Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(156\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43558 | −1.72222 | −0.861109 | − | 0.508420i | \(-0.830230\pi\) | ||||
−0.861109 | + | 0.508420i | \(0.830230\pi\) | |||||||
\(3\) | −1.59767 | −0.922413 | −0.461206 | − | 0.887293i | \(-0.652583\pi\) | ||||
−0.461206 | + | 0.887293i | \(0.652583\pi\) | |||||||
\(4\) | 3.93207 | 1.96604 | ||||||||
\(5\) | −2.50698 | −1.12115 | −0.560577 | − | 0.828102i | \(-0.689421\pi\) | ||||
−0.560577 | + | 0.828102i | \(0.689421\pi\) | |||||||
\(6\) | 3.89125 | 1.58860 | ||||||||
\(7\) | −1.32806 | −0.501959 | −0.250980 | − | 0.967992i | \(-0.580753\pi\) | ||||
−0.250980 | + | 0.967992i | \(0.580753\pi\) | |||||||
\(8\) | −4.70573 | −1.66373 | ||||||||
\(9\) | −0.447465 | −0.149155 | ||||||||
\(10\) | 6.10595 | 1.93087 | ||||||||
\(11\) | −0.0818645 | −0.0246831 | −0.0123415 | − | 0.999924i | \(-0.503929\pi\) | ||||
−0.0123415 | + | 0.999924i | \(0.503929\pi\) | |||||||
\(12\) | −6.28214 | −1.81350 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 3.23460 | 0.864483 | ||||||||
\(15\) | 4.00531 | 1.03417 | ||||||||
\(16\) | 3.59705 | 0.899263 | ||||||||
\(17\) | −3.03467 | −0.736015 | −0.368007 | − | 0.929823i | \(-0.619960\pi\) | ||||
−0.368007 | + | 0.929823i | \(0.619960\pi\) | |||||||
\(18\) | 1.08984 | 0.256877 | ||||||||
\(19\) | 1.84620 | 0.423547 | 0.211774 | − | 0.977319i | \(-0.432076\pi\) | ||||
0.211774 | + | 0.977319i | \(0.432076\pi\) | |||||||
\(20\) | −9.85762 | −2.20423 | ||||||||
\(21\) | 2.12179 | 0.463013 | ||||||||
\(22\) | 0.199388 | 0.0425096 | ||||||||
\(23\) | 1.52399 | 0.317773 | 0.158887 | − | 0.987297i | \(-0.449210\pi\) | ||||
0.158887 | + | 0.987297i | \(0.449210\pi\) | |||||||
\(24\) | 7.51818 | 1.53464 | ||||||||
\(25\) | 1.28493 | 0.256987 | ||||||||
\(26\) | 2.43558 | 0.477657 | ||||||||
\(27\) | 5.50790 | 1.06000 | ||||||||
\(28\) | −5.22203 | −0.986870 | ||||||||
\(29\) | −4.78664 | −0.888856 | −0.444428 | − | 0.895815i | \(-0.646593\pi\) | ||||
−0.444428 | + | 0.895815i | \(0.646593\pi\) | |||||||
\(30\) | −9.75527 | −1.78106 | ||||||||
\(31\) | −8.23735 | −1.47947 | −0.739735 | − | 0.672898i | \(-0.765049\pi\) | ||||
−0.739735 | + | 0.672898i | \(0.765049\pi\) | |||||||
\(32\) | 0.650528 | 0.114998 | ||||||||
\(33\) | 0.130792 | 0.0227680 | ||||||||
\(34\) | 7.39119 | 1.26758 | ||||||||
\(35\) | 3.32941 | 0.562774 | ||||||||
\(36\) | −1.75946 | −0.293244 | ||||||||
\(37\) | −5.92421 | −0.973934 | −0.486967 | − | 0.873420i | \(-0.661897\pi\) | ||||
−0.486967 | + | 0.873420i | \(0.661897\pi\) | |||||||
\(38\) | −4.49658 | −0.729441 | ||||||||
\(39\) | 1.59767 | 0.255831 | ||||||||
\(40\) | 11.7972 | 1.86529 | ||||||||
\(41\) | 4.58663 | 0.716311 | 0.358156 | − | 0.933662i | \(-0.383406\pi\) | ||||
0.358156 | + | 0.933662i | \(0.383406\pi\) | |||||||
\(42\) | −5.16781 | −0.797410 | ||||||||
\(43\) | 3.55579 | 0.542253 | 0.271126 | − | 0.962544i | \(-0.412604\pi\) | ||||
0.271126 | + | 0.962544i | \(0.412604\pi\) | |||||||
\(44\) | −0.321897 | −0.0485278 | ||||||||
\(45\) | 1.12178 | 0.167226 | ||||||||
\(46\) | −3.71180 | −0.547275 | ||||||||
\(47\) | 8.20409 | 1.19669 | 0.598345 | − | 0.801239i | \(-0.295825\pi\) | ||||
0.598345 | + | 0.801239i | \(0.295825\pi\) | |||||||
\(48\) | −5.74689 | −0.829492 | ||||||||
\(49\) | −5.23626 | −0.748037 | ||||||||
\(50\) | −3.12956 | −0.442587 | ||||||||
\(51\) | 4.84838 | 0.678909 | ||||||||
\(52\) | −3.93207 | −0.545280 | ||||||||
\(53\) | −3.16709 | −0.435034 | −0.217517 | − | 0.976057i | \(-0.569796\pi\) | ||||
−0.217517 | + | 0.976057i | \(0.569796\pi\) | |||||||
\(54\) | −13.4149 | −1.82554 | ||||||||
\(55\) | 0.205232 | 0.0276735 | ||||||||
\(56\) | 6.24948 | 0.835123 | ||||||||
\(57\) | −2.94961 | −0.390685 | ||||||||
\(58\) | 11.6583 | 1.53080 | ||||||||
\(59\) | −3.56473 | −0.464088 | −0.232044 | − | 0.972705i | \(-0.574541\pi\) | ||||
−0.232044 | + | 0.972705i | \(0.574541\pi\) | |||||||
\(60\) | 15.7492 | 2.03321 | ||||||||
\(61\) | −9.20735 | −1.17888 | −0.589440 | − | 0.807812i | \(-0.700652\pi\) | ||||
−0.589440 | + | 0.807812i | \(0.700652\pi\) | |||||||
\(62\) | 20.0628 | 2.54797 | ||||||||
\(63\) | 0.594260 | 0.0748697 | ||||||||
\(64\) | −8.77852 | −1.09732 | ||||||||
\(65\) | 2.50698 | 0.310952 | ||||||||
\(66\) | −0.318555 | −0.0392114 | ||||||||
\(67\) | −0.445217 | −0.0543919 | −0.0271960 | − | 0.999630i | \(-0.508658\pi\) | ||||
−0.0271960 | + | 0.999630i | \(0.508658\pi\) | |||||||
\(68\) | −11.9325 | −1.44703 | ||||||||
\(69\) | −2.43482 | −0.293118 | ||||||||
\(70\) | −8.10907 | −0.969219 | ||||||||
\(71\) | 4.51008 | 0.535248 | 0.267624 | − | 0.963523i | \(-0.413761\pi\) | ||||
0.267624 | + | 0.963523i | \(0.413761\pi\) | |||||||
\(72\) | 2.10565 | 0.248153 | ||||||||
\(73\) | −8.94648 | −1.04711 | −0.523553 | − | 0.851993i | \(-0.675394\pi\) | ||||
−0.523553 | + | 0.851993i | \(0.675394\pi\) | |||||||
\(74\) | 14.4289 | 1.67733 | ||||||||
\(75\) | −2.05289 | −0.237048 | ||||||||
\(76\) | 7.25939 | 0.832709 | ||||||||
\(77\) | 0.108721 | 0.0123899 | ||||||||
\(78\) | −3.89125 | −0.440597 | ||||||||
\(79\) | 2.48568 | 0.279661 | 0.139831 | − | 0.990175i | \(-0.455344\pi\) | ||||
0.139831 | + | 0.990175i | \(0.455344\pi\) | |||||||
\(80\) | −9.01773 | −1.00821 | ||||||||
\(81\) | −7.45738 | −0.828598 | ||||||||
\(82\) | −11.1711 | −1.23364 | ||||||||
\(83\) | 5.08585 | 0.558245 | 0.279122 | − | 0.960256i | \(-0.409956\pi\) | ||||
0.279122 | + | 0.960256i | \(0.409956\pi\) | |||||||
\(84\) | 8.34305 | 0.910301 | ||||||||
\(85\) | 7.60784 | 0.825186 | ||||||||
\(86\) | −8.66043 | −0.933878 | ||||||||
\(87\) | 7.64744 | 0.819892 | ||||||||
\(88\) | 0.385232 | 0.0410659 | ||||||||
\(89\) | −8.03176 | −0.851365 | −0.425683 | − | 0.904873i | \(-0.639966\pi\) | ||||
−0.425683 | + | 0.904873i | \(0.639966\pi\) | |||||||
\(90\) | −2.73220 | −0.287999 | ||||||||
\(91\) | 1.32806 | 0.139218 | ||||||||
\(92\) | 5.99243 | 0.624754 | ||||||||
\(93\) | 13.1605 | 1.36468 | ||||||||
\(94\) | −19.9817 | −2.06096 | ||||||||
\(95\) | −4.62838 | −0.474862 | ||||||||
\(96\) | −1.03933 | −0.106076 | ||||||||
\(97\) | −8.27256 | −0.839951 | −0.419975 | − | 0.907535i | \(-0.637961\pi\) | ||||
−0.419975 | + | 0.907535i | \(0.637961\pi\) | |||||||
\(98\) | 12.7534 | 1.28828 | ||||||||
\(99\) | 0.0366315 | 0.00368160 | ||||||||
\(100\) | 5.05245 | 0.505245 | ||||||||
\(101\) | 11.3815 | 1.13250 | 0.566251 | − | 0.824233i | \(-0.308393\pi\) | ||||
0.566251 | + | 0.824233i | \(0.308393\pi\) | |||||||
\(102\) | −11.8086 | −1.16923 | ||||||||
\(103\) | −10.4231 | −1.02701 | −0.513507 | − | 0.858085i | \(-0.671654\pi\) | ||||
−0.513507 | + | 0.858085i | \(0.671654\pi\) | |||||||
\(104\) | 4.70573 | 0.461435 | ||||||||
\(105\) | −5.31929 | −0.519110 | ||||||||
\(106\) | 7.71373 | 0.749223 | ||||||||
\(107\) | 0.472089 | 0.0456386 | 0.0228193 | − | 0.999740i | \(-0.492736\pi\) | ||||
0.0228193 | + | 0.999740i | \(0.492736\pi\) | |||||||
\(108\) | 21.6574 | 2.08399 | ||||||||
\(109\) | −14.7733 | −1.41503 | −0.707513 | − | 0.706700i | \(-0.750183\pi\) | ||||
−0.707513 | + | 0.706700i | \(0.750183\pi\) | |||||||
\(110\) | −0.499861 | −0.0476599 | ||||||||
\(111\) | 9.46490 | 0.898369 | ||||||||
\(112\) | −4.77710 | −0.451393 | ||||||||
\(113\) | −17.4137 | −1.63814 | −0.819072 | − | 0.573690i | \(-0.805511\pi\) | ||||
−0.819072 | + | 0.573690i | \(0.805511\pi\) | |||||||
\(114\) | 7.18402 | 0.672845 | ||||||||
\(115\) | −3.82060 | −0.356273 | ||||||||
\(116\) | −18.8214 | −1.74752 | ||||||||
\(117\) | 0.447465 | 0.0413681 | ||||||||
\(118\) | 8.68221 | 0.799262 | ||||||||
\(119\) | 4.03022 | 0.369449 | ||||||||
\(120\) | −18.8479 | −1.72057 | ||||||||
\(121\) | −10.9933 | −0.999391 | ||||||||
\(122\) | 22.4253 | 2.03029 | ||||||||
\(123\) | −7.32790 | −0.660735 | ||||||||
\(124\) | −32.3898 | −2.90869 | ||||||||
\(125\) | 9.31359 | 0.833032 | ||||||||
\(126\) | −1.44737 | −0.128942 | ||||||||
\(127\) | 8.28930 | 0.735556 | 0.367778 | − | 0.929914i | \(-0.380119\pi\) | ||||
0.367778 | + | 0.929914i | \(0.380119\pi\) | |||||||
\(128\) | 20.0798 | 1.77482 | ||||||||
\(129\) | −5.68096 | −0.500181 | ||||||||
\(130\) | −6.10595 | −0.535528 | ||||||||
\(131\) | 6.50705 | 0.568524 | 0.284262 | − | 0.958747i | \(-0.408251\pi\) | ||||
0.284262 | + | 0.958747i | \(0.408251\pi\) | |||||||
\(132\) | 0.514284 | 0.0447627 | ||||||||
\(133\) | −2.45186 | −0.212603 | ||||||||
\(134\) | 1.08436 | 0.0936748 | ||||||||
\(135\) | −13.8082 | −1.18842 | ||||||||
\(136\) | 14.2803 | 1.22453 | ||||||||
\(137\) | −10.7246 | −0.916260 | −0.458130 | − | 0.888885i | \(-0.651481\pi\) | ||||
−0.458130 | + | 0.888885i | \(0.651481\pi\) | |||||||
\(138\) | 5.93022 | 0.504813 | ||||||||
\(139\) | −7.13823 | −0.605457 | −0.302728 | − | 0.953077i | \(-0.597898\pi\) | ||||
−0.302728 | + | 0.953077i | \(0.597898\pi\) | |||||||
\(140\) | 13.0915 | 1.10643 | ||||||||
\(141\) | −13.1074 | −1.10384 | ||||||||
\(142\) | −10.9847 | −0.921814 | ||||||||
\(143\) | 0.0818645 | 0.00684585 | ||||||||
\(144\) | −1.60955 | −0.134130 | ||||||||
\(145\) | 12.0000 | 0.996545 | ||||||||
\(146\) | 21.7899 | 1.80335 | ||||||||
\(147\) | 8.36579 | 0.689999 | ||||||||
\(148\) | −23.2944 | −1.91479 | ||||||||
\(149\) | −14.9138 | −1.22178 | −0.610892 | − | 0.791714i | \(-0.709189\pi\) | ||||
−0.610892 | + | 0.791714i | \(0.709189\pi\) | |||||||
\(150\) | 5.00000 | 0.408248 | ||||||||
\(151\) | 2.82900 | 0.230221 | 0.115110 | − | 0.993353i | \(-0.463278\pi\) | ||||
0.115110 | + | 0.993353i | \(0.463278\pi\) | |||||||
\(152\) | −8.68771 | −0.704667 | ||||||||
\(153\) | 1.35791 | 0.109780 | ||||||||
\(154\) | −0.264799 | −0.0213381 | ||||||||
\(155\) | 20.6508 | 1.65871 | ||||||||
\(156\) | 6.28214 | 0.502974 | ||||||||
\(157\) | −11.1318 | −0.888416 | −0.444208 | − | 0.895924i | \(-0.646515\pi\) | ||||
−0.444208 | + | 0.895924i | \(0.646515\pi\) | |||||||
\(158\) | −6.05409 | −0.481638 | ||||||||
\(159\) | 5.05996 | 0.401281 | ||||||||
\(160\) | −1.63086 | −0.128931 | ||||||||
\(161\) | −2.02395 | −0.159509 | ||||||||
\(162\) | 18.1631 | 1.42703 | ||||||||
\(163\) | 18.5586 | 1.45362 | 0.726810 | − | 0.686838i | \(-0.241002\pi\) | ||||
0.726810 | + | 0.686838i | \(0.241002\pi\) | |||||||
\(164\) | 18.0350 | 1.40829 | ||||||||
\(165\) | −0.327893 | −0.0255264 | ||||||||
\(166\) | −12.3870 | −0.961420 | ||||||||
\(167\) | −5.34058 | −0.413267 | −0.206633 | − | 0.978418i | \(-0.566251\pi\) | ||||
−0.206633 | + | 0.978418i | \(0.566251\pi\) | |||||||
\(168\) | −9.98459 | −0.770328 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −18.5295 | −1.42115 | ||||||||
\(171\) | −0.826109 | −0.0631742 | ||||||||
\(172\) | 13.9816 | 1.06609 | ||||||||
\(173\) | −3.16590 | −0.240699 | −0.120350 | − | 0.992732i | \(-0.538402\pi\) | ||||
−0.120350 | + | 0.992732i | \(0.538402\pi\) | |||||||
\(174\) | −18.6260 | −1.41203 | ||||||||
\(175\) | −1.70647 | −0.128997 | ||||||||
\(176\) | −0.294471 | −0.0221966 | ||||||||
\(177\) | 5.69525 | 0.428081 | ||||||||
\(178\) | 19.5620 | 1.46624 | ||||||||
\(179\) | −10.0078 | −0.748021 | −0.374011 | − | 0.927424i | \(-0.622018\pi\) | ||||
−0.374011 | + | 0.927424i | \(0.622018\pi\) | |||||||
\(180\) | 4.41094 | 0.328772 | ||||||||
\(181\) | −16.7932 | −1.24823 | −0.624114 | − | 0.781333i | \(-0.714540\pi\) | ||||
−0.624114 | + | 0.781333i | \(0.714540\pi\) | |||||||
\(182\) | −3.23460 | −0.239765 | ||||||||
\(183\) | 14.7103 | 1.08741 | ||||||||
\(184\) | −7.17147 | −0.528688 | ||||||||
\(185\) | 14.8519 | 1.09193 | ||||||||
\(186\) | −32.0536 | −2.35028 | ||||||||
\(187\) | 0.248431 | 0.0181671 | ||||||||
\(188\) | 32.2591 | 2.35273 | ||||||||
\(189\) | −7.31481 | −0.532074 | ||||||||
\(190\) | 11.2728 | 0.817816 | ||||||||
\(191\) | −19.9150 | −1.44100 | −0.720499 | − | 0.693456i | \(-0.756087\pi\) | ||||
−0.720499 | + | 0.693456i | \(0.756087\pi\) | |||||||
\(192\) | 14.0251 | 1.01218 | ||||||||
\(193\) | −9.22002 | −0.663672 | −0.331836 | − | 0.943337i | \(-0.607668\pi\) | ||||
−0.331836 | + | 0.943337i | \(0.607668\pi\) | |||||||
\(194\) | 20.1485 | 1.44658 | ||||||||
\(195\) | −4.00531 | −0.286826 | ||||||||
\(196\) | −20.5894 | −1.47067 | ||||||||
\(197\) | 3.25996 | 0.232262 | 0.116131 | − | 0.993234i | \(-0.462951\pi\) | ||||
0.116131 | + | 0.993234i | \(0.462951\pi\) | |||||||
\(198\) | −0.0892191 | −0.00634052 | ||||||||
\(199\) | −0.0915695 | −0.00649119 | −0.00324559 | − | 0.999995i | \(-0.501033\pi\) | ||||
−0.00324559 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(200\) | −6.04655 | −0.427555 | ||||||||
\(201\) | 0.711308 | 0.0501718 | ||||||||
\(202\) | −27.7206 | −1.95042 | ||||||||
\(203\) | 6.35694 | 0.446169 | ||||||||
\(204\) | 19.0642 | 1.33476 | ||||||||
\(205\) | −11.4986 | −0.803095 | ||||||||
\(206\) | 25.3863 | 1.76874 | ||||||||
\(207\) | −0.681931 | −0.0473975 | ||||||||
\(208\) | −3.59705 | −0.249411 | ||||||||
\(209\) | −0.151138 | −0.0104544 | ||||||||
\(210\) | 12.9556 | 0.894020 | ||||||||
\(211\) | −27.5262 | −1.89498 | −0.947492 | − | 0.319779i | \(-0.896391\pi\) | ||||
−0.947492 | + | 0.319779i | \(0.896391\pi\) | |||||||
\(212\) | −12.4532 | −0.855292 | ||||||||
\(213\) | −7.20560 | −0.493720 | ||||||||
\(214\) | −1.14981 | −0.0785996 | ||||||||
\(215\) | −8.91428 | −0.607949 | ||||||||
\(216\) | −25.9187 | −1.76354 | ||||||||
\(217\) | 10.9397 | 0.742634 | ||||||||
\(218\) | 35.9816 | 2.43698 | ||||||||
\(219\) | 14.2935 | 0.965864 | ||||||||
\(220\) | 0.806989 | 0.0544072 | ||||||||
\(221\) | 3.03467 | 0.204134 | ||||||||
\(222\) | −23.0526 | −1.54719 | ||||||||
\(223\) | −20.7384 | −1.38874 | −0.694372 | − | 0.719616i | \(-0.744318\pi\) | ||||
−0.694372 | + | 0.719616i | \(0.744318\pi\) | |||||||
\(224\) | −0.863940 | −0.0577244 | ||||||||
\(225\) | −0.574963 | −0.0383308 | ||||||||
\(226\) | 42.4126 | 2.82124 | ||||||||
\(227\) | −2.74059 | −0.181899 | −0.0909497 | − | 0.995855i | \(-0.528990\pi\) | ||||
−0.0909497 | + | 0.995855i | \(0.528990\pi\) | |||||||
\(228\) | −11.5981 | −0.768102 | ||||||||
\(229\) | 20.1930 | 1.33439 | 0.667196 | − | 0.744882i | \(-0.267494\pi\) | ||||
0.667196 | + | 0.744882i | \(0.267494\pi\) | |||||||
\(230\) | 9.30540 | 0.613580 | ||||||||
\(231\) | −0.173700 | −0.0114286 | ||||||||
\(232\) | 22.5246 | 1.47881 | ||||||||
\(233\) | 23.2831 | 1.52533 | 0.762665 | − | 0.646794i | \(-0.223891\pi\) | ||||
0.762665 | + | 0.646794i | \(0.223891\pi\) | |||||||
\(234\) | −1.08984 | −0.0712450 | ||||||||
\(235\) | −20.5675 | −1.34167 | ||||||||
\(236\) | −14.0168 | −0.912415 | ||||||||
\(237\) | −3.97129 | −0.257963 | ||||||||
\(238\) | −9.81593 | −0.636272 | ||||||||
\(239\) | −0.494455 | −0.0319836 | −0.0159918 | − | 0.999872i | \(-0.505091\pi\) | ||||
−0.0159918 | + | 0.999872i | \(0.505091\pi\) | |||||||
\(240\) | 14.4073 | 0.929988 | ||||||||
\(241\) | 25.7368 | 1.65786 | 0.828928 | − | 0.559355i | \(-0.188951\pi\) | ||||
0.828928 | + | 0.559355i | \(0.188951\pi\) | |||||||
\(242\) | 26.7751 | 1.72117 | ||||||||
\(243\) | −4.60929 | −0.295686 | ||||||||
\(244\) | −36.2040 | −2.31772 | ||||||||
\(245\) | 13.1272 | 0.838665 | ||||||||
\(246\) | 17.8477 | 1.13793 | ||||||||
\(247\) | −1.84620 | −0.117471 | ||||||||
\(248\) | 38.7627 | 2.46143 | ||||||||
\(249\) | −8.12549 | −0.514932 | ||||||||
\(250\) | −22.6840 | −1.43466 | ||||||||
\(251\) | −11.7881 | −0.744057 | −0.372029 | − | 0.928221i | \(-0.621338\pi\) | ||||
−0.372029 | + | 0.928221i | \(0.621338\pi\) | |||||||
\(252\) | 2.33667 | 0.147197 | ||||||||
\(253\) | −0.124760 | −0.00784362 | ||||||||
\(254\) | −20.1893 | −1.26679 | ||||||||
\(255\) | −12.1548 | −0.761162 | ||||||||
\(256\) | −31.3490 | −1.95931 | ||||||||
\(257\) | −1.52470 | −0.0951081 | −0.0475541 | − | 0.998869i | \(-0.515143\pi\) | ||||
−0.0475541 | + | 0.998869i | \(0.515143\pi\) | |||||||
\(258\) | 13.8365 | 0.861421 | ||||||||
\(259\) | 7.86770 | 0.488875 | ||||||||
\(260\) | 9.85762 | 0.611343 | ||||||||
\(261\) | 2.14185 | 0.132577 | ||||||||
\(262\) | −15.8485 | −0.979122 | ||||||||
\(263\) | −5.65818 | −0.348898 | −0.174449 | − | 0.984666i | \(-0.555814\pi\) | ||||
−0.174449 | + | 0.984666i | \(0.555814\pi\) | |||||||
\(264\) | −0.615472 | −0.0378797 | ||||||||
\(265\) | 7.93983 | 0.487740 | ||||||||
\(266\) | 5.97172 | 0.366150 | ||||||||
\(267\) | 12.8321 | 0.785310 | ||||||||
\(268\) | −1.75063 | −0.106937 | ||||||||
\(269\) | −13.1069 | −0.799142 | −0.399571 | − | 0.916702i | \(-0.630841\pi\) | ||||
−0.399571 | + | 0.916702i | \(0.630841\pi\) | |||||||
\(270\) | 33.6310 | 2.04672 | ||||||||
\(271\) | −20.1402 | −1.22343 | −0.611716 | − | 0.791078i | \(-0.709520\pi\) | ||||
−0.611716 | + | 0.791078i | \(0.709520\pi\) | |||||||
\(272\) | −10.9159 | −0.661871 | ||||||||
\(273\) | −2.12179 | −0.128417 | ||||||||
\(274\) | 26.1206 | 1.57800 | ||||||||
\(275\) | −0.105190 | −0.00634322 | ||||||||
\(276\) | −9.57390 | −0.576281 | ||||||||
\(277\) | 8.49900 | 0.510655 | 0.255328 | − | 0.966855i | \(-0.417817\pi\) | ||||
0.255328 | + | 0.966855i | \(0.417817\pi\) | |||||||
\(278\) | 17.3858 | 1.04273 | ||||||||
\(279\) | 3.68592 | 0.220670 | ||||||||
\(280\) | −15.6673 | −0.936301 | ||||||||
\(281\) | −7.97738 | −0.475891 | −0.237945 | − | 0.971279i | \(-0.576474\pi\) | ||||
−0.237945 | + | 0.971279i | \(0.576474\pi\) | |||||||
\(282\) | 31.9242 | 1.90106 | ||||||||
\(283\) | −12.1424 | −0.721792 | −0.360896 | − | 0.932606i | \(-0.617529\pi\) | ||||
−0.360896 | + | 0.932606i | \(0.617529\pi\) | |||||||
\(284\) | 17.7340 | 1.05232 | ||||||||
\(285\) | 7.39460 | 0.438018 | ||||||||
\(286\) | −0.199388 | −0.0117901 | ||||||||
\(287\) | −6.09132 | −0.359559 | ||||||||
\(288\) | −0.291089 | −0.0171526 | ||||||||
\(289\) | −7.79080 | −0.458283 | ||||||||
\(290\) | −29.2270 | −1.71627 | ||||||||
\(291\) | 13.2168 | 0.774781 | ||||||||
\(292\) | −35.1782 | −2.05865 | ||||||||
\(293\) | 11.9372 | 0.697376 | 0.348688 | − | 0.937239i | \(-0.386627\pi\) | ||||
0.348688 | + | 0.937239i | \(0.386627\pi\) | |||||||
\(294\) | −20.3756 | −1.18833 | ||||||||
\(295\) | 8.93670 | 0.520315 | ||||||||
\(296\) | 27.8777 | 1.62036 | ||||||||
\(297\) | −0.450901 | −0.0261639 | ||||||||
\(298\) | 36.3237 | 2.10418 | ||||||||
\(299\) | −1.52399 | −0.0881345 | ||||||||
\(300\) | −8.07213 | −0.466045 | ||||||||
\(301\) | −4.72230 | −0.272189 | ||||||||
\(302\) | −6.89027 | −0.396490 | ||||||||
\(303\) | −18.1838 | −1.04463 | ||||||||
\(304\) | 6.64088 | 0.380880 | ||||||||
\(305\) | 23.0826 | 1.32171 | ||||||||
\(306\) | −3.30730 | −0.189065 | ||||||||
\(307\) | −15.9848 | −0.912303 | −0.456152 | − | 0.889902i | \(-0.650773\pi\) | ||||
−0.456152 | + | 0.889902i | \(0.650773\pi\) | |||||||
\(308\) | 0.427499 | 0.0243590 | ||||||||
\(309\) | 16.6526 | 0.947332 | ||||||||
\(310\) | −50.2969 | −2.85667 | ||||||||
\(311\) | −6.98418 | −0.396037 | −0.198018 | − | 0.980198i | \(-0.563451\pi\) | ||||
−0.198018 | + | 0.980198i | \(0.563451\pi\) | |||||||
\(312\) | −7.51818 | −0.425633 | ||||||||
\(313\) | −30.3023 | −1.71279 | −0.856394 | − | 0.516323i | \(-0.827300\pi\) | ||||
−0.856394 | + | 0.516323i | \(0.827300\pi\) | |||||||
\(314\) | 27.1125 | 1.53005 | ||||||||
\(315\) | −1.48980 | −0.0839405 | ||||||||
\(316\) | 9.77389 | 0.549824 | ||||||||
\(317\) | −20.2025 | −1.13468 | −0.567342 | − | 0.823482i | \(-0.692028\pi\) | ||||
−0.567342 | + | 0.823482i | \(0.692028\pi\) | |||||||
\(318\) | −12.3240 | −0.691093 | ||||||||
\(319\) | 0.391856 | 0.0219397 | ||||||||
\(320\) | 22.0076 | 1.23026 | ||||||||
\(321\) | −0.754240 | −0.0420976 | ||||||||
\(322\) | 4.92949 | 0.274710 | ||||||||
\(323\) | −5.60260 | −0.311737 | ||||||||
\(324\) | −29.3230 | −1.62905 | ||||||||
\(325\) | −1.28493 | −0.0712753 | ||||||||
\(326\) | −45.2010 | −2.50345 | ||||||||
\(327\) | 23.6028 | 1.30524 | ||||||||
\(328\) | −21.5834 | −1.19175 | ||||||||
\(329\) | −10.8955 | −0.600689 | ||||||||
\(330\) | 0.798611 | 0.0439621 | ||||||||
\(331\) | −5.94385 | −0.326703 | −0.163352 | − | 0.986568i | \(-0.552231\pi\) | ||||
−0.163352 | + | 0.986568i | \(0.552231\pi\) | |||||||
\(332\) | 19.9979 | 1.09753 | ||||||||
\(333\) | 2.65087 | 0.145267 | ||||||||
\(334\) | 13.0074 | 0.711736 | ||||||||
\(335\) | 1.11615 | 0.0609817 | ||||||||
\(336\) | 7.63221 | 0.416371 | ||||||||
\(337\) | 25.5594 | 1.39231 | 0.696155 | − | 0.717891i | \(-0.254892\pi\) | ||||
0.696155 | + | 0.717891i | \(0.254892\pi\) | |||||||
\(338\) | −2.43558 | −0.132478 | ||||||||
\(339\) | 27.8213 | 1.51105 | ||||||||
\(340\) | 29.9146 | 1.62235 | ||||||||
\(341\) | 0.674346 | 0.0365179 | ||||||||
\(342\) | 2.01206 | 0.108800 | ||||||||
\(343\) | 16.2505 | 0.877443 | ||||||||
\(344\) | −16.7326 | −0.902160 | ||||||||
\(345\) | 6.10404 | 0.328631 | ||||||||
\(346\) | 7.71082 | 0.414536 | ||||||||
\(347\) | −10.3442 | −0.555304 | −0.277652 | − | 0.960682i | \(-0.589556\pi\) | ||||
−0.277652 | + | 0.960682i | \(0.589556\pi\) | |||||||
\(348\) | 30.0703 | 1.61194 | ||||||||
\(349\) | −35.0327 | −1.87525 | −0.937627 | − | 0.347642i | \(-0.886983\pi\) | ||||
−0.937627 | + | 0.347642i | \(0.886983\pi\) | |||||||
\(350\) | 4.15625 | 0.222161 | ||||||||
\(351\) | −5.50790 | −0.293990 | ||||||||
\(352\) | −0.0532552 | −0.00283851 | ||||||||
\(353\) | −8.36434 | −0.445189 | −0.222594 | − | 0.974911i | \(-0.571453\pi\) | ||||
−0.222594 | + | 0.974911i | \(0.571453\pi\) | |||||||
\(354\) | −13.8713 | −0.737249 | ||||||||
\(355\) | −11.3067 | −0.600096 | ||||||||
\(356\) | −31.5815 | −1.67382 | ||||||||
\(357\) | −6.43894 | −0.340785 | ||||||||
\(358\) | 24.3750 | 1.28826 | ||||||||
\(359\) | 5.65616 | 0.298521 | 0.149260 | − | 0.988798i | \(-0.452311\pi\) | ||||
0.149260 | + | 0.988798i | \(0.452311\pi\) | |||||||
\(360\) | −5.27881 | −0.278218 | ||||||||
\(361\) | −15.5915 | −0.820608 | ||||||||
\(362\) | 40.9013 | 2.14972 | ||||||||
\(363\) | 17.5636 | 0.921851 | ||||||||
\(364\) | 5.22203 | 0.273709 | ||||||||
\(365\) | 22.4286 | 1.17397 | ||||||||
\(366\) | −35.8281 | −1.87276 | ||||||||
\(367\) | −10.4385 | −0.544885 | −0.272442 | − | 0.962172i | \(-0.587831\pi\) | ||||
−0.272442 | + | 0.962172i | \(0.587831\pi\) | |||||||
\(368\) | 5.48186 | 0.285762 | ||||||||
\(369\) | −2.05236 | −0.106841 | ||||||||
\(370\) | −36.1730 | −1.88054 | ||||||||
\(371\) | 4.20609 | 0.218369 | ||||||||
\(372\) | 51.7481 | 2.68302 | ||||||||
\(373\) | −1.50418 | −0.0778833 | −0.0389417 | − | 0.999241i | \(-0.512399\pi\) | ||||
−0.0389417 | + | 0.999241i | \(0.512399\pi\) | |||||||
\(374\) | −0.605076 | −0.0312877 | ||||||||
\(375\) | −14.8800 | −0.768400 | ||||||||
\(376\) | −38.6062 | −1.99096 | ||||||||
\(377\) | 4.78664 | 0.246524 | ||||||||
\(378\) | 17.8158 | 0.916348 | ||||||||
\(379\) | −14.0096 | −0.719625 | −0.359813 | − | 0.933025i | \(-0.617159\pi\) | ||||
−0.359813 | + | 0.933025i | \(0.617159\pi\) | |||||||
\(380\) | −18.1991 | −0.933596 | ||||||||
\(381\) | −13.2435 | −0.678487 | ||||||||
\(382\) | 48.5046 | 2.48171 | ||||||||
\(383\) | 18.7117 | 0.956124 | 0.478062 | − | 0.878326i | \(-0.341339\pi\) | ||||
0.478062 | + | 0.878326i | \(0.341339\pi\) | |||||||
\(384\) | −32.0808 | −1.63712 | ||||||||
\(385\) | −0.272561 | −0.0138910 | ||||||||
\(386\) | 22.4561 | 1.14299 | ||||||||
\(387\) | −1.59109 | −0.0808797 | ||||||||
\(388\) | −32.5283 | −1.65137 | ||||||||
\(389\) | −24.2764 | −1.23086 | −0.615431 | − | 0.788191i | \(-0.711018\pi\) | ||||
−0.615431 | + | 0.788191i | \(0.711018\pi\) | |||||||
\(390\) | 9.75527 | 0.493977 | ||||||||
\(391\) | −4.62479 | −0.233886 | ||||||||
\(392\) | 24.6404 | 1.24453 | ||||||||
\(393\) | −10.3961 | −0.524414 | ||||||||
\(394\) | −7.93990 | −0.400006 | ||||||||
\(395\) | −6.23155 | −0.313543 | ||||||||
\(396\) | 0.144038 | 0.00723817 | ||||||||
\(397\) | −0.951470 | −0.0477529 | −0.0238764 | − | 0.999715i | \(-0.507601\pi\) | ||||
−0.0238764 | + | 0.999715i | \(0.507601\pi\) | |||||||
\(398\) | 0.223025 | 0.0111792 | ||||||||
\(399\) | 3.91726 | 0.196108 | ||||||||
\(400\) | 4.62197 | 0.231099 | ||||||||
\(401\) | 4.08644 | 0.204067 | 0.102033 | − | 0.994781i | \(-0.467465\pi\) | ||||
0.102033 | + | 0.994781i | \(0.467465\pi\) | |||||||
\(402\) | −1.73245 | −0.0864068 | ||||||||
\(403\) | 8.23735 | 0.410331 | ||||||||
\(404\) | 44.7529 | 2.22654 | ||||||||
\(405\) | 18.6955 | 0.928986 | ||||||||
\(406\) | −15.4829 | −0.768401 | ||||||||
\(407\) | 0.484982 | 0.0240397 | ||||||||
\(408\) | −22.8152 | −1.12952 | ||||||||
\(409\) | −17.8488 | −0.882565 | −0.441282 | − | 0.897368i | \(-0.645476\pi\) | ||||
−0.441282 | + | 0.897368i | \(0.645476\pi\) | |||||||
\(410\) | 28.0058 | 1.38311 | ||||||||
\(411\) | 17.1342 | 0.845170 | ||||||||
\(412\) | −40.9842 | −2.01915 | ||||||||
\(413\) | 4.73417 | 0.232953 | ||||||||
\(414\) | 1.66090 | 0.0816288 | ||||||||
\(415\) | −12.7501 | −0.625879 | ||||||||
\(416\) | −0.650528 | −0.0318948 | ||||||||
\(417\) | 11.4045 | 0.558481 | ||||||||
\(418\) | 0.368110 | 0.0180048 | ||||||||
\(419\) | −15.1391 | −0.739594 | −0.369797 | − | 0.929112i | \(-0.620573\pi\) | ||||
−0.369797 | + | 0.929112i | \(0.620573\pi\) | |||||||
\(420\) | −20.9158 | −1.02059 | ||||||||
\(421\) | 9.99427 | 0.487091 | 0.243545 | − | 0.969889i | \(-0.421690\pi\) | ||||
0.243545 | + | 0.969889i | \(0.421690\pi\) | |||||||
\(422\) | 67.0425 | 3.26358 | ||||||||
\(423\) | −3.67104 | −0.178492 | ||||||||
\(424\) | 14.9035 | 0.723777 | ||||||||
\(425\) | −3.89934 | −0.189146 | ||||||||
\(426\) | 17.5498 | 0.850293 | ||||||||
\(427\) | 12.2279 | 0.591750 | ||||||||
\(428\) | 1.85629 | 0.0897271 | ||||||||
\(429\) | −0.130792 | −0.00631470 | ||||||||
\(430\) | 21.7115 | 1.04702 | ||||||||
\(431\) | −38.6975 | −1.86399 | −0.931996 | − | 0.362468i | \(-0.881934\pi\) | ||||
−0.931996 | + | 0.362468i | \(0.881934\pi\) | |||||||
\(432\) | 19.8122 | 0.953215 | ||||||||
\(433\) | −8.70363 | −0.418270 | −0.209135 | − | 0.977887i | \(-0.567065\pi\) | ||||
−0.209135 | + | 0.977887i | \(0.567065\pi\) | |||||||
\(434\) | −26.6445 | −1.27898 | ||||||||
\(435\) | −19.1720 | −0.919226 | ||||||||
\(436\) | −58.0897 | −2.78199 | ||||||||
\(437\) | 2.81358 | 0.134592 | ||||||||
\(438\) | −34.8130 | −1.66343 | ||||||||
\(439\) | 7.77716 | 0.371184 | 0.185592 | − | 0.982627i | \(-0.440580\pi\) | ||||
0.185592 | + | 0.982627i | \(0.440580\pi\) | |||||||
\(440\) | −0.965768 | −0.0460412 | ||||||||
\(441\) | 2.34304 | 0.111573 | ||||||||
\(442\) | −7.39119 | −0.351563 | ||||||||
\(443\) | 2.82133 | 0.134046 | 0.0670228 | − | 0.997751i | \(-0.478650\pi\) | ||||
0.0670228 | + | 0.997751i | \(0.478650\pi\) | |||||||
\(444\) | 37.2167 | 1.76623 | ||||||||
\(445\) | 20.1354 | 0.954512 | ||||||||
\(446\) | 50.5100 | 2.39172 | ||||||||
\(447\) | 23.8272 | 1.12699 | ||||||||
\(448\) | 11.6584 | 0.550808 | ||||||||
\(449\) | −24.9130 | −1.17572 | −0.587860 | − | 0.808963i | \(-0.700029\pi\) | ||||
−0.587860 | + | 0.808963i | \(0.700029\pi\) | |||||||
\(450\) | 1.40037 | 0.0660141 | ||||||||
\(451\) | −0.375482 | −0.0176808 | ||||||||
\(452\) | −68.4720 | −3.22065 | ||||||||
\(453\) | −4.51979 | −0.212358 | ||||||||
\(454\) | 6.67494 | 0.313270 | ||||||||
\(455\) | −3.32941 | −0.156085 | ||||||||
\(456\) | 13.8801 | 0.649993 | ||||||||
\(457\) | 27.1922 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(458\) | −49.1818 | −2.29811 | ||||||||
\(459\) | −16.7146 | −0.780172 | ||||||||
\(460\) | −15.0229 | −0.700445 | ||||||||
\(461\) | −23.4038 | −1.09003 | −0.545013 | − | 0.838428i | \(-0.683475\pi\) | ||||
−0.545013 | + | 0.838428i | \(0.683475\pi\) | |||||||
\(462\) | 0.423060 | 0.0196825 | ||||||||
\(463\) | 34.8865 | 1.62131 | 0.810657 | − | 0.585521i | \(-0.199110\pi\) | ||||
0.810657 | + | 0.585521i | \(0.199110\pi\) | |||||||
\(464\) | −17.2178 | −0.799316 | ||||||||
\(465\) | −32.9931 | −1.53002 | ||||||||
\(466\) | −56.7081 | −2.62695 | ||||||||
\(467\) | 19.9207 | 0.921819 | 0.460910 | − | 0.887447i | \(-0.347523\pi\) | ||||
0.460910 | + | 0.887447i | \(0.347523\pi\) | |||||||
\(468\) | 1.75946 | 0.0813313 | ||||||||
\(469\) | 0.591275 | 0.0273025 | ||||||||
\(470\) | 50.0938 | 2.31065 | ||||||||
\(471\) | 17.7849 | 0.819486 | ||||||||
\(472\) | 16.7747 | 0.772116 | ||||||||
\(473\) | −0.291093 | −0.0133845 | ||||||||
\(474\) | 9.67241 | 0.444269 | ||||||||
\(475\) | 2.37224 | 0.108846 | ||||||||
\(476\) | 15.8471 | 0.726351 | ||||||||
\(477\) | 1.41716 | 0.0648874 | ||||||||
\(478\) | 1.20429 | 0.0550828 | ||||||||
\(479\) | 3.70213 | 0.169155 | 0.0845774 | − | 0.996417i | \(-0.473046\pi\) | ||||
0.0845774 | + | 0.996417i | \(0.473046\pi\) | |||||||
\(480\) | 2.60557 | 0.118927 | ||||||||
\(481\) | 5.92421 | 0.270121 | ||||||||
\(482\) | −62.6843 | −2.85519 | ||||||||
\(483\) | 3.23359 | 0.147133 | ||||||||
\(484\) | −43.2265 | −1.96484 | ||||||||
\(485\) | 20.7391 | 0.941714 | ||||||||
\(486\) | 11.2263 | 0.509236 | ||||||||
\(487\) | 6.57823 | 0.298088 | 0.149044 | − | 0.988831i | \(-0.452380\pi\) | ||||
0.149044 | + | 0.988831i | \(0.452380\pi\) | |||||||
\(488\) | 43.3273 | 1.96133 | ||||||||
\(489\) | −29.6504 | −1.34084 | ||||||||
\(490\) | −31.9724 | −1.44436 | ||||||||
\(491\) | −28.0197 | −1.26451 | −0.632255 | − | 0.774761i | \(-0.717870\pi\) | ||||
−0.632255 | + | 0.774761i | \(0.717870\pi\) | |||||||
\(492\) | −28.8138 | −1.29903 | ||||||||
\(493\) | 14.5258 | 0.654211 | ||||||||
\(494\) | 4.49658 | 0.202311 | ||||||||
\(495\) | −0.0918343 | −0.00412764 | ||||||||
\(496\) | −29.6302 | −1.33043 | ||||||||
\(497\) | −5.98965 | −0.268673 | ||||||||
\(498\) | 19.7903 | 0.886826 | ||||||||
\(499\) | 33.5776 | 1.50314 | 0.751571 | − | 0.659652i | \(-0.229296\pi\) | ||||
0.751571 | + | 0.659652i | \(0.229296\pi\) | |||||||
\(500\) | 36.6217 | 1.63777 | ||||||||
\(501\) | 8.53247 | 0.381202 | ||||||||
\(502\) | 28.7109 | 1.28143 | ||||||||
\(503\) | 4.23301 | 0.188741 | 0.0943703 | − | 0.995537i | \(-0.469916\pi\) | ||||
0.0943703 | + | 0.995537i | \(0.469916\pi\) | |||||||
\(504\) | −2.79642 | −0.124563 | ||||||||
\(505\) | −28.5332 | −1.26971 | ||||||||
\(506\) | 0.303865 | 0.0135084 | ||||||||
\(507\) | −1.59767 | −0.0709548 | ||||||||
\(508\) | 32.5941 | 1.44613 | ||||||||
\(509\) | 12.5482 | 0.556191 | 0.278095 | − | 0.960553i | \(-0.410297\pi\) | ||||
0.278095 | + | 0.960553i | \(0.410297\pi\) | |||||||
\(510\) | 29.6040 | 1.31089 | ||||||||
\(511\) | 11.8815 | 0.525605 | ||||||||
\(512\) | 36.1935 | 1.59954 | ||||||||
\(513\) | 10.1687 | 0.448958 | ||||||||
\(514\) | 3.71353 | 0.163797 | ||||||||
\(515\) | 26.1304 | 1.15144 | ||||||||
\(516\) | −22.3380 | −0.983374 | ||||||||
\(517\) | −0.671623 | −0.0295380 | ||||||||
\(518\) | −19.1624 | −0.841950 | ||||||||
\(519\) | 5.05805 | 0.222024 | ||||||||
\(520\) | −11.7972 | −0.517339 | ||||||||
\(521\) | −21.7258 | −0.951827 | −0.475913 | − | 0.879492i | \(-0.657882\pi\) | ||||
−0.475913 | + | 0.879492i | \(0.657882\pi\) | |||||||
\(522\) | −5.21666 | −0.228327 | ||||||||
\(523\) | −44.3723 | −1.94026 | −0.970132 | − | 0.242577i | \(-0.922007\pi\) | ||||
−0.970132 | + | 0.242577i | \(0.922007\pi\) | |||||||
\(524\) | 25.5862 | 1.11774 | ||||||||
\(525\) | 2.72636 | 0.118988 | ||||||||
\(526\) | 13.7810 | 0.600879 | ||||||||
\(527\) | 24.9976 | 1.08891 | ||||||||
\(528\) | 0.470466 | 0.0204744 | ||||||||
\(529\) | −20.6775 | −0.899020 | ||||||||
\(530\) | −19.3381 | −0.839995 | ||||||||
\(531\) | 1.59509 | 0.0692211 | ||||||||
\(532\) | −9.64090 | −0.417986 | ||||||||
\(533\) | −4.58663 | −0.198669 | ||||||||
\(534\) | −31.2536 | −1.35248 | ||||||||
\(535\) | −1.18352 | −0.0511679 | ||||||||
\(536\) | 2.09507 | 0.0904933 | ||||||||
\(537\) | 15.9892 | 0.689984 | ||||||||
\(538\) | 31.9230 | 1.37630 | ||||||||
\(539\) | 0.428664 | 0.0184639 | ||||||||
\(540\) | −54.2947 | −2.33647 | ||||||||
\(541\) | 8.11716 | 0.348984 | 0.174492 | − | 0.984659i | \(-0.444172\pi\) | ||||
0.174492 | + | 0.984659i | \(0.444172\pi\) | |||||||
\(542\) | 49.0532 | 2.10702 | ||||||||
\(543\) | 26.8299 | 1.15138 | ||||||||
\(544\) | −1.97414 | −0.0846404 | ||||||||
\(545\) | 37.0363 | 1.58646 | ||||||||
\(546\) | 5.16781 | 0.221162 | ||||||||
\(547\) | 27.2581 | 1.16547 | 0.582735 | − | 0.812662i | \(-0.301982\pi\) | ||||
0.582735 | + | 0.812662i | \(0.301982\pi\) | |||||||
\(548\) | −42.1697 | −1.80140 | ||||||||
\(549\) | 4.11996 | 0.175836 | ||||||||
\(550\) | 0.256200 | 0.0109244 | ||||||||
\(551\) | −8.83709 | −0.376473 | ||||||||
\(552\) | 11.4576 | 0.487668 | ||||||||
\(553\) | −3.30113 | −0.140379 | ||||||||
\(554\) | −20.7000 | −0.879460 | ||||||||
\(555\) | −23.7283 | −1.00721 | ||||||||
\(556\) | −28.0680 | −1.19035 | ||||||||
\(557\) | −1.12080 | −0.0474897 | −0.0237448 | − | 0.999718i | \(-0.507559\pi\) | ||||
−0.0237448 | + | 0.999718i | \(0.507559\pi\) | |||||||
\(558\) | −8.97738 | −0.380043 | ||||||||
\(559\) | −3.55579 | −0.150394 | ||||||||
\(560\) | 11.9761 | 0.506082 | ||||||||
\(561\) | −0.396910 | −0.0167576 | ||||||||
\(562\) | 19.4296 | 0.819588 | ||||||||
\(563\) | 6.69766 | 0.282273 | 0.141136 | − | 0.989990i | \(-0.454924\pi\) | ||||
0.141136 | + | 0.989990i | \(0.454924\pi\) | |||||||
\(564\) | −51.5392 | −2.17019 | ||||||||
\(565\) | 43.6558 | 1.83661 | ||||||||
\(566\) | 29.5739 | 1.24308 | ||||||||
\(567\) | 9.90384 | 0.415922 | ||||||||
\(568\) | −21.2232 | −0.890506 | ||||||||
\(569\) | 21.4844 | 0.900672 | 0.450336 | − | 0.892859i | \(-0.351304\pi\) | ||||
0.450336 | + | 0.892859i | \(0.351304\pi\) | |||||||
\(570\) | −18.0102 | −0.754364 | ||||||||
\(571\) | −13.9764 | −0.584895 | −0.292448 | − | 0.956282i | \(-0.594470\pi\) | ||||
−0.292448 | + | 0.956282i | \(0.594470\pi\) | |||||||
\(572\) | 0.321897 | 0.0134592 | ||||||||
\(573\) | 31.8175 | 1.32919 | ||||||||
\(574\) | 14.8359 | 0.619239 | ||||||||
\(575\) | 1.95822 | 0.0816635 | ||||||||
\(576\) | 3.92808 | 0.163670 | ||||||||
\(577\) | −10.1516 | −0.422618 | −0.211309 | − | 0.977419i | \(-0.567773\pi\) | ||||
−0.211309 | + | 0.977419i | \(0.567773\pi\) | |||||||
\(578\) | 18.9752 | 0.789263 | ||||||||
\(579\) | 14.7305 | 0.612179 | ||||||||
\(580\) | 47.1848 | 1.95924 | ||||||||
\(581\) | −6.75431 | −0.280216 | ||||||||
\(582\) | −32.1906 | −1.33434 | ||||||||
\(583\) | 0.259273 | 0.0107380 | ||||||||
\(584\) | 42.0997 | 1.74210 | ||||||||
\(585\) | −1.12178 | −0.0463801 | ||||||||
\(586\) | −29.0739 | −1.20103 | ||||||||
\(587\) | 39.4332 | 1.62758 | 0.813791 | − | 0.581157i | \(-0.197400\pi\) | ||||
0.813791 | + | 0.581157i | \(0.197400\pi\) | |||||||
\(588\) | 32.8949 | 1.35656 | ||||||||
\(589\) | −15.2078 | −0.626626 | ||||||||
\(590\) | −21.7661 | −0.896096 | ||||||||
\(591\) | −5.20832 | −0.214242 | ||||||||
\(592\) | −21.3097 | −0.875823 | ||||||||
\(593\) | −34.5303 | −1.41799 | −0.708995 | − | 0.705214i | \(-0.750851\pi\) | ||||
−0.708995 | + | 0.705214i | \(0.750851\pi\) | |||||||
\(594\) | 1.09821 | 0.0450600 | ||||||||
\(595\) | −10.1037 | −0.414210 | ||||||||
\(596\) | −58.6420 | −2.40207 | ||||||||
\(597\) | 0.146297 | 0.00598756 | ||||||||
\(598\) | 3.71180 | 0.151787 | ||||||||
\(599\) | 1.88807 | 0.0771446 | 0.0385723 | − | 0.999256i | \(-0.487719\pi\) | ||||
0.0385723 | + | 0.999256i | \(0.487719\pi\) | |||||||
\(600\) | 9.66036 | 0.394383 | ||||||||
\(601\) | 14.1595 | 0.577576 | 0.288788 | − | 0.957393i | \(-0.406748\pi\) | ||||
0.288788 | + | 0.957393i | \(0.406748\pi\) | |||||||
\(602\) | 11.5016 | 0.468768 | ||||||||
\(603\) | 0.199219 | 0.00811283 | ||||||||
\(604\) | 11.1238 | 0.452622 | ||||||||
\(605\) | 27.5599 | 1.12047 | ||||||||
\(606\) | 44.2883 | 1.79909 | ||||||||
\(607\) | 19.7947 | 0.803443 | 0.401721 | − | 0.915762i | \(-0.368412\pi\) | ||||
0.401721 | + | 0.915762i | \(0.368412\pi\) | |||||||
\(608\) | 1.20101 | 0.0487072 | ||||||||
\(609\) | −10.1563 | −0.411552 | ||||||||
\(610\) | −56.2196 | −2.27627 | ||||||||
\(611\) | −8.20409 | −0.331902 | ||||||||
\(612\) | 5.33939 | 0.215832 | ||||||||
\(613\) | −9.61688 | −0.388422 | −0.194211 | − | 0.980960i | \(-0.562215\pi\) | ||||
−0.194211 | + | 0.980960i | \(0.562215\pi\) | |||||||
\(614\) | 38.9324 | 1.57119 | ||||||||
\(615\) | 18.3709 | 0.740785 | ||||||||
\(616\) | −0.511611 | −0.0206134 | ||||||||
\(617\) | 27.3971 | 1.10297 | 0.551484 | − | 0.834186i | \(-0.314062\pi\) | ||||
0.551484 | + | 0.834186i | \(0.314062\pi\) | |||||||
\(618\) | −40.5587 | −1.63151 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 81.2006 | 3.26109 | ||||||||
\(621\) | 8.39396 | 0.336838 | ||||||||
\(622\) | 17.0106 | 0.682062 | ||||||||
\(623\) | 10.6667 | 0.427351 | ||||||||
\(624\) | 5.74689 | 0.230060 | ||||||||
\(625\) | −29.7736 | −1.19094 | ||||||||
\(626\) | 73.8038 | 2.94979 | ||||||||
\(627\) | 0.241468 | 0.00964332 | ||||||||
\(628\) | −43.7711 | −1.74666 | ||||||||
\(629\) | 17.9780 | 0.716830 | ||||||||
\(630\) | 3.62852 | 0.144564 | ||||||||
\(631\) | 7.45598 | 0.296818 | 0.148409 | − | 0.988926i | \(-0.452585\pi\) | ||||
0.148409 | + | 0.988926i | \(0.452585\pi\) | |||||||
\(632\) | −11.6969 | −0.465280 | ||||||||
\(633\) | 43.9777 | 1.74796 | ||||||||
\(634\) | 49.2048 | 1.95417 | ||||||||
\(635\) | −20.7811 | −0.824672 | ||||||||
\(636\) | 19.8961 | 0.788933 | ||||||||
\(637\) | 5.23626 | 0.207468 | ||||||||
\(638\) | −0.954398 | −0.0377850 | ||||||||
\(639\) | −2.01810 | −0.0798349 | ||||||||
\(640\) | −50.3395 | −1.98985 | ||||||||
\(641\) | −25.8869 | −1.02247 | −0.511236 | − | 0.859441i | \(-0.670812\pi\) | ||||
−0.511236 | + | 0.859441i | \(0.670812\pi\) | |||||||
\(642\) | 1.83702 | 0.0725012 | ||||||||
\(643\) | 42.1205 | 1.66107 | 0.830536 | − | 0.556965i | \(-0.188034\pi\) | ||||
0.830536 | + | 0.556965i | \(0.188034\pi\) | |||||||
\(644\) | −7.95830 | −0.313601 | ||||||||
\(645\) | 14.2420 | 0.560780 | ||||||||
\(646\) | 13.6456 | 0.536879 | ||||||||
\(647\) | −1.28092 | −0.0503582 | −0.0251791 | − | 0.999683i | \(-0.508016\pi\) | ||||
−0.0251791 | + | 0.999683i | \(0.508016\pi\) | |||||||
\(648\) | 35.0924 | 1.37856 | ||||||||
\(649\) | 0.291825 | 0.0114551 | ||||||||
\(650\) | 3.12956 | 0.122752 | ||||||||
\(651\) | −17.4780 | −0.685015 | ||||||||
\(652\) | 72.9737 | 2.85787 | ||||||||
\(653\) | 26.3148 | 1.02978 | 0.514888 | − | 0.857257i | \(-0.327834\pi\) | ||||
0.514888 | + | 0.857257i | \(0.327834\pi\) | |||||||
\(654\) | −57.4866 | −2.24790 | ||||||||
\(655\) | −16.3130 | −0.637403 | ||||||||
\(656\) | 16.4984 | 0.644152 | ||||||||
\(657\) | 4.00323 | 0.156181 | ||||||||
\(658\) | 26.5369 | 1.03452 | ||||||||
\(659\) | 6.72659 | 0.262031 | 0.131015 | − | 0.991380i | \(-0.458176\pi\) | ||||
0.131015 | + | 0.991380i | \(0.458176\pi\) | |||||||
\(660\) | −1.28930 | −0.0501859 | ||||||||
\(661\) | −19.5946 | −0.762142 | −0.381071 | − | 0.924546i | \(-0.624445\pi\) | ||||
−0.381071 | + | 0.924546i | \(0.624445\pi\) | |||||||
\(662\) | 14.4767 | 0.562654 | ||||||||
\(663\) | −4.84838 | −0.188296 | ||||||||
\(664\) | −23.9326 | −0.928767 | ||||||||
\(665\) | 6.14676 | 0.238361 | ||||||||
\(666\) | −6.45643 | −0.250182 | ||||||||
\(667\) | −7.29477 | −0.282455 | ||||||||
\(668\) | −20.9996 | −0.812498 | ||||||||
\(669\) | 33.1330 | 1.28099 | ||||||||
\(670\) | −2.71848 | −0.105024 | ||||||||
\(671\) | 0.753755 | 0.0290984 | ||||||||
\(672\) | 1.38029 | 0.0532458 | ||||||||
\(673\) | −2.18594 | −0.0842617 | −0.0421308 | − | 0.999112i | \(-0.513415\pi\) | ||||
−0.0421308 | + | 0.999112i | \(0.513415\pi\) | |||||||
\(674\) | −62.2521 | −2.39786 | ||||||||
\(675\) | 7.07728 | 0.272405 | ||||||||
\(676\) | 3.93207 | 0.151234 | ||||||||
\(677\) | −0.112317 | −0.00431668 | −0.00215834 | − | 0.999998i | \(-0.500687\pi\) | ||||
−0.00215834 | + | 0.999998i | \(0.500687\pi\) | |||||||
\(678\) | −67.7611 | −2.60235 | ||||||||
\(679\) | 10.9864 | 0.421621 | ||||||||
\(680\) | −35.8004 | −1.37288 | ||||||||
\(681\) | 4.37855 | 0.167786 | ||||||||
\(682\) | −1.64243 | −0.0628918 | ||||||||
\(683\) | 14.4955 | 0.554656 | 0.277328 | − | 0.960775i | \(-0.410551\pi\) | ||||
0.277328 | + | 0.960775i | \(0.410551\pi\) | |||||||
\(684\) | −3.24832 | −0.124203 | ||||||||
\(685\) | 26.8862 | 1.02727 | ||||||||
\(686\) | −39.5794 | −1.51115 | ||||||||
\(687\) | −32.2617 | −1.23086 | ||||||||
\(688\) | 12.7904 | 0.487628 | ||||||||
\(689\) | 3.16709 | 0.120657 | ||||||||
\(690\) | −14.8669 | −0.565974 | ||||||||
\(691\) | 28.7993 | 1.09558 | 0.547788 | − | 0.836617i | \(-0.315470\pi\) | ||||
0.547788 | + | 0.836617i | \(0.315470\pi\) | |||||||
\(692\) | −12.4486 | −0.473223 | ||||||||
\(693\) | −0.0486488 | −0.00184801 | ||||||||
\(694\) | 25.1941 | 0.956354 | ||||||||
\(695\) | 17.8954 | 0.678810 | ||||||||
\(696\) | −35.9868 | −1.36408 | ||||||||
\(697\) | −13.9189 | −0.527216 | ||||||||
\(698\) | 85.3250 | 3.22960 | ||||||||
\(699\) | −37.1987 | −1.40698 | ||||||||
\(700\) | −6.70996 | −0.253613 | ||||||||
\(701\) | −12.3663 | −0.467069 | −0.233535 | − | 0.972349i | \(-0.575029\pi\) | ||||
−0.233535 | + | 0.972349i | \(0.575029\pi\) | |||||||
\(702\) | 13.4149 | 0.506315 | ||||||||
\(703\) | −10.9373 | −0.412507 | ||||||||
\(704\) | 0.718649 | 0.0270851 | ||||||||
\(705\) | 32.8599 | 1.23758 | ||||||||
\(706\) | 20.3721 | 0.766712 | ||||||||
\(707\) | −15.1153 | −0.568470 | ||||||||
\(708\) | 22.3941 | 0.841623 | ||||||||
\(709\) | −19.0132 | −0.714056 | −0.357028 | − | 0.934094i | \(-0.616210\pi\) | ||||
−0.357028 | + | 0.934094i | \(0.616210\pi\) | |||||||
\(710\) | 27.5383 | 1.03350 | ||||||||
\(711\) | −1.11226 | −0.0417128 | ||||||||
\(712\) | 37.7953 | 1.41644 | ||||||||
\(713\) | −12.5536 | −0.470136 | ||||||||
\(714\) | 15.6826 | 0.586906 | ||||||||
\(715\) | −0.205232 | −0.00767526 | ||||||||
\(716\) | −39.3516 | −1.47064 | ||||||||
\(717\) | 0.789973 | 0.0295021 | ||||||||
\(718\) | −13.7761 | −0.514118 | ||||||||
\(719\) | 34.8903 | 1.30119 | 0.650594 | − | 0.759426i | \(-0.274520\pi\) | ||||
0.650594 | + | 0.759426i | \(0.274520\pi\) | |||||||
\(720\) | 4.03512 | 0.150380 | ||||||||
\(721\) | 13.8424 | 0.515520 | ||||||||
\(722\) | 37.9745 | 1.41327 | ||||||||
\(723\) | −41.1189 | −1.52923 | ||||||||
\(724\) | −66.0321 | −2.45406 | ||||||||
\(725\) | −6.15051 | −0.228424 | ||||||||
\(726\) | −42.7777 | −1.58763 | ||||||||
\(727\) | −46.6534 | −1.73028 | −0.865139 | − | 0.501532i | \(-0.832770\pi\) | ||||
−0.865139 | + | 0.501532i | \(0.832770\pi\) | |||||||
\(728\) | −6.24948 | −0.231621 | ||||||||
\(729\) | 29.7362 | 1.10134 | ||||||||
\(730\) | −54.6268 | −2.02183 | ||||||||
\(731\) | −10.7906 | −0.399106 | ||||||||
\(732\) | 57.8418 | 2.13790 | ||||||||
\(733\) | −6.29810 | −0.232626 | −0.116313 | − | 0.993213i | \(-0.537108\pi\) | ||||
−0.116313 | + | 0.993213i | \(0.537108\pi\) | |||||||
\(734\) | 25.4238 | 0.938411 | ||||||||
\(735\) | −20.9728 | −0.773595 | ||||||||
\(736\) | 0.991397 | 0.0365434 | ||||||||
\(737\) | 0.0364475 | 0.00134256 | ||||||||
\(738\) | 4.99869 | 0.184004 | ||||||||
\(739\) | −2.76728 | −0.101796 | −0.0508979 | − | 0.998704i | \(-0.516208\pi\) | ||||
−0.0508979 | + | 0.998704i | \(0.516208\pi\) | |||||||
\(740\) | 58.3986 | 2.14677 | ||||||||
\(741\) | 2.94961 | 0.108357 | ||||||||
\(742\) | −10.2443 | −0.376080 | ||||||||
\(743\) | −15.0759 | −0.553083 | −0.276541 | − | 0.961002i | \(-0.589188\pi\) | ||||
−0.276541 | + | 0.961002i | \(0.589188\pi\) | |||||||
\(744\) | −61.9298 | −2.27046 | ||||||||
\(745\) | 37.3885 | 1.36981 | ||||||||
\(746\) | 3.66355 | 0.134132 | ||||||||
\(747\) | −2.27574 | −0.0832650 | ||||||||
\(748\) | 0.976850 | 0.0357172 | ||||||||
\(749\) | −0.626962 | −0.0229087 | ||||||||
\(750\) | 36.2415 | 1.32335 | ||||||||
\(751\) | 30.6701 | 1.11917 | 0.559584 | − | 0.828774i | \(-0.310961\pi\) | ||||
0.559584 | + | 0.828774i | \(0.310961\pi\) | |||||||
\(752\) | 29.5105 | 1.07614 | ||||||||
\(753\) | 18.8334 | 0.686328 | ||||||||
\(754\) | −11.6583 | −0.424569 | ||||||||
\(755\) | −7.09223 | −0.258113 | ||||||||
\(756\) | −28.7624 | −1.04608 | ||||||||
\(757\) | −38.8986 | −1.41379 | −0.706897 | − | 0.707316i | \(-0.749906\pi\) | ||||
−0.706897 | + | 0.707316i | \(0.749906\pi\) | |||||||
\(758\) | 34.1216 | 1.23935 | ||||||||
\(759\) | 0.199325 | 0.00723506 | ||||||||
\(760\) | 21.7799 | 0.790040 | ||||||||
\(761\) | 38.1964 | 1.38462 | 0.692309 | − | 0.721601i | \(-0.256593\pi\) | ||||
0.692309 | + | 0.721601i | \(0.256593\pi\) | |||||||
\(762\) | 32.2557 | 1.16850 | ||||||||
\(763\) | 19.6198 | 0.710285 | ||||||||
\(764\) | −78.3072 | −2.83305 | ||||||||
\(765\) | −3.40424 | −0.123081 | ||||||||
\(766\) | −45.5740 | −1.64665 | ||||||||
\(767\) | 3.56473 | 0.128715 | ||||||||
\(768\) | 50.0852 | 1.80729 | ||||||||
\(769\) | 26.9390 | 0.971444 | 0.485722 | − | 0.874113i | \(-0.338557\pi\) | ||||
0.485722 | + | 0.874113i | \(0.338557\pi\) | |||||||
\(770\) | 0.663845 | 0.0239233 | ||||||||
\(771\) | 2.43596 | 0.0877289 | ||||||||
\(772\) | −36.2538 | −1.30480 | ||||||||
\(773\) | −9.06703 | −0.326119 | −0.163059 | − | 0.986616i | \(-0.552136\pi\) | ||||
−0.163059 | + | 0.986616i | \(0.552136\pi\) | |||||||
\(774\) | 3.87524 | 0.139292 | ||||||||
\(775\) | −10.5844 | −0.380204 | ||||||||
\(776\) | 38.9284 | 1.39745 | ||||||||
\(777\) | −12.5700 | −0.450945 | ||||||||
\(778\) | 59.1272 | 2.11981 | ||||||||
\(779\) | 8.46783 | 0.303392 | ||||||||
\(780\) | −15.7492 | −0.563911 | ||||||||
\(781\) | −0.369215 | −0.0132116 | ||||||||
\(782\) | 11.2641 | 0.402802 | ||||||||
\(783\) | −26.3643 | −0.942183 | ||||||||
\(784\) | −18.8351 | −0.672682 | ||||||||
\(785\) | 27.9072 | 0.996051 | ||||||||
\(786\) | 25.3206 | 0.903155 | ||||||||
\(787\) | 21.5905 | 0.769619 | 0.384809 | − | 0.922996i | \(-0.374267\pi\) | ||||
0.384809 | + | 0.922996i | \(0.374267\pi\) | |||||||
\(788\) | 12.8184 | 0.456636 | ||||||||
\(789\) | 9.03988 | 0.321828 | ||||||||
\(790\) | 15.1775 | 0.539990 | ||||||||
\(791\) | 23.1264 | 0.822282 | ||||||||
\(792\) | −0.172378 | −0.00612518 | ||||||||
\(793\) | 9.20735 | 0.326962 | ||||||||
\(794\) | 2.31738 | 0.0822409 | ||||||||
\(795\) | −12.6852 | −0.449898 | ||||||||
\(796\) | −0.360058 | −0.0127619 | ||||||||
\(797\) | −36.6348 | −1.29767 | −0.648836 | − | 0.760929i | \(-0.724744\pi\) | ||||
−0.648836 | + | 0.760929i | \(0.724744\pi\) | |||||||
\(798\) | −9.54081 | −0.337741 | ||||||||
\(799\) | −24.8967 | −0.880781 | ||||||||
\(800\) | 0.835886 | 0.0295530 | ||||||||
\(801\) | 3.59393 | 0.126985 | ||||||||
\(802\) | −9.95286 | −0.351448 | ||||||||
\(803\) | 0.732399 | 0.0258458 | ||||||||
\(804\) | 2.79692 | 0.0986396 | ||||||||
\(805\) | 5.07398 | 0.178834 | ||||||||
\(806\) | −20.0628 | −0.706680 | ||||||||
\(807\) | 20.9405 | 0.737139 | ||||||||
\(808\) | −53.5583 | −1.88417 | ||||||||
\(809\) | 26.4326 | 0.929320 | 0.464660 | − | 0.885489i | \(-0.346177\pi\) | ||||
0.464660 | + | 0.885489i | \(0.346177\pi\) | |||||||
\(810\) | −45.5344 | −1.59992 | ||||||||
\(811\) | 33.1354 | 1.16354 | 0.581770 | − | 0.813353i | \(-0.302360\pi\) | ||||
0.581770 | + | 0.813353i | \(0.302360\pi\) | |||||||
\(812\) | 24.9959 | 0.877186 | ||||||||
\(813\) | 32.1773 | 1.12851 | ||||||||
\(814\) | −1.18122 | −0.0414016 | ||||||||
\(815\) | −46.5260 | −1.62973 | ||||||||
\(816\) | 17.4399 | 0.610518 | ||||||||
\(817\) | 6.56470 | 0.229670 | ||||||||
\(818\) | 43.4722 | 1.51997 | ||||||||
\(819\) | −0.594260 | −0.0207651 | ||||||||
\(820\) | −45.2132 | −1.57891 | ||||||||
\(821\) | −27.6169 | −0.963837 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(822\) | −41.7319 | −1.45557 | ||||||||
\(823\) | −49.5308 | −1.72653 | −0.863267 | − | 0.504748i | \(-0.831585\pi\) | ||||
−0.863267 | + | 0.504748i | \(0.831585\pi\) | |||||||
\(824\) | 49.0481 | 1.70867 | ||||||||
\(825\) | 0.168059 | 0.00585107 | ||||||||
\(826\) | −11.5305 | −0.401197 | ||||||||
\(827\) | −11.1783 | −0.388708 | −0.194354 | − | 0.980931i | \(-0.562261\pi\) | ||||
−0.194354 | + | 0.980931i | \(0.562261\pi\) | |||||||
\(828\) | −2.68140 | −0.0931851 | ||||||||
\(829\) | 5.36437 | 0.186312 | 0.0931562 | − | 0.995652i | \(-0.470304\pi\) | ||||
0.0931562 | + | 0.995652i | \(0.470304\pi\) | |||||||
\(830\) | 31.0540 | 1.07790 | ||||||||
\(831\) | −13.5786 | −0.471035 | ||||||||
\(832\) | 8.77852 | 0.304341 | ||||||||
\(833\) | 15.8903 | 0.550566 | ||||||||
\(834\) | −27.7766 | −0.961826 | ||||||||
\(835\) | 13.3887 | 0.463336 | ||||||||
\(836\) | −0.594286 | −0.0205538 | ||||||||
\(837\) | −45.3704 | −1.56823 | ||||||||
\(838\) | 36.8726 | 1.27374 | ||||||||
\(839\) | 17.6587 | 0.609645 | 0.304823 | − | 0.952409i | \(-0.401403\pi\) | ||||
0.304823 | + | 0.952409i | \(0.401403\pi\) | |||||||
\(840\) | 25.0311 | 0.863656 | ||||||||
\(841\) | −6.08811 | −0.209935 | ||||||||
\(842\) | −24.3419 | −0.838877 | ||||||||
\(843\) | 12.7452 | 0.438968 | ||||||||
\(844\) | −108.235 | −3.72561 | ||||||||
\(845\) | −2.50698 | −0.0862426 | ||||||||
\(846\) | 8.94113 | 0.307402 | ||||||||
\(847\) | 14.5997 | 0.501653 | ||||||||
\(848\) | −11.3922 | −0.391210 | ||||||||
\(849\) | 19.3995 | 0.665790 | ||||||||
\(850\) | 9.49718 | 0.325751 | ||||||||
\(851\) | −9.02842 | −0.309490 | ||||||||
\(852\) | −28.3329 | −0.970671 | ||||||||
\(853\) | −17.4016 | −0.595819 | −0.297910 | − | 0.954594i | \(-0.596289\pi\) | ||||
−0.297910 | + | 0.954594i | \(0.596289\pi\) | |||||||
\(854\) | −29.7821 | −1.01912 | ||||||||
\(855\) | 2.07104 | 0.0708280 | ||||||||
\(856\) | −2.22152 | −0.0759301 | ||||||||
\(857\) | 23.8492 | 0.814675 | 0.407337 | − | 0.913278i | \(-0.366457\pi\) | ||||
0.407337 | + | 0.913278i | \(0.366457\pi\) | |||||||
\(858\) | 0.318555 | 0.0108753 | ||||||||
\(859\) | 35.2878 | 1.20400 | 0.602002 | − | 0.798495i | \(-0.294370\pi\) | ||||
0.602002 | + | 0.798495i | \(0.294370\pi\) | |||||||
\(860\) | −35.0516 | −1.19525 | ||||||||
\(861\) | 9.73189 | 0.331662 | ||||||||
\(862\) | 94.2510 | 3.21020 | ||||||||
\(863\) | −23.6797 | −0.806065 | −0.403033 | − | 0.915186i | \(-0.632044\pi\) | ||||
−0.403033 | + | 0.915186i | \(0.632044\pi\) | |||||||
\(864\) | 3.58304 | 0.121898 | ||||||||
\(865\) | 7.93684 | 0.269861 | ||||||||
\(866\) | 21.1984 | 0.720352 | ||||||||
\(867\) | 12.4471 | 0.422726 | ||||||||
\(868\) | 43.0156 | 1.46005 | ||||||||
\(869\) | −0.203489 | −0.00690290 | ||||||||
\(870\) | 46.6950 | 1.58311 | ||||||||
\(871\) | 0.445217 | 0.0150856 | ||||||||
\(872\) | 69.5192 | 2.35422 | ||||||||
\(873\) | 3.70168 | 0.125283 | ||||||||
\(874\) | −6.85272 | −0.231797 | ||||||||
\(875\) | −12.3690 | −0.418148 | ||||||||
\(876\) | 56.2030 | 1.89892 | ||||||||
\(877\) | 39.4084 | 1.33073 | 0.665364 | − | 0.746519i | \(-0.268276\pi\) | ||||
0.665364 | + | 0.746519i | \(0.268276\pi\) | |||||||
\(878\) | −18.9419 | −0.639259 | ||||||||
\(879\) | −19.0716 | −0.643268 | ||||||||
\(880\) | 0.738232 | 0.0248858 | ||||||||
\(881\) | 18.9999 | 0.640123 | 0.320061 | − | 0.947397i | \(-0.396297\pi\) | ||||
0.320061 | + | 0.947397i | \(0.396297\pi\) | |||||||
\(882\) | −5.70668 | −0.192154 | ||||||||
\(883\) | 6.24984 | 0.210324 | 0.105162 | − | 0.994455i | \(-0.466464\pi\) | ||||
0.105162 | + | 0.994455i | \(0.466464\pi\) | |||||||
\(884\) | 11.9325 | 0.401334 | ||||||||
\(885\) | −14.2779 | −0.479945 | ||||||||
\(886\) | −6.87160 | −0.230856 | ||||||||
\(887\) | 3.52826 | 0.118467 | 0.0592337 | − | 0.998244i | \(-0.481134\pi\) | ||||
0.0592337 | + | 0.998244i | \(0.481134\pi\) | |||||||
\(888\) | −44.5393 | −1.49464 | ||||||||
\(889\) | −11.0087 | −0.369219 | ||||||||
\(890\) | −49.0416 | −1.64388 | ||||||||
\(891\) | 0.610495 | 0.0204523 | ||||||||
\(892\) | −81.5448 | −2.73032 | ||||||||
\(893\) | 15.1464 | 0.506854 | ||||||||
\(894\) | −58.0332 | −1.94092 | ||||||||
\(895\) | 25.0894 | 0.838647 | ||||||||
\(896\) | −26.6671 | −0.890886 | ||||||||
\(897\) | 2.43482 | 0.0812963 | ||||||||
\(898\) | 60.6778 | 2.02485 | ||||||||
\(899\) | 39.4292 | 1.31504 | ||||||||
\(900\) | −2.26079 | −0.0753598 | ||||||||
\(901\) | 9.61107 | 0.320191 | ||||||||
\(902\) | 0.914519 | 0.0304501 | ||||||||
\(903\) | 7.54465 | 0.251070 | ||||||||
\(904\) | 81.9442 | 2.72542 | ||||||||
\(905\) | 42.1002 | 1.39946 | ||||||||
\(906\) | 11.0083 | 0.365728 | ||||||||
\(907\) | −14.4197 | −0.478797 | −0.239399 | − | 0.970921i | \(-0.576950\pi\) | ||||
−0.239399 | + | 0.970921i | \(0.576950\pi\) | |||||||
\(908\) | −10.7762 | −0.357621 | ||||||||
\(909\) | −5.09282 | −0.168918 | ||||||||
\(910\) | 8.10907 | 0.268813 | ||||||||
\(911\) | 18.5078 | 0.613191 | 0.306596 | − | 0.951840i | \(-0.400810\pi\) | ||||
0.306596 | + | 0.951840i | \(0.400810\pi\) | |||||||
\(912\) | −10.6099 | −0.351329 | ||||||||
\(913\) | −0.416351 | −0.0137792 | ||||||||
\(914\) | −66.2290 | −2.19066 | ||||||||
\(915\) | −36.8783 | −1.21916 | ||||||||
\(916\) | 79.4004 | 2.62346 | ||||||||
\(917\) | −8.64175 | −0.285376 | ||||||||
\(918\) | 40.7099 | 1.34363 | ||||||||
\(919\) | 6.62327 | 0.218482 | 0.109241 | − | 0.994015i | \(-0.465158\pi\) | ||||
0.109241 | + | 0.994015i | \(0.465158\pi\) | |||||||
\(920\) | 17.9787 | 0.592740 | ||||||||
\(921\) | 25.5384 | 0.841520 | ||||||||
\(922\) | 57.0020 | 1.87726 | ||||||||
\(923\) | −4.51008 | −0.148451 | ||||||||
\(924\) | −0.683000 | −0.0224690 | ||||||||
\(925\) | −7.61221 | −0.250288 | ||||||||
\(926\) | −84.9691 | −2.79226 | ||||||||
\(927\) | 4.66395 | 0.153184 | ||||||||
\(928\) | −3.11384 | −0.102217 | ||||||||
\(929\) | 1.45448 | 0.0477200 | 0.0238600 | − | 0.999715i | \(-0.492404\pi\) | ||||
0.0238600 | + | 0.999715i | \(0.492404\pi\) | |||||||
\(930\) | 80.3576 | 2.63503 | ||||||||
\(931\) | −9.66718 | −0.316829 | ||||||||
\(932\) | 91.5510 | 2.99885 | ||||||||
\(933\) | 11.1584 | 0.365309 | ||||||||
\(934\) | −48.5185 | −1.58757 | ||||||||
\(935\) | −0.622812 | −0.0203681 | ||||||||
\(936\) | −2.10565 | −0.0688252 | ||||||||
\(937\) | 50.4817 | 1.64916 | 0.824582 | − | 0.565742i | \(-0.191410\pi\) | ||||
0.824582 | + | 0.565742i | \(0.191410\pi\) | |||||||
\(938\) | −1.44010 | −0.0470209 | ||||||||
\(939\) | 48.4130 | 1.57990 | ||||||||
\(940\) | −80.8727 | −2.63778 | ||||||||
\(941\) | 15.0323 | 0.490040 | 0.245020 | − | 0.969518i | \(-0.421206\pi\) | ||||
0.245020 | + | 0.969518i | \(0.421206\pi\) | |||||||
\(942\) | −43.3167 | −1.41133 | ||||||||
\(943\) | 6.98997 | 0.227625 | ||||||||
\(944\) | −12.8225 | −0.417338 | ||||||||
\(945\) | 18.3381 | 0.596537 | ||||||||
\(946\) | 0.708981 | 0.0230510 | ||||||||
\(947\) | 25.9346 | 0.842760 | 0.421380 | − | 0.906884i | \(-0.361546\pi\) | ||||
0.421380 | + | 0.906884i | \(0.361546\pi\) | |||||||
\(948\) | −15.6154 | −0.507165 | ||||||||
\(949\) | 8.94648 | 0.290415 | ||||||||
\(950\) | −5.77780 | −0.187457 | ||||||||
\(951\) | 32.2768 | 1.04665 | ||||||||
\(952\) | −18.9651 | −0.614662 | ||||||||
\(953\) | 14.7463 | 0.477678 | 0.238839 | − | 0.971059i | \(-0.423233\pi\) | ||||
0.238839 | + | 0.971059i | \(0.423233\pi\) | |||||||
\(954\) | −3.45162 | −0.111750 | ||||||||
\(955\) | 49.9264 | 1.61558 | ||||||||
\(956\) | −1.94423 | −0.0628809 | ||||||||
\(957\) | −0.626054 | −0.0202375 | ||||||||
\(958\) | −9.01686 | −0.291321 | ||||||||
\(959\) | 14.2428 | 0.459925 | ||||||||
\(960\) | −35.1607 | −1.13481 | ||||||||
\(961\) | 36.8539 | 1.18883 | ||||||||
\(962\) | −14.4289 | −0.465207 | ||||||||
\(963\) | −0.211243 | −0.00680722 | ||||||||
\(964\) | 101.199 | 3.25941 | ||||||||
\(965\) | 23.1144 | 0.744078 | ||||||||
\(966\) | −7.87568 | −0.253396 | ||||||||
\(967\) | 11.5228 | 0.370547 | 0.185274 | − | 0.982687i | \(-0.440683\pi\) | ||||
0.185274 | + | 0.982687i | \(0.440683\pi\) | |||||||
\(968\) | 51.7315 | 1.66271 | ||||||||
\(969\) | 8.95108 | 0.287550 | ||||||||
\(970\) | −50.5119 | −1.62184 | ||||||||
\(971\) | −8.33017 | −0.267328 | −0.133664 | − | 0.991027i | \(-0.542674\pi\) | ||||
−0.133664 | + | 0.991027i | \(0.542674\pi\) | |||||||
\(972\) | −18.1241 | −0.581329 | ||||||||
\(973\) | 9.47999 | 0.303915 | ||||||||
\(974\) | −16.0218 | −0.513373 | ||||||||
\(975\) | 2.05289 | 0.0657452 | ||||||||
\(976\) | −33.1193 | −1.06012 | ||||||||
\(977\) | 51.3905 | 1.64413 | 0.822064 | − | 0.569395i | \(-0.192823\pi\) | ||||
0.822064 | + | 0.569395i | \(0.192823\pi\) | |||||||
\(978\) | 72.2161 | 2.30922 | ||||||||
\(979\) | 0.657516 | 0.0210143 | ||||||||
\(980\) | 51.6170 | 1.64885 | ||||||||
\(981\) | 6.61053 | 0.211058 | ||||||||
\(982\) | 68.2442 | 2.17776 | ||||||||
\(983\) | 59.5944 | 1.90077 | 0.950383 | − | 0.311082i | \(-0.100691\pi\) | ||||
0.950383 | + | 0.311082i | \(0.100691\pi\) | |||||||
\(984\) | 34.4831 | 1.09928 | ||||||||
\(985\) | −8.17264 | −0.260402 | ||||||||
\(986\) | −35.3789 | −1.12669 | ||||||||
\(987\) | 17.4074 | 0.554083 | ||||||||
\(988\) | −7.25939 | −0.230952 | ||||||||
\(989\) | 5.41898 | 0.172313 | ||||||||
\(990\) | 0.223670 | 0.00710870 | ||||||||
\(991\) | −32.5170 | −1.03294 | −0.516468 | − | 0.856307i | \(-0.672753\pi\) | ||||
−0.516468 | + | 0.856307i | \(0.672753\pi\) | |||||||
\(992\) | −5.35863 | −0.170137 | ||||||||
\(993\) | 9.49628 | 0.301355 | ||||||||
\(994\) | 14.5883 | 0.462713 | ||||||||
\(995\) | 0.229563 | 0.00727762 | ||||||||
\(996\) | −31.9500 | −1.01238 | ||||||||
\(997\) | 42.5266 | 1.34683 | 0.673416 | − | 0.739264i | \(-0.264826\pi\) | ||||
0.673416 | + | 0.739264i | \(0.264826\pi\) | |||||||
\(998\) | −81.7812 | −2.58874 | ||||||||
\(999\) | −32.6299 | −1.03237 |
(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 | 8047.2.a.d.1.11 | ✓ | 156 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.d.1.11 | ✓ | 156 | 1.1 | even | 1 | trivial |