Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.77641\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | −1.77641 | −1.02561 | −0.512807 | − | 0.858504i | \(-0.671394\pi\) | ||||
−0.512807 | + | 0.858504i | \(0.671394\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.716761 | −0.320545 | −0.160273 | − | 0.987073i | \(-0.551237\pi\) | ||||
−0.160273 | + | 0.987073i | \(0.551237\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.155650 | 0.0518832 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.69774 | 0.511887 | 0.255943 | − | 0.966692i | \(-0.417614\pi\) | ||||
0.255943 | + | 0.966692i | \(0.417614\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.41385 | −1.22418 | −0.612091 | − | 0.790787i | \(-0.709671\pi\) | ||||
−0.612091 | + | 0.790787i | \(0.709671\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.27327 | 0.328756 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.35813 | 0.329394 | 0.164697 | − | 0.986344i | \(-0.447335\pi\) | ||||
0.164697 | + | 0.986344i | \(0.447335\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.61457 | 1.51749 | 0.758743 | − | 0.651390i | \(-0.225814\pi\) | ||||
0.758743 | + | 0.651390i | \(0.225814\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.94432 | −1.03096 | −0.515481 | − | 0.856901i | \(-0.672387\pi\) | ||||
−0.515481 | + | 0.856901i | \(0.672387\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.48625 | −0.897251 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.05275 | 0.972401 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.711000 | −0.132029 | −0.0660147 | − | 0.997819i | \(-0.521028\pi\) | ||||
−0.0660147 | + | 0.997819i | \(0.521028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.41573 | 0.613483 | 0.306742 | − | 0.951793i | \(-0.400761\pi\) | ||||
0.306742 | + | 0.951793i | \(0.400761\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.01588 | −0.524998 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.21830 | −0.857883 | −0.428942 | − | 0.903332i | \(-0.641113\pi\) | ||||
−0.428942 | + | 0.903332i | \(0.641113\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.84083 | 1.25554 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.26787 | −0.955841 | −0.477921 | − | 0.878403i | \(-0.658609\pi\) | ||||
−0.477921 | + | 0.878403i | \(0.658609\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.111564 | −0.0166309 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.29375 | 1.06390 | 0.531952 | − | 0.846775i | \(-0.321459\pi\) | ||||
0.531952 | + | 0.846775i | \(0.321459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41260 | −0.337831 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1698 | −1.67165 | −0.835827 | − | 0.548994i | \(-0.815011\pi\) | ||||
−0.835827 | + | 0.548994i | \(0.815011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.21687 | −0.164083 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.7502 | −1.55635 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.69715 | −0.220950 | −0.110475 | − | 0.993879i | \(-0.535237\pi\) | ||||
−0.110475 | + | 0.993879i | \(0.535237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.76380 | 0.994053 | 0.497027 | − | 0.867735i | \(-0.334425\pi\) | ||||
0.497027 | + | 0.867735i | \(0.334425\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.16368 | 0.392406 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.13992 | 0.383602 | 0.191801 | − | 0.981434i | \(-0.438567\pi\) | ||||
0.191801 | + | 0.981434i | \(0.438567\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.78317 | 1.05737 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.54572 | 0.420799 | 0.210400 | − | 0.977615i | \(-0.432523\pi\) | ||||
0.210400 | + | 0.977615i | \(0.432523\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.4366 | 1.33856 | 0.669278 | − | 0.743012i | \(-0.266603\pi\) | ||||
0.669278 | + | 0.743012i | \(0.266603\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.96945 | 0.920232 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.90590 | 1.00199 | 0.500996 | − | 0.865450i | \(-0.332967\pi\) | ||||
0.500996 | + | 0.865450i | \(0.332967\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.44272 | −1.04919 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.4174 | −1.36299 | −0.681494 | − | 0.731824i | \(-0.738669\pi\) | ||||
−0.681494 | + | 0.731824i | \(0.738669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.973454 | −0.105586 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.26303 | 0.135411 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.08357 | −0.644857 | −0.322429 | − | 0.946594i | \(-0.604499\pi\) | ||||
−0.322429 | + | 0.946594i | \(0.604499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.06775 | −0.629197 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.74107 | −0.486423 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.9366 | −1.61812 | −0.809059 | − | 0.587728i | \(-0.800023\pi\) | ||||
−0.809059 | + | 0.587728i | \(0.800023\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.264252 | 0.0265583 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.1504 | 1.50752 | 0.753759 | − | 0.657151i | \(-0.228239\pi\) | ||||
0.753759 | + | 0.657151i | \(0.228239\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.4235 | −1.81532 | −0.907662 | − | 0.419702i | \(-0.862134\pi\) | ||||
−0.907662 | + | 0.419702i | \(0.862134\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.0184 | −1.54855 | −0.774277 | − | 0.632847i | \(-0.781886\pi\) | ||||
−0.774277 | + | 0.632847i | \(0.781886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.59424 | 0.535831 | 0.267916 | − | 0.963442i | \(-0.413665\pi\) | ||||
0.267916 | + | 0.963442i | \(0.413665\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.26986 | 0.879856 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.8004 | −1.39231 | −0.696153 | − | 0.717893i | \(-0.745107\pi\) | ||||
−0.696153 | + | 0.717893i | \(0.745107\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.54390 | 0.330470 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.687014 | −0.0635145 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.11769 | −0.737972 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.77641 | 0.160174 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.79938 | 0.608155 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.17883 | −0.193340 | −0.0966700 | − | 0.995316i | \(-0.530819\pi\) | ||||
−0.0966700 | + | 0.995316i | \(0.530819\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.1343 | 0.980324 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.33225 | 0.553251 | 0.276625 | − | 0.960978i | \(-0.410784\pi\) | ||||
0.276625 | + | 0.960978i | \(0.410784\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.62161 | −0.311699 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.0536 | 1.79873 | 0.899365 | − | 0.437198i | \(-0.144029\pi\) | ||||
0.899365 | + | 0.437198i | \(0.144029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.86444 | −0.667053 | −0.333526 | − | 0.942741i | \(-0.608239\pi\) | ||||
−0.333526 | + | 0.942741i | \(0.608239\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.9567 | −1.09115 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.49356 | −0.626643 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.509617 | 0.0423214 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.33573 | 0.764813 | 0.382407 | − | 0.923994i | \(-0.375095\pi\) | ||||
0.382407 | + | 0.923994i | \(0.375095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.50195 | −0.122227 | −0.0611135 | − | 0.998131i | \(-0.519465\pi\) | ||||
−0.0611135 | + | 0.998131i | \(0.519465\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.211392 | 0.0170900 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.44826 | −0.196649 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.5894 | 1.08455 | 0.542276 | − | 0.840201i | \(-0.317563\pi\) | ||||
0.542276 | + | 0.840201i | \(0.317563\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.6186 | 1.71447 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1671 | 1.10966 | 0.554828 | − | 0.831965i | \(-0.312784\pi\) | ||||
0.554828 | + | 0.831965i | \(0.312784\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.16167 | 0.168286 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.61946 | −0.589611 | −0.294806 | − | 0.955557i | \(-0.595255\pi\) | ||||
−0.294806 | + | 0.955557i | \(0.595255\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.48208 | 0.498621 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.02955 | 0.0787320 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.78468 | 0.515830 | 0.257915 | − | 0.966168i | \(-0.416965\pi\) | ||||
0.257915 | + | 0.966168i | \(0.416965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.01484 | 0.226609 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.4212 | 1.00315 | 0.501575 | − | 0.865114i | \(-0.332754\pi\) | ||||
0.501575 | + | 0.865114i | \(0.332754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.4891 | −1.74593 | −0.872964 | − | 0.487784i | \(-0.837805\pi\) | ||||
−0.872964 | + | 0.487784i | \(0.837805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.7917 | −1.01951 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.74027 | 0.274990 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.30574 | 0.168613 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.74296 | 0.270831 | 0.135416 | − | 0.990789i | \(-0.456763\pi\) | ||||
0.135416 | + | 0.990789i | \(0.456763\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.3013 | 1.60528 | 0.802640 | − | 0.596464i | \(-0.203428\pi\) | ||||
0.802640 | + | 0.596464i | \(0.203428\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.62000 | −0.402457 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.1467 | 0.865415 | 0.432708 | − | 0.901534i | \(-0.357558\pi\) | ||||
0.432708 | + | 0.901534i | \(0.357558\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.7447 | 0.903445 | 0.451722 | − | 0.892159i | \(-0.350810\pi\) | ||||
0.451722 | + | 0.892159i | \(0.350810\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.57780 | −0.393427 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.716761 | 0.0500608 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.769582 | −0.0534896 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.2298 | 0.776781 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.56860 | 0.176830 | 0.0884149 | − | 0.996084i | \(-0.471820\pi\) | ||||
0.0884149 | + | 0.996084i | \(0.471820\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.29866 | −0.431577 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.49257 | 0.306391 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.3162 | −1.37284 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.99458 | −0.403239 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.3812 | −1.36483 | −0.682413 | − | 0.730967i | \(-0.739069\pi\) | ||||
−0.682413 | + | 0.730967i | \(0.739069\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.698283 | −0.0465522 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.8696 | −1.71703 | −0.858513 | − | 0.512792i | \(-0.828611\pi\) | ||||
−0.858513 | + | 0.512792i | \(0.828611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.2042 | 1.53338 | 0.766689 | − | 0.642018i | \(-0.221903\pi\) | ||||
0.766689 | + | 0.642018i | \(0.221903\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.8849 | 1.17168 | 0.585838 | − | 0.810428i | \(-0.300765\pi\) | ||||
0.585838 | + | 0.810428i | \(0.300765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.22788 | −0.341029 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.8206 | −1.02766 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.03234 | −0.584254 | −0.292127 | − | 0.956380i | \(-0.594363\pi\) | ||||
−0.292127 | + | 0.956380i | \(0.594363\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.99359 | −0.257250 | −0.128625 | − | 0.991693i | \(-0.541056\pi\) | ||||
−0.128625 | + | 0.991693i | \(0.541056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.61595 | 0.103663 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.1957 | −1.85768 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.0585 | 1.39790 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.9887 | 1.64039 | 0.820195 | − | 0.572084i | \(-0.193865\pi\) | ||||
0.820195 | + | 0.572084i | \(0.193865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.39416 | −0.527736 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.72926 | 0.108290 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.1578 | 1.50692 | 0.753460 | − | 0.657494i | \(-0.228384\pi\) | ||||
0.753460 | + | 0.657494i | \(0.228384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.110667 | −0.00685010 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.3693 | −0.947712 | −0.473856 | − | 0.880602i | \(-0.657138\pi\) | ||||
−0.473856 | + | 0.880602i | \(0.657138\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.72286 | 0.535841 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.8069 | 0.661374 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.8438 | −0.844074 | −0.422037 | − | 0.906579i | \(-0.638685\pi\) | ||||
−0.422037 | + | 0.906579i | \(0.638685\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.5459 | 1.06584 | 0.532919 | − | 0.846167i | \(-0.321095\pi\) | ||||
0.532919 | + | 0.846167i | \(0.321095\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.61648 | −0.459291 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9385 | −0.897568 | −0.448784 | − | 0.893640i | \(-0.648143\pi\) | ||||
−0.448784 | + | 0.893640i | \(0.648143\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.531657 | 0.0318295 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.8574 | −1.06529 | −0.532643 | − | 0.846340i | \(-0.678801\pi\) | ||||
−0.532643 | + | 0.846340i | \(0.678801\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5195 | 0.625317 | 0.312658 | − | 0.949866i | \(-0.398780\pi\) | ||||
0.312658 | + | 0.949866i | \(0.398780\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.42210 | 0.498882 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1555 | −0.891499 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.3100 | 1.65956 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.08524 | −0.121821 | −0.0609105 | − | 0.998143i | \(-0.519400\pi\) | ||||
−0.0609105 | + | 0.998143i | \(0.519400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.21645 | 0.0708244 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.57823 | 0.497760 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.8235 | 1.26209 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.9133 | −1.54613 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.56480 | −0.318639 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.1415 | 1.77734 | 0.888669 | − | 0.458549i | \(-0.151631\pi\) | ||||
0.888669 | + | 0.458549i | \(0.151631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.7278 | 1.86182 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.29468 | 0.0734144 | 0.0367072 | − | 0.999326i | \(-0.488313\pi\) | ||||
0.0367072 | + | 0.999326i | \(0.488313\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.26088 | 0.184316 | 0.0921580 | − | 0.995744i | \(-0.470624\pi\) | ||||
0.0921580 | + | 0.995744i | \(0.470624\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.6758 | 1.49826 | 0.749131 | − | 0.662422i | \(-0.230472\pi\) | ||||
0.749131 | + | 0.662422i | \(0.230472\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.20709 | −0.0675841 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.4553 | 1.58822 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.98343 | 0.499852 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.8017 | 1.09840 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.93769 | −0.549556 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.3959 | −0.846237 | −0.423118 | − | 0.906074i | \(-0.639065\pi\) | ||||
−0.423118 | + | 0.906074i | \(0.639065\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.812226 | −0.0445097 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.25057 | −0.122962 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.41514 | 0.512875 | 0.256438 | − | 0.966561i | \(-0.417451\pi\) | ||||
0.256438 | + | 0.966561i | \(0.417451\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.2917 | 1.42797 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.79901 | 0.314034 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.29544 | −0.338935 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.8029 | 0.955707 | 0.477854 | − | 0.878440i | \(-0.341415\pi\) | ||||
0.477854 | + | 0.878440i | \(0.341415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.62781 | 0.461836 | 0.230918 | − | 0.972973i | \(-0.425827\pi\) | ||||
0.230918 | + | 0.972973i | \(0.425827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.3021 | −1.19040 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.87764 | 0.312835 | 0.156418 | − | 0.987691i | \(-0.450005\pi\) | ||||
0.156418 | + | 0.987691i | \(0.450005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.54143 | −0.134885 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.18050 | 0.220638 | 0.110319 | − | 0.993896i | \(-0.464813\pi\) | ||||
0.110319 | + | 0.993896i | \(0.464813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.7525 | 1.30276 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.4204 | 0.756874 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.19734 | −0.429068 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.3369 | −0.643980 | −0.321990 | − | 0.946743i | \(-0.604352\pi\) | ||||
−0.321990 | + | 0.946743i | \(0.604352\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.155650 | −0.00810279 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6356 | −0.550690 | −0.275345 | − | 0.961345i | \(-0.588792\pi\) | ||||
−0.275345 | + | 0.961345i | \(0.588792\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0785 | −0.623732 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.13825 | 0.161628 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0037 | 0.513857 | 0.256929 | − | 0.966430i | \(-0.417289\pi\) | ||||
0.256929 | + | 0.966430i | \(0.417289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.87051 | 0.198292 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.42654 | 0.430576 | 0.215288 | − | 0.976551i | \(-0.430931\pi\) | ||||
0.215288 | + | 0.976551i | \(0.430931\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.975591 | −0.0495921 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0941 | 1.06951 | 0.534756 | − | 0.845007i | \(-0.320404\pi\) | ||||
0.534756 | + | 0.845007i | \(0.320404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.71502 | −0.339593 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.2487 | −0.567422 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.38340 | −0.321184 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.46045 | −0.374429 | −0.187215 | − | 0.982319i | \(-0.559946\pi\) | ||||
−0.187215 | + | 0.982319i | \(0.559946\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.2028 | −0.958940 | −0.479470 | − | 0.877558i | \(-0.659171\pi\) | ||||
−0.479470 | + | 0.877558i | \(0.659171\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.0765 | −0.751015 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.76818 | 0.336313 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.85930 | −0.439139 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.7835 | 0.928784 | 0.464392 | − | 0.885630i | \(-0.346273\pi\) | ||||
0.464392 | + | 0.885630i | \(0.346273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −37.3999 | −1.84480 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.90031 | 0.436899 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.9705 | 0.684139 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.94543 | −0.143894 | −0.0719469 | − | 0.997408i | \(-0.522921\pi\) | ||||
−0.0719469 | + | 0.997408i | \(0.522921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.1692 | −1.17793 | −0.588967 | − | 0.808157i | \(-0.700465\pi\) | ||||
−0.588967 | + | 0.808157i | \(0.700465\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.13527 | 0.0551987 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.09291 | −0.295549 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.3117 | 0.642693 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.2317 | 0.926359 | 0.463179 | − | 0.886265i | \(-0.346709\pi\) | ||||
0.463179 | + | 0.886265i | \(0.346709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3115 | 1.21639 | 0.608196 | − | 0.793787i | \(-0.291894\pi\) | ||||
0.608196 | + | 0.793787i | \(0.291894\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.905291 | −0.0434054 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.7046 | −1.56447 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.2047 | 1.01205 | 0.506023 | − | 0.862520i | \(-0.331115\pi\) | ||||
0.506023 | + | 0.862520i | \(0.331115\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.2976 | −1.43948 | −0.719741 | − | 0.694242i | \(-0.755740\pi\) | ||||
−0.719741 | + | 0.694242i | \(0.755740\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.36047 | 0.206706 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.5841 | −0.784403 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.56127 | −0.356838 | −0.178419 | − | 0.983955i | \(-0.557098\pi\) | ||||
−0.178419 | + | 0.983955i | \(0.557098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.69774 | −0.0799433 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.66809 | 0.125358 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.5520 | 1.52272 | 0.761360 | − | 0.648329i | \(-0.224532\pi\) | ||||
0.761360 | + | 0.648329i | \(0.224532\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.86228 | 0.320304 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.1030 | 0.936289 | 0.468145 | − | 0.883652i | \(-0.344923\pi\) | ||||
0.468145 | + | 0.883652i | \(0.344923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.92239 | −0.461133 | −0.230566 | − | 0.973057i | \(-0.574058\pi\) | ||||
−0.230566 | + | 0.973057i | \(0.574058\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.34913 | 0.201686 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.88181 | −0.272178 | −0.136089 | − | 0.990697i | \(-0.543453\pi\) | ||||
−0.136089 | + | 0.990697i | \(0.543453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.1404 | −1.11233 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.6412 | −0.489283 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.6746 | −1.36157 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.89423 | −0.0867307 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.5129 | −0.663109 | −0.331555 | − | 0.943436i | \(-0.607573\pi\) | ||||
−0.331555 | + | 0.943436i | \(0.607573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.0328 | 1.05020 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.4227 | 0.518680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.8829 | 1.44475 | 0.722375 | − | 0.691501i | \(-0.243050\pi\) | ||||
0.722375 | + | 0.691501i | \(0.243050\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.1667 | −1.13808 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3079 | 1.32265 | 0.661323 | − | 0.750101i | \(-0.269995\pi\) | ||||
0.661323 | + | 0.750101i | \(0.269995\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.965629 | −0.0434897 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.189406 | −0.00851315 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.4677 | 0.961024 | 0.480512 | − | 0.876988i | \(-0.340451\pi\) | ||||
0.480512 | + | 0.876988i | \(0.340451\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.5353 | 0.604713 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.79250 | −0.213687 | −0.106844 | − | 0.994276i | \(-0.534074\pi\) | ||||
−0.106844 | + | 0.994276i | \(0.534074\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.8592 | −0.483228 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.5149 | −0.511393 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.25958 | 0.233127 | 0.116563 | − | 0.993183i | \(-0.462812\pi\) | ||||
0.116563 | + | 0.993183i | \(0.462812\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 33.4217 | 1.47561 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.2053 | 0.581894 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.3829 | 0.544598 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0524 | −0.529042 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.492973 | −0.0215976 | −0.0107988 | − | 0.999942i | \(-0.503437\pi\) | ||||
−0.0107988 | + | 0.999942i | \(0.503437\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.1976 | 0.445908 | 0.222954 | − | 0.974829i | \(-0.428430\pi\) | ||||
0.222954 | + | 0.974829i | \(0.428430\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.63900 | 0.202078 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.44633 | 0.0628840 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.264160 | −0.0114636 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.41385 | 0.191185 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4813 | 0.496382 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.8417 | −1.02884 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.80961 | −0.249775 | −0.124887 | − | 0.992171i | \(-0.539857\pi\) | ||||
−0.124887 | + | 0.992171i | \(0.539857\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 41.7263 | 1.79065 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00974 | −0.171758 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.3728 | 1.89724 | 0.948621 | − | 0.316413i | \(-0.102479\pi\) | ||||
0.948621 | + | 0.316413i | \(0.102479\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.20843 | 0.0515746 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.70296 | −0.200353 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.64428 | −0.282034 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.2088 | 1.19525 | 0.597624 | − | 0.801777i | \(-0.296112\pi\) | ||||
0.597624 | + | 0.801777i | \(0.296112\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.6654 | 1.17012 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.09596 | −0.172931 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.1476 | 1.81845 | 0.909226 | − | 0.416302i | \(-0.136674\pi\) | ||||
0.909226 | + | 0.416302i | \(0.136674\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.6084 | 0.446298 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.4484 | 0.983009 | 0.491504 | − | 0.870875i | \(-0.336447\pi\) | ||||
0.491504 | + | 0.870875i | \(0.336447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.7679 | 0.659865 | 0.329933 | − | 0.944005i | \(-0.392974\pi\) | ||||
0.329933 | + | 0.944005i | \(0.392974\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.64905 | −0.277768 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.1815 | 0.925032 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.7488 | 1.44661 | 0.723306 | − | 0.690528i | \(-0.242622\pi\) | ||||
0.723306 | + | 0.690528i | \(0.242622\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39.6163 | −1.64640 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.6611 | −0.855697 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.492425 | 0.0203593 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.23176 | 0.381036 | 0.190518 | − | 0.981684i | \(-0.438983\pi\) | ||||
0.190518 | + | 0.981684i | \(0.438983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.5936 | 0.930952 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.5775 | −0.887581 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.6848 | 1.75285 | 0.876427 | − | 0.481535i | \(-0.159920\pi\) | ||||
0.876427 | + | 0.481535i | \(0.159920\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.6398 | −0.926585 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.3442 | −1.23983 | −0.619915 | − | 0.784669i | \(-0.712833\pi\) | ||||
−0.619915 | + | 0.784669i | \(0.712833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.9452 | 0.772792 | 0.386396 | − | 0.922333i | \(-0.373720\pi\) | ||||
0.386396 | + | 0.922333i | \(0.373720\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.488727 | 0.0199025 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.81845 | 0.236554 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6141 | 0.999057 | 0.499529 | − | 0.866297i | \(-0.333507\pi\) | ||||
0.499529 | + | 0.866297i | \(0.333507\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.1935 | −1.30241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.3723 | −1.06517 | −0.532583 | − | 0.846378i | \(-0.678779\pi\) | ||||
−0.532583 | + | 0.846378i | \(0.678779\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.27327 | −0.0513430 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.8189 | 0.717361 | 0.358681 | − | 0.933460i | \(-0.383227\pi\) | ||||
0.358681 | + | 0.933460i | \(0.383227\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.78205 | −0.312787 | −0.156393 | − | 0.987695i | \(-0.549987\pi\) | ||||
−0.156393 | + | 0.987695i | \(0.549987\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.9824 | −1.00251 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.5577 | 0.702309 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.9488 | −0.796677 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.08712 | −0.282582 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.4583 | 1.53100 | 0.765499 | − | 0.643437i | \(-0.222492\pi\) | ||||
0.765499 | + | 0.643437i | \(0.222492\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.56290 | −0.181359 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.56170 | 0.0619743 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.551889 | 0.0218324 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.2535 | 1.07645 | 0.538224 | − | 0.842802i | \(-0.319096\pi\) | ||||
0.538224 | + | 0.842802i | \(0.319096\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3283 | 0.959414 | 0.479707 | − | 0.877429i | \(-0.340743\pi\) | ||||
0.479707 | + | 0.877429i | \(0.340743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.98066 | −0.314238 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.86154 | −0.309069 | −0.154535 | − | 0.987987i | \(-0.549388\pi\) | ||||
−0.154535 | + | 0.987987i | \(0.549388\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.88131 | −0.113101 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −44.8914 | −1.75674 | −0.878368 | − | 0.477986i | \(-0.841367\pi\) | ||||
−0.878368 | + | 0.477986i | \(0.841367\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.53871 | −0.177342 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.78011 | 0.0694486 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.8974 | −1.28150 | −0.640750 | − | 0.767750i | \(-0.721376\pi\) | ||||
−0.640750 | + | 0.767750i | \(0.721376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.4082 | −1.06606 | −0.533028 | − | 0.846098i | \(-0.678946\pi\) | ||||
−0.533028 | + | 0.846098i | \(0.678946\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.6489 | 0.413567 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.51541 | 0.136117 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.2055 | 1.39978 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.1809 | 0.508843 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.7433 | −0.452673 | −0.226336 | − | 0.974049i | \(-0.572675\pi\) | ||||
−0.226336 | + | 0.974049i | \(0.572675\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.6679 | −0.872488 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.8790 | 1.34051 | 0.670255 | − | 0.742131i | \(-0.266185\pi\) | ||||
0.670255 | + | 0.742131i | \(0.266185\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.9552 | 1.76101 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.1265 | 1.07623 | 0.538115 | − | 0.842871i | \(-0.319137\pi\) | ||||
0.538115 | + | 0.842871i | \(0.319137\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0904 | −0.576575 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41.2203 | −1.57265 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 53.7158 | 2.04641 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0866 | −0.840216 | −0.420108 | − | 0.907474i | \(-0.638008\pi\) | ||||
−0.420108 | + | 0.907474i | \(0.638008\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.63693 | 0.213821 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.35813 | −0.0514428 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31.7709 | −1.20169 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.4355 | 0.734067 | 0.367034 | − | 0.930208i | \(-0.380373\pi\) | ||||
0.367034 | + | 0.930208i | \(0.380373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.5168 | −1.30183 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.28688 | 0.349764 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.3317 | 1.06402 | 0.532010 | − | 0.846738i | \(-0.321437\pi\) | ||||
0.532010 | + | 0.846738i | \(0.321437\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.38620 | 0.0519865 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.8885 | −0.632478 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.37109 | 0.200867 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0452 | 0.599218 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.2419 | −1.46348 | −0.731738 | − | 0.681586i | \(-0.761291\pi\) | ||||
−0.731738 | + | 0.681586i | \(0.761291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.09428 | 0.263839 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.18972 | 0.118463 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.1234 | 1.26557 | 0.632784 | − | 0.774328i | \(-0.281912\pi\) | ||||
0.632784 | + | 0.774328i | \(0.281912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.4576 | 0.942873 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.51257 | −0.314849 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4573 | 0.755607 | 0.377804 | − | 0.925886i | \(-0.376679\pi\) | ||||
0.377804 | + | 0.925886i | \(0.376679\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.33075 | 0.196361 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.2786 | 0.635603 | 0.317801 | − | 0.948157i | \(-0.397056\pi\) | ||||
0.317801 | + | 0.948157i | \(0.397056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 51.8637 | 1.90526 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.0023 | −1.46754 | −0.733771 | − | 0.679397i | \(-0.762241\pi\) | ||||
−0.733771 | + | 0.679397i | \(0.762241\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.69149 | −0.245157 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.93276 | −0.0707161 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.8954 | −0.871955 | −0.435977 | − | 0.899958i | \(-0.643597\pi\) | ||||
−0.435977 | + | 0.899958i | \(0.643597\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −46.1667 | −1.68241 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.07654 | 0.0391793 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8809 | 0.686239 | 0.343120 | − | 0.939292i | \(-0.388516\pi\) | ||||
0.343120 | + | 0.939292i | \(0.388516\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.9115 | 0.541253 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.3709 | −1.31844 | −0.659222 | − | 0.751949i | \(-0.729114\pi\) | ||||
−0.659222 | + | 0.751949i | \(0.729114\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.151518 | −0.00547813 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.49095 | 0.270483 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.8688 | 0.716488 | 0.358244 | − | 0.933628i | \(-0.383376\pi\) | ||||
0.358244 | + | 0.933628i | \(0.383376\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.9142 | −1.54552 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −52.9289 | −1.90372 | −0.951860 | − | 0.306533i | \(-0.900831\pi\) | ||||
−0.951860 | + | 0.306533i | \(0.900831\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.3238 | −0.550448 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.61457 | −0.236992 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.01969 | 0.215402 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.59250 | −0.128386 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.74035 | −0.347648 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.5636 | −1.19641 | −0.598207 | − | 0.801341i | \(-0.704120\pi\) | ||||
−0.598207 | + | 0.801341i | \(0.704120\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.3023 | 0.971986 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.2683 | −1.21690 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.4954 | −0.549566 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.71633 | −0.0607957 | −0.0303978 | − | 0.999538i | \(-0.509677\pi\) | ||||
−0.0303978 | + | 0.999538i | \(0.509677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.90585 | 0.350444 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.946905 | −0.0334572 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.4164 | 0.685189 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.5924 | 0.865694 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5588 | 0.687650 | 0.343825 | − | 0.939034i | \(-0.388277\pi\) | ||||
0.343825 | + | 0.939034i | \(0.388277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.68156 | −0.339966 | −0.169983 | − | 0.985447i | \(-0.554371\pi\) | ||||
−0.169983 | + | 0.985447i | \(0.554371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.1688 | −1.09314 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.1545 | −0.355695 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.4593 | −1.45048 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.1857 | 1.08839 | 0.544195 | − | 0.838959i | \(-0.316835\pi\) | ||||
0.544195 | + | 0.838959i | \(0.316835\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.1768 | 0.668462 | 0.334231 | − | 0.942491i | \(-0.391523\pi\) | ||||
0.334231 | + | 0.942491i | \(0.391523\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.5300 | 0.471055 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.5616 | 0.402037 | 0.201018 | − | 0.979587i | \(-0.435575\pi\) | ||||
0.201018 | + | 0.979587i | \(0.435575\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.7231 | 1.17125 | 0.585626 | − | 0.810582i | \(-0.300849\pi\) | ||||
0.585626 | + | 0.810582i | \(0.300849\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.5370 | 0.920557 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.46133 | 0.188997 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.2588 | 0.596552 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.17987 | 0.213353 | 0.106676 | − | 0.994294i | \(-0.465979\pi\) | ||||
0.106676 | + | 0.994294i | \(0.465979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4945 | −0.982568 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.7222 | 1.09257 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.64610 | −0.159831 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.6869 | −0.641333 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.8010 | 0.884445 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.00381 | −0.0343698 | −0.0171849 | − | 0.999852i | \(-0.505470\pi\) | ||||
−0.0171849 | + | 0.999852i | \(0.505470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.737945 | −0.0252372 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.1622 | 1.30360 | 0.651798 | − | 0.758393i | \(-0.274015\pi\) | ||||
0.651798 | + | 0.758393i | \(0.274015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.2597 | 0.895970 | 0.447985 | − | 0.894041i | \(-0.352142\pi\) | ||||
0.447985 | + | 0.894041i | \(0.352142\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.57453 | −0.189759 | −0.0948796 | − | 0.995489i | \(-0.530247\pi\) | ||||
−0.0948796 | + | 0.995489i | \(0.530247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.86300 | −0.165347 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.9224 | 0.914334 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.1199 | 0.512906 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8591 | −0.469599 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.48053 | −0.0839531 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.2734 | −0.718353 | −0.359177 | − | 0.933270i | \(-0.616942\pi\) | ||||
−0.359177 | + | 0.933270i | \(0.616942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.70425 | 0.124941 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.3317 | 0.516538 | 0.258269 | − | 0.966073i | \(-0.416848\pi\) | ||||
0.258269 | + | 0.966073i | \(0.416848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.6633 | 1.57034 | 0.785172 | − | 0.619278i | \(-0.212574\pi\) | ||||
0.785172 | + | 0.619278i | \(0.212574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.16092 | −0.0726385 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.3270 | −1.62266 | −0.811332 | − | 0.584586i | \(-0.801257\pi\) | ||||
−0.811332 | + | 0.584586i | \(0.801257\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.0313 | −0.537067 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.2450 | 1.61446 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.61982 | −0.321555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −38.7676 | −1.29441 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.42858 | −0.0809978 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.5282 | −0.550633 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.8361 | 0.559649 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.4253 | −1.37550 | −0.687752 | − | 0.725946i | \(-0.741402\pi\) | ||||
−0.687752 | + | 0.725946i | \(0.741402\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.35815 | 0.0782148 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.6815 | 0.552682 | 0.276341 | − | 0.961060i | \(-0.410878\pi\) | ||||
0.276341 | + | 0.961060i | \(0.410878\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.0815 | −0.697695 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.88538 | 0.326801 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.0748 | 0.860128 | 0.430064 | − | 0.902798i | \(-0.358491\pi\) | ||||
0.430064 | + | 0.902798i | \(0.358491\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −55.3202 | −1.82286 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.6503 | −0.515135 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.4106 | 0.769736 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.86761 | −0.0941848 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.10830 | −0.167598 | −0.0837990 | − | 0.996483i | \(-0.526705\pi\) | ||||
−0.0837990 | + | 0.996483i | \(0.526705\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.29988 | −0.0752948 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.65267 | −0.0540480 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.5517 | 0.932743 | 0.466372 | − | 0.884589i | \(-0.345561\pi\) | ||||
0.466372 | + | 0.884589i | \(0.345561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.79268 | −0.189037 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.2333 | 0.822582 | 0.411291 | − | 0.911504i | \(-0.365078\pi\) | ||||
0.411291 | + | 0.911504i | \(0.365078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.94432 | 0.161009 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.8090 | −0.481226 | −0.240613 | − | 0.970621i | \(-0.577349\pi\) | ||||
−0.240613 | + | 0.970621i | \(0.577349\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.4796 | −1.63864 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.3872 | −1.53664 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.0779 | −1.07150 | −0.535750 | − | 0.844377i | \(-0.679971\pi\) | ||||
−0.535750 | + | 0.844377i | \(0.679971\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.68281 | −0.0868137 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.14429 | 0.0693152 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.3328 | −0.623638 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.49325 | −0.0803439 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.9847 | −0.514565 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.0778 | −0.902920 | −0.451460 | − | 0.892291i | \(-0.649097\pi\) | ||||
−0.451460 | + | 0.892291i | \(0.649097\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.9583 | −0.512655 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.1577 | 1.19245 | 0.596224 | − | 0.802818i | \(-0.296667\pi\) | ||||
0.596224 | + | 0.802818i | \(0.296667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −35.1759 | −1.12653 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.9199 | −1.72505 | −0.862526 | − | 0.506013i | \(-0.831119\pi\) | ||||
−0.862526 | + | 0.506013i | \(0.831119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.3283 | −0.330094 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.870741 | 0.0278006 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.1739 | −0.579658 | −0.289829 | − | 0.957078i | \(-0.593598\pi\) | ||||
−0.289829 | + | 0.957078i | \(0.593598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.70627 | −0.277405 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.9904 | 0.985437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.2275 | −1.94496 | −0.972478 | − | 0.232996i | \(-0.925147\pi\) | ||||
−0.972478 | + | 0.232996i | \(0.925147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.3496 | 0.867912 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.13488 | −0.289595 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.0328 | 1.20451 | 0.602256 | − | 0.798303i | \(-0.294269\pi\) | ||||
0.602256 | + | 0.798303i | \(0.294269\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.3667 | −0.834207 |
(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 | 8036.2.a.t.1.5 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.16 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.16 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.5 | yes | 20 | 1.1 | even | 1 | trivial |