Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(149,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.r (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: | \(5.58952814149\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.149 |
Dual form | 700.2.r.b.249.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | −0.728714 | − | 0.684819i | \(-0.759881\pi\) |
0.228714 | + | 0.973494i | \(0.426548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 1.73205i | −0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.59808 | − | 1.50000i | 0.630126 | − | 0.363803i | −0.150675 | − | 0.988583i | \(-0.548145\pi\) |
0.780801 | + | 0.624780i | \(0.214811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | + | 2.59808i | −0.109109 | + | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.59808 | + | 1.50000i | 0.541736 | + | 0.312772i | 0.745782 | − | 0.666190i | \(-0.232076\pi\) |
−0.204046 | + | 0.978961i | \(0.565409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.00000i | − | 0.962250i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.50000 | + | 6.06218i | 0.628619 | + | 1.08880i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.59808 | − | 1.50000i | −0.452267 | − | 0.261116i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.866025 | + | 0.500000i | 0.142374 | + | 0.0821995i | 0.569495 | − | 0.821995i | \(-0.307139\pi\) |
−0.427121 | + | 0.904194i | \(0.640472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | + | 1.73205i | 0.160128 | + | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.79423 | + | 4.50000i | 1.13691 | + | 0.656392i | 0.945662 | − | 0.325150i | \(-0.105415\pi\) |
0.191243 | + | 0.981543i | \(0.438748\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.59808 | + | 1.50000i | −0.356873 | + | 0.206041i | −0.667708 | − | 0.744423i | \(-0.732725\pi\) |
0.310835 | + | 0.950464i | \(0.399391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.00000i | − | 0.132453i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.50000 | + | 7.79423i | 0.585850 | + | 1.01472i | 0.994769 | + | 0.102151i | \(0.0325726\pi\) |
−0.408919 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.73205 | + | 5.00000i | 0.218218 | + | 0.629941i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.06218 | + | 3.50000i | −0.740613 | + | 0.427593i | −0.822292 | − | 0.569066i | \(-0.807305\pi\) |
0.0816792 | + | 0.996659i | \(0.473972\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.866025 | − | 0.500000i | 0.101361 | − | 0.0585206i | −0.448463 | − | 0.893801i | \(-0.648028\pi\) |
0.549823 | + | 0.835281i | \(0.314695\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.79423 | + | 1.50000i | 0.888235 | + | 0.170941i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.50000 | + | 11.2583i | −0.731307 | + | 1.26666i | 0.225018 | + | 0.974355i | \(0.427756\pi\) |
−0.956325 | + | 0.292306i | \(0.905577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 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 | ||||||||
\(87\) | −5.19615 | + | 3.00000i | −0.557086 | + | 0.321634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.50000 | − | 12.9904i | 0.794998 | − | 1.37698i | −0.127842 | − | 0.991795i | \(-0.540805\pi\) |
0.922840 | − | 0.385183i | \(-0.125862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | − | 3.46410i | −0.419314 | − | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.06218 | − | 3.50000i | −0.628619 | − | 0.362933i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.0000i | − | 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.50000 | − | 12.9904i | −0.746278 | − | 1.29259i | −0.949595 | − | 0.313478i | \(-0.898506\pi\) |
0.203317 | − | 0.979113i | \(-0.434828\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.52628 | + | 5.50000i | 0.938652 | + | 0.541931i | 0.889538 | − | 0.456862i | \(-0.151027\pi\) |
0.0491146 | + | 0.998793i | \(0.484360\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.9904 | − | 7.50000i | −1.25583 | − | 0.725052i | −0.283567 | − | 0.958952i | \(-0.591518\pi\) |
−0.972261 | + | 0.233900i | \(0.924851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.500000 | − | 0.866025i | −0.0478913 | − | 0.0829502i | 0.841086 | − | 0.540901i | \(-0.181917\pi\) |
−0.888977 | + | 0.457951i | \(0.848583\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.46410 | + | 2.00000i | 0.320256 | + | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50000 | − | 7.79423i | 0.137505 | − | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.19615 | + | 3.00000i | −0.468521 | + | 0.270501i | ||||
\(124\) | 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 | ||||||||
\(129\) | −2.00000 | − | 3.46410i | −0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.50000 | + | 2.59808i | −0.131056 | + | 0.226995i | −0.924084 | − | 0.382190i | \(-0.875170\pi\) |
0.793028 | + | 0.609185i | \(0.208503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.866025 | + | 2.50000i | 0.0750939 | + | 0.216777i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.1865 | + | 10.5000i | −1.55378 | + | 0.897076i | −0.555952 | + | 0.831215i | \(0.687646\pi\) |
−0.997829 | + | 0.0658609i | \(0.979021\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.00000 | −0.757937 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.19615 | − | 3.00000i | 0.434524 | − | 0.250873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.33013 | + | 5.50000i | 0.357143 | + | 0.453632i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.50000 | − | 2.59808i | 0.122885 | − | 0.212843i | −0.798019 | − | 0.602632i | \(-0.794119\pi\) |
0.920904 | + | 0.389789i | \(0.127452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.50000 | − | 14.7224i | −0.691720 | − | 1.19809i | −0.971274 | − | 0.237964i | \(-0.923520\pi\) |
0.279554 | − | 0.960130i | \(-0.409814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000i | 0.485071i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2583 | + | 6.50000i | −0.898513 | + | 0.518756i | −0.876717 | − | 0.481006i | \(-0.840272\pi\) |
−0.0217953 | + | 0.999762i | \(0.506938\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.50000 | − | 2.59808i | 0.118958 | − | 0.206041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.50000 | − | 2.59808i | 0.591083 | − | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.52628 | + | 5.50000i | 0.746156 | + | 0.430793i | 0.824303 | − | 0.566149i | \(-0.191567\pi\) |
−0.0781474 | + | 0.996942i | \(0.524900\pi\) | |||||||
\(164\) | 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 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 1.73205i | −0.0764719 | − | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.79423 | − | 4.50000i | −0.592584 | − | 0.342129i | 0.173534 | − | 0.984828i | \(-0.444481\pi\) |
−0.766119 | + | 0.642699i | \(0.777815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.79423 | − | 4.50000i | −0.585850 | − | 0.338241i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5000 | + | 18.1865i | 0.784807 | + | 1.35933i | 0.929114 | + | 0.369792i | \(0.120571\pi\) |
−0.144308 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00000i | 0.0739221i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.79423 | + | 4.50000i | 0.569970 | + | 0.329073i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.0000 | − | 8.66025i | −0.727393 | − | 0.629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.50000 | − | 7.79423i | 0.325609 | − | 0.563971i | −0.656027 | − | 0.754738i | \(-0.727764\pi\) |
0.981635 | + | 0.190767i | \(0.0610975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.52628 | + | 5.50000i | −0.685717 | + | 0.395899i | −0.802005 | − | 0.597317i | \(-0.796234\pi\) |
0.116289 | + | 0.993215i | \(0.462900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.50000 | − | 6.06218i | −0.248108 | − | 0.429736i | 0.714893 | − | 0.699234i | \(-0.246476\pi\) |
−0.963001 | + | 0.269498i | \(0.913142\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | − | 6.06218i | 0.246871 | − | 0.427593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3923 | − | 12.0000i | 0.729397 | − | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.19615 | + | 3.00000i | −0.361158 | + | 0.208514i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.1865 | + | 3.50000i | 1.23458 | + | 0.237595i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.500000 | + | 0.866025i | −0.0337869 | + | 0.0585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.59808 | + | 1.50000i | −0.172440 | + | 0.0995585i | −0.583736 | − | 0.811943i | \(-0.698410\pi\) |
0.411296 | + | 0.911502i | \(0.365076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.50000 | − | 9.52628i | 0.363450 | − | 0.629514i | −0.625076 | − | 0.780564i | \(-0.714932\pi\) |
0.988526 | + | 0.151050i | \(0.0482653\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.50000 | + | 2.59808i | −0.493464 | + | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.1865 | − | 10.5000i | −1.19144 | − | 0.687878i | −0.232806 | − | 0.972523i | \(-0.574791\pi\) |
−0.958633 | + | 0.284645i | \(0.908124\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 13.0000i | − | 0.844441i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.8564 | + | 8.00000i | 0.888889 | + | 0.513200i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.73205 | + | 1.00000i | 0.110208 | + | 0.0636285i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | + | 10.3923i | 0.380235 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000i | 0.565825i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.59808 | − | 1.50000i | −0.162064 | − | 0.0935674i | 0.416775 | − | 0.909010i | \(-0.363160\pi\) |
−0.578838 | + | 0.815442i | \(0.696494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50000 | − | 0.866025i | 0.155342 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | + | 10.3923i | −0.371391 | + | 0.643268i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.59808 | − | 1.50000i | 0.160204 | − | 0.0924940i | −0.417755 | − | 0.908560i | \(-0.637183\pi\) |
0.577959 | + | 0.816066i | \(0.303849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.0000i | 0.917985i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.50000 | + | 2.59808i | 0.0914566 | + | 0.158408i | 0.908124 | − | 0.418701i | \(-0.137514\pi\) |
−0.816668 | + | 0.577108i | \(0.804181\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.50000 | + | 9.52628i | −0.334101 | + | 0.578680i | −0.983312 | − | 0.181928i | \(-0.941766\pi\) |
0.649211 | + | 0.760609i | \(0.275099\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.19615 | + | 1.00000i | 0.314485 | + | 0.0605228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2583 | + | 6.50000i | −0.676448 | + | 0.390547i | −0.798515 | − | 0.601975i | \(-0.794381\pi\) |
0.122068 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.0000 | −0.838158 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.1147 | + | 14.5000i | −1.49292 | + | 0.861936i | −0.999967 | − | 0.00812260i | \(-0.997414\pi\) |
−0.492949 | + | 0.870058i | \(0.664081\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | 5.00000 | + | 8.66025i | 0.293105 | + | 0.507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.9904 | − | 7.50000i | 0.753778 | − | 0.435194i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 6.92820i | 0.461112 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.9904 | + | 7.50000i | 0.746278 | + | 0.430864i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.0000i | − | 1.59804i | −0.601302 | − | 0.799022i | \(-0.705351\pi\) | ||
0.601302 | − | 0.799022i | \(-0.294649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.0000 | −0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5000 | + | 23.3827i | 0.765515 | + | 1.32591i | 0.939974 | + | 0.341246i | \(0.110849\pi\) |
−0.174459 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.9186 | + | 11.5000i | 1.12586 | + | 0.650018i | 0.942892 | − | 0.333099i | \(-0.108094\pi\) |
0.182973 | + | 0.983118i | \(0.441428\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.79423 | + | 4.50000i | 0.437767 | + | 0.252745i | 0.702650 | − | 0.711535i | \(-0.252000\pi\) |
−0.264883 | + | 0.964281i | \(0.585333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.0000 | 0.837218 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00000i | 0.166924i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.866025 | + | 0.500000i | 0.0478913 | + | 0.0276501i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.5000 | − | 7.79423i | 1.24047 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.50000 | − | 11.2583i | 0.357272 | − | 0.618814i | −0.630232 | − | 0.776407i | \(-0.717040\pi\) |
0.987504 | + | 0.157593i | \(0.0503735\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.73205 | + | 1.00000i | −0.0949158 | + | 0.0547997i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 34.0000i | − | 1.85210i | −0.377403 | − | 0.926049i | \(-0.623183\pi\) | ||
0.377403 | − | 0.926049i | \(-0.376817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | + | 5.19615i | 0.162938 | + | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5000 | + | 18.1865i | −0.568607 | + | 0.984856i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.79423 | − | 4.50000i | 0.418416 | − | 0.241573i | −0.275983 | − | 0.961162i | \(-0.589003\pi\) |
0.694399 | + | 0.719590i | \(0.255670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.0000 | −0.533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.1865 | − | 10.5000i | 0.967972 | − | 0.558859i | 0.0693543 | − | 0.997592i | \(-0.477906\pi\) |
0.898617 | + | 0.438733i | \(0.144573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.59808 | + | 7.50000i | 0.137505 | + | 0.396942i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.50000 | − | 12.9904i | 0.395835 | − | 0.685606i | −0.597372 | − | 0.801964i | \(-0.703789\pi\) |
0.993207 | + | 0.116358i | \(0.0371219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000i | 0.104973i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.33013 | − | 2.50000i | 0.226031 | − | 0.130499i | −0.382709 | − | 0.923869i | \(-0.625009\pi\) |
0.608740 | + | 0.793370i | \(0.291675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.00000 | + | 10.3923i | −0.312348 | + | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.50000 | + | 7.79423i | −0.0778761 | + | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.6506 | − | 12.5000i | −1.12103 | − | 0.647225i | −0.179364 | − | 0.983783i | \(-0.557404\pi\) |
−0.941663 | + | 0.336557i | \(0.890737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | − | 6.92820i | −0.204926 | − | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.5788 | − | 16.5000i | −1.46031 | − | 0.843111i | −0.461285 | − | 0.887252i | \(-0.652611\pi\) |
−0.999025 | + | 0.0441413i | \(0.985945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.92820 | − | 4.00000i | −0.352180 | − | 0.203331i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.50000 | + | 12.9904i | 0.380265 | + | 0.658638i | 0.991100 | − | 0.133120i | \(-0.0424994\pi\) |
−0.610835 | + | 0.791758i | \(0.709166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | 0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.00000i | − | 0.151330i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.0429 | + | 18.5000i | 1.60819 | + | 0.928488i | 0.989775 | + | 0.142636i | \(0.0455577\pi\) |
0.618414 | + | 0.785853i | \(0.287776\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.00000 | − | 1.73205i | −0.100125 | − | 0.0867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.1244 | − | 7.00000i | 0.603957 | − | 0.348695i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000i | 0.148704i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.50000 | + | 9.52628i | 0.271957 | + | 0.471044i | 0.969363 | − | 0.245633i | \(-0.0789957\pi\) |
−0.697406 | + | 0.716677i | \(0.745662\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.5000 | − | 18.1865i | 0.517927 | − | 0.897076i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.3827 | + | 4.50000i | 1.15059 | + | 0.221431i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.3205 | − | 10.0000i | 0.848189 | − | 0.489702i | ||||
\(418\) | 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 | ||||||||
\(423\) | −15.5885 | + | 9.00000i | −0.757937 | + | 0.437595i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.866025 | − | 2.50000i | −0.0419099 | − | 0.120983i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.00000 | + | 5.19615i | −0.144841 | + | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.50000 | + | 12.9904i | 0.361262 | + | 0.625725i | 0.988169 | − | 0.153370i | \(-0.0490126\pi\) |
−0.626907 | + | 0.779094i | \(0.715679\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000i | 0.480569i | 0.970702 | + | 0.240285i | \(0.0772408\pi\) | ||||
−0.970702 | + | 0.240285i | \(0.922759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.59808 | + | 1.50000i | −0.124283 | + | 0.0717547i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.500000 | + | 0.866025i | −0.0238637 | + | 0.0413331i | −0.877711 | − | 0.479191i | \(-0.840930\pi\) |
0.853847 | + | 0.520524i | \(0.174263\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | + | 5.19615i | 0.619048 | + | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.79423 | − | 4.50000i | −0.370315 | − | 0.213801i | 0.303281 | − | 0.952901i | \(-0.401918\pi\) |
−0.673596 | + | 0.739100i | \(0.735251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.00000i | 0.141895i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | + | 15.5885i | 0.423793 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.7224 | + | 8.50000i | 0.691720 | + | 0.399365i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9186 | − | 11.5000i | −0.931752 | − | 0.537947i | −0.0443868 | − | 0.999014i | \(-0.514133\pi\) |
−0.887365 | + | 0.461067i | \(0.847467\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.50000 | − | 12.9904i | −0.350070 | − | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | 18.1865 | + | 10.5000i | 0.841572 | + | 0.485882i | 0.857798 | − | 0.513986i | \(-0.171832\pi\) |
−0.0162260 | + | 0.999868i | \(0.505165\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.50000 | + | 18.1865i | −0.161615 | + | 0.839776i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.50000 | − | 11.2583i | 0.299504 | − | 0.518756i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.3923 | + | 6.00000i | −0.477839 | + | 0.275880i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.00000i | − | 0.274721i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.50000 | − | 2.59808i | −0.0685367 | − | 0.118709i | 0.829721 | − | 0.558179i | \(-0.188500\pi\) |
−0.898257 | + | 0.439470i | \(0.855166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.00000 | − | 1.73205i | 0.0455961 | − | 0.0789747i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.19615 | + | 6.00000i | −0.236433 | + | 0.273009i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.4545 | + | 9.50000i | −0.745624 | + | 0.430486i | −0.824110 | − | 0.566429i | \(-0.808325\pi\) |
0.0784867 | + | 0.996915i | \(0.474991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.0000 | −0.497437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.0000 | 1.08310 | 0.541552 | − | 0.840667i | \(-0.317837\pi\) | ||||
0.541552 | + | 0.840667i | \(0.317837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5885 | − | 9.00000i | 0.702069 | − | 0.405340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.50000 | − | 9.52628i | 0.246214 | − | 0.426455i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
0.962472 | + | 0.271380i | \(0.0874801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | + | 10.3923i | 0.268060 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.79423 | + | 4.50000i | −0.346154 | + | 0.199852i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.50000 | − | 2.59808i | 0.0664863 | − | 0.115158i | −0.830866 | − | 0.556473i | \(-0.812154\pi\) |
0.897352 | + | 0.441315i | \(0.145488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.500000 | − | 2.59808i | 0.0221187 | − | 0.114932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.33013 | + | 2.50000i | 0.191180 | + | 0.110378i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.0000i | 1.18746i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.5000 | − | 33.7750i | −0.854311 | − | 1.47971i | −0.877283 | − | 0.479973i | \(-0.840646\pi\) |
0.0229727 | − | 0.999736i | \(-0.492687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.866025 | − | 0.500000i | −0.0378686 | − | 0.0218635i | 0.480946 | − | 0.876750i | \(-0.340293\pi\) |
−0.518815 | + | 0.854887i | \(0.673627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.1865 | + | 10.5000i | 0.792218 | + | 0.457387i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.0000 | −0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12.0000i | − | 0.519778i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.1865 | − | 10.5000i | −0.784807 | − | 0.453108i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5000 | − | 12.9904i | 0.710705 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5000 | + | 30.3109i | −0.752384 | + | 1.30317i | 0.194281 | + | 0.980946i | \(0.437763\pi\) |
−0.946664 | + | 0.322221i | \(0.895571\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.66025 | − | 5.00000i | 0.371647 | − | 0.214571i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000i | 0.342055i | 0.985266 | + | 0.171028i | \(0.0547087\pi\) | ||||
−0.985266 | + | 0.171028i | \(0.945291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.00000 | + | 1.73205i | 0.0426790 | + | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | + | 5.19615i | −0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.2583 | + | 32.5000i | 0.478753 | + | 1.38204i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.5788 | + | 16.5000i | −1.21092 | + | 0.699127i | −0.962961 | − | 0.269642i | \(-0.913095\pi\) |
−0.247964 | + | 0.968769i | \(0.579761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | −0.379980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.79423 | + | 4.50000i | −0.328488 | + | 0.189652i | −0.655169 | − | 0.755482i | \(-0.727403\pi\) |
0.326682 | + | 0.945134i | \(0.394069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.59808 | − | 0.500000i | −0.109109 | − | 0.0209980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.50000 | + | 7.79423i | −0.188650 | + | 0.326751i | −0.944800 | − | 0.327647i | \(-0.893744\pi\) |
0.756151 | + | 0.654398i | \(0.227078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5000 | − | 25.1147i | −0.606806 | − | 1.05102i | −0.991763 | − | 0.128085i | \(-0.959117\pi\) |
0.384957 | − | 0.922934i | \(-0.374216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.00000i | 0.375980i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.866025 | + | 0.500000i | −0.0360531 | + | 0.0208153i | −0.517918 | − | 0.855430i | \(-0.673293\pi\) |
0.481865 | + | 0.876245i | \(0.339960\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.50000 | − | 9.52628i | 0.228572 | − | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | − | 20.7846i | −0.995688 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.79423 | − | 4.50000i | −0.322804 | − | 0.186371i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.00000 | −0.288430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00000 | − | 15.5885i | −0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.1865 | − | 10.5000i | −0.746831 | − | 0.431183i | 0.0777165 | − | 0.996976i | \(-0.475237\pi\) |
−0.824548 | + | 0.565792i | \(0.808570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.06218 | + | 3.50000i | 0.248108 | + | 0.143245i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.5000 | − | 23.3827i | −0.551595 | − | 0.955391i | −0.998160 | − | 0.0606393i | \(-0.980686\pi\) |
0.446565 | − | 0.894751i | \(-0.352647\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 14.0000i | − | 0.570124i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.7032 | − | 23.5000i | −1.65209 | − | 0.953836i | −0.976210 | − | 0.216825i | \(-0.930430\pi\) |
−0.675881 | − | 0.737011i | \(-0.736237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.00000 | + | 15.5885i | −0.121566 | + | 0.631676i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.00000 | − | 15.5885i | 0.364101 | − | 0.630641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.6506 | − | 12.5000i | 0.874461 | − | 0.504870i | 0.00563283 | − | 0.999984i | \(-0.498207\pi\) |
0.868828 | + | 0.495114i | \(0.164874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000i | 0.241551i | 0.992680 | + | 0.120775i | \(0.0385381\pi\) | ||||
−0.992680 | + | 0.120775i | \(0.961462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.5000 | − | 26.8468i | −0.622998 | − | 1.07906i | −0.988924 | − | 0.148420i | \(-0.952581\pi\) |
0.365927 | − | 0.930644i | \(-0.380752\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.50000 | − | 12.9904i | 0.300965 | − | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.9904 | − | 37.5000i | −0.520449 | − | 1.50241i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.59808 | − | 1.50000i | 0.103757 | − | 0.0599042i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.00000 | 0.119618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.46410 | − | 2.00000i | 0.137686 | − | 0.0794929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.8564 | + | 2.00000i | −0.549011 | + | 0.0792429i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.50000 | − | 12.9904i | −0.296232 | − | 0.513089i | 0.679039 | − | 0.734103i | \(-0.262397\pi\) |
−0.975271 | + | 0.221013i | \(0.929064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 20.0000i | − | 0.788723i | −0.918955 | − | 0.394362i | \(-0.870966\pi\) | ||
0.918955 | − | 0.394362i | \(-0.129034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.1865 | − | 10.5000i | 0.714986 | − | 0.412798i | −0.0979182 | − | 0.995194i | \(-0.531218\pi\) |
0.812905 | + | 0.582397i | \(0.197885\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.5000 | + | 23.3827i | −0.529921 | + | 0.917851i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.5000 | + | 6.06218i | −0.685879 | + | 0.237595i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.7750 | + | 19.5000i | 1.32172 | + | 0.763094i | 0.984003 | − | 0.178154i | \(-0.0570127\pi\) |
0.337715 | + | 0.941248i | \(0.390346\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000i | 0.0780274i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.50000 | − | 9.52628i | −0.213925 | − | 0.370529i | 0.739014 | − | 0.673690i | \(-0.235292\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.19615 | + | 3.00000i | 0.201802 | + | 0.116510i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.5885 | + | 9.00000i | 0.603587 | + | 0.348481i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | + | 6.92820i | 0.154649 | + | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.00000 | 0.115814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 14.0000i | − | 0.539660i | −0.962908 | − | 0.269830i | \(-0.913032\pi\) | ||
0.962908 | − | 0.269830i | \(-0.0869676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.3827 | − | 13.5000i | −0.898670 | − | 0.518847i | −0.0219013 | − | 0.999760i | \(-0.506972\pi\) |
−0.876768 | + | 0.480913i | \(0.840305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.0000 | − | 17.3205i | −0.767530 | − | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50000 | − | 2.59808i | 0.0574801 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.1865 | + | 10.5000i | −0.695888 | + | 0.401771i | −0.805814 | − | 0.592168i | \(-0.798272\pi\) |
0.109926 | + | 0.993940i | \(0.464939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.0000i | 0.419676i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.00000 | + | 5.19615i | 0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.50000 | − | 11.2583i | 0.247272 | − | 0.428287i | −0.715496 | − | 0.698617i | \(-0.753799\pi\) |
0.962768 | + | 0.270330i | \(0.0871327\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.3923 | + | 12.0000i | −0.394771 | + | 0.455842i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.5885 | − | 9.00000i | 0.590455 | − | 0.340899i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.0000 | 0.794293 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.866025 | + | 0.500000i | −0.0326628 | + | 0.0188579i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.9711 | − | 7.50000i | −1.46566 | − | 0.282067i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.500000 | + | 0.866025i | −0.0187779 | + | 0.0325243i | −0.875262 | − | 0.483650i | \(-0.839311\pi\) |
0.856484 | + | 0.516174i | \(0.172644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.0000 | − | 22.5167i | −0.487538 | − | 0.844441i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.0000i | 0.786456i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.3923 | + | 6.00000i | −0.388108 | + | 0.224074i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.5000 | + | 18.1865i | −0.391584 | + | 0.678243i | −0.992659 | − | 0.120950i | \(-0.961406\pi\) |
0.601075 | + | 0.799193i | \(0.294739\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5000 | − | 9.52628i | 1.02415 | − | 0.354777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.866025 | − | 0.500000i | −0.0322078 | − | 0.0185952i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000i | 1.18681i | 0.804902 | + | 0.593407i | \(0.202218\pi\) | ||||
−0.804902 | + | 0.593407i | \(0.797782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | + | 10.3923i | 0.221918 | + | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.6506 | − | 12.5000i | −0.799684 | − | 0.461698i | 0.0436764 | − | 0.999046i | \(-0.486093\pi\) |
−0.843361 | + | 0.537348i | \(0.819426\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.1865 | − | 10.5000i | −0.669910 | − | 0.386772i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.50000 | − | 16.4545i | −0.349463 | − | 0.605288i | 0.636691 | − | 0.771119i | \(-0.280303\pi\) |
−0.986154 | + | 0.165831i | \(0.946969\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.0000i | 1.76095i | 0.474093 | + | 0.880475i | \(0.342776\pi\) | ||||
−0.474093 | + | 0.880475i | \(0.657224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.7846 | + | 12.0000i | 0.760469 | + | 0.439057i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.5000 | + | 12.9904i | −1.37022 | + | 0.474658i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5000 | − | 21.6506i | 0.456131 | − | 0.790043i | −0.542621 | − | 0.839978i | \(-0.682568\pi\) |
0.998752 | + | 0.0499348i | \(0.0159013\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.50000 | − | 7.79423i | −0.163340 | − | 0.282913i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.50000 | + | 2.59808i | −0.0543750 | + | 0.0941802i | −0.891932 | − | 0.452170i | \(-0.850650\pi\) |
0.837557 | + | 0.546350i | \(0.183983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.59808 | − | 0.500000i | −0.0940567 | − | 0.0181012i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5885 | − | 9.00000i | 0.562867 | − | 0.324971i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.0000 | 1.22607 | 0.613036 | − | 0.790055i | \(-0.289948\pi\) | ||||
0.613036 | + | 0.790055i | \(0.289948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | 0.108042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.5788 | − | 16.5000i | 1.02791 | − | 0.593464i | 0.111524 | − | 0.993762i | \(-0.464427\pi\) |
0.916385 | + | 0.400298i | \(0.131093\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.73205 | + | 2.00000i | −0.0621370 | + | 0.0717496i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.00000 | + | 5.19615i | −0.107486 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 30.0000i | − | 1.07211i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.8468 | + | 15.5000i | −0.956985 | + | 0.552515i | −0.895244 | − | 0.445577i | \(-0.852999\pi\) |
−0.0617409 | + | 0.998092i | \(0.519665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.50000 | + | 2.59808i | −0.0534014 | + | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | − | 10.3923i | −0.426671 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.73205 | − | 1.00000i | −0.0615069 | − | 0.0355110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.0000i | 1.48772i | 0.668338 | + | 0.743858i | \(0.267006\pi\) | ||||
−0.668338 | + | 0.743858i | \(0.732994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.0000 | 0.955191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0000 | + | 25.9808i | 0.529999 | + | 0.917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.59808 | + | 1.50000i | 0.0916841 | + | 0.0529339i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.59808 | − | 1.50000i | −0.0914566 | − | 0.0528025i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.5000 | − | 28.5788i | −0.580109 | − | 1.00478i | −0.995466 | − | 0.0951198i | \(-0.969677\pi\) |
0.415357 | − | 0.909659i | \(-0.363657\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.0000 | −1.82597 | −0.912983 | − | 0.407997i | \(-0.866228\pi\) | ||||
−0.912983 | + | 0.407997i | \(0.866228\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 11.0000i | − | 0.385787i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.46410 | − | 2.00000i | −0.121194 | − | 0.0699711i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.0000 | − | 3.46410i | 0.349428 | − | 0.121046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5000 | + | 23.3827i | −0.471153 | + | 0.816061i | −0.999456 | − | 0.0329950i | \(-0.989495\pi\) |
0.528302 | + | 0.849056i | \(0.322829\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.33013 | + | 2.50000i | −0.150939 | + | 0.0871445i | −0.573567 | − | 0.819159i | \(-0.694441\pi\) |
0.422628 | + | 0.906303i | \(0.361108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.0000i | − | 1.25184i | −0.779886 | − | 0.625921i | \(-0.784723\pi\) | ||
0.779886 | − | 0.625921i | \(-0.215277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.500000 | − | 0.866025i | −0.0173657 | − | 0.0300783i | 0.857212 | − | 0.514964i | \(-0.172195\pi\) |
−0.874578 | + | 0.484885i | \(0.838861\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.50000 | − | 11.2583i | 0.225483 | − | 0.390547i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.9904 | − | 16.5000i | −0.450090 | − | 0.571691i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.3109 | − | 17.5000i | 1.04770 | − | 0.604888i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.9808 | + | 15.0000i | −0.894825 | + | 0.516627i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.73205 | − | 5.00000i | −0.0595140 | − | 0.171802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.5000 | − | 25.1147i | 0.497639 | − | 0.861936i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.50000 | + | 2.59808i | 0.0514193 | + | 0.0890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000i | 0.753266i | 0.926363 | + | 0.376633i | \(0.122918\pi\) | ||||
−0.926363 | + | 0.376633i | \(0.877082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.9904 | − | 7.50000i | 0.443743 | − | 0.256195i | −0.261441 | − | 0.965219i | \(-0.584198\pi\) |
0.705184 | + | 0.709024i | \(0.250864\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.5000 | − | 19.9186i | 0.392375 | − | 0.679613i | −0.600387 | − | 0.799709i | \(-0.704987\pi\) |
0.992762 | + | 0.120096i | \(0.0383202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.00000 | + | 15.5885i | −0.102240 | + | 0.531253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.1673 | + | 25.5000i | 1.50347 | + | 0.868030i | 0.999992 | + | 0.00402340i | \(0.00128069\pi\) |
0.503480 | + | 0.864007i | \(0.332053\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 8.00000i | − | 0.271694i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.0000 | −1.32298 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | + | 12.1244i | 0.237186 | + | 0.410818i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.3205 | + | 10.0000i | 0.586210 | + | 0.338449i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2583 | + | 6.50000i | 0.380167 | + | 0.219489i | 0.677891 | − | 0.735163i | \(-0.262894\pi\) |
−0.297724 | + | 0.954652i | \(0.596228\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.00000 | + | 5.19615i | 0.101187 | + | 0.175262i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 44.0000i | − | 1.48072i | −0.672212 | − | 0.740359i | \(-0.734656\pi\) | ||
0.672212 | − | 0.740359i | \(-0.265344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.7750 | − | 19.5000i | −1.13405 | − | 0.654746i | −0.189102 | − | 0.981957i | \(-0.560558\pi\) |
−0.944951 | + | 0.327212i | \(0.893891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | + | 13.8564i | 0.536623 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | − | 2.59808i | 0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.79423 | + | 4.50000i | −0.260824 | + | 0.150587i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.00000i | 0.200334i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.0000 | + | 36.3731i | 0.700389 | + | 1.21311i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.50000 | + | 7.79423i | −0.149917 | + | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.3923 | − | 2.00000i | −0.345834 | − | 0.0665558i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.5070 | − | 20.5000i | 1.17899 | − | 0.680691i | 0.223211 | − | 0.974770i | \(-0.428346\pi\) |
0.955781 | + | 0.294079i | \(0.0950128\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.0000 | 0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.1769 | − | 18.0000i | 1.03181 | − | 0.595713i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.59808 | + | 7.50000i | 0.0857960 | + | 0.247672i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.500000 | + | 0.866025i | −0.0164935 | + | 0.0285675i | −0.874154 | − | 0.485648i | \(-0.838584\pi\) |
0.857661 | + | 0.514216i | \(0.171917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.0526 | + | 11.0000i | −0.625768 | + | 0.361287i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.50000 | + | 7.79423i | −0.147640 | + | 0.255720i | −0.930355 | − | 0.366660i | \(-0.880501\pi\) |
0.782715 | + | 0.622381i | \(0.213834\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.50000 | + | 2.59808i | 0.213029 | + | 0.0851485i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.3827 | − | 13.5000i | −0.765515 | − | 0.441970i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000i | 0.849383i | 0.905338 | + | 0.424691i | \(0.139617\pi\) | ||||
−0.905338 | + | 0.424691i | \(0.860383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.0000 | −0.750577 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5000 | − | 23.3827i | −0.440087 | − | 0.762254i | 0.557608 | − | 0.830104i | \(-0.311719\pi\) |
−0.997695 | + | 0.0678506i | \(0.978386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.5885 | + | 9.00000i | 0.507630 | + | 0.293080i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.9711 | + | 22.5000i | 1.26639 | + | 0.731152i | 0.974303 | − | 0.225240i | \(-0.0723165\pi\) |
0.292089 | + | 0.956391i | \(0.405650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.00000 | − | 1.73205i | −0.0324614 | − | 0.0562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.00000 | −0.291845 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000i | 0.583077i | 0.956559 | + | 0.291539i | \(0.0941672\pi\) | ||||
−0.956559 | + | 0.291539i | \(0.905833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.5885 | − | 9.00000i | −0.503903 | − | 0.290929i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.5000 | + | 54.5596i | −0.339063 | + | 1.76182i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.9808 | − | 15.0000i | 0.837218 | − | 0.483368i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.0000i | − | 0.514525i | −0.966342 | − | 0.257263i | \(-0.917179\pi\) | ||
0.966342 | − | 0.257263i | \(-0.0828206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.50000 | − | 2.59808i | −0.0481869 | − | 0.0834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.5000 | + | 44.1673i | −0.818334 | + | 1.41740i | 0.0885751 | + | 0.996070i | \(0.471769\pi\) |
−0.906909 | + | 0.421326i | \(0.861565\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.6410 | + | 40.0000i | −1.11054 | + | 1.28234i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.3827 | − | 13.5000i | 0.748078 | − | 0.431903i | −0.0769208 | − | 0.997037i | \(-0.524509\pi\) |
0.824999 | + | 0.565134i | \(0.191176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.0000 | 1.43821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.5788 | + | 16.5000i | −0.911523 | + | 0.526268i | −0.880921 | − | 0.473263i | \(-0.843076\pi\) |
−0.0306024 | + | 0.999532i | \(0.509743\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.5885 | + | 18.0000i | −0.496186 | + | 0.572946i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.00000 | + | 10.3923i | −0.190789 | + | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.50000 | + | 16.4545i | 0.301777 | + | 0.522694i | 0.976539 | − | 0.215342i | \(-0.0690867\pi\) |
−0.674761 | + | 0.738036i | \(0.735753\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.0000i | 0.412543i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.0955 | − | 29.5000i | 1.61821 | − | 0.934274i | 0.630828 | − | 0.775923i | \(-0.282715\pi\) |
0.987383 | − | 0.158352i | \(-0.0506179\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.50000 | − | 4.33013i | 0.0790965 | − | 0.136999i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))