Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.35123 | −0.780134 | −0.390067 | − | 0.920787i | \(-0.627548\pi\) | ||||
−0.390067 | + | 0.920787i | \(0.627548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.606242 | 0.229138 | 0.114569 | − | 0.993415i | \(-0.463451\pi\) | ||||
0.114569 | + | 0.993415i | \(0.463451\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.17417 | −0.391391 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.513496 | −0.154825 | −0.0774124 | − | 0.996999i | \(-0.524666\pi\) | ||||
−0.0774124 | + | 0.996999i | \(0.524666\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.05546 | −1.12478 | −0.562391 | − | 0.826871i | \(-0.690118\pi\) | ||||
−0.562391 | + | 0.826871i | \(0.690118\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.35123 | −0.348886 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.21613 | 0.294956 | 0.147478 | − | 0.989065i | \(-0.452884\pi\) | ||||
0.147478 | + | 0.989065i | \(0.452884\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.41563 | −0.783598 | −0.391799 | − | 0.920051i | \(-0.628147\pi\) | ||||
−0.391799 | + | 0.920051i | \(0.628147\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.819174 | −0.178758 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.56762 | 1.16093 | 0.580464 | − | 0.814286i | \(-0.302871\pi\) | ||||
0.580464 | + | 0.814286i | \(0.302871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64027 | 1.08547 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.352723 | −0.0654991 | −0.0327495 | − | 0.999464i | \(-0.510426\pi\) | ||||
−0.0327495 | + | 0.999464i | \(0.510426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.19863 | −0.574491 | −0.287245 | − | 0.957857i | \(-0.592740\pi\) | ||||
−0.287245 | + | 0.957857i | \(0.592740\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.693852 | 0.120784 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.606242 | 0.102474 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.97893 | 0.489733 | 0.244866 | − | 0.969557i | \(-0.421256\pi\) | ||||
0.244866 | + | 0.969557i | \(0.421256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.47987 | 0.877481 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.88938 | 1.54446 | 0.772231 | − | 0.635342i | \(-0.219141\pi\) | ||||
0.772231 | + | 0.635342i | \(0.219141\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.95245 | −0.907741 | −0.453870 | − | 0.891068i | \(-0.649957\pi\) | ||||
−0.453870 | + | 0.891068i | \(0.649957\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.17417 | −0.175036 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.73581 | 0.982519 | 0.491259 | − | 0.871013i | \(-0.336537\pi\) | ||||
0.491259 | + | 0.871013i | \(0.336537\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.63247 | −0.947496 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.64328 | −0.230105 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.8930 | 1.90835 | 0.954177 | − | 0.299244i | \(-0.0967344\pi\) | ||||
0.954177 | + | 0.299244i | \(0.0967344\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.513496 | −0.0692398 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.61530 | 0.611311 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.57824 | −1.24698 | −0.623491 | − | 0.781831i | \(-0.714286\pi\) | ||||
−0.623491 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.75403 | 0.352617 | 0.176309 | − | 0.984335i | \(-0.443584\pi\) | ||||
0.176309 | + | 0.984335i | \(0.443584\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.711834 | −0.0896827 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.05546 | −0.503018 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.461052 | −0.0563264 | −0.0281632 | − | 0.999603i | \(-0.508966\pi\) | ||||
−0.0281632 | + | 0.999603i | \(0.508966\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.52314 | −0.905680 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2366 | 1.92693 | 0.963463 | − | 0.267841i | \(-0.0863100\pi\) | ||||
0.963463 | + | 0.267841i | \(0.0863100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.9847 | −1.75383 | −0.876915 | − | 0.480646i | \(-0.840402\pi\) | ||||
−0.876915 | + | 0.480646i | \(0.840402\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.35123 | −0.156027 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.311303 | −0.0354763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.62051 | −0.857374 | −0.428687 | − | 0.903453i | \(-0.641024\pi\) | ||||
−0.428687 | + | 0.903453i | \(0.641024\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.09879 | −0.455421 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.6545 | 1.49878 | 0.749389 | − | 0.662130i | \(-0.230348\pi\) | ||||
0.749389 | + | 0.662130i | \(0.230348\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.21613 | 0.131908 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.476611 | 0.0510980 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.2210 | −1.40142 | −0.700710 | − | 0.713446i | \(-0.747133\pi\) | ||||
−0.700710 | + | 0.713446i | \(0.747133\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.45859 | −0.257730 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.32209 | 0.448180 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.41563 | −0.350436 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.8774 | −1.71365 | −0.856823 | − | 0.515611i | \(-0.827565\pi\) | ||||
−0.856823 | + | 0.515611i | \(0.827565\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.602933 | 0.0605971 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.35478 | 0.134806 | 0.0674028 | − | 0.997726i | \(-0.478529\pi\) | ||||
0.0674028 | + | 0.997726i | \(0.478529\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.08356 | 0.500898 | 0.250449 | − | 0.968130i | \(-0.419422\pi\) | ||||
0.250449 | + | 0.968130i | \(0.419422\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.819174 | −0.0799432 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.2058 | −1.66335 | −0.831674 | − | 0.555265i | \(-0.812617\pi\) | ||||
−0.831674 | + | 0.555265i | \(0.812617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.45022 | 0.809385 | 0.404692 | − | 0.914453i | \(-0.367379\pi\) | ||||
0.404692 | + | 0.914453i | \(0.367379\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.02522 | −0.382057 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.192700 | 0.0181277 | 0.00906387 | − | 0.999959i | \(-0.497115\pi\) | ||||
0.00906387 | + | 0.999959i | \(0.497115\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.56762 | 0.519183 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.76182 | 0.440230 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.737271 | 0.0675856 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7363 | −0.976029 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.3628 | −1.20489 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.0814 | −1.24952 | −0.624759 | − | 0.780818i | \(-0.714803\pi\) | ||||
−0.624759 | + | 0.780818i | \(0.714803\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.04314 | 0.708159 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.05974 | 0.616813 | 0.308406 | − | 0.951255i | \(-0.400204\pi\) | ||||
0.308406 | + | 0.951255i | \(0.400204\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.07070 | −0.179552 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.64027 | 0.485438 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.6083 | −1.58981 | −0.794907 | − | 0.606731i | \(-0.792481\pi\) | ||||
−0.794907 | + | 0.606731i | \(0.792481\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.381840 | −0.0323872 | −0.0161936 | − | 0.999869i | \(-0.505155\pi\) | ||||
−0.0161936 | + | 0.999869i | \(0.505155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.10164 | −0.766496 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.08246 | 0.174144 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.352723 | −0.0292921 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.96200 | 0.739173 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.95647 | 0.569896 | 0.284948 | − | 0.958543i | \(-0.408024\pi\) | ||||
0.284948 | + | 0.958543i | \(0.408024\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.74046 | 0.141636 | 0.0708181 | − | 0.997489i | \(-0.477439\pi\) | ||||
0.0708181 | + | 0.997489i | \(0.477439\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.42795 | −0.115443 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.19863 | −0.256920 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.6679 | −0.851393 | −0.425697 | − | 0.904866i | \(-0.639971\pi\) | ||||
−0.425697 | + | 0.904866i | \(0.639971\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.7727 | −1.48877 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.37533 | 0.266013 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0911 | −0.868722 | −0.434361 | − | 0.900739i | \(-0.643026\pi\) | ||||
−0.434361 | + | 0.900739i | \(0.643026\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.693852 | 0.0540163 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.08839 | 0.238987 | 0.119494 | − | 0.992835i | \(-0.461873\pi\) | ||||
0.119494 | + | 0.992835i | \(0.461873\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.44676 | 0.265136 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.01054 | 0.306694 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.29434 | 0.706636 | 0.353318 | − | 0.935503i | \(-0.385053\pi\) | ||||
0.353318 | + | 0.935503i | \(0.385053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.606242 | 0.0458276 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.9424 | 0.972812 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.66882 | −0.274220 | −0.137110 | − | 0.990556i | \(-0.543781\pi\) | ||||
−0.137110 | + | 0.990556i | \(0.543781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.87094 | 0.585042 | 0.292521 | − | 0.956259i | \(-0.405506\pi\) | ||||
0.292521 | + | 0.956259i | \(0.405506\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.72133 | −0.275089 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.97893 | 0.219015 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.624479 | −0.0456665 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.41937 | 0.248723 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.8532 | −1.36417 | −0.682086 | − | 0.731272i | \(-0.738927\pi\) | ||||
−0.682086 | + | 0.731272i | \(0.738927\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.300821 | −0.0216536 | −0.0108268 | − | 0.999941i | \(-0.503446\pi\) | ||||
−0.0108268 | + | 0.999941i | \(0.503446\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.47987 | 0.392421 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.83775 | −0.700911 | −0.350455 | − | 0.936579i | \(-0.613973\pi\) | ||||
−0.350455 | + | 0.936579i | \(0.613973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.48116 | 0.459437 | 0.229719 | − | 0.973257i | \(-0.426219\pi\) | ||||
0.229719 | + | 0.973257i | \(0.426219\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.622987 | 0.0439421 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.213836 | −0.0150083 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.88938 | 0.690704 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.53735 | −0.454378 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.75391 | 0.121320 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.81870 | −0.125205 | −0.0626023 | − | 0.998039i | \(-0.519940\pi\) | ||||
−0.0626023 | + | 0.998039i | \(0.519940\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.9394 | −1.50326 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.95245 | −0.405954 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.93914 | −0.131638 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.2478 | 1.36822 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.93198 | −0.331761 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.4401 | −1.23484 | −0.617421 | − | 0.786633i | \(-0.711823\pi\) | ||||
−0.617421 | + | 0.786633i | \(0.711823\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.17417 | −0.0782783 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.40400 | 0.358676 | 0.179338 | − | 0.983788i | \(-0.442604\pi\) | ||||
0.179338 | + | 0.983788i | \(0.442604\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.60956 | 0.238526 | 0.119263 | − | 0.992863i | \(-0.461947\pi\) | ||||
0.119263 | + | 0.992863i | \(0.461947\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.420642 | 0.0276762 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.57605 | −0.430811 | −0.215406 | − | 0.976525i | \(-0.569107\pi\) | ||||
−0.215406 | + | 0.976525i | \(0.569107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.73581 | 0.439396 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.2971 | 0.668867 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.0971 | −0.847181 | −0.423591 | − | 0.905854i | \(-0.639231\pi\) | ||||
−0.423591 | + | 0.905854i | \(0.639231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2302 | 0.658985 | 0.329493 | − | 0.944158i | \(-0.393122\pi\) | ||||
0.329493 | + | 0.944158i | \(0.393122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.3824 | −0.730182 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.63247 | −0.423733 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8519 | 0.881378 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.4504 | −1.16925 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.6762 | 1.36819 | 0.684096 | − | 0.729392i | \(-0.260197\pi\) | ||||
0.684096 | + | 0.729392i | \(0.260197\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.85895 | −0.179741 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.64328 | −0.102906 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.8062 | −1.73450 | −0.867252 | − | 0.497870i | \(-0.834116\pi\) | ||||
−0.867252 | + | 0.497870i | \(0.834116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.80595 | 0.112216 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.414158 | 0.0256358 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.6195 | 1.20979 | 0.604896 | − | 0.796304i | \(-0.293215\pi\) | ||||
0.604896 | + | 0.796304i | \(0.293215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.8930 | 0.853442 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.8646 | 1.09330 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.05968 | 0.0646100 | 0.0323050 | − | 0.999478i | \(-0.489715\pi\) | ||||
0.0323050 | + | 0.999478i | \(0.489715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.87140 | −0.113679 | −0.0568397 | − | 0.998383i | \(-0.518102\pi\) | ||||
−0.0568397 | + | 0.998383i | \(0.518102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.32213 | 0.201064 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.513496 | −0.0309650 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.40614 | −0.204655 | −0.102327 | − | 0.994751i | \(-0.532629\pi\) | ||||
−0.102327 | + | 0.994751i | \(0.532629\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.75575 | 0.224851 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.23600 | −0.252699 | −0.126349 | − | 0.991986i | \(-0.540326\pi\) | ||||
−0.126349 | + | 0.991986i | \(0.540326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.68934 | −0.219309 | −0.109654 | − | 0.993970i | \(-0.534974\pi\) | ||||
−0.109654 | + | 0.993970i | \(0.534974\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.61530 | 0.273387 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.99536 | 0.353895 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5210 | −0.913001 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.8053 | 1.33687 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.66371 | −0.447719 | −0.223859 | − | 0.974621i | \(-0.571866\pi\) | ||||
−0.223859 | + | 0.974621i | \(0.571866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.57824 | −0.557667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.89626 | −0.168058 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.5793 | −1.30579 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.60863 | −0.207998 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.83062 | −0.105166 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.75403 | 0.157695 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.2147 | 1.21079 | 0.605395 | − | 0.795926i | \(-0.293015\pi\) | ||||
0.605395 | + | 0.795926i | \(0.293015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.86906 | −0.390767 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.8089 | 0.783028 | 0.391514 | − | 0.920172i | \(-0.371951\pi\) | ||||
0.391514 | + | 0.920172i | \(0.371951\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.79116 | −0.553429 | −0.276715 | − | 0.960952i | \(-0.589246\pi\) | ||||
−0.276715 | + | 0.960952i | \(0.589246\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.711834 | −0.0401073 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.81819 | −0.495279 | −0.247639 | − | 0.968852i | \(-0.579655\pi\) | ||||
−0.247639 | + | 0.968852i | \(0.579655\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.181122 | 0.0101409 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.2490 | 1.29763 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.15386 | −0.231127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.05546 | −0.224956 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.4182 | −0.631428 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.08353 | 0.225132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9908 | 0.823972 | 0.411986 | − | 0.911190i | \(-0.364835\pi\) | ||||
0.411986 | + | 0.911190i | \(0.364835\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.49778 | −0.191677 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.461052 | −0.0251899 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.6680 | −1.01691 | −0.508455 | − | 0.861089i | \(-0.669783\pi\) | ||||
−0.508455 | + | 0.861089i | \(0.669783\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.260383 | −0.0141421 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.64248 | 0.0889454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.26458 | −0.446245 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.52314 | −0.405032 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.1547 | 0.813547 | 0.406773 | − | 0.913529i | \(-0.366654\pi\) | ||||
0.406773 | + | 0.913529i | \(0.366654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.805271 | 0.0431052 | 0.0215526 | − | 0.999768i | \(-0.493139\pi\) | ||||
0.0215526 | + | 0.999768i | \(0.493139\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.8739 | −1.22092 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.9920 | 0.638268 | 0.319134 | − | 0.947710i | \(-0.396608\pi\) | ||||
0.319134 | + | 0.947710i | \(0.396608\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.2366 | 0.861748 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.996224 | −0.0527258 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.30187 | 0.121488 | 0.0607441 | − | 0.998153i | \(-0.480653\pi\) | ||||
0.0607441 | + | 0.998153i | \(0.480653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.33350 | −0.385974 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.5073 | 0.761433 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.9847 | −0.784336 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.8192 | 1.03455 | 0.517277 | − | 0.855818i | \(-0.326946\pi\) | ||||
0.517277 | + | 0.855818i | \(0.326946\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.6118 | −0.604489 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.42254 | 0.437276 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1130 | −0.834297 | −0.417149 | − | 0.908838i | \(-0.636971\pi\) | ||||
−0.417149 | + | 0.908838i | \(0.636971\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.35123 | −0.0697773 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.43046 | 0.0736722 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.258072 | −0.0132563 | −0.00662815 | − | 0.999978i | \(-0.502110\pi\) | ||||
−0.00662815 | + | 0.999978i | \(0.502110\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.0272 | 0.974791 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.5346 | −1.35586 | −0.677928 | − | 0.735128i | \(-0.737122\pi\) | ||||
−0.677928 | + | 0.735128i | \(0.737122\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.311303 | −0.0158655 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.98922 | 0.355282 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.0038 | −0.557915 | −0.278957 | − | 0.960303i | \(-0.589989\pi\) | ||||
−0.278957 | + | 0.960303i | \(0.589989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.77097 | 0.342423 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.53935 | −0.481196 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.62051 | −0.383429 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.33962 | 0.0672335 | 0.0336168 | − | 0.999435i | \(-0.489297\pi\) | ||||
0.0336168 | + | 0.999435i | \(0.489297\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.79799 | 0.140075 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.9719 | 0.646177 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.09879 | −0.203671 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.52967 | −0.0758228 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.10382 | 0.0545805 | 0.0272902 | − | 0.999628i | \(-0.491312\pi\) | ||||
0.0272902 | + | 0.999628i | \(0.491312\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.1441 | 1.24027 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.80674 | −0.285731 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.6545 | 0.670274 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.515954 | 0.0252664 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.64055 | −0.275559 | −0.137780 | − | 0.990463i | \(-0.543997\pi\) | ||||
−0.137780 | + | 0.990463i | \(0.543997\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.44108 | 0.0702340 | 0.0351170 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351170 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.90901 | −0.384549 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.21613 | 0.0589911 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.66961 | 0.0807981 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.81389 | −0.135856 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.3145 | −0.785840 | −0.392920 | − | 0.919573i | \(-0.628535\pi\) | ||||
−0.392920 | + | 0.919573i | \(0.628535\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.9287 | −1.63051 | −0.815255 | − | 0.579102i | \(-0.803403\pi\) | ||||
−0.815255 | + | 0.579102i | \(0.803403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.476611 | 0.0228517 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.0169 | −0.909702 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.02962 | 0.0968684 | 0.0484342 | − | 0.998826i | \(-0.484577\pi\) | ||||
0.0484342 | + | 0.998826i | \(0.484577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.78767 | 0.370842 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.0894 | −0.954476 | −0.477238 | − | 0.878774i | \(-0.658362\pi\) | ||||
−0.477238 | + | 0.878774i | \(0.658362\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.2210 | −0.626734 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.39980 | −0.444595 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.82741 | −0.322205 | −0.161103 | − | 0.986938i | \(-0.551505\pi\) | ||||
−0.161103 | + | 0.986938i | \(0.551505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.07815 | −0.239121 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.35176 | −0.110495 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.45859 | −0.115261 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.7368 | −1.34425 | −0.672125 | − | 0.740437i | \(-0.734618\pi\) | ||||
−0.672125 | + | 0.740437i | \(0.734618\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.85933 | 0.320166 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.94545 | −0.370057 | −0.185028 | − | 0.982733i | \(-0.559238\pi\) | ||||
−0.185028 | + | 0.982733i | \(0.559238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.4474 | 1.69385 | 0.846927 | − | 0.531709i | \(-0.178450\pi\) | ||||
0.846927 | + | 0.531709i | \(0.178450\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.32209 | 0.200432 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.50055 | −0.300810 | −0.150405 | − | 0.988625i | \(-0.548058\pi\) | ||||
−0.150405 | + | 0.988625i | \(0.548058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.279509 | −0.0129065 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4148 | 0.664201 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.05656 | 0.140541 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.41563 | −0.156720 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.3128 | −0.746913 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.7454 | −0.993571 | −0.496786 | − | 0.867873i | \(-0.665486\pi\) | ||||
−0.496786 | + | 0.867873i | \(0.665486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0809 | −0.550843 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.56085 | −0.207526 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.8774 | −0.766365 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.0984 | −1.36389 | −0.681944 | − | 0.731404i | \(-0.738865\pi\) | ||||
−0.681944 | + | 0.731404i | \(0.738865\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.9866 | 0.677719 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.5954 | 0.884326 | 0.442163 | − | 0.896935i | \(-0.354211\pi\) | ||||
0.442163 | + | 0.896935i | \(0.354211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.428958 | −0.0193193 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.602933 | 0.0270998 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.84330 | 0.441532 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.5906 | 0.518865 | 0.259432 | − | 0.965761i | \(-0.416465\pi\) | ||||
0.259432 | + | 0.965761i | \(0.416465\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.17313 | −0.186442 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.3163 | 0.459983 | 0.229992 | − | 0.973193i | \(-0.426130\pi\) | ||||
0.229992 | + | 0.973193i | \(0.426130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.35478 | 0.0602869 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.65737 | −0.206841 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.0107739 | −0.000477543 0 | −0.000238771 | − | 1.00000i | \(-0.500076\pi\) | ||||
−0.000238771 | 1.00000i | \(0.500076\pi\) | ||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.08438 | −0.401869 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.2651 | −0.850574 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.08356 | 0.224008 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.45881 | −0.152118 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.5588 | −0.551270 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.7674 | −1.43557 | −0.717783 | − | 0.696266i | \(-0.754843\pi\) | ||||
−0.717783 | + | 0.696266i | \(0.754843\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.424493 | 0.0185618 | 0.00928089 | − | 0.999957i | \(-0.497046\pi\) | ||||
0.00928089 | + | 0.999957i | \(0.497046\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.819174 | −0.0357517 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.88996 | −0.169449 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.99839 | 0.347756 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2465 | 0.488058 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.1060 | −1.73718 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.2058 | −0.743872 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.95742 | 0.213929 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.40575 | 0.146696 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.3644 | 0.875535 | 0.437768 | − | 0.899088i | \(-0.355769\pi\) | ||||
0.437768 | + | 0.899088i | \(0.355769\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.6355 | −0.456411 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.45022 | 0.361968 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.5191 | −1.68971 | −0.844857 | − | 0.534993i | \(-0.820314\pi\) | ||||
−0.844857 | + | 0.534993i | \(0.820314\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.23371 | −0.138011 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.20477 | 0.0513250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.61988 | −0.196457 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.02522 | −0.170861 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.8261 | −1.64512 | −0.822558 | − | 0.568682i | \(-0.807454\pi\) | ||||
−0.822558 | + | 0.568682i | \(0.807454\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.1399 | 1.02101 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.843816 | 0.0356259 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.85778 | 0.373311 | 0.186656 | − | 0.982425i | \(-0.440235\pi\) | ||||
0.186656 | + | 0.982425i | \(0.440235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.192700 | 0.00810697 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.48486 | −0.104354 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.34442 | 0.0563611 | 0.0281806 | − | 0.999603i | \(-0.491029\pi\) | ||||
0.0281806 | + | 0.999603i | \(0.491029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4542 | −1.19077 | −0.595385 | − | 0.803440i | \(-0.703001\pi\) | ||||
−0.595385 | + | 0.803440i | \(0.703001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.4751 | 1.06424 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.56762 | 0.232186 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.69718 | −0.112285 | −0.0561426 | − | 0.998423i | \(-0.517880\pi\) | ||||
−0.0561426 | + | 0.998423i | \(0.517880\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.406478 | 0.0168927 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.27794 | 0.343427 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.13401 | −0.295460 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.76182 | 0.196877 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.0125 | −1.32130 | −0.660649 | − | 0.750695i | \(-0.729719\pi\) | ||||
−0.660649 | + | 0.750695i | \(0.729719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.9253 | 0.450170 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.2931 | 0.546804 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.2380 | 0.584684 | 0.292342 | − | 0.956314i | \(-0.405565\pi\) | ||||
0.292342 | + | 0.956314i | \(0.405565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.737271 | 0.0302252 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.75755 | −0.358422 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.3223 | 1.11636 | 0.558179 | − | 0.829720i | \(-0.311500\pi\) | ||||
0.558179 | + | 0.829720i | \(0.311500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.94346 | −0.405602 | −0.202801 | − | 0.979220i | \(-0.565004\pi\) | ||||
−0.202801 | + | 0.979220i | \(0.565004\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.541355 | 0.0220457 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.7363 | −0.436494 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.1269 | 0.857515 | 0.428758 | − | 0.903420i | \(-0.358951\pi\) | ||||
0.428758 | + | 0.903420i | \(0.358951\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.288942 | 0.0117085 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.3168 | −1.10512 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.21101 | −0.291250 | −0.145625 | − | 0.989340i | \(-0.546519\pi\) | ||||
−0.145625 | + | 0.989340i | \(0.546519\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.3628 | −0.538842 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.1082 | −0.970558 | −0.485279 | − | 0.874359i | \(-0.661282\pi\) | ||||
−0.485279 | + | 0.874359i | \(0.661282\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.2831 | −1.33776 | −0.668881 | − | 0.743370i | \(-0.733226\pi\) | ||||
−0.668881 | + | 0.743370i | \(0.733226\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.4029 | 1.26016 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.01512 | −0.321119 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.36994 | −0.0946462 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.62277 | 0.144449 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.2142 | −1.04357 | −0.521786 | − | 0.853076i | \(-0.674734\pi\) | ||||
−0.521786 | + | 0.853076i | \(0.674734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.45749 | 0.0976764 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.0814 | −0.558802 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.8977 | 1.06573 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.0646 | −0.754182 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.99830 | 0.0789281 | 0.0394641 | − | 0.999221i | \(-0.487435\pi\) | ||||
0.0394641 | + | 0.999221i | \(0.487435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.0283 | −1.26307 | −0.631536 | − | 0.775347i | \(-0.717575\pi\) | ||||
−0.631536 | + | 0.775347i | \(0.717575\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.04314 | 0.316698 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.9388 | 0.823188 | 0.411594 | − | 0.911367i | \(-0.364972\pi\) | ||||
0.411594 | + | 0.911367i | \(0.364972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.91839 | 0.193064 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.62023 | 0.102695 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.7532 | −0.890402 | −0.445201 | − | 0.895431i | \(-0.646868\pi\) | ||||
−0.445201 | + | 0.895431i | \(0.646868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.05974 | 0.275847 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.5947 | 0.686434 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.57035 | 0.216990 | 0.108495 | − | 0.994097i | \(-0.465397\pi\) | ||||
0.108495 | + | 0.994097i | \(0.465397\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.4326 | −1.06701 | −0.533503 | − | 0.845798i | \(-0.679125\pi\) | ||||
−0.533503 | + | 0.845798i | \(0.679125\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.66425 | 0.258818 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.07070 | −0.0802982 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.96383 | −0.0760398 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.9169 | 0.963342 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.41418 | −0.0545939 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.2708 | −0.742834 | −0.371417 | − | 0.928466i | \(-0.621128\pi\) | ||||
−0.371417 | + | 0.928466i | \(0.621128\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.64027 | 0.217094 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.8792 | 1.18678 | 0.593392 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593392 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2318 | −0.392661 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.30206 | −0.279815 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.2044 | 1.80623 | 0.903113 | − | 0.429402i | \(-0.141276\pi\) | ||||
0.903113 | + | 0.429402i | \(0.141276\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.6083 | −0.710987 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.87735 | −0.186083 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −56.3426 | −2.14648 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.5424 | −0.591261 | −0.295631 | − | 0.955302i | \(-0.595530\pi\) | ||||
−0.295631 | + | 0.955302i | \(0.595530\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.365524 | 0.0138851 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.381840 | −0.0144840 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0268 | 0.455548 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.88576 | 0.336090 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.7092 | 1.12210 | 0.561050 | − | 0.827782i | \(-0.310398\pi\) | ||||
0.561050 | + | 0.827782i | \(0.310398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.1749 | −0.383754 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.10164 | −0.342787 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.821325 | 0.0308891 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00686 | 0.300704 | 0.150352 | − | 0.988633i | \(-0.451959\pi\) | ||||
0.150352 | + | 0.988633i | \(0.451959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.94780 | 0.335569 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.8087 | −0.666943 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.08246 | 0.0778797 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.6972 | 0.660915 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.28015 | 0.0477417 | 0.0238708 | − | 0.999715i | \(-0.492401\pi\) | ||||
0.0238708 | + | 0.999715i | \(0.492401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.08187 | 0.114775 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.8234 | −0.514096 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.352723 | −0.0130998 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.19885 | 0.192815 | 0.0964073 | − | 0.995342i | \(-0.469265\pi\) | ||||
0.0964073 | + | 0.995342i | \(0.469265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.6766 | 1.02506 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.23898 | −0.267743 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.04235 | 0.149308 | 0.0746538 | − | 0.997210i | \(-0.476215\pi\) | ||||
0.0746538 | + | 0.997210i | \(0.476215\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.96200 | 0.330568 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.236748 | 0.00872073 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.7039 | −0.393748 | −0.196874 | − | 0.980429i | \(-0.563079\pi\) | ||||
−0.196874 | + | 0.980429i | \(0.563079\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.7172 | −0.687592 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.8808 | −0.729358 | −0.364679 | − | 0.931133i | \(-0.618821\pi\) | ||||
−0.364679 | + | 0.931133i | \(0.618821\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.95647 | 0.254865 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.0328 | −0.586608 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.4309 | −0.381136 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.1013 | 0.733505 | 0.366753 | − | 0.930318i | \(-0.380470\pi\) | ||||
0.366753 | + | 0.930318i | \(0.380470\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.2896 | −1.06737 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.74046 | 0.0633417 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.3432 | −1.57534 | −0.787669 | − | 0.616099i | \(-0.788712\pi\) | ||||
−0.787669 | + | 0.616099i | \(0.788712\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.86310 | 0.140222 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.5161 | 0.997459 | 0.498730 | − | 0.866758i | \(-0.333800\pi\) | ||||
0.498730 | + | 0.866758i | \(0.333800\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.12288 | 0.185461 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.42795 | −0.0516277 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38.8442 | 1.40258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.781969 | 0.0281985 | 0.0140993 | − | 0.999901i | \(-0.495512\pi\) | ||||
0.0140993 | + | 0.999901i | \(0.495512\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.5726 | 1.35314 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.3231 | −0.659035 | −0.329518 | − | 0.944149i | \(-0.606886\pi\) | ||||
−0.329518 | + | 0.944149i | \(0.606886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.19863 | −0.114898 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.44026 | −0.0875438 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.7784 | −1.21024 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.33741 | −0.298336 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.98946 | −0.0710974 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.6679 | −0.380755 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.4284 | 1.04901 | 0.524504 | − | 0.851408i | \(-0.324251\pi\) | ||||
0.524504 | + | 0.851408i | \(0.324251\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.5105 | −0.943800 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.116823 | 0.00415375 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.1689 | −0.396618 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.7727 | −0.665799 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.5547 | 1.11772 | 0.558862 | − | 0.829261i | \(-0.311238\pi\) | ||||
0.558862 | + | 0.829261i | \(0.311238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.19164 | 0.289799 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.5237 | 0.548504 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.69459 | 0.271536 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.37533 | 0.118965 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.43188 | −0.0504045 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.6008 | −1.42745 | −0.713725 | − | 0.700426i | \(-0.752993\pi\) | ||||
−0.713725 | + | 0.700426i | \(0.752993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.5995 | 1.07449 | 0.537247 | − | 0.843425i | \(-0.319464\pi\) | ||||
0.537247 | + | 0.843425i | \(0.319464\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.52869 | 0.0886851 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.0911 | −0.388504 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.3314 | 0.711304 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.88681 | 0.100873 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.7574 | −1.56204 | −0.781022 | − | 0.624503i | \(-0.785302\pi\) | ||||
−0.781022 | + | 0.624503i | \(0.785302\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.8903 | 1.25106 | 0.625528 | − | 0.780202i | \(-0.284884\pi\) | ||||
0.625528 | + | 0.780202i | \(0.284884\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.693852 | 0.0241568 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.49205 | 0.295297 | 0.147649 | − | 0.989040i | \(-0.452829\pi\) | ||||
0.147649 | + | 0.989040i | \(0.452829\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.67364 | 0.197054 | 0.0985268 | − | 0.995134i | \(-0.468587\pi\) | ||||
0.0985268 | + | 0.995134i | \(0.468587\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.60248 | 0.159658 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.06597 | −0.279469 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.08839 | 0.106878 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.0411 | −0.623593 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.5868 | 0.538115 | 0.269057 | − | 0.963124i | \(-0.413288\pi\) | ||||
0.269057 | + | 0.963124i | \(0.413288\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8756 | −0.995710 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.72382 | 0.197139 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.44676 | 0.118572 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.50881 | −0.223645 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.98516 | 0.171090 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.5855 | 0.568545 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.86186 | −0.234946 | −0.117473 | − | 0.993076i | \(-0.537479\pi\) | ||||
−0.117473 | + | 0.993076i | \(0.537479\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.01054 | 0.137158 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.6735 | −0.842830 | −0.421415 | − | 0.906868i | \(-0.638466\pi\) | ||||
−0.421415 | + | 0.906868i | \(0.638466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.0722 | 0.650735 | 0.325368 | − | 0.945588i | \(-0.394512\pi\) | ||||
0.325368 | + | 0.945588i | \(0.394512\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.10112 | −0.276085 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.8497 | 1.22034 | 0.610169 | − | 0.792271i | \(-0.291102\pi\) | ||||
0.610169 | + | 0.792271i | \(0.291102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.29434 | 0.316017 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.9725 | 0.712263 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.91310 | 0.132743 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.86978 | 0.0633550 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.8171 | 0.670706 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.606242 | 0.0204947 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.3777 | −0.721874 | −0.360937 | − | 0.932590i | \(-0.617543\pi\) | ||||
−0.360937 | + | 0.932590i | \(0.617543\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.3554 | 0.349280 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.9093 | 1.37827 | 0.689134 | − | 0.724634i | \(-0.257991\pi\) | ||||
0.689134 | + | 0.724634i | \(0.257991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5093 | −0.454624 | −0.227312 | − | 0.973822i | \(-0.572994\pi\) | ||||
−0.227312 | + | 0.973822i | \(0.572994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.9424 | 0.435055 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.14262 | −0.239826 | −0.119913 | − | 0.992784i | \(-0.538262\pi\) | ||||
−0.119913 | + | 0.992784i | \(0.538262\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.53671 | −0.286312 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.10471 | 0.0705105 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.0070 | −0.769900 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.66882 | −0.122635 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.5098 | 1.01869 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.12823 | 0.0376286 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.8958 | 0.562880 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.87609 | 0.162266 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.87094 | 0.261639 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.156907 | −0.00521001 | −0.00260501 | − | 0.999997i | \(-0.500829\pi\) | ||||
−0.00260501 | + | 0.999997i | \(0.500829\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.59075 | −0.0527618 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.2640 | 1.36714 | 0.683568 | − | 0.729886i | \(-0.260427\pi\) | ||||
0.683568 | + | 0.729886i | \(0.260427\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.01153 | −0.232048 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.72133 | −0.123023 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.27992 | 0.141335 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.3237 | 1.23120 | 0.615598 | − | 0.788060i | \(-0.288915\pi\) | ||||
0.615598 | + | 0.788060i | \(0.288915\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.6660 | −0.944577 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −65.8468 | −2.16737 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.97893 | 0.0979465 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.96898 | −0.196047 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.3747 | −1.48870 | −0.744348 | − | 0.667792i | \(-0.767240\pi\) | ||||
−0.744348 | + | 0.667792i | \(0.767240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.6540 | 0.742456 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.6590 | −0.610867 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.624479 | −0.0204227 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.2456 | −0.334708 | −0.167354 | − | 0.985897i | \(-0.553522\pi\) | ||||
−0.167354 | + | 0.985897i | \(0.553522\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.2301 | 0.431749 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0036 | −0.326107 | −0.163054 | − | 0.986617i | \(-0.552134\pi\) | ||||
−0.163054 | + | 0.986617i | \(0.552134\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.0603 | 1.79301 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.41937 | 0.111232 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.9561 | 0.388521 | 0.194261 | − | 0.980950i | \(-0.437769\pi\) | ||||
0.194261 | + | 0.980950i | \(0.437769\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.7700 | 1.97268 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.9154 | 0.386384 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.4471 | −1.69893 | −0.849464 | − | 0.527646i | \(-0.823075\pi\) | ||||
−0.849464 | + | 0.527646i | \(0.823075\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.8532 | −0.610077 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.244738 | −0.00791124 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.2811 | −0.364287 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7688 | −0.669960 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.2026 | 0.651020 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.300821 | −0.00968376 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0265 | −0.418903 | −0.209451 | − | 0.977819i | \(-0.567168\pi\) | ||||
−0.209451 | + | 0.977819i | \(0.567168\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.61282 | 0.180310 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.2746 | −0.329728 | −0.164864 | − | 0.986316i | \(-0.552719\pi\) | ||||
−0.164864 | + | 0.986316i | \(0.552719\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.231487 | −0.00742114 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.47987 | 0.175496 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.1490 | −0.420675 | −0.210337 | − | 0.977629i | \(-0.567456\pi\) | ||||
−0.210337 | + | 0.977629i | \(0.567456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.78892 | 0.216975 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.92203 | −0.316786 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.2903 | −0.679054 | −0.339527 | − | 0.940596i | \(-0.610267\pi\) | ||||
−0.339527 | + | 0.940596i | \(0.610267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.83775 | −0.313457 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.51780 | −0.175633 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.1410 | −1.05382 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.78392 | 0.215498 | 0.107749 | − | 0.994178i | \(-0.465636\pi\) | ||||
0.107749 | + | 0.994178i | \(0.465636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.2561 | −0.642808 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.48116 | 0.205467 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.4226 | −0.488439 | −0.244220 | − | 0.969720i | \(-0.578532\pi\) | ||||
−0.244220 | + | 0.969720i | \(0.578532\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.8020 | 0.531591 |
(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 | 8020.2.a.d.1.9 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.d.1.9 | ✓ | 29 | 1.1 | even | 1 | trivial |