Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(1,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, 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("625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.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: | \(4.99065012633\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6152203125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 26x^{4} - 35x^{3} - 27x^{2} + 16x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.32610\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32610 | −1.64480 | −0.822401 | − | 0.568908i | \(-0.807366\pi\) | ||||
−0.822401 | + | 0.568908i | \(0.807366\pi\) | |||||||
\(3\) | 2.30231 | 1.32924 | 0.664621 | − | 0.747181i | \(-0.268593\pi\) | ||||
0.664621 | + | 0.747181i | \(0.268593\pi\) | |||||||
\(4\) | 3.41075 | 1.70537 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.35542 | −2.18634 | ||||||||
\(7\) | −3.59425 | −1.35850 | −0.679249 | − | 0.733908i | \(-0.737694\pi\) | ||||
−0.679249 | + | 0.733908i | \(0.737694\pi\) | |||||||
\(8\) | −3.28154 | −1.16020 | ||||||||
\(9\) | 2.30065 | 0.766883 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.497788 | −0.150089 | −0.0750443 | − | 0.997180i | \(-0.523910\pi\) | ||||
−0.0750443 | + | 0.997180i | \(0.523910\pi\) | |||||||
\(12\) | 7.85261 | 2.26685 | ||||||||
\(13\) | −2.64789 | −0.734392 | −0.367196 | − | 0.930143i | \(-0.619682\pi\) | ||||
−0.367196 | + | 0.930143i | \(0.619682\pi\) | |||||||
\(14\) | 8.36058 | 2.23446 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.811708 | 0.202927 | ||||||||
\(17\) | −5.10719 | −1.23867 | −0.619337 | − | 0.785125i | \(-0.712599\pi\) | ||||
−0.619337 | + | 0.785125i | \(0.712599\pi\) | |||||||
\(18\) | −5.35154 | −1.26137 | ||||||||
\(19\) | −0.987277 | −0.226497 | −0.113248 | − | 0.993567i | \(-0.536126\pi\) | ||||
−0.113248 | + | 0.993567i | \(0.536126\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.27508 | −1.80577 | ||||||||
\(22\) | 1.15790 | 0.246866 | ||||||||
\(23\) | −6.41382 | −1.33737 | −0.668687 | − | 0.743544i | \(-0.733143\pi\) | ||||
−0.668687 | + | 0.743544i | \(0.733143\pi\) | |||||||
\(24\) | −7.55514 | −1.54219 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.15926 | 1.20793 | ||||||||
\(27\) | −1.61013 | −0.309869 | ||||||||
\(28\) | −12.2591 | −2.31675 | ||||||||
\(29\) | −5.57001 | −1.03432 | −0.517162 | − | 0.855887i | \(-0.673012\pi\) | ||||
−0.517162 | + | 0.855887i | \(0.673012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.05507 | 1.08752 | 0.543762 | − | 0.839240i | \(-0.317000\pi\) | ||||
0.543762 | + | 0.839240i | \(0.317000\pi\) | |||||||
\(32\) | 4.67497 | 0.826426 | ||||||||
\(33\) | −1.14606 | −0.199504 | ||||||||
\(34\) | 11.8798 | 2.03738 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.84693 | 1.30782 | ||||||||
\(37\) | 4.59612 | 0.755598 | 0.377799 | − | 0.925888i | \(-0.376681\pi\) | ||||
0.377799 | + | 0.925888i | \(0.376681\pi\) | |||||||
\(38\) | 2.29651 | 0.372543 | ||||||||
\(39\) | −6.09627 | −0.976185 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.87475 | −0.448960 | −0.224480 | − | 0.974479i | \(-0.572068\pi\) | ||||
−0.224480 | + | 0.974479i | \(0.572068\pi\) | |||||||
\(42\) | 19.2487 | 2.97014 | ||||||||
\(43\) | 9.48858 | 1.44700 | 0.723498 | − | 0.690327i | \(-0.242533\pi\) | ||||
0.723498 | + | 0.690327i | \(0.242533\pi\) | |||||||
\(44\) | −1.69783 | −0.255957 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.9192 | 2.19972 | ||||||||
\(47\) | −5.36834 | −0.783053 | −0.391527 | − | 0.920167i | \(-0.628053\pi\) | ||||
−0.391527 | + | 0.920167i | \(0.628053\pi\) | |||||||
\(48\) | 1.86881 | 0.269739 | ||||||||
\(49\) | 5.91861 | 0.845515 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.7583 | −1.64650 | ||||||||
\(52\) | −9.03129 | −1.25241 | ||||||||
\(53\) | 0.307600 | 0.0422521 | 0.0211261 | − | 0.999777i | \(-0.493275\pi\) | ||||
0.0211261 | + | 0.999777i | \(0.493275\pi\) | |||||||
\(54\) | 3.74532 | 0.509673 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.7947 | 1.57613 | ||||||||
\(57\) | −2.27302 | −0.301069 | ||||||||
\(58\) | 12.9564 | 1.70126 | ||||||||
\(59\) | −1.26645 | −0.164878 | −0.0824389 | − | 0.996596i | \(-0.526271\pi\) | ||||
−0.0824389 | + | 0.996596i | \(0.526271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.22625 | −0.797190 | −0.398595 | − | 0.917127i | \(-0.630502\pi\) | ||||
−0.398595 | + | 0.917127i | \(0.630502\pi\) | |||||||
\(62\) | −14.0847 | −1.78876 | ||||||||
\(63\) | −8.26910 | −1.04181 | ||||||||
\(64\) | −12.4979 | −1.56223 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.66586 | 0.328145 | ||||||||
\(67\) | 5.28626 | 0.645819 | 0.322910 | − | 0.946430i | \(-0.395339\pi\) | ||||
0.322910 | + | 0.946430i | \(0.395339\pi\) | |||||||
\(68\) | −17.4193 | −2.11240 | ||||||||
\(69\) | −14.7666 | −1.77769 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.151963 | −0.0180347 | −0.00901734 | − | 0.999959i | \(-0.502870\pi\) | ||||
−0.00901734 | + | 0.999959i | \(0.502870\pi\) | |||||||
\(72\) | −7.54968 | −0.889738 | ||||||||
\(73\) | 14.8741 | 1.74088 | 0.870439 | − | 0.492276i | \(-0.163835\pi\) | ||||
0.870439 | + | 0.492276i | \(0.163835\pi\) | |||||||
\(74\) | −10.6910 | −1.24281 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.36735 | −0.386262 | ||||||||
\(77\) | 1.78917 | 0.203895 | ||||||||
\(78\) | 14.1805 | 1.60563 | ||||||||
\(79\) | −16.5886 | −1.86636 | −0.933181 | − | 0.359406i | \(-0.882979\pi\) | ||||
−0.933181 | + | 0.359406i | \(0.882979\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6090 | −1.17877 | ||||||||
\(82\) | 6.68696 | 0.738451 | ||||||||
\(83\) | −14.5960 | −1.60212 | −0.801058 | − | 0.598587i | \(-0.795729\pi\) | ||||
−0.801058 | + | 0.598587i | \(0.795729\pi\) | |||||||
\(84\) | −28.2242 | −3.07952 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −22.0714 | −2.38002 | ||||||||
\(87\) | −12.8239 | −1.37487 | ||||||||
\(88\) | 1.63351 | 0.174133 | ||||||||
\(89\) | 11.3822 | 1.20652 | 0.603258 | − | 0.797546i | \(-0.293869\pi\) | ||||
0.603258 | + | 0.797546i | \(0.293869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.51717 | 0.997670 | ||||||||
\(92\) | −21.8759 | −2.28072 | ||||||||
\(93\) | 13.9407 | 1.44558 | ||||||||
\(94\) | 12.4873 | 1.28797 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.7633 | 1.09852 | ||||||||
\(97\) | −0.849192 | −0.0862223 | −0.0431112 | − | 0.999070i | \(-0.513727\pi\) | ||||
−0.0431112 | + | 0.999070i | \(0.513727\pi\) | |||||||
\(98\) | −13.7673 | −1.39070 | ||||||||
\(99\) | −1.14523 | −0.115100 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.2498 | −1.31841 | −0.659203 | − | 0.751965i | \(-0.729106\pi\) | ||||
−0.659203 | + | 0.751965i | \(0.729106\pi\) | |||||||
\(102\) | 27.3511 | 2.70816 | ||||||||
\(103\) | −0.830909 | −0.0818719 | −0.0409360 | − | 0.999162i | \(-0.513034\pi\) | ||||
−0.0409360 | + | 0.999162i | \(0.513034\pi\) | |||||||
\(104\) | 8.68917 | 0.852043 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.715509 | −0.0694964 | ||||||||
\(107\) | 0.0722844 | 0.00698800 | 0.00349400 | − | 0.999994i | \(-0.498888\pi\) | ||||
0.00349400 | + | 0.999994i | \(0.498888\pi\) | |||||||
\(108\) | −5.49174 | −0.528443 | ||||||||
\(109\) | 5.59621 | 0.536020 | 0.268010 | − | 0.963416i | \(-0.413634\pi\) | ||||
0.268010 | + | 0.963416i | \(0.413634\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.5817 | 1.00437 | ||||||||
\(112\) | −2.91748 | −0.275676 | ||||||||
\(113\) | 2.60239 | 0.244812 | 0.122406 | − | 0.992480i | \(-0.460939\pi\) | ||||
0.122406 | + | 0.992480i | \(0.460939\pi\) | |||||||
\(114\) | 5.28728 | 0.495199 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −18.9979 | −1.76391 | ||||||||
\(117\) | −6.09186 | −0.563193 | ||||||||
\(118\) | 2.94589 | 0.271191 | ||||||||
\(119\) | 18.3565 | 1.68274 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7522 | −0.977473 | ||||||||
\(122\) | 14.4829 | 1.31122 | ||||||||
\(123\) | −6.61857 | −0.596777 | ||||||||
\(124\) | 20.6523 | 1.85463 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 19.2348 | 1.71357 | ||||||||
\(127\) | −4.94483 | −0.438783 | −0.219391 | − | 0.975637i | \(-0.570407\pi\) | ||||
−0.219391 | + | 0.975637i | \(0.570407\pi\) | |||||||
\(128\) | 19.7214 | 1.74314 | ||||||||
\(129\) | 21.8457 | 1.92341 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.70342 | 0.236199 | 0.118099 | − | 0.993002i | \(-0.462320\pi\) | ||||
0.118099 | + | 0.993002i | \(0.462320\pi\) | |||||||
\(132\) | −3.90893 | −0.340229 | ||||||||
\(133\) | 3.54852 | 0.307695 | ||||||||
\(134\) | −12.2964 | −1.06224 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.7595 | 1.43711 | ||||||||
\(137\) | 2.24838 | 0.192092 | 0.0960459 | − | 0.995377i | \(-0.469380\pi\) | ||||
0.0960459 | + | 0.995377i | \(0.469380\pi\) | |||||||
\(138\) | 34.3487 | 2.92395 | ||||||||
\(139\) | −10.8032 | −0.916317 | −0.458159 | − | 0.888870i | \(-0.651491\pi\) | ||||
−0.458159 | + | 0.888870i | \(0.651491\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.3596 | −1.04087 | ||||||||
\(142\) | 0.353481 | 0.0296635 | ||||||||
\(143\) | 1.31809 | 0.110224 | ||||||||
\(144\) | 1.86745 | 0.155621 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −34.5986 | −2.86340 | ||||||||
\(147\) | 13.6265 | 1.12389 | ||||||||
\(148\) | 15.6762 | 1.28858 | ||||||||
\(149\) | 12.1878 | 0.998460 | 0.499230 | − | 0.866469i | \(-0.333616\pi\) | ||||
0.499230 | + | 0.866469i | \(0.333616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0860 | 1.39044 | 0.695220 | − | 0.718797i | \(-0.255307\pi\) | ||||
0.695220 | + | 0.718797i | \(0.255307\pi\) | |||||||
\(152\) | 3.23979 | 0.262782 | ||||||||
\(153\) | −11.7498 | −0.949918 | ||||||||
\(154\) | −4.16179 | −0.335367 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −20.7929 | −1.66476 | ||||||||
\(157\) | 7.49835 | 0.598433 | 0.299217 | − | 0.954185i | \(-0.403275\pi\) | ||||
0.299217 | + | 0.954185i | \(0.403275\pi\) | |||||||
\(158\) | 38.5868 | 3.06980 | ||||||||
\(159\) | 0.708192 | 0.0561633 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.0529 | 1.81682 | ||||||||
\(162\) | 24.6775 | 1.93885 | ||||||||
\(163\) | −1.95259 | −0.152939 | −0.0764693 | − | 0.997072i | \(-0.524365\pi\) | ||||
−0.0764693 | + | 0.997072i | \(0.524365\pi\) | |||||||
\(164\) | −9.80504 | −0.765645 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 33.9517 | 2.63516 | ||||||||
\(167\) | 0.356578 | 0.0275928 | 0.0137964 | − | 0.999905i | \(-0.495608\pi\) | ||||
0.0137964 | + | 0.999905i | \(0.495608\pi\) | |||||||
\(168\) | 27.1550 | 2.09506 | ||||||||
\(169\) | −5.98868 | −0.460668 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.27138 | −0.173697 | ||||||||
\(172\) | 32.3632 | 2.46767 | ||||||||
\(173\) | 9.95032 | 0.756509 | 0.378254 | − | 0.925702i | \(-0.376524\pi\) | ||||
0.378254 | + | 0.925702i | \(0.376524\pi\) | |||||||
\(174\) | 29.8297 | 2.26138 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.404058 | −0.0304570 | ||||||||
\(177\) | −2.91577 | −0.219162 | ||||||||
\(178\) | −26.4763 | −1.98448 | ||||||||
\(179\) | 15.3824 | 1.14973 | 0.574867 | − | 0.818247i | \(-0.305054\pi\) | ||||
0.574867 | + | 0.818247i | \(0.305054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.91917 | 0.662957 | 0.331478 | − | 0.943463i | \(-0.392453\pi\) | ||||
0.331478 | + | 0.943463i | \(0.392453\pi\) | |||||||
\(182\) | −22.1379 | −1.64097 | ||||||||
\(183\) | −14.3348 | −1.05966 | ||||||||
\(184\) | 21.0472 | 1.55162 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −32.4274 | −2.37769 | ||||||||
\(187\) | 2.54230 | 0.185911 | ||||||||
\(188\) | −18.3101 | −1.33540 | ||||||||
\(189\) | 5.78719 | 0.420956 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3887 | −0.824056 | −0.412028 | − | 0.911171i | \(-0.635179\pi\) | ||||
−0.412028 | + | 0.911171i | \(0.635179\pi\) | |||||||
\(192\) | −28.7740 | −2.07659 | ||||||||
\(193\) | −17.3321 | −1.24759 | −0.623795 | − | 0.781588i | \(-0.714410\pi\) | ||||
−0.623795 | + | 0.781588i | \(0.714410\pi\) | |||||||
\(194\) | 1.97531 | 0.141819 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20.1869 | 1.44192 | ||||||||
\(197\) | −25.9609 | −1.84964 | −0.924820 | − | 0.380405i | \(-0.875785\pi\) | ||||
−0.924820 | + | 0.380405i | \(0.875785\pi\) | |||||||
\(198\) | 2.66393 | 0.189317 | ||||||||
\(199\) | −8.38571 | −0.594447 | −0.297223 | − | 0.954808i | \(-0.596061\pi\) | ||||
−0.297223 | + | 0.954808i | \(0.596061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.1706 | 0.858450 | ||||||||
\(202\) | 30.8204 | 2.16852 | ||||||||
\(203\) | 20.0200 | 1.40513 | ||||||||
\(204\) | −40.1048 | −2.80790 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.93278 | 0.134663 | ||||||||
\(207\) | −14.7559 | −1.02561 | ||||||||
\(208\) | −2.14931 | −0.149028 | ||||||||
\(209\) | 0.491454 | 0.0339946 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.9135 | 1.09553 | 0.547765 | − | 0.836632i | \(-0.315479\pi\) | ||||
0.547765 | + | 0.836632i | \(0.315479\pi\) | |||||||
\(212\) | 1.04915 | 0.0720557 | ||||||||
\(213\) | −0.349866 | −0.0239724 | ||||||||
\(214\) | −0.168141 | −0.0114939 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.28370 | 0.359510 | ||||||||
\(217\) | −21.7634 | −1.47740 | ||||||||
\(218\) | −13.0174 | −0.881647 | ||||||||
\(219\) | 34.2448 | 2.31405 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.5233 | 0.909674 | ||||||||
\(222\) | −24.6142 | −1.65199 | ||||||||
\(223\) | 0.379706 | 0.0254270 | 0.0127135 | − | 0.999919i | \(-0.495953\pi\) | ||||
0.0127135 | + | 0.999919i | \(0.495953\pi\) | |||||||
\(224\) | −16.8030 | −1.12270 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.05343 | −0.402668 | ||||||||
\(227\) | −20.3009 | −1.34742 | −0.673710 | − | 0.738996i | \(-0.735300\pi\) | ||||
−0.673710 | + | 0.738996i | \(0.735300\pi\) | |||||||
\(228\) | −7.75270 | −0.513435 | ||||||||
\(229\) | −11.9107 | −0.787078 | −0.393539 | − | 0.919308i | \(-0.628749\pi\) | ||||
−0.393539 | + | 0.919308i | \(0.628749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.11923 | 0.271026 | ||||||||
\(232\) | 18.2782 | 1.20002 | ||||||||
\(233\) | 19.0610 | 1.24873 | 0.624364 | − | 0.781133i | \(-0.285358\pi\) | ||||
0.624364 | + | 0.781133i | \(0.285358\pi\) | |||||||
\(234\) | 14.1703 | 0.926341 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.31954 | −0.281178 | ||||||||
\(237\) | −38.1922 | −2.48085 | ||||||||
\(238\) | −42.6991 | −2.76777 | ||||||||
\(239\) | 4.12493 | 0.266819 | 0.133410 | − | 0.991061i | \(-0.457407\pi\) | ||||
0.133410 | + | 0.991061i | \(0.457407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1858 | 1.04262 | 0.521310 | − | 0.853367i | \(-0.325444\pi\) | ||||
0.521310 | + | 0.853367i | \(0.325444\pi\) | |||||||
\(242\) | 25.0107 | 1.60775 | ||||||||
\(243\) | −19.5948 | −1.25701 | ||||||||
\(244\) | −21.2362 | −1.35951 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.3955 | 0.981580 | ||||||||
\(247\) | 2.61420 | 0.166338 | ||||||||
\(248\) | −19.8700 | −1.26175 | ||||||||
\(249\) | −33.6045 | −2.12960 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8718 | 0.749344 | 0.374672 | − | 0.927157i | \(-0.377755\pi\) | ||||
0.374672 | + | 0.927157i | \(0.377755\pi\) | |||||||
\(252\) | −28.2038 | −1.77667 | ||||||||
\(253\) | 3.19272 | 0.200725 | ||||||||
\(254\) | 11.5022 | 0.721711 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −20.8782 | −1.30489 | ||||||||
\(257\) | 18.9164 | 1.17997 | 0.589986 | − | 0.807414i | \(-0.299133\pi\) | ||||
0.589986 | + | 0.807414i | \(0.299133\pi\) | |||||||
\(258\) | −50.8153 | −3.16362 | ||||||||
\(259\) | −16.5196 | −1.02648 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.8146 | −0.793206 | ||||||||
\(262\) | −6.28843 | −0.388501 | ||||||||
\(263\) | 6.74703 | 0.416040 | 0.208020 | − | 0.978125i | \(-0.433298\pi\) | ||||
0.208020 | + | 0.978125i | \(0.433298\pi\) | |||||||
\(264\) | 3.76086 | 0.231465 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.25421 | −0.506098 | ||||||||
\(267\) | 26.2055 | 1.60375 | ||||||||
\(268\) | 18.0301 | 1.10136 | ||||||||
\(269\) | −25.3329 | −1.54457 | −0.772286 | − | 0.635275i | \(-0.780887\pi\) | ||||
−0.772286 | + | 0.635275i | \(0.780887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.40735 | 0.571456 | 0.285728 | − | 0.958311i | \(-0.407765\pi\) | ||||
0.285728 | + | 0.958311i | \(0.407765\pi\) | |||||||
\(272\) | −4.14555 | −0.251361 | ||||||||
\(273\) | 21.9115 | 1.32614 | ||||||||
\(274\) | −5.22995 | −0.315953 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −50.3653 | −3.03163 | ||||||||
\(277\) | 5.96736 | 0.358544 | 0.179272 | − | 0.983800i | \(-0.442626\pi\) | ||||
0.179272 | + | 0.983800i | \(0.442626\pi\) | |||||||
\(278\) | 25.1294 | 1.50716 | ||||||||
\(279\) | 13.9306 | 0.834003 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0723 | 0.660516 | 0.330258 | − | 0.943891i | \(-0.392864\pi\) | ||||
0.330258 | + | 0.943891i | \(0.392864\pi\) | |||||||
\(282\) | 28.7497 | 1.71202 | ||||||||
\(283\) | 3.02406 | 0.179762 | 0.0898810 | − | 0.995953i | \(-0.471351\pi\) | ||||
0.0898810 | + | 0.995953i | \(0.471351\pi\) | |||||||
\(284\) | −0.518307 | −0.0307559 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.06600 | −0.181297 | ||||||||
\(287\) | 10.3326 | 0.609911 | ||||||||
\(288\) | 10.7555 | 0.633772 | ||||||||
\(289\) | 9.08337 | 0.534316 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.95511 | −0.114610 | ||||||||
\(292\) | 50.7317 | 2.96885 | ||||||||
\(293\) | −6.26426 | −0.365962 | −0.182981 | − | 0.983116i | \(-0.558575\pi\) | ||||
−0.182981 | + | 0.983116i | \(0.558575\pi\) | |||||||
\(294\) | −31.6966 | −1.84858 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.0824 | −0.876646 | ||||||||
\(297\) | 0.801501 | 0.0465078 | ||||||||
\(298\) | −28.3500 | −1.64227 | ||||||||
\(299\) | 16.9831 | 0.982158 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.1043 | −1.96574 | ||||||||
\(302\) | −39.7438 | −2.28700 | ||||||||
\(303\) | −30.5052 | −1.75248 | ||||||||
\(304\) | −0.801381 | −0.0459623 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 27.3313 | 1.56243 | ||||||||
\(307\) | −25.8734 | −1.47667 | −0.738337 | − | 0.674432i | \(-0.764388\pi\) | ||||
−0.738337 | + | 0.674432i | \(0.764388\pi\) | |||||||
\(308\) | 6.10241 | 0.347717 | ||||||||
\(309\) | −1.91301 | −0.108828 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.00277 | −0.510500 | −0.255250 | − | 0.966875i | \(-0.582158\pi\) | ||||
−0.255250 | + | 0.966875i | \(0.582158\pi\) | |||||||
\(312\) | 20.0052 | 1.13257 | ||||||||
\(313\) | 33.2274 | 1.87812 | 0.939062 | − | 0.343748i | \(-0.111696\pi\) | ||||
0.939062 | + | 0.343748i | \(0.111696\pi\) | |||||||
\(314\) | −17.4419 | −0.984304 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −56.5795 | −3.18285 | ||||||||
\(317\) | 25.9693 | 1.45858 | 0.729290 | − | 0.684204i | \(-0.239850\pi\) | ||||
0.729290 | + | 0.684204i | \(0.239850\pi\) | |||||||
\(318\) | −1.64733 | −0.0923774 | ||||||||
\(319\) | 2.77268 | 0.155240 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.166421 | 0.00928874 | ||||||||
\(322\) | −53.6233 | −2.98831 | ||||||||
\(323\) | 5.04221 | 0.280556 | ||||||||
\(324\) | −36.1845 | −2.01025 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.54192 | 0.251554 | ||||||||
\(327\) | 12.8842 | 0.712500 | ||||||||
\(328\) | 9.43361 | 0.520884 | ||||||||
\(329\) | 19.2951 | 1.06378 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.1284 | 0.666636 | 0.333318 | − | 0.942814i | \(-0.391832\pi\) | ||||
0.333318 | + | 0.942814i | \(0.391832\pi\) | |||||||
\(332\) | −49.7832 | −2.73221 | ||||||||
\(333\) | 10.5741 | 0.579455 | ||||||||
\(334\) | −0.829436 | −0.0453847 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.71695 | −0.366440 | ||||||||
\(337\) | 30.2519 | 1.64793 | 0.823963 | − | 0.566644i | \(-0.191759\pi\) | ||||
0.823963 | + | 0.566644i | \(0.191759\pi\) | |||||||
\(338\) | 13.9303 | 0.757707 | ||||||||
\(339\) | 5.99152 | 0.325415 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.01414 | −0.163225 | ||||||||
\(342\) | 5.28345 | 0.285696 | ||||||||
\(343\) | 3.88680 | 0.209867 | ||||||||
\(344\) | −31.1372 | −1.67881 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.1455 | −1.24431 | ||||||||
\(347\) | 13.3283 | 0.715502 | 0.357751 | − | 0.933817i | \(-0.383544\pi\) | ||||
0.357751 | + | 0.933817i | \(0.383544\pi\) | |||||||
\(348\) | −43.7391 | −2.34466 | ||||||||
\(349\) | −27.4444 | −1.46906 | −0.734532 | − | 0.678574i | \(-0.762598\pi\) | ||||
−0.734532 | + | 0.678574i | \(0.762598\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.26344 | 0.227566 | ||||||||
\(352\) | −2.32714 | −0.124037 | ||||||||
\(353\) | −15.5564 | −0.827983 | −0.413992 | − | 0.910281i | \(-0.635866\pi\) | ||||
−0.413992 | + | 0.910281i | \(0.635866\pi\) | |||||||
\(354\) | 6.78237 | 0.360479 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 38.8220 | 2.05756 | ||||||||
\(357\) | 42.2624 | 2.23676 | ||||||||
\(358\) | −35.7810 | −1.89109 | ||||||||
\(359\) | −21.9829 | −1.16021 | −0.580107 | − | 0.814540i | \(-0.696989\pi\) | ||||
−0.580107 | + | 0.814540i | \(0.696989\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0253 | −0.948699 | ||||||||
\(362\) | −20.7469 | −1.09043 | ||||||||
\(363\) | −24.7550 | −1.29930 | ||||||||
\(364\) | 32.4607 | 1.70140 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 33.3442 | 1.74293 | ||||||||
\(367\) | −12.1103 | −0.632155 | −0.316078 | − | 0.948733i | \(-0.602366\pi\) | ||||
−0.316078 | + | 0.948733i | \(0.602366\pi\) | |||||||
\(368\) | −5.20615 | −0.271389 | ||||||||
\(369\) | −6.61379 | −0.344300 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.10559 | −0.0573994 | ||||||||
\(372\) | 47.5481 | 2.46526 | ||||||||
\(373\) | −7.08604 | −0.366901 | −0.183451 | − | 0.983029i | \(-0.558727\pi\) | ||||
−0.183451 | + | 0.983029i | \(0.558727\pi\) | |||||||
\(374\) | −5.91364 | −0.305787 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.6164 | 0.908499 | ||||||||
\(377\) | 14.7488 | 0.759600 | ||||||||
\(378\) | −13.4616 | −0.692390 | ||||||||
\(379\) | −21.5030 | −1.10453 | −0.552266 | − | 0.833668i | \(-0.686237\pi\) | ||||
−0.552266 | + | 0.833668i | \(0.686237\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3845 | −0.583248 | ||||||||
\(382\) | 26.4912 | 1.35541 | ||||||||
\(383\) | −24.8816 | −1.27139 | −0.635696 | − | 0.771940i | \(-0.719287\pi\) | ||||
−0.635696 | + | 0.771940i | \(0.719287\pi\) | |||||||
\(384\) | 45.4048 | 2.31706 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 40.3161 | 2.05204 | ||||||||
\(387\) | 21.8299 | 1.10968 | ||||||||
\(388\) | −2.89638 | −0.147041 | ||||||||
\(389\) | −35.4142 | −1.79557 | −0.897785 | − | 0.440434i | \(-0.854825\pi\) | ||||
−0.897785 | + | 0.440434i | \(0.854825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.7566 | 1.65657 | ||||||||
\(392\) | −19.4222 | −0.980967 | ||||||||
\(393\) | 6.22412 | 0.313965 | ||||||||
\(394\) | 60.3878 | 3.04229 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.90611 | −0.196289 | ||||||||
\(397\) | −5.49705 | −0.275889 | −0.137944 | − | 0.990440i | \(-0.544050\pi\) | ||||
−0.137944 | + | 0.990440i | \(0.544050\pi\) | |||||||
\(398\) | 19.5060 | 0.977748 | ||||||||
\(399\) | 8.16980 | 0.409001 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.8463 | 1.24077 | 0.620383 | − | 0.784299i | \(-0.286977\pi\) | ||||
0.620383 | + | 0.784299i | \(0.286977\pi\) | |||||||
\(402\) | −28.3101 | −1.41198 | ||||||||
\(403\) | −16.0332 | −0.798669 | ||||||||
\(404\) | −45.1918 | −2.24838 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −46.5685 | −2.31116 | ||||||||
\(407\) | −2.28789 | −0.113407 | ||||||||
\(408\) | 38.5855 | 1.91027 | ||||||||
\(409\) | 3.93157 | 0.194404 | 0.0972019 | − | 0.995265i | \(-0.469011\pi\) | ||||
0.0972019 | + | 0.995265i | \(0.469011\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.17647 | 0.255336 | ||||||||
\(412\) | −2.83402 | −0.139622 | ||||||||
\(413\) | 4.55194 | 0.223986 | ||||||||
\(414\) | 34.3238 | 1.68692 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.3788 | −0.606921 | ||||||||
\(417\) | −24.8724 | −1.21801 | ||||||||
\(418\) | −1.14317 | −0.0559144 | ||||||||
\(419\) | −4.76604 | −0.232836 | −0.116418 | − | 0.993200i | \(-0.537141\pi\) | ||||
−0.116418 | + | 0.993200i | \(0.537141\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0581 | 0.782625 | 0.391312 | − | 0.920258i | \(-0.372021\pi\) | ||||
0.391312 | + | 0.920258i | \(0.372021\pi\) | |||||||
\(422\) | −37.0164 | −1.80193 | ||||||||
\(423\) | −12.3507 | −0.600510 | ||||||||
\(424\) | −1.00940 | −0.0490209 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.813824 | 0.0394299 | ||||||||
\(427\) | 22.3787 | 1.08298 | ||||||||
\(428\) | 0.246544 | 0.0119172 | ||||||||
\(429\) | 3.03465 | 0.146514 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −41.3693 | −1.99269 | −0.996344 | − | 0.0854360i | \(-0.972772\pi\) | ||||
−0.996344 | + | 0.0854360i | \(0.972772\pi\) | |||||||
\(432\) | −1.30695 | −0.0628808 | ||||||||
\(433\) | −15.1854 | −0.729763 | −0.364881 | − | 0.931054i | \(-0.618890\pi\) | ||||
−0.364881 | + | 0.931054i | \(0.618890\pi\) | |||||||
\(434\) | 50.6239 | 2.43003 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.0873 | 0.914115 | ||||||||
\(437\) | 6.33222 | 0.302911 | ||||||||
\(438\) | −79.6568 | −3.80615 | ||||||||
\(439\) | 17.1194 | 0.817063 | 0.408532 | − | 0.912744i | \(-0.366041\pi\) | ||||
0.408532 | + | 0.912744i | \(0.366041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.6166 | 0.648411 | ||||||||
\(442\) | −31.4565 | −1.49623 | ||||||||
\(443\) | −35.3909 | −1.68147 | −0.840736 | − | 0.541445i | \(-0.817877\pi\) | ||||
−0.840736 | + | 0.541445i | \(0.817877\pi\) | |||||||
\(444\) | 36.0916 | 1.71283 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.883234 | −0.0418223 | ||||||||
\(447\) | 28.0601 | 1.32719 | ||||||||
\(448\) | 44.9204 | 2.12229 | ||||||||
\(449\) | 20.6830 | 0.976090 | 0.488045 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488045 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.43101 | 0.0673838 | ||||||||
\(452\) | 8.87610 | 0.417497 | ||||||||
\(453\) | 39.3374 | 1.84823 | ||||||||
\(454\) | 47.2220 | 2.21624 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.45902 | 0.349301 | ||||||||
\(457\) | −41.7664 | −1.95375 | −0.976876 | − | 0.213807i | \(-0.931414\pi\) | ||||
−0.976876 | + | 0.213807i | \(0.931414\pi\) | |||||||
\(458\) | 27.7054 | 1.29459 | ||||||||
\(459\) | 8.22322 | 0.383827 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6783 | −0.497340 | −0.248670 | − | 0.968588i | \(-0.579993\pi\) | ||||
−0.248670 | + | 0.968588i | \(0.579993\pi\) | |||||||
\(462\) | −9.58176 | −0.445784 | ||||||||
\(463\) | 7.83033 | 0.363906 | 0.181953 | − | 0.983307i | \(-0.441758\pi\) | ||||
0.181953 | + | 0.983307i | \(0.441758\pi\) | |||||||
\(464\) | −4.52122 | −0.209892 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −44.3379 | −2.05391 | ||||||||
\(467\) | −4.98100 | −0.230493 | −0.115246 | − | 0.993337i | \(-0.536766\pi\) | ||||
−0.115246 | + | 0.993337i | \(0.536766\pi\) | |||||||
\(468\) | −20.7778 | −0.960455 | ||||||||
\(469\) | −19.0001 | −0.877344 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.2635 | 0.795462 | ||||||||
\(472\) | 4.15591 | 0.191291 | ||||||||
\(473\) | −4.72330 | −0.217178 | ||||||||
\(474\) | 88.8388 | 4.08050 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 62.6094 | 2.86970 | ||||||||
\(477\) | 0.707679 | 0.0324024 | ||||||||
\(478\) | −9.59500 | −0.438865 | ||||||||
\(479\) | −16.3981 | −0.749247 | −0.374623 | − | 0.927177i | \(-0.622228\pi\) | ||||
−0.374623 | + | 0.927177i | \(0.622228\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.1700 | −0.554906 | ||||||||
\(482\) | −37.6498 | −1.71490 | ||||||||
\(483\) | 53.0749 | 2.41499 | ||||||||
\(484\) | −36.6731 | −1.66696 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 45.5794 | 2.06753 | ||||||||
\(487\) | −0.876508 | −0.0397184 | −0.0198592 | − | 0.999803i | \(-0.506322\pi\) | ||||
−0.0198592 | + | 0.999803i | \(0.506322\pi\) | |||||||
\(488\) | 20.4317 | 0.924901 | ||||||||
\(489\) | −4.49547 | −0.203292 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2118 | 0.551112 | 0.275556 | − | 0.961285i | \(-0.411138\pi\) | ||||
0.275556 | + | 0.961285i | \(0.411138\pi\) | |||||||
\(492\) | −22.5743 | −1.01773 | ||||||||
\(493\) | 28.4471 | 1.28119 | ||||||||
\(494\) | −6.08090 | −0.273592 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.91495 | 0.220688 | ||||||||
\(497\) | 0.546192 | 0.0245001 | ||||||||
\(498\) | 78.1675 | 3.50277 | ||||||||
\(499\) | −3.34603 | −0.149789 | −0.0748945 | − | 0.997191i | \(-0.523862\pi\) | ||||
−0.0748945 | + | 0.997191i | \(0.523862\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.820954 | 0.0366775 | ||||||||
\(502\) | −27.6151 | −1.23252 | ||||||||
\(503\) | −11.8820 | −0.529792 | −0.264896 | − | 0.964277i | \(-0.585338\pi\) | ||||
−0.264896 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(504\) | 27.1354 | 1.20871 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.42660 | −0.330152 | ||||||||
\(507\) | −13.7878 | −0.612339 | ||||||||
\(508\) | −16.8656 | −0.748289 | ||||||||
\(509\) | 36.3183 | 1.60978 | 0.804890 | − | 0.593424i | \(-0.202224\pi\) | ||||
0.804890 | + | 0.593424i | \(0.202224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53.4611 | −2.36498 | ||||||||
\(512\) | 9.12203 | 0.403140 | ||||||||
\(513\) | 1.58964 | 0.0701844 | ||||||||
\(514\) | −44.0014 | −1.94082 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 74.5102 | 3.28013 | ||||||||
\(517\) | 2.67229 | 0.117527 | ||||||||
\(518\) | 38.4263 | 1.68835 | ||||||||
\(519\) | 22.9088 | 1.00558 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.204224 | 0.00894722 | 0.00447361 | − | 0.999990i | \(-0.498576\pi\) | ||||
0.00447361 | + | 0.999990i | \(0.498576\pi\) | |||||||
\(522\) | 29.8081 | 1.30467 | ||||||||
\(523\) | −28.0312 | −1.22572 | −0.612859 | − | 0.790192i | \(-0.709981\pi\) | ||||
−0.612859 | + | 0.790192i | \(0.709981\pi\) | |||||||
\(524\) | 9.22069 | 0.402808 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.6943 | −0.684303 | ||||||||
\(527\) | −30.9244 | −1.34709 | ||||||||
\(528\) | −0.930269 | −0.0404848 | ||||||||
\(529\) | 18.1371 | 0.788570 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.91366 | −0.126442 | ||||||||
\(532\) | 12.1031 | 0.524736 | ||||||||
\(533\) | 7.61202 | 0.329713 | ||||||||
\(534\) | −60.9567 | −2.63785 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −17.3471 | −0.749280 | ||||||||
\(537\) | 35.4151 | 1.52827 | ||||||||
\(538\) | 58.9268 | 2.54052 | ||||||||
\(539\) | −2.94621 | −0.126902 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.32216 | −0.400791 | −0.200396 | − | 0.979715i | \(-0.564223\pi\) | ||||
−0.200396 | + | 0.979715i | \(0.564223\pi\) | |||||||
\(542\) | −21.8824 | −0.939931 | ||||||||
\(543\) | 20.5347 | 0.881230 | ||||||||
\(544\) | −23.8760 | −1.02367 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −50.9684 | −2.18125 | ||||||||
\(547\) | 20.0378 | 0.856755 | 0.428378 | − | 0.903600i | \(-0.359085\pi\) | ||||
0.428378 | + | 0.903600i | \(0.359085\pi\) | |||||||
\(548\) | 7.66865 | 0.327588 | ||||||||
\(549\) | −14.3244 | −0.611351 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.49914 | 0.234271 | ||||||||
\(552\) | 48.4573 | 2.06248 | ||||||||
\(553\) | 59.6235 | 2.53545 | ||||||||
\(554\) | −13.8807 | −0.589734 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36.8471 | −1.56266 | ||||||||
\(557\) | 28.9839 | 1.22809 | 0.614043 | − | 0.789272i | \(-0.289542\pi\) | ||||
0.614043 | + | 0.789272i | \(0.289542\pi\) | |||||||
\(558\) | −32.4040 | −1.37177 | ||||||||
\(559\) | −25.1247 | −1.06266 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.85316 | 0.247121 | ||||||||
\(562\) | −25.7552 | −1.08642 | ||||||||
\(563\) | −13.7025 | −0.577492 | −0.288746 | − | 0.957406i | \(-0.593238\pi\) | ||||
−0.288746 | + | 0.957406i | \(0.593238\pi\) | |||||||
\(564\) | −42.1555 | −1.77507 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.03428 | −0.295673 | ||||||||
\(567\) | 38.1312 | 1.60136 | ||||||||
\(568\) | 0.498673 | 0.0209239 | ||||||||
\(569\) | 34.6152 | 1.45115 | 0.725573 | − | 0.688146i | \(-0.241575\pi\) | ||||
0.725573 | + | 0.688146i | \(0.241575\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.4197 | −1.77521 | −0.887604 | − | 0.460607i | \(-0.847632\pi\) | ||||
−0.887604 | + | 0.460607i | \(0.847632\pi\) | |||||||
\(572\) | 4.49566 | 0.187973 | ||||||||
\(573\) | −26.2203 | −1.09537 | ||||||||
\(574\) | −24.0346 | −1.00318 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −28.7532 | −1.19805 | ||||||||
\(577\) | 34.3049 | 1.42813 | 0.714067 | − | 0.700078i | \(-0.246851\pi\) | ||||
0.714067 | + | 0.700078i | \(0.246851\pi\) | |||||||
\(578\) | −21.1288 | −0.878844 | ||||||||
\(579\) | −39.9039 | −1.65835 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.4615 | 2.17647 | ||||||||
\(582\) | 4.54777 | 0.188511 | ||||||||
\(583\) | −0.153120 | −0.00634156 | ||||||||
\(584\) | −48.8099 | −2.01977 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5713 | 0.601935 | ||||||||
\(587\) | −29.7521 | −1.22800 | −0.614001 | − | 0.789305i | \(-0.710441\pi\) | ||||
−0.614001 | + | 0.789305i | \(0.710441\pi\) | |||||||
\(588\) | 46.4765 | 1.91666 | ||||||||
\(589\) | −5.97803 | −0.246321 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −59.7702 | −2.45862 | ||||||||
\(592\) | 3.73071 | 0.153331 | ||||||||
\(593\) | 14.8105 | 0.608195 | 0.304098 | − | 0.952641i | \(-0.401645\pi\) | ||||
0.304098 | + | 0.952641i | \(0.401645\pi\) | |||||||
\(594\) | −1.86437 | −0.0764962 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 41.5694 | 1.70275 | ||||||||
\(597\) | −19.3065 | −0.790163 | ||||||||
\(598\) | −39.5044 | −1.61545 | ||||||||
\(599\) | 27.2394 | 1.11297 | 0.556486 | − | 0.830857i | \(-0.312149\pi\) | ||||
0.556486 | + | 0.830857i | \(0.312149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.1682 | 1.35296 | 0.676480 | − | 0.736461i | \(-0.263505\pi\) | ||||
0.676480 | + | 0.736461i | \(0.263505\pi\) | |||||||
\(602\) | 79.3301 | 3.23325 | ||||||||
\(603\) | 12.1618 | 0.495268 | ||||||||
\(604\) | 58.2761 | 2.37122 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 70.9583 | 2.88248 | ||||||||
\(607\) | −5.79849 | −0.235353 | −0.117677 | − | 0.993052i | \(-0.537545\pi\) | ||||
−0.117677 | + | 0.993052i | \(0.537545\pi\) | |||||||
\(608\) | −4.61549 | −0.187183 | ||||||||
\(609\) | 46.0923 | 1.86775 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.2148 | 0.575068 | ||||||||
\(612\) | −40.0758 | −1.61997 | ||||||||
\(613\) | −4.04653 | −0.163438 | −0.0817189 | − | 0.996655i | \(-0.526041\pi\) | ||||
−0.0817189 | + | 0.996655i | \(0.526041\pi\) | |||||||
\(614\) | 60.1842 | 2.42884 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.87125 | −0.236559 | ||||||||
\(617\) | −37.1749 | −1.49661 | −0.748303 | − | 0.663357i | \(-0.769131\pi\) | ||||
−0.748303 | + | 0.663357i | \(0.769131\pi\) | |||||||
\(618\) | 4.44986 | 0.179000 | ||||||||
\(619\) | −37.7118 | −1.51576 | −0.757882 | − | 0.652391i | \(-0.773766\pi\) | ||||
−0.757882 | + | 0.652391i | \(0.773766\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.3271 | 0.414411 | ||||||||
\(622\) | 20.9413 | 0.839672 | ||||||||
\(623\) | −40.9106 | −1.63905 | ||||||||
\(624\) | −4.94839 | −0.198094 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −77.2903 | −3.08914 | ||||||||
\(627\) | 1.13148 | 0.0451870 | ||||||||
\(628\) | 25.5750 | 1.02055 | ||||||||
\(629\) | −23.4733 | −0.935940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.5225 | 0.737368 | 0.368684 | − | 0.929555i | \(-0.379808\pi\) | ||||
0.368684 | + | 0.929555i | \(0.379808\pi\) | |||||||
\(632\) | 54.4362 | 2.16536 | ||||||||
\(633\) | 36.6379 | 1.45622 | ||||||||
\(634\) | −60.4072 | −2.39908 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.41546 | 0.0957794 | ||||||||
\(637\) | −15.6718 | −0.620940 | ||||||||
\(638\) | −6.44954 | −0.255340 | ||||||||
\(639\) | −0.349613 | −0.0138305 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.7116 | −0.778560 | −0.389280 | − | 0.921120i | \(-0.627276\pi\) | ||||
−0.389280 | + | 0.921120i | \(0.627276\pi\) | |||||||
\(642\) | −0.387113 | −0.0152781 | ||||||||
\(643\) | −42.5897 | −1.67957 | −0.839787 | − | 0.542916i | \(-0.817320\pi\) | ||||
−0.839787 | + | 0.542916i | \(0.817320\pi\) | |||||||
\(644\) | 78.6275 | 3.09836 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.7287 | −0.461459 | ||||||||
\(647\) | −27.4018 | −1.07728 | −0.538638 | − | 0.842537i | \(-0.681061\pi\) | ||||
−0.538638 | + | 0.842537i | \(0.681061\pi\) | |||||||
\(648\) | 34.8138 | 1.36761 | ||||||||
\(649\) | 0.630424 | 0.0247463 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −50.1062 | −1.96382 | ||||||||
\(652\) | −6.65979 | −0.260818 | ||||||||
\(653\) | −21.4414 | −0.839068 | −0.419534 | − | 0.907740i | \(-0.637807\pi\) | ||||
−0.419534 | + | 0.907740i | \(0.637807\pi\) | |||||||
\(654\) | −29.9701 | −1.17192 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.33346 | −0.0911062 | ||||||||
\(657\) | 34.2200 | 1.33505 | ||||||||
\(658\) | −44.8825 | −1.74970 | ||||||||
\(659\) | −36.7342 | −1.43096 | −0.715480 | − | 0.698633i | \(-0.753792\pi\) | ||||
−0.715480 | + | 0.698633i | \(0.753792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.7515 | −0.612664 | −0.306332 | − | 0.951925i | \(-0.599102\pi\) | ||||
−0.306332 | + | 0.951925i | \(0.599102\pi\) | |||||||
\(662\) | −28.2118 | −1.09648 | ||||||||
\(663\) | 31.1348 | 1.20918 | ||||||||
\(664\) | 47.8973 | 1.85878 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.5963 | −0.953089 | ||||||||
\(667\) | 35.7250 | 1.38328 | ||||||||
\(668\) | 1.21620 | 0.0470561 | ||||||||
\(669\) | 0.874201 | 0.0337986 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.09935 | 0.119649 | ||||||||
\(672\) | −38.6858 | −1.49234 | ||||||||
\(673\) | −31.0107 | −1.19537 | −0.597687 | − | 0.801730i | \(-0.703913\pi\) | ||||
−0.597687 | + | 0.801730i | \(0.703913\pi\) | |||||||
\(674\) | −70.3690 | −2.71051 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.4259 | −0.785611 | ||||||||
\(677\) | 9.59882 | 0.368912 | 0.184456 | − | 0.982841i | \(-0.440948\pi\) | ||||
0.184456 | + | 0.982841i | \(0.440948\pi\) | |||||||
\(678\) | −13.9369 | −0.535243 | ||||||||
\(679\) | 3.05220 | 0.117133 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −46.7391 | −1.79105 | ||||||||
\(682\) | 7.01120 | 0.268473 | ||||||||
\(683\) | 0.868350 | 0.0332265 | 0.0166132 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166132 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(684\) | −7.74710 | −0.296218 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.04109 | −0.345190 | ||||||||
\(687\) | −27.4221 | −1.04622 | ||||||||
\(688\) | 7.70196 | 0.293635 | ||||||||
\(689\) | −0.814491 | −0.0310296 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.1375 | −0.499772 | −0.249886 | − | 0.968275i | \(-0.580393\pi\) | ||||
−0.249886 | + | 0.968275i | \(0.580393\pi\) | |||||||
\(692\) | 33.9380 | 1.29013 | ||||||||
\(693\) | 4.11625 | 0.156364 | ||||||||
\(694\) | −31.0030 | −1.17686 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 42.0822 | 1.59512 | ||||||||
\(697\) | 14.6819 | 0.556116 | ||||||||
\(698\) | 63.8384 | 2.41632 | ||||||||
\(699\) | 43.8844 | 1.65986 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.13602 | 0.269524 | 0.134762 | − | 0.990878i | \(-0.456973\pi\) | ||||
0.134762 | + | 0.990878i | \(0.456973\pi\) | |||||||
\(702\) | −9.91719 | −0.374300 | ||||||||
\(703\) | −4.53765 | −0.171141 | ||||||||
\(704\) | 6.22129 | 0.234474 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.1858 | 1.36187 | ||||||||
\(707\) | 47.6231 | 1.79105 | ||||||||
\(708\) | −9.94495 | −0.373754 | ||||||||
\(709\) | −8.00513 | −0.300639 | −0.150319 | − | 0.988637i | \(-0.548030\pi\) | ||||
−0.150319 | + | 0.988637i | \(0.548030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.1645 | −1.43128 | ||||||||
\(712\) | −37.3513 | −1.39980 | ||||||||
\(713\) | −38.8362 | −1.45443 | ||||||||
\(714\) | −98.3066 | −3.67903 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 52.4655 | 1.96073 | ||||||||
\(717\) | 9.49688 | 0.354667 | ||||||||
\(718\) | 51.1345 | 1.90832 | ||||||||
\(719\) | −41.2567 | −1.53861 | −0.769307 | − | 0.638879i | \(-0.779398\pi\) | ||||
−0.769307 | + | 0.638879i | \(0.779398\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.98649 | 0.111223 | ||||||||
\(722\) | 41.9286 | 1.56042 | ||||||||
\(723\) | 37.2648 | 1.38589 | ||||||||
\(724\) | 30.4210 | 1.13059 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 57.5825 | 2.13709 | ||||||||
\(727\) | −39.2602 | −1.45608 | −0.728040 | − | 0.685534i | \(-0.759569\pi\) | ||||
−0.728040 | + | 0.685534i | \(0.759569\pi\) | |||||||
\(728\) | −31.2310 | −1.15750 | ||||||||
\(729\) | −13.2864 | −0.492090 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.4600 | −1.79236 | ||||||||
\(732\) | −48.8924 | −1.80711 | ||||||||
\(733\) | −0.912055 | −0.0336875 | −0.0168438 | − | 0.999858i | \(-0.505362\pi\) | ||||
−0.0168438 | + | 0.999858i | \(0.505362\pi\) | |||||||
\(734\) | 28.1699 | 1.03977 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.9844 | −1.10524 | ||||||||
\(737\) | −2.63143 | −0.0969301 | ||||||||
\(738\) | 15.3843 | 0.566305 | ||||||||
\(739\) | −11.6941 | −0.430174 | −0.215087 | − | 0.976595i | \(-0.569003\pi\) | ||||
−0.215087 | + | 0.976595i | \(0.569003\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.01871 | 0.221103 | ||||||||
\(742\) | 2.57171 | 0.0944106 | ||||||||
\(743\) | −11.5631 | −0.424211 | −0.212105 | − | 0.977247i | \(-0.568032\pi\) | ||||
−0.212105 | + | 0.977247i | \(0.568032\pi\) | |||||||
\(744\) | −45.7470 | −1.67716 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.4828 | 0.603480 | ||||||||
\(747\) | −33.5802 | −1.22863 | ||||||||
\(748\) | 8.67113 | 0.317048 | ||||||||
\(749\) | −0.259808 | −0.00949318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.2430 | −0.994112 | −0.497056 | − | 0.867718i | \(-0.665586\pi\) | ||||
−0.497056 | + | 0.867718i | \(0.665586\pi\) | |||||||
\(752\) | −4.35753 | −0.158903 | ||||||||
\(753\) | 27.3327 | 0.996059 | ||||||||
\(754\) | −34.3071 | −1.24939 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19.7387 | 0.717888 | ||||||||
\(757\) | −17.1080 | −0.621800 | −0.310900 | − | 0.950443i | \(-0.600630\pi\) | ||||
−0.310900 | + | 0.950443i | \(0.600630\pi\) | |||||||
\(758\) | 50.0181 | 1.81674 | ||||||||
\(759\) | 7.35065 | 0.266812 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.7173 | 1.36725 | 0.683625 | − | 0.729833i | \(-0.260402\pi\) | ||||
0.683625 | + | 0.729833i | \(0.260402\pi\) | |||||||
\(762\) | 26.4816 | 0.959328 | ||||||||
\(763\) | −20.1142 | −0.728182 | ||||||||
\(764\) | −38.8439 | −1.40532 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 57.8772 | 2.09119 | ||||||||
\(767\) | 3.35342 | 0.121085 | ||||||||
\(768\) | −48.0682 | −1.73451 | ||||||||
\(769\) | −5.93347 | −0.213966 | −0.106983 | − | 0.994261i | \(-0.534119\pi\) | ||||
−0.106983 | + | 0.994261i | \(0.534119\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.5514 | 1.56847 | ||||||||
\(772\) | −59.1153 | −2.12761 | ||||||||
\(773\) | −23.5908 | −0.848503 | −0.424252 | − | 0.905544i | \(-0.639463\pi\) | ||||
−0.424252 | + | 0.905544i | \(0.639463\pi\) | |||||||
\(774\) | −50.7786 | −1.82520 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.78666 | 0.100035 | ||||||||
\(777\) | −38.0333 | −1.36444 | ||||||||
\(778\) | 82.3770 | 2.95336 | ||||||||
\(779\) | 2.83817 | 0.101688 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0756453 | 0.00270680 | ||||||||
\(782\) | −76.1952 | −2.72473 | ||||||||
\(783\) | 8.96842 | 0.320505 | ||||||||
\(784\) | 4.80418 | 0.171578 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.4779 | −0.516411 | ||||||||
\(787\) | 18.2307 | 0.649854 | 0.324927 | − | 0.945739i | \(-0.394660\pi\) | ||||
0.324927 | + | 0.945739i | \(0.394660\pi\) | |||||||
\(788\) | −88.5462 | −3.15433 | ||||||||
\(789\) | 15.5338 | 0.553017 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.35364 | −0.332577 | ||||||||
\(792\) | 3.75814 | 0.133540 | ||||||||
\(793\) | 16.4864 | 0.585451 | ||||||||
\(794\) | 12.7867 | 0.453783 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −28.6015 | −1.01375 | ||||||||
\(797\) | 10.8296 | 0.383603 | 0.191801 | − | 0.981434i | \(-0.438567\pi\) | ||||
0.191801 | + | 0.981434i | \(0.438567\pi\) | |||||||
\(798\) | −19.0038 | −0.672727 | ||||||||
\(799\) | 27.4171 | 0.969948 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.1865 | 0.925256 | ||||||||
\(802\) | −57.7950 | −2.04081 | ||||||||
\(803\) | −7.40413 | −0.261286 | ||||||||
\(804\) | 41.5109 | 1.46398 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 37.2948 | 1.31365 | ||||||||
\(807\) | −58.3242 | −2.05311 | ||||||||
\(808\) | 43.4799 | 1.52962 | ||||||||
\(809\) | 44.8177 | 1.57571 | 0.787854 | − | 0.615863i | \(-0.211192\pi\) | ||||
0.787854 | + | 0.615863i | \(0.211192\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.06296 | −0.107555 | −0.0537775 | − | 0.998553i | \(-0.517126\pi\) | ||||
−0.0537775 | + | 0.998553i | \(0.517126\pi\) | |||||||
\(812\) | 68.2831 | 2.39627 | ||||||||
\(813\) | 21.6587 | 0.759602 | ||||||||
\(814\) | 5.32187 | 0.186532 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9.54435 | −0.334119 | ||||||||
\(817\) | −9.36786 | −0.327740 | ||||||||
\(818\) | −9.14524 | −0.319756 | ||||||||
\(819\) | 21.8957 | 0.765096 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.3210 | 0.709208 | 0.354604 | − | 0.935017i | \(-0.384616\pi\) | ||||
0.354604 | + | 0.935017i | \(0.384616\pi\) | |||||||
\(822\) | −12.0410 | −0.419978 | ||||||||
\(823\) | 50.0369 | 1.74418 | 0.872089 | − | 0.489348i | \(-0.162765\pi\) | ||||
0.872089 | + | 0.489348i | \(0.162765\pi\) | |||||||
\(824\) | 2.72666 | 0.0949879 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.5883 | −0.368413 | ||||||||
\(827\) | 31.6293 | 1.09986 | 0.549929 | − | 0.835211i | \(-0.314655\pi\) | ||||
0.549929 | + | 0.835211i | \(0.314655\pi\) | |||||||
\(828\) | −50.3288 | −1.74905 | ||||||||
\(829\) | 33.1369 | 1.15089 | 0.575446 | − | 0.817840i | \(-0.304829\pi\) | ||||
0.575446 | + | 0.817840i | \(0.304829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.7387 | 0.476591 | ||||||||
\(832\) | 33.0930 | 1.14729 | ||||||||
\(833\) | −30.2274 | −1.04732 | ||||||||
\(834\) | 57.8557 | 2.00338 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.67623 | 0.0579735 | ||||||||
\(837\) | −9.74944 | −0.336990 | ||||||||
\(838\) | 11.0863 | 0.382970 | ||||||||
\(839\) | 10.3854 | 0.358543 | 0.179271 | − | 0.983800i | \(-0.442626\pi\) | ||||
0.179271 | + | 0.983800i | \(0.442626\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.02500 | 0.0698275 | ||||||||
\(842\) | −37.3528 | −1.28726 | ||||||||
\(843\) | 25.4918 | 0.877986 | ||||||||
\(844\) | 54.2769 | 1.86829 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 28.7289 | 0.987720 | ||||||||
\(847\) | 38.6461 | 1.32790 | ||||||||
\(848\) | 0.249681 | 0.00857410 | ||||||||
\(849\) | 6.96235 | 0.238947 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.4787 | −1.01052 | ||||||||
\(852\) | −1.19331 | −0.0408820 | ||||||||
\(853\) | 9.31456 | 0.318924 | 0.159462 | − | 0.987204i | \(-0.449024\pi\) | ||||
0.159462 | + | 0.987204i | \(0.449024\pi\) | |||||||
\(854\) | −52.0551 | −1.78129 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.237204 | −0.00810748 | ||||||||
\(857\) | 34.0314 | 1.16249 | 0.581245 | − | 0.813729i | \(-0.302566\pi\) | ||||
0.581245 | + | 0.813729i | \(0.302566\pi\) | |||||||
\(858\) | −7.05890 | −0.240987 | ||||||||
\(859\) | 33.4243 | 1.14042 | 0.570211 | − | 0.821498i | \(-0.306861\pi\) | ||||
0.570211 | + | 0.821498i | \(0.306861\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.7888 | 0.810719 | ||||||||
\(862\) | 96.2291 | 3.27758 | ||||||||
\(863\) | −16.5900 | −0.564730 | −0.282365 | − | 0.959307i | \(-0.591119\pi\) | ||||
−0.282365 | + | 0.959307i | \(0.591119\pi\) | |||||||
\(864\) | −7.52730 | −0.256084 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.3227 | 1.20032 | ||||||||
\(867\) | 20.9128 | 0.710235 | ||||||||
\(868\) | −74.2296 | −2.51952 | ||||||||
\(869\) | 8.25760 | 0.280120 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.9974 | −0.474285 | ||||||||
\(872\) | −18.3642 | −0.621891 | ||||||||
\(873\) | −1.95369 | −0.0661224 | ||||||||
\(874\) | −14.7294 | −0.498229 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 116.800 | 3.94632 | ||||||||
\(877\) | 32.9538 | 1.11277 | 0.556385 | − | 0.830925i | \(-0.312188\pi\) | ||||
0.556385 | + | 0.830925i | \(0.312188\pi\) | |||||||
\(878\) | −39.8214 | −1.34391 | ||||||||
\(879\) | −14.4223 | −0.486452 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.0755 | −1.68709 | −0.843544 | − | 0.537061i | \(-0.819535\pi\) | ||||
−0.843544 | + | 0.537061i | \(0.819535\pi\) | |||||||
\(882\) | −31.6737 | −1.06651 | ||||||||
\(883\) | −12.5335 | −0.421786 | −0.210893 | − | 0.977509i | \(-0.567637\pi\) | ||||
−0.210893 | + | 0.977509i | \(0.567637\pi\) | |||||||
\(884\) | 46.1245 | 1.55133 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 82.3228 | 2.76569 | ||||||||
\(887\) | −26.9358 | −0.904415 | −0.452207 | − | 0.891913i | \(-0.649363\pi\) | ||||
−0.452207 | + | 0.891913i | \(0.649363\pi\) | |||||||
\(888\) | −34.7244 | −1.16527 | ||||||||
\(889\) | 17.7729 | 0.596085 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.28101 | 0.176921 | ||||||||
\(892\) | 1.29508 | 0.0433625 | ||||||||
\(893\) | 5.30004 | 0.177359 | ||||||||
\(894\) | −65.2705 | −2.18297 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −70.8835 | −2.36805 | ||||||||
\(897\) | 39.1004 | 1.30552 | ||||||||
\(898\) | −48.1107 | −1.60548 | ||||||||
\(899\) | −33.7268 | −1.12485 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.57097 | −0.0523366 | ||||||||
\(902\) | −3.32869 | −0.110833 | ||||||||
\(903\) | −78.5188 | −2.61294 | ||||||||
\(904\) | −8.53986 | −0.284032 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −91.5027 | −3.03997 | ||||||||
\(907\) | 28.6510 | 0.951342 | 0.475671 | − | 0.879623i | \(-0.342205\pi\) | ||||
0.475671 | + | 0.879623i | \(0.342205\pi\) | |||||||
\(908\) | −69.2414 | −2.29786 | ||||||||
\(909\) | −30.4832 | −1.01106 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.90071 | −0.294894 | −0.147447 | − | 0.989070i | \(-0.547106\pi\) | ||||
−0.147447 | + | 0.989070i | \(0.547106\pi\) | |||||||
\(912\) | −1.84503 | −0.0610950 | ||||||||
\(913\) | 7.26569 | 0.240459 | ||||||||
\(914\) | 97.1530 | 3.21354 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −40.6242 | −1.34226 | ||||||||
\(917\) | −9.71676 | −0.320876 | ||||||||
\(918\) | −19.1280 | −0.631320 | ||||||||
\(919\) | 17.1901 | 0.567049 | 0.283525 | − | 0.958965i | \(-0.408496\pi\) | ||||
0.283525 | + | 0.958965i | \(0.408496\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −59.5687 | −1.96286 | ||||||||
\(922\) | 24.8389 | 0.818025 | ||||||||
\(923\) | 0.402381 | 0.0132445 | ||||||||
\(924\) | 14.0497 | 0.462200 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.2141 | −0.598554 | ||||||||
\(927\) | −1.91163 | −0.0627861 | ||||||||
\(928\) | −26.0396 | −0.854793 | ||||||||
\(929\) | 34.7789 | 1.14106 | 0.570530 | − | 0.821277i | \(-0.306738\pi\) | ||||
0.570530 | + | 0.821277i | \(0.306738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.84330 | −0.191507 | ||||||||
\(932\) | 65.0123 | 2.12955 | ||||||||
\(933\) | −20.7272 | −0.678578 | ||||||||
\(934\) | 11.5863 | 0.379115 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19.9907 | 0.653417 | ||||||||
\(937\) | 16.5386 | 0.540292 | 0.270146 | − | 0.962819i | \(-0.412928\pi\) | ||||
0.270146 | + | 0.962819i | \(0.412928\pi\) | |||||||
\(938\) | 44.1962 | 1.44306 | ||||||||
\(939\) | 76.4999 | 2.49648 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.1982 | 1.34302 | 0.671512 | − | 0.740994i | \(-0.265645\pi\) | ||||
0.671512 | + | 0.740994i | \(0.265645\pi\) | |||||||
\(942\) | −40.1568 | −1.30838 | ||||||||
\(943\) | 18.4381 | 0.600428 | ||||||||
\(944\) | −1.02799 | −0.0334582 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.9869 | 0.357214 | ||||||||
\(947\) | 37.1110 | 1.20594 | 0.602972 | − | 0.797762i | \(-0.293983\pi\) | ||||
0.602972 | + | 0.797762i | \(0.293983\pi\) | |||||||
\(948\) | −130.264 | −4.23077 | ||||||||
\(949\) | −39.3849 | −1.27849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 59.7895 | 1.93881 | ||||||||
\(952\) | −60.2376 | −1.95231 | ||||||||
\(953\) | −20.8962 | −0.676895 | −0.338447 | − | 0.940985i | \(-0.609902\pi\) | ||||
−0.338447 | + | 0.940985i | \(0.609902\pi\) | |||||||
\(954\) | −1.64613 | −0.0532956 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.0691 | 0.455027 | ||||||||
\(957\) | 6.38358 | 0.206352 | ||||||||
\(958\) | 38.1436 | 1.23236 | ||||||||
\(959\) | −8.08122 | −0.260956 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.66391 | 0.182707 | ||||||||
\(962\) | 28.3087 | 0.912710 | ||||||||
\(963\) | 0.166301 | 0.00535897 | ||||||||
\(964\) | 55.2057 | 1.77806 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −123.458 | −3.97218 | ||||||||
\(967\) | −8.28057 | −0.266285 | −0.133143 | − | 0.991097i | \(-0.542507\pi\) | ||||
−0.133143 | + | 0.991097i | \(0.542507\pi\) | |||||||
\(968\) | 35.2838 | 1.13407 | ||||||||
\(969\) | 11.6087 | 0.372927 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.4077 | −0.847463 | −0.423731 | − | 0.905788i | \(-0.639280\pi\) | ||||
−0.423731 | + | 0.905788i | \(0.639280\pi\) | |||||||
\(972\) | −66.8329 | −2.14366 | ||||||||
\(973\) | 38.8294 | 1.24481 | ||||||||
\(974\) | 2.03885 | 0.0653289 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.05390 | −0.161771 | ||||||||
\(977\) | −25.3280 | −0.810314 | −0.405157 | − | 0.914247i | \(-0.632783\pi\) | ||||
−0.405157 | + | 0.914247i | \(0.632783\pi\) | |||||||
\(978\) | 10.4569 | 0.334376 | ||||||||
\(979\) | −5.66594 | −0.181084 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.8749 | 0.411065 | ||||||||
\(982\) | −28.4059 | −0.906470 | ||||||||
\(983\) | 5.12811 | 0.163561 | 0.0817807 | − | 0.996650i | \(-0.473939\pi\) | ||||
0.0817807 | + | 0.996650i | \(0.473939\pi\) | |||||||
\(984\) | 21.7191 | 0.692381 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −66.1708 | −2.10731 | ||||||||
\(987\) | 44.4235 | 1.41401 | ||||||||
\(988\) | 8.91638 | 0.283668 | ||||||||
\(989\) | −60.8581 | −1.93517 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.5396 | −0.843059 | −0.421530 | − | 0.906815i | \(-0.638507\pi\) | ||||
−0.421530 | + | 0.906815i | \(0.638507\pi\) | |||||||
\(992\) | 28.3073 | 0.898758 | ||||||||
\(993\) | 27.9233 | 0.886120 | ||||||||
\(994\) | −1.27050 | −0.0402978 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −114.616 | −3.63176 | ||||||||
\(997\) | −44.4973 | −1.40924 | −0.704622 | − | 0.709583i | \(-0.748883\pi\) | ||||
−0.704622 | + | 0.709583i | \(0.748883\pi\) | |||||||
\(998\) | 7.78321 | 0.246373 | ||||||||
\(999\) | −7.40034 | −0.234136 |
(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 | 625.2.a.e.1.3 | ✓ | 8 | |
3.2 | odd | 2 | 5625.2.a.be.1.6 | 8 | |||
4.3 | odd | 2 | 10000.2.a.bn.1.1 | 8 | |||
5.2 | odd | 4 | 625.2.b.d.624.3 | 16 | |||
5.3 | odd | 4 | 625.2.b.d.624.14 | 16 | |||
5.4 | even | 2 | 625.2.a.g.1.6 | yes | 8 | ||
15.14 | odd | 2 | 5625.2.a.s.1.3 | 8 | |||
20.19 | odd | 2 | 10000.2.a.be.1.8 | 8 | |||
25.2 | odd | 20 | 625.2.e.k.124.2 | 32 | |||
25.3 | odd | 20 | 625.2.e.j.249.7 | 32 | |||
25.4 | even | 10 | 625.2.d.m.376.2 | 16 | |||
25.6 | even | 5 | 625.2.d.q.251.3 | 16 | |||
25.8 | odd | 20 | 625.2.e.j.374.2 | 32 | |||
25.9 | even | 10 | 625.2.d.n.126.3 | 16 | |||
25.11 | even | 5 | 625.2.d.p.501.2 | 16 | |||
25.12 | odd | 20 | 625.2.e.k.499.7 | 32 | |||
25.13 | odd | 20 | 625.2.e.k.499.2 | 32 | |||
25.14 | even | 10 | 625.2.d.n.501.3 | 16 | |||
25.16 | even | 5 | 625.2.d.p.126.2 | 16 | |||
25.17 | odd | 20 | 625.2.e.j.374.7 | 32 | |||
25.19 | even | 10 | 625.2.d.m.251.2 | 16 | |||
25.21 | even | 5 | 625.2.d.q.376.3 | 16 | |||
25.22 | odd | 20 | 625.2.e.j.249.2 | 32 | |||
25.23 | odd | 20 | 625.2.e.k.124.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
625.2.a.g.1.6 | yes | 8 | 5.4 | even | 2 | ||
625.2.b.d.624.3 | 16 | 5.2 | odd | 4 | |||
625.2.b.d.624.14 | 16 | 5.3 | odd | 4 | |||
625.2.d.m.251.2 | 16 | 25.19 | even | 10 | |||
625.2.d.m.376.2 | 16 | 25.4 | even | 10 | |||
625.2.d.n.126.3 | 16 | 25.9 | even | 10 | |||
625.2.d.n.501.3 | 16 | 25.14 | even | 10 | |||
625.2.d.p.126.2 | 16 | 25.16 | even | 5 | |||
625.2.d.p.501.2 | 16 | 25.11 | even | 5 | |||
625.2.d.q.251.3 | 16 | 25.6 | even | 5 | |||
625.2.d.q.376.3 | 16 | 25.21 | even | 5 | |||
625.2.e.j.249.2 | 32 | 25.22 | odd | 20 | |||
625.2.e.j.249.7 | 32 | 25.3 | odd | 20 | |||
625.2.e.j.374.2 | 32 | 25.8 | odd | 20 | |||
625.2.e.j.374.7 | 32 | 25.17 | odd | 20 | |||
625.2.e.k.124.2 | 32 | 25.2 | odd | 20 | |||
625.2.e.k.124.7 | 32 | 25.23 | odd | 20 | |||
625.2.e.k.499.2 | 32 | 25.13 | odd | 20 | |||
625.2.e.k.499.7 | 32 | 25.12 | odd | 20 | |||
5625.2.a.s.1.3 | 8 | 15.14 | odd | 2 | |||
5625.2.a.be.1.6 | 8 | 3.2 | odd | 2 | |||
10000.2.a.be.1.8 | 8 | 20.19 | odd | 2 | |||
10000.2.a.bn.1.1 | 8 | 4.3 | odd | 2 |