Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.60951 | −1.13810 | −0.569049 | − | 0.822304i | \(-0.692688\pi\) | ||||
−0.569049 | + | 0.822304i | \(0.692688\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.590533 | 0.295266 | ||||||||
\(5\) | 2.17104 | 0.970917 | 0.485459 | − | 0.874260i | \(-0.338653\pi\) | ||||
0.485459 | + | 0.874260i | \(0.338653\pi\) | |||||||
\(6\) | 1.60951 | 0.657081 | ||||||||
\(7\) | 3.27452 | 1.23765 | 0.618825 | − | 0.785529i | \(-0.287609\pi\) | ||||
0.618825 | + | 0.785529i | \(0.287609\pi\) | |||||||
\(8\) | 2.26856 | 0.802056 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.49431 | −1.10500 | ||||||||
\(11\) | 0.0669844 | 0.0201966 | 0.0100983 | − | 0.999949i | \(-0.496786\pi\) | ||||
0.0100983 | + | 0.999949i | \(0.496786\pi\) | |||||||
\(12\) | −0.590533 | −0.170472 | ||||||||
\(13\) | 0.443428 | 0.122985 | 0.0614924 | − | 0.998108i | \(-0.480414\pi\) | ||||
0.0614924 | + | 0.998108i | \(0.480414\pi\) | |||||||
\(14\) | −5.27038 | −1.40857 | ||||||||
\(15\) | −2.17104 | −0.560559 | ||||||||
\(16\) | −4.83234 | −1.20808 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.60951 | −0.379366 | ||||||||
\(19\) | −3.50112 | −0.803212 | −0.401606 | − | 0.915813i | \(-0.631548\pi\) | ||||
−0.401606 | + | 0.915813i | \(0.631548\pi\) | |||||||
\(20\) | 1.28207 | 0.286679 | ||||||||
\(21\) | −3.27452 | −0.714558 | ||||||||
\(22\) | −0.107812 | −0.0229857 | ||||||||
\(23\) | −4.40532 | −0.918572 | −0.459286 | − | 0.888288i | \(-0.651895\pi\) | ||||
−0.459286 | + | 0.888288i | \(0.651895\pi\) | |||||||
\(24\) | −2.26856 | −0.463067 | ||||||||
\(25\) | −0.286599 | −0.0573197 | ||||||||
\(26\) | −0.713703 | −0.139969 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.93371 | 0.365437 | ||||||||
\(29\) | 8.76824 | 1.62822 | 0.814111 | − | 0.580709i | \(-0.197225\pi\) | ||||
0.814111 | + | 0.580709i | \(0.197225\pi\) | |||||||
\(30\) | 3.49431 | 0.637971 | ||||||||
\(31\) | 9.92020 | 1.78172 | 0.890860 | − | 0.454277i | \(-0.150103\pi\) | ||||
0.890860 | + | 0.454277i | \(0.150103\pi\) | |||||||
\(32\) | 3.24060 | 0.572862 | ||||||||
\(33\) | −0.0669844 | −0.0116605 | ||||||||
\(34\) | −1.60951 | −0.276029 | ||||||||
\(35\) | 7.10909 | 1.20166 | ||||||||
\(36\) | 0.590533 | 0.0984221 | ||||||||
\(37\) | −3.50206 | −0.575735 | −0.287868 | − | 0.957670i | \(-0.592946\pi\) | ||||
−0.287868 | + | 0.957670i | \(0.592946\pi\) | |||||||
\(38\) | 5.63510 | 0.914134 | ||||||||
\(39\) | −0.443428 | −0.0710053 | ||||||||
\(40\) | 4.92512 | 0.778730 | ||||||||
\(41\) | −8.85328 | −1.38265 | −0.691325 | − | 0.722544i | \(-0.742973\pi\) | ||||
−0.691325 | + | 0.722544i | \(0.742973\pi\) | |||||||
\(42\) | 5.27038 | 0.813237 | ||||||||
\(43\) | −0.643560 | −0.0981420 | −0.0490710 | − | 0.998795i | \(-0.515626\pi\) | ||||
−0.0490710 | + | 0.998795i | \(0.515626\pi\) | |||||||
\(44\) | 0.0395565 | 0.00596337 | ||||||||
\(45\) | 2.17104 | 0.323639 | ||||||||
\(46\) | 7.09041 | 1.04542 | ||||||||
\(47\) | −10.7581 | −1.56924 | −0.784618 | − | 0.619980i | \(-0.787141\pi\) | ||||
−0.784618 | + | 0.619980i | \(0.787141\pi\) | |||||||
\(48\) | 4.83234 | 0.697488 | ||||||||
\(49\) | 3.72245 | 0.531779 | ||||||||
\(50\) | 0.461284 | 0.0652355 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0.261859 | 0.0363133 | ||||||||
\(53\) | −10.1229 | −1.39048 | −0.695242 | − | 0.718776i | \(-0.744703\pi\) | ||||
−0.695242 | + | 0.718776i | \(0.744703\pi\) | |||||||
\(54\) | 1.60951 | 0.219027 | ||||||||
\(55\) | 0.145426 | 0.0196092 | ||||||||
\(56\) | 7.42842 | 0.992665 | ||||||||
\(57\) | 3.50112 | 0.463735 | ||||||||
\(58\) | −14.1126 | −1.85308 | ||||||||
\(59\) | 7.39311 | 0.962502 | 0.481251 | − | 0.876583i | \(-0.340183\pi\) | ||||
0.481251 | + | 0.876583i | \(0.340183\pi\) | |||||||
\(60\) | −1.28207 | −0.165514 | ||||||||
\(61\) | −7.94758 | −1.01758 | −0.508791 | − | 0.860890i | \(-0.669908\pi\) | ||||
−0.508791 | + | 0.860890i | \(0.669908\pi\) | |||||||
\(62\) | −15.9667 | −2.02777 | ||||||||
\(63\) | 3.27452 | 0.412550 | ||||||||
\(64\) | 4.44889 | 0.556111 | ||||||||
\(65\) | 0.962699 | 0.119408 | ||||||||
\(66\) | 0.107812 | 0.0132708 | ||||||||
\(67\) | −15.6509 | −1.91207 | −0.956033 | − | 0.293261i | \(-0.905260\pi\) | ||||
−0.956033 | + | 0.293261i | \(0.905260\pi\) | |||||||
\(68\) | 0.590533 | 0.0716126 | ||||||||
\(69\) | 4.40532 | 0.530338 | ||||||||
\(70\) | −11.4422 | −1.36760 | ||||||||
\(71\) | −2.66761 | −0.316587 | −0.158293 | − | 0.987392i | \(-0.550599\pi\) | ||||
−0.158293 | + | 0.987392i | \(0.550599\pi\) | |||||||
\(72\) | 2.26856 | 0.267352 | ||||||||
\(73\) | 11.0205 | 1.28985 | 0.644925 | − | 0.764246i | \(-0.276889\pi\) | ||||
0.644925 | + | 0.764246i | \(0.276889\pi\) | |||||||
\(74\) | 5.63661 | 0.655243 | ||||||||
\(75\) | 0.286599 | 0.0330936 | ||||||||
\(76\) | −2.06753 | −0.237162 | ||||||||
\(77\) | 0.219342 | 0.0249963 | ||||||||
\(78\) | 0.713703 | 0.0808110 | ||||||||
\(79\) | −6.51709 | −0.733230 | −0.366615 | − | 0.930373i | \(-0.619483\pi\) | ||||
−0.366615 | + | 0.930373i | \(0.619483\pi\) | |||||||
\(80\) | −10.4912 | −1.17295 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.2495 | 1.57359 | ||||||||
\(83\) | −3.88084 | −0.425978 | −0.212989 | − | 0.977055i | \(-0.568320\pi\) | ||||
−0.212989 | + | 0.977055i | \(0.568320\pi\) | |||||||
\(84\) | −1.93371 | −0.210985 | ||||||||
\(85\) | 2.17104 | 0.235482 | ||||||||
\(86\) | 1.03582 | 0.111695 | ||||||||
\(87\) | −8.76824 | −0.940054 | ||||||||
\(88\) | 0.151958 | 0.0161988 | ||||||||
\(89\) | −12.6880 | −1.34492 | −0.672462 | − | 0.740132i | \(-0.734763\pi\) | ||||
−0.672462 | + | 0.740132i | \(0.734763\pi\) | |||||||
\(90\) | −3.49431 | −0.368333 | ||||||||
\(91\) | 1.45201 | 0.152212 | ||||||||
\(92\) | −2.60148 | −0.271223 | ||||||||
\(93\) | −9.92020 | −1.02868 | ||||||||
\(94\) | 17.3154 | 1.78594 | ||||||||
\(95\) | −7.60106 | −0.779852 | ||||||||
\(96\) | −3.24060 | −0.330742 | ||||||||
\(97\) | −10.3181 | −1.04765 | −0.523823 | − | 0.851827i | \(-0.675495\pi\) | ||||
−0.523823 | + | 0.851827i | \(0.675495\pi\) | |||||||
\(98\) | −5.99134 | −0.605217 | ||||||||
\(99\) | 0.0669844 | 0.00673219 | ||||||||
\(100\) | −0.169246 | −0.0169246 | ||||||||
\(101\) | −4.57205 | −0.454936 | −0.227468 | − | 0.973786i | \(-0.573045\pi\) | ||||
−0.227468 | + | 0.973786i | \(0.573045\pi\) | |||||||
\(102\) | 1.60951 | 0.159366 | ||||||||
\(103\) | −9.90284 | −0.975756 | −0.487878 | − | 0.872912i | \(-0.662229\pi\) | ||||
−0.487878 | + | 0.872912i | \(0.662229\pi\) | |||||||
\(104\) | 1.00594 | 0.0986407 | ||||||||
\(105\) | −7.10909 | −0.693777 | ||||||||
\(106\) | 16.2929 | 1.58251 | ||||||||
\(107\) | −0.405221 | −0.0391742 | −0.0195871 | − | 0.999808i | \(-0.506235\pi\) | ||||
−0.0195871 | + | 0.999808i | \(0.506235\pi\) | |||||||
\(108\) | −0.590533 | −0.0568241 | ||||||||
\(109\) | −13.8464 | −1.32625 | −0.663123 | − | 0.748510i | \(-0.730770\pi\) | ||||
−0.663123 | + | 0.748510i | \(0.730770\pi\) | |||||||
\(110\) | −0.234065 | −0.0223172 | ||||||||
\(111\) | 3.50206 | 0.332401 | ||||||||
\(112\) | −15.8236 | −1.49519 | ||||||||
\(113\) | −6.23069 | −0.586134 | −0.293067 | − | 0.956092i | \(-0.594676\pi\) | ||||
−0.293067 | + | 0.956092i | \(0.594676\pi\) | |||||||
\(114\) | −5.63510 | −0.527775 | ||||||||
\(115\) | −9.56410 | −0.891857 | ||||||||
\(116\) | 5.17794 | 0.480759 | ||||||||
\(117\) | 0.443428 | 0.0409949 | ||||||||
\(118\) | −11.8993 | −1.09542 | ||||||||
\(119\) | 3.27452 | 0.300174 | ||||||||
\(120\) | −4.92512 | −0.449600 | ||||||||
\(121\) | −10.9955 | −0.999592 | ||||||||
\(122\) | 12.7917 | 1.15811 | ||||||||
\(123\) | 8.85328 | 0.798274 | ||||||||
\(124\) | 5.85820 | 0.526082 | ||||||||
\(125\) | −11.4774 | −1.02657 | ||||||||
\(126\) | −5.27038 | −0.469522 | ||||||||
\(127\) | 0.307558 | 0.0272913 | 0.0136457 | − | 0.999907i | \(-0.495656\pi\) | ||||
0.0136457 | + | 0.999907i | \(0.495656\pi\) | |||||||
\(128\) | −13.6417 | −1.20577 | ||||||||
\(129\) | 0.643560 | 0.0566623 | ||||||||
\(130\) | −1.54948 | −0.135898 | ||||||||
\(131\) | 1.76409 | 0.154130 | 0.0770648 | − | 0.997026i | \(-0.475445\pi\) | ||||
0.0770648 | + | 0.997026i | \(0.475445\pi\) | |||||||
\(132\) | −0.0395565 | −0.00344295 | ||||||||
\(133\) | −11.4645 | −0.994096 | ||||||||
\(134\) | 25.1904 | 2.17612 | ||||||||
\(135\) | −2.17104 | −0.186853 | ||||||||
\(136\) | 2.26856 | 0.194527 | ||||||||
\(137\) | 13.5368 | 1.15653 | 0.578264 | − | 0.815850i | \(-0.303730\pi\) | ||||
0.578264 | + | 0.815850i | \(0.303730\pi\) | |||||||
\(138\) | −7.09041 | −0.603576 | ||||||||
\(139\) | −13.9370 | −1.18212 | −0.591062 | − | 0.806626i | \(-0.701291\pi\) | ||||
−0.591062 | + | 0.806626i | \(0.701291\pi\) | |||||||
\(140\) | 4.19815 | 0.354809 | ||||||||
\(141\) | 10.7581 | 0.905999 | ||||||||
\(142\) | 4.29355 | 0.360306 | ||||||||
\(143\) | 0.0297028 | 0.00248387 | ||||||||
\(144\) | −4.83234 | −0.402695 | ||||||||
\(145\) | 19.0362 | 1.58087 | ||||||||
\(146\) | −17.7376 | −1.46797 | ||||||||
\(147\) | −3.72245 | −0.307023 | ||||||||
\(148\) | −2.06808 | −0.169995 | ||||||||
\(149\) | −15.3787 | −1.25987 | −0.629936 | − | 0.776647i | \(-0.716919\pi\) | ||||
−0.629936 | + | 0.776647i | \(0.716919\pi\) | |||||||
\(150\) | −0.461284 | −0.0376637 | ||||||||
\(151\) | 1.02768 | 0.0836313 | 0.0418157 | − | 0.999125i | \(-0.486686\pi\) | ||||
0.0418157 | + | 0.999125i | \(0.486686\pi\) | |||||||
\(152\) | −7.94249 | −0.644221 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −0.353033 | −0.0284482 | ||||||||
\(155\) | 21.5371 | 1.72990 | ||||||||
\(156\) | −0.261859 | −0.0209655 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 10.4893 | 0.834488 | ||||||||
\(159\) | 10.1229 | 0.802796 | ||||||||
\(160\) | 7.03546 | 0.556202 | ||||||||
\(161\) | −14.4253 | −1.13687 | ||||||||
\(162\) | −1.60951 | −0.126455 | ||||||||
\(163\) | −15.8596 | −1.24222 | −0.621110 | − | 0.783723i | \(-0.713318\pi\) | ||||
−0.621110 | + | 0.783723i | \(0.713318\pi\) | |||||||
\(164\) | −5.22815 | −0.408250 | ||||||||
\(165\) | −0.145426 | −0.0113214 | ||||||||
\(166\) | 6.24627 | 0.484805 | ||||||||
\(167\) | 2.41485 | 0.186867 | 0.0934333 | − | 0.995626i | \(-0.470216\pi\) | ||||
0.0934333 | + | 0.995626i | \(0.470216\pi\) | |||||||
\(168\) | −7.42842 | −0.573115 | ||||||||
\(169\) | −12.8034 | −0.984875 | ||||||||
\(170\) | −3.49431 | −0.268002 | ||||||||
\(171\) | −3.50112 | −0.267737 | ||||||||
\(172\) | −0.380043 | −0.0289780 | ||||||||
\(173\) | 4.41983 | 0.336034 | 0.168017 | − | 0.985784i | \(-0.446264\pi\) | ||||
0.168017 | + | 0.985784i | \(0.446264\pi\) | |||||||
\(174\) | 14.1126 | 1.06987 | ||||||||
\(175\) | −0.938472 | −0.0709418 | ||||||||
\(176\) | −0.323691 | −0.0243992 | ||||||||
\(177\) | −7.39311 | −0.555701 | ||||||||
\(178\) | 20.4215 | 1.53065 | ||||||||
\(179\) | 17.2209 | 1.28715 | 0.643574 | − | 0.765384i | \(-0.277451\pi\) | ||||
0.643574 | + | 0.765384i | \(0.277451\pi\) | |||||||
\(180\) | 1.28207 | 0.0955598 | ||||||||
\(181\) | 12.4907 | 0.928429 | 0.464215 | − | 0.885723i | \(-0.346337\pi\) | ||||
0.464215 | + | 0.885723i | \(0.346337\pi\) | |||||||
\(182\) | −2.33703 | −0.173232 | ||||||||
\(183\) | 7.94758 | 0.587502 | ||||||||
\(184\) | −9.99371 | −0.736746 | ||||||||
\(185\) | −7.60310 | −0.558991 | ||||||||
\(186\) | 15.9667 | 1.17073 | ||||||||
\(187\) | 0.0669844 | 0.00489839 | ||||||||
\(188\) | −6.35303 | −0.463343 | ||||||||
\(189\) | −3.27452 | −0.238186 | ||||||||
\(190\) | 12.2340 | 0.887548 | ||||||||
\(191\) | 16.5568 | 1.19801 | 0.599003 | − | 0.800747i | \(-0.295564\pi\) | ||||
0.599003 | + | 0.800747i | \(0.295564\pi\) | |||||||
\(192\) | −4.44889 | −0.321071 | ||||||||
\(193\) | 2.28013 | 0.164127 | 0.0820636 | − | 0.996627i | \(-0.473849\pi\) | ||||
0.0820636 | + | 0.996627i | \(0.473849\pi\) | |||||||
\(194\) | 16.6071 | 1.19232 | ||||||||
\(195\) | −0.962699 | −0.0689403 | ||||||||
\(196\) | 2.19823 | 0.157017 | ||||||||
\(197\) | 9.31037 | 0.663337 | 0.331668 | − | 0.943396i | \(-0.392389\pi\) | ||||
0.331668 | + | 0.943396i | \(0.392389\pi\) | |||||||
\(198\) | −0.107812 | −0.00766189 | ||||||||
\(199\) | −25.4449 | −1.80374 | −0.901870 | − | 0.432008i | \(-0.857805\pi\) | ||||
−0.901870 | + | 0.432008i | \(0.857805\pi\) | |||||||
\(200\) | −0.650165 | −0.0459736 | ||||||||
\(201\) | 15.6509 | 1.10393 | ||||||||
\(202\) | 7.35878 | 0.517762 | ||||||||
\(203\) | 28.7118 | 2.01517 | ||||||||
\(204\) | −0.590533 | −0.0413456 | ||||||||
\(205\) | −19.2208 | −1.34244 | ||||||||
\(206\) | 15.9388 | 1.11051 | ||||||||
\(207\) | −4.40532 | −0.306191 | ||||||||
\(208\) | −2.14279 | −0.148576 | ||||||||
\(209\) | −0.234521 | −0.0162221 | ||||||||
\(210\) | 11.4422 | 0.789586 | ||||||||
\(211\) | 19.0396 | 1.31074 | 0.655369 | − | 0.755309i | \(-0.272513\pi\) | ||||
0.655369 | + | 0.755309i | \(0.272513\pi\) | |||||||
\(212\) | −5.97789 | −0.410563 | ||||||||
\(213\) | 2.66761 | 0.182781 | ||||||||
\(214\) | 0.652209 | 0.0445841 | ||||||||
\(215\) | −1.39719 | −0.0952877 | ||||||||
\(216\) | −2.26856 | −0.154356 | ||||||||
\(217\) | 32.4839 | 2.20515 | ||||||||
\(218\) | 22.2860 | 1.50940 | ||||||||
\(219\) | −11.0205 | −0.744695 | ||||||||
\(220\) | 0.0858787 | 0.00578994 | ||||||||
\(221\) | 0.443428 | 0.0298282 | ||||||||
\(222\) | −5.63661 | −0.378305 | ||||||||
\(223\) | 27.9824 | 1.87384 | 0.936920 | − | 0.349543i | \(-0.113663\pi\) | ||||
0.936920 | + | 0.349543i | \(0.113663\pi\) | |||||||
\(224\) | 10.6114 | 0.709003 | ||||||||
\(225\) | −0.286599 | −0.0191066 | ||||||||
\(226\) | 10.0284 | 0.667078 | ||||||||
\(227\) | −16.0912 | −1.06801 | −0.534004 | − | 0.845482i | \(-0.679313\pi\) | ||||
−0.534004 | + | 0.845482i | \(0.679313\pi\) | |||||||
\(228\) | 2.06753 | 0.136925 | ||||||||
\(229\) | 20.3353 | 1.34380 | 0.671899 | − | 0.740643i | \(-0.265479\pi\) | ||||
0.671899 | + | 0.740643i | \(0.265479\pi\) | |||||||
\(230\) | 15.3936 | 1.01502 | ||||||||
\(231\) | −0.219342 | −0.0144316 | ||||||||
\(232\) | 19.8913 | 1.30592 | ||||||||
\(233\) | −1.86976 | −0.122492 | −0.0612460 | − | 0.998123i | \(-0.519507\pi\) | ||||
−0.0612460 | + | 0.998123i | \(0.519507\pi\) | |||||||
\(234\) | −0.713703 | −0.0466562 | ||||||||
\(235\) | −23.3563 | −1.52360 | ||||||||
\(236\) | 4.36588 | 0.284194 | ||||||||
\(237\) | 6.51709 | 0.423331 | ||||||||
\(238\) | −5.27038 | −0.341628 | ||||||||
\(239\) | 10.3252 | 0.667883 | 0.333941 | − | 0.942594i | \(-0.391621\pi\) | ||||
0.333941 | + | 0.942594i | \(0.391621\pi\) | |||||||
\(240\) | 10.4912 | 0.677203 | ||||||||
\(241\) | −13.4017 | −0.863279 | −0.431639 | − | 0.902046i | \(-0.642065\pi\) | ||||
−0.431639 | + | 0.902046i | \(0.642065\pi\) | |||||||
\(242\) | 17.6974 | 1.13763 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.69330 | −0.300458 | ||||||||
\(245\) | 8.08159 | 0.516314 | ||||||||
\(246\) | −14.2495 | −0.908513 | ||||||||
\(247\) | −1.55249 | −0.0987829 | ||||||||
\(248\) | 22.5045 | 1.42904 | ||||||||
\(249\) | 3.88084 | 0.245938 | ||||||||
\(250\) | 18.4730 | 1.16834 | ||||||||
\(251\) | 2.90309 | 0.183241 | 0.0916206 | − | 0.995794i | \(-0.470795\pi\) | ||||
0.0916206 | + | 0.995794i | \(0.470795\pi\) | |||||||
\(252\) | 1.93371 | 0.121812 | ||||||||
\(253\) | −0.295088 | −0.0185520 | ||||||||
\(254\) | −0.495018 | −0.0310602 | ||||||||
\(255\) | −2.17104 | −0.135956 | ||||||||
\(256\) | 13.0588 | 0.816174 | ||||||||
\(257\) | −0.639767 | −0.0399076 | −0.0199538 | − | 0.999801i | \(-0.506352\pi\) | ||||
−0.0199538 | + | 0.999801i | \(0.506352\pi\) | |||||||
\(258\) | −1.03582 | −0.0644872 | ||||||||
\(259\) | −11.4676 | −0.712559 | ||||||||
\(260\) | 0.568505 | 0.0352572 | ||||||||
\(261\) | 8.76824 | 0.542741 | ||||||||
\(262\) | −2.83933 | −0.175414 | ||||||||
\(263\) | 13.8260 | 0.852549 | 0.426274 | − | 0.904594i | \(-0.359826\pi\) | ||||
0.426274 | + | 0.904594i | \(0.359826\pi\) | |||||||
\(264\) | −0.151958 | −0.00935237 | ||||||||
\(265\) | −21.9771 | −1.35004 | ||||||||
\(266\) | 18.4522 | 1.13138 | ||||||||
\(267\) | 12.6880 | 0.776492 | ||||||||
\(268\) | −9.24239 | −0.564569 | ||||||||
\(269\) | 13.1386 | 0.801073 | 0.400536 | − | 0.916281i | \(-0.368824\pi\) | ||||
0.400536 | + | 0.916281i | \(0.368824\pi\) | |||||||
\(270\) | 3.49431 | 0.212657 | ||||||||
\(271\) | 8.33061 | 0.506049 | 0.253024 | − | 0.967460i | \(-0.418575\pi\) | ||||
0.253024 | + | 0.967460i | \(0.418575\pi\) | |||||||
\(272\) | −4.83234 | −0.293003 | ||||||||
\(273\) | −1.45201 | −0.0878798 | ||||||||
\(274\) | −21.7877 | −1.31624 | ||||||||
\(275\) | −0.0191977 | −0.00115766 | ||||||||
\(276\) | 2.60148 | 0.156591 | ||||||||
\(277\) | −13.9593 | −0.838730 | −0.419365 | − | 0.907818i | \(-0.637747\pi\) | ||||
−0.419365 | + | 0.907818i | \(0.637747\pi\) | |||||||
\(278\) | 22.4319 | 1.34537 | ||||||||
\(279\) | 9.92020 | 0.593907 | ||||||||
\(280\) | 16.1274 | 0.963795 | ||||||||
\(281\) | −26.8581 | −1.60222 | −0.801109 | − | 0.598518i | \(-0.795756\pi\) | ||||
−0.801109 | + | 0.598518i | \(0.795756\pi\) | |||||||
\(282\) | −17.3154 | −1.03111 | ||||||||
\(283\) | −4.53638 | −0.269660 | −0.134830 | − | 0.990869i | \(-0.543049\pi\) | ||||
−0.134830 | + | 0.990869i | \(0.543049\pi\) | |||||||
\(284\) | −1.57531 | −0.0934774 | ||||||||
\(285\) | 7.60106 | 0.450248 | ||||||||
\(286\) | −0.0478070 | −0.00282689 | ||||||||
\(287\) | −28.9902 | −1.71124 | ||||||||
\(288\) | 3.24060 | 0.190954 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −30.6390 | −1.79918 | ||||||||
\(291\) | 10.3181 | 0.604858 | ||||||||
\(292\) | 6.50795 | 0.380849 | ||||||||
\(293\) | −11.6603 | −0.681203 | −0.340601 | − | 0.940208i | \(-0.610631\pi\) | ||||
−0.340601 | + | 0.940208i | \(0.610631\pi\) | |||||||
\(294\) | 5.99134 | 0.349422 | ||||||||
\(295\) | 16.0507 | 0.934509 | ||||||||
\(296\) | −7.94462 | −0.461772 | ||||||||
\(297\) | −0.0669844 | −0.00388683 | ||||||||
\(298\) | 24.7522 | 1.43386 | ||||||||
\(299\) | −1.95344 | −0.112970 | ||||||||
\(300\) | 0.169246 | 0.00977142 | ||||||||
\(301\) | −2.10735 | −0.121465 | ||||||||
\(302\) | −1.65406 | −0.0951806 | ||||||||
\(303\) | 4.57205 | 0.262658 | ||||||||
\(304\) | 16.9186 | 0.970348 | ||||||||
\(305\) | −17.2545 | −0.987989 | ||||||||
\(306\) | −1.60951 | −0.0920097 | ||||||||
\(307\) | 15.3874 | 0.878208 | 0.439104 | − | 0.898436i | \(-0.355296\pi\) | ||||
0.439104 | + | 0.898436i | \(0.355296\pi\) | |||||||
\(308\) | 0.129528 | 0.00738057 | ||||||||
\(309\) | 9.90284 | 0.563353 | ||||||||
\(310\) | −34.6643 | −1.96880 | ||||||||
\(311\) | 8.52143 | 0.483206 | 0.241603 | − | 0.970375i | \(-0.422327\pi\) | ||||
0.241603 | + | 0.970375i | \(0.422327\pi\) | |||||||
\(312\) | −1.00594 | −0.0569502 | ||||||||
\(313\) | −16.7701 | −0.947900 | −0.473950 | − | 0.880552i | \(-0.657172\pi\) | ||||
−0.473950 | + | 0.880552i | \(0.657172\pi\) | |||||||
\(314\) | −1.60951 | −0.0908301 | ||||||||
\(315\) | 7.10909 | 0.400552 | ||||||||
\(316\) | −3.84856 | −0.216498 | ||||||||
\(317\) | 33.4976 | 1.88141 | 0.940707 | − | 0.339220i | \(-0.110163\pi\) | ||||
0.940707 | + | 0.339220i | \(0.110163\pi\) | |||||||
\(318\) | −16.2929 | −0.913660 | ||||||||
\(319\) | 0.587336 | 0.0328845 | ||||||||
\(320\) | 9.65870 | 0.539938 | ||||||||
\(321\) | 0.405221 | 0.0226172 | ||||||||
\(322\) | 23.2177 | 1.29387 | ||||||||
\(323\) | −3.50112 | −0.194808 | ||||||||
\(324\) | 0.590533 | 0.0328074 | ||||||||
\(325\) | −0.127086 | −0.00704946 | ||||||||
\(326\) | 25.5262 | 1.41377 | ||||||||
\(327\) | 13.8464 | 0.765709 | ||||||||
\(328\) | −20.0842 | −1.10896 | ||||||||
\(329\) | −35.2277 | −1.94217 | ||||||||
\(330\) | 0.234065 | 0.0128848 | ||||||||
\(331\) | −17.3634 | −0.954379 | −0.477190 | − | 0.878800i | \(-0.658344\pi\) | ||||
−0.477190 | + | 0.878800i | \(0.658344\pi\) | |||||||
\(332\) | −2.29177 | −0.125777 | ||||||||
\(333\) | −3.50206 | −0.191912 | ||||||||
\(334\) | −3.88673 | −0.212672 | ||||||||
\(335\) | −33.9787 | −1.85646 | ||||||||
\(336\) | 15.8236 | 0.863246 | ||||||||
\(337\) | −20.3177 | −1.10677 | −0.553387 | − | 0.832924i | \(-0.686665\pi\) | ||||
−0.553387 | + | 0.832924i | \(0.686665\pi\) | |||||||
\(338\) | 20.6072 | 1.12088 | ||||||||
\(339\) | 6.23069 | 0.338405 | ||||||||
\(340\) | 1.28207 | 0.0695299 | ||||||||
\(341\) | 0.664499 | 0.0359846 | ||||||||
\(342\) | 5.63510 | 0.304711 | ||||||||
\(343\) | −10.7324 | −0.579494 | ||||||||
\(344\) | −1.45995 | −0.0787153 | ||||||||
\(345\) | 9.56410 | 0.514914 | ||||||||
\(346\) | −7.11378 | −0.382439 | ||||||||
\(347\) | 8.12404 | 0.436121 | 0.218061 | − | 0.975935i | \(-0.430027\pi\) | ||||
0.218061 | + | 0.975935i | \(0.430027\pi\) | |||||||
\(348\) | −5.17794 | −0.277567 | ||||||||
\(349\) | −9.01081 | −0.482338 | −0.241169 | − | 0.970483i | \(-0.577531\pi\) | ||||
−0.241169 | + | 0.970483i | \(0.577531\pi\) | |||||||
\(350\) | 1.51048 | 0.0807387 | ||||||||
\(351\) | −0.443428 | −0.0236684 | ||||||||
\(352\) | 0.217070 | 0.0115699 | ||||||||
\(353\) | 21.5948 | 1.14937 | 0.574687 | − | 0.818373i | \(-0.305124\pi\) | ||||
0.574687 | + | 0.818373i | \(0.305124\pi\) | |||||||
\(354\) | 11.8993 | 0.632441 | ||||||||
\(355\) | −5.79147 | −0.307379 | ||||||||
\(356\) | −7.49267 | −0.397111 | ||||||||
\(357\) | −3.27452 | −0.173306 | ||||||||
\(358\) | −27.7172 | −1.46490 | ||||||||
\(359\) | 3.96063 | 0.209034 | 0.104517 | − | 0.994523i | \(-0.466670\pi\) | ||||
0.104517 | + | 0.994523i | \(0.466670\pi\) | |||||||
\(360\) | 4.92512 | 0.259577 | ||||||||
\(361\) | −6.74216 | −0.354850 | ||||||||
\(362\) | −20.1040 | −1.05664 | ||||||||
\(363\) | 10.9955 | 0.577115 | ||||||||
\(364\) | 0.857461 | 0.0449432 | ||||||||
\(365\) | 23.9259 | 1.25234 | ||||||||
\(366\) | −12.7917 | −0.668634 | ||||||||
\(367\) | −0.346579 | −0.0180913 | −0.00904564 | − | 0.999959i | \(-0.502879\pi\) | ||||
−0.00904564 | + | 0.999959i | \(0.502879\pi\) | |||||||
\(368\) | 21.2880 | 1.10971 | ||||||||
\(369\) | −8.85328 | −0.460883 | ||||||||
\(370\) | 12.2373 | 0.636187 | ||||||||
\(371\) | −33.1475 | −1.72093 | ||||||||
\(372\) | −5.85820 | −0.303734 | ||||||||
\(373\) | 3.29447 | 0.170581 | 0.0852905 | − | 0.996356i | \(-0.472818\pi\) | ||||
0.0852905 | + | 0.996356i | \(0.472818\pi\) | |||||||
\(374\) | −0.107812 | −0.00557484 | ||||||||
\(375\) | 11.4774 | 0.592690 | ||||||||
\(376\) | −24.4054 | −1.25861 | ||||||||
\(377\) | 3.88808 | 0.200247 | ||||||||
\(378\) | 5.27038 | 0.271079 | ||||||||
\(379\) | 13.9258 | 0.715319 | 0.357660 | − | 0.933852i | \(-0.383575\pi\) | ||||
0.357660 | + | 0.933852i | \(0.383575\pi\) | |||||||
\(380\) | −4.48868 | −0.230264 | ||||||||
\(381\) | −0.307558 | −0.0157567 | ||||||||
\(382\) | −26.6483 | −1.36345 | ||||||||
\(383\) | −17.7613 | −0.907562 | −0.453781 | − | 0.891113i | \(-0.649925\pi\) | ||||
−0.453781 | + | 0.891113i | \(0.649925\pi\) | |||||||
\(384\) | 13.6417 | 0.696152 | ||||||||
\(385\) | 0.476199 | 0.0242693 | ||||||||
\(386\) | −3.66990 | −0.186793 | ||||||||
\(387\) | −0.643560 | −0.0327140 | ||||||||
\(388\) | −6.09318 | −0.309335 | ||||||||
\(389\) | 21.5899 | 1.09465 | 0.547326 | − | 0.836920i | \(-0.315646\pi\) | ||||
0.547326 | + | 0.836920i | \(0.315646\pi\) | |||||||
\(390\) | 1.54948 | 0.0784608 | ||||||||
\(391\) | −4.40532 | −0.222786 | ||||||||
\(392\) | 8.44460 | 0.426517 | ||||||||
\(393\) | −1.76409 | −0.0889867 | ||||||||
\(394\) | −14.9852 | −0.754942 | ||||||||
\(395\) | −14.1488 | −0.711906 | ||||||||
\(396\) | 0.0395565 | 0.00198779 | ||||||||
\(397\) | −17.2324 | −0.864871 | −0.432436 | − | 0.901665i | \(-0.642346\pi\) | ||||
−0.432436 | + | 0.901665i | \(0.642346\pi\) | |||||||
\(398\) | 40.9539 | 2.05283 | ||||||||
\(399\) | 11.4645 | 0.573942 | ||||||||
\(400\) | 1.38494 | 0.0692471 | ||||||||
\(401\) | 19.0021 | 0.948919 | 0.474460 | − | 0.880277i | \(-0.342644\pi\) | ||||
0.474460 | + | 0.880277i | \(0.342644\pi\) | |||||||
\(402\) | −25.1904 | −1.25638 | ||||||||
\(403\) | 4.39889 | 0.219125 | ||||||||
\(404\) | −2.69995 | −0.134327 | ||||||||
\(405\) | 2.17104 | 0.107880 | ||||||||
\(406\) | −46.2119 | −2.29346 | ||||||||
\(407\) | −0.234584 | −0.0116279 | ||||||||
\(408\) | −2.26856 | −0.112310 | ||||||||
\(409\) | 20.7015 | 1.02362 | 0.511811 | − | 0.859098i | \(-0.328975\pi\) | ||||
0.511811 | + | 0.859098i | \(0.328975\pi\) | |||||||
\(410\) | 30.9361 | 1.52783 | ||||||||
\(411\) | −13.5368 | −0.667722 | ||||||||
\(412\) | −5.84795 | −0.288108 | ||||||||
\(413\) | 24.2089 | 1.19124 | ||||||||
\(414\) | 7.09041 | 0.348475 | ||||||||
\(415\) | −8.42546 | −0.413589 | ||||||||
\(416\) | 1.43697 | 0.0704533 | ||||||||
\(417\) | 13.9370 | 0.682500 | ||||||||
\(418\) | 0.377464 | 0.0184624 | ||||||||
\(419\) | 20.9715 | 1.02452 | 0.512262 | − | 0.858829i | \(-0.328808\pi\) | ||||
0.512262 | + | 0.858829i | \(0.328808\pi\) | |||||||
\(420\) | −4.19815 | −0.204849 | ||||||||
\(421\) | −32.3863 | −1.57841 | −0.789207 | − | 0.614127i | \(-0.789508\pi\) | ||||
−0.789207 | + | 0.614127i | \(0.789508\pi\) | |||||||
\(422\) | −30.6445 | −1.49175 | ||||||||
\(423\) | −10.7581 | −0.523079 | ||||||||
\(424\) | −22.9643 | −1.11524 | ||||||||
\(425\) | −0.286599 | −0.0139021 | ||||||||
\(426\) | −4.29355 | −0.208023 | ||||||||
\(427\) | −26.0245 | −1.25941 | ||||||||
\(428\) | −0.239296 | −0.0115668 | ||||||||
\(429\) | −0.0297028 | −0.00143406 | ||||||||
\(430\) | 2.24880 | 0.108447 | ||||||||
\(431\) | 16.5496 | 0.797166 | 0.398583 | − | 0.917132i | \(-0.369502\pi\) | ||||
0.398583 | + | 0.917132i | \(0.369502\pi\) | |||||||
\(432\) | 4.83234 | 0.232496 | ||||||||
\(433\) | −17.0293 | −0.818378 | −0.409189 | − | 0.912450i | \(-0.634188\pi\) | ||||
−0.409189 | + | 0.912450i | \(0.634188\pi\) | |||||||
\(434\) | −52.2832 | −2.50967 | ||||||||
\(435\) | −19.0362 | −0.912715 | ||||||||
\(436\) | −8.17677 | −0.391596 | ||||||||
\(437\) | 15.4235 | 0.737808 | ||||||||
\(438\) | 17.7376 | 0.847536 | ||||||||
\(439\) | 20.6196 | 0.984118 | 0.492059 | − | 0.870562i | \(-0.336244\pi\) | ||||
0.492059 | + | 0.870562i | \(0.336244\pi\) | |||||||
\(440\) | 0.329906 | 0.0157277 | ||||||||
\(441\) | 3.72245 | 0.177260 | ||||||||
\(442\) | −0.713703 | −0.0339474 | ||||||||
\(443\) | −13.8670 | −0.658841 | −0.329420 | − | 0.944183i | \(-0.606853\pi\) | ||||
−0.329420 | + | 0.944183i | \(0.606853\pi\) | |||||||
\(444\) | 2.06808 | 0.0981468 | ||||||||
\(445\) | −27.5461 | −1.30581 | ||||||||
\(446\) | −45.0381 | −2.13261 | ||||||||
\(447\) | 15.3787 | 0.727387 | ||||||||
\(448\) | 14.5680 | 0.688271 | ||||||||
\(449\) | −22.0658 | −1.04135 | −0.520675 | − | 0.853755i | \(-0.674319\pi\) | ||||
−0.520675 | + | 0.853755i | \(0.674319\pi\) | |||||||
\(450\) | 0.461284 | 0.0217452 | ||||||||
\(451\) | −0.593032 | −0.0279248 | ||||||||
\(452\) | −3.67943 | −0.173066 | ||||||||
\(453\) | −1.02768 | −0.0482846 | ||||||||
\(454\) | 25.8990 | 1.21550 | ||||||||
\(455\) | 3.15237 | 0.147785 | ||||||||
\(456\) | 7.94249 | 0.371941 | ||||||||
\(457\) | 37.4863 | 1.75353 | 0.876767 | − | 0.480915i | \(-0.159695\pi\) | ||||
0.876767 | + | 0.480915i | \(0.159695\pi\) | |||||||
\(458\) | −32.7300 | −1.52937 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −5.64792 | −0.263335 | ||||||||
\(461\) | 16.2066 | 0.754818 | 0.377409 | − | 0.926047i | \(-0.376815\pi\) | ||||
0.377409 | + | 0.926047i | \(0.376815\pi\) | |||||||
\(462\) | 0.353033 | 0.0164246 | ||||||||
\(463\) | −5.22576 | −0.242861 | −0.121431 | − | 0.992600i | \(-0.538748\pi\) | ||||
−0.121431 | + | 0.992600i | \(0.538748\pi\) | |||||||
\(464\) | −42.3711 | −1.96703 | ||||||||
\(465\) | −21.5371 | −0.998760 | ||||||||
\(466\) | 3.00940 | 0.139408 | ||||||||
\(467\) | −0.858711 | −0.0397364 | −0.0198682 | − | 0.999803i | \(-0.506325\pi\) | ||||
−0.0198682 | + | 0.999803i | \(0.506325\pi\) | |||||||
\(468\) | 0.261859 | 0.0121044 | ||||||||
\(469\) | −51.2492 | −2.36647 | ||||||||
\(470\) | 37.5923 | 1.73400 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | 16.7717 | 0.771980 | ||||||||
\(473\) | −0.0431085 | −0.00198213 | ||||||||
\(474\) | −10.4893 | −0.481792 | ||||||||
\(475\) | 1.00342 | 0.0460399 | ||||||||
\(476\) | 1.93371 | 0.0886314 | ||||||||
\(477\) | −10.1229 | −0.463494 | ||||||||
\(478\) | −16.6186 | −0.760116 | ||||||||
\(479\) | −16.8868 | −0.771579 | −0.385789 | − | 0.922587i | \(-0.626071\pi\) | ||||
−0.385789 | + | 0.922587i | \(0.626071\pi\) | |||||||
\(480\) | −7.03546 | −0.321123 | ||||||||
\(481\) | −1.55291 | −0.0708067 | ||||||||
\(482\) | 21.5702 | 0.982496 | ||||||||
\(483\) | 14.4253 | 0.656373 | ||||||||
\(484\) | −6.49321 | −0.295146 | ||||||||
\(485\) | −22.4010 | −1.01718 | ||||||||
\(486\) | 1.60951 | 0.0730090 | ||||||||
\(487\) | 8.20424 | 0.371770 | 0.185885 | − | 0.982572i | \(-0.440485\pi\) | ||||
0.185885 | + | 0.982572i | \(0.440485\pi\) | |||||||
\(488\) | −18.0295 | −0.816158 | ||||||||
\(489\) | 15.8596 | 0.717196 | ||||||||
\(490\) | −13.0074 | −0.587615 | ||||||||
\(491\) | −10.5890 | −0.477875 | −0.238937 | − | 0.971035i | \(-0.576799\pi\) | ||||
−0.238937 | + | 0.971035i | \(0.576799\pi\) | |||||||
\(492\) | 5.22815 | 0.235703 | ||||||||
\(493\) | 8.76824 | 0.394902 | ||||||||
\(494\) | 2.49876 | 0.112425 | ||||||||
\(495\) | 0.145426 | 0.00653640 | ||||||||
\(496\) | −47.9377 | −2.15247 | ||||||||
\(497\) | −8.73512 | −0.391824 | ||||||||
\(498\) | −6.24627 | −0.279902 | ||||||||
\(499\) | 42.4502 | 1.90033 | 0.950167 | − | 0.311742i | \(-0.100912\pi\) | ||||
0.950167 | + | 0.311742i | \(0.100912\pi\) | |||||||
\(500\) | −6.77778 | −0.303112 | ||||||||
\(501\) | −2.41485 | −0.107888 | ||||||||
\(502\) | −4.67256 | −0.208546 | ||||||||
\(503\) | 2.89522 | 0.129091 | 0.0645457 | − | 0.997915i | \(-0.479440\pi\) | ||||
0.0645457 | + | 0.997915i | \(0.479440\pi\) | |||||||
\(504\) | 7.42842 | 0.330888 | ||||||||
\(505\) | −9.92609 | −0.441705 | ||||||||
\(506\) | 0.474947 | 0.0211140 | ||||||||
\(507\) | 12.8034 | 0.568618 | ||||||||
\(508\) | 0.181623 | 0.00805821 | ||||||||
\(509\) | 20.6225 | 0.914074 | 0.457037 | − | 0.889448i | \(-0.348911\pi\) | ||||
0.457037 | + | 0.889448i | \(0.348911\pi\) | |||||||
\(510\) | 3.49431 | 0.154731 | ||||||||
\(511\) | 36.0867 | 1.59638 | ||||||||
\(512\) | 6.26519 | 0.276885 | ||||||||
\(513\) | 3.50112 | 0.154578 | ||||||||
\(514\) | 1.02971 | 0.0454187 | ||||||||
\(515\) | −21.4994 | −0.947378 | ||||||||
\(516\) | 0.380043 | 0.0167305 | ||||||||
\(517\) | −0.720628 | −0.0316932 | ||||||||
\(518\) | 18.4572 | 0.810962 | ||||||||
\(519\) | −4.41983 | −0.194009 | ||||||||
\(520\) | 2.18394 | 0.0957719 | ||||||||
\(521\) | 2.79472 | 0.122439 | 0.0612196 | − | 0.998124i | \(-0.480501\pi\) | ||||
0.0612196 | + | 0.998124i | \(0.480501\pi\) | |||||||
\(522\) | −14.1126 | −0.617692 | ||||||||
\(523\) | −13.1975 | −0.577086 | −0.288543 | − | 0.957467i | \(-0.593171\pi\) | ||||
−0.288543 | + | 0.957467i | \(0.593171\pi\) | |||||||
\(524\) | 1.04175 | 0.0455093 | ||||||||
\(525\) | 0.938472 | 0.0409583 | ||||||||
\(526\) | −22.2532 | −0.970284 | ||||||||
\(527\) | 9.92020 | 0.432131 | ||||||||
\(528\) | 0.323691 | 0.0140869 | ||||||||
\(529\) | −3.59319 | −0.156226 | ||||||||
\(530\) | 35.3725 | 1.53648 | ||||||||
\(531\) | 7.39311 | 0.320834 | ||||||||
\(532\) | −6.77015 | −0.293523 | ||||||||
\(533\) | −3.92579 | −0.170045 | ||||||||
\(534\) | −20.4215 | −0.883724 | ||||||||
\(535\) | −0.879750 | −0.0380349 | ||||||||
\(536\) | −35.5050 | −1.53358 | ||||||||
\(537\) | −17.2209 | −0.743135 | ||||||||
\(538\) | −21.1467 | −0.911699 | ||||||||
\(539\) | 0.249347 | 0.0107401 | ||||||||
\(540\) | −1.28207 | −0.0551714 | ||||||||
\(541\) | −11.7990 | −0.507277 | −0.253638 | − | 0.967299i | \(-0.581627\pi\) | ||||
−0.253638 | + | 0.967299i | \(0.581627\pi\) | |||||||
\(542\) | −13.4082 | −0.575933 | ||||||||
\(543\) | −12.4907 | −0.536029 | ||||||||
\(544\) | 3.24060 | 0.138939 | ||||||||
\(545\) | −30.0611 | −1.28768 | ||||||||
\(546\) | 2.33703 | 0.100016 | ||||||||
\(547\) | 25.4673 | 1.08890 | 0.544452 | − | 0.838792i | \(-0.316738\pi\) | ||||
0.544452 | + | 0.838792i | \(0.316738\pi\) | |||||||
\(548\) | 7.99393 | 0.341484 | ||||||||
\(549\) | −7.94758 | −0.339194 | ||||||||
\(550\) | 0.0308989 | 0.00131753 | ||||||||
\(551\) | −30.6987 | −1.30781 | ||||||||
\(552\) | 9.99371 | 0.425360 | ||||||||
\(553\) | −21.3403 | −0.907483 | ||||||||
\(554\) | 22.4676 | 0.954557 | ||||||||
\(555\) | 7.60310 | 0.322734 | ||||||||
\(556\) | −8.23028 | −0.349042 | ||||||||
\(557\) | 33.5873 | 1.42314 | 0.711571 | − | 0.702614i | \(-0.247984\pi\) | ||||
0.711571 | + | 0.702614i | \(0.247984\pi\) | |||||||
\(558\) | −15.9667 | −0.675924 | ||||||||
\(559\) | −0.285373 | −0.0120700 | ||||||||
\(560\) | −34.3535 | −1.45170 | ||||||||
\(561\) | −0.0669844 | −0.00282809 | ||||||||
\(562\) | 43.2284 | 1.82348 | ||||||||
\(563\) | −15.6933 | −0.661392 | −0.330696 | − | 0.943737i | \(-0.607284\pi\) | ||||
−0.330696 | + | 0.943737i | \(0.607284\pi\) | |||||||
\(564\) | 6.35303 | 0.267511 | ||||||||
\(565\) | −13.5271 | −0.569087 | ||||||||
\(566\) | 7.30137 | 0.306899 | ||||||||
\(567\) | 3.27452 | 0.137517 | ||||||||
\(568\) | −6.05161 | −0.253920 | ||||||||
\(569\) | 14.0025 | 0.587016 | 0.293508 | − | 0.955957i | \(-0.405177\pi\) | ||||
0.293508 | + | 0.955957i | \(0.405177\pi\) | |||||||
\(570\) | −12.2340 | −0.512426 | ||||||||
\(571\) | −37.9480 | −1.58807 | −0.794037 | − | 0.607870i | \(-0.792024\pi\) | ||||
−0.794037 | + | 0.607870i | \(0.792024\pi\) | |||||||
\(572\) | 0.0175405 | 0.000733404 0 | ||||||||
\(573\) | −16.5568 | −0.691669 | ||||||||
\(574\) | 46.6601 | 1.94756 | ||||||||
\(575\) | 1.26256 | 0.0526523 | ||||||||
\(576\) | 4.44889 | 0.185370 | ||||||||
\(577\) | −5.35312 | −0.222853 | −0.111427 | − | 0.993773i | \(-0.535542\pi\) | ||||
−0.111427 | + | 0.993773i | \(0.535542\pi\) | |||||||
\(578\) | −1.60951 | −0.0669469 | ||||||||
\(579\) | −2.28013 | −0.0947589 | ||||||||
\(580\) | 11.2415 | 0.466777 | ||||||||
\(581\) | −12.7079 | −0.527212 | ||||||||
\(582\) | −16.6071 | −0.688388 | ||||||||
\(583\) | −0.678075 | −0.0280830 | ||||||||
\(584\) | 25.0006 | 1.03453 | ||||||||
\(585\) | 0.962699 | 0.0398027 | ||||||||
\(586\) | 18.7674 | 0.775275 | ||||||||
\(587\) | 26.0412 | 1.07484 | 0.537418 | − | 0.843316i | \(-0.319400\pi\) | ||||
0.537418 | + | 0.843316i | \(0.319400\pi\) | |||||||
\(588\) | −2.19823 | −0.0906535 | ||||||||
\(589\) | −34.7318 | −1.43110 | ||||||||
\(590\) | −25.8339 | −1.06356 | ||||||||
\(591\) | −9.31037 | −0.382978 | ||||||||
\(592\) | 16.9231 | 0.695537 | ||||||||
\(593\) | 9.03662 | 0.371089 | 0.185545 | − | 0.982636i | \(-0.440595\pi\) | ||||
0.185545 | + | 0.982636i | \(0.440595\pi\) | |||||||
\(594\) | 0.107812 | 0.00442359 | ||||||||
\(595\) | 7.10909 | 0.291444 | ||||||||
\(596\) | −9.08162 | −0.371998 | ||||||||
\(597\) | 25.4449 | 1.04139 | ||||||||
\(598\) | 3.14409 | 0.128571 | ||||||||
\(599\) | −15.7529 | −0.643645 | −0.321823 | − | 0.946800i | \(-0.604295\pi\) | ||||
−0.321823 | + | 0.946800i | \(0.604295\pi\) | |||||||
\(600\) | 0.650165 | 0.0265429 | ||||||||
\(601\) | 4.91630 | 0.200540 | 0.100270 | − | 0.994960i | \(-0.468029\pi\) | ||||
0.100270 | + | 0.994960i | \(0.468029\pi\) | |||||||
\(602\) | 3.39180 | 0.138240 | ||||||||
\(603\) | −15.6509 | −0.637355 | ||||||||
\(604\) | 0.606878 | 0.0246935 | ||||||||
\(605\) | −23.8717 | −0.970521 | ||||||||
\(606\) | −7.35878 | −0.298930 | ||||||||
\(607\) | −45.4549 | −1.84496 | −0.922480 | − | 0.386046i | \(-0.873841\pi\) | ||||
−0.922480 | + | 0.386046i | \(0.873841\pi\) | |||||||
\(608\) | −11.3457 | −0.460130 | ||||||||
\(609\) | −28.7118 | −1.16346 | ||||||||
\(610\) | 27.7713 | 1.12443 | ||||||||
\(611\) | −4.77046 | −0.192992 | ||||||||
\(612\) | 0.590533 | 0.0238709 | ||||||||
\(613\) | 37.9669 | 1.53347 | 0.766734 | − | 0.641965i | \(-0.221880\pi\) | ||||
0.766734 | + | 0.641965i | \(0.221880\pi\) | |||||||
\(614\) | −24.7663 | −0.999486 | ||||||||
\(615\) | 19.2208 | 0.775058 | ||||||||
\(616\) | 0.497589 | 0.0200484 | ||||||||
\(617\) | 22.4257 | 0.902824 | 0.451412 | − | 0.892316i | \(-0.350920\pi\) | ||||
0.451412 | + | 0.892316i | \(0.350920\pi\) | |||||||
\(618\) | −15.9388 | −0.641151 | ||||||||
\(619\) | 24.8136 | 0.997342 | 0.498671 | − | 0.866791i | \(-0.333822\pi\) | ||||
0.498671 | + | 0.866791i | \(0.333822\pi\) | |||||||
\(620\) | 12.7184 | 0.510782 | ||||||||
\(621\) | 4.40532 | 0.176779 | ||||||||
\(622\) | −13.7154 | −0.549935 | ||||||||
\(623\) | −41.5470 | −1.66455 | ||||||||
\(624\) | 2.14279 | 0.0857804 | ||||||||
\(625\) | −23.4849 | −0.939395 | ||||||||
\(626\) | 26.9916 | 1.07880 | ||||||||
\(627\) | 0.234521 | 0.00936585 | ||||||||
\(628\) | 0.590533 | 0.0235648 | ||||||||
\(629\) | −3.50206 | −0.139636 | ||||||||
\(630\) | −11.4422 | −0.455867 | ||||||||
\(631\) | −2.38149 | −0.0948057 | −0.0474028 | − | 0.998876i | \(-0.515094\pi\) | ||||
−0.0474028 | + | 0.998876i | \(0.515094\pi\) | |||||||
\(632\) | −14.7844 | −0.588091 | ||||||||
\(633\) | −19.0396 | −0.756755 | ||||||||
\(634\) | −53.9149 | −2.14123 | ||||||||
\(635\) | 0.667719 | 0.0264976 | ||||||||
\(636\) | 5.97789 | 0.237039 | ||||||||
\(637\) | 1.65064 | 0.0654008 | ||||||||
\(638\) | −0.945325 | −0.0374258 | ||||||||
\(639\) | −2.66761 | −0.105529 | ||||||||
\(640\) | −29.6167 | −1.17070 | ||||||||
\(641\) | 3.98300 | 0.157319 | 0.0786595 | − | 0.996902i | \(-0.474936\pi\) | ||||
0.0786595 | + | 0.996902i | \(0.474936\pi\) | |||||||
\(642\) | −0.652209 | −0.0257406 | ||||||||
\(643\) | 37.9999 | 1.49857 | 0.749285 | − | 0.662248i | \(-0.230397\pi\) | ||||
0.749285 | + | 0.662248i | \(0.230397\pi\) | |||||||
\(644\) | −8.51860 | −0.335680 | ||||||||
\(645\) | 1.39719 | 0.0550144 | ||||||||
\(646\) | 5.63510 | 0.221710 | ||||||||
\(647\) | 21.9666 | 0.863598 | 0.431799 | − | 0.901970i | \(-0.357879\pi\) | ||||
0.431799 | + | 0.901970i | \(0.357879\pi\) | |||||||
\(648\) | 2.26856 | 0.0891173 | ||||||||
\(649\) | 0.495224 | 0.0194392 | ||||||||
\(650\) | 0.204546 | 0.00802297 | ||||||||
\(651\) | −32.4839 | −1.27314 | ||||||||
\(652\) | −9.36562 | −0.366786 | ||||||||
\(653\) | 11.2081 | 0.438607 | 0.219303 | − | 0.975657i | \(-0.429622\pi\) | ||||
0.219303 | + | 0.975657i | \(0.429622\pi\) | |||||||
\(654\) | −22.2860 | −0.871451 | ||||||||
\(655\) | 3.82991 | 0.149647 | ||||||||
\(656\) | 42.7820 | 1.67036 | ||||||||
\(657\) | 11.0205 | 0.429950 | ||||||||
\(658\) | 56.6994 | 2.21037 | ||||||||
\(659\) | −13.9551 | −0.543612 | −0.271806 | − | 0.962352i | \(-0.587621\pi\) | ||||
−0.271806 | + | 0.962352i | \(0.587621\pi\) | |||||||
\(660\) | −0.0858787 | −0.00334282 | ||||||||
\(661\) | −17.8764 | −0.695311 | −0.347656 | − | 0.937622i | \(-0.613022\pi\) | ||||
−0.347656 | + | 0.937622i | \(0.613022\pi\) | |||||||
\(662\) | 27.9466 | 1.08618 | ||||||||
\(663\) | −0.443428 | −0.0172213 | ||||||||
\(664\) | −8.80391 | −0.341658 | ||||||||
\(665\) | −24.8898 | −0.965185 | ||||||||
\(666\) | 5.63661 | 0.218414 | ||||||||
\(667\) | −38.6269 | −1.49564 | ||||||||
\(668\) | 1.42605 | 0.0551754 | ||||||||
\(669\) | −27.9824 | −1.08186 | ||||||||
\(670\) | 54.6892 | 2.11283 | ||||||||
\(671\) | −0.532364 | −0.0205517 | ||||||||
\(672\) | −10.6114 | −0.409343 | ||||||||
\(673\) | 11.4088 | 0.439776 | 0.219888 | − | 0.975525i | \(-0.429431\pi\) | ||||
0.219888 | + | 0.975525i | \(0.429431\pi\) | |||||||
\(674\) | 32.7016 | 1.25962 | ||||||||
\(675\) | 0.286599 | 0.0110312 | ||||||||
\(676\) | −7.56081 | −0.290800 | ||||||||
\(677\) | −37.2245 | −1.43065 | −0.715327 | − | 0.698790i | \(-0.753722\pi\) | ||||
−0.715327 | + | 0.698790i | \(0.753722\pi\) | |||||||
\(678\) | −10.0284 | −0.385137 | ||||||||
\(679\) | −33.7868 | −1.29662 | ||||||||
\(680\) | 4.92512 | 0.188870 | ||||||||
\(681\) | 16.0912 | 0.616615 | ||||||||
\(682\) | −1.06952 | −0.0409540 | ||||||||
\(683\) | −16.0374 | −0.613655 | −0.306828 | − | 0.951765i | \(-0.599267\pi\) | ||||
−0.306828 | + | 0.951765i | \(0.599267\pi\) | |||||||
\(684\) | −2.06753 | −0.0790539 | ||||||||
\(685\) | 29.3889 | 1.12289 | ||||||||
\(686\) | 17.2739 | 0.659521 | ||||||||
\(687\) | −20.3353 | −0.775842 | ||||||||
\(688\) | 3.10990 | 0.118564 | ||||||||
\(689\) | −4.48876 | −0.171008 | ||||||||
\(690\) | −15.3936 | −0.586022 | ||||||||
\(691\) | 1.77741 | 0.0676160 | 0.0338080 | − | 0.999428i | \(-0.489237\pi\) | ||||
0.0338080 | + | 0.999428i | \(0.489237\pi\) | |||||||
\(692\) | 2.61006 | 0.0992195 | ||||||||
\(693\) | 0.219342 | 0.00833210 | ||||||||
\(694\) | −13.0758 | −0.496349 | ||||||||
\(695\) | −30.2578 | −1.14775 | ||||||||
\(696\) | −19.8913 | −0.753976 | ||||||||
\(697\) | −8.85328 | −0.335342 | ||||||||
\(698\) | 14.5030 | 0.548947 | ||||||||
\(699\) | 1.86976 | 0.0707208 | ||||||||
\(700\) | −0.554198 | −0.0209467 | ||||||||
\(701\) | 35.0386 | 1.32339 | 0.661695 | − | 0.749773i | \(-0.269837\pi\) | ||||
0.661695 | + | 0.749773i | \(0.269837\pi\) | |||||||
\(702\) | 0.713703 | 0.0269370 | ||||||||
\(703\) | 12.2611 | 0.462437 | ||||||||
\(704\) | 0.298006 | 0.0112315 | ||||||||
\(705\) | 23.3563 | 0.879650 | ||||||||
\(706\) | −34.7571 | −1.30810 | ||||||||
\(707\) | −14.9713 | −0.563052 | ||||||||
\(708\) | −4.36588 | −0.164080 | ||||||||
\(709\) | −47.9107 | −1.79932 | −0.899661 | − | 0.436589i | \(-0.856187\pi\) | ||||
−0.899661 | + | 0.436589i | \(0.856187\pi\) | |||||||
\(710\) | 9.32145 | 0.349828 | ||||||||
\(711\) | −6.51709 | −0.244410 | ||||||||
\(712\) | −28.7834 | −1.07870 | ||||||||
\(713\) | −43.7016 | −1.63664 | ||||||||
\(714\) | 5.27038 | 0.197239 | ||||||||
\(715\) | 0.0644858 | 0.00241163 | ||||||||
\(716\) | 10.1695 | 0.380052 | ||||||||
\(717\) | −10.3252 | −0.385602 | ||||||||
\(718\) | −6.37469 | −0.237901 | ||||||||
\(719\) | 36.8251 | 1.37334 | 0.686672 | − | 0.726967i | \(-0.259071\pi\) | ||||
0.686672 | + | 0.726967i | \(0.259071\pi\) | |||||||
\(720\) | −10.4912 | −0.390983 | ||||||||
\(721\) | −32.4270 | −1.20765 | ||||||||
\(722\) | 10.8516 | 0.403854 | ||||||||
\(723\) | 13.4017 | 0.498414 | ||||||||
\(724\) | 7.37619 | 0.274134 | ||||||||
\(725\) | −2.51297 | −0.0933292 | ||||||||
\(726\) | −17.6974 | −0.656813 | ||||||||
\(727\) | −7.33881 | −0.272181 | −0.136091 | − | 0.990696i | \(-0.543454\pi\) | ||||
−0.136091 | + | 0.990696i | \(0.543454\pi\) | |||||||
\(728\) | 3.29397 | 0.122083 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −38.5090 | −1.42528 | ||||||||
\(731\) | −0.643560 | −0.0238029 | ||||||||
\(732\) | 4.69330 | 0.173470 | ||||||||
\(733\) | −47.0217 | −1.73679 | −0.868394 | − | 0.495876i | \(-0.834847\pi\) | ||||
−0.868394 | + | 0.495876i | \(0.834847\pi\) | |||||||
\(734\) | 0.557823 | 0.0205896 | ||||||||
\(735\) | −8.08159 | −0.298094 | ||||||||
\(736\) | −14.2759 | −0.526215 | ||||||||
\(737\) | −1.04837 | −0.0386172 | ||||||||
\(738\) | 14.2495 | 0.524530 | ||||||||
\(739\) | −7.96828 | −0.293118 | −0.146559 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146559 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(740\) | −4.48988 | −0.165051 | ||||||||
\(741\) | 1.55249 | 0.0570323 | ||||||||
\(742\) | 53.3513 | 1.95859 | ||||||||
\(743\) | 32.1751 | 1.18039 | 0.590195 | − | 0.807261i | \(-0.299051\pi\) | ||||
0.590195 | + | 0.807261i | \(0.299051\pi\) | |||||||
\(744\) | −22.5045 | −0.825056 | ||||||||
\(745\) | −33.3877 | −1.22323 | ||||||||
\(746\) | −5.30249 | −0.194138 | ||||||||
\(747\) | −3.88084 | −0.141993 | ||||||||
\(748\) | 0.0395565 | 0.00144633 | ||||||||
\(749\) | −1.32690 | −0.0484840 | ||||||||
\(750\) | −18.4730 | −0.674540 | ||||||||
\(751\) | 18.9490 | 0.691457 | 0.345729 | − | 0.938335i | \(-0.387632\pi\) | ||||
0.345729 | + | 0.938335i | \(0.387632\pi\) | |||||||
\(752\) | 51.9869 | 1.89577 | ||||||||
\(753\) | −2.90309 | −0.105794 | ||||||||
\(754\) | −6.25792 | −0.227900 | ||||||||
\(755\) | 2.23113 | 0.0811991 | ||||||||
\(756\) | −1.93371 | −0.0703283 | ||||||||
\(757\) | −16.7262 | −0.607925 | −0.303963 | − | 0.952684i | \(-0.598310\pi\) | ||||
−0.303963 | + | 0.952684i | \(0.598310\pi\) | |||||||
\(758\) | −22.4137 | −0.814103 | ||||||||
\(759\) | 0.295088 | 0.0107110 | ||||||||
\(760\) | −17.2434 | −0.625485 | ||||||||
\(761\) | 9.47778 | 0.343569 | 0.171785 | − | 0.985135i | \(-0.445047\pi\) | ||||
0.171785 | + | 0.985135i | \(0.445047\pi\) | |||||||
\(762\) | 0.495018 | 0.0179326 | ||||||||
\(763\) | −45.3403 | −1.64143 | ||||||||
\(764\) | 9.77732 | 0.353731 | ||||||||
\(765\) | 2.17104 | 0.0784940 | ||||||||
\(766\) | 28.5871 | 1.03289 | ||||||||
\(767\) | 3.27831 | 0.118373 | ||||||||
\(768\) | −13.0588 | −0.471218 | ||||||||
\(769\) | −39.5360 | −1.42570 | −0.712851 | − | 0.701315i | \(-0.752597\pi\) | ||||
−0.712851 | + | 0.701315i | \(0.752597\pi\) | |||||||
\(770\) | −0.766448 | −0.0276209 | ||||||||
\(771\) | 0.639767 | 0.0230407 | ||||||||
\(772\) | 1.34649 | 0.0484613 | ||||||||
\(773\) | 24.1185 | 0.867481 | 0.433740 | − | 0.901038i | \(-0.357194\pi\) | ||||
0.433740 | + | 0.901038i | \(0.357194\pi\) | |||||||
\(774\) | 1.03582 | 0.0372317 | ||||||||
\(775\) | −2.84312 | −0.102128 | ||||||||
\(776\) | −23.4072 | −0.840270 | ||||||||
\(777\) | 11.4676 | 0.411396 | ||||||||
\(778\) | −34.7492 | −1.24582 | ||||||||
\(779\) | 30.9964 | 1.11056 | ||||||||
\(780\) | −0.568505 | −0.0203557 | ||||||||
\(781\) | −0.178688 | −0.00639396 | ||||||||
\(782\) | 7.09041 | 0.253553 | ||||||||
\(783\) | −8.76824 | −0.313351 | ||||||||
\(784\) | −17.9882 | −0.642434 | ||||||||
\(785\) | 2.17104 | 0.0774876 | ||||||||
\(786\) | 2.83933 | 0.101276 | ||||||||
\(787\) | −22.3996 | −0.798459 | −0.399230 | − | 0.916851i | \(-0.630722\pi\) | ||||
−0.399230 | + | 0.916851i | \(0.630722\pi\) | |||||||
\(788\) | 5.49808 | 0.195861 | ||||||||
\(789\) | −13.8260 | −0.492219 | ||||||||
\(790\) | 22.7728 | 0.810218 | ||||||||
\(791\) | −20.4025 | −0.725429 | ||||||||
\(792\) | 0.151958 | 0.00539959 | ||||||||
\(793\) | −3.52418 | −0.125147 | ||||||||
\(794\) | 27.7358 | 0.984308 | ||||||||
\(795\) | 21.9771 | 0.779448 | ||||||||
\(796\) | −15.0260 | −0.532584 | ||||||||
\(797\) | −7.86697 | −0.278662 | −0.139331 | − | 0.990246i | \(-0.544495\pi\) | ||||
−0.139331 | + | 0.990246i | \(0.544495\pi\) | |||||||
\(798\) | −18.4522 | −0.653202 | ||||||||
\(799\) | −10.7581 | −0.380596 | ||||||||
\(800\) | −0.928751 | −0.0328363 | ||||||||
\(801\) | −12.6880 | −0.448308 | ||||||||
\(802\) | −30.5841 | −1.07996 | ||||||||
\(803\) | 0.738201 | 0.0260505 | ||||||||
\(804\) | 9.24239 | 0.325954 | ||||||||
\(805\) | −31.3178 | −1.10381 | ||||||||
\(806\) | −7.08008 | −0.249385 | ||||||||
\(807\) | −13.1386 | −0.462500 | ||||||||
\(808\) | −10.3720 | −0.364884 | ||||||||
\(809\) | −14.1202 | −0.496441 | −0.248220 | − | 0.968704i | \(-0.579846\pi\) | ||||
−0.248220 | + | 0.968704i | \(0.579846\pi\) | |||||||
\(810\) | −3.49431 | −0.122778 | ||||||||
\(811\) | −44.7232 | −1.57044 | −0.785222 | − | 0.619214i | \(-0.787451\pi\) | ||||
−0.785222 | + | 0.619214i | \(0.787451\pi\) | |||||||
\(812\) | 16.9552 | 0.595012 | ||||||||
\(813\) | −8.33061 | −0.292167 | ||||||||
\(814\) | 0.377565 | 0.0132337 | ||||||||
\(815\) | −34.4318 | −1.20609 | ||||||||
\(816\) | 4.83234 | 0.169166 | ||||||||
\(817\) | 2.25318 | 0.0788288 | ||||||||
\(818\) | −33.3193 | −1.16498 | ||||||||
\(819\) | 1.45201 | 0.0507374 | ||||||||
\(820\) | −11.3505 | −0.396377 | ||||||||
\(821\) | −24.8849 | −0.868488 | −0.434244 | − | 0.900795i | \(-0.642985\pi\) | ||||
−0.434244 | + | 0.900795i | \(0.642985\pi\) | |||||||
\(822\) | 21.7877 | 0.759933 | ||||||||
\(823\) | −4.27302 | −0.148948 | −0.0744741 | − | 0.997223i | \(-0.523728\pi\) | ||||
−0.0744741 | + | 0.997223i | \(0.523728\pi\) | |||||||
\(824\) | −22.4652 | −0.782611 | ||||||||
\(825\) | 0.0191977 | 0.000668376 0 | ||||||||
\(826\) | −38.9645 | −1.35575 | ||||||||
\(827\) | 46.9913 | 1.63405 | 0.817024 | − | 0.576604i | \(-0.195623\pi\) | ||||
0.817024 | + | 0.576604i | \(0.195623\pi\) | |||||||
\(828\) | −2.60148 | −0.0904078 | ||||||||
\(829\) | 12.9630 | 0.450224 | 0.225112 | − | 0.974333i | \(-0.427725\pi\) | ||||
0.225112 | + | 0.974333i | \(0.427725\pi\) | |||||||
\(830\) | 13.5609 | 0.470705 | ||||||||
\(831\) | 13.9593 | 0.484241 | ||||||||
\(832\) | 1.97276 | 0.0683932 | ||||||||
\(833\) | 3.72245 | 0.128975 | ||||||||
\(834\) | −22.4319 | −0.776752 | ||||||||
\(835\) | 5.24273 | 0.181432 | ||||||||
\(836\) | −0.138492 | −0.00478985 | ||||||||
\(837\) | −9.92020 | −0.342892 | ||||||||
\(838\) | −33.7539 | −1.16601 | ||||||||
\(839\) | −37.1402 | −1.28222 | −0.641111 | − | 0.767448i | \(-0.721526\pi\) | ||||
−0.641111 | + | 0.767448i | \(0.721526\pi\) | |||||||
\(840\) | −16.1274 | −0.556447 | ||||||||
\(841\) | 47.8821 | 1.65111 | ||||||||
\(842\) | 52.1263 | 1.79639 | ||||||||
\(843\) | 26.8581 | 0.925041 | ||||||||
\(844\) | 11.2435 | 0.387017 | ||||||||
\(845\) | −27.7966 | −0.956232 | ||||||||
\(846\) | 17.3154 | 0.595315 | ||||||||
\(847\) | −36.0050 | −1.23715 | ||||||||
\(848\) | 48.9171 | 1.67982 | ||||||||
\(849\) | 4.53638 | 0.155688 | ||||||||
\(850\) | 0.461284 | 0.0158219 | ||||||||
\(851\) | 15.4277 | 0.528854 | ||||||||
\(852\) | 1.57531 | 0.0539692 | ||||||||
\(853\) | −52.0333 | −1.78159 | −0.890793 | − | 0.454409i | \(-0.849850\pi\) | ||||
−0.890793 | + | 0.454409i | \(0.849850\pi\) | |||||||
\(854\) | 41.8867 | 1.43333 | ||||||||
\(855\) | −7.60106 | −0.259951 | ||||||||
\(856\) | −0.919267 | −0.0314199 | ||||||||
\(857\) | 14.3706 | 0.490890 | 0.245445 | − | 0.969411i | \(-0.421066\pi\) | ||||
0.245445 | + | 0.969411i | \(0.421066\pi\) | |||||||
\(858\) | 0.0478070 | 0.00163210 | ||||||||
\(859\) | 31.8322 | 1.08610 | 0.543050 | − | 0.839700i | \(-0.317269\pi\) | ||||
0.543050 | + | 0.839700i | \(0.317269\pi\) | |||||||
\(860\) | −0.825088 | −0.0281353 | ||||||||
\(861\) | 28.9902 | 0.987984 | ||||||||
\(862\) | −26.6368 | −0.907253 | ||||||||
\(863\) | 8.00074 | 0.272348 | 0.136174 | − | 0.990685i | \(-0.456519\pi\) | ||||
0.136174 | + | 0.990685i | \(0.456519\pi\) | |||||||
\(864\) | −3.24060 | −0.110247 | ||||||||
\(865\) | 9.59562 | 0.326261 | ||||||||
\(866\) | 27.4089 | 0.931394 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 19.1828 | 0.651106 | ||||||||
\(869\) | −0.436544 | −0.0148087 | ||||||||
\(870\) | 30.6390 | 1.03876 | ||||||||
\(871\) | −6.94006 | −0.235155 | ||||||||
\(872\) | −31.4114 | −1.06372 | ||||||||
\(873\) | −10.3181 | −0.349215 | ||||||||
\(874\) | −24.8244 | −0.839698 | ||||||||
\(875\) | −37.5829 | −1.27053 | ||||||||
\(876\) | −6.50795 | −0.219883 | ||||||||
\(877\) | −31.0189 | −1.04743 | −0.523717 | − | 0.851892i | \(-0.675455\pi\) | ||||
−0.523717 | + | 0.851892i | \(0.675455\pi\) | |||||||
\(878\) | −33.1875 | −1.12002 | ||||||||
\(879\) | 11.6603 | 0.393293 | ||||||||
\(880\) | −0.702746 | −0.0236896 | ||||||||
\(881\) | −6.54277 | −0.220432 | −0.110216 | − | 0.993908i | \(-0.535154\pi\) | ||||
−0.110216 | + | 0.993908i | \(0.535154\pi\) | |||||||
\(882\) | −5.99134 | −0.201739 | ||||||||
\(883\) | 0.496200 | 0.0166985 | 0.00834923 | − | 0.999965i | \(-0.497342\pi\) | ||||
0.00834923 | + | 0.999965i | \(0.497342\pi\) | |||||||
\(884\) | 0.261859 | 0.00880726 | ||||||||
\(885\) | −16.0507 | −0.539539 | ||||||||
\(886\) | 22.3191 | 0.749825 | ||||||||
\(887\) | 16.5058 | 0.554211 | 0.277105 | − | 0.960840i | \(-0.410625\pi\) | ||||
0.277105 | + | 0.960840i | \(0.410625\pi\) | |||||||
\(888\) | 7.94462 | 0.266604 | ||||||||
\(889\) | 1.00710 | 0.0337771 | ||||||||
\(890\) | 44.3358 | 1.48614 | ||||||||
\(891\) | 0.0669844 | 0.00224406 | ||||||||
\(892\) | 16.5245 | 0.553282 | ||||||||
\(893\) | 37.6655 | 1.26043 | ||||||||
\(894\) | −24.7522 | −0.827838 | ||||||||
\(895\) | 37.3871 | 1.24971 | ||||||||
\(896\) | −44.6701 | −1.49232 | ||||||||
\(897\) | 1.95344 | 0.0652235 | ||||||||
\(898\) | 35.5152 | 1.18516 | ||||||||
\(899\) | 86.9827 | 2.90104 | ||||||||
\(900\) | −0.169246 | −0.00564153 | ||||||||
\(901\) | −10.1229 | −0.337242 | ||||||||
\(902\) | 0.954493 | 0.0317811 | ||||||||
\(903\) | 2.10735 | 0.0701281 | ||||||||
\(904\) | −14.1347 | −0.470112 | ||||||||
\(905\) | 27.1179 | 0.901428 | ||||||||
\(906\) | 1.65406 | 0.0549526 | ||||||||
\(907\) | 37.1504 | 1.23356 | 0.616779 | − | 0.787136i | \(-0.288437\pi\) | ||||
0.616779 | + | 0.787136i | \(0.288437\pi\) | |||||||
\(908\) | −9.50237 | −0.315347 | ||||||||
\(909\) | −4.57205 | −0.151645 | ||||||||
\(910\) | −5.07378 | −0.168194 | ||||||||
\(911\) | −11.7297 | −0.388622 | −0.194311 | − | 0.980940i | \(-0.562247\pi\) | ||||
−0.194311 | + | 0.980940i | \(0.562247\pi\) | |||||||
\(912\) | −16.9186 | −0.560231 | ||||||||
\(913\) | −0.259956 | −0.00860329 | ||||||||
\(914\) | −60.3347 | −1.99569 | ||||||||
\(915\) | 17.2545 | 0.570416 | ||||||||
\(916\) | 12.0087 | 0.396778 | ||||||||
\(917\) | 5.77655 | 0.190759 | ||||||||
\(918\) | 1.60951 | 0.0531219 | ||||||||
\(919\) | 21.8157 | 0.719634 | 0.359817 | − | 0.933023i | \(-0.382839\pi\) | ||||
0.359817 | + | 0.933023i | \(0.382839\pi\) | |||||||
\(920\) | −21.6967 | −0.715319 | ||||||||
\(921\) | −15.3874 | −0.507033 | ||||||||
\(922\) | −26.0848 | −0.859057 | ||||||||
\(923\) | −1.18289 | −0.0389353 | ||||||||
\(924\) | −0.129528 | −0.00426117 | ||||||||
\(925\) | 1.00369 | 0.0330010 | ||||||||
\(926\) | 8.41092 | 0.276400 | ||||||||
\(927\) | −9.90284 | −0.325252 | ||||||||
\(928\) | 28.4144 | 0.932747 | ||||||||
\(929\) | 41.0704 | 1.34747 | 0.673737 | − | 0.738971i | \(-0.264688\pi\) | ||||
0.673737 | + | 0.738971i | \(0.264688\pi\) | |||||||
\(930\) | 34.6643 | 1.13669 | ||||||||
\(931\) | −13.0328 | −0.427131 | ||||||||
\(932\) | −1.10415 | −0.0361678 | ||||||||
\(933\) | −8.52143 | −0.278979 | ||||||||
\(934\) | 1.38211 | 0.0452239 | ||||||||
\(935\) | 0.145426 | 0.00475593 | ||||||||
\(936\) | 1.00594 | 0.0328802 | ||||||||
\(937\) | −18.3496 | −0.599456 | −0.299728 | − | 0.954025i | \(-0.596896\pi\) | ||||
−0.299728 | + | 0.954025i | \(0.596896\pi\) | |||||||
\(938\) | 82.4863 | 2.69327 | ||||||||
\(939\) | 16.7701 | 0.547270 | ||||||||
\(940\) | −13.7927 | −0.449867 | ||||||||
\(941\) | 1.36282 | 0.0444267 | 0.0222133 | − | 0.999753i | \(-0.492929\pi\) | ||||
0.0222133 | + | 0.999753i | \(0.492929\pi\) | |||||||
\(942\) | 1.60951 | 0.0524408 | ||||||||
\(943\) | 39.0015 | 1.27006 | ||||||||
\(944\) | −35.7260 | −1.16278 | ||||||||
\(945\) | −7.10909 | −0.231259 | ||||||||
\(946\) | 0.0693837 | 0.00225586 | ||||||||
\(947\) | 8.20840 | 0.266737 | 0.133369 | − | 0.991067i | \(-0.457421\pi\) | ||||
0.133369 | + | 0.991067i | \(0.457421\pi\) | |||||||
\(948\) | 3.84856 | 0.124995 | ||||||||
\(949\) | 4.88679 | 0.158632 | ||||||||
\(950\) | −1.61501 | −0.0523979 | ||||||||
\(951\) | −33.4976 | −1.08624 | ||||||||
\(952\) | 7.42842 | 0.240757 | ||||||||
\(953\) | −58.9189 | −1.90857 | −0.954284 | − | 0.298900i | \(-0.903380\pi\) | ||||
−0.954284 | + | 0.298900i | \(0.903380\pi\) | |||||||
\(954\) | 16.2929 | 0.527502 | ||||||||
\(955\) | 35.9454 | 1.16316 | ||||||||
\(956\) | 6.09738 | 0.197203 | ||||||||
\(957\) | −0.587336 | −0.0189859 | ||||||||
\(958\) | 27.1796 | 0.878132 | ||||||||
\(959\) | 44.3265 | 1.43138 | ||||||||
\(960\) | −9.65870 | −0.311733 | ||||||||
\(961\) | 67.4104 | 2.17453 | ||||||||
\(962\) | 2.49943 | 0.0805849 | ||||||||
\(963\) | −0.405221 | −0.0130581 | ||||||||
\(964\) | −7.91414 | −0.254897 | ||||||||
\(965\) | 4.95024 | 0.159354 | ||||||||
\(966\) | −23.2177 | −0.747016 | ||||||||
\(967\) | 25.3510 | 0.815233 | 0.407616 | − | 0.913153i | \(-0.366360\pi\) | ||||
0.407616 | + | 0.913153i | \(0.366360\pi\) | |||||||
\(968\) | −24.9439 | −0.801729 | ||||||||
\(969\) | 3.50112 | 0.112472 | ||||||||
\(970\) | 36.0547 | 1.15765 | ||||||||
\(971\) | 4.92467 | 0.158040 | 0.0790201 | − | 0.996873i | \(-0.474821\pi\) | ||||
0.0790201 | + | 0.996873i | \(0.474821\pi\) | |||||||
\(972\) | −0.590533 | −0.0189414 | ||||||||
\(973\) | −45.6371 | −1.46306 | ||||||||
\(974\) | −13.2048 | −0.423110 | ||||||||
\(975\) | 0.127086 | 0.00407000 | ||||||||
\(976\) | 38.4054 | 1.22933 | ||||||||
\(977\) | 8.17517 | 0.261547 | 0.130773 | − | 0.991412i | \(-0.458254\pi\) | ||||
0.130773 | + | 0.991412i | \(0.458254\pi\) | |||||||
\(978\) | −25.5262 | −0.816239 | ||||||||
\(979\) | −0.849897 | −0.0271628 | ||||||||
\(980\) | 4.77244 | 0.152450 | ||||||||
\(981\) | −13.8464 | −0.442082 | ||||||||
\(982\) | 17.0431 | 0.543868 | ||||||||
\(983\) | −14.0328 | −0.447576 | −0.223788 | − | 0.974638i | \(-0.571842\pi\) | ||||
−0.223788 | + | 0.974638i | \(0.571842\pi\) | |||||||
\(984\) | 20.0842 | 0.640260 | ||||||||
\(985\) | 20.2132 | 0.644045 | ||||||||
\(986\) | −14.1126 | −0.449437 | ||||||||
\(987\) | 35.2277 | 1.12131 | ||||||||
\(988\) | −0.916799 | −0.0291673 | ||||||||
\(989\) | 2.83509 | 0.0901505 | ||||||||
\(990\) | −0.234065 | −0.00743906 | ||||||||
\(991\) | −16.2156 | −0.515105 | −0.257553 | − | 0.966264i | \(-0.582916\pi\) | ||||
−0.257553 | + | 0.966264i | \(0.582916\pi\) | |||||||
\(992\) | 32.1474 | 1.02068 | ||||||||
\(993\) | 17.3634 | 0.551011 | ||||||||
\(994\) | 14.0593 | 0.445933 | ||||||||
\(995\) | −55.2418 | −1.75128 | ||||||||
\(996\) | 2.29177 | 0.0726174 | ||||||||
\(997\) | 34.4790 | 1.09196 | 0.545980 | − | 0.837798i | \(-0.316157\pi\) | ||||
0.545980 | + | 0.837798i | \(0.316157\pi\) | |||||||
\(998\) | −68.3242 | −2.16277 | ||||||||
\(999\) | 3.50206 | 0.110800 |
(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 | 8007.2.a.c.1.11 | ✓ | 39 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.c.1.11 | ✓ | 39 | 1.1 | even | 1 | trivial |