Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9801,2,Mod(1,9801)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9801, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9801.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9801 = 3^{4} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9801.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: | \(78.2613790211\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{18} - 2 x^{17} - 22 x^{16} + 42 x^{15} + 198 x^{14} - 357 x^{13} - 944 x^{12} + 1579 x^{11} + \cdots - 55 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-1.54614\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9801.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.54614 | 1.09328 | 0.546642 | − | 0.837367i | \(-0.315906\pi\) | ||||
0.546642 | + | 0.837367i | \(0.315906\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.390538 | 0.195269 | ||||||||
\(5\) | −0.592032 | −0.264765 | −0.132382 | − | 0.991199i | \(-0.542263\pi\) | ||||
−0.132382 | + | 0.991199i | \(0.542263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.721951 | −0.272872 | −0.136436 | − | 0.990649i | \(-0.543565\pi\) | ||||
−0.136436 | + | 0.990649i | \(0.543565\pi\) | |||||||
\(8\) | −2.48845 | −0.879799 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.915362 | −0.289463 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57496 | 0.436817 | 0.218408 | − | 0.975857i | \(-0.429914\pi\) | ||||
0.218408 | + | 0.975857i | \(0.429914\pi\) | |||||||
\(14\) | −1.11623 | −0.298326 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.62856 | −1.15714 | ||||||||
\(17\) | 4.59200 | 1.11372 | 0.556862 | − | 0.830605i | \(-0.312005\pi\) | ||||
0.556862 | + | 0.830605i | \(0.312005\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50860 | −0.575512 | −0.287756 | − | 0.957704i | \(-0.592909\pi\) | ||||
−0.287756 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(20\) | −0.231211 | −0.0517004 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.45200 | 0.928306 | 0.464153 | − | 0.885755i | \(-0.346359\pi\) | ||||
0.464153 | + | 0.885755i | \(0.346359\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.64950 | −0.929900 | ||||||||
\(26\) | 2.43511 | 0.477564 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.281949 | −0.0532834 | ||||||||
\(29\) | 6.97862 | 1.29590 | 0.647949 | − | 0.761684i | \(-0.275627\pi\) | ||||
0.647949 | + | 0.761684i | \(0.275627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.12824 | −1.63948 | −0.819740 | − | 0.572735i | \(-0.805882\pi\) | ||||
−0.819740 | + | 0.572735i | \(0.805882\pi\) | |||||||
\(32\) | −2.17948 | −0.385282 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.09986 | 1.21762 | ||||||||
\(35\) | 0.427418 | 0.0722468 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.89170 | 0.475392 | 0.237696 | − | 0.971340i | \(-0.423608\pi\) | ||||
0.237696 | + | 0.971340i | \(0.423608\pi\) | |||||||
\(38\) | −3.87864 | −0.629198 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.47324 | 0.232940 | ||||||||
\(41\) | −1.15412 | −0.180243 | −0.0901216 | − | 0.995931i | \(-0.528726\pi\) | ||||
−0.0901216 | + | 0.995931i | \(0.528726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.21448 | 0.642702 | 0.321351 | − | 0.946960i | \(-0.395863\pi\) | ||||
0.321351 | + | 0.946960i | \(0.395863\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.88340 | 1.01490 | ||||||||
\(47\) | 0.227555 | 0.0331924 | 0.0165962 | − | 0.999862i | \(-0.494717\pi\) | ||||
0.0165962 | + | 0.999862i | \(0.494717\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.47879 | −0.925541 | ||||||||
\(50\) | −7.18876 | −1.01664 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.615084 | 0.0852967 | ||||||||
\(53\) | 5.70359 | 0.783449 | 0.391724 | − | 0.920083i | \(-0.371879\pi\) | ||||
0.391724 | + | 0.920083i | \(0.371879\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.79654 | 0.240072 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.7899 | 1.41678 | ||||||||
\(59\) | −7.13355 | −0.928710 | −0.464355 | − | 0.885649i | \(-0.653714\pi\) | ||||
−0.464355 | + | 0.885649i | \(0.653714\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.55896 | −0.583715 | −0.291857 | − | 0.956462i | \(-0.594273\pi\) | ||||
−0.291857 | + | 0.956462i | \(0.594273\pi\) | |||||||
\(62\) | −14.1135 | −1.79242 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.88733 | 0.735917 | ||||||||
\(65\) | −0.932429 | −0.115654 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.09142 | −0.988524 | −0.494262 | − | 0.869313i | \(-0.664562\pi\) | ||||
−0.494262 | + | 0.869313i | \(0.664562\pi\) | |||||||
\(68\) | 1.79335 | 0.217476 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.660846 | 0.0789862 | ||||||||
\(71\) | 12.3094 | 1.46086 | 0.730429 | − | 0.682989i | \(-0.239320\pi\) | ||||
0.730429 | + | 0.682989i | \(0.239320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.4833 | −1.81219 | −0.906093 | − | 0.423078i | \(-0.860950\pi\) | ||||
−0.906093 | + | 0.423078i | \(0.860950\pi\) | |||||||
\(74\) | 4.47096 | 0.519738 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.979704 | −0.112380 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6196 | 1.64483 | 0.822414 | − | 0.568889i | \(-0.192627\pi\) | ||||
0.822414 | + | 0.568889i | \(0.192627\pi\) | |||||||
\(80\) | 2.74025 | 0.306370 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.78443 | −0.197057 | ||||||||
\(83\) | −6.95300 | −0.763191 | −0.381596 | − | 0.924329i | \(-0.624625\pi\) | ||||
−0.381596 | + | 0.924329i | \(0.624625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.71861 | −0.294875 | ||||||||
\(86\) | 6.51616 | 0.702656 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.4803 | −1.32291 | −0.661453 | − | 0.749986i | \(-0.730060\pi\) | ||||
−0.661453 | + | 0.749986i | \(0.730060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.13705 | −0.119195 | ||||||||
\(92\) | 1.73868 | 0.181269 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.351832 | 0.0362887 | ||||||||
\(95\) | 1.48517 | 0.152375 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.1805 | 1.43981 | 0.719904 | − | 0.694073i | \(-0.244186\pi\) | ||||
0.719904 | + | 0.694073i | \(0.244186\pi\) | |||||||
\(98\) | −10.0171 | −1.01188 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.81581 | −0.181581 | ||||||||
\(101\) | −14.3685 | −1.42972 | −0.714861 | − | 0.699266i | \(-0.753510\pi\) | ||||
−0.714861 | + | 0.699266i | \(0.753510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.42885 | −0.436388 | −0.218194 | − | 0.975905i | \(-0.570017\pi\) | ||||
−0.218194 | + | 0.975905i | \(0.570017\pi\) | |||||||
\(104\) | −3.91922 | −0.384311 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.81853 | 0.856532 | ||||||||
\(107\) | −15.7444 | −1.52207 | −0.761035 | − | 0.648711i | \(-0.775308\pi\) | ||||
−0.761035 | + | 0.648711i | \(0.775308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.6970 | 1.31194 | 0.655969 | − | 0.754788i | \(-0.272260\pi\) | ||||
0.655969 | + | 0.754788i | \(0.272260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.34159 | 0.315750 | ||||||||
\(113\) | −8.03013 | −0.755411 | −0.377706 | − | 0.925926i | \(-0.623287\pi\) | ||||
−0.377706 | + | 0.925926i | \(0.623287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.63573 | −0.245783 | ||||||||
\(116\) | 2.72542 | 0.253049 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.0294 | −1.01534 | ||||||||
\(119\) | −3.31520 | −0.303904 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −7.04877 | −0.638166 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.56493 | −0.320140 | ||||||||
\(125\) | 5.71281 | 0.510969 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.9963 | 1.06450 | 0.532250 | − | 0.846587i | \(-0.321347\pi\) | ||||
0.532250 | + | 0.846587i | \(0.321347\pi\) | |||||||
\(128\) | 13.4616 | 1.18985 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.44166 | −0.126442 | ||||||||
\(131\) | −6.89109 | −0.602077 | −0.301039 | − | 0.953612i | \(-0.597333\pi\) | ||||
−0.301039 | + | 0.953612i | \(0.597333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.81109 | 0.157041 | ||||||||
\(134\) | −12.5104 | −1.08074 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.4270 | −0.979854 | ||||||||
\(137\) | −9.24655 | −0.789986 | −0.394993 | − | 0.918684i | \(-0.629253\pi\) | ||||
−0.394993 | + | 0.918684i | \(0.629253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.6113 | −1.83305 | −0.916523 | − | 0.399982i | \(-0.869016\pi\) | ||||
−0.916523 | + | 0.399982i | \(0.869016\pi\) | |||||||
\(140\) | 0.166923 | 0.0141076 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.0320 | 1.59713 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.13157 | −0.343108 | ||||||||
\(146\) | −23.9393 | −1.98123 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.12932 | 0.0928293 | ||||||||
\(149\) | −1.14643 | −0.0939194 | −0.0469597 | − | 0.998897i | \(-0.514953\pi\) | ||||
−0.0469597 | + | 0.998897i | \(0.514953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.880640 | −0.0716655 | −0.0358327 | − | 0.999358i | \(-0.511408\pi\) | ||||
−0.0358327 | + | 0.999358i | \(0.511408\pi\) | |||||||
\(152\) | 6.24252 | 0.506335 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.40421 | 0.434077 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.78621 | −0.781025 | −0.390512 | − | 0.920598i | \(-0.627702\pi\) | ||||
−0.390512 | + | 0.920598i | \(0.627702\pi\) | |||||||
\(158\) | 22.6038 | 1.79826 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.29032 | 0.102009 | ||||||||
\(161\) | −3.21412 | −0.253308 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.62976 | 0.362631 | 0.181315 | − | 0.983425i | \(-0.441965\pi\) | ||||
0.181315 | + | 0.983425i | \(0.441965\pi\) | |||||||
\(164\) | −0.450728 | −0.0351959 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.7503 | −0.834384 | ||||||||
\(167\) | −16.9874 | −1.31452 | −0.657262 | − | 0.753663i | \(-0.728285\pi\) | ||||
−0.657262 | + | 0.753663i | \(0.728285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5195 | −0.809191 | ||||||||
\(170\) | −4.20335 | −0.322382 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.64592 | 0.125500 | ||||||||
\(173\) | −0.591056 | −0.0449371 | −0.0224686 | − | 0.999748i | \(-0.507153\pi\) | ||||
−0.0224686 | + | 0.999748i | \(0.507153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.35671 | 0.253743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −19.2962 | −1.44631 | ||||||||
\(179\) | 9.64093 | 0.720597 | 0.360298 | − | 0.932837i | \(-0.382675\pi\) | ||||
0.360298 | + | 0.932837i | \(0.382675\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.76187 | −0.353947 | −0.176973 | − | 0.984216i | \(-0.556631\pi\) | ||||
−0.176973 | + | 0.984216i | \(0.556631\pi\) | |||||||
\(182\) | −1.75803 | −0.130314 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.0786 | −0.816723 | ||||||||
\(185\) | −1.71198 | −0.125867 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.0888691 | 0.00648144 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.29628 | 0.166590 | ||||||||
\(191\) | 5.19802 | 0.376116 | 0.188058 | − | 0.982158i | \(-0.439781\pi\) | ||||
0.188058 | + | 0.982158i | \(0.439781\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.26805 | −0.235239 | −0.117620 | − | 0.993059i | \(-0.537526\pi\) | ||||
−0.117620 | + | 0.993059i | \(0.537526\pi\) | |||||||
\(194\) | 21.9249 | 1.57412 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.53021 | −0.180730 | ||||||||
\(197\) | −22.4626 | −1.60039 | −0.800197 | − | 0.599737i | \(-0.795272\pi\) | ||||
−0.800197 | + | 0.599737i | \(0.795272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.8291 | −1.47654 | −0.738269 | − | 0.674507i | \(-0.764356\pi\) | ||||
−0.738269 | + | 0.674507i | \(0.764356\pi\) | |||||||
\(200\) | 11.5700 | 0.818125 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −22.2157 | −1.56309 | ||||||||
\(203\) | −5.03822 | −0.353614 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.683276 | 0.0477220 | ||||||||
\(206\) | −6.84761 | −0.477096 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.28981 | −0.505457 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.39202 | −0.233517 | −0.116758 | − | 0.993160i | \(-0.537250\pi\) | ||||
−0.116758 | + | 0.993160i | \(0.537250\pi\) | |||||||
\(212\) | 2.22747 | 0.152983 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −24.3430 | −1.66405 | ||||||||
\(215\) | −2.49511 | −0.170165 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.59014 | 0.447368 | ||||||||
\(218\) | 21.1775 | 1.43432 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.23224 | 0.486493 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0264 | −0.738382 | −0.369191 | − | 0.929354i | \(-0.620365\pi\) | ||||
−0.369191 | + | 0.929354i | \(0.620365\pi\) | |||||||
\(224\) | 1.57348 | 0.105133 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.4157 | −0.825879 | ||||||||
\(227\) | −5.96689 | −0.396036 | −0.198018 | − | 0.980198i | \(-0.563451\pi\) | ||||
−0.198018 | + | 0.980198i | \(0.563451\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.7507 | 1.63557 | 0.817785 | − | 0.575523i | \(-0.195202\pi\) | ||||
0.817785 | + | 0.575523i | \(0.195202\pi\) | |||||||
\(230\) | −4.07519 | −0.268710 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.3659 | −1.14013 | ||||||||
\(233\) | 4.18842 | 0.274392 | 0.137196 | − | 0.990544i | \(-0.456191\pi\) | ||||
0.137196 | + | 0.990544i | \(0.456191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.134720 | −0.00878817 | ||||||||
\(236\) | −2.78592 | −0.181348 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.12575 | −0.332253 | ||||||||
\(239\) | −7.37284 | −0.476910 | −0.238455 | − | 0.971154i | \(-0.576641\pi\) | ||||
−0.238455 | + | 0.971154i | \(0.576641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.82924 | 0.568741 | 0.284371 | − | 0.958714i | \(-0.408215\pi\) | ||||
0.284371 | + | 0.958714i | \(0.408215\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.78045 | −0.113981 | ||||||||
\(245\) | 3.83565 | 0.245051 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.95096 | −0.251393 | ||||||||
\(248\) | 22.7152 | 1.44241 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.83279 | 0.558634 | ||||||||
\(251\) | −20.5731 | −1.29856 | −0.649280 | − | 0.760550i | \(-0.724930\pi\) | ||||
−0.649280 | + | 0.760550i | \(0.724930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 18.5479 | 1.16380 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.03879 | 0.564924 | ||||||||
\(257\) | 3.38239 | 0.210987 | 0.105494 | − | 0.994420i | \(-0.466358\pi\) | ||||
0.105494 | + | 0.994420i | \(0.466358\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.08766 | −0.129721 | ||||||||
\(260\) | −0.364149 | −0.0225836 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.6546 | −0.658241 | ||||||||
\(263\) | −14.2822 | −0.880681 | −0.440341 | − | 0.897831i | \(-0.645142\pi\) | ||||
−0.440341 | + | 0.897831i | \(0.645142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.37671 | −0.207430 | ||||||||
\(266\) | 2.80019 | 0.171690 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.16001 | −0.193028 | ||||||||
\(269\) | −6.72041 | −0.409751 | −0.204875 | − | 0.978788i | \(-0.565679\pi\) | ||||
−0.204875 | + | 0.978788i | \(0.565679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.98035 | 0.241789 | 0.120895 | − | 0.992665i | \(-0.461424\pi\) | ||||
0.120895 | + | 0.992665i | \(0.461424\pi\) | |||||||
\(272\) | −21.2543 | −1.28873 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.2964 | −0.863679 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.1320 | 0.789026 | 0.394513 | − | 0.918890i | \(-0.370913\pi\) | ||||
0.394513 | + | 0.918890i | \(0.370913\pi\) | |||||||
\(278\) | −33.4140 | −2.00404 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.06361 | −0.0635627 | ||||||||
\(281\) | −2.96787 | −0.177048 | −0.0885241 | − | 0.996074i | \(-0.528215\pi\) | ||||
−0.0885241 | + | 0.996074i | \(0.528215\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.09278 | −0.481066 | −0.240533 | − | 0.970641i | \(-0.577322\pi\) | ||||
−0.240533 | + | 0.970641i | \(0.577322\pi\) | |||||||
\(284\) | 4.80729 | 0.285260 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.833217 | 0.0491833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.08649 | 0.240382 | ||||||||
\(290\) | −6.38797 | −0.375114 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.04683 | −0.353864 | ||||||||
\(293\) | −15.7156 | −0.918114 | −0.459057 | − | 0.888407i | \(-0.651813\pi\) | ||||
−0.459057 | + | 0.888407i | \(0.651813\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.22329 | 0.245890 | ||||||||
\(296\) | −7.19584 | −0.418249 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.77254 | −0.102681 | ||||||||
\(299\) | 7.01174 | 0.405499 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.04265 | −0.175375 | ||||||||
\(302\) | −1.36159 | −0.0783507 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.6112 | 0.665948 | ||||||||
\(305\) | 2.69905 | 0.154547 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.51315 | 0.200506 | 0.100253 | − | 0.994962i | \(-0.468035\pi\) | ||||
0.100253 | + | 0.994962i | \(0.468035\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.35565 | 0.474569 | ||||||||
\(311\) | −26.3344 | −1.49329 | −0.746644 | − | 0.665224i | \(-0.768336\pi\) | ||||
−0.746644 | + | 0.665224i | \(0.768336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.46114 | −0.139112 | −0.0695560 | − | 0.997578i | \(-0.522158\pi\) | ||||
−0.0695560 | + | 0.997578i | \(0.522158\pi\) | |||||||
\(314\) | −15.1308 | −0.853882 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.70949 | 0.321184 | ||||||||
\(317\) | 26.5071 | 1.48879 | 0.744395 | − | 0.667740i | \(-0.232738\pi\) | ||||
0.744395 | + | 0.667740i | \(0.232738\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.48549 | −0.194845 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.96947 | −0.276938 | ||||||||
\(323\) | −11.5195 | −0.640962 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.32279 | −0.406196 | ||||||||
\(326\) | 7.15824 | 0.396458 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.87197 | 0.158578 | ||||||||
\(329\) | −0.164284 | −0.00905726 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.10397 | 0.445434 | 0.222717 | − | 0.974883i | \(-0.428507\pi\) | ||||
0.222717 | + | 0.974883i | \(0.428507\pi\) | |||||||
\(332\) | −2.71541 | −0.149028 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −26.2648 | −1.43715 | ||||||||
\(335\) | 4.79038 | 0.261726 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.7206 | −1.34662 | −0.673309 | − | 0.739361i | \(-0.735128\pi\) | ||||
−0.673309 | + | 0.739361i | \(0.735128\pi\) | |||||||
\(338\) | −16.2646 | −0.884676 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.06172 | −0.0575799 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.73102 | 0.525426 | ||||||||
\(344\) | −10.4875 | −0.565449 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.913853 | −0.0491290 | ||||||||
\(347\) | −2.06964 | −0.111104 | −0.0555522 | − | 0.998456i | \(-0.517692\pi\) | ||||
−0.0555522 | + | 0.998456i | \(0.517692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.21427 | 0.279113 | 0.139557 | − | 0.990214i | \(-0.455432\pi\) | ||||
0.139557 | + | 0.990214i | \(0.455432\pi\) | |||||||
\(350\) | 5.18993 | 0.277413 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.6725 | −1.15351 | −0.576756 | − | 0.816917i | \(-0.695681\pi\) | ||||
−0.576756 | + | 0.816917i | \(0.695681\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.28756 | −0.386784 | ||||||||
\(356\) | −4.87402 | −0.258323 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.9062 | 0.787817 | ||||||||
\(359\) | 8.75285 | 0.461958 | 0.230979 | − | 0.972959i | \(-0.425807\pi\) | ||||
0.230979 | + | 0.972959i | \(0.425807\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.7069 | −0.668786 | ||||||||
\(362\) | −7.36250 | −0.386964 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.444060 | −0.0232751 | ||||||||
\(365\) | 9.16662 | 0.479803 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.76623 | −0.353194 | −0.176597 | − | 0.984283i | \(-0.556509\pi\) | ||||
−0.176597 | + | 0.984283i | \(0.556509\pi\) | |||||||
\(368\) | −20.6063 | −1.07418 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.64695 | −0.137608 | ||||||||
\(371\) | −4.11771 | −0.213781 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.8933 | 1.13359 | 0.566797 | − | 0.823857i | \(-0.308182\pi\) | ||||
0.566797 | + | 0.823857i | \(0.308182\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.566260 | −0.0292026 | ||||||||
\(377\) | 10.9911 | 0.566069 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.8236 | −1.73740 | −0.868701 | − | 0.495337i | \(-0.835045\pi\) | ||||
−0.868701 | + | 0.495337i | \(0.835045\pi\) | |||||||
\(380\) | 0.580016 | 0.0297542 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.03686 | 0.411201 | ||||||||
\(383\) | 18.3739 | 0.938862 | 0.469431 | − | 0.882969i | \(-0.344459\pi\) | ||||
0.469431 | + | 0.882969i | \(0.344459\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.05284 | −0.257183 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.53801 | 0.281150 | ||||||||
\(389\) | 30.8065 | 1.56195 | 0.780977 | − | 0.624560i | \(-0.214722\pi\) | ||||
0.780977 | + | 0.624560i | \(0.214722\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.4436 | 1.03388 | ||||||||
\(392\) | 16.1221 | 0.814290 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −34.7302 | −1.74968 | ||||||||
\(395\) | −8.65524 | −0.435493 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.29578 | −0.416353 | −0.208177 | − | 0.978091i | \(-0.566753\pi\) | ||||
−0.208177 | + | 0.978091i | \(0.566753\pi\) | |||||||
\(398\) | −32.2047 | −1.61427 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.5205 | 1.07602 | ||||||||
\(401\) | 3.93362 | 0.196436 | 0.0982179 | − | 0.995165i | \(-0.468686\pi\) | ||||
0.0982179 | + | 0.995165i | \(0.468686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.3767 | −0.716152 | ||||||||
\(404\) | −5.61146 | −0.279181 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.78977 | −0.386600 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.50425 | 0.123827 | 0.0619137 | − | 0.998082i | \(-0.480280\pi\) | ||||
0.0619137 | + | 0.998082i | \(0.480280\pi\) | |||||||
\(410\) | 1.05644 | 0.0521737 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.72964 | −0.0852130 | ||||||||
\(413\) | 5.15007 | 0.253418 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.11640 | 0.202066 | ||||||||
\(416\) | −3.43261 | −0.168298 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.7394 | −0.524654 | −0.262327 | − | 0.964979i | \(-0.584490\pi\) | ||||
−0.262327 | + | 0.964979i | \(0.584490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.1875 | 1.08135 | 0.540675 | − | 0.841232i | \(-0.318169\pi\) | ||||
0.540675 | + | 0.841232i | \(0.318169\pi\) | |||||||
\(422\) | −5.24453 | −0.255300 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.1931 | −0.689278 | ||||||||
\(425\) | −21.3505 | −1.03565 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.29134 | 0.159279 | ||||||||
\(428\) | −6.14879 | −0.297213 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.85778 | −0.186038 | ||||||||
\(431\) | −18.4582 | −0.889100 | −0.444550 | − | 0.895754i | \(-0.646636\pi\) | ||||
−0.444550 | + | 0.895754i | \(0.646636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.1166 | 0.726459 | 0.363230 | − | 0.931700i | \(-0.381674\pi\) | ||||
0.363230 | + | 0.931700i | \(0.381674\pi\) | |||||||
\(434\) | 10.1893 | 0.489100 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.34921 | 0.256181 | ||||||||
\(437\) | −11.1683 | −0.534252 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.9553 | −1.14333 | −0.571663 | − | 0.820488i | \(-0.693702\pi\) | ||||
−0.571663 | + | 0.820488i | \(0.693702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.1820 | 0.531875 | ||||||||
\(443\) | −25.4977 | −1.21143 | −0.605716 | − | 0.795681i | \(-0.707113\pi\) | ||||
−0.605716 | + | 0.795681i | \(0.707113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.38872 | 0.350259 | ||||||||
\(446\) | −17.0483 | −0.807261 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.25036 | −0.200811 | ||||||||
\(449\) | 22.4824 | 1.06101 | 0.530505 | − | 0.847682i | \(-0.322002\pi\) | ||||
0.530505 | + | 0.847682i | \(0.322002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.13607 | −0.147508 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.22562 | −0.432980 | ||||||||
\(455\) | 0.673168 | 0.0315586 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.6896 | −1.01460 | −0.507298 | − | 0.861771i | \(-0.669356\pi\) | ||||
−0.507298 | + | 0.861771i | \(0.669356\pi\) | |||||||
\(458\) | 38.2679 | 1.78814 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.02935 | −0.0479938 | ||||||||
\(461\) | −12.1036 | −0.563722 | −0.281861 | − | 0.959455i | \(-0.590952\pi\) | ||||
−0.281861 | + | 0.959455i | \(0.590952\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0308 | 0.930910 | 0.465455 | − | 0.885071i | \(-0.345891\pi\) | ||||
0.465455 | + | 0.885071i | \(0.345891\pi\) | |||||||
\(464\) | −32.3009 | −1.49953 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.47586 | 0.299988 | ||||||||
\(467\) | −6.06750 | −0.280770 | −0.140385 | − | 0.990097i | \(-0.544834\pi\) | ||||
−0.140385 | + | 0.990097i | \(0.544834\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.84161 | 0.269740 | ||||||||
\(470\) | −0.208296 | −0.00960796 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17.7515 | 0.817078 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.6637 | 0.535169 | ||||||||
\(476\) | −1.29471 | −0.0593430 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.3994 | −0.521397 | ||||||||
\(479\) | 36.2728 | 1.65735 | 0.828673 | − | 0.559732i | \(-0.189096\pi\) | ||||
0.828673 | + | 0.559732i | \(0.189096\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.55432 | 0.207659 | ||||||||
\(482\) | 13.6512 | 0.621795 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.39529 | −0.381211 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.68493 | −0.393552 | −0.196776 | − | 0.980449i | \(-0.563047\pi\) | ||||
−0.196776 | + | 0.980449i | \(0.563047\pi\) | |||||||
\(488\) | 11.3447 | 0.513552 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.93044 | 0.267910 | ||||||||
\(491\) | −33.1973 | −1.49817 | −0.749087 | − | 0.662472i | \(-0.769508\pi\) | ||||
−0.749087 | + | 0.662472i | \(0.769508\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.0458 | 1.44327 | ||||||||
\(494\) | −6.10872 | −0.274844 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 42.2506 | 1.89711 | ||||||||
\(497\) | −8.88678 | −0.398627 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8769 | 0.934578 | 0.467289 | − | 0.884105i | \(-0.345231\pi\) | ||||
0.467289 | + | 0.884105i | \(0.345231\pi\) | |||||||
\(500\) | 2.23107 | 0.0997765 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −31.8087 | −1.41969 | ||||||||
\(503\) | 23.3189 | 1.03974 | 0.519869 | − | 0.854246i | \(-0.325981\pi\) | ||||
0.519869 | + | 0.854246i | \(0.325981\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.50663 | 0.378540 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.68502 | 0.207864 | ||||||||
\(509\) | −6.48121 | −0.287275 | −0.143637 | − | 0.989630i | \(-0.545880\pi\) | ||||
−0.143637 | + | 0.989630i | \(0.545880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1782 | 0.494494 | ||||||||
\(512\) | −12.9480 | −0.572225 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.22963 | 0.230669 | ||||||||
\(515\) | 2.62202 | 0.115540 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.22781 | −0.141822 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.32030 | 0.101752 | ||||||||
\(521\) | 33.2103 | 1.45497 | 0.727484 | − | 0.686124i | \(-0.240689\pi\) | ||||
0.727484 | + | 0.686124i | \(0.240689\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.1386 | 1.75514 | 0.877569 | − | 0.479451i | \(-0.159164\pi\) | ||||
0.877569 | + | 0.479451i | \(0.159164\pi\) | |||||||
\(524\) | −2.69123 | −0.117567 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.0823 | −0.962834 | ||||||||
\(527\) | −41.9169 | −1.82593 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.17970 | −0.138248 | ||||||||
\(530\) | −5.22085 | −0.226779 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.707298 | 0.0306652 | ||||||||
\(533\) | −1.81770 | −0.0787332 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.32119 | 0.402990 | ||||||||
\(536\) | 20.1351 | 0.869703 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.3907 | −0.447974 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.6485 | −1.05972 | −0.529860 | − | 0.848085i | \(-0.677756\pi\) | ||||
−0.529860 | + | 0.848085i | \(0.677756\pi\) | |||||||
\(542\) | 6.15417 | 0.264344 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.0082 | −0.429098 | ||||||||
\(545\) | −8.10908 | −0.347355 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.7204 | −1.09972 | −0.549861 | − | 0.835256i | \(-0.685319\pi\) | ||||
−0.549861 | + | 0.835256i | \(0.685319\pi\) | |||||||
\(548\) | −3.61113 | −0.154260 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.5066 | −0.745805 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.5546 | −0.448827 | ||||||||
\(554\) | 20.3039 | 0.862629 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.44003 | −0.357937 | ||||||||
\(557\) | 11.6815 | 0.494962 | 0.247481 | − | 0.968893i | \(-0.420397\pi\) | ||||
0.247481 | + | 0.968893i | \(0.420397\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.63766 | 0.280743 | ||||||||
\(560\) | −1.97833 | −0.0835996 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.58873 | −0.193564 | ||||||||
\(563\) | 8.12210 | 0.342306 | 0.171153 | − | 0.985244i | \(-0.445251\pi\) | ||||
0.171153 | + | 0.985244i | \(0.445251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.75409 | 0.200006 | ||||||||
\(566\) | −12.5125 | −0.525941 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −30.6313 | −1.28526 | ||||||||
\(569\) | −18.0066 | −0.754877 | −0.377438 | − | 0.926035i | \(-0.623195\pi\) | ||||
−0.377438 | + | 0.926035i | \(0.623195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.60645 | 0.109076 | 0.0545382 | − | 0.998512i | \(-0.482631\pi\) | ||||
0.0545382 | + | 0.998512i | \(0.482631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.28827 | 0.0537712 | ||||||||
\(575\) | −20.6996 | −0.863231 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.1888 | 1.46493 | 0.732465 | − | 0.680805i | \(-0.238370\pi\) | ||||
0.732465 | + | 0.680805i | \(0.238370\pi\) | |||||||
\(578\) | 6.31827 | 0.262805 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.61353 | −0.0669984 | ||||||||
\(581\) | 5.01972 | 0.208253 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 38.5294 | 1.59436 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.2984 | −1.00376 | ||||||||
\(587\) | −23.5524 | −0.972112 | −0.486056 | − | 0.873928i | \(-0.661565\pi\) | ||||
−0.486056 | + | 0.873928i | \(0.661565\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.8991 | 0.943541 | ||||||||
\(590\) | 6.52979 | 0.268827 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.3844 | −0.550095 | ||||||||
\(593\) | 13.1828 | 0.541354 | 0.270677 | − | 0.962670i | \(-0.412752\pi\) | ||||
0.270677 | + | 0.962670i | \(0.412752\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.96270 | 0.0804630 | ||||||||
\(596\) | −0.447726 | −0.0183396 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.8411 | 0.443326 | ||||||||
\(599\) | −34.2164 | −1.39804 | −0.699022 | − | 0.715100i | \(-0.746381\pi\) | ||||
−0.699022 | + | 0.715100i | \(0.746381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.0285 | −1.18410 | −0.592049 | − | 0.805902i | \(-0.701681\pi\) | ||||
−0.592049 | + | 0.805902i | \(0.701681\pi\) | |||||||
\(602\) | −4.70435 | −0.191735 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.343924 | −0.0139941 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.15635 | 0.128112 | 0.0640562 | − | 0.997946i | \(-0.479596\pi\) | ||||
0.0640562 | + | 0.997946i | \(0.479596\pi\) | |||||||
\(608\) | 5.46745 | 0.221735 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.17310 | 0.168964 | ||||||||
\(611\) | 0.358392 | 0.0144990 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.9410 | −1.37086 | −0.685432 | − | 0.728136i | \(-0.740387\pi\) | ||||
−0.685432 | + | 0.728136i | \(0.740387\pi\) | |||||||
\(614\) | 5.43181 | 0.219210 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6077 | 0.869895 | 0.434948 | − | 0.900456i | \(-0.356767\pi\) | ||||
0.434948 | + | 0.900456i | \(0.356767\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.5126 | 0.824471 | 0.412235 | − | 0.911077i | \(-0.364748\pi\) | ||||
0.412235 | + | 0.911077i | \(0.364748\pi\) | |||||||
\(620\) | 2.11055 | 0.0847617 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −40.7166 | −1.63259 | ||||||||
\(623\) | 9.01014 | 0.360984 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.8653 | 0.794613 | ||||||||
\(626\) | −3.80526 | −0.152089 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.82189 | −0.152510 | ||||||||
\(629\) | 13.2787 | 0.529456 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8645 | 1.18889 | 0.594443 | − | 0.804138i | \(-0.297372\pi\) | ||||
0.594443 | + | 0.804138i | \(0.297372\pi\) | |||||||
\(632\) | −36.3800 | −1.44712 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 40.9837 | 1.62767 | ||||||||
\(635\) | −7.10220 | −0.281842 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.2039 | −0.404292 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.96969 | −0.315030 | ||||||||
\(641\) | 38.1201 | 1.50565 | 0.752826 | − | 0.658220i | \(-0.228690\pi\) | ||||
0.752826 | + | 0.658220i | \(0.228690\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.8251 | −0.663519 | −0.331759 | − | 0.943364i | \(-0.607642\pi\) | ||||
−0.331759 | + | 0.943364i | \(0.607642\pi\) | |||||||
\(644\) | −1.25524 | −0.0494633 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.8107 | −0.700753 | ||||||||
\(647\) | 20.9745 | 0.824592 | 0.412296 | − | 0.911050i | \(-0.364727\pi\) | ||||
0.412296 | + | 0.911050i | \(0.364727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −11.3220 | −0.444087 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.80810 | 0.0708106 | ||||||||
\(653\) | −19.7665 | −0.773522 | −0.386761 | − | 0.922180i | \(-0.626406\pi\) | ||||
−0.386761 | + | 0.922180i | \(0.626406\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.07975 | 0.159409 | ||||||||
\(656\) | 5.34191 | 0.208566 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.254005 | −0.00990215 | ||||||||
\(659\) | −11.8055 | −0.459879 | −0.229939 | − | 0.973205i | \(-0.573853\pi\) | ||||
−0.229939 | + | 0.973205i | \(0.573853\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8076 | 0.692637 | 0.346318 | − | 0.938117i | \(-0.387432\pi\) | ||||
0.346318 | + | 0.938117i | \(0.387432\pi\) | |||||||
\(662\) | 12.5298 | 0.486986 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.3022 | 0.671455 | ||||||||
\(665\) | −1.07222 | −0.0415789 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.0688 | 1.20299 | ||||||||
\(668\) | −6.63422 | −0.256686 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.40658 | 0.286141 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.7053 | −0.759583 | −0.379791 | − | 0.925072i | \(-0.624004\pi\) | ||||
−0.379791 | + | 0.925072i | \(0.624004\pi\) | |||||||
\(674\) | −38.2215 | −1.47224 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.10826 | −0.158010 | ||||||||
\(677\) | −12.4139 | −0.477105 | −0.238553 | − | 0.971130i | \(-0.576673\pi\) | ||||
−0.238553 | + | 0.971130i | \(0.576673\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2376 | −0.392883 | ||||||||
\(680\) | 6.76512 | 0.259431 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.02837 | −0.0776135 | −0.0388068 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388068 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.47425 | 0.209160 | ||||||||
\(686\) | 15.0455 | 0.574439 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19.5070 | −0.743696 | ||||||||
\(689\) | 8.98296 | 0.342223 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.34287 | 0.0891270 | 0.0445635 | − | 0.999007i | \(-0.485810\pi\) | ||||
0.0445635 | + | 0.999007i | \(0.485810\pi\) | |||||||
\(692\) | −0.230830 | −0.00877483 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.19995 | −0.121469 | ||||||||
\(695\) | 12.7946 | 0.485326 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.29972 | −0.200741 | ||||||||
\(698\) | 8.06197 | 0.305150 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.31092 | 0.0495482 | ||||||||
\(701\) | −4.43368 | −0.167458 | −0.0837289 | − | 0.996489i | \(-0.526683\pi\) | ||||
−0.0837289 | + | 0.996489i | \(0.526683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.25411 | −0.273594 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.5087 | −1.26111 | ||||||||
\(707\) | 10.3734 | 0.390131 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.8825 | 1.12226 | 0.561131 | − | 0.827727i | \(-0.310366\pi\) | ||||
0.561131 | + | 0.827727i | \(0.310366\pi\) | |||||||
\(710\) | −11.2676 | −0.422864 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 31.0565 | 1.16389 | ||||||||
\(713\) | −40.6389 | −1.52194 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.76515 | 0.140710 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.5331 | 0.505051 | ||||||||
\(719\) | 21.6321 | 0.806742 | 0.403371 | − | 0.915037i | \(-0.367838\pi\) | ||||
0.403371 | + | 0.915037i | \(0.367838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.19741 | 0.119078 | ||||||||
\(722\) | −19.6466 | −0.731172 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.85969 | −0.0691149 | ||||||||
\(725\) | −32.4471 | −1.20505 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.4422 | −0.461455 | −0.230727 | − | 0.973018i | \(-0.574111\pi\) | ||||
−0.230727 | + | 0.973018i | \(0.574111\pi\) | |||||||
\(728\) | 2.82948 | 0.104868 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.1729 | 0.524561 | ||||||||
\(731\) | 19.3529 | 0.715793 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.3522 | 1.93367 | 0.966836 | − | 0.255396i | \(-0.0822060\pi\) | ||||
0.966836 | + | 0.255396i | \(0.0822060\pi\) | |||||||
\(734\) | −10.4615 | −0.386141 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.70306 | −0.357660 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.6760 | 1.71701 | 0.858503 | − | 0.512809i | \(-0.171395\pi\) | ||||
0.858503 | + | 0.512809i | \(0.171395\pi\) | |||||||
\(740\) | −0.668592 | −0.0245779 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.36655 | −0.233723 | ||||||||
\(743\) | −21.8719 | −0.802401 | −0.401201 | − | 0.915990i | \(-0.631407\pi\) | ||||
−0.401201 | + | 0.915990i | \(0.631407\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.678725 | 0.0248665 | ||||||||
\(746\) | 33.8501 | 1.23934 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.3667 | 0.415330 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.5921 | 1.44474 | 0.722369 | − | 0.691508i | \(-0.243053\pi\) | ||||
0.722369 | + | 0.691508i | \(0.243053\pi\) | |||||||
\(752\) | −1.05325 | −0.0384082 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.9937 | 0.618874 | ||||||||
\(755\) | 0.521367 | 0.0189745 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.1457 | 0.841246 | 0.420623 | − | 0.907235i | \(-0.361811\pi\) | ||||
0.420623 | + | 0.907235i | \(0.361811\pi\) | |||||||
\(758\) | −52.2959 | −1.89947 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.69577 | −0.134060 | ||||||||
\(761\) | −14.8929 | −0.539866 | −0.269933 | − | 0.962879i | \(-0.587002\pi\) | ||||
−0.269933 | + | 0.962879i | \(0.587002\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.88858 | −0.357991 | ||||||||
\(764\) | 2.03003 | 0.0734438 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.4085 | 1.02644 | ||||||||
\(767\) | −11.2351 | −0.405676 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.6233 | −0.779757 | −0.389879 | − | 0.920866i | \(-0.627483\pi\) | ||||
−0.389879 | + | 0.920866i | \(0.627483\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.27630 | −0.0459349 | ||||||||
\(773\) | 6.07292 | 0.218428 | 0.109214 | − | 0.994018i | \(-0.465167\pi\) | ||||
0.109214 | + | 0.994018i | \(0.465167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 42.4417 | 1.52455 | ||||||||
\(776\) | −35.2874 | −1.26674 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 47.6311 | 1.70766 | ||||||||
\(779\) | 2.89522 | 0.103732 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 31.6086 | 1.13032 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 29.9874 | 1.07098 | ||||||||
\(785\) | 5.79375 | 0.206788 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.1554 | −1.82349 | −0.911746 | − | 0.410754i | \(-0.865265\pi\) | ||||
−0.911746 | + | 0.410754i | \(0.865265\pi\) | |||||||
\(788\) | −8.77250 | −0.312507 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.3822 | −0.476117 | ||||||||
\(791\) | 5.79736 | 0.206130 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.18019 | −0.254976 | ||||||||
\(794\) | −12.8264 | −0.455192 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.13457 | −0.288322 | ||||||||
\(797\) | 25.2612 | 0.894798 | 0.447399 | − | 0.894334i | \(-0.352350\pi\) | ||||
0.447399 | + | 0.894334i | \(0.352350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.04494 | 0.0369672 | ||||||||
\(800\) | 10.1335 | 0.358274 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.08192 | 0.214760 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.90286 | 0.0670671 | ||||||||
\(806\) | −22.2283 | −0.782957 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 35.7554 | 1.25787 | ||||||||
\(809\) | 51.3275 | 1.80458 | 0.902290 | − | 0.431130i | \(-0.141885\pi\) | ||||
0.902290 | + | 0.431130i | \(0.141885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.54589 | −0.159628 | −0.0798138 | − | 0.996810i | \(-0.525433\pi\) | ||||
−0.0798138 | + | 0.996810i | \(0.525433\pi\) | |||||||
\(812\) | −1.96762 | −0.0690498 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.74097 | −0.0960119 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5724 | −0.369883 | ||||||||
\(818\) | 3.87192 | 0.135378 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.266845 | 0.00931864 | ||||||||
\(821\) | 10.8738 | 0.379498 | 0.189749 | − | 0.981833i | \(-0.439233\pi\) | ||||
0.189749 | + | 0.981833i | \(0.439233\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.6161 | −0.823207 | −0.411604 | − | 0.911363i | \(-0.635031\pi\) | ||||
−0.411604 | + | 0.911363i | \(0.635031\pi\) | |||||||
\(824\) | 11.0210 | 0.383934 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.96271 | 0.277058 | ||||||||
\(827\) | −27.6040 | −0.959886 | −0.479943 | − | 0.877300i | \(-0.659343\pi\) | ||||
−0.479943 | + | 0.877300i | \(0.659343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.1009 | −0.559208 | −0.279604 | − | 0.960115i | \(-0.590203\pi\) | ||||
−0.279604 | + | 0.960115i | \(0.590203\pi\) | |||||||
\(830\) | 6.36452 | 0.220916 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.27234 | 0.321461 | ||||||||
\(833\) | −29.7506 | −1.03080 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0571 | 0.348039 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.6046 | −0.573596 | ||||||||
\(839\) | 19.4319 | 0.670865 | 0.335432 | − | 0.942064i | \(-0.391118\pi\) | ||||
0.335432 | + | 0.942064i | \(0.391118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.7012 | 0.679350 | ||||||||
\(842\) | 34.3048 | 1.18222 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.32471 | −0.0455986 | ||||||||
\(845\) | 6.22787 | 0.214245 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −26.3994 | −0.906559 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −33.0108 | −1.13226 | ||||||||
\(851\) | 12.8738 | 0.441309 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.7855 | 0.677443 | 0.338722 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338722 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(854\) | 5.08886 | 0.174137 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.1791 | 1.33912 | ||||||||
\(857\) | −4.34065 | −0.148274 | −0.0741369 | − | 0.997248i | \(-0.523620\pi\) | ||||
−0.0741369 | + | 0.997248i | \(0.523620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.17935 | −0.176717 | −0.0883586 | − | 0.996089i | \(-0.528162\pi\) | ||||
−0.0883586 | + | 0.996089i | \(0.528162\pi\) | |||||||
\(860\) | −0.974434 | −0.0332279 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.5389 | −0.972039 | ||||||||
\(863\) | 2.69392 | 0.0917021 | 0.0458510 | − | 0.998948i | \(-0.485400\pi\) | ||||
0.0458510 | + | 0.998948i | \(0.485400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.349924 | 0.0118978 | ||||||||
\(866\) | 23.3724 | 0.794226 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.57370 | 0.0873571 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.7437 | −0.431804 | ||||||||
\(872\) | −34.0843 | −1.15424 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.2677 | −0.584088 | ||||||||
\(875\) | −4.12437 | −0.139429 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.8448 | 0.703878 | 0.351939 | − | 0.936023i | \(-0.385522\pi\) | ||||
0.351939 | + | 0.936023i | \(0.385522\pi\) | |||||||
\(878\) | −37.0382 | −1.24998 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.5843 | −0.390286 | −0.195143 | − | 0.980775i | \(-0.562517\pi\) | ||||
−0.195143 | + | 0.980775i | \(0.562517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.3973 | 0.518159 | 0.259079 | − | 0.965856i | \(-0.416581\pi\) | ||||
0.259079 | + | 0.965856i | \(0.416581\pi\) | |||||||
\(884\) | 2.82447 | 0.0949970 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39.4229 | −1.32444 | ||||||||
\(887\) | −5.90996 | −0.198437 | −0.0992185 | − | 0.995066i | \(-0.531634\pi\) | ||||
−0.0992185 | + | 0.995066i | \(0.531634\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.66074 | −0.290472 | ||||||||
\(890\) | 11.4240 | 0.382932 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.30623 | −0.144183 | ||||||||
\(893\) | −0.570846 | −0.0191026 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.70774 | −0.190789 | ||||||||
\(896\) | −9.71860 | −0.324676 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.7609 | 1.15999 | ||||||||
\(899\) | −63.7025 | −2.12460 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.1909 | 0.872546 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.9826 | 0.664610 | ||||||||
\(905\) | 2.81918 | 0.0937127 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.39332 | −0.245491 | −0.122746 | − | 0.992438i | \(-0.539170\pi\) | ||||
−0.122746 | + | 0.992438i | \(0.539170\pi\) | |||||||
\(908\) | −2.33030 | −0.0773336 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.04081 | 0.0345025 | ||||||||
\(911\) | 14.1988 | 0.470427 | 0.235214 | − | 0.971944i | \(-0.424421\pi\) | ||||
0.235214 | + | 0.971944i | \(0.424421\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −33.5350 | −1.10924 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.66608 | 0.319376 | ||||||||
\(917\) | 4.97503 | 0.164290 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.6426 | 1.37366 | 0.686831 | − | 0.726817i | \(-0.259001\pi\) | ||||
0.686831 | + | 0.726817i | \(0.259001\pi\) | |||||||
\(920\) | 6.55887 | 0.216239 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.7139 | −0.616308 | ||||||||
\(923\) | 19.3869 | 0.638127 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.4449 | −0.442067 | ||||||||
\(926\) | 30.9703 | 1.01775 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.2098 | −0.499286 | ||||||||
\(929\) | 34.1328 | 1.11986 | 0.559930 | − | 0.828540i | \(-0.310828\pi\) | ||||
0.559930 | + | 0.828540i | \(0.310828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.2527 | 0.532660 | ||||||||
\(932\) | 1.63574 | 0.0535803 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.38118 | −0.306962 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.6822 | −1.68838 | −0.844192 | − | 0.536041i | \(-0.819919\pi\) | ||||
−0.844192 | + | 0.536041i | \(0.819919\pi\) | |||||||
\(938\) | 9.03192 | 0.294903 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0526133 | −0.00171606 | ||||||||
\(941\) | 18.0062 | 0.586985 | 0.293492 | − | 0.955961i | \(-0.405182\pi\) | ||||
0.293492 | + | 0.955961i | \(0.405182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.13814 | −0.167321 | ||||||||
\(944\) | 33.0181 | 1.07465 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.6303 | −0.930360 | −0.465180 | − | 0.885216i | \(-0.654010\pi\) | ||||
−0.465180 | + | 0.885216i | \(0.654010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.3857 | −0.791593 | ||||||||
\(950\) | 18.0337 | 0.585091 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.24970 | 0.267374 | ||||||||
\(953\) | 16.6893 | 0.540620 | 0.270310 | − | 0.962773i | \(-0.412874\pi\) | ||||
0.270310 | + | 0.962773i | \(0.412874\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.07740 | −0.0995822 | ||||||||
\(956\) | −2.87938 | −0.0931257 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 56.0827 | 1.81195 | ||||||||
\(959\) | 6.67555 | 0.215565 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.3248 | 1.68790 | ||||||||
\(962\) | 7.04160 | 0.227030 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.44815 | 0.111058 | ||||||||
\(965\) | 1.93479 | 0.0622830 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.3193 | −0.782057 | −0.391029 | − | 0.920379i | \(-0.627881\pi\) | ||||
−0.391029 | + | 0.920379i | \(0.627881\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.9803 | −0.416771 | ||||||||
\(971\) | −7.55191 | −0.242352 | −0.121176 | − | 0.992631i | \(-0.538667\pi\) | ||||
−0.121176 | + | 0.992631i | \(0.538667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.6023 | 0.500186 | ||||||||
\(974\) | −13.4281 | −0.430264 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.1014 | 0.675439 | ||||||||
\(977\) | −2.03229 | −0.0650186 | −0.0325093 | − | 0.999471i | \(-0.510350\pi\) | ||||
−0.0325093 | + | 0.999471i | \(0.510350\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.49797 | 0.0478508 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −51.3276 | −1.63793 | ||||||||
\(983\) | −33.4396 | −1.06656 | −0.533279 | − | 0.845940i | \(-0.679040\pi\) | ||||
−0.533279 | + | 0.845940i | \(0.679040\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.2986 | 0.423728 | ||||||||
\(986\) | 49.5473 | 1.57791 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.54300 | −0.0490893 | ||||||||
\(989\) | 18.7629 | 0.596624 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.1009 | 1.27385 | 0.636923 | − | 0.770927i | \(-0.280207\pi\) | ||||
0.636923 | + | 0.770927i | \(0.280207\pi\) | |||||||
\(992\) | 19.8949 | 0.631662 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13.7402 | −0.435812 | ||||||||
\(995\) | 12.3315 | 0.390935 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.1301 | −0.510845 | −0.255423 | − | 0.966829i | \(-0.582215\pi\) | ||||
−0.255423 | + | 0.966829i | \(0.582215\pi\) | |||||||
\(998\) | 32.2785 | 1.02176 | ||||||||
\(999\) | 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 | 9801.2.a.cn.1.15 | 18 | ||
3.2 | odd | 2 | 9801.2.a.co.1.4 | 18 | |||
9.2 | odd | 6 | 1089.2.e.o.364.15 | 36 | |||
9.5 | odd | 6 | 1089.2.e.o.727.15 | 36 | |||
11.2 | odd | 10 | 891.2.f.e.730.8 | 36 | |||
11.6 | odd | 10 | 891.2.f.e.487.8 | 36 | |||
11.10 | odd | 2 | 9801.2.a.cp.1.4 | 18 | |||
33.2 | even | 10 | 891.2.f.f.730.2 | 36 | |||
33.17 | even | 10 | 891.2.f.f.487.2 | 36 | |||
33.32 | even | 2 | 9801.2.a.cm.1.15 | 18 | |||
99.2 | even | 30 | 99.2.m.b.4.2 | ✓ | 72 | ||
99.13 | odd | 30 | 297.2.n.b.235.2 | 72 | |||
99.32 | even | 6 | 1089.2.e.p.727.4 | 36 | |||
99.50 | even | 30 | 99.2.m.b.25.2 | yes | 72 | ||
99.61 | odd | 30 | 297.2.n.b.91.2 | 72 | |||
99.65 | even | 6 | 1089.2.e.p.364.4 | 36 | |||
99.68 | even | 30 | 99.2.m.b.70.8 | yes | 72 | ||
99.79 | odd | 30 | 297.2.n.b.37.8 | 72 | |||
99.83 | even | 30 | 99.2.m.b.58.8 | yes | 72 | ||
99.94 | odd | 30 | 297.2.n.b.289.8 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.4.2 | ✓ | 72 | 99.2 | even | 30 | ||
99.2.m.b.25.2 | yes | 72 | 99.50 | even | 30 | ||
99.2.m.b.58.8 | yes | 72 | 99.83 | even | 30 | ||
99.2.m.b.70.8 | yes | 72 | 99.68 | even | 30 | ||
297.2.n.b.37.8 | 72 | 99.79 | odd | 30 | |||
297.2.n.b.91.2 | 72 | 99.61 | odd | 30 | |||
297.2.n.b.235.2 | 72 | 99.13 | odd | 30 | |||
297.2.n.b.289.8 | 72 | 99.94 | odd | 30 | |||
891.2.f.e.487.8 | 36 | 11.6 | odd | 10 | |||
891.2.f.e.730.8 | 36 | 11.2 | odd | 10 | |||
891.2.f.f.487.2 | 36 | 33.17 | even | 10 | |||
891.2.f.f.730.2 | 36 | 33.2 | even | 10 | |||
1089.2.e.o.364.15 | 36 | 9.2 | odd | 6 | |||
1089.2.e.o.727.15 | 36 | 9.5 | odd | 6 | |||
1089.2.e.p.364.4 | 36 | 99.65 | even | 6 | |||
1089.2.e.p.727.4 | 36 | 99.32 | even | 6 | |||
9801.2.a.cm.1.15 | 18 | 33.32 | even | 2 | |||
9801.2.a.cn.1.15 | 18 | 1.1 | even | 1 | trivial | ||
9801.2.a.co.1.4 | 18 | 3.2 | odd | 2 | |||
9801.2.a.cp.1.4 | 18 | 11.10 | odd | 2 |