Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, 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("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.9248.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.13578\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.19935 | 0.692447 | 0.346223 | − | 0.938152i | \(-0.387464\pi\) | ||||
0.346223 | + | 0.938152i | \(0.387464\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.13578 | 0.955149 | 0.477575 | − | 0.878591i | \(-0.341516\pi\) | ||||
0.477575 | + | 0.878591i | \(0.341516\pi\) | |||||||
\(6\) | −1.19935 | −0.489634 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.56155 | −0.520518 | ||||||||
\(10\) | −2.13578 | −0.675393 | ||||||||
\(11\) | −4.56155 | −1.37536 | −0.687680 | − | 0.726014i | \(-0.741371\pi\) | ||||
−0.687680 | + | 0.726014i | \(0.741371\pi\) | |||||||
\(12\) | 1.19935 | 0.346223 | ||||||||
\(13\) | −4.53448 | −1.25764 | −0.628820 | − | 0.777551i | \(-0.716462\pi\) | ||||
−0.628820 | + | 0.777551i | \(0.716462\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.56155 | 0.661390 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.20798 | 1.26312 | 0.631561 | − | 0.775326i | \(-0.282415\pi\) | ||||
0.631561 | + | 0.775326i | \(0.282415\pi\) | |||||||
\(18\) | 1.56155 | 0.368062 | ||||||||
\(19\) | −6.14441 | −1.40962 | −0.704812 | − | 0.709394i | \(-0.748969\pi\) | ||||
−0.704812 | + | 0.709394i | \(0.748969\pi\) | |||||||
\(20\) | 2.13578 | 0.477575 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.56155 | 0.972526 | ||||||||
\(23\) | 8.24621 | 1.71945 | 0.859727 | − | 0.510754i | \(-0.170634\pi\) | ||||
0.859727 | + | 0.510754i | \(0.170634\pi\) | |||||||
\(24\) | −1.19935 | −0.244817 | ||||||||
\(25\) | −0.438447 | −0.0876894 | ||||||||
\(26\) | 4.53448 | 0.889286 | ||||||||
\(27\) | −5.47091 | −1.05288 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −2.56155 | −0.467673 | ||||||||
\(31\) | −4.53448 | −0.814418 | −0.407209 | − | 0.913335i | \(-0.633498\pi\) | ||||
−0.407209 | + | 0.913335i | \(0.633498\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.47091 | −0.952363 | ||||||||
\(34\) | −5.20798 | −0.893162 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.56155 | −0.260259 | ||||||||
\(37\) | −1.12311 | −0.184637 | −0.0923187 | − | 0.995730i | \(-0.529428\pi\) | ||||
−0.0923187 | + | 0.995730i | \(0.529428\pi\) | |||||||
\(38\) | 6.14441 | 0.996755 | ||||||||
\(39\) | −5.43845 | −0.870849 | ||||||||
\(40\) | −2.13578 | −0.337696 | ||||||||
\(41\) | 5.20798 | 0.813351 | 0.406675 | − | 0.913573i | \(-0.366688\pi\) | ||||
0.406675 | + | 0.913573i | \(0.366688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.68466 | 1.17190 | 0.585950 | − | 0.810347i | \(-0.300722\pi\) | ||||
0.585950 | + | 0.810347i | \(0.300722\pi\) | |||||||
\(44\) | −4.56155 | −0.687680 | ||||||||
\(45\) | −3.33513 | −0.497172 | ||||||||
\(46\) | −8.24621 | −1.21584 | ||||||||
\(47\) | 2.13578 | 0.311535 | 0.155768 | − | 0.987794i | \(-0.450215\pi\) | ||||
0.155768 | + | 0.987794i | \(0.450215\pi\) | |||||||
\(48\) | 1.19935 | 0.173112 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.438447 | 0.0620058 | ||||||||
\(51\) | 6.24621 | 0.874645 | ||||||||
\(52\) | −4.53448 | −0.628820 | ||||||||
\(53\) | −7.43845 | −1.02175 | −0.510875 | − | 0.859655i | \(-0.670678\pi\) | ||||
−0.510875 | + | 0.859655i | \(0.670678\pi\) | |||||||
\(54\) | 5.47091 | 0.744497 | ||||||||
\(55\) | −9.74247 | −1.31367 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.36932 | −0.976090 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −5.20798 | −0.678022 | −0.339011 | − | 0.940782i | \(-0.610092\pi\) | ||||
−0.339011 | + | 0.940782i | \(0.610092\pi\) | |||||||
\(60\) | 2.56155 | 0.330695 | ||||||||
\(61\) | −4.27156 | −0.546917 | −0.273459 | − | 0.961884i | \(-0.588168\pi\) | ||||
−0.273459 | + | 0.961884i | \(0.588168\pi\) | |||||||
\(62\) | 4.53448 | 0.575880 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.68466 | −1.20123 | ||||||||
\(66\) | 5.47091 | 0.673423 | ||||||||
\(67\) | −13.1231 | −1.60324 | −0.801621 | − | 0.597832i | \(-0.796029\pi\) | ||||
−0.801621 | + | 0.597832i | \(0.796029\pi\) | |||||||
\(68\) | 5.20798 | 0.631561 | ||||||||
\(69\) | 9.89012 | 1.19063 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.3693 | −1.58665 | −0.793323 | − | 0.608801i | \(-0.791651\pi\) | ||||
−0.793323 | + | 0.608801i | \(0.791651\pi\) | |||||||
\(72\) | 1.56155 | 0.184031 | ||||||||
\(73\) | −16.6757 | −1.95174 | −0.975869 | − | 0.218356i | \(-0.929931\pi\) | ||||
−0.975869 | + | 0.218356i | \(0.929931\pi\) | |||||||
\(74\) | 1.12311 | 0.130558 | ||||||||
\(75\) | −0.525853 | −0.0607203 | ||||||||
\(76\) | −6.14441 | −0.704812 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.43845 | 0.615783 | ||||||||
\(79\) | −12.8078 | −1.44099 | −0.720493 | − | 0.693462i | \(-0.756084\pi\) | ||||
−0.720493 | + | 0.693462i | \(0.756084\pi\) | |||||||
\(80\) | 2.13578 | 0.238787 | ||||||||
\(81\) | −1.87689 | −0.208544 | ||||||||
\(82\) | −5.20798 | −0.575126 | ||||||||
\(83\) | −10.0054 | −1.09823 | −0.549117 | − | 0.835745i | \(-0.685036\pi\) | ||||
−0.549117 | + | 0.835745i | \(0.685036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.1231 | 1.20647 | ||||||||
\(86\) | −7.68466 | −0.828658 | ||||||||
\(87\) | 1.19935 | 0.128584 | ||||||||
\(88\) | 4.56155 | 0.486263 | ||||||||
\(89\) | 2.80928 | 0.297783 | 0.148891 | − | 0.988854i | \(-0.452429\pi\) | ||||
0.148891 | + | 0.988854i | \(0.452429\pi\) | |||||||
\(90\) | 3.33513 | 0.351554 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.24621 | 0.859727 | ||||||||
\(93\) | −5.43845 | −0.563941 | ||||||||
\(94\) | −2.13578 | −0.220289 | ||||||||
\(95\) | −13.1231 | −1.34640 | ||||||||
\(96\) | −1.19935 | −0.122408 | ||||||||
\(97\) | 13.7511 | 1.39621 | 0.698106 | − | 0.715994i | \(-0.254026\pi\) | ||||
0.698106 | + | 0.715994i | \(0.254026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.12311 | 0.715899 | ||||||||
\(100\) | −0.438447 | −0.0438447 | ||||||||
\(101\) | −18.9591 | −1.88650 | −0.943250 | − | 0.332084i | \(-0.892248\pi\) | ||||
−0.943250 | + | 0.332084i | \(0.892248\pi\) | |||||||
\(102\) | −6.24621 | −0.618467 | ||||||||
\(103\) | 11.4677 | 1.12994 | 0.564972 | − | 0.825110i | \(-0.308887\pi\) | ||||
0.564972 | + | 0.825110i | \(0.308887\pi\) | |||||||
\(104\) | 4.53448 | 0.444643 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.43845 | 0.722486 | ||||||||
\(107\) | −9.12311 | −0.881964 | −0.440982 | − | 0.897516i | \(-0.645370\pi\) | ||||
−0.440982 | + | 0.897516i | \(0.645370\pi\) | |||||||
\(108\) | −5.47091 | −0.526439 | ||||||||
\(109\) | −1.68466 | −0.161361 | −0.0806805 | − | 0.996740i | \(-0.525709\pi\) | ||||
−0.0806805 | + | 0.996740i | \(0.525709\pi\) | |||||||
\(110\) | 9.74247 | 0.928908 | ||||||||
\(111\) | −1.34700 | −0.127852 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.36932 | 0.505103 | 0.252551 | − | 0.967583i | \(-0.418730\pi\) | ||||
0.252551 | + | 0.967583i | \(0.418730\pi\) | |||||||
\(114\) | 7.36932 | 0.690200 | ||||||||
\(115\) | 17.6121 | 1.64234 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 7.08084 | 0.654624 | ||||||||
\(118\) | 5.20798 | 0.479434 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.56155 | −0.233837 | ||||||||
\(121\) | 9.80776 | 0.891615 | ||||||||
\(122\) | 4.27156 | 0.386729 | ||||||||
\(123\) | 6.24621 | 0.563202 | ||||||||
\(124\) | −4.53448 | −0.407209 | ||||||||
\(125\) | −11.6153 | −1.03891 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.2462 | 1.26415 | 0.632073 | − | 0.774909i | \(-0.282204\pi\) | ||||
0.632073 | + | 0.774909i | \(0.282204\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.21662 | 0.811478 | ||||||||
\(130\) | 9.68466 | 0.849401 | ||||||||
\(131\) | −10.9418 | −0.955991 | −0.477996 | − | 0.878362i | \(-0.658637\pi\) | ||||
−0.477996 | + | 0.878362i | \(0.658637\pi\) | |||||||
\(132\) | −5.47091 | −0.476182 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.1231 | 1.13366 | ||||||||
\(135\) | −11.6847 | −1.00566 | ||||||||
\(136\) | −5.20798 | −0.446581 | ||||||||
\(137\) | 8.24621 | 0.704521 | 0.352261 | − | 0.935902i | \(-0.385413\pi\) | ||||
0.352261 | + | 0.935902i | \(0.385413\pi\) | |||||||
\(138\) | −9.89012 | −0.841903 | ||||||||
\(139\) | 18.0227 | 1.52866 | 0.764331 | − | 0.644824i | \(-0.223069\pi\) | ||||
0.764331 | + | 0.644824i | \(0.223069\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.56155 | 0.215722 | ||||||||
\(142\) | 13.3693 | 1.12193 | ||||||||
\(143\) | 20.6843 | 1.72971 | ||||||||
\(144\) | −1.56155 | −0.130129 | ||||||||
\(145\) | 2.13578 | 0.177367 | ||||||||
\(146\) | 16.6757 | 1.38009 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.12311 | −0.0923187 | ||||||||
\(149\) | −9.68466 | −0.793398 | −0.396699 | − | 0.917949i | \(-0.629844\pi\) | ||||
−0.396699 | + | 0.917949i | \(0.629844\pi\) | |||||||
\(150\) | 0.525853 | 0.0429357 | ||||||||
\(151\) | −12.2462 | −0.996583 | −0.498291 | − | 0.867010i | \(-0.666039\pi\) | ||||
−0.498291 | + | 0.867010i | \(0.666039\pi\) | |||||||
\(152\) | 6.14441 | 0.498378 | ||||||||
\(153\) | −8.13254 | −0.657477 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.68466 | −0.777890 | ||||||||
\(156\) | −5.43845 | −0.435424 | ||||||||
\(157\) | 20.8319 | 1.66257 | 0.831285 | − | 0.555847i | \(-0.187606\pi\) | ||||
0.831285 | + | 0.555847i | \(0.187606\pi\) | |||||||
\(158\) | 12.8078 | 1.01893 | ||||||||
\(159\) | −8.92132 | −0.707507 | ||||||||
\(160\) | −2.13578 | −0.168848 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.87689 | 0.147463 | ||||||||
\(163\) | −8.56155 | −0.670593 | −0.335296 | − | 0.942113i | \(-0.608836\pi\) | ||||
−0.335296 | + | 0.942113i | \(0.608836\pi\) | |||||||
\(164\) | 5.20798 | 0.406675 | ||||||||
\(165\) | −11.6847 | −0.909649 | ||||||||
\(166\) | 10.0054 | 0.776569 | ||||||||
\(167\) | 4.79741 | 0.371235 | 0.185617 | − | 0.982622i | \(-0.440571\pi\) | ||||
0.185617 | + | 0.982622i | \(0.440571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.56155 | 0.581658 | ||||||||
\(170\) | −11.1231 | −0.853103 | ||||||||
\(171\) | 9.59482 | 0.733734 | ||||||||
\(172\) | 7.68466 | 0.585950 | ||||||||
\(173\) | 8.13254 | 0.618306 | 0.309153 | − | 0.951012i | \(-0.399955\pi\) | ||||
0.309153 | + | 0.951012i | \(0.399955\pi\) | |||||||
\(174\) | −1.19935 | −0.0909227 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.56155 | −0.343840 | ||||||||
\(177\) | −6.24621 | −0.469494 | ||||||||
\(178\) | −2.80928 | −0.210564 | ||||||||
\(179\) | −18.2462 | −1.36379 | −0.681893 | − | 0.731452i | \(-0.738843\pi\) | ||||
−0.681893 | + | 0.731452i | \(0.738843\pi\) | |||||||
\(180\) | −3.33513 | −0.248586 | ||||||||
\(181\) | −1.08407 | −0.0805785 | −0.0402893 | − | 0.999188i | \(-0.512828\pi\) | ||||
−0.0402893 | + | 0.999188i | \(0.512828\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.12311 | −0.378711 | ||||||||
\(184\) | −8.24621 | −0.607919 | ||||||||
\(185\) | −2.39871 | −0.176356 | ||||||||
\(186\) | 5.43845 | 0.398766 | ||||||||
\(187\) | −23.7565 | −1.73725 | ||||||||
\(188\) | 2.13578 | 0.155768 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.1231 | 0.952050 | ||||||||
\(191\) | 6.24621 | 0.451960 | 0.225980 | − | 0.974132i | \(-0.427442\pi\) | ||||
0.225980 | + | 0.974132i | \(0.427442\pi\) | |||||||
\(192\) | 1.19935 | 0.0865558 | ||||||||
\(193\) | 21.3693 | 1.53820 | 0.769099 | − | 0.639130i | \(-0.220706\pi\) | ||||
0.769099 | + | 0.639130i | \(0.220706\pi\) | |||||||
\(194\) | −13.7511 | −0.987272 | ||||||||
\(195\) | −11.6153 | −0.831791 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.2462 | −1.44248 | −0.721241 | − | 0.692684i | \(-0.756428\pi\) | ||||
−0.721241 | + | 0.692684i | \(0.756428\pi\) | |||||||
\(198\) | −7.12311 | −0.506217 | ||||||||
\(199\) | −14.1617 | −1.00389 | −0.501947 | − | 0.864898i | \(-0.667383\pi\) | ||||
−0.501947 | + | 0.864898i | \(0.667383\pi\) | |||||||
\(200\) | 0.438447 | 0.0310029 | ||||||||
\(201\) | −15.7392 | −1.11016 | ||||||||
\(202\) | 18.9591 | 1.33396 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.24621 | 0.437322 | ||||||||
\(205\) | 11.1231 | 0.776871 | ||||||||
\(206\) | −11.4677 | −0.798991 | ||||||||
\(207\) | −12.8769 | −0.895006 | ||||||||
\(208\) | −4.53448 | −0.314410 | ||||||||
\(209\) | 28.0281 | 1.93874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.68466 | −0.529034 | −0.264517 | − | 0.964381i | \(-0.585212\pi\) | ||||
−0.264517 | + | 0.964381i | \(0.585212\pi\) | |||||||
\(212\) | −7.43845 | −0.510875 | ||||||||
\(213\) | −16.0345 | −1.09867 | ||||||||
\(214\) | 9.12311 | 0.623643 | ||||||||
\(215\) | 16.4127 | 1.11934 | ||||||||
\(216\) | 5.47091 | 0.372248 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.68466 | 0.114099 | ||||||||
\(219\) | −20.0000 | −1.35147 | ||||||||
\(220\) | −9.74247 | −0.656837 | ||||||||
\(221\) | −23.6155 | −1.58855 | ||||||||
\(222\) | 1.34700 | 0.0904047 | ||||||||
\(223\) | 6.67026 | 0.446674 | 0.223337 | − | 0.974741i | \(-0.428305\pi\) | ||||
0.223337 | + | 0.974741i | \(0.428305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.684658 | 0.0456439 | ||||||||
\(226\) | −5.36932 | −0.357162 | ||||||||
\(227\) | 3.86098 | 0.256263 | 0.128131 | − | 0.991757i | \(-0.459102\pi\) | ||||
0.128131 | + | 0.991757i | \(0.459102\pi\) | |||||||
\(228\) | −7.36932 | −0.488045 | ||||||||
\(229\) | 11.9935 | 0.792555 | 0.396277 | − | 0.918131i | \(-0.370302\pi\) | ||||
0.396277 | + | 0.918131i | \(0.370302\pi\) | |||||||
\(230\) | −17.6121 | −1.16131 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 15.9309 | 1.04367 | 0.521833 | − | 0.853048i | \(-0.325248\pi\) | ||||
0.521833 | + | 0.853048i | \(0.325248\pi\) | |||||||
\(234\) | −7.08084 | −0.462889 | ||||||||
\(235\) | 4.56155 | 0.297563 | ||||||||
\(236\) | −5.20798 | −0.339011 | ||||||||
\(237\) | −15.3610 | −0.997806 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 2.56155 | 0.165348 | ||||||||
\(241\) | −17.4644 | −1.12498 | −0.562492 | − | 0.826803i | \(-0.690157\pi\) | ||||
−0.562492 | + | 0.826803i | \(0.690157\pi\) | |||||||
\(242\) | −9.80776 | −0.630467 | ||||||||
\(243\) | 14.1617 | 0.908472 | ||||||||
\(244\) | −4.27156 | −0.273459 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.24621 | −0.398244 | ||||||||
\(247\) | 27.8617 | 1.77280 | ||||||||
\(248\) | 4.53448 | 0.287940 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | 11.6153 | 0.734617 | ||||||||
\(251\) | 6.52262 | 0.411704 | 0.205852 | − | 0.978583i | \(-0.434003\pi\) | ||||
0.205852 | + | 0.978583i | \(0.434003\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.6155 | −2.36487 | ||||||||
\(254\) | −14.2462 | −0.893887 | ||||||||
\(255\) | 13.3405 | 0.835416 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.9386 | 1.05660 | 0.528300 | − | 0.849058i | \(-0.322830\pi\) | ||||
0.528300 | + | 0.849058i | \(0.322830\pi\) | |||||||
\(258\) | −9.21662 | −0.573801 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.68466 | −0.600617 | ||||||||
\(261\) | −1.56155 | −0.0966577 | ||||||||
\(262\) | 10.9418 | 0.675988 | ||||||||
\(263\) | 4.80776 | 0.296459 | 0.148230 | − | 0.988953i | \(-0.452643\pi\) | ||||
0.148230 | + | 0.988953i | \(0.452643\pi\) | |||||||
\(264\) | 5.47091 | 0.336711 | ||||||||
\(265\) | −15.8869 | −0.975923 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.36932 | 0.206199 | ||||||||
\(268\) | −13.1231 | −0.801621 | ||||||||
\(269\) | 7.72197 | 0.470817 | 0.235408 | − | 0.971897i | \(-0.424357\pi\) | ||||
0.235408 | + | 0.971897i | \(0.424357\pi\) | |||||||
\(270\) | 11.6847 | 0.711106 | ||||||||
\(271\) | 21.0949 | 1.28142 | 0.640711 | − | 0.767782i | \(-0.278640\pi\) | ||||
0.640711 | + | 0.767782i | \(0.278640\pi\) | |||||||
\(272\) | 5.20798 | 0.315780 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.24621 | −0.498172 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 9.89012 | 0.595315 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | −18.0227 | −1.08093 | ||||||||
\(279\) | 7.08084 | 0.423919 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.1771 | 0.965044 | 0.482522 | − | 0.875884i | \(-0.339721\pi\) | ||||
0.482522 | + | 0.875884i | \(0.339721\pi\) | |||||||
\(282\) | −2.56155 | −0.152538 | ||||||||
\(283\) | 27.6175 | 1.64169 | 0.820844 | − | 0.571152i | \(-0.193503\pi\) | ||||
0.820844 | + | 0.571152i | \(0.193503\pi\) | |||||||
\(284\) | −13.3693 | −0.793323 | ||||||||
\(285\) | −15.7392 | −0.932312 | ||||||||
\(286\) | −20.6843 | −1.22309 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.56155 | 0.0920154 | ||||||||
\(289\) | 10.1231 | 0.595477 | ||||||||
\(290\) | −2.13578 | −0.125417 | ||||||||
\(291\) | 16.4924 | 0.966803 | ||||||||
\(292\) | −16.6757 | −0.975869 | ||||||||
\(293\) | −15.7392 | −0.919496 | −0.459748 | − | 0.888049i | \(-0.652060\pi\) | ||||
−0.459748 | + | 0.888049i | \(0.652060\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.1231 | −0.647612 | ||||||||
\(296\) | 1.12311 | 0.0652792 | ||||||||
\(297\) | 24.9559 | 1.44809 | ||||||||
\(298\) | 9.68466 | 0.561017 | ||||||||
\(299\) | −37.3923 | −2.16245 | ||||||||
\(300\) | −0.525853 | −0.0303601 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.2462 | 0.704690 | ||||||||
\(303\) | −22.7386 | −1.30630 | ||||||||
\(304\) | −6.14441 | −0.352406 | ||||||||
\(305\) | −9.12311 | −0.522388 | ||||||||
\(306\) | 8.13254 | 0.464907 | ||||||||
\(307\) | 25.4817 | 1.45432 | 0.727159 | − | 0.686469i | \(-0.240840\pi\) | ||||
0.727159 | + | 0.686469i | \(0.240840\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.7538 | 0.782426 | ||||||||
\(310\) | 9.68466 | 0.550052 | ||||||||
\(311\) | −12.4041 | −0.703372 | −0.351686 | − | 0.936118i | \(-0.614392\pi\) | ||||
−0.351686 | + | 0.936118i | \(0.614392\pi\) | |||||||
\(312\) | 5.43845 | 0.307891 | ||||||||
\(313\) | 8.92132 | 0.504263 | 0.252131 | − | 0.967693i | \(-0.418868\pi\) | ||||
0.252131 | + | 0.967693i | \(0.418868\pi\) | |||||||
\(314\) | −20.8319 | −1.17561 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.8078 | −0.720493 | ||||||||
\(317\) | −18.4924 | −1.03864 | −0.519319 | − | 0.854580i | \(-0.673814\pi\) | ||||
−0.519319 | + | 0.854580i | \(0.673814\pi\) | |||||||
\(318\) | 8.92132 | 0.500283 | ||||||||
\(319\) | −4.56155 | −0.255398 | ||||||||
\(320\) | 2.13578 | 0.119394 | ||||||||
\(321\) | −10.9418 | −0.610713 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.0000 | −1.78053 | ||||||||
\(324\) | −1.87689 | −0.104272 | ||||||||
\(325\) | 1.98813 | 0.110282 | ||||||||
\(326\) | 8.56155 | 0.474181 | ||||||||
\(327\) | −2.02050 | −0.111734 | ||||||||
\(328\) | −5.20798 | −0.287563 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 11.6847 | 0.643219 | ||||||||
\(331\) | −17.3002 | −0.950904 | −0.475452 | − | 0.879742i | \(-0.657716\pi\) | ||||
−0.475452 | + | 0.879742i | \(0.657716\pi\) | |||||||
\(332\) | −10.0054 | −0.549117 | ||||||||
\(333\) | 1.75379 | 0.0961070 | ||||||||
\(334\) | −4.79741 | −0.262503 | ||||||||
\(335\) | −28.0281 | −1.53134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.75379 | −0.422376 | −0.211188 | − | 0.977445i | \(-0.567733\pi\) | ||||
−0.211188 | + | 0.977445i | \(0.567733\pi\) | |||||||
\(338\) | −7.56155 | −0.411294 | ||||||||
\(339\) | 6.43971 | 0.349757 | ||||||||
\(340\) | 11.1231 | 0.603235 | ||||||||
\(341\) | 20.6843 | 1.12012 | ||||||||
\(342\) | −9.59482 | −0.518829 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.68466 | −0.414329 | ||||||||
\(345\) | 21.1231 | 1.13723 | ||||||||
\(346\) | −8.13254 | −0.437208 | ||||||||
\(347\) | −22.8769 | −1.22810 | −0.614048 | − | 0.789269i | \(-0.710460\pi\) | ||||
−0.614048 | + | 0.789269i | \(0.710460\pi\) | |||||||
\(348\) | 1.19935 | 0.0642921 | ||||||||
\(349\) | −14.1293 | −0.756324 | −0.378162 | − | 0.925739i | \(-0.623444\pi\) | ||||
−0.378162 | + | 0.925739i | \(0.623444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.8078 | 1.32414 | ||||||||
\(352\) | 4.56155 | 0.243132 | ||||||||
\(353\) | −4.79741 | −0.255340 | −0.127670 | − | 0.991817i | \(-0.540750\pi\) | ||||
−0.127670 | + | 0.991817i | \(0.540750\pi\) | |||||||
\(354\) | 6.24621 | 0.331982 | ||||||||
\(355\) | −28.5539 | −1.51548 | ||||||||
\(356\) | 2.80928 | 0.148891 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.2462 | 0.964342 | ||||||||
\(359\) | −16.3153 | −0.861091 | −0.430545 | − | 0.902569i | \(-0.641679\pi\) | ||||
−0.430545 | + | 0.902569i | \(0.641679\pi\) | |||||||
\(360\) | 3.33513 | 0.175777 | ||||||||
\(361\) | 18.7538 | 0.987042 | ||||||||
\(362\) | 1.08407 | 0.0569776 | ||||||||
\(363\) | 11.7630 | 0.617396 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −35.6155 | −1.86420 | ||||||||
\(366\) | 5.12311 | 0.267789 | ||||||||
\(367\) | −7.60669 | −0.397066 | −0.198533 | − | 0.980094i | \(-0.563618\pi\) | ||||
−0.198533 | + | 0.980094i | \(0.563618\pi\) | |||||||
\(368\) | 8.24621 | 0.429863 | ||||||||
\(369\) | −8.13254 | −0.423363 | ||||||||
\(370\) | 2.39871 | 0.124703 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.43845 | −0.281970 | ||||||||
\(373\) | −1.19224 | −0.0617316 | −0.0308658 | − | 0.999524i | \(-0.509826\pi\) | ||||
−0.0308658 | + | 0.999524i | \(0.509826\pi\) | |||||||
\(374\) | 23.7565 | 1.22842 | ||||||||
\(375\) | −13.9309 | −0.719387 | ||||||||
\(376\) | −2.13578 | −0.110144 | ||||||||
\(377\) | −4.53448 | −0.233538 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.492423 | −0.0252940 | −0.0126470 | − | 0.999920i | \(-0.504026\pi\) | ||||
−0.0126470 | + | 0.999920i | \(0.504026\pi\) | |||||||
\(380\) | −13.1231 | −0.673201 | ||||||||
\(381\) | 17.0862 | 0.875354 | ||||||||
\(382\) | −6.24621 | −0.319584 | ||||||||
\(383\) | 6.14441 | 0.313965 | 0.156982 | − | 0.987601i | \(-0.449823\pi\) | ||||
0.156982 | + | 0.987601i | \(0.449823\pi\) | |||||||
\(384\) | −1.19935 | −0.0612042 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.3693 | −1.08767 | ||||||||
\(387\) | −12.0000 | −0.609994 | ||||||||
\(388\) | 13.7511 | 0.698106 | ||||||||
\(389\) | 32.9848 | 1.67240 | 0.836199 | − | 0.548426i | \(-0.184773\pi\) | ||||
0.836199 | + | 0.548426i | \(0.184773\pi\) | |||||||
\(390\) | 11.6153 | 0.588165 | ||||||||
\(391\) | 42.9461 | 2.17188 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.1231 | −0.661973 | ||||||||
\(394\) | 20.2462 | 1.01999 | ||||||||
\(395\) | −27.3546 | −1.37636 | ||||||||
\(396\) | 7.12311 | 0.357950 | ||||||||
\(397\) | 37.3600 | 1.87504 | 0.937521 | − | 0.347928i | \(-0.113115\pi\) | ||||
0.937521 | + | 0.347928i | \(0.113115\pi\) | |||||||
\(398\) | 14.1617 | 0.709861 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.438447 | −0.0219224 | ||||||||
\(401\) | 34.8078 | 1.73822 | 0.869108 | − | 0.494622i | \(-0.164693\pi\) | ||||
0.869108 | + | 0.494622i | \(0.164693\pi\) | |||||||
\(402\) | 15.7392 | 0.785002 | ||||||||
\(403\) | 20.5616 | 1.02424 | ||||||||
\(404\) | −18.9591 | −0.943250 | ||||||||
\(405\) | −4.00863 | −0.199191 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.12311 | 0.253943 | ||||||||
\(408\) | −6.24621 | −0.309234 | ||||||||
\(409\) | −17.7274 | −0.876562 | −0.438281 | − | 0.898838i | \(-0.644412\pi\) | ||||
−0.438281 | + | 0.898838i | \(0.644412\pi\) | |||||||
\(410\) | −11.1231 | −0.549331 | ||||||||
\(411\) | 9.89012 | 0.487843 | ||||||||
\(412\) | 11.4677 | 0.564972 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.8769 | 0.632865 | ||||||||
\(415\) | −21.3693 | −1.04898 | ||||||||
\(416\) | 4.53448 | 0.222321 | ||||||||
\(417\) | 21.6155 | 1.05852 | ||||||||
\(418\) | −28.0281 | −1.37090 | ||||||||
\(419\) | −25.2188 | −1.23202 | −0.616009 | − | 0.787739i | \(-0.711251\pi\) | ||||
−0.616009 | + | 0.787739i | \(0.711251\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.8769 | −1.11495 | −0.557476 | − | 0.830193i | \(-0.688230\pi\) | ||||
−0.557476 | + | 0.830193i | \(0.688230\pi\) | |||||||
\(422\) | 7.68466 | 0.374083 | ||||||||
\(423\) | −3.33513 | −0.162160 | ||||||||
\(424\) | 7.43845 | 0.361243 | ||||||||
\(425\) | −2.28343 | −0.110762 | ||||||||
\(426\) | 16.0345 | 0.776875 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.12311 | −0.440982 | ||||||||
\(429\) | 24.8078 | 1.19773 | ||||||||
\(430\) | −16.4127 | −0.791492 | ||||||||
\(431\) | 8.00000 | 0.385346 | 0.192673 | − | 0.981263i | \(-0.438284\pi\) | ||||
0.192673 | + | 0.981263i | \(0.438284\pi\) | |||||||
\(432\) | −5.47091 | −0.263219 | ||||||||
\(433\) | 25.7446 | 1.23721 | 0.618604 | − | 0.785703i | \(-0.287699\pi\) | ||||
0.618604 | + | 0.785703i | \(0.287699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.56155 | 0.122817 | ||||||||
\(436\) | −1.68466 | −0.0806805 | ||||||||
\(437\) | −50.6681 | −2.42378 | ||||||||
\(438\) | 20.0000 | 0.955637 | ||||||||
\(439\) | −8.24782 | −0.393647 | −0.196824 | − | 0.980439i | \(-0.563063\pi\) | ||||
−0.196824 | + | 0.980439i | \(0.563063\pi\) | |||||||
\(440\) | 9.74247 | 0.464454 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.6155 | 1.12328 | ||||||||
\(443\) | 24.8769 | 1.18194 | 0.590968 | − | 0.806695i | \(-0.298746\pi\) | ||||
0.590968 | + | 0.806695i | \(0.298746\pi\) | |||||||
\(444\) | −1.34700 | −0.0639258 | ||||||||
\(445\) | 6.00000 | 0.284427 | ||||||||
\(446\) | −6.67026 | −0.315846 | ||||||||
\(447\) | −11.6153 | −0.549386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.36932 | 0.253394 | 0.126697 | − | 0.991941i | \(-0.459562\pi\) | ||||
0.126697 | + | 0.991941i | \(0.459562\pi\) | |||||||
\(450\) | −0.684658 | −0.0322751 | ||||||||
\(451\) | −23.7565 | −1.11865 | ||||||||
\(452\) | 5.36932 | 0.252551 | ||||||||
\(453\) | −14.6875 | −0.690080 | ||||||||
\(454\) | −3.86098 | −0.181205 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.36932 | 0.345100 | ||||||||
\(457\) | 4.63068 | 0.216614 | 0.108307 | − | 0.994117i | \(-0.465457\pi\) | ||||
0.108307 | + | 0.994117i | \(0.465457\pi\) | |||||||
\(458\) | −11.9935 | −0.560421 | ||||||||
\(459\) | −28.4924 | −1.32991 | ||||||||
\(460\) | 17.6121 | 0.821168 | ||||||||
\(461\) | 22.7048 | 1.05747 | 0.528734 | − | 0.848788i | \(-0.322667\pi\) | ||||
0.528734 | + | 0.848788i | \(0.322667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.36932 | 0.0636376 | 0.0318188 | − | 0.999494i | \(-0.489870\pi\) | ||||
0.0318188 | + | 0.999494i | \(0.489870\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −11.6153 | −0.538648 | ||||||||
\(466\) | −15.9309 | −0.737983 | ||||||||
\(467\) | 11.6153 | 0.537493 | 0.268747 | − | 0.963211i | \(-0.413391\pi\) | ||||
0.268747 | + | 0.963211i | \(0.413391\pi\) | |||||||
\(468\) | 7.08084 | 0.327312 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.56155 | −0.210409 | ||||||||
\(471\) | 24.9848 | 1.15124 | ||||||||
\(472\) | 5.20798 | 0.239717 | ||||||||
\(473\) | −35.0540 | −1.61178 | ||||||||
\(474\) | 15.3610 | 0.705555 | ||||||||
\(475\) | 2.69400 | 0.123609 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.6155 | 0.531838 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.70263 | 0.306251 | 0.153126 | − | 0.988207i | \(-0.451066\pi\) | ||||
0.153126 | + | 0.988207i | \(0.451066\pi\) | |||||||
\(480\) | −2.56155 | −0.116918 | ||||||||
\(481\) | 5.09271 | 0.232207 | ||||||||
\(482\) | 17.4644 | 0.795483 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.80776 | 0.445807 | ||||||||
\(485\) | 29.3693 | 1.33359 | ||||||||
\(486\) | −14.1617 | −0.642387 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | 4.27156 | 0.193364 | ||||||||
\(489\) | −10.2683 | −0.464350 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.1771 | 0.910579 | 0.455289 | − | 0.890343i | \(-0.349536\pi\) | ||||
0.455289 | + | 0.890343i | \(0.349536\pi\) | |||||||
\(492\) | 6.24621 | 0.281601 | ||||||||
\(493\) | 5.20798 | 0.234556 | ||||||||
\(494\) | −27.8617 | −1.25356 | ||||||||
\(495\) | 15.2134 | 0.683791 | ||||||||
\(496\) | −4.53448 | −0.203604 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.0000 | 0.537733 | ||||||||
\(499\) | −5.12311 | −0.229342 | −0.114671 | − | 0.993404i | \(-0.536581\pi\) | ||||
−0.114671 | + | 0.993404i | \(0.536581\pi\) | |||||||
\(500\) | −11.6153 | −0.519453 | ||||||||
\(501\) | 5.75379 | 0.257060 | ||||||||
\(502\) | −6.52262 | −0.291119 | ||||||||
\(503\) | 14.6552 | 0.653441 | 0.326721 | − | 0.945121i | \(-0.394056\pi\) | ||||
0.326721 | + | 0.945121i | \(0.394056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.4924 | −1.80189 | ||||||||
\(506\) | 37.6155 | 1.67221 | ||||||||
\(507\) | 9.06897 | 0.402767 | ||||||||
\(508\) | 14.2462 | 0.632073 | ||||||||
\(509\) | 29.8685 | 1.32390 | 0.661950 | − | 0.749548i | \(-0.269729\pi\) | ||||
0.661950 | + | 0.749548i | \(0.269729\pi\) | |||||||
\(510\) | −13.3405 | −0.590729 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 33.6155 | 1.48416 | ||||||||
\(514\) | −16.9386 | −0.747129 | ||||||||
\(515\) | 24.4924 | 1.07927 | ||||||||
\(516\) | 9.21662 | 0.405739 | ||||||||
\(517\) | −9.74247 | −0.428473 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.75379 | 0.428144 | ||||||||
\(520\) | 9.68466 | 0.424700 | ||||||||
\(521\) | 17.2339 | 0.755030 | 0.377515 | − | 0.926003i | \(-0.376779\pi\) | ||||
0.377515 | + | 0.926003i | \(0.376779\pi\) | |||||||
\(522\) | 1.56155 | 0.0683473 | ||||||||
\(523\) | −44.4732 | −1.94468 | −0.972338 | − | 0.233580i | \(-0.924956\pi\) | ||||
−0.972338 | + | 0.233580i | \(0.924956\pi\) | |||||||
\(524\) | −10.9418 | −0.477996 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.80776 | −0.209628 | ||||||||
\(527\) | −23.6155 | −1.02871 | ||||||||
\(528\) | −5.47091 | −0.238091 | ||||||||
\(529\) | 45.0000 | 1.95652 | ||||||||
\(530\) | 15.8869 | 0.690082 | ||||||||
\(531\) | 8.13254 | 0.352922 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.6155 | −1.02290 | ||||||||
\(534\) | −3.36932 | −0.145805 | ||||||||
\(535\) | −19.4849 | −0.842407 | ||||||||
\(536\) | 13.1231 | 0.566832 | ||||||||
\(537\) | −21.8836 | −0.944349 | ||||||||
\(538\) | −7.72197 | −0.332918 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −11.6847 | −0.502828 | ||||||||
\(541\) | 0.876894 | 0.0377006 | 0.0188503 | − | 0.999822i | \(-0.493999\pi\) | ||||
0.0188503 | + | 0.999822i | \(0.493999\pi\) | |||||||
\(542\) | −21.0949 | −0.906102 | ||||||||
\(543\) | −1.30019 | −0.0557963 | ||||||||
\(544\) | −5.20798 | −0.223291 | ||||||||
\(545\) | −3.59806 | −0.154124 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.6155 | −1.43730 | −0.718648 | − | 0.695374i | \(-0.755239\pi\) | ||||
−0.718648 | + | 0.695374i | \(0.755239\pi\) | |||||||
\(548\) | 8.24621 | 0.352261 | ||||||||
\(549\) | 6.67026 | 0.284680 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | −6.14441 | −0.261761 | ||||||||
\(552\) | −9.89012 | −0.420951 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | −2.87689 | −0.122117 | ||||||||
\(556\) | 18.0227 | 0.764331 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | −7.08084 | −0.299756 | ||||||||
\(559\) | −34.8460 | −1.47383 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.4924 | −1.20295 | ||||||||
\(562\) | −16.1771 | −0.682389 | ||||||||
\(563\) | −15.3610 | −0.647390 | −0.323695 | − | 0.946161i | \(-0.604925\pi\) | ||||
−0.323695 | + | 0.946161i | \(0.604925\pi\) | |||||||
\(564\) | 2.56155 | 0.107861 | ||||||||
\(565\) | 11.4677 | 0.482449 | ||||||||
\(566\) | −27.6175 | −1.16085 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.3693 | 0.560964 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 15.7392 | 0.659244 | ||||||||
\(571\) | 25.1231 | 1.05137 | 0.525685 | − | 0.850680i | \(-0.323809\pi\) | ||||
0.525685 | + | 0.850680i | \(0.323809\pi\) | |||||||
\(572\) | 20.6843 | 0.864854 | ||||||||
\(573\) | 7.49141 | 0.312958 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.61553 | −0.150778 | ||||||||
\(576\) | −1.56155 | −0.0650647 | ||||||||
\(577\) | −39.9063 | −1.66132 | −0.830661 | − | 0.556779i | \(-0.812037\pi\) | ||||
−0.830661 | + | 0.556779i | \(0.812037\pi\) | |||||||
\(578\) | −10.1231 | −0.421066 | ||||||||
\(579\) | 25.6294 | 1.06512 | ||||||||
\(580\) | 2.13578 | 0.0886834 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −16.4924 | −0.683633 | ||||||||
\(583\) | 33.9309 | 1.40527 | ||||||||
\(584\) | 16.6757 | 0.690044 | ||||||||
\(585\) | 15.1231 | 0.625263 | ||||||||
\(586\) | 15.7392 | 0.650182 | ||||||||
\(587\) | −18.8438 | −0.777767 | −0.388884 | − | 0.921287i | \(-0.627139\pi\) | ||||
−0.388884 | + | 0.921287i | \(0.627139\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.8617 | 1.14802 | ||||||||
\(590\) | 11.1231 | 0.457931 | ||||||||
\(591\) | −24.2824 | −0.998842 | ||||||||
\(592\) | −1.12311 | −0.0461594 | ||||||||
\(593\) | 28.7016 | 1.17863 | 0.589316 | − | 0.807903i | \(-0.299397\pi\) | ||||
0.589316 | + | 0.807903i | \(0.299397\pi\) | |||||||
\(594\) | −24.9559 | −1.02395 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.68466 | −0.396699 | ||||||||
\(597\) | −16.9848 | −0.695143 | ||||||||
\(598\) | 37.3923 | 1.52909 | ||||||||
\(599\) | −12.3153 | −0.503191 | −0.251596 | − | 0.967832i | \(-0.580955\pi\) | ||||
−0.251596 | + | 0.967832i | \(0.580955\pi\) | |||||||
\(600\) | 0.525853 | 0.0214679 | ||||||||
\(601\) | 25.2188 | 1.02870 | 0.514348 | − | 0.857582i | \(-0.328034\pi\) | ||||
0.514348 | + | 0.857582i | \(0.328034\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.4924 | 0.834516 | ||||||||
\(604\) | −12.2462 | −0.498291 | ||||||||
\(605\) | 20.9472 | 0.851626 | ||||||||
\(606\) | 22.7386 | 0.923694 | ||||||||
\(607\) | −0.558221 | −0.0226575 | −0.0113287 | − | 0.999936i | \(-0.503606\pi\) | ||||
−0.0113287 | + | 0.999936i | \(0.503606\pi\) | |||||||
\(608\) | 6.14441 | 0.249189 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.12311 | 0.369384 | ||||||||
\(611\) | −9.68466 | −0.391799 | ||||||||
\(612\) | −8.13254 | −0.328739 | ||||||||
\(613\) | −17.0540 | −0.688804 | −0.344402 | − | 0.938822i | \(-0.611918\pi\) | ||||
−0.344402 | + | 0.938822i | \(0.611918\pi\) | |||||||
\(614\) | −25.4817 | −1.02836 | ||||||||
\(615\) | 13.3405 | 0.537942 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.3693 | −0.699262 | −0.349631 | − | 0.936887i | \(-0.613693\pi\) | ||||
−0.349631 | + | 0.936887i | \(0.613693\pi\) | |||||||
\(618\) | −13.7538 | −0.553259 | ||||||||
\(619\) | 30.8050 | 1.23816 | 0.619078 | − | 0.785329i | \(-0.287506\pi\) | ||||
0.619078 | + | 0.785329i | \(0.287506\pi\) | |||||||
\(620\) | −9.68466 | −0.388945 | ||||||||
\(621\) | −45.1143 | −1.81037 | ||||||||
\(622\) | 12.4041 | 0.497359 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.43845 | −0.217712 | ||||||||
\(625\) | −22.6155 | −0.904621 | ||||||||
\(626\) | −8.92132 | −0.356568 | ||||||||
\(627\) | 33.6155 | 1.34247 | ||||||||
\(628\) | 20.8319 | 0.831285 | ||||||||
\(629\) | −5.84912 | −0.233220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.75379 | 0.229055 | 0.114527 | − | 0.993420i | \(-0.463465\pi\) | ||||
0.114527 | + | 0.993420i | \(0.463465\pi\) | |||||||
\(632\) | 12.8078 | 0.509465 | ||||||||
\(633\) | −9.21662 | −0.366328 | ||||||||
\(634\) | 18.4924 | 0.734428 | ||||||||
\(635\) | 30.4268 | 1.20745 | ||||||||
\(636\) | −8.92132 | −0.353753 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.56155 | 0.180594 | ||||||||
\(639\) | 20.8769 | 0.825877 | ||||||||
\(640\) | −2.13578 | −0.0844241 | ||||||||
\(641\) | −17.3693 | −0.686047 | −0.343023 | − | 0.939327i | \(-0.611451\pi\) | ||||
−0.343023 | + | 0.939327i | \(0.611451\pi\) | |||||||
\(642\) | 10.9418 | 0.431839 | ||||||||
\(643\) | 15.6240 | 0.616149 | 0.308074 | − | 0.951362i | \(-0.400315\pi\) | ||||
0.308074 | + | 0.951362i | \(0.400315\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.6847 | 0.775083 | ||||||||
\(646\) | 32.0000 | 1.25902 | ||||||||
\(647\) | 15.2134 | 0.598100 | 0.299050 | − | 0.954237i | \(-0.403330\pi\) | ||||
0.299050 | + | 0.954237i | \(0.403330\pi\) | |||||||
\(648\) | 1.87689 | 0.0737314 | ||||||||
\(649\) | 23.7565 | 0.932524 | ||||||||
\(650\) | −1.98813 | −0.0779810 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.56155 | −0.335296 | ||||||||
\(653\) | −9.86174 | −0.385920 | −0.192960 | − | 0.981207i | \(-0.561809\pi\) | ||||
−0.192960 | + | 0.981207i | \(0.561809\pi\) | |||||||
\(654\) | 2.02050 | 0.0790078 | ||||||||
\(655\) | −23.3693 | −0.913115 | ||||||||
\(656\) | 5.20798 | 0.203338 | ||||||||
\(657\) | 26.0399 | 1.01591 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.3002 | 0.751829 | 0.375914 | − | 0.926654i | \(-0.377329\pi\) | ||||
0.375914 | + | 0.926654i | \(0.377329\pi\) | |||||||
\(660\) | −11.6847 | −0.454825 | ||||||||
\(661\) | 4.15628 | 0.161661 | 0.0808303 | − | 0.996728i | \(-0.474243\pi\) | ||||
0.0808303 | + | 0.996728i | \(0.474243\pi\) | |||||||
\(662\) | 17.3002 | 0.672391 | ||||||||
\(663\) | −28.3234 | −1.09999 | ||||||||
\(664\) | 10.0054 | 0.388285 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.75379 | −0.0679579 | ||||||||
\(667\) | 8.24621 | 0.319295 | ||||||||
\(668\) | 4.79741 | 0.185617 | ||||||||
\(669\) | 8.00000 | 0.309298 | ||||||||
\(670\) | 28.0281 | 1.08282 | ||||||||
\(671\) | 19.4849 | 0.752208 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.6695 | −1.41351 | −0.706753 | − | 0.707461i | \(-0.749841\pi\) | ||||
−0.706753 | + | 0.707461i | \(0.749841\pi\) | |||||||
\(674\) | 7.75379 | 0.298665 | ||||||||
\(675\) | 2.39871 | 0.0923262 | ||||||||
\(676\) | 7.56155 | 0.290829 | ||||||||
\(677\) | −38.9699 | −1.49773 | −0.748867 | − | 0.662720i | \(-0.769402\pi\) | ||||
−0.748867 | + | 0.662720i | \(0.769402\pi\) | |||||||
\(678\) | −6.43971 | −0.247315 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.1231 | −0.426552 | ||||||||
\(681\) | 4.63068 | 0.177448 | ||||||||
\(682\) | −20.6843 | −0.792042 | ||||||||
\(683\) | −5.75379 | −0.220163 | −0.110081 | − | 0.993923i | \(-0.535111\pi\) | ||||
−0.110081 | + | 0.993923i | \(0.535111\pi\) | |||||||
\(684\) | 9.59482 | 0.366867 | ||||||||
\(685\) | 17.6121 | 0.672923 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.3845 | 0.548802 | ||||||||
\(688\) | 7.68466 | 0.292975 | ||||||||
\(689\) | 33.7295 | 1.28499 | ||||||||
\(690\) | −21.1231 | −0.804143 | ||||||||
\(691\) | −17.7274 | −0.674381 | −0.337190 | − | 0.941436i | \(-0.609477\pi\) | ||||
−0.337190 | + | 0.941436i | \(0.609477\pi\) | |||||||
\(692\) | 8.13254 | 0.309153 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.8769 | 0.868395 | ||||||||
\(695\) | 38.4924 | 1.46010 | ||||||||
\(696\) | −1.19935 | −0.0454614 | ||||||||
\(697\) | 27.1231 | 1.02736 | ||||||||
\(698\) | 14.1293 | 0.534802 | ||||||||
\(699\) | 19.1067 | 0.722683 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.0540 | 0.946276 | 0.473138 | − | 0.880988i | \(-0.343121\pi\) | ||||
0.473138 | + | 0.880988i | \(0.343121\pi\) | |||||||
\(702\) | −24.8078 | −0.936309 | ||||||||
\(703\) | 6.90082 | 0.260269 | ||||||||
\(704\) | −4.56155 | −0.171920 | ||||||||
\(705\) | 5.47091 | 0.206046 | ||||||||
\(706\) | 4.79741 | 0.180553 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.24621 | −0.234747 | ||||||||
\(709\) | 31.9309 | 1.19919 | 0.599594 | − | 0.800304i | \(-0.295329\pi\) | ||||
0.599594 | + | 0.800304i | \(0.295329\pi\) | |||||||
\(710\) | 28.5539 | 1.07161 | ||||||||
\(711\) | 20.0000 | 0.750059 | ||||||||
\(712\) | −2.80928 | −0.105282 | ||||||||
\(713\) | −37.3923 | −1.40035 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44.1771 | 1.65213 | ||||||||
\(716\) | −18.2462 | −0.681893 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.3153 | 0.608883 | ||||||||
\(719\) | −10.1207 | −0.377438 | −0.188719 | − | 0.982031i | \(-0.560433\pi\) | ||||
−0.188719 | + | 0.982031i | \(0.560433\pi\) | |||||||
\(720\) | −3.33513 | −0.124293 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.7538 | −0.697944 | ||||||||
\(723\) | −20.9460 | −0.778991 | ||||||||
\(724\) | −1.08407 | −0.0402893 | ||||||||
\(725\) | −0.438447 | −0.0162835 | ||||||||
\(726\) | −11.7630 | −0.436565 | ||||||||
\(727\) | −20.1261 | −0.746435 | −0.373217 | − | 0.927744i | \(-0.621745\pi\) | ||||
−0.373217 | + | 0.927744i | \(0.621745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.6155 | 0.837612 | ||||||||
\(730\) | 35.6155 | 1.31819 | ||||||||
\(731\) | 40.0216 | 1.48025 | ||||||||
\(732\) | −5.12311 | −0.189355 | ||||||||
\(733\) | 27.2069 | 1.00491 | 0.502455 | − | 0.864603i | \(-0.332430\pi\) | ||||
0.502455 | + | 0.864603i | \(0.332430\pi\) | |||||||
\(734\) | 7.60669 | 0.280768 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.24621 | −0.303959 | ||||||||
\(737\) | 59.8617 | 2.20504 | ||||||||
\(738\) | 8.13254 | 0.299363 | ||||||||
\(739\) | 15.0540 | 0.553769 | 0.276885 | − | 0.960903i | \(-0.410698\pi\) | ||||
0.276885 | + | 0.960903i | \(0.410698\pi\) | |||||||
\(740\) | −2.39871 | −0.0881782 | ||||||||
\(741\) | 33.4161 | 1.22757 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.9848 | −0.769859 | −0.384930 | − | 0.922946i | \(-0.625774\pi\) | ||||
−0.384930 | + | 0.922946i | \(0.625774\pi\) | |||||||
\(744\) | 5.43845 | 0.199383 | ||||||||
\(745\) | −20.6843 | −0.757814 | ||||||||
\(746\) | 1.19224 | 0.0436509 | ||||||||
\(747\) | 15.6240 | 0.571651 | ||||||||
\(748\) | −23.7565 | −0.868624 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 13.9309 | 0.508683 | ||||||||
\(751\) | −18.7386 | −0.683782 | −0.341891 | − | 0.939740i | \(-0.611067\pi\) | ||||
−0.341891 | + | 0.939740i | \(0.611067\pi\) | |||||||
\(752\) | 2.13578 | 0.0778839 | ||||||||
\(753\) | 7.82292 | 0.285083 | ||||||||
\(754\) | 4.53448 | 0.165136 | ||||||||
\(755\) | −26.1552 | −0.951885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.4924 | 1.18096 | 0.590479 | − | 0.807053i | \(-0.298939\pi\) | ||||
0.590479 | + | 0.807053i | \(0.298939\pi\) | |||||||
\(758\) | 0.492423 | 0.0178856 | ||||||||
\(759\) | −45.1143 | −1.63754 | ||||||||
\(760\) | 13.1231 | 0.476025 | ||||||||
\(761\) | −53.3621 | −1.93438 | −0.967188 | − | 0.254064i | \(-0.918233\pi\) | ||||
−0.967188 | + | 0.254064i | \(0.918233\pi\) | |||||||
\(762\) | −17.0862 | −0.618969 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.24621 | 0.225980 | ||||||||
\(765\) | −17.3693 | −0.627989 | ||||||||
\(766\) | −6.14441 | −0.222007 | ||||||||
\(767\) | 23.6155 | 0.852707 | ||||||||
\(768\) | 1.19935 | 0.0432779 | ||||||||
\(769\) | −34.8136 | −1.25541 | −0.627705 | − | 0.778451i | \(-0.716006\pi\) | ||||
−0.627705 | + | 0.778451i | \(0.716006\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.3153 | 0.731639 | ||||||||
\(772\) | 21.3693 | 0.769099 | ||||||||
\(773\) | 2.10341 | 0.0756545 | 0.0378272 | − | 0.999284i | \(-0.487956\pi\) | ||||
0.0378272 | + | 0.999284i | \(0.487956\pi\) | |||||||
\(774\) | 12.0000 | 0.431331 | ||||||||
\(775\) | 1.98813 | 0.0714158 | ||||||||
\(776\) | −13.7511 | −0.493636 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −32.9848 | −1.18256 | ||||||||
\(779\) | −32.0000 | −1.14652 | ||||||||
\(780\) | −11.6153 | −0.415895 | ||||||||
\(781\) | 60.9848 | 2.18221 | ||||||||
\(782\) | −42.9461 | −1.53575 | ||||||||
\(783\) | −5.47091 | −0.195514 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44.4924 | 1.58800 | ||||||||
\(786\) | 13.1231 | 0.468086 | ||||||||
\(787\) | 17.7274 | 0.631912 | 0.315956 | − | 0.948774i | \(-0.397675\pi\) | ||||
0.315956 | + | 0.948774i | \(0.397675\pi\) | |||||||
\(788\) | −20.2462 | −0.721241 | ||||||||
\(789\) | 5.76621 | 0.205282 | ||||||||
\(790\) | 27.3546 | 0.973231 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.12311 | −0.253109 | ||||||||
\(793\) | 19.3693 | 0.687825 | ||||||||
\(794\) | −37.3600 | −1.32586 | ||||||||
\(795\) | −19.0540 | −0.675775 | ||||||||
\(796\) | −14.1617 | −0.501947 | ||||||||
\(797\) | 23.9871 | 0.849665 | 0.424833 | − | 0.905272i | \(-0.360333\pi\) | ||||
0.424833 | + | 0.905272i | \(0.360333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.1231 | 0.393507 | ||||||||
\(800\) | 0.438447 | 0.0155014 | ||||||||
\(801\) | −4.38684 | −0.155001 | ||||||||
\(802\) | −34.8078 | −1.22910 | ||||||||
\(803\) | 76.0669 | 2.68434 | ||||||||
\(804\) | −15.7392 | −0.555080 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.5616 | −0.724250 | ||||||||
\(807\) | 9.26137 | 0.326016 | ||||||||
\(808\) | 18.9591 | 0.666978 | ||||||||
\(809\) | −22.9848 | −0.808104 | −0.404052 | − | 0.914736i | \(-0.632399\pi\) | ||||
−0.404052 | + | 0.914736i | \(0.632399\pi\) | |||||||
\(810\) | 4.00863 | 0.140849 | ||||||||
\(811\) | −9.24898 | −0.324776 | −0.162388 | − | 0.986727i | \(-0.551920\pi\) | ||||
−0.162388 | + | 0.986727i | \(0.551920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.3002 | 0.887316 | ||||||||
\(814\) | −5.12311 | −0.179565 | ||||||||
\(815\) | −18.2856 | −0.640516 | ||||||||
\(816\) | 6.24621 | 0.218661 | ||||||||
\(817\) | −47.2177 | −1.65194 | ||||||||
\(818\) | 17.7274 | 0.619823 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.1231 | 0.388436 | ||||||||
\(821\) | 11.9309 | 0.416390 | 0.208195 | − | 0.978087i | \(-0.433241\pi\) | ||||
0.208195 | + | 0.978087i | \(0.433241\pi\) | |||||||
\(822\) | −9.89012 | −0.344957 | ||||||||
\(823\) | 9.75379 | 0.339996 | 0.169998 | − | 0.985444i | \(-0.445624\pi\) | ||||
0.169998 | + | 0.985444i | \(0.445624\pi\) | |||||||
\(824\) | −11.4677 | −0.399495 | ||||||||
\(825\) | 2.39871 | 0.0835122 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.6847 | −1.31042 | −0.655212 | − | 0.755445i | \(-0.727421\pi\) | ||||
−0.655212 | + | 0.755445i | \(0.727421\pi\) | |||||||
\(828\) | −12.8769 | −0.447503 | ||||||||
\(829\) | 16.2651 | 0.564910 | 0.282455 | − | 0.959281i | \(-0.408851\pi\) | ||||
0.282455 | + | 0.959281i | \(0.408851\pi\) | |||||||
\(830\) | 21.3693 | 0.741740 | ||||||||
\(831\) | −11.9935 | −0.416051 | ||||||||
\(832\) | −4.53448 | −0.157205 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −21.6155 | −0.748485 | ||||||||
\(835\) | 10.2462 | 0.354585 | ||||||||
\(836\) | 28.0281 | 0.969371 | ||||||||
\(837\) | 24.8078 | 0.857482 | ||||||||
\(838\) | 25.2188 | 0.871168 | ||||||||
\(839\) | −16.2975 | −0.562651 | −0.281325 | − | 0.959612i | \(-0.590774\pi\) | ||||
−0.281325 | + | 0.959612i | \(0.590774\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 22.8769 | 0.788390 | ||||||||
\(843\) | 19.4020 | 0.668241 | ||||||||
\(844\) | −7.68466 | −0.264517 | ||||||||
\(845\) | 16.1498 | 0.555570 | ||||||||
\(846\) | 3.33513 | 0.114664 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.43845 | −0.255437 | ||||||||
\(849\) | 33.1231 | 1.13678 | ||||||||
\(850\) | 2.28343 | 0.0783209 | ||||||||
\(851\) | −9.26137 | −0.317476 | ||||||||
\(852\) | −16.0345 | −0.549334 | ||||||||
\(853\) | −45.9354 | −1.57280 | −0.786400 | − | 0.617718i | \(-0.788057\pi\) | ||||
−0.786400 | + | 0.617718i | \(0.788057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.4924 | 0.700826 | ||||||||
\(856\) | 9.12311 | 0.311821 | ||||||||
\(857\) | 8.16491 | 0.278908 | 0.139454 | − | 0.990229i | \(-0.455465\pi\) | ||||
0.139454 | + | 0.990229i | \(0.455465\pi\) | |||||||
\(858\) | −24.8078 | −0.846923 | ||||||||
\(859\) | 12.4365 | 0.424327 | 0.212163 | − | 0.977234i | \(-0.431949\pi\) | ||||
0.212163 | + | 0.977234i | \(0.431949\pi\) | |||||||
\(860\) | 16.4127 | 0.559670 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.00000 | −0.272481 | ||||||||
\(863\) | −14.0000 | −0.476566 | −0.238283 | − | 0.971196i | \(-0.576585\pi\) | ||||
−0.238283 | + | 0.971196i | \(0.576585\pi\) | |||||||
\(864\) | 5.47091 | 0.186124 | ||||||||
\(865\) | 17.3693 | 0.590574 | ||||||||
\(866\) | −25.7446 | −0.874838 | ||||||||
\(867\) | 12.1412 | 0.412336 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 58.4233 | 1.98187 | ||||||||
\(870\) | −2.56155 | −0.0868448 | ||||||||
\(871\) | 59.5065 | 2.01630 | ||||||||
\(872\) | 1.68466 | 0.0570497 | ||||||||
\(873\) | −21.4731 | −0.726753 | ||||||||
\(874\) | 50.6681 | 1.71387 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20.0000 | −0.675737 | ||||||||
\(877\) | −18.3153 | −0.618465 | −0.309233 | − | 0.950986i | \(-0.600072\pi\) | ||||
−0.309233 | + | 0.950986i | \(0.600072\pi\) | |||||||
\(878\) | 8.24782 | 0.278351 | ||||||||
\(879\) | −18.8769 | −0.636702 | ||||||||
\(880\) | −9.74247 | −0.328419 | ||||||||
\(881\) | −25.5141 | −0.859591 | −0.429795 | − | 0.902926i | \(-0.641414\pi\) | ||||
−0.429795 | + | 0.902926i | \(0.641414\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.8769 | −0.904480 | −0.452240 | − | 0.891896i | \(-0.649375\pi\) | ||||
−0.452240 | + | 0.891896i | \(0.649375\pi\) | |||||||
\(884\) | −23.6155 | −0.794276 | ||||||||
\(885\) | −13.3405 | −0.448437 | ||||||||
\(886\) | −24.8769 | −0.835756 | ||||||||
\(887\) | −50.1746 | −1.68470 | −0.842350 | − | 0.538932i | \(-0.818828\pi\) | ||||
−0.842350 | + | 0.538932i | \(0.818828\pi\) | |||||||
\(888\) | 1.34700 | 0.0452024 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.00000 | −0.201120 | ||||||||
\(891\) | 8.56155 | 0.286823 | ||||||||
\(892\) | 6.67026 | 0.223337 | ||||||||
\(893\) | −13.1231 | −0.439148 | ||||||||
\(894\) | 11.6153 | 0.388474 | ||||||||
\(895\) | −38.9699 | −1.30262 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.8466 | −1.49738 | ||||||||
\(898\) | −5.36932 | −0.179176 | ||||||||
\(899\) | −4.53448 | −0.151234 | ||||||||
\(900\) | 0.684658 | 0.0228219 | ||||||||
\(901\) | −38.7393 | −1.29059 | ||||||||
\(902\) | 23.7565 | 0.791005 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.36932 | −0.178581 | ||||||||
\(905\) | −2.31534 | −0.0769646 | ||||||||
\(906\) | 14.6875 | 0.487960 | ||||||||
\(907\) | −5.36932 | −0.178285 | −0.0891426 | − | 0.996019i | \(-0.528413\pi\) | ||||
−0.0891426 | + | 0.996019i | \(0.528413\pi\) | |||||||
\(908\) | 3.86098 | 0.128131 | ||||||||
\(909\) | 29.6056 | 0.981956 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.3002 | −1.76591 | −0.882957 | − | 0.469454i | \(-0.844451\pi\) | ||||
−0.882957 | + | 0.469454i | \(0.844451\pi\) | |||||||
\(912\) | −7.36932 | −0.244022 | ||||||||
\(913\) | 45.6401 | 1.51047 | ||||||||
\(914\) | −4.63068 | −0.153169 | ||||||||
\(915\) | −10.9418 | −0.361725 | ||||||||
\(916\) | 11.9935 | 0.396277 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 28.4924 | 0.940390 | ||||||||
\(919\) | 18.0000 | 0.593765 | 0.296883 | − | 0.954914i | \(-0.404053\pi\) | ||||
0.296883 | + | 0.954914i | \(0.404053\pi\) | |||||||
\(920\) | −17.6121 | −0.580653 | ||||||||
\(921\) | 30.5616 | 1.00704 | ||||||||
\(922\) | −22.7048 | −0.747743 | ||||||||
\(923\) | 60.6230 | 1.99543 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.492423 | 0.0161908 | ||||||||
\(926\) | −1.36932 | −0.0449985 | ||||||||
\(927\) | −17.9074 | −0.588156 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 7.49141 | 0.245785 | 0.122893 | − | 0.992420i | \(-0.460783\pi\) | ||||
0.122893 | + | 0.992420i | \(0.460783\pi\) | |||||||
\(930\) | 11.6153 | 0.380881 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.9309 | 0.521833 | ||||||||
\(933\) | −14.8769 | −0.487048 | ||||||||
\(934\) | −11.6153 | −0.380065 | ||||||||
\(935\) | −50.7386 | −1.65933 | ||||||||
\(936\) | −7.08084 | −0.231444 | ||||||||
\(937\) | −57.1078 | −1.86563 | −0.932816 | − | 0.360354i | \(-0.882656\pi\) | ||||
−0.932816 | + | 0.360354i | \(0.882656\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.6998 | 0.349175 | ||||||||
\(940\) | 4.56155 | 0.148781 | ||||||||
\(941\) | 2.66163 | 0.0867667 | 0.0433834 | − | 0.999058i | \(-0.486186\pi\) | ||||
0.0433834 | + | 0.999058i | \(0.486186\pi\) | |||||||
\(942\) | −24.9848 | −0.814050 | ||||||||
\(943\) | 42.9461 | 1.39852 | ||||||||
\(944\) | −5.20798 | −0.169505 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.0540 | 1.13970 | ||||||||
\(947\) | −40.3153 | −1.31007 | −0.655036 | − | 0.755597i | \(-0.727347\pi\) | ||||
−0.655036 | + | 0.755597i | \(0.727347\pi\) | |||||||
\(948\) | −15.3610 | −0.498903 | ||||||||
\(949\) | 75.6155 | 2.45458 | ||||||||
\(950\) | −2.69400 | −0.0874049 | ||||||||
\(951\) | −22.1789 | −0.719201 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.946025 | −0.0306447 | −0.0153224 | − | 0.999883i | \(-0.504877\pi\) | ||||
−0.0153224 | + | 0.999883i | \(0.504877\pi\) | |||||||
\(954\) | −11.6155 | −0.376067 | ||||||||
\(955\) | 13.3405 | 0.431689 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.47091 | −0.176849 | ||||||||
\(958\) | −6.70263 | −0.216552 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.56155 | 0.0826738 | ||||||||
\(961\) | −10.4384 | −0.336724 | ||||||||
\(962\) | −5.09271 | −0.164195 | ||||||||
\(963\) | 14.2462 | 0.459078 | ||||||||
\(964\) | −17.4644 | −0.562492 | ||||||||
\(965\) | 45.6401 | 1.46921 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.93087 | 0.190724 | 0.0953620 | − | 0.995443i | \(-0.469599\pi\) | ||||
0.0953620 | + | 0.995443i | \(0.469599\pi\) | |||||||
\(968\) | −9.80776 | −0.315233 | ||||||||
\(969\) | −38.3793 | −1.23292 | ||||||||
\(970\) | −29.3693 | −0.942992 | ||||||||
\(971\) | −15.7392 | −0.505096 | −0.252548 | − | 0.967584i | \(-0.581269\pi\) | ||||
−0.252548 | + | 0.967584i | \(0.581269\pi\) | |||||||
\(972\) | 14.1617 | 0.454236 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.00000 | 0.256337 | ||||||||
\(975\) | 2.38447 | 0.0763642 | ||||||||
\(976\) | −4.27156 | −0.136729 | ||||||||
\(977\) | −60.6695 | −1.94099 | −0.970495 | − | 0.241122i | \(-0.922484\pi\) | ||||
−0.970495 | + | 0.241122i | \(0.922484\pi\) | |||||||
\(978\) | 10.2683 | 0.328345 | ||||||||
\(979\) | −12.8147 | −0.409559 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.63068 | 0.0839912 | ||||||||
\(982\) | −20.1771 | −0.643877 | ||||||||
\(983\) | 32.2672 | 1.02917 | 0.514583 | − | 0.857441i | \(-0.327947\pi\) | ||||
0.514583 | + | 0.857441i | \(0.327947\pi\) | |||||||
\(984\) | −6.24621 | −0.199122 | ||||||||
\(985\) | −43.2414 | −1.37779 | ||||||||
\(986\) | −5.20798 | −0.165856 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 27.8617 | 0.886400 | ||||||||
\(989\) | 63.3693 | 2.01503 | ||||||||
\(990\) | −15.2134 | −0.483513 | ||||||||
\(991\) | 1.61553 | 0.0513189 | 0.0256595 | − | 0.999671i | \(-0.491831\pi\) | ||||
0.0256595 | + | 0.999671i | \(0.491831\pi\) | |||||||
\(992\) | 4.53448 | 0.143970 | ||||||||
\(993\) | −20.7490 | −0.658450 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.2462 | −0.958869 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 11.7630 | 0.372537 | 0.186268 | − | 0.982499i | \(-0.440361\pi\) | ||||
0.186268 | + | 0.982499i | \(0.440361\pi\) | |||||||
\(998\) | 5.12311 | 0.162169 | ||||||||
\(999\) | 6.14441 | 0.194401 |
(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 | 2842.2.a.p.1.3 | yes | 4 | |
7.6 | odd | 2 | inner | 2842.2.a.p.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2842.2.a.p.1.2 | ✓ | 4 | 7.6 | odd | 2 | inner | |
2842.2.a.p.1.3 | yes | 4 | 1.1 | even | 1 | trivial |