Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2254,2,Mod(1,2254)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2254, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2254.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2254 = 2 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2254.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: | \(17.9982806156\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1957.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 322) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.06150\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2254.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.57641 | 1.48749 | 0.743747 | − | 0.668461i | \(-0.233047\pi\) | ||||
0.743747 | + | 0.668461i | \(0.233047\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.32664 | 0.593290 | 0.296645 | − | 0.954988i | \(-0.404132\pi\) | ||||
0.296645 | + | 0.954988i | \(0.404132\pi\) | |||||||
\(6\) | 2.57641 | 1.05182 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.63791 | 1.21264 | ||||||||
\(10\) | 1.32664 | 0.419520 | ||||||||
\(11\) | 2.09133 | 0.630560 | 0.315280 | − | 0.948999i | \(-0.397902\pi\) | ||||
0.315280 | + | 0.948999i | \(0.397902\pi\) | |||||||
\(12\) | 2.57641 | 0.743747 | ||||||||
\(13\) | 3.11142 | 0.862952 | 0.431476 | − | 0.902124i | \(-0.357993\pi\) | ||||
0.431476 | + | 0.902124i | \(0.357993\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41797 | 0.882516 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.94919 | −1.68543 | −0.842713 | − | 0.538363i | \(-0.819043\pi\) | ||||
−0.842713 | + | 0.538363i | \(0.819043\pi\) | |||||||
\(18\) | 3.63791 | 0.857464 | ||||||||
\(19\) | 7.76653 | 1.78176 | 0.890882 | − | 0.454235i | \(-0.150087\pi\) | ||||
0.890882 | + | 0.454235i | \(0.150087\pi\) | |||||||
\(20\) | 1.32664 | 0.296645 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.09133 | 0.445873 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.57641 | 0.525908 | ||||||||
\(25\) | −3.24003 | −0.648007 | ||||||||
\(26\) | 3.11142 | 0.610199 | ||||||||
\(27\) | 1.64353 | 0.316298 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.15845 | 0.215118 | 0.107559 | − | 0.994199i | \(-0.465697\pi\) | ||||
0.107559 | + | 0.994199i | \(0.465697\pi\) | |||||||
\(30\) | 3.41797 | 0.624033 | ||||||||
\(31\) | −8.71388 | −1.56506 | −0.782530 | − | 0.622613i | \(-0.786071\pi\) | ||||
−0.782530 | + | 0.622613i | \(0.786071\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.38814 | 0.937954 | ||||||||
\(34\) | −6.94919 | −1.19178 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.63791 | 0.606319 | ||||||||
\(37\) | −3.30944 | −0.544069 | −0.272034 | − | 0.962288i | \(-0.587696\pi\) | ||||
−0.272034 | + | 0.962288i | \(0.587696\pi\) | |||||||
\(38\) | 7.76653 | 1.25990 | ||||||||
\(39\) | 8.01631 | 1.28364 | ||||||||
\(40\) | 1.32664 | 0.209760 | ||||||||
\(41\) | −4.26425 | −0.665964 | −0.332982 | − | 0.942933i | \(-0.608055\pi\) | ||||
−0.332982 | + | 0.942933i | \(0.608055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.36716 | −1.27598 | −0.637990 | − | 0.770045i | \(-0.720234\pi\) | ||||
−0.637990 | + | 0.770045i | \(0.720234\pi\) | |||||||
\(44\) | 2.09133 | 0.315280 | ||||||||
\(45\) | 4.82619 | 0.719446 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −3.48130 | −0.507800 | −0.253900 | − | 0.967230i | \(-0.581713\pi\) | ||||
−0.253900 | + | 0.967230i | \(0.581713\pi\) | |||||||
\(48\) | 2.57641 | 0.371873 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.24003 | −0.458210 | ||||||||
\(51\) | −17.9040 | −2.50706 | ||||||||
\(52\) | 3.11142 | 0.431476 | ||||||||
\(53\) | 4.24003 | 0.582413 | 0.291207 | − | 0.956660i | \(-0.405943\pi\) | ||||
0.291207 | + | 0.956660i | \(0.405943\pi\) | |||||||
\(54\) | 1.64353 | 0.223656 | ||||||||
\(55\) | 2.77444 | 0.374105 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 20.0098 | 2.65036 | ||||||||
\(58\) | 1.15845 | 0.152111 | ||||||||
\(59\) | 9.18450 | 1.19572 | 0.597860 | − | 0.801601i | \(-0.296018\pi\) | ||||
0.597860 | + | 0.801601i | \(0.296018\pi\) | |||||||
\(60\) | 3.41797 | 0.441258 | ||||||||
\(61\) | 12.0387 | 1.54140 | 0.770698 | − | 0.637201i | \(-0.219908\pi\) | ||||
0.770698 | + | 0.637201i | \(0.219908\pi\) | |||||||
\(62\) | −8.71388 | −1.10666 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.12772 | 0.511981 | ||||||||
\(66\) | 5.38814 | 0.663234 | ||||||||
\(67\) | −7.26319 | −0.887340 | −0.443670 | − | 0.896190i | \(-0.646324\pi\) | ||||
−0.443670 | + | 0.896190i | \(0.646324\pi\) | |||||||
\(68\) | −6.94919 | −0.842713 | ||||||||
\(69\) | −2.57641 | −0.310164 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.41708 | −0.880245 | −0.440123 | − | 0.897938i | \(-0.645065\pi\) | ||||
−0.440123 | + | 0.897938i | \(0.645065\pi\) | |||||||
\(72\) | 3.63791 | 0.428732 | ||||||||
\(73\) | −4.36805 | −0.511241 | −0.255621 | − | 0.966777i | \(-0.582280\pi\) | ||||
−0.255621 | + | 0.966777i | \(0.582280\pi\) | |||||||
\(74\) | −3.30944 | −0.384715 | ||||||||
\(75\) | −8.34767 | −0.963906 | ||||||||
\(76\) | 7.76653 | 0.890882 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.01631 | 0.907668 | ||||||||
\(79\) | −0.797250 | −0.0896977 | −0.0448488 | − | 0.998994i | \(-0.514281\pi\) | ||||
−0.0448488 | + | 0.998994i | \(0.514281\pi\) | |||||||
\(80\) | 1.32664 | 0.148323 | ||||||||
\(81\) | −6.67932 | −0.742147 | ||||||||
\(82\) | −4.26425 | −0.470907 | ||||||||
\(83\) | 10.3746 | 1.13876 | 0.569381 | − | 0.822074i | \(-0.307183\pi\) | ||||
0.569381 | + | 0.822074i | \(0.307183\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.21906 | −0.999947 | ||||||||
\(86\) | −8.36716 | −0.902254 | ||||||||
\(87\) | 2.98464 | 0.319987 | ||||||||
\(88\) | 2.09133 | 0.222937 | ||||||||
\(89\) | 16.6426 | 1.76412 | 0.882058 | − | 0.471140i | \(-0.156158\pi\) | ||||
0.882058 | + | 0.471140i | \(0.156158\pi\) | |||||||
\(90\) | 4.82619 | 0.508725 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −22.4506 | −2.32802 | ||||||||
\(94\) | −3.48130 | −0.359069 | ||||||||
\(95\) | 10.3034 | 1.05710 | ||||||||
\(96\) | 2.57641 | 0.262954 | ||||||||
\(97\) | 6.65800 | 0.676018 | 0.338009 | − | 0.941143i | \(-0.390247\pi\) | ||||
0.338009 | + | 0.941143i | \(0.390247\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.60808 | 0.764641 | ||||||||
\(100\) | −3.24003 | −0.324003 | ||||||||
\(101\) | 9.15879 | 0.911334 | 0.455667 | − | 0.890150i | \(-0.349401\pi\) | ||||
0.455667 | + | 0.890150i | \(0.349401\pi\) | |||||||
\(102\) | −17.9040 | −1.77276 | ||||||||
\(103\) | 4.53211 | 0.446562 | 0.223281 | − | 0.974754i | \(-0.428323\pi\) | ||||
0.223281 | + | 0.974754i | \(0.428323\pi\) | |||||||
\(104\) | 3.11142 | 0.305100 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.24003 | 0.411828 | ||||||||
\(107\) | −12.3344 | −1.19241 | −0.596207 | − | 0.802830i | \(-0.703326\pi\) | ||||
−0.596207 | + | 0.802830i | \(0.703326\pi\) | |||||||
\(108\) | 1.64353 | 0.158149 | ||||||||
\(109\) | −1.09984 | −0.105346 | −0.0526728 | − | 0.998612i | \(-0.516774\pi\) | ||||
−0.0526728 | + | 0.998612i | \(0.516774\pi\) | |||||||
\(110\) | 2.77444 | 0.264532 | ||||||||
\(111\) | −8.52649 | −0.809299 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.44278 | 0.417942 | 0.208971 | − | 0.977922i | \(-0.432989\pi\) | ||||
0.208971 | + | 0.977922i | \(0.432989\pi\) | |||||||
\(114\) | 20.0098 | 1.87409 | ||||||||
\(115\) | −1.32664 | −0.123710 | ||||||||
\(116\) | 1.15845 | 0.107559 | ||||||||
\(117\) | 11.3191 | 1.04645 | ||||||||
\(118\) | 9.18450 | 0.845501 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.41797 | 0.312016 | ||||||||
\(121\) | −6.62633 | −0.602394 | ||||||||
\(122\) | 12.0387 | 1.08993 | ||||||||
\(123\) | −10.9865 | −0.990617 | ||||||||
\(124\) | −8.71388 | −0.782530 | ||||||||
\(125\) | −10.9315 | −0.977746 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.41201 | 0.214031 | 0.107015 | − | 0.994257i | \(-0.465871\pi\) | ||||
0.107015 | + | 0.994257i | \(0.465871\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −21.5573 | −1.89801 | ||||||||
\(130\) | 4.12772 | 0.362025 | ||||||||
\(131\) | 1.52342 | 0.133102 | 0.0665511 | − | 0.997783i | \(-0.478800\pi\) | ||||
0.0665511 | + | 0.997783i | \(0.478800\pi\) | |||||||
\(132\) | 5.38814 | 0.468977 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.26319 | −0.627444 | ||||||||
\(135\) | 2.18037 | 0.187656 | ||||||||
\(136\) | −6.94919 | −0.595888 | ||||||||
\(137\) | 9.62668 | 0.822463 | 0.411231 | − | 0.911531i | \(-0.365099\pi\) | ||||
0.411231 | + | 0.911531i | \(0.365099\pi\) | |||||||
\(138\) | −2.57641 | −0.219319 | ||||||||
\(139\) | 8.57676 | 0.727471 | 0.363736 | − | 0.931502i | \(-0.381501\pi\) | ||||
0.363736 | + | 0.931502i | \(0.381501\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.96928 | −0.755349 | ||||||||
\(142\) | −7.41708 | −0.622427 | ||||||||
\(143\) | 6.50701 | 0.544143 | ||||||||
\(144\) | 3.63791 | 0.303159 | ||||||||
\(145\) | 1.53684 | 0.127627 | ||||||||
\(146\) | −4.36805 | −0.361502 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.30944 | −0.272034 | ||||||||
\(149\) | 16.0214 | 1.31252 | 0.656261 | − | 0.754534i | \(-0.272137\pi\) | ||||
0.656261 | + | 0.754534i | \(0.272137\pi\) | |||||||
\(150\) | −8.34767 | −0.681584 | ||||||||
\(151\) | −13.9358 | −1.13408 | −0.567039 | − | 0.823691i | \(-0.691911\pi\) | ||||
−0.567039 | + | 0.823691i | \(0.691911\pi\) | |||||||
\(152\) | 7.76653 | 0.629949 | ||||||||
\(153\) | −25.2806 | −2.04381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.5602 | −0.928535 | ||||||||
\(156\) | 8.01631 | 0.641818 | ||||||||
\(157\) | −15.4227 | −1.23087 | −0.615433 | − | 0.788190i | \(-0.711019\pi\) | ||||
−0.615433 | + | 0.788190i | \(0.711019\pi\) | |||||||
\(158\) | −0.797250 | −0.0634258 | ||||||||
\(159\) | 10.9241 | 0.866336 | ||||||||
\(160\) | 1.32664 | 0.104880 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.67932 | −0.524777 | ||||||||
\(163\) | −8.61387 | −0.674690 | −0.337345 | − | 0.941381i | \(-0.609529\pi\) | ||||
−0.337345 | + | 0.941381i | \(0.609529\pi\) | |||||||
\(164\) | −4.26425 | −0.332982 | ||||||||
\(165\) | 7.14810 | 0.556479 | ||||||||
\(166\) | 10.3746 | 0.805226 | ||||||||
\(167\) | 11.9693 | 0.926211 | 0.463105 | − | 0.886303i | \(-0.346735\pi\) | ||||
0.463105 | + | 0.886303i | \(0.346735\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.31907 | −0.255313 | ||||||||
\(170\) | −9.21906 | −0.707069 | ||||||||
\(171\) | 28.2540 | 2.16063 | ||||||||
\(172\) | −8.36716 | −0.637990 | ||||||||
\(173\) | −19.8197 | −1.50686 | −0.753431 | − | 0.657527i | \(-0.771603\pi\) | ||||
−0.753431 | + | 0.657527i | \(0.771603\pi\) | |||||||
\(174\) | 2.98464 | 0.226265 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.09133 | 0.157640 | ||||||||
\(177\) | 23.6631 | 1.77863 | ||||||||
\(178\) | 16.6426 | 1.24742 | ||||||||
\(179\) | −16.4096 | −1.22651 | −0.613257 | − | 0.789884i | \(-0.710141\pi\) | ||||
−0.613257 | + | 0.789884i | \(0.710141\pi\) | |||||||
\(180\) | 4.82619 | 0.359723 | ||||||||
\(181\) | −11.2306 | −0.834766 | −0.417383 | − | 0.908731i | \(-0.637053\pi\) | ||||
−0.417383 | + | 0.908731i | \(0.637053\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.0167 | 2.29282 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −4.39043 | −0.322791 | ||||||||
\(186\) | −22.4506 | −1.64616 | ||||||||
\(187\) | −14.5331 | −1.06276 | ||||||||
\(188\) | −3.48130 | −0.253900 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.3034 | 0.747485 | ||||||||
\(191\) | 6.36805 | 0.460776 | 0.230388 | − | 0.973099i | \(-0.426000\pi\) | ||||
0.230388 | + | 0.973099i | \(0.426000\pi\) | |||||||
\(192\) | 2.57641 | 0.185937 | ||||||||
\(193\) | −14.0550 | −1.01170 | −0.505850 | − | 0.862621i | \(-0.668821\pi\) | ||||
−0.505850 | + | 0.862621i | \(0.668821\pi\) | |||||||
\(194\) | 6.65800 | 0.478017 | ||||||||
\(195\) | 10.6347 | 0.761569 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.95570 | −0.495573 | −0.247786 | − | 0.968815i | \(-0.579703\pi\) | ||||
−0.247786 | + | 0.968815i | \(0.579703\pi\) | |||||||
\(198\) | 7.60808 | 0.540683 | ||||||||
\(199\) | 21.0897 | 1.49501 | 0.747506 | − | 0.664255i | \(-0.231251\pi\) | ||||
0.747506 | + | 0.664255i | \(0.231251\pi\) | |||||||
\(200\) | −3.24003 | −0.229105 | ||||||||
\(201\) | −18.7130 | −1.31991 | ||||||||
\(202\) | 9.15879 | 0.644410 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −17.9040 | −1.25353 | ||||||||
\(205\) | −5.65711 | −0.395110 | ||||||||
\(206\) | 4.53211 | 0.315767 | ||||||||
\(207\) | −3.63791 | −0.252852 | ||||||||
\(208\) | 3.11142 | 0.215738 | ||||||||
\(209\) | 16.2424 | 1.12351 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.5036 | 1.82458 | 0.912290 | − | 0.409544i | \(-0.134312\pi\) | ||||
0.912290 | + | 0.409544i | \(0.134312\pi\) | |||||||
\(212\) | 4.24003 | 0.291207 | ||||||||
\(213\) | −19.1095 | −1.30936 | ||||||||
\(214\) | −12.3344 | −0.843165 | ||||||||
\(215\) | −11.1002 | −0.757026 | ||||||||
\(216\) | 1.64353 | 0.111828 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.09984 | −0.0744906 | ||||||||
\(219\) | −11.2539 | −0.760468 | ||||||||
\(220\) | 2.77444 | 0.187053 | ||||||||
\(221\) | −21.6218 | −1.45444 | ||||||||
\(222\) | −8.52649 | −0.572261 | ||||||||
\(223\) | −9.80109 | −0.656329 | −0.328165 | − | 0.944621i | \(-0.606430\pi\) | ||||
−0.328165 | + | 0.944621i | \(0.606430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.7870 | −0.785797 | ||||||||
\(226\) | 4.44278 | 0.295530 | ||||||||
\(227\) | −28.4962 | −1.89136 | −0.945679 | − | 0.325103i | \(-0.894601\pi\) | ||||
−0.945679 | + | 0.325103i | \(0.894601\pi\) | |||||||
\(228\) | 20.0098 | 1.32518 | ||||||||
\(229\) | −25.1914 | −1.66469 | −0.832347 | − | 0.554254i | \(-0.813004\pi\) | ||||
−0.832347 | + | 0.554254i | \(0.813004\pi\) | |||||||
\(230\) | −1.32664 | −0.0874759 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.15845 | 0.0760557 | ||||||||
\(233\) | −13.1625 | −0.862302 | −0.431151 | − | 0.902280i | \(-0.641892\pi\) | ||||
−0.431151 | + | 0.902280i | \(0.641892\pi\) | |||||||
\(234\) | 11.3191 | 0.739951 | ||||||||
\(235\) | −4.61843 | −0.301273 | ||||||||
\(236\) | 9.18450 | 0.597860 | ||||||||
\(237\) | −2.05405 | −0.133425 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.78283 | −0.568114 | −0.284057 | − | 0.958807i | \(-0.591681\pi\) | ||||
−0.284057 | + | 0.958807i | \(0.591681\pi\) | |||||||
\(240\) | 3.41797 | 0.220629 | ||||||||
\(241\) | 1.52755 | 0.0983983 | 0.0491992 | − | 0.998789i | \(-0.484333\pi\) | ||||
0.0491992 | + | 0.998789i | \(0.484333\pi\) | |||||||
\(242\) | −6.62633 | −0.425957 | ||||||||
\(243\) | −22.1393 | −1.42024 | ||||||||
\(244\) | 12.0387 | 0.770698 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.9865 | −0.700472 | ||||||||
\(247\) | 24.1649 | 1.53758 | ||||||||
\(248\) | −8.71388 | −0.553332 | ||||||||
\(249\) | 26.7293 | 1.69390 | ||||||||
\(250\) | −10.9315 | −0.691371 | ||||||||
\(251\) | 1.04230 | 0.0657895 | 0.0328947 | − | 0.999459i | \(-0.489527\pi\) | ||||
0.0328947 | + | 0.999459i | \(0.489527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.09133 | −0.131481 | ||||||||
\(254\) | 2.41201 | 0.151343 | ||||||||
\(255\) | −23.7521 | −1.48741 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.77409 | −0.422556 | −0.211278 | − | 0.977426i | \(-0.567763\pi\) | ||||
−0.211278 | + | 0.977426i | \(0.567763\pi\) | |||||||
\(258\) | −21.5573 | −1.34210 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.12772 | 0.255991 | ||||||||
\(261\) | 4.21433 | 0.260860 | ||||||||
\(262\) | 1.52342 | 0.0941175 | ||||||||
\(263\) | 0.457086 | 0.0281852 | 0.0140926 | − | 0.999901i | \(-0.495514\pi\) | ||||
0.0140926 | + | 0.999901i | \(0.495514\pi\) | |||||||
\(264\) | 5.38814 | 0.331617 | ||||||||
\(265\) | 5.62499 | 0.345540 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 42.8783 | 2.62411 | ||||||||
\(268\) | −7.26319 | −0.443670 | ||||||||
\(269\) | 18.5535 | 1.13123 | 0.565613 | − | 0.824671i | \(-0.308640\pi\) | ||||
0.565613 | + | 0.824671i | \(0.308640\pi\) | |||||||
\(270\) | 2.18037 | 0.132693 | ||||||||
\(271\) | 18.2909 | 1.11109 | 0.555546 | − | 0.831485i | \(-0.312509\pi\) | ||||
0.555546 | + | 0.831485i | \(0.312509\pi\) | |||||||
\(272\) | −6.94919 | −0.421357 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.62668 | 0.581569 | ||||||||
\(275\) | −6.77598 | −0.408607 | ||||||||
\(276\) | −2.57641 | −0.155082 | ||||||||
\(277\) | 20.1567 | 1.21110 | 0.605548 | − | 0.795809i | \(-0.292954\pi\) | ||||
0.605548 | + | 0.795809i | \(0.292954\pi\) | |||||||
\(278\) | 8.57676 | 0.514400 | ||||||||
\(279\) | −31.7004 | −1.89785 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.27365 | −0.433909 | −0.216955 | − | 0.976182i | \(-0.569612\pi\) | ||||
−0.216955 | + | 0.976182i | \(0.569612\pi\) | |||||||
\(282\) | −8.96928 | −0.534113 | ||||||||
\(283\) | −2.76240 | −0.164208 | −0.0821038 | − | 0.996624i | \(-0.526164\pi\) | ||||
−0.0821038 | + | 0.996624i | \(0.526164\pi\) | |||||||
\(284\) | −7.41708 | −0.440123 | ||||||||
\(285\) | 26.5457 | 1.57243 | ||||||||
\(286\) | 6.50701 | 0.384767 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.63791 | 0.214366 | ||||||||
\(289\) | 31.2912 | 1.84066 | ||||||||
\(290\) | 1.53684 | 0.0902463 | ||||||||
\(291\) | 17.1538 | 1.00557 | ||||||||
\(292\) | −4.36805 | −0.255621 | ||||||||
\(293\) | 25.3756 | 1.48246 | 0.741228 | − | 0.671253i | \(-0.234244\pi\) | ||||
0.741228 | + | 0.671253i | \(0.234244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1845 | 0.709409 | ||||||||
\(296\) | −3.30944 | −0.192357 | ||||||||
\(297\) | 3.43717 | 0.199445 | ||||||||
\(298\) | 16.0214 | 0.928094 | ||||||||
\(299\) | −3.11142 | −0.179938 | ||||||||
\(300\) | −8.34767 | −0.481953 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.9358 | −0.801914 | ||||||||
\(303\) | 23.5968 | 1.35560 | ||||||||
\(304\) | 7.76653 | 0.445441 | ||||||||
\(305\) | 15.9710 | 0.914495 | ||||||||
\(306\) | −25.2806 | −1.44519 | ||||||||
\(307\) | −29.2469 | −1.66921 | −0.834606 | − | 0.550848i | \(-0.814304\pi\) | ||||
−0.834606 | + | 0.550848i | \(0.814304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6766 | 0.664259 | ||||||||
\(310\) | −11.5602 | −0.656573 | ||||||||
\(311\) | 27.2828 | 1.54707 | 0.773534 | − | 0.633755i | \(-0.218487\pi\) | ||||
0.773534 | + | 0.633755i | \(0.218487\pi\) | |||||||
\(312\) | 8.01631 | 0.453834 | ||||||||
\(313\) | 2.57676 | 0.145647 | 0.0728236 | − | 0.997345i | \(-0.476799\pi\) | ||||
0.0728236 | + | 0.997345i | \(0.476799\pi\) | |||||||
\(314\) | −15.4227 | −0.870353 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.797250 | −0.0448488 | ||||||||
\(317\) | −12.5065 | −0.702433 | −0.351216 | − | 0.936294i | \(-0.614232\pi\) | ||||
−0.351216 | + | 0.936294i | \(0.614232\pi\) | |||||||
\(318\) | 10.9241 | 0.612592 | ||||||||
\(319\) | 2.42270 | 0.135645 | ||||||||
\(320\) | 1.32664 | 0.0741613 | ||||||||
\(321\) | −31.7786 | −1.77371 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −53.9711 | −3.00303 | ||||||||
\(324\) | −6.67932 | −0.371074 | ||||||||
\(325\) | −10.0811 | −0.559199 | ||||||||
\(326\) | −8.61387 | −0.477078 | ||||||||
\(327\) | −2.83364 | −0.156701 | ||||||||
\(328\) | −4.26425 | −0.235454 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.14810 | 0.393490 | ||||||||
\(331\) | 2.73397 | 0.150273 | 0.0751363 | − | 0.997173i | \(-0.476061\pi\) | ||||
0.0751363 | + | 0.997173i | \(0.476061\pi\) | |||||||
\(332\) | 10.3746 | 0.569381 | ||||||||
\(333\) | −12.0395 | −0.659759 | ||||||||
\(334\) | 11.9693 | 0.654930 | ||||||||
\(335\) | −9.63562 | −0.526450 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4355 | 0.677405 | 0.338703 | − | 0.940893i | \(-0.390012\pi\) | ||||
0.338703 | + | 0.940893i | \(0.390012\pi\) | |||||||
\(338\) | −3.31907 | −0.180534 | ||||||||
\(339\) | 11.4465 | 0.621686 | ||||||||
\(340\) | −9.21906 | −0.499973 | ||||||||
\(341\) | −18.2236 | −0.986864 | ||||||||
\(342\) | 28.2540 | 1.52780 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.36716 | −0.451127 | ||||||||
\(345\) | −3.41797 | −0.184017 | ||||||||
\(346\) | −19.8197 | −1.06551 | ||||||||
\(347\) | 2.20748 | 0.118504 | 0.0592518 | − | 0.998243i | \(-0.481129\pi\) | ||||
0.0592518 | + | 0.998243i | \(0.481129\pi\) | |||||||
\(348\) | 2.98464 | 0.159993 | ||||||||
\(349\) | 10.7710 | 0.576558 | 0.288279 | − | 0.957546i | \(-0.406917\pi\) | ||||
0.288279 | + | 0.957546i | \(0.406917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.11371 | 0.272950 | ||||||||
\(352\) | 2.09133 | 0.111468 | ||||||||
\(353\) | −13.8970 | −0.739661 | −0.369831 | − | 0.929099i | \(-0.620584\pi\) | ||||
−0.369831 | + | 0.929099i | \(0.620584\pi\) | |||||||
\(354\) | 23.6631 | 1.25768 | ||||||||
\(355\) | −9.83977 | −0.522241 | ||||||||
\(356\) | 16.6426 | 0.882058 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.4096 | −0.867276 | ||||||||
\(359\) | −19.4670 | −1.02743 | −0.513714 | − | 0.857961i | \(-0.671731\pi\) | ||||
−0.513714 | + | 0.857961i | \(0.671731\pi\) | |||||||
\(360\) | 4.82619 | 0.254363 | ||||||||
\(361\) | 41.3190 | 2.17468 | ||||||||
\(362\) | −11.2306 | −0.590269 | ||||||||
\(363\) | −17.0722 | −0.896057 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.79482 | −0.303315 | ||||||||
\(366\) | 31.0167 | 1.62127 | ||||||||
\(367\) | 17.1874 | 0.897174 | 0.448587 | − | 0.893739i | \(-0.351927\pi\) | ||||
0.448587 | + | 0.893739i | \(0.351927\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −15.5130 | −0.807573 | ||||||||
\(370\) | −4.39043 | −0.228248 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −22.4506 | −1.16401 | ||||||||
\(373\) | −9.43657 | −0.488607 | −0.244303 | − | 0.969699i | \(-0.578559\pi\) | ||||
−0.244303 | + | 0.969699i | \(0.578559\pi\) | |||||||
\(374\) | −14.5331 | −0.751486 | ||||||||
\(375\) | −28.1642 | −1.45439 | ||||||||
\(376\) | −3.48130 | −0.179534 | ||||||||
\(377\) | 3.60441 | 0.185637 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.99131 | 0.359120 | 0.179560 | − | 0.983747i | \(-0.442533\pi\) | ||||
0.179560 | + | 0.983747i | \(0.442533\pi\) | |||||||
\(380\) | 10.3034 | 0.528552 | ||||||||
\(381\) | 6.21433 | 0.318370 | ||||||||
\(382\) | 6.36805 | 0.325818 | ||||||||
\(383\) | 27.5410 | 1.40728 | 0.703640 | − | 0.710556i | \(-0.251557\pi\) | ||||
0.703640 | + | 0.710556i | \(0.251557\pi\) | |||||||
\(384\) | 2.57641 | 0.131477 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0550 | −0.715380 | ||||||||
\(387\) | −30.4390 | −1.54730 | ||||||||
\(388\) | 6.65800 | 0.338009 | ||||||||
\(389\) | 6.70443 | 0.339928 | 0.169964 | − | 0.985450i | \(-0.445635\pi\) | ||||
0.169964 | + | 0.985450i | \(0.445635\pi\) | |||||||
\(390\) | 10.6347 | 0.538511 | ||||||||
\(391\) | 6.94919 | 0.351436 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.92497 | 0.197989 | ||||||||
\(394\) | −6.95570 | −0.350423 | ||||||||
\(395\) | −1.05766 | −0.0532168 | ||||||||
\(396\) | 7.60808 | 0.382320 | ||||||||
\(397\) | 22.6052 | 1.13452 | 0.567262 | − | 0.823537i | \(-0.308003\pi\) | ||||
0.567262 | + | 0.823537i | \(0.308003\pi\) | |||||||
\(398\) | 21.0897 | 1.05713 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.24003 | −0.162002 | ||||||||
\(401\) | −9.70827 | −0.484808 | −0.242404 | − | 0.970175i | \(-0.577936\pi\) | ||||
−0.242404 | + | 0.970175i | \(0.577936\pi\) | |||||||
\(402\) | −18.7130 | −0.933319 | ||||||||
\(403\) | −27.1125 | −1.35057 | ||||||||
\(404\) | 9.15879 | 0.455667 | ||||||||
\(405\) | −8.86104 | −0.440309 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.92114 | −0.343068 | ||||||||
\(408\) | −17.9040 | −0.886380 | ||||||||
\(409\) | −36.3360 | −1.79670 | −0.898350 | − | 0.439281i | \(-0.855233\pi\) | ||||
−0.898350 | + | 0.439281i | \(0.855233\pi\) | |||||||
\(410\) | −5.65711 | −0.279385 | ||||||||
\(411\) | 24.8023 | 1.22341 | ||||||||
\(412\) | 4.53211 | 0.223281 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.63791 | −0.178794 | ||||||||
\(415\) | 13.7633 | 0.675616 | ||||||||
\(416\) | 3.11142 | 0.152550 | ||||||||
\(417\) | 22.0973 | 1.08211 | ||||||||
\(418\) | 16.2424 | 0.794441 | ||||||||
\(419\) | 9.98642 | 0.487868 | 0.243934 | − | 0.969792i | \(-0.421562\pi\) | ||||
0.243934 | + | 0.969792i | \(0.421562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.1053 | 0.687448 | 0.343724 | − | 0.939071i | \(-0.388312\pi\) | ||||
0.343724 | + | 0.939071i | \(0.388312\pi\) | |||||||
\(422\) | 26.5036 | 1.29017 | ||||||||
\(423\) | −12.6647 | −0.615778 | ||||||||
\(424\) | 4.24003 | 0.205914 | ||||||||
\(425\) | 22.5156 | 1.09217 | ||||||||
\(426\) | −19.1095 | −0.925857 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.3344 | −0.596207 | ||||||||
\(429\) | 16.7647 | 0.809410 | ||||||||
\(430\) | −11.1002 | −0.535298 | ||||||||
\(431\) | −3.54369 | −0.170694 | −0.0853468 | − | 0.996351i | \(-0.527200\pi\) | ||||
−0.0853468 | + | 0.996351i | \(0.527200\pi\) | |||||||
\(432\) | 1.64353 | 0.0790744 | ||||||||
\(433\) | −16.2680 | −0.781792 | −0.390896 | − | 0.920435i | \(-0.627835\pi\) | ||||
−0.390896 | + | 0.920435i | \(0.627835\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.95953 | 0.189845 | ||||||||
\(436\) | −1.09984 | −0.0526728 | ||||||||
\(437\) | −7.76653 | −0.371523 | ||||||||
\(438\) | −11.2539 | −0.537732 | ||||||||
\(439\) | 1.17003 | 0.0558423 | 0.0279211 | − | 0.999610i | \(-0.491111\pi\) | ||||
0.0279211 | + | 0.999610i | \(0.491111\pi\) | |||||||
\(440\) | 2.77444 | 0.132266 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.6218 | −1.02845 | ||||||||
\(443\) | 39.0073 | 1.85329 | 0.926647 | − | 0.375934i | \(-0.122678\pi\) | ||||
0.926647 | + | 0.375934i | \(0.122678\pi\) | |||||||
\(444\) | −8.52649 | −0.404650 | ||||||||
\(445\) | 22.0787 | 1.04663 | ||||||||
\(446\) | −9.80109 | −0.464095 | ||||||||
\(447\) | 41.2777 | 1.95237 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.1714 | 1.51826 | 0.759130 | − | 0.650939i | \(-0.225624\pi\) | ||||
0.759130 | + | 0.650939i | \(0.225624\pi\) | |||||||
\(450\) | −11.7870 | −0.555643 | ||||||||
\(451\) | −8.91796 | −0.419930 | ||||||||
\(452\) | 4.44278 | 0.208971 | ||||||||
\(453\) | −35.9043 | −1.68693 | ||||||||
\(454\) | −28.4962 | −1.33739 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.0098 | 0.937045 | ||||||||
\(457\) | −34.3548 | −1.60705 | −0.803524 | − | 0.595273i | \(-0.797044\pi\) | ||||
−0.803524 | + | 0.595273i | \(0.797044\pi\) | |||||||
\(458\) | −25.1914 | −1.17712 | ||||||||
\(459\) | −11.4212 | −0.533096 | ||||||||
\(460\) | −1.32664 | −0.0618548 | ||||||||
\(461\) | 10.5155 | 0.489756 | 0.244878 | − | 0.969554i | \(-0.421252\pi\) | ||||
0.244878 | + | 0.969554i | \(0.421252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.9943 | −0.929213 | −0.464606 | − | 0.885517i | \(-0.653804\pi\) | ||||
−0.464606 | + | 0.885517i | \(0.653804\pi\) | |||||||
\(464\) | 1.15845 | 0.0537795 | ||||||||
\(465\) | −29.7838 | −1.38119 | ||||||||
\(466\) | −13.1625 | −0.609739 | ||||||||
\(467\) | −27.4643 | −1.27090 | −0.635448 | − | 0.772144i | \(-0.719184\pi\) | ||||
−0.635448 | + | 0.772144i | \(0.719184\pi\) | |||||||
\(468\) | 11.3191 | 0.523224 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.61843 | −0.213032 | ||||||||
\(471\) | −39.7353 | −1.83090 | ||||||||
\(472\) | 9.18450 | 0.422751 | ||||||||
\(473\) | −17.4985 | −0.804582 | ||||||||
\(474\) | −2.05405 | −0.0943455 | ||||||||
\(475\) | −25.1638 | −1.15459 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.4249 | 0.706257 | ||||||||
\(478\) | −8.78283 | −0.401717 | ||||||||
\(479\) | −8.44551 | −0.385885 | −0.192943 | − | 0.981210i | \(-0.561803\pi\) | ||||
−0.192943 | + | 0.981210i | \(0.561803\pi\) | |||||||
\(480\) | 3.41797 | 0.156008 | ||||||||
\(481\) | −10.2971 | −0.469505 | ||||||||
\(482\) | 1.52755 | 0.0695781 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.62633 | −0.301197 | ||||||||
\(485\) | 8.83275 | 0.401075 | ||||||||
\(486\) | −22.1393 | −1.00426 | ||||||||
\(487\) | 33.2791 | 1.50802 | 0.754009 | − | 0.656864i | \(-0.228117\pi\) | ||||
0.754009 | + | 0.656864i | \(0.228117\pi\) | |||||||
\(488\) | 12.0387 | 0.544966 | ||||||||
\(489\) | −22.1929 | −1.00360 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8532 | 0.715444 | 0.357722 | − | 0.933828i | \(-0.383553\pi\) | ||||
0.357722 | + | 0.933828i | \(0.383553\pi\) | |||||||
\(492\) | −10.9865 | −0.495308 | ||||||||
\(493\) | −8.05027 | −0.362566 | ||||||||
\(494\) | 24.1649 | 1.08723 | ||||||||
\(495\) | 10.0932 | 0.453654 | ||||||||
\(496\) | −8.71388 | −0.391265 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 26.7293 | 1.19777 | ||||||||
\(499\) | −19.3323 | −0.865433 | −0.432717 | − | 0.901530i | \(-0.642445\pi\) | ||||
−0.432717 | + | 0.901530i | \(0.642445\pi\) | |||||||
\(500\) | −10.9315 | −0.488873 | ||||||||
\(501\) | 30.8378 | 1.37773 | ||||||||
\(502\) | 1.04230 | 0.0465202 | ||||||||
\(503\) | 40.9220 | 1.82462 | 0.912310 | − | 0.409500i | \(-0.134297\pi\) | ||||
0.912310 | + | 0.409500i | \(0.134297\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1504 | 0.540686 | ||||||||
\(506\) | −2.09133 | −0.0929710 | ||||||||
\(507\) | −8.55131 | −0.379777 | ||||||||
\(508\) | 2.41201 | 0.107015 | ||||||||
\(509\) | 0.521823 | 0.0231294 | 0.0115647 | − | 0.999933i | \(-0.496319\pi\) | ||||
0.0115647 | + | 0.999933i | \(0.496319\pi\) | |||||||
\(510\) | −23.7521 | −1.05176 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 12.7645 | 0.563568 | ||||||||
\(514\) | −6.77409 | −0.298792 | ||||||||
\(515\) | 6.01247 | 0.264941 | ||||||||
\(516\) | −21.5573 | −0.949006 | ||||||||
\(517\) | −7.28055 | −0.320198 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −51.0637 | −2.24145 | ||||||||
\(520\) | 4.12772 | 0.181013 | ||||||||
\(521\) | 12.2977 | 0.538774 | 0.269387 | − | 0.963032i | \(-0.413179\pi\) | ||||
0.269387 | + | 0.963032i | \(0.413179\pi\) | |||||||
\(522\) | 4.21433 | 0.184456 | ||||||||
\(523\) | 31.3781 | 1.37207 | 0.686034 | − | 0.727569i | \(-0.259350\pi\) | ||||
0.686034 | + | 0.727569i | \(0.259350\pi\) | |||||||
\(524\) | 1.52342 | 0.0665511 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.457086 | 0.0199299 | ||||||||
\(527\) | 60.5544 | 2.63779 | ||||||||
\(528\) | 5.38814 | 0.234489 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 5.62499 | 0.244334 | ||||||||
\(531\) | 33.4124 | 1.44997 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.2679 | −0.574695 | ||||||||
\(534\) | 42.8783 | 1.85553 | ||||||||
\(535\) | −16.3633 | −0.707448 | ||||||||
\(536\) | −7.26319 | −0.313722 | ||||||||
\(537\) | −42.2780 | −1.82443 | ||||||||
\(538\) | 18.5535 | 0.799898 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.18037 | 0.0938281 | ||||||||
\(541\) | 0.751971 | 0.0323298 | 0.0161649 | − | 0.999869i | \(-0.494854\pi\) | ||||
0.0161649 | + | 0.999869i | \(0.494854\pi\) | |||||||
\(542\) | 18.2909 | 0.785661 | ||||||||
\(543\) | −28.9348 | −1.24171 | ||||||||
\(544\) | −6.94919 | −0.297944 | ||||||||
\(545\) | −1.45909 | −0.0625005 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.3113 | −1.16775 | −0.583874 | − | 0.811844i | \(-0.698464\pi\) | ||||
−0.583874 | + | 0.811844i | \(0.698464\pi\) | |||||||
\(548\) | 9.62668 | 0.411231 | ||||||||
\(549\) | 43.7957 | 1.86916 | ||||||||
\(550\) | −6.77598 | −0.288929 | ||||||||
\(551\) | 8.99711 | 0.383290 | ||||||||
\(552\) | −2.57641 | −0.109660 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.1567 | 0.856375 | ||||||||
\(555\) | −11.3116 | −0.480149 | ||||||||
\(556\) | 8.57676 | 0.363736 | ||||||||
\(557\) | 29.2485 | 1.23930 | 0.619650 | − | 0.784878i | \(-0.287274\pi\) | ||||
0.619650 | + | 0.784878i | \(0.287274\pi\) | |||||||
\(558\) | −31.7004 | −1.34198 | ||||||||
\(559\) | −26.0337 | −1.10111 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.4432 | −1.58085 | ||||||||
\(562\) | −7.27365 | −0.306820 | ||||||||
\(563\) | 0.514516 | 0.0216843 | 0.0108421 | − | 0.999941i | \(-0.496549\pi\) | ||||
0.0108421 | + | 0.999941i | \(0.496549\pi\) | |||||||
\(564\) | −8.96928 | −0.377675 | ||||||||
\(565\) | 5.89396 | 0.247961 | ||||||||
\(566\) | −2.76240 | −0.116112 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.41708 | −0.311214 | ||||||||
\(569\) | 33.8004 | 1.41699 | 0.708493 | − | 0.705718i | \(-0.249375\pi\) | ||||
0.708493 | + | 0.705718i | \(0.249375\pi\) | |||||||
\(570\) | 26.5457 | 1.11188 | ||||||||
\(571\) | −13.3829 | −0.560055 | −0.280028 | − | 0.959992i | \(-0.590344\pi\) | ||||
−0.280028 | + | 0.959992i | \(0.590344\pi\) | |||||||
\(572\) | 6.50701 | 0.272072 | ||||||||
\(573\) | 16.4067 | 0.685401 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.24003 | 0.135119 | ||||||||
\(576\) | 3.63791 | 0.151580 | ||||||||
\(577\) | −36.6482 | −1.52568 | −0.762842 | − | 0.646585i | \(-0.776196\pi\) | ||||
−0.762842 | + | 0.646585i | \(0.776196\pi\) | |||||||
\(578\) | 31.2912 | 1.30154 | ||||||||
\(579\) | −36.2115 | −1.50490 | ||||||||
\(580\) | 1.53684 | 0.0638137 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.1538 | 0.711047 | ||||||||
\(583\) | 8.86731 | 0.367247 | ||||||||
\(584\) | −4.36805 | −0.180751 | ||||||||
\(585\) | 15.0163 | 0.620848 | ||||||||
\(586\) | 25.3756 | 1.04825 | ||||||||
\(587\) | −10.8300 | −0.447003 | −0.223502 | − | 0.974704i | \(-0.571749\pi\) | ||||
−0.223502 | + | 0.974704i | \(0.571749\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −67.6766 | −2.78857 | ||||||||
\(590\) | 12.1845 | 0.501628 | ||||||||
\(591\) | −17.9208 | −0.737162 | ||||||||
\(592\) | −3.30944 | −0.136017 | ||||||||
\(593\) | −7.80794 | −0.320634 | −0.160317 | − | 0.987066i | \(-0.551252\pi\) | ||||
−0.160317 | + | 0.987066i | \(0.551252\pi\) | |||||||
\(594\) | 3.43717 | 0.141029 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.0214 | 0.656261 | ||||||||
\(597\) | 54.3359 | 2.22382 | ||||||||
\(598\) | −3.11142 | −0.127235 | ||||||||
\(599\) | −34.7398 | −1.41943 | −0.709715 | − | 0.704489i | \(-0.751176\pi\) | ||||
−0.709715 | + | 0.704489i | \(0.751176\pi\) | |||||||
\(600\) | −8.34767 | −0.340792 | ||||||||
\(601\) | −33.4939 | −1.36625 | −0.683123 | − | 0.730303i | \(-0.739379\pi\) | ||||
−0.683123 | + | 0.730303i | \(0.739379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.4229 | −1.07602 | ||||||||
\(604\) | −13.9358 | −0.567039 | ||||||||
\(605\) | −8.79074 | −0.357395 | ||||||||
\(606\) | 23.5968 | 0.958556 | ||||||||
\(607\) | −33.0399 | −1.34105 | −0.670523 | − | 0.741888i | \(-0.733930\pi\) | ||||
−0.670523 | + | 0.741888i | \(0.733930\pi\) | |||||||
\(608\) | 7.76653 | 0.314974 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.9710 | 0.646646 | ||||||||
\(611\) | −10.8318 | −0.438207 | ||||||||
\(612\) | −25.2806 | −1.02191 | ||||||||
\(613\) | 0.344610 | 0.0139187 | 0.00695934 | − | 0.999976i | \(-0.497785\pi\) | ||||
0.00695934 | + | 0.999976i | \(0.497785\pi\) | |||||||
\(614\) | −29.2469 | −1.18031 | ||||||||
\(615\) | −14.5751 | −0.587723 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.8997 | 0.760872 | 0.380436 | − | 0.924807i | \(-0.375774\pi\) | ||||
0.380436 | + | 0.924807i | \(0.375774\pi\) | |||||||
\(618\) | 11.6766 | 0.469702 | ||||||||
\(619\) | 22.4272 | 0.901424 | 0.450712 | − | 0.892669i | \(-0.351170\pi\) | ||||
0.450712 | + | 0.892669i | \(0.351170\pi\) | |||||||
\(620\) | −11.5602 | −0.464267 | ||||||||
\(621\) | −1.64353 | −0.0659526 | ||||||||
\(622\) | 27.2828 | 1.09394 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.01631 | 0.320909 | ||||||||
\(625\) | 1.69798 | 0.0679193 | ||||||||
\(626\) | 2.57676 | 0.102988 | ||||||||
\(627\) | 41.8471 | 1.67121 | ||||||||
\(628\) | −15.4227 | −0.615433 | ||||||||
\(629\) | 22.9979 | 0.916988 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.9749 | 1.83023 | 0.915117 | − | 0.403189i | \(-0.132098\pi\) | ||||
0.915117 | + | 0.403189i | \(0.132098\pi\) | |||||||
\(632\) | −0.797250 | −0.0317129 | ||||||||
\(633\) | 68.2842 | 2.71405 | ||||||||
\(634\) | −12.5065 | −0.496695 | ||||||||
\(635\) | 3.19986 | 0.126982 | ||||||||
\(636\) | 10.9241 | 0.433168 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.42270 | 0.0959154 | ||||||||
\(639\) | −26.9827 | −1.06742 | ||||||||
\(640\) | 1.32664 | 0.0524399 | ||||||||
\(641\) | −11.8457 | −0.467876 | −0.233938 | − | 0.972251i | \(-0.575161\pi\) | ||||
−0.233938 | + | 0.972251i | \(0.575161\pi\) | |||||||
\(642\) | −31.7786 | −1.25420 | ||||||||
\(643\) | 40.7199 | 1.60584 | 0.802918 | − | 0.596089i | \(-0.203280\pi\) | ||||
0.802918 | + | 0.596089i | \(0.203280\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −28.5987 | −1.12607 | ||||||||
\(646\) | −53.9711 | −2.12346 | ||||||||
\(647\) | 0.721680 | 0.0283722 | 0.0141861 | − | 0.999899i | \(-0.495484\pi\) | ||||
0.0141861 | + | 0.999899i | \(0.495484\pi\) | |||||||
\(648\) | −6.67932 | −0.262389 | ||||||||
\(649\) | 19.2078 | 0.753973 | ||||||||
\(650\) | −10.0811 | −0.395413 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.61387 | −0.337345 | ||||||||
\(653\) | −0.746263 | −0.0292035 | −0.0146018 | − | 0.999893i | \(-0.504648\pi\) | ||||
−0.0146018 | + | 0.999893i | \(0.504648\pi\) | |||||||
\(654\) | −2.83364 | −0.110804 | ||||||||
\(655\) | 2.02103 | 0.0789683 | ||||||||
\(656\) | −4.26425 | −0.166491 | ||||||||
\(657\) | −15.8906 | −0.619951 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.85325 | 0.266965 | 0.133482 | − | 0.991051i | \(-0.457384\pi\) | ||||
0.133482 | + | 0.991051i | \(0.457384\pi\) | |||||||
\(660\) | 7.14810 | 0.278240 | ||||||||
\(661\) | 33.7836 | 1.31403 | 0.657016 | − | 0.753877i | \(-0.271819\pi\) | ||||
0.657016 | + | 0.753877i | \(0.271819\pi\) | |||||||
\(662\) | 2.73397 | 0.106259 | ||||||||
\(663\) | −55.7068 | −2.16347 | ||||||||
\(664\) | 10.3746 | 0.402613 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.0395 | −0.466520 | ||||||||
\(667\) | −1.15845 | −0.0448552 | ||||||||
\(668\) | 11.9693 | 0.463105 | ||||||||
\(669\) | −25.2517 | −0.976286 | ||||||||
\(670\) | −9.63562 | −0.372257 | ||||||||
\(671\) | 25.1769 | 0.971943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.6054 | 1.25684 | 0.628422 | − | 0.777873i | \(-0.283701\pi\) | ||||
0.628422 | + | 0.777873i | \(0.283701\pi\) | |||||||
\(674\) | 12.4355 | 0.478998 | ||||||||
\(675\) | −5.32509 | −0.204963 | ||||||||
\(676\) | −3.31907 | −0.127657 | ||||||||
\(677\) | 25.1527 | 0.966697 | 0.483349 | − | 0.875428i | \(-0.339420\pi\) | ||||
0.483349 | + | 0.875428i | \(0.339420\pi\) | |||||||
\(678\) | 11.4465 | 0.439598 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.21906 | −0.353535 | ||||||||
\(681\) | −73.4180 | −2.81338 | ||||||||
\(682\) | −18.2236 | −0.697818 | ||||||||
\(683\) | −33.7015 | −1.28955 | −0.644776 | − | 0.764372i | \(-0.723049\pi\) | ||||
−0.644776 | + | 0.764372i | \(0.723049\pi\) | |||||||
\(684\) | 28.2540 | 1.08032 | ||||||||
\(685\) | 12.7711 | 0.487959 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −64.9035 | −2.47622 | ||||||||
\(688\) | −8.36716 | −0.318995 | ||||||||
\(689\) | 13.1925 | 0.502595 | ||||||||
\(690\) | −3.41797 | −0.130120 | ||||||||
\(691\) | 25.1004 | 0.954863 | 0.477431 | − | 0.878669i | \(-0.341568\pi\) | ||||
0.477431 | + | 0.878669i | \(0.341568\pi\) | |||||||
\(692\) | −19.8197 | −0.753431 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.20748 | 0.0837947 | ||||||||
\(695\) | 11.3783 | 0.431602 | ||||||||
\(696\) | 2.98464 | 0.113132 | ||||||||
\(697\) | 29.6331 | 1.12243 | ||||||||
\(698\) | 10.7710 | 0.407688 | ||||||||
\(699\) | −33.9120 | −1.28267 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.8099 | −1.23921 | −0.619607 | − | 0.784912i | \(-0.712708\pi\) | ||||
−0.619607 | + | 0.784912i | \(0.712708\pi\) | |||||||
\(702\) | 5.11371 | 0.193005 | ||||||||
\(703\) | −25.7029 | −0.969402 | ||||||||
\(704\) | 2.09133 | 0.0788200 | ||||||||
\(705\) | −11.8990 | −0.448141 | ||||||||
\(706\) | −13.8970 | −0.523020 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 23.6631 | 0.889313 | ||||||||
\(709\) | −19.0921 | −0.717019 | −0.358510 | − | 0.933526i | \(-0.616715\pi\) | ||||
−0.358510 | + | 0.933526i | \(0.616715\pi\) | |||||||
\(710\) | −9.83977 | −0.369280 | ||||||||
\(711\) | −2.90033 | −0.108771 | ||||||||
\(712\) | 16.6426 | 0.623709 | ||||||||
\(713\) | 8.71388 | 0.326338 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.63244 | 0.322835 | ||||||||
\(716\) | −16.4096 | −0.613257 | ||||||||
\(717\) | −22.6282 | −0.845067 | ||||||||
\(718\) | −19.4670 | −0.726502 | ||||||||
\(719\) | 21.0449 | 0.784842 | 0.392421 | − | 0.919786i | \(-0.371638\pi\) | ||||
0.392421 | + | 0.919786i | \(0.371638\pi\) | |||||||
\(720\) | 4.82619 | 0.179862 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 41.3190 | 1.53773 | ||||||||
\(723\) | 3.93561 | 0.146367 | ||||||||
\(724\) | −11.2306 | −0.417383 | ||||||||
\(725\) | −3.75341 | −0.139398 | ||||||||
\(726\) | −17.0722 | −0.633608 | ||||||||
\(727\) | 11.6826 | 0.433282 | 0.216641 | − | 0.976251i | \(-0.430490\pi\) | ||||
0.216641 | + | 0.976251i | \(0.430490\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.0021 | −1.37045 | ||||||||
\(730\) | −5.79482 | −0.214476 | ||||||||
\(731\) | 58.1450 | 2.15057 | ||||||||
\(732\) | 31.0167 | 1.14641 | ||||||||
\(733\) | −24.2475 | −0.895603 | −0.447802 | − | 0.894133i | \(-0.647793\pi\) | ||||
−0.447802 | + | 0.894133i | \(0.647793\pi\) | |||||||
\(734\) | 17.1874 | 0.634398 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −15.1897 | −0.559521 | ||||||||
\(738\) | −15.5130 | −0.571040 | ||||||||
\(739\) | −27.1189 | −0.997586 | −0.498793 | − | 0.866721i | \(-0.666223\pi\) | ||||
−0.498793 | + | 0.866721i | \(0.666223\pi\) | |||||||
\(740\) | −4.39043 | −0.161395 | ||||||||
\(741\) | 62.2589 | 2.28714 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.3281 | −0.378902 | −0.189451 | − | 0.981890i | \(-0.560671\pi\) | ||||
−0.189451 | + | 0.981890i | \(0.560671\pi\) | |||||||
\(744\) | −22.4506 | −0.823078 | ||||||||
\(745\) | 21.2546 | 0.778707 | ||||||||
\(746\) | −9.43657 | −0.345497 | ||||||||
\(747\) | 37.7419 | 1.38091 | ||||||||
\(748\) | −14.5331 | −0.531381 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −28.1642 | −1.02841 | ||||||||
\(751\) | −10.3067 | −0.376095 | −0.188048 | − | 0.982160i | \(-0.560216\pi\) | ||||
−0.188048 | + | 0.982160i | \(0.560216\pi\) | |||||||
\(752\) | −3.48130 | −0.126950 | ||||||||
\(753\) | 2.68540 | 0.0978614 | ||||||||
\(754\) | 3.60441 | 0.131265 | ||||||||
\(755\) | −18.4877 | −0.672837 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.6243 | −1.44017 | −0.720084 | − | 0.693887i | \(-0.755897\pi\) | ||||
−0.720084 | + | 0.693887i | \(0.755897\pi\) | |||||||
\(758\) | 6.99131 | 0.253936 | ||||||||
\(759\) | −5.38814 | −0.195577 | ||||||||
\(760\) | 10.3034 | 0.373742 | ||||||||
\(761\) | −53.4638 | −1.93806 | −0.969031 | − | 0.246941i | \(-0.920575\pi\) | ||||
−0.969031 | + | 0.246941i | \(0.920575\pi\) | |||||||
\(762\) | 6.21433 | 0.225121 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.36805 | 0.230388 | ||||||||
\(765\) | −33.5381 | −1.21257 | ||||||||
\(766\) | 27.5410 | 0.995098 | ||||||||
\(767\) | 28.5768 | 1.03185 | ||||||||
\(768\) | 2.57641 | 0.0929684 | ||||||||
\(769\) | 8.56383 | 0.308820 | 0.154410 | − | 0.988007i | \(-0.450652\pi\) | ||||
0.154410 | + | 0.988007i | \(0.450652\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.4529 | −0.628550 | ||||||||
\(772\) | −14.0550 | −0.505850 | ||||||||
\(773\) | −31.7891 | −1.14338 | −0.571688 | − | 0.820471i | \(-0.693711\pi\) | ||||
−0.571688 | + | 0.820471i | \(0.693711\pi\) | |||||||
\(774\) | −30.4390 | −1.09411 | ||||||||
\(775\) | 28.2333 | 1.01417 | ||||||||
\(776\) | 6.65800 | 0.239008 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.70443 | 0.240365 | ||||||||
\(779\) | −33.1184 | −1.18659 | ||||||||
\(780\) | 10.6347 | 0.380784 | ||||||||
\(781\) | −15.5116 | −0.555047 | ||||||||
\(782\) | 6.94919 | 0.248503 | ||||||||
\(783\) | 1.90394 | 0.0680413 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.4603 | −0.730260 | ||||||||
\(786\) | 3.92497 | 0.139999 | ||||||||
\(787\) | 10.4395 | 0.372130 | 0.186065 | − | 0.982537i | \(-0.440427\pi\) | ||||
0.186065 | + | 0.982537i | \(0.440427\pi\) | |||||||
\(788\) | −6.95570 | −0.247786 | ||||||||
\(789\) | 1.17764 | 0.0419253 | ||||||||
\(790\) | −1.05766 | −0.0376299 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.60808 | 0.270341 | ||||||||
\(793\) | 37.4574 | 1.33015 | ||||||||
\(794\) | 22.6052 | 0.802230 | ||||||||
\(795\) | 14.4923 | 0.513989 | ||||||||
\(796\) | 21.0897 | 0.747506 | ||||||||
\(797\) | 2.70514 | 0.0958211 | 0.0479105 | − | 0.998852i | \(-0.484744\pi\) | ||||
0.0479105 | + | 0.998852i | \(0.484744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.1922 | 0.855860 | ||||||||
\(800\) | −3.24003 | −0.114552 | ||||||||
\(801\) | 60.5445 | 2.13923 | ||||||||
\(802\) | −9.70827 | −0.342811 | ||||||||
\(803\) | −9.13503 | −0.322368 | ||||||||
\(804\) | −18.7130 | −0.659956 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.1125 | −0.954999 | ||||||||
\(807\) | 47.8015 | 1.68269 | ||||||||
\(808\) | 9.15879 | 0.322205 | ||||||||
\(809\) | 22.3936 | 0.787318 | 0.393659 | − | 0.919257i | \(-0.371209\pi\) | ||||
0.393659 | + | 0.919257i | \(0.371209\pi\) | |||||||
\(810\) | −8.86104 | −0.311345 | ||||||||
\(811\) | −23.7712 | −0.834719 | −0.417359 | − | 0.908742i | \(-0.637044\pi\) | ||||
−0.417359 | + | 0.908742i | \(0.637044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.1249 | 1.65274 | ||||||||
\(814\) | −6.92114 | −0.242586 | ||||||||
\(815\) | −11.4275 | −0.400287 | ||||||||
\(816\) | −17.9040 | −0.626765 | ||||||||
\(817\) | −64.9838 | −2.27349 | ||||||||
\(818\) | −36.3360 | −1.27046 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.65711 | −0.197555 | ||||||||
\(821\) | −21.8755 | −0.763459 | −0.381729 | − | 0.924274i | \(-0.624671\pi\) | ||||
−0.381729 | + | 0.924274i | \(0.624671\pi\) | |||||||
\(822\) | 24.8023 | 0.865080 | ||||||||
\(823\) | −27.6968 | −0.965449 | −0.482724 | − | 0.875772i | \(-0.660353\pi\) | ||||
−0.482724 | + | 0.875772i | \(0.660353\pi\) | |||||||
\(824\) | 4.53211 | 0.157884 | ||||||||
\(825\) | −17.4577 | −0.607801 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.6016 | 1.55095 | 0.775475 | − | 0.631378i | \(-0.217510\pi\) | ||||
0.775475 | + | 0.631378i | \(0.217510\pi\) | |||||||
\(828\) | −3.63791 | −0.126426 | ||||||||
\(829\) | −36.3293 | −1.26177 | −0.630884 | − | 0.775877i | \(-0.717308\pi\) | ||||
−0.630884 | + | 0.775877i | \(0.717308\pi\) | |||||||
\(830\) | 13.7633 | 0.477733 | ||||||||
\(831\) | 51.9319 | 1.80150 | ||||||||
\(832\) | 3.11142 | 0.107869 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 22.0973 | 0.765167 | ||||||||
\(835\) | 15.8789 | 0.549512 | ||||||||
\(836\) | 16.2424 | 0.561754 | ||||||||
\(837\) | −14.3215 | −0.495025 | ||||||||
\(838\) | 9.98642 | 0.344975 | ||||||||
\(839\) | 51.3975 | 1.77444 | 0.887219 | − | 0.461348i | \(-0.152634\pi\) | ||||
0.887219 | + | 0.461348i | \(0.152634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6580 | −0.953724 | ||||||||
\(842\) | 14.1053 | 0.486099 | ||||||||
\(843\) | −18.7399 | −0.645438 | ||||||||
\(844\) | 26.5036 | 0.912290 | ||||||||
\(845\) | −4.40321 | −0.151475 | ||||||||
\(846\) | −12.6647 | −0.435421 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.24003 | 0.145603 | ||||||||
\(849\) | −7.11709 | −0.244258 | ||||||||
\(850\) | 22.5156 | 0.772279 | ||||||||
\(851\) | 3.30944 | 0.113446 | ||||||||
\(852\) | −19.1095 | −0.654680 | ||||||||
\(853\) | −36.8505 | −1.26174 | −0.630868 | − | 0.775890i | \(-0.717301\pi\) | ||||
−0.630868 | + | 0.775890i | \(0.717301\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 37.4828 | 1.28188 | ||||||||
\(856\) | −12.3344 | −0.421582 | ||||||||
\(857\) | −15.7872 | −0.539282 | −0.269641 | − | 0.962961i | \(-0.586905\pi\) | ||||
−0.269641 | + | 0.962961i | \(0.586905\pi\) | |||||||
\(858\) | 16.7647 | 0.572339 | ||||||||
\(859\) | 30.2068 | 1.03064 | 0.515322 | − | 0.856997i | \(-0.327672\pi\) | ||||
0.515322 | + | 0.856997i | \(0.327672\pi\) | |||||||
\(860\) | −11.1002 | −0.378513 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.54369 | −0.120699 | ||||||||
\(863\) | 51.9316 | 1.76777 | 0.883886 | − | 0.467702i | \(-0.154918\pi\) | ||||
0.883886 | + | 0.467702i | \(0.154918\pi\) | |||||||
\(864\) | 1.64353 | 0.0559140 | ||||||||
\(865\) | −26.2935 | −0.894007 | ||||||||
\(866\) | −16.2680 | −0.552810 | ||||||||
\(867\) | 80.6192 | 2.73797 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.66731 | −0.0565598 | ||||||||
\(870\) | 3.95953 | 0.134241 | ||||||||
\(871\) | −22.5988 | −0.765732 | ||||||||
\(872\) | −1.09984 | −0.0372453 | ||||||||
\(873\) | 24.2212 | 0.819765 | ||||||||
\(874\) | −7.76653 | −0.262707 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.2539 | −0.380234 | ||||||||
\(877\) | −11.3012 | −0.381615 | −0.190807 | − | 0.981627i | \(-0.561111\pi\) | ||||
−0.190807 | + | 0.981627i | \(0.561111\pi\) | |||||||
\(878\) | 1.17003 | 0.0394864 | ||||||||
\(879\) | 65.3780 | 2.20514 | ||||||||
\(880\) | 2.77444 | 0.0935263 | ||||||||
\(881\) | 17.4345 | 0.587384 | 0.293692 | − | 0.955900i | \(-0.405116\pi\) | ||||
0.293692 | + | 0.955900i | \(0.405116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.0567 | 1.61724 | 0.808618 | − | 0.588333i | \(-0.200216\pi\) | ||||
0.808618 | + | 0.588333i | \(0.200216\pi\) | |||||||
\(884\) | −21.6218 | −0.727221 | ||||||||
\(885\) | 31.3923 | 1.05524 | ||||||||
\(886\) | 39.0073 | 1.31048 | ||||||||
\(887\) | −2.19433 | −0.0736783 | −0.0368391 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368391 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(888\) | −8.52649 | −0.286130 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 22.0787 | 0.740081 | ||||||||
\(891\) | −13.9687 | −0.467968 | ||||||||
\(892\) | −9.80109 | −0.328165 | ||||||||
\(893\) | −27.0376 | −0.904780 | ||||||||
\(894\) | 41.2777 | 1.38053 | ||||||||
\(895\) | −21.7696 | −0.727678 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.01631 | −0.267657 | ||||||||
\(898\) | 32.1714 | 1.07357 | ||||||||
\(899\) | −10.0946 | −0.336673 | ||||||||
\(900\) | −11.7870 | −0.392899 | ||||||||
\(901\) | −29.4648 | −0.981615 | ||||||||
\(902\) | −8.91796 | −0.296935 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.44278 | 0.147765 | ||||||||
\(905\) | −14.8990 | −0.495259 | ||||||||
\(906\) | −35.9043 | −1.19284 | ||||||||
\(907\) | −30.3570 | −1.00799 | −0.503993 | − | 0.863708i | \(-0.668136\pi\) | ||||
−0.503993 | + | 0.863708i | \(0.668136\pi\) | |||||||
\(908\) | −28.4962 | −0.945679 | ||||||||
\(909\) | 33.3189 | 1.10512 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.09959 | −0.0364309 | −0.0182155 | − | 0.999834i | \(-0.505798\pi\) | ||||
−0.0182155 | + | 0.999834i | \(0.505798\pi\) | |||||||
\(912\) | 20.0098 | 0.662591 | ||||||||
\(913\) | 21.6967 | 0.718057 | ||||||||
\(914\) | −34.3548 | −1.13635 | ||||||||
\(915\) | 41.1478 | 1.36031 | ||||||||
\(916\) | −25.1914 | −0.832347 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.4212 | −0.376956 | ||||||||
\(919\) | −9.67342 | −0.319097 | −0.159548 | − | 0.987190i | \(-0.551004\pi\) | ||||
−0.159548 | + | 0.987190i | \(0.551004\pi\) | |||||||
\(920\) | −1.32664 | −0.0437379 | ||||||||
\(921\) | −75.3523 | −2.48294 | ||||||||
\(922\) | 10.5155 | 0.346310 | ||||||||
\(923\) | −23.0776 | −0.759610 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.7227 | 0.352560 | ||||||||
\(926\) | −19.9943 | −0.657052 | ||||||||
\(927\) | 16.4874 | 0.541518 | ||||||||
\(928\) | 1.15845 | 0.0380279 | ||||||||
\(929\) | 11.3437 | 0.372175 | 0.186088 | − | 0.982533i | \(-0.440419\pi\) | ||||
0.186088 | + | 0.982533i | \(0.440419\pi\) | |||||||
\(930\) | −29.7838 | −0.976649 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −13.1625 | −0.431151 | ||||||||
\(933\) | 70.2919 | 2.30125 | ||||||||
\(934\) | −27.4643 | −0.898658 | ||||||||
\(935\) | −19.2801 | −0.630527 | ||||||||
\(936\) | 11.3191 | 0.369975 | ||||||||
\(937\) | −1.06500 | −0.0347921 | −0.0173960 | − | 0.999849i | \(-0.505538\pi\) | ||||
−0.0173960 | + | 0.999849i | \(0.505538\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.63880 | 0.216649 | ||||||||
\(940\) | −4.61843 | −0.150636 | ||||||||
\(941\) | 46.7079 | 1.52263 | 0.761317 | − | 0.648379i | \(-0.224553\pi\) | ||||
0.761317 | + | 0.648379i | \(0.224553\pi\) | |||||||
\(942\) | −39.7353 | −1.29464 | ||||||||
\(943\) | 4.26425 | 0.138863 | ||||||||
\(944\) | 9.18450 | 0.298930 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.4985 | −0.568925 | ||||||||
\(947\) | 46.8692 | 1.52305 | 0.761523 | − | 0.648138i | \(-0.224452\pi\) | ||||
0.761523 | + | 0.648138i | \(0.224452\pi\) | |||||||
\(948\) | −2.05405 | −0.0667124 | ||||||||
\(949\) | −13.5908 | −0.441177 | ||||||||
\(950\) | −25.1638 | −0.816422 | ||||||||
\(951\) | −32.2218 | −1.04486 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.2926 | −1.36999 | −0.684996 | − | 0.728547i | \(-0.740196\pi\) | ||||
−0.684996 | + | 0.728547i | \(0.740196\pi\) | |||||||
\(954\) | 15.4249 | 0.499399 | ||||||||
\(955\) | 8.44809 | 0.273374 | ||||||||
\(956\) | −8.78283 | −0.284057 | ||||||||
\(957\) | 6.24187 | 0.201771 | ||||||||
\(958\) | −8.44551 | −0.272862 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.41797 | 0.110314 | ||||||||
\(961\) | 44.9318 | 1.44941 | ||||||||
\(962\) | −10.2971 | −0.331991 | ||||||||
\(963\) | −44.8716 | −1.44597 | ||||||||
\(964\) | 1.52755 | 0.0491992 | ||||||||
\(965\) | −18.6459 | −0.600232 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.5007 | 1.36673 | 0.683366 | − | 0.730076i | \(-0.260515\pi\) | ||||
0.683366 | + | 0.730076i | \(0.260515\pi\) | |||||||
\(968\) | −6.62633 | −0.212978 | ||||||||
\(969\) | −139.052 | −4.46699 | ||||||||
\(970\) | 8.83275 | 0.283603 | ||||||||
\(971\) | 1.03232 | 0.0331289 | 0.0165644 | − | 0.999863i | \(-0.494727\pi\) | ||||
0.0165644 | + | 0.999863i | \(0.494727\pi\) | |||||||
\(972\) | −22.1393 | −0.710118 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 33.2791 | 1.06633 | ||||||||
\(975\) | −25.9731 | −0.831805 | ||||||||
\(976\) | 12.0387 | 0.385349 | ||||||||
\(977\) | 0.852420 | 0.0272713 | 0.0136357 | − | 0.999907i | \(-0.495659\pi\) | ||||
0.0136357 | + | 0.999907i | \(0.495659\pi\) | |||||||
\(978\) | −22.1929 | −0.709650 | ||||||||
\(979\) | 34.8053 | 1.11238 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00112 | −0.127746 | ||||||||
\(982\) | 15.8532 | 0.505896 | ||||||||
\(983\) | −6.92136 | −0.220757 | −0.110379 | − | 0.993890i | \(-0.535206\pi\) | ||||
−0.110379 | + | 0.993890i | \(0.535206\pi\) | |||||||
\(984\) | −10.9865 | −0.350236 | ||||||||
\(985\) | −9.22769 | −0.294019 | ||||||||
\(986\) | −8.05027 | −0.256373 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.1649 | 0.768789 | ||||||||
\(989\) | 8.36716 | 0.266060 | ||||||||
\(990\) | 10.0932 | 0.320782 | ||||||||
\(991\) | −1.34596 | −0.0427558 | −0.0213779 | − | 0.999771i | \(-0.506805\pi\) | ||||
−0.0213779 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(992\) | −8.71388 | −0.276666 | ||||||||
\(993\) | 7.04384 | 0.223530 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.9784 | 0.886976 | ||||||||
\(996\) | 26.7293 | 0.846950 | ||||||||
\(997\) | 4.84179 | 0.153341 | 0.0766705 | − | 0.997056i | \(-0.475571\pi\) | ||||
0.0766705 | + | 0.997056i | \(0.475571\pi\) | |||||||
\(998\) | −19.3323 | −0.611954 | ||||||||
\(999\) | −5.43917 | −0.172088 |
(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 | 2254.2.a.z.1.4 | 4 | ||
7.2 | even | 3 | 322.2.e.a.277.1 | yes | 8 | ||
7.4 | even | 3 | 322.2.e.a.93.1 | ✓ | 8 | ||
7.6 | odd | 2 | 2254.2.a.x.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.e.a.93.1 | ✓ | 8 | 7.4 | even | 3 | ||
322.2.e.a.277.1 | yes | 8 | 7.2 | even | 3 | ||
2254.2.a.x.1.1 | 4 | 7.6 | odd | 2 | |||
2254.2.a.z.1.4 | 4 | 1.1 | even | 1 | trivial |