Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(899,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.bc (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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 899.2 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.899 |
Dual form | 1575.2.bc.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 \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(1226\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 1.22474i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59808 | + | 0.500000i | 0.981981 | + | 0.188982i | ||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.22474 | − | 0.707107i | −0.369274 | − | 0.213201i | 0.303867 | − | 0.952714i | \(-0.401722\pi\) |
−0.673141 | + | 0.739514i | \(0.735055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.19615 | 1.44115 | 0.720577 | − | 0.693375i | \(-0.243877\pi\) | ||||
0.720577 | + | 0.693375i | \(0.243877\pi\) | |||||||
\(14\) | −1.22474 | − | 3.53553i | −0.327327 | − | 0.944911i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 4.24264 | + | 2.44949i | 1.02899 | + | 0.594089i | 0.916696 | − | 0.399586i | \(-0.130846\pi\) |
0.112296 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | 2.82843 | + | 4.89898i | 0.589768 | + | 1.02151i | 0.994263 | + | 0.106967i | \(0.0341141\pi\) |
−0.404495 | + | 0.914540i | \(0.632553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.67423 | − | 6.36396i | −0.720577 | − | 1.24808i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843i | 0.525226i | 0.964901 | + | 0.262613i | \(0.0845842\pi\) | ||||
−0.964901 | + | 0.262613i | \(0.915416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 0.866025i | 0.269408 | + | 0.155543i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.92820i | − | 1.18818i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.866025 | − | 0.500000i | 0.142374 | − | 0.0821995i | −0.427121 | − | 0.904194i | \(-0.640472\pi\) |
0.569495 | + | 0.821995i | \(0.307139\pi\) | |||||||
\(38\) | 2.12132 | + | 1.22474i | 0.344124 | + | 0.198680i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.34847 | −1.14764 | −0.573819 | − | 0.818982i | \(-0.694539\pi\) | ||||
−0.573819 | + | 0.818982i | \(0.694539\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.00000i | − | 0.152499i | −0.997089 | − | 0.0762493i | \(-0.975706\pi\) | ||
0.997089 | − | 0.0762493i | \(-0.0242945\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | − | 6.92820i | 0.589768 | − | 1.02151i | ||||
\(47\) | 10.6066 | − | 6.12372i | 1.54713 | − | 0.893237i | 0.548773 | − | 0.835971i | \(-0.315095\pi\) |
0.998359 | − | 0.0572655i | \(-0.0182382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.50000 | + | 2.59808i | 0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.41421 | + | 2.44949i | −0.194257 | + | 0.336463i | −0.946657 | − | 0.322244i | \(-0.895563\pi\) |
0.752400 | + | 0.658707i | \(0.228896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.34847 | − | 1.41421i | −0.981981 | − | 0.188982i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.46410 | − | 2.00000i | 0.454859 | − | 0.262613i | ||||
\(59\) | 2.44949 | − | 4.24264i | 0.318896 | − | 0.552345i | −0.661362 | − | 0.750067i | \(-0.730021\pi\) |
0.980258 | + | 0.197722i | \(0.0633545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | + | 1.73205i | −0.384111 | + | 0.221766i | −0.679605 | − | 0.733578i | \(-0.737849\pi\) |
0.295495 | + | 0.955344i | \(0.404516\pi\) | |||||||
\(62\) | − | 2.44949i | − | 0.311086i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.52628 | + | 5.50000i | 1.16382 | + | 0.671932i | 0.952217 | − | 0.305424i | \(-0.0987981\pi\) |
0.211604 | + | 0.977356i | \(0.432131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.07107i | − | 0.839181i | −0.907713 | − | 0.419591i | \(-0.862174\pi\) | ||
0.907713 | − | 0.419591i | \(-0.137826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.866025 | + | 1.50000i | −0.101361 | + | 0.175562i | −0.912245 | − | 0.409644i | \(-0.865653\pi\) |
0.810885 | + | 0.585206i | \(0.198986\pi\) | |||||||
\(74\) | −1.22474 | − | 0.707107i | −0.142374 | − | 0.0821995i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.82843 | − | 2.44949i | −0.322329 | − | 0.279145i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.50000 | + | 4.33013i | 0.281272 | + | 0.487177i | 0.971698 | − | 0.236225i | \(-0.0759104\pi\) |
−0.690426 | + | 0.723403i | \(0.742577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.19615 | + | 9.00000i | 0.573819 | + | 0.993884i | ||||
\(83\) | 7.34847i | 0.806599i | 0.915068 | + | 0.403300i | \(0.132137\pi\) | ||||
−0.915068 | + | 0.403300i | \(0.867863\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.22474 | + | 0.707107i | −0.132068 | + | 0.0762493i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.46410 | + | 2.00000i | 0.369274 | + | 0.213201i | ||||
\(89\) | −2.44949 | − | 4.24264i | −0.259645 | − | 0.449719i | 0.706502 | − | 0.707712i | \(-0.250272\pi\) |
−0.966147 | + | 0.257993i | \(0.916939\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5000 | + | 2.59808i | 1.41518 | + | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.0000 | − | 8.66025i | −1.54713 | − | 0.893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.3923 | −1.05518 | −0.527589 | − | 0.849500i | \(-0.676904\pi\) | ||||
−0.527589 | + | 0.849500i | \(0.676904\pi\) | |||||||
\(98\) | −1.41421 | − | 9.79796i | −0.142857 | − | 0.989743i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.57321 | − | 14.8492i | 0.853067 | − | 1.47755i | −0.0253604 | − | 0.999678i | \(-0.508073\pi\) |
0.878427 | − | 0.477876i | \(-0.158593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.33013 | − | 7.50000i | −0.426660 | − | 0.738997i | 0.569914 | − | 0.821705i | \(-0.306977\pi\) |
−0.996574 | + | 0.0827075i | \(0.973643\pi\) | |||||||
\(104\) | −14.6969 | −1.44115 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00000 | 0.388514 | ||||||||
\(107\) | 1.41421 | + | 2.44949i | 0.136717 | + | 0.236801i | 0.926252 | − | 0.376905i | \(-0.123012\pi\) |
−0.789535 | + | 0.613706i | \(0.789678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.500000 | + | 0.866025i | −0.0478913 | + | 0.0829502i | −0.888977 | − | 0.457951i | \(-0.848583\pi\) |
0.841086 | + | 0.540901i | \(0.181917\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.46410 | + | 10.0000i | 0.327327 | + | 0.944911i | ||||
\(113\) | −1.41421 | −0.133038 | −0.0665190 | − | 0.997785i | \(-0.521189\pi\) | ||||
−0.0665190 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.92820 | −0.637793 | ||||||||
\(119\) | 9.79796 | + | 8.48528i | 0.898177 | + | 0.777844i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.50000 | − | 7.79423i | −0.409091 | − | 0.708566i | ||||
\(122\) | 4.24264 | + | 2.44949i | 0.384111 | + | 0.221766i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.0000i | − | 0.976092i | −0.872818 | − | 0.488046i | \(-0.837710\pi\) | ||
0.872818 | − | 0.488046i | \(-0.162290\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.500000 | − | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.22474 | − | 2.12132i | −0.107006 | − | 0.185341i | 0.807550 | − | 0.589799i | \(-0.200793\pi\) |
−0.914556 | + | 0.404459i | \(0.867460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.33013 | + | 1.50000i | −0.375470 | + | 0.130066i | ||||
\(134\) | − | 15.5563i | − | 1.34386i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.0000 | − | 6.92820i | −1.02899 | − | 0.594089i | ||||
\(137\) | 5.65685 | − | 9.79796i | 0.483298 | − | 0.837096i | −0.516518 | − | 0.856276i | \(-0.672772\pi\) |
0.999816 | + | 0.0191800i | \(0.00610555\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.19615i | 0.440732i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) | ||||
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.66025 | + | 5.00000i | −0.726752 | + | 0.419591i | ||||
\(143\) | −6.36396 | − | 3.67423i | −0.532181 | − | 0.307255i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.44949 | 0.202721 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.89898 | + | 2.82843i | −0.401340 | + | 0.231714i | −0.687062 | − | 0.726599i | \(-0.741100\pi\) |
0.285722 | + | 0.958313i | \(0.407767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0000 | − | 19.0526i | 0.895167 | − | 1.55048i | 0.0615699 | − | 0.998103i | \(-0.480389\pi\) |
0.833597 | − | 0.552372i | \(-0.186277\pi\) | |||||||
\(152\) | 4.24264 | − | 2.44949i | 0.344124 | − | 0.198680i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | + | 5.19615i | −0.0805823 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.66025 | − | 15.0000i | 0.691164 | − | 1.19713i | −0.280293 | − | 0.959914i | \(-0.590432\pi\) |
0.971457 | − | 0.237216i | \(-0.0762349\pi\) | |||||||
\(158\) | 3.53553 | − | 6.12372i | 0.281272 | − | 0.487177i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.89898 | + | 14.1421i | 0.386094 | + | 1.11456i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.66025 | + | 5.00000i | −0.678323 | + | 0.391630i | −0.799223 | − | 0.601035i | \(-0.794755\pi\) |
0.120900 | + | 0.992665i | \(0.461422\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.00000 | − | 5.19615i | 0.698535 | − | 0.403300i | ||||
\(167\) | 7.34847i | 0.568642i | 0.958729 | + | 0.284321i | \(0.0917681\pi\) | ||||
−0.958729 | + | 0.284321i | \(0.908232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.0000 | 1.07692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.48528 | − | 4.89898i | 0.645124 | − | 0.372463i | −0.141462 | − | 0.989944i | \(-0.545180\pi\) |
0.786586 | + | 0.617481i | \(0.211847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.65685i | − | 0.426401i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.46410 | + | 6.00000i | −0.259645 | + | 0.449719i | ||||
\(179\) | 8.57321 | + | 4.94975i | 0.640792 | + | 0.369961i | 0.784920 | − | 0.619598i | \(-0.212704\pi\) |
−0.144127 | + | 0.989559i | \(0.546038\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5885i | 1.15868i | 0.815086 | + | 0.579340i | \(0.196690\pi\) | ||||
−0.815086 | + | 0.579340i | \(0.803310\pi\) | |||||||
\(182\) | −6.36396 | − | 18.3712i | −0.471728 | − | 1.36176i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.00000 | − | 13.8564i | −0.589768 | − | 1.02151i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.46410 | − | 6.00000i | −0.253320 | − | 0.438763i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.22474 | − | 0.707107i | 0.0886194 | − | 0.0511645i | −0.455035 | − | 0.890473i | \(-0.650373\pi\) |
0.543655 | + | 0.839309i | \(0.317040\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.52628 | − | 5.50000i | −0.685717 | − | 0.395899i | 0.116289 | − | 0.993215i | \(-0.462900\pi\) |
−0.802005 | + | 0.597317i | \(0.796234\pi\) | |||||||
\(194\) | 7.34847 | + | 12.7279i | 0.527589 | + | 0.913812i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.7990 | −1.41062 | −0.705310 | − | 0.708899i | \(-0.749192\pi\) | ||||
−0.705310 | + | 0.708899i | \(0.749192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0000 | + | 6.92820i | 0.850657 | + | 0.491127i | 0.860873 | − | 0.508821i | \(-0.169918\pi\) |
−0.0102152 | + | 0.999948i | \(0.503252\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −24.2487 | −1.70613 | ||||||||
\(203\) | −1.41421 | + | 7.34847i | −0.0992583 | + | 0.515761i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.12372 | + | 10.6066i | −0.426660 | + | 0.738997i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.3923 | + | 18.0000i | 0.720577 | + | 1.24808i | ||||
\(209\) | 2.44949 | 0.169435 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0000 | −1.51454 | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||||
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.00000 | − | 3.46410i | 0.136717 | − | 0.236801i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.46410 | + | 3.00000i | 0.235159 | + | 0.203653i | ||||
\(218\) | 1.41421 | 0.0957826 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.0454 | + | 12.7279i | 1.48293 | + | 0.856173i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.7846 | −1.39184 | −0.695920 | − | 0.718119i | \(-0.745003\pi\) | ||||
−0.695920 | + | 0.718119i | \(0.745003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.00000 | + | 1.73205i | 0.0665190 | + | 0.115214i | ||||
\(227\) | 23.3345 | + | 13.4722i | 1.54877 | + | 0.894181i | 0.998236 | + | 0.0593658i | \(0.0189078\pi\) |
0.550530 | + | 0.834815i | \(0.314425\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 8.00000i | − | 0.525226i | ||||||
\(233\) | 4.94975 | + | 8.57321i | 0.324269 | + | 0.561650i | 0.981364 | − | 0.192158i | \(-0.0615485\pi\) |
−0.657095 | + | 0.753807i | \(0.728215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.46410 | − | 18.0000i | 0.224544 | − | 1.16677i | ||||
\(239\) | − | 26.8701i | − | 1.73808i | −0.494742 | − | 0.869040i | \(-0.664738\pi\) | ||
0.494742 | − | 0.869040i | \(-0.335262\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0000 | − | 6.92820i | −0.772988 | − | 0.446285i | 0.0609515 | − | 0.998141i | \(-0.480586\pi\) |
−0.833939 | + | 0.551856i | \(0.813920\pi\) | |||||||
\(242\) | −6.36396 | + | 11.0227i | −0.409091 | + | 0.708566i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.79423 | + | 4.50000i | −0.495935 | + | 0.286328i | ||||
\(248\) | −4.24264 | − | 2.44949i | −0.269408 | − | 0.155543i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.00000i | − | 0.502956i | ||||||
\(254\) | −13.4722 | + | 7.77817i | −0.845321 | + | 0.488046i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.12132 | + | 1.22474i | −0.132324 | + | 0.0763975i | −0.564701 | − | 0.825296i | \(-0.691008\pi\) |
0.432377 | + | 0.901693i | \(0.357675\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50000 | − | 0.866025i | 0.155342 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.73205 | + | 3.00000i | −0.107006 | + | 0.185341i | ||||
\(263\) | 7.07107 | − | 12.2474i | 0.436021 | − | 0.755210i | −0.561358 | − | 0.827573i | \(-0.689721\pi\) |
0.997378 | + | 0.0723633i | \(0.0230541\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.89898 | + | 4.24264i | 0.300376 | + | 0.260133i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.57321 | + | 14.8492i | −0.522718 | + | 0.905374i | 0.476932 | + | 0.878940i | \(0.341749\pi\) |
−0.999651 | + | 0.0264343i | \(0.991585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | + | 6.92820i | −0.728948 | + | 0.420858i | −0.818037 | − | 0.575165i | \(-0.804938\pi\) |
0.0890891 | + | 0.996024i | \(0.471604\pi\) | |||||||
\(272\) | 19.5959i | 1.18818i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.0000 | −0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.9186 | + | 11.5000i | 1.19679 | + | 0.690968i | 0.959839 | − | 0.280553i | \(-0.0905179\pi\) |
0.236953 | + | 0.971521i | \(0.423851\pi\) | |||||||
\(278\) | 6.36396 | − | 3.67423i | 0.381685 | − | 0.220366i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.6274i | 1.34984i | 0.737892 | + | 0.674919i | \(0.235822\pi\) | ||||
−0.737892 | + | 0.674919i | \(0.764178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.866025 | + | 1.50000i | −0.0514799 | + | 0.0891657i | −0.890617 | − | 0.454754i | \(-0.849727\pi\) |
0.839137 | + | 0.543920i | \(0.183060\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.3923i | 0.614510i | ||||||||
\(287\) | −19.0919 | − | 3.67423i | −1.12696 | − | 0.216883i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.50000 | + | 6.06218i | 0.205882 | + | 0.356599i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.6969i | 0.858604i | 0.903161 | + | 0.429302i | \(0.141240\pi\) | ||||
−0.903161 | + | 0.429302i | \(0.858760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.44949 | + | 1.41421i | −0.142374 | + | 0.0821995i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.92820 | + | 4.00000i | 0.401340 | + | 0.231714i | ||||
\(299\) | 14.6969 | + | 25.4558i | 0.849946 | + | 1.47215i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | − | 2.59808i | 0.0288195 | − | 0.149751i | ||||
\(302\) | −31.1127 | −1.79033 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.00000 | − | 3.46410i | −0.344124 | − | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5885 | −0.889680 | −0.444840 | − | 0.895610i | \(-0.646740\pi\) | ||||
−0.444840 | + | 0.895610i | \(0.646740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.57321 | − | 14.8492i | 0.486142 | − | 0.842023i | −0.513731 | − | 0.857951i | \(-0.671737\pi\) |
0.999873 | + | 0.0159282i | \(0.00507031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.06218 | + | 10.5000i | 0.342655 | + | 0.593495i | 0.984925 | − | 0.172983i | \(-0.0553406\pi\) |
−0.642270 | + | 0.766478i | \(0.722007\pi\) | |||||||
\(314\) | −24.4949 | −1.38233 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.07107 | − | 12.2474i | −0.397151 | − | 0.687885i | 0.596222 | − | 0.802819i | \(-0.296668\pi\) |
−0.993373 | + | 0.114934i | \(0.963334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.8564 | − | 16.0000i | 0.772187 | − | 0.891645i | ||||
\(323\) | −8.48528 | −0.472134 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.2474 | + | 7.07107i | 0.678323 | + | 0.391630i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.7846 | 1.14764 | ||||||||
\(329\) | 30.6186 | − | 10.6066i | 1.68806 | − | 0.584761i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5000 | + | 26.8468i | 0.851957 | + | 1.47563i | 0.879440 | + | 0.476011i | \(0.157918\pi\) |
−0.0274825 | + | 0.999622i | \(0.508749\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.00000 | − | 5.19615i | 0.492458 | − | 0.284321i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 23.0000i | − | 1.25289i | −0.779466 | − | 0.626445i | \(-0.784509\pi\) | ||
0.779466 | − | 0.626445i | \(-0.215491\pi\) | |||||||
\(338\) | −9.89949 | − | 17.1464i | −0.538462 | − | 0.932643i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.22474 | − | 2.12132i | −0.0663237 | − | 0.114876i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 2.82843i | 0.152499i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | − | 6.92820i | −0.645124 | − | 0.372463i | ||||
\(347\) | −15.5563 | + | 26.9444i | −0.835109 | + | 1.44645i | 0.0588334 | + | 0.998268i | \(0.481262\pi\) |
−0.893942 | + | 0.448183i | \(0.852071\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3923i | 0.556287i | 0.960539 | + | 0.278144i | \(0.0897191\pi\) | ||||
−0.960539 | + | 0.278144i | \(0.910281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.8492 | + | 8.57321i | 0.790345 | + | 0.456306i | 0.840084 | − | 0.542456i | \(-0.182506\pi\) |
−0.0497387 | + | 0.998762i | \(0.515839\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 14.0000i | − | 0.739923i | ||||||
\(359\) | 24.4949 | − | 14.1421i | 1.29279 | − | 0.746393i | 0.313643 | − | 0.949541i | \(-0.398450\pi\) |
0.979148 | + | 0.203148i | \(0.0651171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 19.0919 | − | 11.0227i | 1.00345 | − | 0.579340i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.866025 | − | 1.50000i | 0.0452062 | − | 0.0782994i | −0.842537 | − | 0.538639i | \(-0.818939\pi\) |
0.887743 | + | 0.460339i | \(0.152272\pi\) | |||||||
\(368\) | −11.3137 | + | 19.5959i | −0.589768 | + | 1.02151i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.89898 | + | 5.65685i | −0.254342 | + | 0.293689i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.1147 | − | 14.5000i | 1.30039 | − | 0.750782i | 0.319921 | − | 0.947444i | \(-0.396344\pi\) |
0.980471 | + | 0.196663i | \(0.0630104\pi\) | |||||||
\(374\) | −4.89898 | + | 8.48528i | −0.253320 | + | 0.438763i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −30.0000 | + | 17.3205i | −1.54713 | + | 0.893237i | ||||
\(377\) | 14.6969i | 0.756931i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.00000 | 0.359566 | 0.179783 | − | 0.983706i | \(-0.442460\pi\) | ||||
0.179783 | + | 0.983706i | \(0.442460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.73205 | − | 1.00000i | −0.0886194 | − | 0.0511645i | ||||
\(383\) | −16.9706 | + | 9.79796i | −0.867155 | + | 0.500652i | −0.866402 | − | 0.499347i | \(-0.833573\pi\) |
−0.000753393 | 1.00000i | \(0.500240\pi\) | ||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.5563i | 0.791797i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.2702 | + | 13.4350i | 1.17984 | + | 0.681183i | 0.955978 | − | 0.293437i | \(-0.0947991\pi\) |
0.223865 | + | 0.974620i | \(0.428132\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.7128i | 1.40150i | ||||||||
\(392\) | −18.3848 | − | 7.34847i | −0.928571 | − | 0.371154i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.0000 | + | 24.2487i | 0.705310 | + | 1.22163i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.866025 | − | 1.50000i | −0.0434646 | − | 0.0752828i | 0.843475 | − | 0.537169i | \(-0.180506\pi\) |
−0.886939 | + | 0.461886i | \(0.847173\pi\) | |||||||
\(398\) | − | 19.5959i | − | 0.982255i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.1464 | + | 9.89949i | −0.856252 | + | 0.494357i | −0.862755 | − | 0.505622i | \(-0.831263\pi\) |
0.00650355 | + | 0.999979i | \(0.497930\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.79423 | + | 4.50000i | 0.388258 | + | 0.224161i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.0000 | − | 3.46410i | 0.496292 | − | 0.171920i | ||||
\(407\) | −1.41421 | −0.0701000 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.5000 | − | 16.4545i | −1.40923 | − | 0.813622i | −0.413920 | − | 0.910313i | \(-0.635841\pi\) |
−0.995314 | + | 0.0966915i | \(0.969174\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.48528 | − | 9.79796i | 0.417533 | − | 0.482126i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.73205 | − | 3.00000i | −0.0847174 | − | 0.146735i | ||||
\(419\) | −36.7423 | −1.79498 | −0.897491 | − | 0.441034i | \(-0.854612\pi\) | ||||
−0.897491 | + | 0.441034i | \(0.854612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 15.5563 | + | 26.9444i | 0.757271 | + | 1.31163i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.00000 | − | 6.92820i | 0.194257 | − | 0.336463i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.66025 | + | 3.00000i | −0.419099 | + | 0.145180i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.4722 | + | 7.77817i | 0.648933 | + | 0.374661i | 0.788047 | − | 0.615615i | \(-0.211092\pi\) |
−0.139114 | + | 0.990276i | \(0.544426\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.5885 | −0.749133 | −0.374567 | − | 0.927200i | \(-0.622209\pi\) | ||||
−0.374567 | + | 0.927200i | \(0.622209\pi\) | |||||||
\(434\) | 1.22474 | − | 6.36396i | 0.0587896 | − | 0.305480i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.48528 | − | 4.89898i | −0.405906 | − | 0.234350i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.0000 | + | 13.8564i | −1.14546 | + | 0.661330i | −0.947776 | − | 0.318936i | \(-0.896674\pi\) |
−0.197681 | + | 0.980266i | \(0.563341\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 36.0000i | − | 1.71235i | ||||||
\(443\) | 19.7990 | + | 34.2929i | 0.940678 | + | 1.62930i | 0.764181 | + | 0.645002i | \(0.223143\pi\) |
0.176497 | + | 0.984301i | \(0.443523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.6969 | + | 25.4558i | 0.695920 | + | 1.20537i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.7846 | + | 4.00000i | 0.981981 | + | 0.188982i | ||||
\(449\) | 7.07107i | 0.333704i | 0.985982 | + | 0.166852i | \(0.0533603\pi\) | ||||
−0.985982 | + | 0.166852i | \(0.946640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | + | 5.19615i | 0.423793 | + | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 38.1051i | − | 1.78836i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.33013 | + | 2.50000i | −0.202555 | + | 0.116945i | −0.597847 | − | 0.801611i | \(-0.703977\pi\) |
0.395292 | + | 0.918556i | \(0.370643\pi\) | |||||||
\(458\) | 27.5772 | + | 15.9217i | 1.28860 | + | 0.743971i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.6969 | −0.684505 | −0.342252 | − | 0.939608i | \(-0.611190\pi\) | ||||
−0.342252 | + | 0.939608i | \(0.611190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.0000i | − | 0.604161i | −0.953282 | − | 0.302081i | \(-0.902319\pi\) | ||
0.953282 | − | 0.302081i | \(-0.0976812\pi\) | |||||||
\(464\) | −9.79796 | + | 5.65685i | −0.454859 | + | 0.262613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.00000 | − | 12.1244i | 0.324269 | − | 0.561650i | ||||
\(467\) | 23.3345 | − | 13.4722i | 1.07979 | − | 0.623419i | 0.148952 | − | 0.988844i | \(-0.452410\pi\) |
0.930841 | + | 0.365426i | \(0.119077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.0000 | + | 19.0526i | 1.01587 | + | 0.879765i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.92820 | + | 12.0000i | −0.318896 | + | 0.552345i | ||||
\(473\) | −0.707107 | + | 1.22474i | −0.0325128 | + | 0.0563138i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −32.9090 | + | 19.0000i | −1.50522 | + | 0.869040i | ||||
\(479\) | 2.44949 | − | 4.24264i | 0.111920 | − | 0.193851i | −0.804624 | − | 0.593784i | \(-0.797633\pi\) |
0.916544 | + | 0.399933i | \(0.130967\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50000 | − | 2.59808i | 0.205182 | − | 0.118462i | ||||
\(482\) | 19.5959i | 0.892570i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7224 | + | 8.50000i | 0.667137 | + | 0.385172i | 0.794991 | − | 0.606621i | \(-0.207476\pi\) |
−0.127854 | + | 0.991793i | \(0.540809\pi\) | |||||||
\(488\) | 8.48528 | − | 4.89898i | 0.384111 | − | 0.221766i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.3137i | − | 0.510581i | −0.966864 | − | 0.255290i | \(-0.917829\pi\) | ||
0.966864 | − | 0.255290i | \(-0.0821710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.92820 | + | 12.0000i | −0.312031 | + | 0.540453i | ||||
\(494\) | 11.0227 | + | 6.36396i | 0.495935 | + | 0.286328i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.92820i | 0.311086i | ||||||||
\(497\) | 3.53553 | − | 18.3712i | 0.158590 | − | 0.824060i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5000 | − | 21.6506i | −0.559577 | − | 0.969216i | −0.997532 | − | 0.0702185i | \(-0.977630\pi\) |
0.437955 | − | 0.898997i | \(-0.355703\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.0454i | 0.982956i | 0.870890 | + | 0.491478i | \(0.163543\pi\) | ||||
−0.870890 | + | 0.491478i | \(0.836457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.79796 | + | 5.65685i | −0.435572 | + | 0.251478i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.22474 | + | 2.12132i | 0.0542859 | + | 0.0940259i | 0.891891 | − | 0.452250i | \(-0.149378\pi\) |
−0.837605 | + | 0.546276i | \(0.816045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | + | 3.46410i | −0.132712 | + | 0.153243i | ||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.00000 | + | 1.73205i | 0.132324 | + | 0.0763975i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.3205 | −0.761755 | ||||||||
\(518\) | −2.82843 | − | 2.44949i | −0.124274 | − | 0.107624i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.44949 | + | 4.24264i | −0.107314 | + | 0.185873i | −0.914681 | − | 0.404176i | \(-0.867558\pi\) |
0.807367 | + | 0.590049i | \(0.200892\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.866025 | + | 1.50000i | 0.0378686 | + | 0.0655904i | 0.884339 | − | 0.466846i | \(-0.154610\pi\) |
−0.846470 | + | 0.532437i | \(0.821276\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.0000 | −0.872041 | ||||||||
\(527\) | 4.24264 | + | 7.34847i | 0.184812 | + | 0.320104i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.50000 | + | 7.79423i | −0.195652 | + | 0.338880i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.1838 | −1.65392 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −26.9444 | − | 15.5563i | −1.16382 | − | 0.671932i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.2487 | 1.04544 | ||||||||
\(539\) | −6.12372 | − | 7.77817i | −0.263767 | − | 0.335030i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.50000 | − | 14.7224i | −0.365444 | − | 0.632967i | 0.623404 | − | 0.781900i | \(-0.285749\pi\) |
−0.988847 | + | 0.148933i | \(0.952416\pi\) | |||||||
\(542\) | 16.9706 | + | 9.79796i | 0.728948 | + | 0.420858i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0000i | 0.427569i | 0.976881 | + | 0.213785i | \(0.0685791\pi\) | ||||
−0.976881 | + | 0.213785i | \(0.931421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.44949 | − | 4.24264i | −0.104352 | − | 0.180743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.33013 | + | 12.5000i | 0.184136 | + | 0.531554i | ||||
\(554\) | − | 32.5269i | − | 1.38194i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.77817 | − | 13.4722i | 0.329572 | − | 0.570835i | −0.652855 | − | 0.757483i | \(-0.726429\pi\) |
0.982427 | + | 0.186648i | \(0.0597623\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.19615i | − | 0.219774i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.7128 | − | 16.0000i | 1.16899 | − | 0.674919i | ||||
\(563\) | −23.3345 | − | 13.4722i | −0.983433 | − | 0.567785i | −0.0801281 | − | 0.996785i | \(-0.525533\pi\) |
−0.903305 | + | 0.428999i | \(0.858866\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.44949 | 0.102960 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.0000i | 0.839181i | ||||||||
\(569\) | −1.22474 | + | 0.707107i | −0.0513440 | + | 0.0296435i | −0.525452 | − | 0.850823i | \(-0.676104\pi\) |
0.474108 | + | 0.880467i | \(0.342771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.50000 | + | 9.52628i | −0.230168 | + | 0.398662i | −0.957857 | − | 0.287244i | \(-0.907261\pi\) |
0.727690 | + | 0.685907i | \(0.240594\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.00000 | + | 25.9808i | 0.375653 | + | 1.08442i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.866025 | − | 1.50000i | 0.0360531 | − | 0.0624458i | −0.847436 | − | 0.530898i | \(-0.821855\pi\) |
0.883489 | + | 0.468452i | \(0.155188\pi\) | |||||||
\(578\) | 4.94975 | − | 8.57321i | 0.205882 | − | 0.356599i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.67423 | + | 19.0919i | −0.152433 | + | 0.792065i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.46410 | − | 2.00000i | 0.143468 | − | 0.0828315i | ||||
\(584\) | 2.44949 | − | 4.24264i | 0.101361 | − | 0.175562i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.0000 | − | 10.3923i | 0.743573 | − | 0.429302i | ||||
\(587\) | 14.6969i | 0.606608i | 0.952894 | + | 0.303304i | \(0.0980897\pi\) | ||||
−0.952894 | + | 0.303304i | \(0.901910\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00000 | −0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.46410 | + | 2.00000i | 0.142374 | + | 0.0821995i | ||||
\(593\) | 14.8492 | − | 8.57321i | 0.609785 | − | 0.352060i | −0.163096 | − | 0.986610i | \(-0.552148\pi\) |
0.772881 | + | 0.634550i | \(0.218815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.7846 | − | 36.0000i | 0.849946 | − | 1.47215i | ||||
\(599\) | 4.89898 | + | 2.82843i | 0.200167 | + | 0.115566i | 0.596733 | − | 0.802440i | \(-0.296465\pi\) |
−0.396566 | + | 0.918006i | \(0.629798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.9808i | − | 1.05978i | −0.848067 | − | 0.529889i | \(-0.822234\pi\) | ||
0.848067 | − | 0.529889i | \(-0.177766\pi\) | |||||||
\(602\) | −3.53553 | + | 1.22474i | −0.144098 | + | 0.0499169i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.9186 | + | 34.5000i | 0.808470 | + | 1.40031i | 0.913923 | + | 0.405887i | \(0.133038\pi\) |
−0.105453 | + | 0.994424i | \(0.533629\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 55.1135 | − | 31.8198i | 2.22965 | − | 1.28729i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.92820 | − | 4.00000i | −0.279827 | − | 0.161558i | 0.353518 | − | 0.935428i | \(-0.384985\pi\) |
−0.633345 | + | 0.773869i | \(0.718319\pi\) | |||||||
\(614\) | 11.0227 | + | 19.0919i | 0.444840 | + | 0.770486i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.00000 | + | 6.92820i | 0.322329 | + | 0.279145i | ||||
\(617\) | −24.0416 | −0.967880 | −0.483940 | − | 0.875101i | \(-0.660795\pi\) | ||||
−0.483940 | + | 0.875101i | \(0.660795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.5000 | + | 14.7224i | 1.02493 | + | 0.591744i | 0.915529 | − | 0.402253i | \(-0.131773\pi\) |
0.109403 | + | 0.993997i | \(0.465106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.2487 | −0.972285 | ||||||||
\(623\) | −4.24264 | − | 12.2474i | −0.169978 | − | 0.490684i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.57321 | − | 14.8492i | 0.342655 | − | 0.593495i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.89898 | 0.195335 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0000 | 1.51276 | 0.756378 | − | 0.654135i | \(-0.226967\pi\) | ||||
0.756378 | + | 0.654135i | \(0.226967\pi\) | |||||||
\(632\) | −7.07107 | − | 12.2474i | −0.281272 | − | 0.487177i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.0000 | + | 17.3205i | −0.397151 | + | 0.687885i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.7750 | + | 13.5000i | 1.33821 | + | 0.534889i | ||||
\(638\) | −5.65685 | −0.223957 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.2474 | − | 7.07107i | −0.483745 | − | 0.279290i | 0.238231 | − | 0.971209i | \(-0.423433\pi\) |
−0.721976 | + | 0.691918i | \(0.756766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.9808 | −1.02458 | −0.512291 | − | 0.858812i | \(-0.671203\pi\) | ||||
−0.512291 | + | 0.858812i | \(0.671203\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | + | 10.3923i | 0.236067 | + | 0.408880i | ||||
\(647\) | −14.8492 | − | 8.57321i | −0.583784 | − | 0.337048i | 0.178852 | − | 0.983876i | \(-0.442762\pi\) |
−0.762636 | + | 0.646828i | \(0.776095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | + | 3.46410i | −0.235521 | + | 0.135978i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.53553 | − | 6.12372i | −0.138356 | − | 0.239640i | 0.788518 | − | 0.615011i | \(-0.210849\pi\) |
−0.926875 | + | 0.375371i | \(0.877515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.6969 | − | 25.4558i | −0.573819 | − | 0.993884i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −34.6410 | − | 30.0000i | −1.35045 | − | 1.16952i | ||||
\(659\) | − | 22.6274i | − | 0.881439i | −0.897645 | − | 0.440720i | \(-0.854723\pi\) | ||
0.897645 | − | 0.440720i | \(-0.145277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.5000 | − | 14.7224i | −0.991835 | − | 0.572636i | −0.0860127 | − | 0.996294i | \(-0.527413\pi\) |
−0.905822 | + | 0.423658i | \(0.860746\pi\) | |||||||
\(662\) | 21.9203 | − | 37.9671i | 0.851957 | − | 1.47563i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 20.7846i | − | 0.806599i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8564 | + | 8.00000i | −0.536522 | + | 0.309761i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.89898 | 0.189123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.0000i | 1.34915i | 0.738206 | + | 0.674575i | \(0.235673\pi\) | ||||
−0.738206 | + | 0.674575i | \(0.764327\pi\) | |||||||
\(674\) | −28.1691 | + | 16.2635i | −1.08503 | + | 0.626445i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.48528 | + | 4.89898i | −0.326116 | + | 0.188283i | −0.654115 | − | 0.756395i | \(-0.726959\pi\) |
0.327999 | + | 0.944678i | \(0.393626\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.0000 | − | 5.19615i | −1.03616 | − | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.73205 | + | 3.00000i | −0.0663237 | + | 0.114876i | ||||
\(683\) | 24.0416 | − | 41.6413i | 0.919927 | − | 1.59336i | 0.120405 | − | 0.992725i | \(-0.461581\pi\) |
0.799522 | − | 0.600636i | \(-0.205086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.22474 | − | 26.1630i | 0.0467610 | − | 0.998906i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.46410 | − | 2.00000i | 0.132068 | − | 0.0762493i | ||||
\(689\) | −7.34847 | + | 12.7279i | −0.279954 | + | 0.484895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.5000 | − | 21.6506i | 1.42657 | − | 0.823629i | 0.429719 | − | 0.902963i | \(-0.358613\pi\) |
0.996848 | + | 0.0793336i | \(0.0252792\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44.0000 | 1.67022 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.1769 | − | 18.0000i | −1.18091 | − | 0.681799i | ||||
\(698\) | 12.7279 | − | 7.34847i | 0.481759 | − | 0.278144i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.65685i | 0.213656i | 0.994277 | + | 0.106828i | \(0.0340695\pi\) | ||||
−0.994277 | + | 0.106828i | \(0.965931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.866025 | + | 1.50000i | −0.0326628 | + | 0.0565736i | ||||
\(704\) | −9.79796 | − | 5.65685i | −0.369274 | − | 0.213201i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 24.2487i | − | 0.912612i | ||||||
\(707\) | 29.6985 | − | 34.2929i | 1.11693 | − | 1.28972i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.0000 | − | 34.6410i | −0.751116 | − | 1.30097i | −0.947282 | − | 0.320400i | \(-0.896183\pi\) |
0.196167 | − | 0.980571i | \(-0.437151\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.92820 | + | 12.0000i | 0.259645 | + | 0.449719i | ||||
\(713\) | 9.79796i | 0.366936i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −34.6410 | − | 20.0000i | −1.29279 | − | 0.746393i | ||||
\(719\) | −13.4722 | − | 23.3345i | −0.502428 | − | 0.870231i | −0.999996 | − | 0.00280593i | \(-0.999107\pi\) |
0.497568 | − | 0.867425i | \(-0.334226\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.50000 | − | 21.6506i | −0.279315 | − | 0.806312i | ||||
\(722\) | 22.6274 | 0.842105 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9808 | −0.963573 | −0.481787 | − | 0.876289i | \(-0.660012\pi\) | ||||
−0.481787 | + | 0.876289i | \(0.660012\pi\) | |||||||
\(728\) | −38.1838 | − | 7.34847i | −1.41518 | − | 0.272352i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.44949 | − | 4.24264i | 0.0905977 | − | 0.156920i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.9186 | − | 34.5000i | −0.735710 | − | 1.27429i | −0.954411 | − | 0.298495i | \(-0.903515\pi\) |
0.218702 | − | 0.975792i | \(-0.429818\pi\) | |||||||
\(734\) | −2.44949 | −0.0904123 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.77817 | − | 13.4722i | −0.286513 | − | 0.496255i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.500000 | + | 0.866025i | −0.0183928 | + | 0.0318573i | −0.875075 | − | 0.483987i | \(-0.839188\pi\) |
0.856683 | + | 0.515844i | \(0.172522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.3923 | + | 2.00000i | 0.381514 | + | 0.0734223i | ||||
\(743\) | 24.0416 | 0.882002 | 0.441001 | − | 0.897507i | \(-0.354624\pi\) | ||||
0.441001 | + | 0.897507i | \(0.354624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35.5176 | − | 20.5061i | −1.30039 | − | 0.750782i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.44949 | + | 7.07107i | 0.0895024 | + | 0.258371i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.5000 | − | 25.1147i | −0.529113 | − | 0.916450i | −0.999424 | − | 0.0339490i | \(-0.989192\pi\) |
0.470311 | − | 0.882501i | \(-0.344142\pi\) | |||||||
\(752\) | 42.4264 | + | 24.4949i | 1.54713 | + | 0.893237i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.0000 | − | 10.3923i | 0.655521 | − | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.00000i | − | 0.0726912i | −0.999339 | − | 0.0363456i | \(-0.988428\pi\) | ||
0.999339 | − | 0.0363456i | \(-0.0115717\pi\) | |||||||
\(758\) | −4.94975 | − | 8.57321i | −0.179783 | − | 0.311393i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2474 | − | 21.2132i | −0.443970 | − | 0.768978i | 0.554010 | − | 0.832510i | \(-0.313097\pi\) |
−0.997980 | + | 0.0635319i | \(0.979764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.73205 | + | 2.00000i | −0.0627044 | + | 0.0724049i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | + | 13.8564i | 0.867155 | + | 0.500652i | ||||
\(767\) | 12.7279 | − | 22.0454i | 0.459579 | − | 0.796014i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.9808i | − | 0.936890i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) | ||
0.883493 | − | 0.468445i | \(-0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.3345 | − | 13.4722i | −0.839284 | − | 0.484561i | 0.0177365 | − | 0.999843i | \(-0.494354\pi\) |
−0.857021 | + | 0.515282i | \(0.827687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29.3939 | 1.05518 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 38.0000i | − | 1.36237i | ||||||
\(779\) | 11.0227 | − | 6.36396i | 0.394929 | − | 0.228013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.00000 | + | 8.66025i | −0.178914 | + | 0.309888i | ||||
\(782\) | 33.9411 | − | 19.5959i | 1.21373 | − | 0.700749i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.00000 | + | 27.7128i | 0.142857 | + | 0.989743i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.5167 | + | 39.0000i | −0.802632 | + | 1.39020i | 0.115246 | + | 0.993337i | \(0.463234\pi\) |
−0.917878 | + | 0.396863i | \(0.870099\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.67423 | − | 0.707107i | −0.130641 | − | 0.0251418i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.5885 | + | 9.00000i | −0.553562 | + | 0.319599i | ||||
\(794\) | −1.22474 | + | 2.12132i | −0.0434646 | + | 0.0752828i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.3939i | 1.04118i | 0.853805 | + | 0.520592i | \(0.174289\pi\) | ||||
−0.853805 | + | 0.520592i | \(0.825711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.0000 | 2.12265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.2487 | + | 14.0000i | 0.856252 | + | 0.494357i | ||||
\(803\) | 2.12132 | − | 1.22474i | 0.0748598 | − | 0.0432203i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 12.7279i | − | 0.448322i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −24.2487 | + | 42.0000i | −0.853067 | + | 1.47755i | ||||
\(809\) | −35.5176 | − | 20.5061i | −1.24873 | − | 0.720956i | −0.277876 | − | 0.960617i | \(-0.589630\pi\) |
−0.970857 | + | 0.239661i | \(0.922964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.00000 | + | 1.73205i | 0.0350500 | + | 0.0607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.866025 | + | 1.50000i | 0.0302984 | + | 0.0524784i | ||||
\(818\) | 46.5403i | 1.62724i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.8207 | + | 12.0208i | −0.726646 | + | 0.419529i | −0.817194 | − | 0.576363i | \(-0.804472\pi\) |
0.0905478 | + | 0.995892i | \(0.471138\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.4449 | + | 17.0000i | 1.02638 | + | 0.592583i | 0.915947 | − | 0.401300i | \(-0.131442\pi\) |
0.110437 | + | 0.993883i | \(0.464775\pi\) | |||||||
\(824\) | 12.2474 | + | 21.2132i | 0.426660 | + | 0.738997i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0000 | − | 3.46410i | −0.626300 | − | 0.120532i | ||||
\(827\) | −7.07107 | −0.245885 | −0.122943 | − | 0.992414i | \(-0.539233\pi\) | ||||
−0.122943 | + | 0.992414i | \(0.539233\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.5692 | 1.44115 | ||||||||
\(833\) | 21.2132 | + | 26.9444i | 0.734994 | + | 0.933568i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.9808 | + | 45.0000i | 0.897491 | + | 1.55450i | ||||
\(839\) | 14.6969 | 0.507395 | 0.253697 | − | 0.967284i | \(-0.418353\pi\) | ||||
0.253697 | + | 0.967284i | \(0.418353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0.707107 | + | 1.22474i | 0.0243685 | + | 0.0422075i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.79423 | − | 22.5000i | −0.267813 | − | 0.773109i | ||||
\(848\) | −11.3137 | −0.388514 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.89898 | + | 2.82843i | 0.167935 | + | 0.0969572i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.3731 | −1.24539 | −0.622695 | − | 0.782465i | \(-0.713962\pi\) | ||||
−0.622695 | + | 0.782465i | \(0.713962\pi\) | |||||||
\(854\) | 9.79796 | + | 8.48528i | 0.335279 | + | 0.290360i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | − | 6.92820i | −0.136717 | − | 0.236801i | ||||
\(857\) | −33.9411 | − | 19.5959i | −1.15941 | − | 0.669384i | −0.208245 | − | 0.978077i | \(-0.566775\pi\) |
−0.951162 | + | 0.308693i | \(0.900108\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.0000 | + | 19.0526i | −1.12595 | + | 0.650065i | −0.942912 | − | 0.333042i | \(-0.891925\pi\) |
−0.183033 | + | 0.983107i | \(0.558592\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 22.0000i | − | 0.749323i | ||||||
\(863\) | −20.5061 | − | 35.5176i | −0.698036 | − | 1.20903i | −0.969147 | − | 0.246485i | \(-0.920724\pi\) |
0.271111 | − | 0.962548i | \(-0.412609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.0227 | + | 19.0919i | 0.374567 | + | 0.648769i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.07107i | − | 0.239870i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.5000 | + | 28.5788i | 1.67724 | + | 0.968357i | ||||
\(872\) | 1.41421 | − | 2.44949i | 0.0478913 | − | 0.0829502i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.8564i | 0.468700i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.3205 | + | 10.0000i | −0.584872 | + | 0.337676i | −0.763067 | − | 0.646319i | \(-0.776307\pi\) |
0.178195 | + | 0.983995i | \(0.442974\pi\) | |||||||
\(878\) | 33.9411 | + | 19.5959i | 1.14546 | + | 0.661330i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.0000i | 0.370179i | 0.982722 | + | 0.185090i | \(0.0592576\pi\) | ||||
−0.982722 | + | 0.185090i | \(0.940742\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.0000 | − | 48.4974i | 0.940678 | − | 1.62930i | ||||
\(887\) | 36.0624 | − | 20.8207i | 1.21086 | − | 0.699089i | 0.247912 | − | 0.968783i | \(-0.420256\pi\) |
0.962946 | + | 0.269693i | \(0.0869222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.50000 | − | 28.5788i | 0.184464 | − | 0.958503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.6066 | + | 18.3712i | −0.354936 | + | 0.614768i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.79796 | − | 28.2843i | −0.327327 | − | 0.944911i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.66025 | − | 5.00000i | 0.288996 | − | 0.166852i | ||||
\(899\) | −2.44949 | + | 4.24264i | −0.0816951 | + | 0.141500i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | + | 6.92820i | −0.399778 | + | 0.230812i | ||||
\(902\) | − | 14.6969i | − | 0.489355i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.00000 | 0.133038 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.33013 | + | 2.50000i | 0.143780 | + | 0.0830111i | 0.570164 | − | 0.821531i | \(-0.306880\pi\) |
−0.426385 | + | 0.904542i | \(0.640213\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 53.7401i | − | 1.78049i | −0.455483 | − | 0.890245i | \(-0.650533\pi\) | ||
0.455483 | − | 0.890245i | \(-0.349467\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.19615 | − | 9.00000i | 0.171968 | − | 0.297857i | ||||
\(914\) | 6.12372 | + | 3.53553i | 0.202555 | + | 0.116945i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.12132 | − | 6.12372i | −0.0700522 | − | 0.202223i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.50000 | + | 14.7224i | 0.280389 | + | 0.485648i | 0.971481 | − | 0.237119i | \(-0.0762032\pi\) |
−0.691091 | + | 0.722767i | \(0.742870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.3923 | + | 18.0000i | 0.342252 | + | 0.592798i | ||||
\(923\) | − | 36.7423i | − | 1.20939i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.9217 | + | 9.19239i | −0.523219 | + | 0.302081i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.1691 | − | 48.7904i | −0.924199 | − | 1.60076i | −0.792844 | − | 0.609425i | \(-0.791400\pi\) |
−0.131355 | − | 0.991335i | \(-0.541933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.0000 | + | 1.73205i | −0.393284 | + | 0.0567657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.0000 | − | 19.0526i | −1.07979 | − | 0.623419i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.7654 | 1.52776 | 0.763879 | − | 0.645359i | \(-0.223292\pi\) | ||||
0.763879 | + | 0.645359i | \(0.223292\pi\) | |||||||
\(938\) | 7.77817 | − | 40.4166i | 0.253966 | − | 1.31965i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.4949 | + | 42.4264i | −0.798511 | + | 1.38306i | 0.122075 | + | 0.992521i | \(0.461045\pi\) |
−0.920586 | + | 0.390540i | \(0.872288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.7846 | − | 36.0000i | −0.676840 | − | 1.17232i | ||||
\(944\) | 19.5959 | 0.637793 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | 24.7487 | + | 42.8661i | 0.804226 | + | 1.39296i | 0.916812 | + | 0.399318i | \(0.130753\pi\) |
−0.112586 | + | 0.993642i | \(0.535914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.50000 | + | 7.79423i | −0.146076 | + | 0.253011i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −27.7128 | − | 24.0000i | −0.898177 | − | 0.777844i | ||||
\(953\) | −5.65685 | −0.183243 | −0.0916217 | − | 0.995794i | \(-0.529205\pi\) | ||||
−0.0916217 | + | 0.995794i | \(0.529205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.92820 | −0.223840 | ||||||||
\(959\) | 19.5959 | − | 22.6274i | 0.632785 | − | 0.730677i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | −6.36396 | − | 3.67423i | −0.205182 | − | 0.118462i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0000i | 0.418052i | 0.977910 | + | 0.209026i | \(0.0670293\pi\) | ||||
−0.977910 | + | 0.209026i | \(0.932971\pi\) | |||||||
\(968\) | 12.7279 | + | 22.0454i | 0.409091 | + | 0.708566i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.5959 | − | 33.9411i | −0.628863 | − | 1.08922i | −0.987780 | − | 0.155853i | \(-0.950187\pi\) |
0.358917 | − | 0.933369i | \(-0.383146\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.59808 | + | 13.5000i | −0.0832905 | + | 0.432790i | ||||
\(974\) | − | 24.0416i | − | 0.770344i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0000 | − | 6.92820i | −0.384111 | − | 0.221766i | ||||
\(977\) | 3.53553 | − | 6.12372i | 0.113112 | − | 0.195915i | −0.803912 | − | 0.594749i | \(-0.797252\pi\) |
0.917023 | + | 0.398833i | \(0.130585\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.92820i | 0.221426i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.8564 | + | 8.00000i | −0.442176 | + | 0.255290i | ||||
\(983\) | −4.24264 | − | 2.44949i | −0.135319 | − | 0.0781266i | 0.430812 | − | 0.902442i | \(-0.358227\pi\) |
−0.566131 | + | 0.824315i | \(0.691561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19.5959 | 0.624061 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.89898 | − | 2.82843i | 0.155778 | − | 0.0899388i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5000 | + | 30.3109i | −0.555906 | + | 0.962857i | 0.441927 | + | 0.897051i | \(0.354295\pi\) |
−0.997832 | + | 0.0658059i | \(0.979038\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.0000 | + | 8.66025i | −0.792952 | + | 0.274687i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.7224 | + | 25.5000i | −0.466264 | + | 0.807593i | −0.999258 | − | 0.0385262i | \(-0.987734\pi\) |
0.532993 | + | 0.846119i | \(0.321067\pi\) | |||||||
\(998\) | −17.6777 | + | 30.6186i | −0.559577 | + | 0.969216i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))