Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(881,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("882.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.d (of order \(2\), degree \(1\), 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: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.6 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.881 |
Dual form | 882.2.d.a.881.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.717439 | −0.320848 | −0.160424 | − | 0.987048i | \(-0.551286\pi\) | ||||
−0.160424 | + | 0.987048i | \(0.551286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 0.717439i | − 0.226874i | ||||||||
\(11\) | 3.00000i | 0.904534i | 0.891883 | + | 0.452267i | \(0.149385\pi\) | ||||
−0.891883 | + | 0.452267i | \(0.850615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.44949i | − 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.91359 | −1.43426 | −0.717128 | − | 0.696941i | \(-0.754544\pi\) | ||||
−0.717128 | + | 0.696941i | \(0.754544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.91359i | 1.35667i | 0.734752 | + | 0.678335i | \(0.237298\pi\) | ||||
−0.734752 | + | 0.678335i | \(0.762702\pi\) | |||||||
\(20\) | 0.717439 | 0.160424 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | 4.24264i | 0.884652i | 0.896854 | + | 0.442326i | \(0.145847\pi\) | ||||
−0.896854 | + | 0.442326i | \(0.854153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.48528 | −0.897056 | ||||||||
\(26\) | 2.44949 | 0.480384 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.24264i | 1.34492i | 0.740131 | + | 0.672462i | \(0.234763\pi\) | ||||
−0.740131 | + | 0.672462i | \(0.765237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 9.08052i | − 1.63091i | −0.578821 | − | 0.815455i | \(-0.696487\pi\) | ||||
0.578821 | − | 0.815455i | \(-0.303513\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 5.91359i | − 1.01417i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.242641 | −0.0398899 | −0.0199449 | − | 0.999801i | \(-0.506349\pi\) | ||||
−0.0199449 | + | 0.999801i | \(0.506349\pi\) | |||||||
\(38\) | −5.91359 | −0.959311 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.717439i | 0.113437i | ||||||||
\(41\) | −11.8272 | −1.84710 | −0.923548 | − | 0.383483i | \(-0.874724\pi\) | ||||
−0.923548 | + | 0.383483i | \(0.874724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.242641 | −0.0370024 | −0.0185012 | − | 0.999829i | \(-0.505889\pi\) | ||||
−0.0185012 | + | 0.999829i | \(0.505889\pi\) | |||||||
\(44\) | − 3.00000i | − 0.452267i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.24264 | −0.625543 | ||||||||
\(47\) | −5.91359 | −0.862586 | −0.431293 | − | 0.902212i | \(-0.641942\pi\) | ||||
−0.431293 | + | 0.902212i | \(0.641942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 4.48528i | − 0.634315i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.44949i | 0.339683i | ||||||||
\(53\) | 7.24264i | 0.994853i | 0.867506 | + | 0.497427i | \(0.165722\pi\) | ||||
−0.867506 | + | 0.497427i | \(0.834278\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.15232i | − 0.290218i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.24264 | −0.951005 | ||||||||
\(59\) | 8.06591 | 1.05009 | 0.525046 | − | 0.851074i | \(-0.324048\pi\) | ||||
0.525046 | + | 0.851074i | \(0.324048\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.01461i | − 0.129908i | −0.997888 | − | 0.0649539i | \(-0.979310\pi\) | ||||
0.997888 | − | 0.0649539i | \(-0.0206900\pi\) | |||||||
\(62\) | 9.08052 | 1.15323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.75736i | 0.217974i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0000 | −1.22169 | −0.610847 | − | 0.791748i | \(-0.709171\pi\) | ||||
−0.610847 | + | 0.791748i | \(0.709171\pi\) | |||||||
\(68\) | 5.91359 | 0.717128 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 1.75736i | − 0.208560i | −0.994548 | − | 0.104280i | \(-0.966746\pi\) | ||||
0.994548 | − | 0.104280i | \(-0.0332538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1.43488i | − 0.167940i | −0.996468 | − | 0.0839699i | \(-0.973240\pi\) | ||||
0.996468 | − | 0.0839699i | \(-0.0267600\pi\) | |||||||
\(74\) | − 0.242641i | − 0.0282064i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 5.91359i | − 0.678335i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.75736 | −0.310227 | −0.155114 | − | 0.987897i | \(-0.549574\pi\) | ||||
−0.155114 | + | 0.987897i | \(0.549574\pi\) | |||||||
\(80\) | −0.717439 | −0.0802121 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 11.8272i | − 1.30609i | ||||||||
\(83\) | −6.63103 | −0.727850 | −0.363925 | − | 0.931428i | \(-0.618564\pi\) | ||||
−0.363925 | + | 0.931428i | \(0.618564\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24264 | 0.460179 | ||||||||
\(86\) | − 0.242641i | − 0.0261646i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | 10.3923 | 1.10158 | 0.550791 | − | 0.834643i | \(-0.314326\pi\) | ||||
0.550791 | + | 0.834643i | \(0.314326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 4.24264i | − 0.442326i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 5.91359i | − 0.609940i | ||||||||
\(95\) | − 4.24264i | − 0.435286i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5592i | 1.37673i | 0.725364 | + | 0.688366i | \(0.241672\pi\) | ||||
−0.725364 | + | 0.688366i | \(0.758328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.48528 | 0.448528 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.49333i | 0.541273i | 0.962682 | + | 0.270637i | \(0.0872342\pi\) | ||||
−0.962682 | + | 0.270637i | \(0.912766\pi\) | |||||||
\(104\) | −2.44949 | −0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.24264 | −0.703467 | ||||||||
\(107\) | − 11.4853i | − 1.11032i | −0.831742 | − | 0.555162i | \(-0.812656\pi\) | ||||
0.831742 | − | 0.555162i | \(-0.187344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.4853 | 1.77057 | 0.885284 | − | 0.465050i | \(-0.153964\pi\) | ||||
0.885284 | + | 0.465050i | \(0.153964\pi\) | |||||||
\(110\) | 2.15232 | 0.205215 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.48528i | 0.798228i | 0.916901 | + | 0.399114i | \(0.130682\pi\) | ||||
−0.916901 | + | 0.399114i | \(0.869318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.04384i | − 0.283839i | ||||||||
\(116\) | − 7.24264i | − 0.672462i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.06591i | 0.742527i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | 1.01461 | 0.0918586 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.08052i | 0.815455i | ||||||||
\(125\) | 6.80511 | 0.608668 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.24264 | 0.287738 | 0.143869 | − | 0.989597i | \(-0.454046\pi\) | ||||
0.143869 | + | 0.989597i | \(0.454046\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.75736 | −0.154131 | ||||||||
\(131\) | −5.19615 | −0.453990 | −0.226995 | − | 0.973896i | \(-0.572890\pi\) | ||||
−0.226995 | + | 0.973896i | \(0.572890\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 10.0000i | − 0.863868i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.91359i | 0.507086i | ||||||||
\(137\) | 2.48528i | 0.212332i | 0.994348 | + | 0.106166i | \(0.0338575\pi\) | ||||
−0.994348 | + | 0.106166i | \(0.966143\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 0.594346i | − 0.0504118i | −0.999682 | − | 0.0252059i | \(-0.991976\pi\) | ||||
0.999682 | − | 0.0252059i | \(-0.00802413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.75736 | 0.147474 | ||||||||
\(143\) | 7.34847 | 0.614510 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 5.19615i | − 0.431517i | ||||||||
\(146\) | 1.43488 | 0.118751 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.242641 | 0.0199449 | ||||||||
\(149\) | − 3.51472i | − 0.287937i | −0.989582 | − | 0.143968i | \(-0.954014\pi\) | ||||
0.989582 | − | 0.143968i | \(-0.0459864\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.24264 | 0.426640 | 0.213320 | − | 0.976982i | \(-0.431572\pi\) | ||||
0.213320 | + | 0.976982i | \(0.431572\pi\) | |||||||
\(152\) | 5.91359 | 0.479656 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.51472i | 0.523275i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.6969i | 1.17294i | 0.809970 | + | 0.586472i | \(0.199483\pi\) | ||||
−0.809970 | + | 0.586472i | \(0.800517\pi\) | |||||||
\(158\) | − 2.75736i | − 0.219364i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 0.717439i | − 0.0567185i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.24264 | −0.175657 | −0.0878286 | − | 0.996136i | \(-0.527993\pi\) | ||||
−0.0878286 | + | 0.996136i | \(0.527993\pi\) | |||||||
\(164\) | 11.8272 | 0.923548 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 6.63103i | − 0.514668i | ||||||||
\(167\) | 16.1318 | 1.24832 | 0.624159 | − | 0.781298i | \(-0.285442\pi\) | ||||
0.624159 | + | 0.781298i | \(0.285442\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 4.24264i | 0.325396i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.242641 | 0.0185012 | ||||||||
\(173\) | −20.7846 | −1.58022 | −0.790112 | − | 0.612962i | \(-0.789978\pi\) | ||||
−0.790112 | + | 0.612962i | \(0.789978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.3923i | 0.778936i | ||||||||
\(179\) | − 26.4853i | − 1.97960i | −0.142454 | − | 0.989801i | \(-0.545499\pi\) | ||||
0.142454 | − | 0.989801i | \(-0.454501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8272i | 0.879108i | 0.898216 | + | 0.439554i | \(0.144863\pi\) | ||||
−0.898216 | + | 0.439554i | \(0.855137\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.24264 | 0.312772 | ||||||||
\(185\) | 0.174080 | 0.0127986 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 17.7408i | − 1.29733i | ||||||||
\(188\) | 5.91359 | 0.431293 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.24264 | 0.307794 | ||||||||
\(191\) | 8.48528i | 0.613973i | 0.951714 | + | 0.306987i | \(0.0993207\pi\) | ||||
−0.951714 | + | 0.306987i | \(0.900679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.48528 | 0.682765 | 0.341383 | − | 0.939924i | \(-0.389105\pi\) | ||||
0.341383 | + | 0.939924i | \(0.389105\pi\) | |||||||
\(194\) | −13.5592 | −0.973496 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 26.4853i | − 1.88700i | −0.331375 | − | 0.943499i | \(-0.607513\pi\) | ||||
0.331375 | − | 0.943499i | \(-0.392487\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0600i | 1.63468i | 0.576155 | + | 0.817341i | \(0.304553\pi\) | ||||
−0.576155 | + | 0.817341i | \(0.695447\pi\) | |||||||
\(200\) | 4.48528i | 0.317157i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.48528 | 0.592638 | ||||||||
\(206\) | −5.49333 | −0.382738 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 2.44949i | − 0.169842i | ||||||||
\(209\) | −17.7408 | −1.22716 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.242641 | −0.0167041 | −0.00835204 | − | 0.999965i | \(-0.502659\pi\) | ||||
−0.00835204 | + | 0.999965i | \(0.502659\pi\) | |||||||
\(212\) | − 7.24264i | − 0.497427i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.4853 | 0.785118 | ||||||||
\(215\) | 0.174080 | 0.0118721 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.4853i | 1.25198i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.15232i | 0.145109i | ||||||||
\(221\) | 14.4853i | 0.974385i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.15232i | 0.144130i | 0.997400 | + | 0.0720649i | \(0.0229589\pi\) | ||||
−0.997400 | + | 0.0720649i | \(0.977041\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.48528 | −0.564433 | ||||||||
\(227\) | 15.5885 | 1.03464 | 0.517321 | − | 0.855791i | \(-0.326929\pi\) | ||||
0.517321 | + | 0.855791i | \(0.326929\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8564i | 0.915657i | 0.889041 | + | 0.457829i | \(0.151373\pi\) | ||||
−0.889041 | + | 0.457829i | \(0.848627\pi\) | |||||||
\(230\) | 3.04384 | 0.200705 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.24264 | 0.475503 | ||||||||
\(233\) | 18.7279i | 1.22691i | 0.789731 | + | 0.613453i | \(0.210220\pi\) | ||||
−0.789731 | + | 0.613453i | \(0.789780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.24264 | 0.276759 | ||||||||
\(236\) | −8.06591 | −0.525046 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7279i | 0.823301i | 0.911342 | + | 0.411650i | \(0.135048\pi\) | ||||
−0.911342 | + | 0.411650i | \(0.864952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.22538i | 0.465427i | 0.972545 | + | 0.232714i | \(0.0747605\pi\) | ||||
−0.972545 | + | 0.232714i | \(0.925239\pi\) | |||||||
\(242\) | 2.00000i | 0.128565i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.01461i | 0.0649539i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.4853 | 0.921676 | ||||||||
\(248\) | −9.08052 | −0.576614 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.80511i | 0.430393i | ||||||||
\(251\) | 27.4156 | 1.73046 | 0.865230 | − | 0.501375i | \(-0.167172\pi\) | ||||
0.865230 | + | 0.501375i | \(0.167172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.7279 | −0.800198 | ||||||||
\(254\) | 3.24264i | 0.203461i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.30463 | 0.268516 | 0.134258 | − | 0.990946i | \(-0.457135\pi\) | ||||
0.134258 | + | 0.990946i | \(0.457135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 1.75736i | − 0.108987i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 5.19615i | − 0.321019i | ||||||||
\(263\) | − 15.2132i | − 0.938086i | −0.883175 | − | 0.469043i | \(-0.844599\pi\) | ||||
0.883175 | − | 0.469043i | \(-0.155401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 5.19615i | − 0.319197i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.0000 | 0.610847 | ||||||||
\(269\) | −13.9795 | −0.852345 | −0.426173 | − | 0.904642i | \(-0.640138\pi\) | ||||
−0.426173 | + | 0.904642i | \(0.640138\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.21076i | 0.377277i | 0.982047 | + | 0.188639i | \(0.0604075\pi\) | ||||
−0.982047 | + | 0.188639i | \(0.939593\pi\) | |||||||
\(272\) | −5.91359 | −0.358564 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.48528 | −0.150141 | ||||||||
\(275\) | − 13.4558i | − 0.811418i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9706 | 0.779326 | 0.389663 | − | 0.920958i | \(-0.372592\pi\) | ||||
0.389663 | + | 0.920958i | \(0.372592\pi\) | |||||||
\(278\) | 0.594346 | 0.0356465 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 21.2049i | − 1.26050i | −0.776393 | − | 0.630250i | \(-0.782953\pi\) | ||||
0.776393 | − | 0.630250i | \(-0.217047\pi\) | |||||||
\(284\) | 1.75736i | 0.104280i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.34847i | 0.434524i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.9706 | 1.05709 | ||||||||
\(290\) | 5.19615 | 0.305129 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.43488i | 0.0839699i | ||||||||
\(293\) | 0.717439 | 0.0419132 | 0.0209566 | − | 0.999780i | \(-0.493329\pi\) | ||||
0.0209566 | + | 0.999780i | \(0.493329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.78680 | −0.336920 | ||||||||
\(296\) | 0.242641i | 0.0141032i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.51472 | 0.203602 | ||||||||
\(299\) | 10.3923 | 0.601003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.24264i | 0.301680i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.91359i | 0.339168i | ||||||||
\(305\) | 0.727922i | 0.0416807i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9.97204i | − 0.569134i | −0.958656 | − | 0.284567i | \(-0.908150\pi\) | ||||
0.958656 | − | 0.284567i | \(-0.0918499\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.51472 | −0.370011 | ||||||||
\(311\) | −8.95743 | −0.507929 | −0.253965 | − | 0.967214i | \(-0.581735\pi\) | ||||
−0.253965 | + | 0.967214i | \(0.581735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 18.4582i | − 1.04332i | −0.853154 | − | 0.521660i | \(-0.825313\pi\) | ||||
0.853154 | − | 0.521660i | \(-0.174687\pi\) | |||||||
\(314\) | −14.6969 | −0.829396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.75736 | 0.155114 | ||||||||
\(317\) | 1.24264i | 0.0697937i | 0.999391 | + | 0.0348968i | \(0.0111103\pi\) | ||||
−0.999391 | + | 0.0348968i | \(0.988890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.7279 | −1.21653 | ||||||||
\(320\) | 0.717439 | 0.0401061 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 34.9706i | − 1.94581i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.9867i | 0.609430i | ||||||||
\(326\) | − 2.24264i | − 0.124208i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.8272i | 0.653047i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.4558 | −1.83890 | −0.919450 | − | 0.393208i | \(-0.871365\pi\) | ||||
−0.919450 | + | 0.393208i | \(0.871365\pi\) | |||||||
\(332\) | 6.63103 | 0.363925 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.1318i | 0.882694i | ||||||||
\(335\) | 7.17439 | 0.391979 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00000 | −0.272367 | −0.136184 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(338\) | 7.00000i | 0.380750i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.24264 | −0.230089 | ||||||||
\(341\) | 27.2416 | 1.47521 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.242641i | 0.0130823i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 20.7846i | − 1.11739i | ||||||||
\(347\) | − 2.48528i | − 0.133417i | −0.997773 | − | 0.0667084i | \(-0.978750\pi\) | ||||
0.997773 | − | 0.0667084i | \(-0.0212497\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 2.27541i | − 0.121800i | −0.998144 | − | 0.0608999i | \(-0.980603\pi\) | ||||
0.998144 | − | 0.0608999i | \(-0.0193971\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | −8.95743 | −0.476756 | −0.238378 | − | 0.971172i | \(-0.576616\pi\) | ||||
−0.238378 | + | 0.971172i | \(0.576616\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.26080i | 0.0669162i | ||||||||
\(356\) | −10.3923 | −0.550791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.4853 | 1.39979 | ||||||||
\(359\) | − 18.0000i | − 0.950004i | −0.879985 | − | 0.475002i | \(-0.842447\pi\) | ||||
0.879985 | − | 0.475002i | \(-0.157553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.9706 | −0.840556 | ||||||||
\(362\) | −11.8272 | −0.621623 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.02944i | 0.0538832i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 15.4144i | − 0.804624i | −0.915503 | − | 0.402312i | \(-0.868207\pi\) | ||||
0.915503 | − | 0.402312i | \(-0.131793\pi\) | |||||||
\(368\) | 4.24264i | 0.221163i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.174080i | 0.00904998i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.4558 | −1.52517 | −0.762583 | − | 0.646891i | \(-0.776069\pi\) | ||||
−0.762583 | + | 0.646891i | \(0.776069\pi\) | |||||||
\(374\) | 17.7408 | 0.917354 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.91359i | 0.304970i | ||||||||
\(377\) | 17.7408 | 0.913696 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4853 | 0.641326 | 0.320663 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320663 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(380\) | 4.24264i | 0.217643i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.48528 | −0.434145 | ||||||||
\(383\) | −22.2195 | −1.13536 | −0.567681 | − | 0.823248i | \(-0.692159\pi\) | ||||
−0.567681 | + | 0.823248i | \(0.692159\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.48528i | 0.482788i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 13.5592i | − 0.688366i | ||||||||
\(389\) | 31.4558i | 1.59487i | 0.603402 | + | 0.797437i | \(0.293812\pi\) | ||||
−0.603402 | + | 0.797437i | \(0.706188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 25.0892i | − 1.26882i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 26.4853 | 1.33431 | ||||||||
\(395\) | 1.97824 | 0.0995359 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 13.8564i | − 0.695433i | −0.937600 | − | 0.347717i | \(-0.886957\pi\) | ||||
0.937600 | − | 0.347717i | \(-0.113043\pi\) | |||||||
\(398\) | −23.0600 | −1.15589 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.48528 | −0.224264 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.2426 | −1.10798 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 0.727922i | − 0.0360818i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9941i | 0.741411i | 0.928750 | + | 0.370706i | \(0.120884\pi\) | ||||
−0.928750 | + | 0.370706i | \(0.879116\pi\) | |||||||
\(410\) | 8.48528i | 0.419058i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 5.49333i | − 0.270637i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.75736 | 0.233530 | ||||||||
\(416\) | 2.44949 | 0.120096 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 17.7408i | − 0.867730i | ||||||||
\(419\) | −23.6544 | −1.15559 | −0.577796 | − | 0.816181i | \(-0.696087\pi\) | ||||
−0.577796 | + | 0.816181i | \(0.696087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.2426 | −0.694144 | −0.347072 | − | 0.937839i | \(-0.612824\pi\) | ||||
−0.347072 | + | 0.937839i | \(0.612824\pi\) | |||||||
\(422\) | − 0.242641i | − 0.0118116i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.24264 | 0.351734 | ||||||||
\(425\) | 26.5241 | 1.28661 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.4853i | 0.555162i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.174080i | 0.00839488i | ||||||||
\(431\) | 3.51472i | 0.169298i | 0.996411 | + | 0.0846490i | \(0.0269769\pi\) | ||||
−0.996411 | + | 0.0846490i | \(0.973023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 3.46410i | − 0.166474i | −0.996530 | − | 0.0832370i | \(-0.973474\pi\) | ||||
0.996530 | − | 0.0832370i | \(-0.0265259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.4853 | −0.885284 | ||||||||
\(437\) | −25.0892 | −1.20018 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.8493i | 0.804171i | 0.915602 | + | 0.402086i | \(0.131715\pi\) | ||||
−0.915602 | + | 0.402086i | \(0.868285\pi\) | |||||||
\(440\) | −2.15232 | −0.102608 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.4853 | −0.688995 | ||||||||
\(443\) | − 16.4558i | − 0.781841i | −0.920425 | − | 0.390920i | \(-0.872157\pi\) | ||||
0.920425 | − | 0.390920i | \(-0.127843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.45584 | −0.353441 | ||||||||
\(446\) | −2.15232 | −0.101915 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 1.75736i | − 0.0829349i | −0.999140 | − | 0.0414675i | \(-0.986797\pi\) | ||||
0.999140 | − | 0.0414675i | \(-0.0132033\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 35.4815i | − 1.67076i | ||||||||
\(452\) | − 8.48528i | − 0.399114i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.5885i | 0.731603i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0000 | −1.07589 | −0.537947 | − | 0.842978i | \(-0.680800\pi\) | ||||
−0.537947 | + | 0.842978i | \(0.680800\pi\) | |||||||
\(458\) | −13.8564 | −0.647467 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.04384i | 0.141920i | ||||||||
\(461\) | −32.6118 | −1.51888 | −0.759441 | − | 0.650576i | \(-0.774528\pi\) | ||||
−0.759441 | + | 0.650576i | \(0.774528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4558 | −1.36893 | −0.684465 | − | 0.729046i | \(-0.739964\pi\) | ||||
−0.684465 | + | 0.729046i | \(0.739964\pi\) | |||||||
\(464\) | 7.24264i | 0.336231i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.7279 | −0.867554 | ||||||||
\(467\) | 39.7862 | 1.84108 | 0.920542 | − | 0.390643i | \(-0.127747\pi\) | ||||
0.920542 | + | 0.390643i | \(0.127747\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.24264i | 0.195698i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 8.06591i | − 0.371264i | ||||||||
\(473\) | − 0.727922i | − 0.0334699i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 26.5241i | − 1.21701i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.7279 | −0.582162 | ||||||||
\(479\) | 12.0013 | 0.548352 | 0.274176 | − | 0.961680i | \(-0.411595\pi\) | ||||
0.274176 | + | 0.961680i | \(0.411595\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.594346i | 0.0270998i | ||||||||
\(482\) | −7.22538 | −0.329107 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | − 9.72792i | − 0.441722i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.2132 | −0.644062 | −0.322031 | − | 0.946729i | \(-0.604365\pi\) | ||||
−0.322031 | + | 0.946729i | \(0.604365\pi\) | |||||||
\(488\) | −1.01461 | −0.0459293 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 13.9706i | − 0.630483i | −0.949012 | − | 0.315241i | \(-0.897915\pi\) | ||||
0.949012 | − | 0.315241i | \(-0.102085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 42.8300i | − 1.92897i | ||||||||
\(494\) | 14.4853i | 0.651724i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 9.08052i | − 0.407727i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.9411 | 1.42988 | 0.714941 | − | 0.699185i | \(-0.246454\pi\) | ||||
0.714941 | + | 0.699185i | \(0.246454\pi\) | |||||||
\(500\) | −6.80511 | −0.304334 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.4156i | 1.22362i | ||||||||
\(503\) | 31.0028 | 1.38235 | 0.691174 | − | 0.722688i | \(-0.257094\pi\) | ||||
0.691174 | + | 0.722688i | \(0.257094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − 12.7279i | − 0.565825i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.24264 | −0.143869 | ||||||||
\(509\) | 17.1974 | 0.762262 | 0.381131 | − | 0.924521i | \(-0.375535\pi\) | ||||
0.381131 | + | 0.924521i | \(0.375535\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.30463i | 0.189869i | ||||||||
\(515\) | − 3.94113i | − 0.173667i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 17.7408i | − 0.780238i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.75736 | 0.0770653 | ||||||||
\(521\) | −33.8726 | −1.48399 | −0.741993 | − | 0.670408i | \(-0.766119\pi\) | ||||
−0.741993 | + | 0.670408i | \(0.766119\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 6.75412i | − 0.295337i | −0.989037 | − | 0.147669i | \(-0.952823\pi\) | ||||
0.989037 | − | 0.147669i | \(-0.0471769\pi\) | |||||||
\(524\) | 5.19615 | 0.226995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.2132 | 0.663327 | ||||||||
\(527\) | 53.6985i | 2.33914i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.00000 | 0.217391 | ||||||||
\(530\) | 5.19615 | 0.225706 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.9706i | 1.25485i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.23999i | 0.356246i | ||||||||
\(536\) | 10.0000i | 0.431934i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 13.9795i | − 0.602699i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7279 | 0.633203 | 0.316601 | − | 0.948559i | \(-0.397458\pi\) | ||||
0.316601 | + | 0.948559i | \(0.397458\pi\) | |||||||
\(542\) | −6.21076 | −0.266775 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 5.91359i | − 0.253543i | ||||||||
\(545\) | −13.2621 | −0.568084 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.6985 | −1.69738 | −0.848692 | − | 0.528887i | \(-0.822610\pi\) | ||||
−0.848692 | + | 0.528887i | \(0.822610\pi\) | |||||||
\(548\) | − 2.48528i | − 0.106166i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.4558 | 0.573759 | ||||||||
\(551\) | −42.8300 | −1.82462 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.9706i | 0.551066i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.594346i | 0.0252059i | ||||||||
\(557\) | − 9.72792i | − 0.412185i | −0.978532 | − | 0.206093i | \(-0.933925\pi\) | ||||
0.978532 | − | 0.206093i | \(-0.0660748\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.594346i | 0.0251382i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | 34.5900 | 1.45780 | 0.728898 | − | 0.684622i | \(-0.240033\pi\) | ||||
0.728898 | + | 0.684622i | \(0.240033\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 6.08767i | − 0.256110i | ||||||||
\(566\) | 21.2049 | 0.891307 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.75736 | −0.0737372 | ||||||||
\(569\) | − 10.2426i | − 0.429394i | −0.976681 | − | 0.214697i | \(-0.931124\pi\) | ||||
0.976681 | − | 0.214697i | \(-0.0688764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.72792 | 0.365252 | 0.182626 | − | 0.983182i | \(-0.441540\pi\) | ||||
0.182626 | + | 0.983182i | \(0.441540\pi\) | |||||||
\(572\) | −7.34847 | −0.307255 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 19.0294i | − 0.793582i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.6895i | 0.445009i | 0.974932 | + | 0.222504i | \(0.0714232\pi\) | ||||
−0.974932 | + | 0.222504i | \(0.928577\pi\) | |||||||
\(578\) | 17.9706i | 0.747477i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.19615i | 0.215758i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.7279 | −0.899879 | ||||||||
\(584\) | −1.43488 | −0.0593757 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.717439i | 0.0296371i | ||||||||
\(587\) | −5.19615 | −0.214468 | −0.107234 | − | 0.994234i | \(-0.534199\pi\) | ||||
−0.107234 | + | 0.994234i | \(0.534199\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.6985 | 2.21261 | ||||||||
\(590\) | − 5.78680i | − 0.238239i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.242641 | −0.00997247 | ||||||||
\(593\) | −23.4803 | −0.964220 | −0.482110 | − | 0.876111i | \(-0.660129\pi\) | ||||
−0.482110 | + | 0.876111i | \(0.660129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.51472i | 0.143968i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.3923i | 0.424973i | ||||||||
\(599\) | 7.45584i | 0.304638i | 0.988331 | + | 0.152319i | \(0.0486740\pi\) | ||||
−0.988331 | + | 0.152319i | \(0.951326\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.3572i | 0.952760i | 0.879240 | + | 0.476380i | \(0.158051\pi\) | ||||
−0.879240 | + | 0.476380i | \(0.841949\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.24264 | −0.213320 | ||||||||
\(605\) | −1.43488 | −0.0583361 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0672i | 0.814501i | 0.913316 | + | 0.407251i | \(0.133512\pi\) | ||||
−0.913316 | + | 0.407251i | \(0.866488\pi\) | |||||||
\(608\) | −5.91359 | −0.239828 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.727922 | −0.0294727 | ||||||||
\(611\) | 14.4853i | 0.586012i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.2132 | −1.50303 | −0.751514 | − | 0.659718i | \(-0.770676\pi\) | ||||
−0.751514 | + | 0.659718i | \(0.770676\pi\) | |||||||
\(614\) | 9.97204 | 0.402439 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 17.6985i | − 0.712514i | −0.934388 | − | 0.356257i | \(-0.884053\pi\) | ||||
0.934388 | − | 0.356257i | \(-0.115947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.15978i | 0.247582i | 0.992308 | + | 0.123791i | \(0.0395053\pi\) | ||||
−0.992308 | + | 0.123791i | \(0.960495\pi\) | |||||||
\(620\) | − 6.51472i | − 0.261637i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 8.95743i | − 0.359160i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.5442 | 0.701766 | ||||||||
\(626\) | 18.4582 | 0.737739 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 14.6969i | − 0.586472i | ||||||||
\(629\) | 1.43488 | 0.0572123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.7574 | 0.985575 | 0.492787 | − | 0.870150i | \(-0.335978\pi\) | ||||
0.492787 | + | 0.870150i | \(0.335978\pi\) | |||||||
\(632\) | 2.75736i | 0.109682i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.24264 | −0.0493516 | ||||||||
\(635\) | −2.32640 | −0.0923202 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 21.7279i | − 0.860217i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.717439i | 0.0283593i | ||||||||
\(641\) | 17.6985i | 0.699048i | 0.936927 | + | 0.349524i | \(0.113657\pi\) | ||||
−0.936927 | + | 0.349524i | \(0.886343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.0174i | 1.26264i | 0.775520 | + | 0.631322i | \(0.217488\pi\) | ||||
−0.775520 | + | 0.631322i | \(0.782512\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.9706 | 1.37590 | ||||||||
\(647\) | −32.4377 | −1.27526 | −0.637629 | − | 0.770344i | \(-0.720085\pi\) | ||||
−0.637629 | + | 0.770344i | \(0.720085\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.1977i | 0.949844i | ||||||||
\(650\) | −10.9867 | −0.430932 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.24264 | 0.0878286 | ||||||||
\(653\) | 19.2426i | 0.753023i | 0.926412 | + | 0.376511i | \(0.122876\pi\) | ||||
−0.926412 | + | 0.376511i | \(0.877124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.72792 | 0.145662 | ||||||||
\(656\) | −11.8272 | −0.461774 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000i | 0.233727i | 0.993148 | + | 0.116863i | \(0.0372840\pi\) | ||||
−0.993148 | + | 0.116863i | \(0.962716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.6556i | 1.38684i | 0.720532 | + | 0.693422i | \(0.243898\pi\) | ||||
−0.720532 | + | 0.693422i | \(0.756102\pi\) | |||||||
\(662\) | − 33.4558i | − 1.30030i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.63103i | 0.257334i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.7279 | −1.18979 | ||||||||
\(668\) | −16.1318 | −0.624159 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.17439i | 0.277171i | ||||||||
\(671\) | 3.04384 | 0.117506 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.9706 | 0.692714 | 0.346357 | − | 0.938103i | \(-0.387419\pi\) | ||||
0.346357 | + | 0.938103i | \(0.387419\pi\) | |||||||
\(674\) | − 5.00000i | − 0.192593i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | 2.15232 | 0.0827203 | 0.0413601 | − | 0.999144i | \(-0.486831\pi\) | ||||
0.0413601 | + | 0.999144i | \(0.486831\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 4.24264i | − 0.162698i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.2416i | 1.04313i | ||||||||
\(683\) | 7.97056i | 0.304985i | 0.988305 | + | 0.152493i | \(0.0487300\pi\) | ||||
−0.988305 | + | 0.152493i | \(0.951270\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.78304i | − 0.0681264i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.242641 | −0.00925059 | ||||||||
\(689\) | 17.7408 | 0.675870 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 28.5533i | − 1.08622i | −0.839661 | − | 0.543110i | \(-0.817247\pi\) | ||||
0.839661 | − | 0.543110i | \(-0.182753\pi\) | |||||||
\(692\) | 20.7846 | 0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.48528 | 0.0943400 | ||||||||
\(695\) | 0.426407i | 0.0161745i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 69.9411 | 2.64921 | ||||||||
\(698\) | 2.27541 | 0.0861255 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.6985i | 0.781771i | 0.920439 | + | 0.390885i | \(0.127831\pi\) | ||||
−0.920439 | + | 0.390885i | \(0.872169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.43488i | − 0.0541174i | ||||||||
\(704\) | − 3.00000i | − 0.113067i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 8.95743i | − 0.337117i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.9706 | 1.01290 | 0.506450 | − | 0.862269i | \(-0.330957\pi\) | ||||
0.506450 | + | 0.862269i | \(0.330957\pi\) | |||||||
\(710\) | −1.26080 | −0.0473169 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 10.3923i | − 0.389468i | ||||||||
\(713\) | 38.5254 | 1.44279 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.27208 | −0.197165 | ||||||||
\(716\) | 26.4853i | 0.989801i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.0000 | 0.671754 | ||||||||
\(719\) | −16.1318 | −0.601615 | −0.300808 | − | 0.953685i | \(-0.597256\pi\) | ||||
−0.300808 | + | 0.953685i | \(0.597256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 15.9706i | − 0.594363i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 11.8272i | − 0.439554i | ||||||||
\(725\) | − 32.4853i | − 1.20647i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 11.7041i | − 0.434081i | −0.976163 | − | 0.217040i | \(-0.930360\pi\) | ||||
0.976163 | − | 0.217040i | \(-0.0696403\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.02944 | −0.0381012 | ||||||||
\(731\) | 1.43488 | 0.0530709 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4.72490i | − 0.174518i | −0.996186 | − | 0.0872591i | \(-0.972189\pi\) | ||||
0.996186 | − | 0.0872591i | \(-0.0278108\pi\) | |||||||
\(734\) | 15.4144 | 0.568955 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.24264 | −0.156386 | ||||||||
\(737\) | − 30.0000i | − 1.10506i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.4558 | 0.568552 | 0.284276 | − | 0.958742i | \(-0.408247\pi\) | ||||
0.284276 | + | 0.958742i | \(0.408247\pi\) | |||||||
\(740\) | −0.174080 | −0.00639930 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.4853i | 1.41189i | 0.708268 | + | 0.705944i | \(0.249477\pi\) | ||||
−0.708268 | + | 0.705944i | \(0.750523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.52160i | 0.0923841i | ||||||||
\(746\) | − 29.4558i | − 1.07846i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.7408i | 0.648667i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.2426 | 1.28602 | 0.643011 | − | 0.765857i | \(-0.277685\pi\) | ||||
0.643011 | + | 0.765857i | \(0.277685\pi\) | |||||||
\(752\) | −5.91359 | −0.215646 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.7408i | 0.646081i | ||||||||
\(755\) | −3.76127 | −0.136887 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.7574 | −1.22693 | −0.613466 | − | 0.789721i | \(-0.710225\pi\) | ||||
−0.613466 | + | 0.789721i | \(0.710225\pi\) | |||||||
\(758\) | 12.4853i | 0.453486i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.24264 | −0.153897 | ||||||||
\(761\) | −29.5680 | −1.07184 | −0.535919 | − | 0.844270i | \(-0.680035\pi\) | ||||
−0.535919 | + | 0.844270i | \(0.680035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 8.48528i | − 0.306987i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 22.2195i | − 0.802823i | ||||||||
\(767\) | − 19.7574i | − 0.713397i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.84895i | 0.355162i | 0.984106 | + | 0.177581i | \(0.0568272\pi\) | ||||
−0.984106 | + | 0.177581i | \(0.943173\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.48528 | −0.341383 | ||||||||
\(773\) | 16.1318 | 0.580221 | 0.290111 | − | 0.956993i | \(-0.406308\pi\) | ||||
0.290111 | + | 0.956993i | \(0.406308\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.7287i | 1.46302i | ||||||||
\(776\) | 13.5592 | 0.486748 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.4558 | −1.12775 | ||||||||
\(779\) | − 69.9411i | − 2.50590i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.27208 | 0.188650 | ||||||||
\(782\) | 25.0892 | 0.897190 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 10.5442i | − 0.376337i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.1915i | 1.14750i | 0.819029 | + | 0.573752i | \(0.194513\pi\) | ||||
−0.819029 | + | 0.573752i | \(0.805487\pi\) | |||||||
\(788\) | 26.4853i | 0.943499i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.97824i | 0.0703825i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.48528 | −0.0882549 | ||||||||
\(794\) | 13.8564 | 0.491745 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 23.0600i | − 0.817341i | ||||||||
\(797\) | −6.45695 | −0.228717 | −0.114358 | − | 0.993440i | \(-0.536481\pi\) | ||||
−0.114358 | + | 0.993440i | \(0.536481\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.9706 | 1.23717 | ||||||||
\(800\) | − 4.48528i | − 0.158579i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.30463 | 0.151907 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 22.2426i | − 0.783464i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.02944i | 0.247142i | 0.992336 | + | 0.123571i | \(0.0394346\pi\) | ||||
−0.992336 | + | 0.123571i | \(0.960565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.727922 | 0.0255137 | ||||||||
\(815\) | 1.60896 | 0.0563593 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.43488i | − 0.0502000i | ||||||||
\(818\) | −14.9941 | −0.524257 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.48528 | −0.296319 | ||||||||
\(821\) | 40.7574i | 1.42244i | 0.702969 | + | 0.711221i | \(0.251857\pi\) | ||||
−0.702969 | + | 0.711221i | \(0.748143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.9411 | 1.04368 | 0.521841 | − | 0.853043i | \(-0.325245\pi\) | ||||
0.521841 | + | 0.853043i | \(0.325245\pi\) | |||||||
\(824\) | 5.49333 | 0.191369 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.9706i | 1.32037i | 0.751105 | + | 0.660183i | \(0.229521\pi\) | ||||
−0.751105 | + | 0.660183i | \(0.770479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0880i | 0.454564i | 0.973829 | + | 0.227282i | \(0.0729840\pi\) | ||||
−0.973829 | + | 0.227282i | \(0.927016\pi\) | |||||||
\(830\) | 4.75736i | 0.165130i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.44949i | 0.0849208i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.5736 | −0.400521 | ||||||||
\(836\) | 17.7408 | 0.613578 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 23.6544i | − 0.817126i | ||||||||
\(839\) | −10.2182 | −0.352772 | −0.176386 | − | 0.984321i | \(-0.556441\pi\) | ||||
−0.176386 | + | 0.984321i | \(0.556441\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4558 | −0.808822 | ||||||||
\(842\) | − 14.2426i | − 0.490834i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.242641 | 0.00835204 | ||||||||
\(845\) | −5.02207 | −0.172765 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.24264i | 0.248713i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.5241i | 0.909770i | ||||||||
\(851\) | − 1.02944i | − 0.0352887i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.9164i | 1.26399i | 0.774971 | + | 0.631997i | \(0.217765\pi\) | ||||
−0.774971 | + | 0.631997i | \(0.782235\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.4853 | −0.392559 | ||||||||
\(857\) | 33.8726 | 1.15707 | 0.578533 | − | 0.815659i | \(-0.303625\pi\) | ||||
0.578533 | + | 0.815659i | \(0.303625\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 9.37769i | − 0.319963i | −0.987120 | − | 0.159981i | \(-0.948857\pi\) | ||||
0.987120 | − | 0.159981i | \(-0.0511434\pi\) | |||||||
\(860\) | −0.174080 | −0.00593607 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.51472 | −0.119712 | ||||||||
\(863\) | 33.5147i | 1.14085i | 0.821348 | + | 0.570427i | \(0.193222\pi\) | ||||
−0.821348 | + | 0.570427i | \(0.806778\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.9117 | 0.507013 | ||||||||
\(866\) | 3.46410 | 0.117715 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 8.27208i | − 0.280611i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4949i | 0.829978i | ||||||||
\(872\) | − 18.4853i | − 0.625991i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 25.0892i | − 0.848656i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.48528 | 0.151457 | 0.0757286 | − | 0.997128i | \(-0.475872\pi\) | ||||
0.0757286 | + | 0.997128i | \(0.475872\pi\) | |||||||
\(878\) | −16.8493 | −0.568635 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 2.15232i | − 0.0725546i | ||||||||
\(881\) | −19.0016 | −0.640179 | −0.320090 | − | 0.947387i | \(-0.603713\pi\) | ||||
−0.320090 | + | 0.947387i | \(0.603713\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.4558 | 1.39510 | 0.697550 | − | 0.716536i | \(-0.254273\pi\) | ||||
0.697550 | + | 0.716536i | \(0.254273\pi\) | |||||||
\(884\) | − 14.4853i | − 0.487193i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.4558 | 0.552845 | ||||||||
\(887\) | 10.5664 | 0.354784 | 0.177392 | − | 0.984140i | \(-0.443234\pi\) | ||||
0.177392 | + | 0.984140i | \(0.443234\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 7.45584i | − 0.249920i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 2.15232i | − 0.0720649i | ||||||||
\(893\) | − 34.9706i | − 1.17025i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.0016i | 0.635153i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.75736 | 0.0586438 | ||||||||
\(899\) | 65.7669 | 2.19345 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 42.8300i | − 1.42687i | ||||||||
\(902\) | 35.4815 | 1.18141 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.48528 | 0.282216 | ||||||||
\(905\) | − 8.48528i | − 0.282060i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.6985 | −1.05253 | −0.526265 | − | 0.850320i | \(-0.676408\pi\) | ||||
−0.526265 | + | 0.850320i | \(0.676408\pi\) | |||||||
\(908\) | −15.5885 | −0.517321 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 6.72792i | − 0.222906i | −0.993770 | − | 0.111453i | \(-0.964450\pi\) | ||||
0.993770 | − | 0.111453i | \(-0.0355505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 19.8931i | − 0.658365i | ||||||||
\(914\) | − 23.0000i | − 0.760772i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 13.8564i | − 0.457829i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.4853 | 1.20354 | 0.601769 | − | 0.798670i | \(-0.294463\pi\) | ||||
0.601769 | + | 0.798670i | \(0.294463\pi\) | |||||||
\(920\) | −3.04384 | −0.100352 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 32.6118i | − 1.07401i | ||||||||
\(923\) | −4.30463 | −0.141689 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.08831 | 0.0357835 | ||||||||
\(926\) | − 29.4558i | − 0.967979i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.24264 | −0.237751 | ||||||||
\(929\) | −31.0028 | −1.01717 | −0.508585 | − | 0.861012i | \(-0.669831\pi\) | ||||
−0.508585 | + | 0.861012i | \(0.669831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 18.7279i | − 0.613453i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39.7862i | 1.30184i | ||||||||
\(935\) | 12.7279i | 0.416248i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 35.1844i | − 1.14942i | −0.818356 | − | 0.574712i | \(-0.805114\pi\) | ||||
0.818356 | − | 0.574712i | \(-0.194886\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.24264 | −0.138380 | ||||||||
\(941\) | 27.5897 | 0.899399 | 0.449700 | − | 0.893180i | \(-0.351531\pi\) | ||||
0.449700 | + | 0.893180i | \(0.351531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 50.1785i | − 1.63404i | ||||||||
\(944\) | 8.06591 | 0.262523 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.727922 | 0.0236668 | ||||||||
\(947\) | − 10.9706i | − 0.356495i | −0.983986 | − | 0.178248i | \(-0.942957\pi\) | ||||
0.983986 | − | 0.178248i | \(-0.0570428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.51472 | −0.114093 | ||||||||
\(950\) | 26.5241 | 0.860556 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 17.6985i | − 0.573310i | −0.958034 | − | 0.286655i | \(-0.907457\pi\) | ||||
0.958034 | − | 0.286655i | \(-0.0925434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 6.08767i | − 0.196992i | ||||||||
\(956\) | − 12.7279i | − 0.411650i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0013i | 0.387743i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −51.4558 | −1.65987 | ||||||||
\(962\) | −0.594346 | −0.0191625 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 7.22538i | − 0.232714i | ||||||||
\(965\) | −6.80511 | −0.219064 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.7279 | 1.53483 | 0.767413 | − | 0.641153i | \(-0.221544\pi\) | ||||
0.767413 | + | 0.641153i | \(0.221544\pi\) | |||||||
\(968\) | − 2.00000i | − 0.0642824i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.72792 | 0.312345 | ||||||||
\(971\) | 27.0675 | 0.868637 | 0.434318 | − | 0.900759i | \(-0.356989\pi\) | ||||
0.434318 | + | 0.900759i | \(0.356989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 14.2132i | − 0.455420i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 1.01461i | − 0.0324769i | ||||||||
\(977\) | 40.2426i | 1.28748i | 0.765246 | + | 0.643738i | \(0.222617\pi\) | ||||
−0.765246 | + | 0.643738i | \(0.777383\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.1769i | 0.996419i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.9706 | 0.445819 | ||||||||
\(983\) | −47.3087 | −1.50891 | −0.754457 | − | 0.656349i | \(-0.772100\pi\) | ||||
−0.754457 | + | 0.656349i | \(0.772100\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.0016i | 0.605440i | ||||||||
\(986\) | 42.8300 | 1.36399 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.4853 | −0.460838 | ||||||||
\(989\) | − 1.02944i | − 0.0327342i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.2132 | 1.65861 | 0.829304 | − | 0.558798i | \(-0.188737\pi\) | ||||
0.829304 | + | 0.558798i | \(0.188737\pi\) | |||||||
\(992\) | 9.08052 | 0.288307 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 16.5442i | − 0.524485i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 38.9456i | − 1.23342i | −0.787190 | − | 0.616711i | \(-0.788465\pi\) | ||||
0.787190 | − | 0.616711i | \(-0.211535\pi\) | |||||||
\(998\) | 31.9411i | 1.01108i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))