Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −1.45785 | −0.841692 | −0.420846 | − | 0.907132i | \(-0.638267\pi\) | ||||
−0.420846 | + | 0.907132i | \(0.638267\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.272726 | 0.121967 | 0.0609834 | − | 0.998139i | \(-0.480576\pi\) | ||||
0.0609834 | + | 0.998139i | \(0.480576\pi\) | |||||||
\(6\) | −1.45785 | −0.595166 | ||||||||
\(7\) | 4.58744 | 1.73389 | 0.866945 | − | 0.498403i | \(-0.166080\pi\) | ||||
0.866945 | + | 0.498403i | \(0.166080\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.874665 | −0.291555 | ||||||||
\(10\) | 0.272726 | 0.0862435 | ||||||||
\(11\) | −1.88209 | −0.567472 | −0.283736 | − | 0.958902i | \(-0.591574\pi\) | ||||
−0.283736 | + | 0.958902i | \(0.591574\pi\) | |||||||
\(12\) | −1.45785 | −0.420846 | ||||||||
\(13\) | −4.55484 | −1.26329 | −0.631643 | − | 0.775260i | \(-0.717619\pi\) | ||||
−0.631643 | + | 0.775260i | \(0.717619\pi\) | |||||||
\(14\) | 4.58744 | 1.22605 | ||||||||
\(15\) | −0.397594 | −0.102658 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.81630 | −1.16812 | −0.584062 | − | 0.811709i | \(-0.698538\pi\) | ||||
−0.584062 | + | 0.811709i | \(0.698538\pi\) | |||||||
\(18\) | −0.874665 | −0.206161 | ||||||||
\(19\) | 3.57600 | 0.820390 | 0.410195 | − | 0.911998i | \(-0.365461\pi\) | ||||
0.410195 | + | 0.911998i | \(0.365461\pi\) | |||||||
\(20\) | 0.272726 | 0.0609834 | ||||||||
\(21\) | −6.68782 | −1.45940 | ||||||||
\(22\) | −1.88209 | −0.401263 | ||||||||
\(23\) | 2.91478 | 0.607774 | 0.303887 | − | 0.952708i | \(-0.401715\pi\) | ||||
0.303887 | + | 0.952708i | \(0.401715\pi\) | |||||||
\(24\) | −1.45785 | −0.297583 | ||||||||
\(25\) | −4.92562 | −0.985124 | ||||||||
\(26\) | −4.55484 | −0.893278 | ||||||||
\(27\) | 5.64869 | 1.08709 | ||||||||
\(28\) | 4.58744 | 0.866945 | ||||||||
\(29\) | 6.32421 | 1.17438 | 0.587188 | − | 0.809451i | \(-0.300235\pi\) | ||||
0.587188 | + | 0.809451i | \(0.300235\pi\) | |||||||
\(30\) | −0.397594 | −0.0725904 | ||||||||
\(31\) | 4.00085 | 0.718573 | 0.359287 | − | 0.933227i | \(-0.383020\pi\) | ||||
0.359287 | + | 0.933227i | \(0.383020\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.74381 | 0.477636 | ||||||||
\(34\) | −4.81630 | −0.825989 | ||||||||
\(35\) | 1.25111 | 0.211477 | ||||||||
\(36\) | −0.874665 | −0.145778 | ||||||||
\(37\) | 6.09247 | 1.00160 | 0.500798 | − | 0.865564i | \(-0.333040\pi\) | ||||
0.500798 | + | 0.865564i | \(0.333040\pi\) | |||||||
\(38\) | 3.57600 | 0.580103 | ||||||||
\(39\) | 6.64029 | 1.06330 | ||||||||
\(40\) | 0.272726 | 0.0431217 | ||||||||
\(41\) | 3.62123 | 0.565542 | 0.282771 | − | 0.959187i | \(-0.408746\pi\) | ||||
0.282771 | + | 0.959187i | \(0.408746\pi\) | |||||||
\(42\) | −6.68782 | −1.03195 | ||||||||
\(43\) | 3.58714 | 0.547033 | 0.273517 | − | 0.961867i | \(-0.411813\pi\) | ||||
0.273517 | + | 0.961867i | \(0.411813\pi\) | |||||||
\(44\) | −1.88209 | −0.283736 | ||||||||
\(45\) | −0.238544 | −0.0355600 | ||||||||
\(46\) | 2.91478 | 0.429761 | ||||||||
\(47\) | 3.64602 | 0.531826 | 0.265913 | − | 0.963997i | \(-0.414327\pi\) | ||||
0.265913 | + | 0.963997i | \(0.414327\pi\) | |||||||
\(48\) | −1.45785 | −0.210423 | ||||||||
\(49\) | 14.0446 | 2.00638 | ||||||||
\(50\) | −4.92562 | −0.696588 | ||||||||
\(51\) | 7.02146 | 0.983201 | ||||||||
\(52\) | −4.55484 | −0.631643 | ||||||||
\(53\) | −0.684641 | −0.0940427 | −0.0470214 | − | 0.998894i | \(-0.514973\pi\) | ||||
−0.0470214 | + | 0.998894i | \(0.514973\pi\) | |||||||
\(54\) | 5.64869 | 0.768690 | ||||||||
\(55\) | −0.513295 | −0.0692126 | ||||||||
\(56\) | 4.58744 | 0.613023 | ||||||||
\(57\) | −5.21328 | −0.690515 | ||||||||
\(58\) | 6.32421 | 0.830409 | ||||||||
\(59\) | 12.0566 | 1.56963 | 0.784815 | − | 0.619730i | \(-0.212758\pi\) | ||||
0.784815 | + | 0.619730i | \(0.212758\pi\) | |||||||
\(60\) | −0.397594 | −0.0513292 | ||||||||
\(61\) | −11.4376 | −1.46443 | −0.732214 | − | 0.681075i | \(-0.761513\pi\) | ||||
−0.732214 | + | 0.681075i | \(0.761513\pi\) | |||||||
\(62\) | 4.00085 | 0.508108 | ||||||||
\(63\) | −4.01248 | −0.505524 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.24222 | −0.154079 | ||||||||
\(66\) | 2.74381 | 0.337740 | ||||||||
\(67\) | 0.692854 | 0.0846456 | 0.0423228 | − | 0.999104i | \(-0.486524\pi\) | ||||
0.0423228 | + | 0.999104i | \(0.486524\pi\) | |||||||
\(68\) | −4.81630 | −0.584062 | ||||||||
\(69\) | −4.24932 | −0.511558 | ||||||||
\(70\) | 1.25111 | 0.149537 | ||||||||
\(71\) | −2.37181 | −0.281481 | −0.140741 | − | 0.990046i | \(-0.544948\pi\) | ||||
−0.140741 | + | 0.990046i | \(0.544948\pi\) | |||||||
\(72\) | −0.874665 | −0.103080 | ||||||||
\(73\) | 7.13870 | 0.835522 | 0.417761 | − | 0.908557i | \(-0.362815\pi\) | ||||
0.417761 | + | 0.908557i | \(0.362815\pi\) | |||||||
\(74\) | 6.09247 | 0.708235 | ||||||||
\(75\) | 7.18083 | 0.829171 | ||||||||
\(76\) | 3.57600 | 0.410195 | ||||||||
\(77\) | −8.63398 | −0.983934 | ||||||||
\(78\) | 6.64029 | 0.751865 | ||||||||
\(79\) | 8.92250 | 1.00386 | 0.501930 | − | 0.864908i | \(-0.332623\pi\) | ||||
0.501930 | + | 0.864908i | \(0.332623\pi\) | |||||||
\(80\) | 0.272726 | 0.0304917 | ||||||||
\(81\) | −5.61097 | −0.623441 | ||||||||
\(82\) | 3.62123 | 0.399898 | ||||||||
\(83\) | 6.97015 | 0.765074 | 0.382537 | − | 0.923940i | \(-0.375051\pi\) | ||||
0.382537 | + | 0.923940i | \(0.375051\pi\) | |||||||
\(84\) | −6.68782 | −0.729701 | ||||||||
\(85\) | −1.31353 | −0.142472 | ||||||||
\(86\) | 3.58714 | 0.386811 | ||||||||
\(87\) | −9.21976 | −0.988462 | ||||||||
\(88\) | −1.88209 | −0.200632 | ||||||||
\(89\) | −5.64258 | −0.598113 | −0.299056 | − | 0.954235i | \(-0.596672\pi\) | ||||
−0.299056 | + | 0.954235i | \(0.596672\pi\) | |||||||
\(90\) | −0.238544 | −0.0251447 | ||||||||
\(91\) | −20.8951 | −2.19040 | ||||||||
\(92\) | 2.91478 | 0.303887 | ||||||||
\(93\) | −5.83265 | −0.604817 | ||||||||
\(94\) | 3.64602 | 0.376058 | ||||||||
\(95\) | 0.975267 | 0.100060 | ||||||||
\(96\) | −1.45785 | −0.148791 | ||||||||
\(97\) | 6.48014 | 0.657959 | 0.328979 | − | 0.944337i | \(-0.393295\pi\) | ||||
0.328979 | + | 0.944337i | \(0.393295\pi\) | |||||||
\(98\) | 14.0446 | 1.41872 | ||||||||
\(99\) | 1.64620 | 0.165449 | ||||||||
\(100\) | −4.92562 | −0.492562 | ||||||||
\(101\) | 8.58012 | 0.853754 | 0.426877 | − | 0.904310i | \(-0.359614\pi\) | ||||
0.426877 | + | 0.904310i | \(0.359614\pi\) | |||||||
\(102\) | 7.02146 | 0.695228 | ||||||||
\(103\) | −3.22241 | −0.317514 | −0.158757 | − | 0.987318i | \(-0.550749\pi\) | ||||
−0.158757 | + | 0.987318i | \(0.550749\pi\) | |||||||
\(104\) | −4.55484 | −0.446639 | ||||||||
\(105\) | −1.82394 | −0.177998 | ||||||||
\(106\) | −0.684641 | −0.0664982 | ||||||||
\(107\) | −2.60671 | −0.252000 | −0.126000 | − | 0.992030i | \(-0.540214\pi\) | ||||
−0.126000 | + | 0.992030i | \(0.540214\pi\) | |||||||
\(108\) | 5.64869 | 0.543546 | ||||||||
\(109\) | −5.81982 | −0.557438 | −0.278719 | − | 0.960373i | \(-0.589910\pi\) | ||||
−0.278719 | + | 0.960373i | \(0.589910\pi\) | |||||||
\(110\) | −0.513295 | −0.0489407 | ||||||||
\(111\) | −8.88192 | −0.843035 | ||||||||
\(112\) | 4.58744 | 0.433473 | ||||||||
\(113\) | −8.17856 | −0.769375 | −0.384687 | − | 0.923047i | \(-0.625691\pi\) | ||||
−0.384687 | + | 0.923047i | \(0.625691\pi\) | |||||||
\(114\) | −5.21328 | −0.488268 | ||||||||
\(115\) | 0.794936 | 0.0741282 | ||||||||
\(116\) | 6.32421 | 0.587188 | ||||||||
\(117\) | 3.98396 | 0.368317 | ||||||||
\(118\) | 12.0566 | 1.10990 | ||||||||
\(119\) | −22.0945 | −2.02540 | ||||||||
\(120\) | −0.397594 | −0.0362952 | ||||||||
\(121\) | −7.45774 | −0.677976 | ||||||||
\(122\) | −11.4376 | −1.03551 | ||||||||
\(123\) | −5.27923 | −0.476012 | ||||||||
\(124\) | 4.00085 | 0.359287 | ||||||||
\(125\) | −2.70697 | −0.242119 | ||||||||
\(126\) | −4.01248 | −0.357460 | ||||||||
\(127\) | 10.5022 | 0.931917 | 0.465958 | − | 0.884807i | \(-0.345710\pi\) | ||||
0.465958 | + | 0.884807i | \(0.345710\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.22952 | −0.460434 | ||||||||
\(130\) | −1.24222 | −0.108950 | ||||||||
\(131\) | 14.3205 | 1.25119 | 0.625595 | − | 0.780148i | \(-0.284856\pi\) | ||||
0.625595 | + | 0.780148i | \(0.284856\pi\) | |||||||
\(132\) | 2.74381 | 0.238818 | ||||||||
\(133\) | 16.4047 | 1.42247 | ||||||||
\(134\) | 0.692854 | 0.0598535 | ||||||||
\(135\) | 1.54054 | 0.132589 | ||||||||
\(136\) | −4.81630 | −0.412995 | ||||||||
\(137\) | −8.86989 | −0.757806 | −0.378903 | − | 0.925436i | \(-0.623699\pi\) | ||||
−0.378903 | + | 0.925436i | \(0.623699\pi\) | |||||||
\(138\) | −4.24932 | −0.361726 | ||||||||
\(139\) | 18.8865 | 1.60193 | 0.800964 | − | 0.598712i | \(-0.204321\pi\) | ||||
0.800964 | + | 0.598712i | \(0.204321\pi\) | |||||||
\(140\) | 1.25111 | 0.105738 | ||||||||
\(141\) | −5.31536 | −0.447634 | ||||||||
\(142\) | −2.37181 | −0.199037 | ||||||||
\(143\) | 8.57262 | 0.716879 | ||||||||
\(144\) | −0.874665 | −0.0728888 | ||||||||
\(145\) | 1.72477 | 0.143235 | ||||||||
\(146\) | 7.13870 | 0.590803 | ||||||||
\(147\) | −20.4750 | −1.68875 | ||||||||
\(148\) | 6.09247 | 0.500798 | ||||||||
\(149\) | −11.0950 | −0.908936 | −0.454468 | − | 0.890763i | \(-0.650171\pi\) | ||||
−0.454468 | + | 0.890763i | \(0.650171\pi\) | |||||||
\(150\) | 7.18083 | 0.586312 | ||||||||
\(151\) | 17.8872 | 1.45564 | 0.727821 | − | 0.685767i | \(-0.240533\pi\) | ||||
0.727821 | + | 0.685767i | \(0.240533\pi\) | |||||||
\(152\) | 3.57600 | 0.290052 | ||||||||
\(153\) | 4.21265 | 0.340573 | ||||||||
\(154\) | −8.63398 | −0.695746 | ||||||||
\(155\) | 1.09113 | 0.0876420 | ||||||||
\(156\) | 6.64029 | 0.531649 | ||||||||
\(157\) | −13.4535 | −1.07371 | −0.536854 | − | 0.843675i | \(-0.680388\pi\) | ||||
−0.536854 | + | 0.843675i | \(0.680388\pi\) | |||||||
\(158\) | 8.92250 | 0.709836 | ||||||||
\(159\) | 0.998106 | 0.0791550 | ||||||||
\(160\) | 0.272726 | 0.0215609 | ||||||||
\(161\) | 13.3714 | 1.05381 | ||||||||
\(162\) | −5.61097 | −0.440839 | ||||||||
\(163\) | 12.6837 | 0.993467 | 0.496733 | − | 0.867903i | \(-0.334533\pi\) | ||||
0.496733 | + | 0.867903i | \(0.334533\pi\) | |||||||
\(164\) | 3.62123 | 0.282771 | ||||||||
\(165\) | 0.748308 | 0.0582557 | ||||||||
\(166\) | 6.97015 | 0.540989 | ||||||||
\(167\) | −15.5279 | −1.20159 | −0.600793 | − | 0.799405i | \(-0.705148\pi\) | ||||
−0.600793 | + | 0.799405i | \(0.705148\pi\) | |||||||
\(168\) | −6.68782 | −0.515976 | ||||||||
\(169\) | 7.74658 | 0.595891 | ||||||||
\(170\) | −1.31353 | −0.100743 | ||||||||
\(171\) | −3.12780 | −0.239189 | ||||||||
\(172\) | 3.58714 | 0.273517 | ||||||||
\(173\) | 19.7193 | 1.49923 | 0.749614 | − | 0.661876i | \(-0.230239\pi\) | ||||
0.749614 | + | 0.661876i | \(0.230239\pi\) | |||||||
\(174\) | −9.21976 | −0.698949 | ||||||||
\(175\) | −22.5960 | −1.70810 | ||||||||
\(176\) | −1.88209 | −0.141868 | ||||||||
\(177\) | −17.5767 | −1.32114 | ||||||||
\(178\) | −5.64258 | −0.422930 | ||||||||
\(179\) | −6.74100 | −0.503846 | −0.251923 | − | 0.967747i | \(-0.581063\pi\) | ||||
−0.251923 | + | 0.967747i | \(0.581063\pi\) | |||||||
\(180\) | −0.238544 | −0.0177800 | ||||||||
\(181\) | 7.20245 | 0.535354 | 0.267677 | − | 0.963509i | \(-0.413744\pi\) | ||||
0.267677 | + | 0.963509i | \(0.413744\pi\) | |||||||
\(182\) | −20.8951 | −1.54885 | ||||||||
\(183\) | 16.6743 | 1.23260 | ||||||||
\(184\) | 2.91478 | 0.214881 | ||||||||
\(185\) | 1.66157 | 0.122161 | ||||||||
\(186\) | −5.83265 | −0.427670 | ||||||||
\(187\) | 9.06472 | 0.662878 | ||||||||
\(188\) | 3.64602 | 0.265913 | ||||||||
\(189\) | 25.9131 | 1.88490 | ||||||||
\(190\) | 0.975267 | 0.0707533 | ||||||||
\(191\) | −7.02014 | −0.507959 | −0.253980 | − | 0.967210i | \(-0.581740\pi\) | ||||
−0.253980 | + | 0.967210i | \(0.581740\pi\) | |||||||
\(192\) | −1.45785 | −0.105211 | ||||||||
\(193\) | −10.5912 | −0.762370 | −0.381185 | − | 0.924499i | \(-0.624484\pi\) | ||||
−0.381185 | + | 0.924499i | \(0.624484\pi\) | |||||||
\(194\) | 6.48014 | 0.465247 | ||||||||
\(195\) | 1.81098 | 0.129687 | ||||||||
\(196\) | 14.0446 | 1.00319 | ||||||||
\(197\) | 7.58015 | 0.540063 | 0.270032 | − | 0.962851i | \(-0.412966\pi\) | ||||
0.270032 | + | 0.962851i | \(0.412966\pi\) | |||||||
\(198\) | 1.64620 | 0.116990 | ||||||||
\(199\) | 18.3153 | 1.29834 | 0.649168 | − | 0.760645i | \(-0.275117\pi\) | ||||
0.649168 | + | 0.760645i | \(0.275117\pi\) | |||||||
\(200\) | −4.92562 | −0.348294 | ||||||||
\(201\) | −1.01008 | −0.0712455 | ||||||||
\(202\) | 8.58012 | 0.603695 | ||||||||
\(203\) | 29.0119 | 2.03624 | ||||||||
\(204\) | 7.02146 | 0.491601 | ||||||||
\(205\) | 0.987604 | 0.0689773 | ||||||||
\(206\) | −3.22241 | −0.224516 | ||||||||
\(207\) | −2.54946 | −0.177200 | ||||||||
\(208\) | −4.55484 | −0.315821 | ||||||||
\(209\) | −6.73035 | −0.465548 | ||||||||
\(210\) | −1.82394 | −0.125864 | ||||||||
\(211\) | −3.91259 | −0.269354 | −0.134677 | − | 0.990890i | \(-0.543000\pi\) | ||||
−0.134677 | + | 0.990890i | \(0.543000\pi\) | |||||||
\(212\) | −0.684641 | −0.0470214 | ||||||||
\(213\) | 3.45774 | 0.236921 | ||||||||
\(214\) | −2.60671 | −0.178191 | ||||||||
\(215\) | 0.978305 | 0.0667199 | ||||||||
\(216\) | 5.64869 | 0.384345 | ||||||||
\(217\) | 18.3537 | 1.24593 | ||||||||
\(218\) | −5.81982 | −0.394168 | ||||||||
\(219\) | −10.4072 | −0.703252 | ||||||||
\(220\) | −0.513295 | −0.0346063 | ||||||||
\(221\) | 21.9375 | 1.47568 | ||||||||
\(222\) | −8.88192 | −0.596116 | ||||||||
\(223\) | −12.7908 | −0.856536 | −0.428268 | − | 0.903652i | \(-0.640876\pi\) | ||||
−0.428268 | + | 0.903652i | \(0.640876\pi\) | |||||||
\(224\) | 4.58744 | 0.306511 | ||||||||
\(225\) | 4.30827 | 0.287218 | ||||||||
\(226\) | −8.17856 | −0.544030 | ||||||||
\(227\) | −24.4022 | −1.61963 | −0.809815 | − | 0.586686i | \(-0.800432\pi\) | ||||
−0.809815 | + | 0.586686i | \(0.800432\pi\) | |||||||
\(228\) | −5.21328 | −0.345258 | ||||||||
\(229\) | 16.9084 | 1.11734 | 0.558668 | − | 0.829391i | \(-0.311313\pi\) | ||||
0.558668 | + | 0.829391i | \(0.311313\pi\) | |||||||
\(230\) | 0.794936 | 0.0524165 | ||||||||
\(231\) | 12.5871 | 0.828169 | ||||||||
\(232\) | 6.32421 | 0.415205 | ||||||||
\(233\) | 6.29988 | 0.412719 | 0.206360 | − | 0.978476i | \(-0.433838\pi\) | ||||
0.206360 | + | 0.978476i | \(0.433838\pi\) | |||||||
\(234\) | 3.98396 | 0.260440 | ||||||||
\(235\) | 0.994363 | 0.0648651 | ||||||||
\(236\) | 12.0566 | 0.784815 | ||||||||
\(237\) | −13.0077 | −0.844941 | ||||||||
\(238\) | −22.0945 | −1.43217 | ||||||||
\(239\) | 26.9213 | 1.74139 | 0.870696 | − | 0.491821i | \(-0.163669\pi\) | ||||
0.870696 | + | 0.491821i | \(0.163669\pi\) | |||||||
\(240\) | −0.397594 | −0.0256646 | ||||||||
\(241\) | −1.72834 | −0.111332 | −0.0556661 | − | 0.998449i | \(-0.517728\pi\) | ||||
−0.0556661 | + | 0.998449i | \(0.517728\pi\) | |||||||
\(242\) | −7.45774 | −0.479401 | ||||||||
\(243\) | −8.76611 | −0.562346 | ||||||||
\(244\) | −11.4376 | −0.732214 | ||||||||
\(245\) | 3.83034 | 0.244711 | ||||||||
\(246\) | −5.27923 | −0.336591 | ||||||||
\(247\) | −16.2881 | −1.03639 | ||||||||
\(248\) | 4.00085 | 0.254054 | ||||||||
\(249\) | −10.1615 | −0.643956 | ||||||||
\(250\) | −2.70697 | −0.171204 | ||||||||
\(251\) | 6.10643 | 0.385434 | 0.192717 | − | 0.981254i | \(-0.438270\pi\) | ||||
0.192717 | + | 0.981254i | \(0.438270\pi\) | |||||||
\(252\) | −4.01248 | −0.252762 | ||||||||
\(253\) | −5.48588 | −0.344894 | ||||||||
\(254\) | 10.5022 | 0.658965 | ||||||||
\(255\) | 1.91493 | 0.119918 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.844669 | 0.0526890 | 0.0263445 | − | 0.999653i | \(-0.491613\pi\) | ||||
0.0263445 | + | 0.999653i | \(0.491613\pi\) | |||||||
\(258\) | −5.22952 | −0.325576 | ||||||||
\(259\) | 27.9488 | 1.73666 | ||||||||
\(260\) | −1.24222 | −0.0770394 | ||||||||
\(261\) | −5.53156 | −0.342395 | ||||||||
\(262\) | 14.3205 | 0.884725 | ||||||||
\(263\) | −8.09836 | −0.499366 | −0.249683 | − | 0.968328i | \(-0.580326\pi\) | ||||
−0.249683 | + | 0.968328i | \(0.580326\pi\) | |||||||
\(264\) | 2.74381 | 0.168870 | ||||||||
\(265\) | −0.186719 | −0.0114701 | ||||||||
\(266\) | 16.4047 | 1.00584 | ||||||||
\(267\) | 8.22606 | 0.503427 | ||||||||
\(268\) | 0.692854 | 0.0423228 | ||||||||
\(269\) | −10.5581 | −0.643738 | −0.321869 | − | 0.946784i | \(-0.604311\pi\) | ||||
−0.321869 | + | 0.946784i | \(0.604311\pi\) | |||||||
\(270\) | 1.54054 | 0.0937545 | ||||||||
\(271\) | −5.24362 | −0.318527 | −0.159264 | − | 0.987236i | \(-0.550912\pi\) | ||||
−0.159264 | + | 0.987236i | \(0.550912\pi\) | |||||||
\(272\) | −4.81630 | −0.292031 | ||||||||
\(273\) | 30.4619 | 1.84364 | ||||||||
\(274\) | −8.86989 | −0.535850 | ||||||||
\(275\) | 9.27046 | 0.559030 | ||||||||
\(276\) | −4.24932 | −0.255779 | ||||||||
\(277\) | 15.5586 | 0.934828 | 0.467414 | − | 0.884039i | \(-0.345186\pi\) | ||||
0.467414 | + | 0.884039i | \(0.345186\pi\) | |||||||
\(278\) | 18.8865 | 1.13273 | ||||||||
\(279\) | −3.49940 | −0.209504 | ||||||||
\(280\) | 1.25111 | 0.0747684 | ||||||||
\(281\) | −3.50481 | −0.209079 | −0.104540 | − | 0.994521i | \(-0.533337\pi\) | ||||
−0.104540 | + | 0.994521i | \(0.533337\pi\) | |||||||
\(282\) | −5.31536 | −0.316525 | ||||||||
\(283\) | −8.93733 | −0.531269 | −0.265635 | − | 0.964074i | \(-0.585581\pi\) | ||||
−0.265635 | + | 0.964074i | \(0.585581\pi\) | |||||||
\(284\) | −2.37181 | −0.140741 | ||||||||
\(285\) | −1.42180 | −0.0842199 | ||||||||
\(286\) | 8.57262 | 0.506910 | ||||||||
\(287\) | 16.6122 | 0.980588 | ||||||||
\(288\) | −0.874665 | −0.0515401 | ||||||||
\(289\) | 6.19677 | 0.364516 | ||||||||
\(290\) | 1.72477 | 0.101282 | ||||||||
\(291\) | −9.44709 | −0.553798 | ||||||||
\(292\) | 7.13870 | 0.417761 | ||||||||
\(293\) | −2.23322 | −0.130466 | −0.0652330 | − | 0.997870i | \(-0.520779\pi\) | ||||
−0.0652330 | + | 0.997870i | \(0.520779\pi\) | |||||||
\(294\) | −20.4750 | −1.19413 | ||||||||
\(295\) | 3.28813 | 0.191443 | ||||||||
\(296\) | 6.09247 | 0.354117 | ||||||||
\(297\) | −10.6313 | −0.616893 | ||||||||
\(298\) | −11.0950 | −0.642715 | ||||||||
\(299\) | −13.2764 | −0.767792 | ||||||||
\(300\) | 7.18083 | 0.414585 | ||||||||
\(301\) | 16.4558 | 0.948496 | ||||||||
\(302\) | 17.8872 | 1.02929 | ||||||||
\(303\) | −12.5086 | −0.718597 | ||||||||
\(304\) | 3.57600 | 0.205097 | ||||||||
\(305\) | −3.11932 | −0.178611 | ||||||||
\(306\) | 4.21265 | 0.240821 | ||||||||
\(307\) | 19.8899 | 1.13518 | 0.567589 | − | 0.823312i | \(-0.307876\pi\) | ||||
0.567589 | + | 0.823312i | \(0.307876\pi\) | |||||||
\(308\) | −8.63398 | −0.491967 | ||||||||
\(309\) | 4.69780 | 0.267249 | ||||||||
\(310\) | 1.09113 | 0.0619723 | ||||||||
\(311\) | −23.9249 | −1.35665 | −0.678327 | − | 0.734760i | \(-0.737295\pi\) | ||||
−0.678327 | + | 0.734760i | \(0.737295\pi\) | |||||||
\(312\) | 6.64029 | 0.375932 | ||||||||
\(313\) | −5.72885 | −0.323814 | −0.161907 | − | 0.986806i | \(-0.551764\pi\) | ||||
−0.161907 | + | 0.986806i | \(0.551764\pi\) | |||||||
\(314\) | −13.4535 | −0.759227 | ||||||||
\(315\) | −1.09431 | −0.0616572 | ||||||||
\(316\) | 8.92250 | 0.501930 | ||||||||
\(317\) | −34.0783 | −1.91403 | −0.957013 | − | 0.290044i | \(-0.906330\pi\) | ||||
−0.957013 | + | 0.290044i | \(0.906330\pi\) | |||||||
\(318\) | 0.998106 | 0.0559710 | ||||||||
\(319\) | −11.9027 | −0.666425 | ||||||||
\(320\) | 0.272726 | 0.0152458 | ||||||||
\(321\) | 3.80020 | 0.212106 | ||||||||
\(322\) | 13.3714 | 0.745159 | ||||||||
\(323\) | −17.2231 | −0.958318 | ||||||||
\(324\) | −5.61097 | −0.311720 | ||||||||
\(325\) | 22.4354 | 1.24449 | ||||||||
\(326\) | 12.6837 | 0.702487 | ||||||||
\(327\) | 8.48444 | 0.469191 | ||||||||
\(328\) | 3.62123 | 0.199949 | ||||||||
\(329\) | 16.7259 | 0.922128 | ||||||||
\(330\) | 0.748308 | 0.0411930 | ||||||||
\(331\) | −20.6223 | −1.13350 | −0.566752 | − | 0.823889i | \(-0.691800\pi\) | ||||
−0.566752 | + | 0.823889i | \(0.691800\pi\) | |||||||
\(332\) | 6.97015 | 0.382537 | ||||||||
\(333\) | −5.32887 | −0.292020 | ||||||||
\(334\) | −15.5279 | −0.849650 | ||||||||
\(335\) | 0.188959 | 0.0103239 | ||||||||
\(336\) | −6.68782 | −0.364850 | ||||||||
\(337\) | 21.3936 | 1.16538 | 0.582692 | − | 0.812693i | \(-0.301999\pi\) | ||||
0.582692 | + | 0.812693i | \(0.301999\pi\) | |||||||
\(338\) | 7.74658 | 0.421358 | ||||||||
\(339\) | 11.9231 | 0.647576 | ||||||||
\(340\) | −1.31353 | −0.0712362 | ||||||||
\(341\) | −7.52996 | −0.407770 | ||||||||
\(342\) | −3.12780 | −0.169132 | ||||||||
\(343\) | 32.3169 | 1.74495 | ||||||||
\(344\) | 3.58714 | 0.193406 | ||||||||
\(345\) | −1.15890 | −0.0623931 | ||||||||
\(346\) | 19.7193 | 1.06011 | ||||||||
\(347\) | −22.2924 | −1.19672 | −0.598359 | − | 0.801228i | \(-0.704180\pi\) | ||||
−0.598359 | + | 0.801228i | \(0.704180\pi\) | |||||||
\(348\) | −9.21976 | −0.494231 | ||||||||
\(349\) | 29.7073 | 1.59019 | 0.795097 | − | 0.606482i | \(-0.207420\pi\) | ||||
0.795097 | + | 0.606482i | \(0.207420\pi\) | |||||||
\(350\) | −22.5960 | −1.20781 | ||||||||
\(351\) | −25.7289 | −1.37331 | ||||||||
\(352\) | −1.88209 | −0.100316 | ||||||||
\(353\) | −13.8095 | −0.735005 | −0.367502 | − | 0.930023i | \(-0.619787\pi\) | ||||
−0.367502 | + | 0.930023i | \(0.619787\pi\) | |||||||
\(354\) | −17.5767 | −0.934190 | ||||||||
\(355\) | −0.646853 | −0.0343314 | ||||||||
\(356\) | −5.64258 | −0.299056 | ||||||||
\(357\) | 32.2106 | 1.70476 | ||||||||
\(358\) | −6.74100 | −0.356273 | ||||||||
\(359\) | 13.4255 | 0.708570 | 0.354285 | − | 0.935138i | \(-0.384724\pi\) | ||||
0.354285 | + | 0.935138i | \(0.384724\pi\) | |||||||
\(360\) | −0.238544 | −0.0125724 | ||||||||
\(361\) | −6.21225 | −0.326961 | ||||||||
\(362\) | 7.20245 | 0.378552 | ||||||||
\(363\) | 10.8723 | 0.570647 | ||||||||
\(364\) | −20.8951 | −1.09520 | ||||||||
\(365\) | 1.94691 | 0.101906 | ||||||||
\(366\) | 16.6743 | 0.871578 | ||||||||
\(367\) | 33.6156 | 1.75472 | 0.877359 | − | 0.479834i | \(-0.159303\pi\) | ||||
0.877359 | + | 0.479834i | \(0.159303\pi\) | |||||||
\(368\) | 2.91478 | 0.151943 | ||||||||
\(369\) | −3.16737 | −0.164887 | ||||||||
\(370\) | 1.66157 | 0.0863811 | ||||||||
\(371\) | −3.14075 | −0.163060 | ||||||||
\(372\) | −5.83265 | −0.302409 | ||||||||
\(373\) | 14.4484 | 0.748110 | 0.374055 | − | 0.927407i | \(-0.377967\pi\) | ||||
0.374055 | + | 0.927407i | \(0.377967\pi\) | |||||||
\(374\) | 9.06472 | 0.468725 | ||||||||
\(375\) | 3.94637 | 0.203790 | ||||||||
\(376\) | 3.64602 | 0.188029 | ||||||||
\(377\) | −28.8058 | −1.48357 | ||||||||
\(378\) | 25.9131 | 1.33282 | ||||||||
\(379\) | 3.81403 | 0.195914 | 0.0979568 | − | 0.995191i | \(-0.468769\pi\) | ||||
0.0979568 | + | 0.995191i | \(0.468769\pi\) | |||||||
\(380\) | 0.975267 | 0.0500301 | ||||||||
\(381\) | −15.3106 | −0.784387 | ||||||||
\(382\) | −7.02014 | −0.359181 | ||||||||
\(383\) | 13.4704 | 0.688304 | 0.344152 | − | 0.938914i | \(-0.388166\pi\) | ||||
0.344152 | + | 0.938914i | \(0.388166\pi\) | |||||||
\(384\) | −1.45785 | −0.0743957 | ||||||||
\(385\) | −2.35471 | −0.120007 | ||||||||
\(386\) | −10.5912 | −0.539077 | ||||||||
\(387\) | −3.13754 | −0.159490 | ||||||||
\(388\) | 6.48014 | 0.328979 | ||||||||
\(389\) | 22.6974 | 1.15080 | 0.575401 | − | 0.817871i | \(-0.304846\pi\) | ||||
0.575401 | + | 0.817871i | \(0.304846\pi\) | |||||||
\(390\) | 1.81098 | 0.0917024 | ||||||||
\(391\) | −14.0385 | −0.709956 | ||||||||
\(392\) | 14.0446 | 0.709361 | ||||||||
\(393\) | −20.8772 | −1.05312 | ||||||||
\(394\) | 7.58015 | 0.381882 | ||||||||
\(395\) | 2.43340 | 0.122438 | ||||||||
\(396\) | 1.64620 | 0.0827246 | ||||||||
\(397\) | 35.3314 | 1.77323 | 0.886616 | − | 0.462506i | \(-0.153050\pi\) | ||||
0.886616 | + | 0.462506i | \(0.153050\pi\) | |||||||
\(398\) | 18.3153 | 0.918062 | ||||||||
\(399\) | −23.9156 | −1.19728 | ||||||||
\(400\) | −4.92562 | −0.246281 | ||||||||
\(401\) | 24.4662 | 1.22178 | 0.610892 | − | 0.791714i | \(-0.290811\pi\) | ||||
0.610892 | + | 0.791714i | \(0.290811\pi\) | |||||||
\(402\) | −1.01008 | −0.0503782 | ||||||||
\(403\) | −18.2232 | −0.907763 | ||||||||
\(404\) | 8.58012 | 0.426877 | ||||||||
\(405\) | −1.53026 | −0.0760390 | ||||||||
\(406\) | 29.0119 | 1.43984 | ||||||||
\(407\) | −11.4666 | −0.568377 | ||||||||
\(408\) | 7.02146 | 0.347614 | ||||||||
\(409\) | 2.13462 | 0.105550 | 0.0527752 | − | 0.998606i | \(-0.483193\pi\) | ||||
0.0527752 | + | 0.998606i | \(0.483193\pi\) | |||||||
\(410\) | 0.987604 | 0.0487743 | ||||||||
\(411\) | 12.9310 | 0.637839 | ||||||||
\(412\) | −3.22241 | −0.158757 | ||||||||
\(413\) | 55.3088 | 2.72157 | ||||||||
\(414\) | −2.54946 | −0.125299 | ||||||||
\(415\) | 1.90094 | 0.0933135 | ||||||||
\(416\) | −4.55484 | −0.223319 | ||||||||
\(417\) | −27.5337 | −1.34833 | ||||||||
\(418\) | −6.73035 | −0.329192 | ||||||||
\(419\) | −13.2991 | −0.649704 | −0.324852 | − | 0.945765i | \(-0.605314\pi\) | ||||
−0.324852 | + | 0.945765i | \(0.605314\pi\) | |||||||
\(420\) | −1.82394 | −0.0889992 | ||||||||
\(421\) | −16.4472 | −0.801586 | −0.400793 | − | 0.916169i | \(-0.631265\pi\) | ||||
−0.400793 | + | 0.916169i | \(0.631265\pi\) | |||||||
\(422\) | −3.91259 | −0.190462 | ||||||||
\(423\) | −3.18904 | −0.155057 | ||||||||
\(424\) | −0.684641 | −0.0332491 | ||||||||
\(425\) | 23.7233 | 1.15075 | ||||||||
\(426\) | 3.45774 | 0.167528 | ||||||||
\(427\) | −52.4691 | −2.53916 | ||||||||
\(428\) | −2.60671 | −0.126000 | ||||||||
\(429\) | −12.4976 | −0.603391 | ||||||||
\(430\) | 0.978305 | 0.0471781 | ||||||||
\(431\) | −38.1987 | −1.83997 | −0.919984 | − | 0.391957i | \(-0.871798\pi\) | ||||
−0.919984 | + | 0.391957i | \(0.871798\pi\) | |||||||
\(432\) | 5.64869 | 0.271773 | ||||||||
\(433\) | 33.8447 | 1.62647 | 0.813236 | − | 0.581934i | \(-0.197704\pi\) | ||||
0.813236 | + | 0.581934i | \(0.197704\pi\) | |||||||
\(434\) | 18.3537 | 0.881004 | ||||||||
\(435\) | −2.51447 | −0.120560 | ||||||||
\(436\) | −5.81982 | −0.278719 | ||||||||
\(437\) | 10.4232 | 0.498612 | ||||||||
\(438\) | −10.4072 | −0.497274 | ||||||||
\(439\) | −8.27917 | −0.395143 | −0.197572 | − | 0.980288i | \(-0.563305\pi\) | ||||
−0.197572 | + | 0.980288i | \(0.563305\pi\) | |||||||
\(440\) | −0.513295 | −0.0244704 | ||||||||
\(441\) | −12.2844 | −0.584969 | ||||||||
\(442\) | 21.9375 | 1.04346 | ||||||||
\(443\) | −9.44031 | −0.448523 | −0.224261 | − | 0.974529i | \(-0.571997\pi\) | ||||
−0.224261 | + | 0.974529i | \(0.571997\pi\) | |||||||
\(444\) | −8.88192 | −0.421517 | ||||||||
\(445\) | −1.53888 | −0.0729498 | ||||||||
\(446\) | −12.7908 | −0.605662 | ||||||||
\(447\) | 16.1748 | 0.765044 | ||||||||
\(448\) | 4.58744 | 0.216736 | ||||||||
\(449\) | −23.8641 | −1.12622 | −0.563109 | − | 0.826383i | \(-0.690395\pi\) | ||||
−0.563109 | + | 0.826383i | \(0.690395\pi\) | |||||||
\(450\) | 4.30827 | 0.203094 | ||||||||
\(451\) | −6.81549 | −0.320929 | ||||||||
\(452\) | −8.17856 | −0.384687 | ||||||||
\(453\) | −26.0770 | −1.22520 | ||||||||
\(454\) | −24.4022 | −1.14525 | ||||||||
\(455\) | −5.69863 | −0.267156 | ||||||||
\(456\) | −5.21328 | −0.244134 | ||||||||
\(457\) | 15.8047 | 0.739314 | 0.369657 | − | 0.929168i | \(-0.379475\pi\) | ||||
0.369657 | + | 0.929168i | \(0.379475\pi\) | |||||||
\(458\) | 16.9084 | 0.790076 | ||||||||
\(459\) | −27.2058 | −1.26986 | ||||||||
\(460\) | 0.794936 | 0.0370641 | ||||||||
\(461\) | 31.9144 | 1.48640 | 0.743202 | − | 0.669067i | \(-0.233306\pi\) | ||||
0.743202 | + | 0.669067i | \(0.233306\pi\) | |||||||
\(462\) | 12.5871 | 0.585604 | ||||||||
\(463\) | 5.12251 | 0.238063 | 0.119032 | − | 0.992890i | \(-0.462021\pi\) | ||||
0.119032 | + | 0.992890i | \(0.462021\pi\) | |||||||
\(464\) | 6.32421 | 0.293594 | ||||||||
\(465\) | −1.59071 | −0.0737676 | ||||||||
\(466\) | 6.29988 | 0.291836 | ||||||||
\(467\) | −27.3516 | −1.26568 | −0.632841 | − | 0.774282i | \(-0.718111\pi\) | ||||
−0.632841 | + | 0.774282i | \(0.718111\pi\) | |||||||
\(468\) | 3.98396 | 0.184159 | ||||||||
\(469\) | 3.17843 | 0.146766 | ||||||||
\(470\) | 0.994363 | 0.0458665 | ||||||||
\(471\) | 19.6133 | 0.903732 | ||||||||
\(472\) | 12.0566 | 0.554948 | ||||||||
\(473\) | −6.75132 | −0.310426 | ||||||||
\(474\) | −13.0077 | −0.597463 | ||||||||
\(475\) | −17.6140 | −0.808186 | ||||||||
\(476\) | −22.0945 | −1.01270 | ||||||||
\(477\) | 0.598832 | 0.0274186 | ||||||||
\(478\) | 26.9213 | 1.23135 | ||||||||
\(479\) | −38.1374 | −1.74254 | −0.871271 | − | 0.490802i | \(-0.836704\pi\) | ||||
−0.871271 | + | 0.490802i | \(0.836704\pi\) | |||||||
\(480\) | −0.397594 | −0.0181476 | ||||||||
\(481\) | −27.7502 | −1.26530 | ||||||||
\(482\) | −1.72834 | −0.0787237 | ||||||||
\(483\) | −19.4935 | −0.886986 | ||||||||
\(484\) | −7.45774 | −0.338988 | ||||||||
\(485\) | 1.76730 | 0.0802490 | ||||||||
\(486\) | −8.76611 | −0.397639 | ||||||||
\(487\) | −32.6262 | −1.47843 | −0.739217 | − | 0.673468i | \(-0.764804\pi\) | ||||
−0.739217 | + | 0.673468i | \(0.764804\pi\) | |||||||
\(488\) | −11.4376 | −0.517754 | ||||||||
\(489\) | −18.4910 | −0.836193 | ||||||||
\(490\) | 3.83034 | 0.173037 | ||||||||
\(491\) | 5.95061 | 0.268547 | 0.134274 | − | 0.990944i | \(-0.457130\pi\) | ||||
0.134274 | + | 0.990944i | \(0.457130\pi\) | |||||||
\(492\) | −5.27923 | −0.238006 | ||||||||
\(493\) | −30.4593 | −1.37182 | ||||||||
\(494\) | −16.2881 | −0.732836 | ||||||||
\(495\) | 0.448961 | 0.0201793 | ||||||||
\(496\) | 4.00085 | 0.179643 | ||||||||
\(497\) | −10.8805 | −0.488058 | ||||||||
\(498\) | −10.1615 | −0.455346 | ||||||||
\(499\) | −40.3308 | −1.80545 | −0.902727 | − | 0.430213i | \(-0.858438\pi\) | ||||
−0.902727 | + | 0.430213i | \(0.858438\pi\) | |||||||
\(500\) | −2.70697 | −0.121060 | ||||||||
\(501\) | 22.6374 | 1.01137 | ||||||||
\(502\) | 6.10643 | 0.272543 | ||||||||
\(503\) | −12.0073 | −0.535377 | −0.267689 | − | 0.963505i | \(-0.586260\pi\) | ||||
−0.267689 | + | 0.963505i | \(0.586260\pi\) | |||||||
\(504\) | −4.01248 | −0.178730 | ||||||||
\(505\) | 2.34002 | 0.104130 | ||||||||
\(506\) | −5.48588 | −0.243877 | ||||||||
\(507\) | −11.2934 | −0.501556 | ||||||||
\(508\) | 10.5022 | 0.465958 | ||||||||
\(509\) | −39.2735 | −1.74077 | −0.870384 | − | 0.492374i | \(-0.836129\pi\) | ||||
−0.870384 | + | 0.492374i | \(0.836129\pi\) | |||||||
\(510\) | 1.91493 | 0.0847947 | ||||||||
\(511\) | 32.7484 | 1.44870 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 20.1997 | 0.891839 | ||||||||
\(514\) | 0.844669 | 0.0372568 | ||||||||
\(515\) | −0.878835 | −0.0387261 | ||||||||
\(516\) | −5.22952 | −0.230217 | ||||||||
\(517\) | −6.86213 | −0.301796 | ||||||||
\(518\) | 27.9488 | 1.22800 | ||||||||
\(519\) | −28.7478 | −1.26189 | ||||||||
\(520\) | −1.24222 | −0.0544751 | ||||||||
\(521\) | 4.30490 | 0.188601 | 0.0943005 | − | 0.995544i | \(-0.469939\pi\) | ||||
0.0943005 | + | 0.995544i | \(0.469939\pi\) | |||||||
\(522\) | −5.53156 | −0.242110 | ||||||||
\(523\) | 1.68521 | 0.0736892 | 0.0368446 | − | 0.999321i | \(-0.488269\pi\) | ||||
0.0368446 | + | 0.999321i | \(0.488269\pi\) | |||||||
\(524\) | 14.3205 | 0.625595 | ||||||||
\(525\) | 32.9417 | 1.43769 | ||||||||
\(526\) | −8.09836 | −0.353105 | ||||||||
\(527\) | −19.2693 | −0.839384 | ||||||||
\(528\) | 2.74381 | 0.119409 | ||||||||
\(529\) | −14.5040 | −0.630611 | ||||||||
\(530\) | −0.186719 | −0.00811057 | ||||||||
\(531\) | −10.5454 | −0.457633 | ||||||||
\(532\) | 16.4047 | 0.711233 | ||||||||
\(533\) | −16.4941 | −0.714441 | ||||||||
\(534\) | 8.22606 | 0.355976 | ||||||||
\(535\) | −0.710917 | −0.0307356 | ||||||||
\(536\) | 0.692854 | 0.0299267 | ||||||||
\(537\) | 9.82738 | 0.424083 | ||||||||
\(538\) | −10.5581 | −0.455191 | ||||||||
\(539\) | −26.4333 | −1.13856 | ||||||||
\(540\) | 1.54054 | 0.0662945 | ||||||||
\(541\) | 9.92954 | 0.426904 | 0.213452 | − | 0.976954i | \(-0.431529\pi\) | ||||
0.213452 | + | 0.976954i | \(0.431529\pi\) | |||||||
\(542\) | −5.24362 | −0.225233 | ||||||||
\(543\) | −10.5001 | −0.450603 | ||||||||
\(544\) | −4.81630 | −0.206497 | ||||||||
\(545\) | −1.58722 | −0.0679889 | ||||||||
\(546\) | 30.4619 | 1.30365 | ||||||||
\(547\) | −42.8561 | −1.83239 | −0.916197 | − | 0.400729i | \(-0.868757\pi\) | ||||
−0.916197 | + | 0.400729i | \(0.868757\pi\) | |||||||
\(548\) | −8.86989 | −0.378903 | ||||||||
\(549\) | 10.0040 | 0.426961 | ||||||||
\(550\) | 9.27046 | 0.395294 | ||||||||
\(551\) | 22.6153 | 0.963446 | ||||||||
\(552\) | −4.24932 | −0.180863 | ||||||||
\(553\) | 40.9315 | 1.74058 | ||||||||
\(554\) | 15.5586 | 0.661023 | ||||||||
\(555\) | −2.42233 | −0.102822 | ||||||||
\(556\) | 18.8865 | 0.800964 | ||||||||
\(557\) | 2.54870 | 0.107992 | 0.0539960 | − | 0.998541i | \(-0.482804\pi\) | ||||
0.0539960 | + | 0.998541i | \(0.482804\pi\) | |||||||
\(558\) | −3.49940 | −0.148141 | ||||||||
\(559\) | −16.3388 | −0.691060 | ||||||||
\(560\) | 1.25111 | 0.0528692 | ||||||||
\(561\) | −13.2150 | −0.557939 | ||||||||
\(562\) | −3.50481 | −0.147841 | ||||||||
\(563\) | 21.4520 | 0.904093 | 0.452047 | − | 0.891994i | \(-0.350694\pi\) | ||||
0.452047 | + | 0.891994i | \(0.350694\pi\) | |||||||
\(564\) | −5.31536 | −0.223817 | ||||||||
\(565\) | −2.23051 | −0.0938381 | ||||||||
\(566\) | −8.93733 | −0.375664 | ||||||||
\(567\) | −25.7400 | −1.08098 | ||||||||
\(568\) | −2.37181 | −0.0995187 | ||||||||
\(569\) | −26.9069 | −1.12800 | −0.563998 | − | 0.825776i | \(-0.690738\pi\) | ||||
−0.563998 | + | 0.825776i | \(0.690738\pi\) | |||||||
\(570\) | −1.42180 | −0.0595524 | ||||||||
\(571\) | 18.6844 | 0.781917 | 0.390958 | − | 0.920408i | \(-0.372144\pi\) | ||||
0.390958 | + | 0.920408i | \(0.372144\pi\) | |||||||
\(572\) | 8.57262 | 0.358439 | ||||||||
\(573\) | 10.2343 | 0.427545 | ||||||||
\(574\) | 16.6122 | 0.693380 | ||||||||
\(575\) | −14.3571 | −0.598733 | ||||||||
\(576\) | −0.874665 | −0.0364444 | ||||||||
\(577\) | −12.0482 | −0.501574 | −0.250787 | − | 0.968042i | \(-0.580689\pi\) | ||||
−0.250787 | + | 0.968042i | \(0.580689\pi\) | |||||||
\(578\) | 6.19677 | 0.257752 | ||||||||
\(579\) | 15.4404 | 0.641681 | ||||||||
\(580\) | 1.72477 | 0.0716174 | ||||||||
\(581\) | 31.9752 | 1.32655 | ||||||||
\(582\) | −9.44709 | −0.391594 | ||||||||
\(583\) | 1.28856 | 0.0533666 | ||||||||
\(584\) | 7.13870 | 0.295402 | ||||||||
\(585\) | 1.08653 | 0.0449224 | ||||||||
\(586\) | −2.23322 | −0.0922534 | ||||||||
\(587\) | 31.6915 | 1.30805 | 0.654025 | − | 0.756473i | \(-0.273079\pi\) | ||||
0.654025 | + | 0.756473i | \(0.273079\pi\) | |||||||
\(588\) | −20.4750 | −0.844375 | ||||||||
\(589\) | 14.3070 | 0.589510 | ||||||||
\(590\) | 3.28813 | 0.135370 | ||||||||
\(591\) | −11.0507 | −0.454567 | ||||||||
\(592\) | 6.09247 | 0.250399 | ||||||||
\(593\) | −41.6109 | −1.70876 | −0.854378 | − | 0.519652i | \(-0.826062\pi\) | ||||
−0.854378 | + | 0.519652i | \(0.826062\pi\) | |||||||
\(594\) | −10.6313 | −0.436209 | ||||||||
\(595\) | −6.02575 | −0.247031 | ||||||||
\(596\) | −11.0950 | −0.454468 | ||||||||
\(597\) | −26.7010 | −1.09280 | ||||||||
\(598\) | −13.2764 | −0.542911 | ||||||||
\(599\) | −39.8614 | −1.62869 | −0.814347 | − | 0.580378i | \(-0.802905\pi\) | ||||
−0.814347 | + | 0.580378i | \(0.802905\pi\) | |||||||
\(600\) | 7.18083 | 0.293156 | ||||||||
\(601\) | −16.5908 | −0.676751 | −0.338375 | − | 0.941011i | \(-0.609877\pi\) | ||||
−0.338375 | + | 0.941011i | \(0.609877\pi\) | |||||||
\(602\) | 16.4558 | 0.670688 | ||||||||
\(603\) | −0.606015 | −0.0246789 | ||||||||
\(604\) | 17.8872 | 0.727821 | ||||||||
\(605\) | −2.03392 | −0.0826905 | ||||||||
\(606\) | −12.5086 | −0.508125 | ||||||||
\(607\) | −3.52190 | −0.142949 | −0.0714747 | − | 0.997442i | \(-0.522771\pi\) | ||||
−0.0714747 | + | 0.997442i | \(0.522771\pi\) | |||||||
\(608\) | 3.57600 | 0.145026 | ||||||||
\(609\) | −42.2951 | −1.71389 | ||||||||
\(610\) | −3.11932 | −0.126297 | ||||||||
\(611\) | −16.6070 | −0.671848 | ||||||||
\(612\) | 4.21265 | 0.170286 | ||||||||
\(613\) | −19.5830 | −0.790952 | −0.395476 | − | 0.918476i | \(-0.629420\pi\) | ||||
−0.395476 | + | 0.918476i | \(0.629420\pi\) | |||||||
\(614\) | 19.8899 | 0.802692 | ||||||||
\(615\) | −1.43978 | −0.0580576 | ||||||||
\(616\) | −8.63398 | −0.347873 | ||||||||
\(617\) | −10.7978 | −0.434703 | −0.217352 | − | 0.976093i | \(-0.569742\pi\) | ||||
−0.217352 | + | 0.976093i | \(0.569742\pi\) | |||||||
\(618\) | 4.69780 | 0.188973 | ||||||||
\(619\) | −41.5303 | −1.66924 | −0.834621 | − | 0.550824i | \(-0.814313\pi\) | ||||
−0.834621 | + | 0.550824i | \(0.814313\pi\) | |||||||
\(620\) | 1.09113 | 0.0438210 | ||||||||
\(621\) | 16.4647 | 0.660706 | ||||||||
\(622\) | −23.9249 | −0.959299 | ||||||||
\(623\) | −25.8850 | −1.03706 | ||||||||
\(624\) | 6.64029 | 0.265824 | ||||||||
\(625\) | 23.8898 | 0.955594 | ||||||||
\(626\) | −5.72885 | −0.228971 | ||||||||
\(627\) | 9.81186 | 0.391848 | ||||||||
\(628\) | −13.4535 | −0.536854 | ||||||||
\(629\) | −29.3432 | −1.16999 | ||||||||
\(630\) | −1.09431 | −0.0435982 | ||||||||
\(631\) | 10.6832 | 0.425292 | 0.212646 | − | 0.977129i | \(-0.431792\pi\) | ||||
0.212646 | + | 0.977129i | \(0.431792\pi\) | |||||||
\(632\) | 8.92250 | 0.354918 | ||||||||
\(633\) | 5.70398 | 0.226713 | ||||||||
\(634\) | −34.0783 | −1.35342 | ||||||||
\(635\) | 2.86421 | 0.113663 | ||||||||
\(636\) | 0.998106 | 0.0395775 | ||||||||
\(637\) | −63.9711 | −2.53463 | ||||||||
\(638\) | −11.9027 | −0.471234 | ||||||||
\(639\) | 2.07453 | 0.0820673 | ||||||||
\(640\) | 0.272726 | 0.0107804 | ||||||||
\(641\) | −36.0857 | −1.42530 | −0.712650 | − | 0.701520i | \(-0.752505\pi\) | ||||
−0.712650 | + | 0.701520i | \(0.752505\pi\) | |||||||
\(642\) | 3.80020 | 0.149982 | ||||||||
\(643\) | 40.2987 | 1.58923 | 0.794613 | − | 0.607116i | \(-0.207674\pi\) | ||||
0.794613 | + | 0.607116i | \(0.207674\pi\) | |||||||
\(644\) | 13.3714 | 0.526907 | ||||||||
\(645\) | −1.42623 | −0.0561576 | ||||||||
\(646\) | −17.2231 | −0.677633 | ||||||||
\(647\) | 21.3984 | 0.841257 | 0.420629 | − | 0.907233i | \(-0.361810\pi\) | ||||
0.420629 | + | 0.907233i | \(0.361810\pi\) | |||||||
\(648\) | −5.61097 | −0.220420 | ||||||||
\(649\) | −22.6915 | −0.890720 | ||||||||
\(650\) | 22.4354 | 0.879990 | ||||||||
\(651\) | −26.7569 | −1.04869 | ||||||||
\(652\) | 12.6837 | 0.496733 | ||||||||
\(653\) | −10.2723 | −0.401986 | −0.200993 | − | 0.979593i | \(-0.564417\pi\) | ||||
−0.200993 | + | 0.979593i | \(0.564417\pi\) | |||||||
\(654\) | 8.48444 | 0.331768 | ||||||||
\(655\) | 3.90558 | 0.152604 | ||||||||
\(656\) | 3.62123 | 0.141385 | ||||||||
\(657\) | −6.24397 | −0.243601 | ||||||||
\(658\) | 16.7259 | 0.652043 | ||||||||
\(659\) | 18.9604 | 0.738592 | 0.369296 | − | 0.929312i | \(-0.379599\pi\) | ||||
0.369296 | + | 0.929312i | \(0.379599\pi\) | |||||||
\(660\) | 0.748308 | 0.0291279 | ||||||||
\(661\) | 28.9784 | 1.12713 | 0.563564 | − | 0.826072i | \(-0.309430\pi\) | ||||
0.563564 | + | 0.826072i | \(0.309430\pi\) | |||||||
\(662\) | −20.6223 | −0.801508 | ||||||||
\(663\) | −31.9816 | −1.24206 | ||||||||
\(664\) | 6.97015 | 0.270494 | ||||||||
\(665\) | 4.47398 | 0.173494 | ||||||||
\(666\) | −5.32887 | −0.206489 | ||||||||
\(667\) | 18.4337 | 0.713755 | ||||||||
\(668\) | −15.5279 | −0.600793 | ||||||||
\(669\) | 18.6471 | 0.720939 | ||||||||
\(670\) | 0.188959 | 0.00730013 | ||||||||
\(671\) | 21.5265 | 0.831021 | ||||||||
\(672\) | −6.68782 | −0.257988 | ||||||||
\(673\) | 4.61859 | 0.178034 | 0.0890168 | − | 0.996030i | \(-0.471628\pi\) | ||||
0.0890168 | + | 0.996030i | \(0.471628\pi\) | |||||||
\(674\) | 21.3936 | 0.824051 | ||||||||
\(675\) | −27.8233 | −1.07092 | ||||||||
\(676\) | 7.74658 | 0.297945 | ||||||||
\(677\) | 31.4416 | 1.20840 | 0.604200 | − | 0.796833i | \(-0.293493\pi\) | ||||
0.604200 | + | 0.796833i | \(0.293493\pi\) | |||||||
\(678\) | 11.9231 | 0.457906 | ||||||||
\(679\) | 29.7273 | 1.14083 | ||||||||
\(680\) | −1.31353 | −0.0503716 | ||||||||
\(681\) | 35.5748 | 1.36323 | ||||||||
\(682\) | −7.52996 | −0.288337 | ||||||||
\(683\) | 38.7254 | 1.48179 | 0.740893 | − | 0.671623i | \(-0.234402\pi\) | ||||
0.740893 | + | 0.671623i | \(0.234402\pi\) | |||||||
\(684\) | −3.12780 | −0.119594 | ||||||||
\(685\) | −2.41905 | −0.0924271 | ||||||||
\(686\) | 32.3169 | 1.23386 | ||||||||
\(687\) | −24.6499 | −0.940453 | ||||||||
\(688\) | 3.58714 | 0.136758 | ||||||||
\(689\) | 3.11843 | 0.118803 | ||||||||
\(690\) | −1.15890 | −0.0441186 | ||||||||
\(691\) | 30.0841 | 1.14445 | 0.572227 | − | 0.820095i | \(-0.306080\pi\) | ||||
0.572227 | + | 0.820095i | \(0.306080\pi\) | |||||||
\(692\) | 19.7193 | 0.749614 | ||||||||
\(693\) | 7.55184 | 0.286871 | ||||||||
\(694\) | −22.2924 | −0.846207 | ||||||||
\(695\) | 5.15082 | 0.195382 | ||||||||
\(696\) | −9.21976 | −0.349474 | ||||||||
\(697\) | −17.4410 | −0.660624 | ||||||||
\(698\) | 29.7073 | 1.12444 | ||||||||
\(699\) | −9.18430 | −0.347382 | ||||||||
\(700\) | −22.5960 | −0.854049 | ||||||||
\(701\) | −25.0157 | −0.944831 | −0.472415 | − | 0.881376i | \(-0.656618\pi\) | ||||
−0.472415 | + | 0.881376i | \(0.656618\pi\) | |||||||
\(702\) | −25.7289 | −0.971074 | ||||||||
\(703\) | 21.7866 | 0.821699 | ||||||||
\(704\) | −1.88209 | −0.0709339 | ||||||||
\(705\) | −1.44963 | −0.0545964 | ||||||||
\(706\) | −13.8095 | −0.519727 | ||||||||
\(707\) | 39.3608 | 1.48032 | ||||||||
\(708\) | −17.5767 | −0.660572 | ||||||||
\(709\) | 8.28621 | 0.311195 | 0.155598 | − | 0.987821i | \(-0.450270\pi\) | ||||
0.155598 | + | 0.987821i | \(0.450270\pi\) | |||||||
\(710\) | −0.646853 | −0.0242759 | ||||||||
\(711\) | −7.80420 | −0.292680 | ||||||||
\(712\) | −5.64258 | −0.211465 | ||||||||
\(713\) | 11.6616 | 0.436730 | ||||||||
\(714\) | 32.2106 | 1.20545 | ||||||||
\(715\) | 2.33798 | 0.0874353 | ||||||||
\(716\) | −6.74100 | −0.251923 | ||||||||
\(717\) | −39.2473 | −1.46572 | ||||||||
\(718\) | 13.4255 | 0.501035 | ||||||||
\(719\) | 45.2588 | 1.68787 | 0.843933 | − | 0.536448i | \(-0.180234\pi\) | ||||
0.843933 | + | 0.536448i | \(0.180234\pi\) | |||||||
\(720\) | −0.238544 | −0.00889000 | ||||||||
\(721\) | −14.7826 | −0.550534 | ||||||||
\(722\) | −6.21225 | −0.231196 | ||||||||
\(723\) | 2.51967 | 0.0937074 | ||||||||
\(724\) | 7.20245 | 0.267677 | ||||||||
\(725\) | −31.1506 | −1.15691 | ||||||||
\(726\) | 10.8723 | 0.403508 | ||||||||
\(727\) | −47.8798 | −1.77576 | −0.887882 | − | 0.460072i | \(-0.847824\pi\) | ||||
−0.887882 | + | 0.460072i | \(0.847824\pi\) | |||||||
\(728\) | −20.8951 | −0.774423 | ||||||||
\(729\) | 29.6126 | 1.09676 | ||||||||
\(730\) | 1.94691 | 0.0720583 | ||||||||
\(731\) | −17.2767 | −0.639003 | ||||||||
\(732\) | 16.6743 | 0.616299 | ||||||||
\(733\) | 16.6669 | 0.615605 | 0.307803 | − | 0.951450i | \(-0.400406\pi\) | ||||
0.307803 | + | 0.951450i | \(0.400406\pi\) | |||||||
\(734\) | 33.6156 | 1.24077 | ||||||||
\(735\) | −5.58407 | −0.205971 | ||||||||
\(736\) | 2.91478 | 0.107440 | ||||||||
\(737\) | −1.30401 | −0.0480340 | ||||||||
\(738\) | −3.16737 | −0.116592 | ||||||||
\(739\) | 20.2131 | 0.743552 | 0.371776 | − | 0.928323i | \(-0.378749\pi\) | ||||
0.371776 | + | 0.928323i | \(0.378749\pi\) | |||||||
\(740\) | 1.66157 | 0.0610807 | ||||||||
\(741\) | 23.7456 | 0.872318 | ||||||||
\(742\) | −3.14075 | −0.115301 | ||||||||
\(743\) | 16.8568 | 0.618416 | 0.309208 | − | 0.950994i | \(-0.399936\pi\) | ||||
0.309208 | + | 0.950994i | \(0.399936\pi\) | |||||||
\(744\) | −5.83265 | −0.213835 | ||||||||
\(745\) | −3.02589 | −0.110860 | ||||||||
\(746\) | 14.4484 | 0.528993 | ||||||||
\(747\) | −6.09655 | −0.223061 | ||||||||
\(748\) | 9.06472 | 0.331439 | ||||||||
\(749\) | −11.9581 | −0.436941 | ||||||||
\(750\) | 3.94637 | 0.144101 | ||||||||
\(751\) | 11.6969 | 0.426824 | 0.213412 | − | 0.976962i | \(-0.431542\pi\) | ||||
0.213412 | + | 0.976962i | \(0.431542\pi\) | |||||||
\(752\) | 3.64602 | 0.132957 | ||||||||
\(753\) | −8.90227 | −0.324417 | ||||||||
\(754\) | −28.8058 | −1.04904 | ||||||||
\(755\) | 4.87831 | 0.177540 | ||||||||
\(756\) | 25.9131 | 0.942449 | ||||||||
\(757\) | 54.2544 | 1.97191 | 0.985954 | − | 0.167016i | \(-0.0534133\pi\) | ||||
0.985954 | + | 0.167016i | \(0.0534133\pi\) | |||||||
\(758\) | 3.81403 | 0.138532 | ||||||||
\(759\) | 7.99761 | 0.290295 | ||||||||
\(760\) | 0.975267 | 0.0353766 | ||||||||
\(761\) | −20.5485 | −0.744884 | −0.372442 | − | 0.928056i | \(-0.621479\pi\) | ||||
−0.372442 | + | 0.928056i | \(0.621479\pi\) | |||||||
\(762\) | −15.3106 | −0.554645 | ||||||||
\(763\) | −26.6981 | −0.966536 | ||||||||
\(764\) | −7.02014 | −0.253980 | ||||||||
\(765\) | 1.14890 | 0.0415385 | ||||||||
\(766\) | 13.4704 | 0.486704 | ||||||||
\(767\) | −54.9157 | −1.98289 | ||||||||
\(768\) | −1.45785 | −0.0526057 | ||||||||
\(769\) | −13.9108 | −0.501635 | −0.250818 | − | 0.968034i | \(-0.580699\pi\) | ||||
−0.250818 | + | 0.968034i | \(0.580699\pi\) | |||||||
\(770\) | −2.35471 | −0.0848579 | ||||||||
\(771\) | −1.23140 | −0.0443479 | ||||||||
\(772\) | −10.5912 | −0.381185 | ||||||||
\(773\) | −20.7907 | −0.747790 | −0.373895 | − | 0.927471i | \(-0.621978\pi\) | ||||
−0.373895 | + | 0.927471i | \(0.621978\pi\) | |||||||
\(774\) | −3.13754 | −0.112777 | ||||||||
\(775\) | −19.7067 | −0.707884 | ||||||||
\(776\) | 6.48014 | 0.232623 | ||||||||
\(777\) | −40.7453 | −1.46173 | ||||||||
\(778\) | 22.6974 | 0.813740 | ||||||||
\(779\) | 12.9495 | 0.463965 | ||||||||
\(780\) | 1.81098 | 0.0648434 | ||||||||
\(781\) | 4.46395 | 0.159733 | ||||||||
\(782\) | −14.0385 | −0.502015 | ||||||||
\(783\) | 35.7235 | 1.27665 | ||||||||
\(784\) | 14.0446 | 0.501594 | ||||||||
\(785\) | −3.66913 | −0.130957 | ||||||||
\(786\) | −20.8772 | −0.744666 | ||||||||
\(787\) | −33.3231 | −1.18784 | −0.593920 | − | 0.804524i | \(-0.702421\pi\) | ||||
−0.593920 | + | 0.804524i | \(0.702421\pi\) | |||||||
\(788\) | 7.58015 | 0.270032 | ||||||||
\(789\) | 11.8062 | 0.420312 | ||||||||
\(790\) | 2.43340 | 0.0865764 | ||||||||
\(791\) | −37.5187 | −1.33401 | ||||||||
\(792\) | 1.64620 | 0.0584951 | ||||||||
\(793\) | 52.0962 | 1.84999 | ||||||||
\(794\) | 35.3314 | 1.25386 | ||||||||
\(795\) | 0.272209 | 0.00965427 | ||||||||
\(796\) | 18.3153 | 0.649168 | ||||||||
\(797\) | −36.4468 | −1.29101 | −0.645507 | − | 0.763755i | \(-0.723354\pi\) | ||||
−0.645507 | + | 0.763755i | \(0.723354\pi\) | |||||||
\(798\) | −23.9156 | −0.846603 | ||||||||
\(799\) | −17.5603 | −0.621239 | ||||||||
\(800\) | −4.92562 | −0.174147 | ||||||||
\(801\) | 4.93537 | 0.174383 | ||||||||
\(802\) | 24.4662 | 0.863932 | ||||||||
\(803\) | −13.4357 | −0.474135 | ||||||||
\(804\) | −1.01008 | −0.0356228 | ||||||||
\(805\) | 3.64673 | 0.128530 | ||||||||
\(806\) | −18.2232 | −0.641886 | ||||||||
\(807\) | 15.3921 | 0.541829 | ||||||||
\(808\) | 8.58012 | 0.301848 | ||||||||
\(809\) | −8.85480 | −0.311318 | −0.155659 | − | 0.987811i | \(-0.549750\pi\) | ||||
−0.155659 | + | 0.987811i | \(0.549750\pi\) | |||||||
\(810\) | −1.53026 | −0.0537677 | ||||||||
\(811\) | 3.57581 | 0.125564 | 0.0627818 | − | 0.998027i | \(-0.480003\pi\) | ||||
0.0627818 | + | 0.998027i | \(0.480003\pi\) | |||||||
\(812\) | 29.0119 | 1.01812 | ||||||||
\(813\) | 7.64443 | 0.268102 | ||||||||
\(814\) | −11.4666 | −0.401903 | ||||||||
\(815\) | 3.45918 | 0.121170 | ||||||||
\(816\) | 7.02146 | 0.245800 | ||||||||
\(817\) | 12.8276 | 0.448781 | ||||||||
\(818\) | 2.13462 | 0.0746354 | ||||||||
\(819\) | 18.2762 | 0.638622 | ||||||||
\(820\) | 0.987604 | 0.0344886 | ||||||||
\(821\) | 15.5800 | 0.543745 | 0.271873 | − | 0.962333i | \(-0.412357\pi\) | ||||
0.271873 | + | 0.962333i | \(0.412357\pi\) | |||||||
\(822\) | 12.9310 | 0.451020 | ||||||||
\(823\) | −21.7041 | −0.756559 | −0.378279 | − | 0.925691i | \(-0.623484\pi\) | ||||
−0.378279 | + | 0.925691i | \(0.623484\pi\) | |||||||
\(824\) | −3.22241 | −0.112258 | ||||||||
\(825\) | −13.5150 | −0.470531 | ||||||||
\(826\) | 55.3088 | 1.92444 | ||||||||
\(827\) | 20.2410 | 0.703848 | 0.351924 | − | 0.936029i | \(-0.385528\pi\) | ||||
0.351924 | + | 0.936029i | \(0.385528\pi\) | |||||||
\(828\) | −2.54946 | −0.0885998 | ||||||||
\(829\) | 18.6382 | 0.647331 | 0.323666 | − | 0.946172i | \(-0.395085\pi\) | ||||
0.323666 | + | 0.946172i | \(0.395085\pi\) | |||||||
\(830\) | 1.90094 | 0.0659826 | ||||||||
\(831\) | −22.6822 | −0.786837 | ||||||||
\(832\) | −4.55484 | −0.157911 | ||||||||
\(833\) | −67.6432 | −2.34370 | ||||||||
\(834\) | −27.5337 | −0.953413 | ||||||||
\(835\) | −4.23486 | −0.146554 | ||||||||
\(836\) | −6.73035 | −0.232774 | ||||||||
\(837\) | 22.5996 | 0.781155 | ||||||||
\(838\) | −13.2991 | −0.459410 | ||||||||
\(839\) | −22.1060 | −0.763183 | −0.381591 | − | 0.924331i | \(-0.624624\pi\) | ||||
−0.381591 | + | 0.924331i | \(0.624624\pi\) | |||||||
\(840\) | −1.82394 | −0.0629319 | ||||||||
\(841\) | 10.9956 | 0.379159 | ||||||||
\(842\) | −16.4472 | −0.566807 | ||||||||
\(843\) | 5.10949 | 0.175980 | ||||||||
\(844\) | −3.91259 | −0.134677 | ||||||||
\(845\) | 2.11269 | 0.0726788 | ||||||||
\(846\) | −3.18904 | −0.109642 | ||||||||
\(847\) | −34.2119 | −1.17554 | ||||||||
\(848\) | −0.684641 | −0.0235107 | ||||||||
\(849\) | 13.0293 | 0.447165 | ||||||||
\(850\) | 23.7233 | 0.813702 | ||||||||
\(851\) | 17.7582 | 0.608744 | ||||||||
\(852\) | 3.45774 | 0.118460 | ||||||||
\(853\) | −26.6607 | −0.912844 | −0.456422 | − | 0.889764i | \(-0.650869\pi\) | ||||
−0.456422 | + | 0.889764i | \(0.650869\pi\) | |||||||
\(854\) | −52.4691 | −1.79546 | ||||||||
\(855\) | −0.853032 | −0.0291731 | ||||||||
\(856\) | −2.60671 | −0.0890955 | ||||||||
\(857\) | −22.2750 | −0.760898 | −0.380449 | − | 0.924802i | \(-0.624231\pi\) | ||||
−0.380449 | + | 0.924802i | \(0.624231\pi\) | |||||||
\(858\) | −12.4976 | −0.426662 | ||||||||
\(859\) | −33.6768 | −1.14904 | −0.574519 | − | 0.818491i | \(-0.694811\pi\) | ||||
−0.574519 | + | 0.818491i | \(0.694811\pi\) | |||||||
\(860\) | 0.978305 | 0.0333599 | ||||||||
\(861\) | −24.2182 | −0.825353 | ||||||||
\(862\) | −38.1987 | −1.30105 | ||||||||
\(863\) | 21.4571 | 0.730408 | 0.365204 | − | 0.930928i | \(-0.380999\pi\) | ||||
0.365204 | + | 0.930928i | \(0.380999\pi\) | |||||||
\(864\) | 5.64869 | 0.192172 | ||||||||
\(865\) | 5.37795 | 0.182856 | ||||||||
\(866\) | 33.8447 | 1.15009 | ||||||||
\(867\) | −9.03398 | −0.306810 | ||||||||
\(868\) | 18.3537 | 0.622964 | ||||||||
\(869\) | −16.7930 | −0.569662 | ||||||||
\(870\) | −2.51447 | −0.0852484 | ||||||||
\(871\) | −3.15584 | −0.106932 | ||||||||
\(872\) | −5.81982 | −0.197084 | ||||||||
\(873\) | −5.66795 | −0.191831 | ||||||||
\(874\) | 10.4232 | 0.352572 | ||||||||
\(875\) | −12.4181 | −0.419808 | ||||||||
\(876\) | −10.4072 | −0.351626 | ||||||||
\(877\) | 32.9314 | 1.11201 | 0.556007 | − | 0.831177i | \(-0.312333\pi\) | ||||
0.556007 | + | 0.831177i | \(0.312333\pi\) | |||||||
\(878\) | −8.27917 | −0.279408 | ||||||||
\(879\) | 3.25570 | 0.109812 | ||||||||
\(880\) | −0.513295 | −0.0173032 | ||||||||
\(881\) | −16.8413 | −0.567397 | −0.283698 | − | 0.958914i | \(-0.591561\pi\) | ||||
−0.283698 | + | 0.958914i | \(0.591561\pi\) | |||||||
\(882\) | −12.2844 | −0.413636 | ||||||||
\(883\) | 5.55649 | 0.186991 | 0.0934953 | − | 0.995620i | \(-0.470196\pi\) | ||||
0.0934953 | + | 0.995620i | \(0.470196\pi\) | |||||||
\(884\) | 21.9375 | 0.737838 | ||||||||
\(885\) | −4.79362 | −0.161136 | ||||||||
\(886\) | −9.44031 | −0.317153 | ||||||||
\(887\) | −8.27433 | −0.277825 | −0.138912 | − | 0.990305i | \(-0.544361\pi\) | ||||
−0.138912 | + | 0.990305i | \(0.544361\pi\) | |||||||
\(888\) | −8.88192 | −0.298058 | ||||||||
\(889\) | 48.1781 | 1.61584 | ||||||||
\(890\) | −1.53888 | −0.0515833 | ||||||||
\(891\) | 10.5603 | 0.353785 | ||||||||
\(892\) | −12.7908 | −0.428268 | ||||||||
\(893\) | 13.0381 | 0.436305 | ||||||||
\(894\) | 16.1748 | 0.540968 | ||||||||
\(895\) | −1.83844 | −0.0614524 | ||||||||
\(896\) | 4.58744 | 0.153256 | ||||||||
\(897\) | 19.3550 | 0.646244 | ||||||||
\(898\) | −23.8641 | −0.796356 | ||||||||
\(899\) | 25.3022 | 0.843875 | ||||||||
\(900\) | 4.30827 | 0.143609 | ||||||||
\(901\) | 3.29744 | 0.109854 | ||||||||
\(902\) | −6.81549 | −0.226931 | ||||||||
\(903\) | −23.9901 | −0.798341 | ||||||||
\(904\) | −8.17856 | −0.272015 | ||||||||
\(905\) | 1.96429 | 0.0652953 | ||||||||
\(906\) | −26.0770 | −0.866349 | ||||||||
\(907\) | −0.489746 | −0.0162617 | −0.00813087 | − | 0.999967i | \(-0.502588\pi\) | ||||
−0.00813087 | + | 0.999967i | \(0.502588\pi\) | |||||||
\(908\) | −24.4022 | −0.809815 | ||||||||
\(909\) | −7.50473 | −0.248916 | ||||||||
\(910\) | −5.69863 | −0.188908 | ||||||||
\(911\) | 8.68182 | 0.287642 | 0.143821 | − | 0.989604i | \(-0.454061\pi\) | ||||
0.143821 | + | 0.989604i | \(0.454061\pi\) | |||||||
\(912\) | −5.21328 | −0.172629 | ||||||||
\(913\) | −13.1185 | −0.434157 | ||||||||
\(914\) | 15.8047 | 0.522774 | ||||||||
\(915\) | 4.54750 | 0.150336 | ||||||||
\(916\) | 16.9084 | 0.558668 | ||||||||
\(917\) | 65.6946 | 2.16943 | ||||||||
\(918\) | −27.2058 | −0.897925 | ||||||||
\(919\) | −22.5601 | −0.744187 | −0.372094 | − | 0.928195i | \(-0.621360\pi\) | ||||
−0.372094 | + | 0.928195i | \(0.621360\pi\) | |||||||
\(920\) | 0.794936 | 0.0262083 | ||||||||
\(921\) | −28.9966 | −0.955470 | ||||||||
\(922\) | 31.9144 | 1.05105 | ||||||||
\(923\) | 10.8032 | 0.355592 | ||||||||
\(924\) | 12.5871 | 0.414084 | ||||||||
\(925\) | −30.0092 | −0.986696 | ||||||||
\(926\) | 5.12251 | 0.168336 | ||||||||
\(927\) | 2.81853 | 0.0925727 | ||||||||
\(928\) | 6.32421 | 0.207602 | ||||||||
\(929\) | −24.9243 | −0.817738 | −0.408869 | − | 0.912593i | \(-0.634077\pi\) | ||||
−0.408869 | + | 0.912593i | \(0.634077\pi\) | |||||||
\(930\) | −1.59071 | −0.0521616 | ||||||||
\(931\) | 50.2236 | 1.64601 | ||||||||
\(932\) | 6.29988 | 0.206360 | ||||||||
\(933\) | 34.8789 | 1.14188 | ||||||||
\(934\) | −27.3516 | −0.894972 | ||||||||
\(935\) | 2.47218 | 0.0808490 | ||||||||
\(936\) | 3.98396 | 0.130220 | ||||||||
\(937\) | 1.56449 | 0.0511097 | 0.0255548 | − | 0.999673i | \(-0.491865\pi\) | ||||
0.0255548 | + | 0.999673i | \(0.491865\pi\) | |||||||
\(938\) | 3.17843 | 0.103779 | ||||||||
\(939\) | 8.35183 | 0.272552 | ||||||||
\(940\) | 0.994363 | 0.0324325 | ||||||||
\(941\) | 50.4348 | 1.64413 | 0.822065 | − | 0.569394i | \(-0.192822\pi\) | ||||
0.822065 | + | 0.569394i | \(0.192822\pi\) | |||||||
\(942\) | 19.6133 | 0.639035 | ||||||||
\(943\) | 10.5551 | 0.343722 | ||||||||
\(944\) | 12.0566 | 0.392407 | ||||||||
\(945\) | 7.06716 | 0.229895 | ||||||||
\(946\) | −6.75132 | −0.219504 | ||||||||
\(947\) | 15.3263 | 0.498037 | 0.249018 | − | 0.968499i | \(-0.419892\pi\) | ||||
0.249018 | + | 0.968499i | \(0.419892\pi\) | |||||||
\(948\) | −13.0077 | −0.422470 | ||||||||
\(949\) | −32.5157 | −1.05550 | ||||||||
\(950\) | −17.6140 | −0.571474 | ||||||||
\(951\) | 49.6811 | 1.61102 | ||||||||
\(952\) | −22.0945 | −0.716087 | ||||||||
\(953\) | −32.2732 | −1.04543 | −0.522715 | − | 0.852507i | \(-0.675081\pi\) | ||||
−0.522715 | + | 0.852507i | \(0.675081\pi\) | |||||||
\(954\) | 0.598832 | 0.0193879 | ||||||||
\(955\) | −1.91457 | −0.0619541 | ||||||||
\(956\) | 26.9213 | 0.870696 | ||||||||
\(957\) | 17.3524 | 0.560924 | ||||||||
\(958\) | −38.1374 | −1.23216 | ||||||||
\(959\) | −40.6901 | −1.31395 | ||||||||
\(960\) | −0.397594 | −0.0128323 | ||||||||
\(961\) | −14.9932 | −0.483652 | ||||||||
\(962\) | −27.7502 | −0.894703 | ||||||||
\(963\) | 2.28000 | 0.0734719 | ||||||||
\(964\) | −1.72834 | −0.0556661 | ||||||||
\(965\) | −2.88849 | −0.0929838 | ||||||||
\(966\) | −19.4935 | −0.627194 | ||||||||
\(967\) | −30.7470 | −0.988756 | −0.494378 | − | 0.869247i | \(-0.664604\pi\) | ||||
−0.494378 | + | 0.869247i | \(0.664604\pi\) | |||||||
\(968\) | −7.45774 | −0.239701 | ||||||||
\(969\) | 25.1087 | 0.806608 | ||||||||
\(970\) | 1.76730 | 0.0567446 | ||||||||
\(971\) | −1.62463 | −0.0521368 | −0.0260684 | − | 0.999660i | \(-0.508299\pi\) | ||||
−0.0260684 | + | 0.999660i | \(0.508299\pi\) | |||||||
\(972\) | −8.76611 | −0.281173 | ||||||||
\(973\) | 86.6405 | 2.77757 | ||||||||
\(974\) | −32.6262 | −1.04541 | ||||||||
\(975\) | −32.7075 | −1.04748 | ||||||||
\(976\) | −11.4376 | −0.366107 | ||||||||
\(977\) | −20.0462 | −0.641334 | −0.320667 | − | 0.947192i | \(-0.603907\pi\) | ||||
−0.320667 | + | 0.947192i | \(0.603907\pi\) | |||||||
\(978\) | −18.4910 | −0.591278 | ||||||||
\(979\) | 10.6199 | 0.339412 | ||||||||
\(980\) | 3.83034 | 0.122356 | ||||||||
\(981\) | 5.09039 | 0.162524 | ||||||||
\(982\) | 5.95061 | 0.189892 | ||||||||
\(983\) | 11.1380 | 0.355247 | 0.177624 | − | 0.984098i | \(-0.443159\pi\) | ||||
0.177624 | + | 0.984098i | \(0.443159\pi\) | |||||||
\(984\) | −5.27923 | −0.168296 | ||||||||
\(985\) | 2.06730 | 0.0658697 | ||||||||
\(986\) | −30.4593 | −0.970022 | ||||||||
\(987\) | −24.3839 | −0.776148 | ||||||||
\(988\) | −16.2881 | −0.518193 | ||||||||
\(989\) | 10.4557 | 0.332473 | ||||||||
\(990\) | 0.448961 | 0.0142689 | ||||||||
\(991\) | 45.3052 | 1.43917 | 0.719584 | − | 0.694406i | \(-0.244333\pi\) | ||||
0.719584 | + | 0.694406i | \(0.244333\pi\) | |||||||
\(992\) | 4.00085 | 0.127027 | ||||||||
\(993\) | 30.0642 | 0.954060 | ||||||||
\(994\) | −10.8805 | −0.345109 | ||||||||
\(995\) | 4.99505 | 0.158354 | ||||||||
\(996\) | −10.1615 | −0.321978 | ||||||||
\(997\) | 38.0287 | 1.20438 | 0.602190 | − | 0.798352i | \(-0.294295\pi\) | ||||
0.602190 | + | 0.798352i | \(0.294295\pi\) | |||||||
\(998\) | −40.3308 | −1.27665 | ||||||||
\(999\) | 34.4145 | 1.08883 |
(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 | 4034.2.a.d.1.14 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.d.1.14 | ✓ | 52 | 1.1 | even | 1 | trivial |