Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, 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("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.495822 | 0.350599 | 0.175300 | − | 0.984515i | \(-0.443911\pi\) | ||||
0.175300 | + | 0.984515i | \(0.443911\pi\) | |||||||
\(3\) | −0.133739 | −0.0772140 | −0.0386070 | − | 0.999254i | \(-0.512292\pi\) | ||||
−0.0386070 | + | 0.999254i | \(0.512292\pi\) | |||||||
\(4\) | −1.75416 | −0.877080 | ||||||||
\(5\) | −0.493567 | −0.220730 | −0.110365 | − | 0.993891i | \(-0.535202\pi\) | ||||
−0.110365 | + | 0.993891i | \(0.535202\pi\) | |||||||
\(6\) | −0.0663105 | −0.0270712 | ||||||||
\(7\) | 1.67893 | 0.634574 | 0.317287 | − | 0.948330i | \(-0.397228\pi\) | ||||
0.317287 | + | 0.948330i | \(0.397228\pi\) | |||||||
\(8\) | −1.86140 | −0.658103 | ||||||||
\(9\) | −2.98211 | −0.994038 | ||||||||
\(10\) | −0.244721 | −0.0773877 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.234599 | 0.0677229 | ||||||||
\(13\) | 5.28022 | 1.46447 | 0.732234 | − | 0.681053i | \(-0.238478\pi\) | ||||
0.732234 | + | 0.681053i | \(0.238478\pi\) | |||||||
\(14\) | 0.832448 | 0.222481 | ||||||||
\(15\) | 0.0660089 | 0.0170434 | ||||||||
\(16\) | 2.58540 | 0.646350 | ||||||||
\(17\) | 1.59160 | 0.386020 | 0.193010 | − | 0.981197i | \(-0.438175\pi\) | ||||
0.193010 | + | 0.981197i | \(0.438175\pi\) | |||||||
\(18\) | −1.47860 | −0.348509 | ||||||||
\(19\) | −7.18138 | −1.64752 | −0.823761 | − | 0.566937i | \(-0.808128\pi\) | ||||
−0.823761 | + | 0.566937i | \(0.808128\pi\) | |||||||
\(20\) | 0.865796 | 0.193598 | ||||||||
\(21\) | −0.224537 | −0.0489980 | ||||||||
\(22\) | 0.495822 | 0.105710 | ||||||||
\(23\) | −1.46229 | −0.304908 | −0.152454 | − | 0.988311i | \(-0.548718\pi\) | ||||
−0.152454 | + | 0.988311i | \(0.548718\pi\) | |||||||
\(24\) | 0.248940 | 0.0508147 | ||||||||
\(25\) | −4.75639 | −0.951278 | ||||||||
\(26\) | 2.61805 | 0.513441 | ||||||||
\(27\) | 0.800039 | 0.153968 | ||||||||
\(28\) | −2.94510 | −0.556572 | ||||||||
\(29\) | −8.57087 | −1.59157 | −0.795786 | − | 0.605578i | \(-0.792942\pi\) | ||||
−0.795786 | + | 0.605578i | \(0.792942\pi\) | |||||||
\(30\) | 0.0327287 | 0.00597541 | ||||||||
\(31\) | 1.89658 | 0.340636 | 0.170318 | − | 0.985389i | \(-0.445521\pi\) | ||||
0.170318 | + | 0.985389i | \(0.445521\pi\) | |||||||
\(32\) | 5.00469 | 0.884712 | ||||||||
\(33\) | −0.133739 | −0.0232809 | ||||||||
\(34\) | 0.789150 | 0.135338 | ||||||||
\(35\) | −0.828662 | −0.140069 | ||||||||
\(36\) | 5.23111 | 0.871851 | ||||||||
\(37\) | 6.08431 | 1.00026 | 0.500128 | − | 0.865952i | \(-0.333286\pi\) | ||||
0.500128 | + | 0.865952i | \(0.333286\pi\) | |||||||
\(38\) | −3.56069 | −0.577620 | ||||||||
\(39\) | −0.706169 | −0.113077 | ||||||||
\(40\) | 0.918723 | 0.145263 | ||||||||
\(41\) | 1.95977 | 0.306065 | 0.153033 | − | 0.988221i | \(-0.451096\pi\) | ||||
0.153033 | + | 0.988221i | \(0.451096\pi\) | |||||||
\(42\) | −0.111330 | −0.0171786 | ||||||||
\(43\) | −8.81508 | −1.34429 | −0.672143 | − | 0.740421i | \(-0.734626\pi\) | ||||
−0.672143 | + | 0.740421i | \(0.734626\pi\) | |||||||
\(44\) | −1.75416 | −0.264450 | ||||||||
\(45\) | 1.47187 | 0.219414 | ||||||||
\(46\) | −0.725034 | −0.106900 | ||||||||
\(47\) | −8.75989 | −1.27776 | −0.638880 | − | 0.769306i | \(-0.720602\pi\) | ||||
−0.638880 | + | 0.769306i | \(0.720602\pi\) | |||||||
\(48\) | −0.345768 | −0.0499073 | ||||||||
\(49\) | −4.18121 | −0.597316 | ||||||||
\(50\) | −2.35832 | −0.333517 | ||||||||
\(51\) | −0.212858 | −0.0298061 | ||||||||
\(52\) | −9.26235 | −1.28446 | ||||||||
\(53\) | −6.71231 | −0.922006 | −0.461003 | − | 0.887399i | \(-0.652510\pi\) | ||||
−0.461003 | + | 0.887399i | \(0.652510\pi\) | |||||||
\(54\) | 0.396677 | 0.0539809 | ||||||||
\(55\) | −0.493567 | −0.0665525 | ||||||||
\(56\) | −3.12514 | −0.417615 | ||||||||
\(57\) | 0.960428 | 0.127212 | ||||||||
\(58\) | −4.24963 | −0.558003 | ||||||||
\(59\) | −3.43339 | −0.446989 | −0.223494 | − | 0.974705i | \(-0.571746\pi\) | ||||
−0.223494 | + | 0.974705i | \(0.571746\pi\) | |||||||
\(60\) | −0.115790 | −0.0149485 | ||||||||
\(61\) | −5.71897 | −0.732240 | −0.366120 | − | 0.930568i | \(-0.619314\pi\) | ||||
−0.366120 | + | 0.930568i | \(0.619314\pi\) | |||||||
\(62\) | 0.940366 | 0.119427 | ||||||||
\(63\) | −5.00675 | −0.630791 | ||||||||
\(64\) | −2.68937 | −0.336171 | ||||||||
\(65\) | −2.60614 | −0.323252 | ||||||||
\(66\) | −0.0663105 | −0.00816226 | ||||||||
\(67\) | −7.92404 | −0.968075 | −0.484038 | − | 0.875047i | \(-0.660830\pi\) | ||||
−0.484038 | + | 0.875047i | \(0.660830\pi\) | |||||||
\(68\) | −2.79192 | −0.338570 | ||||||||
\(69\) | 0.195564 | 0.0235432 | ||||||||
\(70\) | −0.410869 | −0.0491082 | ||||||||
\(71\) | −7.56641 | −0.897967 | −0.448984 | − | 0.893540i | \(-0.648214\pi\) | ||||
−0.448984 | + | 0.893540i | \(0.648214\pi\) | |||||||
\(72\) | 5.55089 | 0.654179 | ||||||||
\(73\) | −3.61848 | −0.423511 | −0.211756 | − | 0.977323i | \(-0.567918\pi\) | ||||
−0.211756 | + | 0.977323i | \(0.567918\pi\) | |||||||
\(74\) | 3.01674 | 0.350689 | ||||||||
\(75\) | 0.636113 | 0.0734520 | ||||||||
\(76\) | 12.5973 | 1.44501 | ||||||||
\(77\) | 1.67893 | 0.191331 | ||||||||
\(78\) | −0.350134 | −0.0396449 | ||||||||
\(79\) | 15.0966 | 1.69850 | 0.849250 | − | 0.527992i | \(-0.177055\pi\) | ||||
0.849250 | + | 0.527992i | \(0.177055\pi\) | |||||||
\(80\) | −1.27607 | −0.142669 | ||||||||
\(81\) | 8.83935 | 0.982150 | ||||||||
\(82\) | 0.971698 | 0.107306 | ||||||||
\(83\) | −0.0259306 | −0.00284625 | −0.00142312 | − | 0.999999i | \(-0.500453\pi\) | ||||
−0.00142312 | + | 0.999999i | \(0.500453\pi\) | |||||||
\(84\) | 0.393874 | 0.0429752 | ||||||||
\(85\) | −0.785561 | −0.0852060 | ||||||||
\(86\) | −4.37071 | −0.471306 | ||||||||
\(87\) | 1.14626 | 0.122892 | ||||||||
\(88\) | −1.86140 | −0.198425 | ||||||||
\(89\) | −13.2543 | −1.40495 | −0.702474 | − | 0.711709i | \(-0.747921\pi\) | ||||
−0.702474 | + | 0.711709i | \(0.747921\pi\) | |||||||
\(90\) | 0.729787 | 0.0769263 | ||||||||
\(91\) | 8.86509 | 0.929314 | ||||||||
\(92\) | 2.56509 | 0.267429 | ||||||||
\(93\) | −0.253646 | −0.0263019 | ||||||||
\(94\) | −4.34334 | −0.447982 | ||||||||
\(95\) | 3.54449 | 0.363657 | ||||||||
\(96\) | −0.669320 | −0.0683122 | ||||||||
\(97\) | −8.69413 | −0.882756 | −0.441378 | − | 0.897321i | \(-0.645510\pi\) | ||||
−0.441378 | + | 0.897321i | \(0.645510\pi\) | |||||||
\(98\) | −2.07314 | −0.209418 | ||||||||
\(99\) | −2.98211 | −0.299714 | ||||||||
\(100\) | 8.34347 | 0.834347 | ||||||||
\(101\) | 9.03831 | 0.899346 | 0.449673 | − | 0.893193i | \(-0.351541\pi\) | ||||
0.449673 | + | 0.893193i | \(0.351541\pi\) | |||||||
\(102\) | −0.105540 | −0.0104500 | ||||||||
\(103\) | −0.951482 | −0.0937523 | −0.0468762 | − | 0.998901i | \(-0.514927\pi\) | ||||
−0.0468762 | + | 0.998901i | \(0.514927\pi\) | |||||||
\(104\) | −9.82857 | −0.963771 | ||||||||
\(105\) | 0.110824 | 0.0108153 | ||||||||
\(106\) | −3.32811 | −0.323254 | ||||||||
\(107\) | 9.86449 | 0.953636 | 0.476818 | − | 0.879002i | \(-0.341790\pi\) | ||||
0.476818 | + | 0.879002i | \(0.341790\pi\) | |||||||
\(108\) | −1.40340 | −0.135042 | ||||||||
\(109\) | 20.7918 | 1.99149 | 0.995747 | − | 0.0921260i | \(-0.0293663\pi\) | ||||
0.995747 | + | 0.0921260i | \(0.0293663\pi\) | |||||||
\(110\) | −0.244721 | −0.0233333 | ||||||||
\(111\) | −0.813707 | −0.0772337 | ||||||||
\(112\) | 4.34069 | 0.410157 | ||||||||
\(113\) | −14.4582 | −1.36011 | −0.680054 | − | 0.733162i | \(-0.738044\pi\) | ||||
−0.680054 | + | 0.733162i | \(0.738044\pi\) | |||||||
\(114\) | 0.476201 | 0.0446003 | ||||||||
\(115\) | 0.721737 | 0.0673023 | ||||||||
\(116\) | 15.0347 | 1.39594 | ||||||||
\(117\) | −15.7462 | −1.45574 | ||||||||
\(118\) | −1.70235 | −0.156714 | ||||||||
\(119\) | 2.67218 | 0.244958 | ||||||||
\(120\) | −0.122869 | −0.0112163 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.83559 | −0.256723 | ||||||||
\(123\) | −0.262097 | −0.0236325 | ||||||||
\(124\) | −3.32691 | −0.298765 | ||||||||
\(125\) | 4.81543 | 0.430705 | ||||||||
\(126\) | −2.48245 | −0.221155 | ||||||||
\(127\) | −4.96659 | −0.440713 | −0.220357 | − | 0.975419i | \(-0.570722\pi\) | ||||
−0.220357 | + | 0.975419i | \(0.570722\pi\) | |||||||
\(128\) | −11.3428 | −1.00257 | ||||||||
\(129\) | 1.17892 | 0.103798 | ||||||||
\(130\) | −1.29218 | −0.113332 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 0.234599 | 0.0204192 | ||||||||
\(133\) | −12.0570 | −1.04547 | ||||||||
\(134\) | −3.92891 | −0.339406 | ||||||||
\(135\) | −0.394873 | −0.0339852 | ||||||||
\(136\) | −2.96260 | −0.254040 | ||||||||
\(137\) | 11.2713 | 0.962971 | 0.481485 | − | 0.876454i | \(-0.340097\pi\) | ||||
0.481485 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(138\) | 0.0969650 | 0.00825421 | ||||||||
\(139\) | −12.0592 | −1.02285 | −0.511423 | − | 0.859329i | \(-0.670882\pi\) | ||||
−0.511423 | + | 0.859329i | \(0.670882\pi\) | |||||||
\(140\) | 1.45361 | 0.122852 | ||||||||
\(141\) | 1.17153 | 0.0986610 | ||||||||
\(142\) | −3.75159 | −0.314827 | ||||||||
\(143\) | 5.28022 | 0.441554 | ||||||||
\(144\) | −7.70996 | −0.642497 | ||||||||
\(145\) | 4.23030 | 0.351307 | ||||||||
\(146\) | −1.79412 | −0.148483 | ||||||||
\(147\) | 0.559189 | 0.0461211 | ||||||||
\(148\) | −10.6729 | −0.877304 | ||||||||
\(149\) | 1.01857 | 0.0834447 | 0.0417223 | − | 0.999129i | \(-0.486716\pi\) | ||||
0.0417223 | + | 0.999129i | \(0.486716\pi\) | |||||||
\(150\) | 0.315399 | 0.0257522 | ||||||||
\(151\) | 20.9376 | 1.70388 | 0.851939 | − | 0.523642i | \(-0.175427\pi\) | ||||
0.851939 | + | 0.523642i | \(0.175427\pi\) | |||||||
\(152\) | 13.3674 | 1.08424 | ||||||||
\(153\) | −4.74633 | −0.383718 | ||||||||
\(154\) | 0.832448 | 0.0670806 | ||||||||
\(155\) | −0.936089 | −0.0751885 | ||||||||
\(156\) | 1.23873 | 0.0991780 | ||||||||
\(157\) | 5.75439 | 0.459250 | 0.229625 | − | 0.973279i | \(-0.426250\pi\) | ||||
0.229625 | + | 0.973279i | \(0.426250\pi\) | |||||||
\(158\) | 7.48522 | 0.595492 | ||||||||
\(159\) | 0.897694 | 0.0711918 | ||||||||
\(160\) | −2.47015 | −0.195282 | ||||||||
\(161\) | −2.45507 | −0.193487 | ||||||||
\(162\) | 4.38274 | 0.344341 | ||||||||
\(163\) | 0.379296 | 0.0297088 | 0.0148544 | − | 0.999890i | \(-0.495272\pi\) | ||||
0.0148544 | + | 0.999890i | \(0.495272\pi\) | |||||||
\(164\) | −3.43776 | −0.268444 | ||||||||
\(165\) | 0.0660089 | 0.00513879 | ||||||||
\(166\) | −0.0128569 | −0.000997892 0 | ||||||||
\(167\) | −20.7913 | −1.60888 | −0.804439 | − | 0.594036i | \(-0.797534\pi\) | ||||
−0.804439 | + | 0.594036i | \(0.797534\pi\) | |||||||
\(168\) | 0.417952 | 0.0322457 | ||||||||
\(169\) | 14.8807 | 1.14467 | ||||||||
\(170\) | −0.389498 | −0.0298731 | ||||||||
\(171\) | 21.4157 | 1.63770 | ||||||||
\(172\) | 15.4631 | 1.17905 | ||||||||
\(173\) | 1.07921 | 0.0820509 | 0.0410255 | − | 0.999158i | \(-0.486938\pi\) | ||||
0.0410255 | + | 0.999158i | \(0.486938\pi\) | |||||||
\(174\) | 0.568339 | 0.0430857 | ||||||||
\(175\) | −7.98563 | −0.603657 | ||||||||
\(176\) | 2.58540 | 0.194882 | ||||||||
\(177\) | 0.459176 | 0.0345138 | ||||||||
\(178\) | −6.57175 | −0.492574 | ||||||||
\(179\) | −15.2854 | −1.14249 | −0.571244 | − | 0.820780i | \(-0.693539\pi\) | ||||
−0.571244 | + | 0.820780i | \(0.693539\pi\) | |||||||
\(180\) | −2.58190 | −0.192444 | ||||||||
\(181\) | −21.0127 | −1.56186 | −0.780931 | − | 0.624618i | \(-0.785255\pi\) | ||||
−0.780931 | + | 0.624618i | \(0.785255\pi\) | |||||||
\(182\) | 4.39551 | 0.325817 | ||||||||
\(183\) | 0.764847 | 0.0565391 | ||||||||
\(184\) | 2.72189 | 0.200661 | ||||||||
\(185\) | −3.00302 | −0.220786 | ||||||||
\(186\) | −0.125763 | −0.00922141 | ||||||||
\(187\) | 1.59160 | 0.116389 | ||||||||
\(188\) | 15.3662 | 1.12070 | ||||||||
\(189\) | 1.34321 | 0.0977039 | ||||||||
\(190\) | 1.75744 | 0.127498 | ||||||||
\(191\) | −16.7701 | −1.21344 | −0.606720 | − | 0.794916i | \(-0.707515\pi\) | ||||
−0.606720 | + | 0.794916i | \(0.707515\pi\) | |||||||
\(192\) | 0.359672 | 0.0259571 | ||||||||
\(193\) | −18.0268 | −1.29760 | −0.648799 | − | 0.760960i | \(-0.724728\pi\) | ||||
−0.648799 | + | 0.760960i | \(0.724728\pi\) | |||||||
\(194\) | −4.31074 | −0.309493 | ||||||||
\(195\) | 0.348541 | 0.0249596 | ||||||||
\(196\) | 7.33452 | 0.523894 | ||||||||
\(197\) | 13.1321 | 0.935626 | 0.467813 | − | 0.883827i | \(-0.345042\pi\) | ||||
0.467813 | + | 0.883827i | \(0.345042\pi\) | |||||||
\(198\) | −1.47860 | −0.105079 | ||||||||
\(199\) | 18.2178 | 1.29142 | 0.645711 | − | 0.763582i | \(-0.276561\pi\) | ||||
0.645711 | + | 0.763582i | \(0.276561\pi\) | |||||||
\(200\) | 8.85353 | 0.626039 | ||||||||
\(201\) | 1.05975 | 0.0747490 | ||||||||
\(202\) | 4.48139 | 0.315310 | ||||||||
\(203\) | −14.3899 | −1.00997 | ||||||||
\(204\) | 0.373387 | 0.0261423 | ||||||||
\(205\) | −0.967279 | −0.0675577 | ||||||||
\(206\) | −0.471766 | −0.0328695 | ||||||||
\(207\) | 4.36071 | 0.303090 | ||||||||
\(208\) | 13.6515 | 0.946560 | ||||||||
\(209\) | −7.18138 | −0.496747 | ||||||||
\(210\) | 0.0549490 | 0.00379184 | ||||||||
\(211\) | 4.70567 | 0.323951 | 0.161976 | − | 0.986795i | \(-0.448213\pi\) | ||||
0.161976 | + | 0.986795i | \(0.448213\pi\) | |||||||
\(212\) | 11.7745 | 0.808673 | ||||||||
\(213\) | 1.01192 | 0.0693356 | ||||||||
\(214\) | 4.89103 | 0.334344 | ||||||||
\(215\) | 4.35083 | 0.296724 | ||||||||
\(216\) | −1.48919 | −0.101326 | ||||||||
\(217\) | 3.18422 | 0.216159 | ||||||||
\(218\) | 10.3090 | 0.698216 | ||||||||
\(219\) | 0.483930 | 0.0327010 | ||||||||
\(220\) | 0.865796 | 0.0583719 | ||||||||
\(221\) | 8.40399 | 0.565314 | ||||||||
\(222\) | −0.403454 | −0.0270781 | ||||||||
\(223\) | 27.3812 | 1.83358 | 0.916790 | − | 0.399370i | \(-0.130771\pi\) | ||||
0.916790 | + | 0.399370i | \(0.130771\pi\) | |||||||
\(224\) | 8.40250 | 0.561415 | ||||||||
\(225\) | 14.1841 | 0.945607 | ||||||||
\(226\) | −7.16867 | −0.476853 | ||||||||
\(227\) | −13.4949 | −0.895690 | −0.447845 | − | 0.894111i | \(-0.647808\pi\) | ||||
−0.447845 | + | 0.894111i | \(0.647808\pi\) | |||||||
\(228\) | −1.68474 | −0.111575 | ||||||||
\(229\) | 17.2225 | 1.13809 | 0.569047 | − | 0.822305i | \(-0.307312\pi\) | ||||
0.569047 | + | 0.822305i | \(0.307312\pi\) | |||||||
\(230\) | 0.357853 | 0.0235961 | ||||||||
\(231\) | −0.224537 | −0.0147734 | ||||||||
\(232\) | 15.9538 | 1.04742 | ||||||||
\(233\) | 24.1856 | 1.58445 | 0.792226 | − | 0.610227i | \(-0.208922\pi\) | ||||
0.792226 | + | 0.610227i | \(0.208922\pi\) | |||||||
\(234\) | −7.80732 | −0.510380 | ||||||||
\(235\) | 4.32359 | 0.282040 | ||||||||
\(236\) | 6.02271 | 0.392045 | ||||||||
\(237\) | −2.01900 | −0.131148 | ||||||||
\(238\) | 1.32492 | 0.0858820 | ||||||||
\(239\) | 22.4259 | 1.45061 | 0.725307 | − | 0.688426i | \(-0.241698\pi\) | ||||
0.725307 | + | 0.688426i | \(0.241698\pi\) | |||||||
\(240\) | 0.170659 | 0.0110160 | ||||||||
\(241\) | −9.62695 | −0.620127 | −0.310063 | − | 0.950716i | \(-0.600350\pi\) | ||||
−0.310063 | + | 0.950716i | \(0.600350\pi\) | |||||||
\(242\) | 0.495822 | 0.0318726 | ||||||||
\(243\) | −3.58228 | −0.229803 | ||||||||
\(244\) | 10.0320 | 0.642233 | ||||||||
\(245\) | 2.06371 | 0.131845 | ||||||||
\(246\) | −0.129954 | −0.00828553 | ||||||||
\(247\) | −37.9193 | −2.41275 | ||||||||
\(248\) | −3.53029 | −0.224173 | ||||||||
\(249\) | 0.00346792 | 0.000219770 0 | ||||||||
\(250\) | 2.38760 | 0.151005 | ||||||||
\(251\) | 12.4381 | 0.785083 | 0.392542 | − | 0.919734i | \(-0.371596\pi\) | ||||
0.392542 | + | 0.919734i | \(0.371596\pi\) | |||||||
\(252\) | 8.78264 | 0.553254 | ||||||||
\(253\) | −1.46229 | −0.0919332 | ||||||||
\(254\) | −2.46254 | −0.154514 | ||||||||
\(255\) | 0.105060 | 0.00657910 | ||||||||
\(256\) | −0.245289 | −0.0153305 | ||||||||
\(257\) | −14.8275 | −0.924912 | −0.462456 | − | 0.886642i | \(-0.653032\pi\) | ||||
−0.462456 | + | 0.886642i | \(0.653032\pi\) | |||||||
\(258\) | 0.584532 | 0.0363914 | ||||||||
\(259\) | 10.2151 | 0.634736 | ||||||||
\(260\) | 4.57159 | 0.283518 | ||||||||
\(261\) | 25.5593 | 1.58208 | ||||||||
\(262\) | 0.495822 | 0.0306320 | ||||||||
\(263\) | −14.3548 | −0.885153 | −0.442576 | − | 0.896731i | \(-0.645935\pi\) | ||||
−0.442576 | + | 0.896731i | \(0.645935\pi\) | |||||||
\(264\) | 0.248940 | 0.0153212 | ||||||||
\(265\) | 3.31297 | 0.203514 | ||||||||
\(266\) | −5.97813 | −0.366543 | ||||||||
\(267\) | 1.77260 | 0.108482 | ||||||||
\(268\) | 13.9000 | 0.849080 | ||||||||
\(269\) | 11.3186 | 0.690106 | 0.345053 | − | 0.938583i | \(-0.387861\pi\) | ||||
0.345053 | + | 0.938583i | \(0.387861\pi\) | |||||||
\(270\) | −0.195787 | −0.0119152 | ||||||||
\(271\) | −11.8010 | −0.716860 | −0.358430 | − | 0.933557i | \(-0.616688\pi\) | ||||
−0.358430 | + | 0.933557i | \(0.616688\pi\) | |||||||
\(272\) | 4.11492 | 0.249504 | ||||||||
\(273\) | −1.18560 | −0.0717560 | ||||||||
\(274\) | 5.58855 | 0.337617 | ||||||||
\(275\) | −4.75639 | −0.286821 | ||||||||
\(276\) | −0.343051 | −0.0206492 | ||||||||
\(277\) | −15.4341 | −0.927345 | −0.463673 | − | 0.886007i | \(-0.653469\pi\) | ||||
−0.463673 | + | 0.886007i | \(0.653469\pi\) | |||||||
\(278\) | −5.97921 | −0.358609 | ||||||||
\(279\) | −5.65582 | −0.338605 | ||||||||
\(280\) | 1.54247 | 0.0921800 | ||||||||
\(281\) | −12.6262 | −0.753218 | −0.376609 | − | 0.926372i | \(-0.622910\pi\) | ||||
−0.376609 | + | 0.926372i | \(0.622910\pi\) | |||||||
\(282\) | 0.580872 | 0.0345905 | ||||||||
\(283\) | −16.2670 | −0.966975 | −0.483488 | − | 0.875351i | \(-0.660630\pi\) | ||||
−0.483488 | + | 0.875351i | \(0.660630\pi\) | |||||||
\(284\) | 13.2727 | 0.787589 | ||||||||
\(285\) | −0.474035 | −0.0280794 | ||||||||
\(286\) | 2.61805 | 0.154808 | ||||||||
\(287\) | 3.29031 | 0.194221 | ||||||||
\(288\) | −14.9246 | −0.879438 | ||||||||
\(289\) | −14.4668 | −0.850989 | ||||||||
\(290\) | 2.09748 | 0.123168 | ||||||||
\(291\) | 1.16274 | 0.0681611 | ||||||||
\(292\) | 6.34740 | 0.371453 | ||||||||
\(293\) | 32.2542 | 1.88431 | 0.942155 | − | 0.335176i | \(-0.108796\pi\) | ||||
0.942155 | + | 0.335176i | \(0.108796\pi\) | |||||||
\(294\) | 0.277258 | 0.0161700 | ||||||||
\(295\) | 1.69461 | 0.0986637 | ||||||||
\(296\) | −11.3253 | −0.658271 | ||||||||
\(297\) | 0.800039 | 0.0464230 | ||||||||
\(298\) | 0.505030 | 0.0292556 | ||||||||
\(299\) | −7.72119 | −0.446528 | ||||||||
\(300\) | −1.11584 | −0.0644233 | ||||||||
\(301\) | −14.7999 | −0.853050 | ||||||||
\(302\) | 10.3813 | 0.597378 | ||||||||
\(303\) | −1.20877 | −0.0694421 | ||||||||
\(304\) | −18.5668 | −1.06488 | ||||||||
\(305\) | 2.82270 | 0.161627 | ||||||||
\(306\) | −2.35333 | −0.134531 | ||||||||
\(307\) | 11.3179 | 0.645949 | 0.322974 | − | 0.946408i | \(-0.395317\pi\) | ||||
0.322974 | + | 0.946408i | \(0.395317\pi\) | |||||||
\(308\) | −2.94510 | −0.167813 | ||||||||
\(309\) | 0.127250 | 0.00723899 | ||||||||
\(310\) | −0.464134 | −0.0263610 | ||||||||
\(311\) | 20.4740 | 1.16097 | 0.580487 | − | 0.814270i | \(-0.302862\pi\) | ||||
0.580487 | + | 0.814270i | \(0.302862\pi\) | |||||||
\(312\) | 1.31446 | 0.0744166 | ||||||||
\(313\) | −8.88910 | −0.502442 | −0.251221 | − | 0.967930i | \(-0.580832\pi\) | ||||
−0.251221 | + | 0.967930i | \(0.580832\pi\) | |||||||
\(314\) | 2.85315 | 0.161013 | ||||||||
\(315\) | 2.47116 | 0.139234 | ||||||||
\(316\) | −26.4818 | −1.48972 | ||||||||
\(317\) | −18.3295 | −1.02949 | −0.514744 | − | 0.857344i | \(-0.672113\pi\) | ||||
−0.514744 | + | 0.857344i | \(0.672113\pi\) | |||||||
\(318\) | 0.445096 | 0.0249598 | ||||||||
\(319\) | −8.57087 | −0.479877 | ||||||||
\(320\) | 1.32738 | 0.0742029 | ||||||||
\(321\) | −1.31926 | −0.0736341 | ||||||||
\(322\) | −1.21728 | −0.0678362 | ||||||||
\(323\) | −11.4299 | −0.635976 | ||||||||
\(324\) | −15.5056 | −0.861424 | ||||||||
\(325\) | −25.1148 | −1.39312 | ||||||||
\(326\) | 0.188063 | 0.0104159 | ||||||||
\(327\) | −2.78067 | −0.153771 | ||||||||
\(328\) | −3.64791 | −0.201422 | ||||||||
\(329\) | −14.7072 | −0.810834 | ||||||||
\(330\) | 0.0327287 | 0.00180165 | ||||||||
\(331\) | 23.8825 | 1.31270 | 0.656349 | − | 0.754457i | \(-0.272100\pi\) | ||||
0.656349 | + | 0.754457i | \(0.272100\pi\) | |||||||
\(332\) | 0.0454864 | 0.00249639 | ||||||||
\(333\) | −18.1441 | −0.994292 | ||||||||
\(334\) | −10.3088 | −0.564071 | ||||||||
\(335\) | 3.91104 | 0.213683 | ||||||||
\(336\) | −0.580518 | −0.0316699 | ||||||||
\(337\) | 17.9902 | 0.979990 | 0.489995 | − | 0.871725i | \(-0.336999\pi\) | ||||
0.489995 | + | 0.871725i | \(0.336999\pi\) | |||||||
\(338\) | 7.37817 | 0.401320 | ||||||||
\(339\) | 1.93361 | 0.105019 | ||||||||
\(340\) | 1.37800 | 0.0747325 | ||||||||
\(341\) | 1.89658 | 0.102706 | ||||||||
\(342\) | 10.6184 | 0.574176 | ||||||||
\(343\) | −18.7724 | −1.01362 | ||||||||
\(344\) | 16.4083 | 0.884679 | ||||||||
\(345\) | −0.0965240 | −0.00519668 | ||||||||
\(346\) | 0.535097 | 0.0287670 | ||||||||
\(347\) | −14.2631 | −0.765682 | −0.382841 | − | 0.923814i | \(-0.625054\pi\) | ||||
−0.382841 | + | 0.923814i | \(0.625054\pi\) | |||||||
\(348\) | −2.01072 | −0.107786 | ||||||||
\(349\) | −19.5360 | −1.04574 | −0.522870 | − | 0.852413i | \(-0.675139\pi\) | ||||
−0.522870 | + | 0.852413i | \(0.675139\pi\) | |||||||
\(350\) | −3.95945 | −0.211641 | ||||||||
\(351\) | 4.22438 | 0.225481 | ||||||||
\(352\) | 5.00469 | 0.266751 | ||||||||
\(353\) | 15.1166 | 0.804576 | 0.402288 | − | 0.915513i | \(-0.368215\pi\) | ||||
0.402288 | + | 0.915513i | \(0.368215\pi\) | |||||||
\(354\) | 0.227670 | 0.0121005 | ||||||||
\(355\) | 3.73453 | 0.198208 | ||||||||
\(356\) | 23.2501 | 1.23225 | ||||||||
\(357\) | −0.357373 | −0.0189142 | ||||||||
\(358\) | −7.57886 | −0.400555 | ||||||||
\(359\) | −0.696301 | −0.0367494 | −0.0183747 | − | 0.999831i | \(-0.505849\pi\) | ||||
−0.0183747 | + | 0.999831i | \(0.505849\pi\) | |||||||
\(360\) | −2.73974 | −0.144397 | ||||||||
\(361\) | 32.5723 | 1.71433 | ||||||||
\(362\) | −10.4186 | −0.547587 | ||||||||
\(363\) | −0.133739 | −0.00701945 | ||||||||
\(364\) | −15.5508 | −0.815083 | ||||||||
\(365\) | 1.78596 | 0.0934815 | ||||||||
\(366\) | 0.379228 | 0.0198226 | ||||||||
\(367\) | 17.2552 | 0.900714 | 0.450357 | − | 0.892849i | \(-0.351297\pi\) | ||||
0.450357 | + | 0.892849i | \(0.351297\pi\) | |||||||
\(368\) | −3.78060 | −0.197077 | ||||||||
\(369\) | −5.84427 | −0.304240 | ||||||||
\(370\) | −1.48896 | −0.0774074 | ||||||||
\(371\) | −11.2695 | −0.585081 | ||||||||
\(372\) | 0.444936 | 0.0230688 | ||||||||
\(373\) | 36.4711 | 1.88840 | 0.944201 | − | 0.329371i | \(-0.106837\pi\) | ||||
0.944201 | + | 0.329371i | \(0.106837\pi\) | |||||||
\(374\) | 0.789150 | 0.0408060 | ||||||||
\(375\) | −0.644009 | −0.0332565 | ||||||||
\(376\) | 16.3056 | 0.840898 | ||||||||
\(377\) | −45.2561 | −2.33081 | ||||||||
\(378\) | 0.665991 | 0.0342549 | ||||||||
\(379\) | −15.7902 | −0.811088 | −0.405544 | − | 0.914076i | \(-0.632918\pi\) | ||||
−0.405544 | + | 0.914076i | \(0.632918\pi\) | |||||||
\(380\) | −6.21761 | −0.318957 | ||||||||
\(381\) | 0.664224 | 0.0340292 | ||||||||
\(382\) | −8.31497 | −0.425431 | ||||||||
\(383\) | 28.0572 | 1.43366 | 0.716828 | − | 0.697251i | \(-0.245593\pi\) | ||||
0.716828 | + | 0.697251i | \(0.245593\pi\) | |||||||
\(384\) | 1.51697 | 0.0774127 | ||||||||
\(385\) | −0.828662 | −0.0422325 | ||||||||
\(386\) | −8.93809 | −0.454937 | ||||||||
\(387\) | 26.2876 | 1.33627 | ||||||||
\(388\) | 15.2509 | 0.774248 | ||||||||
\(389\) | 35.1657 | 1.78297 | 0.891487 | − | 0.453046i | \(-0.149663\pi\) | ||||
0.891487 | + | 0.453046i | \(0.149663\pi\) | |||||||
\(390\) | 0.172814 | 0.00875080 | ||||||||
\(391\) | −2.32738 | −0.117700 | ||||||||
\(392\) | 7.78289 | 0.393095 | ||||||||
\(393\) | −0.133739 | −0.00674622 | ||||||||
\(394\) | 6.51120 | 0.328030 | ||||||||
\(395\) | −7.45118 | −0.374909 | ||||||||
\(396\) | 5.23111 | 0.262873 | ||||||||
\(397\) | 3.92453 | 0.196966 | 0.0984832 | − | 0.995139i | \(-0.468601\pi\) | ||||
0.0984832 | + | 0.995139i | \(0.468601\pi\) | |||||||
\(398\) | 9.03277 | 0.452772 | ||||||||
\(399\) | 1.61249 | 0.0807253 | ||||||||
\(400\) | −12.2972 | −0.614859 | ||||||||
\(401\) | −29.5493 | −1.47562 | −0.737810 | − | 0.675008i | \(-0.764140\pi\) | ||||
−0.737810 | + | 0.675008i | \(0.764140\pi\) | |||||||
\(402\) | 0.525447 | 0.0262069 | ||||||||
\(403\) | 10.0144 | 0.498851 | ||||||||
\(404\) | −15.8547 | −0.788798 | ||||||||
\(405\) | −4.36281 | −0.216790 | ||||||||
\(406\) | −7.13481 | −0.354095 | ||||||||
\(407\) | 6.08431 | 0.301588 | ||||||||
\(408\) | 0.396213 | 0.0196155 | ||||||||
\(409\) | 11.7281 | 0.579915 | 0.289957 | − | 0.957040i | \(-0.406359\pi\) | ||||
0.289957 | + | 0.957040i | \(0.406359\pi\) | |||||||
\(410\) | −0.479598 | −0.0236857 | ||||||||
\(411\) | −1.50741 | −0.0743548 | ||||||||
\(412\) | 1.66905 | 0.0822283 | ||||||||
\(413\) | −5.76440 | −0.283647 | ||||||||
\(414\) | 2.16213 | 0.106263 | ||||||||
\(415\) | 0.0127985 | 0.000628252 0 | ||||||||
\(416\) | 26.4258 | 1.29563 | ||||||||
\(417\) | 1.61278 | 0.0789781 | ||||||||
\(418\) | −3.56069 | −0.174159 | ||||||||
\(419\) | −11.5393 | −0.563733 | −0.281866 | − | 0.959454i | \(-0.590953\pi\) | ||||
−0.281866 | + | 0.959454i | \(0.590953\pi\) | |||||||
\(420\) | −0.194403 | −0.00948590 | ||||||||
\(421\) | −33.0198 | −1.60928 | −0.804642 | − | 0.593760i | \(-0.797643\pi\) | ||||
−0.804642 | + | 0.593760i | \(0.797643\pi\) | |||||||
\(422\) | 2.33317 | 0.113577 | ||||||||
\(423\) | 26.1230 | 1.27014 | ||||||||
\(424\) | 12.4943 | 0.606775 | ||||||||
\(425\) | −7.57027 | −0.367212 | ||||||||
\(426\) | 0.501732 | 0.0243090 | ||||||||
\(427\) | −9.60173 | −0.464660 | ||||||||
\(428\) | −17.3039 | −0.836416 | ||||||||
\(429\) | −0.706169 | −0.0340941 | ||||||||
\(430\) | 2.15724 | 0.104031 | ||||||||
\(431\) | 1.04523 | 0.0503467 | 0.0251734 | − | 0.999683i | \(-0.491986\pi\) | ||||
0.0251734 | + | 0.999683i | \(0.491986\pi\) | |||||||
\(432\) | 2.06842 | 0.0995170 | ||||||||
\(433\) | −6.26433 | −0.301045 | −0.150522 | − | 0.988607i | \(-0.548096\pi\) | ||||
−0.150522 | + | 0.988607i | \(0.548096\pi\) | |||||||
\(434\) | 1.57880 | 0.0757850 | ||||||||
\(435\) | −0.565754 | −0.0271258 | ||||||||
\(436\) | −36.4722 | −1.74670 | ||||||||
\(437\) | 10.5012 | 0.502343 | ||||||||
\(438\) | 0.239943 | 0.0114649 | ||||||||
\(439\) | −0.0715349 | −0.00341418 | −0.00170709 | − | 0.999999i | \(-0.500543\pi\) | ||||
−0.00170709 | + | 0.999999i | \(0.500543\pi\) | |||||||
\(440\) | 0.918723 | 0.0437984 | ||||||||
\(441\) | 12.4688 | 0.593755 | ||||||||
\(442\) | 4.16688 | 0.198198 | ||||||||
\(443\) | −14.0540 | −0.667727 | −0.333863 | − | 0.942621i | \(-0.608352\pi\) | ||||
−0.333863 | + | 0.942621i | \(0.608352\pi\) | |||||||
\(444\) | 1.42737 | 0.0677402 | ||||||||
\(445\) | 6.54186 | 0.310114 | ||||||||
\(446\) | 13.5762 | 0.642851 | ||||||||
\(447\) | −0.136222 | −0.00644310 | ||||||||
\(448\) | −4.51524 | −0.213325 | ||||||||
\(449\) | 12.9572 | 0.611489 | 0.305745 | − | 0.952114i | \(-0.401095\pi\) | ||||
0.305745 | + | 0.952114i | \(0.401095\pi\) | |||||||
\(450\) | 7.03279 | 0.331529 | ||||||||
\(451\) | 1.95977 | 0.0922821 | ||||||||
\(452\) | 25.3619 | 1.19292 | ||||||||
\(453\) | −2.80016 | −0.131563 | ||||||||
\(454\) | −6.69108 | −0.314028 | ||||||||
\(455\) | −4.37551 | −0.205127 | ||||||||
\(456\) | −1.78774 | −0.0837184 | ||||||||
\(457\) | 33.9436 | 1.58781 | 0.793906 | − | 0.608040i | \(-0.208044\pi\) | ||||
0.793906 | + | 0.608040i | \(0.208044\pi\) | |||||||
\(458\) | 8.53929 | 0.399015 | ||||||||
\(459\) | 1.27334 | 0.0594345 | ||||||||
\(460\) | −1.26604 | −0.0590295 | ||||||||
\(461\) | 0.0276148 | 0.00128615 | 0.000643076 | − | 1.00000i | \(-0.499795\pi\) | ||||
0.000643076 | 1.00000i | \(0.499795\pi\) | ||||||||
\(462\) | −0.111330 | −0.00517956 | ||||||||
\(463\) | −6.87111 | −0.319327 | −0.159664 | − | 0.987171i | \(-0.551041\pi\) | ||||
−0.159664 | + | 0.987171i | \(0.551041\pi\) | |||||||
\(464\) | −22.1591 | −1.02871 | ||||||||
\(465\) | 0.125191 | 0.00580560 | ||||||||
\(466\) | 11.9918 | 0.555508 | ||||||||
\(467\) | −34.8283 | −1.61166 | −0.805831 | − | 0.592146i | \(-0.798281\pi\) | ||||
−0.805831 | + | 0.592146i | \(0.798281\pi\) | |||||||
\(468\) | 27.6214 | 1.27680 | ||||||||
\(469\) | −13.3039 | −0.614315 | ||||||||
\(470\) | 2.14373 | 0.0988829 | ||||||||
\(471\) | −0.769584 | −0.0354605 | ||||||||
\(472\) | 6.39089 | 0.294164 | ||||||||
\(473\) | −8.81508 | −0.405318 | ||||||||
\(474\) | −1.00106 | −0.0459803 | ||||||||
\(475\) | 34.1575 | 1.56725 | ||||||||
\(476\) | −4.68743 | −0.214848 | ||||||||
\(477\) | 20.0169 | 0.916509 | ||||||||
\(478\) | 11.1193 | 0.508584 | ||||||||
\(479\) | −23.5724 | −1.07705 | −0.538526 | − | 0.842609i | \(-0.681019\pi\) | ||||
−0.538526 | + | 0.842609i | \(0.681019\pi\) | |||||||
\(480\) | 0.330354 | 0.0150785 | ||||||||
\(481\) | 32.1265 | 1.46484 | ||||||||
\(482\) | −4.77326 | −0.217416 | ||||||||
\(483\) | 0.328338 | 0.0149399 | ||||||||
\(484\) | −1.75416 | −0.0797346 | ||||||||
\(485\) | 4.29114 | 0.194850 | ||||||||
\(486\) | −1.77617 | −0.0805688 | ||||||||
\(487\) | 22.2936 | 1.01022 | 0.505110 | − | 0.863055i | \(-0.331452\pi\) | ||||
0.505110 | + | 0.863055i | \(0.331452\pi\) | |||||||
\(488\) | 10.6453 | 0.481889 | ||||||||
\(489\) | −0.0507265 | −0.00229393 | ||||||||
\(490\) | 1.02323 | 0.0462249 | ||||||||
\(491\) | −31.6498 | −1.42834 | −0.714168 | − | 0.699974i | \(-0.753195\pi\) | ||||
−0.714168 | + | 0.699974i | \(0.753195\pi\) | |||||||
\(492\) | 0.459761 | 0.0207276 | ||||||||
\(493\) | −13.6414 | −0.614378 | ||||||||
\(494\) | −18.8012 | −0.845906 | ||||||||
\(495\) | 1.47187 | 0.0661558 | ||||||||
\(496\) | 4.90342 | 0.220170 | ||||||||
\(497\) | −12.7034 | −0.569827 | ||||||||
\(498\) | 0.00171947 | 7.70512e−5 0 | ||||||||
\(499\) | 22.5760 | 1.01064 | 0.505319 | − | 0.862933i | \(-0.331375\pi\) | ||||
0.505319 | + | 0.862933i | \(0.331375\pi\) | |||||||
\(500\) | −8.44704 | −0.377763 | ||||||||
\(501\) | 2.78060 | 0.124228 | ||||||||
\(502\) | 6.16706 | 0.275249 | ||||||||
\(503\) | −28.0156 | −1.24915 | −0.624577 | − | 0.780963i | \(-0.714729\pi\) | ||||
−0.624577 | + | 0.780963i | \(0.714729\pi\) | |||||||
\(504\) | 9.31953 | 0.415125 | ||||||||
\(505\) | −4.46101 | −0.198512 | ||||||||
\(506\) | −0.725034 | −0.0322317 | ||||||||
\(507\) | −1.99012 | −0.0883844 | ||||||||
\(508\) | 8.71219 | 0.386541 | ||||||||
\(509\) | 11.8699 | 0.526123 | 0.263062 | − | 0.964779i | \(-0.415268\pi\) | ||||
0.263062 | + | 0.964779i | \(0.415268\pi\) | |||||||
\(510\) | 0.0520909 | 0.00230663 | ||||||||
\(511\) | −6.07516 | −0.268749 | ||||||||
\(512\) | 22.5640 | 0.997199 | ||||||||
\(513\) | −5.74539 | −0.253665 | ||||||||
\(514\) | −7.35179 | −0.324273 | ||||||||
\(515\) | 0.469620 | 0.0206939 | ||||||||
\(516\) | −2.06801 | −0.0910390 | ||||||||
\(517\) | −8.75989 | −0.385259 | ||||||||
\(518\) | 5.06488 | 0.222538 | ||||||||
\(519\) | −0.144332 | −0.00633548 | ||||||||
\(520\) | 4.85106 | 0.212733 | ||||||||
\(521\) | 14.8079 | 0.648747 | 0.324373 | − | 0.945929i | \(-0.394847\pi\) | ||||
0.324373 | + | 0.945929i | \(0.394847\pi\) | |||||||
\(522\) | 12.6729 | 0.554677 | ||||||||
\(523\) | −21.0116 | −0.918772 | −0.459386 | − | 0.888237i | \(-0.651931\pi\) | ||||
−0.459386 | + | 0.888237i | \(0.651931\pi\) | |||||||
\(524\) | −1.75416 | −0.0766309 | ||||||||
\(525\) | 1.06799 | 0.0466107 | ||||||||
\(526\) | −7.11741 | −0.310334 | ||||||||
\(527\) | 3.01860 | 0.131492 | ||||||||
\(528\) | −0.345768 | −0.0150476 | ||||||||
\(529\) | −20.8617 | −0.907031 | ||||||||
\(530\) | 1.64264 | 0.0713519 | ||||||||
\(531\) | 10.2387 | 0.444324 | ||||||||
\(532\) | 21.1499 | 0.916965 | ||||||||
\(533\) | 10.3480 | 0.448223 | ||||||||
\(534\) | 0.878896 | 0.0380336 | ||||||||
\(535\) | −4.86879 | −0.210496 | ||||||||
\(536\) | 14.7498 | 0.637093 | ||||||||
\(537\) | 2.04425 | 0.0882161 | ||||||||
\(538\) | 5.61200 | 0.241951 | ||||||||
\(539\) | −4.18121 | −0.180097 | ||||||||
\(540\) | 0.692670 | 0.0298078 | ||||||||
\(541\) | 16.0002 | 0.687902 | 0.343951 | − | 0.938988i | \(-0.388235\pi\) | ||||
0.343951 | + | 0.938988i | \(0.388235\pi\) | |||||||
\(542\) | −5.85119 | −0.251330 | ||||||||
\(543\) | 2.81021 | 0.120598 | ||||||||
\(544\) | 7.96546 | 0.341516 | ||||||||
\(545\) | −10.2622 | −0.439582 | ||||||||
\(546\) | −0.587849 | −0.0251576 | ||||||||
\(547\) | −14.4429 | −0.617534 | −0.308767 | − | 0.951138i | \(-0.599916\pi\) | ||||
−0.308767 | + | 0.951138i | \(0.599916\pi\) | |||||||
\(548\) | −19.7716 | −0.844603 | ||||||||
\(549\) | 17.0546 | 0.727874 | ||||||||
\(550\) | −2.35832 | −0.100559 | ||||||||
\(551\) | 61.5507 | 2.62215 | ||||||||
\(552\) | −0.364022 | −0.0154938 | ||||||||
\(553\) | 25.3460 | 1.07782 | ||||||||
\(554\) | −7.65257 | −0.325126 | ||||||||
\(555\) | 0.401619 | 0.0170478 | ||||||||
\(556\) | 21.1537 | 0.897119 | ||||||||
\(557\) | −35.5026 | −1.50429 | −0.752146 | − | 0.658997i | \(-0.770981\pi\) | ||||
−0.752146 | + | 0.658997i | \(0.770981\pi\) | |||||||
\(558\) | −2.80428 | −0.118715 | ||||||||
\(559\) | −46.5455 | −1.96867 | ||||||||
\(560\) | −2.14242 | −0.0905339 | ||||||||
\(561\) | −0.212858 | −0.00898688 | ||||||||
\(562\) | −6.26037 | −0.264078 | ||||||||
\(563\) | −32.0306 | −1.34993 | −0.674965 | − | 0.737850i | \(-0.735841\pi\) | ||||
−0.674965 | + | 0.737850i | \(0.735841\pi\) | |||||||
\(564\) | −2.05506 | −0.0865336 | ||||||||
\(565\) | 7.13607 | 0.300217 | ||||||||
\(566\) | −8.06556 | −0.339021 | ||||||||
\(567\) | 14.8406 | 0.623247 | ||||||||
\(568\) | 14.0841 | 0.590955 | ||||||||
\(569\) | −29.7085 | −1.24544 | −0.622722 | − | 0.782443i | \(-0.713973\pi\) | ||||
−0.622722 | + | 0.782443i | \(0.713973\pi\) | |||||||
\(570\) | −0.235037 | −0.00984462 | ||||||||
\(571\) | 10.0609 | 0.421035 | 0.210518 | − | 0.977590i | \(-0.432485\pi\) | ||||
0.210518 | + | 0.977590i | \(0.432485\pi\) | |||||||
\(572\) | −9.26235 | −0.387278 | ||||||||
\(573\) | 2.24280 | 0.0936945 | ||||||||
\(574\) | 1.63141 | 0.0680937 | ||||||||
\(575\) | 6.95521 | 0.290052 | ||||||||
\(576\) | 8.02000 | 0.334167 | ||||||||
\(577\) | 3.65440 | 0.152134 | 0.0760672 | − | 0.997103i | \(-0.475764\pi\) | ||||
0.0760672 | + | 0.997103i | \(0.475764\pi\) | |||||||
\(578\) | −7.17296 | −0.298356 | ||||||||
\(579\) | 2.41088 | 0.100193 | ||||||||
\(580\) | −7.42063 | −0.308125 | ||||||||
\(581\) | −0.0435355 | −0.00180616 | ||||||||
\(582\) | 0.576513 | 0.0238972 | ||||||||
\(583\) | −6.71231 | −0.277995 | ||||||||
\(584\) | 6.73542 | 0.278714 | ||||||||
\(585\) | 7.77181 | 0.321325 | ||||||||
\(586\) | 15.9923 | 0.660638 | ||||||||
\(587\) | −42.0903 | −1.73725 | −0.868627 | − | 0.495467i | \(-0.834997\pi\) | ||||
−0.868627 | + | 0.495467i | \(0.834997\pi\) | |||||||
\(588\) | −0.980907 | −0.0404519 | ||||||||
\(589\) | −13.6201 | −0.561205 | ||||||||
\(590\) | 0.840222 | 0.0345914 | ||||||||
\(591\) | −1.75627 | −0.0722434 | ||||||||
\(592\) | 15.7304 | 0.646515 | ||||||||
\(593\) | −4.67197 | −0.191855 | −0.0959274 | − | 0.995388i | \(-0.530582\pi\) | ||||
−0.0959274 | + | 0.995388i | \(0.530582\pi\) | |||||||
\(594\) | 0.396677 | 0.0162759 | ||||||||
\(595\) | −1.31890 | −0.0540695 | ||||||||
\(596\) | −1.78674 | −0.0731877 | ||||||||
\(597\) | −2.43642 | −0.0997159 | ||||||||
\(598\) | −3.82834 | −0.156552 | ||||||||
\(599\) | −7.98355 | −0.326199 | −0.163100 | − | 0.986610i | \(-0.552149\pi\) | ||||
−0.163100 | + | 0.986610i | \(0.552149\pi\) | |||||||
\(600\) | −1.18406 | −0.0483389 | ||||||||
\(601\) | 9.75081 | 0.397744 | 0.198872 | − | 0.980025i | \(-0.436272\pi\) | ||||
0.198872 | + | 0.980025i | \(0.436272\pi\) | |||||||
\(602\) | −7.33809 | −0.299078 | ||||||||
\(603\) | 23.6304 | 0.962304 | ||||||||
\(604\) | −36.7279 | −1.49444 | ||||||||
\(605\) | −0.493567 | −0.0200663 | ||||||||
\(606\) | −0.599335 | −0.0243463 | ||||||||
\(607\) | 7.41998 | 0.301168 | 0.150584 | − | 0.988597i | \(-0.451885\pi\) | ||||
0.150584 | + | 0.988597i | \(0.451885\pi\) | |||||||
\(608\) | −35.9406 | −1.45758 | ||||||||
\(609\) | 1.92448 | 0.0779838 | ||||||||
\(610\) | 1.39955 | 0.0566663 | ||||||||
\(611\) | −46.2541 | −1.87124 | ||||||||
\(612\) | 8.32583 | 0.336552 | ||||||||
\(613\) | 27.0577 | 1.09285 | 0.546426 | − | 0.837508i | \(-0.315988\pi\) | ||||
0.546426 | + | 0.837508i | \(0.315988\pi\) | |||||||
\(614\) | 5.61168 | 0.226469 | ||||||||
\(615\) | 0.129362 | 0.00521640 | ||||||||
\(616\) | −3.12514 | −0.125916 | ||||||||
\(617\) | 2.03934 | 0.0821009 | 0.0410505 | − | 0.999157i | \(-0.486930\pi\) | ||||
0.0410505 | + | 0.999157i | \(0.486930\pi\) | |||||||
\(618\) | 0.0630933 | 0.00253798 | ||||||||
\(619\) | −11.0858 | −0.445576 | −0.222788 | − | 0.974867i | \(-0.571516\pi\) | ||||
−0.222788 | + | 0.974867i | \(0.571516\pi\) | |||||||
\(620\) | 1.64205 | 0.0659463 | ||||||||
\(621\) | −1.16989 | −0.0469460 | ||||||||
\(622\) | 10.1515 | 0.407036 | ||||||||
\(623\) | −22.2529 | −0.891544 | ||||||||
\(624\) | −1.82573 | −0.0730876 | ||||||||
\(625\) | 21.4052 | 0.856209 | ||||||||
\(626\) | −4.40741 | −0.176156 | ||||||||
\(627\) | 0.960428 | 0.0383558 | ||||||||
\(628\) | −10.0941 | −0.402799 | ||||||||
\(629\) | 9.68379 | 0.386118 | ||||||||
\(630\) | 1.22526 | 0.0488154 | ||||||||
\(631\) | −2.14166 | −0.0852583 | −0.0426291 | − | 0.999091i | \(-0.513573\pi\) | ||||
−0.0426291 | + | 0.999091i | \(0.513573\pi\) | |||||||
\(632\) | −28.1007 | −1.11779 | ||||||||
\(633\) | −0.629329 | −0.0250136 | ||||||||
\(634\) | −9.08818 | −0.360938 | ||||||||
\(635\) | 2.45134 | 0.0972785 | ||||||||
\(636\) | −1.57470 | −0.0624409 | ||||||||
\(637\) | −22.0777 | −0.874750 | ||||||||
\(638\) | −4.24963 | −0.168244 | ||||||||
\(639\) | 22.5639 | 0.892614 | ||||||||
\(640\) | 5.59844 | 0.221298 | ||||||||
\(641\) | 19.3356 | 0.763710 | 0.381855 | − | 0.924222i | \(-0.375285\pi\) | ||||
0.381855 | + | 0.924222i | \(0.375285\pi\) | |||||||
\(642\) | −0.654119 | −0.0258160 | ||||||||
\(643\) | −45.6817 | −1.80151 | −0.900756 | − | 0.434325i | \(-0.856987\pi\) | ||||
−0.900756 | + | 0.434325i | \(0.856987\pi\) | |||||||
\(644\) | 4.30659 | 0.169703 | ||||||||
\(645\) | −0.581874 | −0.0229113 | ||||||||
\(646\) | −5.66719 | −0.222973 | ||||||||
\(647\) | −44.2889 | −1.74118 | −0.870589 | − | 0.492012i | \(-0.836262\pi\) | ||||
−0.870589 | + | 0.492012i | \(0.836262\pi\) | |||||||
\(648\) | −16.4535 | −0.646355 | ||||||||
\(649\) | −3.43339 | −0.134772 | ||||||||
\(650\) | −12.4525 | −0.488426 | ||||||||
\(651\) | −0.425852 | −0.0166905 | ||||||||
\(652\) | −0.665346 | −0.0260570 | ||||||||
\(653\) | 7.33534 | 0.287054 | 0.143527 | − | 0.989646i | \(-0.454156\pi\) | ||||
0.143527 | + | 0.989646i | \(0.454156\pi\) | |||||||
\(654\) | −1.37872 | −0.0539121 | ||||||||
\(655\) | −0.493567 | −0.0192853 | ||||||||
\(656\) | 5.06680 | 0.197825 | ||||||||
\(657\) | 10.7907 | 0.420986 | ||||||||
\(658\) | −7.29215 | −0.284278 | ||||||||
\(659\) | −3.15542 | −0.122918 | −0.0614588 | − | 0.998110i | \(-0.519575\pi\) | ||||
−0.0614588 | + | 0.998110i | \(0.519575\pi\) | |||||||
\(660\) | −0.115790 | −0.00450713 | ||||||||
\(661\) | 30.3021 | 1.17862 | 0.589308 | − | 0.807908i | \(-0.299400\pi\) | ||||
0.589308 | + | 0.807908i | \(0.299400\pi\) | |||||||
\(662\) | 11.8414 | 0.460231 | ||||||||
\(663\) | −1.12394 | −0.0436501 | ||||||||
\(664\) | 0.0482670 | 0.00187312 | ||||||||
\(665\) | 5.95094 | 0.230767 | ||||||||
\(666\) | −8.99625 | −0.348598 | ||||||||
\(667\) | 12.5331 | 0.485283 | ||||||||
\(668\) | 36.4712 | 1.41111 | ||||||||
\(669\) | −3.66192 | −0.141578 | ||||||||
\(670\) | 1.93918 | 0.0749171 | ||||||||
\(671\) | −5.71897 | −0.220779 | ||||||||
\(672\) | −1.12374 | −0.0433491 | ||||||||
\(673\) | 31.2761 | 1.20561 | 0.602803 | − | 0.797890i | \(-0.294050\pi\) | ||||
0.602803 | + | 0.797890i | \(0.294050\pi\) | |||||||
\(674\) | 8.91995 | 0.343583 | ||||||||
\(675\) | −3.80530 | −0.146466 | ||||||||
\(676\) | −26.1031 | −1.00397 | ||||||||
\(677\) | 40.5803 | 1.55963 | 0.779815 | − | 0.626011i | \(-0.215313\pi\) | ||||
0.779815 | + | 0.626011i | \(0.215313\pi\) | |||||||
\(678\) | 0.958727 | 0.0368197 | ||||||||
\(679\) | −14.5968 | −0.560174 | ||||||||
\(680\) | 1.46224 | 0.0560743 | ||||||||
\(681\) | 1.80479 | 0.0691598 | ||||||||
\(682\) | 0.940366 | 0.0360085 | ||||||||
\(683\) | −2.36606 | −0.0905346 | −0.0452673 | − | 0.998975i | \(-0.514414\pi\) | ||||
−0.0452673 | + | 0.998975i | \(0.514414\pi\) | |||||||
\(684\) | −37.5666 | −1.43639 | ||||||||
\(685\) | −5.56313 | −0.212556 | ||||||||
\(686\) | −9.30778 | −0.355373 | ||||||||
\(687\) | −2.30331 | −0.0878768 | ||||||||
\(688\) | −22.7905 | −0.868880 | ||||||||
\(689\) | −35.4424 | −1.35025 | ||||||||
\(690\) | −0.0478587 | −0.00182195 | ||||||||
\(691\) | −23.0434 | −0.876613 | −0.438307 | − | 0.898826i | \(-0.644422\pi\) | ||||
−0.438307 | + | 0.898826i | \(0.644422\pi\) | |||||||
\(692\) | −1.89311 | −0.0719653 | ||||||||
\(693\) | −5.00675 | −0.190191 | ||||||||
\(694\) | −7.07195 | −0.268447 | ||||||||
\(695\) | 5.95201 | 0.225773 | ||||||||
\(696\) | −2.13364 | −0.0808753 | ||||||||
\(697\) | 3.11917 | 0.118147 | ||||||||
\(698\) | −9.68639 | −0.366635 | ||||||||
\(699\) | −3.23455 | −0.122342 | ||||||||
\(700\) | 14.0081 | 0.529455 | ||||||||
\(701\) | −41.0188 | −1.54926 | −0.774629 | − | 0.632416i | \(-0.782063\pi\) | ||||
−0.774629 | + | 0.632416i | \(0.782063\pi\) | |||||||
\(702\) | 2.09454 | 0.0790534 | ||||||||
\(703\) | −43.6938 | −1.64794 | ||||||||
\(704\) | −2.68937 | −0.101359 | ||||||||
\(705\) | −0.578231 | −0.0217774 | ||||||||
\(706\) | 7.49514 | 0.282083 | ||||||||
\(707\) | 15.1747 | 0.570701 | ||||||||
\(708\) | −0.805468 | −0.0302714 | ||||||||
\(709\) | 22.1323 | 0.831197 | 0.415599 | − | 0.909548i | \(-0.363572\pi\) | ||||
0.415599 | + | 0.909548i | \(0.363572\pi\) | |||||||
\(710\) | 1.85166 | 0.0694916 | ||||||||
\(711\) | −45.0198 | −1.68837 | ||||||||
\(712\) | 24.6714 | 0.924600 | ||||||||
\(713\) | −2.77335 | −0.103863 | ||||||||
\(714\) | −0.177193 | −0.00663129 | ||||||||
\(715\) | −2.60614 | −0.0974641 | ||||||||
\(716\) | 26.8131 | 1.00205 | ||||||||
\(717\) | −2.99921 | −0.112008 | ||||||||
\(718\) | −0.345241 | −0.0128843 | ||||||||
\(719\) | −42.8153 | −1.59674 | −0.798370 | − | 0.602167i | \(-0.794304\pi\) | ||||
−0.798370 | + | 0.602167i | \(0.794304\pi\) | |||||||
\(720\) | 3.80538 | 0.141818 | ||||||||
\(721\) | −1.59747 | −0.0594928 | ||||||||
\(722\) | 16.1500 | 0.601043 | ||||||||
\(723\) | 1.28749 | 0.0478825 | ||||||||
\(724\) | 36.8596 | 1.36988 | ||||||||
\(725\) | 40.7664 | 1.51403 | ||||||||
\(726\) | −0.0663105 | −0.00246101 | ||||||||
\(727\) | −3.03429 | −0.112536 | −0.0562678 | − | 0.998416i | \(-0.517920\pi\) | ||||
−0.0562678 | + | 0.998416i | \(0.517920\pi\) | |||||||
\(728\) | −16.5014 | −0.611584 | ||||||||
\(729\) | −26.0389 | −0.964406 | ||||||||
\(730\) | 0.885519 | 0.0327745 | ||||||||
\(731\) | −14.0301 | −0.518921 | ||||||||
\(732\) | −1.34166 | −0.0495894 | ||||||||
\(733\) | 12.6004 | 0.465405 | 0.232702 | − | 0.972548i | \(-0.425243\pi\) | ||||
0.232702 | + | 0.972548i | \(0.425243\pi\) | |||||||
\(734\) | 8.55551 | 0.315789 | ||||||||
\(735\) | −0.275997 | −0.0101803 | ||||||||
\(736\) | −7.31829 | −0.269756 | ||||||||
\(737\) | −7.92404 | −0.291886 | ||||||||
\(738\) | −2.89772 | −0.106666 | ||||||||
\(739\) | 12.8976 | 0.474446 | 0.237223 | − | 0.971455i | \(-0.423763\pi\) | ||||
0.237223 | + | 0.971455i | \(0.423763\pi\) | |||||||
\(740\) | 5.26777 | 0.193647 | ||||||||
\(741\) | 5.07127 | 0.186298 | ||||||||
\(742\) | −5.58764 | −0.205129 | ||||||||
\(743\) | −19.7920 | −0.726098 | −0.363049 | − | 0.931770i | \(-0.618264\pi\) | ||||
−0.363049 | + | 0.931770i | \(0.618264\pi\) | |||||||
\(744\) | 0.472135 | 0.0173093 | ||||||||
\(745\) | −0.502733 | −0.0184187 | ||||||||
\(746\) | 18.0832 | 0.662072 | ||||||||
\(747\) | 0.0773279 | 0.00282928 | ||||||||
\(748\) | −2.79192 | −0.102083 | ||||||||
\(749\) | 16.5617 | 0.605153 | ||||||||
\(750\) | −0.319314 | −0.0116597 | ||||||||
\(751\) | 39.9885 | 1.45920 | 0.729600 | − | 0.683874i | \(-0.239706\pi\) | ||||
0.729600 | + | 0.683874i | \(0.239706\pi\) | |||||||
\(752\) | −22.6478 | −0.825881 | ||||||||
\(753\) | −1.66345 | −0.0606194 | ||||||||
\(754\) | −22.4390 | −0.817179 | ||||||||
\(755\) | −10.3341 | −0.376096 | ||||||||
\(756\) | −2.35620 | −0.0856941 | ||||||||
\(757\) | −26.4640 | −0.961852 | −0.480926 | − | 0.876761i | \(-0.659699\pi\) | ||||
−0.480926 | + | 0.876761i | \(0.659699\pi\) | |||||||
\(758\) | −7.82912 | −0.284367 | ||||||||
\(759\) | 0.195564 | 0.00709853 | ||||||||
\(760\) | −6.59770 | −0.239324 | ||||||||
\(761\) | 6.70772 | 0.243155 | 0.121577 | − | 0.992582i | \(-0.461205\pi\) | ||||
0.121577 | + | 0.992582i | \(0.461205\pi\) | |||||||
\(762\) | 0.329337 | 0.0119306 | ||||||||
\(763\) | 34.9079 | 1.26375 | ||||||||
\(764\) | 29.4174 | 1.06428 | ||||||||
\(765\) | 2.34263 | 0.0846980 | ||||||||
\(766\) | 13.9114 | 0.502638 | ||||||||
\(767\) | −18.1290 | −0.654601 | ||||||||
\(768\) | 0.0328046 | 0.00118373 | ||||||||
\(769\) | 4.82752 | 0.174085 | 0.0870423 | − | 0.996205i | \(-0.472258\pi\) | ||||
0.0870423 | + | 0.996205i | \(0.472258\pi\) | |||||||
\(770\) | −0.410869 | −0.0148067 | ||||||||
\(771\) | 1.98300 | 0.0714162 | ||||||||
\(772\) | 31.6219 | 1.13810 | ||||||||
\(773\) | 42.0235 | 1.51148 | 0.755740 | − | 0.654872i | \(-0.227278\pi\) | ||||
0.755740 | + | 0.654872i | \(0.227278\pi\) | |||||||
\(774\) | 13.0340 | 0.468496 | ||||||||
\(775\) | −9.02088 | −0.324040 | ||||||||
\(776\) | 16.1832 | 0.580944 | ||||||||
\(777\) | −1.36615 | −0.0490105 | ||||||||
\(778\) | 17.4359 | 0.625109 | ||||||||
\(779\) | −14.0739 | −0.504249 | ||||||||
\(780\) | −0.611398 | −0.0218915 | ||||||||
\(781\) | −7.56641 | −0.270747 | ||||||||
\(782\) | −1.15396 | −0.0412657 | ||||||||
\(783\) | −6.85704 | −0.245050 | ||||||||
\(784\) | −10.8101 | −0.386075 | ||||||||
\(785\) | −2.84018 | −0.101370 | ||||||||
\(786\) | −0.0663105 | −0.00236522 | ||||||||
\(787\) | 13.4224 | 0.478457 | 0.239229 | − | 0.970963i | \(-0.423105\pi\) | ||||
0.239229 | + | 0.970963i | \(0.423105\pi\) | |||||||
\(788\) | −23.0359 | −0.820619 | ||||||||
\(789\) | 1.91979 | 0.0683462 | ||||||||
\(790\) | −3.69446 | −0.131443 | ||||||||
\(791\) | −24.2742 | −0.863090 | ||||||||
\(792\) | 5.55089 | 0.197242 | ||||||||
\(793\) | −30.1974 | −1.07234 | ||||||||
\(794\) | 1.94587 | 0.0690562 | ||||||||
\(795\) | −0.443072 | −0.0157141 | ||||||||
\(796\) | −31.9569 | −1.13268 | ||||||||
\(797\) | −29.5569 | −1.04696 | −0.523480 | − | 0.852038i | \(-0.675367\pi\) | ||||
−0.523480 | + | 0.852038i | \(0.675367\pi\) | |||||||
\(798\) | 0.799506 | 0.0283022 | ||||||||
\(799\) | −13.9422 | −0.493241 | ||||||||
\(800\) | −23.8043 | −0.841608 | ||||||||
\(801\) | 39.5257 | 1.39657 | ||||||||
\(802\) | −14.6512 | −0.517351 | ||||||||
\(803\) | −3.61848 | −0.127693 | ||||||||
\(804\) | −1.85897 | −0.0655608 | ||||||||
\(805\) | 1.21174 | 0.0427083 | ||||||||
\(806\) | 4.96534 | 0.174897 | ||||||||
\(807\) | −1.51373 | −0.0532858 | ||||||||
\(808\) | −16.8239 | −0.591862 | ||||||||
\(809\) | −28.8347 | −1.01377 | −0.506886 | − | 0.862013i | \(-0.669204\pi\) | ||||
−0.506886 | + | 0.862013i | \(0.669204\pi\) | |||||||
\(810\) | −2.16318 | −0.0760063 | ||||||||
\(811\) | −6.05999 | −0.212795 | −0.106397 | − | 0.994324i | \(-0.533932\pi\) | ||||
−0.106397 | + | 0.994324i | \(0.533932\pi\) | |||||||
\(812\) | 25.2421 | 0.885825 | ||||||||
\(813\) | 1.57825 | 0.0553516 | ||||||||
\(814\) | 3.01674 | 0.105737 | ||||||||
\(815\) | −0.187208 | −0.00655761 | ||||||||
\(816\) | −0.550324 | −0.0192652 | ||||||||
\(817\) | 63.3045 | 2.21474 | ||||||||
\(818\) | 5.81503 | 0.203318 | ||||||||
\(819\) | −26.4367 | −0.923773 | ||||||||
\(820\) | 1.69676 | 0.0592535 | ||||||||
\(821\) | −13.3298 | −0.465214 | −0.232607 | − | 0.972571i | \(-0.574726\pi\) | ||||
−0.232607 | + | 0.972571i | \(0.574726\pi\) | |||||||
\(822\) | −0.747405 | −0.0260687 | ||||||||
\(823\) | 14.0190 | 0.488672 | 0.244336 | − | 0.969691i | \(-0.421430\pi\) | ||||
0.244336 | + | 0.969691i | \(0.421430\pi\) | |||||||
\(824\) | 1.77108 | 0.0616986 | ||||||||
\(825\) | 0.636113 | 0.0221466 | ||||||||
\(826\) | −2.85811 | −0.0994465 | ||||||||
\(827\) | 4.30220 | 0.149602 | 0.0748011 | − | 0.997198i | \(-0.476168\pi\) | ||||
0.0748011 | + | 0.997198i | \(0.476168\pi\) | |||||||
\(828\) | −7.64938 | −0.265834 | ||||||||
\(829\) | 2.30813 | 0.0801648 | 0.0400824 | − | 0.999196i | \(-0.487238\pi\) | ||||
0.0400824 | + | 0.999196i | \(0.487238\pi\) | |||||||
\(830\) | 0.00634576 | 0.000220265 0 | ||||||||
\(831\) | 2.06413 | 0.0716040 | ||||||||
\(832\) | −14.2004 | −0.492312 | ||||||||
\(833\) | −6.65481 | −0.230576 | ||||||||
\(834\) | 0.799651 | 0.0276896 | ||||||||
\(835\) | 10.2619 | 0.355127 | ||||||||
\(836\) | 12.5973 | 0.435687 | ||||||||
\(837\) | 1.51734 | 0.0524469 | ||||||||
\(838\) | −5.72145 | −0.197644 | ||||||||
\(839\) | 3.84974 | 0.132908 | 0.0664539 | − | 0.997789i | \(-0.478831\pi\) | ||||
0.0664539 | + | 0.997789i | \(0.478831\pi\) | |||||||
\(840\) | −0.206287 | −0.00711759 | ||||||||
\(841\) | 44.4599 | 1.53310 | ||||||||
\(842\) | −16.3719 | −0.564214 | ||||||||
\(843\) | 1.68861 | 0.0581590 | ||||||||
\(844\) | −8.25450 | −0.284131 | ||||||||
\(845\) | −7.34462 | −0.252663 | ||||||||
\(846\) | 12.9523 | 0.445311 | ||||||||
\(847\) | 1.67893 | 0.0576885 | ||||||||
\(848\) | −17.3540 | −0.595939 | ||||||||
\(849\) | 2.17553 | 0.0746640 | ||||||||
\(850\) | −3.75351 | −0.128744 | ||||||||
\(851\) | −8.89702 | −0.304986 | ||||||||
\(852\) | −1.77507 | −0.0608129 | ||||||||
\(853\) | 44.7596 | 1.53254 | 0.766270 | − | 0.642519i | \(-0.222111\pi\) | ||||
0.766270 | + | 0.642519i | \(0.222111\pi\) | |||||||
\(854\) | −4.76075 | −0.162909 | ||||||||
\(855\) | −10.5701 | −0.361489 | ||||||||
\(856\) | −18.3617 | −0.627591 | ||||||||
\(857\) | 29.9863 | 1.02431 | 0.512156 | − | 0.858893i | \(-0.328847\pi\) | ||||
0.512156 | + | 0.858893i | \(0.328847\pi\) | |||||||
\(858\) | −0.350134 | −0.0119534 | ||||||||
\(859\) | 32.9772 | 1.12517 | 0.562584 | − | 0.826740i | \(-0.309807\pi\) | ||||
0.562584 | + | 0.826740i | \(0.309807\pi\) | |||||||
\(860\) | −7.63206 | −0.260251 | ||||||||
\(861\) | −0.440042 | −0.0149966 | ||||||||
\(862\) | 0.518246 | 0.0176515 | ||||||||
\(863\) | −56.3255 | −1.91734 | −0.958672 | − | 0.284515i | \(-0.908167\pi\) | ||||
−0.958672 | + | 0.284515i | \(0.908167\pi\) | |||||||
\(864\) | 4.00395 | 0.136217 | ||||||||
\(865\) | −0.532663 | −0.0181111 | ||||||||
\(866\) | −3.10599 | −0.105546 | ||||||||
\(867\) | 1.93477 | 0.0657082 | ||||||||
\(868\) | −5.58563 | −0.189589 | ||||||||
\(869\) | 15.0966 | 0.512117 | ||||||||
\(870\) | −0.280513 | −0.00951029 | ||||||||
\(871\) | −41.8406 | −1.41772 | ||||||||
\(872\) | −38.7018 | −1.31061 | ||||||||
\(873\) | 25.9269 | 0.877493 | ||||||||
\(874\) | 5.20675 | 0.176121 | ||||||||
\(875\) | 8.08475 | 0.273314 | ||||||||
\(876\) | −0.848892 | −0.0286814 | ||||||||
\(877\) | 16.5114 | 0.557550 | 0.278775 | − | 0.960356i | \(-0.410072\pi\) | ||||
0.278775 | + | 0.960356i | \(0.410072\pi\) | |||||||
\(878\) | −0.0354686 | −0.00119701 | ||||||||
\(879\) | −4.31363 | −0.145495 | ||||||||
\(880\) | −1.27607 | −0.0430162 | ||||||||
\(881\) | −0.219342 | −0.00738981 | −0.00369490 | − | 0.999993i | \(-0.501176\pi\) | ||||
−0.00369490 | + | 0.999993i | \(0.501176\pi\) | |||||||
\(882\) | 6.18233 | 0.208170 | ||||||||
\(883\) | 32.3565 | 1.08888 | 0.544442 | − | 0.838799i | \(-0.316742\pi\) | ||||
0.544442 | + | 0.838799i | \(0.316742\pi\) | |||||||
\(884\) | −14.7419 | −0.495825 | ||||||||
\(885\) | −0.226634 | −0.00761822 | ||||||||
\(886\) | −6.96829 | −0.234104 | ||||||||
\(887\) | −57.3089 | −1.92425 | −0.962123 | − | 0.272617i | \(-0.912111\pi\) | ||||
−0.962123 | + | 0.272617i | \(0.912111\pi\) | |||||||
\(888\) | 1.51463 | 0.0508277 | ||||||||
\(889\) | −8.33852 | −0.279665 | ||||||||
\(890\) | 3.24360 | 0.108726 | ||||||||
\(891\) | 8.83935 | 0.296129 | ||||||||
\(892\) | −48.0310 | −1.60820 | ||||||||
\(893\) | 62.9081 | 2.10514 | ||||||||
\(894\) | −0.0675420 | −0.00225894 | ||||||||
\(895\) | 7.54439 | 0.252181 | ||||||||
\(896\) | −19.0438 | −0.636207 | ||||||||
\(897\) | 1.03262 | 0.0344782 | ||||||||
\(898\) | 6.42448 | 0.214388 | ||||||||
\(899\) | −16.2554 | −0.542146 | ||||||||
\(900\) | −24.8812 | −0.829373 | ||||||||
\(901\) | −10.6833 | −0.355912 | ||||||||
\(902\) | 0.971698 | 0.0323540 | ||||||||
\(903\) | 1.97931 | 0.0658674 | ||||||||
\(904\) | 26.9123 | 0.895091 | ||||||||
\(905\) | 10.3712 | 0.344749 | ||||||||
\(906\) | −1.38838 | −0.0461259 | ||||||||
\(907\) | 21.2091 | 0.704236 | 0.352118 | − | 0.935956i | \(-0.385462\pi\) | ||||
0.352118 | + | 0.935956i | \(0.385462\pi\) | |||||||
\(908\) | 23.6723 | 0.785592 | ||||||||
\(909\) | −26.9533 | −0.893984 | ||||||||
\(910\) | −2.16948 | −0.0719174 | ||||||||
\(911\) | 25.9210 | 0.858803 | 0.429401 | − | 0.903114i | \(-0.358725\pi\) | ||||
0.429401 | + | 0.903114i | \(0.358725\pi\) | |||||||
\(912\) | 2.48309 | 0.0822234 | ||||||||
\(913\) | −0.0259306 | −0.000858176 0 | ||||||||
\(914\) | 16.8300 | 0.556686 | ||||||||
\(915\) | −0.377503 | −0.0124799 | ||||||||
\(916\) | −30.2110 | −0.998200 | ||||||||
\(917\) | 1.67893 | 0.0554430 | ||||||||
\(918\) | 0.631351 | 0.0208377 | ||||||||
\(919\) | 6.73660 | 0.222220 | 0.111110 | − | 0.993808i | \(-0.464559\pi\) | ||||
0.111110 | + | 0.993808i | \(0.464559\pi\) | |||||||
\(920\) | −1.34344 | −0.0442918 | ||||||||
\(921\) | −1.51364 | −0.0498763 | ||||||||
\(922\) | 0.0136920 | 0.000450924 0 | ||||||||
\(923\) | −39.9523 | −1.31505 | ||||||||
\(924\) | 0.393874 | 0.0129575 | ||||||||
\(925\) | −28.9394 | −0.951521 | ||||||||
\(926\) | −3.40684 | −0.111956 | ||||||||
\(927\) | 2.83743 | 0.0931934 | ||||||||
\(928\) | −42.8946 | −1.40808 | ||||||||
\(929\) | 38.9868 | 1.27911 | 0.639557 | − | 0.768744i | \(-0.279118\pi\) | ||||
0.639557 | + | 0.768744i | \(0.279118\pi\) | |||||||
\(930\) | 0.0620726 | 0.00203544 | ||||||||
\(931\) | 30.0269 | 0.984091 | ||||||||
\(932\) | −42.4255 | −1.38969 | ||||||||
\(933\) | −2.73816 | −0.0896434 | ||||||||
\(934\) | −17.2686 | −0.565047 | ||||||||
\(935\) | −0.785561 | −0.0256906 | ||||||||
\(936\) | 29.3099 | 0.958025 | ||||||||
\(937\) | 34.4896 | 1.12673 | 0.563363 | − | 0.826209i | \(-0.309507\pi\) | ||||
0.563363 | + | 0.826209i | \(0.309507\pi\) | |||||||
\(938\) | −6.59635 | −0.215378 | ||||||||
\(939\) | 1.18882 | 0.0387955 | ||||||||
\(940\) | −7.58427 | −0.247372 | ||||||||
\(941\) | 32.6353 | 1.06388 | 0.531940 | − | 0.846782i | \(-0.321463\pi\) | ||||
0.531940 | + | 0.846782i | \(0.321463\pi\) | |||||||
\(942\) | −0.381576 | −0.0124324 | ||||||||
\(943\) | −2.86575 | −0.0933217 | ||||||||
\(944\) | −8.87668 | −0.288911 | ||||||||
\(945\) | −0.662962 | −0.0215662 | ||||||||
\(946\) | −4.37071 | −0.142104 | ||||||||
\(947\) | 5.15503 | 0.167516 | 0.0837580 | − | 0.996486i | \(-0.473308\pi\) | ||||
0.0837580 | + | 0.996486i | \(0.473308\pi\) | |||||||
\(948\) | 3.54164 | 0.115027 | ||||||||
\(949\) | −19.1064 | −0.620219 | ||||||||
\(950\) | 16.9360 | 0.549477 | ||||||||
\(951\) | 2.45136 | 0.0794909 | ||||||||
\(952\) | −4.97398 | −0.161207 | ||||||||
\(953\) | 24.2889 | 0.786795 | 0.393397 | − | 0.919369i | \(-0.371300\pi\) | ||||
0.393397 | + | 0.919369i | \(0.371300\pi\) | |||||||
\(954\) | 9.92480 | 0.321327 | ||||||||
\(955\) | 8.27715 | 0.267842 | ||||||||
\(956\) | −39.3387 | −1.27230 | ||||||||
\(957\) | 1.14626 | 0.0370532 | ||||||||
\(958\) | −11.6877 | −0.377613 | ||||||||
\(959\) | 18.9236 | 0.611076 | ||||||||
\(960\) | −0.177522 | −0.00572950 | ||||||||
\(961\) | −27.4030 | −0.883967 | ||||||||
\(962\) | 15.9290 | 0.513572 | ||||||||
\(963\) | −29.4170 | −0.947951 | ||||||||
\(964\) | 16.8872 | 0.543901 | ||||||||
\(965\) | 8.89744 | 0.286419 | ||||||||
\(966\) | 0.162797 | 0.00523791 | ||||||||
\(967\) | −59.4072 | −1.91041 | −0.955203 | − | 0.295951i | \(-0.904364\pi\) | ||||
−0.955203 | + | 0.295951i | \(0.904364\pi\) | |||||||
\(968\) | −1.86140 | −0.0598275 | ||||||||
\(969\) | 1.52862 | 0.0491062 | ||||||||
\(970\) | 2.12764 | 0.0683144 | ||||||||
\(971\) | −6.97321 | −0.223781 | −0.111890 | − | 0.993721i | \(-0.535691\pi\) | ||||
−0.111890 | + | 0.993721i | \(0.535691\pi\) | |||||||
\(972\) | 6.28389 | 0.201556 | ||||||||
\(973\) | −20.2465 | −0.649072 | ||||||||
\(974\) | 11.0537 | 0.354182 | ||||||||
\(975\) | 3.35881 | 0.107568 | ||||||||
\(976\) | −14.7858 | −0.473283 | ||||||||
\(977\) | 32.2743 | 1.03255 | 0.516273 | − | 0.856424i | \(-0.327319\pi\) | ||||
0.516273 | + | 0.856424i | \(0.327319\pi\) | |||||||
\(978\) | −0.0251513 | −0.000804251 0 | ||||||||
\(979\) | −13.2543 | −0.423608 | ||||||||
\(980\) | −3.62007 | −0.115639 | ||||||||
\(981\) | −62.0036 | −1.97962 | ||||||||
\(982\) | −15.6927 | −0.500773 | ||||||||
\(983\) | −18.8500 | −0.601221 | −0.300611 | − | 0.953747i | \(-0.597190\pi\) | ||||
−0.300611 | + | 0.953747i | \(0.597190\pi\) | |||||||
\(984\) | 0.487866 | 0.0155526 | ||||||||
\(985\) | −6.48159 | −0.206521 | ||||||||
\(986\) | −6.76370 | −0.215400 | ||||||||
\(987\) | 1.96692 | 0.0626077 | ||||||||
\(988\) | 66.5165 | 2.11617 | ||||||||
\(989\) | 12.8902 | 0.409884 | ||||||||
\(990\) | 0.729787 | 0.0231941 | ||||||||
\(991\) | −24.5367 | −0.779436 | −0.389718 | − | 0.920934i | \(-0.627427\pi\) | ||||
−0.389718 | + | 0.920934i | \(0.627427\pi\) | |||||||
\(992\) | 9.49179 | 0.301365 | ||||||||
\(993\) | −3.19400 | −0.101359 | ||||||||
\(994\) | −6.29864 | −0.199781 | ||||||||
\(995\) | −8.99168 | −0.285056 | ||||||||
\(996\) | −0.00608328 | −0.000192756 0 | ||||||||
\(997\) | −43.5102 | −1.37798 | −0.688992 | − | 0.724769i | \(-0.741946\pi\) | ||||
−0.688992 | + | 0.724769i | \(0.741946\pi\) | |||||||
\(998\) | 11.1937 | 0.354329 | ||||||||
\(999\) | 4.86769 | 0.154007 |
(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 | 1441.2.a.c.1.15 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.c.1.15 | ✓ | 23 | 1.1 | even | 1 | trivial |