Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [496,2,Mod(129,496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(496, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("496.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 496 = 2^{4} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 496.i (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: | \(3.96057994026\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 31) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 273.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 496.273 |
Dual form | 496.2.i.h.129.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/496\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) | \(373\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.207107 | + | 0.358719i | 0.119573 | + | 0.207107i | 0.919599 | − | 0.392859i | \(-0.128514\pi\) |
−0.800025 | + | 0.599966i | \(0.795181\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) |
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.207107 | − | 0.358719i | −0.0782790 | − | 0.135583i | 0.824228 | − | 0.566257i | \(-0.191609\pi\) |
−0.902507 | + | 0.430674i | \(0.858276\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41421 | − | 2.44949i | 0.471405 | − | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.62132 | − | 2.80821i | 0.488846 | − | 0.846707i | −0.511071 | − | 0.859538i | \(-0.670751\pi\) |
0.999918 | + | 0.0128314i | \(0.00408449\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.91421 | − | 3.31552i | 0.530907 | − | 0.919558i | −0.468442 | − | 0.883494i | \(-0.655185\pi\) |
0.999349 | − | 0.0360643i | \(-0.0114821\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.414214 | −0.106949 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.91421 | + | 5.04757i | 0.706801 | + | 1.22421i | 0.966038 | + | 0.258401i | \(0.0831955\pi\) |
−0.259237 | + | 0.965814i | \(0.583471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.20711 | + | 3.82282i | 0.506345 | + | 0.877015i | 0.999973 | + | 0.00734216i | \(0.00233710\pi\) |
−0.493628 | + | 0.869673i | \(0.664330\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0857864 | − | 0.148586i | 0.0187201 | − | 0.0324242i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.82843 | −1.26801 | −0.634004 | − | 0.773330i | \(-0.718590\pi\) | ||||
−0.634004 | + | 0.773330i | \(0.718590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | + | 2.44949i | 0.898027 | + | 0.439941i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.34315 | 0.233812 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.414214 | 0.0700149 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.500000 | − | 0.866025i | −0.0821995 | − | 0.142374i | 0.821995 | − | 0.569495i | \(-0.192861\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.58579 | 0.253929 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.74264 | − | 6.48244i | 0.584502 | − | 1.01239i | −0.410435 | − | 0.911890i | \(-0.634623\pi\) |
0.994937 | − | 0.100498i | \(-0.0320435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.44975 | − | 9.43924i | −0.831079 | − | 1.43947i | −0.897184 | − | 0.441658i | \(-0.854391\pi\) |
0.0661049 | − | 0.997813i | \(-0.478943\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421 | + | 2.44949i | 0.210819 | + | 0.365148i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.65685 | −1.40860 | −0.704298 | − | 0.709904i | \(-0.748738\pi\) | ||||
−0.704298 | + | 0.709904i | \(0.748738\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.41421 | − | 5.91359i | 0.487745 | − | 0.844799i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.20711 | + | 2.09077i | −0.169029 | + | 0.292766i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.91421 | + | 5.04757i | −0.400298 | + | 0.693337i | −0.993762 | − | 0.111524i | \(-0.964427\pi\) |
0.593464 | + | 0.804861i | \(0.297760\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.62132 | + | 2.80821i | 0.218619 | + | 0.378659i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.914214 | + | 1.58346i | −0.121091 | + | 0.209735i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.03553 | + | 3.52565i | 0.265004 | + | 0.459000i | 0.967565 | − | 0.252624i | \(-0.0812934\pi\) |
−0.702561 | + | 0.711624i | \(0.747960\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.82843 | −0.362143 | −0.181071 | − | 0.983470i | \(-0.557957\pi\) | ||||
−0.181071 | + | 0.983470i | \(0.557957\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.17157 | −0.147604 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.91421 | + | 3.31552i | 0.237429 | + | 0.411239i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.62132 | − | 2.80821i | 0.198076 | − | 0.343077i | −0.749829 | − | 0.661632i | \(-0.769864\pi\) |
0.947904 | + | 0.318555i | \(0.103197\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.828427 | + | 1.43488i | 0.0997309 | + | 0.172739i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0355339 | − | 0.0615465i | 0.00421710 | − | 0.00730423i | −0.863909 | − | 0.503648i | \(-0.831991\pi\) |
0.868126 | + | 0.496343i | \(0.165324\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.914214 | − | 1.58346i | 0.107001 | − | 0.185330i | −0.807553 | − | 0.589795i | \(-0.799209\pi\) |
0.914554 | + | 0.404464i | \(0.132542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.828427 | + | 1.43488i | −0.0956585 | + | 0.165685i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.34315 | −0.153066 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.37868 | − | 5.85204i | −0.380131 | − | 0.658406i | 0.610950 | − | 0.791670i | \(-0.290788\pi\) |
−0.991081 | + | 0.133263i | \(0.957454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.74264 | − | 6.48244i | −0.415849 | − | 0.720272i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.03553 | + | 8.72180i | −0.552722 | + | 0.957342i | 0.445355 | + | 0.895354i | \(0.353077\pi\) |
−0.998077 | + | 0.0619880i | \(0.980256\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.82843 | −0.632182 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.41421 | − | 2.44949i | −0.151620 | − | 0.262613i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.48528 | 0.475439 | 0.237719 | − | 0.971334i | \(-0.423600\pi\) | ||||
0.237719 | + | 0.971334i | \(0.423600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.58579 | −0.166236 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.156854 | + | 2.30090i | 0.0162650 | + | 0.238593i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.41421 | −0.452889 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.17157 | 0.525094 | 0.262547 | − | 0.964919i | \(-0.415438\pi\) | ||||
0.262547 | + | 0.964919i | \(0.415438\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.58579 | − | 7.94282i | −0.460889 | − | 0.798283i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.48528 | −0.844317 | −0.422159 | − | 0.906522i | \(-0.638727\pi\) | ||||
−0.422159 | + | 0.906522i | \(0.638727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.03553 | − | 1.79360i | 0.102034 | − | 0.176728i | −0.810488 | − | 0.585755i | \(-0.800798\pi\) |
0.912523 | + | 0.409026i | \(0.134132\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0857864 | + | 0.148586i | 0.00837190 | + | 0.0145006i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.20711 | + | 10.7510i | 0.600064 | + | 1.03934i | 0.992811 | + | 0.119694i | \(0.0381914\pi\) |
−0.392747 | + | 0.919646i | \(0.628475\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8284 | −1.03718 | −0.518588 | − | 0.855024i | \(-0.673542\pi\) | ||||
−0.518588 | + | 0.855024i | \(0.673542\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.207107 | − | 0.358719i | 0.0196577 | − | 0.0340481i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.32843 | + | 14.4253i | −0.783473 | + | 1.35701i | 0.146435 | + | 0.989220i | \(0.453220\pi\) |
−0.929907 | + | 0.367794i | \(0.880113\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | + | 3.46410i | −0.186501 | + | 0.323029i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.41421 | − | 9.37769i | −0.500544 | − | 0.866968i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.20711 | − | 2.09077i | 0.110655 | − | 0.191661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.242641 | + | 0.420266i | 0.0220582 | + | 0.0382060i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.10051 | 0.279563 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.44975 | + | 7.70719i | 0.394851 | + | 0.683902i | 0.993082 | − | 0.117421i | \(-0.0374628\pi\) |
−0.598231 | + | 0.801324i | \(0.704129\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.25736 | − | 3.90986i | 0.198749 | − | 0.344244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.62132 | − | 11.4685i | −0.578507 | − | 1.00200i | −0.995651 | − | 0.0931636i | \(-0.970302\pi\) |
0.417143 | − | 0.908841i | \(-0.363031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.914214 | − | 1.58346i | 0.0792724 | − | 0.137304i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.20711 | + | 2.09077i | −0.103891 | + | 0.179945i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.74264 | + | 8.21449i | −0.405191 | + | 0.701812i | −0.994344 | − | 0.106210i | \(-0.966128\pi\) |
0.589153 | + | 0.808022i | \(0.299462\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | − | 3.46410i | −0.168430 | − | 0.291730i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.20711 | − | 10.7510i | −0.519064 | − | 0.899046i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.41421 | − | 5.91359i | 0.283535 | − | 0.491097i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.82843 | 0.233285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.500000 | − | 0.866025i | −0.0409616 | − | 0.0709476i | 0.844818 | − | 0.535054i | \(-0.179709\pi\) |
−0.885779 | + | 0.464107i | \(0.846375\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.31371 | −0.432423 | −0.216212 | − | 0.976346i | \(-0.569370\pi\) | ||||
−0.216212 | + | 0.976346i | \(0.569370\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.4853 | 1.33276 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.62132 | + | 3.10538i | −0.371193 | + | 0.249430i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.17157 | 0.731971 | 0.365986 | − | 0.930621i | \(-0.380732\pi\) | ||||
0.365986 | + | 0.930621i | \(0.380732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.41421 | −0.191460 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.828427 | − | 1.43488i | −0.0652892 | − | 0.113084i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.9706 | −1.64254 | −0.821271 | − | 0.570539i | \(-0.806734\pi\) | ||||
−0.821271 | + | 0.570539i | \(0.806734\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.671573 | + | 1.16320i | −0.0522819 | + | 0.0905549i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.2782 | + | 19.5344i | 0.872731 | + | 1.51162i | 0.859160 | + | 0.511707i | \(0.170987\pi\) |
0.0135714 | + | 0.999908i | \(0.495680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.828427 | − | 1.43488i | −0.0637252 | − | 0.110375i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.4853 | 0.954773 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.15685 | + | 7.19988i | −0.316040 | + | 0.547397i | −0.979658 | − | 0.200674i | \(-0.935687\pi\) |
0.663618 | + | 0.748071i | \(0.269020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.828427 | − | 1.43488i | 0.0626232 | − | 0.108467i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.843146 | + | 1.46037i | −0.0633747 | + | 0.109768i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.62132 | − | 13.2005i | −0.569644 | − | 0.986653i | −0.996601 | − | 0.0823807i | \(-0.973748\pi\) |
0.426957 | − | 0.904272i | \(-0.359586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.15685 | + | 10.6640i | −0.457635 | + | 0.792648i | −0.998835 | − | 0.0482461i | \(-0.984637\pi\) |
0.541200 | + | 0.840894i | \(0.317970\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.585786 | − | 1.01461i | −0.0433026 | − | 0.0750023i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.8995 | 1.38207 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.500000 | − | 0.866025i | −0.0363696 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4497 | + | 18.0995i | −0.756117 | + | 1.30963i | 0.188700 | + | 0.982035i | \(0.439573\pi\) |
−0.944817 | + | 0.327599i | \(0.893761\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.57107 | − | 6.18527i | −0.257051 | − | 0.445226i | 0.708400 | − | 0.705812i | \(-0.249418\pi\) |
−0.965451 | + | 0.260586i | \(0.916084\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.792893 | + | 1.37333i | −0.0567803 | + | 0.0983463i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.74264 | − | 11.6786i | 0.480393 | − | 0.832066i | −0.519354 | − | 0.854559i | \(-0.673827\pi\) |
0.999747 | + | 0.0224938i | \(0.00716061\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.20711 | − | 15.9472i | 0.652674 | − | 1.13047i | −0.329797 | − | 0.944052i | \(-0.606980\pi\) |
0.982471 | − | 0.186413i | \(-0.0596864\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.34315 | 0.0947382 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.41421 | + | 2.44949i | 0.0992583 | + | 0.171920i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.74264 | + | 6.48244i | 0.261397 | + | 0.452754i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.65685 | − | 9.79796i | 0.393179 | − | 0.681005i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.3137 | 0.990100 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.20711 | + | 9.01897i | 0.358472 | + | 0.620892i | 0.987706 | − | 0.156324i | \(-0.0499645\pi\) |
−0.629234 | + | 0.777216i | \(0.716631\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0294373 | 0.00201701 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.8995 | 0.743339 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.156854 | − | 2.30090i | −0.0106480 | − | 0.156195i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.757359 | 0.0511776 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.3137 | 1.50098 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8640 | − | 20.5490i | −0.794470 | − | 1.37606i | −0.923175 | − | 0.384379i | \(-0.874416\pi\) |
0.128706 | − | 0.991683i | \(-0.458918\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.3137 | 0.754247 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.20711 | + | 15.9472i | −0.611097 | + | 1.05845i | 0.379959 | + | 0.925003i | \(0.375938\pi\) |
−0.991056 | + | 0.133448i | \(0.957395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.74264 | + | 4.75039i | 0.181239 | + | 0.313915i | 0.942303 | − | 0.334762i | \(-0.108656\pi\) |
−0.761064 | + | 0.648677i | \(0.775323\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.278175 | − | 0.481813i | −0.0183025 | − | 0.0317009i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.17157 | −0.600850 | −0.300425 | − | 0.953805i | \(-0.597128\pi\) | ||||
−0.300425 | + | 0.953805i | \(0.597128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.82843 | − | 8.36308i | 0.314972 | − | 0.545547i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.39949 | − | 2.42400i | 0.0909070 | − | 0.157455i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.6213 | + | 18.3967i | −0.687036 | + | 1.18998i | 0.285756 | + | 0.958302i | \(0.407755\pi\) |
−0.972792 | + | 0.231679i | \(0.925578\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.67157 | − | 11.5555i | −0.429754 | − | 0.744355i | 0.567097 | − | 0.823651i | \(-0.308066\pi\) |
−0.996851 | + | 0.0792954i | \(0.974733\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.17157 | − | 8.95743i | 0.331757 | − | 0.574619i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.41421 | + | 5.91359i | 0.218126 | + | 0.377805i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.8995 | 1.07529 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.17157 | −0.264363 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.20711 | + | 5.55487i | 0.202431 | + | 0.350620i | 0.949311 | − | 0.314338i | \(-0.101783\pi\) |
−0.746880 | + | 0.664958i | \(0.768449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.48528 | − | 11.2328i | 0.407726 | − | 0.706202i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.20711 | − | 2.09077i | −0.0755920 | − | 0.130929i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1569 | + | 19.3242i | −0.695945 | + | 1.20541i | 0.273915 | + | 0.961754i | \(0.411681\pi\) |
−0.969861 | + | 0.243659i | \(0.921652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.207107 | + | 0.358719i | −0.0128690 | + | 0.0222897i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.65685 | + | 16.7262i | −0.597744 | + | 1.03532i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3137 | 1.43758 | 0.718792 | − | 0.695225i | \(-0.244695\pi\) | ||||
0.718792 | + | 0.695225i | \(0.244695\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.91421 | − | 5.04757i | −0.179019 | − | 0.310070i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.928932 | + | 1.60896i | 0.0568497 | + | 0.0984666i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.0858 | − | 22.6652i | 0.797854 | − | 1.38192i | −0.123156 | − | 0.992387i | \(-0.539302\pi\) |
0.921011 | − | 0.389537i | \(-0.127365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.686292 | 0.0416892 | 0.0208446 | − | 0.999783i | \(-0.493364\pi\) | ||||
0.0208446 | + | 0.999783i | \(0.493364\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.328427 | − | 0.568852i | −0.0198773 | − | 0.0344285i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.9706 | 0.782154 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.1421 | 0.849719 | 0.424859 | − | 0.905259i | \(-0.360324\pi\) | ||||
0.424859 | + | 0.905259i | \(0.360324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.0711 | − | 8.78335i | 0.782544 | − | 0.525845i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6569 | 0.811816 | 0.405908 | − | 0.913914i | \(-0.366955\pi\) | ||||
0.405908 | + | 0.913914i | \(0.366955\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.914214 | − | 1.58346i | −0.0541533 | − | 0.0937963i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.10051 | −0.183017 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.48528 | + | 14.6969i | −0.499134 | + | 0.864526i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.07107 | + | 1.85514i | 0.0627871 | + | 0.108750i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.39949 | − | 12.8163i | −0.432283 | − | 0.748736i | 0.564786 | − | 0.825237i | \(-0.308959\pi\) |
−0.997070 | + | 0.0765008i | \(0.975625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.07107 | −0.237027 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.91421 | − | 6.77962i | 0.227126 | − | 0.393393i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.65685 | − | 13.2621i | 0.442807 | − | 0.766965i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.25736 | + | 3.90986i | −0.130112 | + | 0.225361i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.75736 | − | 3.04384i | −0.100958 | − | 0.174864i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.41421 | − | 2.44949i | 0.0809776 | − | 0.140257i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.62132 | − | 9.73641i | −0.320826 | − | 0.555686i | 0.659833 | − | 0.751412i | \(-0.270627\pi\) |
−0.980659 | + | 0.195726i | \(0.937294\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.857864 | 0.0488022 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3137 | −0.641542 | −0.320771 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320771 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.914214 | + | 1.58346i | 0.0516744 | + | 0.0895027i | 0.890706 | − | 0.454581i | \(-0.150211\pi\) |
−0.839031 | + | 0.544083i | \(0.816878\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.585786 | − | 1.01461i | 0.0330053 | − | 0.0571669i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.91421 | + | 6.77962i | 0.219844 | + | 0.380781i | 0.954760 | − | 0.297377i | \(-0.0961118\pi\) |
−0.734916 | + | 0.678158i | \(0.762778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.0711 | + | 19.1757i | −0.619861 | + | 1.07363i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.57107 | + | 4.45322i | −0.143503 | + | 0.248555i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.8640 | + | 22.2810i | −0.715770 | + | 1.23975i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.3137 | 0.849452 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.24264 | − | 3.88437i | −0.124018 | − | 0.214806i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.00000 | + | 3.46410i | 0.110264 | + | 0.190982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.62132 | − | 8.00436i | 0.254011 | − | 0.439960i | −0.710616 | − | 0.703580i | \(-0.751583\pi\) |
0.964626 | + | 0.263621i | \(0.0849168\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.82843 | −0.154997 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.62132 | + | 2.80821i | 0.0885822 | + | 0.153429i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.31371 | 0.507350 | 0.253675 | − | 0.967290i | \(-0.418361\pi\) | ||||
0.253675 | + | 0.967290i | \(0.418361\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.89949 | −0.374729 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.9853 | − | 10.0696i | 0.811498 | − | 0.545301i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.72792 | −0.309279 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.65685 | −0.0892020 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.27817 | − | 7.41002i | −0.229664 | − | 0.397790i | 0.728044 | − | 0.685530i | \(-0.240430\pi\) |
−0.957709 | + | 0.287740i | \(0.907096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.1127 | −1.45131 | −0.725655 | − | 0.688059i | \(-0.758463\pi\) | ||||
−0.725655 | + | 0.688059i | \(0.758463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.62132 | − | 8.00436i | 0.246668 | − | 0.427241i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | − | 2.59808i | −0.0798369 | − | 0.138282i | 0.823343 | − | 0.567545i | \(-0.192107\pi\) |
−0.903179 | + | 0.429263i | \(0.858773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0355339 | + | 0.0615465i | 0.00188594 | + | 0.00326655i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.00000 | 0.0529256 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.55025 | − | 6.14922i | 0.187375 | − | 0.324543i | −0.756999 | − | 0.653416i | \(-0.773335\pi\) |
0.944374 | + | 0.328873i | \(0.106669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.242641 | + | 0.420266i | −0.0127706 | + | 0.0221193i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.100505 | + | 0.174080i | −0.00527515 | + | 0.00913682i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.914214 | + | 1.58346i | 0.0478521 | + | 0.0828823i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.1066 | + | 20.9692i | −0.631959 | + | 1.09459i | 0.355191 | + | 0.934794i | \(0.384416\pi\) |
−0.987151 | + | 0.159792i | \(0.948918\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.5858 | − | 18.3351i | −0.551074 | − | 0.954488i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.41421 | 0.125340 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.86396 | − | 3.22848i | −0.0962545 | − | 0.166718i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.0711 | + | 22.6398i | −0.673194 | + | 1.16601i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.69239 | + | 6.39540i | 0.189665 | + | 0.328510i | 0.945139 | − | 0.326669i | \(-0.105926\pi\) |
−0.755473 | + | 0.655179i | \(0.772593\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.84315 | + | 3.19242i | −0.0944272 | + | 0.163553i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.55025 | − | 4.41717i | 0.130312 | − | 0.225707i | −0.793485 | − | 0.608590i | \(-0.791735\pi\) |
0.923797 | + | 0.382883i | \(0.125069\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.671573 | − | 1.16320i | 0.0342265 | − | 0.0592821i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.8284 | −1.56710 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.57107 | + | 9.64937i | 0.282464 | + | 0.489243i | 0.971991 | − | 0.235018i | \(-0.0755148\pi\) |
−0.689527 | + | 0.724260i | \(0.742181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.6569 | + | 20.1903i | 0.589512 | + | 1.02107i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.74264 | − | 4.75039i | 0.138348 | − | 0.239626i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.75736 | 0.340000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.7426 | + | 28.9991i | 0.840289 | + | 1.45542i | 0.889650 | + | 0.456642i | \(0.150948\pi\) |
−0.0493613 | + | 0.998781i | \(0.515719\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.757359 | 0.0379154 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.8284 | −1.33975 | −0.669874 | − | 0.742475i | \(-0.733652\pi\) | ||||
−0.669874 | + | 0.742475i | \(0.733652\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.6924 | − | 11.8887i | 0.881321 | − | 0.592220i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.48528 | 0.371947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.24264 | −0.160732 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.3284 | − | 17.8894i | −0.510708 | − | 0.884572i | −0.999923 | − | 0.0124088i | \(-0.996050\pi\) |
0.489215 | − | 0.872163i | \(-0.337283\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.92893 | −0.193800 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.843146 | − | 1.46037i | 0.0414885 | − | 0.0718602i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.03553 | − | 8.72180i | −0.247185 | − | 0.428136i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.5711 | − | 26.9699i | 0.758887 | − | 1.31443i | −0.184531 | − | 0.982827i | \(-0.559077\pi\) |
0.943418 | − | 0.331605i | \(-0.107590\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.6569 | + | 23.6544i | −0.664019 | + | 1.15011i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.6569 | + | 20.1903i | −0.565440 | + | 0.979372i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.585786 | + | 1.01461i | 0.0283482 | + | 0.0491005i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.57107 | − | 4.45322i | 0.124132 | − | 0.215003i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.37868 | − | 14.5123i | −0.403587 | − | 0.699033i | 0.590569 | − | 0.806987i | \(-0.298903\pi\) |
−0.994156 | + | 0.107954i | \(0.965570\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.1127 | 1.30295 | 0.651477 | − | 0.758669i | \(-0.274150\pi\) | ||||
0.651477 | + | 0.758669i | \(0.274150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.82843 | 0.135613 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.82843 | + | 15.2913i | 0.422321 | + | 0.731481i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.03553 | − | 1.79360i | 0.0494233 | − | 0.0856037i | −0.840255 | − | 0.542191i | \(-0.817595\pi\) |
0.889679 | + | 0.456587i | \(0.150928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.65685 | − | 16.7262i | −0.459850 | − | 0.796484i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.37868 | + | 4.11999i | −0.113014 | + | 0.195747i | −0.916984 | − | 0.398923i | \(-0.869384\pi\) |
0.803970 | + | 0.594670i | \(0.202717\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.24264 | + | 3.88437i | −0.106311 | + | 0.184137i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.207107 | − | 0.358719i | 0.00979581 | − | 0.0169668i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.6274 | −1.91733 | −0.958663 | − | 0.284543i | \(-0.908158\pi\) | ||||
−0.958663 | + | 0.284543i | \(0.908158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.1360 | − | 21.0202i | −0.571464 | − | 0.989804i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.10051 | − | 1.90613i | −0.0517062 | − | 0.0895578i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.792893 | − | 1.37333i | 0.0371714 | − | 0.0643828i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.1127 | −1.45539 | −0.727695 | − | 0.685901i | \(-0.759409\pi\) | ||||
−0.727695 | + | 0.685901i | \(0.759409\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.03553 | + | 12.1859i | 0.328391 | + | 0.568789i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.14214 | −0.0997692 | −0.0498846 | − | 0.998755i | \(-0.515885\pi\) | ||||
−0.0498846 | + | 0.998755i | \(0.515885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.97056 | 0.416897 | 0.208449 | − | 0.978033i | \(-0.433159\pi\) | ||||
0.208449 | + | 0.978033i | \(0.433159\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.07107 | − | 1.01461i | −0.0960435 | − | 0.0470515i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.34315 | −0.0620207 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.89949 | + | 3.29002i | 0.0875241 | + | 0.151596i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.3431 | −1.62508 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.82843 | + | 15.2913i | −0.405076 | + | 0.701612i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.24264 | + | 14.2767i | 0.377405 | + | 0.653684i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.86396 | − | 13.6208i | −0.359314 | − | 0.622349i | 0.628533 | − | 0.777783i | \(-0.283656\pi\) |
−0.987846 | + | 0.155434i | \(0.950322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.82843 | −0.174561 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.343146 | − | 0.594346i | 0.0156137 | − | 0.0270437i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.58579 | + | 4.47871i | −0.117415 | + | 0.203368i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.69239 | − | 16.7877i | 0.439204 | − | 0.760724i | −0.558424 | − | 0.829556i | \(-0.688594\pi\) |
0.997628 | + | 0.0688318i | \(0.0219272\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.34315 | − | 7.52255i | −0.196404 | − | 0.340181i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.792893 | − | 1.37333i | 0.0357828 | − | 0.0619776i | −0.847579 | − | 0.530669i | \(-0.821941\pi\) |
0.883362 | + | 0.468691i | \(0.155274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.8995 | − | 34.4669i | −0.896228 | − | 1.55231i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.17157 | 0.412232 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.0294373 | −0.00132044 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.10660 | − | 1.91669i | −0.0495383 | − | 0.0858028i | 0.840193 | − | 0.542288i | \(-0.182442\pi\) |
−0.889731 | + | 0.456485i | \(0.849108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.67157 | + | 8.09140i | −0.208710 | + | 0.361497i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.69239 | − | 11.5916i | −0.298399 | − | 0.516842i | 0.677371 | − | 0.735642i | \(-0.263119\pi\) |
−0.975770 | + | 0.218800i | \(0.929786\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.24264 | − | 7.34847i | 0.188795 | − | 0.327003i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.343146 | − | 0.594346i | 0.0152396 | − | 0.0263958i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.3995 | − | 28.4048i | 0.726895 | − | 1.25902i | −0.231294 | − | 0.972884i | \(-0.574296\pi\) |
0.958189 | − | 0.286135i | \(-0.0923706\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.757359 | −0.0335036 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.32843 | + | 9.22911i | 0.235256 | + | 0.407475i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.03553 | + | 1.79360i | 0.0456311 | + | 0.0790353i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.6569 | + | 27.1185i | −0.688588 | + | 1.19267i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.44365 | −0.151159 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.2279 | + | 17.7153i | 0.448093 | + | 0.776121i | 0.998262 | − | 0.0589331i | \(-0.0187699\pi\) |
−0.550169 | + | 0.835054i | \(0.685437\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.00000 | 0.349816 | 0.174908 | − | 0.984585i | \(-0.444037\pi\) | ||||
0.174908 | + | 0.984585i | \(0.444037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.686292 | 0.0299522 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.20711 | + | 32.3762i | 0.0961431 | + | 1.41033i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.5147 | 0.499696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.3284 | − | 24.8176i | −0.620633 | − | 1.07497i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.4142 | −0.536713 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.15685 | − | 5.46783i | 0.136228 | − | 0.235954i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.0711 | − | 19.1757i | −0.476865 | − | 0.825954i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.6421 | + | 27.0930i | 0.672508 | + | 1.16482i | 0.977191 | + | 0.212364i | \(0.0681162\pi\) |
−0.304683 | + | 0.952454i | \(0.598550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.10051 | −0.218884 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.41421 | − | 9.37769i | 0.231919 | − | 0.401696i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.86396 | + | 17.0849i | −0.421753 | + | 0.730497i | −0.996111 | − | 0.0881071i | \(-0.971918\pi\) |
0.574358 | + | 0.818604i | \(0.305252\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.00000 | + | 6.92820i | −0.170716 | + | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0711 | − | 26.1039i | −0.642049 | − | 1.11206i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.39949 | + | 2.42400i | −0.0595126 | + | 0.103079i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.207107 | + | 0.358719i | 0.00879119 | + | 0.0152268i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.5147 | 1.16584 | 0.582918 | − | 0.812531i | \(-0.301911\pi\) | ||||
0.582918 | + | 0.812531i | \(0.301911\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.7279 | −1.76490 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.91421 | + | 6.77962i | 0.165258 | + | 0.286236i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.62132 | − | 11.4685i | 0.279055 | − | 0.483338i | −0.692095 | − | 0.721807i | \(-0.743312\pi\) |
0.971150 | + | 0.238468i | \(0.0766454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.32843 | − | 14.4253i | −0.350380 | − | 0.606875i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.55025 | + | 2.68512i | −0.0651045 | + | 0.112764i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.57107 | − | 11.3814i | 0.275473 | − | 0.477134i | −0.694781 | − | 0.719221i | \(-0.744499\pi\) |
0.970254 | + | 0.242087i | \(0.0778320\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5503 | + | 18.2736i | −0.441514 | + | 0.764725i | −0.997802 | − | 0.0662645i | \(-0.978892\pi\) |
0.556288 | + | 0.830990i | \(0.312225\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.65685 | −0.361645 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | + | 13.8564i | 0.333623 | + | 0.577852i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.0147186 | + | 0.0254934i | 0.000612744 | + | 0.00106130i | 0.866332 | − | 0.499469i | \(-0.166472\pi\) |
−0.865719 | + | 0.500531i | \(0.833138\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.47918 | − | 2.56202i | 0.0614728 | − | 0.106474i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.17157 | 0.173066 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.44975 | + | 16.3674i | 0.391369 | + | 0.677870i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.8284 | 0.447700 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.6569 | 1.30662 | 0.653309 | − | 0.757091i | \(-0.273380\pi\) | ||||
0.653309 | + | 0.757091i | \(0.273380\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.67157 | + | 24.5204i | 0.0688760 | + | 1.01035i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.58579 | 0.229769 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.31371 | −0.0539475 | −0.0269738 | − | 0.999636i | \(-0.508587\pi\) | ||||
−0.0269738 | + | 0.999636i | \(0.508587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.20711 | + | 2.09077i | 0.0494866 | + | 0.0857132i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.62742 | 0.312169 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.55025 | − | 13.0774i | 0.308495 | − | 0.534329i | −0.669538 | − | 0.742777i | \(-0.733508\pi\) |
0.978033 | + | 0.208449i | \(0.0668414\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.25736 | + | 5.64191i | 0.132870 | + | 0.230138i | 0.924782 | − | 0.380498i | \(-0.124247\pi\) |
−0.791911 | + | 0.610636i | \(0.790914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.58579 | − | 7.94282i | −0.186748 | − | 0.323456i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.485281 | −0.0197295 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.792893 | + | 1.37333i | −0.0321825 | + | 0.0557418i | −0.881668 | − | 0.471870i | \(-0.843579\pi\) |
0.849486 | + | 0.527612i | \(0.176912\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.585786 | + | 1.01461i | −0.0237373 | + | 0.0411141i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.4853 | + | 32.0174i | −0.747834 | + | 1.29529i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.15685 | − | 10.6640i | −0.248673 | − | 0.430714i | 0.714485 | − | 0.699651i | \(-0.246661\pi\) |
−0.963158 | + | 0.268937i | \(0.913328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.55025 | + | 2.68512i | −0.0625122 | + | 0.108274i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.6421 | + | 28.8250i | 0.669987 | + | 1.16045i | 0.977907 | + | 0.209040i | \(0.0670337\pi\) |
−0.307920 | + | 0.951412i | \(0.599633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.3431 | 0.817660 | 0.408830 | − | 0.912611i | \(-0.365937\pi\) | ||||
0.408830 | + | 0.912611i | \(0.365937\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.65685 | 0.387516 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.928932 | − | 1.60896i | −0.0372169 | − | 0.0644615i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.96447 | + | 5.13461i | 0.118389 | + | 0.205056i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.91421 | − | 5.04757i | 0.116197 | − | 0.201260i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.0061 | − | 43.3118i | 0.995477 | − | 1.72422i | 0.415464 | − | 0.909610i | \(-0.363619\pi\) |
0.580013 | − | 0.814607i | \(-0.303047\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.15685 | + | 3.73578i | −0.0857273 | + | 0.148484i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.89949 | −0.353166 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.0711 | − | 22.6398i | −0.517895 | − | 0.897020i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.100505 | − | 0.174080i | −0.00397592 | − | 0.00688649i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.98528 | − | 12.0989i | 0.275902 | − | 0.477876i | −0.694460 | − | 0.719531i | \(-0.744357\pi\) |
0.970362 | + | 0.241655i | \(0.0776901\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.3137 | −1.39264 | −0.696318 | − | 0.717733i | \(-0.745180\pi\) | ||||
−0.696318 | + | 0.717733i | \(0.745180\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.25736 | + | 3.90986i | 0.0888834 | + | 0.153951i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.3137 | 1.78147 | 0.890733 | − | 0.454527i | \(-0.150192\pi\) | ||||
0.890733 | + | 0.454527i | \(0.150192\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.2010 | 0.518185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.792893 | − | 0.532799i | 0.0310759 | − | 0.0208821i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.14214 | −0.240360 | −0.120180 | − | 0.992752i | \(-0.538347\pi\) | ||||
−0.120180 | + | 0.992752i | \(0.538347\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.2426 | 0.517433 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.58579 | − | 4.47871i | −0.100881 | − | 0.174731i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.65685 | 0.0645419 | 0.0322709 | − | 0.999479i | \(-0.489726\pi\) | ||||
0.0322709 | + | 0.999479i | \(0.489726\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.42893 | + | 4.20703i | −0.0944745 | + | 0.163635i | −0.909389 | − | 0.415946i | \(-0.863450\pi\) |
0.814915 | + | 0.579581i | \(0.196784\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.62132 | + | 8.00436i | 0.179477 | + | 0.310864i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.914214 | + | 1.58346i | 0.0354517 | + | 0.0614041i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.3137 | −1.05759 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.91421 | − | 8.51167i | 0.189994 | − | 0.329080i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.58579 | + | 7.94282i | −0.177032 | + | 0.306629i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.67157 | + | 8.09140i | −0.180076 | + | 0.311901i | −0.941906 | − | 0.335876i | \(-0.890968\pi\) |
0.761830 | + | 0.647777i | \(0.224301\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.82843 | + | 8.36308i | 0.185846 | + | 0.321895i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.2990 | − | 33.4268i | 0.741720 | − | 1.28470i | −0.209991 | − | 0.977703i | \(-0.567343\pi\) |
0.951711 | − | 0.306994i | \(-0.0993232\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.07107 | − | 1.85514i | −0.0411038 | − | 0.0711939i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.62742 | −0.292283 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.37258 | 0.0525204 | 0.0262602 | − | 0.999655i | \(-0.491640\pi\) | ||||
0.0262602 | + | 0.999655i | \(0.491640\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.74264 | − | 8.21449i | −0.181207 | − | 0.313860i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.13604 | + | 1.96768i | −0.0433426 | + | 0.0750716i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.1569 | + | 19.3242i | 0.425042 | + | 0.736195i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.0355339 | + | 0.0615465i | −0.00135177 | + | 0.00234134i | −0.866700 | − | 0.498829i | \(-0.833764\pi\) |
0.865349 | + | 0.501170i | \(0.167097\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.89949 | + | 3.29002i | −0.0721558 | + | 0.124978i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.6274 | 1.65251 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.89949 | − | 3.29002i | −0.0718455 | − | 0.124440i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.74264 | + | 11.6786i | 0.254666 | + | 0.441094i | 0.964805 | − | 0.262967i | \(-0.0847011\pi\) |
−0.710139 | + | 0.704062i | \(0.751368\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.20711 | − | 3.82282i | 0.0832426 | − | 0.144180i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.75736 | + | 3.04384i | 0.0660923 | + | 0.114475i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.3137 | 0.650230 | 0.325115 | − | 0.945674i | \(-0.394597\pi\) | ||||
0.325115 | + | 0.945674i | \(0.394597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.1127 | −0.716782 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.0000 | + | 9.79796i | 0.749006 | + | 0.366936i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.4142 | 0.464265 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.79899 | −0.328604 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.03553 | − | 6.98975i | −0.150500 | − | 0.260674i | 0.780911 | − | 0.624642i | \(-0.214755\pi\) |
−0.931411 | + | 0.363968i | \(0.881422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.857864 | −0.0319485 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.76346 | − | 4.78645i | 0.102774 | − | 0.178010i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.6569 | − | 23.6544i | −0.507203 | − | 0.878501i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.4203 | + | 35.3690i | 0.757347 | + | 1.31176i | 0.944199 | + | 0.329376i | \(0.106838\pi\) |
−0.186851 | + | 0.982388i | \(0.559828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.7635 | − | 55.0159i | 1.17481 | − | 2.03484i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.81371 | + | 13.5337i | −0.288606 | + | 0.499880i | −0.973477 | − | 0.228784i | \(-0.926525\pi\) |
0.684871 | + | 0.728664i | \(0.259858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.41421 | + | 2.44949i | −0.0521641 | + | 0.0903508i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.25736 | − | 9.10601i | −0.193657 | − | 0.335424i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.9350 | − | 39.7246i | 0.843679 | − | 1.46129i | −0.0430851 | − | 0.999071i | \(-0.513719\pi\) |
0.886764 | − | 0.462223i | \(-0.152948\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.50000 | + | 6.06218i | 0.128576 | + | 0.222700i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.65685 | −0.207530 | −0.103765 | − | 0.994602i | \(-0.533089\pi\) | ||||
−0.103765 | + | 0.994602i | \(0.533089\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.00000 | 0.0366372 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.2426 | + | 24.6690i | 0.521111 | + | 0.902591i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.57107 | − | 4.45322i | 0.0939448 | − | 0.162717i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.62132 | + | 6.27231i | 0.132144 | + | 0.228880i | 0.924503 | − | 0.381175i | \(-0.124481\pi\) |
−0.792359 | + | 0.610055i | \(0.791147\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.32843 | + | 2.30090i | −0.0484106 | + | 0.0838496i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.65685 | − | 4.60181i | 0.0966928 | − | 0.167477i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.6716 | + | 20.2158i | −0.424211 | + | 0.734754i | −0.996346 | − | 0.0854047i | \(-0.972782\pi\) |
0.572136 | + | 0.820159i | \(0.306115\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.37258 | 0.195012 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.2279 | − | 26.3755i | −0.552012 | − | 0.956112i | −0.998129 | − | 0.0611380i | \(-0.980527\pi\) |
0.446118 | − | 0.894974i | \(-0.352806\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.24264 | + | 3.88437i | 0.0811890 | + | 0.140624i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.24264 | + | 14.2767i | −0.298013 | + | 0.516174i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5858 | 0.562770 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.0563 | − | 31.2745i | −0.651129 | − | 1.12779i | −0.982849 | − | 0.184410i | \(-0.940963\pi\) |
0.331721 | − | 0.943378i | \(-0.392371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.24264 | −0.332866 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.0000 | 0.647415 | 0.323708 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.51472 | + | 22.2195i | 0.0544103 | + | 0.798148i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.171573 | −0.00615514 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.0416 | 1.18384 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.115224 | − | 0.199573i | −0.00412303 | − | 0.00714129i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.4853 | −0.589136 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.58579 | + | 7.94282i | −0.163674 | + | 0.283491i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.2071 | + | 36.7318i | 0.755952 | + | 1.30935i | 0.944900 | + | 0.327360i | \(0.106159\pi\) |
−0.188948 | + | 0.981987i | \(0.560508\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.82843 | + | 8.36308i | 0.171897 | + | 0.297734i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.89949 | 0.245318 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.41421 | + | 9.37769i | −0.192264 | + | 0.333012i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.20711 | − | 2.09077i | 0.0428117 | − | 0.0741520i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.2279 | + | 24.6435i | −0.503979 | + | 0.872917i | 0.496011 | + | 0.868316i | \(0.334798\pi\) |
−0.999989 | + | 0.00460050i | \(0.998536\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.1421 | − | 48.7436i | −0.995597 | − | 1.72442i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.34315 | − | 10.9867i | 0.224124 | − | 0.388194i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.96447 | − | 5.13461i | −0.104614 | − | 0.181196i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.65685 | 0.0583964 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.8406 | 0.381608 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.01472 | + | 10.4178i | 0.211466 | + | 0.366270i | 0.952174 | − | 0.305558i | \(-0.0988428\pi\) |
−0.740707 | + | 0.671828i | \(0.765509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.86396 | + | 11.8887i | −0.241026 | + | 0.417470i | −0.961007 | − | 0.276524i | \(-0.910817\pi\) |
0.719981 | + | 0.693994i | \(0.244151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.142136 | + | 0.246186i | 0.00498491 | + | 0.00863412i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.4853 | − | 18.1610i | 0.367283 | − | 0.636153i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.0563 | − | 41.6668i | 0.841625 | − | 1.45774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.24264 | + | 3.88437i | −0.0783642 | + | 0.135731i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.48528 | 0.296138 | 0.148069 | − | 0.988977i | \(-0.452694\pi\) | ||||
0.148069 | + | 0.988977i | \(0.452694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.1066 | + | 31.3616i | 0.631156 | + | 1.09320i | 0.987316 | + | 0.158770i | \(0.0507528\pi\) |
−0.356159 | + | 0.934425i | \(0.615914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.68629 | + | 4.65279i | 0.0935247 | + | 0.161989i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.4497 | − | 31.9559i | 0.641561 | − | 1.11122i | −0.343524 | − | 0.939144i | \(-0.611621\pi\) |
0.985084 | − | 0.172072i | \(-0.0550460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.4264 | 1.33460 | 0.667302 | − | 0.744787i | \(-0.267449\pi\) | ||||
0.667302 | + | 0.744787i | \(0.267449\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.92893 | + | 5.07306i | 0.101604 | + | 0.175982i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39.7990 | 1.37895 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.5563 | −0.780595 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.0711 | + | 5.91359i | 0.417237 | + | 0.204404i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.6274 | 0.504995 | 0.252497 | − | 0.967598i | \(-0.418748\pi\) | ||||
0.252497 | + | 0.967598i | \(0.418748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.414214 | + | 0.717439i | 0.0142663 | + | 0.0247099i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.65685 | 0.0569975 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.100505 | − | 0.174080i | 0.00345339 | − | 0.00598146i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.82843 | + | 4.89898i | 0.0970714 | + | 0.168133i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00000 | − | 3.46410i | −0.0685591 | − | 0.118748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.5147 | −0.531214 | −0.265607 | − | 0.964081i | \(-0.585572\pi\) | ||||
−0.265607 | + | 0.964081i | \(0.585572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.24264 | + | 10.8126i | −0.213494 | + | 0.369782i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.74264 | − | 16.8747i | 0.332802 | − | 0.576430i | −0.650258 | − | 0.759714i | \(-0.725339\pi\) |
0.983060 | + | 0.183283i | \(0.0586725\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.6924 | + | 42.7685i | −0.842493 | + | 1.45924i | 0.0452869 | + | 0.998974i | \(0.485580\pi\) |
−0.887780 | + | 0.460267i | \(0.847754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.642136 | − | 1.11221i | −0.0218839 | − | 0.0379041i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.30761 | + | 2.26485i | −0.0445116 | + | 0.0770964i | −0.887423 | − | 0.460956i | \(-0.847507\pi\) |
0.842911 | + | 0.538053i | \(0.180840\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.15685 | − | 7.19988i | −0.141337 | − | 0.244803i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.02944 | −0.238732 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.9117 | −0.743303 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.20711 | − | 10.7510i | −0.210320 | − | 0.364285i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.31371 | − | 12.6677i | 0.247532 | − | 0.428737i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.86396 | + | 3.22848i | 0.0630134 | + | 0.109142i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.9142 | + | 46.6168i | −0.908828 | + | 1.57414i | −0.0931343 | + | 0.995654i | \(0.529689\pi\) |
−0.815694 | + | 0.578483i | \(0.803645\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.06497 | − | 5.30869i | 0.103379 | − | 0.179058i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.84315 | + | 10.1206i | −0.196861 | + | 0.340973i | −0.947509 | − | 0.319729i | \(-0.896408\pi\) |
0.750648 | + | 0.660702i | \(0.229741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.2843 | 1.01915 | 0.509573 | − | 0.860427i | \(-0.329803\pi\) | ||||
0.509573 | + | 0.860427i | \(0.329803\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.843146 | − | 1.46037i | −0.0283420 | − | 0.0490898i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.6630 | − | 44.4495i | −0.861678 | − | 1.49247i | −0.870309 | − | 0.492507i | \(-0.836081\pi\) |
0.00863117 | − | 0.999963i | \(-0.497253\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.84315 | − | 3.19242i | 0.0618171 | − | 0.107070i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.2721 | −0.813145 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.3137 | − | 36.9164i | −0.713236 | − | 1.23536i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.2426 | 0.509505 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.34315 | 0.211791 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.1421 | − | 16.7262i | −1.13870 | − | 0.557849i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.9706 | −1.13172 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.87006 | −0.0622316 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.15685 | − | 10.6640i | −0.204661 | − | 0.354483i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.6863 | −1.08533 | −0.542665 | − | 0.839949i | \(-0.682585\pi\) | ||||
−0.542665 | + | 0.839949i | \(0.682585\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.0000 | + | 20.7846i | −0.398015 | + | 0.689382i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.479185 | + | 0.829972i | 0.0158761 | + | 0.0274982i | 0.873854 | − | 0.486188i | \(-0.161613\pi\) |
−0.857978 | + | 0.513686i | \(0.828280\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.3284 | + | 28.2817i | 0.540392 | + | 0.935987i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.17157 | 0.0387310 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.74264 | + | 4.75039i | −0.0905700 | + | 0.156872i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.4497 | + | 30.2238i | −0.575614 | + | 0.996993i | 0.420361 | + | 0.907357i | \(0.361904\pi\) |
−0.995975 | + | 0.0896356i | \(0.971430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.32843 | − | 4.03295i | 0.0767243 | − | 0.132890i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.136039 | − | 0.235626i | −0.00447778 | − | 0.00775574i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | − | 3.46410i | 0.0657596 | − | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.92893 | − | 5.07306i | −0.0961988 | − | 0.166621i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.51472 | 0.246550 | 0.123275 | − | 0.992373i | \(-0.460660\pi\) | ||||
0.123275 | + | 0.992373i | \(0.460660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.1421 | 0.987869 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.34315 | − | 4.05845i | −0.0767111 | − | 0.132868i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.44975 | + | 16.3674i | −0.309040 | + | 0.535273i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.84315 | − | 13.5847i | −0.256224 | − | 0.443794i | 0.709003 | − | 0.705206i | \(-0.249145\pi\) |
−0.965227 | + | 0.261412i | \(0.915812\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.378680 | + | 0.655892i | −0.0123577 | + | 0.0214042i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.5000 | − | 30.3109i | 0.570484 | − | 0.988107i | −0.426033 | − | 0.904708i | \(-0.640089\pi\) |
0.996516 | − | 0.0833989i | \(-0.0265776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.9706 | − | 25.9298i | 0.487509 | − | 0.844390i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.55025 | + | 16.5415i | 0.310342 | + | 0.537527i | 0.978436 | − | 0.206549i | \(-0.0662233\pi\) |
−0.668095 | + | 0.744076i | \(0.732890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.50000 | − | 6.06218i | −0.113615 | − | 0.196787i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.62132 | + | 2.80821i | −0.0525749 | + | 0.0910624i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.51472 | 0.113853 | 0.0569265 | − | 0.998378i | \(-0.481870\pi\) | ||||
0.0569265 | + | 0.998378i | \(0.481870\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.4497 | − | 18.0995i | −0.338146 | − | 0.585686i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.17157 | −0.296475 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.92893 | 0.126872 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | + | 24.4949i | 0.612903 | + | 0.790158i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.1127 | 1.13149 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.14214 | 0.229913 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.72183 | − | 13.3746i | −0.248317 | − | 0.430098i | 0.714742 | − | 0.699388i | \(-0.246544\pi\) |
−0.963059 | + | 0.269290i | \(0.913211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.6569 | −0.342347 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.349242 | + | 0.604906i | −0.0112077 | + | 0.0194123i | −0.871575 | − | 0.490262i | \(-0.836901\pi\) |
0.860367 | + | 0.509675i | \(0.170234\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.17157 | + | 5.49333i | 0.101572 | + | 0.175927i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.485281 | −0.0155255 | −0.00776276 | − | 0.999970i | \(-0.502471\pi\) | ||||
−0.00776276 | + | 0.999970i | \(0.502471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.27208 | − | 12.5956i | 0.232417 | − | 0.402557i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.3137 | + | 26.5241i | −0.488929 | + | 0.846850i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.4203 | + | 33.6370i | −0.619412 | + | 1.07285i | 0.370182 | + | 0.928959i | \(0.379295\pi\) |
−0.989593 | + | 0.143893i | \(0.954038\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.74264 | + | 11.6786i | 0.214838 | + | 0.372111i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.828427 | + | 1.43488i | −0.0263691 | + | 0.0456727i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.7990 | − | 37.7570i | −0.693168 | − | 1.20060i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.9411 | −1.52290 | −0.761450 | − | 0.648224i | \(-0.775512\pi\) | ||||
−0.761450 | + | 0.648224i | \(0.775512\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.82843 | 0.121491 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.20711 | + | 15.9472i | 0.291885 | + | 0.505559i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.2990 | + | 28.2307i | −0.516194 | + | 0.894075i | 0.483629 | + | 0.875273i | \(0.339318\pi\) |
−0.999823 | + | 0.0188015i | \(0.994015\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.20711 | − | 2.09077i | −0.0381912 | − | 0.0661490i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))