Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(649,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1620.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.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: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.301925376.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 14x^{4} + 43x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(1.56613i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.649 |
Dual form | 1620.2.d.c.649.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.20860 | + | 0.349411i | −0.987716 | + | 0.156261i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.26496i | 0.856073i | 0.903761 | + | 0.428036i | \(0.140795\pi\) | ||||
−0.903761 | + | 0.428036i | \(0.859205\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.54722 | −0.768017 | −0.384009 | − | 0.923330i | \(-0.625457\pi\) | ||||
−0.384009 | + | 0.923330i | \(0.625457\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.02510i | − | 1.39371i | −0.717212 | − | 0.696856i | \(-0.754582\pi\) | ||
0.717212 | − | 0.696856i | \(-0.245418\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.72392i | − | 1.38825i | −0.719852 | − | 0.694127i | \(-0.755791\pi\) | ||
0.719852 | − | 0.694127i | \(-0.244209\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.86997 | 0.429002 | 0.214501 | − | 0.976724i | \(-0.431188\pi\) | ||||
0.214501 | + | 0.976724i | \(0.431188\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.39722i | 1.12540i | 0.826662 | + | 0.562699i | \(0.190237\pi\) | ||||
−0.826662 | + | 0.562699i | \(0.809763\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.75582 | − | 1.54342i | 0.951165 | − | 0.308684i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.38162 | 1.68499 | 0.842495 | − | 0.538705i | \(-0.181086\pi\) | ||||
0.842495 | + | 0.538705i | \(0.181086\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.791400 | − | 5.00238i | −0.133771 | − | 0.845557i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.59165i | 0.426065i | 0.977045 | + | 0.213032i | \(0.0683340\pi\) | ||||
−0.977045 | + | 0.213032i | \(0.931666\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.96442 | 0.619139 | 0.309569 | − | 0.950877i | \(-0.399815\pi\) | ||||
0.309569 | + | 0.950877i | \(0.399815\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2084i | 1.55677i | 0.627790 | + | 0.778383i | \(0.283960\pi\) | ||||
−0.627790 | + | 0.778383i | \(0.716040\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.07095i | − | 0.156214i | −0.996945 | − | 0.0781070i | \(-0.975112\pi\) | ||
0.996945 | − | 0.0781070i | \(-0.0248876\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.86997 | 0.267139 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7036i | 1.47025i | 0.677931 | + | 0.735125i | \(0.262877\pi\) | ||||
−0.677931 | + | 0.735125i | \(0.737123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.62580 | − | 0.890028i | 0.758583 | − | 0.120011i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.58280 | 0.206063 | 0.103032 | − | 0.994678i | \(-0.467146\pi\) | ||||
0.103032 | + | 0.994678i | \(0.467146\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.869975 | 0.111389 | 0.0556944 | − | 0.998448i | \(-0.482263\pi\) | ||||
0.0556944 | + | 0.998448i | \(0.482263\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.75582 | + | 11.0984i | 0.217783 | + | 1.37659i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.85661i | 0.593329i | 0.954982 | + | 0.296664i | \(0.0958743\pi\) | ||||
−0.954982 | + | 0.296664i | \(0.904126\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.86997 | −0.221925 | −0.110963 | − | 0.993825i | \(-0.535393\pi\) | ||||
−0.110963 | + | 0.993825i | \(0.535393\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.87652i | 0.453713i | 0.973928 | + | 0.226856i | \(0.0728448\pi\) | ||||
−0.973928 | + | 0.226856i | \(0.927155\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.76935i | − | 0.657479i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.2516 | 1.49092 | 0.745461 | − | 0.666550i | \(-0.232230\pi\) | ||||
0.745461 | + | 0.666550i | \(0.232230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 14.7032i | − | 1.61388i | −0.590632 | − | 0.806941i | \(-0.701122\pi\) | ||
0.590632 | − | 0.806941i | \(-0.298878\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | + | 12.6418i | 0.216930 | + | 1.37120i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.4172 | 1.42222 | 0.711110 | − | 0.703081i | \(-0.248193\pi\) | ||||
0.711110 | + | 0.703081i | \(0.248193\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.3816 | 1.19312 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.13003 | + | 0.653390i | −0.423732 | + | 0.0670364i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 17.6669i | − | 1.79381i | −0.442227 | − | 0.896903i | \(-0.645812\pi\) | ||
0.442227 | − | 0.896903i | \(-0.354188\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.32275 | −0.529633 | −0.264817 | − | 0.964299i | \(-0.585311\pi\) | ||||
−0.264817 | + | 0.964299i | \(0.585311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.01547i | − | 0.592722i | −0.955076 | − | 0.296361i | \(-0.904227\pi\) | ||
0.955076 | − | 0.296361i | \(-0.0957731\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.69840i | 0.454212i | 0.973870 | + | 0.227106i | \(0.0729263\pi\) | ||||
−0.973870 | + | 0.227106i | \(0.927074\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.64167 | 0.636157 | 0.318078 | − | 0.948064i | \(-0.396962\pi\) | ||||
0.318078 | + | 0.948064i | \(0.396962\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.8000i | − | 1.20413i | −0.798448 | − | 0.602064i | \(-0.794345\pi\) | ||
0.798448 | − | 0.602064i | \(-0.205655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.88585 | − | 11.9203i | −0.175856 | − | 1.11157i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.9644 | 1.18845 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.51165 | −0.410150 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.96442 | + | 5.07053i | −0.891245 | + | 0.453522i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.8103i | − | 1.13673i | −0.822775 | − | 0.568367i | \(-0.807576\pi\) | ||
0.822775 | − | 0.568367i | \(-0.192424\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.51165 | −0.831037 | −0.415518 | − | 0.909585i | \(-0.636400\pi\) | ||||
−0.415518 | + | 0.909585i | \(0.636400\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.23541i | 0.367257i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4933i | 0.981936i | 0.871178 | + | 0.490968i | \(0.163357\pi\) | ||||
−0.871178 | + | 0.490968i | \(0.836643\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.5116 | 0.976405 | 0.488203 | − | 0.872730i | \(-0.337653\pi\) | ||||
0.488203 | + | 0.872730i | \(0.337653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.8000i | 1.07039i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.62580 | + | 1.04823i | −0.550243 | + | 0.0870510i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.7044 | 1.61425 | 0.807123 | − | 0.590384i | \(-0.201024\pi\) | ||||
0.807123 | + | 0.590384i | \(0.201024\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3816 | 1.25174 | 0.625869 | − | 0.779928i | \(-0.284744\pi\) | ||||
0.625869 | + | 0.779928i | \(0.284744\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.7202 | + | 3.27804i | −1.66429 | + | 0.263299i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.4836i | 0.996303i | 0.867090 | + | 0.498151i | \(0.165988\pi\) | ||||
−0.867090 | + | 0.498151i | \(0.834012\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.2245 | −0.963424 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.93826i | 0.151816i | 0.997115 | + | 0.0759082i | \(0.0241856\pi\) | ||||
−0.997115 | + | 0.0759082i | \(0.975814\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.326695i | − | 0.0252804i | −0.999920 | − | 0.0126402i | \(-0.995976\pi\) | ||
0.999920 | − | 0.0126402i | \(-0.00402361\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2516 | −0.942431 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 20.7992i | − | 1.58133i | −0.612246 | − | 0.790667i | \(-0.709734\pi\) | ||
0.612246 | − | 0.790667i | \(-0.290266\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.49577 | + | 10.7717i | 0.264256 | + | 0.814266i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.79882 | −0.283937 | −0.141969 | − | 0.989871i | \(-0.545343\pi\) | ||||
−0.141969 | + | 0.989871i | \(0.545343\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.5116 | −1.22730 | −0.613651 | − | 0.789578i | \(-0.710300\pi\) | ||||
−0.613651 | + | 0.789578i | \(0.710300\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.905551 | − | 5.72392i | −0.0665774 | − | 0.420831i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.5801i | 1.06620i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3816 | 0.823545 | 0.411773 | − | 0.911287i | \(-0.364910\pi\) | ||||
0.411773 | + | 0.911287i | \(0.364910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 14.0849i | − | 1.01385i | −0.861989 | − | 0.506927i | \(-0.830781\pi\) | ||
0.861989 | − | 0.506927i | \(-0.169219\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.90830i | − | 0.563443i | −0.959496 | − | 0.281721i | \(-0.909095\pi\) | ||
0.959496 | − | 0.281721i | \(-0.0909054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.86997 | 0.132559 | 0.0662795 | − | 0.997801i | \(-0.478887\pi\) | ||||
0.0662795 | + | 0.997801i | \(0.478887\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.79487i | 0.476906i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.75582 | + | 1.38521i | −0.611533 | + | 0.0967475i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.76325 | −0.329481 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3816 | −0.783543 | −0.391772 | − | 0.920063i | \(-0.628138\pi\) | ||||
−0.391772 | + | 0.920063i | \(0.628138\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.56693 | − | 22.5463i | −0.243262 | − | 1.53764i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.2490i | 1.44247i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.7632 | −1.93483 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.85661i | 0.325222i | 0.986690 | + | 0.162611i | \(0.0519916\pi\) | ||||
−0.986690 | + | 0.162611i | \(0.948008\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.07613i | 0.469659i | 0.972037 | + | 0.234830i | \(0.0754532\pi\) | ||||
−0.972037 | + | 0.234830i | \(0.924547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.73995 | −0.577552 | −0.288776 | − | 0.957397i | \(-0.593248\pi\) | ||||
−0.288776 | + | 0.957397i | \(0.593248\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.26346i | − | 0.606869i | −0.952852 | − | 0.303435i | \(-0.901867\pi\) | ||
0.952852 | − | 0.303435i | \(-0.0981334\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.374201 | + | 2.36530i | 0.0244102 | + | 0.154295i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6772 | 0.820023 | 0.410012 | − | 0.912080i | \(-0.365525\pi\) | ||||
0.410012 | + | 0.912080i | \(0.365525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.6099 | −0.683445 | −0.341723 | − | 0.939801i | \(-0.611010\pi\) | ||||
−0.341723 | + | 0.939801i | \(0.611010\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.13003 | + | 0.653390i | −0.263858 | + | 0.0417435i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 9.39680i | − | 0.597904i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.6332 | 1.17612 | 0.588059 | − | 0.808818i | \(-0.299892\pi\) | ||||
0.588059 | + | 0.808818i | \(0.299892\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.7479i | − | 0.864326i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.3898i | 1.64615i | 0.567933 | + | 0.823075i | \(0.307743\pi\) | ||||
−0.567933 | + | 0.823075i | \(0.692257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.86997 | −0.364742 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.6776i | 0.843400i | 0.906735 | + | 0.421700i | \(0.138566\pi\) | ||||
−0.906735 | + | 0.421700i | \(0.861434\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.73995 | − | 23.6399i | −0.229743 | − | 1.45219i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.6417 | 1.38049 | 0.690244 | − | 0.723577i | \(-0.257503\pi\) | ||||
0.690244 | + | 0.723577i | \(0.257503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.86997 | 0.356576 | 0.178288 | − | 0.983978i | \(-0.442944\pi\) | ||||
0.178288 | + | 0.983978i | \(0.442944\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.1142 | + | 3.93143i | −0.730511 | + | 0.237074i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 0.158205i | − | 0.00950560i | −0.999989 | − | 0.00475280i | \(-0.998487\pi\) | ||
0.999989 | − | 0.00475280i | \(-0.00151287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.39008 | −0.202235 | −0.101117 | − | 0.994874i | \(-0.532242\pi\) | ||||
−0.101117 | + | 0.994874i | \(0.532242\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 11.9782i | − | 0.712028i | −0.934481 | − | 0.356014i | \(-0.884135\pi\) | ||
0.934481 | − | 0.356014i | \(-0.115865\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.97924i | 0.530028i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7632 | −0.927250 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.0753i | 0.880708i | 0.897824 | + | 0.440354i | \(0.145147\pi\) | ||||
−0.897824 | + | 0.440354i | \(0.854853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.49577 | + | 0.553048i | −0.203532 | + | 0.0321997i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.1216 | 1.56848 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.1216 | −1.33271 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.92143 | + | 0.303979i | −0.110021 | + | 0.0174058i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.00518i | − | 0.342734i | −0.985207 | − | 0.171367i | \(-0.945182\pi\) | ||
0.985207 | − | 0.171367i | \(-0.0548183\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.4049 | 1.72410 | 0.862052 | − | 0.506819i | \(-0.169179\pi\) | ||||
0.862052 | + | 0.506819i | \(0.169179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.2984i | 1.03429i | 0.855898 | + | 0.517144i | \(0.173005\pi\) | ||||
−0.855898 | + | 0.517144i | \(0.826995\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.47377i | − | 0.475935i | −0.971273 | − | 0.237967i | \(-0.923519\pi\) | ||
0.971273 | − | 0.237967i | \(-0.0764811\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.64167 | −0.427852 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.7036i | − | 0.595563i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.75582 | − | 23.8985i | −0.430216 | − | 1.32565i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.42565 | 0.133731 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.2516 | −0.838304 | −0.419152 | − | 0.907916i | \(-0.637672\pi\) | ||||
−0.419152 | + | 0.907916i | \(0.637672\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.69695 | − | 10.7263i | −0.0927144 | − | 0.586040i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.9834i | − | 0.979616i | −0.871830 | − | 0.489808i | \(-0.837067\pi\) | ||
0.871830 | − | 0.489808i | \(-0.162933\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.8971 | −1.29410 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0901i | 1.08476i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 16.3821i | − | 0.879436i | −0.898136 | − | 0.439718i | \(-0.855078\pi\) | ||
0.898136 | − | 0.439718i | \(-0.144922\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.7632 | −0.950845 | −0.475422 | − | 0.879758i | \(-0.657705\pi\) | ||||
−0.475422 | + | 0.879758i | \(0.657705\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7083i | 1.10219i | 0.834441 | + | 0.551097i | \(0.185791\pi\) | ||||
−0.834441 | + | 0.551097i | \(0.814209\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.13003 | − | 0.653390i | 0.219199 | − | 0.0346783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.3732 | 1.81415 | 0.907073 | − | 0.420973i | \(-0.138311\pi\) | ||||
0.907073 | + | 0.420973i | \(0.138311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5032 | −0.815958 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.35450 | − | 8.56169i | −0.0708977 | − | 0.448139i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.14857i | 0.0599551i | 0.999551 | + | 0.0299776i | \(0.00954358\pi\) | ||||
−0.999551 | + | 0.0299776i | \(0.990456\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.2431 | −1.25864 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.5435i | 1.11548i | 0.830016 | + | 0.557739i | \(0.188331\pi\) | ||||
−0.830016 | + | 0.557739i | \(0.811669\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 15.0753i | − | 0.776417i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.7632 | −1.27200 | −0.636001 | − | 0.771688i | \(-0.719413\pi\) | ||||
−0.636001 | + | 0.771688i | \(0.719413\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.53659i | 0.180711i | 0.995910 | + | 0.0903556i | \(0.0288004\pi\) | ||||
−0.995910 | + | 0.0903556i | \(0.971200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.01587 | + | 12.7422i | 0.102738 | + | 0.649402i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.7988 | 1.56156 | 0.780781 | − | 0.624805i | \(-0.214821\pi\) | ||||
0.780781 | + | 0.624805i | \(0.214821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.8933 | 1.56234 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.2675 | + | 4.63025i | −1.47261 | + | 0.232973i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 18.1196i | − | 0.909399i | −0.890645 | − | 0.454700i | \(-0.849747\pi\) | ||
0.890645 | − | 0.454700i | \(-0.150253\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5828 | −0.678293 | −0.339146 | − | 0.940734i | \(-0.610138\pi\) | ||||
−0.339146 | + | 0.940734i | \(0.610138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 47.1436i | − | 2.34839i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.60152i | − | 0.327225i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.2749 | −1.39810 | −0.699052 | − | 0.715071i | \(-0.746394\pi\) | ||||
−0.699052 | + | 0.715071i | \(0.746394\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.58497i | 0.176405i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.13745 | + | 32.4734i | 0.252187 | + | 1.59406i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0271 | 1.07610 | 0.538048 | − | 0.842914i | \(-0.319162\pi\) | ||||
0.538048 | + | 0.842914i | \(0.319162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.2749 | −0.793190 | −0.396595 | − | 0.917994i | \(-0.629808\pi\) | ||||
−0.396595 | + | 0.917994i | \(0.629808\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.83440 | − | 27.2219i | −0.428531 | − | 1.32046i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.97045i | 0.0953570i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.6921 | −0.900366 | −0.450183 | − | 0.892936i | \(-0.648641\pi\) | ||||
−0.450183 | + | 0.892936i | \(0.648641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11.9885i | − | 0.576128i | −0.957611 | − | 0.288064i | \(-0.906988\pi\) | ||
0.957611 | − | 0.288064i | \(-0.0930116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.0927i | 0.482798i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2516 | 0.632464 | 0.316232 | − | 0.948682i | \(-0.397582\pi\) | ||||
0.316232 | + | 0.948682i | \(0.397582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.3132i | 1.10765i | 0.832635 | + | 0.553823i | \(0.186831\pi\) | ||||
−0.832635 | + | 0.553823i | \(0.813169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.6332 | + | 4.68812i | −1.40475 | + | 0.222238i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.7632 | −0.507949 | −0.253974 | − | 0.967211i | \(-0.581738\pi\) | ||||
−0.253974 | + | 0.967211i | \(0.581738\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0983 | −0.475509 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.1374 | + | 3.97686i | −1.17846 | + | 0.186438i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 9.55501i | − | 0.446964i | −0.974708 | − | 0.223482i | \(-0.928258\pi\) | ||
0.974708 | − | 0.223482i | \(-0.0717425\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.2601 | −0.803881 | −0.401940 | − | 0.915666i | \(-0.631664\pi\) | ||||
−0.401940 | + | 0.915666i | \(0.631664\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.8291i | 1.66512i | 0.553936 | + | 0.832559i | \(0.313125\pi\) | ||||
−0.553936 | + | 0.832559i | \(0.686875\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.5287i | 1.32015i | 0.751199 | + | 0.660076i | \(0.229476\pi\) | ||||
−0.751199 | + | 0.660076i | \(0.770524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0000 | −0.507933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 26.0031i | − | 1.19562i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.89327 | − | 2.88615i | 0.408051 | − | 0.132426i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.8259 | −1.18002 | −0.590009 | − | 0.807397i | \(-0.700876\pi\) | ||||
−0.590009 | + | 0.807397i | \(0.700876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.0233 | 0.593811 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.17302 | + | 39.0192i | 0.280303 | + | 1.77177i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.88880i | − | 0.221533i | −0.993846 | − | 0.110766i | \(-0.964669\pi\) | ||
0.993846 | − | 0.110766i | \(-0.0353305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.51165 | −0.429255 | −0.214627 | − | 0.976696i | \(-0.568854\pi\) | ||||
−0.214627 | + | 0.976696i | \(0.568854\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 17.1718i | − | 0.773377i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4.23541i | − | 0.189984i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.51165 | −0.425800 | −0.212900 | − | 0.977074i | \(-0.568291\pi\) | ||||
−0.212900 | + | 0.977074i | \(0.568291\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 13.7801i | − | 0.614426i | −0.951641 | − | 0.307213i | \(-0.900604\pi\) | ||
0.951641 | − | 0.307213i | \(-0.0993964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.7558 | − | 1.85983i | 0.523127 | − | 0.0827612i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.97670 | 0.0876159 | 0.0438079 | − | 0.999040i | \(-0.486051\pi\) | ||||
0.0438079 | + | 0.999040i | \(0.486051\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.78015 | −0.388411 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.10187 | + | 13.2858i | 0.0926195 | + | 0.585440i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.72795i | 0.119975i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.1804 | 0.796500 | 0.398250 | − | 0.917277i | \(-0.369618\pi\) | ||||
0.398250 | + | 0.917277i | \(0.369618\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 15.0431i | − | 0.657789i | −0.944367 | − | 0.328894i | \(-0.893324\pi\) | ||
0.944367 | − | 0.328894i | \(-0.106676\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 53.6996i | − | 2.33919i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.13003 | −0.266523 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 19.9216i | − | 0.862901i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.64167 | − | 10.3769i | −0.0709757 | − | 0.448632i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.76325 | −0.205167 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7717 | 0.549098 | 0.274549 | − | 0.961573i | \(-0.411471\pi\) | ||||
0.274549 | + | 0.961573i | \(0.411471\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.6688 | + | 2.32067i | −0.628342 | + | 0.0994067i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.42900i | 0.403155i | 0.979473 | + | 0.201577i | \(0.0646068\pi\) | ||||
−0.979473 | + | 0.201577i | \(0.935393\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.60992 | 0.238991 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.0143i | 1.27634i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.85726i | 0.248180i | 0.992271 | + | 0.124090i | \(0.0396012\pi\) | ||||
−0.992271 | + | 0.124090i | \(0.960399\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.2982 | 2.16968 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 31.3124i | − | 1.31966i | −0.751415 | − | 0.659830i | \(-0.770628\pi\) | ||
0.751415 | − | 0.659830i | \(-0.229372\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.47248 | + | 28.2702i | 0.188159 | + | 1.18934i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.4405 | 1.48574 | 0.742871 | − | 0.669434i | \(-0.233463\pi\) | ||||
0.742871 | + | 0.669434i | \(0.233463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.7950 | −1.62352 | −0.811760 | − | 0.583991i | \(-0.801490\pi\) | ||||
−0.811760 | + | 0.583991i | \(0.801490\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.33017 | + | 25.6682i | 0.347392 | + | 1.07044i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.7634i | 0.822761i | 0.911464 | + | 0.411381i | \(0.134953\pi\) | ||||
−0.911464 | + | 0.411381i | \(0.865047\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.3020 | 1.38160 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 27.2644i | − | 1.12918i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 21.0380i | − | 0.868331i | −0.900833 | − | 0.434165i | \(-0.857043\pi\) | ||
0.900833 | − | 0.434165i | \(-0.142957\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.5434 | 0.722863 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.9390i | − | 0.613471i | −0.951795 | − | 0.306735i | \(-0.900763\pi\) | ||
0.951795 | − | 0.306735i | \(-0.0992367\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.6332 | + | 4.52991i | −1.17385 | + | 0.185708i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.5116 | −0.878942 | −0.439471 | − | 0.898257i | \(-0.644834\pi\) | ||||
−0.439471 | + | 0.898257i | \(0.644834\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.51165 | 0.224825 | 0.112412 | − | 0.993662i | \(-0.464142\pi\) | ||||
0.112412 | + | 0.993662i | \(0.464142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.96442 | − | 1.57642i | 0.405111 | − | 0.0640906i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.70293i | 0.393830i | 0.980421 | + | 0.196915i | \(0.0630923\pi\) | ||||
−0.980421 | + | 0.196915i | \(0.936908\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.38162 | −0.217717 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.25467i | 0.0910653i | 0.998963 | + | 0.0455326i | \(0.0144985\pi\) | ||||
−0.998963 | + | 0.0455326i | \(0.985501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.1553i | 1.61659i | 0.588776 | + | 0.808297i | \(0.299610\pi\) | ||||
−0.588776 | + | 0.808297i | \(0.700390\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.12157 | −0.205853 | −0.102927 | − | 0.994689i | \(-0.532821\pi\) | ||||
−0.102927 | + | 0.994689i | \(0.532821\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.3894i | 1.21752i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.2357 | − | 14.6804i | 0.809429 | − | 0.587218i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.8344 | 0.591486 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.28335 | −0.0510892 | −0.0255446 | − | 0.999674i | \(-0.508132\pi\) | ||||
−0.0255446 | + | 0.999674i | \(0.508132\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.47607 | + | 28.2929i | 0.177627 | + | 1.12277i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 9.39680i | − | 0.372315i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.5388 | −1.12721 | −0.563607 | − | 0.826043i | \(-0.690587\pi\) | ||||
−0.563607 | + | 0.826043i | \(0.690587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.3132i | 0.919384i | 0.888078 | + | 0.459692i | \(0.152040\pi\) | ||||
−0.888078 | + | 0.459692i | \(0.847960\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.93381i | 0.351224i | 0.984459 | + | 0.175612i | \(0.0561905\pi\) | ||||
−0.984459 | + | 0.175612i | \(0.943810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.03175 | −0.158260 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.3310i | 0.560817i | 0.959881 | + | 0.280408i | \(0.0904699\pi\) | ||||
−0.959881 | + | 0.280408i | \(0.909530\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.0074 | − | 3.32347i | 0.820828 | − | 0.129859i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.58280 | 0.295384 | 0.147692 | − | 0.989033i | \(-0.452816\pi\) | ||||
0.147692 | + | 0.989033i | \(0.452816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.5116 | 1.14787 | 0.573935 | − | 0.818901i | \(-0.305416\pi\) | ||||
0.573935 | + | 0.818901i | \(0.305416\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.47990 | − | 9.35433i | −0.0573880 | − | 0.362745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.1917i | 0.626944i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.21602 | −0.0855485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 6.98527i | − | 0.269262i | −0.990896 | − | 0.134631i | \(-0.957015\pi\) | ||
0.990896 | − | 0.134631i | \(-0.0429849\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 20.1033i | − | 0.772634i | −0.922366 | − | 0.386317i | \(-0.873747\pi\) | ||
0.922366 | − | 0.386317i | \(-0.126253\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.0148 | 1.53563 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 44.5270i | − | 1.70378i | −0.523721 | − | 0.851890i | \(-0.675456\pi\) | ||
0.523721 | − | 0.851890i | \(-0.324544\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.01587 | − | 25.3840i | −0.153439 | − | 0.969874i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 53.7865 | 2.04910 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.7717 | 1.28474 | 0.642368 | − | 0.766396i | \(-0.277952\pi\) | ||||
0.642368 | + | 0.766396i | \(0.277952\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.4246 | + | 4.02230i | −0.964411 | + | 0.152574i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 22.6920i | − | 0.859522i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.78398 | −0.256227 | −0.128114 | − | 0.991759i | \(-0.540892\pi\) | ||||
−0.128114 | + | 0.991759i | \(0.540892\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.84632i | 0.182782i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 12.0558i | − | 0.453405i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.7865 | 1.68199 | 0.840997 | − | 0.541040i | \(-0.181969\pi\) | ||||
0.840997 | + | 0.541040i | \(0.181969\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.6347i | 1.89629i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.47248 | − | 28.2702i | −0.167261 | − | 1.05724i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.55105 | −0.207019 | −0.103510 | − | 0.994628i | \(-0.533007\pi\) | ||||
−0.103510 | + | 0.994628i | \(0.533007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.6248 | 0.507413 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.2675 | − | 4.63025i | 0.529881 | − | 0.171963i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.5564i | 1.39289i | 0.717611 | + | 0.696444i | \(0.245236\pi\) | ||||
−0.717611 | + | 0.696444i | \(0.754764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.4320 | 2.16119 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.5442i | − | 1.27592i | −0.770070 | − | 0.637959i | \(-0.779779\pi\) | ||
0.770070 | − | 0.637959i | \(-0.220221\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.3709i | − | 0.455687i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.520101 | 0.0191322 | 0.00956612 | − | 0.999954i | \(-0.496955\pi\) | ||||
0.00956612 | + | 0.999954i | \(0.496955\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.7918i | 1.53319i | 0.642130 | + | 0.766596i | \(0.278051\pi\) | ||||
−0.642130 | + | 0.766596i | \(0.721949\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.5191 | + | 6.88492i | −1.59442 | + | 0.252244i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.6417 | −0.388838 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.1216 | 0.624775 | 0.312388 | − | 0.949955i | \(-0.398871\pi\) | ||||
0.312388 | + | 0.949955i | \(0.398871\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.9718 | + | 5.37451i | −1.23636 | + | 0.195598i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 6.80515i | − | 0.247337i | −0.992324 | − | 0.123669i | \(-0.960534\pi\) | ||
0.992324 | − | 0.123669i | \(-0.0394660\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.2431 | −1.64006 | −0.820031 | − | 0.572319i | \(-0.806044\pi\) | ||||
−0.820031 | + | 0.572319i | \(0.806044\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.0431i | 0.544597i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 7.95373i | − | 0.287192i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.2431 | 0.549682 | 0.274841 | − | 0.961490i | \(-0.411375\pi\) | ||||
0.274841 | + | 0.961490i | \(0.411375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.6173 | − | 14.4798i | 1.60270 | − | 0.520128i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.41337 | 0.265612 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.76325 | 0.170442 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.36192 | − | 27.5714i | −0.155684 | − | 0.984064i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 20.2586i | − | 0.722141i | −0.932539 | − | 0.361070i | \(-0.882411\pi\) | ||
0.932539 | − | 0.361070i | \(-0.117589\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.9915 | 1.03082 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.37171i | − | 0.155244i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.2691i | 0.399171i | 0.979880 | + | 0.199585i | \(0.0639595\pi\) | ||||
−0.979880 | + | 0.199585i | \(0.936040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.13003 | −0.216865 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 9.87437i | − | 0.348459i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.9990 | − | 4.27137i | 0.951589 | − | 0.150546i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.5032 | 0.931803 | 0.465901 | − | 0.884837i | \(-0.345730\pi\) | ||||
0.465901 | + | 0.884837i | \(0.345730\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.54340 | −0.0541960 | −0.0270980 | − | 0.999633i | \(-0.508627\pi\) | ||||
−0.0270980 | + | 0.999633i | \(0.508627\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.677250 | − | 4.28084i | −0.0237230 | − | 0.149951i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.0894i | 0.667855i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.3189 | 0.395033 | 0.197517 | − | 0.980300i | \(-0.436712\pi\) | ||||
0.197517 | + | 0.980300i | \(0.436712\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.72350i | − | 0.338940i | −0.985535 | − | 0.169470i | \(-0.945794\pi\) | ||
0.985535 | − | 0.169470i | \(-0.0542056\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.9722i | − | 0.903143i | −0.892235 | − | 0.451571i | \(-0.850864\pi\) | ||
0.892235 | − | 0.451571i | \(-0.149136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.61838 | 0.334060 | 0.167030 | − | 0.985952i | \(-0.446582\pi\) | ||||
0.167030 | + | 0.985952i | \(0.446582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 10.7036i | − | 0.370857i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.114151 | + | 0.721538i | 0.00395035 | + | 0.0249699i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.0906 | −0.693605 | −0.346803 | − | 0.937938i | \(-0.612733\pi\) | ||||
−0.346803 | + | 0.937938i | \(0.612733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.0589 | − | 4.28084i | 0.930854 | − | 0.147265i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.2187i | − | 0.351118i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.9877 | −0.479493 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.9312i | 0.648193i | 0.946024 | + | 0.324097i | \(0.105060\pi\) | ||||
−0.946024 | + | 0.324097i | \(0.894940\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.0618i | 1.30017i | 0.759863 | + | 0.650084i | \(0.225266\pi\) | ||||
−0.759863 | + | 0.650084i | \(0.774734\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.35833 | −0.216943 | −0.108472 | − | 0.994100i | \(-0.534596\pi\) | ||||
−0.108472 | + | 0.994100i | \(0.534596\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 6.61609i | − | 0.225214i | −0.993640 | − | 0.112607i | \(-0.964080\pi\) | ||
0.993640 | − | 0.112607i | \(-0.0359202\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.26747 | + | 45.9371i | 0.247101 | + | 1.56191i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.7548 | −1.14505 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4049 | 0.826929 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.4845 | − | 22.5690i | −0.388248 | − | 0.762971i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.5654i | 0.728211i | 0.931358 | + | 0.364105i | \(0.118625\pi\) | ||||
−0.931358 | + | 0.364105i | \(0.881375\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.1449 | −1.45359 | −0.726794 | − | 0.686856i | \(-0.758990\pi\) | ||||
−0.726794 | + | 0.686856i | \(0.758990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.3306i | 0.616874i | 0.951245 | + | 0.308437i | \(0.0998060\pi\) | ||||
−0.951245 | + | 0.308437i | \(0.900194\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.0618i | 1.27799i | 0.769210 | + | 0.638996i | \(0.220650\pi\) | ||||
−0.769210 | + | 0.638996i | \(0.779350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.0148 | 0.973127 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2.00265i | − | 0.0670160i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.39008 | − | 1.32735i | 0.280449 | − | 0.0443684i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.1449 | 0.938684 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.2664 | 2.04108 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.4676 | − | 5.76935i | 1.21222 | − | 0.191780i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.1705i | 0.968590i | 0.874905 | + | 0.484295i | \(0.160924\pi\) | ||||
−0.874905 | + | 0.484295i | \(0.839076\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.51165 | −0.116346 | −0.0581730 | − | 0.998307i | \(-0.518528\pi\) | ||||
−0.0581730 | + | 0.998307i | \(0.518528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.4523i | 1.23949i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 21.5435i | − | 0.711428i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.2431 | 0.799708 | 0.399854 | − | 0.916579i | \(-0.369061\pi\) | ||||
0.399854 | + | 0.916579i | \(0.369061\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.39680i | 0.309300i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | + | 12.3254i | 0.131519 | + | 0.405258i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.73150 | 0.286471 | 0.143236 | − | 0.989689i | \(-0.454249\pi\) | ||||
0.143236 | + | 0.989689i | \(0.454249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.49681 | 0.114603 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.09445 | − | 32.2016i | −0.166606 | − | 1.05311i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.9873i | 1.17565i | 0.808987 | + | 0.587826i | \(0.200016\pi\) | ||||
−0.808987 | + | 0.587826i | \(0.799984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6688 | −0.869378 | −0.434689 | − | 0.900581i | \(-0.643142\pi\) | ||||
−0.434689 | + | 0.900581i | \(0.643142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.3969i | 0.696778i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.05917i | 0.261888i | 0.991390 | + | 0.130944i | \(0.0418008\pi\) | ||||
−0.991390 | + | 0.130944i | \(0.958199\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.4799 | 0.632344 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.7733i | 0.770092i | 0.922897 | + | 0.385046i | \(0.125814\pi\) | ||||
−0.922897 | + | 0.385046i | \(0.874186\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.1374 | + | 3.97686i | −0.813429 | + | 0.128688i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.0317 | −0.840609 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.0148 | 1.83919 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.92143 | + | 31.1079i | 0.158426 | + | 1.00140i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.7223i | − | 1.08444i | −0.840238 | − | 0.542218i | \(-0.817585\pi\) | ||
0.840238 | − | 0.542218i | \(-0.182415\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.1766 | 1.16096 | 0.580481 | − | 0.814273i | \(-0.302864\pi\) | ||||
0.580481 | + | 0.814273i | \(0.302864\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.0734i | 0.835874i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 50.0722i | − | 1.60195i | −0.598697 | − | 0.800976i | \(-0.704315\pi\) | ||
0.598697 | − | 0.800976i | \(-0.295685\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.1766 | −1.09229 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 40.3941i | − | 1.28837i | −0.764869 | − | 0.644186i | \(-0.777196\pi\) | ||
0.764869 | − | 0.644186i | \(-0.222804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.76325 | + | 17.4663i | 0.0880443 | + | 0.556521i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −55.0970 | −1.75198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.13003 | + | 0.653390i | −0.130931 | + | 0.0207138i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 42.9506i | − | 1.36026i | −0.733091 | − | 0.680130i | \(-0.761923\pi\) | ||
0.733091 | − | 0.680130i | \(-0.238077\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))