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 | 1.2 | ||
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 | \(-0.612536\pi\) | ||||
−0.346223 | + | 0.938152i | \(0.612536\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.13578 | −0.955149 | −0.477575 | − | 0.878591i | \(-0.658484\pi\) | ||||
−0.477575 | + | 0.878591i | \(0.658484\pi\) | |||||||
\(6\) | 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 | \(-0.283538\pi\) | ||||
0.628820 | + | 0.777551i | \(0.283538\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.56155 | 0.661390 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.20798 | −1.26312 | −0.631561 | − | 0.775326i | \(-0.717585\pi\) | ||||
−0.631561 | + | 0.775326i | \(0.717585\pi\) | |||||||
\(18\) | 1.56155 | 0.368062 | ||||||||
\(19\) | 6.14441 | 1.40962 | 0.704812 | − | 0.709394i | \(-0.251031\pi\) | ||||
0.704812 | + | 0.709394i | \(0.251031\pi\) | |||||||
\(20\) | −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 | \(-0.366502\pi\) | ||||
0.407209 | + | 0.913335i | \(0.366502\pi\) | |||||||
\(32\) | −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 | \(-0.633312\pi\) | ||||
−0.406675 | + | 0.913573i | \(0.633312\pi\) | |||||||
\(42\) | 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 | \(-0.549785\pi\) | ||||
−0.155768 | + | 0.987794i | \(0.549785\pi\) | |||||||
\(48\) | −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 | \(-0.389908\pi\) | ||||
0.339011 | + | 0.940782i | \(0.389908\pi\) | |||||||
\(60\) | 2.56155 | 0.330695 | ||||||||
\(61\) | 4.27156 | 0.546917 | 0.273459 | − | 0.961884i | \(-0.411832\pi\) | ||||
0.273459 | + | 0.961884i | \(0.411832\pi\) | |||||||
\(62\) | −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 | \(-0.0700694\pi\) | ||||
0.975869 | + | 0.218356i | \(0.0700694\pi\) | |||||||
\(74\) | 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 | \(-0.314964\pi\) | ||||
0.549117 | + | 0.835745i | \(0.314964\pi\) | |||||||
\(84\) | 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 | \(-0.547571\pi\) | ||||
−0.148891 | + | 0.988854i | \(0.547571\pi\) | |||||||
\(90\) | −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 | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.12311 | 0.715899 | ||||||||
\(100\) | −0.438447 | −0.0438447 | ||||||||
\(101\) | 18.9591 | 1.88650 | 0.943250 | − | 0.332084i | \(-0.107752\pi\) | ||||
0.943250 | + | 0.332084i | \(0.107752\pi\) | |||||||
\(102\) | −6.24621 | −0.618467 | ||||||||
\(103\) | −11.4677 | −1.12994 | −0.564972 | − | 0.825110i | \(-0.691113\pi\) | ||||
−0.564972 | + | 0.825110i | \(0.691113\pi\) | |||||||
\(104\) | −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 | \(-0.341363\pi\) | ||||
0.477996 | + | 0.878362i | \(0.341363\pi\) | |||||||
\(132\) | 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 | \(-0.776931\pi\) | ||||
−0.764331 | + | 0.644824i | \(0.776931\pi\) | |||||||
\(140\) | 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 | \(-0.812394\pi\) | ||||
−0.831285 | + | 0.555847i | \(0.812394\pi\) | |||||||
\(158\) | 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 | \(-0.559429\pi\) | ||||
−0.185617 | + | 0.982622i | \(0.559429\pi\) | |||||||
\(168\) | 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 | \(-0.600045\pi\) | ||||
−0.309153 | + | 0.951012i | \(0.600045\pi\) | |||||||
\(174\) | 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 | \(-0.487172\pi\) | ||||
0.0402893 | + | 0.999188i | \(0.487172\pi\) | |||||||
\(182\) | 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 | \(-0.332617\pi\) | ||||
0.501947 | + | 0.864898i | \(0.332617\pi\) | |||||||
\(200\) | 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 | \(-0.571695\pi\) | ||||
−0.223337 | + | 0.974741i | \(0.571695\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.684658 | 0.0456439 | ||||||||
\(226\) | −5.36932 | −0.357162 | ||||||||
\(227\) | −3.86098 | −0.256263 | −0.128131 | − | 0.991757i | \(-0.540898\pi\) | ||||
−0.128131 | + | 0.991757i | \(0.540898\pi\) | |||||||
\(228\) | −7.36932 | −0.488045 | ||||||||
\(229\) | −11.9935 | −0.792555 | −0.396277 | − | 0.918131i | \(-0.629698\pi\) | ||||
−0.396277 | + | 0.918131i | \(0.629698\pi\) | |||||||
\(230\) | 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 | \(-0.309843\pi\) | ||||
0.562492 | + | 0.826803i | \(0.309843\pi\) | |||||||
\(242\) | −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 | \(-0.565997\pi\) | ||||
−0.205852 | + | 0.978583i | \(0.565997\pi\) | |||||||
\(252\) | 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 | \(-0.677170\pi\) | ||||
−0.528300 | + | 0.849058i | \(0.677170\pi\) | |||||||
\(258\) | 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 | \(-0.575643\pi\) | ||||
−0.235408 | + | 0.971897i | \(0.575643\pi\) | |||||||
\(270\) | 11.6847 | 0.711106 | ||||||||
\(271\) | −21.0949 | −1.28142 | −0.640711 | − | 0.767782i | \(-0.721360\pi\) | ||||
−0.640711 | + | 0.767782i | \(0.721360\pi\) | |||||||
\(272\) | −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 | \(-0.806497\pi\) | ||||
−0.820844 | + | 0.571152i | \(0.806497\pi\) | |||||||
\(284\) | −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 | \(-0.347940\pi\) | ||||
0.459748 | + | 0.888049i | \(0.347940\pi\) | |||||||
\(294\) | 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 | \(-0.759160\pi\) | ||||
−0.727159 | + | 0.686469i | \(0.759160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.7538 | 0.782426 | ||||||||
\(310\) | 9.68466 | 0.550052 | ||||||||
\(311\) | 12.4041 | 0.703372 | 0.351686 | − | 0.936118i | \(-0.385608\pi\) | ||||
0.351686 | + | 0.936118i | \(0.385608\pi\) | |||||||
\(312\) | 5.43845 | 0.307891 | ||||||||
\(313\) | −8.92132 | −0.504263 | −0.252131 | − | 0.967693i | \(-0.581132\pi\) | ||||
−0.252131 | + | 0.967693i | \(0.581132\pi\) | |||||||
\(314\) | 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 | \(-0.376556\pi\) | ||||
0.378162 | + | 0.925739i | \(0.376556\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.8078 | 1.32414 | ||||||||
\(352\) | 4.56155 | 0.243132 | ||||||||
\(353\) | 4.79741 | 0.255340 | 0.127670 | − | 0.991817i | \(-0.459250\pi\) | ||||
0.127670 | + | 0.991817i | \(0.459250\pi\) | |||||||
\(354\) | 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 | \(-0.436382\pi\) | ||||
0.198533 | + | 0.980094i | \(0.436382\pi\) | |||||||
\(368\) | 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 | \(-0.550177\pi\) | ||||
−0.156982 | + | 0.987601i | \(0.550177\pi\) | |||||||
\(384\) | 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 | \(-0.886885\pi\) | ||||
−0.937521 | + | 0.347928i | \(0.886885\pi\) | |||||||
\(398\) | −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 | \(-0.355588\pi\) | ||||
0.438281 | + | 0.898838i | \(0.355588\pi\) | |||||||
\(410\) | −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 | \(-0.288749\pi\) | ||||
0.616009 | + | 0.787739i | \(0.288749\pi\) | |||||||
\(420\) | 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 | \(-0.712301\pi\) | ||||
−0.618604 | + | 0.785703i | \(0.712301\pi\) | |||||||
\(434\) | 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 | \(-0.436937\pi\) | ||||
0.196824 | + | 0.980439i | \(0.436937\pi\) | |||||||
\(440\) | −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 | \(-0.677333\pi\) | ||||
−0.528734 | + | 0.848788i | \(0.677333\pi\) | |||||||
\(462\) | 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 | \(-0.586609\pi\) | ||||
−0.268747 | + | 0.963211i | \(0.586609\pi\) | |||||||
\(468\) | −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 | \(-0.548934\pi\) | ||||
−0.153126 | + | 0.988207i | \(0.548934\pi\) | |||||||
\(480\) | −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 | \(-0.605944\pi\) | ||||
−0.326721 | + | 0.945121i | \(0.605944\pi\) | |||||||
\(504\) | 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 | \(-0.730271\pi\) | ||||
−0.661950 | + | 0.749548i | \(0.730271\pi\) | |||||||
\(510\) | 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 | \(-0.623221\pi\) | ||||
−0.377515 | + | 0.926003i | \(0.623221\pi\) | |||||||
\(522\) | 1.56155 | 0.0683473 | ||||||||
\(523\) | 44.4732 | 1.94468 | 0.972338 | − | 0.233580i | \(-0.0750439\pi\) | ||||
0.972338 | + | 0.233580i | \(0.0750439\pi\) | |||||||
\(524\) | 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 | \(-0.395075\pi\) | ||||
0.323695 | + | 0.946161i | \(0.395075\pi\) | |||||||
\(564\) | 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 | \(-0.187963\pi\) | ||||
0.830661 | + | 0.556779i | \(0.187963\pi\) | |||||||
\(578\) | −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 | \(-0.372861\pi\) | ||||
0.388884 | + | 0.921287i | \(0.372861\pi\) | |||||||
\(588\) | 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 | \(-0.700603\pi\) | ||||
−0.589316 | + | 0.807903i | \(0.700603\pi\) | |||||||
\(594\) | 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 | \(-0.671966\pi\) | ||||
−0.514348 | + | 0.857582i | \(0.671966\pi\) | |||||||
\(602\) | 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 | \(-0.496394\pi\) | ||||
0.0113287 | + | 0.999936i | \(0.496394\pi\) | |||||||
\(608\) | −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 | \(-0.712494\pi\) | ||||
−0.619078 | + | 0.785329i | \(0.712494\pi\) | |||||||
\(620\) | −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 | \(-0.599685\pi\) | ||||
−0.308074 | + | 0.951362i | \(0.599685\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.6847 | 0.775083 | ||||||||
\(646\) | 32.0000 | 1.25902 | ||||||||
\(647\) | −15.2134 | −0.598100 | −0.299050 | − | 0.954237i | \(-0.596670\pi\) | ||||
−0.299050 | + | 0.954237i | \(0.596670\pi\) | |||||||
\(648\) | 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 | \(-0.525757\pi\) | ||||
−0.0808303 | + | 0.996728i | \(0.525757\pi\) | |||||||
\(662\) | 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 | \(-0.230598\pi\) | ||||
0.748867 | + | 0.662720i | \(0.230598\pi\) | |||||||
\(678\) | 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 | \(-0.390523\pi\) | ||||
0.337190 | + | 0.941436i | \(0.390523\pi\) | |||||||
\(692\) | −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 | \(-0.439567\pi\) | ||||
0.188719 | + | 0.982031i | \(0.439567\pi\) | |||||||
\(720\) | 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 | \(-0.378255\pi\) | ||||
0.373217 | + | 0.927744i | \(0.378255\pi\) | |||||||
\(728\) | 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 | \(-0.667570\pi\) | ||||
−0.502455 | + | 0.864603i | \(0.667570\pi\) | |||||||
\(734\) | −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 | \(-0.0817672\pi\) | ||||
0.967188 | + | 0.254064i | \(0.0817672\pi\) | |||||||
\(762\) | 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 | \(-0.283994\pi\) | ||||
0.627705 | + | 0.778451i | \(0.283994\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.3153 | 0.731639 | ||||||||
\(772\) | 21.3693 | 0.769099 | ||||||||
\(773\) | −2.10341 | −0.0756545 | −0.0378272 | − | 0.999284i | \(-0.512044\pi\) | ||||
−0.0378272 | + | 0.999284i | \(0.512044\pi\) | |||||||
\(774\) | 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 | \(-0.602325\pi\) | ||||
−0.315956 | + | 0.948774i | \(0.602325\pi\) | |||||||
\(788\) | −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 | \(-0.639667\pi\) | ||||
−0.424833 | + | 0.905272i | \(0.639667\pi\) | |||||||
\(798\) | 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 | \(-0.448080\pi\) | ||||
0.162388 | + | 0.986727i | \(0.448080\pi\) | |||||||
\(812\) | 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 | \(-0.591149\pi\) | ||||
−0.282455 | + | 0.959281i | \(0.591149\pi\) | |||||||
\(830\) | 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 | \(-0.409226\pi\) | ||||
0.281325 | + | 0.959612i | \(0.409226\pi\) | |||||||
\(840\) | 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 | \(-0.211943\pi\) | ||||
0.786400 | + | 0.617718i | \(0.211943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.4924 | 0.700826 | ||||||||
\(856\) | 9.12311 | 0.311821 | ||||||||
\(857\) | −8.16491 | −0.278908 | −0.139454 | − | 0.990229i | \(-0.544535\pi\) | ||||
−0.139454 | + | 0.990229i | \(0.544535\pi\) | |||||||
\(858\) | −24.8078 | −0.846923 | ||||||||
\(859\) | −12.4365 | −0.424327 | −0.212163 | − | 0.977234i | \(-0.568051\pi\) | ||||
−0.212163 | + | 0.977234i | \(0.568051\pi\) | |||||||
\(860\) | −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 | \(-0.358586\pi\) | ||||
0.429795 | + | 0.902926i | \(0.358586\pi\) | |||||||
\(882\) | 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 | \(-0.181172\pi\) | ||||
0.842350 | + | 0.538932i | \(0.181172\pi\) | |||||||
\(888\) | −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 | \(-0.539217\pi\) | ||||
−0.122893 | + | 0.992420i | \(0.539217\pi\) | |||||||
\(930\) | −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 | \(-0.117344\pi\) | ||||
0.932816 | + | 0.360354i | \(0.117344\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.6998 | 0.349175 | ||||||||
\(940\) | 4.56155 | 0.148781 | ||||||||
\(941\) | −2.66163 | −0.0867667 | −0.0433834 | − | 0.999058i | \(-0.513814\pi\) | ||||
−0.0433834 | + | 0.999058i | \(0.513814\pi\) | |||||||
\(942\) | −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 | \(-0.418731\pi\) | ||||
0.252548 | + | 0.967584i | \(0.418731\pi\) | |||||||
\(972\) | −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 | \(-0.672053\pi\) | ||||
−0.514583 | + | 0.857441i | \(0.672053\pi\) | |||||||
\(984\) | −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 | \(-0.559639\pi\) | ||||
−0.186268 | + | 0.982499i | \(0.559639\pi\) | |||||||
\(998\) | 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.1.2 | ✓ | 4 | |
7.6 | odd | 2 | inner | 2842.2.a.p.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2842.2.a.p.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2842.2.a.p.1.3 | yes | 4 | 7.6 | odd | 2 | inner |