Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.a (trivial) |
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: | yes |
Analytic conductor: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.12489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.12489 | 1.55906 | 0.779530 | − | 0.626365i | \(-0.215458\pi\) | ||||
0.779530 | + | 0.626365i | \(0.215458\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.64002 | −1.39902 | −0.699510 | − | 0.714623i | \(-0.746598\pi\) | ||||
−0.699510 | + | 0.714623i | \(0.746598\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64002 | 0.732211 | 0.366105 | − | 0.930573i | \(-0.380691\pi\) | ||||
0.366105 | + | 0.930573i | \(0.380691\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.12489 | −1.00043 | −0.500216 | − | 0.865901i | \(-0.666746\pi\) | ||||
−0.500216 | + | 0.865901i | \(0.666746\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.60975 | −0.369301 | −0.184651 | − | 0.982804i | \(-0.559115\pi\) | ||||
−0.184651 | + | 0.982804i | \(0.559115\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.48486 | 0.275732 | 0.137866 | − | 0.990451i | \(-0.455976\pi\) | ||||
0.137866 | + | 0.990451i | \(0.455976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.515138 | −0.0925215 | −0.0462608 | − | 0.998929i | \(-0.514731\pi\) | ||||
−0.0462608 | + | 0.998929i | \(0.514731\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.12489 | −0.697233 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.12489 | −0.349329 | −0.174665 | − | 0.984628i | \(-0.555884\pi\) | ||||
−0.174665 | + | 0.984628i | \(0.555884\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.51514 | −0.705146 | −0.352573 | − | 0.935784i | \(-0.614693\pi\) | ||||
−0.352573 | + | 0.935784i | \(0.614693\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.28005 | 0.805200 | 0.402600 | − | 0.915376i | \(-0.368107\pi\) | ||||
0.402600 | + | 0.915376i | \(0.368107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.39025 | −0.348654 | −0.174327 | − | 0.984688i | \(-0.555775\pi\) | ||||
−0.174327 | + | 0.984688i | \(0.555775\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.0147 | 1.43067 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.12489 | −0.566597 | −0.283298 | − | 0.959032i | \(-0.591429\pi\) | ||||
−0.283298 | + | 0.959032i | \(0.591429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.64002 | 0.625661 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.79518 | 0.494091 | 0.247045 | − | 0.969004i | \(-0.420540\pi\) | ||||
0.247045 | + | 0.969004i | \(0.420540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.32970 | 0.298288 | 0.149144 | − | 0.988816i | \(-0.452348\pi\) | ||||
0.149144 | + | 0.988816i | \(0.452348\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.64002 | −0.327455 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.185438 | −0.0226548 | −0.0113274 | − | 0.999936i | \(-0.503606\pi\) | ||||
−0.0113274 | + | 0.999936i | \(0.503606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.9541 | −1.77473 | −0.887364 | − | 0.461069i | \(-0.847466\pi\) | ||||
−0.887364 | + | 0.461069i | \(0.847466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1698 | −1.19029 | −0.595145 | − | 0.803618i | \(-0.702905\pi\) | ||||
−0.595145 | + | 0.803618i | \(0.702905\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.1396 | −2.18116 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.93945 | −0.218205 | −0.109102 | − | 0.994031i | \(-0.534798\pi\) | ||||
−0.109102 | + | 0.994031i | \(0.534798\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.844838 | −0.0927331 | −0.0463665 | − | 0.998924i | \(-0.514764\pi\) | ||||
−0.0463665 | + | 0.998924i | \(0.514764\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.12489 | 0.447407 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.780505 | 0.0827334 | 0.0413667 | − | 0.999144i | \(-0.486829\pi\) | ||||
0.0413667 | + | 0.999144i | \(0.486829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.8898 | 1.14156 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.60975 | 0.165157 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.21949 | −0.936098 | −0.468049 | − | 0.883703i | \(-0.655043\pi\) | ||||
−0.468049 | + | 0.883703i | \(0.655043\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.23509 | −0.122896 | −0.0614481 | − | 0.998110i | \(-0.519572\pi\) | ||||
−0.0614481 | + | 0.998110i | \(0.519572\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0294 | −1.57942 | −0.789710 | − | 0.613481i | \(-0.789769\pi\) | ||||
−0.789710 | + | 0.613481i | \(0.789769\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.185438 | −0.0179269 | −0.00896347 | − | 0.999960i | \(-0.502853\pi\) | ||||
−0.00896347 | + | 0.999960i | \(0.502853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.92007 | 0.567040 | 0.283520 | − | 0.958966i | \(-0.408498\pi\) | ||||
0.283520 | + | 0.958966i | \(0.408498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.31410 | 0.593981 | 0.296990 | − | 0.954880i | \(-0.404017\pi\) | ||||
0.296990 | + | 0.954880i | \(0.404017\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.0147 | −1.55973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5298 | 0.957256 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0790 | −1.69299 | −0.846494 | − | 0.532398i | \(-0.821291\pi\) | ||||
−0.846494 | + | 0.532398i | \(0.821291\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2800 | 0.985542 | 0.492771 | − | 0.870159i | \(-0.335984\pi\) | ||||
0.492771 | + | 0.870159i | \(0.335984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.64002 | −0.575763 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.310323 | 0.0265127 | 0.0132563 | − | 0.999912i | \(-0.495780\pi\) | ||||
0.0132563 | + | 0.999912i | \(0.495780\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.85574 | −0.666315 | −0.333157 | − | 0.942871i | \(-0.608114\pi\) | ||||
−0.333157 | + | 0.942871i | \(0.608114\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.2498 | −1.02438 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.48486 | −0.123311 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.1698 | 0.833146 | 0.416573 | − | 0.909102i | \(-0.363231\pi\) | ||||
0.416573 | + | 0.909102i | \(0.363231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.03028 | 0.0838427 | 0.0419213 | − | 0.999121i | \(-0.486652\pi\) | ||||
0.0419213 | + | 0.999121i | \(0.486652\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.515138 | 0.0413769 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.06433 | 0.324369 | 0.162185 | − | 0.986760i | \(-0.448146\pi\) | ||||
0.162185 | + | 0.986760i | \(0.448146\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.12489 | 0.325087 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.18922 | 0.484777 | 0.242389 | − | 0.970179i | \(-0.422069\pi\) | ||||
0.242389 | + | 0.970179i | \(0.422069\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3893 | 0.881333 | 0.440667 | − | 0.897671i | \(-0.354742\pi\) | ||||
0.440667 | + | 0.897671i | \(0.354742\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.03028 | −0.463867 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.90917 | −0.525295 | −0.262647 | − | 0.964892i | \(-0.584596\pi\) | ||||
−0.262647 | + | 0.964892i | \(0.584596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.12489 | 0.311812 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0294 | 0.899117 | 0.449558 | − | 0.893251i | \(-0.351581\pi\) | ||||
0.449558 | + | 0.893251i | \(0.351581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.81078 | −0.283253 | −0.141627 | − | 0.989920i | \(-0.545233\pi\) | ||||
−0.141627 | + | 0.989920i | \(0.545233\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.12489 | 0.156225 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.1396 | 1.39962 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0799296 | −0.00578350 | −0.00289175 | − | 0.999996i | \(-0.500920\pi\) | ||||
−0.00289175 | + | 0.999996i | \(0.500920\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.9697 | −1.22151 | −0.610754 | − | 0.791821i | \(-0.709133\pi\) | ||||
−0.610754 | + | 0.791821i | \(0.709133\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.6206 | −0.756690 | −0.378345 | − | 0.925665i | \(-0.623507\pi\) | ||||
−0.378345 | + | 0.925665i | \(0.623507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5298 | −1.24266 | −0.621328 | − | 0.783551i | \(-0.713407\pi\) | ||||
−0.621328 | + | 0.783551i | \(0.713407\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.12489 | 0.429883 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.51514 | 0.315351 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.46927 | 0.516660 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.70436 | −0.186176 | −0.0930878 | − | 0.995658i | \(-0.529674\pi\) | ||||
−0.0930878 | + | 0.995658i | \(0.529674\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.28005 | −0.360096 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.12489 | −0.144247 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.8898 | −0.732527 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.21949 | −0.0816634 | −0.0408317 | − | 0.999166i | \(-0.513001\pi\) | ||||
−0.0408317 | + | 0.999166i | \(0.513001\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.56009 | 0.169919 | 0.0849597 | − | 0.996384i | \(-0.472924\pi\) | ||||
0.0849597 | + | 0.996384i | \(0.472924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.9688 | −1.18741 | −0.593706 | − | 0.804682i | \(-0.702336\pi\) | ||||
−0.593706 | + | 0.804682i | \(0.702336\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.18922 | −0.274445 | −0.137222 | − | 0.990540i | \(-0.543818\pi\) | ||||
−0.137222 | + | 0.990540i | \(0.543818\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.39025 | 0.155923 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.3553 | −1.05794 | −0.528968 | − | 0.848642i | \(-0.677421\pi\) | ||||
−0.528968 | + | 0.848642i | \(0.677421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0790 | 0.713662 | 0.356831 | − | 0.934169i | \(-0.383857\pi\) | ||||
0.356831 | + | 0.934169i | \(0.383857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.0147 | −0.639814 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.24977 | −0.270406 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2800 | −0.964468 | −0.482234 | − | 0.876042i | \(-0.660175\pi\) | ||||
−0.482234 | + | 0.876042i | \(0.660175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.64002 | −0.291716 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.14048 | −0.258276 | −0.129138 | − | 0.991627i | \(-0.541221\pi\) | ||||
−0.129138 | + | 0.991627i | \(0.541221\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.76491 | −0.544625 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.5260 | −0.710726 | −0.355363 | − | 0.934728i | \(-0.615643\pi\) | ||||
−0.355363 | + | 0.934728i | \(0.615643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.12489 | 0.253390 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.5445 | 1.74039 | 0.870194 | − | 0.492709i | \(-0.163993\pi\) | ||||
0.870194 | + | 0.492709i | \(0.163993\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.1736 | 1.34695 | 0.673476 | − | 0.739209i | \(-0.264801\pi\) | ||||
0.673476 | + | 0.739209i | \(0.264801\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.64002 | −0.279804 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.24977 | −0.255344 | −0.127672 | − | 0.991816i | \(-0.540750\pi\) | ||||
−0.127672 | + | 0.991816i | \(0.540750\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0109 | −0.656855 | −0.328428 | − | 0.944529i | \(-0.606519\pi\) | ||||
−0.328428 | + | 0.944529i | \(0.606519\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.21571 | 0.0722667 | 0.0361333 | − | 0.999347i | \(-0.488496\pi\) | ||||
0.0361333 | + | 0.999347i | \(0.488496\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.6244 | −1.09937 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.0146797 | 0.000863513 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.8439 | 0.925612 | 0.462806 | − | 0.886460i | \(-0.346843\pi\) | ||||
0.462806 | + | 0.886460i | \(0.346843\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.79518 | −0.220964 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.64002 | 0.152676 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.7796 | 1.25535 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.32970 | −0.133398 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.86043 | 0.505692 | 0.252846 | − | 0.967507i | \(-0.418633\pi\) | ||||
0.252846 | + | 0.967507i | \(0.418633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.6888 | 1.28656 | 0.643281 | − | 0.765630i | \(-0.277573\pi\) | ||||
0.643281 | + | 0.765630i | \(0.277573\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.6841 | 1.56480 | 0.782398 | − | 0.622779i | \(-0.213996\pi\) | ||||
0.782398 | + | 0.622779i | \(0.213996\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.9192 | −1.51193 | −0.755965 | − | 0.654612i | \(-0.772832\pi\) | ||||
−0.755965 | + | 0.654612i | \(0.772832\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.88979 | −0.385754 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.64002 | 0.369461 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.64002 | 0.146442 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.85952 | −0.543573 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.9541 | 1.70139 | 0.850696 | − | 0.525657i | \(-0.176181\pi\) | ||||
0.850696 | + | 0.525657i | \(0.176181\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.185438 | 0.0101315 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.1892 | −1.09978 | −0.549888 | − | 0.835238i | \(-0.685330\pi\) | ||||
−0.549888 | + | 0.835238i | \(0.685330\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.39025 | 0.129439 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4352 | 0.671438 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0449558 | 0.00240643 | 0.00120321 | − | 0.999999i | \(-0.499617\pi\) | ||||
0.00120321 | + | 0.999999i | \(0.499617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.9797 | 1.11664 | 0.558319 | − | 0.829627i | \(-0.311447\pi\) | ||||
0.558319 | + | 0.829627i | \(0.311447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.9541 | 0.793683 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.1405 | −0.746306 | −0.373153 | − | 0.927770i | \(-0.621723\pi\) | ||||
−0.373153 | + | 0.927770i | \(0.621723\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4087 | −0.863616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1698 | 0.532314 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.93567 | 0.518638 | 0.259319 | − | 0.965792i | \(-0.416502\pi\) | ||||
0.259319 | + | 0.965792i | \(0.416502\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.0147 | −0.883358 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.2110 | −1.46071 | −0.730356 | − | 0.683067i | \(-0.760646\pi\) | ||||
−0.730356 | + | 0.683067i | \(0.760646\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.92007 | 0.201894 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5592 | 1.21015 | 0.605077 | − | 0.796167i | \(-0.293142\pi\) | ||||
0.605077 | + | 0.796167i | \(0.293142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.3444 | −1.49943 | −0.749714 | − | 0.661762i | \(-0.769809\pi\) | ||||
−0.749714 | + | 0.661762i | \(0.769809\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.1396 | 0.975443 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.09839 | −0.258499 | −0.129249 | − | 0.991612i | \(-0.541257\pi\) | ||||
−0.129249 | + | 0.991612i | \(0.541257\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.12489 | −0.208604 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.93945 | 0.0975842 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9385 | −1.15125 | −0.575626 | − | 0.817713i | \(-0.695242\pi\) | ||||
−0.575626 | + | 0.817713i | \(0.695242\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.1892 | −1.10808 | −0.554038 | − | 0.832491i | \(-0.686914\pi\) | ||||
−0.554038 | + | 0.832491i | \(0.686914\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.35998 | −0.0677453 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.85952 | 0.488718 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.6741 | −0.972821 | −0.486410 | − | 0.873730i | \(-0.661694\pi\) | ||||
−0.486410 | + | 0.873730i | \(0.661694\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.6547 | 0.770318 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.844838 | 0.0414715 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.4196 | −1.48610 | −0.743048 | − | 0.669239i | \(-0.766620\pi\) | ||||
−0.743048 | + | 0.669239i | \(0.766620\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.8586 | −1.79638 | −0.898189 | − | 0.439609i | \(-0.855117\pi\) | ||||
−0.898189 | + | 0.439609i | \(0.855117\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.12489 | −0.200086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.60975 | 0.465048 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.0596 | 0.918070 | 0.459035 | − | 0.888418i | \(-0.348195\pi\) | ||||
0.459035 | + | 0.888418i | \(0.348195\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.6244 | −1.37560 | −0.687801 | − | 0.725899i | \(-0.741424\pi\) | ||||
−0.687801 | + | 0.725899i | \(0.741424\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.60975 | −0.0770047 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.2498 | −0.966469 | −0.483234 | − | 0.875491i | \(-0.660538\pi\) | ||||
−0.483234 | + | 0.875491i | \(0.660538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.76869 | −0.321590 | −0.160795 | − | 0.986988i | \(-0.551406\pi\) | ||||
−0.160795 | + | 0.986988i | \(0.551406\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.780505 | −0.0369995 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.3553 | −0.771853 | −0.385927 | − | 0.922529i | \(-0.626118\pi\) | ||||
−0.385927 | + | 0.922529i | \(0.626118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.9503 | 0.986513 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.8898 | −0.510521 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.4655 | −0.723445 | −0.361722 | − | 0.932286i | \(-0.617811\pi\) | ||||
−0.361722 | + | 0.932286i | \(0.617811\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.31032 | −0.200752 | −0.100376 | − | 0.994950i | \(-0.532005\pi\) | ||||
−0.100376 | + | 0.994950i | \(0.532005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.5483 | 0.862012 | 0.431006 | − | 0.902349i | \(-0.358159\pi\) | ||||
0.431006 | + | 0.902349i | \(0.358159\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.2148 | −0.842880 | −0.421440 | − | 0.906856i | \(-0.638475\pi\) | ||||
−0.421440 | + | 0.906856i | \(0.638475\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.764909 | −0.0353202 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.4995 | −1.12649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.60975 | −0.0738603 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.5786 | −1.53424 | −0.767122 | − | 0.641502i | \(-0.778312\pi\) | ||||
−0.767122 | + | 0.641502i | \(0.778312\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.60975 | −0.255782 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.21949 | 0.418636 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.3591 | 1.82884 | 0.914422 | − | 0.404763i | \(-0.132646\pi\) | ||||
0.914422 | + | 0.404763i | \(0.132646\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.16606 | 0.368529 | 0.184265 | − | 0.982877i | \(-0.441010\pi\) | ||||
0.184265 | + | 0.982877i | \(0.441010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.12489 | −0.275851 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −61.6841 | −2.76691 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.0147 | −1.11981 | −0.559905 | − | 0.828557i | \(-0.689163\pi\) | ||||
−0.559905 | + | 0.828557i | \(0.689163\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.9944 | −1.60491 | −0.802455 | − | 0.596712i | \(-0.796473\pi\) | ||||
−0.802455 | + | 0.596712i | \(0.796473\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.23509 | 0.0549608 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.3179 | 0.723278 | 0.361639 | − | 0.932318i | \(-0.382217\pi\) | ||||
0.361639 | + | 0.932318i | \(0.382217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.9494 | −1.85573 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0294 | 0.706338 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0908 | 0.487774 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.8283 | 1.30680 | 0.653401 | − | 0.757012i | \(-0.273341\pi\) | ||||
0.653401 | + | 0.757012i | \(0.273341\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.9688 | 1.57281 | 0.786403 | − | 0.617714i | \(-0.211941\pi\) | ||||
0.786403 | + | 0.617714i | \(0.211941\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.12489 | 0.0925615 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.9201 | −0.516316 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.185438 | 0.00801717 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −46.4683 | −2.00153 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.1287 | −0.951386 | −0.475693 | − | 0.879611i | \(-0.657803\pi\) | ||||
−0.475693 | + | 0.879611i | \(0.657803\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.92007 | −0.253588 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.6206 | 0.881675 | 0.440838 | − | 0.897587i | \(-0.354681\pi\) | ||||
0.440838 | + | 0.897587i | \(0.354681\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.39025 | −0.101828 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | −0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.5251 | 0.784935 | 0.392467 | − | 0.919766i | \(-0.371622\pi\) | ||||
0.392467 | + | 0.919766i | \(0.371622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.9394 | 0.589576 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.87511 | −0.247607 | −0.123803 | − | 0.992307i | \(-0.539509\pi\) | ||||
−0.123803 | + | 0.992307i | \(0.539509\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.31410 | −0.265636 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.03028 | −0.210880 | −0.105440 | − | 0.994426i | \(-0.533625\pi\) | ||||
−0.105440 | + | 0.994426i | \(0.533625\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.8208 | 1.75014 | 0.875072 | − | 0.483992i | \(-0.160814\pi\) | ||||
0.875072 | + | 0.483992i | \(0.160814\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.4314 | −0.684049 | −0.342025 | − | 0.939691i | \(-0.611113\pi\) | ||||
−0.342025 | + | 0.939691i | \(0.611113\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.48486 | −0.144576 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.1396 | 0.792680 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.0294 | 0.579054 | 0.289527 | − | 0.957170i | \(-0.406502\pi\) | ||||
0.289527 | + | 0.957170i | \(0.406502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.829242 | 0.0341683 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.1396 | −1.19662 | −0.598309 | − | 0.801265i | \(-0.704161\pi\) | ||||
−0.598309 | + | 0.801265i | \(0.704161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.0147 | 0.697534 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.7106 | 1.33652 | 0.668259 | − | 0.743929i | \(-0.267040\pi\) | ||||
0.668259 | + | 0.743929i | \(0.267040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.7044 | −0.681385 | −0.340692 | − | 0.940175i | \(-0.610661\pi\) | ||||
−0.340692 | + | 0.940175i | \(0.610661\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.5298 | −0.428098 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.480164 | −0.0194893 | −0.00974463 | − | 0.999953i | \(-0.503102\pi\) | ||||
−0.00974463 | + | 0.999953i | \(0.503102\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.31032 | −0.255288 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.65940 | −0.349750 | −0.174875 | − | 0.984591i | \(-0.555952\pi\) | ||||
−0.174875 | + | 0.984591i | \(0.555952\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.0559 | 0.445092 | 0.222546 | − | 0.974922i | \(-0.428563\pi\) | ||||
0.222546 | + | 0.974922i | \(0.428563\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.6197 | −1.35129 | −0.675646 | − | 0.737227i | \(-0.736135\pi\) | ||||
−0.675646 | + | 0.737227i | \(0.736135\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.21949 | 0.128986 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.76491 | 0.349480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.95883 | 0.157598 | 0.0787992 | − | 0.996891i | \(-0.474891\pi\) | ||||
0.0787992 | + | 0.996891i | \(0.474891\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.0790 | 0.757128 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.4390 | 1.04755 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.26915 | −0.247616 | −0.123808 | − | 0.992306i | \(-0.539511\pi\) | ||||
−0.123808 | + | 0.992306i | \(0.539511\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.9348 | −0.510097 | −0.255048 | − | 0.966928i | \(-0.582091\pi\) | ||||
−0.255048 | + | 0.966928i | \(0.582091\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.9192 | 1.45144 | 0.725721 | − | 0.687989i | \(-0.241506\pi\) | ||||
0.725721 | + | 0.687989i | \(0.241506\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.6097 | −0.691243 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.8898 | −0.660949 | −0.330474 | − | 0.943815i | \(-0.607209\pi\) | ||||
−0.330474 | + | 0.943815i | \(0.607209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.2800 | −0.440748 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.4205 | −0.834425 | −0.417213 | − | 0.908809i | \(-0.636993\pi\) | ||||
−0.417213 | + | 0.908809i | \(0.636993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.81834 | 0.148516 | 0.0742582 | − | 0.997239i | \(-0.476341\pi\) | ||||
0.0742582 | + | 0.997239i | \(0.476341\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.64002 | 0.257489 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.48486 | 0.0574941 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.8099 | −0.417310 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.4802 | −1.56040 | −0.780198 | − | 0.625533i | \(-0.784882\pi\) | ||||
−0.780198 | + | 0.625533i | \(0.784882\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.8751 | −1.07133 | −0.535664 | − | 0.844431i | \(-0.679939\pi\) | ||||
−0.535664 | + | 0.844431i | \(0.679939\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38.0294 | −1.45943 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.3297 | 0.471783 | 0.235891 | − | 0.971779i | \(-0.424199\pi\) | ||||
0.235891 | + | 0.971779i | \(0.424199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.310323 | −0.0118568 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.8898 | −0.414868 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.0890 | 1.86743 | 0.933717 | − | 0.358013i | \(-0.116546\pi\) | ||||
0.933717 | + | 0.358013i | \(0.116546\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.85574 | 0.297985 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.6244 | 0.705450 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.7299 | −1.38727 | −0.693635 | − | 0.720326i | \(-0.743992\pi\) | ||||
−0.693635 | + | 0.720326i | \(0.743992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.42053 | 0.129008 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.09461 | −0.191603 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.33062 | −0.0499724 | −0.0249862 | − | 0.999688i | \(-0.507954\pi\) | ||||
−0.0249862 | + | 0.999688i | \(0.507954\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.515138 | −0.0192921 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.2498 | 0.458115 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.7034 | −1.18234 | −0.591169 | − | 0.806547i | \(-0.701334\pi\) | ||||
−0.591169 | + | 0.806547i | \(0.701334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −66.1193 | −2.46241 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.48486 | 0.0551464 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.7455 | 0.769409 | 0.384705 | − | 0.923040i | \(-0.374303\pi\) | ||||
0.384705 | + | 0.923040i | \(0.374303\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.7796 | −0.805547 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.81456 | −0.140894 | −0.0704470 | − | 0.997516i | \(-0.522443\pi\) | ||||
−0.0704470 | + | 0.997516i | \(0.522443\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.860435 | 0.0316945 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.2654 | 0.451189 | 0.225594 | − | 0.974221i | \(-0.427568\pi\) | ||||
0.225594 | + | 0.974221i | \(0.427568\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.9991 | 0.917127 | 0.458564 | − | 0.888662i | \(-0.348364\pi\) | ||||
0.458564 | + | 0.888662i | \(0.348364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.1698 | −0.372594 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.764909 | −0.0279492 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.7687 | −0.392955 | −0.196478 | − | 0.980508i | \(-0.562950\pi\) | ||||
−0.196478 | + | 0.980508i | \(0.562950\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.03028 | −0.0374956 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.4352 | 0.888113 | 0.444056 | − | 0.895999i | \(-0.353539\pi\) | ||||
0.444056 | + | 0.895999i | \(0.353539\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.98532 | −0.253218 | −0.126609 | − | 0.991953i | \(-0.540409\pi\) | ||||
−0.126609 | + | 0.991953i | \(0.540409\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.4196 | 0.884049 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.0194 | 0.361779 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.0705 | −1.01225 | −0.506125 | − | 0.862460i | \(-0.668922\pi\) | ||||
−0.506125 | + | 0.862460i | \(0.668922\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.2791 | −0.729390 | −0.364695 | − | 0.931127i | \(-0.618827\pi\) | ||||
−0.364695 | + | 0.931127i | \(0.618827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.515138 | −0.0185043 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.26823 | 0.260411 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 69.3875 | 2.48288 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.06433 | −0.145062 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.50424 | 0.0536203 | 0.0268102 | − | 0.999641i | \(-0.491465\pi\) | ||||
0.0268102 | + | 0.999641i | \(0.491465\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.0450 | 0.926052 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.15046 | 0.218409 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −55.0247 | −1.94907 | −0.974537 | − | 0.224228i | \(-0.928014\pi\) | ||||
−0.974537 | + | 0.224228i | \(0.928014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.85952 | 0.348805 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 47.1883 | 1.66524 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.12489 | −0.145383 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.35528 | −0.153123 | −0.0765617 | − | 0.997065i | \(-0.524394\pi\) | ||||
−0.0765617 | + | 0.997065i | \(0.524394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.51422 | −0.0531715 | −0.0265858 | − | 0.999647i | \(-0.508464\pi\) | ||||
−0.0265858 | + | 0.999647i | \(0.508464\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.18922 | −0.216799 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.49954 | −0.297361 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.1807 | 0.739213 | 0.369606 | − | 0.929188i | \(-0.379493\pi\) | ||||
0.369606 | + | 0.929188i | \(0.379493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.12867 | −0.0742006 | −0.0371003 | − | 0.999312i | \(-0.511812\pi\) | ||||
−0.0371003 | + | 0.999312i | \(0.511812\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.0559 | 1.01037 | 0.505186 | − | 0.863011i | \(-0.331424\pi\) | ||||
0.505186 | + | 0.863011i | \(0.331424\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.55298 | 0.123400 | 0.0617000 | − | 0.998095i | \(-0.480348\pi\) | ||||
0.0617000 | + | 0.998095i | \(0.480348\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41.3094 | −1.43129 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.3893 | −0.394144 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.03028 | −0.311760 | −0.155880 | − | 0.987776i | \(-0.549821\pi\) | ||||
−0.155880 | + | 0.987776i | \(0.549821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7952 | −0.923972 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.03028 | 0.207448 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.4343 | 1.49242 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.12489 | −0.0728401 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.530734 | 0.0181720 | 0.00908600 | − | 0.999959i | \(-0.497108\pi\) | ||||
0.00908600 | + | 0.999959i | \(0.497108\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.2800 | 0.931869 | 0.465934 | − | 0.884819i | \(-0.345718\pi\) | ||||
0.465934 | + | 0.884819i | \(0.345718\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.6060 | 0.395990 | 0.197995 | − | 0.980203i | \(-0.436557\pi\) | ||||
0.197995 | + | 0.980203i | \(0.436557\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.5895 | 1.24552 | 0.622760 | − | 0.782413i | \(-0.286011\pi\) | ||||
0.622760 | + | 0.782413i | \(0.286011\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.90917 | 0.234919 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.99908 | 0.305273 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.489560 | −0.0165881 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.12489 | −0.139447 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.9688 | 1.75486 | 0.877431 | − | 0.479703i | \(-0.159256\pi\) | ||||
0.877431 | + | 0.479703i | \(0.159256\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.7384 | −0.867149 | −0.433575 | − | 0.901118i | \(-0.642748\pi\) | ||||
−0.433575 | + | 0.901118i | \(0.642748\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.8889 | −1.34237 | −0.671184 | − | 0.741291i | \(-0.734214\pi\) | ||||
−0.671184 | + | 0.741291i | \(0.734214\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.0908 | 1.17823 | 0.589117 | − | 0.808047i | \(-0.299476\pi\) | ||||
0.589117 | + | 0.808047i | \(0.299476\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −78.6987 | −2.63947 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.84770 | 0.128758 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0294 | −0.402097 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.764909 | −0.0255111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.0147 | 0.566841 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.81078 | 0.126675 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5932 | −0.617378 | −0.308689 | − | 0.951163i | \(-0.599890\pi\) | ||||
−0.308689 | + | 0.951163i | \(0.599890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.8392 | −0.822960 | −0.411480 | − | 0.911419i | \(-0.634988\pi\) | ||||
−0.411480 | + | 0.911419i | \(0.634988\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.92007 | 0.129735 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46.5289 | 1.53652 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.8989 | 1.84393 | 0.921967 | − | 0.387269i | \(-0.126582\pi\) | ||||
0.921967 | + | 0.387269i | \(0.126582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39.4792 | −1.29948 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.12489 | −0.0698658 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.8851 | −0.586791 | −0.293395 | − | 0.955991i | \(-0.594785\pi\) | ||||
−0.293395 | + | 0.955991i | \(0.594785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.1211 | −0.528348 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.1396 | −0.625931 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.4608 | 1.51781 | 0.758904 | − | 0.651203i | \(-0.225735\pi\) | ||||
0.758904 | + | 0.651203i | \(0.225735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.6703 | 0.576035 | 0.288018 | − | 0.957625i | \(-0.407004\pi\) | ||||
0.288018 | + | 0.957625i | \(0.407004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.51514 | −0.147033 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.5374 | −0.699871 | −0.349935 | − | 0.936774i | \(-0.613796\pi\) | ||||
−0.349935 | + | 0.936774i | \(0.613796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.8486 | −0.871543 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.62156 | −0.311673 | −0.155836 | − | 0.987783i | \(-0.549807\pi\) | ||||
−0.155836 | + | 0.987783i | \(0.549807\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0799296 | 0.00258646 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.28005 | 0.0413349 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7346 | −0.991440 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.9697 | 0.546275 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.8586 | 1.44256 | 0.721278 | − | 0.692646i | \(-0.243555\pi\) | ||||
0.721278 | + | 0.692646i | \(0.243555\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.19014 | 0.230742 | 0.115371 | − | 0.993322i | \(-0.463194\pi\) | ||||
0.115371 | + | 0.993322i | \(0.463194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.4040 | −1.03883 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.4428 | 0.590037 | 0.295018 | − | 0.955492i | \(-0.404674\pi\) | ||||
0.295018 | + | 0.955492i | \(0.404674\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.62156 | −0.115746 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.2526 | −0.614064 | −0.307032 | − | 0.951699i | \(-0.599336\pi\) | ||||
−0.307032 | + | 0.951699i | \(0.599336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6206 | 0.338402 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.28005 | 0.167896 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.3846 | −0.456943 | −0.228472 | − | 0.973551i | \(-0.573373\pi\) | ||||
−0.228472 | + | 0.973551i | \(0.573373\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.5298 | 0.555733 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.0606 | 0.698665 | 0.349332 | − | 0.936999i | \(-0.386408\pi\) | ||||
0.349332 | + | 0.936999i | \(0.386408\pi\) | |||||||
\(998\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8280.2.a.bk.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bp.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bk.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
8280.2.a.bp.1.3 | yes | 3 | 3.2 | odd | 2 |