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 | 1.35 | ||
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 | ||||||||
\(3\) | −0.200784 | −0.115923 | −0.0579614 | − | 0.998319i | \(-0.518460\pi\) | ||||
−0.0579614 | + | 0.998319i | \(0.518460\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.29596 | −1.02678 | −0.513392 | − | 0.858154i | \(-0.671611\pi\) | ||||
−0.513392 | + | 0.858154i | \(0.671611\pi\) | |||||||
\(6\) | 0.200784 | 0.0819698 | ||||||||
\(7\) | −0.443206 | −0.167516 | −0.0837581 | − | 0.996486i | \(-0.526692\pi\) | ||||
−0.0837581 | + | 0.996486i | \(0.526692\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.95969 | −0.986562 | ||||||||
\(10\) | 2.29596 | 0.726046 | ||||||||
\(11\) | 0.0657130 | 0.0198132 | 0.00990661 | − | 0.999951i | \(-0.496847\pi\) | ||||
0.00990661 | + | 0.999951i | \(0.496847\pi\) | |||||||
\(12\) | −0.200784 | −0.0579614 | ||||||||
\(13\) | −5.22204 | −1.44833 | −0.724167 | − | 0.689625i | \(-0.757775\pi\) | ||||
−0.724167 | + | 0.689625i | \(0.757775\pi\) | |||||||
\(14\) | 0.443206 | 0.118452 | ||||||||
\(15\) | 0.460992 | 0.119028 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.05974 | −1.46970 | −0.734851 | − | 0.678229i | \(-0.762748\pi\) | ||||
−0.734851 | + | 0.678229i | \(0.762748\pi\) | |||||||
\(18\) | 2.95969 | 0.697605 | ||||||||
\(19\) | 0.987451 | 0.226537 | 0.113268 | − | 0.993564i | \(-0.463868\pi\) | ||||
0.113268 | + | 0.993564i | \(0.463868\pi\) | |||||||
\(20\) | −2.29596 | −0.513392 | ||||||||
\(21\) | 0.0889888 | 0.0194190 | ||||||||
\(22\) | −0.0657130 | −0.0140101 | ||||||||
\(23\) | 5.95236 | 1.24115 | 0.620577 | − | 0.784146i | \(-0.286898\pi\) | ||||
0.620577 | + | 0.784146i | \(0.286898\pi\) | |||||||
\(24\) | 0.200784 | 0.0409849 | ||||||||
\(25\) | 0.271430 | 0.0542859 | ||||||||
\(26\) | 5.22204 | 1.02413 | ||||||||
\(27\) | 1.19661 | 0.230288 | ||||||||
\(28\) | −0.443206 | −0.0837581 | ||||||||
\(29\) | −3.90713 | −0.725536 | −0.362768 | − | 0.931879i | \(-0.618168\pi\) | ||||
−0.362768 | + | 0.931879i | \(0.618168\pi\) | |||||||
\(30\) | −0.460992 | −0.0841653 | ||||||||
\(31\) | −6.48171 | −1.16415 | −0.582075 | − | 0.813135i | \(-0.697759\pi\) | ||||
−0.582075 | + | 0.813135i | \(0.697759\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.0131941 | −0.00229680 | ||||||||
\(34\) | 6.05974 | 1.03924 | ||||||||
\(35\) | 1.01758 | 0.172003 | ||||||||
\(36\) | −2.95969 | −0.493281 | ||||||||
\(37\) | −1.23889 | −0.203672 | −0.101836 | − | 0.994801i | \(-0.532472\pi\) | ||||
−0.101836 | + | 0.994801i | \(0.532472\pi\) | |||||||
\(38\) | −0.987451 | −0.160186 | ||||||||
\(39\) | 1.04850 | 0.167895 | ||||||||
\(40\) | 2.29596 | 0.363023 | ||||||||
\(41\) | 6.05668 | 0.945894 | 0.472947 | − | 0.881091i | \(-0.343190\pi\) | ||||
0.472947 | + | 0.881091i | \(0.343190\pi\) | |||||||
\(42\) | −0.0889888 | −0.0137313 | ||||||||
\(43\) | −4.24894 | −0.647957 | −0.323979 | − | 0.946064i | \(-0.605021\pi\) | ||||
−0.323979 | + | 0.946064i | \(0.605021\pi\) | |||||||
\(44\) | 0.0657130 | 0.00990661 | ||||||||
\(45\) | 6.79532 | 1.01299 | ||||||||
\(46\) | −5.95236 | −0.877628 | ||||||||
\(47\) | −2.96424 | −0.432380 | −0.216190 | − | 0.976351i | \(-0.569363\pi\) | ||||
−0.216190 | + | 0.976351i | \(0.569363\pi\) | |||||||
\(48\) | −0.200784 | −0.0289807 | ||||||||
\(49\) | −6.80357 | −0.971938 | ||||||||
\(50\) | −0.271430 | −0.0383860 | ||||||||
\(51\) | 1.21670 | 0.170372 | ||||||||
\(52\) | −5.22204 | −0.724167 | ||||||||
\(53\) | −11.7849 | −1.61878 | −0.809391 | − | 0.587270i | \(-0.800203\pi\) | ||||
−0.809391 | + | 0.587270i | \(0.800203\pi\) | |||||||
\(54\) | −1.19661 | −0.162838 | ||||||||
\(55\) | −0.150874 | −0.0203439 | ||||||||
\(56\) | 0.443206 | 0.0592260 | ||||||||
\(57\) | −0.198264 | −0.0262608 | ||||||||
\(58\) | 3.90713 | 0.513031 | ||||||||
\(59\) | −10.7757 | −1.40287 | −0.701436 | − | 0.712732i | \(-0.747457\pi\) | ||||
−0.701436 | + | 0.712732i | \(0.747457\pi\) | |||||||
\(60\) | 0.460992 | 0.0595138 | ||||||||
\(61\) | −2.55019 | −0.326519 | −0.163259 | − | 0.986583i | \(-0.552201\pi\) | ||||
−0.163259 | + | 0.986583i | \(0.552201\pi\) | |||||||
\(62\) | 6.48171 | 0.823179 | ||||||||
\(63\) | 1.31175 | 0.165265 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.9896 | 1.48713 | ||||||||
\(66\) | 0.0131941 | 0.00162408 | ||||||||
\(67\) | −3.49450 | −0.426922 | −0.213461 | − | 0.976952i | \(-0.568474\pi\) | ||||
−0.213461 | + | 0.976952i | \(0.568474\pi\) | |||||||
\(68\) | −6.05974 | −0.734851 | ||||||||
\(69\) | −1.19514 | −0.143878 | ||||||||
\(70\) | −1.01758 | −0.121625 | ||||||||
\(71\) | −7.48186 | −0.887933 | −0.443967 | − | 0.896043i | \(-0.646429\pi\) | ||||
−0.443967 | + | 0.896043i | \(0.646429\pi\) | |||||||
\(72\) | 2.95969 | 0.348802 | ||||||||
\(73\) | 4.47735 | 0.524034 | 0.262017 | − | 0.965063i | \(-0.415612\pi\) | ||||
0.262017 | + | 0.965063i | \(0.415612\pi\) | |||||||
\(74\) | 1.23889 | 0.144018 | ||||||||
\(75\) | −0.0544988 | −0.00629298 | ||||||||
\(76\) | 0.987451 | 0.113268 | ||||||||
\(77\) | −0.0291244 | −0.00331904 | ||||||||
\(78\) | −1.04850 | −0.118720 | ||||||||
\(79\) | −13.1542 | −1.47997 | −0.739984 | − | 0.672624i | \(-0.765167\pi\) | ||||
−0.739984 | + | 0.672624i | \(0.765167\pi\) | |||||||
\(80\) | −2.29596 | −0.256696 | ||||||||
\(81\) | 8.63880 | 0.959866 | ||||||||
\(82\) | −6.05668 | −0.668848 | ||||||||
\(83\) | −10.9279 | −1.19949 | −0.599744 | − | 0.800192i | \(-0.704731\pi\) | ||||
−0.599744 | + | 0.800192i | \(0.704731\pi\) | |||||||
\(84\) | 0.0889888 | 0.00970948 | ||||||||
\(85\) | 13.9129 | 1.50907 | ||||||||
\(86\) | 4.24894 | 0.458175 | ||||||||
\(87\) | 0.784490 | 0.0841062 | ||||||||
\(88\) | −0.0657130 | −0.00700503 | ||||||||
\(89\) | −1.90357 | −0.201778 | −0.100889 | − | 0.994898i | \(-0.532169\pi\) | ||||
−0.100889 | + | 0.994898i | \(0.532169\pi\) | |||||||
\(90\) | −6.79532 | −0.716289 | ||||||||
\(91\) | 2.31444 | 0.242619 | ||||||||
\(92\) | 5.95236 | 0.620577 | ||||||||
\(93\) | 1.30143 | 0.134952 | ||||||||
\(94\) | 2.96424 | 0.305738 | ||||||||
\(95\) | −2.26715 | −0.232604 | ||||||||
\(96\) | 0.200784 | 0.0204924 | ||||||||
\(97\) | 3.05381 | 0.310068 | 0.155034 | − | 0.987909i | \(-0.450451\pi\) | ||||
0.155034 | + | 0.987909i | \(0.450451\pi\) | |||||||
\(98\) | 6.80357 | 0.687264 | ||||||||
\(99\) | −0.194490 | −0.0195470 | ||||||||
\(100\) | 0.271430 | 0.0271430 | ||||||||
\(101\) | −1.62540 | −0.161733 | −0.0808666 | − | 0.996725i | \(-0.525769\pi\) | ||||
−0.0808666 | + | 0.996725i | \(0.525769\pi\) | |||||||
\(102\) | −1.21670 | −0.120471 | ||||||||
\(103\) | −0.800128 | −0.0788390 | −0.0394195 | − | 0.999223i | \(-0.512551\pi\) | ||||
−0.0394195 | + | 0.999223i | \(0.512551\pi\) | |||||||
\(104\) | 5.22204 | 0.512063 | ||||||||
\(105\) | −0.204315 | −0.0199391 | ||||||||
\(106\) | 11.7849 | 1.14465 | ||||||||
\(107\) | −8.61465 | −0.832809 | −0.416405 | − | 0.909179i | \(-0.636710\pi\) | ||||
−0.416405 | + | 0.909179i | \(0.636710\pi\) | |||||||
\(108\) | 1.19661 | 0.115144 | ||||||||
\(109\) | −19.3946 | −1.85766 | −0.928831 | − | 0.370505i | \(-0.879185\pi\) | ||||
−0.928831 | + | 0.370505i | \(0.879185\pi\) | |||||||
\(110\) | 0.150874 | 0.0143853 | ||||||||
\(111\) | 0.248749 | 0.0236102 | ||||||||
\(112\) | −0.443206 | −0.0418791 | ||||||||
\(113\) | 6.30110 | 0.592758 | 0.296379 | − | 0.955070i | \(-0.404221\pi\) | ||||
0.296379 | + | 0.955070i | \(0.404221\pi\) | |||||||
\(114\) | 0.198264 | 0.0185692 | ||||||||
\(115\) | −13.6664 | −1.27440 | ||||||||
\(116\) | −3.90713 | −0.362768 | ||||||||
\(117\) | 15.4556 | 1.42887 | ||||||||
\(118\) | 10.7757 | 0.991981 | ||||||||
\(119\) | 2.68571 | 0.246199 | ||||||||
\(120\) | −0.460992 | −0.0420826 | ||||||||
\(121\) | −10.9957 | −0.999607 | ||||||||
\(122\) | 2.55019 | 0.230884 | ||||||||
\(123\) | −1.21608 | −0.109651 | ||||||||
\(124\) | −6.48171 | −0.582075 | ||||||||
\(125\) | 10.8566 | 0.971044 | ||||||||
\(126\) | −1.31175 | −0.116860 | ||||||||
\(127\) | 5.98262 | 0.530872 | 0.265436 | − | 0.964129i | \(-0.414484\pi\) | ||||
0.265436 | + | 0.964129i | \(0.414484\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.853120 | 0.0751130 | ||||||||
\(130\) | −11.9896 | −1.05156 | ||||||||
\(131\) | 10.0759 | 0.880334 | 0.440167 | − | 0.897916i | \(-0.354919\pi\) | ||||
0.440167 | + | 0.897916i | \(0.354919\pi\) | |||||||
\(132\) | −0.0131941 | −0.00114840 | ||||||||
\(133\) | −0.437644 | −0.0379486 | ||||||||
\(134\) | 3.49450 | 0.301879 | ||||||||
\(135\) | −2.74737 | −0.236456 | ||||||||
\(136\) | 6.05974 | 0.519618 | ||||||||
\(137\) | −9.32577 | −0.796755 | −0.398377 | − | 0.917222i | \(-0.630427\pi\) | ||||
−0.398377 | + | 0.917222i | \(0.630427\pi\) | |||||||
\(138\) | 1.19514 | 0.101737 | ||||||||
\(139\) | 6.79434 | 0.576288 | 0.288144 | − | 0.957587i | \(-0.406962\pi\) | ||||
0.288144 | + | 0.957587i | \(0.406962\pi\) | |||||||
\(140\) | 1.01758 | 0.0860015 | ||||||||
\(141\) | 0.595173 | 0.0501226 | ||||||||
\(142\) | 7.48186 | 0.627864 | ||||||||
\(143\) | −0.343156 | −0.0286961 | ||||||||
\(144\) | −2.95969 | −0.246640 | ||||||||
\(145\) | 8.97061 | 0.744969 | ||||||||
\(146\) | −4.47735 | −0.370548 | ||||||||
\(147\) | 1.36605 | 0.112670 | ||||||||
\(148\) | −1.23889 | −0.101836 | ||||||||
\(149\) | 6.30000 | 0.516116 | 0.258058 | − | 0.966129i | \(-0.416917\pi\) | ||||
0.258058 | + | 0.966129i | \(0.416917\pi\) | |||||||
\(150\) | 0.0544988 | 0.00444981 | ||||||||
\(151\) | 6.92286 | 0.563374 | 0.281687 | − | 0.959506i | \(-0.409106\pi\) | ||||
0.281687 | + | 0.959506i | \(0.409106\pi\) | |||||||
\(152\) | −0.987451 | −0.0800928 | ||||||||
\(153\) | 17.9349 | 1.44995 | ||||||||
\(154\) | 0.0291244 | 0.00234691 | ||||||||
\(155\) | 14.8818 | 1.19533 | ||||||||
\(156\) | 1.04850 | 0.0839474 | ||||||||
\(157\) | 14.3252 | 1.14327 | 0.571637 | − | 0.820507i | \(-0.306309\pi\) | ||||
0.571637 | + | 0.820507i | \(0.306309\pi\) | |||||||
\(158\) | 13.1542 | 1.04650 | ||||||||
\(159\) | 2.36622 | 0.187654 | ||||||||
\(160\) | 2.29596 | 0.181512 | ||||||||
\(161\) | −2.63813 | −0.207913 | ||||||||
\(162\) | −8.63880 | −0.678728 | ||||||||
\(163\) | −9.94788 | −0.779178 | −0.389589 | − | 0.920989i | \(-0.627383\pi\) | ||||
−0.389589 | + | 0.920989i | \(0.627383\pi\) | |||||||
\(164\) | 6.05668 | 0.472947 | ||||||||
\(165\) | 0.0302932 | 0.00235832 | ||||||||
\(166\) | 10.9279 | 0.848167 | ||||||||
\(167\) | 12.4132 | 0.960561 | 0.480280 | − | 0.877115i | \(-0.340535\pi\) | ||||
0.480280 | + | 0.877115i | \(0.340535\pi\) | |||||||
\(168\) | −0.0889888 | −0.00686564 | ||||||||
\(169\) | 14.2697 | 1.09767 | ||||||||
\(170\) | −13.9129 | −1.06707 | ||||||||
\(171\) | −2.92254 | −0.223492 | ||||||||
\(172\) | −4.24894 | −0.323979 | ||||||||
\(173\) | −1.69219 | −0.128655 | −0.0643273 | − | 0.997929i | \(-0.520490\pi\) | ||||
−0.0643273 | + | 0.997929i | \(0.520490\pi\) | |||||||
\(174\) | −0.784490 | −0.0594720 | ||||||||
\(175\) | −0.120299 | −0.00909378 | ||||||||
\(176\) | 0.0657130 | 0.00495330 | ||||||||
\(177\) | 2.16358 | 0.162625 | ||||||||
\(178\) | 1.90357 | 0.142679 | ||||||||
\(179\) | −18.2511 | −1.36415 | −0.682074 | − | 0.731283i | \(-0.738922\pi\) | ||||
−0.682074 | + | 0.731283i | \(0.738922\pi\) | |||||||
\(180\) | 6.79532 | 0.506493 | ||||||||
\(181\) | 2.58244 | 0.191951 | 0.0959755 | − | 0.995384i | \(-0.469403\pi\) | ||||
0.0959755 | + | 0.995384i | \(0.469403\pi\) | |||||||
\(182\) | −2.31444 | −0.171558 | ||||||||
\(183\) | 0.512038 | 0.0378509 | ||||||||
\(184\) | −5.95236 | −0.438814 | ||||||||
\(185\) | 2.84443 | 0.209127 | ||||||||
\(186\) | −1.30143 | −0.0954251 | ||||||||
\(187\) | −0.398203 | −0.0291195 | ||||||||
\(188\) | −2.96424 | −0.216190 | ||||||||
\(189\) | −0.530345 | −0.0385770 | ||||||||
\(190\) | 2.26715 | 0.164476 | ||||||||
\(191\) | 4.32691 | 0.313084 | 0.156542 | − | 0.987671i | \(-0.449965\pi\) | ||||
0.156542 | + | 0.987671i | \(0.449965\pi\) | |||||||
\(192\) | −0.200784 | −0.0144903 | ||||||||
\(193\) | 0.877843 | 0.0631885 | 0.0315942 | − | 0.999501i | \(-0.489942\pi\) | ||||
0.0315942 | + | 0.999501i | \(0.489942\pi\) | |||||||
\(194\) | −3.05381 | −0.219251 | ||||||||
\(195\) | −2.40732 | −0.172392 | ||||||||
\(196\) | −6.80357 | −0.485969 | ||||||||
\(197\) | 3.66518 | 0.261133 | 0.130567 | − | 0.991440i | \(-0.458320\pi\) | ||||
0.130567 | + | 0.991440i | \(0.458320\pi\) | |||||||
\(198\) | 0.194490 | 0.0138218 | ||||||||
\(199\) | −5.62262 | −0.398577 | −0.199288 | − | 0.979941i | \(-0.563863\pi\) | ||||
−0.199288 | + | 0.979941i | \(0.563863\pi\) | |||||||
\(200\) | −0.271430 | −0.0191930 | ||||||||
\(201\) | 0.701641 | 0.0494899 | ||||||||
\(202\) | 1.62540 | 0.114363 | ||||||||
\(203\) | 1.73167 | 0.121539 | ||||||||
\(204\) | 1.21670 | 0.0851860 | ||||||||
\(205\) | −13.9059 | −0.971229 | ||||||||
\(206\) | 0.800128 | 0.0557476 | ||||||||
\(207\) | −17.6171 | −1.22448 | ||||||||
\(208\) | −5.22204 | −0.362083 | ||||||||
\(209\) | 0.0648883 | 0.00448842 | ||||||||
\(210\) | 0.204315 | 0.0140991 | ||||||||
\(211\) | −7.70814 | −0.530650 | −0.265325 | − | 0.964159i | \(-0.585479\pi\) | ||||
−0.265325 | + | 0.964159i | \(0.585479\pi\) | |||||||
\(212\) | −11.7849 | −0.809391 | ||||||||
\(213\) | 1.50224 | 0.102932 | ||||||||
\(214\) | 8.61465 | 0.588885 | ||||||||
\(215\) | 9.75539 | 0.665312 | ||||||||
\(216\) | −1.19661 | −0.0814190 | ||||||||
\(217\) | 2.87274 | 0.195014 | ||||||||
\(218\) | 19.3946 | 1.31356 | ||||||||
\(219\) | −0.898980 | −0.0607474 | ||||||||
\(220\) | −0.150874 | −0.0101719 | ||||||||
\(221\) | 31.6442 | 2.12862 | ||||||||
\(222\) | −0.248749 | −0.0166949 | ||||||||
\(223\) | −15.3558 | −1.02830 | −0.514151 | − | 0.857700i | \(-0.671893\pi\) | ||||
−0.514151 | + | 0.857700i | \(0.671893\pi\) | |||||||
\(224\) | 0.443206 | 0.0296130 | ||||||||
\(225\) | −0.803347 | −0.0535564 | ||||||||
\(226\) | −6.30110 | −0.419143 | ||||||||
\(227\) | −21.8972 | −1.45337 | −0.726683 | − | 0.686972i | \(-0.758939\pi\) | ||||
−0.726683 | + | 0.686972i | \(0.758939\pi\) | |||||||
\(228\) | −0.198264 | −0.0131304 | ||||||||
\(229\) | 23.9817 | 1.58475 | 0.792376 | − | 0.610033i | \(-0.208844\pi\) | ||||
0.792376 | + | 0.610033i | \(0.208844\pi\) | |||||||
\(230\) | 13.6664 | 0.901135 | ||||||||
\(231\) | 0.00584772 | 0.000384752 0 | ||||||||
\(232\) | 3.90713 | 0.256516 | ||||||||
\(233\) | 26.2413 | 1.71913 | 0.859564 | − | 0.511029i | \(-0.170735\pi\) | ||||
0.859564 | + | 0.511029i | \(0.170735\pi\) | |||||||
\(234\) | −15.4556 | −1.01036 | ||||||||
\(235\) | 6.80579 | 0.443960 | ||||||||
\(236\) | −10.7757 | −0.701436 | ||||||||
\(237\) | 2.64116 | 0.171562 | ||||||||
\(238\) | −2.68571 | −0.174089 | ||||||||
\(239\) | 0.0739620 | 0.00478420 | 0.00239210 | − | 0.999997i | \(-0.499239\pi\) | ||||
0.00239210 | + | 0.999997i | \(0.499239\pi\) | |||||||
\(240\) | 0.460992 | 0.0297569 | ||||||||
\(241\) | −15.1583 | −0.976430 | −0.488215 | − | 0.872724i | \(-0.662352\pi\) | ||||
−0.488215 | + | 0.872724i | \(0.662352\pi\) | |||||||
\(242\) | 10.9957 | 0.706829 | ||||||||
\(243\) | −5.32436 | −0.341558 | ||||||||
\(244\) | −2.55019 | −0.163259 | ||||||||
\(245\) | 15.6207 | 0.997971 | ||||||||
\(246\) | 1.21608 | 0.0775347 | ||||||||
\(247\) | −5.15651 | −0.328101 | ||||||||
\(248\) | 6.48171 | 0.411589 | ||||||||
\(249\) | 2.19414 | 0.139048 | ||||||||
\(250\) | −10.8566 | −0.686632 | ||||||||
\(251\) | −10.4349 | −0.658643 | −0.329322 | − | 0.944218i | \(-0.606820\pi\) | ||||
−0.329322 | + | 0.944218i | \(0.606820\pi\) | |||||||
\(252\) | 1.31175 | 0.0826326 | ||||||||
\(253\) | 0.391148 | 0.0245912 | ||||||||
\(254\) | −5.98262 | −0.375383 | ||||||||
\(255\) | −2.79349 | −0.174935 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.6077 | −0.786444 | −0.393222 | − | 0.919443i | \(-0.628640\pi\) | ||||
−0.393222 | + | 0.919443i | \(0.628640\pi\) | |||||||
\(258\) | −0.853120 | −0.0531129 | ||||||||
\(259\) | 0.549082 | 0.0341183 | ||||||||
\(260\) | 11.9896 | 0.743563 | ||||||||
\(261\) | 11.5639 | 0.715786 | ||||||||
\(262\) | −10.0759 | −0.622490 | ||||||||
\(263\) | 9.51627 | 0.586799 | 0.293399 | − | 0.955990i | \(-0.405213\pi\) | ||||
0.293399 | + | 0.955990i | \(0.405213\pi\) | |||||||
\(264\) | 0.0131941 | 0.000812042 0 | ||||||||
\(265\) | 27.0577 | 1.66214 | ||||||||
\(266\) | 0.437644 | 0.0268337 | ||||||||
\(267\) | 0.382207 | 0.0233907 | ||||||||
\(268\) | −3.49450 | −0.213461 | ||||||||
\(269\) | −1.30081 | −0.0793117 | −0.0396558 | − | 0.999213i | \(-0.512626\pi\) | ||||
−0.0396558 | + | 0.999213i | \(0.512626\pi\) | |||||||
\(270\) | 2.74737 | 0.167200 | ||||||||
\(271\) | −25.5515 | −1.55214 | −0.776072 | − | 0.630644i | \(-0.782791\pi\) | ||||
−0.776072 | + | 0.630644i | \(0.782791\pi\) | |||||||
\(272\) | −6.05974 | −0.367425 | ||||||||
\(273\) | −0.464703 | −0.0281251 | ||||||||
\(274\) | 9.32577 | 0.563391 | ||||||||
\(275\) | 0.0178365 | 0.00107558 | ||||||||
\(276\) | −1.19514 | −0.0719390 | ||||||||
\(277\) | 12.2527 | 0.736194 | 0.368097 | − | 0.929787i | \(-0.380009\pi\) | ||||
0.368097 | + | 0.929787i | \(0.380009\pi\) | |||||||
\(278\) | −6.79434 | −0.407497 | ||||||||
\(279\) | 19.1838 | 1.14851 | ||||||||
\(280\) | −1.01758 | −0.0608123 | ||||||||
\(281\) | 28.6694 | 1.71027 | 0.855136 | − | 0.518404i | \(-0.173474\pi\) | ||||
0.855136 | + | 0.518404i | \(0.173474\pi\) | |||||||
\(282\) | −0.595173 | −0.0354421 | ||||||||
\(283\) | −7.43240 | −0.441810 | −0.220905 | − | 0.975295i | \(-0.570901\pi\) | ||||
−0.220905 | + | 0.975295i | \(0.570901\pi\) | |||||||
\(284\) | −7.48186 | −0.443967 | ||||||||
\(285\) | 0.455207 | 0.0269641 | ||||||||
\(286\) | 0.343156 | 0.0202912 | ||||||||
\(287\) | −2.68436 | −0.158453 | ||||||||
\(288\) | 2.95969 | 0.174401 | ||||||||
\(289\) | 19.7204 | 1.16002 | ||||||||
\(290\) | −8.97061 | −0.526773 | ||||||||
\(291\) | −0.613158 | −0.0359439 | ||||||||
\(292\) | 4.47735 | 0.262017 | ||||||||
\(293\) | −3.32565 | −0.194286 | −0.0971432 | − | 0.995270i | \(-0.530970\pi\) | ||||
−0.0971432 | + | 0.995270i | \(0.530970\pi\) | |||||||
\(294\) | −1.36605 | −0.0796696 | ||||||||
\(295\) | 24.7405 | 1.44045 | ||||||||
\(296\) | 1.23889 | 0.0720088 | ||||||||
\(297\) | 0.0786328 | 0.00456274 | ||||||||
\(298\) | −6.30000 | −0.364949 | ||||||||
\(299\) | −31.0835 | −1.79760 | ||||||||
\(300\) | −0.0544988 | −0.00314649 | ||||||||
\(301\) | 1.88316 | 0.108543 | ||||||||
\(302\) | −6.92286 | −0.398366 | ||||||||
\(303\) | 0.326354 | 0.0187486 | ||||||||
\(304\) | 0.987451 | 0.0566342 | ||||||||
\(305\) | 5.85514 | 0.335264 | ||||||||
\(306\) | −17.9349 | −1.02527 | ||||||||
\(307\) | −1.30079 | −0.0742399 | −0.0371199 | − | 0.999311i | \(-0.511818\pi\) | ||||
−0.0371199 | + | 0.999311i | \(0.511818\pi\) | |||||||
\(308\) | −0.0291244 | −0.00165952 | ||||||||
\(309\) | 0.160653 | 0.00913923 | ||||||||
\(310\) | −14.8818 | −0.845227 | ||||||||
\(311\) | 20.0764 | 1.13843 | 0.569214 | − | 0.822189i | \(-0.307248\pi\) | ||||
0.569214 | + | 0.822189i | \(0.307248\pi\) | |||||||
\(312\) | −1.04850 | −0.0593598 | ||||||||
\(313\) | −24.8721 | −1.40586 | −0.702928 | − | 0.711261i | \(-0.748125\pi\) | ||||
−0.702928 | + | 0.711261i | \(0.748125\pi\) | |||||||
\(314\) | −14.3252 | −0.808417 | ||||||||
\(315\) | −3.01173 | −0.169692 | ||||||||
\(316\) | −13.1542 | −0.739984 | ||||||||
\(317\) | 20.8234 | 1.16956 | 0.584779 | − | 0.811193i | \(-0.301181\pi\) | ||||
0.584779 | + | 0.811193i | \(0.301181\pi\) | |||||||
\(318\) | −2.36622 | −0.132691 | ||||||||
\(319\) | −0.256749 | −0.0143752 | ||||||||
\(320\) | −2.29596 | −0.128348 | ||||||||
\(321\) | 1.72968 | 0.0965416 | ||||||||
\(322\) | 2.63813 | 0.147017 | ||||||||
\(323\) | −5.98369 | −0.332941 | ||||||||
\(324\) | 8.63880 | 0.479933 | ||||||||
\(325\) | −1.41742 | −0.0786242 | ||||||||
\(326\) | 9.94788 | 0.550962 | ||||||||
\(327\) | 3.89412 | 0.215345 | ||||||||
\(328\) | −6.05668 | −0.334424 | ||||||||
\(329\) | 1.31377 | 0.0724306 | ||||||||
\(330\) | −0.0302932 | −0.00166758 | ||||||||
\(331\) | 9.65365 | 0.530613 | 0.265306 | − | 0.964164i | \(-0.414527\pi\) | ||||
0.265306 | + | 0.964164i | \(0.414527\pi\) | |||||||
\(332\) | −10.9279 | −0.599744 | ||||||||
\(333\) | 3.66671 | 0.200935 | ||||||||
\(334\) | −12.4132 | −0.679219 | ||||||||
\(335\) | 8.02324 | 0.438356 | ||||||||
\(336\) | 0.0889888 | 0.00485474 | ||||||||
\(337\) | −26.7884 | −1.45926 | −0.729629 | − | 0.683844i | \(-0.760307\pi\) | ||||
−0.729629 | + | 0.683844i | \(0.760307\pi\) | |||||||
\(338\) | −14.2697 | −0.776170 | ||||||||
\(339\) | −1.26516 | −0.0687142 | ||||||||
\(340\) | 13.9129 | 0.754533 | ||||||||
\(341\) | −0.425933 | −0.0230656 | ||||||||
\(342\) | 2.92254 | 0.158033 | ||||||||
\(343\) | 6.11783 | 0.330332 | ||||||||
\(344\) | 4.24894 | 0.229087 | ||||||||
\(345\) | 2.74399 | 0.147732 | ||||||||
\(346\) | 1.69219 | 0.0909725 | ||||||||
\(347\) | 28.4888 | 1.52936 | 0.764679 | − | 0.644411i | \(-0.222898\pi\) | ||||
0.764679 | + | 0.644411i | \(0.222898\pi\) | |||||||
\(348\) | 0.784490 | 0.0420531 | ||||||||
\(349\) | −11.6593 | −0.624108 | −0.312054 | − | 0.950064i | \(-0.601017\pi\) | ||||
−0.312054 | + | 0.950064i | \(0.601017\pi\) | |||||||
\(350\) | 0.120299 | 0.00643027 | ||||||||
\(351\) | −6.24875 | −0.333534 | ||||||||
\(352\) | −0.0657130 | −0.00350251 | ||||||||
\(353\) | 18.6552 | 0.992916 | 0.496458 | − | 0.868061i | \(-0.334634\pi\) | ||||
0.496458 | + | 0.868061i | \(0.334634\pi\) | |||||||
\(354\) | −2.16358 | −0.114993 | ||||||||
\(355\) | 17.1780 | 0.911716 | ||||||||
\(356\) | −1.90357 | −0.100889 | ||||||||
\(357\) | −0.539249 | −0.0285401 | ||||||||
\(358\) | 18.2511 | 0.964598 | ||||||||
\(359\) | 31.2009 | 1.64672 | 0.823360 | − | 0.567519i | \(-0.192097\pi\) | ||||
0.823360 | + | 0.567519i | \(0.192097\pi\) | |||||||
\(360\) | −6.79532 | −0.358145 | ||||||||
\(361\) | −18.0249 | −0.948681 | ||||||||
\(362\) | −2.58244 | −0.135730 | ||||||||
\(363\) | 2.20776 | 0.115877 | ||||||||
\(364\) | 2.31444 | 0.121310 | ||||||||
\(365\) | −10.2798 | −0.538070 | ||||||||
\(366\) | −0.512038 | −0.0267647 | ||||||||
\(367\) | 34.7404 | 1.81343 | 0.906717 | − | 0.421740i | \(-0.138581\pi\) | ||||
0.906717 | + | 0.421740i | \(0.138581\pi\) | |||||||
\(368\) | 5.95236 | 0.310288 | ||||||||
\(369\) | −17.9259 | −0.933183 | ||||||||
\(370\) | −2.84443 | −0.147875 | ||||||||
\(371\) | 5.22315 | 0.271172 | ||||||||
\(372\) | 1.30143 | 0.0674758 | ||||||||
\(373\) | −21.2826 | −1.10197 | −0.550987 | − | 0.834514i | \(-0.685748\pi\) | ||||
−0.550987 | + | 0.834514i | \(0.685748\pi\) | |||||||
\(374\) | 0.398203 | 0.0205906 | ||||||||
\(375\) | −2.17983 | −0.112566 | ||||||||
\(376\) | 2.96424 | 0.152869 | ||||||||
\(377\) | 20.4032 | 1.05082 | ||||||||
\(378\) | 0.530345 | 0.0272780 | ||||||||
\(379\) | −18.6158 | −0.956230 | −0.478115 | − | 0.878297i | \(-0.658680\pi\) | ||||
−0.478115 | + | 0.878297i | \(0.658680\pi\) | |||||||
\(380\) | −2.26715 | −0.116302 | ||||||||
\(381\) | −1.20122 | −0.0615401 | ||||||||
\(382\) | −4.32691 | −0.221384 | ||||||||
\(383\) | −13.4246 | −0.685965 | −0.342983 | − | 0.939342i | \(-0.611437\pi\) | ||||
−0.342983 | + | 0.939342i | \(0.611437\pi\) | |||||||
\(384\) | 0.200784 | 0.0102462 | ||||||||
\(385\) | 0.0668685 | 0.00340793 | ||||||||
\(386\) | −0.877843 | −0.0446810 | ||||||||
\(387\) | 12.5755 | 0.639250 | ||||||||
\(388\) | 3.05381 | 0.155034 | ||||||||
\(389\) | −1.44707 | −0.0733695 | −0.0366847 | − | 0.999327i | \(-0.511680\pi\) | ||||
−0.0366847 | + | 0.999327i | \(0.511680\pi\) | |||||||
\(390\) | 2.40732 | 0.121899 | ||||||||
\(391\) | −36.0698 | −1.82413 | ||||||||
\(392\) | 6.80357 | 0.343632 | ||||||||
\(393\) | −2.02308 | −0.102051 | ||||||||
\(394\) | −3.66518 | −0.184649 | ||||||||
\(395\) | 30.2016 | 1.51961 | ||||||||
\(396\) | −0.194490 | −0.00977348 | ||||||||
\(397\) | 35.7067 | 1.79207 | 0.896034 | − | 0.443985i | \(-0.146436\pi\) | ||||
0.896034 | + | 0.443985i | \(0.146436\pi\) | |||||||
\(398\) | 5.62262 | 0.281836 | ||||||||
\(399\) | 0.0878721 | 0.00439911 | ||||||||
\(400\) | 0.271430 | 0.0135715 | ||||||||
\(401\) | 5.48471 | 0.273893 | 0.136947 | − | 0.990578i | \(-0.456271\pi\) | ||||
0.136947 | + | 0.990578i | \(0.456271\pi\) | |||||||
\(402\) | −0.701641 | −0.0349947 | ||||||||
\(403\) | 33.8478 | 1.68608 | ||||||||
\(404\) | −1.62540 | −0.0808666 | ||||||||
\(405\) | −19.8343 | −0.985576 | ||||||||
\(406\) | −1.73167 | −0.0859411 | ||||||||
\(407\) | −0.0814109 | −0.00403539 | ||||||||
\(408\) | −1.21670 | −0.0602356 | ||||||||
\(409\) | −34.6578 | −1.71372 | −0.856858 | − | 0.515552i | \(-0.827587\pi\) | ||||
−0.856858 | + | 0.515552i | \(0.827587\pi\) | |||||||
\(410\) | 13.9059 | 0.686763 | ||||||||
\(411\) | 1.87247 | 0.0923620 | ||||||||
\(412\) | −0.800128 | −0.0394195 | ||||||||
\(413\) | 4.77585 | 0.235004 | ||||||||
\(414\) | 17.6171 | 0.865835 | ||||||||
\(415\) | 25.0899 | 1.23162 | ||||||||
\(416\) | 5.22204 | 0.256032 | ||||||||
\(417\) | −1.36420 | −0.0668049 | ||||||||
\(418\) | −0.0648883 | −0.00317379 | ||||||||
\(419\) | −0.221011 | −0.0107971 | −0.00539855 | − | 0.999985i | \(-0.501718\pi\) | ||||
−0.00539855 | + | 0.999985i | \(0.501718\pi\) | |||||||
\(420\) | −0.204315 | −0.00996954 | ||||||||
\(421\) | −18.1784 | −0.885962 | −0.442981 | − | 0.896531i | \(-0.646079\pi\) | ||||
−0.442981 | + | 0.896531i | \(0.646079\pi\) | |||||||
\(422\) | 7.70814 | 0.375226 | ||||||||
\(423\) | 8.77323 | 0.426569 | ||||||||
\(424\) | 11.7849 | 0.572326 | ||||||||
\(425\) | −1.64479 | −0.0797842 | ||||||||
\(426\) | −1.50224 | −0.0727837 | ||||||||
\(427\) | 1.13026 | 0.0546972 | ||||||||
\(428\) | −8.61465 | −0.416405 | ||||||||
\(429\) | 0.0689003 | 0.00332654 | ||||||||
\(430\) | −9.75539 | −0.470447 | ||||||||
\(431\) | −12.2671 | −0.590887 | −0.295443 | − | 0.955360i | \(-0.595467\pi\) | ||||
−0.295443 | + | 0.955360i | \(0.595467\pi\) | |||||||
\(432\) | 1.19661 | 0.0575719 | ||||||||
\(433\) | −7.33472 | −0.352484 | −0.176242 | − | 0.984347i | \(-0.556394\pi\) | ||||
−0.176242 | + | 0.984347i | \(0.556394\pi\) | |||||||
\(434\) | −2.87274 | −0.137896 | ||||||||
\(435\) | −1.80116 | −0.0863589 | ||||||||
\(436\) | −19.3946 | −0.928831 | ||||||||
\(437\) | 5.87767 | 0.281167 | ||||||||
\(438\) | 0.898980 | 0.0429549 | ||||||||
\(439\) | −13.6906 | −0.653418 | −0.326709 | − | 0.945125i | \(-0.605940\pi\) | ||||
−0.326709 | + | 0.945125i | \(0.605940\pi\) | |||||||
\(440\) | 0.150874 | 0.00719265 | ||||||||
\(441\) | 20.1364 | 0.958877 | ||||||||
\(442\) | −31.6442 | −1.50516 | ||||||||
\(443\) | 24.6137 | 1.16943 | 0.584715 | − | 0.811239i | \(-0.301206\pi\) | ||||
0.584715 | + | 0.811239i | \(0.301206\pi\) | |||||||
\(444\) | 0.248749 | 0.0118051 | ||||||||
\(445\) | 4.37053 | 0.207183 | ||||||||
\(446\) | 15.3558 | 0.727119 | ||||||||
\(447\) | −1.26494 | −0.0598296 | ||||||||
\(448\) | −0.443206 | −0.0209395 | ||||||||
\(449\) | −39.4678 | −1.86260 | −0.931299 | − | 0.364255i | \(-0.881324\pi\) | ||||
−0.931299 | + | 0.364255i | \(0.881324\pi\) | |||||||
\(450\) | 0.803347 | 0.0378701 | ||||||||
\(451\) | 0.398002 | 0.0187412 | ||||||||
\(452\) | 6.30110 | 0.296379 | ||||||||
\(453\) | −1.39000 | −0.0653079 | ||||||||
\(454\) | 21.8972 | 1.02769 | ||||||||
\(455\) | −5.31387 | −0.249118 | ||||||||
\(456\) | 0.198264 | 0.00928458 | ||||||||
\(457\) | 13.0389 | 0.609933 | 0.304966 | − | 0.952363i | \(-0.401355\pi\) | ||||
0.304966 | + | 0.952363i | \(0.401355\pi\) | |||||||
\(458\) | −23.9817 | −1.12059 | ||||||||
\(459\) | −7.25114 | −0.338454 | ||||||||
\(460\) | −13.6664 | −0.637199 | ||||||||
\(461\) | −29.2682 | −1.36316 | −0.681578 | − | 0.731746i | \(-0.738706\pi\) | ||||
−0.681578 | + | 0.731746i | \(0.738706\pi\) | |||||||
\(462\) | −0.00584772 | −0.000272061 0 | ||||||||
\(463\) | −7.13135 | −0.331422 | −0.165711 | − | 0.986174i | \(-0.552992\pi\) | ||||
−0.165711 | + | 0.986174i | \(0.552992\pi\) | |||||||
\(464\) | −3.90713 | −0.181384 | ||||||||
\(465\) | −2.98802 | −0.138566 | ||||||||
\(466\) | −26.2413 | −1.21561 | ||||||||
\(467\) | 8.86217 | 0.410092 | 0.205046 | − | 0.978752i | \(-0.434266\pi\) | ||||
0.205046 | + | 0.978752i | \(0.434266\pi\) | |||||||
\(468\) | 15.4556 | 0.714435 | ||||||||
\(469\) | 1.54879 | 0.0715163 | ||||||||
\(470\) | −6.80579 | −0.313927 | ||||||||
\(471\) | −2.87627 | −0.132532 | ||||||||
\(472\) | 10.7757 | 0.495990 | ||||||||
\(473\) | −0.279211 | −0.0128381 | ||||||||
\(474\) | −2.64116 | −0.121313 | ||||||||
\(475\) | 0.268023 | 0.0122978 | ||||||||
\(476\) | 2.68571 | 0.123099 | ||||||||
\(477\) | 34.8796 | 1.59703 | ||||||||
\(478\) | −0.0739620 | −0.00338294 | ||||||||
\(479\) | −11.5049 | −0.525672 | −0.262836 | − | 0.964840i | \(-0.584658\pi\) | ||||
−0.262836 | + | 0.964840i | \(0.584658\pi\) | |||||||
\(480\) | −0.460992 | −0.0210413 | ||||||||
\(481\) | 6.46952 | 0.294985 | ||||||||
\(482\) | 15.1583 | 0.690440 | ||||||||
\(483\) | 0.529694 | 0.0241019 | ||||||||
\(484\) | −10.9957 | −0.499804 | ||||||||
\(485\) | −7.01143 | −0.318373 | ||||||||
\(486\) | 5.32436 | 0.241518 | ||||||||
\(487\) | 23.2218 | 1.05228 | 0.526141 | − | 0.850397i | \(-0.323638\pi\) | ||||
0.526141 | + | 0.850397i | \(0.323638\pi\) | |||||||
\(488\) | 2.55019 | 0.115442 | ||||||||
\(489\) | 1.99738 | 0.0903244 | ||||||||
\(490\) | −15.6207 | −0.705672 | ||||||||
\(491\) | 4.66706 | 0.210622 | 0.105311 | − | 0.994439i | \(-0.466416\pi\) | ||||
0.105311 | + | 0.994439i | \(0.466416\pi\) | |||||||
\(492\) | −1.21608 | −0.0548253 | ||||||||
\(493\) | 23.6762 | 1.06632 | ||||||||
\(494\) | 5.15651 | 0.232002 | ||||||||
\(495\) | 0.446541 | 0.0200705 | ||||||||
\(496\) | −6.48171 | −0.291038 | ||||||||
\(497\) | 3.31601 | 0.148743 | ||||||||
\(498\) | −2.19414 | −0.0983218 | ||||||||
\(499\) | −31.4924 | −1.40979 | −0.704896 | − | 0.709311i | \(-0.749006\pi\) | ||||
−0.704896 | + | 0.709311i | \(0.749006\pi\) | |||||||
\(500\) | 10.8566 | 0.485522 | ||||||||
\(501\) | −2.49237 | −0.111351 | ||||||||
\(502\) | 10.4349 | 0.465731 | ||||||||
\(503\) | 5.24643 | 0.233927 | 0.116963 | − | 0.993136i | \(-0.462684\pi\) | ||||
0.116963 | + | 0.993136i | \(0.462684\pi\) | |||||||
\(504\) | −1.31175 | −0.0584301 | ||||||||
\(505\) | 3.73185 | 0.166065 | ||||||||
\(506\) | −0.391148 | −0.0173886 | ||||||||
\(507\) | −2.86513 | −0.127245 | ||||||||
\(508\) | 5.98262 | 0.265436 | ||||||||
\(509\) | 14.0221 | 0.621517 | 0.310759 | − | 0.950489i | \(-0.399417\pi\) | ||||
0.310759 | + | 0.950489i | \(0.399417\pi\) | |||||||
\(510\) | 2.79349 | 0.123698 | ||||||||
\(511\) | −1.98439 | −0.0877842 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.18159 | 0.0521686 | ||||||||
\(514\) | 12.6077 | 0.556100 | ||||||||
\(515\) | 1.83706 | 0.0809506 | ||||||||
\(516\) | 0.853120 | 0.0375565 | ||||||||
\(517\) | −0.194789 | −0.00856683 | ||||||||
\(518\) | −0.549082 | −0.0241253 | ||||||||
\(519\) | 0.339764 | 0.0149140 | ||||||||
\(520\) | −11.9896 | −0.525778 | ||||||||
\(521\) | 43.7531 | 1.91686 | 0.958429 | − | 0.285331i | \(-0.0921035\pi\) | ||||
0.958429 | + | 0.285331i | \(0.0921035\pi\) | |||||||
\(522\) | −11.5639 | −0.506137 | ||||||||
\(523\) | 13.6581 | 0.597226 | 0.298613 | − | 0.954374i | \(-0.403476\pi\) | ||||
0.298613 | + | 0.954374i | \(0.403476\pi\) | |||||||
\(524\) | 10.0759 | 0.440167 | ||||||||
\(525\) | 0.0241542 | 0.00105418 | ||||||||
\(526\) | −9.51627 | −0.414929 | ||||||||
\(527\) | 39.2775 | 1.71095 | ||||||||
\(528\) | −0.0131941 | −0.000574201 0 | ||||||||
\(529\) | 12.4306 | 0.540463 | ||||||||
\(530\) | −27.0577 | −1.17531 | ||||||||
\(531\) | 31.8926 | 1.38402 | ||||||||
\(532\) | −0.437644 | −0.0189743 | ||||||||
\(533\) | −31.6282 | −1.36997 | ||||||||
\(534\) | −0.382207 | −0.0165397 | ||||||||
\(535\) | 19.7789 | 0.855115 | ||||||||
\(536\) | 3.49450 | 0.150940 | ||||||||
\(537\) | 3.66452 | 0.158136 | ||||||||
\(538\) | 1.30081 | 0.0560818 | ||||||||
\(539\) | −0.447083 | −0.0192572 | ||||||||
\(540\) | −2.74737 | −0.118228 | ||||||||
\(541\) | −33.3820 | −1.43520 | −0.717602 | − | 0.696454i | \(-0.754760\pi\) | ||||
−0.717602 | + | 0.696454i | \(0.754760\pi\) | |||||||
\(542\) | 25.5515 | 1.09753 | ||||||||
\(543\) | −0.518512 | −0.0222515 | ||||||||
\(544\) | 6.05974 | 0.259809 | ||||||||
\(545\) | 44.5291 | 1.90742 | ||||||||
\(546\) | 0.464703 | 0.0198875 | ||||||||
\(547\) | −34.4635 | −1.47355 | −0.736775 | − | 0.676138i | \(-0.763652\pi\) | ||||
−0.736775 | + | 0.676138i | \(0.763652\pi\) | |||||||
\(548\) | −9.32577 | −0.398377 | ||||||||
\(549\) | 7.54777 | 0.322131 | ||||||||
\(550\) | −0.0178365 | −0.000760549 0 | ||||||||
\(551\) | −3.85810 | −0.164361 | ||||||||
\(552\) | 1.19514 | 0.0508686 | ||||||||
\(553\) | 5.83005 | 0.247919 | ||||||||
\(554\) | −12.2527 | −0.520568 | ||||||||
\(555\) | −0.571117 | −0.0242426 | ||||||||
\(556\) | 6.79434 | 0.288144 | ||||||||
\(557\) | 12.5151 | 0.530280 | 0.265140 | − | 0.964210i | \(-0.414582\pi\) | ||||
0.265140 | + | 0.964210i | \(0.414582\pi\) | |||||||
\(558\) | −19.1838 | −0.812117 | ||||||||
\(559\) | 22.1881 | 0.938458 | ||||||||
\(560\) | 1.01758 | 0.0430008 | ||||||||
\(561\) | 0.0799529 | 0.00337561 | ||||||||
\(562\) | −28.6694 | −1.20934 | ||||||||
\(563\) | 1.29185 | 0.0544451 | 0.0272225 | − | 0.999629i | \(-0.491334\pi\) | ||||
0.0272225 | + | 0.999629i | \(0.491334\pi\) | |||||||
\(564\) | 0.595173 | 0.0250613 | ||||||||
\(565\) | −14.4671 | −0.608635 | ||||||||
\(566\) | 7.43240 | 0.312407 | ||||||||
\(567\) | −3.82877 | −0.160793 | ||||||||
\(568\) | 7.48186 | 0.313932 | ||||||||
\(569\) | 9.05930 | 0.379786 | 0.189893 | − | 0.981805i | \(-0.439186\pi\) | ||||
0.189893 | + | 0.981805i | \(0.439186\pi\) | |||||||
\(570\) | −0.455207 | −0.0190665 | ||||||||
\(571\) | 2.84133 | 0.118906 | 0.0594529 | − | 0.998231i | \(-0.481064\pi\) | ||||
0.0594529 | + | 0.998231i | \(0.481064\pi\) | |||||||
\(572\) | −0.343156 | −0.0143481 | ||||||||
\(573\) | −0.868775 | −0.0362936 | ||||||||
\(574\) | 2.68436 | 0.112043 | ||||||||
\(575\) | 1.61565 | 0.0673772 | ||||||||
\(576\) | −2.95969 | −0.123320 | ||||||||
\(577\) | 10.5198 | 0.437945 | 0.218972 | − | 0.975731i | \(-0.429730\pi\) | ||||
0.218972 | + | 0.975731i | \(0.429730\pi\) | |||||||
\(578\) | −19.7204 | −0.820260 | ||||||||
\(579\) | −0.176257 | −0.00732499 | ||||||||
\(580\) | 8.97061 | 0.372485 | ||||||||
\(581\) | 4.84330 | 0.200934 | ||||||||
\(582\) | 0.613158 | 0.0254162 | ||||||||
\(583\) | −0.774422 | −0.0320733 | ||||||||
\(584\) | −4.47735 | −0.185274 | ||||||||
\(585\) | −35.4854 | −1.46714 | ||||||||
\(586\) | 3.32565 | 0.137381 | ||||||||
\(587\) | 30.6011 | 1.26304 | 0.631521 | − | 0.775358i | \(-0.282431\pi\) | ||||
0.631521 | + | 0.775358i | \(0.282431\pi\) | |||||||
\(588\) | 1.36605 | 0.0563349 | ||||||||
\(589\) | −6.40037 | −0.263723 | ||||||||
\(590\) | −24.7405 | −1.01855 | ||||||||
\(591\) | −0.735910 | −0.0302713 | ||||||||
\(592\) | −1.23889 | −0.0509179 | ||||||||
\(593\) | 11.6793 | 0.479611 | 0.239806 | − | 0.970821i | \(-0.422916\pi\) | ||||
0.239806 | + | 0.970821i | \(0.422916\pi\) | |||||||
\(594\) | −0.0786328 | −0.00322634 | ||||||||
\(595\) | −6.16629 | −0.252793 | ||||||||
\(596\) | 6.30000 | 0.258058 | ||||||||
\(597\) | 1.12893 | 0.0462041 | ||||||||
\(598\) | 31.0835 | 1.27110 | ||||||||
\(599\) | 6.82646 | 0.278922 | 0.139461 | − | 0.990228i | \(-0.455463\pi\) | ||||
0.139461 | + | 0.990228i | \(0.455463\pi\) | |||||||
\(600\) | 0.0544988 | 0.00222490 | ||||||||
\(601\) | 9.91559 | 0.404465 | 0.202233 | − | 0.979338i | \(-0.435180\pi\) | ||||
0.202233 | + | 0.979338i | \(0.435180\pi\) | |||||||
\(602\) | −1.88316 | −0.0767518 | ||||||||
\(603\) | 10.3426 | 0.421185 | ||||||||
\(604\) | 6.92286 | 0.281687 | ||||||||
\(605\) | 25.2456 | 1.02638 | ||||||||
\(606\) | −0.326354 | −0.0132572 | ||||||||
\(607\) | 2.66158 | 0.108030 | 0.0540151 | − | 0.998540i | \(-0.482798\pi\) | ||||
0.0540151 | + | 0.998540i | \(0.482798\pi\) | |||||||
\(608\) | −0.987451 | −0.0400464 | ||||||||
\(609\) | −0.347691 | −0.0140892 | ||||||||
\(610\) | −5.85514 | −0.237068 | ||||||||
\(611\) | 15.4794 | 0.626230 | ||||||||
\(612\) | 17.9349 | 0.724976 | ||||||||
\(613\) | −11.4946 | −0.464263 | −0.232131 | − | 0.972684i | \(-0.574570\pi\) | ||||
−0.232131 | + | 0.972684i | \(0.574570\pi\) | |||||||
\(614\) | 1.30079 | 0.0524955 | ||||||||
\(615\) | 2.79208 | 0.112588 | ||||||||
\(616\) | 0.0291244 | 0.00117346 | ||||||||
\(617\) | 12.9990 | 0.523319 | 0.261660 | − | 0.965160i | \(-0.415730\pi\) | ||||
0.261660 | + | 0.965160i | \(0.415730\pi\) | |||||||
\(618\) | −0.160653 | −0.00646241 | ||||||||
\(619\) | −9.87474 | −0.396899 | −0.198450 | − | 0.980111i | \(-0.563591\pi\) | ||||
−0.198450 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(620\) | 14.8818 | 0.597666 | ||||||||
\(621\) | 7.12266 | 0.285823 | ||||||||
\(622\) | −20.0764 | −0.804990 | ||||||||
\(623\) | 0.843676 | 0.0338012 | ||||||||
\(624\) | 1.04850 | 0.0419737 | ||||||||
\(625\) | −26.2835 | −1.05134 | ||||||||
\(626\) | 24.8721 | 0.994091 | ||||||||
\(627\) | −0.0130285 | −0.000520310 0 | ||||||||
\(628\) | 14.3252 | 0.571637 | ||||||||
\(629\) | 7.50732 | 0.299337 | ||||||||
\(630\) | 3.01173 | 0.119990 | ||||||||
\(631\) | 23.7102 | 0.943886 | 0.471943 | − | 0.881629i | \(-0.343553\pi\) | ||||
0.471943 | + | 0.881629i | \(0.343553\pi\) | |||||||
\(632\) | 13.1542 | 0.523248 | ||||||||
\(633\) | 1.54767 | 0.0615145 | ||||||||
\(634\) | −20.8234 | −0.827002 | ||||||||
\(635\) | −13.7359 | −0.545091 | ||||||||
\(636\) | 2.36622 | 0.0938269 | ||||||||
\(637\) | 35.5285 | 1.40769 | ||||||||
\(638\) | 0.256749 | 0.0101648 | ||||||||
\(639\) | 22.1440 | 0.876001 | ||||||||
\(640\) | 2.29596 | 0.0907558 | ||||||||
\(641\) | −2.82716 | −0.111666 | −0.0558331 | − | 0.998440i | \(-0.517781\pi\) | ||||
−0.0558331 | + | 0.998440i | \(0.517781\pi\) | |||||||
\(642\) | −1.72968 | −0.0682652 | ||||||||
\(643\) | 27.3536 | 1.07872 | 0.539360 | − | 0.842075i | \(-0.318666\pi\) | ||||
0.539360 | + | 0.842075i | \(0.318666\pi\) | |||||||
\(644\) | −2.63813 | −0.103957 | ||||||||
\(645\) | −1.95873 | −0.0771249 | ||||||||
\(646\) | 5.98369 | 0.235425 | ||||||||
\(647\) | −7.87764 | −0.309702 | −0.154851 | − | 0.987938i | \(-0.549490\pi\) | ||||
−0.154851 | + | 0.987938i | \(0.549490\pi\) | |||||||
\(648\) | −8.63880 | −0.339364 | ||||||||
\(649\) | −0.708101 | −0.0277954 | ||||||||
\(650\) | 1.41742 | 0.0555957 | ||||||||
\(651\) | −0.576800 | −0.0226066 | ||||||||
\(652\) | −9.94788 | −0.389589 | ||||||||
\(653\) | 10.4871 | 0.410392 | 0.205196 | − | 0.978721i | \(-0.434217\pi\) | ||||
0.205196 | + | 0.978721i | \(0.434217\pi\) | |||||||
\(654\) | −3.89412 | −0.152272 | ||||||||
\(655\) | −23.1338 | −0.903913 | ||||||||
\(656\) | 6.05668 | 0.236474 | ||||||||
\(657\) | −13.2515 | −0.516992 | ||||||||
\(658\) | −1.31377 | −0.0512162 | ||||||||
\(659\) | 21.7892 | 0.848787 | 0.424393 | − | 0.905478i | \(-0.360487\pi\) | ||||
0.424393 | + | 0.905478i | \(0.360487\pi\) | |||||||
\(660\) | 0.0302932 | 0.00117916 | ||||||||
\(661\) | −16.9777 | −0.660355 | −0.330178 | − | 0.943919i | \(-0.607109\pi\) | ||||
−0.330178 | + | 0.943919i | \(0.607109\pi\) | |||||||
\(662\) | −9.65365 | −0.375200 | ||||||||
\(663\) | −6.35365 | −0.246755 | ||||||||
\(664\) | 10.9279 | 0.424083 | ||||||||
\(665\) | 1.00481 | 0.0389650 | ||||||||
\(666\) | −3.66671 | −0.142082 | ||||||||
\(667\) | −23.2567 | −0.900502 | ||||||||
\(668\) | 12.4132 | 0.480280 | ||||||||
\(669\) | 3.08320 | 0.119204 | ||||||||
\(670\) | −8.02324 | −0.309965 | ||||||||
\(671\) | −0.167581 | −0.00646938 | ||||||||
\(672\) | −0.0889888 | −0.00343282 | ||||||||
\(673\) | −10.7092 | −0.412808 | −0.206404 | − | 0.978467i | \(-0.566176\pi\) | ||||
−0.206404 | + | 0.978467i | \(0.566176\pi\) | |||||||
\(674\) | 26.7884 | 1.03185 | ||||||||
\(675\) | 0.324796 | 0.0125014 | ||||||||
\(676\) | 14.2697 | 0.548835 | ||||||||
\(677\) | −17.1672 | −0.659790 | −0.329895 | − | 0.944018i | \(-0.607013\pi\) | ||||
−0.329895 | + | 0.944018i | \(0.607013\pi\) | |||||||
\(678\) | 1.26516 | 0.0485882 | ||||||||
\(679\) | −1.35347 | −0.0519414 | ||||||||
\(680\) | −13.9129 | −0.533536 | ||||||||
\(681\) | 4.39661 | 0.168478 | ||||||||
\(682\) | 0.425933 | 0.0163098 | ||||||||
\(683\) | −27.0195 | −1.03387 | −0.516935 | − | 0.856024i | \(-0.672927\pi\) | ||||
−0.516935 | + | 0.856024i | \(0.672927\pi\) | |||||||
\(684\) | −2.92254 | −0.111746 | ||||||||
\(685\) | 21.4116 | 0.818095 | ||||||||
\(686\) | −6.11783 | −0.233580 | ||||||||
\(687\) | −4.81514 | −0.183709 | ||||||||
\(688\) | −4.24894 | −0.161989 | ||||||||
\(689\) | 61.5413 | 2.34454 | ||||||||
\(690\) | −2.74399 | −0.104462 | ||||||||
\(691\) | 3.46776 | 0.131920 | 0.0659599 | − | 0.997822i | \(-0.478989\pi\) | ||||
0.0659599 | + | 0.997822i | \(0.478989\pi\) | |||||||
\(692\) | −1.69219 | −0.0643273 | ||||||||
\(693\) | 0.0861991 | 0.00327443 | ||||||||
\(694\) | −28.4888 | −1.08142 | ||||||||
\(695\) | −15.5995 | −0.591724 | ||||||||
\(696\) | −0.784490 | −0.0297360 | ||||||||
\(697\) | −36.7019 | −1.39018 | ||||||||
\(698\) | 11.6593 | 0.441311 | ||||||||
\(699\) | −5.26885 | −0.199286 | ||||||||
\(700\) | −0.120299 | −0.00454689 | ||||||||
\(701\) | −17.1971 | −0.649525 | −0.324763 | − | 0.945796i | \(-0.605284\pi\) | ||||
−0.324763 | + | 0.945796i | \(0.605284\pi\) | |||||||
\(702\) | 6.24875 | 0.235844 | ||||||||
\(703\) | −1.22334 | −0.0461391 | ||||||||
\(704\) | 0.0657130 | 0.00247665 | ||||||||
\(705\) | −1.36649 | −0.0514651 | ||||||||
\(706\) | −18.6552 | −0.702098 | ||||||||
\(707\) | 0.720387 | 0.0270929 | ||||||||
\(708\) | 2.16358 | 0.0813124 | ||||||||
\(709\) | −25.2893 | −0.949760 | −0.474880 | − | 0.880051i | \(-0.657509\pi\) | ||||
−0.474880 | + | 0.880051i | \(0.657509\pi\) | |||||||
\(710\) | −17.1780 | −0.644681 | ||||||||
\(711\) | 38.9324 | 1.46008 | ||||||||
\(712\) | 1.90357 | 0.0713394 | ||||||||
\(713\) | −38.5815 | −1.44489 | ||||||||
\(714\) | 0.539249 | 0.0201809 | ||||||||
\(715\) | 0.787872 | 0.0294647 | ||||||||
\(716\) | −18.2511 | −0.682074 | ||||||||
\(717\) | −0.0148504 | −0.000554598 0 | ||||||||
\(718\) | −31.2009 | −1.16441 | ||||||||
\(719\) | −4.37890 | −0.163306 | −0.0816528 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816528 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(720\) | 6.79532 | 0.253247 | ||||||||
\(721\) | 0.354622 | 0.0132068 | ||||||||
\(722\) | 18.0249 | 0.670819 | ||||||||
\(723\) | 3.04354 | 0.113190 | ||||||||
\(724\) | 2.58244 | 0.0959755 | ||||||||
\(725\) | −1.06051 | −0.0393864 | ||||||||
\(726\) | −2.20776 | −0.0819376 | ||||||||
\(727\) | −14.5756 | −0.540578 | −0.270289 | − | 0.962779i | \(-0.587119\pi\) | ||||
−0.270289 | + | 0.962779i | \(0.587119\pi\) | |||||||
\(728\) | −2.31444 | −0.0857789 | ||||||||
\(729\) | −24.8473 | −0.920272 | ||||||||
\(730\) | 10.2798 | 0.380473 | ||||||||
\(731\) | 25.7475 | 0.952304 | ||||||||
\(732\) | 0.512038 | 0.0189255 | ||||||||
\(733\) | −21.7938 | −0.804971 | −0.402486 | − | 0.915426i | \(-0.631854\pi\) | ||||
−0.402486 | + | 0.915426i | \(0.631854\pi\) | |||||||
\(734\) | −34.7404 | −1.28229 | ||||||||
\(735\) | −3.13639 | −0.115688 | ||||||||
\(736\) | −5.95236 | −0.219407 | ||||||||
\(737\) | −0.229634 | −0.00845869 | ||||||||
\(738\) | 17.9259 | 0.659860 | ||||||||
\(739\) | 21.6251 | 0.795493 | 0.397746 | − | 0.917495i | \(-0.369792\pi\) | ||||
0.397746 | + | 0.917495i | \(0.369792\pi\) | |||||||
\(740\) | 2.84443 | 0.104563 | ||||||||
\(741\) | 1.03535 | 0.0380343 | ||||||||
\(742\) | −5.22315 | −0.191748 | ||||||||
\(743\) | −40.8632 | −1.49913 | −0.749563 | − | 0.661933i | \(-0.769737\pi\) | ||||
−0.749563 | + | 0.661933i | \(0.769737\pi\) | |||||||
\(744\) | −1.30143 | −0.0477126 | ||||||||
\(745\) | −14.4645 | −0.529940 | ||||||||
\(746\) | 21.2826 | 0.779213 | ||||||||
\(747\) | 32.3430 | 1.18337 | ||||||||
\(748\) | −0.398203 | −0.0145598 | ||||||||
\(749\) | 3.81807 | 0.139509 | ||||||||
\(750\) | 2.17983 | 0.0795963 | ||||||||
\(751\) | −19.2893 | −0.703875 | −0.351937 | − | 0.936024i | \(-0.614477\pi\) | ||||
−0.351937 | + | 0.936024i | \(0.614477\pi\) | |||||||
\(752\) | −2.96424 | −0.108095 | ||||||||
\(753\) | 2.09516 | 0.0763518 | ||||||||
\(754\) | −20.4032 | −0.743041 | ||||||||
\(755\) | −15.8946 | −0.578464 | ||||||||
\(756\) | −0.530345 | −0.0192885 | ||||||||
\(757\) | −15.2005 | −0.552472 | −0.276236 | − | 0.961090i | \(-0.589087\pi\) | ||||
−0.276236 | + | 0.961090i | \(0.589087\pi\) | |||||||
\(758\) | 18.6158 | 0.676156 | ||||||||
\(759\) | −0.0785362 | −0.00285069 | ||||||||
\(760\) | 2.26715 | 0.0822381 | ||||||||
\(761\) | −21.0512 | −0.763104 | −0.381552 | − | 0.924347i | \(-0.624610\pi\) | ||||
−0.381552 | + | 0.924347i | \(0.624610\pi\) | |||||||
\(762\) | 1.20122 | 0.0435154 | ||||||||
\(763\) | 8.59579 | 0.311188 | ||||||||
\(764\) | 4.32691 | 0.156542 | ||||||||
\(765\) | −41.1778 | −1.48879 | ||||||||
\(766\) | 13.4246 | 0.485051 | ||||||||
\(767\) | 56.2710 | 2.03183 | ||||||||
\(768\) | −0.200784 | −0.00724517 | ||||||||
\(769\) | 11.2519 | 0.405753 | 0.202876 | − | 0.979204i | \(-0.434971\pi\) | ||||
0.202876 | + | 0.979204i | \(0.434971\pi\) | |||||||
\(770\) | −0.0668685 | −0.00240977 | ||||||||
\(771\) | 2.53142 | 0.0911668 | ||||||||
\(772\) | 0.877843 | 0.0315942 | ||||||||
\(773\) | 23.2601 | 0.836608 | 0.418304 | − | 0.908307i | \(-0.362625\pi\) | ||||
0.418304 | + | 0.908307i | \(0.362625\pi\) | |||||||
\(774\) | −12.5755 | −0.452018 | ||||||||
\(775\) | −1.75933 | −0.0631970 | ||||||||
\(776\) | −3.05381 | −0.109626 | ||||||||
\(777\) | −0.110247 | −0.00395509 | ||||||||
\(778\) | 1.44707 | 0.0518801 | ||||||||
\(779\) | 5.98067 | 0.214280 | ||||||||
\(780\) | −2.40732 | −0.0861959 | ||||||||
\(781\) | −0.491655 | −0.0175928 | ||||||||
\(782\) | 36.0698 | 1.28985 | ||||||||
\(783\) | −4.67531 | −0.167082 | ||||||||
\(784\) | −6.80357 | −0.242985 | ||||||||
\(785\) | −32.8900 | −1.17390 | ||||||||
\(786\) | 2.02308 | 0.0721608 | ||||||||
\(787\) | −43.5652 | −1.55293 | −0.776465 | − | 0.630160i | \(-0.782989\pi\) | ||||
−0.776465 | + | 0.630160i | \(0.782989\pi\) | |||||||
\(788\) | 3.66518 | 0.130567 | ||||||||
\(789\) | −1.91072 | −0.0680233 | ||||||||
\(790\) | −30.2016 | −1.07453 | ||||||||
\(791\) | −2.79269 | −0.0992966 | ||||||||
\(792\) | 0.194490 | 0.00691089 | ||||||||
\(793\) | 13.3172 | 0.472908 | ||||||||
\(794\) | −35.7067 | −1.26718 | ||||||||
\(795\) | −5.43275 | −0.192680 | ||||||||
\(796\) | −5.62262 | −0.199288 | ||||||||
\(797\) | −24.0864 | −0.853183 | −0.426592 | − | 0.904444i | \(-0.640286\pi\) | ||||
−0.426592 | + | 0.904444i | \(0.640286\pi\) | |||||||
\(798\) | −0.0878721 | −0.00311064 | ||||||||
\(799\) | 17.9625 | 0.635469 | ||||||||
\(800\) | −0.271430 | −0.00959649 | ||||||||
\(801\) | 5.63398 | 0.199067 | ||||||||
\(802\) | −5.48471 | −0.193672 | ||||||||
\(803\) | 0.294220 | 0.0103828 | ||||||||
\(804\) | 0.701641 | 0.0247450 | ||||||||
\(805\) | 6.05703 | 0.213482 | ||||||||
\(806\) | −33.8478 | −1.19224 | ||||||||
\(807\) | 0.261182 | 0.00919403 | ||||||||
\(808\) | 1.62540 | 0.0571813 | ||||||||
\(809\) | −24.6476 | −0.866562 | −0.433281 | − | 0.901259i | \(-0.642644\pi\) | ||||
−0.433281 | + | 0.901259i | \(0.642644\pi\) | |||||||
\(810\) | 19.8343 | 0.696907 | ||||||||
\(811\) | −5.43408 | −0.190816 | −0.0954082 | − | 0.995438i | \(-0.530416\pi\) | ||||
−0.0954082 | + | 0.995438i | \(0.530416\pi\) | |||||||
\(812\) | 1.73167 | 0.0607696 | ||||||||
\(813\) | 5.13034 | 0.179929 | ||||||||
\(814\) | 0.0814109 | 0.00285345 | ||||||||
\(815\) | 22.8399 | 0.800047 | ||||||||
\(816\) | 1.21670 | 0.0425930 | ||||||||
\(817\) | −4.19562 | −0.146786 | ||||||||
\(818\) | 34.6578 | 1.21178 | ||||||||
\(819\) | −6.85002 | −0.239359 | ||||||||
\(820\) | −13.9059 | −0.485615 | ||||||||
\(821\) | 34.6219 | 1.20831 | 0.604156 | − | 0.796866i | \(-0.293510\pi\) | ||||
0.604156 | + | 0.796866i | \(0.293510\pi\) | |||||||
\(822\) | −1.87247 | −0.0653098 | ||||||||
\(823\) | −52.4113 | −1.82694 | −0.913472 | − | 0.406902i | \(-0.866609\pi\) | ||||
−0.913472 | + | 0.406902i | \(0.866609\pi\) | |||||||
\(824\) | 0.800128 | 0.0278738 | ||||||||
\(825\) | −0.00358128 | −0.000124684 0 | ||||||||
\(826\) | −4.77585 | −0.166173 | ||||||||
\(827\) | −24.3231 | −0.845797 | −0.422898 | − | 0.906177i | \(-0.638987\pi\) | ||||
−0.422898 | + | 0.906177i | \(0.638987\pi\) | |||||||
\(828\) | −17.6171 | −0.612238 | ||||||||
\(829\) | 30.5861 | 1.06230 | 0.531149 | − | 0.847278i | \(-0.321760\pi\) | ||||
0.531149 | + | 0.847278i | \(0.321760\pi\) | |||||||
\(830\) | −25.0899 | −0.870884 | ||||||||
\(831\) | −2.46015 | −0.0853417 | ||||||||
\(832\) | −5.22204 | −0.181042 | ||||||||
\(833\) | 41.2278 | 1.42846 | ||||||||
\(834\) | 1.36420 | 0.0472382 | ||||||||
\(835\) | −28.5002 | −0.986289 | ||||||||
\(836\) | 0.0648883 | 0.00224421 | ||||||||
\(837\) | −7.75609 | −0.268090 | ||||||||
\(838\) | 0.221011 | 0.00763470 | ||||||||
\(839\) | 0.379687 | 0.0131082 | 0.00655412 | − | 0.999979i | \(-0.497914\pi\) | ||||
0.00655412 | + | 0.999979i | \(0.497914\pi\) | |||||||
\(840\) | 0.204315 | 0.00704953 | ||||||||
\(841\) | −13.7343 | −0.473597 | ||||||||
\(842\) | 18.1784 | 0.626470 | ||||||||
\(843\) | −5.75635 | −0.198259 | ||||||||
\(844\) | −7.70814 | −0.265325 | ||||||||
\(845\) | −32.7627 | −1.12707 | ||||||||
\(846\) | −8.77323 | −0.301630 | ||||||||
\(847\) | 4.87336 | 0.167451 | ||||||||
\(848\) | −11.7849 | −0.404696 | ||||||||
\(849\) | 1.49231 | 0.0512158 | ||||||||
\(850\) | 1.64479 | 0.0564159 | ||||||||
\(851\) | −7.37430 | −0.252788 | ||||||||
\(852\) | 1.50224 | 0.0514659 | ||||||||
\(853\) | 7.19130 | 0.246225 | 0.123113 | − | 0.992393i | \(-0.460712\pi\) | ||||
0.123113 | + | 0.992393i | \(0.460712\pi\) | |||||||
\(854\) | −1.13026 | −0.0386768 | ||||||||
\(855\) | 6.71004 | 0.229479 | ||||||||
\(856\) | 8.61465 | 0.294443 | ||||||||
\(857\) | −4.31879 | −0.147527 | −0.0737635 | − | 0.997276i | \(-0.523501\pi\) | ||||
−0.0737635 | + | 0.997276i | \(0.523501\pi\) | |||||||
\(858\) | −0.0689003 | −0.00235222 | ||||||||
\(859\) | 37.7536 | 1.28814 | 0.644069 | − | 0.764968i | \(-0.277245\pi\) | ||||
0.644069 | + | 0.764968i | \(0.277245\pi\) | |||||||
\(860\) | 9.75539 | 0.332656 | ||||||||
\(861\) | 0.538977 | 0.0183683 | ||||||||
\(862\) | 12.2671 | 0.417820 | ||||||||
\(863\) | −6.52775 | −0.222207 | −0.111104 | − | 0.993809i | \(-0.535439\pi\) | ||||
−0.111104 | + | 0.993809i | \(0.535439\pi\) | |||||||
\(864\) | −1.19661 | −0.0407095 | ||||||||
\(865\) | 3.88519 | 0.132101 | ||||||||
\(866\) | 7.33472 | 0.249244 | ||||||||
\(867\) | −3.95954 | −0.134473 | ||||||||
\(868\) | 2.87274 | 0.0975071 | ||||||||
\(869\) | −0.864405 | −0.0293229 | ||||||||
\(870\) | 1.80116 | 0.0610650 | ||||||||
\(871\) | 18.2484 | 0.618325 | ||||||||
\(872\) | 19.3946 | 0.656782 | ||||||||
\(873\) | −9.03833 | −0.305901 | ||||||||
\(874\) | −5.87767 | −0.198815 | ||||||||
\(875\) | −4.81172 | −0.162666 | ||||||||
\(876\) | −0.898980 | −0.0303737 | ||||||||
\(877\) | 16.5833 | 0.559977 | 0.279988 | − | 0.960003i | \(-0.409669\pi\) | ||||
0.279988 | + | 0.960003i | \(0.409669\pi\) | |||||||
\(878\) | 13.6906 | 0.462036 | ||||||||
\(879\) | 0.667737 | 0.0225222 | ||||||||
\(880\) | −0.150874 | −0.00508597 | ||||||||
\(881\) | −6.22524 | −0.209734 | −0.104867 | − | 0.994486i | \(-0.533442\pi\) | ||||
−0.104867 | + | 0.994486i | \(0.533442\pi\) | |||||||
\(882\) | −20.1364 | −0.678029 | ||||||||
\(883\) | 40.3638 | 1.35835 | 0.679175 | − | 0.733976i | \(-0.262338\pi\) | ||||
0.679175 | + | 0.733976i | \(0.262338\pi\) | |||||||
\(884\) | 31.6442 | 1.06431 | ||||||||
\(885\) | −4.96750 | −0.166981 | ||||||||
\(886\) | −24.6137 | −0.826912 | ||||||||
\(887\) | −25.4303 | −0.853865 | −0.426932 | − | 0.904284i | \(-0.640406\pi\) | ||||
−0.426932 | + | 0.904284i | \(0.640406\pi\) | |||||||
\(888\) | −0.248749 | −0.00834746 | ||||||||
\(889\) | −2.65154 | −0.0889296 | ||||||||
\(890\) | −4.37053 | −0.146500 | ||||||||
\(891\) | 0.567681 | 0.0190180 | ||||||||
\(892\) | −15.3558 | −0.514151 | ||||||||
\(893\) | −2.92705 | −0.0979498 | ||||||||
\(894\) | 1.26494 | 0.0423059 | ||||||||
\(895\) | 41.9037 | 1.40069 | ||||||||
\(896\) | 0.443206 | 0.0148065 | ||||||||
\(897\) | 6.24107 | 0.208383 | ||||||||
\(898\) | 39.4678 | 1.31706 | ||||||||
\(899\) | 25.3249 | 0.844633 | ||||||||
\(900\) | −0.803347 | −0.0267782 | ||||||||
\(901\) | 71.4135 | 2.37913 | ||||||||
\(902\) | −0.398002 | −0.0132520 | ||||||||
\(903\) | −0.378108 | −0.0125827 | ||||||||
\(904\) | −6.30110 | −0.209572 | ||||||||
\(905\) | −5.92917 | −0.197092 | ||||||||
\(906\) | 1.39000 | 0.0461797 | ||||||||
\(907\) | −3.34039 | −0.110916 | −0.0554579 | − | 0.998461i | \(-0.517662\pi\) | ||||
−0.0554579 | + | 0.998461i | \(0.517662\pi\) | |||||||
\(908\) | −21.8972 | −0.726683 | ||||||||
\(909\) | 4.81067 | 0.159560 | ||||||||
\(910\) | 5.31387 | 0.176153 | ||||||||
\(911\) | −0.828856 | −0.0274612 | −0.0137306 | − | 0.999906i | \(-0.504371\pi\) | ||||
−0.0137306 | + | 0.999906i | \(0.504371\pi\) | |||||||
\(912\) | −0.198264 | −0.00656519 | ||||||||
\(913\) | −0.718102 | −0.0237657 | ||||||||
\(914\) | −13.0389 | −0.431287 | ||||||||
\(915\) | −1.17562 | −0.0388648 | ||||||||
\(916\) | 23.9817 | 0.792376 | ||||||||
\(917\) | −4.46570 | −0.147470 | ||||||||
\(918\) | 7.25114 | 0.239323 | ||||||||
\(919\) | 20.9157 | 0.689945 | 0.344972 | − | 0.938613i | \(-0.387888\pi\) | ||||
0.344972 | + | 0.938613i | \(0.387888\pi\) | |||||||
\(920\) | 13.6664 | 0.450567 | ||||||||
\(921\) | 0.261178 | 0.00860610 | ||||||||
\(922\) | 29.2682 | 0.963897 | ||||||||
\(923\) | 39.0706 | 1.28602 | ||||||||
\(924\) | 0.00584772 | 0.000192376 0 | ||||||||
\(925\) | −0.336271 | −0.0110565 | ||||||||
\(926\) | 7.13135 | 0.234351 | ||||||||
\(927\) | 2.36813 | 0.0777795 | ||||||||
\(928\) | 3.90713 | 0.128258 | ||||||||
\(929\) | 19.1309 | 0.627665 | 0.313833 | − | 0.949478i | \(-0.398387\pi\) | ||||
0.313833 | + | 0.949478i | \(0.398387\pi\) | |||||||
\(930\) | 2.98802 | 0.0979810 | ||||||||
\(931\) | −6.71819 | −0.220180 | ||||||||
\(932\) | 26.2413 | 0.859564 | ||||||||
\(933\) | −4.03102 | −0.131970 | ||||||||
\(934\) | −8.86217 | −0.289979 | ||||||||
\(935\) | 0.914259 | 0.0298995 | ||||||||
\(936\) | −15.4556 | −0.505182 | ||||||||
\(937\) | −2.98421 | −0.0974900 | −0.0487450 | − | 0.998811i | \(-0.515522\pi\) | ||||
−0.0487450 | + | 0.998811i | \(0.515522\pi\) | |||||||
\(938\) | −1.54879 | −0.0505697 | ||||||||
\(939\) | 4.99393 | 0.162971 | ||||||||
\(940\) | 6.80579 | 0.221980 | ||||||||
\(941\) | −19.7437 | −0.643626 | −0.321813 | − | 0.946803i | \(-0.604292\pi\) | ||||
−0.321813 | + | 0.946803i | \(0.604292\pi\) | |||||||
\(942\) | 2.87627 | 0.0937139 | ||||||||
\(943\) | 36.0516 | 1.17400 | ||||||||
\(944\) | −10.7757 | −0.350718 | ||||||||
\(945\) | 1.21765 | 0.0396102 | ||||||||
\(946\) | 0.279211 | 0.00907792 | ||||||||
\(947\) | −23.5295 | −0.764605 | −0.382303 | − | 0.924037i | \(-0.624869\pi\) | ||||
−0.382303 | + | 0.924037i | \(0.624869\pi\) | |||||||
\(948\) | 2.64116 | 0.0857810 | ||||||||
\(949\) | −23.3809 | −0.758976 | ||||||||
\(950\) | −0.268023 | −0.00869583 | ||||||||
\(951\) | −4.18100 | −0.135578 | ||||||||
\(952\) | −2.68571 | −0.0870445 | ||||||||
\(953\) | 36.0159 | 1.16667 | 0.583336 | − | 0.812231i | \(-0.301747\pi\) | ||||
0.583336 | + | 0.812231i | \(0.301747\pi\) | |||||||
\(954\) | −34.8796 | −1.12927 | ||||||||
\(955\) | −9.93441 | −0.321470 | ||||||||
\(956\) | 0.0739620 | 0.00239210 | ||||||||
\(957\) | 0.0515512 | 0.00166641 | ||||||||
\(958\) | 11.5049 | 0.371707 | ||||||||
\(959\) | 4.13324 | 0.133469 | ||||||||
\(960\) | 0.460992 | 0.0148785 | ||||||||
\(961\) | 11.0126 | 0.355246 | ||||||||
\(962\) | −6.46952 | −0.208586 | ||||||||
\(963\) | 25.4966 | 0.821618 | ||||||||
\(964\) | −15.1583 | −0.488215 | ||||||||
\(965\) | −2.01549 | −0.0648810 | ||||||||
\(966\) | −0.529694 | −0.0170426 | ||||||||
\(967\) | 53.7919 | 1.72983 | 0.864915 | − | 0.501919i | \(-0.167372\pi\) | ||||
0.864915 | + | 0.501919i | \(0.167372\pi\) | |||||||
\(968\) | 10.9957 | 0.353415 | ||||||||
\(969\) | 1.20143 | 0.0385955 | ||||||||
\(970\) | 7.01143 | 0.225124 | ||||||||
\(971\) | 2.52562 | 0.0810512 | 0.0405256 | − | 0.999179i | \(-0.487097\pi\) | ||||
0.0405256 | + | 0.999179i | \(0.487097\pi\) | |||||||
\(972\) | −5.32436 | −0.170779 | ||||||||
\(973\) | −3.01129 | −0.0965377 | ||||||||
\(974\) | −23.2218 | −0.744076 | ||||||||
\(975\) | 0.284595 | 0.00911433 | ||||||||
\(976\) | −2.55019 | −0.0816297 | ||||||||
\(977\) | 0.833970 | 0.0266811 | 0.0133405 | − | 0.999911i | \(-0.495753\pi\) | ||||
0.0133405 | + | 0.999911i | \(0.495753\pi\) | |||||||
\(978\) | −1.99738 | −0.0638690 | ||||||||
\(979\) | −0.125089 | −0.00399788 | ||||||||
\(980\) | 15.6207 | 0.498985 | ||||||||
\(981\) | 57.4018 | 1.83270 | ||||||||
\(982\) | −4.66706 | −0.148932 | ||||||||
\(983\) | 36.9676 | 1.17908 | 0.589541 | − | 0.807739i | \(-0.299309\pi\) | ||||
0.589541 | + | 0.807739i | \(0.299309\pi\) | |||||||
\(984\) | 1.21608 | 0.0387674 | ||||||||
\(985\) | −8.41511 | −0.268128 | ||||||||
\(986\) | −23.6762 | −0.754003 | ||||||||
\(987\) | −0.263785 | −0.00839636 | ||||||||
\(988\) | −5.15651 | −0.164050 | ||||||||
\(989\) | −25.2912 | −0.804215 | ||||||||
\(990\) | −0.446541 | −0.0141920 | ||||||||
\(991\) | −13.2317 | −0.420319 | −0.210159 | − | 0.977667i | \(-0.567398\pi\) | ||||
−0.210159 | + | 0.977667i | \(0.567398\pi\) | |||||||
\(992\) | 6.48171 | 0.205795 | ||||||||
\(993\) | −1.93830 | −0.0615101 | ||||||||
\(994\) | −3.31601 | −0.105177 | ||||||||
\(995\) | 12.9093 | 0.409252 | ||||||||
\(996\) | 2.19414 | 0.0695240 | ||||||||
\(997\) | 13.2405 | 0.419331 | 0.209666 | − | 0.977773i | \(-0.432762\pi\) | ||||
0.209666 | + | 0.977773i | \(0.432762\pi\) | |||||||
\(998\) | 31.4924 | 0.996873 | ||||||||
\(999\) | −1.48246 | −0.0469031 |
(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.1.35 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.35 | ✓ | 77 | 1.1 | even | 1 | trivial |