Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1349,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 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("2100.1349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bo (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1949.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1949 |
Dual form | 2100.2.bo.a.1349.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | + | 2.00000i | −0.654654 | + | 0.755929i | ||||
\(8\) | 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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.59808 | + | 1.50000i | 0.630126 | + | 0.363803i | 0.780801 | − | 0.624780i | \(-0.214811\pi\) |
−0.150675 | + | 0.988583i | \(0.548145\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50000 | + | 0.866025i | −0.344124 | + | 0.198680i | −0.662094 | − | 0.749421i | \(-0.730332\pi\) |
0.317970 | + | 0.948101i | \(0.396999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.50000 | − | 0.866025i | −0.981981 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59808 | − | 4.50000i | −0.541736 | − | 0.938315i | −0.998805 | − | 0.0488832i | \(-0.984434\pi\) |
0.457068 | − | 0.889432i | \(-0.348900\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 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 | ||||||||
\(33\) | − | 9.00000i | − | 1.56670i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.06218 | − | 3.50000i | 0.996616 | − | 0.575396i | 0.0893706 | − | 0.995998i | \(-0.471514\pi\) |
0.907245 | + | 0.420602i | \(0.138181\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.59808 | + | 1.50000i | −0.378968 | + | 0.218797i | −0.677369 | − | 0.735643i | \(-0.736880\pi\) |
0.298401 | + | 0.954441i | \(0.403547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.19615i | 0.727607i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.59808 | − | 4.50000i | 0.356873 | − | 0.618123i | −0.630563 | − | 0.776138i | \(-0.717176\pi\) |
0.987437 | + | 0.158015i | \(0.0505095\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.59808 | − | 1.50000i | −0.344124 | − | 0.198680i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −2.59808 | − | 7.50000i | −0.327327 | − | 0.944911i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.33013 | − | 2.50000i | −0.529009 | − | 0.305424i | 0.211604 | − | 0.977356i | \(-0.432131\pi\) |
−0.740613 | + | 0.671932i | \(0.765465\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −6.06218 | + | 10.5000i | −0.709524 | + | 1.22893i | 0.255510 | + | 0.966807i | \(0.417757\pi\) |
−0.965034 | + | 0.262126i | \(0.915577\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.9904 | − | 4.50000i | 1.48039 | − | 0.512823i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | − | 0.866025i | −0.0562544 | − | 0.0974355i | 0.836527 | − | 0.547926i | \(-0.184582\pi\) |
−0.892781 | + | 0.450490i | \(0.851249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.50000 | + | 7.79423i | 0.476999 | + | 0.826187i | 0.999653 | − | 0.0263586i | \(-0.00839118\pi\) |
−0.522654 | + | 0.852545i | \(0.675058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.00000i | − | 0.311086i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.92820 | −0.703452 | −0.351726 | − | 0.936103i | \(-0.614405\pi\) | ||||
−0.351726 | + | 0.936103i | \(0.614405\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 2.59808 | + | 4.50000i | 0.255996 | + | 0.443398i | 0.965166 | − | 0.261640i | \(-0.0842633\pi\) |
−0.709170 | + | 0.705038i | \(0.750930\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.79423 | − | 13.5000i | −0.753497 | − | 1.30509i | −0.946118 | − | 0.323821i | \(-0.895032\pi\) |
0.192622 | − | 0.981273i | \(-0.438301\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.50000 | + | 14.7224i | −0.814152 | + | 1.41015i | 0.0957826 | + | 0.995402i | \(0.469465\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.5000 | + | 6.06218i | 0.996616 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.7846 | 1.95525 | 0.977626 | − | 0.210352i | \(-0.0674609\pi\) | ||||
0.977626 | + | 0.210352i | \(0.0674609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||||
\(123\) | −5.19615 | − | 9.00000i | −0.468521 | − | 0.811503i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 0.866025 | − | 4.50000i | 0.0750939 | − | 0.390199i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.59808 | + | 4.50000i | −0.221969 | + | 0.384461i | −0.955406 | − | 0.295296i | \(-0.904582\pi\) |
0.733437 | + | 0.679757i | \(0.237915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3923i | 0.881464i | 0.897639 | + | 0.440732i | \(0.145281\pi\) | ||||
−0.897639 | + | 0.440732i | \(0.854719\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 9.52628 | − | 7.50000i | 0.785714 | − | 0.618590i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.50000 | + | 2.59808i | −0.368654 | + | 0.212843i | −0.672870 | − | 0.739760i | \(-0.734939\pi\) |
0.304216 | + | 0.952603i | \(0.401606\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | −7.79423 | + | 4.50000i | −0.630126 | + | 0.363803i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.59808 | − | 4.50000i | 0.207349 | − | 0.359139i | −0.743530 | − | 0.668703i | \(-0.766850\pi\) |
0.950879 | + | 0.309564i | \(0.100183\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.00000 | 0.713746 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5000 | + | 2.59808i | 1.06395 | + | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.866025 | − | 0.500000i | 0.0678323 | − | 0.0391630i | −0.465700 | − | 0.884943i | \(-0.654198\pi\) |
0.533533 | + | 0.845780i | \(0.320864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.0000i | − | 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.19615i | − | 0.397360i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.79423 | + | 4.50000i | −0.592584 | + | 0.342129i | −0.766119 | − | 0.642699i | \(-0.777815\pi\) |
0.173534 | + | 0.984828i | \(0.444481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.19615 | 0.390567 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.50000 | + | 2.59808i | 0.336346 | + | 0.194189i | 0.658655 | − | 0.752445i | \(-0.271126\pi\) |
−0.322309 | + | 0.946634i | \(0.604459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.1865 | − | 10.5000i | −1.34439 | − | 0.776182i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.79423 | − | 13.5000i | −0.569970 | − | 0.987218i | ||||
\(188\) | 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 | ||||||||
\(193\) | −4.33013 | − | 2.50000i | −0.311689 | − | 0.179954i | 0.335993 | − | 0.941865i | \(-0.390928\pi\) |
−0.647682 | + | 0.761911i | \(0.724262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | + | 0.866025i | 0.106332 | + | 0.0613909i | 0.552223 | − | 0.833696i | \(-0.313780\pi\) |
−0.445891 | + | 0.895087i | \(0.647113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.66025i | − | 0.610847i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.5885 | 1.08347 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 15.5885 | − | 9.00000i | 1.06810 | − | 0.616670i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.33013 | − | 1.50000i | 0.293948 | − | 0.101827i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.0000 | −1.41905 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3923 | 0.695920 | 0.347960 | − | 0.937509i | \(-0.386874\pi\) | ||||
0.347960 | + | 0.937509i | \(0.386874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.79423 | + | 4.50000i | 0.517321 | + | 0.298675i | 0.735838 | − | 0.677158i | \(-0.236789\pi\) |
−0.218517 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.5000 | + | 11.2583i | −1.28860 | + | 0.743971i | −0.978404 | − | 0.206702i | \(-0.933727\pi\) |
−0.310192 | + | 0.950674i | \(0.600393\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0000 | + | 15.5885i | 1.18431 | + | 1.02565i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.59808 | − | 4.50000i | −0.170206 | − | 0.294805i | 0.768286 | − | 0.640107i | \(-0.221110\pi\) |
−0.938492 | + | 0.345302i | \(0.887777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.866025 | − | 1.50000i | 0.0562544 | − | 0.0974355i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | ||||||||
\(253\) | 27.0000i | 1.69748i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.3827 | + | 13.5000i | −1.45857 | + | 0.842107i | −0.998941 | − | 0.0460033i | \(-0.985352\pi\) |
−0.459631 | + | 0.888110i | \(0.652018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.50000 | + | 18.1865i | −0.217479 | + | 1.13006i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.59808 | + | 4.50000i | −0.160204 | + | 0.277482i | −0.934942 | − | 0.354801i | \(-0.884549\pi\) |
0.774738 | + | 0.632283i | \(0.217882\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.79423 | + | 13.5000i | −0.476999 | + | 0.826187i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5000 | − | 18.1865i | 0.640196 | − | 1.10885i | −0.345192 | − | 0.938532i | \(-0.612186\pi\) |
0.985389 | − | 0.170321i | \(-0.0544803\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2583 | + | 6.50000i | 0.676448 | + | 0.390547i | 0.798515 | − | 0.601975i | \(-0.205619\pi\) |
−0.122068 | + | 0.992522i | \(0.538953\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −4.33013 | + | 7.50000i | −0.257399 | + | 0.445829i | −0.965544 | − | 0.260238i | \(-0.916199\pi\) |
0.708145 | + | 0.706067i | \(0.249532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3923 | − | 12.0000i | 0.613438 | − | 0.708338i | ||||
\(288\) | 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 | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.3827 | + | 13.5000i | 1.35680 | + | 0.783349i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 6.92820i | 0.461112 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.5885 | −0.895533 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.3205 | −0.988534 | −0.494267 | − | 0.869310i | \(-0.664563\pi\) | ||||
−0.494267 | + | 0.869310i | \(0.664563\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 6.06218 | + | 10.5000i | 0.342655 | + | 0.593495i | 0.984925 | − | 0.172983i | \(-0.0553406\pi\) |
−0.642270 | + | 0.766478i | \(0.722007\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.9904 | + | 22.5000i | 0.729612 | + | 1.26373i | 0.957047 | + | 0.289933i | \(0.0936329\pi\) |
−0.227435 | + | 0.973793i | \(0.573034\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.5000 | − | 23.3827i | 0.753497 | − | 1.30509i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.19615 | −0.289122 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.4449 | −1.62830 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 21.0000i | 1.15079i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.00000i | − | 0.108947i | −0.998515 | − | 0.0544735i | \(-0.982652\pi\) | ||
0.998515 | − | 0.0544735i | \(-0.0173480\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.79423 | + | 13.5000i | −0.418416 | + | 0.724718i | −0.995780 | − | 0.0917687i | \(-0.970748\pi\) |
0.577364 | + | 0.816487i | \(0.304081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.8564i | − | 0.741716i | −0.928689 | − | 0.370858i | \(-0.879064\pi\) | ||
0.928689 | − | 0.370858i | \(-0.120936\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.59808 | − | 1.50000i | −0.138282 | − | 0.0798369i | 0.429263 | − | 0.903179i | \(-0.358773\pi\) |
−0.567545 | + | 0.823343i | \(0.692107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.3923 | − | 9.00000i | −0.550019 | − | 0.476331i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.5000 | + | 12.9904i | −1.18750 | + | 0.685606i | −0.957739 | − | 0.287640i | \(-0.907129\pi\) |
−0.229766 | + | 0.973246i | \(0.573796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.8564 | + | 24.0000i | −0.727273 | + | 1.25967i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4545 | + | 28.5000i | −0.858917 | + | 1.48769i | 0.0140459 | + | 0.999901i | \(0.495529\pi\) |
−0.872963 | + | 0.487787i | \(0.837804\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | 21.6506 | − | 12.5000i | 1.12103 | − | 0.647225i | 0.179364 | − | 0.983783i | \(-0.442596\pi\) |
0.941663 | + | 0.336557i | \(0.109263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0000 | + | 6.92820i | −0.614779 | + | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.1865 | + | 10.5000i | −0.929288 | + | 0.536525i | −0.886586 | − | 0.462563i | \(-0.846930\pi\) |
−0.0427020 | + | 0.999088i | \(0.513597\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.3923 | + | 6.00000i | 0.528271 | + | 0.304997i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.5000 | − | 12.9904i | −1.14080 | − | 0.658638i | −0.194168 | − | 0.980968i | \(-0.562201\pi\) |
−0.946627 | + | 0.322330i | \(0.895534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.5885i | − | 0.788342i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.79423 | − | 13.5000i | 0.393167 | − | 0.680985i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.33013 | + | 7.50000i | 0.217323 | + | 0.376414i | 0.953989 | − | 0.299843i | \(-0.0969342\pi\) |
−0.736666 | + | 0.676257i | \(0.763601\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.3731 | −1.80295 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.50000 | + | 2.59808i | 0.222511 | + | 0.128467i | 0.607112 | − | 0.794616i | \(-0.292328\pi\) |
−0.384602 | + | 0.923083i | \(0.625661\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | −0.443937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.59808 | + | 7.50000i | 0.127843 | + | 0.369051i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.5885 | + | 9.00000i | −0.763370 | + | 0.440732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 9.00000i | − | 0.437595i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.06218 | − | 31.5000i | 0.293369 | − | 1.52439i | ||||
\(428\) | 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 | ||||||||
\(433\) | 34.6410 | 1.66474 | 0.832370 | − | 0.554220i | \(-0.186983\pi\) | ||||
0.832370 | + | 0.554220i | \(0.186983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.79423 | + | 4.50000i | 0.372849 | + | 0.215264i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.5000 | + | 7.79423i | −0.644320 | + | 0.371998i | −0.786277 | − | 0.617875i | \(-0.787994\pi\) |
0.141957 | + | 0.989873i | \(0.454661\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.5000 | + | 7.79423i | 0.928571 | + | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.79423 | + | 13.5000i | 0.370315 | + | 0.641404i | 0.989614 | − | 0.143751i | \(-0.0459164\pi\) |
−0.619299 | + | 0.785155i | \(0.712583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.79423 | − | 4.50000i | −0.368654 | − | 0.212843i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.7846i | − | 0.980886i | −0.871473 | − | 0.490443i | \(-0.836835\pi\) | ||
0.871473 | − | 0.490443i | \(-0.163165\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0000 | + | 15.5885i | 1.27138 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.5167 | −1.05792 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.8468 | − | 15.5000i | 1.25584 | − | 0.725059i | 0.283577 | − | 0.958950i | \(-0.408479\pi\) |
0.972263 | + | 0.233890i | \(0.0751456\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.79423 | − | 4.50000i | 0.360674 | − | 0.208235i | −0.308702 | − | 0.951159i | \(-0.599895\pi\) |
0.669376 | + | 0.742923i | \(0.266561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.5000 | − | 4.33013i | 0.577196 | − | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.00000 | 0.414698 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.3923 | + | 18.0000i | −0.477839 | + | 0.827641i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.79423 | + | 13.5000i | 0.356873 | + | 0.618123i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.5000 | + | 28.5788i | −0.753904 | + | 1.30580i | 0.192013 | + | 0.981392i | \(0.438498\pi\) |
−0.945917 | + | 0.324408i | \(0.894835\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.79423 | + | 22.5000i | 0.354650 | + | 1.02379i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.866025 | − | 0.500000i | −0.0392434 | − | 0.0226572i | 0.480250 | − | 0.877132i | \(-0.340546\pi\) |
−0.519493 | + | 0.854475i | \(0.673879\pi\) | |||||||
\(488\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.7846 | + | 18.0000i | 0.932317 | + | 0.807410i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.50000 | + | 6.06218i | 0.156682 | + | 0.271380i | 0.933670 | − | 0.358134i | \(-0.116587\pi\) |
−0.776989 | + | 0.629515i | \(0.783254\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0000 | − | 10.3923i | 0.804181 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.2583 | − | 19.5000i | −0.500000 | − | 0.866025i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5000 | + | 18.1865i | 0.465404 | + | 0.806104i | 0.999220 | − | 0.0394971i | \(-0.0125756\pi\) |
−0.533815 | + | 0.845601i | \(0.679242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5000 | − | 30.3109i | −0.464493 | − | 1.34087i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.79423 | − | 4.50000i | 0.344124 | − | 0.198680i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.5885 | 0.685580 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 12.9904 | + | 22.5000i | 0.568030 | + | 0.983856i | 0.996761 | + | 0.0804241i | \(0.0256275\pi\) |
−0.428731 | + | 0.903432i | \(0.641039\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.59808 | − | 4.50000i | −0.113174 | − | 0.196023i | ||||
\(528\) | 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 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.00000i | 0.388379i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 10.3923 | − | 6.00000i | 0.445976 | − | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000i | 1.36822i | 0.729378 | + | 0.684111i | \(0.239809\pi\) | ||||
−0.729378 | + | 0.684111i | \(0.760191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 36.3731i | − | 1.55236i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.59808 | + | 0.500000i | 0.110481 | + | 0.0212622i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.9904 | + | 22.5000i | −0.550420 | + | 0.953356i | 0.447824 | + | 0.894122i | \(0.352199\pi\) |
−0.998244 | + | 0.0592339i | \(0.981134\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5000 | − | 23.3827i | 0.569970 | − | 0.987218i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.3827 | + | 13.5000i | 0.985463 | + | 0.568957i | 0.903915 | − | 0.427712i | \(-0.140680\pi\) |
0.0815478 | + | 0.996669i | \(0.474014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.3827 | + | 4.50000i | 0.981981 | + | 0.188982i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5000 | − | 7.79423i | 0.565949 | − | 0.326751i | −0.189580 | − | 0.981865i | \(-0.560713\pi\) |
0.755530 | + | 0.655114i | \(0.227379\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | −23.3827 | − | 13.5000i | −0.976826 | − | 0.563971i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.9904 | − | 22.5000i | 0.540797 | − | 0.936687i | −0.458062 | − | 0.888920i | \(-0.651456\pi\) |
0.998859 | − | 0.0477669i | \(-0.0152105\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 8.66025i | − | 0.359908i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | + | 20.7846i | 0.995688 | + | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.3827 | + | 13.5000i | −0.968412 | + | 0.559113i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 36.0000i | − | 1.48588i | −0.669359 | − | 0.742940i | \(-0.733431\pi\) | ||
0.669359 | − | 0.742940i | \(-0.266569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | 0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.1865 | + | 10.5000i | −0.746831 | + | 0.431183i | −0.824548 | − | 0.565792i | \(-0.808570\pi\) |
0.0777165 | + | 0.996976i | \(0.475237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.00000i | 0.122782i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.50000 | + | 2.59808i | 0.183865 | + | 0.106155i | 0.589107 | − | 0.808055i | \(-0.299480\pi\) |
−0.405242 | + | 0.914209i | \(0.632813\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.6410i | − | 1.41304i | −0.707695 | − | 0.706518i | \(-0.750265\pi\) | ||
0.707695 | − | 0.706518i | \(-0.249735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.9904 | − | 7.50000i | 0.529009 | − | 0.305424i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.7224 | + | 25.5000i | 0.597565 | + | 1.03501i | 0.993179 | + | 0.116596i | \(0.0371984\pi\) |
−0.395614 | + | 0.918417i | \(0.629468\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.866025 | − | 0.500000i | −0.0349784 | − | 0.0201948i | 0.482409 | − | 0.875946i | \(-0.339762\pi\) |
−0.517387 | + | 0.855751i | \(0.673095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.7846 | −0.836757 | −0.418378 | − | 0.908273i | \(-0.637401\pi\) | ||||
−0.418378 | + | 0.908273i | \(0.637401\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.5000 | − | 12.9904i | −0.904351 | − | 0.522127i | −0.0257420 | − | 0.999669i | \(-0.508195\pi\) |
−0.878609 | + | 0.477541i | \(0.841528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.5000 | + | 23.3827i | 0.541736 | + | 0.938315i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.3827 | − | 4.50000i | −0.936808 | − | 0.180289i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.79423 | + | 13.5000i | 0.311272 | + | 0.539138i | ||||
\(628\) | 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 | ||||||||
\(633\) | −17.3205 | − | 30.0000i | −0.688428 | − | 1.19239i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 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 | ||||||||
\(643\) | 3.46410 | 0.136611 | 0.0683054 | − | 0.997664i | \(-0.478241\pi\) | ||||
0.0683054 | + | 0.997664i | \(0.478241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.79423 | + | 4.50000i | 0.306423 | + | 0.176913i | 0.645325 | − | 0.763908i | \(-0.276722\pi\) |
−0.338902 | + | 0.940822i | \(0.610055\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | 7.79423 | + | 13.5000i | 0.305012 | + | 0.528296i | 0.977264 | − | 0.212026i | \(-0.0680063\pi\) |
−0.672252 | + | 0.740322i | \(0.734673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.1865 | − | 31.5000i | −0.709524 | − | 1.22893i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10.3923i | − | 0.404827i | −0.979300 | − | 0.202413i | \(-0.935122\pi\) | ||
0.979300 | − | 0.202413i | \(-0.0648785\pi\) | |||||||
\(660\) | 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 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | ||||||||
\(673\) | − | 22.0000i | − | 0.848038i | −0.905653 | − | 0.424019i | \(-0.860619\pi\) | ||
0.905653 | − | 0.424019i | \(-0.139381\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.9711 | − | 22.5000i | 1.49778 | − | 0.864745i | 0.497786 | − | 0.867300i | \(-0.334147\pi\) |
0.999997 | + | 0.00255466i | \(0.000813175\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | − | 13.8564i | 0.460518 | − | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.5885i | 0.597351i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.1865 | − | 31.5000i | 0.695888 | − | 1.20531i | −0.273992 | − | 0.961732i | \(-0.588344\pi\) |
0.969880 | − | 0.243582i | \(-0.0783225\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.7750 | − | 19.5000i | −1.28860 | − | 0.743971i | ||||
\(688\) | 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 | ||||||||
\(693\) | −7.79423 | + | 40.5000i | −0.296078 | + | 1.53847i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.5885 | − | 9.00000i | −0.590455 | − | 0.340899i | ||||
\(698\) | 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 | ||||||||
\(703\) | −6.06218 | + | 10.5000i | −0.228639 | + | 0.396015i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.79423 | − | 22.5000i | −0.293132 | − | 0.846200i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5000 | + | 26.8468i | 0.582115 | + | 1.00825i | 0.995228 | + | 0.0975728i | \(0.0311079\pi\) |
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.00000 | 0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.00000i | 0.337053i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.5885 | − | 9.00000i | 0.582162 | − | 0.336111i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.50000 | − | 12.9904i | −0.279703 | − | 0.484459i | 0.691608 | − | 0.722273i | \(-0.256903\pi\) |
−0.971311 | + | 0.237814i | \(0.923569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5000 | − | 2.59808i | −0.502766 | − | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.00000i | 0.111571i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.2487 | −0.899335 | −0.449667 | − | 0.893196i | \(-0.648458\pi\) | ||||
−0.449667 | + | 0.893196i | \(0.648458\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7224 | − | 25.5000i | −0.543785 | − | 0.941864i | −0.998682 | − | 0.0513199i | \(-0.983657\pi\) |
0.454897 | − | 0.890544i | \(-0.349676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9904 | + | 22.5000i | 0.478507 | + | 0.828798i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.50000 | − | 14.7224i | 0.312678 | − | 0.541573i | −0.666264 | − | 0.745716i | \(-0.732107\pi\) |
0.978941 | + | 0.204143i | \(0.0654407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.9615 | −1.90628 | −0.953142 | − | 0.302524i | \(-0.902171\pi\) | ||||
−0.953142 | + | 0.302524i | \(0.902171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.1769 | + | 18.0000i | 1.14070 | + | 0.658586i | ||||
\(748\) | 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 | ||||||||
\(753\) | 20.7846 | + | 36.0000i | 0.757433 | + | 1.31191i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000i | 0.363456i | 0.983349 | + | 0.181728i | \(0.0581691\pi\) | ||||
−0.983349 | + | 0.181728i | \(0.941831\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −14.7224 | − | 42.5000i | −0.532988 | − | 1.53860i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.6410i | 1.24919i | 0.780950 | + | 0.624593i | \(0.214735\pi\) | ||||
−0.780950 | + | 0.624593i | \(0.785265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.5000 | − | 23.3827i | −1.45857 | − | 0.842107i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.7750 | − | 19.5000i | −1.21480 | − | 0.701366i | −0.251000 | − | 0.967987i | \(-0.580760\pi\) |
−0.963802 | + | 0.266621i | \(0.914093\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −30.3109 | + | 10.5000i | −1.08740 | + | 0.376685i | ||||
\(778\) | 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 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.866025 | − | 1.50000i | 0.0308705 | − | 0.0534692i | −0.850177 | − | 0.526496i | \(-0.823505\pi\) |
0.881048 | + | 0.473027i | \(0.156839\pi\) | |||||||
\(788\) | 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 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 18.0000i | − | 0.637593i | −0.947823 | − | 0.318796i | \(-0.896721\pi\) | ||
0.947823 | − | 0.318796i | \(-0.103279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.00000 | −0.318397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.0000 | −0.953998 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.5596 | − | 31.5000i | 1.92537 | − | 1.11161i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 36.3731 | 1.28039 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.5000 | − | 12.9904i | −0.791058 | − | 0.456717i | 0.0492770 | − | 0.998785i | \(-0.484308\pi\) |
−0.840335 | + | 0.542068i | \(0.817642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.9615i | − | 1.82462i | −0.409505 | − | 0.912308i | \(-0.634299\pi\) | ||
0.409505 | − | 0.912308i | \(-0.365701\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.7750 | + | 19.5000i | 1.18454 | + | 0.683895i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.46410 | + | 6.00000i | 0.121194 | + | 0.209913i | ||||
\(818\) | 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 | ||||||||
\(823\) | −6.06218 | − | 3.50000i | −0.211314 | − | 0.122002i | 0.390608 | − | 0.920557i | \(-0.372265\pi\) |
−0.601922 | + | 0.798555i | \(0.705598\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.3923 | −0.361376 | −0.180688 | − | 0.983540i | \(-0.557832\pi\) | ||||
−0.180688 | + | 0.983540i | \(0.557832\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.50000 | − | 0.866025i | −0.0520972 | − | 0.0300783i | 0.473725 | − | 0.880673i | \(-0.342909\pi\) |
−0.525822 | + | 0.850594i | \(0.676242\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.5167i | 0.781094i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.79423 | − | 19.5000i | 0.270054 | − | 0.675635i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.79423 | + | 4.50000i | 0.269408 | + | 0.155543i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.1769 | − | 18.0000i | 1.07379 | − | 0.619953i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −41.5692 | − | 8.00000i | −1.42834 | − | 0.274883i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.0000 | −0.514799 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.5000 | − | 18.1865i | −1.07981 | − | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8564 | 0.474434 | 0.237217 | − | 0.971457i | \(-0.423765\pi\) | ||||
0.237217 | + | 0.971457i | \(0.423765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.5788 | − | 16.5000i | −0.976235 | − | 0.563629i | −0.0751033 | − | 0.997176i | \(-0.523929\pi\) |
−0.901131 | + | 0.433546i | \(0.857262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.5000 | − | 19.9186i | 1.17712 | − | 0.679613i | 0.221777 | − | 0.975097i | \(-0.428814\pi\) |
0.955348 | + | 0.295484i | \(0.0954809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.0000 | + | 5.19615i | 0.920158 | + | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.59808 | − | 4.50000i | −0.0884395 | − | 0.153182i | 0.818412 | − | 0.574632i | \(-0.194855\pi\) |
−0.906852 | + | 0.421450i | \(0.861521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.92820 | − | 12.0000i | 0.235294 | − | 0.407541i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.19615i | 0.176267i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.3923 | − | 18.0000i | 0.351726 | − | 0.609208i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.52628 | − | 5.50000i | 0.321680 | − | 0.185722i | −0.330461 | − | 0.943820i | \(-0.607204\pi\) |
0.652141 | + | 0.758098i | \(0.273871\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 28.0000i | − | 0.942275i | −0.882060 | − | 0.471138i | \(-0.843844\pi\) | ||
0.882060 | − | 0.471138i | \(-0.156156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.59808 | + | 1.50000i | −0.0872349 | + | 0.0503651i | −0.542983 | − | 0.839744i | \(-0.682705\pi\) |
0.455748 | + | 0.890109i | \(0.349372\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0000 | − | 13.8564i | −0.536623 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.7654i | 1.56670i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.59808 | − | 4.50000i | 0.0869413 | − | 0.150587i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 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 | ||||||||
\(903\) | −3.46410 | + | 18.0000i | −0.115278 | + | 0.599002i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.0429 | − | 18.5000i | −1.06397 | − | 0.614282i | −0.137441 | − | 0.990510i | \(-0.543888\pi\) |
−0.926527 | + | 0.376228i | \(0.877221\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −31.1769 | + | 54.0000i | −1.03181 | + | 1.78714i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.3827 | + | 4.50000i | 0.772164 | + | 0.148603i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.50000 | + | 16.4545i | 0.313376 | + | 0.542783i | 0.979091 | − | 0.203423i | \(-0.0652066\pi\) |
−0.665715 | + | 0.746206i | \(0.731873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.0000 | − | 25.9808i | −0.494267 | − | 0.856095i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.5885 | −0.511992 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.5000 | − | 33.7750i | −0.639774 | − | 1.10812i | −0.985482 | − | 0.169779i | \(-0.945695\pi\) |
0.345708 | − | 0.938342i | \(-0.387639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.50000 | + | 9.52628i | 0.245803 | + | 0.312211i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.9808 | −0.850572 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.5692 | 1.35801 | 0.679004 | − | 0.734135i | \(-0.262412\pi\) | ||||
0.679004 | + | 0.734135i | \(0.262412\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 15.5885 | + | 27.0000i | 0.507630 | + | 0.879241i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.3827 | + | 40.5000i | 0.759835 | + | 1.31607i | 0.942934 | + | 0.332979i | \(0.108054\pi\) |
−0.183099 | + | 0.983094i | \(0.558613\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.5000 | + | 38.9711i | −0.729612 | + | 1.26373i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.7846 | 0.673280 | 0.336640 | − | 0.941634i | \(-0.390710\pi\) | ||||
0.336640 | + | 0.941634i | \(0.390710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||||||
\(963\) | 46.7654 | 1.50699 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.0000i | − | 1.28631i | −0.765735 | − | 0.643157i | \(-0.777624\pi\) | ||
0.765735 | − | 0.643157i | \(-0.222376\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −20.7846 | − | 18.0000i | −0.666324 | − | 0.577054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.1865 | − | 31.5000i | 0.581839 | − | 1.00777i | −0.413423 | − | 0.910539i | \(-0.635667\pi\) |
0.995261 | − | 0.0972351i | \(-0.0309999\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 46.7654i | − | 1.49463i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5000 | − | 44.1673i | −0.814152 | − | 1.41015i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.59808 | + | 1.50000i | 0.0828658 | + | 0.0478426i | 0.540860 | − | 0.841112i | \(-0.318099\pi\) |
−0.457995 | + | 0.888955i | \(0.651432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.9904 | − | 4.50000i | 0.413488 | − | 0.143237i | ||||
\(988\) | 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 | ||||||||
\(993\) | 26.8468 | − | 46.5000i | 0.851957 | − | 1.47563i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.2583 | + | 19.5000i | −0.356555 | + | 0.617571i | −0.987383 | − | 0.158352i | \(-0.949382\pi\) |
0.630828 | + | 0.775923i | \(0.282715\pi\) | |||||||
\(998\) | 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 \(a_p\))