Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,2,Mod(5,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.k (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: | \(0.670743376979\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.17 |
Dual form | 84.2.k.a.5.1 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | + | 2.59808i | 0.670820 | + | 1.16190i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.50000 | − | 2.59808i | −1.35680 | − | 0.783349i | −0.367610 | − | 0.929980i | \(-0.619824\pi\) |
−0.989191 | + | 0.146631i | \(0.953157\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.50000 | − | 2.59808i | −1.16190 | − | 0.670820i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50000 | − | 0.866025i | 0.344124 | − | 0.198680i | −0.317970 | − | 0.948101i | \(-0.603001\pi\) |
0.662094 | + | 0.749421i | \(0.269668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.50000 | − | 0.866025i | −0.981981 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.50000 | − | 2.59808i | 0.938315 | − | 0.541736i | 0.0488832 | − | 0.998805i | \(-0.484434\pi\) |
0.889432 | + | 0.457068i | \(0.151100\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.00000 | 1.56670 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.50000 | + | 7.79423i | −0.253546 | + | 1.31747i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | − | 6.06218i | −0.575396 | − | 0.996616i | −0.995998 | − | 0.0893706i | \(-0.971514\pi\) |
0.420602 | − | 0.907245i | \(-0.361819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.00000 | 1.34164 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.50000 | + | 2.59808i | 0.218797 | + | 0.378968i | 0.954441 | − | 0.298401i | \(-0.0964533\pi\) |
−0.735643 | + | 0.677369i | \(0.763120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.19615i | 0.727607i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | + | 2.59808i | 0.618123 | + | 0.356873i | 0.776138 | − | 0.630563i | \(-0.217176\pi\) |
−0.158015 | + | 0.987437i | \(0.550509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 15.5885i | − | 2.10195i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.50000 | + | 2.59808i | −0.198680 | + | 0.344124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5000 | + | 6.06218i | −1.34439 | + | 0.776182i | −0.987448 | − | 0.157945i | \(-0.949513\pi\) |
−0.356939 | + | 0.934128i | \(0.616180\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.50000 | − | 2.59808i | 0.944911 | − | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.50000 | + | 4.33013i | −0.305424 | + | 0.529009i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.50000 | + | 7.79423i | −0.541736 | + | 0.938315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.3923i | − | 1.23334i | −0.787222 | − | 0.616670i | \(-0.788481\pi\) | ||
0.787222 | − | 0.616670i | \(-0.211519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5000 | − | 6.06218i | −1.22893 | − | 0.709524i | −0.262126 | − | 0.965034i | \(-0.584423\pi\) |
−0.966807 | + | 0.255510i | \(0.917757\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 6.92820i | − | 0.800000i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.50000 | − | 12.9904i | −0.512823 | − | 1.48039i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | 0.976187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.50000 | − | 7.79423i | −0.476999 | − | 0.826187i | 0.522654 | − | 0.852545i | \(-0.324942\pi\) |
−0.999653 | + | 0.0263586i | \(0.991609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.00000 | 0.311086 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.50000 | + | 2.59808i | 0.461690 | + | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820i | 0.703452i | 0.936103 | + | 0.351726i | \(0.114405\pi\) | ||||
−0.936103 | + | 0.351726i | \(0.885595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.5000 | + | 7.79423i | −1.35680 | + | 0.783349i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50000 | + | 7.79423i | −0.447767 | + | 0.775555i | −0.998240 | − | 0.0592978i | \(-0.981114\pi\) |
0.550474 | + | 0.834853i | \(0.314447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.50000 | + | 2.59808i | −0.443398 | + | 0.255996i | −0.705038 | − | 0.709170i | \(-0.749070\pi\) |
0.261640 | + | 0.965166i | \(0.415737\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.50000 | − | 12.9904i | −0.439155 | − | 1.26773i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5000 | + | 7.79423i | −1.30509 | + | 0.753497i | −0.981273 | − | 0.192622i | \(-0.938301\pi\) |
−0.323821 | + | 0.946118i | \(0.604968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.50000 | − | 14.7224i | 0.814152 | − | 1.41015i | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) |
0.909935 | − | 0.414751i | \(-0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.5000 | + | 6.06218i | 0.996616 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.7846i | 1.95525i | 0.210352 | + | 0.977626i | \(0.432539\pi\) | ||||
−0.210352 | + | 0.977626i | \(0.567461\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.5000 | + | 7.79423i | 1.25888 | + | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.50000 | − | 2.59808i | 0.687524 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | + | 13.8564i | 0.727273 | + | 1.25967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.00000 | − | 5.19615i | 0.811503 | − | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | + | 3.46410i | −0.528271 | + | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.50000 | − | 7.79423i | −0.393167 | − | 0.680985i | 0.599699 | − | 0.800226i | \(-0.295287\pi\) |
−0.992865 | + | 0.119241i | \(0.961954\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.50000 | + | 0.866025i | 0.390199 | + | 0.0750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.5000 | + | 7.79423i | −1.16190 | + | 0.670820i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50000 | + | 2.59808i | 0.384461 | + | 0.221969i | 0.679757 | − | 0.733437i | \(-0.262085\pi\) |
−0.295296 | + | 0.955406i | \(0.595418\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.3923i | − | 0.881464i | −0.897639 | − | 0.440732i | \(-0.854719\pi\) | ||
0.897639 | − | 0.440732i | \(-0.145281\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.50000 | − | 2.59808i | −0.378968 | − | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.50000 | − | 9.52628i | −0.618590 | − | 0.785714i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.50000 | − | 2.59808i | 0.368654 | − | 0.212843i | −0.304216 | − | 0.952603i | \(-0.598394\pi\) |
0.672870 | + | 0.739760i | \(0.265061\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.50000 | + | 11.2583i | −0.528962 | + | 0.916190i | 0.470467 | + | 0.882418i | \(0.344085\pi\) |
−0.999430 | + | 0.0337724i | \(0.989248\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.50000 | − | 7.79423i | −0.363803 | − | 0.630126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.19615i | − | 0.417365i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.50000 | − | 2.59808i | −0.359139 | − | 0.207349i | 0.309564 | − | 0.950879i | \(-0.399817\pi\) |
−0.668703 | + | 0.743530i | \(0.733150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.00000 | −0.713746 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5000 | + | 2.59808i | 1.06395 | + | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | + | 0.866025i | 0.0391630 | + | 0.0678323i | 0.884943 | − | 0.465700i | \(-0.154198\pi\) |
−0.845780 | + | 0.533533i | \(0.820864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.5000 | + | 23.3827i | 1.05097 | + | 1.82034i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.19615i | − | 0.397360i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.50000 | − | 7.79423i | −0.342129 | − | 0.592584i | 0.642699 | − | 0.766119i | \(-0.277815\pi\) |
−0.984828 | + | 0.173534i | \(0.944481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | + | 3.46410i | −0.755929 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.19615i | − | 0.390567i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.50000 | − | 2.59808i | −0.336346 | − | 0.194189i | 0.322309 | − | 0.946634i | \(-0.395541\pi\) |
−0.658655 | + | 0.752445i | \(0.728874\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.5000 | − | 18.1865i | 0.776182 | − | 1.34439i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.5000 | − | 18.1865i | 0.771975 | − | 1.33710i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.5000 | + | 7.79423i | −0.987218 | + | 0.569970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.00000 | + | 10.3923i | −0.654654 | + | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5000 | + | 7.79423i | −0.976826 | + | 0.563971i | −0.901310 | − | 0.433174i | \(-0.857394\pi\) |
−0.0755154 | + | 0.997145i | \(0.524060\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.50000 | − | 4.33013i | 0.179954 | − | 0.311689i | −0.761911 | − | 0.647682i | \(-0.775738\pi\) |
0.941865 | + | 0.335993i | \(0.109072\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.50000 | − | 0.866025i | −0.106332 | − | 0.0613909i | 0.445891 | − | 0.895087i | \(-0.352887\pi\) |
−0.552223 | + | 0.833696i | \(0.686220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.66025i | − | 0.610847i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | − | 15.5885i | −0.628587 | − | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 15.5885i | − | 1.08347i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.00000 | −0.622543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.00000 | + | 15.5885i | 0.616670 | + | 1.06810i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.00000 | + | 10.3923i | 0.409197 | + | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.50000 | − | 4.33013i | −0.101827 | − | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.0000 | 1.41905 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3923i | 0.695920i | 0.937509 | + | 0.347960i | \(0.113126\pi\) | ||||
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.00000 | + | 10.3923i | 0.400000 | + | 0.692820i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.50000 | − | 7.79423i | 0.298675 | − | 0.517321i | −0.677158 | − | 0.735838i | \(-0.736789\pi\) |
0.975833 | + | 0.218517i | \(0.0701218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5000 | − | 11.2583i | 1.28860 | − | 0.743971i | 0.310192 | − | 0.950674i | \(-0.399607\pi\) |
0.978404 | + | 0.206702i | \(0.0662732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0000 | + | 15.5885i | 1.18431 | + | 1.02565i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.50000 | − | 2.59808i | 0.294805 | − | 0.170206i | −0.345302 | − | 0.938492i | \(-0.612223\pi\) |
0.640107 | + | 0.768286i | \(0.278890\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.50000 | + | 7.79423i | −0.293548 | + | 0.508439i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.50000 | − | 0.866025i | −0.0974355 | − | 0.0562544i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3923i | 0.672222i | 0.941822 | + | 0.336111i | \(0.109112\pi\) | ||||
−0.941822 | + | 0.336111i | \(0.890888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.50000 | + | 0.866025i | 0.0966235 | + | 0.0557856i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.5000 | + | 12.9904i | −1.05415 | + | 0.829925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.0000 | + | 10.3923i | −1.14070 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.0000 | −1.69748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.5000 | + | 7.79423i | −0.845403 | + | 0.488094i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.5000 | + | 23.3827i | 0.842107 | + | 1.45857i | 0.888110 | + | 0.459631i | \(0.152018\pi\) |
−0.0460033 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.50000 | − | 18.1865i | 0.217479 | − | 1.13006i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.50000 | − | 2.59808i | −0.277482 | − | 0.160204i | 0.354801 | − | 0.934942i | \(-0.384549\pi\) |
−0.632283 | + | 0.774738i | \(0.717882\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.5885i | 0.957591i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.5000 | + | 7.79423i | 0.826187 | + | 0.476999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.5000 | + | 18.1865i | −0.640196 | + | 1.10885i | 0.345192 | + | 0.938532i | \(0.387814\pi\) |
−0.985389 | + | 0.170321i | \(0.945520\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5000 | − | 11.2583i | 1.18454 | − | 0.683895i | 0.227480 | − | 0.973783i | \(-0.426951\pi\) |
0.957061 | + | 0.289888i | \(0.0936180\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.0000 | − | 10.3923i | 1.08544 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | − | 11.2583i | 0.390547 | − | 0.676448i | −0.601975 | − | 0.798515i | \(-0.705619\pi\) |
0.992522 | + | 0.122068i | \(0.0389525\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.50000 | + | 2.59808i | −0.269408 | + | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.7846i | − | 1.23991i | −0.784639 | − | 0.619953i | \(-0.787152\pi\) | ||
0.784639 | − | 0.619953i | \(-0.212848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.50000 | − | 4.33013i | −0.445829 | − | 0.257399i | 0.260238 | − | 0.965544i | \(-0.416199\pi\) |
−0.706067 | + | 0.708145i | \(0.749532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.00000 | −0.533114 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | − | 10.3923i | −0.708338 | − | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | − | 10.3923i | −0.351726 | − | 0.609208i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00000 | −0.524000 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | − | 23.3827i | 0.783349 | − | 1.35680i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 6.92820i | 0.461112 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 15.5885i | − | 0.895533i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31.5000 | − | 18.1865i | −1.80368 | − | 1.04136i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3205i | 0.988534i | 0.869310 | + | 0.494267i | \(0.164563\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.50000 | − | 7.79423i | 0.255996 | − | 0.443398i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.50000 | + | 12.9904i | −0.425286 | + | 0.736617i | −0.996447 | − | 0.0842210i | \(-0.973160\pi\) |
0.571161 | + | 0.820838i | \(0.306493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5000 | + | 6.06218i | −0.593495 | + | 0.342655i | −0.766478 | − | 0.642270i | \(-0.777993\pi\) |
0.172983 | + | 0.984925i | \(0.444659\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.0000 | + | 15.5885i | 1.01419 | + | 0.878310i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.5000 | − | 12.9904i | 1.26373 | − | 0.729612i | 0.289933 | − | 0.957047i | \(-0.406367\pi\) |
0.973793 | + | 0.227435i | \(0.0730338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.5000 | − | 23.3827i | 0.753497 | − | 1.30509i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.19615i | − | 0.289122i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.4449i | 1.62830i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.50000 | + | 7.79423i | −0.0826977 | + | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5000 | − | 26.8468i | −0.851957 | − | 1.47563i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) |
0.0274825 | − | 0.999622i | \(-0.491251\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.0000 | −1.15079 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.0000 | −0.819538 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0000 | − | 31.1769i | −0.977626 | − | 1.69330i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.50000 | + | 7.79423i | 0.243689 | + | 0.422081i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −27.0000 | −1.45363 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.5000 | + | 7.79423i | 0.724718 | + | 0.418416i | 0.816487 | − | 0.577364i | \(-0.195919\pi\) |
−0.0917687 | + | 0.995780i | \(0.529252\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.8564i | 0.741716i | 0.928689 | + | 0.370858i | \(0.120936\pi\) | ||||
−0.928689 | + | 0.370858i | \(0.879064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.50000 | − | 2.59808i | 0.0798369 | − | 0.138282i | −0.823343 | − | 0.567545i | \(-0.807893\pi\) |
0.903179 | + | 0.429263i | \(0.141227\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.0000 | − | 15.5885i | 1.43301 | − | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.00000 | + | 10.3923i | −0.476331 | + | 0.550019i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.5000 | − | 12.9904i | 1.18750 | − | 0.685606i | 0.229766 | − | 0.973246i | \(-0.426204\pi\) |
0.957739 | + | 0.287640i | \(0.0928706\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.0000 | − | 13.8564i | −1.25967 | − | 0.727273i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 36.3731i | − | 1.90385i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.5000 | + | 16.4545i | 1.48769 | + | 0.858917i | 0.999901 | − | 0.0140459i | \(-0.00447111\pi\) |
0.487787 | + | 0.872963i | \(0.337804\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.00000 | + | 15.5885i | −0.468521 | + | 0.811503i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.50000 | + | 12.9904i | 0.233628 | + | 0.674427i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | + | 21.6506i | 0.647225 | + | 1.12103i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) |
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.50000 | + | 2.59808i | −0.232379 | + | 0.134164i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0000 | + | 6.92820i | −0.614779 | + | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.5000 | − | 18.1865i | −0.536525 | − | 0.929288i | −0.999088 | − | 0.0427020i | \(-0.986403\pi\) |
0.462563 | − | 0.886586i | \(-0.346930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.0000 | − | 31.1769i | 1.37605 | − | 1.58892i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.00000 | − | 10.3923i | 0.304997 | − | 0.528271i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.5000 | + | 12.9904i | 1.14080 | + | 0.658638i | 0.946627 | − | 0.322330i | \(-0.104466\pi\) |
0.194168 | + | 0.980968i | \(0.437799\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.5885i | − | 0.788342i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.5000 | + | 7.79423i | 0.680985 | + | 0.393167i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.50000 | + | 2.59808i | −0.0754732 | + | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50000 | − | 4.33013i | 0.376414 | − | 0.217323i | −0.299843 | − | 0.953989i | \(-0.596934\pi\) |
0.676257 | + | 0.736666i | \(0.263601\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.50000 | + | 2.59808i | −0.375470 | + | 0.130066i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.5000 | + | 18.1865i | −1.57303 | + | 0.908192i | −0.577241 | + | 0.816574i | \(0.695871\pi\) |
−0.995794 | + | 0.0916181i | \(0.970796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.5000 | − | 23.3827i | 0.670820 | − | 1.16190i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.3731i | 1.80295i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.50000 | − | 2.59808i | −0.222511 | − | 0.128467i | 0.384602 | − | 0.923083i | \(-0.374339\pi\) |
−0.607112 | + | 0.794616i | \(0.707672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | −0.443937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.50000 | + | 2.59808i | −0.369051 | + | 0.127843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | + | 31.1769i | 0.883585 | + | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.00000 | + | 15.5885i | 0.440732 | + | 0.763370i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.00000 | 0.437595 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | + | 10.3923i | 0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.5000 | − | 6.06218i | −1.52439 | − | 0.293369i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5000 | + | 7.79423i | 0.650272 | + | 0.375435i | 0.788560 | − | 0.614957i | \(-0.210827\pi\) |
−0.138288 | + | 0.990392i | \(0.544160\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6410i | 1.66474i | 0.554220 | + | 0.832370i | \(0.313017\pi\) | ||||
−0.554220 | + | 0.832370i | \(0.686983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.50000 | − | 7.79423i | 0.215264 | − | 0.372849i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.5000 | − | 7.79423i | 0.644320 | − | 0.371998i | −0.141957 | − | 0.989873i | \(-0.545339\pi\) |
0.786277 | + | 0.617875i | \(0.212006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.5000 | + | 7.79423i | 0.928571 | + | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.5000 | + | 7.79423i | −0.641404 | + | 0.370315i | −0.785155 | − | 0.619299i | \(-0.787417\pi\) |
0.143751 | + | 0.989614i | \(0.454084\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5000 | − | 23.3827i | 0.639961 | − | 1.10845i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.50000 | + | 7.79423i | −0.212843 | + | 0.368654i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.7846i | 0.980886i | 0.871473 | + | 0.490443i | \(0.163165\pi\) | ||||
−0.871473 | + | 0.490443i | \(0.836835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0000 | + | 15.5885i | 1.27138 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 22.5167i | − | 1.05792i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5000 | − | 26.8468i | −0.725059 | − | 1.25584i | −0.958950 | − | 0.283577i | \(-0.908479\pi\) |
0.233890 | − | 0.972263i | \(-0.424854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.5000 | + | 7.79423i | 0.630126 | + | 0.363803i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0000 | 1.39724 | 0.698620 | − | 0.715493i | \(-0.253798\pi\) | ||||
0.698620 | + | 0.715493i | \(0.253798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.50000 | + | 7.79423i | 0.208683 | + | 0.361449i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.50000 | − | 7.79423i | −0.208235 | − | 0.360674i | 0.742923 | − | 0.669376i | \(-0.233439\pi\) |
−0.951159 | + | 0.308702i | \(0.900105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.5000 | + | 4.33013i | −0.577196 | + | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.00000 | 0.414698 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.0000 | − | 10.3923i | −0.827641 | − | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.92820i | 0.317888i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.5000 | − | 7.79423i | 0.618123 | − | 0.356873i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.5000 | − | 28.5788i | 0.753904 | − | 1.30580i | −0.192013 | − | 0.981392i | \(-0.561502\pi\) |
0.945917 | − | 0.324408i | \(-0.105165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.5000 | + | 7.79423i | −1.02379 | + | 0.354650i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.0000 | + | 10.3923i | −0.817338 | + | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.500000 | + | 0.866025i | −0.0226572 | + | 0.0392434i | −0.877132 | − | 0.480250i | \(-0.840546\pi\) |
0.854475 | + | 0.519493i | \(0.173879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.50000 | − | 0.866025i | −0.0678323 | − | 0.0391630i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.3923i | − | 0.468998i | −0.972116 | − | 0.234499i | \(-0.924655\pi\) | ||
0.972116 | − | 0.234499i | \(-0.0753450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −40.5000 | − | 23.3827i | −1.82034 | − | 1.05097i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.0000 | − | 20.7846i | 0.807410 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50000 | − | 6.06218i | −0.156682 | − | 0.271380i | 0.776989 | − | 0.629515i | \(-0.216746\pi\) |
−0.933670 | + | 0.358134i | \(0.883413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0000 | − | 10.3923i | 0.804181 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0000 | −1.20148 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.5000 | + | 11.2583i | −0.866025 | + | 0.500000i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5000 | − | 18.1865i | −0.465404 | − | 0.806104i | 0.533815 | − | 0.845601i | \(-0.320758\pi\) |
−0.999220 | + | 0.0394971i | \(0.987424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5000 | − | 30.3109i | −0.464493 | − | 1.34087i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.50000 | + | 7.79423i | 0.198680 | + | 0.344124i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.5000 | − | 7.79423i | −0.594881 | − | 0.343455i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15.5885i | − | 0.685580i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.5000 | + | 7.79423i | 0.592584 | + | 0.342129i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.50000 | − | 12.9904i | 0.328581 | − | 0.569119i | −0.653650 | − | 0.756797i | \(-0.726763\pi\) |
0.982231 | + | 0.187678i | \(0.0600963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.5000 | + | 12.9904i | −0.983856 | + | 0.568030i | −0.903432 | − | 0.428731i | \(-0.858961\pi\) |
−0.0804241 | + | 0.996761i | \(0.525627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.0000 | − | 13.8564i | 0.523723 | − | 0.604743i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.50000 | + | 2.59808i | −0.196023 | + | 0.113174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | − | 3.46410i | 0.0869565 | − | 0.150613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.50000 | + | 7.79423i | 0.195283 | + | 0.338241i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.5000 | − | 23.3827i | −1.75097 | − | 1.01092i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.00000 | 0.388379 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.5000 | − | 33.7750i | 0.581486 | − | 1.45479i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5000 | + | 32.0429i | 0.795377 | + | 1.37763i | 0.922599 | + | 0.385759i | \(0.126061\pi\) |
−0.127222 | + | 0.991874i | \(0.540606\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.00000 | + | 10.3923i | 0.257485 | + | 0.445976i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 51.0000 | 2.18460 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000 | 1.36822 | 0.684111 | − | 0.729378i | \(-0.260191\pi\) | ||||
0.684111 | + | 0.729378i | \(0.260191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.3731i | 1.55236i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | + | 2.59808i | −0.0212622 | + | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36.3731i | 1.54395i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.5000 | + | 12.9904i | 0.953356 | + | 0.550420i | 0.894122 | − | 0.447824i | \(-0.147801\pi\) |
0.0592339 | + | 0.998244i | \(0.481134\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5000 | − | 23.3827i | 0.569970 | − | 0.987218i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.5000 | + | 23.3827i | −0.568957 | + | 0.985463i | 0.427712 | + | 0.903915i | \(0.359320\pi\) |
−0.996669 | + | 0.0815478i | \(0.974014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −54.0000 | + | 31.1769i | −2.27180 | + | 1.31162i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.50000 | − | 23.3827i | 0.188982 | − | 0.981981i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5000 | + | 7.79423i | −0.565949 | + | 0.326751i | −0.755530 | − | 0.655114i | \(-0.772621\pi\) |
0.189580 | + | 0.981865i | \(0.439287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50000 | − | 6.06218i | 0.146470 | − | 0.253694i | −0.783450 | − | 0.621455i | \(-0.786542\pi\) |
0.929921 | + | 0.367760i | \(0.119875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.5000 | − | 23.3827i | 0.563971 | − | 0.976826i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.7846i | 0.866778i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.5000 | − | 12.9904i | −0.936687 | − | 0.540797i | −0.0477669 | − | 0.998859i | \(-0.515210\pi\) |
−0.888920 | + | 0.458062i | \(0.848544\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.66025i | 0.359908i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | + | 20.7846i | 0.995688 | + | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.5000 | − | 23.3827i | −0.559113 | − | 0.968412i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.0000 | −1.48588 | −0.742940 | − | 0.669359i | \(-0.766569\pi\) | ||||
−0.742940 | + | 0.669359i | \(0.766569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00000 | −0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.5000 | − | 18.1865i | −0.431183 | − | 0.746831i | 0.565792 | − | 0.824548i | \(-0.308570\pi\) |
−0.996976 | + | 0.0777165i | \(0.975237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.0000 | + | 15.5885i | 0.737928 | + | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.00000 | 0.122782 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.50000 | − | 2.59808i | −0.183865 | − | 0.106155i | 0.405242 | − | 0.914209i | \(-0.367187\pi\) |
−0.589107 | + | 0.808055i | \(0.700520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.6410i | − | 1.41304i | −0.707695 | − | 0.706518i | \(-0.750265\pi\) | ||
0.707695 | − | 0.706518i | \(-0.249735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.50000 | + | 12.9904i | 0.305424 | + | 0.529009i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.0000 | + | 41.5692i | −0.975739 | + | 1.69003i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.5000 | − | 14.7224i | 1.03501 | − | 0.597565i | 0.116596 | − | 0.993179i | \(-0.462802\pi\) |
0.918417 | + | 0.395614i | \(0.129468\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.500000 | − | 0.866025i | 0.0201948 | − | 0.0349784i | −0.855751 | − | 0.517387i | \(-0.826905\pi\) |
0.875946 | + | 0.482409i | \(0.160238\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 27.0000 | + | 15.5885i | 1.08875 | + | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.7846i | 0.836757i | 0.908273 | + | 0.418378i | \(0.137401\pi\) | ||||
−0.908273 | + | 0.418378i | \(0.862599\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.5000 | + | 12.9904i | 0.904351 | + | 0.522127i | 0.878609 | − | 0.477541i | \(-0.158472\pi\) |
0.0257420 | + | 0.999669i | \(0.491805\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.5000 | + | 23.3827i | 0.541736 | + | 0.938315i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.50000 | − | 23.3827i | 0.180289 | − | 0.936808i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.5000 | − | 7.79423i | 0.539138 | − | 0.311272i | ||||
\(628\) | 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 | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.0000 | − | 17.3205i | 1.19239 | − | 0.688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.0000 | + | 20.7846i | 0.476205 | + | 0.824812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.0000 | − | 15.5885i | −1.06810 | − | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5000 | − | 7.79423i | −0.533218 | − | 0.307854i | 0.209108 | − | 0.977893i | \(-0.432944\pi\) |
−0.742326 | + | 0.670039i | \(0.766277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.46410i | 0.136611i | 0.997664 | + | 0.0683054i | \(0.0217592\pi\) | ||||
−0.997664 | + | 0.0683054i | \(0.978241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.0000 | − | 10.3923i | −0.708749 | − | 0.409197i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.50000 | − | 7.79423i | 0.176913 | − | 0.306423i | −0.763908 | − | 0.645325i | \(-0.776722\pi\) |
0.940822 | + | 0.338902i | \(0.110055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5000 | − | 7.79423i | 0.529921 | − | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.00000 | + | 5.19615i | 0.235159 | + | 0.203653i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.5000 | + | 7.79423i | −0.528296 | + | 0.305012i | −0.740322 | − | 0.672252i | \(-0.765327\pi\) |
0.212026 | + | 0.977264i | \(0.431994\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.5000 | − | 23.3827i | 0.527489 | − | 0.913637i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31.5000 | + | 18.1865i | −1.22893 | + | 0.709524i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.3923i | 0.404827i | 0.979300 | + | 0.202413i | \(0.0648785\pi\) | ||||
−0.979300 | + | 0.202413i | \(0.935122\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5000 | + | 11.2583i | 0.758462 | + | 0.437898i | 0.828743 | − | 0.559629i | \(-0.189056\pi\) |
−0.0702812 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.50000 | + | 12.9904i | 0.174503 | + | 0.503745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.00000 | − | 15.5885i | −0.347960 | − | 0.602685i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 63.0000 | 2.43209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0000 | 0.848038 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.0000 | − | 10.3923i | −0.692820 | − | 0.400000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.5000 | − | 38.9711i | −0.864745 | − | 1.49778i | −0.867300 | − | 0.497786i | \(-0.834147\pi\) |
0.00255466 | − | 0.999997i | \(-0.499187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | + | 13.8564i | −0.460518 | + | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.5885i | 0.597351i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.5000 | + | 18.1865i | 1.20531 | + | 0.695888i | 0.961732 | − | 0.273992i | \(-0.0883442\pi\) |
0.243582 | + | 0.969880i | \(0.421677\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5885i | 0.595604i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.5000 | + | 33.7750i | −0.743971 | + | 1.28860i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5000 | + | 16.4545i | −1.08419 | + | 0.625958i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −40.5000 | − | 7.79423i | −1.53847 | − | 0.296078i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.0000 | − | 15.5885i | 1.02417 | − | 0.591304i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.50000 | + | 7.79423i | −0.170206 | + | 0.294805i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 20.7846i | − | 0.785024i | −0.919747 | − | 0.392512i | \(-0.871606\pi\) | ||
0.919747 | − | 0.392512i | \(-0.128394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5000 | − | 6.06218i | −0.396015 | − | 0.228639i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 15.5885i | − | 0.587095i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.5000 | + | 7.79423i | −0.846200 | + | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.5000 | − | 26.8468i | −0.582115 | − | 1.00825i | −0.995228 | − | 0.0975728i | \(-0.968892\pi\) |
0.413114 | − | 0.910679i | \(-0.364441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.00000 | 0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.00000 | −0.337053 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.00000 | − | 15.5885i | −0.336111 | − | 0.582162i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.50000 | + | 12.9904i | 0.279703 | + | 0.484459i | 0.971311 | − | 0.237814i | \(-0.0764307\pi\) |
−0.691608 | + | 0.722273i | \(0.743097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5000 | − | 2.59808i | −0.502766 | − | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.00000 | −0.111571 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2487i | 0.899335i | 0.893196 | + | 0.449667i | \(0.148458\pi\) | ||||
−0.893196 | + | 0.449667i | \(0.851542\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.5000 | − | 14.7224i | 0.941864 | − | 0.543785i | 0.0513199 | − | 0.998682i | \(-0.483657\pi\) |
0.890544 | + | 0.454897i | \(0.150324\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.5000 | − | 33.7750i | 0.497955 | − | 1.24581i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.5000 | − | 12.9904i | 0.828798 | − | 0.478507i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.50000 | + | 14.7224i | −0.312678 | + | 0.541573i | −0.978941 | − | 0.204143i | \(-0.934559\pi\) |
0.666264 | + | 0.745716i | \(0.267893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 51.9615i | − | 1.90628i | −0.302524 | − | 0.953142i | \(-0.597829\pi\) | ||
0.302524 | − | 0.953142i | \(-0.402171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5000 | + | 7.79423i | 0.494602 | + | 0.285558i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.0000 | − | 31.1769i | 0.658586 | − | 1.14070i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.5000 | − | 7.79423i | −1.47984 | − | 0.284795i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5000 | + | 25.1147i | 0.529113 | + | 0.916450i | 0.999424 | + | 0.0339490i | \(0.0108084\pi\) |
−0.470311 | + | 0.882501i | \(0.655858\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.0000 | + | 20.7846i | −1.31191 | + | 0.757433i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.0000 | −1.41936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 40.5000 | − | 23.3827i | 1.47006 | − | 0.848738i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.5000 | − | 18.1865i | −0.380625 | − | 0.659261i | 0.610527 | − | 0.791995i | \(-0.290958\pi\) |
−0.991152 | + | 0.132734i | \(0.957624\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.5000 | − | 14.7224i | 1.53860 | − | 0.532988i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.5000 | − | 23.3827i | 0.488094 | − | 0.845403i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 34.6410i | − | 1.24919i | −0.780950 | − | 0.624593i | \(-0.785265\pi\) | ||
0.780950 | − | 0.624593i | \(-0.214735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.5000 | − | 23.3827i | −1.45857 | − | 0.842107i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.5000 | − | 33.7750i | 0.701366 | − | 1.21480i | −0.266621 | − | 0.963802i | \(-0.585907\pi\) |
0.967987 | − | 0.251000i | \(-0.0807596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | − | 3.46410i | 0.215526 | − | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5000 | + | 30.3109i | 0.376685 | + | 1.08740i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.00000 | + | 5.19615i | −0.322458 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | + | 46.7654i | −0.966136 | + | 1.67340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 15.5885i | − | 0.556376i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.50000 | − | 0.866025i | −0.0534692 | − | 0.0308705i | 0.473027 | − | 0.881048i | \(-0.343161\pi\) |
−0.526496 | + | 0.850177i | \(0.676495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.00000 | 0.320408 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.0000 | + | 41.5692i | −1.28001 | + | 1.47803i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.5000 | − | 23.3827i | −0.478796 | − | 0.829298i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.0000 | −0.637593 | −0.318796 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318796 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.00000 | 0.318397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.0000 | −0.953998 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.5000 | + | 54.5596i | 1.11161 | + | 1.92537i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.5000 | + | 38.9711i | 0.475812 | + | 1.37355i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 36.3731i | − | 1.28039i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.5000 | + | 12.9904i | 0.791058 | + | 0.456717i | 0.840335 | − | 0.542068i | \(-0.182358\pi\) |
−0.0492770 | + | 0.998785i | \(0.515692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.9615i | − | 1.82462i | −0.409505 | − | 0.912308i | \(-0.634299\pi\) | ||
0.409505 | − | 0.912308i | \(-0.365701\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.5000 | + | 33.7750i | −0.683895 | + | 1.18454i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.50000 | + | 2.59808i | −0.0525427 | + | 0.0910066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00000 | − | 3.46410i | 0.209913 | − | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.50000 | − | 2.59808i | 0.157051 | − | 0.0906735i | −0.419415 | − | 0.907795i | \(-0.637765\pi\) |
0.576466 | + | 0.817121i | \(0.304431\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.50000 | − | 6.06218i | 0.122002 | − | 0.211314i | −0.798555 | − | 0.601922i | \(-0.794402\pi\) |
0.920557 | + | 0.390608i | \(0.127735\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.0000 | + | 31.1769i | −0.626680 | + | 1.08544i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.3923i | 0.361376i | 0.983540 | + | 0.180688i | \(0.0578324\pi\) | ||||
−0.983540 | + | 0.180688i | \(0.942168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50000 | + | 0.866025i | 0.0520972 | + | 0.0300783i | 0.525822 | − | 0.850594i | \(-0.323758\pi\) |
−0.473725 | + | 0.880673i | \(0.657091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.5167i | 0.781094i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.5000 | + | 7.79423i | 0.675635 | + | 0.270054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.0000 | − | 31.1769i | −0.622916 | − | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.50000 | − | 7.79423i | 0.155543 | − | 0.269408i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.0000 | + | 31.1769i | 0.619953 | + | 1.07379i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.5000 | + | 33.7750i | 0.670820 | + | 1.16190i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.00000 | + | 41.5692i | −0.274883 | + | 1.42834i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.0000 | 0.514799 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.5000 | − | 18.1865i | −1.07981 | − | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8564i | 0.474434i | 0.971457 | + | 0.237217i | \(0.0762353\pi\) | ||||
−0.971457 | + | 0.237217i | \(0.923765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.5000 | − | 7.79423i | 0.461690 | − | 0.266557i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.5000 | + | 28.5788i | −0.563629 | + | 0.976235i | 0.433546 | + | 0.901131i | \(0.357262\pi\) |
−0.997176 | + | 0.0751033i | \(0.976071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.5000 | + | 19.9186i | −1.17712 | + | 0.679613i | −0.955348 | − | 0.295484i | \(-0.904519\pi\) |
−0.221777 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.0000 | + | 5.19615i | 0.920158 | + | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.50000 | − | 2.59808i | 0.153182 | − | 0.0884395i | −0.421450 | − | 0.906852i | \(-0.638479\pi\) |
0.574632 | + | 0.818412i | \(0.305145\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5000 | − | 23.3827i | 0.459014 | − | 0.795035i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0000 | − | 6.92820i | −0.407541 | − | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.19615i | − | 0.176267i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.0000 | + | 10.3923i | 0.609208 | + | 0.351726i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | + | 5.19615i | 0.202837 | + | 0.175662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.50000 | − | 9.52628i | −0.185722 | − | 0.321680i | 0.758098 | − | 0.652141i | \(-0.226129\pi\) |
−0.943820 | + | 0.330461i | \(0.892796\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.00000 | − | 5.19615i | 0.303562 | − | 0.175262i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5000 | − | 7.79423i | 0.453798 | − | 0.262000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.50000 | + | 2.59808i | 0.0503651 | + | 0.0872349i | 0.890109 | − | 0.455748i | \(-0.150628\pi\) |
−0.839744 | + | 0.542983i | \(0.817295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | + | 13.8564i | 0.536623 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.7654i | 1.56670i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.50000 | + | 2.59808i | 0.150587 | + | 0.0869413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 15.5885i | − | 0.521065i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5000 | − | 7.79423i | 0.449750 | − | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.0000 | − | 3.46410i | −0.599002 | − | 0.115278i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.0000 | − | 10.3923i | 0.598340 | − | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5000 | + | 32.0429i | −0.614282 | + | 1.06397i | 0.376228 | + | 0.926527i | \(0.377221\pi\) |
−0.990510 | + | 0.137441i | \(0.956112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.5000 | + | 23.3827i | 0.447767 | + | 0.775555i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.3923i | − | 0.344312i | −0.985070 | − | 0.172156i | \(-0.944927\pi\) | ||
0.985070 | − | 0.172156i | \(-0.0550734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.0000 | − | 31.1769i | −1.78714 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 63.0000 | 2.08272 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.50000 | − | 23.3827i | 0.148603 | − | 0.772164i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.50000 | − | 16.4545i | −0.313376 | − | 0.542783i | 0.665715 | − | 0.746206i | \(-0.268127\pi\) |
−0.979091 | + | 0.203423i | \(0.934793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.0000 | − | 25.9808i | −0.494267 | − | 0.856095i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.0000 | 0.920634 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5885i | 0.511992i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.5000 | + | 33.7750i | 0.639774 | + | 1.10812i | 0.985482 | + | 0.169779i | \(0.0543055\pi\) |
−0.345708 | + | 0.938342i | \(0.612361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.50000 | + | 9.52628i | 0.245803 | + | 0.312211i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 25.9808i | − | 0.850572i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40.5000 | − | 23.3827i | −1.32449 | − | 0.764696i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.5692i | − | 1.35801i | −0.734135 | − | 0.679004i | \(-0.762412\pi\) | ||
0.734135 | − | 0.679004i | \(-0.237588\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.5000 | − | 18.1865i | 0.342655 | − | 0.593495i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5000 | + | 18.1865i | −0.342290 | + | 0.592864i | −0.984858 | − | 0.173365i | \(-0.944536\pi\) |
0.642567 | + | 0.766229i | \(0.277869\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.0000 | + | 15.5885i | −0.879241 | + | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −40.5000 | − | 7.79423i | −1.31747 | − | 0.253546i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.5000 | − | 23.3827i | 1.31607 | − | 0.759835i | 0.332979 | − | 0.942934i | \(-0.391946\pi\) |
0.983094 | + | 0.183099i | \(0.0586129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.5000 | + | 38.9711i | −0.729612 | + | 1.26373i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.7846i | 0.673280i | 0.941634 | + | 0.336640i | \(0.109290\pi\) | ||||
−0.941634 | + | 0.336640i | \(0.890710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.5000 | − | 23.3827i | −1.31055 | − | 0.756646i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.50000 | + | 12.9904i | 0.145313 | + | 0.419481i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46.7654i | 1.50699i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.0000 | 0.482867 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.0000 | −1.28631 | −0.643157 | − | 0.765735i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765735i | \(0.722376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.50000 | + | 7.79423i | 0.144561 | + | 0.250387i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.5000 | − | 49.3634i | −0.914609 | − | 1.58415i | −0.807473 | − | 0.589904i | \(-0.799166\pi\) |
−0.107135 | − | 0.994244i | \(-0.534168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.0000 | − | 20.7846i | 0.577054 | − | 0.666324i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.5000 | − | 18.1865i | −1.00777 | − | 0.581839i | −0.0972351 | − | 0.995261i | \(-0.531000\pi\) |
−0.910539 | + | 0.413423i | \(0.864333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.7654i | 1.49463i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5000 | − | 44.1673i | −0.814152 | − | 1.41015i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.50000 | + | 2.59808i | −0.0478426 | + | 0.0828658i | −0.888955 | − | 0.457995i | \(-0.848568\pi\) |
0.841112 | + | 0.540860i | \(0.181901\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.50000 | − | 12.9904i | −0.143237 | − | 0.413488i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0000 | − | 10.3923i | 0.572367 | − | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5000 | + | 21.6506i | −0.397076 | + | 0.687755i | −0.993364 | − | 0.115015i | \(-0.963308\pi\) |
0.596288 | + | 0.802771i | \(0.296642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 46.5000 | + | 26.8468i | 1.47563 | + | 0.851957i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.19615i | − | 0.164729i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.5000 | + | 11.2583i | 0.617571 | + | 0.356555i | 0.775923 | − | 0.630828i | \(-0.217285\pi\) |
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 \(a_p\))