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: | \(1\) |
Dimension: | \(151\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36725 | −1.67390 | −0.836949 | − | 0.547281i | \(-0.815663\pi\) | ||||
−0.836949 | + | 0.547281i | \(0.815663\pi\) | |||||||
\(3\) | 0.254210 | 0.146768 | 0.0733842 | − | 0.997304i | \(-0.476620\pi\) | ||||
0.0733842 | + | 0.997304i | \(0.476620\pi\) | |||||||
\(4\) | 3.60387 | 1.80193 | ||||||||
\(5\) | 1.17067 | 0.523539 | 0.261770 | − | 0.965130i | \(-0.415694\pi\) | ||||
0.261770 | + | 0.965130i | \(0.415694\pi\) | |||||||
\(6\) | −0.601779 | −0.245675 | ||||||||
\(7\) | −2.57756 | −0.974227 | −0.487113 | − | 0.873339i | \(-0.661950\pi\) | ||||
−0.487113 | + | 0.873339i | \(0.661950\pi\) | |||||||
\(8\) | −3.79676 | −1.34236 | ||||||||
\(9\) | −2.93538 | −0.978459 | ||||||||
\(10\) | −2.77126 | −0.876351 | ||||||||
\(11\) | −2.66016 | −0.802069 | −0.401035 | − | 0.916063i | \(-0.631349\pi\) | ||||
−0.401035 | + | 0.916063i | \(0.631349\pi\) | |||||||
\(12\) | 0.916140 | 0.264467 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 6.10173 | 1.63076 | ||||||||
\(15\) | 0.297596 | 0.0768389 | ||||||||
\(16\) | 1.78014 | 0.445034 | ||||||||
\(17\) | 3.09731 | 0.751209 | 0.375604 | − | 0.926780i | \(-0.377435\pi\) | ||||
0.375604 | + | 0.926780i | \(0.377435\pi\) | |||||||
\(18\) | 6.94877 | 1.63784 | ||||||||
\(19\) | −6.16603 | −1.41458 | −0.707292 | − | 0.706922i | \(-0.750083\pi\) | ||||
−0.707292 | + | 0.706922i | \(0.750083\pi\) | |||||||
\(20\) | 4.21894 | 0.943383 | ||||||||
\(21\) | −0.655243 | −0.142986 | ||||||||
\(22\) | 6.29727 | 1.34258 | ||||||||
\(23\) | 8.37256 | 1.74580 | 0.872899 | − | 0.487900i | \(-0.162237\pi\) | ||||
0.872899 | + | 0.487900i | \(0.162237\pi\) | |||||||
\(24\) | −0.965175 | −0.197015 | ||||||||
\(25\) | −3.62953 | −0.725907 | ||||||||
\(26\) | 2.36725 | 0.464256 | ||||||||
\(27\) | −1.50883 | −0.290375 | ||||||||
\(28\) | −9.28920 | −1.75549 | ||||||||
\(29\) | −2.73366 | −0.507629 | −0.253814 | − | 0.967253i | \(-0.581685\pi\) | ||||
−0.253814 | + | 0.967253i | \(0.581685\pi\) | |||||||
\(30\) | −0.704484 | −0.128621 | ||||||||
\(31\) | 0.535016 | 0.0960917 | 0.0480458 | − | 0.998845i | \(-0.484701\pi\) | ||||
0.0480458 | + | 0.998845i | \(0.484701\pi\) | |||||||
\(32\) | 3.37949 | 0.597416 | ||||||||
\(33\) | −0.676240 | −0.117718 | ||||||||
\(34\) | −7.33211 | −1.25745 | ||||||||
\(35\) | −3.01747 | −0.510046 | ||||||||
\(36\) | −10.5787 | −1.76312 | ||||||||
\(37\) | 10.5604 | 1.73611 | 0.868056 | − | 0.496467i | \(-0.165370\pi\) | ||||
0.868056 | + | 0.496467i | \(0.165370\pi\) | |||||||
\(38\) | 14.5965 | 2.36787 | ||||||||
\(39\) | −0.254210 | −0.0407062 | ||||||||
\(40\) | −4.44475 | −0.702776 | ||||||||
\(41\) | −4.18761 | −0.653995 | −0.326998 | − | 0.945025i | \(-0.606037\pi\) | ||||
−0.326998 | + | 0.945025i | \(0.606037\pi\) | |||||||
\(42\) | 1.55112 | 0.239343 | ||||||||
\(43\) | 8.17993 | 1.24743 | 0.623714 | − | 0.781653i | \(-0.285623\pi\) | ||||
0.623714 | + | 0.781653i | \(0.285623\pi\) | |||||||
\(44\) | −9.58688 | −1.44528 | ||||||||
\(45\) | −3.43635 | −0.512261 | ||||||||
\(46\) | −19.8199 | −2.92229 | ||||||||
\(47\) | 9.39988 | 1.37111 | 0.685557 | − | 0.728019i | \(-0.259559\pi\) | ||||
0.685557 | + | 0.728019i | \(0.259559\pi\) | |||||||
\(48\) | 0.452529 | 0.0653169 | ||||||||
\(49\) | −0.356173 | −0.0508818 | ||||||||
\(50\) | 8.59201 | 1.21509 | ||||||||
\(51\) | 0.787368 | 0.110254 | ||||||||
\(52\) | −3.60387 | −0.499767 | ||||||||
\(53\) | −0.512259 | −0.0703642 | −0.0351821 | − | 0.999381i | \(-0.511201\pi\) | ||||
−0.0351821 | + | 0.999381i | \(0.511201\pi\) | |||||||
\(54\) | 3.57178 | 0.486058 | ||||||||
\(55\) | −3.11417 | −0.419914 | ||||||||
\(56\) | 9.78638 | 1.30776 | ||||||||
\(57\) | −1.56747 | −0.207616 | ||||||||
\(58\) | 6.47126 | 0.849718 | ||||||||
\(59\) | 3.78589 | 0.492881 | 0.246441 | − | 0.969158i | \(-0.420739\pi\) | ||||
0.246441 | + | 0.969158i | \(0.420739\pi\) | |||||||
\(60\) | 1.07250 | 0.138459 | ||||||||
\(61\) | 2.00673 | 0.256935 | 0.128468 | − | 0.991714i | \(-0.458994\pi\) | ||||
0.128468 | + | 0.991714i | \(0.458994\pi\) | |||||||
\(62\) | −1.26652 | −0.160848 | ||||||||
\(63\) | 7.56612 | 0.953241 | ||||||||
\(64\) | −11.5604 | −1.44505 | ||||||||
\(65\) | −1.17067 | −0.145204 | ||||||||
\(66\) | 1.60083 | 0.197048 | ||||||||
\(67\) | −9.55948 | −1.16788 | −0.583938 | − | 0.811798i | \(-0.698489\pi\) | ||||
−0.583938 | + | 0.811798i | \(0.698489\pi\) | |||||||
\(68\) | 11.1623 | 1.35363 | ||||||||
\(69\) | 2.12839 | 0.256228 | ||||||||
\(70\) | 7.14311 | 0.853765 | ||||||||
\(71\) | −3.63682 | −0.431611 | −0.215806 | − | 0.976436i | \(-0.569238\pi\) | ||||
−0.215806 | + | 0.976436i | \(0.569238\pi\) | |||||||
\(72\) | 11.1449 | 1.31344 | ||||||||
\(73\) | 10.8378 | 1.26847 | 0.634237 | − | 0.773139i | \(-0.281314\pi\) | ||||
0.634237 | + | 0.773139i | \(0.281314\pi\) | |||||||
\(74\) | −24.9990 | −2.90607 | ||||||||
\(75\) | −0.922665 | −0.106540 | ||||||||
\(76\) | −22.2216 | −2.54899 | ||||||||
\(77\) | 6.85673 | 0.781397 | ||||||||
\(78\) | 0.601779 | 0.0681380 | ||||||||
\(79\) | 11.7148 | 1.31802 | 0.659012 | − | 0.752133i | \(-0.270975\pi\) | ||||
0.659012 | + | 0.752133i | \(0.270975\pi\) | |||||||
\(80\) | 2.08395 | 0.232993 | ||||||||
\(81\) | 8.42257 | 0.935841 | ||||||||
\(82\) | 9.91312 | 1.09472 | ||||||||
\(83\) | 0.465564 | 0.0511023 | 0.0255512 | − | 0.999674i | \(-0.491866\pi\) | ||||
0.0255512 | + | 0.999674i | \(0.491866\pi\) | |||||||
\(84\) | −2.36141 | −0.257651 | ||||||||
\(85\) | 3.62593 | 0.393287 | ||||||||
\(86\) | −19.3639 | −2.08807 | ||||||||
\(87\) | −0.694925 | −0.0745038 | ||||||||
\(88\) | 10.1000 | 1.07666 | ||||||||
\(89\) | 0.472409 | 0.0500753 | 0.0250376 | − | 0.999687i | \(-0.492029\pi\) | ||||
0.0250376 | + | 0.999687i | \(0.492029\pi\) | |||||||
\(90\) | 8.13471 | 0.857473 | ||||||||
\(91\) | 2.57756 | 0.270202 | ||||||||
\(92\) | 30.1736 | 3.14582 | ||||||||
\(93\) | 0.136006 | 0.0141032 | ||||||||
\(94\) | −22.2519 | −2.29510 | ||||||||
\(95\) | −7.21838 | −0.740590 | ||||||||
\(96\) | 0.859101 | 0.0876817 | ||||||||
\(97\) | 1.20908 | 0.122764 | 0.0613819 | − | 0.998114i | \(-0.480449\pi\) | ||||
0.0613819 | + | 0.998114i | \(0.480449\pi\) | |||||||
\(98\) | 0.843150 | 0.0851710 | ||||||||
\(99\) | 7.80858 | 0.784792 | ||||||||
\(100\) | −13.0804 | −1.30804 | ||||||||
\(101\) | 16.1150 | 1.60351 | 0.801753 | − | 0.597655i | \(-0.203901\pi\) | ||||
0.801753 | + | 0.597655i | \(0.203901\pi\) | |||||||
\(102\) | −1.86390 | −0.184553 | ||||||||
\(103\) | −1.82301 | −0.179627 | −0.0898134 | − | 0.995959i | \(-0.528627\pi\) | ||||
−0.0898134 | + | 0.995959i | \(0.528627\pi\) | |||||||
\(104\) | 3.79676 | 0.372303 | ||||||||
\(105\) | −0.767072 | −0.0748586 | ||||||||
\(106\) | 1.21264 | 0.117782 | ||||||||
\(107\) | 1.22156 | 0.118093 | 0.0590465 | − | 0.998255i | \(-0.481194\pi\) | ||||
0.0590465 | + | 0.998255i | \(0.481194\pi\) | |||||||
\(108\) | −5.43764 | −0.523237 | ||||||||
\(109\) | −10.7167 | −1.02647 | −0.513237 | − | 0.858247i | \(-0.671554\pi\) | ||||
−0.513237 | + | 0.858247i | \(0.671554\pi\) | |||||||
\(110\) | 7.37201 | 0.702894 | ||||||||
\(111\) | 2.68455 | 0.254806 | ||||||||
\(112\) | −4.58841 | −0.433564 | ||||||||
\(113\) | 10.8624 | 1.02185 | 0.510925 | − | 0.859625i | \(-0.329303\pi\) | ||||
0.510925 | + | 0.859625i | \(0.329303\pi\) | |||||||
\(114\) | 3.71059 | 0.347528 | ||||||||
\(115\) | 9.80149 | 0.913994 | ||||||||
\(116\) | −9.85177 | −0.914713 | ||||||||
\(117\) | 2.93538 | 0.271376 | ||||||||
\(118\) | −8.96215 | −0.825033 | ||||||||
\(119\) | −7.98352 | −0.731848 | ||||||||
\(120\) | −1.12990 | −0.103145 | ||||||||
\(121\) | −3.92354 | −0.356685 | ||||||||
\(122\) | −4.75043 | −0.430083 | ||||||||
\(123\) | −1.06453 | −0.0959858 | ||||||||
\(124\) | 1.92813 | 0.173151 | ||||||||
\(125\) | −10.1023 | −0.903580 | ||||||||
\(126\) | −17.9109 | −1.59563 | ||||||||
\(127\) | 4.25493 | 0.377564 | 0.188782 | − | 0.982019i | \(-0.439546\pi\) | ||||
0.188782 | + | 0.982019i | \(0.439546\pi\) | |||||||
\(128\) | 20.6073 | 1.82145 | ||||||||
\(129\) | 2.07942 | 0.183083 | ||||||||
\(130\) | 2.77126 | 0.243056 | ||||||||
\(131\) | 16.2566 | 1.42035 | 0.710174 | − | 0.704026i | \(-0.248616\pi\) | ||||
0.710174 | + | 0.704026i | \(0.248616\pi\) | |||||||
\(132\) | −2.43708 | −0.212121 | ||||||||
\(133\) | 15.8933 | 1.37813 | ||||||||
\(134\) | 22.6297 | 1.95491 | ||||||||
\(135\) | −1.76634 | −0.152023 | ||||||||
\(136\) | −11.7597 | −1.00839 | ||||||||
\(137\) | −10.8802 | −0.929561 | −0.464780 | − | 0.885426i | \(-0.653867\pi\) | ||||
−0.464780 | + | 0.885426i | \(0.653867\pi\) | |||||||
\(138\) | −5.03843 | −0.428899 | ||||||||
\(139\) | 4.68524 | 0.397397 | 0.198699 | − | 0.980061i | \(-0.436329\pi\) | ||||
0.198699 | + | 0.980061i | \(0.436329\pi\) | |||||||
\(140\) | −10.8746 | −0.919069 | ||||||||
\(141\) | 2.38955 | 0.201236 | ||||||||
\(142\) | 8.60926 | 0.722473 | ||||||||
\(143\) | 2.66016 | 0.222454 | ||||||||
\(144\) | −5.22537 | −0.435447 | ||||||||
\(145\) | −3.20021 | −0.265763 | ||||||||
\(146\) | −25.6559 | −2.12330 | ||||||||
\(147\) | −0.0905428 | −0.00746784 | ||||||||
\(148\) | 38.0581 | 3.12836 | ||||||||
\(149\) | 3.99003 | 0.326876 | 0.163438 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163438 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(150\) | 2.18418 | 0.178337 | ||||||||
\(151\) | −6.15106 | −0.500566 | −0.250283 | − | 0.968173i | \(-0.580524\pi\) | ||||
−0.250283 | + | 0.968173i | \(0.580524\pi\) | |||||||
\(152\) | 23.4109 | 1.89888 | ||||||||
\(153\) | −9.09178 | −0.735027 | ||||||||
\(154\) | −16.2316 | −1.30798 | ||||||||
\(155\) | 0.626326 | 0.0503077 | ||||||||
\(156\) | −0.916140 | −0.0733499 | ||||||||
\(157\) | −7.53876 | −0.601659 | −0.300829 | − | 0.953678i | \(-0.597263\pi\) | ||||
−0.300829 | + | 0.953678i | \(0.597263\pi\) | |||||||
\(158\) | −27.7320 | −2.20624 | ||||||||
\(159\) | −0.130221 | −0.0103272 | ||||||||
\(160\) | 3.95627 | 0.312770 | ||||||||
\(161\) | −21.5808 | −1.70080 | ||||||||
\(162\) | −19.9383 | −1.56650 | ||||||||
\(163\) | −22.4555 | −1.75885 | −0.879425 | − | 0.476038i | \(-0.842072\pi\) | ||||
−0.879425 | + | 0.476038i | \(0.842072\pi\) | |||||||
\(164\) | −15.0916 | −1.17846 | ||||||||
\(165\) | −0.791653 | −0.0616301 | ||||||||
\(166\) | −1.10211 | −0.0855401 | ||||||||
\(167\) | 1.94999 | 0.150895 | 0.0754475 | − | 0.997150i | \(-0.475961\pi\) | ||||
0.0754475 | + | 0.997150i | \(0.475961\pi\) | |||||||
\(168\) | 2.48780 | 0.191938 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −8.58347 | −0.658322 | ||||||||
\(171\) | 18.0996 | 1.38411 | ||||||||
\(172\) | 29.4794 | 2.24778 | ||||||||
\(173\) | −17.5205 | −1.33206 | −0.666031 | − | 0.745924i | \(-0.732008\pi\) | ||||
−0.666031 | + | 0.745924i | \(0.732008\pi\) | |||||||
\(174\) | 1.64506 | 0.124712 | ||||||||
\(175\) | 9.35535 | 0.707198 | ||||||||
\(176\) | −4.73545 | −0.356948 | ||||||||
\(177\) | 0.962413 | 0.0723394 | ||||||||
\(178\) | −1.11831 | −0.0838209 | ||||||||
\(179\) | −3.89016 | −0.290764 | −0.145382 | − | 0.989376i | \(-0.546441\pi\) | ||||
−0.145382 | + | 0.989376i | \(0.546441\pi\) | |||||||
\(180\) | −12.3842 | −0.923062 | ||||||||
\(181\) | 12.7087 | 0.944631 | 0.472316 | − | 0.881429i | \(-0.343418\pi\) | ||||
0.472316 | + | 0.881429i | \(0.343418\pi\) | |||||||
\(182\) | −6.10173 | −0.452291 | ||||||||
\(183\) | 0.510131 | 0.0377099 | ||||||||
\(184\) | −31.7886 | −2.34349 | ||||||||
\(185\) | 12.3627 | 0.908922 | ||||||||
\(186\) | −0.321961 | −0.0236073 | ||||||||
\(187\) | −8.23935 | −0.602521 | ||||||||
\(188\) | 33.8759 | 2.47066 | ||||||||
\(189\) | 3.88911 | 0.282891 | ||||||||
\(190\) | 17.0877 | 1.23967 | ||||||||
\(191\) | −23.7992 | −1.72205 | −0.861024 | − | 0.508564i | \(-0.830177\pi\) | ||||
−0.861024 | + | 0.508564i | \(0.830177\pi\) | |||||||
\(192\) | −2.93876 | −0.212087 | ||||||||
\(193\) | −23.6873 | −1.70505 | −0.852523 | − | 0.522690i | \(-0.824929\pi\) | ||||
−0.852523 | + | 0.522690i | \(0.824929\pi\) | |||||||
\(194\) | −2.86220 | −0.205494 | ||||||||
\(195\) | −0.297596 | −0.0213113 | ||||||||
\(196\) | −1.28360 | −0.0916858 | ||||||||
\(197\) | −18.5672 | −1.32286 | −0.661428 | − | 0.750009i | \(-0.730049\pi\) | ||||
−0.661428 | + | 0.750009i | \(0.730049\pi\) | |||||||
\(198\) | −18.4849 | −1.31366 | ||||||||
\(199\) | −28.1323 | −1.99425 | −0.997123 | − | 0.0758013i | \(-0.975849\pi\) | ||||
−0.997123 | + | 0.0758013i | \(0.975849\pi\) | |||||||
\(200\) | 13.7805 | 0.974426 | ||||||||
\(201\) | −2.43012 | −0.171407 | ||||||||
\(202\) | −38.1483 | −2.68411 | ||||||||
\(203\) | 7.04619 | 0.494545 | ||||||||
\(204\) | 2.83757 | 0.198670 | ||||||||
\(205\) | −4.90231 | −0.342392 | ||||||||
\(206\) | 4.31553 | 0.300677 | ||||||||
\(207\) | −24.5766 | −1.70819 | ||||||||
\(208\) | −1.78014 | −0.123430 | ||||||||
\(209\) | 16.4026 | 1.13459 | ||||||||
\(210\) | 1.81585 | 0.125306 | ||||||||
\(211\) | −17.5114 | −1.20554 | −0.602768 | − | 0.797917i | \(-0.705935\pi\) | ||||
−0.602768 | + | 0.797917i | \(0.705935\pi\) | |||||||
\(212\) | −1.84611 | −0.126792 | ||||||||
\(213\) | −0.924517 | −0.0633468 | ||||||||
\(214\) | −2.89174 | −0.197676 | ||||||||
\(215\) | 9.57599 | 0.653077 | ||||||||
\(216\) | 5.72868 | 0.389787 | ||||||||
\(217\) | −1.37904 | −0.0936151 | ||||||||
\(218\) | 25.3691 | 1.71821 | ||||||||
\(219\) | 2.75509 | 0.186172 | ||||||||
\(220\) | −11.2231 | −0.756658 | ||||||||
\(221\) | −3.09731 | −0.208348 | ||||||||
\(222\) | −6.35500 | −0.426520 | ||||||||
\(223\) | 17.5161 | 1.17296 | 0.586482 | − | 0.809962i | \(-0.300512\pi\) | ||||
0.586482 | + | 0.809962i | \(0.300512\pi\) | |||||||
\(224\) | −8.71085 | −0.582018 | ||||||||
\(225\) | 10.6541 | 0.710270 | ||||||||
\(226\) | −25.7141 | −1.71047 | ||||||||
\(227\) | −6.85422 | −0.454931 | −0.227465 | − | 0.973786i | \(-0.573044\pi\) | ||||
−0.227465 | + | 0.973786i | \(0.573044\pi\) | |||||||
\(228\) | −5.64895 | −0.374111 | ||||||||
\(229\) | −24.8303 | −1.64083 | −0.820416 | − | 0.571767i | \(-0.806258\pi\) | ||||
−0.820416 | + | 0.571767i | \(0.806258\pi\) | |||||||
\(230\) | −23.2026 | −1.52993 | ||||||||
\(231\) | 1.74305 | 0.114684 | ||||||||
\(232\) | 10.3791 | 0.681419 | ||||||||
\(233\) | 14.5096 | 0.950559 | 0.475279 | − | 0.879835i | \(-0.342347\pi\) | ||||
0.475279 | + | 0.879835i | \(0.342347\pi\) | |||||||
\(234\) | −6.94877 | −0.454255 | ||||||||
\(235\) | 11.0041 | 0.717831 | ||||||||
\(236\) | 13.6439 | 0.888140 | ||||||||
\(237\) | 2.97803 | 0.193444 | ||||||||
\(238\) | 18.8990 | 1.22504 | ||||||||
\(239\) | −18.9850 | −1.22804 | −0.614020 | − | 0.789290i | \(-0.710449\pi\) | ||||
−0.614020 | + | 0.789290i | \(0.710449\pi\) | |||||||
\(240\) | 0.529761 | 0.0341959 | ||||||||
\(241\) | 17.2473 | 1.11099 | 0.555497 | − | 0.831519i | \(-0.312528\pi\) | ||||
0.555497 | + | 0.831519i | \(0.312528\pi\) | |||||||
\(242\) | 9.28799 | 0.597055 | ||||||||
\(243\) | 6.66760 | 0.427727 | ||||||||
\(244\) | 7.23198 | 0.462980 | ||||||||
\(245\) | −0.416961 | −0.0266386 | ||||||||
\(246\) | 2.52002 | 0.160670 | ||||||||
\(247\) | 6.16603 | 0.392335 | ||||||||
\(248\) | −2.03133 | −0.128989 | ||||||||
\(249\) | 0.118351 | 0.00750020 | ||||||||
\(250\) | 23.9147 | 1.51250 | ||||||||
\(251\) | −28.6309 | −1.80716 | −0.903582 | − | 0.428415i | \(-0.859072\pi\) | ||||
−0.903582 | + | 0.428415i | \(0.859072\pi\) | |||||||
\(252\) | 27.2673 | 1.71768 | ||||||||
\(253\) | −22.2724 | −1.40025 | ||||||||
\(254\) | −10.0725 | −0.632003 | ||||||||
\(255\) | 0.921748 | 0.0577221 | ||||||||
\(256\) | −25.6619 | −1.60387 | ||||||||
\(257\) | −10.9530 | −0.683231 | −0.341615 | − | 0.939840i | \(-0.610974\pi\) | ||||
−0.341615 | + | 0.939840i | \(0.610974\pi\) | |||||||
\(258\) | −4.92251 | −0.306462 | ||||||||
\(259\) | −27.2200 | −1.69137 | ||||||||
\(260\) | −4.21894 | −0.261647 | ||||||||
\(261\) | 8.02433 | 0.496694 | ||||||||
\(262\) | −38.4835 | −2.37752 | ||||||||
\(263\) | −13.7632 | −0.848674 | −0.424337 | − | 0.905504i | \(-0.639493\pi\) | ||||
−0.424337 | + | 0.905504i | \(0.639493\pi\) | |||||||
\(264\) | 2.56752 | 0.158020 | ||||||||
\(265\) | −0.599685 | −0.0368384 | ||||||||
\(266\) | −37.6235 | −2.30684 | ||||||||
\(267\) | 0.120091 | 0.00734947 | ||||||||
\(268\) | −34.4511 | −2.10444 | ||||||||
\(269\) | −6.23289 | −0.380026 | −0.190013 | − | 0.981782i | \(-0.560853\pi\) | ||||
−0.190013 | + | 0.981782i | \(0.560853\pi\) | |||||||
\(270\) | 4.18138 | 0.254470 | ||||||||
\(271\) | 5.34314 | 0.324573 | 0.162286 | − | 0.986744i | \(-0.448113\pi\) | ||||
0.162286 | + | 0.986744i | \(0.448113\pi\) | |||||||
\(272\) | 5.51364 | 0.334313 | ||||||||
\(273\) | 0.655243 | 0.0396571 | ||||||||
\(274\) | 25.7562 | 1.55599 | ||||||||
\(275\) | 9.65515 | 0.582227 | ||||||||
\(276\) | 7.67044 | 0.461706 | ||||||||
\(277\) | 2.51617 | 0.151182 | 0.0755909 | − | 0.997139i | \(-0.475916\pi\) | ||||
0.0755909 | + | 0.997139i | \(0.475916\pi\) | |||||||
\(278\) | −11.0911 | −0.665202 | ||||||||
\(279\) | −1.57047 | −0.0940218 | ||||||||
\(280\) | 11.4566 | 0.684664 | ||||||||
\(281\) | 5.17983 | 0.309003 | 0.154501 | − | 0.987993i | \(-0.450623\pi\) | ||||
0.154501 | + | 0.987993i | \(0.450623\pi\) | |||||||
\(282\) | −5.65665 | −0.336849 | ||||||||
\(283\) | 27.2815 | 1.62172 | 0.810860 | − | 0.585241i | \(-0.199000\pi\) | ||||
0.810860 | + | 0.585241i | \(0.199000\pi\) | |||||||
\(284\) | −13.1066 | −0.777735 | ||||||||
\(285\) | −1.83498 | −0.108695 | ||||||||
\(286\) | −6.29727 | −0.372365 | ||||||||
\(287\) | 10.7938 | 0.637140 | ||||||||
\(288\) | −9.92009 | −0.584547 | ||||||||
\(289\) | −7.40666 | −0.435686 | ||||||||
\(290\) | 7.57571 | 0.444861 | ||||||||
\(291\) | 0.307361 | 0.0180178 | ||||||||
\(292\) | 39.0582 | 2.28571 | ||||||||
\(293\) | −6.46192 | −0.377509 | −0.188755 | − | 0.982024i | \(-0.560445\pi\) | ||||
−0.188755 | + | 0.982024i | \(0.560445\pi\) | |||||||
\(294\) | 0.214337 | 0.0125004 | ||||||||
\(295\) | 4.43203 | 0.258043 | ||||||||
\(296\) | −40.0951 | −2.33048 | ||||||||
\(297\) | 4.01374 | 0.232901 | ||||||||
\(298\) | −9.44538 | −0.547156 | ||||||||
\(299\) | −8.37256 | −0.484197 | ||||||||
\(300\) | −3.32516 | −0.191978 | ||||||||
\(301\) | −21.0843 | −1.21528 | ||||||||
\(302\) | 14.5611 | 0.837897 | ||||||||
\(303\) | 4.09661 | 0.235344 | ||||||||
\(304\) | −10.9764 | −0.629538 | ||||||||
\(305\) | 2.34921 | 0.134516 | ||||||||
\(306\) | 21.5225 | 1.23036 | ||||||||
\(307\) | 19.5316 | 1.11472 | 0.557362 | − | 0.830269i | \(-0.311813\pi\) | ||||
0.557362 | + | 0.830269i | \(0.311813\pi\) | |||||||
\(308\) | 24.7108 | 1.40803 | ||||||||
\(309\) | −0.463429 | −0.0263635 | ||||||||
\(310\) | −1.48267 | −0.0842100 | ||||||||
\(311\) | −14.8043 | −0.839474 | −0.419737 | − | 0.907646i | \(-0.637878\pi\) | ||||
−0.419737 | + | 0.907646i | \(0.637878\pi\) | |||||||
\(312\) | 0.965175 | 0.0546423 | ||||||||
\(313\) | 4.74272 | 0.268074 | 0.134037 | − | 0.990976i | \(-0.457206\pi\) | ||||
0.134037 | + | 0.990976i | \(0.457206\pi\) | |||||||
\(314\) | 17.8461 | 1.00712 | ||||||||
\(315\) | 8.85742 | 0.499059 | ||||||||
\(316\) | 42.2188 | 2.37499 | ||||||||
\(317\) | −14.0678 | −0.790124 | −0.395062 | − | 0.918654i | \(-0.629277\pi\) | ||||
−0.395062 | + | 0.918654i | \(0.629277\pi\) | |||||||
\(318\) | 0.308267 | 0.0172867 | ||||||||
\(319\) | 7.27199 | 0.407153 | ||||||||
\(320\) | −13.5334 | −0.756538 | ||||||||
\(321\) | 0.310534 | 0.0173323 | ||||||||
\(322\) | 51.0871 | 2.84697 | ||||||||
\(323\) | −19.0981 | −1.06265 | ||||||||
\(324\) | 30.3538 | 1.68632 | ||||||||
\(325\) | 3.62953 | 0.201330 | ||||||||
\(326\) | 53.1577 | 2.94413 | ||||||||
\(327\) | −2.72430 | −0.150654 | ||||||||
\(328\) | 15.8994 | 0.877895 | ||||||||
\(329\) | −24.2288 | −1.33578 | ||||||||
\(330\) | 1.87404 | 0.103163 | ||||||||
\(331\) | 10.8321 | 0.595388 | 0.297694 | − | 0.954661i | \(-0.403783\pi\) | ||||
0.297694 | + | 0.954661i | \(0.403783\pi\) | |||||||
\(332\) | 1.67783 | 0.0920830 | ||||||||
\(333\) | −30.9986 | −1.69871 | ||||||||
\(334\) | −4.61612 | −0.252583 | ||||||||
\(335\) | −11.1910 | −0.611429 | ||||||||
\(336\) | −1.16642 | −0.0636335 | ||||||||
\(337\) | 13.9217 | 0.758363 | 0.379182 | − | 0.925322i | \(-0.376206\pi\) | ||||
0.379182 | + | 0.925322i | \(0.376206\pi\) | |||||||
\(338\) | −2.36725 | −0.128761 | ||||||||
\(339\) | 2.76134 | 0.149975 | ||||||||
\(340\) | 13.0674 | 0.708678 | ||||||||
\(341\) | −1.42323 | −0.0770722 | ||||||||
\(342\) | −42.8463 | −2.31686 | ||||||||
\(343\) | 18.9610 | 1.02380 | ||||||||
\(344\) | −31.0572 | −1.67449 | ||||||||
\(345\) | 2.49164 | 0.134145 | ||||||||
\(346\) | 41.4755 | 2.22974 | ||||||||
\(347\) | 12.5692 | 0.674748 | 0.337374 | − | 0.941371i | \(-0.390461\pi\) | ||||
0.337374 | + | 0.941371i | \(0.390461\pi\) | |||||||
\(348\) | −2.50442 | −0.134251 | ||||||||
\(349\) | 19.6054 | 1.04946 | 0.524728 | − | 0.851270i | \(-0.324167\pi\) | ||||
0.524728 | + | 0.851270i | \(0.324167\pi\) | |||||||
\(350\) | −22.1464 | −1.18378 | ||||||||
\(351\) | 1.50883 | 0.0805356 | ||||||||
\(352\) | −8.99000 | −0.479168 | ||||||||
\(353\) | −31.3603 | −1.66914 | −0.834569 | − | 0.550903i | \(-0.814283\pi\) | ||||
−0.834569 | + | 0.550903i | \(0.814283\pi\) | |||||||
\(354\) | −2.27827 | −0.121089 | ||||||||
\(355\) | −4.25751 | −0.225965 | ||||||||
\(356\) | 1.70250 | 0.0902324 | ||||||||
\(357\) | −2.02949 | −0.107412 | ||||||||
\(358\) | 9.20898 | 0.486710 | ||||||||
\(359\) | −12.4242 | −0.655726 | −0.327863 | − | 0.944725i | \(-0.606328\pi\) | ||||
−0.327863 | + | 0.944725i | \(0.606328\pi\) | |||||||
\(360\) | 13.0470 | 0.687638 | ||||||||
\(361\) | 19.0199 | 1.00105 | ||||||||
\(362\) | −30.0847 | −1.58122 | ||||||||
\(363\) | −0.997403 | −0.0523501 | ||||||||
\(364\) | 9.28920 | 0.486886 | ||||||||
\(365\) | 12.6875 | 0.664095 | ||||||||
\(366\) | −1.20761 | −0.0631226 | ||||||||
\(367\) | 27.9206 | 1.45744 | 0.728722 | − | 0.684810i | \(-0.240115\pi\) | ||||
0.728722 | + | 0.684810i | \(0.240115\pi\) | |||||||
\(368\) | 14.9043 | 0.776940 | ||||||||
\(369\) | 12.2922 | 0.639908 | ||||||||
\(370\) | −29.2655 | −1.52144 | ||||||||
\(371\) | 1.32038 | 0.0685507 | ||||||||
\(372\) | 0.490150 | 0.0254131 | ||||||||
\(373\) | −15.1658 | −0.785257 | −0.392629 | − | 0.919697i | \(-0.628434\pi\) | ||||
−0.392629 | + | 0.919697i | \(0.628434\pi\) | |||||||
\(374\) | 19.5046 | 1.00856 | ||||||||
\(375\) | −2.56811 | −0.132617 | ||||||||
\(376\) | −35.6891 | −1.84052 | ||||||||
\(377\) | 2.73366 | 0.140791 | ||||||||
\(378\) | −9.20650 | −0.473531 | ||||||||
\(379\) | −1.91443 | −0.0983379 | −0.0491690 | − | 0.998790i | \(-0.515657\pi\) | ||||
−0.0491690 | + | 0.998790i | \(0.515657\pi\) | |||||||
\(380\) | −26.0141 | −1.33449 | ||||||||
\(381\) | 1.08165 | 0.0554144 | ||||||||
\(382\) | 56.3386 | 2.88253 | ||||||||
\(383\) | −30.8204 | −1.57485 | −0.787425 | − | 0.616411i | \(-0.788586\pi\) | ||||
−0.787425 | + | 0.616411i | \(0.788586\pi\) | |||||||
\(384\) | 5.23859 | 0.267330 | ||||||||
\(385\) | 8.02696 | 0.409092 | ||||||||
\(386\) | 56.0736 | 2.85407 | ||||||||
\(387\) | −24.0112 | −1.22056 | ||||||||
\(388\) | 4.35738 | 0.221212 | ||||||||
\(389\) | 15.4395 | 0.782816 | 0.391408 | − | 0.920217i | \(-0.371988\pi\) | ||||
0.391408 | + | 0.920217i | \(0.371988\pi\) | |||||||
\(390\) | 0.704484 | 0.0356729 | ||||||||
\(391\) | 25.9324 | 1.31146 | ||||||||
\(392\) | 1.35230 | 0.0683016 | ||||||||
\(393\) | 4.13260 | 0.208462 | ||||||||
\(394\) | 43.9531 | 2.21433 | ||||||||
\(395\) | 13.7142 | 0.690037 | ||||||||
\(396\) | 28.1411 | 1.41414 | ||||||||
\(397\) | −8.74317 | −0.438807 | −0.219404 | − | 0.975634i | \(-0.570411\pi\) | ||||
−0.219404 | + | 0.975634i | \(0.570411\pi\) | |||||||
\(398\) | 66.5962 | 3.33816 | ||||||||
\(399\) | 4.04024 | 0.202265 | ||||||||
\(400\) | −6.46106 | −0.323053 | ||||||||
\(401\) | 23.0924 | 1.15318 | 0.576590 | − | 0.817033i | \(-0.304383\pi\) | ||||
0.576590 | + | 0.817033i | \(0.304383\pi\) | |||||||
\(402\) | 5.75269 | 0.286918 | ||||||||
\(403\) | −0.535016 | −0.0266510 | ||||||||
\(404\) | 58.0765 | 2.88941 | ||||||||
\(405\) | 9.86004 | 0.489949 | ||||||||
\(406\) | −16.6801 | −0.827819 | ||||||||
\(407\) | −28.0923 | −1.39248 | ||||||||
\(408\) | −2.98945 | −0.148000 | ||||||||
\(409\) | 0.519002 | 0.0256630 | 0.0128315 | − | 0.999918i | \(-0.495915\pi\) | ||||
0.0128315 | + | 0.999918i | \(0.495915\pi\) | |||||||
\(410\) | 11.6050 | 0.573129 | ||||||||
\(411\) | −2.76586 | −0.136430 | ||||||||
\(412\) | −6.56990 | −0.323676 | ||||||||
\(413\) | −9.75838 | −0.480178 | ||||||||
\(414\) | 58.1790 | 2.85934 | ||||||||
\(415\) | 0.545022 | 0.0267541 | ||||||||
\(416\) | −3.37949 | −0.165693 | ||||||||
\(417\) | 1.19104 | 0.0583253 | ||||||||
\(418\) | −38.8291 | −1.89919 | ||||||||
\(419\) | −14.4316 | −0.705032 | −0.352516 | − | 0.935806i | \(-0.614674\pi\) | ||||
−0.352516 | + | 0.935806i | \(0.614674\pi\) | |||||||
\(420\) | −2.76443 | −0.134890 | ||||||||
\(421\) | −4.55122 | −0.221813 | −0.110906 | − | 0.993831i | \(-0.535375\pi\) | ||||
−0.110906 | + | 0.993831i | \(0.535375\pi\) | |||||||
\(422\) | 41.4539 | 2.01794 | ||||||||
\(423\) | −27.5922 | −1.34158 | ||||||||
\(424\) | 1.94492 | 0.0944538 | ||||||||
\(425\) | −11.2418 | −0.545308 | ||||||||
\(426\) | 2.18856 | 0.106036 | ||||||||
\(427\) | −5.17247 | −0.250313 | ||||||||
\(428\) | 4.40235 | 0.212796 | ||||||||
\(429\) | 0.676240 | 0.0326492 | ||||||||
\(430\) | −22.6687 | −1.09318 | ||||||||
\(431\) | 10.7454 | 0.517589 | 0.258794 | − | 0.965932i | \(-0.416675\pi\) | ||||
0.258794 | + | 0.965932i | \(0.416675\pi\) | |||||||
\(432\) | −2.68593 | −0.129227 | ||||||||
\(433\) | 19.0730 | 0.916589 | 0.458294 | − | 0.888801i | \(-0.348461\pi\) | ||||
0.458294 | + | 0.888801i | \(0.348461\pi\) | |||||||
\(434\) | 3.26452 | 0.156702 | ||||||||
\(435\) | −0.813527 | −0.0390056 | ||||||||
\(436\) | −38.6216 | −1.84964 | ||||||||
\(437\) | −51.6254 | −2.46958 | ||||||||
\(438\) | −6.52199 | −0.311633 | ||||||||
\(439\) | 5.78468 | 0.276088 | 0.138044 | − | 0.990426i | \(-0.455918\pi\) | ||||
0.138044 | + | 0.990426i | \(0.455918\pi\) | |||||||
\(440\) | 11.8237 | 0.563675 | ||||||||
\(441\) | 1.04550 | 0.0497858 | ||||||||
\(442\) | 7.33211 | 0.348753 | ||||||||
\(443\) | 3.97399 | 0.188810 | 0.0944049 | − | 0.995534i | \(-0.469905\pi\) | ||||
0.0944049 | + | 0.995534i | \(0.469905\pi\) | |||||||
\(444\) | 9.67477 | 0.459144 | ||||||||
\(445\) | 0.553035 | 0.0262164 | ||||||||
\(446\) | −41.4650 | −1.96342 | ||||||||
\(447\) | 1.01431 | 0.0479750 | ||||||||
\(448\) | 29.7976 | 1.40780 | ||||||||
\(449\) | −20.9464 | −0.988523 | −0.494262 | − | 0.869313i | \(-0.664562\pi\) | ||||
−0.494262 | + | 0.869313i | \(0.664562\pi\) | |||||||
\(450\) | −25.2208 | −1.18892 | ||||||||
\(451\) | 11.1397 | 0.524549 | ||||||||
\(452\) | 39.1467 | 1.84131 | ||||||||
\(453\) | −1.56366 | −0.0734673 | ||||||||
\(454\) | 16.2257 | 0.761508 | ||||||||
\(455\) | 3.01747 | 0.141461 | ||||||||
\(456\) | 5.95129 | 0.278695 | ||||||||
\(457\) | 14.7098 | 0.688094 | 0.344047 | − | 0.938952i | \(-0.388202\pi\) | ||||
0.344047 | + | 0.938952i | \(0.388202\pi\) | |||||||
\(458\) | 58.7795 | 2.74659 | ||||||||
\(459\) | −4.67333 | −0.218132 | ||||||||
\(460\) | 35.3233 | 1.64696 | ||||||||
\(461\) | 13.0128 | 0.606064 | 0.303032 | − | 0.952980i | \(-0.402001\pi\) | ||||
0.303032 | + | 0.952980i | \(0.402001\pi\) | |||||||
\(462\) | −4.12624 | −0.191970 | ||||||||
\(463\) | −26.3695 | −1.22549 | −0.612747 | − | 0.790279i | \(-0.709936\pi\) | ||||
−0.612747 | + | 0.790279i | \(0.709936\pi\) | |||||||
\(464\) | −4.86629 | −0.225912 | ||||||||
\(465\) | 0.159219 | 0.00738358 | ||||||||
\(466\) | −34.3480 | −1.59114 | ||||||||
\(467\) | 10.8100 | 0.500226 | 0.250113 | − | 0.968217i | \(-0.419532\pi\) | ||||
0.250113 | + | 0.968217i | \(0.419532\pi\) | |||||||
\(468\) | 10.5787 | 0.489001 | ||||||||
\(469\) | 24.6402 | 1.13778 | ||||||||
\(470\) | −26.0496 | −1.20158 | ||||||||
\(471\) | −1.91643 | −0.0883044 | ||||||||
\(472\) | −14.3741 | −0.661623 | ||||||||
\(473\) | −21.7599 | −1.00052 | ||||||||
\(474\) | −7.04975 | −0.323806 | ||||||||
\(475\) | 22.3798 | 1.02686 | ||||||||
\(476\) | −28.7715 | −1.31874 | ||||||||
\(477\) | 1.50367 | 0.0688484 | ||||||||
\(478\) | 44.9423 | 2.05561 | ||||||||
\(479\) | 26.3405 | 1.20353 | 0.601765 | − | 0.798673i | \(-0.294464\pi\) | ||||
0.601765 | + | 0.798673i | \(0.294464\pi\) | |||||||
\(480\) | 1.00572 | 0.0459048 | ||||||||
\(481\) | −10.5604 | −0.481511 | ||||||||
\(482\) | −40.8286 | −1.85969 | ||||||||
\(483\) | −5.48606 | −0.249624 | ||||||||
\(484\) | −14.1399 | −0.642723 | ||||||||
\(485\) | 1.41544 | 0.0642716 | ||||||||
\(486\) | −15.7839 | −0.715971 | ||||||||
\(487\) | −36.6265 | −1.65970 | −0.829852 | − | 0.557984i | \(-0.811575\pi\) | ||||
−0.829852 | + | 0.557984i | \(0.811575\pi\) | |||||||
\(488\) | −7.61906 | −0.344899 | ||||||||
\(489\) | −5.70841 | −0.258143 | ||||||||
\(490\) | 0.987049 | 0.0445904 | ||||||||
\(491\) | 19.3589 | 0.873653 | 0.436826 | − | 0.899546i | \(-0.356102\pi\) | ||||
0.436826 | + | 0.899546i | \(0.356102\pi\) | |||||||
\(492\) | −3.83644 | −0.172960 | ||||||||
\(493\) | −8.46701 | −0.381335 | ||||||||
\(494\) | −14.5965 | −0.656729 | ||||||||
\(495\) | 9.14126 | 0.410869 | ||||||||
\(496\) | 0.952401 | 0.0427641 | ||||||||
\(497\) | 9.37413 | 0.420487 | ||||||||
\(498\) | −0.280167 | −0.0125546 | ||||||||
\(499\) | 12.2245 | 0.547243 | 0.273622 | − | 0.961837i | \(-0.411778\pi\) | ||||
0.273622 | + | 0.961837i | \(0.411778\pi\) | |||||||
\(500\) | −36.4075 | −1.62819 | ||||||||
\(501\) | 0.495708 | 0.0221466 | ||||||||
\(502\) | 67.7764 | 3.02501 | ||||||||
\(503\) | 42.2576 | 1.88417 | 0.942086 | − | 0.335371i | \(-0.108862\pi\) | ||||
0.942086 | + | 0.335371i | \(0.108862\pi\) | |||||||
\(504\) | −28.7267 | −1.27959 | ||||||||
\(505\) | 18.8654 | 0.839498 | ||||||||
\(506\) | 52.7242 | 2.34388 | ||||||||
\(507\) | 0.254210 | 0.0112899 | ||||||||
\(508\) | 15.3342 | 0.680345 | ||||||||
\(509\) | −37.5291 | −1.66345 | −0.831724 | − | 0.555189i | \(-0.812646\pi\) | ||||
−0.831724 | + | 0.555189i | \(0.812646\pi\) | |||||||
\(510\) | −2.18201 | −0.0966209 | ||||||||
\(511\) | −27.9352 | −1.23578 | ||||||||
\(512\) | 19.5334 | 0.863264 | ||||||||
\(513\) | 9.30351 | 0.410760 | ||||||||
\(514\) | 25.9285 | 1.14366 | ||||||||
\(515\) | −2.13415 | −0.0940417 | ||||||||
\(516\) | 7.49396 | 0.329903 | ||||||||
\(517\) | −25.0052 | −1.09973 | ||||||||
\(518\) | 64.4365 | 2.83118 | ||||||||
\(519\) | −4.45390 | −0.195504 | ||||||||
\(520\) | 4.44475 | 0.194915 | ||||||||
\(521\) | −9.99951 | −0.438087 | −0.219043 | − | 0.975715i | \(-0.570294\pi\) | ||||
−0.219043 | + | 0.975715i | \(0.570294\pi\) | |||||||
\(522\) | −18.9956 | −0.831415 | ||||||||
\(523\) | 10.5497 | 0.461306 | 0.230653 | − | 0.973036i | \(-0.425914\pi\) | ||||
0.230653 | + | 0.973036i | \(0.425914\pi\) | |||||||
\(524\) | 58.5867 | 2.55937 | ||||||||
\(525\) | 2.37823 | 0.103794 | ||||||||
\(526\) | 32.5809 | 1.42059 | ||||||||
\(527\) | 1.65711 | 0.0721849 | ||||||||
\(528\) | −1.20380 | −0.0523886 | ||||||||
\(529\) | 47.0997 | 2.04781 | ||||||||
\(530\) | 1.41960 | 0.0616637 | ||||||||
\(531\) | −11.1130 | −0.482264 | ||||||||
\(532\) | 57.2774 | 2.48329 | ||||||||
\(533\) | 4.18761 | 0.181386 | ||||||||
\(534\) | −0.284286 | −0.0123023 | ||||||||
\(535\) | 1.43005 | 0.0618263 | ||||||||
\(536\) | 36.2950 | 1.56771 | ||||||||
\(537\) | −0.988919 | −0.0426750 | ||||||||
\(538\) | 14.7548 | 0.636124 | ||||||||
\(539\) | 0.947478 | 0.0408108 | ||||||||
\(540\) | −6.36567 | −0.273935 | ||||||||
\(541\) | −0.372435 | −0.0160122 | −0.00800612 | − | 0.999968i | \(-0.502548\pi\) | ||||
−0.00800612 | + | 0.999968i | \(0.502548\pi\) | |||||||
\(542\) | −12.6485 | −0.543301 | ||||||||
\(543\) | 3.23068 | 0.138642 | ||||||||
\(544\) | 10.4673 | 0.448784 | ||||||||
\(545\) | −12.5457 | −0.537399 | ||||||||
\(546\) | −1.55112 | −0.0663819 | ||||||||
\(547\) | −9.31392 | −0.398235 | −0.199117 | − | 0.979976i | \(-0.563807\pi\) | ||||
−0.199117 | + | 0.979976i | \(0.563807\pi\) | |||||||
\(548\) | −39.2109 | −1.67501 | ||||||||
\(549\) | −5.89050 | −0.251401 | ||||||||
\(550\) | −22.8561 | −0.974589 | ||||||||
\(551\) | 16.8558 | 0.718083 | ||||||||
\(552\) | −8.08098 | −0.343949 | ||||||||
\(553\) | −30.1957 | −1.28405 | ||||||||
\(554\) | −5.95639 | −0.253063 | ||||||||
\(555\) | 3.14272 | 0.133401 | ||||||||
\(556\) | 16.8850 | 0.716083 | ||||||||
\(557\) | 21.8874 | 0.927397 | 0.463699 | − | 0.885993i | \(-0.346522\pi\) | ||||
0.463699 | + | 0.885993i | \(0.346522\pi\) | |||||||
\(558\) | 3.71770 | 0.157383 | ||||||||
\(559\) | −8.17993 | −0.345974 | ||||||||
\(560\) | −5.37151 | −0.226988 | ||||||||
\(561\) | −2.09453 | −0.0884310 | ||||||||
\(562\) | −12.2619 | −0.517239 | ||||||||
\(563\) | 21.4734 | 0.904997 | 0.452498 | − | 0.891765i | \(-0.350533\pi\) | ||||
0.452498 | + | 0.891765i | \(0.350533\pi\) | |||||||
\(564\) | 8.61161 | 0.362614 | ||||||||
\(565\) | 12.7163 | 0.534979 | ||||||||
\(566\) | −64.5822 | −2.71459 | ||||||||
\(567\) | −21.7097 | −0.911722 | ||||||||
\(568\) | 13.8081 | 0.579376 | ||||||||
\(569\) | −35.8201 | −1.50166 | −0.750829 | − | 0.660496i | \(-0.770346\pi\) | ||||
−0.750829 | + | 0.660496i | \(0.770346\pi\) | |||||||
\(570\) | 4.34387 | 0.181945 | ||||||||
\(571\) | 4.45961 | 0.186629 | 0.0933144 | − | 0.995637i | \(-0.470254\pi\) | ||||
0.0933144 | + | 0.995637i | \(0.470254\pi\) | |||||||
\(572\) | 9.58688 | 0.400847 | ||||||||
\(573\) | −6.04999 | −0.252742 | ||||||||
\(574\) | −25.5517 | −1.06651 | ||||||||
\(575\) | −30.3885 | −1.26729 | ||||||||
\(576\) | 33.9341 | 1.41392 | ||||||||
\(577\) | −9.95024 | −0.414234 | −0.207117 | − | 0.978316i | \(-0.566408\pi\) | ||||
−0.207117 | + | 0.978316i | \(0.566408\pi\) | |||||||
\(578\) | 17.5334 | 0.729293 | ||||||||
\(579\) | −6.02154 | −0.250247 | ||||||||
\(580\) | −11.5332 | −0.478888 | ||||||||
\(581\) | −1.20002 | −0.0497853 | ||||||||
\(582\) | −0.727601 | −0.0301600 | ||||||||
\(583\) | 1.36269 | 0.0564369 | ||||||||
\(584\) | −41.1487 | −1.70274 | ||||||||
\(585\) | 3.43635 | 0.142076 | ||||||||
\(586\) | 15.2970 | 0.631912 | ||||||||
\(587\) | −20.0626 | −0.828073 | −0.414036 | − | 0.910260i | \(-0.635881\pi\) | ||||
−0.414036 | + | 0.910260i | \(0.635881\pi\) | |||||||
\(588\) | −0.326304 | −0.0134566 | ||||||||
\(589\) | −3.29892 | −0.135930 | ||||||||
\(590\) | −10.4917 | −0.431937 | ||||||||
\(591\) | −4.71996 | −0.194153 | ||||||||
\(592\) | 18.7989 | 0.772628 | ||||||||
\(593\) | −40.0251 | −1.64363 | −0.821817 | − | 0.569751i | \(-0.807039\pi\) | ||||
−0.821817 | + | 0.569751i | \(0.807039\pi\) | |||||||
\(594\) | −9.50153 | −0.389852 | ||||||||
\(595\) | −9.34605 | −0.383151 | ||||||||
\(596\) | 14.3795 | 0.589008 | ||||||||
\(597\) | −7.15152 | −0.292692 | ||||||||
\(598\) | 19.8199 | 0.810497 | ||||||||
\(599\) | 19.8508 | 0.811083 | 0.405541 | − | 0.914077i | \(-0.367083\pi\) | ||||
0.405541 | + | 0.914077i | \(0.367083\pi\) | |||||||
\(600\) | 3.50313 | 0.143015 | ||||||||
\(601\) | 7.19057 | 0.293310 | 0.146655 | − | 0.989188i | \(-0.453149\pi\) | ||||
0.146655 | + | 0.989188i | \(0.453149\pi\) | |||||||
\(602\) | 49.9117 | 2.03425 | ||||||||
\(603\) | 28.0607 | 1.14272 | ||||||||
\(604\) | −22.1676 | −0.901988 | ||||||||
\(605\) | −4.59316 | −0.186739 | ||||||||
\(606\) | −9.69769 | −0.393942 | ||||||||
\(607\) | 5.62132 | 0.228162 | 0.114081 | − | 0.993471i | \(-0.463608\pi\) | ||||
0.114081 | + | 0.993471i | \(0.463608\pi\) | |||||||
\(608\) | −20.8380 | −0.845094 | ||||||||
\(609\) | 1.79121 | 0.0725836 | ||||||||
\(610\) | −5.56117 | −0.225165 | ||||||||
\(611\) | −9.39988 | −0.380278 | ||||||||
\(612\) | −32.7656 | −1.32447 | ||||||||
\(613\) | −28.8128 | −1.16374 | −0.581870 | − | 0.813282i | \(-0.697679\pi\) | ||||
−0.581870 | + | 0.813282i | \(0.697679\pi\) | |||||||
\(614\) | −46.2361 | −1.86594 | ||||||||
\(615\) | −1.24622 | −0.0502523 | ||||||||
\(616\) | −26.0334 | −1.04891 | ||||||||
\(617\) | −7.81520 | −0.314628 | −0.157314 | − | 0.987549i | \(-0.550283\pi\) | ||||
−0.157314 | + | 0.987549i | \(0.550283\pi\) | |||||||
\(618\) | 1.09705 | 0.0441299 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | 2.25720 | 0.0906513 | ||||||||
\(621\) | −12.6328 | −0.506936 | ||||||||
\(622\) | 35.0454 | 1.40519 | ||||||||
\(623\) | −1.21766 | −0.0487847 | ||||||||
\(624\) | −0.452529 | −0.0181156 | ||||||||
\(625\) | 6.32119 | 0.252848 | ||||||||
\(626\) | −11.2272 | −0.448729 | ||||||||
\(627\) | 4.16972 | 0.166522 | ||||||||
\(628\) | −27.1687 | −1.08415 | ||||||||
\(629\) | 32.7087 | 1.30418 | ||||||||
\(630\) | −20.9677 | −0.835374 | ||||||||
\(631\) | −44.9706 | −1.79025 | −0.895125 | − | 0.445815i | \(-0.852914\pi\) | ||||
−0.895125 | + | 0.445815i | \(0.852914\pi\) | |||||||
\(632\) | −44.4784 | −1.76926 | ||||||||
\(633\) | −4.45158 | −0.176934 | ||||||||
\(634\) | 33.3019 | 1.32259 | ||||||||
\(635\) | 4.98111 | 0.197669 | ||||||||
\(636\) | −0.469301 | −0.0186090 | ||||||||
\(637\) | 0.356173 | 0.0141121 | ||||||||
\(638\) | −17.2146 | −0.681533 | ||||||||
\(639\) | 10.6754 | 0.422314 | ||||||||
\(640\) | 24.1243 | 0.953598 | ||||||||
\(641\) | −8.39444 | −0.331560 | −0.165780 | − | 0.986163i | \(-0.553014\pi\) | ||||
−0.165780 | + | 0.986163i | \(0.553014\pi\) | |||||||
\(642\) | −0.735111 | −0.0290125 | ||||||||
\(643\) | −11.2465 | −0.443517 | −0.221759 | − | 0.975102i | \(-0.571180\pi\) | ||||
−0.221759 | + | 0.975102i | \(0.571180\pi\) | |||||||
\(644\) | −77.7743 | −3.06474 | ||||||||
\(645\) | 2.43431 | 0.0958510 | ||||||||
\(646\) | 45.2100 | 1.77876 | ||||||||
\(647\) | −35.8394 | −1.40899 | −0.704497 | − | 0.709707i | \(-0.748827\pi\) | ||||
−0.704497 | + | 0.709707i | \(0.748827\pi\) | |||||||
\(648\) | −31.9785 | −1.25623 | ||||||||
\(649\) | −10.0711 | −0.395325 | ||||||||
\(650\) | −8.59201 | −0.337006 | ||||||||
\(651\) | −0.350565 | −0.0137397 | ||||||||
\(652\) | −80.9266 | −3.16933 | ||||||||
\(653\) | −39.7379 | −1.55506 | −0.777531 | − | 0.628844i | \(-0.783528\pi\) | ||||
−0.777531 | + | 0.628844i | \(0.783528\pi\) | |||||||
\(654\) | 6.44909 | 0.252179 | ||||||||
\(655\) | 19.0311 | 0.743607 | ||||||||
\(656\) | −7.45452 | −0.291050 | ||||||||
\(657\) | −31.8132 | −1.24115 | ||||||||
\(658\) | 57.3556 | 2.23595 | ||||||||
\(659\) | −5.49785 | −0.214166 | −0.107083 | − | 0.994250i | \(-0.534151\pi\) | ||||
−0.107083 | + | 0.994250i | \(0.534151\pi\) | |||||||
\(660\) | −2.85302 | −0.111053 | ||||||||
\(661\) | 33.3406 | 1.29680 | 0.648399 | − | 0.761301i | \(-0.275439\pi\) | ||||
0.648399 | + | 0.761301i | \(0.275439\pi\) | |||||||
\(662\) | −25.6424 | −0.996619 | ||||||||
\(663\) | −0.787368 | −0.0305789 | ||||||||
\(664\) | −1.76764 | −0.0685976 | ||||||||
\(665\) | 18.6058 | 0.721503 | ||||||||
\(666\) | 73.3815 | 2.84347 | ||||||||
\(667\) | −22.8878 | −0.886217 | ||||||||
\(668\) | 7.02752 | 0.271903 | ||||||||
\(669\) | 4.45277 | 0.172154 | ||||||||
\(670\) | 26.4919 | 1.02347 | ||||||||
\(671\) | −5.33822 | −0.206080 | ||||||||
\(672\) | −2.21439 | −0.0854218 | ||||||||
\(673\) | −23.3947 | −0.901800 | −0.450900 | − | 0.892574i | \(-0.648897\pi\) | ||||
−0.450900 | + | 0.892574i | \(0.648897\pi\) | |||||||
\(674\) | −32.9561 | −1.26942 | ||||||||
\(675\) | 5.47636 | 0.210785 | ||||||||
\(676\) | 3.60387 | 0.138610 | ||||||||
\(677\) | −0.287333 | −0.0110431 | −0.00552155 | − | 0.999985i | \(-0.501758\pi\) | ||||
−0.00552155 | + | 0.999985i | \(0.501758\pi\) | |||||||
\(678\) | −6.53677 | −0.251043 | ||||||||
\(679\) | −3.11649 | −0.119600 | ||||||||
\(680\) | −13.7668 | −0.527932 | ||||||||
\(681\) | −1.74241 | −0.0667694 | ||||||||
\(682\) | 3.36914 | 0.129011 | ||||||||
\(683\) | 44.7800 | 1.71346 | 0.856729 | − | 0.515767i | \(-0.172493\pi\) | ||||
0.856729 | + | 0.515767i | \(0.172493\pi\) | |||||||
\(684\) | 65.2287 | 2.49408 | ||||||||
\(685\) | −12.7371 | −0.486661 | ||||||||
\(686\) | −44.8854 | −1.71373 | ||||||||
\(687\) | −6.31211 | −0.240822 | ||||||||
\(688\) | 14.5614 | 0.555147 | ||||||||
\(689\) | 0.512259 | 0.0195155 | ||||||||
\(690\) | −5.89833 | −0.224546 | ||||||||
\(691\) | 33.9291 | 1.29073 | 0.645363 | − | 0.763876i | \(-0.276706\pi\) | ||||
0.645363 | + | 0.763876i | \(0.276706\pi\) | |||||||
\(692\) | −63.1417 | −2.40029 | ||||||||
\(693\) | −20.1271 | −0.764565 | ||||||||
\(694\) | −29.7543 | −1.12946 | ||||||||
\(695\) | 5.48487 | 0.208053 | ||||||||
\(696\) | 2.63846 | 0.100011 | ||||||||
\(697\) | −12.9703 | −0.491287 | ||||||||
\(698\) | −46.4110 | −1.75668 | ||||||||
\(699\) | 3.68850 | 0.139512 | ||||||||
\(700\) | 33.7155 | 1.27432 | ||||||||
\(701\) | −46.7646 | −1.76627 | −0.883137 | − | 0.469115i | \(-0.844573\pi\) | ||||
−0.883137 | + | 0.469115i | \(0.844573\pi\) | |||||||
\(702\) | −3.57178 | −0.134808 | ||||||||
\(703\) | −65.1154 | −2.45588 | ||||||||
\(704\) | 30.7525 | 1.15903 | ||||||||
\(705\) | 2.79737 | 0.105355 | ||||||||
\(706\) | 74.2375 | 2.79397 | ||||||||
\(707\) | −41.5375 | −1.56218 | ||||||||
\(708\) | 3.46841 | 0.130351 | ||||||||
\(709\) | −6.07482 | −0.228145 | −0.114072 | − | 0.993472i | \(-0.536390\pi\) | ||||
−0.114072 | + | 0.993472i | \(0.536390\pi\) | |||||||
\(710\) | 10.0786 | 0.378243 | ||||||||
\(711\) | −34.3875 | −1.28963 | ||||||||
\(712\) | −1.79362 | −0.0672189 | ||||||||
\(713\) | 4.47945 | 0.167757 | ||||||||
\(714\) | 4.80431 | 0.179797 | ||||||||
\(715\) | 3.11417 | 0.116463 | ||||||||
\(716\) | −14.0196 | −0.523938 | ||||||||
\(717\) | −4.82619 | −0.180237 | ||||||||
\(718\) | 29.4112 | 1.09762 | ||||||||
\(719\) | −23.6083 | −0.880441 | −0.440221 | − | 0.897890i | \(-0.645100\pi\) | ||||
−0.440221 | + | 0.897890i | \(0.645100\pi\) | |||||||
\(720\) | −6.11718 | −0.227974 | ||||||||
\(721\) | 4.69893 | 0.174997 | ||||||||
\(722\) | −45.0248 | −1.67565 | ||||||||
\(723\) | 4.38443 | 0.163059 | ||||||||
\(724\) | 45.8005 | 1.70216 | ||||||||
\(725\) | 9.92193 | 0.368491 | ||||||||
\(726\) | 2.36110 | 0.0876287 | ||||||||
\(727\) | 42.1944 | 1.56490 | 0.782452 | − | 0.622711i | \(-0.213969\pi\) | ||||
0.782452 | + | 0.622711i | \(0.213969\pi\) | |||||||
\(728\) | −9.78638 | −0.362707 | ||||||||
\(729\) | −23.5727 | −0.873064 | ||||||||
\(730\) | −30.0345 | −1.11163 | ||||||||
\(731\) | 25.3358 | 0.937078 | ||||||||
\(732\) | 1.83844 | 0.0679509 | ||||||||
\(733\) | 10.9044 | 0.402763 | 0.201381 | − | 0.979513i | \(-0.435457\pi\) | ||||
0.201381 | + | 0.979513i | \(0.435457\pi\) | |||||||
\(734\) | −66.0950 | −2.43961 | ||||||||
\(735\) | −0.105996 | −0.00390971 | ||||||||
\(736\) | 28.2950 | 1.04297 | ||||||||
\(737\) | 25.4298 | 0.936718 | ||||||||
\(738\) | −29.0988 | −1.07114 | ||||||||
\(739\) | 29.8737 | 1.09892 | 0.549460 | − | 0.835520i | \(-0.314833\pi\) | ||||
0.549460 | + | 0.835520i | \(0.314833\pi\) | |||||||
\(740\) | 44.5535 | 1.63782 | ||||||||
\(741\) | 1.56747 | 0.0575823 | ||||||||
\(742\) | −3.12567 | −0.114747 | ||||||||
\(743\) | −36.3622 | −1.33400 | −0.666999 | − | 0.745058i | \(-0.732422\pi\) | ||||
−0.666999 | + | 0.745058i | \(0.732422\pi\) | |||||||
\(744\) | −0.516384 | −0.0189315 | ||||||||
\(745\) | 4.67100 | 0.171132 | ||||||||
\(746\) | 35.9013 | 1.31444 | ||||||||
\(747\) | −1.36661 | −0.0500015 | ||||||||
\(748\) | −29.6936 | −1.08570 | ||||||||
\(749\) | −3.14866 | −0.115049 | ||||||||
\(750\) | 6.07937 | 0.221987 | ||||||||
\(751\) | 17.3540 | 0.633257 | 0.316628 | − | 0.948550i | \(-0.397449\pi\) | ||||
0.316628 | + | 0.948550i | \(0.397449\pi\) | |||||||
\(752\) | 16.7331 | 0.610192 | ||||||||
\(753\) | −7.27826 | −0.265234 | ||||||||
\(754\) | −6.47126 | −0.235669 | ||||||||
\(755\) | −7.20086 | −0.262066 | ||||||||
\(756\) | 14.0159 | 0.509752 | ||||||||
\(757\) | 40.7801 | 1.48218 | 0.741090 | − | 0.671406i | \(-0.234309\pi\) | ||||
0.741090 | + | 0.671406i | \(0.234309\pi\) | |||||||
\(758\) | 4.53194 | 0.164608 | ||||||||
\(759\) | −5.66186 | −0.205513 | ||||||||
\(760\) | 27.4064 | 0.994136 | ||||||||
\(761\) | 6.63784 | 0.240621 | 0.120311 | − | 0.992736i | \(-0.461611\pi\) | ||||
0.120311 | + | 0.992736i | \(0.461611\pi\) | |||||||
\(762\) | −2.56053 | −0.0927581 | ||||||||
\(763\) | 27.6230 | 1.00002 | ||||||||
\(764\) | −85.7691 | −3.10302 | ||||||||
\(765\) | −10.6435 | −0.384815 | ||||||||
\(766\) | 72.9596 | 2.63614 | ||||||||
\(767\) | −3.78589 | −0.136701 | ||||||||
\(768\) | −6.52351 | −0.235397 | ||||||||
\(769\) | −19.9729 | −0.720242 | −0.360121 | − | 0.932906i | \(-0.617265\pi\) | ||||
−0.360121 | + | 0.932906i | \(0.617265\pi\) | |||||||
\(770\) | −19.0018 | −0.684778 | ||||||||
\(771\) | −2.78437 | −0.100277 | ||||||||
\(772\) | −85.3658 | −3.07238 | ||||||||
\(773\) | −14.2866 | −0.513852 | −0.256926 | − | 0.966431i | \(-0.582710\pi\) | ||||
−0.256926 | + | 0.966431i | \(0.582710\pi\) | |||||||
\(774\) | 56.8404 | 2.04309 | ||||||||
\(775\) | −1.94186 | −0.0697536 | ||||||||
\(776\) | −4.59060 | −0.164793 | ||||||||
\(777\) | −6.91959 | −0.248239 | ||||||||
\(778\) | −36.5492 | −1.31035 | ||||||||
\(779\) | 25.8209 | 0.925131 | ||||||||
\(780\) | −1.07250 | −0.0384015 | ||||||||
\(781\) | 9.67453 | 0.346182 | ||||||||
\(782\) | −61.3885 | −2.19525 | ||||||||
\(783\) | 4.12464 | 0.147403 | ||||||||
\(784\) | −0.634036 | −0.0226441 | ||||||||
\(785\) | −8.82539 | −0.314992 | ||||||||
\(786\) | −9.78289 | −0.348944 | ||||||||
\(787\) | −8.47130 | −0.301969 | −0.150985 | − | 0.988536i | \(-0.548244\pi\) | ||||
−0.150985 | + | 0.988536i | \(0.548244\pi\) | |||||||
\(788\) | −66.9136 | −2.38370 | ||||||||
\(789\) | −3.49874 | −0.124558 | ||||||||
\(790\) | −32.4649 | −1.15505 | ||||||||
\(791\) | −27.9986 | −0.995514 | ||||||||
\(792\) | −29.6473 | −1.05347 | ||||||||
\(793\) | −2.00673 | −0.0712610 | ||||||||
\(794\) | 20.6973 | 0.734518 | ||||||||
\(795\) | −0.152446 | −0.00540671 | ||||||||
\(796\) | −101.385 | −3.59350 | ||||||||
\(797\) | −16.4470 | −0.582582 | −0.291291 | − | 0.956634i | \(-0.594085\pi\) | ||||
−0.291291 | + | 0.956634i | \(0.594085\pi\) | |||||||
\(798\) | −9.56426 | −0.338571 | ||||||||
\(799\) | 29.1144 | 1.02999 | ||||||||
\(800\) | −12.2660 | −0.433668 | ||||||||
\(801\) | −1.38670 | −0.0489966 | ||||||||
\(802\) | −54.6655 | −1.93031 | ||||||||
\(803\) | −28.8304 | −1.01740 | ||||||||
\(804\) | −8.75783 | −0.308865 | ||||||||
\(805\) | −25.2640 | −0.890437 | ||||||||
\(806\) | 1.26652 | 0.0446111 | ||||||||
\(807\) | −1.58446 | −0.0557757 | ||||||||
\(808\) | −61.1849 | −2.15248 | ||||||||
\(809\) | 43.9842 | 1.54640 | 0.773202 | − | 0.634160i | \(-0.218654\pi\) | ||||
0.773202 | + | 0.634160i | \(0.218654\pi\) | |||||||
\(810\) | −23.3412 | −0.820125 | ||||||||
\(811\) | 45.2574 | 1.58920 | 0.794602 | − | 0.607131i | \(-0.207680\pi\) | ||||
0.794602 | + | 0.607131i | \(0.207680\pi\) | |||||||
\(812\) | 25.3935 | 0.891138 | ||||||||
\(813\) | 1.35828 | 0.0476370 | ||||||||
\(814\) | 66.5014 | 2.33087 | ||||||||
\(815\) | −26.2879 | −0.920826 | ||||||||
\(816\) | 1.40162 | 0.0490666 | ||||||||
\(817\) | −50.4377 | −1.76459 | ||||||||
\(818\) | −1.22861 | −0.0429573 | ||||||||
\(819\) | −7.56612 | −0.264382 | ||||||||
\(820\) | −17.6673 | −0.616968 | ||||||||
\(821\) | −0.572243 | −0.0199714 | −0.00998571 | − | 0.999950i | \(-0.503179\pi\) | ||||
−0.00998571 | + | 0.999950i | \(0.503179\pi\) | |||||||
\(822\) | 6.54749 | 0.228370 | ||||||||
\(823\) | −35.6804 | −1.24374 | −0.621871 | − | 0.783120i | \(-0.713627\pi\) | ||||
−0.621871 | + | 0.783120i | \(0.713627\pi\) | |||||||
\(824\) | 6.92154 | 0.241123 | ||||||||
\(825\) | 2.45444 | 0.0854525 | ||||||||
\(826\) | 23.1005 | 0.803770 | ||||||||
\(827\) | −11.1929 | −0.389215 | −0.194608 | − | 0.980881i | \(-0.562343\pi\) | ||||
−0.194608 | + | 0.980881i | \(0.562343\pi\) | |||||||
\(828\) | −88.5709 | −3.07805 | ||||||||
\(829\) | 26.5929 | 0.923611 | 0.461805 | − | 0.886981i | \(-0.347202\pi\) | ||||
0.461805 | + | 0.886981i | \(0.347202\pi\) | |||||||
\(830\) | −1.29020 | −0.0447836 | ||||||||
\(831\) | 0.639635 | 0.0221887 | ||||||||
\(832\) | 11.5604 | 0.400784 | ||||||||
\(833\) | −1.10318 | −0.0382229 | ||||||||
\(834\) | −2.81948 | −0.0976306 | ||||||||
\(835\) | 2.28280 | 0.0789994 | ||||||||
\(836\) | 59.1129 | 2.04446 | ||||||||
\(837\) | −0.807250 | −0.0279026 | ||||||||
\(838\) | 34.1633 | 1.18015 | ||||||||
\(839\) | 44.3237 | 1.53022 | 0.765112 | − | 0.643897i | \(-0.222683\pi\) | ||||
0.765112 | + | 0.643897i | \(0.222683\pi\) | |||||||
\(840\) | 2.91239 | 0.100487 | ||||||||
\(841\) | −21.5271 | −0.742313 | ||||||||
\(842\) | 10.7739 | 0.371292 | ||||||||
\(843\) | 1.31677 | 0.0453518 | ||||||||
\(844\) | −63.1089 | −2.17230 | ||||||||
\(845\) | 1.17067 | 0.0402722 | ||||||||
\(846\) | 65.3176 | 2.24567 | ||||||||
\(847\) | 10.1132 | 0.347492 | ||||||||
\(848\) | −0.911890 | −0.0313144 | ||||||||
\(849\) | 6.93524 | 0.238017 | ||||||||
\(850\) | 26.6122 | 0.912789 | ||||||||
\(851\) | 88.4172 | 3.03090 | ||||||||
\(852\) | −3.33184 | −0.114147 | ||||||||
\(853\) | 4.07104 | 0.139390 | 0.0696948 | − | 0.997568i | \(-0.477797\pi\) | ||||
0.0696948 | + | 0.997568i | \(0.477797\pi\) | |||||||
\(854\) | 12.2445 | 0.418999 | ||||||||
\(855\) | 21.1887 | 0.724637 | ||||||||
\(856\) | −4.63798 | −0.158523 | ||||||||
\(857\) | 5.86818 | 0.200453 | 0.100227 | − | 0.994965i | \(-0.468043\pi\) | ||||
0.100227 | + | 0.994965i | \(0.468043\pi\) | |||||||
\(858\) | −1.60083 | −0.0546514 | ||||||||
\(859\) | 11.2912 | 0.385251 | 0.192625 | − | 0.981272i | \(-0.438300\pi\) | ||||
0.192625 | + | 0.981272i | \(0.438300\pi\) | |||||||
\(860\) | 34.5106 | 1.17680 | ||||||||
\(861\) | 2.74390 | 0.0935119 | ||||||||
\(862\) | −25.4371 | −0.866391 | ||||||||
\(863\) | 56.3109 | 1.91685 | 0.958423 | − | 0.285353i | \(-0.0921107\pi\) | ||||
0.958423 | + | 0.285353i | \(0.0921107\pi\) | |||||||
\(864\) | −5.09909 | −0.173475 | ||||||||
\(865\) | −20.5107 | −0.697386 | ||||||||
\(866\) | −45.1505 | −1.53428 | ||||||||
\(867\) | −1.88285 | −0.0639448 | ||||||||
\(868\) | −4.96987 | −0.168688 | ||||||||
\(869\) | −31.1634 | −1.05715 | ||||||||
\(870\) | 1.92582 | 0.0652915 | ||||||||
\(871\) | 9.55948 | 0.323911 | ||||||||
\(872\) | 40.6888 | 1.37790 | ||||||||
\(873\) | −3.54911 | −0.120119 | ||||||||
\(874\) | 122.210 | 4.13382 | ||||||||
\(875\) | 26.0394 | 0.880292 | ||||||||
\(876\) | 9.92899 | 0.335469 | ||||||||
\(877\) | −38.2820 | −1.29269 | −0.646346 | − | 0.763044i | \(-0.723704\pi\) | ||||
−0.646346 | + | 0.763044i | \(0.723704\pi\) | |||||||
\(878\) | −13.6938 | −0.462143 | ||||||||
\(879\) | −1.64268 | −0.0554064 | ||||||||
\(880\) | −5.54364 | −0.186876 | ||||||||
\(881\) | −47.6529 | −1.60547 | −0.802734 | − | 0.596338i | \(-0.796622\pi\) | ||||
−0.802734 | + | 0.596338i | \(0.796622\pi\) | |||||||
\(882\) | −2.47496 | −0.0833364 | ||||||||
\(883\) | 17.6246 | 0.593114 | 0.296557 | − | 0.955015i | \(-0.404162\pi\) | ||||
0.296557 | + | 0.955015i | \(0.404162\pi\) | |||||||
\(884\) | −11.1623 | −0.375429 | ||||||||
\(885\) | 1.12667 | 0.0378725 | ||||||||
\(886\) | −9.40742 | −0.316048 | ||||||||
\(887\) | 12.0489 | 0.404564 | 0.202282 | − | 0.979327i | \(-0.435164\pi\) | ||||
0.202282 | + | 0.979327i | \(0.435164\pi\) | |||||||
\(888\) | −10.1926 | −0.342041 | ||||||||
\(889\) | −10.9673 | −0.367833 | ||||||||
\(890\) | −1.30917 | −0.0438835 | ||||||||
\(891\) | −22.4054 | −0.750609 | ||||||||
\(892\) | 63.1257 | 2.11360 | ||||||||
\(893\) | −57.9599 | −1.93955 | ||||||||
\(894\) | −2.40111 | −0.0803052 | ||||||||
\(895\) | −4.55409 | −0.152226 | ||||||||
\(896\) | −53.1166 | −1.77450 | ||||||||
\(897\) | −2.12839 | −0.0710648 | ||||||||
\(898\) | 49.5854 | 1.65469 | ||||||||
\(899\) | −1.46255 | −0.0487789 | ||||||||
\(900\) | 38.3958 | 1.27986 | ||||||||
\(901\) | −1.58663 | −0.0528582 | ||||||||
\(902\) | −26.3705 | −0.878042 | ||||||||
\(903\) | −5.35984 | −0.178364 | ||||||||
\(904\) | −41.2420 | −1.37169 | ||||||||
\(905\) | 14.8777 | 0.494551 | ||||||||
\(906\) | 3.70158 | 0.122977 | ||||||||
\(907\) | 12.7168 | 0.422256 | 0.211128 | − | 0.977458i | \(-0.432286\pi\) | ||||
0.211128 | + | 0.977458i | \(0.432286\pi\) | |||||||
\(908\) | −24.7017 | −0.819756 | ||||||||
\(909\) | −47.3037 | −1.56897 | ||||||||
\(910\) | −7.14311 | −0.236792 | ||||||||
\(911\) | 3.44702 | 0.114205 | 0.0571024 | − | 0.998368i | \(-0.481814\pi\) | ||||
0.0571024 | + | 0.998368i | \(0.481814\pi\) | |||||||
\(912\) | −2.79030 | −0.0923962 | ||||||||
\(913\) | −1.23848 | −0.0409876 | ||||||||
\(914\) | −34.8217 | −1.15180 | ||||||||
\(915\) | 0.597194 | 0.0197426 | ||||||||
\(916\) | −89.4851 | −2.95667 | ||||||||
\(917\) | −41.9025 | −1.38374 | ||||||||
\(918\) | 11.0629 | 0.365131 | ||||||||
\(919\) | −44.1399 | −1.45604 | −0.728020 | − | 0.685556i | \(-0.759559\pi\) | ||||
−0.728020 | + | 0.685556i | \(0.759559\pi\) | |||||||
\(920\) | −37.2139 | −1.22691 | ||||||||
\(921\) | 4.96512 | 0.163606 | ||||||||
\(922\) | −30.8044 | −1.01449 | ||||||||
\(923\) | 3.63682 | 0.119707 | ||||||||
\(924\) | 6.28173 | 0.206654 | ||||||||
\(925\) | −38.3292 | −1.26026 | ||||||||
\(926\) | 62.4232 | 2.05135 | ||||||||
\(927\) | 5.35123 | 0.175758 | ||||||||
\(928\) | −9.23839 | −0.303265 | ||||||||
\(929\) | −29.1404 | −0.956064 | −0.478032 | − | 0.878342i | \(-0.658650\pi\) | ||||
−0.478032 | + | 0.878342i | \(0.658650\pi\) | |||||||
\(930\) | −0.376910 | −0.0123594 | ||||||||
\(931\) | 2.19617 | 0.0719766 | ||||||||
\(932\) | 52.2909 | 1.71284 | ||||||||
\(933\) | −3.76340 | −0.123208 | ||||||||
\(934\) | −25.5899 | −0.837327 | ||||||||
\(935\) | −9.64555 | −0.315443 | ||||||||
\(936\) | −11.1449 | −0.364283 | ||||||||
\(937\) | 4.85175 | 0.158500 | 0.0792499 | − | 0.996855i | \(-0.474748\pi\) | ||||
0.0792499 | + | 0.996855i | \(0.474748\pi\) | |||||||
\(938\) | −58.3294 | −1.90452 | ||||||||
\(939\) | 1.20565 | 0.0393448 | ||||||||
\(940\) | 39.6575 | 1.29349 | ||||||||
\(941\) | 39.0103 | 1.27170 | 0.635849 | − | 0.771813i | \(-0.280650\pi\) | ||||
0.635849 | + | 0.771813i | \(0.280650\pi\) | |||||||
\(942\) | 4.53667 | 0.147813 | ||||||||
\(943\) | −35.0610 | −1.14174 | ||||||||
\(944\) | 6.73940 | 0.219349 | ||||||||
\(945\) | 4.55286 | 0.148105 | ||||||||
\(946\) | 51.5112 | 1.67477 | ||||||||
\(947\) | 57.3354 | 1.86315 | 0.931575 | − | 0.363550i | \(-0.118435\pi\) | ||||
0.931575 | + | 0.363550i | \(0.118435\pi\) | |||||||
\(948\) | 10.7324 | 0.348574 | ||||||||
\(949\) | −10.8378 | −0.351811 | ||||||||
\(950\) | −52.9786 | −1.71885 | ||||||||
\(951\) | −3.57617 | −0.115965 | ||||||||
\(952\) | 30.3115 | 0.982401 | ||||||||
\(953\) | −56.2867 | −1.82330 | −0.911652 | − | 0.410964i | \(-0.865192\pi\) | ||||
−0.911652 | + | 0.410964i | \(0.865192\pi\) | |||||||
\(954\) | −3.55957 | −0.115245 | ||||||||
\(955\) | −27.8610 | −0.901560 | ||||||||
\(956\) | −68.4196 | −2.21285 | ||||||||
\(957\) | 1.84861 | 0.0597572 | ||||||||
\(958\) | −62.3546 | −2.01459 | ||||||||
\(959\) | 28.0445 | 0.905603 | ||||||||
\(960\) | −3.44032 | −0.111036 | ||||||||
\(961\) | −30.7138 | −0.990766 | ||||||||
\(962\) | 24.9990 | 0.806000 | ||||||||
\(963\) | −3.58575 | −0.115549 | ||||||||
\(964\) | 62.1569 | 2.00194 | ||||||||
\(965\) | −27.7299 | −0.892658 | ||||||||
\(966\) | 12.9869 | 0.417845 | ||||||||
\(967\) | −60.0770 | −1.93195 | −0.965973 | − | 0.258642i | \(-0.916725\pi\) | ||||
−0.965973 | + | 0.258642i | \(0.916725\pi\) | |||||||
\(968\) | 14.8967 | 0.478799 | ||||||||
\(969\) | −4.85494 | −0.155963 | ||||||||
\(970\) | −3.35069 | −0.107584 | ||||||||
\(971\) | 33.6589 | 1.08017 | 0.540083 | − | 0.841612i | \(-0.318393\pi\) | ||||
0.540083 | + | 0.841612i | \(0.318393\pi\) | |||||||
\(972\) | 24.0292 | 0.770736 | ||||||||
\(973\) | −12.0765 | −0.387155 | ||||||||
\(974\) | 86.7040 | 2.77817 | ||||||||
\(975\) | 0.922665 | 0.0295489 | ||||||||
\(976\) | 3.57225 | 0.114345 | ||||||||
\(977\) | 18.8800 | 0.604026 | 0.302013 | − | 0.953304i | \(-0.402341\pi\) | ||||
0.302013 | + | 0.953304i | \(0.402341\pi\) | |||||||
\(978\) | 13.5132 | 0.432106 | ||||||||
\(979\) | −1.25669 | −0.0401638 | ||||||||
\(980\) | −1.50267 | −0.0480011 | ||||||||
\(981\) | 31.4576 | 1.00436 | ||||||||
\(982\) | −45.8272 | −1.46241 | ||||||||
\(983\) | −5.58231 | −0.178048 | −0.0890240 | − | 0.996029i | \(-0.528375\pi\) | ||||
−0.0890240 | + | 0.996029i | \(0.528375\pi\) | |||||||
\(984\) | 4.04178 | 0.128847 | ||||||||
\(985\) | −21.7360 | −0.692567 | ||||||||
\(986\) | 20.0435 | 0.638316 | ||||||||
\(987\) | −6.15920 | −0.196050 | ||||||||
\(988\) | 22.2216 | 0.706962 | ||||||||
\(989\) | 68.4869 | 2.17776 | ||||||||
\(990\) | −21.6396 | −0.687753 | ||||||||
\(991\) | −6.12039 | −0.194421 | −0.0972103 | − | 0.995264i | \(-0.530992\pi\) | ||||
−0.0972103 | + | 0.995264i | \(0.530992\pi\) | |||||||
\(992\) | 1.80808 | 0.0574067 | ||||||||
\(993\) | 2.75364 | 0.0873841 | ||||||||
\(994\) | −22.1909 | −0.703853 | ||||||||
\(995\) | −32.9336 | −1.04407 | ||||||||
\(996\) | 0.426522 | 0.0135149 | ||||||||
\(997\) | −46.8442 | −1.48357 | −0.741786 | − | 0.670637i | \(-0.766021\pi\) | ||||
−0.741786 | + | 0.670637i | \(0.766021\pi\) | |||||||
\(998\) | −28.9384 | −0.916029 | ||||||||
\(999\) | −15.9338 | −0.504124 |
(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.c.1.16 | ✓ | 151 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.c.1.16 | ✓ | 151 | 1.1 | even | 1 | trivial |