Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(447,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.447");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.f (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: | \(3.57729801055\) |
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 | 447.2 | ||
Root | \(0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.447 |
Dual form | 448.2.f.d.447.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.61313 | −1.50869 | −0.754344 | − | 0.656479i | \(-0.772045\pi\) | ||||
−0.754344 | + | 0.656479i | \(0.772045\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.08239i | 0.484061i | 0.970269 | + | 0.242030i | \(0.0778133\pi\) | ||||
−0.970269 | + | 0.242030i | \(0.922187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.08239 | − | 2.41421i | −0.409106 | − | 0.912487i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.82843 | 1.27614 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.14386i | − | 1.14930i | −0.818399 | − | 0.574650i | \(-0.805138\pi\) | ||
0.818399 | − | 0.574650i | \(-0.194862\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 4.77791 | 1.09613 | 0.548064 | − | 0.836436i | \(-0.315365\pi\) | ||||
0.548064 | + | 0.836436i | \(0.315365\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | + | 6.30864i | 0.617213 | + | 1.37666i | ||||
\(22\) | 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 | ||||||||
\(27\) | −2.16478 | −0.416613 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.65685 | 1.42184 | 0.710921 | − | 0.703272i | \(-0.248278\pi\) | ||||
0.710921 | + | 0.703272i | \(0.248278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.39104 | 1.32747 | 0.663735 | − | 0.747968i | \(-0.268970\pi\) | ||||
0.663735 | + | 0.747968i | \(0.268970\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5.22625i | − | 0.909774i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.61313 | − | 1.17157i | 0.441699 | − | 0.198032i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.65685 | −0.601183 | −0.300592 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300592 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.8284i | 1.73394i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.28772i | − | 1.29432i | −0.762352 | − | 0.647162i | \(-0.775956\pi\) | ||
0.762352 | − | 0.647162i | \(-0.224044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.65685i | 1.16766i | 0.811876 | + | 0.583830i | \(0.198446\pi\) | ||||
−0.811876 | + | 0.583830i | \(0.801554\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.14386i | 0.617730i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.06147 | −0.446561 | −0.223280 | − | 0.974754i | \(-0.571677\pi\) | ||||
−0.223280 | + | 0.974754i | \(0.571677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.65685 | + | 5.22625i | −0.665265 | + | 0.746607i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 19.3137i | − | 2.70446i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.16478 | −0.291899 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.4853 | −1.65372 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.67459 | 0.738769 | 0.369385 | − | 0.929277i | \(-0.379569\pi\) | ||||
0.369385 | + | 0.929277i | \(0.379569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.08239i | − | 0.138586i | −0.997596 | − | 0.0692931i | \(-0.977926\pi\) | ||
0.997596 | − | 0.0692931i | \(-0.0220744\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.14386 | − | 9.24264i | −0.522077 | − | 1.16446i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.48528 | 0.556331 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.34315i | 0.530600i | 0.964166 | + | 0.265300i | \(0.0854709\pi\) | ||||
−0.964166 | + | 0.265300i | \(0.914529\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 9.55582i | − | 1.15039i | ||||||
\(70\) | 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 | \(0.0167108\pi\) | ||||
−0.998622 | + | 0.0524744i | \(0.983289\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.0042 | −1.15518 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.82843 | − | 2.16478i | 0.550250 | − | 0.246700i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.17157i | − | 0.806865i | −0.915009 | − | 0.403432i | \(-0.867817\pi\) | ||
0.915009 | − | 0.403432i | \(-0.132183\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.82843 | −0.647603 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.71644 | 0.188404 | 0.0942020 | − | 0.995553i | \(-0.469970\pi\) | ||||
0.0942020 | + | 0.995553i | \(0.469970\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.0083 | −2.14512 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.22625i | 0.553982i | 0.960873 | + | 0.276991i | \(0.0893372\pi\) | ||||
−0.960873 | + | 0.276991i | \(0.910663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0042 | + | 4.48528i | −1.04872 | + | 0.470185i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −19.3137 | −2.00274 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 7.65685i | 0.769543i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.47343i | 0.843138i | 0.906796 | + | 0.421569i | \(0.138520\pi\) | ||||
−0.906796 | + | 0.421569i | \(0.861480\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | − | 11.6569i | − | 1.12691i | −0.826147 | − | 0.563455i | \(-0.809472\pi\) | ||
0.826147 | − | 0.563455i | \(-0.190528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3137 | −1.65835 | −0.829176 | − | 0.558987i | \(-0.811190\pi\) | ||||
−0.829176 | + | 0.558987i | \(0.811190\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −3.95815 | −0.369099 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 15.8645i | − | 1.46667i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.8435 | − | 8.00000i | 1.63571 | − | 0.733359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.6569i | 1.95273i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.55582i | 0.854699i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.65685i | − | 0.679436i | −0.940527 | − | 0.339718i | \(-0.889668\pi\) | ||
0.940527 | − | 0.339718i | \(-0.110332\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 20.0083i | − | 1.76163i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.50981 | 0.306653 | 0.153327 | − | 0.988176i | \(-0.451001\pi\) | ||||
0.153327 | + | 0.988176i | \(0.451001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.17157 | − | 11.5349i | −0.448432 | − | 1.00020i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.34315i | − | 0.201666i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0042 | 0.848542 | 0.424271 | − | 0.905535i | \(-0.360530\pi\) | ||||
0.424271 | + | 0.905535i | \(0.360530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.28772 | 0.693054 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.28772i | 0.688258i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.1689 | − | 13.6569i | 1.00368 | − | 1.12640i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 8.00000i | 0.642575i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.47343i | − | 0.676253i | −0.941101 | − | 0.338127i | \(-0.890207\pi\) | ||
0.941101 | − | 0.338127i | \(-0.109793\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.22625 | −0.414469 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.82843 | − | 3.95815i | 0.695778 | − | 0.311946i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.31371i | 0.416202i | 0.978107 | + | 0.208101i | \(0.0667282\pi\) | ||||
−0.978107 | + | 0.208101i | \(0.933272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.65685 | 0.440386 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 18.2919 | 1.39882 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6382i | 0.808808i | 0.914580 | + | 0.404404i | \(0.132521\pi\) | ||||
−0.914580 | + | 0.404404i | \(0.867479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.14386 | − | 9.24264i | −0.313246 | − | 0.698678i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.8284 | −1.11457 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000i | 0.149487i | 0.997203 | + | 0.0747435i | \(0.0238138\pi\) | ||||
−0.997203 | + | 0.0747435i | \(0.976186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5349i | 0.857382i | 0.903451 | + | 0.428691i | \(0.141025\pi\) | ||||
−0.903451 | + | 0.428691i | \(0.858975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.82843i | 0.209083i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.95815i | − | 0.291009i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.7821 | −1.08097 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.34315 | + | 5.22625i | 0.170439 | + | 0.380154i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.828427i | 0.0599429i | 0.999551 | + | 0.0299714i | \(0.00954164\pi\) | ||||
−0.999551 | + | 0.0299714i | \(0.990458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.48528 | 0.466821 | 0.233410 | − | 0.972378i | \(-0.425011\pi\) | ||||
0.233410 | + | 0.972378i | \(0.425011\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.7206 | −0.839330 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.65685 | 0.545528 | 0.272764 | − | 0.962081i | \(-0.412062\pi\) | ||||
0.272764 | + | 0.962081i | \(0.412062\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | −8.28772 | − | 18.4853i | −0.581684 | − | 1.29741i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.97056 | 0.626531 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.0000i | 0.973067i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.55582i | 0.660990i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 22.9706i | − | 1.58136i | −0.612230 | − | 0.790679i | \(-0.709728\pi\) | ||
0.612230 | − | 0.790679i | \(-0.290272\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.28772i | − | 0.567865i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.28772 | −0.565218 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | − | 17.8435i | −0.543075 | − | 1.21130i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 2.34315i | − | 0.158335i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.6274 | 2.06022 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | −29.1158 | −1.93248 | −0.966242 | − | 0.257637i | \(-0.917056\pi\) | ||||
−0.966242 | + | 0.257637i | \(0.917056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.3784i | 1.94138i | 0.240332 | + | 0.970691i | \(0.422744\pi\) | ||||
−0.240332 | + | 0.970691i | \(0.577256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.6173 | + | 5.65685i | −0.830157 | + | 0.372194i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.31371i | − | 0.216163i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.7402i | 1.21731i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.6569i | 1.27150i | 0.771897 | + | 0.635748i | \(0.219308\pi\) | ||||
−0.771897 | + | 0.635748i | \(0.780692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0502i | 1.03388i | 0.856021 | + | 0.516941i | \(0.172929\pi\) | ||||
−0.856021 | + | 0.516941i | \(0.827071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.7248 | 1.39364 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.65685 | − | 5.04054i | −0.361403 | − | 0.322028i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 19.7990i | − | 1.25978i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.48528 | −0.284243 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.61313 | 0.164939 | 0.0824695 | − | 0.996594i | \(-0.473719\pi\) | ||||
0.0824695 | + | 0.996594i | \(0.473719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.31371 | −0.459809 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 3.95815 | + | 8.82843i | 0.245948 | + | 0.548572i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 29.3137 | 1.81447 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | − | 13.6569i | − | 0.835786i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 25.0489i | − | 1.52726i | −0.645656 | − | 0.763628i | \(-0.723416\pi\) | ||
0.645656 | − | 0.763628i | \(-0.276584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.2346 | −1.53289 | −0.766446 | − | 0.642309i | \(-0.777977\pi\) | ||||
−0.766446 | + | 0.642309i | \(0.777977\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.1421 | − | 11.7206i | 1.58219 | − | 0.709363i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.65685i | 0.461726i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.97056 | −0.418821 | −0.209410 | − | 0.977828i | \(-0.567154\pi\) | ||||
−0.209410 | + | 0.977828i | \(0.567154\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.2960 | 1.69404 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.6274 | 0.991909 | 0.495954 | − | 0.868349i | \(-0.334818\pi\) | ||||
0.495954 | + | 0.868349i | \(0.334818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.61313 | 0.155334 | 0.0776671 | − | 0.996979i | \(-0.475253\pi\) | ||||
0.0776671 | + | 0.996979i | \(0.475253\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 13.5140i | − | 0.800499i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.0083 | + | 8.97056i | −1.18105 | + | 0.529516i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −37.6274 | −2.21338 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.6274i | 1.79541i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.47343i | 0.495023i | 0.968885 | + | 0.247511i | \(0.0796128\pi\) | ||||
−0.968885 | + | 0.247511i | \(0.920387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.14214i | 0.357609i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.32957i | − | 0.251227i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.1535 | 0.876349 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.4853 | − | 8.28772i | 1.06547 | − | 0.477696i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 22.1421i | − | 1.27203i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.17157 | 0.0670841 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.71644 | 0.0979626 | 0.0489813 | − | 0.998800i | \(-0.484403\pi\) | ||||
0.0489813 | + | 0.998800i | \(0.484403\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.6569 | −1.68712 | ||||||||
\(310\) | 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 | \(-0.941244\pi\) | ||
0.983012 | − | 0.183541i | \(-0.0587561\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.0042 | − | 4.48528i | 0.563671 | − | 0.252717i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.3431 | −0.917923 | −0.458961 | − | 0.888456i | \(-0.651778\pi\) | ||||
−0.458961 | + | 0.888456i | \(0.651778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.3137i | 0.857403i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.4608i | 1.70016i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.3137i | 1.96491i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 15.8645i | − | 0.880002i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 45.2429 | 2.50194 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.31371 | + | 7.39104i | 0.182691 | + | 0.407481i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.31371i | 0.292068i | 0.989280 | + | 0.146034i | \(0.0466509\pi\) | ||||
−0.989280 | + | 0.146034i | \(0.953349\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.0000 | −0.767195 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −8.28772 | −0.450127 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.7821i | 0.800494i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6578 | + | 5.58579i | 0.953433 | + | 0.301604i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.3431 | 0.556856 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8.34315i | − | 0.447884i | −0.974603 | − | 0.223942i | \(-0.928107\pi\) | ||
0.974603 | − | 0.223942i | \(-0.0718925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.8645i | − | 0.849205i | −0.905380 | − | 0.424603i | \(-0.860414\pi\) | ||
0.905380 | − | 0.424603i | \(-0.139586\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | −3.43289 | −0.182199 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −46.6274 | + | 20.9050i | −2.46778 | + | 1.10641i | ||||
\(358\) | 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 | ||||||||
\(363\) | −18.2919 | −0.960075 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.970563 | −0.0508016 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.32957 | 0.226002 | 0.113001 | − | 0.993595i | \(-0.463954\pi\) | ||||
0.113001 | + | 0.993595i | \(0.463954\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 31.7289i | − | 1.65174i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.16478 | − | 4.82843i | −0.112390 | − | 0.250679i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.9706 | 1.39648 | 0.698241 | − | 0.715862i | \(-0.253966\pi\) | ||||
0.698241 | + | 0.715862i | \(0.253966\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 24.9706i | − | 1.28947i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 31.7289i | − | 1.63412i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.3137i | − | 0.889345i | −0.895693 | − | 0.444673i | \(-0.853320\pi\) | ||
0.895693 | − | 0.444673i | \(-0.146680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.0083i | 1.02506i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5140 | 0.690532 | 0.345266 | − | 0.938505i | \(-0.387789\pi\) | ||||
0.345266 | + | 0.938505i | \(0.387789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.34315 | + | 5.22625i | 0.119418 | + | 0.266354i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.3137i | 1.49010i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.34315 | −0.423014 | −0.211507 | − | 0.977376i | \(-0.567837\pi\) | ||||
−0.211507 | + | 0.977376i | \(0.567837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.0279 | −1.36686 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.17157 | −0.462645 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.76245 | 0.390571 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 14.0711i | − | 0.706208i | −0.935584 | − | 0.353104i | \(-0.885126\pi\) | ||
0.935584 | − | 0.353104i | \(-0.114874\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − | 30.6274i | − | 1.52566i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 6.30864i | − | 0.313479i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.31371i | − | 0.362527i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.6173i | − | 0.623885i | −0.950101 | − | 0.311942i | \(-0.899020\pi\) | ||
0.950101 | − | 0.311942i | \(-0.100980\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.22625 | −0.257792 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.14214 | − | 13.6997i | −0.302235 | − | 0.674117i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.85786i | 0.0911990i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.1421 | −1.28019 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.14933 | −0.251561 | −0.125781 | − | 0.992058i | \(-0.540144\pi\) | ||||
−0.125781 | + | 0.992058i | \(0.540144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.31371 | −0.0640262 | −0.0320131 | − | 0.999487i | \(-0.510192\pi\) | ||||
−0.0320131 | + | 0.999487i | \(0.510192\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.7206 | −0.569875 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 28.2960i | 1.37256i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.61313 | + | 1.17157i | −0.126458 | + | 0.0566964i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.6569 | −1.04560 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 23.6569i | − | 1.13951i | −0.821814 | − | 0.569755i | \(-0.807038\pi\) | ||
0.821814 | − | 0.569755i | \(-0.192962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 28.2960i | − | 1.35982i | −0.733295 | − | 0.679911i | \(-0.762019\pi\) | ||
0.733295 | − | 0.679911i | \(-0.237981\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 21.6569i | − | 1.03837i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.4721i | 0.835805i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | 10.0000i | 0.475114i | 0.971374 | + | 0.237557i | \(0.0763467\pi\) | ||||
−0.971374 | + | 0.237557i | \(0.923653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.65685 | −0.268161 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | 16.5754 | 0.780507 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 51.3658i | − | 2.41338i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.85483 | − | 10.8284i | −0.227598 | − | 0.507644i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.1127 | −1.17472 | −0.587361 | − | 0.809325i | \(-0.699833\pi\) | ||||
−0.587361 | + | 0.809325i | \(0.699833\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 16.0000i | − | 0.746816i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 32.4399i | − | 1.51088i | −0.655220 | − | 0.755438i | \(-0.727424\pi\) | ||
0.655220 | − | 0.755438i | \(-0.272576\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1421i | 0.564293i | 0.959371 | + | 0.282146i | \(0.0910464\pi\) | ||||
−0.959371 | + | 0.282146i | \(0.908954\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 20.9050i | − | 0.969447i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.7862 | −1.14697 | −0.573485 | − | 0.819216i | \(-0.694409\pi\) | ||||
−0.573485 | + | 0.819216i | \(0.694409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4853 | − | 4.70099i | 0.484165 | − | 0.217071i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.1421i | 1.02026i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.3137 | −0.704125 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.2919 | 0.839289 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.65685 | 0.350583 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.8322 | −1.40876 | −0.704381 | − | 0.709822i | \(-0.748775\pi\) | ||||
−0.704381 | + | 0.709822i | \(0.748775\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.1535i | 0.690940i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23.0698 | + | 10.3431i | −1.04971 | + | 0.470629i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.6863 | 0.576055 | ||||||||
\(486\) | 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 | ||||||||
\(491\) | − | 26.2843i | − | 1.18619i | −0.805132 | − | 0.593096i | \(-0.797905\pi\) | ||
0.805132 | − | 0.593096i | \(-0.202095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 56.5921i | 2.54878i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.28772 | −0.372505 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.65685 | − | 3.43289i | 0.343457 | − | 0.153986i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.31371i | 0.237874i | 0.992902 | + | 0.118937i | \(0.0379487\pi\) | ||||
−0.992902 | + | 0.118937i | \(0.962051\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 40.9706 | 1.83043 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 10.9008 | 0.484124 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.9456i | 1.15002i | 0.818148 | + | 0.575008i | \(0.195001\pi\) | ||||
−0.818148 | + | 0.575008i | \(0.804999\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.16478 | − | 0.970563i | 0.0957644 | − | 0.0429352i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.3431 | −0.456661 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.2843i | 0.541310i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.12293i | − | 0.269286i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 27.7990i | − | 1.22024i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6173i | 0.552773i | 0.961047 | + | 0.276387i | \(0.0891371\pi\) | ||||
−0.961047 | + | 0.276387i | \(0.910863\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.34502 | 0.0588138 | 0.0294069 | − | 0.999568i | \(-0.490638\pi\) | ||||
0.0294069 | + | 0.999568i | \(0.490638\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.8284 | + | 24.1522i | 0.472591 | + | 1.05409i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 54.6274i | 2.37961i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.62742 | 0.418583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.7248 | 0.942775 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.3431 | −1.48757 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6173 | 0.545493 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5.22625i | − | 0.225529i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.4525 | − | 9.31371i | −0.450221 | − | 0.401170i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.68629 | −0.115493 | −0.0577463 | − | 0.998331i | \(-0.518391\pi\) | ||||
−0.0577463 | + | 0.998331i | \(0.518391\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 30.1421i | − | 1.29352i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 18.7402i | − | 0.802743i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.6863i | − | 0.456913i | −0.973554 | − | 0.228456i | \(-0.926632\pi\) | ||
0.973554 | − | 0.228456i | \(-0.0733678\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 4.14386i | − | 0.176856i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.5838 | 1.55852 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.3137 | + | 7.76245i | −0.736254 | + | 0.330093i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.3431i | 0.439042i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.3137 | −0.733605 | −0.366803 | − | 0.930299i | \(-0.619548\pi\) | ||||
−0.366803 | + | 0.930299i | \(0.619548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.7289 | 1.34199 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.6274 | 1.63085 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.6829 | 1.08241 | 0.541203 | − | 0.840892i | \(-0.317969\pi\) | ||||
0.541203 | + | 0.840892i | \(0.317969\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.43289i | 0.144423i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.30864 | + | 14.0711i | 0.264938 | + | 0.590929i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.1421 | 1.51516 | 0.757579 | − | 0.652744i | \(-0.226382\pi\) | ||||
0.757579 | + | 0.652744i | \(0.226382\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 19.6569i | − | 0.822614i | −0.911497 | − | 0.411307i | \(-0.865072\pi\) | ||
0.911497 | − | 0.411307i | \(-0.134928\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.16478i | − | 0.0904352i | ||||||
\(574\) | 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 | ||||||||
\(579\) | −16.9469 | −0.704287 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.85786 | − | 4.14386i | −0.0770772 | − | 0.171916i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.1716 | 0.709957 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.4454 | 1.38044 | 0.690219 | − | 0.723600i | \(-0.257514\pi\) | ||||
0.690219 | + | 0.723600i | \(0.257514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.3137 | 1.45508 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 8.65914 | + | 19.3137i | 0.354990 | + | 0.791785i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.34315 | 0.0958986 | ||||||||
\(598\) | 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 | \(-0.913621\pi\) | ||
0.963406 | − | 0.268048i | \(-0.0863786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.6274i | 0.677121i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.57675i | 0.308039i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.8100 | 1.69702 | 0.848508 | − | 0.529182i | \(-0.177501\pi\) | ||||
0.848508 | + | 0.529182i | \(0.177501\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.6569 | + | 48.3044i | 0.877580 | + | 1.95739i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.6863i | 0.513232i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3137 | −0.699294 | −0.349647 | − | 0.936881i | \(-0.613698\pi\) | ||||
−0.349647 | + | 0.936881i | \(0.613698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23.4412 | −0.945241 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −49.1127 | −1.97720 | −0.988601 | − | 0.150557i | \(-0.951893\pi\) | ||||
−0.988601 | + | 0.150557i | \(0.951893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6215 | −0.909233 | −0.454616 | − | 0.890687i | \(-0.650224\pi\) | ||||
−0.454616 | + | 0.890687i | \(0.650224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 7.91630i | − | 0.317670i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.6173 | − | 5.65685i | 0.505501 | − | 0.226637i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.79899 | 0.351960 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 24.9706i | − | 0.997228i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 27.0279i | − | 1.07767i | ||||||
\(630\) | 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 | ||||||||
\(635\) | 8.28772 | 0.328888 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.6569 | + | 19.2974i | 0.858076 | + | 0.764589i | ||||
\(638\) | 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 | ||||||||
\(643\) | −26.5796 | −1.04820 | −0.524099 | − | 0.851658i | \(-0.675598\pi\) | ||||
−0.524099 | + | 0.851658i | \(0.675598\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.6569 | 0.852738 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 20.9050 | + | 46.6274i | 0.819332 | + | 1.82747i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.3137 | −0.990602 | −0.495301 | − | 0.868721i | \(-0.664942\pi\) | ||||
−0.495301 | + | 0.868721i | \(0.664942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.79899i | 0.148439i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.43289i | 0.133930i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 50.9706i | 1.98553i | 0.120068 | + | 0.992766i | \(0.461689\pi\) | ||||
−0.120068 | + | 0.992766i | \(0.538311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.68006i | 0.259824i | 0.991526 | + | 0.129912i | \(0.0414695\pi\) | ||||
−0.991526 | + | 0.129912i | \(0.958530\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −80.0333 | −3.10824 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.4853 | − | 5.59767i | 0.484158 | − | 0.217068i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.0000i | 1.08416i | ||||||||
\(668\) | 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 | ||||||||
\(675\) | −8.28772 | −0.318994 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 22.3588i | − | 0.859319i | −0.902991 | − | 0.429660i | \(-0.858634\pi\) | ||
0.902991 | − | 0.429660i | \(-0.141366\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.2960 | + | 12.6863i | −1.08590 | + | 0.486855i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 76.0833 | 2.91552 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 32.3431i | − | 1.23758i | −0.785558 | − | 0.618788i | \(-0.787624\pi\) | ||
0.785558 | − | 0.618788i | \(-0.212376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.16478i | 0.0827122i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 76.7696i | − | 2.92894i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 8.28772i | − | 0.315737i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.3756 | 0.394706 | 0.197353 | − | 0.980333i | \(-0.436766\pi\) | ||||
0.197353 | + | 0.980333i | \(0.436766\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.4853 | − | 8.28772i | 0.702198 | − | 0.314824i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.8284i | 0.410746i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.2548 | 2.32019 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −47.0363 | −1.77907 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3137 | 0.502852 | 0.251426 | − | 0.967877i | \(-0.419101\pi\) | ||||
0.251426 | + | 0.967877i | \(0.419101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.4721 | −0.658974 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.65914i | 0.326122i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.4567 | − | 9.17157i | 0.769352 | − | 0.344932i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0000 | 0.676004 | 0.338002 | − | 0.941145i | \(-0.390249\pi\) | ||||
0.338002 | + | 0.941145i | \(0.390249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 27.4558i | − | 1.02967i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.0279i | 1.01220i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.97056i | 0.335480i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 51.3658i | − | 1.91829i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.3797 | −0.760036 | −0.380018 | − | 0.924979i | \(-0.624082\pi\) | ||||
−0.380018 | + | 0.924979i | \(0.624082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.2843 | − | 27.3994i | −0.457490 | − | 1.02041i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 41.9411i | − | 1.55981i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.3137 | 1.08868 | ||||||||
\(726\) | 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 | ||||||||
\(731\) | −56.5921 | −2.09313 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.3588i | 0.825842i | 0.910767 | + | 0.412921i | \(0.135491\pi\) | ||||
−0.910767 | + | 0.412921i | \(0.864509\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.7821 | + | 13.1716i | 0.545245 | + | 0.485841i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.68629 | −0.319964 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 28.6274i | − | 1.05308i | −0.850151 | − | 0.526538i | \(-0.823490\pi\) | ||
0.850151 | − | 0.526538i | \(-0.176510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 51.7373i | 1.90062i | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 6.57128 | 0.240430 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.1421 | + | 12.6173i | −1.02829 | + | 0.461026i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 18.9706i | − | 0.692246i | −0.938189 | − | 0.346123i | \(-0.887498\pi\) | ||
0.938189 | − | 0.346123i | \(-0.112502\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.82843 | −0.248842 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.2764 | −0.774328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.6863 | −0.969930 | −0.484965 | − | 0.874534i | \(-0.661168\pi\) | ||||
−0.484965 | + | 0.874534i | \(0.661168\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.1116 | 0.693709 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 33.5223i | − | 1.21518i | −0.794250 | − | 0.607591i | \(-0.792136\pi\) | ||
0.794250 | − | 0.607591i | \(-0.207864\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.7402 | + | 41.7990i | 0.678442 | + | 1.51323i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −30.6274 | −1.10734 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − | 38.6274i | − | 1.39113i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.3283i | 0.479384i | 0.970849 | + | 0.239692i | \(0.0770465\pi\) | ||||
−0.970849 | + | 0.239692i | \(0.922953\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.2960 | 1.01642 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.3431 | − | 23.0698i | −0.371058 | − | 0.827624i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 39.5980i | − | 1.41874i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.34315 | −0.226976 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.5754 | −0.592358 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.17157 | 0.327347 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.6829 | 0.915497 | 0.457749 | − | 0.889082i | \(-0.348656\pi\) | ||||
0.457749 | + | 0.889082i | \(0.348656\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 63.0864i | 2.24594i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.43289 | − | 7.65685i | −0.122059 | − | 0.272246i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.48528 | −0.159277 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 5.65685i | − | 0.200628i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 11.0096i | − | 0.389981i | −0.980805 | − | 0.194991i | \(-0.937532\pi\) | ||
0.980805 | − | 0.194991i | \(-0.0624676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 22.6274i | − | 0.800500i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.0083i | 0.706959i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.79337 | −0.0632865 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.28427 | + | 9.55582i | 0.151001 | + | 0.336798i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 65.4558i | 2.30415i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.4853 | −1.21244 | −0.606219 | − | 0.795298i | \(-0.707314\pi\) | ||||
−0.606219 | + | 0.795298i | \(0.707314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.1577 | −0.883405 | −0.441702 | − | 0.897162i | \(-0.645625\pi\) | ||||
−0.441702 | + | 0.897162i | \(0.645625\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 65.9411 | 2.31266 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.75152 | −0.201467 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.5838i | 1.27990i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38.3002 | + | 17.1716i | −1.33832 | + | 0.600023i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.5980 | −1.03298 | −0.516488 | − | 0.856294i | \(-0.672761\pi\) | ||||
−0.516488 | + | 0.856294i | \(0.672761\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | 47.2548i | 1.64321i | 0.570056 | + | 0.821606i | \(0.306921\pi\) | ||||
−0.570056 | + | 0.821606i | \(0.693079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 51.5515i | − | 1.79046i | −0.445605 | − | 0.895230i | \(-0.647011\pi\) | ||
0.445605 | − | 0.895230i | \(-0.352989\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2150 | 0.631870 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.6274 | − | 34.4190i | −1.33836 | − | 1.19255i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 16.9706i | − | 0.587291i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0000 | −0.553041 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | −43.4495 | −1.49648 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 4.51528i | − | 0.155330i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.57675 | − | 16.8995i | −0.260340 | − | 0.580674i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.82843 | −0.234351 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 13.3726i | − | 0.458406i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.2974i | − | 0.660729i | −0.943853 | − | 0.330364i | \(-0.892828\pi\) | ||
0.943853 | − | 0.330364i | \(-0.107172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.7990i | 0.677111i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 27.3994i | − | 0.935944i | −0.883743 | − | 0.467972i | \(-0.844985\pi\) | ||
0.883743 | − | 0.467972i | \(-0.155015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.0823 | 1.81114 | 0.905572 | − | 0.424193i | \(-0.139442\pi\) | ||||
0.905572 | + | 0.424193i | \(0.139442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 52.2843 | − | 23.4412i | 1.78184 | − | 0.798874i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.4558i | 0.798446i | 0.916854 | + | 0.399223i | \(0.130720\pi\) | ||||
−0.916854 | + | 0.399223i | \(0.869280\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5147 | −0.391512 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 98.3252 | 3.33930 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.3431 | 0.486558 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.9974 | 0.609818 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 44.8715i | − | 1.51867i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.0698 | − | 10.3431i | 0.779901 | − | 0.349662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.6569 | −0.393624 | −0.196812 | − | 0.980441i | \(-0.563059\pi\) | ||||
−0.196812 | + | 0.980441i | \(0.563059\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 35.6569i | − | 1.19995i | −0.800019 | − | 0.599974i | \(-0.795177\pi\) | ||
0.800019 | − | 0.599974i | \(-0.204823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 16.0502i | − | 0.539521i | ||||||
\(886\) | 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 | ||||||||
\(891\) | − | 11.6569i | − | 0.390519i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.6274 | −0.489488 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.16478 | −0.0723608 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −39.5980 | −1.32214 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 56.5921 | 1.88745 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.7821i | 0.492462i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −48.3044 | + | 21.6569i | −1.60747 | + | 0.720695i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.4853 | −0.415025 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.0000i | 0.863316i | 0.902037 | + | 0.431658i | \(0.142071\pi\) | ||||
−0.902037 | + | 0.431658i | \(0.857929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.4399i | 1.07596i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.6569i | 1.18136i | 0.806904 | + | 0.590682i | \(0.201141\pi\) | ||||
−0.806904 | + | 0.590682i | \(0.798859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.43289i | 0.113612i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.06147 | −0.101209 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.79899 | − | 8.47343i | −0.125454 | − | 0.279817i | ||||
\(918\) | 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 | ||||||||
\(923\) | 13.1426 | 0.432592 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0000 | −0.460317 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | −22.2500 | + | 24.9706i | −0.729215 | + | 0.818377i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.3431 | 0.338619 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 16.0000i | − | 0.523256i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.8296i | 1.59519i | 0.603190 | + | 0.797597i | \(0.293896\pi\) | ||||
−0.603190 | + | 0.797597i | \(0.706104\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9706i | 0.553813i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.10201i | 0.264118i | 0.991242 | + | 0.132059i | \(0.0421588\pi\) | ||||
−0.991242 | + | 0.132059i | \(0.957841\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.3070 | 0.986931 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.65685 | + | 2.53620i | −0.184017 | + | 0.0825027i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.6569i | 1.28867i | 0.764741 | + | 0.644337i | \(0.222867\pi\) | ||||
−0.764741 | + | 0.644337i | \(0.777133\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.71573 | 0.120618 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.7067 | 1.38486 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.6274 | −1.44562 | −0.722812 | − | 0.691045i | \(-0.757151\pi\) | ||||
−0.722812 | + | 0.691045i | \(0.757151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.896683 | −0.0290160 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 40.0166i | − | 1.29355i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.16478 | − | 4.82843i | −0.0699045 | − | 0.155918i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.6274 | 0.762175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 44.6274i | − | 1.43810i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.01962i | 0.225969i | ||||||||
\(966\) | 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 | ||||||||
\(971\) | −4.77791 | −0.153330 | −0.0766652 | − | 0.997057i | \(-0.524427\pi\) | ||||
−0.0766652 | + | 0.997057i | \(0.524427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.8284 | − | 24.1522i | −0.347143 | − | 0.774283i | ||||
\(974\) | 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 | ||||||||
\(979\) | −10.4525 | −0.334063 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −66.2843 | −2.11629 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | −8.65914 | − | 19.3137i | −0.275623 | − | 0.614762i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.0000 | −0.890348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2.48528i | − | 0.0789476i | −0.999221 | − | 0.0394738i | \(-0.987432\pi\) | ||
0.999221 | − | 0.0394738i | \(-0.0125682\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.8854i | − | 0.440640i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 0.970563i | − | 0.0307689i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5.04054i | − | 0.159636i | −0.996809 | − | 0.0798178i | \(-0.974566\pi\) | ||
0.996809 | − | 0.0798178i | \(-0.0254338\pi\) | |||||||
\(998\) | 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 \(a_p\))