Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 56 x^{10} + 26 x^{9} - 263 x^{8} + 50 x^{7} + 478 x^{6} - 174 x^{5} + \cdots - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.46649\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46649 | 1.03696 | 0.518481 | − | 0.855089i | \(-0.326498\pi\) | ||||
0.518481 | + | 0.855089i | \(0.326498\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.150578 | 0.0752892 | ||||||||
\(5\) | 1.27945 | 0.572189 | 0.286095 | − | 0.958201i | \(-0.407643\pi\) | ||||
0.286095 | + | 0.958201i | \(0.407643\pi\) | |||||||
\(6\) | 1.46649 | 0.598690 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.71215 | −0.958890 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.87630 | 0.593338 | ||||||||
\(11\) | 4.55512 | 1.37342 | 0.686710 | − | 0.726931i | \(-0.259054\pi\) | ||||
0.686710 | + | 0.726931i | \(0.259054\pi\) | |||||||
\(12\) | 0.150578 | 0.0434682 | ||||||||
\(13\) | −3.82930 | −1.06206 | −0.531029 | − | 0.847354i | \(-0.678194\pi\) | ||||
−0.531029 | + | 0.847354i | \(0.678194\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.27945 | 0.330354 | ||||||||
\(16\) | −4.27848 | −1.06962 | ||||||||
\(17\) | −3.03199 | −0.735366 | −0.367683 | − | 0.929951i | \(-0.619849\pi\) | ||||
−0.367683 | + | 0.929951i | \(0.619849\pi\) | |||||||
\(18\) | 1.46649 | 0.345654 | ||||||||
\(19\) | −4.80420 | −1.10216 | −0.551080 | − | 0.834453i | \(-0.685784\pi\) | ||||
−0.551080 | + | 0.834453i | \(0.685784\pi\) | |||||||
\(20\) | 0.192658 | 0.0430797 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.68002 | 1.42418 | ||||||||
\(23\) | −6.82949 | −1.42405 | −0.712023 | − | 0.702156i | \(-0.752221\pi\) | ||||
−0.712023 | + | 0.702156i | \(0.752221\pi\) | |||||||
\(24\) | −2.71215 | −0.553615 | ||||||||
\(25\) | −3.36300 | −0.672599 | ||||||||
\(26\) | −5.61561 | −1.10131 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.73574 | −1.62219 | −0.811093 | − | 0.584917i | \(-0.801127\pi\) | ||||
−0.811093 | + | 0.584917i | \(0.801127\pi\) | |||||||
\(30\) | 1.87630 | 0.342564 | ||||||||
\(31\) | 0.252900 | 0.0454221 | 0.0227111 | − | 0.999742i | \(-0.492770\pi\) | ||||
0.0227111 | + | 0.999742i | \(0.492770\pi\) | |||||||
\(32\) | −0.850033 | −0.150266 | ||||||||
\(33\) | 4.55512 | 0.792945 | ||||||||
\(34\) | −4.44637 | −0.762546 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.150578 | 0.0250964 | ||||||||
\(37\) | 1.57080 | 0.258238 | 0.129119 | − | 0.991629i | \(-0.458785\pi\) | ||||
0.129119 | + | 0.991629i | \(0.458785\pi\) | |||||||
\(38\) | −7.04529 | −1.14290 | ||||||||
\(39\) | −3.82930 | −0.613179 | ||||||||
\(40\) | −3.47007 | −0.548666 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.30779 | 0.504434 | 0.252217 | − | 0.967671i | \(-0.418840\pi\) | ||||
0.252217 | + | 0.967671i | \(0.418840\pi\) | |||||||
\(44\) | 0.685903 | 0.103404 | ||||||||
\(45\) | 1.27945 | 0.190730 | ||||||||
\(46\) | −10.0153 | −1.47668 | ||||||||
\(47\) | −7.07743 | −1.03235 | −0.516175 | − | 0.856483i | \(-0.672645\pi\) | ||||
−0.516175 | + | 0.856483i | \(0.672645\pi\) | |||||||
\(48\) | −4.27848 | −0.617546 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.93178 | −0.697460 | ||||||||
\(51\) | −3.03199 | −0.424564 | ||||||||
\(52\) | −0.576610 | −0.0799615 | ||||||||
\(53\) | 3.70905 | 0.509477 | 0.254738 | − | 0.967010i | \(-0.418011\pi\) | ||||
0.254738 | + | 0.967010i | \(0.418011\pi\) | |||||||
\(54\) | 1.46649 | 0.199563 | ||||||||
\(55\) | 5.82807 | 0.785857 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.80420 | −0.636332 | ||||||||
\(58\) | −12.8108 | −1.68214 | ||||||||
\(59\) | 10.7021 | 1.39329 | 0.696645 | − | 0.717416i | \(-0.254675\pi\) | ||||
0.696645 | + | 0.717416i | \(0.254675\pi\) | |||||||
\(60\) | 0.192658 | 0.0248721 | ||||||||
\(61\) | −11.5919 | −1.48419 | −0.742096 | − | 0.670294i | \(-0.766168\pi\) | ||||
−0.742096 | + | 0.670294i | \(0.766168\pi\) | |||||||
\(62\) | 0.370874 | 0.0471010 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.31041 | 0.913801 | ||||||||
\(65\) | −4.89942 | −0.607698 | ||||||||
\(66\) | 6.68002 | 0.822253 | ||||||||
\(67\) | −9.19482 | −1.12333 | −0.561663 | − | 0.827366i | \(-0.689838\pi\) | ||||
−0.561663 | + | 0.827366i | \(0.689838\pi\) | |||||||
\(68\) | −0.456553 | −0.0553651 | ||||||||
\(69\) | −6.82949 | −0.822174 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.31030 | −0.748894 | −0.374447 | − | 0.927248i | \(-0.622168\pi\) | ||||
−0.374447 | + | 0.927248i | \(0.622168\pi\) | |||||||
\(72\) | −2.71215 | −0.319630 | ||||||||
\(73\) | 1.54239 | 0.180523 | 0.0902616 | − | 0.995918i | \(-0.471230\pi\) | ||||
0.0902616 | + | 0.995918i | \(0.471230\pi\) | |||||||
\(74\) | 2.30356 | 0.267783 | ||||||||
\(75\) | −3.36300 | −0.388325 | ||||||||
\(76\) | −0.723409 | −0.0829807 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.61561 | −0.635843 | ||||||||
\(79\) | 12.1437 | 1.36628 | 0.683139 | − | 0.730288i | \(-0.260614\pi\) | ||||
0.683139 | + | 0.730288i | \(0.260614\pi\) | |||||||
\(80\) | −5.47412 | −0.612026 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.46649 | 0.161946 | ||||||||
\(83\) | −11.4396 | −1.25566 | −0.627830 | − | 0.778350i | \(-0.716057\pi\) | ||||
−0.627830 | + | 0.778350i | \(0.716057\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.87930 | −0.420769 | ||||||||
\(86\) | 4.85083 | 0.523079 | ||||||||
\(87\) | −8.73574 | −0.936569 | ||||||||
\(88\) | −12.3542 | −1.31696 | ||||||||
\(89\) | −6.14545 | −0.651416 | −0.325708 | − | 0.945470i | \(-0.605603\pi\) | ||||
−0.325708 | + | 0.945470i | \(0.605603\pi\) | |||||||
\(90\) | 1.87630 | 0.197779 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.02837 | −0.107215 | ||||||||
\(93\) | 0.252900 | 0.0262245 | ||||||||
\(94\) | −10.3790 | −1.07051 | ||||||||
\(95\) | −6.14675 | −0.630644 | ||||||||
\(96\) | −0.850033 | −0.0867561 | ||||||||
\(97\) | −9.51325 | −0.965925 | −0.482962 | − | 0.875641i | \(-0.660439\pi\) | ||||
−0.482962 | + | 0.875641i | \(0.660439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.55512 | 0.457807 | ||||||||
\(100\) | −0.506395 | −0.0506395 | ||||||||
\(101\) | 18.8292 | 1.87358 | 0.936788 | − | 0.349898i | \(-0.113784\pi\) | ||||
0.936788 | + | 0.349898i | \(0.113784\pi\) | |||||||
\(102\) | −4.44637 | −0.440256 | ||||||||
\(103\) | −9.78428 | −0.964074 | −0.482037 | − | 0.876151i | \(-0.660103\pi\) | ||||
−0.482037 | + | 0.876151i | \(0.660103\pi\) | |||||||
\(104\) | 10.3856 | 1.01840 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.43926 | 0.528308 | ||||||||
\(107\) | 9.64440 | 0.932359 | 0.466180 | − | 0.884690i | \(-0.345630\pi\) | ||||
0.466180 | + | 0.884690i | \(0.345630\pi\) | |||||||
\(108\) | 0.150578 | 0.0144894 | ||||||||
\(109\) | 7.19766 | 0.689411 | 0.344705 | − | 0.938711i | \(-0.387979\pi\) | ||||
0.344705 | + | 0.938711i | \(0.387979\pi\) | |||||||
\(110\) | 8.54678 | 0.814903 | ||||||||
\(111\) | 1.57080 | 0.149094 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.2060 | 1.52453 | 0.762265 | − | 0.647265i | \(-0.224087\pi\) | ||||
0.762265 | + | 0.647265i | \(0.224087\pi\) | |||||||
\(114\) | −7.04529 | −0.659852 | ||||||||
\(115\) | −8.73802 | −0.814824 | ||||||||
\(116\) | −1.31541 | −0.122133 | ||||||||
\(117\) | −3.82930 | −0.354019 | ||||||||
\(118\) | 15.6944 | 1.44479 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.47007 | −0.316773 | ||||||||
\(121\) | 9.74912 | 0.886284 | ||||||||
\(122\) | −16.9994 | −1.53905 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 0.0380812 | 0.00341980 | ||||||||
\(125\) | −10.7001 | −0.957044 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.30123 | −0.825350 | −0.412675 | − | 0.910878i | \(-0.635406\pi\) | ||||
−0.412675 | + | 0.910878i | \(0.635406\pi\) | |||||||
\(128\) | 12.4207 | 1.09784 | ||||||||
\(129\) | 3.30779 | 0.291235 | ||||||||
\(130\) | −7.18492 | −0.630159 | ||||||||
\(131\) | 2.36148 | 0.206323 | 0.103162 | − | 0.994665i | \(-0.467104\pi\) | ||||
0.103162 | + | 0.994665i | \(0.467104\pi\) | |||||||
\(132\) | 0.685903 | 0.0597002 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.4841 | −1.16485 | ||||||||
\(135\) | 1.27945 | 0.110118 | ||||||||
\(136\) | 8.22322 | 0.705135 | ||||||||
\(137\) | −8.05057 | −0.687807 | −0.343903 | − | 0.939005i | \(-0.611749\pi\) | ||||
−0.343903 | + | 0.939005i | \(0.611749\pi\) | |||||||
\(138\) | −10.0153 | −0.852563 | ||||||||
\(139\) | −4.36913 | −0.370585 | −0.185292 | − | 0.982683i | \(-0.559323\pi\) | ||||
−0.185292 | + | 0.982683i | \(0.559323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.07743 | −0.596027 | ||||||||
\(142\) | −9.25396 | −0.776575 | ||||||||
\(143\) | −17.4429 | −1.45865 | ||||||||
\(144\) | −4.27848 | −0.356540 | ||||||||
\(145\) | −11.1770 | −0.928197 | ||||||||
\(146\) | 2.26189 | 0.187196 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.236529 | 0.0194425 | ||||||||
\(149\) | 21.7122 | 1.77873 | 0.889365 | − | 0.457198i | \(-0.151147\pi\) | ||||
0.889365 | + | 0.457198i | \(0.151147\pi\) | |||||||
\(150\) | −4.93178 | −0.402679 | ||||||||
\(151\) | 8.17544 | 0.665308 | 0.332654 | − | 0.943049i | \(-0.392056\pi\) | ||||
0.332654 | + | 0.943049i | \(0.392056\pi\) | |||||||
\(152\) | 13.0297 | 1.05685 | ||||||||
\(153\) | −3.03199 | −0.245122 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.323574 | 0.0259901 | ||||||||
\(156\) | −0.576610 | −0.0461658 | ||||||||
\(157\) | 16.4197 | 1.31043 | 0.655216 | − | 0.755442i | \(-0.272578\pi\) | ||||
0.655216 | + | 0.755442i | \(0.272578\pi\) | |||||||
\(158\) | 17.8086 | 1.41678 | ||||||||
\(159\) | 3.70905 | 0.294146 | ||||||||
\(160\) | −1.08758 | −0.0859806 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.46649 | 0.115218 | ||||||||
\(163\) | −7.65254 | −0.599393 | −0.299697 | − | 0.954035i | \(-0.596885\pi\) | ||||
−0.299697 | + | 0.954035i | \(0.596885\pi\) | |||||||
\(164\) | 0.150578 | 0.0117582 | ||||||||
\(165\) | 5.82807 | 0.453715 | ||||||||
\(166\) | −16.7760 | −1.30207 | ||||||||
\(167\) | −0.211772 | −0.0163874 | −0.00819369 | − | 0.999966i | \(-0.502608\pi\) | ||||
−0.00819369 | + | 0.999966i | \(0.502608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.66355 | 0.127966 | ||||||||
\(170\) | −5.68893 | −0.436321 | ||||||||
\(171\) | −4.80420 | −0.367386 | ||||||||
\(172\) | 0.498082 | 0.0379784 | ||||||||
\(173\) | −0.100684 | −0.00765484 | −0.00382742 | − | 0.999993i | \(-0.501218\pi\) | ||||
−0.00382742 | + | 0.999993i | \(0.501218\pi\) | |||||||
\(174\) | −12.8108 | −0.971187 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.4890 | −1.46904 | ||||||||
\(177\) | 10.7021 | 0.804416 | ||||||||
\(178\) | −9.01221 | −0.675494 | ||||||||
\(179\) | 5.96037 | 0.445499 | 0.222750 | − | 0.974876i | \(-0.428497\pi\) | ||||
0.222750 | + | 0.974876i | \(0.428497\pi\) | |||||||
\(180\) | 0.192658 | 0.0143599 | ||||||||
\(181\) | −8.73411 | −0.649201 | −0.324601 | − | 0.945851i | \(-0.605230\pi\) | ||||
−0.324601 | + | 0.945851i | \(0.605230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.5919 | −0.856899 | ||||||||
\(184\) | 18.5226 | 1.36550 | ||||||||
\(185\) | 2.00977 | 0.147761 | ||||||||
\(186\) | 0.370874 | 0.0271938 | ||||||||
\(187\) | −13.8111 | −1.00997 | ||||||||
\(188\) | −1.06571 | −0.0777248 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.01412 | −0.653953 | ||||||||
\(191\) | 21.8499 | 1.58100 | 0.790502 | − | 0.612459i | \(-0.209819\pi\) | ||||
0.790502 | + | 0.612459i | \(0.209819\pi\) | |||||||
\(192\) | 7.31041 | 0.527583 | ||||||||
\(193\) | 1.99809 | 0.143826 | 0.0719129 | − | 0.997411i | \(-0.477090\pi\) | ||||
0.0719129 | + | 0.997411i | \(0.477090\pi\) | |||||||
\(194\) | −13.9510 | −1.00163 | ||||||||
\(195\) | −4.89942 | −0.350855 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.78972 | −0.198760 | −0.0993798 | − | 0.995050i | \(-0.531686\pi\) | ||||
−0.0993798 | + | 0.995050i | \(0.531686\pi\) | |||||||
\(198\) | 6.68002 | 0.474728 | ||||||||
\(199\) | −22.1261 | −1.56848 | −0.784238 | − | 0.620460i | \(-0.786946\pi\) | ||||
−0.784238 | + | 0.620460i | \(0.786946\pi\) | |||||||
\(200\) | 9.12095 | 0.644948 | ||||||||
\(201\) | −9.19482 | −0.648553 | ||||||||
\(202\) | 27.6127 | 1.94283 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.456553 | −0.0319651 | ||||||||
\(205\) | 1.27945 | 0.0893610 | ||||||||
\(206\) | −14.3485 | −0.999708 | ||||||||
\(207\) | −6.82949 | −0.474682 | ||||||||
\(208\) | 16.3836 | 1.13600 | ||||||||
\(209\) | −21.8837 | −1.51373 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.11123 | −0.145343 | −0.0726717 | − | 0.997356i | \(-0.523153\pi\) | ||||
−0.0726717 | + | 0.997356i | \(0.523153\pi\) | |||||||
\(212\) | 0.558502 | 0.0383581 | ||||||||
\(213\) | −6.31030 | −0.432374 | ||||||||
\(214\) | 14.1434 | 0.966820 | ||||||||
\(215\) | 4.23217 | 0.288632 | ||||||||
\(216\) | −2.71215 | −0.184538 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.5553 | 0.714892 | ||||||||
\(219\) | 1.54239 | 0.104225 | ||||||||
\(220\) | 0.877581 | 0.0591665 | ||||||||
\(221\) | 11.6104 | 0.781001 | ||||||||
\(222\) | 2.30356 | 0.154605 | ||||||||
\(223\) | −24.2366 | −1.62300 | −0.811501 | − | 0.584351i | \(-0.801349\pi\) | ||||
−0.811501 | + | 0.584351i | \(0.801349\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.36300 | −0.224200 | ||||||||
\(226\) | 23.7658 | 1.58088 | ||||||||
\(227\) | 2.14939 | 0.142660 | 0.0713301 | − | 0.997453i | \(-0.477276\pi\) | ||||
0.0713301 | + | 0.997453i | \(0.477276\pi\) | |||||||
\(228\) | −0.723409 | −0.0479089 | ||||||||
\(229\) | 3.06900 | 0.202805 | 0.101402 | − | 0.994845i | \(-0.467667\pi\) | ||||
0.101402 | + | 0.994845i | \(0.467667\pi\) | |||||||
\(230\) | −12.8142 | −0.844942 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 23.6926 | 1.55550 | ||||||||
\(233\) | 9.37576 | 0.614227 | 0.307113 | − | 0.951673i | \(-0.400637\pi\) | ||||
0.307113 | + | 0.951673i | \(0.400637\pi\) | |||||||
\(234\) | −5.61561 | −0.367104 | ||||||||
\(235\) | −9.05525 | −0.590700 | ||||||||
\(236\) | 1.61150 | 0.104900 | ||||||||
\(237\) | 12.1437 | 0.788821 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.5926 | 1.00860 | 0.504300 | − | 0.863528i | \(-0.331750\pi\) | ||||
0.504300 | + | 0.863528i | \(0.331750\pi\) | |||||||
\(240\) | −5.47412 | −0.353353 | ||||||||
\(241\) | 4.22330 | 0.272047 | 0.136023 | − | 0.990706i | \(-0.456568\pi\) | ||||
0.136023 | + | 0.990706i | \(0.456568\pi\) | |||||||
\(242\) | 14.2969 | 0.919042 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.74549 | −0.111744 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.46649 | 0.0934997 | ||||||||
\(247\) | 18.3967 | 1.17056 | ||||||||
\(248\) | −0.685902 | −0.0435548 | ||||||||
\(249\) | −11.4396 | −0.724956 | ||||||||
\(250\) | −15.6915 | −0.992417 | ||||||||
\(251\) | −4.51217 | −0.284806 | −0.142403 | − | 0.989809i | \(-0.545483\pi\) | ||||
−0.142403 | + | 0.989809i | \(0.545483\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.1091 | −1.95582 | ||||||||
\(254\) | −13.6401 | −0.855857 | ||||||||
\(255\) | −3.87930 | −0.242931 | ||||||||
\(256\) | 3.59391 | 0.224619 | ||||||||
\(257\) | −4.76009 | −0.296927 | −0.148463 | − | 0.988918i | \(-0.547433\pi\) | ||||
−0.148463 | + | 0.988918i | \(0.547433\pi\) | |||||||
\(258\) | 4.85083 | 0.302000 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.737746 | −0.0457531 | ||||||||
\(261\) | −8.73574 | −0.540729 | ||||||||
\(262\) | 3.46307 | 0.213949 | ||||||||
\(263\) | −28.7541 | −1.77305 | −0.886527 | − | 0.462678i | \(-0.846889\pi\) | ||||
−0.886527 | + | 0.462678i | \(0.846889\pi\) | |||||||
\(264\) | −12.3542 | −0.760346 | ||||||||
\(265\) | 4.74555 | 0.291517 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.14545 | −0.376095 | ||||||||
\(268\) | −1.38454 | −0.0845744 | ||||||||
\(269\) | −25.0023 | −1.52442 | −0.762208 | − | 0.647332i | \(-0.775885\pi\) | ||||
−0.762208 | + | 0.647332i | \(0.775885\pi\) | |||||||
\(270\) | 1.87630 | 0.114188 | ||||||||
\(271\) | −25.4980 | −1.54890 | −0.774448 | − | 0.632638i | \(-0.781972\pi\) | ||||
−0.774448 | + | 0.632638i | \(0.781972\pi\) | |||||||
\(272\) | 12.9723 | 0.786563 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.8060 | −0.713229 | ||||||||
\(275\) | −15.3189 | −0.923762 | ||||||||
\(276\) | −1.02837 | −0.0619008 | ||||||||
\(277\) | 22.6527 | 1.36107 | 0.680535 | − | 0.732716i | \(-0.261748\pi\) | ||||
0.680535 | + | 0.732716i | \(0.261748\pi\) | |||||||
\(278\) | −6.40727 | −0.384282 | ||||||||
\(279\) | 0.252900 | 0.0151407 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.4784 | −1.57957 | −0.789784 | − | 0.613385i | \(-0.789807\pi\) | ||||
−0.789784 | + | 0.613385i | \(0.789807\pi\) | |||||||
\(282\) | −10.3790 | −0.618058 | ||||||||
\(283\) | −19.4386 | −1.15550 | −0.577752 | − | 0.816212i | \(-0.696070\pi\) | ||||
−0.577752 | + | 0.816212i | \(0.696070\pi\) | |||||||
\(284\) | −0.950195 | −0.0563837 | ||||||||
\(285\) | −6.14675 | −0.364102 | ||||||||
\(286\) | −25.5798 | −1.51257 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.850033 | −0.0500887 | ||||||||
\(289\) | −7.80702 | −0.459237 | ||||||||
\(290\) | −16.3909 | −0.962505 | ||||||||
\(291\) | −9.51325 | −0.557677 | ||||||||
\(292\) | 0.232251 | 0.0135915 | ||||||||
\(293\) | −19.8355 | −1.15880 | −0.579400 | − | 0.815043i | \(-0.696713\pi\) | ||||
−0.579400 | + | 0.815043i | \(0.696713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6928 | 0.797226 | ||||||||
\(296\) | −4.26025 | −0.247622 | ||||||||
\(297\) | 4.55512 | 0.264315 | ||||||||
\(298\) | 31.8406 | 1.84447 | ||||||||
\(299\) | 26.1522 | 1.51242 | ||||||||
\(300\) | −0.506395 | −0.0292367 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.9892 | 0.689899 | ||||||||
\(303\) | 18.8292 | 1.08171 | ||||||||
\(304\) | 20.5547 | 1.17889 | ||||||||
\(305\) | −14.8313 | −0.849239 | ||||||||
\(306\) | −4.44637 | −0.254182 | ||||||||
\(307\) | 18.8959 | 1.07845 | 0.539223 | − | 0.842163i | \(-0.318718\pi\) | ||||
0.539223 | + | 0.842163i | \(0.318718\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.78428 | −0.556608 | ||||||||
\(310\) | 0.474516 | 0.0269507 | ||||||||
\(311\) | 22.0458 | 1.25011 | 0.625053 | − | 0.780583i | \(-0.285077\pi\) | ||||
0.625053 | + | 0.780583i | \(0.285077\pi\) | |||||||
\(312\) | 10.3856 | 0.587971 | ||||||||
\(313\) | 11.6199 | 0.656795 | 0.328397 | − | 0.944540i | \(-0.393491\pi\) | ||||
0.328397 | + | 0.944540i | \(0.393491\pi\) | |||||||
\(314\) | 24.0792 | 1.35887 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.82859 | 0.102866 | ||||||||
\(317\) | −6.76104 | −0.379738 | −0.189869 | − | 0.981809i | \(-0.560806\pi\) | ||||
−0.189869 | + | 0.981809i | \(0.560806\pi\) | |||||||
\(318\) | 5.43926 | 0.305019 | ||||||||
\(319\) | −39.7923 | −2.22794 | ||||||||
\(320\) | 9.35333 | 0.522867 | ||||||||
\(321\) | 9.64440 | 0.538298 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.5663 | 0.810490 | ||||||||
\(324\) | 0.150578 | 0.00836547 | ||||||||
\(325\) | 12.8779 | 0.714339 | ||||||||
\(326\) | −11.2223 | −0.621548 | ||||||||
\(327\) | 7.19766 | 0.398031 | ||||||||
\(328\) | −2.71215 | −0.149753 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 8.54678 | 0.470485 | ||||||||
\(331\) | 27.7408 | 1.52477 | 0.762387 | − | 0.647122i | \(-0.224028\pi\) | ||||
0.762387 | + | 0.647122i | \(0.224028\pi\) | |||||||
\(332\) | −1.72256 | −0.0945377 | ||||||||
\(333\) | 1.57080 | 0.0860794 | ||||||||
\(334\) | −0.310560 | −0.0169931 | ||||||||
\(335\) | −11.7644 | −0.642755 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.1071 | 0.877411 | 0.438706 | − | 0.898631i | \(-0.355437\pi\) | ||||
0.438706 | + | 0.898631i | \(0.355437\pi\) | |||||||
\(338\) | 2.43958 | 0.132696 | ||||||||
\(339\) | 16.2060 | 0.880188 | ||||||||
\(340\) | −0.584138 | −0.0316793 | ||||||||
\(341\) | 1.15199 | 0.0623837 | ||||||||
\(342\) | −7.04529 | −0.380966 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.97123 | −0.483696 | ||||||||
\(345\) | −8.73802 | −0.470439 | ||||||||
\(346\) | −0.147651 | −0.00793777 | ||||||||
\(347\) | −22.8151 | −1.22478 | −0.612390 | − | 0.790556i | \(-0.709792\pi\) | ||||
−0.612390 | + | 0.790556i | \(0.709792\pi\) | |||||||
\(348\) | −1.31541 | −0.0705136 | ||||||||
\(349\) | −35.0143 | −1.87427 | −0.937136 | − | 0.348965i | \(-0.886533\pi\) | ||||
−0.937136 | + | 0.348965i | \(0.886533\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.82930 | −0.204393 | ||||||||
\(352\) | −3.87200 | −0.206378 | ||||||||
\(353\) | −20.4057 | −1.08609 | −0.543044 | − | 0.839704i | \(-0.682728\pi\) | ||||
−0.543044 | + | 0.839704i | \(0.682728\pi\) | |||||||
\(354\) | 15.6944 | 0.834149 | ||||||||
\(355\) | −8.07374 | −0.428509 | ||||||||
\(356\) | −0.925372 | −0.0490446 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.74080 | 0.461966 | ||||||||
\(359\) | −12.3014 | −0.649242 | −0.324621 | − | 0.945844i | \(-0.605237\pi\) | ||||
−0.324621 | + | 0.945844i | \(0.605237\pi\) | |||||||
\(360\) | −3.47007 | −0.182889 | ||||||||
\(361\) | 4.08034 | 0.214755 | ||||||||
\(362\) | −12.8084 | −0.673197 | ||||||||
\(363\) | 9.74912 | 0.511696 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.97342 | 0.103293 | ||||||||
\(366\) | −16.9994 | −0.888571 | ||||||||
\(367\) | 20.8417 | 1.08793 | 0.543963 | − | 0.839109i | \(-0.316923\pi\) | ||||
0.543963 | + | 0.839109i | \(0.316923\pi\) | |||||||
\(368\) | 29.2199 | 1.52319 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 2.94730 | 0.153223 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.0380812 | 0.00197442 | ||||||||
\(373\) | −5.74240 | −0.297330 | −0.148665 | − | 0.988888i | \(-0.547498\pi\) | ||||
−0.148665 | + | 0.988888i | \(0.547498\pi\) | |||||||
\(374\) | −20.2538 | −1.04730 | ||||||||
\(375\) | −10.7001 | −0.552549 | ||||||||
\(376\) | 19.1951 | 0.989909 | ||||||||
\(377\) | 33.4518 | 1.72285 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.9770 | 1.23162 | 0.615808 | − | 0.787896i | \(-0.288830\pi\) | ||||
0.615808 | + | 0.787896i | \(0.288830\pi\) | |||||||
\(380\) | −0.925569 | −0.0474807 | ||||||||
\(381\) | −9.30123 | −0.476516 | ||||||||
\(382\) | 32.0426 | 1.63944 | ||||||||
\(383\) | −32.3926 | −1.65518 | −0.827591 | − | 0.561331i | \(-0.810290\pi\) | ||||
−0.827591 | + | 0.561331i | \(0.810290\pi\) | |||||||
\(384\) | 12.4207 | 0.633839 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.93017 | 0.149142 | ||||||||
\(387\) | 3.30779 | 0.168145 | ||||||||
\(388\) | −1.43249 | −0.0727237 | ||||||||
\(389\) | 5.10993 | 0.259084 | 0.129542 | − | 0.991574i | \(-0.458649\pi\) | ||||
0.129542 | + | 0.991574i | \(0.458649\pi\) | |||||||
\(390\) | −7.18492 | −0.363823 | ||||||||
\(391\) | 20.7070 | 1.04720 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.36148 | 0.119121 | ||||||||
\(394\) | −4.09109 | −0.206106 | ||||||||
\(395\) | 15.5374 | 0.781770 | ||||||||
\(396\) | 0.685903 | 0.0344679 | ||||||||
\(397\) | −4.25431 | −0.213518 | −0.106759 | − | 0.994285i | \(-0.534047\pi\) | ||||
−0.106759 | + | 0.994285i | \(0.534047\pi\) | |||||||
\(398\) | −32.4476 | −1.62645 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.3885 | 0.719426 | ||||||||
\(401\) | −22.6592 | −1.13155 | −0.565774 | − | 0.824561i | \(-0.691422\pi\) | ||||
−0.565774 | + | 0.824561i | \(0.691422\pi\) | |||||||
\(402\) | −13.4841 | −0.672524 | ||||||||
\(403\) | −0.968430 | −0.0482409 | ||||||||
\(404\) | 2.83527 | 0.141060 | ||||||||
\(405\) | 1.27945 | 0.0635766 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.15519 | 0.354670 | ||||||||
\(408\) | 8.22322 | 0.407110 | ||||||||
\(409\) | 8.95406 | 0.442750 | 0.221375 | − | 0.975189i | \(-0.428946\pi\) | ||||
0.221375 | + | 0.975189i | \(0.428946\pi\) | |||||||
\(410\) | 1.87630 | 0.0926639 | ||||||||
\(411\) | −8.05057 | −0.397106 | ||||||||
\(412\) | −1.47330 | −0.0725844 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −10.0153 | −0.492227 | ||||||||
\(415\) | −14.6365 | −0.718475 | ||||||||
\(416\) | 3.25503 | 0.159591 | ||||||||
\(417\) | −4.36913 | −0.213957 | ||||||||
\(418\) | −32.0921 | −1.56968 | ||||||||
\(419\) | 2.97330 | 0.145255 | 0.0726276 | − | 0.997359i | \(-0.476862\pi\) | ||||
0.0726276 | + | 0.997359i | \(0.476862\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.2554 | −1.37708 | −0.688541 | − | 0.725197i | \(-0.741749\pi\) | ||||
−0.688541 | + | 0.725197i | \(0.741749\pi\) | |||||||
\(422\) | −3.09609 | −0.150715 | ||||||||
\(423\) | −7.07743 | −0.344117 | ||||||||
\(424\) | −10.0595 | −0.488532 | ||||||||
\(425\) | 10.1966 | 0.494607 | ||||||||
\(426\) | −9.25396 | −0.448356 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.45224 | 0.0701966 | ||||||||
\(429\) | −17.4429 | −0.842153 | ||||||||
\(430\) | 6.20642 | 0.299300 | ||||||||
\(431\) | −3.95002 | −0.190266 | −0.0951330 | − | 0.995465i | \(-0.530328\pi\) | ||||
−0.0951330 | + | 0.995465i | \(0.530328\pi\) | |||||||
\(432\) | −4.27848 | −0.205849 | ||||||||
\(433\) | 26.0349 | 1.25116 | 0.625578 | − | 0.780162i | \(-0.284863\pi\) | ||||
0.625578 | + | 0.780162i | \(0.284863\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.1770 | −0.535895 | ||||||||
\(436\) | 1.08381 | 0.0519052 | ||||||||
\(437\) | 32.8102 | 1.56953 | ||||||||
\(438\) | 2.26189 | 0.108077 | ||||||||
\(439\) | −11.7277 | −0.559731 | −0.279865 | − | 0.960039i | \(-0.590290\pi\) | ||||
−0.279865 | + | 0.960039i | \(0.590290\pi\) | |||||||
\(440\) | −15.8066 | −0.753550 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.0265 | 0.809868 | ||||||||
\(443\) | −19.0476 | −0.904979 | −0.452490 | − | 0.891770i | \(-0.649464\pi\) | ||||
−0.452490 | + | 0.891770i | \(0.649464\pi\) | |||||||
\(444\) | 0.236529 | 0.0112252 | ||||||||
\(445\) | −7.86282 | −0.372733 | ||||||||
\(446\) | −35.5426 | −1.68299 | ||||||||
\(447\) | 21.7122 | 1.02695 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.3284 | 1.24252 | 0.621258 | − | 0.783606i | \(-0.286622\pi\) | ||||
0.621258 | + | 0.783606i | \(0.286622\pi\) | |||||||
\(450\) | −4.93178 | −0.232487 | ||||||||
\(451\) | 4.55512 | 0.214492 | ||||||||
\(452\) | 2.44027 | 0.114781 | ||||||||
\(453\) | 8.17544 | 0.384116 | ||||||||
\(454\) | 3.15205 | 0.147933 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.0297 | 0.610172 | ||||||||
\(457\) | 21.8307 | 1.02120 | 0.510598 | − | 0.859820i | \(-0.329424\pi\) | ||||
0.510598 | + | 0.859820i | \(0.329424\pi\) | |||||||
\(458\) | 4.50064 | 0.210301 | ||||||||
\(459\) | −3.03199 | −0.141521 | ||||||||
\(460\) | −1.31576 | −0.0613475 | ||||||||
\(461\) | 24.3400 | 1.13363 | 0.566813 | − | 0.823847i | \(-0.308176\pi\) | ||||
0.566813 | + | 0.823847i | \(0.308176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.6333 | −1.98134 | −0.990669 | − | 0.136288i | \(-0.956483\pi\) | ||||
−0.990669 | + | 0.136288i | \(0.956483\pi\) | |||||||
\(464\) | 37.3757 | 1.73512 | ||||||||
\(465\) | 0.323574 | 0.0150054 | ||||||||
\(466\) | 13.7494 | 0.636929 | ||||||||
\(467\) | 20.2806 | 0.938473 | 0.469237 | − | 0.883072i | \(-0.344529\pi\) | ||||
0.469237 | + | 0.883072i | \(0.344529\pi\) | |||||||
\(468\) | −0.576610 | −0.0266538 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −13.2794 | −0.612533 | ||||||||
\(471\) | 16.4197 | 0.756578 | ||||||||
\(472\) | −29.0256 | −1.33601 | ||||||||
\(473\) | 15.0674 | 0.692800 | ||||||||
\(474\) | 17.8086 | 0.817977 | ||||||||
\(475\) | 16.1565 | 0.741311 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.70905 | 0.169826 | ||||||||
\(478\) | 22.8663 | 1.04588 | ||||||||
\(479\) | −9.77588 | −0.446671 | −0.223336 | − | 0.974742i | \(-0.571695\pi\) | ||||
−0.223336 | + | 0.974742i | \(0.571695\pi\) | |||||||
\(480\) | −1.08758 | −0.0496409 | ||||||||
\(481\) | −6.01507 | −0.274264 | ||||||||
\(482\) | 6.19340 | 0.282102 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.46801 | 0.0667276 | ||||||||
\(485\) | −12.1718 | −0.552692 | ||||||||
\(486\) | 1.46649 | 0.0665211 | ||||||||
\(487\) | 41.3316 | 1.87291 | 0.936456 | − | 0.350784i | \(-0.114085\pi\) | ||||
0.936456 | + | 0.350784i | \(0.114085\pi\) | |||||||
\(488\) | 31.4390 | 1.42318 | ||||||||
\(489\) | −7.65254 | −0.346060 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1552 | 0.458297 | 0.229149 | − | 0.973391i | \(-0.426406\pi\) | ||||
0.229149 | + | 0.973391i | \(0.426406\pi\) | |||||||
\(492\) | 0.150578 | 0.00678860 | ||||||||
\(493\) | 26.4867 | 1.19290 | ||||||||
\(494\) | 26.9785 | 1.21382 | ||||||||
\(495\) | 5.82807 | 0.261952 | ||||||||
\(496\) | −1.08203 | −0.0485845 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.7760 | −0.751751 | ||||||||
\(499\) | −31.2177 | −1.39750 | −0.698748 | − | 0.715368i | \(-0.746259\pi\) | ||||
−0.698748 | + | 0.715368i | \(0.746259\pi\) | |||||||
\(500\) | −1.61120 | −0.0720551 | ||||||||
\(501\) | −0.211772 | −0.00946126 | ||||||||
\(502\) | −6.61703 | −0.295332 | ||||||||
\(503\) | 7.06660 | 0.315084 | 0.157542 | − | 0.987512i | \(-0.449643\pi\) | ||||
0.157542 | + | 0.987512i | \(0.449643\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0911 | 1.07204 | ||||||||
\(506\) | −45.6211 | −2.02811 | ||||||||
\(507\) | 1.66355 | 0.0738811 | ||||||||
\(508\) | −1.40056 | −0.0621400 | ||||||||
\(509\) | 31.3182 | 1.38815 | 0.694077 | − | 0.719901i | \(-0.255813\pi\) | ||||
0.694077 | + | 0.719901i | \(0.255813\pi\) | |||||||
\(510\) | −5.68893 | −0.251910 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.5709 | −0.864920 | ||||||||
\(513\) | −4.80420 | −0.212111 | ||||||||
\(514\) | −6.98061 | −0.307901 | ||||||||
\(515\) | −12.5185 | −0.551633 | ||||||||
\(516\) | 0.498082 | 0.0219269 | ||||||||
\(517\) | −32.2386 | −1.41785 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.100684 | −0.00441952 | ||||||||
\(520\) | 13.2879 | 0.582715 | ||||||||
\(521\) | 31.3657 | 1.37415 | 0.687077 | − | 0.726584i | \(-0.258893\pi\) | ||||
0.687077 | + | 0.726584i | \(0.258893\pi\) | |||||||
\(522\) | −12.8108 | −0.560715 | ||||||||
\(523\) | −1.05298 | −0.0460435 | −0.0230217 | − | 0.999735i | \(-0.507329\pi\) | ||||
−0.0230217 | + | 0.999735i | \(0.507329\pi\) | |||||||
\(524\) | 0.355587 | 0.0155339 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −42.1674 | −1.83859 | ||||||||
\(527\) | −0.766790 | −0.0334019 | ||||||||
\(528\) | −19.4890 | −0.848150 | ||||||||
\(529\) | 23.6419 | 1.02791 | ||||||||
\(530\) | 6.95928 | 0.302292 | ||||||||
\(531\) | 10.7021 | 0.464430 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.82930 | −0.165865 | ||||||||
\(534\) | −9.01221 | −0.389996 | ||||||||
\(535\) | 12.3396 | 0.533486 | ||||||||
\(536\) | 24.9377 | 1.07715 | ||||||||
\(537\) | 5.96037 | 0.257209 | ||||||||
\(538\) | −36.6655 | −1.58076 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.192658 | 0.00829069 | ||||||||
\(541\) | −29.4388 | −1.26567 | −0.632836 | − | 0.774286i | \(-0.718109\pi\) | ||||
−0.632836 | + | 0.774286i | \(0.718109\pi\) | |||||||
\(542\) | −37.3925 | −1.60615 | ||||||||
\(543\) | −8.73411 | −0.374816 | ||||||||
\(544\) | 2.57729 | 0.110501 | ||||||||
\(545\) | 9.20908 | 0.394473 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.9838 | −0.726173 | −0.363087 | − | 0.931755i | \(-0.618277\pi\) | ||||
−0.363087 | + | 0.931755i | \(0.618277\pi\) | |||||||
\(548\) | −1.21224 | −0.0517844 | ||||||||
\(549\) | −11.5919 | −0.494731 | ||||||||
\(550\) | −22.4649 | −0.957905 | ||||||||
\(551\) | 41.9682 | 1.78791 | ||||||||
\(552\) | 18.5226 | 0.788374 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 33.2199 | 1.41138 | ||||||||
\(555\) | 2.00977 | 0.0853099 | ||||||||
\(556\) | −0.657897 | −0.0279010 | ||||||||
\(557\) | 34.1849 | 1.44846 | 0.724231 | − | 0.689557i | \(-0.242195\pi\) | ||||
0.724231 | + | 0.689557i | \(0.242195\pi\) | |||||||
\(558\) | 0.370874 | 0.0157003 | ||||||||
\(559\) | −12.6665 | −0.535738 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.8111 | −0.583105 | ||||||||
\(562\) | −38.8301 | −1.63795 | ||||||||
\(563\) | −11.3775 | −0.479505 | −0.239752 | − | 0.970834i | \(-0.577066\pi\) | ||||
−0.239752 | + | 0.970834i | \(0.577066\pi\) | |||||||
\(564\) | −1.06571 | −0.0448744 | ||||||||
\(565\) | 20.7348 | 0.872320 | ||||||||
\(566\) | −28.5064 | −1.19821 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.1145 | 0.718107 | ||||||||
\(569\) | 15.5552 | 0.652108 | 0.326054 | − | 0.945351i | \(-0.394281\pi\) | ||||
0.326054 | + | 0.945351i | \(0.394281\pi\) | |||||||
\(570\) | −9.01412 | −0.377560 | ||||||||
\(571\) | −4.44306 | −0.185936 | −0.0929682 | − | 0.995669i | \(-0.529636\pi\) | ||||
−0.0929682 | + | 0.995669i | \(0.529636\pi\) | |||||||
\(572\) | −2.62653 | −0.109821 | ||||||||
\(573\) | 21.8499 | 0.912794 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.9675 | 0.957813 | ||||||||
\(576\) | 7.31041 | 0.304600 | ||||||||
\(577\) | −10.9014 | −0.453831 | −0.226916 | − | 0.973914i | \(-0.572864\pi\) | ||||
−0.226916 | + | 0.973914i | \(0.572864\pi\) | |||||||
\(578\) | −11.4489 | −0.476211 | ||||||||
\(579\) | 1.99809 | 0.0830378 | ||||||||
\(580\) | −1.68301 | −0.0698833 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.9510 | −0.578289 | ||||||||
\(583\) | 16.8952 | 0.699726 | ||||||||
\(584\) | −4.18320 | −0.173102 | ||||||||
\(585\) | −4.89942 | −0.202566 | ||||||||
\(586\) | −29.0884 | −1.20163 | ||||||||
\(587\) | 24.0069 | 0.990870 | 0.495435 | − | 0.868645i | \(-0.335009\pi\) | ||||
0.495435 | + | 0.868645i | \(0.335009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.21498 | −0.0500624 | ||||||||
\(590\) | 20.0803 | 0.826692 | ||||||||
\(591\) | −2.78972 | −0.114754 | ||||||||
\(592\) | −6.72065 | −0.276217 | ||||||||
\(593\) | −22.1604 | −0.910019 | −0.455009 | − | 0.890487i | \(-0.650364\pi\) | ||||
−0.455009 | + | 0.890487i | \(0.650364\pi\) | |||||||
\(594\) | 6.68002 | 0.274084 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.26938 | 0.133919 | ||||||||
\(597\) | −22.1261 | −0.905560 | ||||||||
\(598\) | 38.3518 | 1.56832 | ||||||||
\(599\) | 14.8012 | 0.604760 | 0.302380 | − | 0.953188i | \(-0.402219\pi\) | ||||
0.302380 | + | 0.953188i | \(0.402219\pi\) | |||||||
\(600\) | 9.12095 | 0.372361 | ||||||||
\(601\) | −14.5905 | −0.595159 | −0.297580 | − | 0.954697i | \(-0.596179\pi\) | ||||
−0.297580 | + | 0.954697i | \(0.596179\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.19482 | −0.374442 | ||||||||
\(604\) | 1.23105 | 0.0500905 | ||||||||
\(605\) | 12.4736 | 0.507122 | ||||||||
\(606\) | 27.6127 | 1.12169 | ||||||||
\(607\) | 27.2613 | 1.10650 | 0.553252 | − | 0.833014i | \(-0.313387\pi\) | ||||
0.553252 | + | 0.833014i | \(0.313387\pi\) | |||||||
\(608\) | 4.08373 | 0.165617 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.7499 | −0.880628 | ||||||||
\(611\) | 27.1016 | 1.09641 | ||||||||
\(612\) | −0.456553 | −0.0184550 | ||||||||
\(613\) | −15.2639 | −0.616505 | −0.308252 | − | 0.951305i | \(-0.599744\pi\) | ||||
−0.308252 | + | 0.951305i | \(0.599744\pi\) | |||||||
\(614\) | 27.7106 | 1.11831 | ||||||||
\(615\) | 1.27945 | 0.0515926 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.36538 | −0.135485 | −0.0677425 | − | 0.997703i | \(-0.521580\pi\) | ||||
−0.0677425 | + | 0.997703i | \(0.521580\pi\) | |||||||
\(618\) | −14.3485 | −0.577182 | ||||||||
\(619\) | 40.1468 | 1.61363 | 0.806817 | − | 0.590801i | \(-0.201188\pi\) | ||||
0.806817 | + | 0.590801i | \(0.201188\pi\) | |||||||
\(620\) | 0.0487232 | 0.00195677 | ||||||||
\(621\) | −6.82949 | −0.274058 | ||||||||
\(622\) | 32.3299 | 1.29631 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 16.3836 | 0.655869 | ||||||||
\(625\) | 3.12473 | 0.124989 | ||||||||
\(626\) | 17.0404 | 0.681071 | ||||||||
\(627\) | −21.8837 | −0.873951 | ||||||||
\(628\) | 2.47245 | 0.0986613 | ||||||||
\(629\) | −4.76266 | −0.189900 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.02333 | 0.160166 | 0.0800832 | − | 0.996788i | \(-0.474481\pi\) | ||||
0.0800832 | + | 0.996788i | \(0.474481\pi\) | |||||||
\(632\) | −32.9356 | −1.31011 | ||||||||
\(633\) | −2.11123 | −0.0839140 | ||||||||
\(634\) | −9.91496 | −0.393773 | ||||||||
\(635\) | −11.9005 | −0.472257 | ||||||||
\(636\) | 0.558502 | 0.0221461 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −58.3549 | −2.31029 | ||||||||
\(639\) | −6.31030 | −0.249631 | ||||||||
\(640\) | 15.8917 | 0.628174 | ||||||||
\(641\) | 18.6090 | 0.735012 | 0.367506 | − | 0.930021i | \(-0.380212\pi\) | ||||
0.367506 | + | 0.930021i | \(0.380212\pi\) | |||||||
\(642\) | 14.1434 | 0.558194 | ||||||||
\(643\) | 29.4661 | 1.16203 | 0.581015 | − | 0.813893i | \(-0.302656\pi\) | ||||
0.581015 | + | 0.813893i | \(0.302656\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.23217 | 0.166642 | ||||||||
\(646\) | 21.3613 | 0.840447 | ||||||||
\(647\) | −24.1937 | −0.951152 | −0.475576 | − | 0.879675i | \(-0.657760\pi\) | ||||
−0.475576 | + | 0.879675i | \(0.657760\pi\) | |||||||
\(648\) | −2.71215 | −0.106543 | ||||||||
\(649\) | 48.7492 | 1.91357 | ||||||||
\(650\) | 18.8853 | 0.740742 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.15231 | −0.0451278 | ||||||||
\(653\) | 6.14391 | 0.240430 | 0.120215 | − | 0.992748i | \(-0.461642\pi\) | ||||
0.120215 | + | 0.992748i | \(0.461642\pi\) | |||||||
\(654\) | 10.5553 | 0.412743 | ||||||||
\(655\) | 3.02140 | 0.118056 | ||||||||
\(656\) | −4.27848 | −0.167047 | ||||||||
\(657\) | 1.54239 | 0.0601744 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.3257 | −1.10341 | −0.551707 | − | 0.834038i | \(-0.686023\pi\) | ||||
−0.551707 | + | 0.834038i | \(0.686023\pi\) | |||||||
\(660\) | 0.877581 | 0.0341598 | ||||||||
\(661\) | −19.0553 | −0.741164 | −0.370582 | − | 0.928800i | \(-0.620842\pi\) | ||||
−0.370582 | + | 0.928800i | \(0.620842\pi\) | |||||||
\(662\) | 40.6815 | 1.58113 | ||||||||
\(663\) | 11.6104 | 0.450911 | ||||||||
\(664\) | 31.0259 | 1.20404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.30356 | 0.0892610 | ||||||||
\(667\) | 59.6606 | 2.31007 | ||||||||
\(668\) | −0.0318882 | −0.00123379 | ||||||||
\(669\) | −24.2366 | −0.937041 | ||||||||
\(670\) | −17.2523 | −0.666513 | ||||||||
\(671\) | −52.8025 | −2.03842 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6442 | 0.718682 | 0.359341 | − | 0.933206i | \(-0.383001\pi\) | ||||
0.359341 | + | 0.933206i | \(0.383001\pi\) | |||||||
\(674\) | 23.6209 | 0.909842 | ||||||||
\(675\) | −3.36300 | −0.129442 | ||||||||
\(676\) | 0.250495 | 0.00963444 | ||||||||
\(677\) | 3.36750 | 0.129424 | 0.0647118 | − | 0.997904i | \(-0.479387\pi\) | ||||
0.0647118 | + | 0.997904i | \(0.479387\pi\) | |||||||
\(678\) | 23.7658 | 0.912721 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10.5212 | 0.403471 | ||||||||
\(681\) | 2.14939 | 0.0823649 | ||||||||
\(682\) | 1.68937 | 0.0646895 | ||||||||
\(683\) | 19.9474 | 0.763266 | 0.381633 | − | 0.924314i | \(-0.375362\pi\) | ||||
0.381633 | + | 0.924314i | \(0.375362\pi\) | |||||||
\(684\) | −0.723409 | −0.0276602 | ||||||||
\(685\) | −10.3003 | −0.393556 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.06900 | 0.117089 | ||||||||
\(688\) | −14.1523 | −0.539553 | ||||||||
\(689\) | −14.2031 | −0.541093 | ||||||||
\(690\) | −12.8142 | −0.487827 | ||||||||
\(691\) | 14.3012 | 0.544042 | 0.272021 | − | 0.962291i | \(-0.412308\pi\) | ||||
0.272021 | + | 0.962291i | \(0.412308\pi\) | |||||||
\(692\) | −0.0151608 | −0.000576327 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −33.4580 | −1.27005 | ||||||||
\(695\) | −5.59010 | −0.212045 | ||||||||
\(696\) | 23.6926 | 0.898067 | ||||||||
\(697\) | −3.03199 | −0.114845 | ||||||||
\(698\) | −51.3479 | −1.94355 | ||||||||
\(699\) | 9.37576 | 0.354624 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.464844 | 0.0175569 | 0.00877846 | − | 0.999961i | \(-0.497206\pi\) | ||||
0.00877846 | + | 0.999961i | \(0.497206\pi\) | |||||||
\(702\) | −5.61561 | −0.211948 | ||||||||
\(703\) | −7.54644 | −0.284620 | ||||||||
\(704\) | 33.2998 | 1.25503 | ||||||||
\(705\) | −9.05525 | −0.341041 | ||||||||
\(706\) | −29.9247 | −1.12623 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.61150 | 0.0605639 | ||||||||
\(709\) | 13.2728 | 0.498472 | 0.249236 | − | 0.968443i | \(-0.419821\pi\) | ||||
0.249236 | + | 0.968443i | \(0.419821\pi\) | |||||||
\(710\) | −11.8400 | −0.444348 | ||||||||
\(711\) | 12.1437 | 0.455426 | ||||||||
\(712\) | 16.6674 | 0.624636 | ||||||||
\(713\) | −1.72718 | −0.0646833 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.3174 | −0.834625 | ||||||||
\(716\) | 0.897504 | 0.0335413 | ||||||||
\(717\) | 15.5926 | 0.582316 | ||||||||
\(718\) | −18.0398 | −0.673239 | ||||||||
\(719\) | −34.4829 | −1.28600 | −0.642998 | − | 0.765868i | \(-0.722310\pi\) | ||||
−0.642998 | + | 0.765868i | \(0.722310\pi\) | |||||||
\(720\) | −5.47412 | −0.204009 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.98375 | 0.222692 | ||||||||
\(723\) | 4.22330 | 0.157066 | ||||||||
\(724\) | −1.31517 | −0.0488778 | ||||||||
\(725\) | 29.3783 | 1.09108 | ||||||||
\(726\) | 14.2969 | 0.530609 | ||||||||
\(727\) | −21.6773 | −0.803967 | −0.401984 | − | 0.915647i | \(-0.631679\pi\) | ||||
−0.401984 | + | 0.915647i | \(0.631679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.89399 | 0.107111 | ||||||||
\(731\) | −10.0292 | −0.370944 | ||||||||
\(732\) | −1.74549 | −0.0645152 | ||||||||
\(733\) | −22.6515 | −0.836652 | −0.418326 | − | 0.908297i | \(-0.637383\pi\) | ||||
−0.418326 | + | 0.908297i | \(0.637383\pi\) | |||||||
\(734\) | 30.5640 | 1.12814 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.80529 | 0.213986 | ||||||||
\(737\) | −41.8835 | −1.54280 | ||||||||
\(738\) | 1.46649 | 0.0539821 | ||||||||
\(739\) | 48.9365 | 1.80016 | 0.900079 | − | 0.435727i | \(-0.143509\pi\) | ||||
0.900079 | + | 0.435727i | \(0.143509\pi\) | |||||||
\(740\) | 0.302628 | 0.0111248 | ||||||||
\(741\) | 18.3967 | 0.675821 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.4774 | −1.11811 | −0.559054 | − | 0.829131i | \(-0.688835\pi\) | ||||
−0.559054 | + | 0.829131i | \(0.688835\pi\) | |||||||
\(744\) | −0.685902 | −0.0251464 | ||||||||
\(745\) | 27.7797 | 1.01777 | ||||||||
\(746\) | −8.42114 | −0.308320 | ||||||||
\(747\) | −11.4396 | −0.418553 | ||||||||
\(748\) | −2.07965 | −0.0760396 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −15.6915 | −0.572972 | ||||||||
\(751\) | −38.1654 | −1.39268 | −0.696338 | − | 0.717714i | \(-0.745188\pi\) | ||||
−0.696338 | + | 0.717714i | \(0.745188\pi\) | |||||||
\(752\) | 30.2807 | 1.10422 | ||||||||
\(753\) | −4.51217 | −0.164433 | ||||||||
\(754\) | 49.0565 | 1.78653 | ||||||||
\(755\) | 10.4601 | 0.380682 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.1752 | 0.587898 | 0.293949 | − | 0.955821i | \(-0.405030\pi\) | ||||
0.293949 | + | 0.955821i | \(0.405030\pi\) | |||||||
\(758\) | 35.1619 | 1.27714 | ||||||||
\(759\) | −31.1091 | −1.12919 | ||||||||
\(760\) | 16.6709 | 0.604718 | ||||||||
\(761\) | 3.03664 | 0.110078 | 0.0550391 | − | 0.998484i | \(-0.482472\pi\) | ||||
0.0550391 | + | 0.998484i | \(0.482472\pi\) | |||||||
\(762\) | −13.6401 | −0.494129 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.29013 | 0.119033 | ||||||||
\(765\) | −3.87930 | −0.140256 | ||||||||
\(766\) | −47.5032 | −1.71636 | ||||||||
\(767\) | −40.9814 | −1.47975 | ||||||||
\(768\) | 3.59391 | 0.129684 | ||||||||
\(769\) | −31.1611 | −1.12370 | −0.561848 | − | 0.827240i | \(-0.689909\pi\) | ||||
−0.561848 | + | 0.827240i | \(0.689909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.76009 | −0.171431 | ||||||||
\(772\) | 0.300869 | 0.0108285 | ||||||||
\(773\) | −23.7229 | −0.853252 | −0.426626 | − | 0.904428i | \(-0.640298\pi\) | ||||
−0.426626 | + | 0.904428i | \(0.640298\pi\) | |||||||
\(774\) | 4.85083 | 0.174360 | ||||||||
\(775\) | −0.850501 | −0.0305509 | ||||||||
\(776\) | 25.8014 | 0.926215 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.49364 | 0.268660 | ||||||||
\(779\) | −4.80420 | −0.172128 | ||||||||
\(780\) | −0.737746 | −0.0264156 | ||||||||
\(781\) | −28.7442 | −1.02855 | ||||||||
\(782\) | 30.3664 | 1.08590 | ||||||||
\(783\) | −8.73574 | −0.312190 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.0082 | 0.749815 | ||||||||
\(786\) | 3.46307 | 0.123524 | ||||||||
\(787\) | −15.3274 | −0.546363 | −0.273182 | − | 0.961962i | \(-0.588076\pi\) | ||||
−0.273182 | + | 0.961962i | \(0.588076\pi\) | |||||||
\(788\) | −0.420072 | −0.0149645 | ||||||||
\(789\) | −28.7541 | −1.02367 | ||||||||
\(790\) | 22.7853 | 0.810665 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.3542 | −0.438986 | ||||||||
\(793\) | 44.3889 | 1.57630 | ||||||||
\(794\) | −6.23889 | −0.221410 | ||||||||
\(795\) | 4.74555 | 0.168307 | ||||||||
\(796\) | −3.33171 | −0.118089 | ||||||||
\(797\) | 12.7798 | 0.452683 | 0.226342 | − | 0.974048i | \(-0.427323\pi\) | ||||
0.226342 | + | 0.974048i | \(0.427323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.4587 | 0.759155 | ||||||||
\(800\) | 2.85866 | 0.101069 | ||||||||
\(801\) | −6.14545 | −0.217139 | ||||||||
\(802\) | −33.2294 | −1.17337 | ||||||||
\(803\) | 7.02578 | 0.247934 | ||||||||
\(804\) | −1.38454 | −0.0488290 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.42019 | −0.0500240 | ||||||||
\(807\) | −25.0023 | −0.880122 | ||||||||
\(808\) | −51.0676 | −1.79655 | ||||||||
\(809\) | 36.0453 | 1.26729 | 0.633643 | − | 0.773625i | \(-0.281559\pi\) | ||||
0.633643 | + | 0.773625i | \(0.281559\pi\) | |||||||
\(810\) | 1.87630 | 0.0659265 | ||||||||
\(811\) | 50.0804 | 1.75856 | 0.879281 | − | 0.476304i | \(-0.158024\pi\) | ||||
0.879281 | + | 0.476304i | \(0.158024\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.4980 | −0.894255 | ||||||||
\(814\) | 10.4930 | 0.367779 | ||||||||
\(815\) | −9.79108 | −0.342966 | ||||||||
\(816\) | 12.9723 | 0.454122 | ||||||||
\(817\) | −15.8913 | −0.555966 | ||||||||
\(818\) | 13.1310 | 0.459114 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.192658 | 0.00672792 | ||||||||
\(821\) | 6.58081 | 0.229672 | 0.114836 | − | 0.993384i | \(-0.463366\pi\) | ||||
0.114836 | + | 0.993384i | \(0.463366\pi\) | |||||||
\(822\) | −11.8060 | −0.411783 | ||||||||
\(823\) | −47.0271 | −1.63926 | −0.819630 | − | 0.572893i | \(-0.805821\pi\) | ||||
−0.819630 | + | 0.572893i | \(0.805821\pi\) | |||||||
\(824\) | 26.5364 | 0.924441 | ||||||||
\(825\) | −15.3189 | −0.533334 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.7549 | −1.41719 | −0.708593 | − | 0.705617i | \(-0.750670\pi\) | ||||
−0.708593 | + | 0.705617i | \(0.750670\pi\) | |||||||
\(828\) | −1.02837 | −0.0357385 | ||||||||
\(829\) | −3.84526 | −0.133551 | −0.0667757 | − | 0.997768i | \(-0.521271\pi\) | ||||
−0.0667757 | + | 0.997768i | \(0.521271\pi\) | |||||||
\(830\) | −21.4641 | −0.745031 | ||||||||
\(831\) | 22.6527 | 0.785814 | ||||||||
\(832\) | −27.9937 | −0.970509 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.40727 | −0.221865 | ||||||||
\(835\) | −0.270952 | −0.00937669 | ||||||||
\(836\) | −3.29521 | −0.113967 | ||||||||
\(837\) | 0.252900 | 0.00874149 | ||||||||
\(838\) | 4.36030 | 0.150624 | ||||||||
\(839\) | 6.17902 | 0.213323 | 0.106662 | − | 0.994295i | \(-0.465984\pi\) | ||||
0.106662 | + | 0.994295i | \(0.465984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.3131 | 1.63149 | ||||||||
\(842\) | −41.4361 | −1.42798 | ||||||||
\(843\) | −26.4784 | −0.911964 | ||||||||
\(844\) | −0.317906 | −0.0109428 | ||||||||
\(845\) | 2.12844 | 0.0732206 | ||||||||
\(846\) | −10.3790 | −0.356836 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.8691 | −0.544947 | ||||||||
\(849\) | −19.4386 | −0.667131 | ||||||||
\(850\) | 14.9531 | 0.512888 | ||||||||
\(851\) | −10.7278 | −0.367743 | ||||||||
\(852\) | −0.950195 | −0.0325531 | ||||||||
\(853\) | −46.9552 | −1.60772 | −0.803859 | − | 0.594821i | \(-0.797223\pi\) | ||||
−0.803859 | + | 0.594821i | \(0.797223\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.14675 | −0.210215 | ||||||||
\(856\) | −26.1570 | −0.894029 | ||||||||
\(857\) | −26.3427 | −0.899851 | −0.449925 | − | 0.893066i | \(-0.648549\pi\) | ||||
−0.449925 | + | 0.893066i | \(0.648549\pi\) | |||||||
\(858\) | −25.5798 | −0.873280 | ||||||||
\(859\) | −49.5524 | −1.69071 | −0.845354 | − | 0.534207i | \(-0.820610\pi\) | ||||
−0.845354 | + | 0.534207i | \(0.820610\pi\) | |||||||
\(860\) | 0.637274 | 0.0217309 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.79265 | −0.197298 | ||||||||
\(863\) | 28.2906 | 0.963024 | 0.481512 | − | 0.876439i | \(-0.340088\pi\) | ||||
0.481512 | + | 0.876439i | \(0.340088\pi\) | |||||||
\(864\) | −0.850033 | −0.0289187 | ||||||||
\(865\) | −0.128820 | −0.00438002 | ||||||||
\(866\) | 38.1798 | 1.29740 | ||||||||
\(867\) | −7.80702 | −0.265140 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 55.3162 | 1.87647 | ||||||||
\(870\) | −16.3909 | −0.555703 | ||||||||
\(871\) | 35.2098 | 1.19304 | ||||||||
\(872\) | −19.5211 | −0.661069 | ||||||||
\(873\) | −9.51325 | −0.321975 | ||||||||
\(874\) | 48.1157 | 1.62754 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.232251 | 0.00784703 | ||||||||
\(877\) | 30.9380 | 1.04470 | 0.522351 | − | 0.852731i | \(-0.325055\pi\) | ||||
0.522351 | + | 0.852731i | \(0.325055\pi\) | |||||||
\(878\) | −17.1984 | −0.580419 | ||||||||
\(879\) | −19.8355 | −0.669033 | ||||||||
\(880\) | −24.9353 | −0.840569 | ||||||||
\(881\) | −16.8026 | −0.566093 | −0.283046 | − | 0.959106i | \(-0.591345\pi\) | ||||
−0.283046 | + | 0.959106i | \(0.591345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.2149 | 0.915853 | 0.457926 | − | 0.888990i | \(-0.348592\pi\) | ||||
0.457926 | + | 0.888990i | \(0.348592\pi\) | |||||||
\(884\) | 1.74828 | 0.0588010 | ||||||||
\(885\) | 13.6928 | 0.460278 | ||||||||
\(886\) | −27.9330 | −0.938428 | ||||||||
\(887\) | 18.8116 | 0.631630 | 0.315815 | − | 0.948821i | \(-0.397722\pi\) | ||||
0.315815 | + | 0.948821i | \(0.397722\pi\) | |||||||
\(888\) | −4.26025 | −0.142965 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.5307 | −0.386510 | ||||||||
\(891\) | 4.55512 | 0.152602 | ||||||||
\(892\) | −3.64951 | −0.122195 | ||||||||
\(893\) | 34.0014 | 1.13781 | ||||||||
\(894\) | 31.8406 | 1.06491 | ||||||||
\(895\) | 7.62603 | 0.254910 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.1522 | 0.873196 | ||||||||
\(898\) | 38.6102 | 1.28844 | ||||||||
\(899\) | −2.20927 | −0.0736832 | ||||||||
\(900\) | −0.506395 | −0.0168798 | ||||||||
\(901\) | −11.2458 | −0.374652 | ||||||||
\(902\) | 6.68002 | 0.222420 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −43.9530 | −1.46186 | ||||||||
\(905\) | −11.1749 | −0.371466 | ||||||||
\(906\) | 11.9892 | 0.398313 | ||||||||
\(907\) | −9.49673 | −0.315334 | −0.157667 | − | 0.987492i | \(-0.550397\pi\) | ||||
−0.157667 | + | 0.987492i | \(0.550397\pi\) | |||||||
\(908\) | 0.323652 | 0.0107408 | ||||||||
\(909\) | 18.8292 | 0.624525 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.27058 | −0.141491 | −0.0707454 | − | 0.997494i | \(-0.522538\pi\) | ||||
−0.0707454 | + | 0.997494i | \(0.522538\pi\) | |||||||
\(912\) | 20.5547 | 0.680634 | ||||||||
\(913\) | −52.1088 | −1.72455 | ||||||||
\(914\) | 32.0143 | 1.05894 | ||||||||
\(915\) | −14.8313 | −0.490308 | ||||||||
\(916\) | 0.462125 | 0.0152690 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.44637 | −0.146752 | ||||||||
\(919\) | 17.0686 | 0.563040 | 0.281520 | − | 0.959555i | \(-0.409161\pi\) | ||||
0.281520 | + | 0.959555i | \(0.409161\pi\) | |||||||
\(920\) | 23.6988 | 0.781327 | ||||||||
\(921\) | 18.8959 | 0.622641 | ||||||||
\(922\) | 35.6942 | 1.17553 | ||||||||
\(923\) | 24.1640 | 0.795369 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.28260 | −0.173691 | ||||||||
\(926\) | −62.5211 | −2.05457 | ||||||||
\(927\) | −9.78428 | −0.321358 | ||||||||
\(928\) | 7.42567 | 0.243759 | ||||||||
\(929\) | −7.76360 | −0.254716 | −0.127358 | − | 0.991857i | \(-0.540650\pi\) | ||||
−0.127358 | + | 0.991857i | \(0.540650\pi\) | |||||||
\(930\) | 0.474516 | 0.0155600 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.41179 | 0.0462446 | ||||||||
\(933\) | 22.0458 | 0.721749 | ||||||||
\(934\) | 29.7412 | 0.973161 | ||||||||
\(935\) | −17.6707 | −0.577892 | ||||||||
\(936\) | 10.3856 | 0.339465 | ||||||||
\(937\) | 15.7893 | 0.515815 | 0.257907 | − | 0.966170i | \(-0.416967\pi\) | ||||
0.257907 | + | 0.966170i | \(0.416967\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.6199 | 0.379201 | ||||||||
\(940\) | −1.36353 | −0.0444733 | ||||||||
\(941\) | 4.84076 | 0.157804 | 0.0789022 | − | 0.996882i | \(-0.474859\pi\) | ||||
0.0789022 | + | 0.996882i | \(0.474859\pi\) | |||||||
\(942\) | 24.0792 | 0.784542 | ||||||||
\(943\) | −6.82949 | −0.222399 | ||||||||
\(944\) | −45.7886 | −1.49029 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.0961 | 0.718407 | ||||||||
\(947\) | 29.4532 | 0.957101 | 0.478550 | − | 0.878060i | \(-0.341162\pi\) | ||||
0.478550 | + | 0.878060i | \(0.341162\pi\) | |||||||
\(948\) | 1.82859 | 0.0593897 | ||||||||
\(949\) | −5.90628 | −0.191726 | ||||||||
\(950\) | 23.6933 | 0.768711 | ||||||||
\(951\) | −6.76104 | −0.219242 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.3799 | −1.37282 | −0.686410 | − | 0.727215i | \(-0.740814\pi\) | ||||
−0.686410 | + | 0.727215i | \(0.740814\pi\) | |||||||
\(954\) | 5.43926 | 0.176103 | ||||||||
\(955\) | 27.9560 | 0.904634 | ||||||||
\(956\) | 2.34791 | 0.0759367 | ||||||||
\(957\) | −39.7923 | −1.28630 | ||||||||
\(958\) | −14.3362 | −0.463181 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.35333 | 0.301877 | ||||||||
\(961\) | −30.9360 | −0.997937 | ||||||||
\(962\) | −8.82101 | −0.284401 | ||||||||
\(963\) | 9.64440 | 0.310786 | ||||||||
\(964\) | 0.635938 | 0.0204822 | ||||||||
\(965\) | 2.55647 | 0.0822956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.7551 | 1.72865 | 0.864324 | − | 0.502935i | \(-0.167747\pi\) | ||||
0.864324 | + | 0.502935i | \(0.167747\pi\) | |||||||
\(968\) | −26.4411 | −0.849848 | ||||||||
\(969\) | 14.5663 | 0.467937 | ||||||||
\(970\) | −17.8497 | −0.573120 | ||||||||
\(971\) | 59.8654 | 1.92117 | 0.960586 | − | 0.277984i | \(-0.0896662\pi\) | ||||
0.960586 | + | 0.277984i | \(0.0896662\pi\) | |||||||
\(972\) | 0.150578 | 0.00482981 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 60.6121 | 1.94214 | ||||||||
\(975\) | 12.8779 | 0.412424 | ||||||||
\(976\) | 49.5958 | 1.58752 | ||||||||
\(977\) | −40.7952 | −1.30515 | −0.652577 | − | 0.757722i | \(-0.726312\pi\) | ||||
−0.652577 | + | 0.757722i | \(0.726312\pi\) | |||||||
\(978\) | −11.2223 | −0.358851 | ||||||||
\(979\) | −27.9933 | −0.894669 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.19766 | 0.229804 | ||||||||
\(982\) | 14.8924 | 0.475237 | ||||||||
\(983\) | 5.14025 | 0.163948 | 0.0819742 | − | 0.996634i | \(-0.473877\pi\) | ||||
0.0819742 | + | 0.996634i | \(0.473877\pi\) | |||||||
\(984\) | −2.71215 | −0.0864602 | ||||||||
\(985\) | −3.56933 | −0.113728 | ||||||||
\(986\) | 38.8423 | 1.23699 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.77015 | 0.0881302 | ||||||||
\(989\) | −22.5905 | −0.718338 | ||||||||
\(990\) | 8.54678 | 0.271634 | ||||||||
\(991\) | 10.6227 | 0.337440 | 0.168720 | − | 0.985664i | \(-0.446037\pi\) | ||||
0.168720 | + | 0.985664i | \(0.446037\pi\) | |||||||
\(992\) | −0.214973 | −0.00682541 | ||||||||
\(993\) | 27.7408 | 0.880328 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.3093 | −0.897465 | ||||||||
\(996\) | −1.72256 | −0.0545814 | ||||||||
\(997\) | 33.9535 | 1.07532 | 0.537659 | − | 0.843162i | \(-0.319309\pi\) | ||||
0.537659 | + | 0.843162i | \(0.319309\pi\) | |||||||
\(998\) | −45.7803 | −1.44915 | ||||||||
\(999\) | 1.57080 | 0.0496980 |
(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 | 6027.2.a.bi.1.11 | 13 | ||
7.2 | even | 3 | 861.2.i.f.739.3 | yes | 26 | ||
7.4 | even | 3 | 861.2.i.f.247.3 | ✓ | 26 | ||
7.6 | odd | 2 | 6027.2.a.bh.1.11 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.f.247.3 | ✓ | 26 | 7.4 | even | 3 | ||
861.2.i.f.739.3 | yes | 26 | 7.2 | even | 3 | ||
6027.2.a.bh.1.11 | 13 | 7.6 | odd | 2 | |||
6027.2.a.bi.1.11 | 13 | 1.1 | even | 1 | trivial |