Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,2,Mod(165,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.e (of order \(3\), 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: | \(1.56506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 177.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.177 |
Dual form | 196.2.e.a.165.1 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) |
−0.684819 | + | 0.728714i | \(0.740119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 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 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 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 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50000 | − | 6.06218i | −0.628619 | − | 1.08880i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | + | 2.59808i | −0.261116 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | − | 0.866025i | 0.0821995 | − | 0.142374i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | − | 1.73205i | −0.160128 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | − | 5.19615i | −0.447214 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.50000 | + | 7.79423i | −0.656392 | + | 1.13691i | 0.325150 | + | 0.945662i | \(0.394585\pi\) |
−0.981543 | + | 0.191243i | \(0.938748\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000 | 1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 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 | −0.896258 | − | 0.443533i | \(-0.853725\pi\) |
0.832240 | + | 0.554416i | \(0.187058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | + | 5.19615i | −0.372104 | + | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | + | 6.06218i | 0.427593 | + | 0.740613i | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −0.500000 | − | 0.866025i | −0.0585206 | − | 0.101361i | 0.835281 | − | 0.549823i | \(-0.185305\pi\) |
−0.893801 | + | 0.448463i | \(0.851972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.00000 | − | 3.46410i | 0.230940 | − | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | 0.976187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.00000 | − | 5.19615i | −0.321634 | − | 0.557086i | ||||
\(88\) | 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 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.50000 | − | 6.06218i | 0.362933 | − | 0.628619i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.50000 | + | 2.59808i | 0.153897 | + | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 1.01535 | 0.507673 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.50000 | + | 12.9904i | 0.746278 | + | 1.29259i | 0.949595 | + | 0.313478i | \(0.101494\pi\) |
−0.203317 | + | 0.979113i | \(0.565172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.50000 | − | 9.52628i | 0.541931 | − | 0.938652i | −0.456862 | − | 0.889538i | \(-0.651027\pi\) |
0.998793 | − | 0.0491146i | \(-0.0156400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.50000 | + | 12.9904i | −0.725052 | + | 1.25583i | 0.233900 | + | 0.972261i | \(0.424851\pi\) |
−0.958952 | + | 0.283567i | \(0.908482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | + | 0.866025i | 0.0478913 | + | 0.0829502i | 0.888977 | − | 0.457951i | \(-0.151417\pi\) |
−0.841086 | + | 0.540901i | \(0.818083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.00000 | 0.0949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | + | 7.79423i | 0.419627 | + | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | + | 3.46410i | −0.184900 | + | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00000 | − | 5.19615i | −0.270501 | − | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | − | 3.46410i | −0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.50000 | − | 2.59808i | 0.131056 | − | 0.226995i | −0.793028 | − | 0.609185i | \(-0.791497\pi\) |
0.924084 | + | 0.382190i | \(0.124830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.50000 | − | 12.9904i | 0.645497 | − | 1.11803i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5000 | + | 18.1865i | 0.897076 | + | 1.55378i | 0.831215 | + | 0.555952i | \(0.187646\pi\) |
0.0658609 | + | 0.997829i | \(0.479021\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | −3.00000 | − | 5.19615i | −0.250873 | − | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.00000 | + | 15.5885i | −0.747409 | + | 1.29455i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.50000 | + | 2.59808i | −0.122885 | + | 0.212843i | −0.920904 | − | 0.389789i | \(-0.872548\pi\) |
0.798019 | + | 0.602632i | \(0.205881\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.0000 | −1.68676 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.50000 | − | 11.2583i | −0.518756 | − | 0.898513i | −0.999762 | − | 0.0217953i | \(-0.993062\pi\) |
0.481006 | − | 0.876717i | \(-0.340272\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.50000 | − | 2.59808i | 0.118958 | − | 0.206041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | + | 9.52628i | −0.430793 | + | 0.746156i | −0.996942 | − | 0.0781474i | \(-0.975100\pi\) |
0.566149 | + | 0.824303i | \(0.308433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.50000 | + | 7.79423i | 0.350325 | + | 0.606780i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | + | 1.73205i | 0.0764719 | + | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.50000 | + | 7.79423i | −0.342129 | + | 0.592584i | −0.984828 | − | 0.173534i | \(-0.944481\pi\) |
0.642699 | + | 0.766119i | \(0.277815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.50000 | + | 7.79423i | −0.338241 | + | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5000 | − | 18.1865i | −0.784807 | − | 1.35933i | −0.929114 | − | 0.369792i | \(-0.879429\pi\) |
0.144308 | − | 0.989533i | \(-0.453905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.50000 | − | 2.59808i | −0.110282 | − | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.50000 | + | 7.79423i | −0.329073 | + | 0.569970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | ||||||||
\(193\) | −5.50000 | − | 9.52628i | −0.395899 | − | 0.685717i | 0.597317 | − | 0.802005i | \(-0.296234\pi\) |
−0.993215 | + | 0.116289i | \(0.962900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.00000 | −0.429669 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | + | 15.5885i | −0.628587 | + | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | + | 5.19615i | 0.208514 | + | 0.361158i | ||||
\(208\) | 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 | ||||||||
\(215\) | −6.00000 | + | 10.3923i | −0.409197 | + | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 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 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.00000 | −0.533333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5000 | − | 18.1865i | 0.687878 | − | 1.19144i | −0.284645 | − | 0.958633i | \(-0.591876\pi\) |
0.972523 | − | 0.232806i | \(-0.0747909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5000 | + | 23.3827i | 0.880643 | + | 1.52532i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.0000 | 0.844441 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | − | 0.866025i | −0.0322078 | − | 0.0557856i | 0.849472 | − | 0.527633i | \(-0.176921\pi\) |
−0.881680 | + | 0.471848i | \(0.843587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.00000 | − | 13.8564i | 0.513200 | − | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | − | 1.73205i | 0.0636285 | − | 0.110208i | ||||
\(248\) | 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 | ||||||||
\(253\) | −9.00000 | −0.565825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.50000 | + | 7.79423i | 0.281801 | + | 0.488094i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.50000 | − | 2.59808i | 0.0935674 | − | 0.162064i | −0.815442 | − | 0.578838i | \(-0.803506\pi\) |
0.909010 | + | 0.416775i | \(0.136840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | + | 10.3923i | −0.371391 | + | 0.643268i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.50000 | + | 2.59808i | 0.0924940 | + | 0.160204i | 0.908560 | − | 0.417755i | \(-0.137183\pi\) |
−0.816066 | + | 0.577959i | \(0.803849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.0000 | 0.917985 | ||||||||
\(268\) | 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 | −0.649211 | − | 0.760609i | \(-0.724901\pi\) |
0.983312 | + | 0.181928i | \(0.0582339\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.00000 | − | 10.3923i | 0.361814 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | + | 11.2583i | 0.390547 | + | 0.676448i | 0.992522 | − | 0.122068i | \(-0.0389525\pi\) |
−0.601975 | + | 0.798515i | \(0.705619\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 14.5000 | + | 25.1147i | 0.861936 | + | 1.49292i | 0.870058 | + | 0.492949i | \(0.164081\pi\) |
−0.00812260 | + | 0.999967i | \(0.502586\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.50000 | + | 2.59808i | −0.0888523 | + | 0.153897i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 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 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.0000 | 1.57200 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.50000 | + | 12.9904i | 0.435194 | + | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.50000 | + | 12.9904i | −0.430864 | + | 0.746278i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.50000 | + | 2.59808i | 0.0858898 | + | 0.148765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.0000 | 0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5000 | − | 23.3827i | −0.765515 | − | 1.32591i | −0.939974 | − | 0.341246i | \(-0.889151\pi\) |
0.174459 | − | 0.984664i | \(-0.444182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5000 | − | 19.9186i | 0.650018 | − | 1.12586i | −0.333099 | − | 0.942892i | \(-0.608094\pi\) |
0.983118 | − | 0.182973i | \(-0.0585722\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.50000 | − | 7.79423i | 0.252745 | − | 0.437767i | −0.711535 | − | 0.702650i | \(-0.752000\pi\) |
0.964281 | + | 0.264883i | \(0.0853332\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | − | 15.5885i | −0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0000 | −0.837218 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | + | 6.92820i | 0.221880 | + | 0.384308i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.500000 | + | 0.866025i | −0.0276501 | + | 0.0478913i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(333\) | −1.00000 | − | 1.73205i | −0.0547997 | − | 0.0949158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.0000 | 1.14735 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.0000 | −1.85210 | −0.926049 | − | 0.377403i | \(-0.876817\pi\) | ||||
−0.926049 | + | 0.377403i | \(0.876817\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.50000 | + | 7.79423i | −0.242272 | + | 0.419627i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.50000 | − | 7.79423i | −0.241573 | − | 0.418416i | 0.719590 | − | 0.694399i | \(-0.244330\pi\) |
−0.961162 | + | 0.275983i | \(0.910997\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | −10.5000 | − | 18.1865i | −0.558859 | − | 0.967972i | −0.997592 | − | 0.0693543i | \(-0.977906\pi\) |
0.438733 | − | 0.898617i | \(-0.355427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.50000 | + | 12.9904i | −0.395835 | + | 0.685606i | −0.993207 | − | 0.116358i | \(-0.962878\pi\) |
0.597372 | + | 0.801964i | \(0.296211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.00000 | −0.157027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.50000 | + | 4.33013i | 0.130499 | + | 0.226031i | 0.923869 | − | 0.382709i | \(-0.125009\pi\) |
−0.793370 | + | 0.608740i | \(0.791675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.00000 | + | 10.3923i | −0.312348 | + | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | − | 21.6506i | 0.647225 | − | 1.12103i | −0.336557 | − | 0.941663i | \(-0.609263\pi\) |
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.50000 | + | 2.59808i | 0.0774597 | + | 0.134164i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.00000 | + | 6.92820i | 0.204926 | + | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.5000 | + | 28.5788i | −0.843111 | + | 1.46031i | 0.0441413 | + | 0.999025i | \(0.485945\pi\) |
−0.887252 | + | 0.461285i | \(0.847389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | + | 6.92820i | −0.203331 | + | 0.352180i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.50000 | − | 12.9904i | −0.380265 | − | 0.658638i | 0.610835 | − | 0.791758i | \(-0.290834\pi\) |
−0.991100 | + | 0.133120i | \(0.957501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00000 | 0.151330 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.5000 | − | 33.7750i | −0.981151 | − | 1.69940i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.5000 | + | 32.0429i | −0.928488 | + | 1.60819i | −0.142636 | + | 0.989775i | \(0.545558\pi\) |
−0.785853 | + | 0.618414i | \(0.787776\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 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 | ||||||||
\(403\) | 7.00000 | + | 12.1244i | 0.348695 | + | 0.603957i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.00000 | −0.149071 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000 | 0.148704 | ||||||||
\(408\) | 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 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | + | 31.1769i | −0.883585 | + | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.0000 | − | 17.3205i | −0.489702 | − | 0.848189i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.00000 | + | 15.5885i | 0.437595 | + | 0.757937i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | − | 10.3923i | 0.291043 | − | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 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 | ||||||||
\(433\) | 10.0000 | 0.480569 | 0.240285 | − | 0.970702i | \(-0.422759\pi\) | ||||
0.240285 | + | 0.970702i | \(0.422759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0000 | −0.863034 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.50000 | − | 2.59808i | −0.0717547 | − | 0.124283i | ||||
\(438\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.50000 | − | 7.79423i | 0.213801 | − | 0.370315i | −0.739100 | − | 0.673596i | \(-0.764749\pi\) |
0.952901 | + | 0.303281i | \(0.0980821\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.5000 | − | 38.9711i | −1.06660 | − | 1.84741i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.00000 | −0.141895 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.50000 | − | 14.7224i | 0.399365 | − | 0.691720i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | + | 19.9186i | −0.537947 | + | 0.931752i | 0.461067 | + | 0.887365i | \(0.347467\pi\) |
−0.999014 | + | 0.0443868i | \(0.985867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.50000 | + | 12.9904i | 0.350070 | + | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.5000 | − | 18.1865i | −0.486926 | − | 0.843380i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.5000 | + | 18.1865i | −0.485882 | + | 0.841572i | −0.999868 | − | 0.0162260i | \(-0.994835\pi\) |
0.513986 | + | 0.857798i | \(0.328168\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.50000 | − | 11.2583i | 0.299504 | − | 0.518756i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | − | 10.3923i | −0.275880 | − | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.0000 | − | 25.9808i | 0.681115 | − | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.50000 | + | 16.4545i | 0.430486 | + | 0.745624i | 0.996915 | − | 0.0784867i | \(-0.0250088\pi\) |
−0.566429 | + | 0.824110i | \(0.691675\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | −9.00000 | − | 15.5885i | −0.405340 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.00000 | − | 15.5885i | 0.404520 | − | 0.700649i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.50000 | + | 9.52628i | −0.246214 | + | 0.426455i | −0.962472 | − | 0.271380i | \(-0.912520\pi\) |
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | + | 10.3923i | 0.268060 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.0000 | 2.00247 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.50000 | − | 7.79423i | −0.199852 | − | 0.346154i | ||||
\(508\) | 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 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.50000 | + | 4.33013i | −0.110378 | + | 0.191180i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.5000 | − | 28.5788i | −0.727077 | − | 1.25933i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.0000 | −1.18746 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.00000 | −0.395056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.5000 | + | 33.7750i | 0.854311 | + | 1.47971i | 0.877283 | + | 0.479973i | \(0.159354\pi\) |
−0.0229727 | + | 0.999736i | \(0.507313\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.500000 | + | 0.866025i | −0.0218635 | + | 0.0378686i | −0.876750 | − | 0.480946i | \(-0.840293\pi\) |
0.854887 | + | 0.518815i | \(0.173627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.5000 | − | 18.1865i | 0.457387 | − | 0.792218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.0000 | 0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.5000 | + | 38.9711i | 0.972760 | + | 1.68487i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.5000 | − | 18.1865i | 0.453108 | − | 0.784807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 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 | ||||||||
\(543\) | 5.00000 | + | 8.66025i | 0.214571 | + | 0.371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.00000 | 0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.50000 | − | 2.59808i | 0.0636715 | − | 0.110282i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.5000 | + | 28.5788i | 0.699127 | + | 1.21092i | 0.968769 | + | 0.247964i | \(0.0797613\pi\) |
−0.269642 | + | 0.962961i | \(0.586905\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | −0.379980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.50000 | + | 7.79423i | 0.189652 | + | 0.328488i | 0.945134 | − | 0.326682i | \(-0.105931\pi\) |
−0.755482 | + | 0.655169i | \(0.772597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | − | 15.5885i | 0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.50000 | − | 7.79423i | 0.188650 | − | 0.326751i | −0.756151 | − | 0.654398i | \(-0.772922\pi\) |
0.944800 | + | 0.327647i | \(0.106256\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 9.00000 | 0.375980 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.500000 | − | 0.866025i | −0.0208153 | − | 0.0360531i | 0.855430 | − | 0.517918i | \(-0.173293\pi\) |
−0.876245 | + | 0.481865i | \(0.839960\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.50000 | − | 9.52628i | 0.228572 | − | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.50000 | − | 7.79423i | 0.186371 | − | 0.322804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000 | + | 10.3923i | 0.248069 | + | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.00000 | 0.288430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | + | 15.5885i | 0.370211 | + | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.5000 | + | 18.1865i | −0.431183 | + | 0.746831i | −0.996976 | − | 0.0777165i | \(-0.975237\pi\) |
0.565792 | + | 0.824548i | \(0.308570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.50000 | − | 6.06218i | 0.143245 | − | 0.248108i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.5000 | + | 23.3827i | 0.551595 | + | 0.955391i | 0.998160 | + | 0.0606393i | \(0.0193139\pi\) |
−0.446565 | + | 0.894751i | \(0.647353\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0000 | 0.570124 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.00000 | − | 5.19615i | −0.121967 | − | 0.211254i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.5000 | − | 40.7032i | 0.953836 | − | 1.65209i | 0.216825 | − | 0.976210i | \(-0.430430\pi\) |
0.737011 | − | 0.675881i | \(-0.236237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.00000 | − | 15.5885i | 0.364101 | − | 0.630641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5000 | + | 21.6506i | 0.504870 | + | 0.874461i | 0.999984 | + | 0.00563283i | \(0.00179300\pi\) |
−0.495114 | + | 0.868828i | \(0.664874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0000 | −0.725830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.50000 | − | 2.59808i | −0.0599042 | − | 0.103757i | ||||
\(628\) | 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 | ||||||||
\(633\) | −2.00000 | − | 3.46410i | −0.0794929 | − | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.0000 | − | 20.7846i | 0.476205 | − | 0.824812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | −20.0000 | −0.788723 | −0.394362 | − | 0.918955i | \(-0.629034\pi\) | ||||
−0.394362 | + | 0.918955i | \(0.629034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0000 | −0.472500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.5000 | + | 18.1865i | 0.412798 | + | 0.714986i | 0.995194 | − | 0.0979182i | \(-0.0312184\pi\) |
−0.582397 | + | 0.812905i | \(0.697885\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.5000 | + | 23.3827i | −0.529921 | + | 0.917851i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.5000 | + | 33.7750i | −0.763094 | + | 1.32172i | 0.178154 | + | 0.984003i | \(0.442987\pi\) |
−0.941248 | + | 0.337715i | \(0.890346\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.50000 | − | 7.79423i | −0.175830 | − | 0.304546i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.00000 | −0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.50000 | + | 9.52628i | 0.213925 | + | 0.370529i | 0.952940 | − | 0.303160i | \(-0.0980418\pi\) |
−0.739014 | + | 0.673690i | \(0.764708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.00000 | − | 5.19615i | 0.116510 | − | 0.201802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | − | 15.5885i | 0.348481 | − | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.00000 | − | 6.92820i | −0.154649 | − | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.00000 | −0.115814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.0000 | − | 17.3205i | −0.384900 | − | 0.666667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5000 | − | 23.3827i | 0.518847 | − | 0.898670i | −0.480913 | − | 0.876768i | \(-0.659695\pi\) |
0.999760 | − | 0.0219013i | \(-0.00697196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50000 | − | 2.59808i | 0.0574801 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.5000 | − | 18.1865i | −0.401771 | − | 0.695888i | 0.592168 | − | 0.805814i | \(-0.298272\pi\) |
−0.993940 | + | 0.109926i | \(0.964939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 63.0000 | 2.40711 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.0000 | 0.419676 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.00000 | + | 5.19615i | 0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.50000 | + | 11.2583i | −0.247272 | + | 0.428287i | −0.962768 | − | 0.270330i | \(-0.912867\pi\) |
0.715496 | + | 0.698617i | \(0.246201\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.0000 | + | 51.9615i | −1.13796 | + | 1.97101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | − | 15.5885i | −0.340899 | − | 0.590455i | ||||
\(698\) | 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 | ||||||||
\(703\) | 0.500000 | + | 0.866025i | 0.0188579 | + | 0.0326628i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.5000 | + | 23.3827i | −0.508439 | + | 0.880643i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.500000 | − | 0.866025i | 0.0187779 | − | 0.0325243i | −0.856484 | − | 0.516174i | \(-0.827356\pi\) |
0.875262 | + | 0.483650i | \(0.160689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.0000 | − | 22.5167i | −0.487538 | − | 0.844441i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.0000 | 0.786456 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.00000 | − | 10.3923i | −0.224074 | − | 0.388108i | ||||
\(718\) | 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 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.500000 | − | 0.866025i | 0.0185952 | − | 0.0322078i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0000 | + | 20.7846i | 0.445669 | + | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.00000 | − | 10.3923i | −0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5000 | + | 21.6506i | −0.461698 | + | 0.799684i | −0.999046 | − | 0.0436764i | \(-0.986093\pi\) |
0.537348 | + | 0.843361i | \(0.319426\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.5000 | + | 18.1865i | −0.386772 | + | 0.669910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.50000 | + | 16.4545i | 0.349463 | + | 0.605288i | 0.986154 | − | 0.165831i | \(-0.0530307\pi\) |
−0.636691 | + | 0.771119i | \(0.719697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00000 | 0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.0000 | −1.76095 | −0.880475 | − | 0.474093i | \(-0.842776\pi\) | ||||
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.50000 | + | 7.79423i | 0.164867 | + | 0.285558i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.0000 | + | 20.7846i | −0.439057 | + | 0.760469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | −51.0000 | −1.85608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.50000 | − | 7.79423i | −0.163340 | − | 0.282913i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.50000 | − | 2.59808i | 0.0543750 | − | 0.0941802i | −0.837557 | − | 0.546350i | \(-0.816017\pi\) |
0.891932 | + | 0.452170i | \(0.149350\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.00000 | − | 15.5885i | 0.325396 | − | 0.563602i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.00000 | − | 15.5885i | −0.324971 | − | 0.562867i | ||||
\(768\) | 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 | ||||||||
\(773\) | −16.5000 | − | 28.5788i | −0.593464 | − | 1.02791i | −0.993762 | − | 0.111524i | \(-0.964427\pi\) |
0.400298 | − | 0.916385i | \(-0.368907\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.0000 | + | 24.2487i | −0.502895 | + | 0.871039i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.00000 | − | 5.19615i | 0.107486 | − | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −30.0000 | −1.07211 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.0000 | −1.39197 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5000 | − | 26.8468i | −0.552515 | − | 0.956985i | −0.998092 | − | 0.0617409i | \(-0.980335\pi\) |
0.445577 | − | 0.895244i | \(-0.352999\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.50000 | + | 2.59808i | −0.0534014 | + | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | − | 1.73205i | 0.0355110 | − | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.50000 | − | 7.79423i | −0.159599 | − | 0.276433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0000 | −1.48772 | −0.743858 | − | 0.668338i | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.0000 | −0.955191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.0000 | − | 25.9808i | −0.529999 | − | 0.917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.50000 | − | 2.59808i | 0.0529339 | − | 0.0916841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.50000 | + | 2.59808i | −0.0528025 | + | 0.0914566i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.5000 | + | 28.5788i | 0.580109 | + | 1.00478i | 0.995466 | + | 0.0951198i | \(0.0303234\pi\) |
−0.415357 | + | 0.909659i | \(0.636343\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0000 | 1.82597 | 0.912983 | − | 0.407997i | \(-0.133772\pi\) | ||||
0.912983 | + | 0.407997i | \(0.133772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.0000 | 0.385787 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.5000 | + | 28.5788i | 0.577970 | + | 1.00107i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | − | 3.46410i | 0.0699711 | − | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | ||||||||
\(823\) | −2.50000 | − | 4.33013i | −0.0871445 | − | 0.150939i | 0.819159 | − | 0.573567i | \(-0.194441\pi\) |
−0.906303 | + | 0.422628i | \(0.861108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | − | 31.1769i | 0.622916 | − | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.5000 | − | 30.3109i | −0.604888 | − | 1.04770i | ||||
\(838\) | 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 | ||||||||
\(843\) | 15.0000 | + | 25.9808i | 0.516627 | + | 0.894825i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.5000 | + | 23.3827i | −0.464414 | + | 0.804389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 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 | ||||||||
\(853\) | 22.0000 | 0.753266 | 0.376633 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.50000 | + | 12.9904i | 0.256195 | + | 0.443743i | 0.965219 | − | 0.261441i | \(-0.0841977\pi\) |
−0.709024 | + | 0.705184i | \(0.750864\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.5000 | + | 44.1673i | −0.868030 | + | 1.50347i | −0.00402340 | + | 0.999992i | \(0.501281\pi\) |
−0.864007 | + | 0.503480i | \(0.832053\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5000 | + | 23.3827i | 0.459014 | + | 0.795035i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.0000 | 1.32298 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.00000 | − | 12.1244i | −0.237186 | − | 0.410818i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.0000 | − | 17.3205i | 0.338449 | − | 0.586210i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.50000 | − | 11.2583i | 0.219489 | − | 0.380167i | −0.735163 | − | 0.677891i | \(-0.762894\pi\) |
0.954652 | + | 0.297724i | \(0.0962275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.00000 | − | 5.19615i | −0.101187 | − | 0.175262i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5000 | + | 23.3827i | 0.453798 | + | 0.786000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.5000 | − | 33.7750i | 0.654746 | − | 1.13405i | −0.327212 | − | 0.944951i | \(-0.606109\pi\) |
0.981957 | − | 0.189102i | \(-0.0605577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | − | 2.59808i | 0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.50000 | − | 7.79423i | −0.150587 | − | 0.260824i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −63.0000 | −2.10586 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.00000 | 0.200334 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.0000 | − | 25.9808i | 0.498617 | − | 0.863630i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.5000 | − | 35.5070i | −0.680691 | − | 1.17899i | −0.974770 | − | 0.223211i | \(-0.928346\pi\) |
0.294079 | − | 0.955781i | \(-0.404987\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.50000 | + | 2.59808i | −0.0495885 | + | 0.0858898i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.500000 | − | 0.866025i | 0.0164935 | − | 0.0285675i | −0.857661 | − | 0.514216i | \(-0.828083\pi\) |
0.874154 | + | 0.485648i | \(0.161416\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.0000 | − | 19.0526i | −0.361287 | − | 0.625768i | ||||
\(928\) | 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 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.5000 | − | 23.3827i | 0.441970 | − | 0.765515i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.5000 | + | 23.3827i | 0.441497 | + | 0.764696i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.0000 | 0.750577 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.5000 | + | 23.3827i | 0.440087 | + | 0.762254i | 0.997695 | − | 0.0678506i | \(-0.0216141\pi\) |
−0.557608 | + | 0.830104i | \(0.688281\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | − | 15.5885i | 0.293080 | − | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.5000 | − | 38.9711i | 0.731152 | − | 1.26639i | −0.225240 | − | 0.974303i | \(-0.572316\pi\) |
0.956391 | − | 0.292089i | \(-0.0943502\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00000 | + | 1.73205i | 0.0324614 | + | 0.0562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.00000 | 0.291845 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.5000 | − | 23.3827i | −0.436850 | − | 0.756646i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.00000 | − | 15.5885i | 0.290929 | − | 0.503903i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.0000 | + | 25.9808i | 0.483368 | + | 0.837218i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.0000 | −1.06231 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0000 | −0.514525 | −0.257263 | − | 0.966342i | \(-0.582821\pi\) | ||||
−0.257263 | + | 0.966342i | \(0.582821\pi\) | |||||||
\(968\) | 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 | \(-0.528231\pi\) |
0.906909 | − | 0.421326i | \(-0.138435\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.00000 | + | 6.92820i | −0.128103 | + | 0.221880i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.5000 | − | 23.3827i | −0.431903 | − | 0.748078i | 0.565134 | − | 0.824999i | \(-0.308824\pi\) |
−0.997037 | + | 0.0769208i | \(0.975491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.0000 | 1.43821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.5000 | + | 28.5788i | 0.526268 | + | 0.911523i | 0.999532 | + | 0.0306024i | \(0.00974257\pi\) |
−0.473263 | + | 0.880921i | \(0.656924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0000 | − | 46.7654i | 0.860292 | − | 1.49007i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 13.0000 | 0.412543 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0000 | −0.665745 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.5000 | + | 51.0955i | 0.934274 | + | 1.61821i | 0.775923 | + | 0.630828i | \(0.217285\pi\) |
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | 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 \(a_p\))