Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.74912\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.47363 | −1.10624 | −0.553120 | − | 0.833102i | \(-0.686563\pi\) | ||||
−0.553120 | + | 0.833102i | \(0.686563\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.47363 | −0.782229 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.03127 | 0.840724 | 0.420362 | − | 0.907357i | \(-0.361903\pi\) | ||||
0.420362 | + | 0.907357i | \(0.361903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.47363 | 0.638687 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.64167 | −1.61084 | −0.805421 | − | 0.592704i | \(-0.798061\pi\) | ||||
−0.805421 | + | 0.592704i | \(0.798061\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.557647 | 0.127933 | 0.0639665 | − | 0.997952i | \(-0.479625\pi\) | ||||
0.0639665 | + | 0.997952i | \(0.479625\pi\) | |||||||
\(20\) | −2.47363 | −0.553120 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.66981 | −0.556693 | −0.278347 | − | 0.960481i | \(-0.589786\pi\) | ||||
−0.278347 | + | 0.960481i | \(0.589786\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.11882 | 0.223765 | ||||||||
\(26\) | 3.03127 | 0.594482 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.77568 | 0.701126 | 0.350563 | − | 0.936539i | \(-0.385990\pi\) | ||||
0.350563 | + | 0.936539i | \(0.385990\pi\) | |||||||
\(30\) | 2.47363 | 0.451620 | ||||||||
\(31\) | 2.00666 | 0.360407 | 0.180204 | − | 0.983629i | \(-0.442324\pi\) | ||||
0.180204 | + | 0.983629i | \(0.442324\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −6.64167 | −1.13904 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.158619 | −0.0260768 | −0.0130384 | − | 0.999915i | \(-0.504150\pi\) | ||||
−0.0130384 | + | 0.999915i | \(0.504150\pi\) | |||||||
\(38\) | 0.557647 | 0.0904623 | ||||||||
\(39\) | −3.03127 | −0.485392 | ||||||||
\(40\) | −2.47363 | −0.391115 | ||||||||
\(41\) | −5.93207 | −0.926433 | −0.463217 | − | 0.886245i | \(-0.653305\pi\) | ||||
−0.463217 | + | 0.886245i | \(0.653305\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.32666 | 0.659810 | 0.329905 | − | 0.944014i | \(-0.392983\pi\) | ||||
0.329905 | + | 0.944014i | \(0.392983\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −2.47363 | −0.368746 | ||||||||
\(46\) | −2.66981 | −0.393642 | ||||||||
\(47\) | −7.38607 | −1.07737 | −0.538685 | − | 0.842507i | \(-0.681079\pi\) | ||||
−0.538685 | + | 0.842507i | \(0.681079\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.11882 | 0.158226 | ||||||||
\(51\) | 6.64167 | 0.930020 | ||||||||
\(52\) | 3.03127 | 0.420362 | ||||||||
\(53\) | 2.83785 | 0.389809 | 0.194904 | − | 0.980822i | \(-0.437560\pi\) | ||||
0.194904 | + | 0.980822i | \(0.437560\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.47363 | −0.333544 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.557647 | −0.0738622 | ||||||||
\(58\) | 3.77568 | 0.495771 | ||||||||
\(59\) | −1.48881 | −0.193827 | −0.0969134 | − | 0.995293i | \(-0.530897\pi\) | ||||
−0.0969134 | + | 0.995293i | \(0.530897\pi\) | |||||||
\(60\) | 2.47363 | 0.319344 | ||||||||
\(61\) | 3.19932 | 0.409630 | 0.204815 | − | 0.978801i | \(-0.434341\pi\) | ||||
0.204815 | + | 0.978801i | \(0.434341\pi\) | |||||||
\(62\) | 2.00666 | 0.254847 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.49824 | −0.930042 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −11.2739 | −1.37733 | −0.688664 | − | 0.725081i | \(-0.741802\pi\) | ||||
−0.688664 | + | 0.725081i | \(0.741802\pi\) | |||||||
\(68\) | −6.64167 | −0.805421 | ||||||||
\(69\) | 2.66981 | 0.321407 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0098 | −1.30662 | −0.653311 | − | 0.757089i | \(-0.726621\pi\) | ||||
−0.653311 | + | 0.757089i | \(0.726621\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 3.18323 | 0.372569 | 0.186284 | − | 0.982496i | \(-0.440355\pi\) | ||||
0.186284 | + | 0.982496i | \(0.440355\pi\) | |||||||
\(74\) | −0.158619 | −0.0184391 | ||||||||
\(75\) | −1.11882 | −0.129191 | ||||||||
\(76\) | 0.557647 | 0.0639665 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.03127 | −0.343224 | ||||||||
\(79\) | −6.95668 | −0.782687 | −0.391344 | − | 0.920245i | \(-0.627990\pi\) | ||||
−0.391344 | + | 0.920245i | \(0.627990\pi\) | |||||||
\(80\) | −2.47363 | −0.276560 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.93207 | −0.655087 | ||||||||
\(83\) | 4.59744 | 0.504635 | 0.252317 | − | 0.967645i | \(-0.418807\pi\) | ||||
0.252317 | + | 0.967645i | \(0.418807\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.4290 | 1.78198 | ||||||||
\(86\) | 4.32666 | 0.466556 | ||||||||
\(87\) | −3.77568 | −0.404795 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −6.62558 | −0.702310 | −0.351155 | − | 0.936317i | \(-0.614211\pi\) | ||||
−0.351155 | + | 0.936317i | \(0.614211\pi\) | |||||||
\(90\) | −2.47363 | −0.260743 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.66981 | −0.278347 | ||||||||
\(93\) | −2.00666 | −0.208081 | ||||||||
\(94\) | −7.38607 | −0.761815 | ||||||||
\(95\) | −1.37941 | −0.141525 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −1.17656 | −0.119462 | −0.0597310 | − | 0.998215i | \(-0.519024\pi\) | ||||
−0.0597310 | + | 0.998215i | \(0.519024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.11882 | 0.111882 | ||||||||
\(101\) | −14.5295 | −1.44574 | −0.722870 | − | 0.690984i | \(-0.757177\pi\) | ||||
−0.722870 | + | 0.690984i | \(0.757177\pi\) | |||||||
\(102\) | 6.64167 | 0.657623 | ||||||||
\(103\) | −12.2239 | −1.20446 | −0.602230 | − | 0.798323i | \(-0.705721\pi\) | ||||
−0.602230 | + | 0.798323i | \(0.705721\pi\) | |||||||
\(104\) | 3.03127 | 0.297241 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.83785 | 0.275636 | ||||||||
\(107\) | −2.81900 | −0.272523 | −0.136262 | − | 0.990673i | \(-0.543509\pi\) | ||||
−0.136262 | + | 0.990673i | \(0.543509\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −20.5478 | −1.96812 | −0.984062 | − | 0.177823i | \(-0.943095\pi\) | ||||
−0.984062 | + | 0.177823i | \(0.943095\pi\) | |||||||
\(110\) | −2.47363 | −0.235851 | ||||||||
\(111\) | 0.158619 | 0.0150555 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.7194 | 1.10247 | 0.551234 | − | 0.834351i | \(-0.314157\pi\) | ||||
0.551234 | + | 0.834351i | \(0.314157\pi\) | |||||||
\(114\) | −0.557647 | −0.0522285 | ||||||||
\(115\) | 6.60411 | 0.615836 | ||||||||
\(116\) | 3.77568 | 0.350563 | ||||||||
\(117\) | 3.03127 | 0.280241 | ||||||||
\(118\) | −1.48881 | −0.137056 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.47363 | 0.225810 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.19932 | 0.289652 | ||||||||
\(123\) | 5.93207 | 0.534876 | ||||||||
\(124\) | 2.00666 | 0.180204 | ||||||||
\(125\) | 9.60058 | 0.858702 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0397948 | 0.00353121 | 0.00176561 | − | 0.999998i | \(-0.499438\pi\) | ||||
0.00176561 | + | 0.999998i | \(0.499438\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.32666 | −0.380941 | ||||||||
\(130\) | −7.49824 | −0.657639 | ||||||||
\(131\) | −9.60097 | −0.838841 | −0.419420 | − | 0.907792i | \(-0.637767\pi\) | ||||
−0.419420 | + | 0.907792i | \(0.637767\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.2739 | −0.973918 | ||||||||
\(135\) | 2.47363 | 0.212896 | ||||||||
\(136\) | −6.64167 | −0.569518 | ||||||||
\(137\) | −18.6667 | −1.59480 | −0.797400 | − | 0.603451i | \(-0.793792\pi\) | ||||
−0.797400 | + | 0.603451i | \(0.793792\pi\) | |||||||
\(138\) | 2.66981 | 0.227269 | ||||||||
\(139\) | −8.33333 | −0.706823 | −0.353412 | − | 0.935468i | \(-0.614979\pi\) | ||||
−0.353412 | + | 0.935468i | \(0.614979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.38607 | 0.622020 | ||||||||
\(142\) | −11.0098 | −0.923922 | ||||||||
\(143\) | 3.03127 | 0.253488 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −9.33962 | −0.775613 | ||||||||
\(146\) | 3.18323 | 0.263446 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.158619 | −0.0130384 | ||||||||
\(149\) | −15.2341 | −1.24803 | −0.624014 | − | 0.781413i | \(-0.714499\pi\) | ||||
−0.624014 | + | 0.781413i | \(0.714499\pi\) | |||||||
\(150\) | −1.11882 | −0.0913516 | ||||||||
\(151\) | −8.31724 | −0.676847 | −0.338424 | − | 0.940994i | \(-0.609894\pi\) | ||||
−0.338424 | + | 0.940994i | \(0.609894\pi\) | |||||||
\(152\) | 0.557647 | 0.0452312 | ||||||||
\(153\) | −6.64167 | −0.536947 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.96374 | −0.398697 | ||||||||
\(156\) | −3.03127 | −0.242696 | ||||||||
\(157\) | 9.13401 | 0.728973 | 0.364487 | − | 0.931209i | \(-0.381244\pi\) | ||||
0.364487 | + | 0.931209i | \(0.381244\pi\) | |||||||
\(158\) | −6.95668 | −0.553443 | ||||||||
\(159\) | −2.83785 | −0.225056 | ||||||||
\(160\) | −2.47363 | −0.195557 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.33609 | 0.652933 | 0.326466 | − | 0.945209i | \(-0.394142\pi\) | ||||
0.326466 | + | 0.945209i | \(0.394142\pi\) | |||||||
\(164\) | −5.93207 | −0.463217 | ||||||||
\(165\) | 2.47363 | 0.192572 | ||||||||
\(166\) | 4.59744 | 0.356831 | ||||||||
\(167\) | 22.1610 | 1.71487 | 0.857434 | − | 0.514594i | \(-0.172057\pi\) | ||||
0.857434 | + | 0.514594i | \(0.172057\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.81138 | −0.293183 | ||||||||
\(170\) | 16.4290 | 1.26005 | ||||||||
\(171\) | 0.557647 | 0.0426444 | ||||||||
\(172\) | 4.32666 | 0.329905 | ||||||||
\(173\) | −20.9656 | −1.59398 | −0.796991 | − | 0.603991i | \(-0.793576\pi\) | ||||
−0.796991 | + | 0.603991i | \(0.793576\pi\) | |||||||
\(174\) | −3.77568 | −0.286233 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 1.48881 | 0.111906 | ||||||||
\(178\) | −6.62558 | −0.496608 | ||||||||
\(179\) | −12.3759 | −0.925017 | −0.462508 | − | 0.886615i | \(-0.653050\pi\) | ||||
−0.462508 | + | 0.886615i | \(0.653050\pi\) | |||||||
\(180\) | −2.47363 | −0.184373 | ||||||||
\(181\) | −20.5595 | −1.52817 | −0.764087 | − | 0.645113i | \(-0.776810\pi\) | ||||
−0.764087 | + | 0.645113i | \(0.776810\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.19932 | −0.236500 | ||||||||
\(184\) | −2.66981 | −0.196821 | ||||||||
\(185\) | 0.392364 | 0.0288472 | ||||||||
\(186\) | −2.00666 | −0.147136 | ||||||||
\(187\) | −6.64167 | −0.485687 | ||||||||
\(188\) | −7.38607 | −0.538685 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.37941 | −0.100073 | ||||||||
\(191\) | −20.3267 | −1.47079 | −0.735393 | − | 0.677641i | \(-0.763002\pi\) | ||||
−0.735393 | + | 0.677641i | \(0.763002\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −13.0761 | −0.941235 | −0.470618 | − | 0.882337i | \(-0.655969\pi\) | ||||
−0.470618 | + | 0.882337i | \(0.655969\pi\) | |||||||
\(194\) | −1.17656 | −0.0844724 | ||||||||
\(195\) | 7.49824 | 0.536960 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.80159 | −0.270852 | −0.135426 | − | 0.990787i | \(-0.543240\pi\) | ||||
−0.135426 | + | 0.990787i | \(0.543240\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 6.87098 | 0.487071 | 0.243536 | − | 0.969892i | \(-0.421693\pi\) | ||||
0.243536 | + | 0.969892i | \(0.421693\pi\) | |||||||
\(200\) | 1.11882 | 0.0791128 | ||||||||
\(201\) | 11.2739 | 0.795201 | ||||||||
\(202\) | −14.5295 | −1.02229 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.64167 | 0.465010 | ||||||||
\(205\) | 14.6737 | 1.02486 | ||||||||
\(206\) | −12.2239 | −0.851681 | ||||||||
\(207\) | −2.66981 | −0.185564 | ||||||||
\(208\) | 3.03127 | 0.210181 | ||||||||
\(209\) | 0.557647 | 0.0385733 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7984 | 0.812237 | 0.406119 | − | 0.913820i | \(-0.366882\pi\) | ||||
0.406119 | + | 0.913820i | \(0.366882\pi\) | |||||||
\(212\) | 2.83785 | 0.194904 | ||||||||
\(213\) | 11.0098 | 0.754379 | ||||||||
\(214\) | −2.81900 | −0.192703 | ||||||||
\(215\) | −10.7025 | −0.729907 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −20.5478 | −1.39167 | ||||||||
\(219\) | −3.18323 | −0.215103 | ||||||||
\(220\) | −2.47363 | −0.166772 | ||||||||
\(221\) | −20.1327 | −1.35427 | ||||||||
\(222\) | 0.158619 | 0.0106458 | ||||||||
\(223\) | 21.0031 | 1.40647 | 0.703237 | − | 0.710956i | \(-0.251737\pi\) | ||||
0.703237 | + | 0.710956i | \(0.251737\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.11882 | 0.0745883 | ||||||||
\(226\) | 11.7194 | 0.779563 | ||||||||
\(227\) | 29.4884 | 1.95721 | 0.978607 | − | 0.205736i | \(-0.0659590\pi\) | ||||
0.978607 | + | 0.205736i | \(0.0659590\pi\) | |||||||
\(228\) | −0.557647 | −0.0369311 | ||||||||
\(229\) | 17.3254 | 1.14489 | 0.572446 | − | 0.819942i | \(-0.305995\pi\) | ||||
0.572446 | + | 0.819942i | \(0.305995\pi\) | |||||||
\(230\) | 6.60411 | 0.435462 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.77568 | 0.247885 | ||||||||
\(233\) | 29.4388 | 1.92860 | 0.964300 | − | 0.264812i | \(-0.0853100\pi\) | ||||
0.964300 | + | 0.264812i | \(0.0853100\pi\) | |||||||
\(234\) | 3.03127 | 0.198161 | ||||||||
\(235\) | 18.2704 | 1.19183 | ||||||||
\(236\) | −1.48881 | −0.0969134 | ||||||||
\(237\) | 6.95668 | 0.451885 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.2047 | 1.56567 | 0.782835 | − | 0.622229i | \(-0.213773\pi\) | ||||
0.782835 | + | 0.622229i | \(0.213773\pi\) | |||||||
\(240\) | 2.47363 | 0.159672 | ||||||||
\(241\) | 15.3083 | 0.986096 | 0.493048 | − | 0.870002i | \(-0.335883\pi\) | ||||
0.493048 | + | 0.870002i | \(0.335883\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.19932 | 0.204815 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.93207 | 0.378215 | ||||||||
\(247\) | 1.69038 | 0.107556 | ||||||||
\(248\) | 2.00666 | 0.127423 | ||||||||
\(249\) | −4.59744 | −0.291351 | ||||||||
\(250\) | 9.60058 | 0.607194 | ||||||||
\(251\) | −7.79453 | −0.491986 | −0.245993 | − | 0.969272i | \(-0.579114\pi\) | ||||
−0.245993 | + | 0.969272i | \(0.579114\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.66981 | −0.167849 | ||||||||
\(254\) | 0.0397948 | 0.00249695 | ||||||||
\(255\) | −16.4290 | −1.02882 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.0973 | −0.879368 | −0.439684 | − | 0.898152i | \(-0.644910\pi\) | ||||
−0.439684 | + | 0.898152i | \(0.644910\pi\) | |||||||
\(258\) | −4.32666 | −0.269366 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.49824 | −0.465021 | ||||||||
\(261\) | 3.77568 | 0.233709 | ||||||||
\(262\) | −9.60097 | −0.593150 | ||||||||
\(263\) | 4.61353 | 0.284482 | 0.142241 | − | 0.989832i | \(-0.454569\pi\) | ||||
0.142241 | + | 0.989832i | \(0.454569\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −7.01978 | −0.431222 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.62558 | 0.405479 | ||||||||
\(268\) | −11.2739 | −0.688664 | ||||||||
\(269\) | 3.18323 | 0.194085 | 0.0970424 | − | 0.995280i | \(-0.469062\pi\) | ||||
0.0970424 | + | 0.995280i | \(0.469062\pi\) | |||||||
\(270\) | 2.47363 | 0.150540 | ||||||||
\(271\) | −0.722930 | −0.0439149 | −0.0219574 | − | 0.999759i | \(-0.506990\pi\) | ||||
−0.0219574 | + | 0.999759i | \(0.506990\pi\) | |||||||
\(272\) | −6.64167 | −0.402710 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.6667 | −1.12769 | ||||||||
\(275\) | 1.11882 | 0.0674676 | ||||||||
\(276\) | 2.66981 | 0.160704 | ||||||||
\(277\) | 1.18490 | 0.0711938 | 0.0355969 | − | 0.999366i | \(-0.488667\pi\) | ||||
0.0355969 | + | 0.999366i | \(0.488667\pi\) | |||||||
\(278\) | −8.33333 | −0.499800 | ||||||||
\(279\) | 2.00666 | 0.120136 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.89097 | 0.172461 | 0.0862305 | − | 0.996275i | \(-0.472518\pi\) | ||||
0.0862305 | + | 0.996275i | \(0.472518\pi\) | |||||||
\(282\) | 7.38607 | 0.439834 | ||||||||
\(283\) | 5.32353 | 0.316451 | 0.158225 | − | 0.987403i | \(-0.449423\pi\) | ||||
0.158225 | + | 0.987403i | \(0.449423\pi\) | |||||||
\(284\) | −11.0098 | −0.653311 | ||||||||
\(285\) | 1.37941 | 0.0817092 | ||||||||
\(286\) | 3.03127 | 0.179243 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 27.1118 | 1.59481 | ||||||||
\(290\) | −9.33962 | −0.548441 | ||||||||
\(291\) | 1.17656 | 0.0689714 | ||||||||
\(292\) | 3.18323 | 0.186284 | ||||||||
\(293\) | −10.6413 | −0.621670 | −0.310835 | − | 0.950464i | \(-0.600609\pi\) | ||||
−0.310835 | + | 0.950464i | \(0.600609\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.68276 | 0.214419 | ||||||||
\(296\) | −0.158619 | −0.00921955 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −15.2341 | −0.882489 | ||||||||
\(299\) | −8.09292 | −0.468025 | ||||||||
\(300\) | −1.11882 | −0.0645954 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.31724 | −0.478603 | ||||||||
\(303\) | 14.5295 | 0.834698 | ||||||||
\(304\) | 0.557647 | 0.0319833 | ||||||||
\(305\) | −7.91391 | −0.453149 | ||||||||
\(306\) | −6.64167 | −0.379679 | ||||||||
\(307\) | −28.9733 | −1.65359 | −0.826797 | − | 0.562500i | \(-0.809840\pi\) | ||||
−0.826797 | + | 0.562500i | \(0.809840\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.2239 | 0.695395 | ||||||||
\(310\) | −4.96374 | −0.281921 | ||||||||
\(311\) | −2.62019 | −0.148578 | −0.0742888 | − | 0.997237i | \(-0.523669\pi\) | ||||
−0.0742888 | + | 0.997237i | \(0.523669\pi\) | |||||||
\(312\) | −3.03127 | −0.171612 | ||||||||
\(313\) | 31.7566 | 1.79499 | 0.897494 | − | 0.441027i | \(-0.145386\pi\) | ||||
0.897494 | + | 0.441027i | \(0.145386\pi\) | |||||||
\(314\) | 9.13401 | 0.515462 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.95668 | −0.391344 | ||||||||
\(317\) | −24.8308 | −1.39464 | −0.697318 | − | 0.716762i | \(-0.745623\pi\) | ||||
−0.697318 | + | 0.716762i | \(0.745623\pi\) | |||||||
\(318\) | −2.83785 | −0.159139 | ||||||||
\(319\) | 3.77568 | 0.211397 | ||||||||
\(320\) | −2.47363 | −0.138280 | ||||||||
\(321\) | 2.81900 | 0.157341 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.70371 | −0.206080 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.39146 | 0.188124 | ||||||||
\(326\) | 8.33609 | 0.461693 | ||||||||
\(327\) | 20.5478 | 1.13630 | ||||||||
\(328\) | −5.93207 | −0.327544 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.47363 | 0.136169 | ||||||||
\(331\) | 21.2669 | 1.16893 | 0.584466 | − | 0.811418i | \(-0.301304\pi\) | ||||
0.584466 | + | 0.811418i | \(0.301304\pi\) | |||||||
\(332\) | 4.59744 | 0.252317 | ||||||||
\(333\) | −0.158619 | −0.00869228 | ||||||||
\(334\) | 22.1610 | 1.21260 | ||||||||
\(335\) | 27.8874 | 1.52365 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.3927 | 1.27428 | 0.637142 | − | 0.770747i | \(-0.280117\pi\) | ||||
0.637142 | + | 0.770747i | \(0.280117\pi\) | |||||||
\(338\) | −3.81138 | −0.207312 | ||||||||
\(339\) | −11.7194 | −0.636510 | ||||||||
\(340\) | 16.4290 | 0.890988 | ||||||||
\(341\) | 2.00666 | 0.108667 | ||||||||
\(342\) | 0.557647 | 0.0301541 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.32666 | 0.233278 | ||||||||
\(345\) | −6.60411 | −0.355553 | ||||||||
\(346\) | −20.9656 | −1.12712 | ||||||||
\(347\) | 6.60020 | 0.354317 | 0.177159 | − | 0.984182i | \(-0.443309\pi\) | ||||
0.177159 | + | 0.984182i | \(0.443309\pi\) | |||||||
\(348\) | −3.77568 | −0.202398 | ||||||||
\(349\) | −5.06164 | −0.270944 | −0.135472 | − | 0.990781i | \(-0.543255\pi\) | ||||
−0.135472 | + | 0.990781i | \(0.543255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.03127 | −0.161797 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 11.5166 | 0.612964 | 0.306482 | − | 0.951876i | \(-0.400848\pi\) | ||||
0.306482 | + | 0.951876i | \(0.400848\pi\) | |||||||
\(354\) | 1.48881 | 0.0791294 | ||||||||
\(355\) | 27.2341 | 1.44544 | ||||||||
\(356\) | −6.62558 | −0.351155 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.3759 | −0.654086 | ||||||||
\(359\) | −10.5080 | −0.554593 | −0.277296 | − | 0.960784i | \(-0.589438\pi\) | ||||
−0.277296 | + | 0.960784i | \(0.589438\pi\) | |||||||
\(360\) | −2.47363 | −0.130372 | ||||||||
\(361\) | −18.6890 | −0.983633 | ||||||||
\(362\) | −20.5595 | −1.08058 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.87412 | −0.412150 | ||||||||
\(366\) | −3.19932 | −0.167231 | ||||||||
\(367\) | −10.8976 | −0.568852 | −0.284426 | − | 0.958698i | \(-0.591803\pi\) | ||||
−0.284426 | + | 0.958698i | \(0.591803\pi\) | |||||||
\(368\) | −2.66981 | −0.139173 | ||||||||
\(369\) | −5.93207 | −0.308811 | ||||||||
\(370\) | 0.392364 | 0.0203981 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.00666 | −0.104041 | ||||||||
\(373\) | 21.3459 | 1.10525 | 0.552624 | − | 0.833431i | \(-0.313627\pi\) | ||||
0.552624 | + | 0.833431i | \(0.313627\pi\) | |||||||
\(374\) | −6.64167 | −0.343433 | ||||||||
\(375\) | −9.60058 | −0.495772 | ||||||||
\(376\) | −7.38607 | −0.380908 | ||||||||
\(377\) | 11.4451 | 0.589453 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.3066 | −1.09445 | −0.547225 | − | 0.836986i | \(-0.684316\pi\) | ||||
−0.547225 | + | 0.836986i | \(0.684316\pi\) | |||||||
\(380\) | −1.37941 | −0.0707623 | ||||||||
\(381\) | −0.0397948 | −0.00203875 | ||||||||
\(382\) | −20.3267 | −1.04000 | ||||||||
\(383\) | 34.6202 | 1.76901 | 0.884505 | − | 0.466531i | \(-0.154497\pi\) | ||||
0.884505 | + | 0.466531i | \(0.154497\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0761 | −0.665554 | ||||||||
\(387\) | 4.32666 | 0.219937 | ||||||||
\(388\) | −1.17656 | −0.0597310 | ||||||||
\(389\) | −9.68276 | −0.490936 | −0.245468 | − | 0.969405i | \(-0.578942\pi\) | ||||
−0.245468 | + | 0.969405i | \(0.578942\pi\) | |||||||
\(390\) | 7.49824 | 0.379688 | ||||||||
\(391\) | 17.7320 | 0.896745 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.60097 | 0.484305 | ||||||||
\(394\) | −3.80159 | −0.191521 | ||||||||
\(395\) | 17.2082 | 0.865839 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 11.8928 | 0.596884 | 0.298442 | − | 0.954428i | \(-0.403533\pi\) | ||||
0.298442 | + | 0.954428i | \(0.403533\pi\) | |||||||
\(398\) | 6.87098 | 0.344411 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.11882 | 0.0559412 | ||||||||
\(401\) | 33.9804 | 1.69690 | 0.848449 | − | 0.529277i | \(-0.177537\pi\) | ||||
0.848449 | + | 0.529277i | \(0.177537\pi\) | |||||||
\(402\) | 11.2739 | 0.562292 | ||||||||
\(403\) | 6.08275 | 0.303003 | ||||||||
\(404\) | −14.5295 | −0.722870 | ||||||||
\(405\) | −2.47363 | −0.122915 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.158619 | −0.00786246 | ||||||||
\(408\) | 6.64167 | 0.328812 | ||||||||
\(409\) | −9.51305 | −0.470390 | −0.235195 | − | 0.971948i | \(-0.575573\pi\) | ||||
−0.235195 | + | 0.971948i | \(0.575573\pi\) | |||||||
\(410\) | 14.6737 | 0.724683 | ||||||||
\(411\) | 18.6667 | 0.920758 | ||||||||
\(412\) | −12.2239 | −0.602230 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.66981 | −0.131214 | ||||||||
\(415\) | −11.3724 | −0.558247 | ||||||||
\(416\) | 3.03127 | 0.148620 | ||||||||
\(417\) | 8.33333 | 0.408085 | ||||||||
\(418\) | 0.557647 | 0.0272754 | ||||||||
\(419\) | 15.9249 | 0.777981 | 0.388990 | − | 0.921242i | \(-0.372824\pi\) | ||||
0.388990 | + | 0.921242i | \(0.372824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.55842 | 0.173427 | 0.0867133 | − | 0.996233i | \(-0.472364\pi\) | ||||
0.0867133 | + | 0.996233i | \(0.472364\pi\) | |||||||
\(422\) | 11.7984 | 0.574339 | ||||||||
\(423\) | −7.38607 | −0.359123 | ||||||||
\(424\) | 2.83785 | 0.137818 | ||||||||
\(425\) | −7.43086 | −0.360450 | ||||||||
\(426\) | 11.0098 | 0.533426 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.81900 | −0.136262 | ||||||||
\(429\) | −3.03127 | −0.146351 | ||||||||
\(430\) | −10.7025 | −0.516122 | ||||||||
\(431\) | 20.2774 | 0.976730 | 0.488365 | − | 0.872639i | \(-0.337593\pi\) | ||||
0.488365 | + | 0.872639i | \(0.337593\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −27.7144 | −1.33187 | −0.665935 | − | 0.746010i | \(-0.731967\pi\) | ||||
−0.665935 | + | 0.746010i | \(0.731967\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.33962 | 0.447800 | ||||||||
\(436\) | −20.5478 | −0.984062 | ||||||||
\(437\) | −1.48881 | −0.0712195 | ||||||||
\(438\) | −3.18323 | −0.152101 | ||||||||
\(439\) | −4.85433 | −0.231685 | −0.115842 | − | 0.993268i | \(-0.536957\pi\) | ||||
−0.115842 | + | 0.993268i | \(0.536957\pi\) | |||||||
\(440\) | −2.47363 | −0.117925 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.1327 | −0.957615 | ||||||||
\(443\) | −30.5269 | −1.45038 | −0.725188 | − | 0.688551i | \(-0.758247\pi\) | ||||
−0.725188 | + | 0.688551i | \(0.758247\pi\) | |||||||
\(444\) | 0.158619 | 0.00752773 | ||||||||
\(445\) | 16.3892 | 0.776923 | ||||||||
\(446\) | 21.0031 | 0.994527 | ||||||||
\(447\) | 15.2341 | 0.720549 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.3986 | −1.43460 | −0.717300 | − | 0.696764i | \(-0.754622\pi\) | ||||
−0.717300 | + | 0.696764i | \(0.754622\pi\) | |||||||
\(450\) | 1.11882 | 0.0527419 | ||||||||
\(451\) | −5.93207 | −0.279330 | ||||||||
\(452\) | 11.7194 | 0.551234 | ||||||||
\(453\) | 8.31724 | 0.390778 | ||||||||
\(454\) | 29.4884 | 1.38396 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.557647 | −0.0261142 | ||||||||
\(457\) | 11.1020 | 0.519328 | 0.259664 | − | 0.965699i | \(-0.416388\pi\) | ||||
0.259664 | + | 0.965699i | \(0.416388\pi\) | |||||||
\(458\) | 17.3254 | 0.809561 | ||||||||
\(459\) | 6.64167 | 0.310007 | ||||||||
\(460\) | 6.60411 | 0.307918 | ||||||||
\(461\) | −38.1693 | −1.77772 | −0.888861 | − | 0.458177i | \(-0.848503\pi\) | ||||
−0.888861 | + | 0.458177i | \(0.848503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.4388 | −1.46108 | −0.730542 | − | 0.682867i | \(-0.760733\pi\) | ||||
−0.730542 | + | 0.682867i | \(0.760733\pi\) | |||||||
\(464\) | 3.77568 | 0.175281 | ||||||||
\(465\) | 4.96374 | 0.230188 | ||||||||
\(466\) | 29.4388 | 1.36373 | ||||||||
\(467\) | 11.9204 | 0.551611 | 0.275805 | − | 0.961213i | \(-0.411055\pi\) | ||||
0.275805 | + | 0.961213i | \(0.411055\pi\) | |||||||
\(468\) | 3.03127 | 0.140121 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 18.2704 | 0.842750 | ||||||||
\(471\) | −9.13401 | −0.420873 | ||||||||
\(472\) | −1.48881 | −0.0685281 | ||||||||
\(473\) | 4.32666 | 0.198940 | ||||||||
\(474\) | 6.95668 | 0.319531 | ||||||||
\(475\) | 0.623909 | 0.0286269 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.83785 | 0.129936 | ||||||||
\(478\) | 24.2047 | 1.10710 | ||||||||
\(479\) | 39.4155 | 1.80094 | 0.900470 | − | 0.434918i | \(-0.143223\pi\) | ||||
0.900470 | + | 0.434918i | \(0.143223\pi\) | |||||||
\(480\) | 2.47363 | 0.112905 | ||||||||
\(481\) | −0.480818 | −0.0219234 | ||||||||
\(482\) | 15.3083 | 0.697275 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 2.91038 | 0.132154 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 23.1551 | 1.04926 | 0.524629 | − | 0.851331i | \(-0.324204\pi\) | ||||
0.524629 | + | 0.851331i | \(0.324204\pi\) | |||||||
\(488\) | 3.19932 | 0.144826 | ||||||||
\(489\) | −8.33609 | −0.376971 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.47530 | −0.201967 | −0.100984 | − | 0.994888i | \(-0.532199\pi\) | ||||
−0.100984 | + | 0.994888i | \(0.532199\pi\) | |||||||
\(492\) | 5.93207 | 0.267438 | ||||||||
\(493\) | −25.0768 | −1.12940 | ||||||||
\(494\) | 1.69038 | 0.0760538 | ||||||||
\(495\) | −2.47363 | −0.111181 | ||||||||
\(496\) | 2.00666 | 0.0901019 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.59744 | −0.206016 | ||||||||
\(499\) | −16.7727 | −0.750850 | −0.375425 | − | 0.926853i | \(-0.622503\pi\) | ||||
−0.375425 | + | 0.926853i | \(0.622503\pi\) | |||||||
\(500\) | 9.60058 | 0.429351 | ||||||||
\(501\) | −22.1610 | −0.990080 | ||||||||
\(502\) | −7.79453 | −0.347887 | ||||||||
\(503\) | 41.1653 | 1.83547 | 0.917734 | − | 0.397195i | \(-0.130016\pi\) | ||||
0.917734 | + | 0.397195i | \(0.130016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.9406 | 1.59933 | ||||||||
\(506\) | −2.66981 | −0.118687 | ||||||||
\(507\) | 3.81138 | 0.169269 | ||||||||
\(508\) | 0.0397948 | 0.00176561 | ||||||||
\(509\) | −14.5987 | −0.647077 | −0.323538 | − | 0.946215i | \(-0.604872\pi\) | ||||
−0.323538 | + | 0.946215i | \(0.604872\pi\) | |||||||
\(510\) | −16.4290 | −0.727488 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.557647 | −0.0246207 | ||||||||
\(514\) | −14.0973 | −0.621807 | ||||||||
\(515\) | 30.2374 | 1.33242 | ||||||||
\(516\) | −4.32666 | −0.190471 | ||||||||
\(517\) | −7.38607 | −0.324839 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.9656 | 0.920286 | ||||||||
\(520\) | −7.49824 | −0.328819 | ||||||||
\(521\) | −17.0054 | −0.745019 | −0.372509 | − | 0.928028i | \(-0.621503\pi\) | ||||
−0.372509 | + | 0.928028i | \(0.621503\pi\) | |||||||
\(522\) | 3.77568 | 0.165257 | ||||||||
\(523\) | −32.8874 | −1.43807 | −0.719033 | − | 0.694976i | \(-0.755415\pi\) | ||||
−0.719033 | + | 0.694976i | \(0.755415\pi\) | |||||||
\(524\) | −9.60097 | −0.419420 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.61353 | 0.201159 | ||||||||
\(527\) | −13.3276 | −0.580559 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −15.8721 | −0.690092 | ||||||||
\(530\) | −7.01978 | −0.304920 | ||||||||
\(531\) | −1.48881 | −0.0646089 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.9817 | −0.778874 | ||||||||
\(534\) | 6.62558 | 0.286717 | ||||||||
\(535\) | 6.97316 | 0.301476 | ||||||||
\(536\) | −11.2739 | −0.486959 | ||||||||
\(537\) | 12.3759 | 0.534059 | ||||||||
\(538\) | 3.18323 | 0.137239 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.47363 | 0.106448 | ||||||||
\(541\) | −3.11529 | −0.133937 | −0.0669685 | − | 0.997755i | \(-0.521333\pi\) | ||||
−0.0669685 | + | 0.997755i | \(0.521333\pi\) | |||||||
\(542\) | −0.722930 | −0.0310525 | ||||||||
\(543\) | 20.5595 | 0.882292 | ||||||||
\(544\) | −6.64167 | −0.284759 | ||||||||
\(545\) | 50.8276 | 2.17722 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.58706 | −0.196129 | −0.0980643 | − | 0.995180i | \(-0.531265\pi\) | ||||
−0.0980643 | + | 0.995180i | \(0.531265\pi\) | |||||||
\(548\) | −18.6667 | −0.797400 | ||||||||
\(549\) | 3.19932 | 0.136543 | ||||||||
\(550\) | 1.11882 | 0.0477068 | ||||||||
\(551\) | 2.10550 | 0.0896972 | ||||||||
\(552\) | 2.66981 | 0.113635 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.18490 | 0.0503416 | ||||||||
\(555\) | −0.392364 | −0.0166549 | ||||||||
\(556\) | −8.33333 | −0.353412 | ||||||||
\(557\) | 18.4290 | 0.780862 | 0.390431 | − | 0.920632i | \(-0.372326\pi\) | ||||
0.390431 | + | 0.920632i | \(0.372326\pi\) | |||||||
\(558\) | 2.00666 | 0.0849488 | ||||||||
\(559\) | 13.1153 | 0.554718 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.64167 | 0.280411 | ||||||||
\(562\) | 2.89097 | 0.121948 | ||||||||
\(563\) | −7.03903 | −0.296660 | −0.148330 | − | 0.988938i | \(-0.547390\pi\) | ||||
−0.148330 | + | 0.988938i | \(0.547390\pi\) | |||||||
\(564\) | 7.38607 | 0.311010 | ||||||||
\(565\) | −28.9894 | −1.21959 | ||||||||
\(566\) | 5.32353 | 0.223765 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.0098 | −0.461961 | ||||||||
\(569\) | −20.2913 | −0.850657 | −0.425328 | − | 0.905039i | \(-0.639841\pi\) | ||||
−0.425328 | + | 0.905039i | \(0.639841\pi\) | |||||||
\(570\) | 1.37941 | 0.0577772 | ||||||||
\(571\) | 10.8517 | 0.454131 | 0.227066 | − | 0.973879i | \(-0.427087\pi\) | ||||
0.227066 | + | 0.973879i | \(0.427087\pi\) | |||||||
\(572\) | 3.03127 | 0.126744 | ||||||||
\(573\) | 20.3267 | 0.849158 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.98705 | −0.124568 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 15.0944 | 0.628387 | 0.314194 | − | 0.949359i | \(-0.398266\pi\) | ||||
0.314194 | + | 0.949359i | \(0.398266\pi\) | |||||||
\(578\) | 27.1118 | 1.12770 | ||||||||
\(579\) | 13.0761 | 0.543422 | ||||||||
\(580\) | −9.33962 | −0.387806 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.17656 | 0.0487702 | ||||||||
\(583\) | 2.83785 | 0.117532 | ||||||||
\(584\) | 3.18323 | 0.131723 | ||||||||
\(585\) | −7.49824 | −0.310014 | ||||||||
\(586\) | −10.6413 | −0.439587 | ||||||||
\(587\) | −8.46197 | −0.349263 | −0.174631 | − | 0.984634i | \(-0.555873\pi\) | ||||
−0.174631 | + | 0.984634i | \(0.555873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.11901 | 0.0461080 | ||||||||
\(590\) | 3.68276 | 0.151617 | ||||||||
\(591\) | 3.80159 | 0.156376 | ||||||||
\(592\) | −0.158619 | −0.00651921 | ||||||||
\(593\) | −28.2234 | −1.15900 | −0.579498 | − | 0.814974i | \(-0.696751\pi\) | ||||
−0.579498 | + | 0.814974i | \(0.696751\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.2341 | −0.624014 | ||||||||
\(597\) | −6.87098 | −0.281211 | ||||||||
\(598\) | −8.09292 | −0.330944 | ||||||||
\(599\) | 15.4396 | 0.630845 | 0.315422 | − | 0.948951i | \(-0.397854\pi\) | ||||
0.315422 | + | 0.948951i | \(0.397854\pi\) | |||||||
\(600\) | −1.11882 | −0.0456758 | ||||||||
\(601\) | 10.8464 | 0.442432 | 0.221216 | − | 0.975225i | \(-0.428997\pi\) | ||||
0.221216 | + | 0.975225i | \(0.428997\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.2739 | −0.459109 | ||||||||
\(604\) | −8.31724 | −0.338424 | ||||||||
\(605\) | −2.47363 | −0.100567 | ||||||||
\(606\) | 14.5295 | 0.590221 | ||||||||
\(607\) | 13.9134 | 0.564725 | 0.282363 | − | 0.959308i | \(-0.408882\pi\) | ||||
0.282363 | + | 0.959308i | \(0.408882\pi\) | |||||||
\(608\) | 0.557647 | 0.0226156 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.91391 | −0.320425 | ||||||||
\(611\) | −22.3892 | −0.905770 | ||||||||
\(612\) | −6.64167 | −0.268474 | ||||||||
\(613\) | 6.82843 | 0.275798 | 0.137899 | − | 0.990446i | \(-0.455965\pi\) | ||||
0.137899 | + | 0.990446i | \(0.455965\pi\) | |||||||
\(614\) | −28.9733 | −1.16927 | ||||||||
\(615\) | −14.6737 | −0.591701 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.0688 | −1.29104 | −0.645521 | − | 0.763743i | \(-0.723360\pi\) | ||||
−0.645521 | + | 0.763743i | \(0.723360\pi\) | |||||||
\(618\) | 12.2239 | 0.491718 | ||||||||
\(619\) | 18.0492 | 0.725459 | 0.362730 | − | 0.931894i | \(-0.381845\pi\) | ||||
0.362730 | + | 0.931894i | \(0.381845\pi\) | |||||||
\(620\) | −4.96374 | −0.199348 | ||||||||
\(621\) | 2.66981 | 0.107136 | ||||||||
\(622\) | −2.62019 | −0.105060 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.03127 | −0.121348 | ||||||||
\(625\) | −29.3424 | −1.17369 | ||||||||
\(626\) | 31.7566 | 1.26925 | ||||||||
\(627\) | −0.557647 | −0.0222703 | ||||||||
\(628\) | 9.13401 | 0.364487 | ||||||||
\(629\) | 1.05350 | 0.0420056 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.28724 | 0.369719 | 0.184860 | − | 0.982765i | \(-0.440817\pi\) | ||||
0.184860 | + | 0.982765i | \(0.440817\pi\) | |||||||
\(632\) | −6.95668 | −0.276722 | ||||||||
\(633\) | −11.7984 | −0.468945 | ||||||||
\(634\) | −24.8308 | −0.986157 | ||||||||
\(635\) | −0.0984373 | −0.00390637 | ||||||||
\(636\) | −2.83785 | −0.112528 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.77568 | 0.149481 | ||||||||
\(639\) | −11.0098 | −0.435541 | ||||||||
\(640\) | −2.47363 | −0.0977786 | ||||||||
\(641\) | −15.3700 | −0.607078 | −0.303539 | − | 0.952819i | \(-0.598168\pi\) | ||||
−0.303539 | + | 0.952819i | \(0.598168\pi\) | |||||||
\(642\) | 2.81900 | 0.111257 | ||||||||
\(643\) | 11.3833 | 0.448914 | 0.224457 | − | 0.974484i | \(-0.427939\pi\) | ||||
0.224457 | + | 0.974484i | \(0.427939\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.7025 | 0.421412 | ||||||||
\(646\) | −3.70371 | −0.145720 | ||||||||
\(647\) | 20.1464 | 0.792038 | 0.396019 | − | 0.918242i | \(-0.370391\pi\) | ||||
0.396019 | + | 0.918242i | \(0.370391\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −1.48881 | −0.0584410 | ||||||||
\(650\) | 3.39146 | 0.133024 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.33609 | 0.326466 | ||||||||
\(653\) | −38.1062 | −1.49121 | −0.745606 | − | 0.666387i | \(-0.767840\pi\) | ||||
−0.745606 | + | 0.666387i | \(0.767840\pi\) | |||||||
\(654\) | 20.5478 | 0.803484 | ||||||||
\(655\) | 23.7492 | 0.927958 | ||||||||
\(656\) | −5.93207 | −0.231608 | ||||||||
\(657\) | 3.18323 | 0.124190 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.4653 | 0.836168 | 0.418084 | − | 0.908408i | \(-0.362702\pi\) | ||||
0.418084 | + | 0.908408i | \(0.362702\pi\) | |||||||
\(660\) | 2.47363 | 0.0962858 | ||||||||
\(661\) | −6.01166 | −0.233826 | −0.116913 | − | 0.993142i | \(-0.537300\pi\) | ||||
−0.116913 | + | 0.993142i | \(0.537300\pi\) | |||||||
\(662\) | 21.2669 | 0.826560 | ||||||||
\(663\) | 20.1327 | 0.781890 | ||||||||
\(664\) | 4.59744 | 0.178415 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.158619 | −0.00614637 | ||||||||
\(667\) | −10.0803 | −0.390312 | ||||||||
\(668\) | 22.1610 | 0.857434 | ||||||||
\(669\) | −21.0031 | −0.812028 | ||||||||
\(670\) | 27.8874 | 1.07739 | ||||||||
\(671\) | 3.19932 | 0.123508 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.415116 | 0.0160015 | 0.00800077 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800077 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(674\) | 23.3927 | 0.901055 | ||||||||
\(675\) | −1.11882 | −0.0430636 | ||||||||
\(676\) | −3.81138 | −0.146592 | ||||||||
\(677\) | 18.2067 | 0.699742 | 0.349871 | − | 0.936798i | \(-0.386225\pi\) | ||||
0.349871 | + | 0.936798i | \(0.386225\pi\) | |||||||
\(678\) | −11.7194 | −0.450081 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 16.4290 | 0.630024 | ||||||||
\(681\) | −29.4884 | −1.13000 | ||||||||
\(682\) | 2.00666 | 0.0768391 | ||||||||
\(683\) | −44.9763 | −1.72097 | −0.860485 | − | 0.509476i | \(-0.829839\pi\) | ||||
−0.860485 | + | 0.509476i | \(0.829839\pi\) | |||||||
\(684\) | 0.557647 | 0.0213222 | ||||||||
\(685\) | 46.1743 | 1.76423 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.3254 | −0.661004 | ||||||||
\(688\) | 4.32666 | 0.164952 | ||||||||
\(689\) | 8.60230 | 0.327722 | ||||||||
\(690\) | −6.60411 | −0.251414 | ||||||||
\(691\) | 30.7910 | 1.17134 | 0.585672 | − | 0.810548i | \(-0.300831\pi\) | ||||
0.585672 | + | 0.810548i | \(0.300831\pi\) | |||||||
\(692\) | −20.9656 | −0.796991 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.60020 | 0.250540 | ||||||||
\(695\) | 20.6135 | 0.781916 | ||||||||
\(696\) | −3.77568 | −0.143117 | ||||||||
\(697\) | 39.3988 | 1.49234 | ||||||||
\(698\) | −5.06164 | −0.191586 | ||||||||
\(699\) | −29.4388 | −1.11348 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.83376 | −0.295877 | −0.147939 | − | 0.988997i | \(-0.547264\pi\) | ||||
−0.147939 | + | 0.988997i | \(0.547264\pi\) | |||||||
\(702\) | −3.03127 | −0.114408 | ||||||||
\(703\) | −0.0884535 | −0.00333609 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −18.2704 | −0.688102 | ||||||||
\(706\) | 11.5166 | 0.433431 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.48881 | 0.0559530 | ||||||||
\(709\) | 44.2507 | 1.66187 | 0.830936 | − | 0.556368i | \(-0.187806\pi\) | ||||
0.830936 | + | 0.556368i | \(0.187806\pi\) | |||||||
\(710\) | 27.2341 | 1.02208 | ||||||||
\(711\) | −6.95668 | −0.260896 | ||||||||
\(712\) | −6.62558 | −0.248304 | ||||||||
\(713\) | −5.35741 | −0.200636 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.49824 | −0.280418 | ||||||||
\(716\) | −12.3759 | −0.462508 | ||||||||
\(717\) | −24.2047 | −0.903940 | ||||||||
\(718\) | −10.5080 | −0.392156 | ||||||||
\(719\) | 6.50843 | 0.242723 | 0.121362 | − | 0.992608i | \(-0.461274\pi\) | ||||
0.121362 | + | 0.992608i | \(0.461274\pi\) | |||||||
\(720\) | −2.47363 | −0.0921866 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.6890 | −0.695534 | ||||||||
\(723\) | −15.3083 | −0.569323 | ||||||||
\(724\) | −20.5595 | −0.764087 | ||||||||
\(725\) | 4.22432 | 0.156887 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | −18.9110 | −0.701369 | −0.350684 | − | 0.936494i | \(-0.614051\pi\) | ||||
−0.350684 | + | 0.936494i | \(0.614051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.87412 | −0.291434 | ||||||||
\(731\) | −28.7363 | −1.06285 | ||||||||
\(732\) | −3.19932 | −0.118250 | ||||||||
\(733\) | 10.2146 | 0.377286 | 0.188643 | − | 0.982046i | \(-0.439591\pi\) | ||||
0.188643 | + | 0.982046i | \(0.439591\pi\) | |||||||
\(734\) | −10.8976 | −0.402239 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.66981 | −0.0984104 | ||||||||
\(737\) | −11.2739 | −0.415280 | ||||||||
\(738\) | −5.93207 | −0.218362 | ||||||||
\(739\) | 7.08939 | 0.260787 | 0.130394 | − | 0.991462i | \(-0.458376\pi\) | ||||
0.130394 | + | 0.991462i | \(0.458376\pi\) | |||||||
\(740\) | 0.392364 | 0.0144236 | ||||||||
\(741\) | −1.69038 | −0.0620977 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.5408 | −1.19380 | −0.596902 | − | 0.802314i | \(-0.703602\pi\) | ||||
−0.596902 | + | 0.802314i | \(0.703602\pi\) | |||||||
\(744\) | −2.00666 | −0.0735679 | ||||||||
\(745\) | 37.6835 | 1.38062 | ||||||||
\(746\) | 21.3459 | 0.781528 | ||||||||
\(747\) | 4.59744 | 0.168212 | ||||||||
\(748\) | −6.64167 | −0.242843 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.60058 | −0.350563 | ||||||||
\(751\) | −29.0496 | −1.06003 | −0.530017 | − | 0.847987i | \(-0.677815\pi\) | ||||
−0.530017 | + | 0.847987i | \(0.677815\pi\) | |||||||
\(752\) | −7.38607 | −0.269342 | ||||||||
\(753\) | 7.79453 | 0.284048 | ||||||||
\(754\) | 11.4451 | 0.416806 | ||||||||
\(755\) | 20.5737 | 0.748755 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4151 | 1.03276 | 0.516382 | − | 0.856358i | \(-0.327278\pi\) | ||||
0.516382 | + | 0.856358i | \(0.327278\pi\) | |||||||
\(758\) | −21.3066 | −0.773892 | ||||||||
\(759\) | 2.66981 | 0.0969079 | ||||||||
\(760\) | −1.37941 | −0.0500365 | ||||||||
\(761\) | 25.7999 | 0.935245 | 0.467622 | − | 0.883928i | \(-0.345111\pi\) | ||||
0.467622 | + | 0.883928i | \(0.345111\pi\) | |||||||
\(762\) | −0.0397948 | −0.00144161 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.3267 | −0.735393 | ||||||||
\(765\) | 16.4290 | 0.593992 | ||||||||
\(766\) | 34.6202 | 1.25088 | ||||||||
\(767\) | −4.51299 | −0.162955 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −27.1932 | −0.980612 | −0.490306 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490306 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0973 | 0.507704 | ||||||||
\(772\) | −13.0761 | −0.470618 | ||||||||
\(773\) | 24.5032 | 0.881319 | 0.440660 | − | 0.897674i | \(-0.354745\pi\) | ||||
0.440660 | + | 0.897674i | \(0.354745\pi\) | |||||||
\(774\) | 4.32666 | 0.155519 | ||||||||
\(775\) | 2.24510 | 0.0806465 | ||||||||
\(776\) | −1.17656 | −0.0422362 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.68276 | −0.347144 | ||||||||
\(779\) | −3.30800 | −0.118521 | ||||||||
\(780\) | 7.49824 | 0.268480 | ||||||||
\(781\) | −11.0098 | −0.393962 | ||||||||
\(782\) | 17.7320 | 0.634094 | ||||||||
\(783\) | −3.77568 | −0.134932 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.5941 | −0.806419 | ||||||||
\(786\) | 9.60097 | 0.342455 | ||||||||
\(787\) | 52.8741 | 1.88476 | 0.942379 | − | 0.334547i | \(-0.108583\pi\) | ||||
0.942379 | + | 0.334547i | \(0.108583\pi\) | |||||||
\(788\) | −3.80159 | −0.135426 | ||||||||
\(789\) | −4.61353 | −0.164246 | ||||||||
\(790\) | 17.2082 | 0.612241 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 9.69800 | 0.344386 | ||||||||
\(794\) | 11.8928 | 0.422061 | ||||||||
\(795\) | 7.01978 | 0.248966 | ||||||||
\(796\) | 6.87098 | 0.243536 | ||||||||
\(797\) | −27.1028 | −0.960032 | −0.480016 | − | 0.877260i | \(-0.659369\pi\) | ||||
−0.480016 | + | 0.877260i | \(0.659369\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.0559 | 1.73547 | ||||||||
\(800\) | 1.11882 | 0.0395564 | ||||||||
\(801\) | −6.62558 | −0.234103 | ||||||||
\(802\) | 33.9804 | 1.19989 | ||||||||
\(803\) | 3.18323 | 0.112334 | ||||||||
\(804\) | 11.2739 | 0.397600 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.08275 | 0.214256 | ||||||||
\(807\) | −3.18323 | −0.112055 | ||||||||
\(808\) | −14.5295 | −0.511146 | ||||||||
\(809\) | −3.58488 | −0.126038 | −0.0630189 | − | 0.998012i | \(-0.520073\pi\) | ||||
−0.0630189 | + | 0.998012i | \(0.520073\pi\) | |||||||
\(810\) | −2.47363 | −0.0869143 | ||||||||
\(811\) | −50.2933 | −1.76604 | −0.883018 | − | 0.469339i | \(-0.844492\pi\) | ||||
−0.883018 | + | 0.469339i | \(0.844492\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.722930 | 0.0253543 | ||||||||
\(814\) | −0.158619 | −0.00555960 | ||||||||
\(815\) | −20.6204 | −0.722300 | ||||||||
\(816\) | 6.64167 | 0.232505 | ||||||||
\(817\) | 2.41275 | 0.0844115 | ||||||||
\(818\) | −9.51305 | −0.332616 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.6737 | 0.512428 | ||||||||
\(821\) | −11.1556 | −0.389335 | −0.194667 | − | 0.980869i | \(-0.562363\pi\) | ||||
−0.194667 | + | 0.980869i | \(0.562363\pi\) | |||||||
\(822\) | 18.6667 | 0.651074 | ||||||||
\(823\) | 22.7860 | 0.794271 | 0.397136 | − | 0.917760i | \(-0.370004\pi\) | ||||
0.397136 | + | 0.917760i | \(0.370004\pi\) | |||||||
\(824\) | −12.2239 | −0.425841 | ||||||||
\(825\) | −1.11882 | −0.0389525 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.0490 | 0.592853 | 0.296426 | − | 0.955056i | \(-0.404205\pi\) | ||||
0.296426 | + | 0.955056i | \(0.404205\pi\) | |||||||
\(828\) | −2.66981 | −0.0927822 | ||||||||
\(829\) | 11.6952 | 0.406190 | 0.203095 | − | 0.979159i | \(-0.434900\pi\) | ||||
0.203095 | + | 0.979159i | \(0.434900\pi\) | |||||||
\(830\) | −11.3724 | −0.394740 | ||||||||
\(831\) | −1.18490 | −0.0411037 | ||||||||
\(832\) | 3.03127 | 0.105090 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.33333 | 0.288559 | ||||||||
\(835\) | −54.8180 | −1.89705 | ||||||||
\(836\) | 0.557647 | 0.0192866 | ||||||||
\(837\) | −2.00666 | −0.0693604 | ||||||||
\(838\) | 15.9249 | 0.550116 | ||||||||
\(839\) | −30.2833 | −1.04550 | −0.522748 | − | 0.852487i | \(-0.675093\pi\) | ||||
−0.522748 | + | 0.852487i | \(0.675093\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7443 | −0.508422 | ||||||||
\(842\) | 3.55842 | 0.122631 | ||||||||
\(843\) | −2.89097 | −0.0995704 | ||||||||
\(844\) | 11.7984 | 0.406119 | ||||||||
\(845\) | 9.42794 | 0.324331 | ||||||||
\(846\) | −7.38607 | −0.253938 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.83785 | 0.0974522 | ||||||||
\(849\) | −5.32353 | −0.182703 | ||||||||
\(850\) | −7.43086 | −0.254876 | ||||||||
\(851\) | 0.423483 | 0.0145168 | ||||||||
\(852\) | 11.0098 | 0.377189 | ||||||||
\(853\) | 34.7318 | 1.18920 | 0.594598 | − | 0.804023i | \(-0.297311\pi\) | ||||
0.594598 | + | 0.804023i | \(0.297311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.37941 | −0.0471749 | ||||||||
\(856\) | −2.81900 | −0.0963515 | ||||||||
\(857\) | −21.7344 | −0.742433 | −0.371216 | − | 0.928546i | \(-0.621059\pi\) | ||||
−0.371216 | + | 0.928546i | \(0.621059\pi\) | |||||||
\(858\) | −3.03127 | −0.103486 | ||||||||
\(859\) | 39.9241 | 1.36219 | 0.681096 | − | 0.732194i | \(-0.261504\pi\) | ||||
0.681096 | + | 0.732194i | \(0.261504\pi\) | |||||||
\(860\) | −10.7025 | −0.364954 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.2774 | 0.690652 | ||||||||
\(863\) | 57.8380 | 1.96883 | 0.984414 | − | 0.175866i | \(-0.0562726\pi\) | ||||
0.984414 | + | 0.175866i | \(0.0562726\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 51.8610 | 1.76333 | ||||||||
\(866\) | −27.7144 | −0.941774 | ||||||||
\(867\) | −27.1118 | −0.920764 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.95668 | −0.235989 | ||||||||
\(870\) | 9.33962 | 0.316643 | ||||||||
\(871\) | −34.1743 | −1.15795 | ||||||||
\(872\) | −20.5478 | −0.695837 | ||||||||
\(873\) | −1.17656 | −0.0398207 | ||||||||
\(874\) | −1.48881 | −0.0503598 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.18323 | −0.107551 | ||||||||
\(877\) | −38.1717 | −1.28897 | −0.644484 | − | 0.764618i | \(-0.722928\pi\) | ||||
−0.644484 | + | 0.764618i | \(0.722928\pi\) | |||||||
\(878\) | −4.85433 | −0.163826 | ||||||||
\(879\) | 10.6413 | 0.358921 | ||||||||
\(880\) | −2.47363 | −0.0833859 | ||||||||
\(881\) | 50.5818 | 1.70415 | 0.852073 | − | 0.523423i | \(-0.175345\pi\) | ||||
0.852073 | + | 0.523423i | \(0.175345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.3333 | −1.52559 | −0.762794 | − | 0.646642i | \(-0.776173\pi\) | ||||
−0.762794 | + | 0.646642i | \(0.776173\pi\) | |||||||
\(884\) | −20.1327 | −0.677136 | ||||||||
\(885\) | −3.68276 | −0.123795 | ||||||||
\(886\) | −30.5269 | −1.02557 | ||||||||
\(887\) | 14.6337 | 0.491353 | 0.245676 | − | 0.969352i | \(-0.420990\pi\) | ||||
0.245676 | + | 0.969352i | \(0.420990\pi\) | |||||||
\(888\) | 0.158619 | 0.00532291 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.3892 | 0.549368 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 21.0031 | 0.703237 | ||||||||
\(893\) | −4.11882 | −0.137831 | ||||||||
\(894\) | 15.2341 | 0.509505 | ||||||||
\(895\) | 30.6133 | 1.02329 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.09292 | 0.270215 | ||||||||
\(898\) | −30.3986 | −1.01442 | ||||||||
\(899\) | 7.57652 | 0.252691 | ||||||||
\(900\) | 1.11882 | 0.0372941 | ||||||||
\(901\) | −18.8481 | −0.627920 | ||||||||
\(902\) | −5.93207 | −0.197516 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.7194 | 0.389781 | ||||||||
\(905\) | 50.8565 | 1.69053 | ||||||||
\(906\) | 8.31724 | 0.276322 | ||||||||
\(907\) | 51.4597 | 1.70869 | 0.854346 | − | 0.519704i | \(-0.173958\pi\) | ||||
0.854346 | + | 0.519704i | \(0.173958\pi\) | |||||||
\(908\) | 29.4884 | 0.978607 | ||||||||
\(909\) | −14.5295 | −0.481913 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.27373 | 0.141595 | 0.0707975 | − | 0.997491i | \(-0.477446\pi\) | ||||
0.0707975 | + | 0.997491i | \(0.477446\pi\) | |||||||
\(912\) | −0.557647 | −0.0184655 | ||||||||
\(913\) | 4.59744 | 0.152153 | ||||||||
\(914\) | 11.1020 | 0.367220 | ||||||||
\(915\) | 7.91391 | 0.261626 | ||||||||
\(916\) | 17.3254 | 0.572446 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.64167 | 0.219208 | ||||||||
\(919\) | 46.0992 | 1.52067 | 0.760336 | − | 0.649530i | \(-0.225034\pi\) | ||||
0.760336 | + | 0.649530i | \(0.225034\pi\) | |||||||
\(920\) | 6.60411 | 0.217731 | ||||||||
\(921\) | 28.9733 | 0.954703 | ||||||||
\(922\) | −38.1693 | −1.25704 | ||||||||
\(923\) | −33.3737 | −1.09851 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.177467 | −0.00583508 | ||||||||
\(926\) | −31.4388 | −1.03314 | ||||||||
\(927\) | −12.2239 | −0.401486 | ||||||||
\(928\) | 3.77568 | 0.123943 | ||||||||
\(929\) | −46.3287 | −1.51999 | −0.759997 | − | 0.649926i | \(-0.774800\pi\) | ||||
−0.759997 | + | 0.649926i | \(0.774800\pi\) | |||||||
\(930\) | 4.96374 | 0.162767 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 29.4388 | 0.964300 | ||||||||
\(933\) | 2.62019 | 0.0857813 | ||||||||
\(934\) | 11.9204 | 0.390048 | ||||||||
\(935\) | 16.4290 | 0.537286 | ||||||||
\(936\) | 3.03127 | 0.0990803 | ||||||||
\(937\) | −50.7016 | −1.65635 | −0.828175 | − | 0.560470i | \(-0.810621\pi\) | ||||
−0.828175 | + | 0.560470i | \(0.810621\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.7566 | −1.03634 | ||||||||
\(940\) | 18.2704 | 0.595914 | ||||||||
\(941\) | −23.8736 | −0.778257 | −0.389128 | − | 0.921184i | \(-0.627224\pi\) | ||||
−0.389128 | + | 0.921184i | \(0.627224\pi\) | |||||||
\(942\) | −9.13401 | −0.297602 | ||||||||
\(943\) | 15.8375 | 0.515739 | ||||||||
\(944\) | −1.48881 | −0.0484567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.32666 | 0.140672 | ||||||||
\(947\) | −21.8678 | −0.710610 | −0.355305 | − | 0.934751i | \(-0.615623\pi\) | ||||
−0.355305 | + | 0.934751i | \(0.615623\pi\) | |||||||
\(948\) | 6.95668 | 0.225942 | ||||||||
\(949\) | 9.64923 | 0.313227 | ||||||||
\(950\) | 0.623909 | 0.0202423 | ||||||||
\(951\) | 24.8308 | 0.805194 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.42292 | 0.143273 | 0.0716363 | − | 0.997431i | \(-0.477178\pi\) | ||||
0.0716363 | + | 0.997431i | \(0.477178\pi\) | |||||||
\(954\) | 2.83785 | 0.0918788 | ||||||||
\(955\) | 50.2806 | 1.62704 | ||||||||
\(956\) | 24.2047 | 0.782835 | ||||||||
\(957\) | −3.77568 | −0.122050 | ||||||||
\(958\) | 39.4155 | 1.27346 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.47363 | 0.0798359 | ||||||||
\(961\) | −26.9733 | −0.870106 | ||||||||
\(962\) | −0.480818 | −0.0155022 | ||||||||
\(963\) | −2.81900 | −0.0908411 | ||||||||
\(964\) | 15.3083 | 0.493048 | ||||||||
\(965\) | 32.3453 | 1.04123 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.1894 | 0.552773 | 0.276386 | − | 0.961047i | \(-0.410863\pi\) | ||||
0.276386 | + | 0.961047i | \(0.410863\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 3.70371 | 0.118980 | ||||||||
\(970\) | 2.91038 | 0.0934467 | ||||||||
\(971\) | 25.4614 | 0.817094 | 0.408547 | − | 0.912737i | \(-0.366036\pi\) | ||||
0.408547 | + | 0.912737i | \(0.366036\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.1551 | 0.741937 | ||||||||
\(975\) | −3.39146 | −0.108614 | ||||||||
\(976\) | 3.19932 | 0.102408 | ||||||||
\(977\) | 16.9143 | 0.541136 | 0.270568 | − | 0.962701i | \(-0.412789\pi\) | ||||
0.270568 | + | 0.962701i | \(0.412789\pi\) | |||||||
\(978\) | −8.33609 | −0.266559 | ||||||||
\(979\) | −6.62558 | −0.211754 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.5478 | −0.656042 | ||||||||
\(982\) | −4.47530 | −0.142812 | ||||||||
\(983\) | −20.3763 | −0.649902 | −0.324951 | − | 0.945731i | \(-0.605348\pi\) | ||||
−0.324951 | + | 0.945731i | \(0.605348\pi\) | |||||||
\(984\) | 5.93207 | 0.189107 | ||||||||
\(985\) | 9.40370 | 0.299627 | ||||||||
\(986\) | −25.0768 | −0.798608 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.69038 | 0.0537782 | ||||||||
\(989\) | −11.5514 | −0.367312 | ||||||||
\(990\) | −2.47363 | −0.0786170 | ||||||||
\(991\) | 35.1482 | 1.11652 | 0.558260 | − | 0.829666i | \(-0.311469\pi\) | ||||
0.558260 | + | 0.829666i | \(0.311469\pi\) | |||||||
\(992\) | 2.00666 | 0.0637116 | ||||||||
\(993\) | −21.2669 | −0.674883 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.9962 | −0.538817 | ||||||||
\(996\) | −4.59744 | −0.145676 | ||||||||
\(997\) | −43.8660 | −1.38925 | −0.694625 | − | 0.719372i | \(-0.744429\pi\) | ||||
−0.694625 | + | 0.719372i | \(0.744429\pi\) | |||||||
\(998\) | −16.7727 | −0.530931 | ||||||||
\(999\) | 0.158619 | 0.00501849 |
(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 | 3234.2.a.bl.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 9702.2.a.ea.1.3 | 4 | |||
7.6 | odd | 2 | 3234.2.a.bm.1.3 | yes | 4 | ||
21.20 | even | 2 | 9702.2.a.dz.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bl.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3234.2.a.bm.1.3 | yes | 4 | 7.6 | odd | 2 | ||
9702.2.a.dz.1.2 | 4 | 21.20 | even | 2 | |||
9702.2.a.ea.1.3 | 4 | 3.2 | odd | 2 |