Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(895,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.895");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.e (of order \(2\), degree \(1\), 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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.8 | ||
Root | \(0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.895 |
Dual form | 1792.2.e.f.895.2 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.61313i | 1.50869i | 0.656479 | + | 0.754344i | \(0.272045\pi\) | ||||
−0.656479 | + | 0.754344i | \(0.727955\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.08239 | 0.484061 | 0.242030 | − | 0.970269i | \(-0.422187\pi\) | ||||
0.242030 | + | 0.970269i | \(0.422187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.08239 | − | 2.41421i | −0.409106 | − | 0.912487i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.82843 | −1.27614 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.14386 | 1.14930 | 0.574650 | − | 0.818399i | \(-0.305138\pi\) | ||||
0.574650 | + | 0.818399i | \(0.305138\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843i | 0.730297i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.39104i | 1.79259i | 0.443459 | + | 0.896295i | \(0.353751\pi\) | ||||
−0.443459 | + | 0.896295i | \(0.646249\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.77791i | − | 1.09613i | −0.836436 | − | 0.548064i | \(-0.815365\pi\) | ||
0.836436 | − | 0.548064i | \(-0.184635\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.30864 | − | 2.82843i | 1.37666 | − | 0.617213i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.65685i | 0.762507i | 0.924471 | + | 0.381253i | \(0.124507\pi\) | ||||
−0.924471 | + | 0.381253i | \(0.875493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.82843 | −0.765685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.16478i | − | 0.416613i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.65685i | 1.42184i | 0.703272 | + | 0.710921i | \(0.251722\pi\) | ||||
−0.703272 | + | 0.710921i | \(0.748278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.39104 | −1.32747 | −0.663735 | − | 0.747968i | \(-0.731030\pi\) | ||||
−0.663735 | + | 0.747968i | \(0.731030\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5.22625i | − | 0.909774i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.17157 | − | 2.61313i | −0.198032 | − | 0.441699i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.65685i | 0.601183i | 0.953753 | + | 0.300592i | \(0.0971841\pi\) | ||||
−0.953753 | + | 0.300592i | \(0.902816\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.8284i | 1.73394i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.28772i | 1.29432i | 0.762352 | + | 0.647162i | \(0.224044\pi\) | ||||
−0.762352 | + | 0.647162i | \(0.775956\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.65685 | −1.16766 | −0.583830 | − | 0.811876i | \(-0.698446\pi\) | ||||
−0.583830 | + | 0.811876i | \(0.698446\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.14386 | −0.617730 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.06147 | 0.446561 | 0.223280 | − | 0.974754i | \(-0.428323\pi\) | ||||
0.223280 | + | 0.974754i | \(0.428323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.65685 | + | 5.22625i | −0.665265 | + | 0.746607i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.3137 | −2.70446 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.16478 | −0.291899 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.4853 | 1.65372 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.67459i | 0.738769i | 0.929277 | + | 0.369385i | \(0.120431\pi\) | ||||
−0.929277 | + | 0.369385i | \(0.879569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.08239 | 0.138586 | 0.0692931 | − | 0.997596i | \(-0.477926\pi\) | ||||
0.0692931 | + | 0.997596i | \(0.477926\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.14386 | + | 9.24264i | 0.522077 | + | 1.16446i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.48528 | 0.556331 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.34315 | 0.530600 | 0.265300 | − | 0.964166i | \(-0.414529\pi\) | ||||
0.265300 | + | 0.964166i | \(0.414529\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.55582 | −1.15039 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.17157i | 0.376396i | 0.982131 | + | 0.188198i | \(0.0602647\pi\) | ||||
−0.982131 | + | 0.188198i | \(0.939735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.896683i | − | 0.104949i | −0.998622 | − | 0.0524744i | \(-0.983289\pi\) | ||
0.998622 | − | 0.0524744i | \(-0.0167108\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 10.0042i | − | 1.15518i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.16478 | + | 4.82843i | 0.246700 | + | 0.550250i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.17157i | 0.806865i | 0.915009 | + | 0.403432i | \(0.132183\pi\) | ||||
−0.915009 | + | 0.403432i | \(0.867817\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.82843 | −0.647603 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.71644i | − | 0.188404i | −0.995553 | − | 0.0942020i | \(-0.969970\pi\) | ||
0.995553 | − | 0.0942020i | \(-0.0300300\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000i | 0.867722i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.0083 | −2.14512 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.22625i | − | 0.553982i | −0.960873 | − | 0.276991i | \(-0.910663\pi\) | ||
0.960873 | − | 0.276991i | \(-0.0893372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.48528 | − | 10.0042i | −0.470185 | − | 1.04872i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 19.3137i | − | 2.00274i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.17157i | − | 0.530592i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.7206i | − | 1.19005i | −0.803708 | − | 0.595024i | \(-0.797143\pi\) | ||
0.803708 | − | 0.595024i | \(-0.202857\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.65685 | 0.769543 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.47343 | 0.843138 | 0.421569 | − | 0.906796i | \(-0.361480\pi\) | ||||
0.421569 | + | 0.906796i | \(0.361480\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3492 | 1.11827 | 0.559134 | − | 0.829077i | \(-0.311134\pi\) | ||||
0.559134 | + | 0.829077i | \(0.311134\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.82843 | − | 3.06147i | 0.666386 | − | 0.298769i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.6569 | 1.12691 | 0.563455 | − | 0.826147i | \(-0.309472\pi\) | ||||
0.563455 | + | 0.826147i | \(0.309472\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.3137i | − | 1.65835i | −0.558987 | − | 0.829176i | \(-0.688810\pi\) | ||
0.558987 | − | 0.829176i | \(-0.311190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.55582 | −0.906998 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.17157 | 0.298356 | 0.149178 | − | 0.988810i | \(-0.452337\pi\) | ||||
0.149178 | + | 0.988810i | \(0.452337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.95815i | 0.369099i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.8645 | −1.46667 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.8435 | − | 8.00000i | 1.63571 | − | 0.733359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.6569 | −1.95273 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.55582 | −0.854699 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.65685i | 0.679436i | 0.940527 | + | 0.339718i | \(0.110332\pi\) | ||||
−0.940527 | + | 0.339718i | \(0.889668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 20.0083i | − | 1.76163i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 3.50981i | − | 0.306653i | −0.988176 | − | 0.153327i | \(-0.951001\pi\) | ||
0.988176 | − | 0.153327i | \(-0.0489987\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.5349 | + | 5.17157i | −1.00020 | + | 0.448432i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.34315i | − | 0.201666i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0042i | 0.848542i | 0.905535 | + | 0.424271i | \(0.139470\pi\) | ||||
−0.905535 | + | 0.424271i | \(0.860530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000i | 0.673722i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.28772 | −0.693054 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.28772i | 0.688258i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.6569 | − | 12.1689i | −1.12640 | − | 1.00368i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.0000i | − | 0.819232i | −0.912258 | − | 0.409616i | \(-0.865663\pi\) | ||
0.912258 | − | 0.409616i | \(-0.134337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.6569i | 1.59965i | 0.600232 | + | 0.799826i | \(0.295075\pi\) | ||||
−0.600232 | + | 0.799826i | \(0.704925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 28.2960i | − | 2.28760i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.47343 | 0.676253 | 0.338127 | − | 0.941101i | \(-0.390207\pi\) | ||||
0.338127 | + | 0.941101i | \(0.390207\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.22625 | 0.414469 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.82843 | − | 3.95815i | 0.695778 | − | 0.311946i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.31371 | 0.416202 | 0.208101 | − | 0.978107i | \(-0.433272\pi\) | ||||
0.208101 | + | 0.978107i | \(0.433272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 5.65685i | − | 0.440386i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.6788 | −1.21326 | −0.606629 | − | 0.794985i | \(-0.707479\pi\) | ||||
−0.606629 | + | 0.794985i | \(0.707479\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.17157 | 0.320890 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.2919i | 1.39882i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.6382 | −0.808808 | −0.404404 | − | 0.914580i | \(-0.632521\pi\) | ||||
−0.404404 | + | 0.914580i | \(0.632521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.14386 | + | 9.24264i | 0.313246 | + | 0.698678i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.8284 | −1.11457 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000 | 0.149487 | 0.0747435 | − | 0.997203i | \(-0.476186\pi\) | ||||
0.0747435 | + | 0.997203i | \(0.476186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5349 | 0.857382 | 0.428691 | − | 0.903451i | \(-0.358975\pi\) | ||||
0.428691 | + | 0.903451i | \(0.358975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.82843i | 0.209083i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.95815i | 0.291009i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 14.7821i | − | 1.08097i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.22625 | + | 2.34315i | −0.380154 | + | 0.170439i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.828427i | − | 0.0599429i | −0.999551 | − | 0.0299714i | \(-0.990458\pi\) | ||
0.999551 | − | 0.0299714i | \(-0.00954164\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.48528 | 0.466821 | 0.233410 | − | 0.972378i | \(-0.425011\pi\) | ||||
0.233410 | + | 0.972378i | \(0.425011\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.7206i | 0.839330i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.65685i | − | 0.545528i | −0.962081 | − | 0.272764i | \(-0.912062\pi\) | ||
0.962081 | − | 0.272764i | \(-0.0879379\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.896683 | −0.0635642 | −0.0317821 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317821 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.3492i | 0.800510i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.4853 | − | 8.28772i | 1.29741 | − | 0.581684i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.97056i | 0.626531i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 14.0000i | − | 0.973067i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.55582i | 0.660990i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.9706 | −1.58136 | −0.790679 | − | 0.612230i | \(-0.790272\pi\) | ||||
−0.790679 | + | 0.612230i | \(0.790272\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.28772 | −0.567865 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.28772 | −0.565218 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | + | 17.8435i | 0.543075 | + | 1.21130i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.34315 | 0.158335 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.6274i | 2.06022i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.6569 | 0.977124 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 29.1158i | 1.93248i | 0.257637 | + | 0.966242i | \(0.417056\pi\) | ||||
−0.257637 | + | 0.966242i | \(0.582944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.3784 | 1.94138 | 0.970691 | − | 0.240332i | \(-0.0772562\pi\) | ||||
0.970691 | + | 0.240332i | \(0.0772562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.6173 | + | 5.65685i | −0.830157 | + | 0.372194i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.31371 | 0.216163 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.7402 | −1.21731 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.6569i | − | 1.27150i | −0.771897 | − | 0.635748i | \(-0.780692\pi\) | ||
0.771897 | − | 0.635748i | \(-0.219308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0502i | 1.03388i | 0.856021 | + | 0.516941i | \(0.172929\pi\) | ||||
−0.856021 | + | 0.516941i | \(0.827071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 21.7248i | − | 1.39364i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.04054 | + | 5.65685i | −0.322028 | + | 0.361403i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 19.7990i | − | 1.25978i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.48528 | 0.284243 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.61313i | 0.164939i | 0.996594 | + | 0.0824695i | \(0.0262807\pi\) | ||||
−0.996594 | + | 0.0824695i | \(0.973719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.31371i | − | 0.459809i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.9050 | −1.30912 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.7821i | 0.922080i | 0.887379 | + | 0.461040i | \(0.152524\pi\) | ||||
−0.887379 | + | 0.461040i | \(0.847476\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.82843 | − | 3.95815i | 0.548572 | − | 0.245948i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 29.3137i | − | 1.81447i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 24.1421i | − | 1.48867i | −0.667808 | − | 0.744334i | \(-0.732767\pi\) | ||
0.667808 | − | 0.744334i | \(-0.267233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.16478i | − | 0.132982i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.6569 | 0.835786 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.0489 | 1.52726 | 0.763628 | − | 0.645656i | \(-0.223416\pi\) | ||||
0.763628 | + | 0.645656i | \(0.223416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.2346 | 1.53289 | 0.766446 | − | 0.642309i | \(-0.222023\pi\) | ||||
0.766446 | + | 0.642309i | \(0.222023\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.1421 | − | 11.7206i | 1.58219 | − | 0.709363i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.65685 | 0.461726 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.97056i | 0.418821i | 0.977828 | + | 0.209410i | \(0.0671544\pi\) | ||||
−0.977828 | + | 0.209410i | \(0.932846\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.2960 | 1.69404 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.6274 | −0.991909 | −0.495954 | − | 0.868349i | \(-0.665182\pi\) | ||||
−0.495954 | + | 0.868349i | \(0.665182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.61313i | 0.155334i | 0.996979 | + | 0.0776671i | \(0.0247471\pi\) | ||||
−0.996979 | + | 0.0776671i | \(0.975253\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.5140 | 0.800499 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0083 | − | 8.97056i | 1.18105 | − | 0.529516i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −37.6274 | −2.21338 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.6274 | 1.79541 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.47343 | 0.495023 | 0.247511 | − | 0.968885i | \(-0.420387\pi\) | ||||
0.247511 | + | 0.968885i | \(0.420387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.14214i | 0.357609i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.32957i | 0.251227i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.1535i | 0.876349i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.28772 | + | 18.4853i | 0.477696 | + | 1.06547i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.1421i | 1.27203i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.17157 | 0.0670841 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.71644i | − | 0.0979626i | −0.998800 | − | 0.0489813i | \(-0.984403\pi\) | ||
0.998800 | − | 0.0489813i | \(-0.0155975\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 29.6569i | 1.68712i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.95815 | −0.224446 | −0.112223 | − | 0.993683i | \(-0.535797\pi\) | ||||
−0.112223 | + | 0.993683i | \(0.535797\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.49435i | 0.367083i | 0.983012 | + | 0.183541i | \(0.0587561\pi\) | ||||
−0.983012 | + | 0.183541i | \(0.941244\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.48528 | + | 10.0042i | 0.252717 | + | 0.563671i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 16.3431i | − | 0.917923i | −0.888456 | − | 0.458961i | \(-0.848222\pi\) | ||
0.888456 | − | 0.458961i | \(-0.151778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 15.3137i | − | 0.857403i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.4608i | 1.70016i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.3137 | 1.96491 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.8645 | −0.880002 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 45.2429 | 2.50194 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.31371 | − | 7.39104i | −0.182691 | − | 0.407481i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.31371 | −0.292068 | −0.146034 | − | 0.989280i | \(-0.546651\pi\) | ||||
−0.146034 | + | 0.989280i | \(0.546651\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 14.0000i | − | 0.767195i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.70099 | 0.256842 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.17157 | 0.172767 | 0.0863833 | − | 0.996262i | \(-0.472469\pi\) | ||||
0.0863833 | + | 0.996262i | \(0.472469\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.28772i | 0.450127i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.7821 | 0.800494 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6578 | + | 5.58579i | 0.953433 | + | 0.301604i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.3431 | −0.556856 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.34315 | 0.447884 | 0.223942 | − | 0.974603i | \(-0.428107\pi\) | ||||
0.223942 | + | 0.974603i | \(0.428107\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8645 | 0.849205 | 0.424603 | − | 0.905380i | \(-0.360414\pi\) | ||||
0.424603 | + | 0.905380i | \(0.360414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 8.97056i | − | 0.478813i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.2459i | 0.651782i | 0.945407 | + | 0.325891i | \(0.105664\pi\) | ||||
−0.945407 | + | 0.325891i | \(0.894336\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.43289i | 0.182199i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.9050 | + | 46.6274i | 1.10641 | + | 2.46778i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.9706i | − | 1.00123i | −0.865671 | − | 0.500614i | \(-0.833108\pi\) | ||
0.865671 | − | 0.500614i | \(-0.166892\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.82843 | −0.201496 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 18.2919i | − | 0.960075i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.970563i | − | 0.0508016i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.32957 | −0.226002 | −0.113001 | − | 0.993595i | \(-0.536046\pi\) | ||||
−0.113001 | + | 0.993595i | \(0.536046\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 31.7289i | − | 1.65174i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.82843 | + | 2.16478i | −0.250679 | + | 0.112390i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.9706i | − | 1.39648i | −0.715862 | − | 0.698241i | \(-0.753966\pi\) | ||
0.715862 | − | 0.698241i | \(-0.246034\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 24.9706i | − | 1.28947i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.7289i | 1.63412i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3137 | 0.889345 | 0.444673 | − | 0.895693i | \(-0.353320\pi\) | ||||
0.444673 | + | 0.895693i | \(0.353320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.0083 | −1.02506 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.5140 | −0.690532 | −0.345266 | − | 0.938505i | \(-0.612211\pi\) | ||||
−0.345266 | + | 0.938505i | \(0.612211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.34315 | + | 5.22625i | 0.119418 | + | 0.266354i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.3137 | 1.49010 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.34315i | 0.423014i | 0.977376 | + | 0.211507i | \(0.0678372\pi\) | ||||
−0.977376 | + | 0.211507i | \(0.932163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.0279 | −1.36686 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.17157 | 0.462645 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.76245i | 0.390571i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0711 | 0.706208 | 0.353104 | − | 0.935584i | \(-0.385126\pi\) | ||||
0.353104 | + | 0.935584i | \(0.385126\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.5140 | − | 30.1421i | −0.676545 | − | 1.50899i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.8284 | −1.04012 | −0.520061 | − | 0.854129i | \(-0.674091\pi\) | ||||
−0.520061 | + | 0.854129i | \(0.674091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.6274 | −1.52566 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.30864 | −0.313479 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.31371i | − | 0.362527i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.6173i | 0.623885i | 0.950101 | + | 0.311942i | \(0.100980\pi\) | ||||
−0.950101 | + | 0.311942i | \(0.899020\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.22625i | − | 0.257792i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.6997 | − | 6.14214i | 0.674117 | − | 0.302235i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.85786i | − | 0.0911990i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.1421 | −1.28019 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.14933i | 0.251561i | 0.992058 | + | 0.125781i | \(0.0401435\pi\) | ||||
−0.992058 | + | 0.125781i | \(0.959856\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.31371i | 0.0640262i | 0.999487 | + | 0.0320131i | \(0.0101918\pi\) | ||||
−0.999487 | + | 0.0320131i | \(0.989808\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.7206 | −0.569875 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 28.2960i | − | 1.37256i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.17157 | − | 2.61313i | −0.0566964 | − | 0.126458i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 21.6569i | − | 1.04560i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.6569i | 1.13951i | 0.821814 | + | 0.569755i | \(0.192962\pi\) | ||||
−0.821814 | + | 0.569755i | \(0.807038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 28.2960i | − | 1.35982i | −0.733295 | − | 0.679911i | \(-0.762019\pi\) | ||
0.733295 | − | 0.679911i | \(-0.237981\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.6569 | −1.03837 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.4721 | 0.835805 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.6452 | −1.89216 | −0.946082 | − | 0.323928i | \(-0.894997\pi\) | ||||
−0.946082 | + | 0.323928i | \(0.894997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.8284 | − | 20.0083i | 0.848973 | − | 0.952777i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0000 | −0.475114 | −0.237557 | − | 0.971374i | \(-0.576347\pi\) | ||||
−0.237557 | + | 0.971374i | \(0.576347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.65685i | − | 0.268161i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.1313 | 1.23597 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.31371 | −0.0619977 | −0.0309989 | − | 0.999519i | \(-0.509869\pi\) | ||||
−0.0309989 | + | 0.999519i | \(0.509869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.5754i | − | 0.780507i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −51.3658 | −2.41338 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.85483 | − | 10.8284i | −0.227598 | − | 0.507644i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.1127 | 1.17472 | 0.587361 | − | 0.809325i | \(-0.300167\pi\) | ||||
0.587361 | + | 0.809325i | \(0.300167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.0000 | 0.746816 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.4399 | 1.51088 | 0.755438 | − | 0.655220i | \(-0.227424\pi\) | ||||
0.755438 | + | 0.655220i | \(0.227424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.1421i | − | 0.564293i | −0.959371 | − | 0.282146i | \(-0.908954\pi\) | ||
0.959371 | − | 0.282146i | \(-0.0910464\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 20.9050i | − | 0.969447i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.7862i | 1.14697i | 0.819216 | + | 0.573485i | \(0.194409\pi\) | ||||
−0.819216 | + | 0.573485i | \(0.805591\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.70099 | − | 10.4853i | −0.217071 | − | 0.484165i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.1421i | 1.02026i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.3137 | 0.704125 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.2919i | 0.839289i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.65685i | 0.350583i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.8322 | 1.40876 | 0.704381 | − | 0.709822i | \(-0.251225\pi\) | ||||
0.704381 | + | 0.709822i | \(0.251225\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.1535i | 0.690940i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.3431 | + | 23.0698i | 0.470629 | + | 1.04971i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 12.6863i | − | 0.576055i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.2843i | 1.19105i | 0.803335 | + | 0.595527i | \(0.203057\pi\) | ||||
−0.803335 | + | 0.595527i | \(0.796943\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.8854i | 0.627919i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.2843 | 1.18619 | 0.593096 | − | 0.805132i | \(-0.297905\pi\) | ||||
0.593096 | + | 0.805132i | \(0.297905\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −56.5921 | −2.54878 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.28772 | 0.372505 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.65685 | − | 3.43289i | 0.343457 | − | 0.153986i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.31371 | 0.237874 | 0.118937 | − | 0.992902i | \(-0.462051\pi\) | ||||
0.118937 | + | 0.992902i | \(0.462051\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 40.9706i | − | 1.83043i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.7289 | 1.41472 | 0.707362 | − | 0.706852i | \(-0.249885\pi\) | ||||
0.707362 | + | 0.706852i | \(0.249885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.17157 | 0.408130 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.9008i | 0.484124i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.9456 | −1.15002 | −0.575008 | − | 0.818148i | \(-0.695001\pi\) | ||||
−0.575008 | + | 0.818148i | \(0.695001\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.16478 | + | 0.970563i | −0.0957644 | + | 0.0429352i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.3431 | −0.456661 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.2843 | 0.541310 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.12293 | −0.269286 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 27.7990i | − | 1.22024i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.6173i | − | 0.552773i | −0.961047 | − | 0.276387i | \(-0.910863\pi\) | ||
0.961047 | − | 0.276387i | \(-0.0891371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.34502i | 0.0588138i | 0.999568 | + | 0.0294069i | \(0.00936186\pi\) | ||||
−0.999568 | + | 0.0294069i | \(0.990638\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.1522 | + | 10.8284i | −1.05409 | + | 0.472591i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 54.6274i | − | 2.37961i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.62742 | 0.418583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 21.7248i | − | 0.942775i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.3431i | 1.48757i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6173 | 0.545493 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.22625i | 0.225529i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.31371 | − | 10.4525i | 0.401170 | − | 0.450221i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 2.68629i | − | 0.115493i | −0.998331 | − | 0.0577463i | \(-0.981609\pi\) | ||
0.998331 | − | 0.0577463i | \(-0.0183915\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.1421i | 1.29352i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 18.7402i | − | 0.802743i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6863 | −0.456913 | −0.228456 | − | 0.973554i | \(-0.573368\pi\) | ||||
−0.228456 | + | 0.973554i | \(0.573368\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.14386 | −0.176856 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.5838 | 1.55852 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.3137 | − | 7.76245i | 0.736254 | − | 0.330093i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.3431 | −0.439042 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 17.3137i | − | 0.733605i | −0.930299 | − | 0.366803i | \(-0.880452\pi\) | ||
0.930299 | − | 0.366803i | \(-0.119548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.7289 | −1.34199 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.6274 | 1.63085 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 25.6829i | − | 1.08241i | −0.840892 | − | 0.541203i | \(-0.817969\pi\) | ||
0.840892 | − | 0.541203i | \(-0.182031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.43289 | 0.144423 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.30864 | + | 14.0711i | 0.264938 | + | 0.590929i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.1421 | −1.51516 | −0.757579 | − | 0.652744i | \(-0.773618\pi\) | ||||
−0.757579 | + | 0.652744i | \(0.773618\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.6569 | 0.822614 | 0.411307 | − | 0.911497i | \(-0.365072\pi\) | ||||
0.411307 | + | 0.911497i | \(0.365072\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.16478 | 0.0904352 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 14.0000i | − | 0.583840i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.53620i | − | 0.105583i | −0.998606 | − | 0.0527917i | \(-0.983188\pi\) | ||
0.998606 | − | 0.0527917i | \(-0.0168120\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.9469i | 0.704287i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.14386 | + | 1.85786i | −0.171916 | + | 0.0770772i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.1716 | −0.709957 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.4454i | 1.38044i | 0.723600 | + | 0.690219i | \(0.242486\pi\) | ||||
−0.723600 | + | 0.690219i | \(0.757514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.3137i | 1.45508i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.0083 | 0.823032 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.2346i | − | 1.03626i | −0.855302 | − | 0.518130i | \(-0.826628\pi\) | ||
0.855302 | − | 0.518130i | \(-0.173372\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.3137 | − | 8.65914i | 0.791785 | − | 0.354990i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 2.34315i | − | 0.0958986i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.8284i | − | 1.50477i | −0.658724 | − | 0.752384i | \(-0.728904\pi\) | ||
0.658724 | − | 0.752384i | \(-0.271096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.1426i | 0.536096i | 0.963406 | + | 0.268048i | \(0.0863786\pi\) | ||||
−0.963406 | + | 0.268048i | \(0.913621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.6274 | −0.677121 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.57675 | −0.308039 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.8100 | −1.69702 | −0.848508 | − | 0.529182i | \(-0.822499\pi\) | ||||
−0.848508 | + | 0.529182i | \(0.822499\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.6569 | + | 48.3044i | 0.877580 | + | 1.95739i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.6863 | 0.513232 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.3137i | 0.699294i | 0.936881 | + | 0.349647i | \(0.113698\pi\) | ||||
−0.936881 | + | 0.349647i | \(0.886302\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23.4412 | −0.945241 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 49.1127 | 1.97720 | 0.988601 | − | 0.150557i | \(-0.0481066\pi\) | ||||
0.988601 | + | 0.150557i | \(0.0481066\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 22.6215i | − | 0.909233i | −0.890687 | − | 0.454616i | \(-0.849776\pi\) | ||
0.890687 | − | 0.454616i | \(-0.150224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.91630 | 0.317670 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.6173 | + | 5.65685i | −0.505501 | + | 0.226637i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.79899 | 0.351960 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.9706 | −0.997228 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.0279 | −1.07767 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.51472i | − | 0.378775i | −0.981902 | − | 0.189387i | \(-0.939350\pi\) | ||
0.981902 | − | 0.189387i | \(-0.0606502\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 60.0250i | − | 2.38578i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.28772i | 0.328888i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.2974 | + | 21.6569i | −0.764589 | + | 0.858076i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 12.1421i | − | 0.480335i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.142136 | −0.00561402 | −0.00280701 | − | 0.999996i | \(-0.500894\pi\) | ||||
−0.00280701 | + | 0.999996i | \(0.500894\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.5796i | 1.04820i | 0.851658 | + | 0.524099i | \(0.175598\pi\) | ||||
−0.851658 | + | 0.524099i | \(0.824402\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 21.6569i | − | 0.852738i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.9133 | 1.60847 | 0.804235 | − | 0.594312i | \(-0.202576\pi\) | ||||
0.804235 | + | 0.594312i | \(0.202576\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.3492i | − | 0.445495i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −46.6274 | + | 20.9050i | −1.82747 | + | 0.819332i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 25.3137i | − | 0.990602i | −0.868721 | − | 0.495301i | \(-0.835058\pi\) | ||
0.868721 | − | 0.495301i | \(-0.164942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.79899i | − | 0.148439i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.43289i | 0.133930i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 50.9706 | 1.98553 | 0.992766 | − | 0.120068i | \(-0.0383114\pi\) | ||||
0.992766 | + | 0.120068i | \(0.0383114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.68006 | 0.259824 | 0.129912 | − | 0.991526i | \(-0.458530\pi\) | ||||
0.129912 | + | 0.991526i | \(0.458530\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −80.0333 | −3.10824 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.4853 | + | 5.59767i | −0.484158 | + | 0.217068i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.0000 | −1.08416 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.16478 | −0.0835706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.3137 | 1.12996 | 0.564980 | − | 0.825104i | \(-0.308884\pi\) | ||||
0.564980 | + | 0.825104i | \(0.308884\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.28772i | 0.318994i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.3588 | −0.859319 | −0.429660 | − | 0.902991i | \(-0.641366\pi\) | ||||
−0.429660 | + | 0.902991i | \(0.641366\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.2960 | + | 12.6863i | −1.08590 | + | 0.486855i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −76.0833 | −2.91552 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.3431 | 1.23758 | 0.618788 | − | 0.785558i | \(-0.287624\pi\) | ||||
0.618788 | + | 0.785558i | \(0.287624\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.16478 | −0.0827122 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 76.7696i | 2.92894i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 8.28772i | − | 0.315737i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 10.3756i | − | 0.394706i | −0.980333 | − | 0.197353i | \(-0.936766\pi\) | ||
0.980333 | − | 0.197353i | \(-0.0632345\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.28772 | − | 18.4853i | −0.314824 | − | 0.702198i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.8284i | 0.410746i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −61.2548 | −2.32019 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 47.0363i | − | 1.77907i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3137i | 0.502852i | 0.967877 | + | 0.251426i | \(0.0808995\pi\) | ||||
−0.967877 | + | 0.251426i | \(0.919101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.4721 | 0.658974 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.65914i | 0.326122i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.17157 | − | 20.4567i | −0.344932 | − | 0.769352i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 18.0000i | − | 0.676004i | −0.941145 | − | 0.338002i | \(-0.890249\pi\) | ||
0.941145 | − | 0.338002i | \(-0.109751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 27.4558i | − | 1.02967i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 27.0279i | − | 1.01220i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.97056 | −0.335480 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 51.3658 | 1.91829 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.3797 | 0.760036 | 0.380018 | − | 0.924979i | \(-0.375918\pi\) | ||||
0.380018 | + | 0.924979i | \(0.375918\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.2843 | − | 27.3994i | −0.457490 | − | 1.02041i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −41.9411 | −1.55981 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 29.3137i | − | 1.08868i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.1426 | 0.487430 | 0.243715 | − | 0.969847i | \(-0.421634\pi\) | ||||
0.243715 | + | 0.969847i | \(0.421634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 39.2843 | 1.45497 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 56.5921i | − | 2.09313i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.3588 | −0.825842 | −0.412921 | − | 0.910767i | \(-0.635491\pi\) | ||||
−0.412921 | + | 0.910767i | \(0.635491\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.7821 | − | 13.1716i | −0.545245 | − | 0.485841i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.68629 | −0.319964 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.6274 | −1.05308 | −0.526538 | − | 0.850151i | \(-0.676510\pi\) | ||||
−0.526538 | + | 0.850151i | \(0.676510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 51.7373 | 1.90062 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.6569i | 1.30812i | 0.756441 | + | 0.654062i | \(0.226936\pi\) | ||||
−0.756441 | + | 0.654062i | \(0.773064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 10.8239i | − | 0.396558i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.57128i | 0.240430i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.6173 | − | 28.1421i | −0.461026 | − | 1.02829i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.9706i | 0.692246i | 0.938189 | + | 0.346123i | \(0.112502\pi\) | ||||
−0.938189 | + | 0.346123i | \(0.887498\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.82843 | −0.248842 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.2764i | 0.774328i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.6863i | 0.969930i | 0.874534 | + | 0.484965i | \(0.161168\pi\) | ||||
−0.874534 | + | 0.484965i | \(0.838832\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.1116 | 0.693709 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.5223i | 1.21518i | 0.794250 | + | 0.607591i | \(0.207864\pi\) | ||||
−0.794250 | + | 0.607591i | \(0.792136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.7990 | + | 18.7402i | −1.51323 | + | 0.678442i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 30.6274i | − | 1.10734i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.5147i | 0.849067i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.7206i | 0.422656i | 0.977415 | + | 0.211328i | \(0.0677788\pi\) | ||||
−0.977415 | + | 0.211328i | \(0.932221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.6274 | −1.39113 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.3283 | 0.479384 | 0.239692 | − | 0.970849i | \(-0.422953\pi\) | ||||
0.239692 | + | 0.970849i | \(0.422953\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.2960 | 1.01642 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.3431 | + | 23.0698i | 0.371058 | + | 0.827624i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.5980 | 1.41874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.34315i | − | 0.226976i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.5754 | 0.592358 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.17157 | 0.327347 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25.6829i | − | 0.915497i | −0.889082 | − | 0.457749i | \(-0.848656\pi\) | ||
0.889082 | − | 0.457749i | \(-0.151344\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 63.0864 | 2.24594 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.43289 | − | 7.65685i | −0.122059 | − | 0.272246i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.48528 | 0.159277 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.65685 | 0.200628 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.0096 | 0.389981 | 0.194991 | − | 0.980805i | \(-0.437532\pi\) | ||||
0.194991 | + | 0.980805i | \(0.437532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.6274i | 0.800500i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.0083i | 0.706959i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.79337i | 0.0632865i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.55582 | − | 4.28427i | 0.336798 | − | 0.151001i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 65.4558i | 2.30415i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.4853 | 1.21244 | 0.606219 | − | 0.795298i | \(-0.292686\pi\) | ||||
0.606219 | + | 0.795298i | \(0.292686\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.1577i | − | 0.883405i | −0.897162 | − | 0.441702i | \(-0.854375\pi\) | ||
0.897162 | − | 0.441702i | \(-0.145625\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 65.9411i | 2.31266i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.75152 | 0.201467 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.5838i | 1.27990i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.1716 | + | 38.3002i | 0.600023 | + | 1.33832i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.5980i | 1.03298i | 0.856294 | + | 0.516488i | \(0.172761\pi\) | ||||
−0.856294 | + | 0.516488i | \(0.827239\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.1127i | 1.29367i | 0.762631 | + | 0.646834i | \(0.223907\pi\) | ||||
−0.762631 | + | 0.646834i | \(0.776093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.0083i | 0.696600i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.2548 | −1.64321 | −0.821606 | − | 0.570056i | \(-0.806921\pi\) | ||||
−0.821606 | + | 0.570056i | \(0.806921\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.5515 | 1.79046 | 0.895230 | − | 0.445605i | \(-0.147011\pi\) | ||||
0.895230 | + | 0.445605i | \(0.147011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.2150 | −0.631870 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.6274 | − | 34.4190i | −1.33836 | − | 1.19255i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.9706 | −0.587291 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0000i | 0.553041i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.1426 | −0.453731 | −0.226866 | − | 0.973926i | \(-0.572848\pi\) | ||||
−0.226866 | + | 0.973926i | \(0.572848\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.6274 | −1.02164 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 43.4495i | − | 1.49648i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.51528 | 0.155330 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.57675 | + | 16.8995i | 0.260340 | + | 0.580674i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.82843 | −0.234351 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.3726 | −0.458406 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2974 | −0.660729 | −0.330364 | − | 0.943853i | \(-0.607172\pi\) | ||||
−0.330364 | + | 0.943853i | \(0.607172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.7990i | 0.677111i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.3994i | 0.935944i | 0.883743 | + | 0.467972i | \(0.155015\pi\) | ||||
−0.883743 | + | 0.467972i | \(0.844985\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.0823i | 1.81114i | 0.424193 | + | 0.905572i | \(0.360558\pi\) | ||||
−0.424193 | + | 0.905572i | \(0.639442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.4412 | + | 52.2843i | 0.798874 | + | 1.78184i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 23.4558i | − | 0.798446i | −0.916854 | − | 0.399223i | \(-0.869280\pi\) | ||
0.916854 | − | 0.399223i | \(-0.130720\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5147 | −0.391512 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 98.3252i | − | 3.33930i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 14.3431i | − | 0.486558i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.9974 | 0.609818 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 44.8715i | 1.51867i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.3431 | + | 23.0698i | 0.349662 | + | 0.779901i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 11.6569i | − | 0.393624i | −0.980441 | − | 0.196812i | \(-0.936941\pi\) | ||
0.980441 | − | 0.196812i | \(-0.0630589\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.1421i | 0.746836i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.4804i | 1.26275i | 0.775478 | + | 0.631374i | \(0.217509\pi\) | ||||
−0.775478 | + | 0.631374i | \(0.782491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6569 | −1.19995 | −0.599974 | − | 0.800019i | \(-0.704823\pi\) | ||||
−0.599974 | + | 0.800019i | \(0.704823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.0502 | −0.539521 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.5001 | −1.49417 | −0.747083 | − | 0.664731i | \(-0.768546\pi\) | ||||
−0.747083 | + | 0.664731i | \(0.768546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.4853 | − | 8.28772i | 0.619976 | − | 0.277961i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.6569 | 0.390519 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 14.6274i | − | 0.489488i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.16478 | 0.0723608 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −39.5980 | −1.32214 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 56.5921i | − | 1.88745i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.7821 | 0.492462 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −48.3044 | + | 21.6569i | −1.60747 | + | 0.720695i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.4853 | 0.415025 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.0000 | −0.863316 | −0.431658 | − | 0.902037i | \(-0.642071\pi\) | ||||
−0.431658 | + | 0.902037i | \(0.642071\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32.4399 | −1.07596 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 35.6569i | − | 1.18136i | −0.806904 | − | 0.590682i | \(-0.798859\pi\) | ||
0.806904 | − | 0.590682i | \(-0.201141\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.43289i | 0.113612i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.06147i | 0.101209i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.47343 | + | 3.79899i | −0.279817 | + | 0.125454i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.79899i | 0.323239i | 0.986853 | + | 0.161619i | \(0.0516717\pi\) | ||||
−0.986853 | + | 0.161619i | \(0.948328\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.48528 | 0.147795 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.1426i | 0.432592i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 14.0000i | − | 0.460317i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −43.4495 | −1.42707 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.64820i | 0.218120i | 0.994035 | + | 0.109060i | \(0.0347841\pi\) | ||||
−0.994035 | + | 0.109060i | \(0.965216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.9706 | + | 22.2500i | 0.818377 | + | 0.729215i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 10.3431i | − | 0.338619i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 16.0000i | − | 0.523256i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 48.8296i | − | 1.59519i | −0.603190 | − | 0.797597i | \(-0.706104\pi\) | ||
0.603190 | − | 0.797597i | \(-0.293896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.9706 | −0.553813 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.10201 | −0.264118 | −0.132059 | − | 0.991242i | \(-0.542159\pi\) | ||||
−0.132059 | + | 0.991242i | \(0.542159\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.3070 | −0.986931 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.65685 | + | 2.53620i | −0.184017 | + | 0.0825027i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.6569 | 1.28867 | 0.644337 | − | 0.764741i | \(-0.277133\pi\) | ||||
0.644337 | + | 0.764741i | \(0.277133\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.71573i | − | 0.120618i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.7067 | 1.38486 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.6274 | 1.44562 | 0.722812 | − | 0.691045i | \(-0.242849\pi\) | ||||
0.722812 | + | 0.691045i | \(0.242849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.896683i | − | 0.0290160i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.0166 | 1.29355 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.16478 | + | 4.82843i | 0.0699045 | + | 0.155918i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.6274 | 0.762175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −44.6274 | −1.43810 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.01962 | 0.225969 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.9706i | − | 1.63910i | −0.573006 | − | 0.819551i | \(-0.694223\pi\) | ||
0.573006 | − | 0.819551i | \(-0.305777\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 92.2792i | 2.96443i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.77791i | − | 0.153330i | −0.997057 | − | 0.0766652i | \(-0.975573\pi\) | ||
0.997057 | − | 0.0766652i | \(-0.0244273\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.1522 | − | 10.8284i | 0.774283 | − | 0.347143i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 41.4558i | − | 1.32765i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.6274 | −0.915872 | −0.457936 | − | 0.888985i | \(-0.651411\pi\) | ||||
−0.457936 | + | 0.888985i | \(0.651411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.4525i | 0.334063i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 66.2843i | 2.11629i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.76245 | −0.247584 | −0.123792 | − | 0.992308i | \(-0.539506\pi\) | ||||
−0.123792 | + | 0.992308i | \(0.539506\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8.28772i | − | 0.264069i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.3137 | − | 8.65914i | 0.614762 | − | 0.275623i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 28.0000i | − | 0.890348i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.48528i | 0.0789476i | 0.999221 | + | 0.0394738i | \(0.0125682\pi\) | ||||
−0.999221 | + | 0.0394738i | \(0.987432\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.8854i | − | 0.440640i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.970563 | −0.0307689 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.04054 | −0.159636 | −0.0798178 | − | 0.996809i | \(-0.525434\pi\) | ||||
−0.0798178 | + | 0.996809i | \(0.525434\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.91630 | 0.250461 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))