Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 18 x^{14} + 83 x^{13} + 112 x^{12} - 668 x^{11} - 235 x^{10} + 2648 x^{9} - 298 x^{8} - 5422 x^{7} + 2075 x^{6} + 5385 x^{5} - 3163 x^{4} - 1882 x^{3} + \cdots - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-2.35145\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.35145 | 1.66273 | 0.831364 | − | 0.555729i | \(-0.187561\pi\) | ||||
0.831364 | + | 0.555729i | \(0.187561\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.52933 | 1.76466 | ||||||||
\(5\) | 2.01529 | 0.901266 | 0.450633 | − | 0.892709i | \(-0.351198\pi\) | ||||
0.450633 | + | 0.892709i | \(0.351198\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.59614 | 1.27143 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.73886 | 1.49856 | ||||||||
\(11\) | −0.0911513 | −0.0274832 | −0.0137416 | − | 0.999906i | \(-0.504374\pi\) | ||||
−0.0137416 | + | 0.999906i | \(0.504374\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.36528 | −0.656011 | −0.328005 | − | 0.944676i | \(-0.606376\pi\) | ||||
−0.328005 | + | 0.944676i | \(0.606376\pi\) | |||||||
\(14\) | −2.35145 | −0.628452 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.39749 | 0.349373 | ||||||||
\(17\) | 4.89667 | 1.18762 | 0.593808 | − | 0.804607i | \(-0.297624\pi\) | ||||
0.593808 | + | 0.804607i | \(0.297624\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.257348 | −0.0590396 | −0.0295198 | − | 0.999564i | \(-0.509398\pi\) | ||||
−0.0295198 | + | 0.999564i | \(0.509398\pi\) | |||||||
\(20\) | 7.11262 | 1.59043 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.214338 | −0.0456970 | ||||||||
\(23\) | −1.91105 | −0.398482 | −0.199241 | − | 0.979951i | \(-0.563848\pi\) | ||||
−0.199241 | + | 0.979951i | \(0.563848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.938597 | −0.187719 | ||||||||
\(26\) | −5.56184 | −1.09077 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.52933 | −0.666980 | ||||||||
\(29\) | 5.21144 | 0.967740 | 0.483870 | − | 0.875140i | \(-0.339231\pi\) | ||||
0.483870 | + | 0.875140i | \(0.339231\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.91024 | 0.522694 | 0.261347 | − | 0.965245i | \(-0.415833\pi\) | ||||
0.261347 | + | 0.965245i | \(0.415833\pi\) | |||||||
\(32\) | −3.90614 | −0.690514 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.5143 | 1.97468 | ||||||||
\(35\) | −2.01529 | −0.340647 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.61218 | 1.25143 | 0.625717 | − | 0.780050i | \(-0.284806\pi\) | ||||
0.625717 | + | 0.780050i | \(0.284806\pi\) | |||||||
\(38\) | −0.605141 | −0.0981668 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.24727 | 1.14589 | ||||||||
\(41\) | 4.73944 | 0.740177 | 0.370088 | − | 0.928997i | \(-0.379327\pi\) | ||||
0.370088 | + | 0.928997i | \(0.379327\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.38103 | 1.43059 | 0.715297 | − | 0.698821i | \(-0.246291\pi\) | ||||
0.715297 | + | 0.698821i | \(0.246291\pi\) | |||||||
\(44\) | −0.321703 | −0.0484985 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.49374 | −0.662566 | ||||||||
\(47\) | 1.49159 | 0.217571 | 0.108785 | − | 0.994065i | \(-0.465304\pi\) | ||||
0.108785 | + | 0.994065i | \(0.465304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.20707 | −0.312126 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.34785 | −1.15764 | ||||||||
\(53\) | 11.8399 | 1.62634 | 0.813171 | − | 0.582025i | \(-0.197740\pi\) | ||||
0.813171 | + | 0.582025i | \(0.197740\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.183697 | −0.0247696 | ||||||||
\(56\) | −3.59614 | −0.480554 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.2544 | 1.60909 | ||||||||
\(59\) | 5.10974 | 0.665231 | 0.332616 | − | 0.943063i | \(-0.392069\pi\) | ||||
0.332616 | + | 0.943063i | \(0.392069\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.51881 | 0.962686 | 0.481343 | − | 0.876532i | \(-0.340149\pi\) | ||||
0.481343 | + | 0.876532i | \(0.340149\pi\) | |||||||
\(62\) | 6.84329 | 0.869098 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.9801 | −1.49751 | ||||||||
\(65\) | −4.76673 | −0.591240 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.09291 | 0.744368 | 0.372184 | − | 0.928159i | \(-0.378609\pi\) | ||||
0.372184 | + | 0.928159i | \(0.378609\pi\) | |||||||
\(68\) | 17.2819 | 2.09574 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.73886 | −0.566402 | ||||||||
\(71\) | 5.28553 | 0.627277 | 0.313639 | − | 0.949542i | \(-0.398452\pi\) | ||||
0.313639 | + | 0.949542i | \(0.398452\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.70061 | 0.316082 | 0.158041 | − | 0.987433i | \(-0.449482\pi\) | ||||
0.158041 | + | 0.987433i | \(0.449482\pi\) | |||||||
\(74\) | 17.8997 | 2.08079 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.908264 | −0.104185 | ||||||||
\(77\) | 0.0911513 | 0.0103877 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.8809 | 1.78674 | 0.893370 | − | 0.449322i | \(-0.148335\pi\) | ||||
0.893370 | + | 0.449322i | \(0.148335\pi\) | |||||||
\(80\) | 2.81635 | 0.314878 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.1446 | 1.23071 | ||||||||
\(83\) | −12.3986 | −1.36092 | −0.680462 | − | 0.732783i | \(-0.738221\pi\) | ||||
−0.680462 | + | 0.732783i | \(0.738221\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.86822 | 1.07036 | ||||||||
\(86\) | 22.0590 | 2.37869 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.327793 | −0.0349428 | ||||||||
\(89\) | −2.65998 | −0.281958 | −0.140979 | − | 0.990013i | \(-0.545025\pi\) | ||||
−0.140979 | + | 0.990013i | \(0.545025\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.36528 | 0.247949 | ||||||||
\(92\) | −6.74472 | −0.703186 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.50740 | 0.361761 | ||||||||
\(95\) | −0.518631 | −0.0532104 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.3630 | −1.45834 | −0.729170 | − | 0.684332i | \(-0.760094\pi\) | ||||
−0.729170 | + | 0.684332i | \(0.760094\pi\) | |||||||
\(98\) | 2.35145 | 0.237533 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.31262 | −0.331262 | ||||||||
\(101\) | 3.72951 | 0.371100 | 0.185550 | − | 0.982635i | \(-0.440593\pi\) | ||||
0.185550 | + | 0.982635i | \(0.440593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8352 | 1.06762 | 0.533812 | − | 0.845603i | \(-0.320759\pi\) | ||||
0.533812 | + | 0.845603i | \(0.320759\pi\) | |||||||
\(104\) | −8.50587 | −0.834070 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 27.8411 | 2.70416 | ||||||||
\(107\) | −17.2741 | −1.66995 | −0.834976 | − | 0.550287i | \(-0.814518\pi\) | ||||
−0.834976 | + | 0.550287i | \(0.814518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5617 | −1.01163 | −0.505814 | − | 0.862643i | \(-0.668808\pi\) | ||||
−0.505814 | + | 0.862643i | \(0.668808\pi\) | |||||||
\(110\) | −0.431954 | −0.0411852 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.39749 | −0.132051 | ||||||||
\(113\) | −12.0474 | −1.13333 | −0.566663 | − | 0.823949i | \(-0.691766\pi\) | ||||
−0.566663 | + | 0.823949i | \(0.691766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.85132 | −0.359138 | ||||||||
\(116\) | 18.3929 | 1.70773 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.0153 | 1.10610 | ||||||||
\(119\) | −4.89667 | −0.448877 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9917 | −0.999245 | ||||||||
\(122\) | 17.6801 | 1.60068 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.2712 | 0.922379 | ||||||||
\(125\) | −11.9680 | −1.07045 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −20.3583 | −1.79944 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.2087 | −0.983072 | ||||||||
\(131\) | 20.8416 | 1.82094 | 0.910468 | − | 0.413579i | \(-0.135721\pi\) | ||||
0.910468 | + | 0.413579i | \(0.135721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.257348 | 0.0223149 | ||||||||
\(134\) | 14.3272 | 1.23768 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.6091 | 1.50997 | ||||||||
\(137\) | −4.51432 | −0.385685 | −0.192842 | − | 0.981230i | \(-0.561771\pi\) | ||||
−0.192842 | + | 0.981230i | \(0.561771\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.83048 | 0.494535 | 0.247267 | − | 0.968947i | \(-0.420467\pi\) | ||||
0.247267 | + | 0.968947i | \(0.420467\pi\) | |||||||
\(140\) | −7.11262 | −0.601126 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.4287 | 1.04299 | ||||||||
\(143\) | 0.215598 | 0.0180292 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.5026 | 0.872191 | ||||||||
\(146\) | 6.35035 | 0.525559 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 26.8659 | 2.20836 | ||||||||
\(149\) | −8.09500 | −0.663168 | −0.331584 | − | 0.943426i | \(-0.607583\pi\) | ||||
−0.331584 | + | 0.943426i | \(0.607583\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.34672 | 0.679247 | 0.339623 | − | 0.940562i | \(-0.389700\pi\) | ||||
0.339623 | + | 0.940562i | \(0.389700\pi\) | |||||||
\(152\) | −0.925458 | −0.0750645 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.214338 | 0.0172718 | ||||||||
\(155\) | 5.86498 | 0.471087 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0614 | −1.04242 | −0.521208 | − | 0.853430i | \(-0.674518\pi\) | ||||
−0.521208 | + | 0.853430i | \(0.674518\pi\) | |||||||
\(158\) | 37.3431 | 2.97086 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.87201 | −0.622337 | ||||||||
\(161\) | 1.91105 | 0.150612 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.88655 | −0.539396 | −0.269698 | − | 0.962945i | \(-0.586924\pi\) | ||||
−0.269698 | + | 0.962945i | \(0.586924\pi\) | |||||||
\(164\) | 16.7270 | 1.30616 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.1547 | −2.26285 | ||||||||
\(167\) | −12.0030 | −0.928817 | −0.464408 | − | 0.885621i | \(-0.653733\pi\) | ||||
−0.464408 | + | 0.885621i | \(0.653733\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.40545 | −0.569650 | ||||||||
\(170\) | 23.2046 | 1.77971 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 33.1087 | 2.52452 | ||||||||
\(173\) | −19.3994 | −1.47491 | −0.737456 | − | 0.675396i | \(-0.763973\pi\) | ||||
−0.737456 | + | 0.675396i | \(0.763973\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.938597 | 0.0709513 | ||||||||
\(176\) | −0.127383 | −0.00960187 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.25482 | −0.468819 | ||||||||
\(179\) | 15.3418 | 1.14670 | 0.573349 | − | 0.819311i | \(-0.305644\pi\) | ||||
0.573349 | + | 0.819311i | \(0.305644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.81836 | −0.729793 | −0.364896 | − | 0.931048i | \(-0.618896\pi\) | ||||
−0.364896 | + | 0.931048i | \(0.618896\pi\) | |||||||
\(182\) | 5.56184 | 0.412271 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.87240 | −0.506640 | ||||||||
\(185\) | 15.3408 | 1.12788 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.446338 | −0.0326394 | ||||||||
\(188\) | 5.26431 | 0.383939 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.21954 | −0.0884744 | ||||||||
\(191\) | −21.9444 | −1.58784 | −0.793921 | − | 0.608020i | \(-0.791964\pi\) | ||||
−0.793921 | + | 0.608020i | \(0.791964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.55014 | −0.543471 | −0.271736 | − | 0.962372i | \(-0.587598\pi\) | ||||
−0.271736 | + | 0.962372i | \(0.587598\pi\) | |||||||
\(194\) | −33.7739 | −2.42482 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.52933 | 0.252095 | ||||||||
\(197\) | −19.1551 | −1.36475 | −0.682374 | − | 0.731004i | \(-0.739052\pi\) | ||||
−0.682374 | + | 0.731004i | \(0.739052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.4063 | 1.44656 | 0.723281 | − | 0.690554i | \(-0.242633\pi\) | ||||
0.723281 | + | 0.690554i | \(0.242633\pi\) | |||||||
\(200\) | −3.37532 | −0.238671 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.76976 | 0.617038 | ||||||||
\(203\) | −5.21144 | −0.365771 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.55136 | 0.667096 | ||||||||
\(206\) | 25.4785 | 1.77517 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.30546 | −0.229192 | ||||||||
\(209\) | 0.0234576 | 0.00162260 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.34925 | 0.299415 | 0.149707 | − | 0.988730i | \(-0.452167\pi\) | ||||
0.149707 | + | 0.988730i | \(0.452167\pi\) | |||||||
\(212\) | 41.7870 | 2.86994 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −40.6192 | −2.77667 | ||||||||
\(215\) | 18.9055 | 1.28935 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.91024 | −0.197560 | ||||||||
\(218\) | −24.8353 | −1.68206 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.648325 | −0.0437101 | ||||||||
\(221\) | −11.5820 | −0.779089 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.11821 | 0.141846 | 0.0709229 | − | 0.997482i | \(-0.477406\pi\) | ||||
0.0709229 | + | 0.997482i | \(0.477406\pi\) | |||||||
\(224\) | 3.90614 | 0.260990 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −28.3290 | −1.88441 | ||||||||
\(227\) | −4.20493 | −0.279091 | −0.139546 | − | 0.990216i | \(-0.544564\pi\) | ||||
−0.139546 | + | 0.990216i | \(0.544564\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.69447 | −0.244137 | −0.122069 | − | 0.992522i | \(-0.538953\pi\) | ||||
−0.122069 | + | 0.992522i | \(0.538953\pi\) | |||||||
\(230\) | −9.05620 | −0.597148 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.7410 | 1.23041 | ||||||||
\(233\) | −13.1218 | −0.859635 | −0.429818 | − | 0.902916i | \(-0.641422\pi\) | ||||
−0.429818 | + | 0.902916i | \(0.641422\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00599 | 0.196089 | ||||||||
\(236\) | 18.0339 | 1.17391 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.5143 | −0.746360 | ||||||||
\(239\) | −17.2224 | −1.11402 | −0.557012 | − | 0.830504i | \(-0.688052\pi\) | ||||
−0.557012 | + | 0.830504i | \(0.688052\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0726 | 0.970912 | 0.485456 | − | 0.874261i | \(-0.338654\pi\) | ||||
0.485456 | + | 0.874261i | \(0.338654\pi\) | |||||||
\(242\) | −25.8464 | −1.66147 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26.5364 | 1.69882 | ||||||||
\(245\) | 2.01529 | 0.128752 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.608700 | 0.0387306 | ||||||||
\(248\) | 10.4656 | 0.664567 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −28.1422 | −1.77987 | ||||||||
\(251\) | 17.3625 | 1.09591 | 0.547956 | − | 0.836507i | \(-0.315406\pi\) | ||||
0.547956 | + | 0.836507i | \(0.315406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.174195 | 0.0109515 | ||||||||
\(254\) | −2.35145 | −0.147543 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −23.9114 | −1.49446 | ||||||||
\(257\) | 15.7891 | 0.984895 | 0.492448 | − | 0.870342i | \(-0.336102\pi\) | ||||
0.492448 | + | 0.870342i | \(0.336102\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.61218 | −0.472998 | ||||||||
\(260\) | −16.8234 | −1.04334 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 49.0080 | 3.02772 | ||||||||
\(263\) | −11.0415 | −0.680850 | −0.340425 | − | 0.940272i | \(-0.610571\pi\) | ||||
−0.340425 | + | 0.940272i | \(0.610571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.8609 | 1.46577 | ||||||||
\(266\) | 0.605141 | 0.0371036 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.5039 | 1.31356 | ||||||||
\(269\) | 0.794820 | 0.0484610 | 0.0242305 | − | 0.999706i | \(-0.492286\pi\) | ||||
0.0242305 | + | 0.999706i | \(0.492286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.86100 | 0.234539 | 0.117269 | − | 0.993100i | \(-0.462586\pi\) | ||||
0.117269 | + | 0.993100i | \(0.462586\pi\) | |||||||
\(272\) | 6.84305 | 0.414921 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.6152 | −0.641289 | ||||||||
\(275\) | 0.0855544 | 0.00515912 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.9785 | −0.659636 | −0.329818 | − | 0.944045i | \(-0.606987\pi\) | ||||
−0.329818 | + | 0.944045i | \(0.606987\pi\) | |||||||
\(278\) | 13.7101 | 0.822277 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.24727 | −0.433107 | ||||||||
\(281\) | −0.451302 | −0.0269224 | −0.0134612 | − | 0.999909i | \(-0.504285\pi\) | ||||
−0.0134612 | + | 0.999909i | \(0.504285\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.68388 | 0.516203 | 0.258102 | − | 0.966118i | \(-0.416903\pi\) | ||||
0.258102 | + | 0.966118i | \(0.416903\pi\) | |||||||
\(284\) | 18.6544 | 1.10693 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.506969 | 0.0299777 | ||||||||
\(287\) | −4.73944 | −0.279761 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.97735 | 0.410432 | ||||||||
\(290\) | 24.6963 | 1.45022 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.53132 | 0.557779 | ||||||||
\(293\) | −10.6634 | −0.622963 | −0.311482 | − | 0.950252i | \(-0.600825\pi\) | ||||
−0.311482 | + | 0.950252i | \(0.600825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2976 | 0.599550 | ||||||||
\(296\) | 27.3744 | 1.59111 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.0350 | −1.10267 | ||||||||
\(299\) | 4.52017 | 0.261408 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.38103 | −0.540714 | ||||||||
\(302\) | 19.6269 | 1.12940 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.359641 | −0.0206269 | ||||||||
\(305\) | 15.1526 | 0.867636 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.4364 | 1.05222 | 0.526110 | − | 0.850417i | \(-0.323650\pi\) | ||||
0.526110 | + | 0.850417i | \(0.323650\pi\) | |||||||
\(308\) | 0.321703 | 0.0183307 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.7912 | 0.783289 | ||||||||
\(311\) | −4.89702 | −0.277684 | −0.138842 | − | 0.990315i | \(-0.544338\pi\) | ||||
−0.138842 | + | 0.990315i | \(0.544338\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.9637 | −1.29798 | −0.648991 | − | 0.760796i | \(-0.724809\pi\) | ||||
−0.648991 | + | 0.760796i | \(0.724809\pi\) | |||||||
\(314\) | −30.7133 | −1.73325 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 56.0488 | 3.15299 | ||||||||
\(317\) | −27.7698 | −1.55971 | −0.779853 | − | 0.625963i | \(-0.784706\pi\) | ||||
−0.779853 | + | 0.625963i | \(0.784706\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.475029 | −0.0265965 | ||||||||
\(320\) | −24.1434 | −1.34966 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.49374 | 0.250426 | ||||||||
\(323\) | −1.26015 | −0.0701164 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.22005 | 0.123146 | ||||||||
\(326\) | −16.1934 | −0.896869 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.0437 | 0.941080 | ||||||||
\(329\) | −1.49159 | −0.0822340 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.7608 | 1.03118 | 0.515592 | − | 0.856834i | \(-0.327572\pi\) | ||||
0.515592 | + | 0.856834i | \(0.327572\pi\) | |||||||
\(332\) | −43.7587 | −2.40157 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.2244 | −1.54437 | ||||||||
\(335\) | 12.2790 | 0.670874 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.0118 | 1.47143 | 0.735714 | − | 0.677292i | \(-0.236847\pi\) | ||||
0.735714 | + | 0.677292i | \(0.236847\pi\) | |||||||
\(338\) | −17.4136 | −0.947173 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 34.8282 | 1.88882 | ||||||||
\(341\) | −0.265272 | −0.0143653 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 33.7355 | 1.81890 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −45.6168 | −2.45238 | ||||||||
\(347\) | 10.4238 | 0.559579 | 0.279790 | − | 0.960061i | \(-0.409735\pi\) | ||||
0.279790 | + | 0.960061i | \(0.409735\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.23034 | 0.387031 | 0.193516 | − | 0.981097i | \(-0.438011\pi\) | ||||
0.193516 | + | 0.981097i | \(0.438011\pi\) | |||||||
\(350\) | 2.20707 | 0.117973 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.356050 | 0.0189775 | ||||||||
\(353\) | −28.2757 | −1.50497 | −0.752483 | − | 0.658612i | \(-0.771144\pi\) | ||||
−0.752483 | + | 0.658612i | \(0.771144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.6519 | 0.565344 | ||||||||
\(356\) | −9.38795 | −0.497560 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 36.0755 | 1.90665 | ||||||||
\(359\) | −19.7759 | −1.04373 | −0.521867 | − | 0.853027i | \(-0.674764\pi\) | ||||
−0.521867 | + | 0.853027i | \(0.674764\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9338 | −0.996514 | ||||||||
\(362\) | −23.0874 | −1.21345 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.34785 | 0.437546 | ||||||||
\(365\) | 5.44251 | 0.284874 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.12967 | 0.111168 | 0.0555839 | − | 0.998454i | \(-0.482298\pi\) | ||||
0.0555839 | + | 0.998454i | \(0.482298\pi\) | |||||||
\(368\) | −2.67068 | −0.139219 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 36.0731 | 1.87535 | ||||||||
\(371\) | −11.8399 | −0.614699 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.5519 | 0.753470 | 0.376735 | − | 0.926321i | \(-0.377047\pi\) | ||||
0.376735 | + | 0.926321i | \(0.377047\pi\) | |||||||
\(374\) | −1.04954 | −0.0542705 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.36396 | 0.276625 | ||||||||
\(377\) | −12.3265 | −0.634848 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.5680 | 1.26198 | 0.630988 | − | 0.775793i | \(-0.282650\pi\) | ||||
0.630988 | + | 0.775793i | \(0.282650\pi\) | |||||||
\(380\) | −1.83042 | −0.0938985 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −51.6013 | −2.64015 | ||||||||
\(383\) | 3.12168 | 0.159510 | 0.0797552 | − | 0.996814i | \(-0.474586\pi\) | ||||
0.0797552 | + | 0.996814i | \(0.474586\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.183697 | 0.00936204 | ||||||||
\(386\) | −17.7538 | −0.903645 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −50.6917 | −2.57348 | ||||||||
\(389\) | −28.2302 | −1.43133 | −0.715665 | − | 0.698444i | \(-0.753876\pi\) | ||||
−0.715665 | + | 0.698444i | \(0.753876\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.35778 | −0.473243 | ||||||||
\(392\) | 3.59614 | 0.181632 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −45.0424 | −2.26920 | ||||||||
\(395\) | 32.0046 | 1.61033 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.6300 | 1.43690 | 0.718450 | − | 0.695579i | \(-0.244852\pi\) | ||||
0.718450 | + | 0.695579i | \(0.244852\pi\) | |||||||
\(398\) | 47.9844 | 2.40524 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.31168 | −0.0655841 | ||||||||
\(401\) | −19.6061 | −0.979081 | −0.489540 | − | 0.871981i | \(-0.662835\pi\) | ||||
−0.489540 | + | 0.871981i | \(0.662835\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.88353 | −0.342893 | ||||||||
\(404\) | 13.1627 | 0.654866 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.2544 | −0.608178 | ||||||||
\(407\) | −0.693860 | −0.0343934 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.62163 | 0.0801844 | 0.0400922 | − | 0.999196i | \(-0.487235\pi\) | ||||
0.0400922 | + | 0.999196i | \(0.487235\pi\) | |||||||
\(410\) | 22.4596 | 1.10920 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 38.2410 | 1.88400 | ||||||||
\(413\) | −5.10974 | −0.251434 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.9868 | −1.22655 | ||||||||
\(416\) | 9.23912 | 0.452985 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.0551594 | 0.00269793 | ||||||||
\(419\) | 7.91033 | 0.386445 | 0.193223 | − | 0.981155i | \(-0.438106\pi\) | ||||
0.193223 | + | 0.981155i | \(0.438106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.5793 | −1.05171 | −0.525855 | − | 0.850574i | \(-0.676255\pi\) | ||||
−0.525855 | + | 0.850574i | \(0.676255\pi\) | |||||||
\(422\) | 10.2271 | 0.497845 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 42.5781 | 2.06777 | ||||||||
\(425\) | −4.59600 | −0.222939 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.51881 | −0.363861 | ||||||||
\(428\) | −60.9660 | −2.94690 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 44.4554 | 2.14383 | ||||||||
\(431\) | −16.6583 | −0.802402 | −0.401201 | − | 0.915990i | \(-0.631407\pi\) | ||||
−0.401201 | + | 0.915990i | \(0.631407\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.31119 | 0.303296 | 0.151648 | − | 0.988435i | \(-0.451542\pi\) | ||||
0.151648 | + | 0.988435i | \(0.451542\pi\) | |||||||
\(434\) | −6.84329 | −0.328488 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −37.2757 | −1.78518 | ||||||||
\(437\) | 0.491804 | 0.0235262 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8300 | −0.898706 | −0.449353 | − | 0.893354i | \(-0.648346\pi\) | ||||
−0.449353 | + | 0.893354i | \(0.648346\pi\) | |||||||
\(440\) | −0.660598 | −0.0314928 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −27.2345 | −1.29541 | ||||||||
\(443\) | −8.24573 | −0.391766 | −0.195883 | − | 0.980627i | \(-0.562757\pi\) | ||||
−0.195883 | + | 0.980627i | \(0.562757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.36064 | −0.254119 | ||||||||
\(446\) | 4.98087 | 0.235851 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.9801 | 0.566006 | ||||||||
\(449\) | −0.272917 | −0.0128798 | −0.00643988 | − | 0.999979i | \(-0.502050\pi\) | ||||
−0.00643988 | + | 0.999979i | \(0.502050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.432007 | −0.0203424 | ||||||||
\(452\) | −42.5193 | −1.99994 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.88770 | −0.464053 | ||||||||
\(455\) | 4.76673 | 0.223468 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.2477 | 1.60204 | 0.801019 | − | 0.598639i | \(-0.204291\pi\) | ||||
0.801019 | + | 0.598639i | \(0.204291\pi\) | |||||||
\(458\) | −8.68736 | −0.405934 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.5926 | −0.633757 | ||||||||
\(461\) | 39.4342 | 1.83664 | 0.918318 | − | 0.395844i | \(-0.129548\pi\) | ||||
0.918318 | + | 0.395844i | \(0.129548\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.1924 | −0.984895 | −0.492447 | − | 0.870342i | \(-0.663898\pi\) | ||||
−0.492447 | + | 0.870342i | \(0.663898\pi\) | |||||||
\(464\) | 7.28294 | 0.338102 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.8552 | −1.42934 | ||||||||
\(467\) | 12.1148 | 0.560605 | 0.280303 | − | 0.959912i | \(-0.409565\pi\) | ||||
0.280303 | + | 0.959912i | \(0.409565\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.09291 | −0.281345 | ||||||||
\(470\) | 7.06844 | 0.326043 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.3753 | 0.845792 | ||||||||
\(473\) | −0.855094 | −0.0393172 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.241546 | 0.0110829 | ||||||||
\(476\) | −17.2819 | −0.792116 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −40.4976 | −1.85232 | ||||||||
\(479\) | −29.5864 | −1.35184 | −0.675918 | − | 0.736976i | \(-0.736253\pi\) | ||||
−0.675918 | + | 0.736976i | \(0.736253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0049 | −0.820954 | ||||||||
\(482\) | 35.4425 | 1.61436 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −38.7933 | −1.76333 | ||||||||
\(485\) | −28.9456 | −1.31435 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4625 | −0.474100 | −0.237050 | − | 0.971497i | \(-0.576180\pi\) | ||||
−0.237050 | + | 0.971497i | \(0.576180\pi\) | |||||||
\(488\) | 27.0387 | 1.22398 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.73886 | 0.214080 | ||||||||
\(491\) | −26.9269 | −1.21519 | −0.607597 | − | 0.794245i | \(-0.707867\pi\) | ||||
−0.607597 | + | 0.794245i | \(0.707867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.5187 | 1.14930 | ||||||||
\(494\) | 1.43133 | 0.0643985 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.06703 | 0.182615 | ||||||||
\(497\) | −5.28553 | −0.237089 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.5790 | 1.05554 | 0.527771 | − | 0.849387i | \(-0.323028\pi\) | ||||
0.527771 | + | 0.849387i | \(0.323028\pi\) | |||||||
\(500\) | −42.2390 | −1.88899 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 40.8271 | 1.82220 | ||||||||
\(503\) | 20.5970 | 0.918374 | 0.459187 | − | 0.888340i | \(-0.348141\pi\) | ||||
0.459187 | + | 0.888340i | \(0.348141\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.51605 | 0.334460 | ||||||||
\(506\) | 0.409611 | 0.0182094 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.52933 | −0.156589 | ||||||||
\(509\) | 24.5972 | 1.09025 | 0.545126 | − | 0.838354i | \(-0.316482\pi\) | ||||
0.545126 | + | 0.838354i | \(0.316482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.70061 | −0.119468 | ||||||||
\(512\) | −15.5099 | −0.685449 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 37.1272 | 1.63761 | ||||||||
\(515\) | 21.8361 | 0.962213 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.135960 | −0.00597953 | ||||||||
\(518\) | −17.8997 | −0.786466 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.1418 | −0.751719 | ||||||||
\(521\) | 33.6158 | 1.47274 | 0.736368 | − | 0.676582i | \(-0.236539\pi\) | ||||
0.736368 | + | 0.676582i | \(0.236539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.8429 | −1.21748 | −0.608742 | − | 0.793368i | \(-0.708326\pi\) | ||||
−0.608742 | + | 0.793368i | \(0.708326\pi\) | |||||||
\(524\) | 73.5567 | 3.21334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.9636 | −1.13207 | ||||||||
\(527\) | 14.2505 | 0.620760 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.3479 | −0.841212 | ||||||||
\(530\) | 56.1079 | 2.43717 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.908264 | 0.0393782 | ||||||||
\(533\) | −11.2101 | −0.485564 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.8124 | −1.50507 | ||||||||
\(536\) | 21.9110 | 0.946409 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.86898 | 0.0805775 | ||||||||
\(539\) | −0.0911513 | −0.00392617 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.4932 | −0.666104 | −0.333052 | − | 0.942908i | \(-0.608078\pi\) | ||||
−0.333052 | + | 0.942908i | \(0.608078\pi\) | |||||||
\(542\) | 9.07895 | 0.389974 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.1271 | −0.820066 | ||||||||
\(545\) | −21.2849 | −0.911746 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.9739 | 1.36710 | 0.683552 | − | 0.729902i | \(-0.260434\pi\) | ||||
0.683552 | + | 0.729902i | \(0.260434\pi\) | |||||||
\(548\) | −15.9325 | −0.680604 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.201177 | 0.00857822 | ||||||||
\(551\) | −1.34115 | −0.0571350 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.8809 | −0.675324 | ||||||||
\(554\) | −25.8155 | −1.09680 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.5777 | 0.872688 | ||||||||
\(557\) | 15.6867 | 0.664666 | 0.332333 | − | 0.943162i | \(-0.392164\pi\) | ||||
0.332333 | + | 0.943162i | \(0.392164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.1888 | −0.938485 | ||||||||
\(560\) | −2.81635 | −0.119013 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.06121 | −0.0447646 | ||||||||
\(563\) | 4.58303 | 0.193152 | 0.0965758 | − | 0.995326i | \(-0.469211\pi\) | ||||
0.0965758 | + | 0.995326i | \(0.469211\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.2791 | −1.02143 | ||||||||
\(566\) | 20.4197 | 0.858305 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.0075 | 0.797537 | ||||||||
\(569\) | 12.8151 | 0.537239 | 0.268619 | − | 0.963246i | \(-0.413433\pi\) | ||||
0.268619 | + | 0.963246i | \(0.413433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.1522 | −1.30368 | −0.651839 | − | 0.758357i | \(-0.726002\pi\) | ||||
−0.651839 | + | 0.758357i | \(0.726002\pi\) | |||||||
\(572\) | 0.760917 | 0.0318156 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.1446 | −0.465166 | ||||||||
\(575\) | 1.79371 | 0.0748027 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.42009 | −0.100750 | −0.0503748 | − | 0.998730i | \(-0.516042\pi\) | ||||
−0.0503748 | + | 0.998730i | \(0.516042\pi\) | |||||||
\(578\) | 16.4069 | 0.682437 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 37.0670 | 1.53912 | ||||||||
\(581\) | 12.3986 | 0.514381 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.07923 | −0.0446970 | ||||||||
\(584\) | 9.71175 | 0.401875 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.0745 | −1.03582 | ||||||||
\(587\) | 18.6165 | 0.768386 | 0.384193 | − | 0.923253i | \(-0.374480\pi\) | ||||
0.384193 | + | 0.923253i | \(0.374480\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.748943 | −0.0308597 | ||||||||
\(590\) | 24.2143 | 0.996889 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.6380 | 0.437217 | ||||||||
\(593\) | 12.2093 | 0.501375 | 0.250688 | − | 0.968068i | \(-0.419343\pi\) | ||||
0.250688 | + | 0.968068i | \(0.419343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.86822 | −0.404557 | ||||||||
\(596\) | −28.5699 | −1.17027 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.6290 | 0.434651 | ||||||||
\(599\) | −22.9849 | −0.939137 | −0.469569 | − | 0.882896i | \(-0.655591\pi\) | ||||
−0.469569 | + | 0.882896i | \(0.655591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.719373 | 0.0293438 | 0.0146719 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146719 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(602\) | −22.0590 | −0.899060 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 29.4583 | 1.19864 | ||||||||
\(605\) | −22.1515 | −0.900585 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.71769 | 0.150897 | 0.0754483 | − | 0.997150i | \(-0.475961\pi\) | ||||
0.0754483 | + | 0.997150i | \(0.475961\pi\) | |||||||
\(608\) | 1.00524 | 0.0407677 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 35.6306 | 1.44264 | ||||||||
\(611\) | −3.52803 | −0.142729 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.97409 | −0.402850 | −0.201425 | − | 0.979504i | \(-0.564557\pi\) | ||||
−0.201425 | + | 0.979504i | \(0.564557\pi\) | |||||||
\(614\) | 43.3522 | 1.74955 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.327793 | 0.0132071 | ||||||||
\(617\) | 25.4593 | 1.02495 | 0.512476 | − | 0.858702i | \(-0.328728\pi\) | ||||
0.512476 | + | 0.858702i | \(0.328728\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.0978 | 1.45089 | 0.725446 | − | 0.688280i | \(-0.241634\pi\) | ||||
0.725446 | + | 0.688280i | \(0.241634\pi\) | |||||||
\(620\) | 20.6994 | 0.831309 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.5151 | −0.461713 | ||||||||
\(623\) | 2.65998 | 0.106570 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.4261 | −0.777042 | ||||||||
\(626\) | −53.9979 | −2.15819 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −46.0981 | −1.83951 | ||||||||
\(629\) | 37.2743 | 1.48622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.17238 | 0.126291 | 0.0631453 | − | 0.998004i | \(-0.479887\pi\) | ||||
0.0631453 | + | 0.998004i | \(0.479887\pi\) | |||||||
\(632\) | 57.1099 | 2.27171 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −65.2993 | −2.59337 | ||||||||
\(635\) | −2.01529 | −0.0799744 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.36528 | −0.0937158 | ||||||||
\(638\) | −1.11701 | −0.0442228 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −41.0280 | −1.62177 | ||||||||
\(641\) | 32.5163 | 1.28432 | 0.642159 | − | 0.766571i | \(-0.278039\pi\) | ||||
0.642159 | + | 0.766571i | \(0.278039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.62164 | −0.300568 | −0.150284 | − | 0.988643i | \(-0.548019\pi\) | ||||
−0.150284 | + | 0.988643i | \(0.548019\pi\) | |||||||
\(644\) | 6.74472 | 0.265779 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.96317 | −0.116585 | ||||||||
\(647\) | 16.9965 | 0.668202 | 0.334101 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.465759 | −0.0182827 | ||||||||
\(650\) | 5.22033 | 0.204758 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.3049 | −0.951853 | ||||||||
\(653\) | 32.8417 | 1.28520 | 0.642598 | − | 0.766203i | \(-0.277856\pi\) | ||||
0.642598 | + | 0.766203i | \(0.277856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 42.0019 | 1.64115 | ||||||||
\(656\) | 6.62333 | 0.258598 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.50740 | −0.136733 | ||||||||
\(659\) | −12.1276 | −0.472422 | −0.236211 | − | 0.971702i | \(-0.575906\pi\) | ||||
−0.236211 | + | 0.971702i | \(0.575906\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.30251 | 0.128453 | 0.0642263 | − | 0.997935i | \(-0.479542\pi\) | ||||
0.0642263 | + | 0.997935i | \(0.479542\pi\) | |||||||
\(662\) | 44.1150 | 1.71458 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −44.5871 | −1.73032 | ||||||||
\(665\) | 0.518631 | 0.0201116 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.95932 | −0.385626 | ||||||||
\(668\) | −42.3624 | −1.63905 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 28.8735 | 1.11548 | ||||||||
\(671\) | −0.685350 | −0.0264576 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.8503 | −0.957907 | −0.478954 | − | 0.877840i | \(-0.658984\pi\) | ||||
−0.478954 | + | 0.877840i | \(0.658984\pi\) | |||||||
\(674\) | 63.5170 | 2.44658 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.1362 | −1.00524 | ||||||||
\(677\) | −15.2521 | −0.586185 | −0.293092 | − | 0.956084i | \(-0.594684\pi\) | ||||
−0.293092 | + | 0.956084i | \(0.594684\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.3630 | 0.551201 | ||||||||
\(680\) | 35.4875 | 1.36088 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.623775 | −0.0238856 | ||||||||
\(683\) | −7.38509 | −0.282583 | −0.141291 | − | 0.989968i | \(-0.545125\pi\) | ||||
−0.141291 | + | 0.989968i | \(0.545125\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.09768 | −0.347605 | ||||||||
\(686\) | −2.35145 | −0.0897789 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.1099 | 0.499811 | ||||||||
\(689\) | −28.0048 | −1.06690 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.7340 | 0.674634 | 0.337317 | − | 0.941391i | \(-0.390481\pi\) | ||||
0.337317 | + | 0.941391i | \(0.390481\pi\) | |||||||
\(692\) | −68.4669 | −2.60272 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.5111 | 0.930428 | ||||||||
\(695\) | 11.7501 | 0.445708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.2075 | 0.879046 | ||||||||
\(698\) | 17.0018 | 0.643528 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.31262 | 0.125205 | ||||||||
\(701\) | 42.2300 | 1.59500 | 0.797502 | − | 0.603316i | \(-0.206154\pi\) | ||||
0.797502 | + | 0.603316i | \(0.206154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.95898 | −0.0738842 | ||||||||
\(704\) | 1.09200 | 0.0411563 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −66.4890 | −2.50235 | ||||||||
\(707\) | −3.72951 | −0.140263 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.71968 | 0.327474 | 0.163737 | − | 0.986504i | \(-0.447645\pi\) | ||||
0.163737 | + | 0.986504i | \(0.447645\pi\) | |||||||
\(710\) | 25.0474 | 0.940013 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.56567 | −0.358489 | ||||||||
\(713\) | −5.56161 | −0.208284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.434494 | 0.0162492 | ||||||||
\(716\) | 54.1462 | 2.02354 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −46.5021 | −1.73544 | ||||||||
\(719\) | −41.1755 | −1.53559 | −0.767793 | − | 0.640698i | \(-0.778645\pi\) | ||||
−0.767793 | + | 0.640698i | \(0.778645\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8352 | −0.403524 | ||||||||
\(722\) | −44.5219 | −1.65693 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −34.6522 | −1.28784 | ||||||||
\(725\) | −4.89144 | −0.181664 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.4228 | 1.09123 | 0.545615 | − | 0.838036i | \(-0.316296\pi\) | ||||
0.545615 | + | 0.838036i | \(0.316296\pi\) | |||||||
\(728\) | 8.50587 | 0.315249 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.7978 | 0.473668 | ||||||||
\(731\) | 45.9358 | 1.69900 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.0969 | 0.890040 | 0.445020 | − | 0.895521i | \(-0.353197\pi\) | ||||
0.445020 | + | 0.895521i | \(0.353197\pi\) | |||||||
\(734\) | 5.00782 | 0.184842 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.46483 | 0.275157 | ||||||||
\(737\) | −0.555377 | −0.0204576 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.4406 | 0.494420 | 0.247210 | − | 0.968962i | \(-0.420486\pi\) | ||||
0.247210 | + | 0.968962i | \(0.420486\pi\) | |||||||
\(740\) | 54.1426 | 1.99032 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27.8411 | −1.02208 | ||||||||
\(743\) | 39.8981 | 1.46372 | 0.731860 | − | 0.681455i | \(-0.238652\pi\) | ||||
0.731860 | + | 0.681455i | \(0.238652\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.3138 | −0.597691 | ||||||||
\(746\) | 34.2182 | 1.25282 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.57527 | −0.0575976 | ||||||||
\(749\) | 17.2741 | 0.631182 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5801 | −0.823959 | −0.411979 | − | 0.911193i | \(-0.635162\pi\) | ||||
−0.411979 | + | 0.911193i | \(0.635162\pi\) | |||||||
\(752\) | 2.08449 | 0.0760134 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −28.9852 | −1.05558 | ||||||||
\(755\) | 16.8211 | 0.612182 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.3023 | −0.556171 | −0.278086 | − | 0.960556i | \(-0.589700\pi\) | ||||
−0.278086 | + | 0.960556i | \(0.589700\pi\) | |||||||
\(758\) | 57.7706 | 2.09832 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.86507 | −0.0676531 | ||||||||
\(761\) | −1.97788 | −0.0716980 | −0.0358490 | − | 0.999357i | \(-0.511414\pi\) | ||||
−0.0358490 | + | 0.999357i | \(0.511414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.5617 | 0.382359 | ||||||||
\(764\) | −77.4490 | −2.80201 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.34048 | 0.265222 | ||||||||
\(767\) | −12.0860 | −0.436399 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.2480 | −1.34320 | −0.671598 | − | 0.740916i | \(-0.734392\pi\) | ||||
−0.671598 | + | 0.740916i | \(0.734392\pi\) | |||||||
\(770\) | 0.431954 | 0.0155665 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26.6469 | −0.959044 | ||||||||
\(773\) | −32.5873 | −1.17208 | −0.586042 | − | 0.810281i | \(-0.699315\pi\) | ||||
−0.586042 | + | 0.810281i | \(0.699315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.73154 | −0.0981199 | ||||||||
\(776\) | −51.6513 | −1.85417 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −66.3821 | −2.37991 | ||||||||
\(779\) | −1.21969 | −0.0436998 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.481783 | −0.0172396 | ||||||||
\(782\) | −22.0044 | −0.786874 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.39749 | 0.0499104 | ||||||||
\(785\) | −26.3226 | −0.939494 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.02321 | 0.250350 | 0.125175 | − | 0.992135i | \(-0.460051\pi\) | ||||
0.125175 | + | 0.992135i | \(0.460051\pi\) | |||||||
\(788\) | −67.6047 | −2.40832 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 75.2573 | 2.67754 | ||||||||
\(791\) | 12.0474 | 0.428357 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.7841 | −0.631532 | ||||||||
\(794\) | 67.3221 | 2.38917 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 72.0204 | 2.55269 | ||||||||
\(797\) | −43.7885 | −1.55107 | −0.775535 | − | 0.631305i | \(-0.782520\pi\) | ||||
−0.775535 | + | 0.631305i | \(0.782520\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.30382 | 0.258391 | ||||||||
\(800\) | 3.66629 | 0.129623 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −46.1027 | −1.62794 | ||||||||
\(803\) | −0.246164 | −0.00868694 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.85132 | 0.135741 | ||||||||
\(806\) | −16.1863 | −0.570138 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.4118 | 0.471826 | ||||||||
\(809\) | −11.3663 | −0.399618 | −0.199809 | − | 0.979835i | \(-0.564032\pi\) | ||||
−0.199809 | + | 0.979835i | \(0.564032\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.3608 | −1.38214 | −0.691072 | − | 0.722786i | \(-0.742861\pi\) | ||||
−0.691072 | + | 0.722786i | \(0.742861\pi\) | |||||||
\(812\) | −18.3929 | −0.645463 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.63158 | −0.0571868 | ||||||||
\(815\) | −13.8784 | −0.486140 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.41419 | −0.0844617 | ||||||||
\(818\) | 3.81318 | 0.133325 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 33.7099 | 1.17720 | ||||||||
\(821\) | −11.6097 | −0.405183 | −0.202591 | − | 0.979263i | \(-0.564936\pi\) | ||||
−0.202591 | + | 0.979263i | \(0.564936\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.3330 | −0.499619 | −0.249809 | − | 0.968295i | \(-0.580368\pi\) | ||||
−0.249809 | + | 0.968295i | \(0.580368\pi\) | |||||||
\(824\) | 38.9649 | 1.35741 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.0153 | −0.418066 | ||||||||
\(827\) | −37.2619 | −1.29572 | −0.647862 | − | 0.761758i | \(-0.724337\pi\) | ||||
−0.647862 | + | 0.761758i | \(0.724337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.9915 | 1.38896 | 0.694481 | − | 0.719511i | \(-0.255634\pi\) | ||||
0.694481 | + | 0.719511i | \(0.255634\pi\) | |||||||
\(830\) | −58.7553 | −2.03943 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.3363 | 0.982383 | ||||||||
\(833\) | 4.89667 | 0.169659 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.1895 | −0.837111 | ||||||||
\(836\) | 0.0827895 | 0.00286333 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.6008 | 0.642553 | ||||||||
\(839\) | −10.8582 | −0.374868 | −0.187434 | − | 0.982277i | \(-0.560017\pi\) | ||||
−0.187434 | + | 0.982277i | \(0.560017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.84092 | −0.0634801 | ||||||||
\(842\) | −50.7427 | −1.74871 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.3499 | 0.528366 | ||||||||
\(845\) | −14.9241 | −0.513406 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9917 | 0.377679 | ||||||||
\(848\) | 16.5462 | 0.568200 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.8073 | −0.370686 | ||||||||
\(851\) | −14.5473 | −0.498673 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.22075 | 0.110276 | 0.0551382 | − | 0.998479i | \(-0.482440\pi\) | ||||
0.0551382 | + | 0.998479i | \(0.482440\pi\) | |||||||
\(854\) | −17.6801 | −0.605002 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −62.1201 | −2.12322 | ||||||||
\(857\) | −27.1752 | −0.928288 | −0.464144 | − | 0.885760i | \(-0.653638\pi\) | ||||
−0.464144 | + | 0.885760i | \(0.653638\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.73152 | −0.263796 | −0.131898 | − | 0.991263i | \(-0.542107\pi\) | ||||
−0.131898 | + | 0.991263i | \(0.542107\pi\) | |||||||
\(860\) | 66.7238 | 2.27526 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39.1712 | −1.33418 | ||||||||
\(863\) | 40.5701 | 1.38102 | 0.690511 | − | 0.723322i | \(-0.257386\pi\) | ||||
0.690511 | + | 0.723322i | \(0.257386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.0955 | −1.32929 | ||||||||
\(866\) | 14.8405 | 0.504299 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.2712 | −0.348627 | ||||||||
\(869\) | −1.44756 | −0.0491052 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4115 | −0.488313 | ||||||||
\(872\) | −37.9813 | −1.28621 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.15645 | 0.0391177 | ||||||||
\(875\) | 11.9680 | 0.404593 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.5801 | −0.863780 | −0.431890 | − | 0.901926i | \(-0.642153\pi\) | ||||
−0.431890 | + | 0.901926i | \(0.642153\pi\) | |||||||
\(878\) | −44.2778 | −1.49430 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.256715 | −0.00865384 | ||||||||
\(881\) | −2.14538 | −0.0722797 | −0.0361398 | − | 0.999347i | \(-0.511506\pi\) | ||||
−0.0361398 | + | 0.999347i | \(0.511506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.7069 | −1.03337 | −0.516685 | − | 0.856176i | \(-0.672834\pi\) | ||||
−0.516685 | + | 0.856176i | \(0.672834\pi\) | |||||||
\(884\) | −40.8766 | −1.37483 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.3894 | −0.651401 | ||||||||
\(887\) | −3.09857 | −0.104040 | −0.0520199 | − | 0.998646i | \(-0.516566\pi\) | ||||
−0.0520199 | + | 0.998646i | \(0.516566\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −12.6053 | −0.422531 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.47585 | 0.250310 | ||||||||
\(893\) | −0.383857 | −0.0128453 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.9182 | 1.03348 | ||||||||
\(896\) | 20.3583 | 0.680124 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.641752 | −0.0214155 | ||||||||
\(899\) | 15.1665 | 0.505832 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 57.9763 | 1.93147 | ||||||||
\(902\) | −1.01584 | −0.0338239 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −43.3242 | −1.44094 | ||||||||
\(905\) | −19.7869 | −0.657737 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.1556 | 0.470029 | 0.235015 | − | 0.971992i | \(-0.424486\pi\) | ||||
0.235015 | + | 0.971992i | \(0.424486\pi\) | |||||||
\(908\) | −14.8406 | −0.492502 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.2087 | 0.371566 | ||||||||
\(911\) | 29.6771 | 0.983247 | 0.491624 | − | 0.870808i | \(-0.336404\pi\) | ||||
0.491624 | + | 0.870808i | \(0.336404\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.13015 | 0.0374025 | ||||||||
\(914\) | 80.5318 | 2.66375 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.0390 | −0.430820 | ||||||||
\(917\) | −20.8416 | −0.688249 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.9253 | −1.77883 | −0.889415 | − | 0.457100i | \(-0.848888\pi\) | ||||
−0.889415 | + | 0.457100i | \(0.848888\pi\) | |||||||
\(920\) | −13.8499 | −0.456617 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 92.7277 | 3.05382 | ||||||||
\(923\) | −12.5018 | −0.411501 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.14477 | −0.234918 | ||||||||
\(926\) | −49.8329 | −1.63761 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.3566 | −0.668238 | ||||||||
\(929\) | −36.9355 | −1.21181 | −0.605906 | − | 0.795536i | \(-0.707189\pi\) | ||||
−0.605906 | + | 0.795536i | \(0.707189\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.257348 | −0.00843423 | ||||||||
\(932\) | −46.3110 | −1.51697 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.4873 | 0.932134 | ||||||||
\(935\) | −0.899501 | −0.0294168 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.40870 | 0.111357 | 0.0556787 | − | 0.998449i | \(-0.482268\pi\) | ||||
0.0556787 | + | 0.998449i | \(0.482268\pi\) | |||||||
\(938\) | −14.3272 | −0.467799 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.6091 | 0.346031 | ||||||||
\(941\) | 47.8418 | 1.55960 | 0.779799 | − | 0.626029i | \(-0.215321\pi\) | ||||
0.779799 | + | 0.626029i | \(0.215321\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.05731 | −0.294947 | ||||||||
\(944\) | 7.14082 | 0.232414 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.01071 | −0.0653739 | ||||||||
\(947\) | 5.90288 | 0.191818 | 0.0959088 | − | 0.995390i | \(-0.469424\pi\) | ||||
0.0959088 | + | 0.995390i | \(0.469424\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.38769 | −0.207353 | ||||||||
\(950\) | 0.567983 | 0.0184278 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.6091 | −0.570714 | ||||||||
\(953\) | 35.7438 | 1.15785 | 0.578927 | − | 0.815379i | \(-0.303472\pi\) | ||||
0.578927 | + | 0.815379i | \(0.303472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.2244 | −1.43107 | ||||||||
\(956\) | −60.7835 | −1.96588 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −69.5710 | −2.24774 | ||||||||
\(959\) | 4.51432 | 0.145775 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.5305 | −0.726791 | ||||||||
\(962\) | −42.3377 | −1.36502 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 53.1962 | 1.71333 | ||||||||
\(965\) | −15.2157 | −0.489812 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.5305 | 0.981796 | 0.490898 | − | 0.871217i | \(-0.336669\pi\) | ||||
0.490898 | + | 0.871217i | \(0.336669\pi\) | |||||||
\(968\) | −39.5276 | −1.27047 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −68.0643 | −2.18541 | ||||||||
\(971\) | 24.6280 | 0.790351 | 0.395176 | − | 0.918606i | \(-0.370684\pi\) | ||||
0.395176 | + | 0.918606i | \(0.370684\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.83048 | −0.186917 | ||||||||
\(974\) | −24.6020 | −0.788299 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.5075 | 0.336336 | ||||||||
\(977\) | 42.8486 | 1.37085 | 0.685423 | − | 0.728145i | \(-0.259617\pi\) | ||||
0.685423 | + | 0.728145i | \(0.259617\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.242461 | 0.00774909 | ||||||||
\(980\) | 7.11262 | 0.227204 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −63.3173 | −2.02054 | ||||||||
\(983\) | 48.7528 | 1.55497 | 0.777486 | − | 0.628900i | \(-0.216495\pi\) | ||||
0.777486 | + | 0.628900i | \(0.216495\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.6032 | −1.23000 | ||||||||
\(986\) | 60.0059 | 1.91098 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.14830 | 0.0683465 | ||||||||
\(989\) | −17.9276 | −0.570065 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.0445 | 0.859096 | 0.429548 | − | 0.903044i | \(-0.358673\pi\) | ||||
0.429548 | + | 0.903044i | \(0.358673\pi\) | |||||||
\(992\) | −11.3678 | −0.360928 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.4287 | −0.394214 | ||||||||
\(995\) | 41.1246 | 1.30374 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.1373 | −1.01780 | −0.508900 | − | 0.860826i | \(-0.669948\pi\) | ||||
−0.508900 | + | 0.860826i | \(0.669948\pi\) | |||||||
\(998\) | 55.4449 | 1.75508 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.s.1.15 | 16 | ||
3.2 | odd | 2 | 2667.2.a.n.1.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.n.1.2 | ✓ | 16 | 3.2 | odd | 2 | ||
8001.2.a.s.1.15 | 16 | 1.1 | even | 1 | trivial |