Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.14716 | −1.81701 | −0.908506 | − | 0.417873i | \(-0.862776\pi\) | ||||
−0.908506 | + | 0.417873i | \(0.862776\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.17339 | −0.971971 | −0.485986 | − | 0.873967i | \(-0.661539\pi\) | ||||
−0.485986 | + | 0.873967i | \(0.661539\pi\) | |||||||
\(6\) | 3.14716 | 1.28482 | ||||||||
\(7\) | 4.77090 | 1.80323 | 0.901616 | − | 0.432537i | \(-0.142382\pi\) | ||||
0.901616 | + | 0.432537i | \(0.142382\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.90459 | 2.30153 | ||||||||
\(10\) | 2.17339 | 0.687287 | ||||||||
\(11\) | 0.464609 | 0.140085 | 0.0700425 | − | 0.997544i | \(-0.477687\pi\) | ||||
0.0700425 | + | 0.997544i | \(0.477687\pi\) | |||||||
\(12\) | −3.14716 | −0.908506 | ||||||||
\(13\) | −3.54045 | −0.981943 | −0.490972 | − | 0.871176i | \(-0.663358\pi\) | ||||
−0.490972 | + | 0.871176i | \(0.663358\pi\) | |||||||
\(14\) | −4.77090 | −1.27508 | ||||||||
\(15\) | 6.84001 | 1.76608 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.17248 | 0.526903 | 0.263452 | − | 0.964673i | \(-0.415139\pi\) | ||||
0.263452 | + | 0.964673i | \(0.415139\pi\) | |||||||
\(18\) | −6.90459 | −1.62743 | ||||||||
\(19\) | −7.81420 | −1.79270 | −0.896350 | − | 0.443347i | \(-0.853791\pi\) | ||||
−0.896350 | + | 0.443347i | \(0.853791\pi\) | |||||||
\(20\) | −2.17339 | −0.485986 | ||||||||
\(21\) | −15.0148 | −3.27649 | ||||||||
\(22\) | −0.464609 | −0.0990551 | ||||||||
\(23\) | −2.67609 | −0.558004 | −0.279002 | − | 0.960290i | \(-0.590004\pi\) | ||||
−0.279002 | + | 0.960290i | \(0.590004\pi\) | |||||||
\(24\) | 3.14716 | 0.642410 | ||||||||
\(25\) | −0.276360 | −0.0552720 | ||||||||
\(26\) | 3.54045 | 0.694339 | ||||||||
\(27\) | −12.2884 | −2.36489 | ||||||||
\(28\) | 4.77090 | 0.901616 | ||||||||
\(29\) | −4.66474 | −0.866220 | −0.433110 | − | 0.901341i | \(-0.642584\pi\) | ||||
−0.433110 | + | 0.901341i | \(0.642584\pi\) | |||||||
\(30\) | −6.84001 | −1.24881 | ||||||||
\(31\) | −2.75066 | −0.494032 | −0.247016 | − | 0.969011i | \(-0.579450\pi\) | ||||
−0.247016 | + | 0.969011i | \(0.579450\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.46220 | −0.254536 | ||||||||
\(34\) | −2.17248 | −0.372577 | ||||||||
\(35\) | −10.3691 | −1.75269 | ||||||||
\(36\) | 6.90459 | 1.15076 | ||||||||
\(37\) | −3.49564 | −0.574679 | −0.287340 | − | 0.957829i | \(-0.592771\pi\) | ||||
−0.287340 | + | 0.957829i | \(0.592771\pi\) | |||||||
\(38\) | 7.81420 | 1.26763 | ||||||||
\(39\) | 11.1423 | 1.78420 | ||||||||
\(40\) | 2.17339 | 0.343644 | ||||||||
\(41\) | 0.752133 | 0.117463 | 0.0587317 | − | 0.998274i | \(-0.481294\pi\) | ||||
0.0587317 | + | 0.998274i | \(0.481294\pi\) | |||||||
\(42\) | 15.0148 | 2.31683 | ||||||||
\(43\) | 0.446218 | 0.0680476 | 0.0340238 | − | 0.999421i | \(-0.489168\pi\) | ||||
0.0340238 | + | 0.999421i | \(0.489168\pi\) | |||||||
\(44\) | 0.464609 | 0.0700425 | ||||||||
\(45\) | −15.0064 | −2.23702 | ||||||||
\(46\) | 2.67609 | 0.394569 | ||||||||
\(47\) | 6.33329 | 0.923805 | 0.461903 | − | 0.886931i | \(-0.347167\pi\) | ||||
0.461903 | + | 0.886931i | \(0.347167\pi\) | |||||||
\(48\) | −3.14716 | −0.454253 | ||||||||
\(49\) | 15.7615 | 2.25165 | ||||||||
\(50\) | 0.276360 | 0.0390832 | ||||||||
\(51\) | −6.83713 | −0.957389 | ||||||||
\(52\) | −3.54045 | −0.490972 | ||||||||
\(53\) | −5.24165 | −0.719996 | −0.359998 | − | 0.932953i | \(-0.617223\pi\) | ||||
−0.359998 | + | 0.932953i | \(0.617223\pi\) | |||||||
\(54\) | 12.2884 | 1.67223 | ||||||||
\(55\) | −1.00978 | −0.136159 | ||||||||
\(56\) | −4.77090 | −0.637539 | ||||||||
\(57\) | 24.5925 | 3.25736 | ||||||||
\(58\) | 4.66474 | 0.612510 | ||||||||
\(59\) | 12.6820 | 1.65105 | 0.825525 | − | 0.564365i | \(-0.190879\pi\) | ||||
0.825525 | + | 0.564365i | \(0.190879\pi\) | |||||||
\(60\) | 6.84001 | 0.883041 | ||||||||
\(61\) | −6.29902 | −0.806507 | −0.403254 | − | 0.915088i | \(-0.632121\pi\) | ||||
−0.403254 | + | 0.915088i | \(0.632121\pi\) | |||||||
\(62\) | 2.75066 | 0.349334 | ||||||||
\(63\) | 32.9411 | 4.15019 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.69478 | 0.954421 | ||||||||
\(66\) | 1.46220 | 0.179984 | ||||||||
\(67\) | −7.37205 | −0.900639 | −0.450320 | − | 0.892867i | \(-0.648690\pi\) | ||||
−0.450320 | + | 0.892867i | \(0.648690\pi\) | |||||||
\(68\) | 2.17248 | 0.263452 | ||||||||
\(69\) | 8.42209 | 1.01390 | ||||||||
\(70\) | 10.3691 | 1.23934 | ||||||||
\(71\) | −10.7392 | −1.27451 | −0.637257 | − | 0.770652i | \(-0.719931\pi\) | ||||
−0.637257 | + | 0.770652i | \(0.719931\pi\) | |||||||
\(72\) | −6.90459 | −0.813714 | ||||||||
\(73\) | 14.9326 | 1.74773 | 0.873866 | − | 0.486167i | \(-0.161605\pi\) | ||||
0.873866 | + | 0.486167i | \(0.161605\pi\) | |||||||
\(74\) | 3.49564 | 0.406360 | ||||||||
\(75\) | 0.869748 | 0.100430 | ||||||||
\(76\) | −7.81420 | −0.896350 | ||||||||
\(77\) | 2.21661 | 0.252606 | ||||||||
\(78\) | −11.1423 | −1.26162 | ||||||||
\(79\) | −2.14485 | −0.241314 | −0.120657 | − | 0.992694i | \(-0.538500\pi\) | ||||
−0.120657 | + | 0.992694i | \(0.538500\pi\) | |||||||
\(80\) | −2.17339 | −0.242993 | ||||||||
\(81\) | 17.9596 | 1.99551 | ||||||||
\(82\) | −0.752133 | −0.0830592 | ||||||||
\(83\) | −1.26263 | −0.138592 | −0.0692960 | − | 0.997596i | \(-0.522075\pi\) | ||||
−0.0692960 | + | 0.997596i | \(0.522075\pi\) | |||||||
\(84\) | −15.0148 | −1.63825 | ||||||||
\(85\) | −4.72165 | −0.512135 | ||||||||
\(86\) | −0.446218 | −0.0481169 | ||||||||
\(87\) | 14.6807 | 1.57393 | ||||||||
\(88\) | −0.464609 | −0.0495275 | ||||||||
\(89\) | 10.3386 | 1.09589 | 0.547945 | − | 0.836514i | \(-0.315410\pi\) | ||||
0.547945 | + | 0.836514i | \(0.315410\pi\) | |||||||
\(90\) | 15.0064 | 1.58181 | ||||||||
\(91\) | −16.8911 | −1.77067 | ||||||||
\(92\) | −2.67609 | −0.279002 | ||||||||
\(93\) | 8.65674 | 0.897662 | ||||||||
\(94\) | −6.33329 | −0.653229 | ||||||||
\(95\) | 16.9833 | 1.74245 | ||||||||
\(96\) | 3.14716 | 0.321205 | ||||||||
\(97\) | −5.61370 | −0.569984 | −0.284992 | − | 0.958530i | \(-0.591991\pi\) | ||||
−0.284992 | + | 0.958530i | \(0.591991\pi\) | |||||||
\(98\) | −15.7615 | −1.59215 | ||||||||
\(99\) | 3.20794 | 0.322410 | ||||||||
\(100\) | −0.276360 | −0.0276360 | ||||||||
\(101\) | 4.91550 | 0.489110 | 0.244555 | − | 0.969635i | \(-0.421358\pi\) | ||||
0.244555 | + | 0.969635i | \(0.421358\pi\) | |||||||
\(102\) | 6.83713 | 0.676976 | ||||||||
\(103\) | −13.7917 | −1.35894 | −0.679468 | − | 0.733705i | \(-0.737789\pi\) | ||||
−0.679468 | + | 0.733705i | \(0.737789\pi\) | |||||||
\(104\) | 3.54045 | 0.347169 | ||||||||
\(105\) | 32.6330 | 3.18466 | ||||||||
\(106\) | 5.24165 | 0.509114 | ||||||||
\(107\) | 14.6420 | 1.41550 | 0.707750 | − | 0.706463i | \(-0.249710\pi\) | ||||
0.707750 | + | 0.706463i | \(0.249710\pi\) | |||||||
\(108\) | −12.2884 | −1.18245 | ||||||||
\(109\) | −11.7987 | −1.13011 | −0.565057 | − | 0.825052i | \(-0.691146\pi\) | ||||
−0.565057 | + | 0.825052i | \(0.691146\pi\) | |||||||
\(110\) | 1.00978 | 0.0962787 | ||||||||
\(111\) | 11.0013 | 1.04420 | ||||||||
\(112\) | 4.77090 | 0.450808 | ||||||||
\(113\) | −16.7188 | −1.57277 | −0.786387 | − | 0.617735i | \(-0.788051\pi\) | ||||
−0.786387 | + | 0.617735i | \(0.788051\pi\) | |||||||
\(114\) | −24.5925 | −2.30330 | ||||||||
\(115\) | 5.81621 | 0.542364 | ||||||||
\(116\) | −4.66474 | −0.433110 | ||||||||
\(117\) | −24.4453 | −2.25997 | ||||||||
\(118\) | −12.6820 | −1.16747 | ||||||||
\(119\) | 10.3647 | 0.950129 | ||||||||
\(120\) | −6.84001 | −0.624404 | ||||||||
\(121\) | −10.7841 | −0.980376 | ||||||||
\(122\) | 6.29902 | 0.570287 | ||||||||
\(123\) | −2.36708 | −0.213432 | ||||||||
\(124\) | −2.75066 | −0.247016 | ||||||||
\(125\) | 11.4676 | 1.02569 | ||||||||
\(126\) | −32.9411 | −2.93463 | ||||||||
\(127\) | −6.91452 | −0.613564 | −0.306782 | − | 0.951780i | \(-0.599252\pi\) | ||||
−0.306782 | + | 0.951780i | \(0.599252\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.40432 | −0.123643 | ||||||||
\(130\) | −7.69478 | −0.674877 | ||||||||
\(131\) | 2.61568 | 0.228533 | 0.114267 | − | 0.993450i | \(-0.463548\pi\) | ||||
0.114267 | + | 0.993450i | \(0.463548\pi\) | |||||||
\(132\) | −1.46220 | −0.127268 | ||||||||
\(133\) | −37.2808 | −3.23265 | ||||||||
\(134\) | 7.37205 | 0.636848 | ||||||||
\(135\) | 26.7074 | 2.29861 | ||||||||
\(136\) | −2.17248 | −0.186288 | ||||||||
\(137\) | −2.09352 | −0.178861 | −0.0894307 | − | 0.995993i | \(-0.528505\pi\) | ||||
−0.0894307 | + | 0.995993i | \(0.528505\pi\) | |||||||
\(138\) | −8.42209 | −0.716936 | ||||||||
\(139\) | 0.169351 | 0.0143642 | 0.00718208 | − | 0.999974i | \(-0.497714\pi\) | ||||
0.00718208 | + | 0.999974i | \(0.497714\pi\) | |||||||
\(140\) | −10.3691 | −0.876345 | ||||||||
\(141\) | −19.9318 | −1.67856 | ||||||||
\(142\) | 10.7392 | 0.901217 | ||||||||
\(143\) | −1.64493 | −0.137556 | ||||||||
\(144\) | 6.90459 | 0.575382 | ||||||||
\(145\) | 10.1383 | 0.841941 | ||||||||
\(146\) | −14.9326 | −1.23583 | ||||||||
\(147\) | −49.6040 | −4.09127 | ||||||||
\(148\) | −3.49564 | −0.287340 | ||||||||
\(149\) | 16.4336 | 1.34629 | 0.673145 | − | 0.739511i | \(-0.264943\pi\) | ||||
0.673145 | + | 0.739511i | \(0.264943\pi\) | |||||||
\(150\) | −0.869748 | −0.0710147 | ||||||||
\(151\) | 8.57860 | 0.698116 | 0.349058 | − | 0.937101i | \(-0.386502\pi\) | ||||
0.349058 | + | 0.937101i | \(0.386502\pi\) | |||||||
\(152\) | 7.81420 | 0.633815 | ||||||||
\(153\) | 15.0001 | 1.21268 | ||||||||
\(154\) | −2.21661 | −0.178619 | ||||||||
\(155\) | 5.97826 | 0.480185 | ||||||||
\(156\) | 11.1423 | 0.892101 | ||||||||
\(157\) | −10.6449 | −0.849558 | −0.424779 | − | 0.905297i | \(-0.639648\pi\) | ||||
−0.424779 | + | 0.905297i | \(0.639648\pi\) | |||||||
\(158\) | 2.14485 | 0.170635 | ||||||||
\(159\) | 16.4963 | 1.30824 | ||||||||
\(160\) | 2.17339 | 0.171822 | ||||||||
\(161\) | −12.7674 | −1.00621 | ||||||||
\(162\) | −17.9596 | −1.41104 | ||||||||
\(163\) | 8.77566 | 0.687363 | 0.343681 | − | 0.939086i | \(-0.388326\pi\) | ||||
0.343681 | + | 0.939086i | \(0.388326\pi\) | |||||||
\(164\) | 0.752133 | 0.0587317 | ||||||||
\(165\) | 3.17793 | 0.247402 | ||||||||
\(166\) | 1.26263 | 0.0979994 | ||||||||
\(167\) | −14.8025 | −1.14545 | −0.572725 | − | 0.819748i | \(-0.694114\pi\) | ||||
−0.572725 | + | 0.819748i | \(0.694114\pi\) | |||||||
\(168\) | 15.0148 | 1.15842 | ||||||||
\(169\) | −0.465237 | −0.0357874 | ||||||||
\(170\) | 4.72165 | 0.362134 | ||||||||
\(171\) | −53.9538 | −4.12595 | ||||||||
\(172\) | 0.446218 | 0.0340238 | ||||||||
\(173\) | 11.2411 | 0.854648 | 0.427324 | − | 0.904099i | \(-0.359456\pi\) | ||||
0.427324 | + | 0.904099i | \(0.359456\pi\) | |||||||
\(174\) | −14.6807 | −1.11294 | ||||||||
\(175\) | −1.31849 | −0.0996683 | ||||||||
\(176\) | 0.464609 | 0.0350213 | ||||||||
\(177\) | −39.9121 | −2.99998 | ||||||||
\(178\) | −10.3386 | −0.774912 | ||||||||
\(179\) | −8.63646 | −0.645519 | −0.322760 | − | 0.946481i | \(-0.604611\pi\) | ||||
−0.322760 | + | 0.946481i | \(0.604611\pi\) | |||||||
\(180\) | −15.0064 | −1.11851 | ||||||||
\(181\) | 9.03712 | 0.671724 | 0.335862 | − | 0.941911i | \(-0.390972\pi\) | ||||
0.335862 | + | 0.941911i | \(0.390972\pi\) | |||||||
\(182\) | 16.8911 | 1.25205 | ||||||||
\(183\) | 19.8240 | 1.46543 | ||||||||
\(184\) | 2.67609 | 0.197284 | ||||||||
\(185\) | 7.59740 | 0.558572 | ||||||||
\(186\) | −8.65674 | −0.634743 | ||||||||
\(187\) | 1.00935 | 0.0738113 | ||||||||
\(188\) | 6.33329 | 0.461903 | ||||||||
\(189\) | −58.6265 | −4.26445 | ||||||||
\(190\) | −16.9833 | −1.23210 | ||||||||
\(191\) | −9.35417 | −0.676844 | −0.338422 | − | 0.940994i | \(-0.609893\pi\) | ||||
−0.338422 | + | 0.940994i | \(0.609893\pi\) | |||||||
\(192\) | −3.14716 | −0.227126 | ||||||||
\(193\) | −4.91824 | −0.354023 | −0.177012 | − | 0.984209i | \(-0.556643\pi\) | ||||
−0.177012 | + | 0.984209i | \(0.556643\pi\) | |||||||
\(194\) | 5.61370 | 0.403040 | ||||||||
\(195\) | −24.2167 | −1.73419 | ||||||||
\(196\) | 15.7615 | 1.12582 | ||||||||
\(197\) | 14.7015 | 1.04744 | 0.523718 | − | 0.851892i | \(-0.324544\pi\) | ||||
0.523718 | + | 0.851892i | \(0.324544\pi\) | |||||||
\(198\) | −3.20794 | −0.227978 | ||||||||
\(199\) | 10.5778 | 0.749844 | 0.374922 | − | 0.927056i | \(-0.377670\pi\) | ||||
0.374922 | + | 0.927056i | \(0.377670\pi\) | |||||||
\(200\) | 0.276360 | 0.0195416 | ||||||||
\(201\) | 23.2010 | 1.63647 | ||||||||
\(202\) | −4.91550 | −0.345853 | ||||||||
\(203\) | −22.2550 | −1.56200 | ||||||||
\(204\) | −6.83713 | −0.478695 | ||||||||
\(205\) | −1.63468 | −0.114171 | ||||||||
\(206\) | 13.7917 | 0.960913 | ||||||||
\(207\) | −18.4773 | −1.28426 | ||||||||
\(208\) | −3.54045 | −0.245486 | ||||||||
\(209\) | −3.63055 | −0.251130 | ||||||||
\(210\) | −32.6330 | −2.25189 | ||||||||
\(211\) | −10.8499 | −0.746937 | −0.373469 | − | 0.927643i | \(-0.621832\pi\) | ||||
−0.373469 | + | 0.927643i | \(0.621832\pi\) | |||||||
\(212\) | −5.24165 | −0.359998 | ||||||||
\(213\) | 33.7981 | 2.31581 | ||||||||
\(214\) | −14.6420 | −1.00091 | ||||||||
\(215\) | −0.969807 | −0.0661403 | ||||||||
\(216\) | 12.2884 | 0.836116 | ||||||||
\(217\) | −13.1231 | −0.890855 | ||||||||
\(218\) | 11.7987 | 0.799111 | ||||||||
\(219\) | −46.9953 | −3.17565 | ||||||||
\(220\) | −1.00978 | −0.0680793 | ||||||||
\(221\) | −7.69154 | −0.517389 | ||||||||
\(222\) | −11.0013 | −0.738360 | ||||||||
\(223\) | 22.6580 | 1.51729 | 0.758646 | − | 0.651503i | \(-0.225861\pi\) | ||||
0.758646 | + | 0.651503i | \(0.225861\pi\) | |||||||
\(224\) | −4.77090 | −0.318769 | ||||||||
\(225\) | −1.90815 | −0.127210 | ||||||||
\(226\) | 16.7188 | 1.11212 | ||||||||
\(227\) | 7.21310 | 0.478750 | 0.239375 | − | 0.970927i | \(-0.423057\pi\) | ||||
0.239375 | + | 0.970927i | \(0.423057\pi\) | |||||||
\(228\) | 24.5925 | 1.62868 | ||||||||
\(229\) | 22.7121 | 1.50086 | 0.750430 | − | 0.660950i | \(-0.229847\pi\) | ||||
0.750430 | + | 0.660950i | \(0.229847\pi\) | |||||||
\(230\) | −5.81621 | −0.383509 | ||||||||
\(231\) | −6.97601 | −0.458988 | ||||||||
\(232\) | 4.66474 | 0.306255 | ||||||||
\(233\) | 3.14012 | 0.205716 | 0.102858 | − | 0.994696i | \(-0.467201\pi\) | ||||
0.102858 | + | 0.994696i | \(0.467201\pi\) | |||||||
\(234\) | 24.4453 | 1.59804 | ||||||||
\(235\) | −13.7647 | −0.897912 | ||||||||
\(236\) | 12.6820 | 0.825525 | ||||||||
\(237\) | 6.75016 | 0.438470 | ||||||||
\(238\) | −10.3647 | −0.671843 | ||||||||
\(239\) | 16.9961 | 1.09939 | 0.549694 | − | 0.835366i | \(-0.314744\pi\) | ||||
0.549694 | + | 0.835366i | \(0.314744\pi\) | |||||||
\(240\) | 6.84001 | 0.441521 | ||||||||
\(241\) | −23.5304 | −1.51573 | −0.757863 | − | 0.652414i | \(-0.773756\pi\) | ||||
−0.757863 | + | 0.652414i | \(0.773756\pi\) | |||||||
\(242\) | 10.7841 | 0.693231 | ||||||||
\(243\) | −19.6566 | −1.26097 | ||||||||
\(244\) | −6.29902 | −0.403254 | ||||||||
\(245\) | −34.2560 | −2.18853 | ||||||||
\(246\) | 2.36708 | 0.150919 | ||||||||
\(247\) | 27.6658 | 1.76033 | ||||||||
\(248\) | 2.75066 | 0.174667 | ||||||||
\(249\) | 3.97370 | 0.251823 | ||||||||
\(250\) | −11.4676 | −0.725275 | ||||||||
\(251\) | −1.14462 | −0.0722479 | −0.0361239 | − | 0.999347i | \(-0.511501\pi\) | ||||
−0.0361239 | + | 0.999347i | \(0.511501\pi\) | |||||||
\(252\) | 32.9411 | 2.07510 | ||||||||
\(253\) | −1.24334 | −0.0781680 | ||||||||
\(254\) | 6.91452 | 0.433855 | ||||||||
\(255\) | 14.8598 | 0.930555 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.7954 | 0.985288 | 0.492644 | − | 0.870231i | \(-0.336031\pi\) | ||||
0.492644 | + | 0.870231i | \(0.336031\pi\) | |||||||
\(258\) | 1.40432 | 0.0874290 | ||||||||
\(259\) | −16.6774 | −1.03628 | ||||||||
\(260\) | 7.69478 | 0.477210 | ||||||||
\(261\) | −32.2081 | −1.99363 | ||||||||
\(262\) | −2.61568 | −0.161597 | ||||||||
\(263\) | −4.88652 | −0.301316 | −0.150658 | − | 0.988586i | \(-0.548139\pi\) | ||||
−0.150658 | + | 0.988586i | \(0.548139\pi\) | |||||||
\(264\) | 1.46220 | 0.0899921 | ||||||||
\(265\) | 11.3922 | 0.699816 | ||||||||
\(266\) | 37.2808 | 2.28583 | ||||||||
\(267\) | −32.5372 | −1.99125 | ||||||||
\(268\) | −7.37205 | −0.450320 | ||||||||
\(269\) | 5.45781 | 0.332769 | 0.166384 | − | 0.986061i | \(-0.446791\pi\) | ||||
0.166384 | + | 0.986061i | \(0.446791\pi\) | |||||||
\(270\) | −26.7074 | −1.62536 | ||||||||
\(271\) | −2.93812 | −0.178478 | −0.0892391 | − | 0.996010i | \(-0.528444\pi\) | ||||
−0.0892391 | + | 0.996010i | \(0.528444\pi\) | |||||||
\(272\) | 2.17248 | 0.131726 | ||||||||
\(273\) | 53.1590 | 3.21733 | ||||||||
\(274\) | 2.09352 | 0.126474 | ||||||||
\(275\) | −0.128400 | −0.00774278 | ||||||||
\(276\) | 8.42209 | 0.506950 | ||||||||
\(277\) | 9.57581 | 0.575354 | 0.287677 | − | 0.957727i | \(-0.407117\pi\) | ||||
0.287677 | + | 0.957727i | \(0.407117\pi\) | |||||||
\(278\) | −0.169351 | −0.0101570 | ||||||||
\(279\) | −18.9921 | −1.13703 | ||||||||
\(280\) | 10.3691 | 0.619669 | ||||||||
\(281\) | −29.9556 | −1.78700 | −0.893502 | − | 0.449059i | \(-0.851759\pi\) | ||||
−0.893502 | + | 0.449059i | \(0.851759\pi\) | |||||||
\(282\) | 19.9318 | 1.18692 | ||||||||
\(283\) | −11.7339 | −0.697506 | −0.348753 | − | 0.937215i | \(-0.613395\pi\) | ||||
−0.348753 | + | 0.937215i | \(0.613395\pi\) | |||||||
\(284\) | −10.7392 | −0.637257 | ||||||||
\(285\) | −53.4492 | −3.16606 | ||||||||
\(286\) | 1.64493 | 0.0972665 | ||||||||
\(287\) | 3.58835 | 0.211814 | ||||||||
\(288\) | −6.90459 | −0.406857 | ||||||||
\(289\) | −12.2803 | −0.722373 | ||||||||
\(290\) | −10.1383 | −0.595342 | ||||||||
\(291\) | 17.6672 | 1.03567 | ||||||||
\(292\) | 14.9326 | 0.873866 | ||||||||
\(293\) | 2.11245 | 0.123411 | 0.0617053 | − | 0.998094i | \(-0.480346\pi\) | ||||
0.0617053 | + | 0.998094i | \(0.480346\pi\) | |||||||
\(294\) | 49.6040 | 2.89296 | ||||||||
\(295\) | −27.5629 | −1.60477 | ||||||||
\(296\) | 3.49564 | 0.203180 | ||||||||
\(297\) | −5.70928 | −0.331286 | ||||||||
\(298\) | −16.4336 | −0.951970 | ||||||||
\(299\) | 9.47457 | 0.547928 | ||||||||
\(300\) | 0.869748 | 0.0502149 | ||||||||
\(301\) | 2.12886 | 0.122706 | ||||||||
\(302\) | −8.57860 | −0.493643 | ||||||||
\(303\) | −15.4698 | −0.888719 | ||||||||
\(304\) | −7.81420 | −0.448175 | ||||||||
\(305\) | 13.6903 | 0.783902 | ||||||||
\(306\) | −15.0001 | −0.857497 | ||||||||
\(307\) | −17.9660 | −1.02538 | −0.512688 | − | 0.858575i | \(-0.671350\pi\) | ||||
−0.512688 | + | 0.858575i | \(0.671350\pi\) | |||||||
\(308\) | 2.21661 | 0.126303 | ||||||||
\(309\) | 43.4046 | 2.46920 | ||||||||
\(310\) | −5.97826 | −0.339542 | ||||||||
\(311\) | −11.6408 | −0.660089 | −0.330045 | − | 0.943965i | \(-0.607064\pi\) | ||||
−0.330045 | + | 0.943965i | \(0.607064\pi\) | |||||||
\(312\) | −11.1423 | −0.630811 | ||||||||
\(313\) | −4.03950 | −0.228326 | −0.114163 | − | 0.993462i | \(-0.536419\pi\) | ||||
−0.114163 | + | 0.993462i | \(0.536419\pi\) | |||||||
\(314\) | 10.6449 | 0.600728 | ||||||||
\(315\) | −71.5940 | −4.03387 | ||||||||
\(316\) | −2.14485 | −0.120657 | ||||||||
\(317\) | 30.2160 | 1.69710 | 0.848549 | − | 0.529117i | \(-0.177477\pi\) | ||||
0.848549 | + | 0.529117i | \(0.177477\pi\) | |||||||
\(318\) | −16.4963 | −0.925066 | ||||||||
\(319\) | −2.16728 | −0.121345 | ||||||||
\(320\) | −2.17339 | −0.121496 | ||||||||
\(321\) | −46.0808 | −2.57198 | ||||||||
\(322\) | 12.7674 | 0.711499 | ||||||||
\(323\) | −16.9762 | −0.944579 | ||||||||
\(324\) | 17.9596 | 0.997755 | ||||||||
\(325\) | 0.978438 | 0.0542740 | ||||||||
\(326\) | −8.77566 | −0.486039 | ||||||||
\(327\) | 37.1324 | 2.05343 | ||||||||
\(328\) | −0.752133 | −0.0415296 | ||||||||
\(329\) | 30.2155 | 1.66583 | ||||||||
\(330\) | −3.17793 | −0.174939 | ||||||||
\(331\) | −9.39681 | −0.516496 | −0.258248 | − | 0.966079i | \(-0.583145\pi\) | ||||
−0.258248 | + | 0.966079i | \(0.583145\pi\) | |||||||
\(332\) | −1.26263 | −0.0692960 | ||||||||
\(333\) | −24.1359 | −1.32264 | ||||||||
\(334\) | 14.8025 | 0.809955 | ||||||||
\(335\) | 16.0224 | 0.875396 | ||||||||
\(336\) | −15.0148 | −0.819123 | ||||||||
\(337\) | 36.6938 | 1.99884 | 0.999419 | − | 0.0340823i | \(-0.0108508\pi\) | ||||
0.999419 | + | 0.0340823i | \(0.0108508\pi\) | |||||||
\(338\) | 0.465237 | 0.0253055 | ||||||||
\(339\) | 52.6167 | 2.85775 | ||||||||
\(340\) | −4.72165 | −0.256067 | ||||||||
\(341\) | −1.27798 | −0.0692065 | ||||||||
\(342\) | 53.9538 | 2.91749 | ||||||||
\(343\) | 41.8004 | 2.25701 | ||||||||
\(344\) | −0.446218 | −0.0240585 | ||||||||
\(345\) | −18.3045 | −0.985482 | ||||||||
\(346\) | −11.2411 | −0.604327 | ||||||||
\(347\) | 6.79205 | 0.364616 | 0.182308 | − | 0.983241i | \(-0.441643\pi\) | ||||
0.182308 | + | 0.983241i | \(0.441643\pi\) | |||||||
\(348\) | 14.6807 | 0.786966 | ||||||||
\(349\) | −23.8020 | −1.27409 | −0.637047 | − | 0.770825i | \(-0.719844\pi\) | ||||
−0.637047 | + | 0.770825i | \(0.719844\pi\) | |||||||
\(350\) | 1.31849 | 0.0704761 | ||||||||
\(351\) | 43.5063 | 2.32219 | ||||||||
\(352\) | −0.464609 | −0.0247638 | ||||||||
\(353\) | −28.7773 | −1.53166 | −0.765830 | − | 0.643043i | \(-0.777672\pi\) | ||||
−0.765830 | + | 0.643043i | \(0.777672\pi\) | |||||||
\(354\) | 39.9121 | 2.12130 | ||||||||
\(355\) | 23.3406 | 1.23879 | ||||||||
\(356\) | 10.3386 | 0.547945 | ||||||||
\(357\) | −32.6193 | −1.72639 | ||||||||
\(358\) | 8.63646 | 0.456451 | ||||||||
\(359\) | −10.3470 | −0.546093 | −0.273046 | − | 0.962001i | \(-0.588031\pi\) | ||||
−0.273046 | + | 0.962001i | \(0.588031\pi\) | |||||||
\(360\) | 15.0064 | 0.790906 | ||||||||
\(361\) | 42.0617 | 2.21377 | ||||||||
\(362\) | −9.03712 | −0.474980 | ||||||||
\(363\) | 33.9394 | 1.78135 | ||||||||
\(364\) | −16.8911 | −0.885336 | ||||||||
\(365\) | −32.4545 | −1.69874 | ||||||||
\(366\) | −19.8240 | −1.03622 | ||||||||
\(367\) | 16.8307 | 0.878557 | 0.439278 | − | 0.898351i | \(-0.355234\pi\) | ||||
0.439278 | + | 0.898351i | \(0.355234\pi\) | |||||||
\(368\) | −2.67609 | −0.139501 | ||||||||
\(369\) | 5.19317 | 0.270345 | ||||||||
\(370\) | −7.59740 | −0.394970 | ||||||||
\(371\) | −25.0074 | −1.29832 | ||||||||
\(372\) | 8.65674 | 0.448831 | ||||||||
\(373\) | −21.1791 | −1.09661 | −0.548307 | − | 0.836277i | \(-0.684727\pi\) | ||||
−0.548307 | + | 0.836277i | \(0.684727\pi\) | |||||||
\(374\) | −1.00935 | −0.0521924 | ||||||||
\(375\) | −36.0903 | −1.86370 | ||||||||
\(376\) | −6.33329 | −0.326614 | ||||||||
\(377\) | 16.5153 | 0.850579 | ||||||||
\(378\) | 58.6265 | 3.01542 | ||||||||
\(379\) | 14.5322 | 0.746469 | 0.373234 | − | 0.927737i | \(-0.378249\pi\) | ||||
0.373234 | + | 0.927737i | \(0.378249\pi\) | |||||||
\(380\) | 16.9833 | 0.871226 | ||||||||
\(381\) | 21.7611 | 1.11485 | ||||||||
\(382\) | 9.35417 | 0.478601 | ||||||||
\(383\) | 20.0820 | 1.02614 | 0.513070 | − | 0.858347i | \(-0.328508\pi\) | ||||
0.513070 | + | 0.858347i | \(0.328508\pi\) | |||||||
\(384\) | 3.14716 | 0.160603 | ||||||||
\(385\) | −4.81756 | −0.245526 | ||||||||
\(386\) | 4.91824 | 0.250332 | ||||||||
\(387\) | 3.08095 | 0.156614 | ||||||||
\(388\) | −5.61370 | −0.284992 | ||||||||
\(389\) | −17.2326 | −0.873727 | −0.436864 | − | 0.899528i | \(-0.643911\pi\) | ||||
−0.436864 | + | 0.899528i | \(0.643911\pi\) | |||||||
\(390\) | 24.2167 | 1.22626 | ||||||||
\(391\) | −5.81376 | −0.294014 | ||||||||
\(392\) | −15.7615 | −0.796077 | ||||||||
\(393\) | −8.23195 | −0.415247 | ||||||||
\(394\) | −14.7015 | −0.740649 | ||||||||
\(395\) | 4.66159 | 0.234550 | ||||||||
\(396\) | 3.20794 | 0.161205 | ||||||||
\(397\) | −4.12386 | −0.206970 | −0.103485 | − | 0.994631i | \(-0.532999\pi\) | ||||
−0.103485 | + | 0.994631i | \(0.532999\pi\) | |||||||
\(398\) | −10.5778 | −0.530219 | ||||||||
\(399\) | 117.328 | 5.87377 | ||||||||
\(400\) | −0.276360 | −0.0138180 | ||||||||
\(401\) | 9.40494 | 0.469660 | 0.234830 | − | 0.972036i | \(-0.424547\pi\) | ||||
0.234830 | + | 0.972036i | \(0.424547\pi\) | |||||||
\(402\) | −23.2010 | −1.15716 | ||||||||
\(403\) | 9.73855 | 0.485112 | ||||||||
\(404\) | 4.91550 | 0.244555 | ||||||||
\(405\) | −39.0332 | −1.93958 | ||||||||
\(406\) | 22.2550 | 1.10450 | ||||||||
\(407\) | −1.62411 | −0.0805040 | ||||||||
\(408\) | 6.83713 | 0.338488 | ||||||||
\(409\) | 21.4215 | 1.05923 | 0.529613 | − | 0.848240i | \(-0.322337\pi\) | ||||
0.529613 | + | 0.848240i | \(0.322337\pi\) | |||||||
\(410\) | 1.63468 | 0.0807311 | ||||||||
\(411\) | 6.58863 | 0.324993 | ||||||||
\(412\) | −13.7917 | −0.679468 | ||||||||
\(413\) | 60.5044 | 2.97723 | ||||||||
\(414\) | 18.4773 | 0.908111 | ||||||||
\(415\) | 2.74420 | 0.134707 | ||||||||
\(416\) | 3.54045 | 0.173585 | ||||||||
\(417\) | −0.532974 | −0.0260999 | ||||||||
\(418\) | 3.63055 | 0.177576 | ||||||||
\(419\) | −5.82387 | −0.284515 | −0.142257 | − | 0.989830i | \(-0.545436\pi\) | ||||
−0.142257 | + | 0.989830i | \(0.545436\pi\) | |||||||
\(420\) | 32.6330 | 1.59233 | ||||||||
\(421\) | 28.3087 | 1.37968 | 0.689841 | − | 0.723961i | \(-0.257680\pi\) | ||||
0.689841 | + | 0.723961i | \(0.257680\pi\) | |||||||
\(422\) | 10.8499 | 0.528165 | ||||||||
\(423\) | 43.7288 | 2.12616 | ||||||||
\(424\) | 5.24165 | 0.254557 | ||||||||
\(425\) | −0.600386 | −0.0291230 | ||||||||
\(426\) | −33.7981 | −1.63752 | ||||||||
\(427\) | −30.0520 | −1.45432 | ||||||||
\(428\) | 14.6420 | 0.707750 | ||||||||
\(429\) | 5.17684 | 0.249940 | ||||||||
\(430\) | 0.969807 | 0.0467683 | ||||||||
\(431\) | −36.3042 | −1.74871 | −0.874356 | − | 0.485285i | \(-0.838716\pi\) | ||||
−0.874356 | + | 0.485285i | \(0.838716\pi\) | |||||||
\(432\) | −12.2884 | −0.591224 | ||||||||
\(433\) | 15.3140 | 0.735944 | 0.367972 | − | 0.929837i | \(-0.380052\pi\) | ||||
0.367972 | + | 0.929837i | \(0.380052\pi\) | |||||||
\(434\) | 13.1231 | 0.629929 | ||||||||
\(435\) | −31.9069 | −1.52982 | ||||||||
\(436\) | −11.7987 | −0.565057 | ||||||||
\(437\) | 20.9115 | 1.00033 | ||||||||
\(438\) | 46.9953 | 2.24552 | ||||||||
\(439\) | 19.2649 | 0.919465 | 0.459732 | − | 0.888057i | \(-0.347945\pi\) | ||||
0.459732 | + | 0.888057i | \(0.347945\pi\) | |||||||
\(440\) | 1.00978 | 0.0481393 | ||||||||
\(441\) | 108.827 | 5.18223 | ||||||||
\(442\) | 7.69154 | 0.365849 | ||||||||
\(443\) | 15.0494 | 0.715019 | 0.357509 | − | 0.933910i | \(-0.383626\pi\) | ||||
0.357509 | + | 0.933910i | \(0.383626\pi\) | |||||||
\(444\) | 11.0013 | 0.522099 | ||||||||
\(445\) | −22.4699 | −1.06517 | ||||||||
\(446\) | −22.6580 | −1.07289 | ||||||||
\(447\) | −51.7190 | −2.44622 | ||||||||
\(448\) | 4.77090 | 0.225404 | ||||||||
\(449\) | −27.0747 | −1.27773 | −0.638867 | − | 0.769317i | \(-0.720597\pi\) | ||||
−0.638867 | + | 0.769317i | \(0.720597\pi\) | |||||||
\(450\) | 1.90815 | 0.0899512 | ||||||||
\(451\) | 0.349448 | 0.0164549 | ||||||||
\(452\) | −16.7188 | −0.786387 | ||||||||
\(453\) | −26.9982 | −1.26848 | ||||||||
\(454\) | −7.21310 | −0.338528 | ||||||||
\(455\) | 36.7111 | 1.72104 | ||||||||
\(456\) | −24.5925 | −1.15165 | ||||||||
\(457\) | −35.3447 | −1.65336 | −0.826678 | − | 0.562675i | \(-0.809772\pi\) | ||||
−0.826678 | + | 0.562675i | \(0.809772\pi\) | |||||||
\(458\) | −22.7121 | −1.06127 | ||||||||
\(459\) | −26.6962 | −1.24607 | ||||||||
\(460\) | 5.81621 | 0.271182 | ||||||||
\(461\) | −28.0998 | −1.30874 | −0.654370 | − | 0.756175i | \(-0.727066\pi\) | ||||
−0.654370 | + | 0.756175i | \(0.727066\pi\) | |||||||
\(462\) | 6.97601 | 0.324553 | ||||||||
\(463\) | −34.2886 | −1.59353 | −0.796764 | − | 0.604290i | \(-0.793457\pi\) | ||||
−0.796764 | + | 0.604290i | \(0.793457\pi\) | |||||||
\(464\) | −4.66474 | −0.216555 | ||||||||
\(465\) | −18.8145 | −0.872502 | ||||||||
\(466\) | −3.14012 | −0.145463 | ||||||||
\(467\) | 35.1965 | 1.62870 | 0.814350 | − | 0.580375i | \(-0.197094\pi\) | ||||
0.814350 | + | 0.580375i | \(0.197094\pi\) | |||||||
\(468\) | −24.4453 | −1.12999 | ||||||||
\(469\) | −35.1713 | −1.62406 | ||||||||
\(470\) | 13.7647 | 0.634920 | ||||||||
\(471\) | 33.5013 | 1.54366 | ||||||||
\(472\) | −12.6820 | −0.583734 | ||||||||
\(473\) | 0.207317 | 0.00953245 | ||||||||
\(474\) | −6.75016 | −0.310045 | ||||||||
\(475\) | 2.15953 | 0.0990862 | ||||||||
\(476\) | 10.3647 | 0.475064 | ||||||||
\(477\) | −36.1915 | −1.65709 | ||||||||
\(478\) | −16.9961 | −0.777384 | ||||||||
\(479\) | 7.85768 | 0.359027 | 0.179513 | − | 0.983756i | \(-0.442548\pi\) | ||||
0.179513 | + | 0.983756i | \(0.442548\pi\) | |||||||
\(480\) | −6.84001 | −0.312202 | ||||||||
\(481\) | 12.3761 | 0.564302 | ||||||||
\(482\) | 23.5304 | 1.07178 | ||||||||
\(483\) | 40.1810 | 1.82830 | ||||||||
\(484\) | −10.7841 | −0.490188 | ||||||||
\(485\) | 12.2008 | 0.554008 | ||||||||
\(486\) | 19.6566 | 0.891640 | ||||||||
\(487\) | 13.9859 | 0.633761 | 0.316880 | − | 0.948465i | \(-0.397365\pi\) | ||||
0.316880 | + | 0.948465i | \(0.397365\pi\) | |||||||
\(488\) | 6.29902 | 0.285143 | ||||||||
\(489\) | −27.6184 | −1.24895 | ||||||||
\(490\) | 34.2560 | 1.54753 | ||||||||
\(491\) | 18.0688 | 0.815433 | 0.407717 | − | 0.913108i | \(-0.366325\pi\) | ||||
0.407717 | + | 0.913108i | \(0.366325\pi\) | |||||||
\(492\) | −2.36708 | −0.106716 | ||||||||
\(493\) | −10.1340 | −0.456414 | ||||||||
\(494\) | −27.6658 | −1.24474 | ||||||||
\(495\) | −6.97211 | −0.313373 | ||||||||
\(496\) | −2.75066 | −0.123508 | ||||||||
\(497\) | −51.2359 | −2.29824 | ||||||||
\(498\) | −3.97370 | −0.178066 | ||||||||
\(499\) | −32.1063 | −1.43728 | −0.718639 | − | 0.695384i | \(-0.755234\pi\) | ||||
−0.718639 | + | 0.695384i | \(0.755234\pi\) | |||||||
\(500\) | 11.4676 | 0.512847 | ||||||||
\(501\) | 46.5857 | 2.08129 | ||||||||
\(502\) | 1.14462 | 0.0510870 | ||||||||
\(503\) | 25.3731 | 1.13133 | 0.565664 | − | 0.824636i | \(-0.308620\pi\) | ||||
0.565664 | + | 0.824636i | \(0.308620\pi\) | |||||||
\(504\) | −32.9411 | −1.46731 | ||||||||
\(505\) | −10.6833 | −0.475401 | ||||||||
\(506\) | 1.24334 | 0.0552732 | ||||||||
\(507\) | 1.46417 | 0.0650262 | ||||||||
\(508\) | −6.91452 | −0.306782 | ||||||||
\(509\) | −19.2114 | −0.851530 | −0.425765 | − | 0.904834i | \(-0.639995\pi\) | ||||
−0.425765 | + | 0.904834i | \(0.639995\pi\) | |||||||
\(510\) | −14.8598 | −0.658001 | ||||||||
\(511\) | 71.2421 | 3.15157 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 96.0236 | 4.23955 | ||||||||
\(514\) | −15.7954 | −0.696704 | ||||||||
\(515\) | 29.9748 | 1.32085 | ||||||||
\(516\) | −1.40432 | −0.0618216 | ||||||||
\(517\) | 2.94251 | 0.129411 | ||||||||
\(518\) | 16.6774 | 0.732761 | ||||||||
\(519\) | −35.3776 | −1.55290 | ||||||||
\(520\) | −7.69478 | −0.337439 | ||||||||
\(521\) | 28.7275 | 1.25858 | 0.629288 | − | 0.777172i | \(-0.283347\pi\) | ||||
0.629288 | + | 0.777172i | \(0.283347\pi\) | |||||||
\(522\) | 32.2081 | 1.40971 | ||||||||
\(523\) | 0.223468 | 0.00977157 | 0.00488579 | − | 0.999988i | \(-0.498445\pi\) | ||||
0.00488579 | + | 0.999988i | \(0.498445\pi\) | |||||||
\(524\) | 2.61568 | 0.114267 | ||||||||
\(525\) | 4.14949 | 0.181098 | ||||||||
\(526\) | 4.88652 | 0.213062 | ||||||||
\(527\) | −5.97574 | −0.260307 | ||||||||
\(528\) | −1.46220 | −0.0636340 | ||||||||
\(529\) | −15.8385 | −0.688631 | ||||||||
\(530\) | −11.3922 | −0.494844 | ||||||||
\(531\) | 87.5637 | 3.79994 | ||||||||
\(532\) | −37.2808 | −1.61633 | ||||||||
\(533\) | −2.66289 | −0.115342 | ||||||||
\(534\) | 32.5372 | 1.40802 | ||||||||
\(535\) | −31.8229 | −1.37582 | ||||||||
\(536\) | 7.37205 | 0.318424 | ||||||||
\(537\) | 27.1803 | 1.17292 | ||||||||
\(538\) | −5.45781 | −0.235303 | ||||||||
\(539\) | 7.32295 | 0.315422 | ||||||||
\(540\) | 26.7074 | 1.14930 | ||||||||
\(541\) | −20.2502 | −0.870626 | −0.435313 | − | 0.900279i | \(-0.643362\pi\) | ||||
−0.435313 | + | 0.900279i | \(0.643362\pi\) | |||||||
\(542\) | 2.93812 | 0.126203 | ||||||||
\(543\) | −28.4412 | −1.22053 | ||||||||
\(544\) | −2.17248 | −0.0931442 | ||||||||
\(545\) | 25.6433 | 1.09844 | ||||||||
\(546\) | −53.1590 | −2.27500 | ||||||||
\(547\) | 35.0313 | 1.49783 | 0.748914 | − | 0.662667i | \(-0.230575\pi\) | ||||
0.748914 | + | 0.662667i | \(0.230575\pi\) | |||||||
\(548\) | −2.09352 | −0.0894307 | ||||||||
\(549\) | −43.4922 | −1.85620 | ||||||||
\(550\) | 0.128400 | 0.00547497 | ||||||||
\(551\) | 36.4512 | 1.55287 | ||||||||
\(552\) | −8.42209 | −0.358468 | ||||||||
\(553\) | −10.2329 | −0.435145 | ||||||||
\(554\) | −9.57581 | −0.406837 | ||||||||
\(555\) | −23.9102 | −1.01493 | ||||||||
\(556\) | 0.169351 | 0.00718208 | ||||||||
\(557\) | 25.8517 | 1.09537 | 0.547686 | − | 0.836684i | \(-0.315509\pi\) | ||||
0.547686 | + | 0.836684i | \(0.315509\pi\) | |||||||
\(558\) | 18.9921 | 0.804002 | ||||||||
\(559\) | −1.57981 | −0.0668189 | ||||||||
\(560\) | −10.3691 | −0.438172 | ||||||||
\(561\) | −3.17659 | −0.134116 | ||||||||
\(562\) | 29.9556 | 1.26360 | ||||||||
\(563\) | 7.04696 | 0.296994 | 0.148497 | − | 0.988913i | \(-0.452556\pi\) | ||||
0.148497 | + | 0.988913i | \(0.452556\pi\) | |||||||
\(564\) | −19.9318 | −0.839282 | ||||||||
\(565\) | 36.3365 | 1.52869 | ||||||||
\(566\) | 11.7339 | 0.493212 | ||||||||
\(567\) | 85.6834 | 3.59837 | ||||||||
\(568\) | 10.7392 | 0.450609 | ||||||||
\(569\) | −21.0373 | −0.881929 | −0.440964 | − | 0.897525i | \(-0.645363\pi\) | ||||
−0.440964 | + | 0.897525i | \(0.645363\pi\) | |||||||
\(570\) | 53.4492 | 2.23874 | ||||||||
\(571\) | −19.3157 | −0.808336 | −0.404168 | − | 0.914685i | \(-0.632439\pi\) | ||||
−0.404168 | + | 0.914685i | \(0.632439\pi\) | |||||||
\(572\) | −1.64493 | −0.0687778 | ||||||||
\(573\) | 29.4390 | 1.22983 | ||||||||
\(574\) | −3.58835 | −0.149775 | ||||||||
\(575\) | 0.739566 | 0.0308420 | ||||||||
\(576\) | 6.90459 | 0.287691 | ||||||||
\(577\) | −24.4322 | −1.01713 | −0.508564 | − | 0.861024i | \(-0.669823\pi\) | ||||
−0.508564 | + | 0.861024i | \(0.669823\pi\) | |||||||
\(578\) | 12.2803 | 0.510795 | ||||||||
\(579\) | 15.4785 | 0.643264 | ||||||||
\(580\) | 10.1383 | 0.420971 | ||||||||
\(581\) | −6.02390 | −0.249914 | ||||||||
\(582\) | −17.6672 | −0.732328 | ||||||||
\(583\) | −2.43532 | −0.100861 | ||||||||
\(584\) | −14.9326 | −0.617916 | ||||||||
\(585\) | 53.1293 | 2.19663 | ||||||||
\(586\) | −2.11245 | −0.0872644 | ||||||||
\(587\) | 7.87924 | 0.325211 | 0.162606 | − | 0.986691i | \(-0.448010\pi\) | ||||
0.162606 | + | 0.986691i | \(0.448010\pi\) | |||||||
\(588\) | −49.6040 | −2.04563 | ||||||||
\(589\) | 21.4942 | 0.885652 | ||||||||
\(590\) | 27.5629 | 1.13475 | ||||||||
\(591\) | −46.2678 | −1.90320 | ||||||||
\(592\) | −3.49564 | −0.143670 | ||||||||
\(593\) | 25.6306 | 1.05252 | 0.526261 | − | 0.850323i | \(-0.323594\pi\) | ||||
0.526261 | + | 0.850323i | \(0.323594\pi\) | |||||||
\(594\) | 5.70928 | 0.234255 | ||||||||
\(595\) | −22.5265 | −0.923498 | ||||||||
\(596\) | 16.4336 | 0.673145 | ||||||||
\(597\) | −33.2901 | −1.36247 | ||||||||
\(598\) | −9.47457 | −0.387444 | ||||||||
\(599\) | 41.5720 | 1.69859 | 0.849294 | − | 0.527921i | \(-0.177028\pi\) | ||||
0.849294 | + | 0.527921i | \(0.177028\pi\) | |||||||
\(600\) | −0.869748 | −0.0355073 | ||||||||
\(601\) | −31.2181 | −1.27341 | −0.636707 | − | 0.771106i | \(-0.719704\pi\) | ||||
−0.636707 | + | 0.771106i | \(0.719704\pi\) | |||||||
\(602\) | −2.12886 | −0.0867660 | ||||||||
\(603\) | −50.9010 | −2.07285 | ||||||||
\(604\) | 8.57860 | 0.349058 | ||||||||
\(605\) | 23.4382 | 0.952897 | ||||||||
\(606\) | 15.4698 | 0.628419 | ||||||||
\(607\) | 46.4830 | 1.88669 | 0.943344 | − | 0.331816i | \(-0.107661\pi\) | ||||
0.943344 | + | 0.331816i | \(0.107661\pi\) | |||||||
\(608\) | 7.81420 | 0.316908 | ||||||||
\(609\) | 70.0400 | 2.83816 | ||||||||
\(610\) | −13.6903 | −0.554302 | ||||||||
\(611\) | −22.4227 | −0.907124 | ||||||||
\(612\) | 15.0001 | 0.606342 | ||||||||
\(613\) | 24.7412 | 0.999288 | 0.499644 | − | 0.866231i | \(-0.333464\pi\) | ||||
0.499644 | + | 0.866231i | \(0.333464\pi\) | |||||||
\(614\) | 17.9660 | 0.725051 | ||||||||
\(615\) | 5.14459 | 0.207450 | ||||||||
\(616\) | −2.21661 | −0.0893096 | ||||||||
\(617\) | 17.0754 | 0.687428 | 0.343714 | − | 0.939074i | \(-0.388315\pi\) | ||||
0.343714 | + | 0.939074i | \(0.388315\pi\) | |||||||
\(618\) | −43.4046 | −1.74599 | ||||||||
\(619\) | −18.3828 | −0.738869 | −0.369434 | − | 0.929257i | \(-0.620449\pi\) | ||||
−0.369434 | + | 0.929257i | \(0.620449\pi\) | |||||||
\(620\) | 5.97826 | 0.240093 | ||||||||
\(621\) | 32.8848 | 1.31962 | ||||||||
\(622\) | 11.6408 | 0.466753 | ||||||||
\(623\) | 49.3245 | 1.97615 | ||||||||
\(624\) | 11.1423 | 0.446050 | ||||||||
\(625\) | −23.5418 | −0.941673 | ||||||||
\(626\) | 4.03950 | 0.161451 | ||||||||
\(627\) | 11.4259 | 0.456307 | ||||||||
\(628\) | −10.6449 | −0.424779 | ||||||||
\(629\) | −7.59420 | −0.302800 | ||||||||
\(630\) | 71.5940 | 2.85237 | ||||||||
\(631\) | 37.7998 | 1.50479 | 0.752393 | − | 0.658714i | \(-0.228899\pi\) | ||||
0.752393 | + | 0.658714i | \(0.228899\pi\) | |||||||
\(632\) | 2.14485 | 0.0853174 | ||||||||
\(633\) | 34.1463 | 1.35719 | ||||||||
\(634\) | −30.2160 | −1.20003 | ||||||||
\(635\) | 15.0280 | 0.596367 | ||||||||
\(636\) | 16.4963 | 0.654121 | ||||||||
\(637\) | −55.8028 | −2.21099 | ||||||||
\(638\) | 2.16728 | 0.0858035 | ||||||||
\(639\) | −74.1501 | −2.93333 | ||||||||
\(640\) | 2.17339 | 0.0859109 | ||||||||
\(641\) | 16.1839 | 0.639226 | 0.319613 | − | 0.947548i | \(-0.396447\pi\) | ||||
0.319613 | + | 0.947548i | \(0.396447\pi\) | |||||||
\(642\) | 46.0808 | 1.81866 | ||||||||
\(643\) | 29.6242 | 1.16826 | 0.584132 | − | 0.811659i | \(-0.301435\pi\) | ||||
0.584132 | + | 0.811659i | \(0.301435\pi\) | |||||||
\(644\) | −12.7674 | −0.503106 | ||||||||
\(645\) | 3.05213 | 0.120178 | ||||||||
\(646\) | 16.9762 | 0.667919 | ||||||||
\(647\) | −7.93801 | −0.312075 | −0.156038 | − | 0.987751i | \(-0.549872\pi\) | ||||
−0.156038 | + | 0.987751i | \(0.549872\pi\) | |||||||
\(648\) | −17.9596 | −0.705519 | ||||||||
\(649\) | 5.89216 | 0.231287 | ||||||||
\(650\) | −0.978438 | −0.0383775 | ||||||||
\(651\) | 41.3005 | 1.61869 | ||||||||
\(652\) | 8.77566 | 0.343681 | ||||||||
\(653\) | 4.28596 | 0.167723 | 0.0838613 | − | 0.996477i | \(-0.473275\pi\) | ||||
0.0838613 | + | 0.996477i | \(0.473275\pi\) | |||||||
\(654\) | −37.1324 | −1.45199 | ||||||||
\(655\) | −5.68490 | −0.222128 | ||||||||
\(656\) | 0.752133 | 0.0293658 | ||||||||
\(657\) | 103.104 | 4.02246 | ||||||||
\(658\) | −30.2155 | −1.17792 | ||||||||
\(659\) | 15.6395 | 0.609227 | 0.304614 | − | 0.952476i | \(-0.401473\pi\) | ||||
0.304614 | + | 0.952476i | \(0.401473\pi\) | |||||||
\(660\) | 3.17793 | 0.123701 | ||||||||
\(661\) | −42.2031 | −1.64151 | −0.820755 | − | 0.571280i | \(-0.806447\pi\) | ||||
−0.820755 | + | 0.571280i | \(0.806447\pi\) | |||||||
\(662\) | 9.39681 | 0.365218 | ||||||||
\(663\) | 24.2065 | 0.940102 | ||||||||
\(664\) | 1.26263 | 0.0489997 | ||||||||
\(665\) | 81.0258 | 3.14205 | ||||||||
\(666\) | 24.1359 | 0.935249 | ||||||||
\(667\) | 12.4833 | 0.483355 | ||||||||
\(668\) | −14.8025 | −0.572725 | ||||||||
\(669\) | −71.3083 | −2.75694 | ||||||||
\(670\) | −16.0224 | −0.618998 | ||||||||
\(671\) | −2.92659 | −0.112980 | ||||||||
\(672\) | 15.0148 | 0.579208 | ||||||||
\(673\) | −9.29626 | −0.358344 | −0.179172 | − | 0.983818i | \(-0.557342\pi\) | ||||
−0.179172 | + | 0.983818i | \(0.557342\pi\) | |||||||
\(674\) | −36.6938 | −1.41339 | ||||||||
\(675\) | 3.39601 | 0.130712 | ||||||||
\(676\) | −0.465237 | −0.0178937 | ||||||||
\(677\) | 30.0770 | 1.15595 | 0.577976 | − | 0.816054i | \(-0.303843\pi\) | ||||
0.577976 | + | 0.816054i | \(0.303843\pi\) | |||||||
\(678\) | −52.6167 | −2.02073 | ||||||||
\(679\) | −26.7824 | −1.02781 | ||||||||
\(680\) | 4.72165 | 0.181067 | ||||||||
\(681\) | −22.7007 | −0.869895 | ||||||||
\(682\) | 1.27798 | 0.0489364 | ||||||||
\(683\) | −11.6634 | −0.446286 | −0.223143 | − | 0.974786i | \(-0.571632\pi\) | ||||
−0.223143 | + | 0.974786i | \(0.571632\pi\) | |||||||
\(684\) | −53.9538 | −2.06298 | ||||||||
\(685\) | 4.55004 | 0.173848 | ||||||||
\(686\) | −41.8004 | −1.59595 | ||||||||
\(687\) | −71.4786 | −2.72708 | ||||||||
\(688\) | 0.446218 | 0.0170119 | ||||||||
\(689\) | 18.5578 | 0.706995 | ||||||||
\(690\) | 18.3045 | 0.696841 | ||||||||
\(691\) | 5.73643 | 0.218224 | 0.109112 | − | 0.994029i | \(-0.465199\pi\) | ||||
0.109112 | + | 0.994029i | \(0.465199\pi\) | |||||||
\(692\) | 11.2411 | 0.427324 | ||||||||
\(693\) | 15.3048 | 0.581380 | ||||||||
\(694\) | −6.79205 | −0.257823 | ||||||||
\(695\) | −0.368066 | −0.0139616 | ||||||||
\(696\) | −14.6807 | −0.556469 | ||||||||
\(697\) | 1.63399 | 0.0618918 | ||||||||
\(698\) | 23.8020 | 0.900921 | ||||||||
\(699\) | −9.88244 | −0.373788 | ||||||||
\(700\) | −1.31849 | −0.0498341 | ||||||||
\(701\) | 20.5718 | 0.776986 | 0.388493 | − | 0.921452i | \(-0.372996\pi\) | ||||
0.388493 | + | 0.921452i | \(0.372996\pi\) | |||||||
\(702\) | −43.5063 | −1.64204 | ||||||||
\(703\) | 27.3156 | 1.03023 | ||||||||
\(704\) | 0.464609 | 0.0175106 | ||||||||
\(705\) | 43.3197 | 1.63152 | ||||||||
\(706\) | 28.7773 | 1.08305 | ||||||||
\(707\) | 23.4514 | 0.881979 | ||||||||
\(708\) | −39.9121 | −1.49999 | ||||||||
\(709\) | −45.7623 | −1.71864 | −0.859320 | − | 0.511438i | \(-0.829113\pi\) | ||||
−0.859320 | + | 0.511438i | \(0.829113\pi\) | |||||||
\(710\) | −23.3406 | −0.875957 | ||||||||
\(711\) | −14.8093 | −0.555391 | ||||||||
\(712\) | −10.3386 | −0.387456 | ||||||||
\(713\) | 7.36101 | 0.275672 | ||||||||
\(714\) | 32.6193 | 1.22075 | ||||||||
\(715\) | 3.57507 | 0.133700 | ||||||||
\(716\) | −8.63646 | −0.322760 | ||||||||
\(717\) | −53.4894 | −1.99760 | ||||||||
\(718\) | 10.3470 | 0.386146 | ||||||||
\(719\) | 21.0808 | 0.786180 | 0.393090 | − | 0.919500i | \(-0.371406\pi\) | ||||
0.393090 | + | 0.919500i | \(0.371406\pi\) | |||||||
\(720\) | −15.0064 | −0.559255 | ||||||||
\(721\) | −65.7988 | −2.45048 | ||||||||
\(722\) | −42.0617 | −1.56537 | ||||||||
\(723\) | 74.0538 | 2.75409 | ||||||||
\(724\) | 9.03712 | 0.335862 | ||||||||
\(725\) | 1.28915 | 0.0478778 | ||||||||
\(726\) | −33.9394 | −1.25961 | ||||||||
\(727\) | 25.3964 | 0.941902 | 0.470951 | − | 0.882159i | \(-0.343911\pi\) | ||||
0.470951 | + | 0.882159i | \(0.343911\pi\) | |||||||
\(728\) | 16.8911 | 0.626027 | ||||||||
\(729\) | 7.98350 | 0.295685 | ||||||||
\(730\) | 32.4545 | 1.20119 | ||||||||
\(731\) | 0.969399 | 0.0358545 | ||||||||
\(732\) | 19.8240 | 0.732716 | ||||||||
\(733\) | 40.0778 | 1.48031 | 0.740153 | − | 0.672438i | \(-0.234753\pi\) | ||||
0.740153 | + | 0.672438i | \(0.234753\pi\) | |||||||
\(734\) | −16.8307 | −0.621233 | ||||||||
\(735\) | 107.809 | 3.97659 | ||||||||
\(736\) | 2.67609 | 0.0986421 | ||||||||
\(737\) | −3.42513 | −0.126166 | ||||||||
\(738\) | −5.19317 | −0.191163 | ||||||||
\(739\) | 26.6738 | 0.981211 | 0.490606 | − | 0.871382i | \(-0.336776\pi\) | ||||
0.490606 | + | 0.871382i | \(0.336776\pi\) | |||||||
\(740\) | 7.59740 | 0.279286 | ||||||||
\(741\) | −87.0684 | −3.19854 | ||||||||
\(742\) | 25.0074 | 0.918051 | ||||||||
\(743\) | 29.5772 | 1.08508 | 0.542541 | − | 0.840029i | \(-0.317462\pi\) | ||||
0.542541 | + | 0.840029i | \(0.317462\pi\) | |||||||
\(744\) | −8.65674 | −0.317371 | ||||||||
\(745\) | −35.7166 | −1.30855 | ||||||||
\(746\) | 21.1791 | 0.775423 | ||||||||
\(747\) | −8.71796 | −0.318974 | ||||||||
\(748\) | 1.00935 | 0.0369056 | ||||||||
\(749\) | 69.8558 | 2.55247 | ||||||||
\(750\) | 36.0903 | 1.31783 | ||||||||
\(751\) | −6.76616 | −0.246901 | −0.123450 | − | 0.992351i | \(-0.539396\pi\) | ||||
−0.123450 | + | 0.992351i | \(0.539396\pi\) | |||||||
\(752\) | 6.33329 | 0.230951 | ||||||||
\(753\) | 3.60230 | 0.131275 | ||||||||
\(754\) | −16.5153 | −0.601450 | ||||||||
\(755\) | −18.6447 | −0.678549 | ||||||||
\(756\) | −58.6265 | −2.13223 | ||||||||
\(757\) | 54.1584 | 1.96842 | 0.984210 | − | 0.177006i | \(-0.0566413\pi\) | ||||
0.984210 | + | 0.177006i | \(0.0566413\pi\) | |||||||
\(758\) | −14.5322 | −0.527833 | ||||||||
\(759\) | 3.91298 | 0.142032 | ||||||||
\(760\) | −16.9833 | −0.616050 | ||||||||
\(761\) | −9.32399 | −0.337995 | −0.168997 | − | 0.985617i | \(-0.554053\pi\) | ||||
−0.168997 | + | 0.985617i | \(0.554053\pi\) | |||||||
\(762\) | −21.7611 | −0.788320 | ||||||||
\(763\) | −56.2906 | −2.03786 | ||||||||
\(764\) | −9.35417 | −0.338422 | ||||||||
\(765\) | −32.6010 | −1.17869 | ||||||||
\(766\) | −20.0820 | −0.725591 | ||||||||
\(767\) | −44.8998 | −1.62124 | ||||||||
\(768\) | −3.14716 | −0.113563 | ||||||||
\(769\) | −32.8772 | −1.18558 | −0.592791 | − | 0.805356i | \(-0.701974\pi\) | ||||
−0.592791 | + | 0.805356i | \(0.701974\pi\) | |||||||
\(770\) | 4.81756 | 0.173613 | ||||||||
\(771\) | −49.7105 | −1.79028 | ||||||||
\(772\) | −4.91824 | −0.177012 | ||||||||
\(773\) | 16.3598 | 0.588423 | 0.294211 | − | 0.955740i | \(-0.404943\pi\) | ||||
0.294211 | + | 0.955740i | \(0.404943\pi\) | |||||||
\(774\) | −3.08095 | −0.110743 | ||||||||
\(775\) | 0.760171 | 0.0273062 | ||||||||
\(776\) | 5.61370 | 0.201520 | ||||||||
\(777\) | 52.4862 | 1.88293 | ||||||||
\(778\) | 17.2326 | 0.617818 | ||||||||
\(779\) | −5.87731 | −0.210577 | ||||||||
\(780\) | −24.2167 | −0.867096 | ||||||||
\(781\) | −4.98955 | −0.178540 | ||||||||
\(782\) | 5.81376 | 0.207899 | ||||||||
\(783\) | 57.3220 | 2.04852 | ||||||||
\(784\) | 15.7615 | 0.562911 | ||||||||
\(785\) | 23.1356 | 0.825746 | ||||||||
\(786\) | 8.23195 | 0.293624 | ||||||||
\(787\) | −3.75331 | −0.133791 | −0.0668956 | − | 0.997760i | \(-0.521309\pi\) | ||||
−0.0668956 | + | 0.997760i | \(0.521309\pi\) | |||||||
\(788\) | 14.7015 | 0.523718 | ||||||||
\(789\) | 15.3786 | 0.547494 | ||||||||
\(790\) | −4.66159 | −0.165852 | ||||||||
\(791\) | −79.7638 | −2.83607 | ||||||||
\(792\) | −3.20794 | −0.113989 | ||||||||
\(793\) | 22.3014 | 0.791944 | ||||||||
\(794\) | 4.12386 | 0.146350 | ||||||||
\(795\) | −35.8529 | −1.27157 | ||||||||
\(796\) | 10.5778 | 0.374922 | ||||||||
\(797\) | −22.0905 | −0.782485 | −0.391243 | − | 0.920288i | \(-0.627955\pi\) | ||||
−0.391243 | + | 0.920288i | \(0.627955\pi\) | |||||||
\(798\) | −117.328 | −4.15338 | ||||||||
\(799\) | 13.7589 | 0.486756 | ||||||||
\(800\) | 0.276360 | 0.00977081 | ||||||||
\(801\) | 71.3839 | 2.52223 | ||||||||
\(802\) | −9.40494 | −0.332100 | ||||||||
\(803\) | 6.93784 | 0.244831 | ||||||||
\(804\) | 23.2010 | 0.818236 | ||||||||
\(805\) | 27.7486 | 0.978008 | ||||||||
\(806\) | −9.73855 | −0.343026 | ||||||||
\(807\) | −17.1766 | −0.604644 | ||||||||
\(808\) | −4.91550 | −0.172927 | ||||||||
\(809\) | −1.98014 | −0.0696181 | −0.0348090 | − | 0.999394i | \(-0.511082\pi\) | ||||
−0.0348090 | + | 0.999394i | \(0.511082\pi\) | |||||||
\(810\) | 39.0332 | 1.37149 | ||||||||
\(811\) | −7.90446 | −0.277563 | −0.138782 | − | 0.990323i | \(-0.544319\pi\) | ||||
−0.138782 | + | 0.990323i | \(0.544319\pi\) | |||||||
\(812\) | −22.2550 | −0.780998 | ||||||||
\(813\) | 9.24672 | 0.324297 | ||||||||
\(814\) | 1.62411 | 0.0569249 | ||||||||
\(815\) | −19.0730 | −0.668097 | ||||||||
\(816\) | −6.83713 | −0.239347 | ||||||||
\(817\) | −3.48684 | −0.121989 | ||||||||
\(818\) | −21.4215 | −0.748986 | ||||||||
\(819\) | −116.626 | −4.07525 | ||||||||
\(820\) | −1.63468 | −0.0570855 | ||||||||
\(821\) | −6.71468 | −0.234344 | −0.117172 | − | 0.993112i | \(-0.537383\pi\) | ||||
−0.117172 | + | 0.993112i | \(0.537383\pi\) | |||||||
\(822\) | −6.58863 | −0.229805 | ||||||||
\(823\) | −0.808931 | −0.0281976 | −0.0140988 | − | 0.999901i | \(-0.504488\pi\) | ||||
−0.0140988 | + | 0.999901i | \(0.504488\pi\) | |||||||
\(824\) | 13.7917 | 0.480456 | ||||||||
\(825\) | 0.404093 | 0.0140687 | ||||||||
\(826\) | −60.5044 | −2.10522 | ||||||||
\(827\) | 17.7160 | 0.616045 | 0.308022 | − | 0.951379i | \(-0.400333\pi\) | ||||
0.308022 | + | 0.951379i | \(0.400333\pi\) | |||||||
\(828\) | −18.4773 | −0.642132 | ||||||||
\(829\) | −23.6672 | −0.821994 | −0.410997 | − | 0.911637i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911637i | \(0.634819\pi\) | |||||||
\(830\) | −2.74420 | −0.0952525 | ||||||||
\(831\) | −30.1366 | −1.04543 | ||||||||
\(832\) | −3.54045 | −0.122743 | ||||||||
\(833\) | 34.2415 | 1.18640 | ||||||||
\(834\) | 0.532974 | 0.0184554 | ||||||||
\(835\) | 32.1716 | 1.11334 | ||||||||
\(836\) | −3.63055 | −0.125565 | ||||||||
\(837\) | 33.8010 | 1.16833 | ||||||||
\(838\) | 5.82387 | 0.201182 | ||||||||
\(839\) | −19.5659 | −0.675491 | −0.337746 | − | 0.941237i | \(-0.609664\pi\) | ||||
−0.337746 | + | 0.941237i | \(0.609664\pi\) | |||||||
\(840\) | −32.6330 | −1.12595 | ||||||||
\(841\) | −7.24020 | −0.249662 | ||||||||
\(842\) | −28.3087 | −0.975583 | ||||||||
\(843\) | 94.2751 | 3.24701 | ||||||||
\(844\) | −10.8499 | −0.373469 | ||||||||
\(845\) | 1.01114 | 0.0347844 | ||||||||
\(846\) | −43.7288 | −1.50343 | ||||||||
\(847\) | −51.4501 | −1.76785 | ||||||||
\(848\) | −5.24165 | −0.179999 | ||||||||
\(849\) | 36.9283 | 1.26738 | ||||||||
\(850\) | 0.600386 | 0.0205931 | ||||||||
\(851\) | 9.35466 | 0.320674 | ||||||||
\(852\) | 33.7981 | 1.15790 | ||||||||
\(853\) | 28.7187 | 0.983309 | 0.491655 | − | 0.870790i | \(-0.336392\pi\) | ||||
0.491655 | + | 0.870790i | \(0.336392\pi\) | |||||||
\(854\) | 30.0520 | 1.02836 | ||||||||
\(855\) | 117.263 | 4.01031 | ||||||||
\(856\) | −14.6420 | −0.500455 | ||||||||
\(857\) | −32.5695 | −1.11255 | −0.556276 | − | 0.830997i | \(-0.687770\pi\) | ||||
−0.556276 | + | 0.830997i | \(0.687770\pi\) | |||||||
\(858\) | −5.17684 | −0.176734 | ||||||||
\(859\) | 13.7296 | 0.468448 | 0.234224 | − | 0.972183i | \(-0.424745\pi\) | ||||
0.234224 | + | 0.972183i | \(0.424745\pi\) | |||||||
\(860\) | −0.969807 | −0.0330702 | ||||||||
\(861\) | −11.2931 | −0.384868 | ||||||||
\(862\) | 36.3042 | 1.23653 | ||||||||
\(863\) | −16.3660 | −0.557104 | −0.278552 | − | 0.960421i | \(-0.589855\pi\) | ||||
−0.278552 | + | 0.960421i | \(0.589855\pi\) | |||||||
\(864\) | 12.2884 | 0.418058 | ||||||||
\(865\) | −24.4314 | −0.830693 | ||||||||
\(866\) | −15.3140 | −0.520391 | ||||||||
\(867\) | 38.6481 | 1.31256 | ||||||||
\(868\) | −13.1231 | −0.445427 | ||||||||
\(869\) | −0.996516 | −0.0338045 | ||||||||
\(870\) | 31.9069 | 1.08174 | ||||||||
\(871\) | 26.1004 | 0.884377 | ||||||||
\(872\) | 11.7987 | 0.399555 | ||||||||
\(873\) | −38.7603 | −1.31184 | ||||||||
\(874\) | −20.9115 | −0.707343 | ||||||||
\(875\) | 54.7108 | 1.84956 | ||||||||
\(876\) | −46.9953 | −1.58782 | ||||||||
\(877\) | −41.0199 | −1.38514 | −0.692572 | − | 0.721349i | \(-0.743522\pi\) | ||||
−0.692572 | + | 0.721349i | \(0.743522\pi\) | |||||||
\(878\) | −19.2649 | −0.650160 | ||||||||
\(879\) | −6.64820 | −0.224238 | ||||||||
\(880\) | −1.00978 | −0.0340397 | ||||||||
\(881\) | −37.5027 | −1.26350 | −0.631749 | − | 0.775173i | \(-0.717663\pi\) | ||||
−0.631749 | + | 0.775173i | \(0.717663\pi\) | |||||||
\(882\) | −108.827 | −3.66439 | ||||||||
\(883\) | 28.2312 | 0.950057 | 0.475028 | − | 0.879970i | \(-0.342438\pi\) | ||||
0.475028 | + | 0.879970i | \(0.342438\pi\) | |||||||
\(884\) | −7.69154 | −0.258695 | ||||||||
\(885\) | 86.7447 | 2.91589 | ||||||||
\(886\) | −15.0494 | −0.505595 | ||||||||
\(887\) | −35.0722 | −1.17761 | −0.588804 | − | 0.808276i | \(-0.700401\pi\) | ||||
−0.588804 | + | 0.808276i | \(0.700401\pi\) | |||||||
\(888\) | −11.0013 | −0.369180 | ||||||||
\(889\) | −32.9885 | −1.10640 | ||||||||
\(890\) | 22.4699 | 0.753192 | ||||||||
\(891\) | 8.34419 | 0.279541 | ||||||||
\(892\) | 22.6580 | 0.758646 | ||||||||
\(893\) | −49.4896 | −1.65611 | ||||||||
\(894\) | 51.7190 | 1.72974 | ||||||||
\(895\) | 18.7704 | 0.627426 | ||||||||
\(896\) | −4.77090 | −0.159385 | ||||||||
\(897\) | −29.8179 | −0.995592 | ||||||||
\(898\) | 27.0747 | 0.903495 | ||||||||
\(899\) | 12.8311 | 0.427941 | ||||||||
\(900\) | −1.90815 | −0.0636051 | ||||||||
\(901\) | −11.3874 | −0.379368 | ||||||||
\(902\) | −0.349448 | −0.0116353 | ||||||||
\(903\) | −6.69986 | −0.222957 | ||||||||
\(904\) | 16.7188 | 0.556059 | ||||||||
\(905\) | −19.6412 | −0.652896 | ||||||||
\(906\) | 26.9982 | 0.896954 | ||||||||
\(907\) | −5.26669 | −0.174877 | −0.0874387 | − | 0.996170i | \(-0.527868\pi\) | ||||
−0.0874387 | + | 0.996170i | \(0.527868\pi\) | |||||||
\(908\) | 7.21310 | 0.239375 | ||||||||
\(909\) | 33.9395 | 1.12570 | ||||||||
\(910\) | −36.7111 | −1.21696 | ||||||||
\(911\) | 57.5271 | 1.90596 | 0.952980 | − | 0.303035i | \(-0.0979998\pi\) | ||||
0.952980 | + | 0.303035i | \(0.0979998\pi\) | |||||||
\(912\) | 24.5925 | 0.814339 | ||||||||
\(913\) | −0.586631 | −0.0194147 | ||||||||
\(914\) | 35.3447 | 1.16910 | ||||||||
\(915\) | −43.0854 | −1.42436 | ||||||||
\(916\) | 22.7121 | 0.750430 | ||||||||
\(917\) | 12.4792 | 0.412098 | ||||||||
\(918\) | 26.6962 | 0.881105 | ||||||||
\(919\) | 33.4468 | 1.10331 | 0.551655 | − | 0.834073i | \(-0.313997\pi\) | ||||
0.551655 | + | 0.834073i | \(0.313997\pi\) | |||||||
\(920\) | −5.81621 | −0.191755 | ||||||||
\(921\) | 56.5419 | 1.86312 | ||||||||
\(922\) | 28.0998 | 0.925418 | ||||||||
\(923\) | 38.0217 | 1.25150 | ||||||||
\(924\) | −6.97601 | −0.229494 | ||||||||
\(925\) | 0.966055 | 0.0317637 | ||||||||
\(926\) | 34.2886 | 1.12679 | ||||||||
\(927\) | −95.2260 | −3.12763 | ||||||||
\(928\) | 4.66474 | 0.153128 | ||||||||
\(929\) | 11.5284 | 0.378233 | 0.189117 | − | 0.981955i | \(-0.439438\pi\) | ||||
0.189117 | + | 0.981955i | \(0.439438\pi\) | |||||||
\(930\) | 18.8145 | 0.616952 | ||||||||
\(931\) | −123.164 | −4.03652 | ||||||||
\(932\) | 3.14012 | 0.102858 | ||||||||
\(933\) | 36.6354 | 1.19939 | ||||||||
\(934\) | −35.1965 | −1.15166 | ||||||||
\(935\) | −2.19372 | −0.0717424 | ||||||||
\(936\) | 24.4453 | 0.799021 | ||||||||
\(937\) | 3.19135 | 0.104257 | 0.0521284 | − | 0.998640i | \(-0.483399\pi\) | ||||
0.0521284 | + | 0.998640i | \(0.483399\pi\) | |||||||
\(938\) | 35.1713 | 1.14839 | ||||||||
\(939\) | 12.7129 | 0.414871 | ||||||||
\(940\) | −13.7647 | −0.448956 | ||||||||
\(941\) | 12.9938 | 0.423586 | 0.211793 | − | 0.977315i | \(-0.432070\pi\) | ||||
0.211793 | + | 0.977315i | \(0.432070\pi\) | |||||||
\(942\) | −33.5013 | −1.09153 | ||||||||
\(943\) | −2.01278 | −0.0655451 | ||||||||
\(944\) | 12.6820 | 0.412763 | ||||||||
\(945\) | 127.419 | 4.14493 | ||||||||
\(946\) | −0.207317 | −0.00674046 | ||||||||
\(947\) | 31.2482 | 1.01543 | 0.507715 | − | 0.861525i | \(-0.330490\pi\) | ||||
0.507715 | + | 0.861525i | \(0.330490\pi\) | |||||||
\(948\) | 6.75016 | 0.219235 | ||||||||
\(949\) | −52.8682 | −1.71617 | ||||||||
\(950\) | −2.15953 | −0.0700645 | ||||||||
\(951\) | −95.0943 | −3.08364 | ||||||||
\(952\) | −10.3647 | −0.335921 | ||||||||
\(953\) | −0.739162 | −0.0239438 | −0.0119719 | − | 0.999928i | \(-0.503811\pi\) | ||||
−0.0119719 | + | 0.999928i | \(0.503811\pi\) | |||||||
\(954\) | 36.1915 | 1.17174 | ||||||||
\(955\) | 20.3303 | 0.657873 | ||||||||
\(956\) | 16.9961 | 0.549694 | ||||||||
\(957\) | 6.82077 | 0.220484 | ||||||||
\(958\) | −7.85768 | −0.253870 | ||||||||
\(959\) | −9.98798 | −0.322529 | ||||||||
\(960\) | 6.84001 | 0.220760 | ||||||||
\(961\) | −23.4339 | −0.755932 | ||||||||
\(962\) | −12.3761 | −0.399022 | ||||||||
\(963\) | 101.097 | 3.25781 | ||||||||
\(964\) | −23.5304 | −0.757863 | ||||||||
\(965\) | 10.6893 | 0.344100 | ||||||||
\(966\) | −40.1810 | −1.29280 | ||||||||
\(967\) | 5.28271 | 0.169881 | 0.0849403 | − | 0.996386i | \(-0.472930\pi\) | ||||
0.0849403 | + | 0.996386i | \(0.472930\pi\) | |||||||
\(968\) | 10.7841 | 0.346615 | ||||||||
\(969\) | 53.4267 | 1.71631 | ||||||||
\(970\) | −12.2008 | −0.391743 | ||||||||
\(971\) | 19.9107 | 0.638963 | 0.319482 | − | 0.947592i | \(-0.396491\pi\) | ||||
0.319482 | + | 0.947592i | \(0.396491\pi\) | |||||||
\(972\) | −19.6566 | −0.630484 | ||||||||
\(973\) | 0.807957 | 0.0259019 | ||||||||
\(974\) | −13.9859 | −0.448137 | ||||||||
\(975\) | −3.07930 | −0.0986165 | ||||||||
\(976\) | −6.29902 | −0.201627 | ||||||||
\(977\) | −33.3537 | −1.06708 | −0.533540 | − | 0.845775i | \(-0.679139\pi\) | ||||
−0.533540 | + | 0.845775i | \(0.679139\pi\) | |||||||
\(978\) | 27.6184 | 0.883138 | ||||||||
\(979\) | 4.80342 | 0.153518 | ||||||||
\(980\) | −34.2560 | −1.09427 | ||||||||
\(981\) | −81.4654 | −2.60099 | ||||||||
\(982\) | −18.0688 | −0.576598 | ||||||||
\(983\) | −10.1301 | −0.323099 | −0.161550 | − | 0.986865i | \(-0.551649\pi\) | ||||
−0.161550 | + | 0.986865i | \(0.551649\pi\) | |||||||
\(984\) | 2.36708 | 0.0754597 | ||||||||
\(985\) | −31.9521 | −1.01808 | ||||||||
\(986\) | 10.1340 | 0.322734 | ||||||||
\(987\) | −95.0929 | −3.02684 | ||||||||
\(988\) | 27.6658 | 0.880165 | ||||||||
\(989\) | −1.19412 | −0.0379709 | ||||||||
\(990\) | 6.97211 | 0.221588 | ||||||||
\(991\) | 11.6121 | 0.368870 | 0.184435 | − | 0.982845i | \(-0.440954\pi\) | ||||
0.184435 | + | 0.982845i | \(0.440954\pi\) | |||||||
\(992\) | 2.75066 | 0.0873334 | ||||||||
\(993\) | 29.5732 | 0.938478 | ||||||||
\(994\) | 51.2359 | 1.62510 | ||||||||
\(995\) | −22.9898 | −0.728826 | ||||||||
\(996\) | 3.97370 | 0.125912 | ||||||||
\(997\) | 7.08944 | 0.224525 | 0.112262 | − | 0.993679i | \(-0.464190\pi\) | ||||
0.112262 | + | 0.993679i | \(0.464190\pi\) | |||||||
\(998\) | 32.1063 | 1.01631 | ||||||||
\(999\) | 42.9556 | 1.35906 |
(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 | 8002.2.a.e.1.2 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.2 | ✓ | 77 | 1.1 | even | 1 | trivial |