Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8022,2,Mod(1,8022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8022.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: | \(64.0559925015\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 11x^{7} + 36x^{6} + 50x^{5} - 70x^{4} - 73x^{3} + 14x^{2} + 22x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.411372\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8022.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.51454 | 0.677322 | 0.338661 | − | 0.940909i | \(-0.390026\pi\) | ||||
0.338661 | + | 0.940909i | \(0.390026\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.51454 | 0.478939 | ||||||||
\(11\) | −1.68070 | −0.506751 | −0.253375 | − | 0.967368i | \(-0.581541\pi\) | ||||
−0.253375 | + | 0.967368i | \(0.581541\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.35713 | −0.376399 | −0.188200 | − | 0.982131i | \(-0.560265\pi\) | ||||
−0.188200 | + | 0.982131i | \(0.560265\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.51454 | −0.391052 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.50273 | −1.09207 | −0.546036 | − | 0.837761i | \(-0.683864\pi\) | ||||
−0.546036 | + | 0.837761i | \(0.683864\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.92466 | 0.900379 | 0.450190 | − | 0.892933i | \(-0.351356\pi\) | ||||
0.450190 | + | 0.892933i | \(0.351356\pi\) | |||||||
\(20\) | 1.51454 | 0.338661 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.68070 | −0.358327 | ||||||||
\(23\) | 3.51870 | 0.733699 | 0.366850 | − | 0.930280i | \(-0.380436\pi\) | ||||
0.366850 | + | 0.930280i | \(0.380436\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.70618 | −0.541235 | ||||||||
\(26\) | −1.35713 | −0.266154 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −8.90561 | −1.65373 | −0.826865 | − | 0.562401i | \(-0.809878\pi\) | ||||
−0.826865 | + | 0.562401i | \(0.809878\pi\) | |||||||
\(30\) | −1.51454 | −0.276515 | ||||||||
\(31\) | 4.29806 | 0.771955 | 0.385977 | − | 0.922508i | \(-0.373864\pi\) | ||||
0.385977 | + | 0.922508i | \(0.373864\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.68070 | 0.292573 | ||||||||
\(34\) | −4.50273 | −0.772212 | ||||||||
\(35\) | −1.51454 | −0.256004 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.83806 | 1.45297 | 0.726484 | − | 0.687183i | \(-0.241153\pi\) | ||||
0.726484 | + | 0.687183i | \(0.241153\pi\) | |||||||
\(38\) | 3.92466 | 0.636664 | ||||||||
\(39\) | 1.35713 | 0.217314 | ||||||||
\(40\) | 1.51454 | 0.239469 | ||||||||
\(41\) | −4.69402 | −0.733083 | −0.366541 | − | 0.930402i | \(-0.619458\pi\) | ||||
−0.366541 | + | 0.930402i | \(0.619458\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −2.40129 | −0.366194 | −0.183097 | − | 0.983095i | \(-0.558612\pi\) | ||||
−0.183097 | + | 0.983095i | \(0.558612\pi\) | |||||||
\(44\) | −1.68070 | −0.253375 | ||||||||
\(45\) | 1.51454 | 0.225774 | ||||||||
\(46\) | 3.51870 | 0.518804 | ||||||||
\(47\) | −2.64404 | −0.385672 | −0.192836 | − | 0.981231i | \(-0.561769\pi\) | ||||
−0.192836 | + | 0.981231i | \(0.561769\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.70618 | −0.382711 | ||||||||
\(51\) | 4.50273 | 0.630508 | ||||||||
\(52\) | −1.35713 | −0.188200 | ||||||||
\(53\) | −5.94440 | −0.816526 | −0.408263 | − | 0.912864i | \(-0.633865\pi\) | ||||
−0.408263 | + | 0.912864i | \(0.633865\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.54549 | −0.343233 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −3.92466 | −0.519834 | ||||||||
\(58\) | −8.90561 | −1.16936 | ||||||||
\(59\) | −9.59202 | −1.24877 | −0.624387 | − | 0.781115i | \(-0.714651\pi\) | ||||
−0.624387 | + | 0.781115i | \(0.714651\pi\) | |||||||
\(60\) | −1.51454 | −0.195526 | ||||||||
\(61\) | 4.89730 | 0.627035 | 0.313518 | − | 0.949582i | \(-0.398492\pi\) | ||||
0.313518 | + | 0.949582i | \(0.398492\pi\) | |||||||
\(62\) | 4.29806 | 0.545854 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.05542 | −0.254943 | ||||||||
\(66\) | 1.68070 | 0.206880 | ||||||||
\(67\) | 8.20435 | 1.00232 | 0.501160 | − | 0.865354i | \(-0.332907\pi\) | ||||
0.501160 | + | 0.865354i | \(0.332907\pi\) | |||||||
\(68\) | −4.50273 | −0.546036 | ||||||||
\(69\) | −3.51870 | −0.423602 | ||||||||
\(70\) | −1.51454 | −0.181022 | ||||||||
\(71\) | −6.75595 | −0.801784 | −0.400892 | − | 0.916125i | \(-0.631300\pi\) | ||||
−0.400892 | + | 0.916125i | \(0.631300\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −4.24487 | −0.496825 | −0.248412 | − | 0.968654i | \(-0.579909\pi\) | ||||
−0.248412 | + | 0.968654i | \(0.579909\pi\) | |||||||
\(74\) | 8.83806 | 1.02740 | ||||||||
\(75\) | 2.70618 | 0.312482 | ||||||||
\(76\) | 3.92466 | 0.450190 | ||||||||
\(77\) | 1.68070 | 0.191534 | ||||||||
\(78\) | 1.35713 | 0.153664 | ||||||||
\(79\) | −12.4406 | −1.39968 | −0.699841 | − | 0.714299i | \(-0.746746\pi\) | ||||
−0.699841 | + | 0.714299i | \(0.746746\pi\) | |||||||
\(80\) | 1.51454 | 0.169330 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.69402 | −0.518368 | ||||||||
\(83\) | −4.27560 | −0.469308 | −0.234654 | − | 0.972079i | \(-0.575396\pi\) | ||||
−0.234654 | + | 0.972079i | \(0.575396\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | −6.81955 | −0.739684 | ||||||||
\(86\) | −2.40129 | −0.258938 | ||||||||
\(87\) | 8.90561 | 0.954781 | ||||||||
\(88\) | −1.68070 | −0.179163 | ||||||||
\(89\) | 6.68911 | 0.709044 | 0.354522 | − | 0.935048i | \(-0.384644\pi\) | ||||
0.354522 | + | 0.935048i | \(0.384644\pi\) | |||||||
\(90\) | 1.51454 | 0.159646 | ||||||||
\(91\) | 1.35713 | 0.142265 | ||||||||
\(92\) | 3.51870 | 0.366850 | ||||||||
\(93\) | −4.29806 | −0.445688 | ||||||||
\(94\) | −2.64404 | −0.272712 | ||||||||
\(95\) | 5.94405 | 0.609846 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 3.02861 | 0.307509 | 0.153754 | − | 0.988109i | \(-0.450864\pi\) | ||||
0.153754 | + | 0.988109i | \(0.450864\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −1.68070 | −0.168917 | ||||||||
\(100\) | −2.70618 | −0.270618 | ||||||||
\(101\) | 12.0400 | 1.19803 | 0.599013 | − | 0.800739i | \(-0.295560\pi\) | ||||
0.599013 | + | 0.800739i | \(0.295560\pi\) | |||||||
\(102\) | 4.50273 | 0.445837 | ||||||||
\(103\) | −7.62868 | −0.751676 | −0.375838 | − | 0.926685i | \(-0.622645\pi\) | ||||
−0.375838 | + | 0.926685i | \(0.622645\pi\) | |||||||
\(104\) | −1.35713 | −0.133077 | ||||||||
\(105\) | 1.51454 | 0.147804 | ||||||||
\(106\) | −5.94440 | −0.577371 | ||||||||
\(107\) | −8.48436 | −0.820214 | −0.410107 | − | 0.912037i | \(-0.634509\pi\) | ||||
−0.410107 | + | 0.912037i | \(0.634509\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 0.166999 | 0.0159956 | 0.00799782 | − | 0.999968i | \(-0.497454\pi\) | ||||
0.00799782 | + | 0.999968i | \(0.497454\pi\) | |||||||
\(110\) | −2.54549 | −0.242703 | ||||||||
\(111\) | −8.83806 | −0.838871 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −10.7808 | −1.01417 | −0.507086 | − | 0.861895i | \(-0.669277\pi\) | ||||
−0.507086 | + | 0.861895i | \(0.669277\pi\) | |||||||
\(114\) | −3.92466 | −0.367578 | ||||||||
\(115\) | 5.32920 | 0.496950 | ||||||||
\(116\) | −8.90561 | −0.826865 | ||||||||
\(117\) | −1.35713 | −0.125466 | ||||||||
\(118\) | −9.59202 | −0.883017 | ||||||||
\(119\) | 4.50273 | 0.412765 | ||||||||
\(120\) | −1.51454 | −0.138258 | ||||||||
\(121\) | −8.17524 | −0.743204 | ||||||||
\(122\) | 4.89730 | 0.443381 | ||||||||
\(123\) | 4.69402 | 0.423245 | ||||||||
\(124\) | 4.29806 | 0.385977 | ||||||||
\(125\) | −11.6713 | −1.04391 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −4.94951 | −0.439198 | −0.219599 | − | 0.975590i | \(-0.570475\pi\) | ||||
−0.219599 | + | 0.975590i | \(0.570475\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.40129 | 0.211422 | ||||||||
\(130\) | −2.05542 | −0.180272 | ||||||||
\(131\) | −12.5335 | −1.09505 | −0.547527 | − | 0.836788i | \(-0.684431\pi\) | ||||
−0.547527 | + | 0.836788i | \(0.684431\pi\) | |||||||
\(132\) | 1.68070 | 0.146286 | ||||||||
\(133\) | −3.92466 | −0.340311 | ||||||||
\(134\) | 8.20435 | 0.708748 | ||||||||
\(135\) | −1.51454 | −0.130351 | ||||||||
\(136\) | −4.50273 | −0.386106 | ||||||||
\(137\) | 19.1587 | 1.63684 | 0.818419 | − | 0.574622i | \(-0.194851\pi\) | ||||
0.818419 | + | 0.574622i | \(0.194851\pi\) | |||||||
\(138\) | −3.51870 | −0.299531 | ||||||||
\(139\) | −10.0578 | −0.853090 | −0.426545 | − | 0.904466i | \(-0.640269\pi\) | ||||
−0.426545 | + | 0.904466i | \(0.640269\pi\) | |||||||
\(140\) | −1.51454 | −0.128002 | ||||||||
\(141\) | 2.64404 | 0.222668 | ||||||||
\(142\) | −6.75595 | −0.566947 | ||||||||
\(143\) | 2.28092 | 0.190740 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −13.4879 | −1.12011 | ||||||||
\(146\) | −4.24487 | −0.351308 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 8.83806 | 0.726484 | ||||||||
\(149\) | −17.9407 | −1.46976 | −0.734881 | − | 0.678196i | \(-0.762762\pi\) | ||||
−0.734881 | + | 0.678196i | \(0.762762\pi\) | |||||||
\(150\) | 2.70618 | 0.220958 | ||||||||
\(151\) | −10.3551 | −0.842687 | −0.421344 | − | 0.906901i | \(-0.638441\pi\) | ||||
−0.421344 | + | 0.906901i | \(0.638441\pi\) | |||||||
\(152\) | 3.92466 | 0.318332 | ||||||||
\(153\) | −4.50273 | −0.364024 | ||||||||
\(154\) | 1.68070 | 0.135435 | ||||||||
\(155\) | 6.50957 | 0.522862 | ||||||||
\(156\) | 1.35713 | 0.108657 | ||||||||
\(157\) | −0.575064 | −0.0458951 | −0.0229476 | − | 0.999737i | \(-0.507305\pi\) | ||||
−0.0229476 | + | 0.999737i | \(0.507305\pi\) | |||||||
\(158\) | −12.4406 | −0.989725 | ||||||||
\(159\) | 5.94440 | 0.471421 | ||||||||
\(160\) | 1.51454 | 0.119735 | ||||||||
\(161\) | −3.51870 | −0.277312 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 5.54296 | 0.434158 | 0.217079 | − | 0.976154i | \(-0.430347\pi\) | ||||
0.217079 | + | 0.976154i | \(0.430347\pi\) | |||||||
\(164\) | −4.69402 | −0.366541 | ||||||||
\(165\) | 2.54549 | 0.198166 | ||||||||
\(166\) | −4.27560 | −0.331851 | ||||||||
\(167\) | 18.4617 | 1.42861 | 0.714306 | − | 0.699834i | \(-0.246742\pi\) | ||||
0.714306 | + | 0.699834i | \(0.246742\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | −11.1582 | −0.858324 | ||||||||
\(170\) | −6.81955 | −0.523036 | ||||||||
\(171\) | 3.92466 | 0.300126 | ||||||||
\(172\) | −2.40129 | −0.183097 | ||||||||
\(173\) | 0.979310 | 0.0744556 | 0.0372278 | − | 0.999307i | \(-0.488147\pi\) | ||||
0.0372278 | + | 0.999307i | \(0.488147\pi\) | |||||||
\(174\) | 8.90561 | 0.675132 | ||||||||
\(175\) | 2.70618 | 0.204568 | ||||||||
\(176\) | −1.68070 | −0.126688 | ||||||||
\(177\) | 9.59202 | 0.720980 | ||||||||
\(178\) | 6.68911 | 0.501370 | ||||||||
\(179\) | −12.0842 | −0.903212 | −0.451606 | − | 0.892217i | \(-0.649149\pi\) | ||||
−0.451606 | + | 0.892217i | \(0.649149\pi\) | |||||||
\(180\) | 1.51454 | 0.112887 | ||||||||
\(181\) | −16.0985 | −1.19659 | −0.598297 | − | 0.801275i | \(-0.704156\pi\) | ||||
−0.598297 | + | 0.801275i | \(0.704156\pi\) | |||||||
\(182\) | 1.35713 | 0.100597 | ||||||||
\(183\) | −4.89730 | −0.362019 | ||||||||
\(184\) | 3.51870 | 0.259402 | ||||||||
\(185\) | 13.3856 | 0.984126 | ||||||||
\(186\) | −4.29806 | −0.315149 | ||||||||
\(187\) | 7.56775 | 0.553409 | ||||||||
\(188\) | −2.64404 | −0.192836 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 5.94405 | 0.431226 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.73233 | 0.628567 | 0.314283 | − | 0.949329i | \(-0.398236\pi\) | ||||
0.314283 | + | 0.949329i | \(0.398236\pi\) | |||||||
\(194\) | 3.02861 | 0.217441 | ||||||||
\(195\) | 2.05542 | 0.147192 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −9.75048 | −0.694693 | −0.347346 | − | 0.937737i | \(-0.612917\pi\) | ||||
−0.347346 | + | 0.937737i | \(0.612917\pi\) | |||||||
\(198\) | −1.68070 | −0.119442 | ||||||||
\(199\) | 14.2985 | 1.01360 | 0.506798 | − | 0.862065i | \(-0.330829\pi\) | ||||
0.506798 | + | 0.862065i | \(0.330829\pi\) | |||||||
\(200\) | −2.70618 | −0.191356 | ||||||||
\(201\) | −8.20435 | −0.578690 | ||||||||
\(202\) | 12.0400 | 0.847132 | ||||||||
\(203\) | 8.90561 | 0.625051 | ||||||||
\(204\) | 4.50273 | 0.315254 | ||||||||
\(205\) | −7.10927 | −0.496533 | ||||||||
\(206\) | −7.62868 | −0.531515 | ||||||||
\(207\) | 3.51870 | 0.244566 | ||||||||
\(208\) | −1.35713 | −0.0940998 | ||||||||
\(209\) | −6.59619 | −0.456268 | ||||||||
\(210\) | 1.51454 | 0.104513 | ||||||||
\(211\) | 6.00269 | 0.413242 | 0.206621 | − | 0.978421i | \(-0.433753\pi\) | ||||
0.206621 | + | 0.978421i | \(0.433753\pi\) | |||||||
\(212\) | −5.94440 | −0.408263 | ||||||||
\(213\) | 6.75595 | 0.462910 | ||||||||
\(214\) | −8.48436 | −0.579979 | ||||||||
\(215\) | −3.63685 | −0.248031 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −4.29806 | −0.291771 | ||||||||
\(218\) | 0.166999 | 0.0113106 | ||||||||
\(219\) | 4.24487 | 0.286842 | ||||||||
\(220\) | −2.54549 | −0.171617 | ||||||||
\(221\) | 6.11077 | 0.411055 | ||||||||
\(222\) | −8.83806 | −0.593172 | ||||||||
\(223\) | −16.4263 | −1.09999 | −0.549993 | − | 0.835169i | \(-0.685370\pi\) | ||||
−0.549993 | + | 0.835169i | \(0.685370\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.70618 | −0.180412 | ||||||||
\(226\) | −10.7808 | −0.717128 | ||||||||
\(227\) | −18.4802 | −1.22657 | −0.613287 | − | 0.789860i | \(-0.710153\pi\) | ||||
−0.613287 | + | 0.789860i | \(0.710153\pi\) | |||||||
\(228\) | −3.92466 | −0.259917 | ||||||||
\(229\) | 17.9688 | 1.18741 | 0.593705 | − | 0.804683i | \(-0.297665\pi\) | ||||
0.593705 | + | 0.804683i | \(0.297665\pi\) | |||||||
\(230\) | 5.32920 | 0.351397 | ||||||||
\(231\) | −1.68070 | −0.110582 | ||||||||
\(232\) | −8.90561 | −0.584682 | ||||||||
\(233\) | 29.5440 | 1.93549 | 0.967746 | − | 0.251926i | \(-0.0810640\pi\) | ||||
0.967746 | + | 0.251926i | \(0.0810640\pi\) | |||||||
\(234\) | −1.35713 | −0.0887181 | ||||||||
\(235\) | −4.00449 | −0.261224 | ||||||||
\(236\) | −9.59202 | −0.624387 | ||||||||
\(237\) | 12.4406 | 0.808107 | ||||||||
\(238\) | 4.50273 | 0.291869 | ||||||||
\(239\) | −8.96693 | −0.580023 | −0.290011 | − | 0.957023i | \(-0.593659\pi\) | ||||
−0.290011 | + | 0.957023i | \(0.593659\pi\) | |||||||
\(240\) | −1.51454 | −0.0977630 | ||||||||
\(241\) | 1.20612 | 0.0776933 | 0.0388467 | − | 0.999245i | \(-0.487632\pi\) | ||||
0.0388467 | + | 0.999245i | \(0.487632\pi\) | |||||||
\(242\) | −8.17524 | −0.525524 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.89730 | 0.313518 | ||||||||
\(245\) | 1.51454 | 0.0967602 | ||||||||
\(246\) | 4.69402 | 0.299280 | ||||||||
\(247\) | −5.32626 | −0.338902 | ||||||||
\(248\) | 4.29806 | 0.272927 | ||||||||
\(249\) | 4.27560 | 0.270955 | ||||||||
\(250\) | −11.6713 | −0.738157 | ||||||||
\(251\) | 13.6302 | 0.860334 | 0.430167 | − | 0.902749i | \(-0.358455\pi\) | ||||
0.430167 | + | 0.902749i | \(0.358455\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −5.91388 | −0.371803 | ||||||||
\(254\) | −4.94951 | −0.310560 | ||||||||
\(255\) | 6.81955 | 0.427057 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.82640 | −0.363441 | −0.181721 | − | 0.983350i | \(-0.558167\pi\) | ||||
−0.181721 | + | 0.983350i | \(0.558167\pi\) | |||||||
\(258\) | 2.40129 | 0.149498 | ||||||||
\(259\) | −8.83806 | −0.549170 | ||||||||
\(260\) | −2.05542 | −0.127472 | ||||||||
\(261\) | −8.90561 | −0.551243 | ||||||||
\(262\) | −12.5335 | −0.774321 | ||||||||
\(263\) | −31.0461 | −1.91438 | −0.957191 | − | 0.289458i | \(-0.906525\pi\) | ||||
−0.957191 | + | 0.289458i | \(0.906525\pi\) | |||||||
\(264\) | 1.68070 | 0.103440 | ||||||||
\(265\) | −9.00301 | −0.553051 | ||||||||
\(266\) | −3.92466 | −0.240636 | ||||||||
\(267\) | −6.68911 | −0.409367 | ||||||||
\(268\) | 8.20435 | 0.501160 | ||||||||
\(269\) | 0.696142 | 0.0424445 | 0.0212223 | − | 0.999775i | \(-0.493244\pi\) | ||||
0.0212223 | + | 0.999775i | \(0.493244\pi\) | |||||||
\(270\) | −1.51454 | −0.0921718 | ||||||||
\(271\) | 31.0053 | 1.88344 | 0.941720 | − | 0.336398i | \(-0.109209\pi\) | ||||
0.941720 | + | 0.336398i | \(0.109209\pi\) | |||||||
\(272\) | −4.50273 | −0.273018 | ||||||||
\(273\) | −1.35713 | −0.0821370 | ||||||||
\(274\) | 19.1587 | 1.15742 | ||||||||
\(275\) | 4.54828 | 0.274271 | ||||||||
\(276\) | −3.51870 | −0.211801 | ||||||||
\(277\) | −0.447859 | −0.0269093 | −0.0134546 | − | 0.999909i | \(-0.504283\pi\) | ||||
−0.0134546 | + | 0.999909i | \(0.504283\pi\) | |||||||
\(278\) | −10.0578 | −0.603226 | ||||||||
\(279\) | 4.29806 | 0.257318 | ||||||||
\(280\) | −1.51454 | −0.0905109 | ||||||||
\(281\) | 11.2801 | 0.672915 | 0.336457 | − | 0.941699i | \(-0.390771\pi\) | ||||
0.336457 | + | 0.941699i | \(0.390771\pi\) | |||||||
\(282\) | 2.64404 | 0.157450 | ||||||||
\(283\) | −5.76688 | −0.342806 | −0.171403 | − | 0.985201i | \(-0.554830\pi\) | ||||
−0.171403 | + | 0.985201i | \(0.554830\pi\) | |||||||
\(284\) | −6.75595 | −0.400892 | ||||||||
\(285\) | −5.94405 | −0.352095 | ||||||||
\(286\) | 2.28092 | 0.134874 | ||||||||
\(287\) | 4.69402 | 0.277079 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 3.27459 | 0.192623 | ||||||||
\(290\) | −13.4879 | −0.792035 | ||||||||
\(291\) | −3.02861 | −0.177540 | ||||||||
\(292\) | −4.24487 | −0.248412 | ||||||||
\(293\) | −3.05098 | −0.178240 | −0.0891200 | − | 0.996021i | \(-0.528405\pi\) | ||||
−0.0891200 | + | 0.996021i | \(0.528405\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −14.5275 | −0.845822 | ||||||||
\(296\) | 8.83806 | 0.513702 | ||||||||
\(297\) | 1.68070 | 0.0975242 | ||||||||
\(298\) | −17.9407 | −1.03928 | ||||||||
\(299\) | −4.77532 | −0.276164 | ||||||||
\(300\) | 2.70618 | 0.156241 | ||||||||
\(301\) | 2.40129 | 0.138408 | ||||||||
\(302\) | −10.3551 | −0.595870 | ||||||||
\(303\) | −12.0400 | −0.691681 | ||||||||
\(304\) | 3.92466 | 0.225095 | ||||||||
\(305\) | 7.41715 | 0.424705 | ||||||||
\(306\) | −4.50273 | −0.257404 | ||||||||
\(307\) | −19.5185 | −1.11398 | −0.556991 | − | 0.830518i | \(-0.688044\pi\) | ||||
−0.556991 | + | 0.830518i | \(0.688044\pi\) | |||||||
\(308\) | 1.68070 | 0.0957669 | ||||||||
\(309\) | 7.62868 | 0.433981 | ||||||||
\(310\) | 6.50957 | 0.369719 | ||||||||
\(311\) | 5.73920 | 0.325440 | 0.162720 | − | 0.986672i | \(-0.447973\pi\) | ||||
0.162720 | + | 0.986672i | \(0.447973\pi\) | |||||||
\(312\) | 1.35713 | 0.0768321 | ||||||||
\(313\) | −17.0827 | −0.965574 | −0.482787 | − | 0.875738i | \(-0.660375\pi\) | ||||
−0.482787 | + | 0.875738i | \(0.660375\pi\) | |||||||
\(314\) | −0.575064 | −0.0324528 | ||||||||
\(315\) | −1.51454 | −0.0853345 | ||||||||
\(316\) | −12.4406 | −0.699841 | ||||||||
\(317\) | −13.1001 | −0.735776 | −0.367888 | − | 0.929870i | \(-0.619919\pi\) | ||||
−0.367888 | + | 0.929870i | \(0.619919\pi\) | |||||||
\(318\) | 5.94440 | 0.333345 | ||||||||
\(319\) | 14.9677 | 0.838029 | ||||||||
\(320\) | 1.51454 | 0.0846652 | ||||||||
\(321\) | 8.48436 | 0.473551 | ||||||||
\(322\) | −3.51870 | −0.196089 | ||||||||
\(323\) | −17.6717 | −0.983279 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.67262 | 0.203721 | ||||||||
\(326\) | 5.54296 | 0.306996 | ||||||||
\(327\) | −0.166999 | −0.00923509 | ||||||||
\(328\) | −4.69402 | −0.259184 | ||||||||
\(329\) | 2.64404 | 0.145770 | ||||||||
\(330\) | 2.54549 | 0.140124 | ||||||||
\(331\) | −17.3251 | −0.952271 | −0.476135 | − | 0.879372i | \(-0.657963\pi\) | ||||
−0.476135 | + | 0.879372i | \(0.657963\pi\) | |||||||
\(332\) | −4.27560 | −0.234654 | ||||||||
\(333\) | 8.83806 | 0.484323 | ||||||||
\(334\) | 18.4617 | 1.01018 | ||||||||
\(335\) | 12.4258 | 0.678893 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 0.0407571 | 0.00222018 | 0.00111009 | − | 0.999999i | \(-0.499647\pi\) | ||||
0.00111009 | + | 0.999999i | \(0.499647\pi\) | |||||||
\(338\) | −11.1582 | −0.606927 | ||||||||
\(339\) | 10.7808 | 0.585533 | ||||||||
\(340\) | −6.81955 | −0.369842 | ||||||||
\(341\) | −7.22376 | −0.391189 | ||||||||
\(342\) | 3.92466 | 0.212221 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.40129 | −0.129469 | ||||||||
\(345\) | −5.32920 | −0.286914 | ||||||||
\(346\) | 0.979310 | 0.0526480 | ||||||||
\(347\) | −11.3420 | −0.608868 | −0.304434 | − | 0.952533i | \(-0.598467\pi\) | ||||
−0.304434 | + | 0.952533i | \(0.598467\pi\) | |||||||
\(348\) | 8.90561 | 0.477391 | ||||||||
\(349\) | 14.3535 | 0.768324 | 0.384162 | − | 0.923266i | \(-0.374490\pi\) | ||||
0.384162 | + | 0.923266i | \(0.374490\pi\) | |||||||
\(350\) | 2.70618 | 0.144651 | ||||||||
\(351\) | 1.35713 | 0.0724380 | ||||||||
\(352\) | −1.68070 | −0.0895817 | ||||||||
\(353\) | 7.44716 | 0.396372 | 0.198186 | − | 0.980164i | \(-0.436495\pi\) | ||||
0.198186 | + | 0.980164i | \(0.436495\pi\) | |||||||
\(354\) | 9.59202 | 0.509810 | ||||||||
\(355\) | −10.2321 | −0.543065 | ||||||||
\(356\) | 6.68911 | 0.354522 | ||||||||
\(357\) | −4.50273 | −0.238310 | ||||||||
\(358\) | −12.0842 | −0.638667 | ||||||||
\(359\) | 15.3668 | 0.811028 | 0.405514 | − | 0.914089i | \(-0.367092\pi\) | ||||
0.405514 | + | 0.914089i | \(0.367092\pi\) | |||||||
\(360\) | 1.51454 | 0.0798231 | ||||||||
\(361\) | −3.59703 | −0.189317 | ||||||||
\(362\) | −16.0985 | −0.846119 | ||||||||
\(363\) | 8.17524 | 0.429089 | ||||||||
\(364\) | 1.35713 | 0.0711327 | ||||||||
\(365\) | −6.42902 | −0.336510 | ||||||||
\(366\) | −4.89730 | −0.255986 | ||||||||
\(367\) | −22.3719 | −1.16780 | −0.583902 | − | 0.811824i | \(-0.698475\pi\) | ||||
−0.583902 | + | 0.811824i | \(0.698475\pi\) | |||||||
\(368\) | 3.51870 | 0.183425 | ||||||||
\(369\) | −4.69402 | −0.244361 | ||||||||
\(370\) | 13.3856 | 0.695883 | ||||||||
\(371\) | 5.94440 | 0.308618 | ||||||||
\(372\) | −4.29806 | −0.222844 | ||||||||
\(373\) | 21.7486 | 1.12610 | 0.563049 | − | 0.826423i | \(-0.309628\pi\) | ||||
0.563049 | + | 0.826423i | \(0.309628\pi\) | |||||||
\(374\) | 7.56775 | 0.391319 | ||||||||
\(375\) | 11.6713 | 0.602703 | ||||||||
\(376\) | −2.64404 | −0.136356 | ||||||||
\(377\) | 12.0860 | 0.622462 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 20.1124 | 1.03311 | 0.516554 | − | 0.856255i | \(-0.327215\pi\) | ||||
0.516554 | + | 0.856255i | \(0.327215\pi\) | |||||||
\(380\) | 5.94405 | 0.304923 | ||||||||
\(381\) | 4.94951 | 0.253571 | ||||||||
\(382\) | 1.00000 | 0.0511645 | ||||||||
\(383\) | −24.0159 | −1.22716 | −0.613578 | − | 0.789634i | \(-0.710270\pi\) | ||||
−0.613578 | + | 0.789634i | \(0.710270\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 2.54549 | 0.129730 | ||||||||
\(386\) | 8.73233 | 0.444464 | ||||||||
\(387\) | −2.40129 | −0.122065 | ||||||||
\(388\) | 3.02861 | 0.153754 | ||||||||
\(389\) | 1.60108 | 0.0811781 | 0.0405891 | − | 0.999176i | \(-0.487077\pi\) | ||||
0.0405891 | + | 0.999176i | \(0.487077\pi\) | |||||||
\(390\) | 2.05542 | 0.104080 | ||||||||
\(391\) | −15.8438 | −0.801253 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 12.5335 | 0.632230 | ||||||||
\(394\) | −9.75048 | −0.491222 | ||||||||
\(395\) | −18.8418 | −0.948035 | ||||||||
\(396\) | −1.68070 | −0.0844584 | ||||||||
\(397\) | −4.99455 | −0.250669 | −0.125335 | − | 0.992115i | \(-0.540000\pi\) | ||||
−0.125335 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(398\) | 14.2985 | 0.716721 | ||||||||
\(399\) | 3.92466 | 0.196479 | ||||||||
\(400\) | −2.70618 | −0.135309 | ||||||||
\(401\) | 9.77927 | 0.488354 | 0.244177 | − | 0.969731i | \(-0.421482\pi\) | ||||
0.244177 | + | 0.969731i | \(0.421482\pi\) | |||||||
\(402\) | −8.20435 | −0.409196 | ||||||||
\(403\) | −5.83301 | −0.290563 | ||||||||
\(404\) | 12.0400 | 0.599013 | ||||||||
\(405\) | 1.51454 | 0.0752580 | ||||||||
\(406\) | 8.90561 | 0.441978 | ||||||||
\(407\) | −14.8541 | −0.736292 | ||||||||
\(408\) | 4.50273 | 0.222918 | ||||||||
\(409\) | 14.4342 | 0.713723 | 0.356862 | − | 0.934157i | \(-0.383847\pi\) | ||||
0.356862 | + | 0.934157i | \(0.383847\pi\) | |||||||
\(410\) | −7.10927 | −0.351102 | ||||||||
\(411\) | −19.1587 | −0.945029 | ||||||||
\(412\) | −7.62868 | −0.375838 | ||||||||
\(413\) | 9.59202 | 0.471992 | ||||||||
\(414\) | 3.51870 | 0.172935 | ||||||||
\(415\) | −6.47556 | −0.317873 | ||||||||
\(416\) | −1.35713 | −0.0665386 | ||||||||
\(417\) | 10.0578 | 0.492532 | ||||||||
\(418\) | −6.59619 | −0.322630 | ||||||||
\(419\) | 3.44484 | 0.168292 | 0.0841458 | − | 0.996453i | \(-0.473184\pi\) | ||||
0.0841458 | + | 0.996453i | \(0.473184\pi\) | |||||||
\(420\) | 1.51454 | 0.0739018 | ||||||||
\(421\) | −7.85560 | −0.382859 | −0.191429 | − | 0.981506i | \(-0.561312\pi\) | ||||
−0.191429 | + | 0.981506i | \(0.561312\pi\) | |||||||
\(422\) | 6.00269 | 0.292206 | ||||||||
\(423\) | −2.64404 | −0.128557 | ||||||||
\(424\) | −5.94440 | −0.288685 | ||||||||
\(425\) | 12.1852 | 0.591068 | ||||||||
\(426\) | 6.75595 | 0.327327 | ||||||||
\(427\) | −4.89730 | −0.236997 | ||||||||
\(428\) | −8.48436 | −0.410107 | ||||||||
\(429\) | −2.28092 | −0.110124 | ||||||||
\(430\) | −3.63685 | −0.175384 | ||||||||
\(431\) | −32.8227 | −1.58102 | −0.790508 | − | 0.612452i | \(-0.790183\pi\) | ||||
−0.790508 | + | 0.612452i | \(0.790183\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 30.7560 | 1.47804 | 0.739021 | − | 0.673683i | \(-0.235289\pi\) | ||||
0.739021 | + | 0.673683i | \(0.235289\pi\) | |||||||
\(434\) | −4.29806 | −0.206314 | ||||||||
\(435\) | 13.4879 | 0.646694 | ||||||||
\(436\) | 0.166999 | 0.00799782 | ||||||||
\(437\) | 13.8097 | 0.660608 | ||||||||
\(438\) | 4.24487 | 0.202828 | ||||||||
\(439\) | −10.8474 | −0.517719 | −0.258859 | − | 0.965915i | \(-0.583347\pi\) | ||||
−0.258859 | + | 0.965915i | \(0.583347\pi\) | |||||||
\(440\) | −2.54549 | −0.121351 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 6.11077 | 0.290660 | ||||||||
\(443\) | −15.0722 | −0.716102 | −0.358051 | − | 0.933702i | \(-0.616559\pi\) | ||||
−0.358051 | + | 0.933702i | \(0.616559\pi\) | |||||||
\(444\) | −8.83806 | −0.419436 | ||||||||
\(445\) | 10.1309 | 0.480251 | ||||||||
\(446\) | −16.4263 | −0.777808 | ||||||||
\(447\) | 17.9407 | 0.848567 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 33.9640 | 1.60286 | 0.801431 | − | 0.598088i | \(-0.204073\pi\) | ||||
0.801431 | + | 0.598088i | \(0.204073\pi\) | |||||||
\(450\) | −2.70618 | −0.127570 | ||||||||
\(451\) | 7.88925 | 0.371490 | ||||||||
\(452\) | −10.7808 | −0.507086 | ||||||||
\(453\) | 10.3551 | 0.486526 | ||||||||
\(454\) | −18.4802 | −0.867319 | ||||||||
\(455\) | 2.05542 | 0.0963595 | ||||||||
\(456\) | −3.92466 | −0.183789 | ||||||||
\(457\) | −39.9472 | −1.86865 | −0.934326 | − | 0.356419i | \(-0.883997\pi\) | ||||
−0.934326 | + | 0.356419i | \(0.883997\pi\) | |||||||
\(458\) | 17.9688 | 0.839626 | ||||||||
\(459\) | 4.50273 | 0.210169 | ||||||||
\(460\) | 5.32920 | 0.248475 | ||||||||
\(461\) | 4.14051 | 0.192843 | 0.0964213 | − | 0.995341i | \(-0.469260\pi\) | ||||
0.0964213 | + | 0.995341i | \(0.469260\pi\) | |||||||
\(462\) | −1.68070 | −0.0781933 | ||||||||
\(463\) | −23.7143 | −1.10209 | −0.551047 | − | 0.834474i | \(-0.685772\pi\) | ||||
−0.551047 | + | 0.834474i | \(0.685772\pi\) | |||||||
\(464\) | −8.90561 | −0.413432 | ||||||||
\(465\) | −6.50957 | −0.301874 | ||||||||
\(466\) | 29.5440 | 1.36860 | ||||||||
\(467\) | 35.8186 | 1.65749 | 0.828743 | − | 0.559629i | \(-0.189056\pi\) | ||||
0.828743 | + | 0.559629i | \(0.189056\pi\) | |||||||
\(468\) | −1.35713 | −0.0627332 | ||||||||
\(469\) | −8.20435 | −0.378842 | ||||||||
\(470\) | −4.00449 | −0.184713 | ||||||||
\(471\) | 0.575064 | 0.0264976 | ||||||||
\(472\) | −9.59202 | −0.441508 | ||||||||
\(473\) | 4.03586 | 0.185569 | ||||||||
\(474\) | 12.4406 | 0.571418 | ||||||||
\(475\) | −10.6208 | −0.487317 | ||||||||
\(476\) | 4.50273 | 0.206382 | ||||||||
\(477\) | −5.94440 | −0.272175 | ||||||||
\(478\) | −8.96693 | −0.410138 | ||||||||
\(479\) | −36.2129 | −1.65461 | −0.827305 | − | 0.561753i | \(-0.810127\pi\) | ||||
−0.827305 | + | 0.561753i | \(0.810127\pi\) | |||||||
\(480\) | −1.51454 | −0.0691288 | ||||||||
\(481\) | −11.9944 | −0.546896 | ||||||||
\(482\) | 1.20612 | 0.0549375 | ||||||||
\(483\) | 3.51870 | 0.160106 | ||||||||
\(484\) | −8.17524 | −0.371602 | ||||||||
\(485\) | 4.58694 | 0.208282 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −22.0811 | −1.00059 | −0.500296 | − | 0.865855i | \(-0.666775\pi\) | ||||
−0.500296 | + | 0.865855i | \(0.666775\pi\) | |||||||
\(488\) | 4.89730 | 0.221691 | ||||||||
\(489\) | −5.54296 | −0.250661 | ||||||||
\(490\) | 1.51454 | 0.0684198 | ||||||||
\(491\) | 3.79385 | 0.171214 | 0.0856070 | − | 0.996329i | \(-0.472717\pi\) | ||||
0.0856070 | + | 0.996329i | \(0.472717\pi\) | |||||||
\(492\) | 4.69402 | 0.211623 | ||||||||
\(493\) | 40.0996 | 1.80599 | ||||||||
\(494\) | −5.32626 | −0.239640 | ||||||||
\(495\) | −2.54549 | −0.114411 | ||||||||
\(496\) | 4.29806 | 0.192989 | ||||||||
\(497\) | 6.75595 | 0.303046 | ||||||||
\(498\) | 4.27560 | 0.191594 | ||||||||
\(499\) | 29.5409 | 1.32243 | 0.661216 | − | 0.750196i | \(-0.270041\pi\) | ||||
0.661216 | + | 0.750196i | \(0.270041\pi\) | |||||||
\(500\) | −11.6713 | −0.521956 | ||||||||
\(501\) | −18.4617 | −0.824810 | ||||||||
\(502\) | 13.6302 | 0.608348 | ||||||||
\(503\) | 30.0797 | 1.34119 | 0.670595 | − | 0.741824i | \(-0.266039\pi\) | ||||
0.670595 | + | 0.741824i | \(0.266039\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 18.2350 | 0.811449 | ||||||||
\(506\) | −5.91388 | −0.262904 | ||||||||
\(507\) | 11.1582 | 0.495553 | ||||||||
\(508\) | −4.94951 | −0.219599 | ||||||||
\(509\) | −27.8390 | −1.23394 | −0.616971 | − | 0.786986i | \(-0.711640\pi\) | ||||
−0.616971 | + | 0.786986i | \(0.711640\pi\) | |||||||
\(510\) | 6.81955 | 0.301975 | ||||||||
\(511\) | 4.24487 | 0.187782 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.92466 | −0.173278 | ||||||||
\(514\) | −5.82640 | −0.256992 | ||||||||
\(515\) | −11.5539 | −0.509127 | ||||||||
\(516\) | 2.40129 | 0.105711 | ||||||||
\(517\) | 4.44384 | 0.195440 | ||||||||
\(518\) | −8.83806 | −0.388322 | ||||||||
\(519\) | −0.979310 | −0.0429869 | ||||||||
\(520\) | −2.05542 | −0.0901360 | ||||||||
\(521\) | 19.4835 | 0.853586 | 0.426793 | − | 0.904349i | \(-0.359643\pi\) | ||||
0.426793 | + | 0.904349i | \(0.359643\pi\) | |||||||
\(522\) | −8.90561 | −0.389788 | ||||||||
\(523\) | 10.6141 | 0.464124 | 0.232062 | − | 0.972701i | \(-0.425453\pi\) | ||||
0.232062 | + | 0.972701i | \(0.425453\pi\) | |||||||
\(524\) | −12.5335 | −0.547527 | ||||||||
\(525\) | −2.70618 | −0.118107 | ||||||||
\(526\) | −31.0461 | −1.35367 | ||||||||
\(527\) | −19.3530 | −0.843031 | ||||||||
\(528\) | 1.68070 | 0.0731432 | ||||||||
\(529\) | −10.6188 | −0.461685 | ||||||||
\(530\) | −9.00301 | −0.391066 | ||||||||
\(531\) | −9.59202 | −0.416258 | ||||||||
\(532\) | −3.92466 | −0.170156 | ||||||||
\(533\) | 6.37038 | 0.275932 | ||||||||
\(534\) | −6.68911 | −0.289466 | ||||||||
\(535\) | −12.8499 | −0.555549 | ||||||||
\(536\) | 8.20435 | 0.354374 | ||||||||
\(537\) | 12.0842 | 0.521470 | ||||||||
\(538\) | 0.696142 | 0.0300128 | ||||||||
\(539\) | −1.68070 | −0.0723930 | ||||||||
\(540\) | −1.51454 | −0.0651753 | ||||||||
\(541\) | −2.50986 | −0.107907 | −0.0539537 | − | 0.998543i | \(-0.517182\pi\) | ||||
−0.0539537 | + | 0.998543i | \(0.517182\pi\) | |||||||
\(542\) | 31.0053 | 1.33179 | ||||||||
\(543\) | 16.0985 | 0.690853 | ||||||||
\(544\) | −4.50273 | −0.193053 | ||||||||
\(545\) | 0.252927 | 0.0108342 | ||||||||
\(546\) | −1.35713 | −0.0580796 | ||||||||
\(547\) | −39.1666 | −1.67464 | −0.837321 | − | 0.546711i | \(-0.815879\pi\) | ||||
−0.837321 | + | 0.546711i | \(0.815879\pi\) | |||||||
\(548\) | 19.1587 | 0.818419 | ||||||||
\(549\) | 4.89730 | 0.209012 | ||||||||
\(550\) | 4.54828 | 0.193939 | ||||||||
\(551\) | −34.9515 | −1.48898 | ||||||||
\(552\) | −3.51870 | −0.149766 | ||||||||
\(553\) | 12.4406 | 0.529030 | ||||||||
\(554\) | −0.447859 | −0.0190277 | ||||||||
\(555\) | −13.3856 | −0.568186 | ||||||||
\(556\) | −10.0578 | −0.426545 | ||||||||
\(557\) | −18.2800 | −0.774547 | −0.387273 | − | 0.921965i | \(-0.626583\pi\) | ||||
−0.387273 | + | 0.921965i | \(0.626583\pi\) | |||||||
\(558\) | 4.29806 | 0.181951 | ||||||||
\(559\) | 3.25886 | 0.137835 | ||||||||
\(560\) | −1.51454 | −0.0640009 | ||||||||
\(561\) | −7.56775 | −0.319511 | ||||||||
\(562\) | 11.2801 | 0.475822 | ||||||||
\(563\) | 13.3951 | 0.564537 | 0.282269 | − | 0.959335i | \(-0.408913\pi\) | ||||
0.282269 | + | 0.959335i | \(0.408913\pi\) | |||||||
\(564\) | 2.64404 | 0.111334 | ||||||||
\(565\) | −16.3279 | −0.686921 | ||||||||
\(566\) | −5.76688 | −0.242400 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −6.75595 | −0.283473 | ||||||||
\(569\) | 1.34888 | 0.0565480 | 0.0282740 | − | 0.999600i | \(-0.490999\pi\) | ||||
0.0282740 | + | 0.999600i | \(0.490999\pi\) | |||||||
\(570\) | −5.94405 | −0.248969 | ||||||||
\(571\) | −0.215473 | −0.00901725 | −0.00450863 | − | 0.999990i | \(-0.501435\pi\) | ||||
−0.00450863 | + | 0.999990i | \(0.501435\pi\) | |||||||
\(572\) | 2.28092 | 0.0953702 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | 4.69402 | 0.195925 | ||||||||
\(575\) | −9.52222 | −0.397104 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 4.28061 | 0.178204 | 0.0891021 | − | 0.996022i | \(-0.471600\pi\) | ||||
0.0891021 | + | 0.996022i | \(0.471600\pi\) | |||||||
\(578\) | 3.27459 | 0.136205 | ||||||||
\(579\) | −8.73233 | −0.362903 | ||||||||
\(580\) | −13.4879 | −0.560054 | ||||||||
\(581\) | 4.27560 | 0.177382 | ||||||||
\(582\) | −3.02861 | −0.125540 | ||||||||
\(583\) | 9.99076 | 0.413775 | ||||||||
\(584\) | −4.24487 | −0.175654 | ||||||||
\(585\) | −2.05542 | −0.0849811 | ||||||||
\(586\) | −3.05098 | −0.126035 | ||||||||
\(587\) | −12.4431 | −0.513584 | −0.256792 | − | 0.966467i | \(-0.582665\pi\) | ||||
−0.256792 | + | 0.966467i | \(0.582665\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 16.8684 | 0.695052 | ||||||||
\(590\) | −14.5275 | −0.598086 | ||||||||
\(591\) | 9.75048 | 0.401081 | ||||||||
\(592\) | 8.83806 | 0.363242 | ||||||||
\(593\) | −40.5151 | −1.66375 | −0.831877 | − | 0.554960i | \(-0.812733\pi\) | ||||
−0.831877 | + | 0.554960i | \(0.812733\pi\) | |||||||
\(594\) | 1.68070 | 0.0689600 | ||||||||
\(595\) | 6.81955 | 0.279574 | ||||||||
\(596\) | −17.9407 | −0.734881 | ||||||||
\(597\) | −14.2985 | −0.585200 | ||||||||
\(598\) | −4.77532 | −0.195277 | ||||||||
\(599\) | −45.8522 | −1.87347 | −0.936735 | − | 0.350040i | \(-0.886168\pi\) | ||||
−0.936735 | + | 0.350040i | \(0.886168\pi\) | |||||||
\(600\) | 2.70618 | 0.110479 | ||||||||
\(601\) | 5.92898 | 0.241848 | 0.120924 | − | 0.992662i | \(-0.461414\pi\) | ||||
0.120924 | + | 0.992662i | \(0.461414\pi\) | |||||||
\(602\) | 2.40129 | 0.0978694 | ||||||||
\(603\) | 8.20435 | 0.334107 | ||||||||
\(604\) | −10.3551 | −0.421344 | ||||||||
\(605\) | −12.3817 | −0.503388 | ||||||||
\(606\) | −12.0400 | −0.489092 | ||||||||
\(607\) | 1.24505 | 0.0505351 | 0.0252676 | − | 0.999681i | \(-0.491956\pi\) | ||||
0.0252676 | + | 0.999681i | \(0.491956\pi\) | |||||||
\(608\) | 3.92466 | 0.159166 | ||||||||
\(609\) | −8.90561 | −0.360873 | ||||||||
\(610\) | 7.41715 | 0.300312 | ||||||||
\(611\) | 3.58829 | 0.145167 | ||||||||
\(612\) | −4.50273 | −0.182012 | ||||||||
\(613\) | −28.7860 | −1.16265 | −0.581327 | − | 0.813670i | \(-0.697466\pi\) | ||||
−0.581327 | + | 0.813670i | \(0.697466\pi\) | |||||||
\(614\) | −19.5185 | −0.787704 | ||||||||
\(615\) | 7.10927 | 0.286673 | ||||||||
\(616\) | 1.68070 | 0.0677174 | ||||||||
\(617\) | 7.29625 | 0.293736 | 0.146868 | − | 0.989156i | \(-0.453081\pi\) | ||||
0.146868 | + | 0.989156i | \(0.453081\pi\) | |||||||
\(618\) | 7.62868 | 0.306871 | ||||||||
\(619\) | 19.3366 | 0.777203 | 0.388602 | − | 0.921406i | \(-0.372958\pi\) | ||||
0.388602 | + | 0.921406i | \(0.372958\pi\) | |||||||
\(620\) | 6.50957 | 0.261431 | ||||||||
\(621\) | −3.51870 | −0.141201 | ||||||||
\(622\) | 5.73920 | 0.230121 | ||||||||
\(623\) | −6.68911 | −0.267993 | ||||||||
\(624\) | 1.35713 | 0.0543285 | ||||||||
\(625\) | −4.14572 | −0.165829 | ||||||||
\(626\) | −17.0827 | −0.682764 | ||||||||
\(627\) | 6.59619 | 0.263426 | ||||||||
\(628\) | −0.575064 | −0.0229476 | ||||||||
\(629\) | −39.7954 | −1.58675 | ||||||||
\(630\) | −1.51454 | −0.0603406 | ||||||||
\(631\) | −21.8594 | −0.870210 | −0.435105 | − | 0.900380i | \(-0.643289\pi\) | ||||
−0.435105 | + | 0.900380i | \(0.643289\pi\) | |||||||
\(632\) | −12.4406 | −0.494862 | ||||||||
\(633\) | −6.00269 | −0.238585 | ||||||||
\(634\) | −13.1001 | −0.520272 | ||||||||
\(635\) | −7.49622 | −0.297478 | ||||||||
\(636\) | 5.94440 | 0.235711 | ||||||||
\(637\) | −1.35713 | −0.0537713 | ||||||||
\(638\) | 14.9677 | 0.592576 | ||||||||
\(639\) | −6.75595 | −0.267261 | ||||||||
\(640\) | 1.51454 | 0.0598673 | ||||||||
\(641\) | −14.7589 | −0.582942 | −0.291471 | − | 0.956580i | \(-0.594145\pi\) | ||||
−0.291471 | + | 0.956580i | \(0.594145\pi\) | |||||||
\(642\) | 8.48436 | 0.334851 | ||||||||
\(643\) | 11.5866 | 0.456932 | 0.228466 | − | 0.973552i | \(-0.426629\pi\) | ||||
0.228466 | + | 0.973552i | \(0.426629\pi\) | |||||||
\(644\) | −3.51870 | −0.138656 | ||||||||
\(645\) | 3.63685 | 0.143201 | ||||||||
\(646\) | −17.6717 | −0.695284 | ||||||||
\(647\) | 25.9610 | 1.02063 | 0.510315 | − | 0.859987i | \(-0.329529\pi\) | ||||
0.510315 | + | 0.859987i | \(0.329529\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 16.1213 | 0.632817 | ||||||||
\(650\) | 3.67262 | 0.144052 | ||||||||
\(651\) | 4.29806 | 0.168454 | ||||||||
\(652\) | 5.54296 | 0.217079 | ||||||||
\(653\) | −13.9175 | −0.544633 | −0.272316 | − | 0.962208i | \(-0.587790\pi\) | ||||
−0.272316 | + | 0.962208i | \(0.587790\pi\) | |||||||
\(654\) | −0.166999 | −0.00653019 | ||||||||
\(655\) | −18.9824 | −0.741704 | ||||||||
\(656\) | −4.69402 | −0.183271 | ||||||||
\(657\) | −4.24487 | −0.165608 | ||||||||
\(658\) | 2.64404 | 0.103075 | ||||||||
\(659\) | −11.1201 | −0.433177 | −0.216589 | − | 0.976263i | \(-0.569493\pi\) | ||||
−0.216589 | + | 0.976263i | \(0.569493\pi\) | |||||||
\(660\) | 2.54549 | 0.0990829 | ||||||||
\(661\) | 40.6675 | 1.58178 | 0.790891 | − | 0.611957i | \(-0.209617\pi\) | ||||
0.790891 | + | 0.611957i | \(0.209617\pi\) | |||||||
\(662\) | −17.3251 | −0.673357 | ||||||||
\(663\) | −6.11077 | −0.237323 | ||||||||
\(664\) | −4.27560 | −0.165926 | ||||||||
\(665\) | −5.94405 | −0.230500 | ||||||||
\(666\) | 8.83806 | 0.342468 | ||||||||
\(667\) | −31.3361 | −1.21334 | ||||||||
\(668\) | 18.4617 | 0.714306 | ||||||||
\(669\) | 16.4263 | 0.635077 | ||||||||
\(670\) | 12.4258 | 0.480050 | ||||||||
\(671\) | −8.23091 | −0.317751 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 3.41211 | 0.131527 | 0.0657635 | − | 0.997835i | \(-0.479052\pi\) | ||||
0.0657635 | + | 0.997835i | \(0.479052\pi\) | |||||||
\(674\) | 0.0407571 | 0.00156990 | ||||||||
\(675\) | 2.70618 | 0.104161 | ||||||||
\(676\) | −11.1582 | −0.429162 | ||||||||
\(677\) | 28.5914 | 1.09886 | 0.549429 | − | 0.835540i | \(-0.314845\pi\) | ||||
0.549429 | + | 0.835540i | \(0.314845\pi\) | |||||||
\(678\) | 10.7808 | 0.414034 | ||||||||
\(679\) | −3.02861 | −0.116227 | ||||||||
\(680\) | −6.81955 | −0.261518 | ||||||||
\(681\) | 18.4802 | 0.708163 | ||||||||
\(682\) | −7.22376 | −0.276612 | ||||||||
\(683\) | −20.6210 | −0.789042 | −0.394521 | − | 0.918887i | \(-0.629090\pi\) | ||||
−0.394521 | + | 0.918887i | \(0.629090\pi\) | |||||||
\(684\) | 3.92466 | 0.150063 | ||||||||
\(685\) | 29.0166 | 1.10867 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −17.9688 | −0.685552 | ||||||||
\(688\) | −2.40129 | −0.0915484 | ||||||||
\(689\) | 8.06730 | 0.307340 | ||||||||
\(690\) | −5.32920 | −0.202879 | ||||||||
\(691\) | −9.53559 | −0.362751 | −0.181375 | − | 0.983414i | \(-0.558055\pi\) | ||||
−0.181375 | + | 0.983414i | \(0.558055\pi\) | |||||||
\(692\) | 0.979310 | 0.0372278 | ||||||||
\(693\) | 1.68070 | 0.0638446 | ||||||||
\(694\) | −11.3420 | −0.430535 | ||||||||
\(695\) | −15.2329 | −0.577816 | ||||||||
\(696\) | 8.90561 | 0.337566 | ||||||||
\(697\) | 21.1359 | 0.800580 | ||||||||
\(698\) | 14.3535 | 0.543287 | ||||||||
\(699\) | −29.5440 | −1.11746 | ||||||||
\(700\) | 2.70618 | 0.102284 | ||||||||
\(701\) | −6.59066 | −0.248926 | −0.124463 | − | 0.992224i | \(-0.539721\pi\) | ||||
−0.124463 | + | 0.992224i | \(0.539721\pi\) | |||||||
\(702\) | 1.35713 | 0.0512214 | ||||||||
\(703\) | 34.6864 | 1.30822 | ||||||||
\(704\) | −1.68070 | −0.0633438 | ||||||||
\(705\) | 4.00449 | 0.150818 | ||||||||
\(706\) | 7.44716 | 0.280278 | ||||||||
\(707\) | −12.0400 | −0.452811 | ||||||||
\(708\) | 9.59202 | 0.360490 | ||||||||
\(709\) | 39.7191 | 1.49168 | 0.745841 | − | 0.666124i | \(-0.232048\pi\) | ||||
0.745841 | + | 0.666124i | \(0.232048\pi\) | |||||||
\(710\) | −10.2321 | −0.384005 | ||||||||
\(711\) | −12.4406 | −0.466561 | ||||||||
\(712\) | 6.68911 | 0.250685 | ||||||||
\(713\) | 15.1236 | 0.566383 | ||||||||
\(714\) | −4.50273 | −0.168510 | ||||||||
\(715\) | 3.45455 | 0.129193 | ||||||||
\(716\) | −12.0842 | −0.451606 | ||||||||
\(717\) | 8.96693 | 0.334876 | ||||||||
\(718\) | 15.3668 | 0.573484 | ||||||||
\(719\) | 23.0920 | 0.861188 | 0.430594 | − | 0.902546i | \(-0.358304\pi\) | ||||
0.430594 | + | 0.902546i | \(0.358304\pi\) | |||||||
\(720\) | 1.51454 | 0.0564435 | ||||||||
\(721\) | 7.62868 | 0.284107 | ||||||||
\(722\) | −3.59703 | −0.133868 | ||||||||
\(723\) | −1.20612 | −0.0448563 | ||||||||
\(724\) | −16.0985 | −0.598297 | ||||||||
\(725\) | 24.1002 | 0.895057 | ||||||||
\(726\) | 8.17524 | 0.303412 | ||||||||
\(727\) | −4.50433 | −0.167056 | −0.0835281 | − | 0.996505i | \(-0.526619\pi\) | ||||
−0.0835281 | + | 0.996505i | \(0.526619\pi\) | |||||||
\(728\) | 1.35713 | 0.0502984 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.42902 | −0.237949 | ||||||||
\(731\) | 10.8124 | 0.399910 | ||||||||
\(732\) | −4.89730 | −0.181010 | ||||||||
\(733\) | 20.4381 | 0.754897 | 0.377448 | − | 0.926031i | \(-0.376802\pi\) | ||||
0.377448 | + | 0.926031i | \(0.376802\pi\) | |||||||
\(734\) | −22.3719 | −0.825763 | ||||||||
\(735\) | −1.51454 | −0.0558645 | ||||||||
\(736\) | 3.51870 | 0.129701 | ||||||||
\(737\) | −13.7891 | −0.507927 | ||||||||
\(738\) | −4.69402 | −0.172789 | ||||||||
\(739\) | −26.0039 | −0.956569 | −0.478284 | − | 0.878205i | \(-0.658741\pi\) | ||||
−0.478284 | + | 0.878205i | \(0.658741\pi\) | |||||||
\(740\) | 13.3856 | 0.492063 | ||||||||
\(741\) | 5.32626 | 0.195665 | ||||||||
\(742\) | 5.94440 | 0.218226 | ||||||||
\(743\) | 13.4256 | 0.492536 | 0.246268 | − | 0.969202i | \(-0.420796\pi\) | ||||
0.246268 | + | 0.969202i | \(0.420796\pi\) | |||||||
\(744\) | −4.29806 | −0.157575 | ||||||||
\(745\) | −27.1719 | −0.995501 | ||||||||
\(746\) | 21.7486 | 0.796272 | ||||||||
\(747\) | −4.27560 | −0.156436 | ||||||||
\(748\) | 7.56775 | 0.276704 | ||||||||
\(749\) | 8.48436 | 0.310012 | ||||||||
\(750\) | 11.6713 | 0.426175 | ||||||||
\(751\) | 43.2231 | 1.57723 | 0.788616 | − | 0.614886i | \(-0.210798\pi\) | ||||
0.788616 | + | 0.614886i | \(0.210798\pi\) | |||||||
\(752\) | −2.64404 | −0.0964181 | ||||||||
\(753\) | −13.6302 | −0.496714 | ||||||||
\(754\) | 12.0860 | 0.440147 | ||||||||
\(755\) | −15.6832 | −0.570770 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | −11.5253 | −0.418896 | −0.209448 | − | 0.977820i | \(-0.567167\pi\) | ||||
−0.209448 | + | 0.977820i | \(0.567167\pi\) | |||||||
\(758\) | 20.1124 | 0.730517 | ||||||||
\(759\) | 5.91388 | 0.214660 | ||||||||
\(760\) | 5.94405 | 0.215613 | ||||||||
\(761\) | 41.6182 | 1.50866 | 0.754329 | − | 0.656497i | \(-0.227962\pi\) | ||||
0.754329 | + | 0.656497i | \(0.227962\pi\) | |||||||
\(762\) | 4.94951 | 0.179302 | ||||||||
\(763\) | −0.166999 | −0.00604578 | ||||||||
\(764\) | 1.00000 | 0.0361787 | ||||||||
\(765\) | −6.81955 | −0.246561 | ||||||||
\(766\) | −24.0159 | −0.867730 | ||||||||
\(767\) | 13.0176 | 0.470038 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 4.01075 | 0.144631 | 0.0723157 | − | 0.997382i | \(-0.476961\pi\) | ||||
0.0723157 | + | 0.997382i | \(0.476961\pi\) | |||||||
\(770\) | 2.54549 | 0.0917329 | ||||||||
\(771\) | 5.82640 | 0.209833 | ||||||||
\(772\) | 8.73233 | 0.314283 | ||||||||
\(773\) | 47.5493 | 1.71023 | 0.855115 | − | 0.518438i | \(-0.173486\pi\) | ||||
0.855115 | + | 0.518438i | \(0.173486\pi\) | |||||||
\(774\) | −2.40129 | −0.0863127 | ||||||||
\(775\) | −11.6313 | −0.417809 | ||||||||
\(776\) | 3.02861 | 0.108721 | ||||||||
\(777\) | 8.83806 | 0.317064 | ||||||||
\(778\) | 1.60108 | 0.0574016 | ||||||||
\(779\) | −18.4224 | −0.660052 | ||||||||
\(780\) | 2.05542 | 0.0735958 | ||||||||
\(781\) | 11.3547 | 0.406304 | ||||||||
\(782\) | −15.8438 | −0.566571 | ||||||||
\(783\) | 8.90561 | 0.318260 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −0.870956 | −0.0310858 | ||||||||
\(786\) | 12.5335 | 0.447054 | ||||||||
\(787\) | −5.91975 | −0.211016 | −0.105508 | − | 0.994418i | \(-0.533647\pi\) | ||||
−0.105508 | + | 0.994418i | \(0.533647\pi\) | |||||||
\(788\) | −9.75048 | −0.347346 | ||||||||
\(789\) | 31.0461 | 1.10527 | ||||||||
\(790\) | −18.8418 | −0.670362 | ||||||||
\(791\) | 10.7808 | 0.383321 | ||||||||
\(792\) | −1.68070 | −0.0597211 | ||||||||
\(793\) | −6.64626 | −0.236016 | ||||||||
\(794\) | −4.99455 | −0.177250 | ||||||||
\(795\) | 9.00301 | 0.319304 | ||||||||
\(796\) | 14.2985 | 0.506798 | ||||||||
\(797\) | −7.74622 | −0.274385 | −0.137193 | − | 0.990544i | \(-0.543808\pi\) | ||||
−0.137193 | + | 0.990544i | \(0.543808\pi\) | |||||||
\(798\) | 3.92466 | 0.138932 | ||||||||
\(799\) | 11.9054 | 0.421182 | ||||||||
\(800\) | −2.70618 | −0.0956778 | ||||||||
\(801\) | 6.68911 | 0.236348 | ||||||||
\(802\) | 9.77927 | 0.345318 | ||||||||
\(803\) | 7.13436 | 0.251766 | ||||||||
\(804\) | −8.20435 | −0.289345 | ||||||||
\(805\) | −5.32920 | −0.187830 | ||||||||
\(806\) | −5.83301 | −0.205459 | ||||||||
\(807\) | −0.696142 | −0.0245053 | ||||||||
\(808\) | 12.0400 | 0.423566 | ||||||||
\(809\) | 15.2520 | 0.536230 | 0.268115 | − | 0.963387i | \(-0.413599\pi\) | ||||
0.268115 | + | 0.963387i | \(0.413599\pi\) | |||||||
\(810\) | 1.51454 | 0.0532154 | ||||||||
\(811\) | −11.3203 | −0.397508 | −0.198754 | − | 0.980049i | \(-0.563689\pi\) | ||||
−0.198754 | + | 0.980049i | \(0.563689\pi\) | |||||||
\(812\) | 8.90561 | 0.312526 | ||||||||
\(813\) | −31.0053 | −1.08740 | ||||||||
\(814\) | −14.8541 | −0.520637 | ||||||||
\(815\) | 8.39502 | 0.294065 | ||||||||
\(816\) | 4.50273 | 0.157627 | ||||||||
\(817\) | −9.42426 | −0.329713 | ||||||||
\(818\) | 14.4342 | 0.504678 | ||||||||
\(819\) | 1.35713 | 0.0474218 | ||||||||
\(820\) | −7.10927 | −0.248266 | ||||||||
\(821\) | 52.8540 | 1.84462 | 0.922308 | − | 0.386456i | \(-0.126301\pi\) | ||||
0.922308 | + | 0.386456i | \(0.126301\pi\) | |||||||
\(822\) | −19.1587 | −0.668236 | ||||||||
\(823\) | −18.5931 | −0.648115 | −0.324057 | − | 0.946037i | \(-0.605047\pi\) | ||||
−0.324057 | + | 0.946037i | \(0.605047\pi\) | |||||||
\(824\) | −7.62868 | −0.265758 | ||||||||
\(825\) | −4.54828 | −0.158351 | ||||||||
\(826\) | 9.59202 | 0.333749 | ||||||||
\(827\) | −47.1275 | −1.63878 | −0.819391 | − | 0.573235i | \(-0.805688\pi\) | ||||
−0.819391 | + | 0.573235i | \(0.805688\pi\) | |||||||
\(828\) | 3.51870 | 0.122283 | ||||||||
\(829\) | 39.4965 | 1.37177 | 0.685886 | − | 0.727709i | \(-0.259415\pi\) | ||||
0.685886 | + | 0.727709i | \(0.259415\pi\) | |||||||
\(830\) | −6.47556 | −0.224770 | ||||||||
\(831\) | 0.447859 | 0.0155361 | ||||||||
\(832\) | −1.35713 | −0.0470499 | ||||||||
\(833\) | −4.50273 | −0.156010 | ||||||||
\(834\) | 10.0578 | 0.348272 | ||||||||
\(835\) | 27.9610 | 0.967630 | ||||||||
\(836\) | −6.59619 | −0.228134 | ||||||||
\(837\) | −4.29806 | −0.148563 | ||||||||
\(838\) | 3.44484 | 0.119000 | ||||||||
\(839\) | −25.2536 | −0.871850 | −0.435925 | − | 0.899983i | \(-0.643579\pi\) | ||||
−0.435925 | + | 0.899983i | \(0.643579\pi\) | |||||||
\(840\) | 1.51454 | 0.0522565 | ||||||||
\(841\) | 50.3099 | 1.73482 | ||||||||
\(842\) | −7.85560 | −0.270722 | ||||||||
\(843\) | −11.2801 | −0.388507 | ||||||||
\(844\) | 6.00269 | 0.206621 | ||||||||
\(845\) | −16.8995 | −0.581361 | ||||||||
\(846\) | −2.64404 | −0.0909039 | ||||||||
\(847\) | 8.17524 | 0.280905 | ||||||||
\(848\) | −5.94440 | −0.204131 | ||||||||
\(849\) | 5.76688 | 0.197919 | ||||||||
\(850\) | 12.1852 | 0.417948 | ||||||||
\(851\) | 31.0985 | 1.06604 | ||||||||
\(852\) | 6.75595 | 0.231455 | ||||||||
\(853\) | −27.8781 | −0.954528 | −0.477264 | − | 0.878760i | \(-0.658372\pi\) | ||||
−0.477264 | + | 0.878760i | \(0.658372\pi\) | |||||||
\(854\) | −4.89730 | −0.167582 | ||||||||
\(855\) | 5.94405 | 0.203282 | ||||||||
\(856\) | −8.48436 | −0.289989 | ||||||||
\(857\) | 5.58166 | 0.190666 | 0.0953329 | − | 0.995445i | \(-0.469608\pi\) | ||||
0.0953329 | + | 0.995445i | \(0.469608\pi\) | |||||||
\(858\) | −2.28092 | −0.0778695 | ||||||||
\(859\) | −12.4408 | −0.424475 | −0.212238 | − | 0.977218i | \(-0.568075\pi\) | ||||
−0.212238 | + | 0.977218i | \(0.568075\pi\) | |||||||
\(860\) | −3.63685 | −0.124015 | ||||||||
\(861\) | −4.69402 | −0.159972 | ||||||||
\(862\) | −32.8227 | −1.11795 | ||||||||
\(863\) | −2.57187 | −0.0875473 | −0.0437737 | − | 0.999041i | \(-0.513938\pi\) | ||||
−0.0437737 | + | 0.999041i | \(0.513938\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 1.48320 | 0.0504304 | ||||||||
\(866\) | 30.7560 | 1.04513 | ||||||||
\(867\) | −3.27459 | −0.111211 | ||||||||
\(868\) | −4.29806 | −0.145886 | ||||||||
\(869\) | 20.9090 | 0.709290 | ||||||||
\(870\) | 13.4879 | 0.457282 | ||||||||
\(871\) | −11.1343 | −0.377273 | ||||||||
\(872\) | 0.166999 | 0.00565531 | ||||||||
\(873\) | 3.02861 | 0.102503 | ||||||||
\(874\) | 13.8097 | 0.467120 | ||||||||
\(875\) | 11.6713 | 0.394562 | ||||||||
\(876\) | 4.24487 | 0.143421 | ||||||||
\(877\) | 18.9735 | 0.640688 | 0.320344 | − | 0.947301i | \(-0.396201\pi\) | ||||
0.320344 | + | 0.947301i | \(0.396201\pi\) | |||||||
\(878\) | −10.8474 | −0.366082 | ||||||||
\(879\) | 3.05098 | 0.102907 | ||||||||
\(880\) | −2.54549 | −0.0858083 | ||||||||
\(881\) | −1.43436 | −0.0483247 | −0.0241623 | − | 0.999708i | \(-0.507692\pi\) | ||||
−0.0241623 | + | 0.999708i | \(0.507692\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 21.2692 | 0.715766 | 0.357883 | − | 0.933766i | \(-0.383499\pi\) | ||||
0.357883 | + | 0.933766i | \(0.383499\pi\) | |||||||
\(884\) | 6.11077 | 0.205528 | ||||||||
\(885\) | 14.5275 | 0.488335 | ||||||||
\(886\) | −15.0722 | −0.506361 | ||||||||
\(887\) | −26.2972 | −0.882974 | −0.441487 | − | 0.897268i | \(-0.645549\pi\) | ||||
−0.441487 | + | 0.897268i | \(0.645549\pi\) | |||||||
\(888\) | −8.83806 | −0.296586 | ||||||||
\(889\) | 4.94951 | 0.166001 | ||||||||
\(890\) | 10.1309 | 0.339589 | ||||||||
\(891\) | −1.68070 | −0.0563056 | ||||||||
\(892\) | −16.4263 | −0.549993 | ||||||||
\(893\) | −10.3769 | −0.347251 | ||||||||
\(894\) | 17.9407 | 0.600028 | ||||||||
\(895\) | −18.3019 | −0.611765 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 4.77532 | 0.159443 | ||||||||
\(898\) | 33.9640 | 1.13339 | ||||||||
\(899\) | −38.2769 | −1.27660 | ||||||||
\(900\) | −2.70618 | −0.0902059 | ||||||||
\(901\) | 26.7660 | 0.891706 | ||||||||
\(902\) | 7.88925 | 0.262683 | ||||||||
\(903\) | −2.40129 | −0.0799100 | ||||||||
\(904\) | −10.7808 | −0.358564 | ||||||||
\(905\) | −24.3818 | −0.810478 | ||||||||
\(906\) | 10.3551 | 0.344026 | ||||||||
\(907\) | 13.4014 | 0.444986 | 0.222493 | − | 0.974934i | \(-0.428580\pi\) | ||||
0.222493 | + | 0.974934i | \(0.428580\pi\) | |||||||
\(908\) | −18.4802 | −0.613287 | ||||||||
\(909\) | 12.0400 | 0.399342 | ||||||||
\(910\) | 2.05542 | 0.0681364 | ||||||||
\(911\) | −8.53780 | −0.282870 | −0.141435 | − | 0.989948i | \(-0.545172\pi\) | ||||
−0.141435 | + | 0.989948i | \(0.545172\pi\) | |||||||
\(912\) | −3.92466 | −0.129959 | ||||||||
\(913\) | 7.18601 | 0.237822 | ||||||||
\(914\) | −39.9472 | −1.32134 | ||||||||
\(915\) | −7.41715 | −0.245203 | ||||||||
\(916\) | 17.9688 | 0.593705 | ||||||||
\(917\) | 12.5335 | 0.413892 | ||||||||
\(918\) | 4.50273 | 0.148612 | ||||||||
\(919\) | 15.3686 | 0.506964 | 0.253482 | − | 0.967340i | \(-0.418424\pi\) | ||||
0.253482 | + | 0.967340i | \(0.418424\pi\) | |||||||
\(920\) | 5.32920 | 0.175699 | ||||||||
\(921\) | 19.5185 | 0.643158 | ||||||||
\(922\) | 4.14051 | 0.136360 | ||||||||
\(923\) | 9.16868 | 0.301791 | ||||||||
\(924\) | −1.68070 | −0.0552910 | ||||||||
\(925\) | −23.9174 | −0.786398 | ||||||||
\(926\) | −23.7143 | −0.779299 | ||||||||
\(927\) | −7.62868 | −0.250559 | ||||||||
\(928\) | −8.90561 | −0.292341 | ||||||||
\(929\) | −9.79727 | −0.321438 | −0.160719 | − | 0.987000i | \(-0.551381\pi\) | ||||
−0.160719 | + | 0.987000i | \(0.551381\pi\) | |||||||
\(930\) | −6.50957 | −0.213457 | ||||||||
\(931\) | 3.92466 | 0.128626 | ||||||||
\(932\) | 29.5440 | 0.967746 | ||||||||
\(933\) | −5.73920 | −0.187893 | ||||||||
\(934\) | 35.8186 | 1.17202 | ||||||||
\(935\) | 11.4616 | 0.374836 | ||||||||
\(936\) | −1.35713 | −0.0443591 | ||||||||
\(937\) | 15.9801 | 0.522047 | 0.261024 | − | 0.965332i | \(-0.415940\pi\) | ||||
0.261024 | + | 0.965332i | \(0.415940\pi\) | |||||||
\(938\) | −8.20435 | −0.267881 | ||||||||
\(939\) | 17.0827 | 0.557474 | ||||||||
\(940\) | −4.00449 | −0.130612 | ||||||||
\(941\) | −25.1496 | −0.819855 | −0.409927 | − | 0.912118i | \(-0.634446\pi\) | ||||
−0.409927 | + | 0.912118i | \(0.634446\pi\) | |||||||
\(942\) | 0.575064 | 0.0187366 | ||||||||
\(943\) | −16.5168 | −0.537862 | ||||||||
\(944\) | −9.59202 | −0.312194 | ||||||||
\(945\) | 1.51454 | 0.0492679 | ||||||||
\(946\) | 4.03586 | 0.131217 | ||||||||
\(947\) | 21.8948 | 0.711487 | 0.355743 | − | 0.934584i | \(-0.384228\pi\) | ||||
0.355743 | + | 0.934584i | \(0.384228\pi\) | |||||||
\(948\) | 12.4406 | 0.404053 | ||||||||
\(949\) | 5.76083 | 0.187004 | ||||||||
\(950\) | −10.6208 | −0.344585 | ||||||||
\(951\) | 13.1001 | 0.424800 | ||||||||
\(952\) | 4.50273 | 0.145934 | ||||||||
\(953\) | −13.7032 | −0.443891 | −0.221945 | − | 0.975059i | \(-0.571241\pi\) | ||||
−0.221945 | + | 0.975059i | \(0.571241\pi\) | |||||||
\(954\) | −5.94440 | −0.192457 | ||||||||
\(955\) | 1.51454 | 0.0490093 | ||||||||
\(956\) | −8.96693 | −0.290011 | ||||||||
\(957\) | −14.9677 | −0.483836 | ||||||||
\(958\) | −36.2129 | −1.16999 | ||||||||
\(959\) | −19.1587 | −0.618667 | ||||||||
\(960\) | −1.51454 | −0.0488815 | ||||||||
\(961\) | −12.5267 | −0.404086 | ||||||||
\(962\) | −11.9944 | −0.386714 | ||||||||
\(963\) | −8.48436 | −0.273405 | ||||||||
\(964\) | 1.20612 | 0.0388467 | ||||||||
\(965\) | 13.2254 | 0.425742 | ||||||||
\(966\) | 3.51870 | 0.113212 | ||||||||
\(967\) | 41.4536 | 1.33306 | 0.666528 | − | 0.745480i | \(-0.267779\pi\) | ||||
0.666528 | + | 0.745480i | \(0.267779\pi\) | |||||||
\(968\) | −8.17524 | −0.262762 | ||||||||
\(969\) | 17.6717 | 0.567697 | ||||||||
\(970\) | 4.58694 | 0.147278 | ||||||||
\(971\) | −1.22893 | −0.0394382 | −0.0197191 | − | 0.999806i | \(-0.506277\pi\) | ||||
−0.0197191 | + | 0.999806i | \(0.506277\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 10.0578 | 0.322438 | ||||||||
\(974\) | −22.0811 | −0.707525 | ||||||||
\(975\) | −3.67262 | −0.117618 | ||||||||
\(976\) | 4.89730 | 0.156759 | ||||||||
\(977\) | 21.7929 | 0.697215 | 0.348608 | − | 0.937269i | \(-0.386655\pi\) | ||||
0.348608 | + | 0.937269i | \(0.386655\pi\) | |||||||
\(978\) | −5.54296 | −0.177244 | ||||||||
\(979\) | −11.2424 | −0.359308 | ||||||||
\(980\) | 1.51454 | 0.0483801 | ||||||||
\(981\) | 0.166999 | 0.00533188 | ||||||||
\(982\) | 3.79385 | 0.121067 | ||||||||
\(983\) | 17.0163 | 0.542734 | 0.271367 | − | 0.962476i | \(-0.412524\pi\) | ||||
0.271367 | + | 0.962476i | \(0.412524\pi\) | |||||||
\(984\) | 4.69402 | 0.149640 | ||||||||
\(985\) | −14.7675 | −0.470530 | ||||||||
\(986\) | 40.0996 | 1.27703 | ||||||||
\(987\) | −2.64404 | −0.0841606 | ||||||||
\(988\) | −5.32626 | −0.169451 | ||||||||
\(989\) | −8.44943 | −0.268676 | ||||||||
\(990\) | −2.54549 | −0.0809008 | ||||||||
\(991\) | 36.3089 | 1.15339 | 0.576696 | − | 0.816959i | \(-0.304342\pi\) | ||||
0.576696 | + | 0.816959i | \(0.304342\pi\) | |||||||
\(992\) | 4.29806 | 0.136464 | ||||||||
\(993\) | 17.3251 | 0.549794 | ||||||||
\(994\) | 6.75595 | 0.214286 | ||||||||
\(995\) | 21.6557 | 0.686531 | ||||||||
\(996\) | 4.27560 | 0.135478 | ||||||||
\(997\) | 46.0938 | 1.45980 | 0.729902 | − | 0.683551i | \(-0.239566\pi\) | ||||
0.729902 | + | 0.683551i | \(0.239566\pi\) | |||||||
\(998\) | 29.5409 | 0.935101 | ||||||||
\(999\) | −8.83806 | −0.279624 |
(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 | 8022.2.a.q.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8022.2.a.q.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial |