Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1064,2,Mod(1,1064)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1064, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1064.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1064 = 2^{3} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1064.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: | \(8.49608277506\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1064.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.381966 | −0.220528 | −0.110264 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110264 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.85410 | −1.16206 | −0.581028 | − | 0.813884i | \(-0.697349\pi\) | ||||
−0.581028 | + | 0.813884i | \(0.697349\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.23607 | −1.72957 | −0.864787 | − | 0.502139i | \(-0.832547\pi\) | ||||
−0.864787 | + | 0.502139i | \(0.832547\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.854102 | −0.220528 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.85410 | −1.41983 | −0.709914 | − | 0.704288i | \(-0.751266\pi\) | ||||
−0.709914 | + | 0.704288i | \(0.751266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.381966 | −0.0833518 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.76393 | 0.367805 | 0.183903 | − | 0.982944i | \(-0.441127\pi\) | ||||
0.183903 | + | 0.982944i | \(0.441127\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.61803 | −1.22894 | −0.614469 | − | 0.788941i | \(-0.710630\pi\) | ||||
−0.614469 | + | 0.788941i | \(0.710630\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.61803 | −0.829423 | −0.414712 | − | 0.909953i | \(-0.636118\pi\) | ||||
−0.414712 | + | 0.909953i | \(0.636118\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.47214 | 0.256266 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.23607 | 0.377964 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.47214 | −1.22841 | −0.614206 | − | 0.789146i | \(-0.710524\pi\) | ||||
−0.614206 | + | 0.789146i | \(0.710524\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.38197 | 0.381420 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.56231 | 1.49338 | 0.746691 | − | 0.665171i | \(-0.231642\pi\) | ||||
0.746691 | + | 0.665171i | \(0.231642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9443 | 1.66899 | 0.834493 | − | 0.551019i | \(-0.185761\pi\) | ||||
0.834493 | + | 0.551019i | \(0.185761\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.38197 | −0.951367 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.00000 | 1.02105 | 0.510527 | − | 0.859861i | \(-0.329450\pi\) | ||||
0.510527 | + | 0.859861i | \(0.329450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.23607 | 0.313112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.85410 | 0.666762 | 0.333381 | − | 0.942792i | \(-0.391810\pi\) | ||||
0.333381 | + | 0.942792i | \(0.391810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.61803 | −1.16206 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.381966 | −0.0505926 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.70820 | 0.352578 | 0.176289 | − | 0.984338i | \(-0.443591\pi\) | ||||
0.176289 | + | 0.984338i | \(0.443591\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.708204 | 0.0906762 | 0.0453381 | − | 0.998972i | \(-0.485563\pi\) | ||||
0.0453381 | + | 0.998972i | \(0.485563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.85410 | −0.359583 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.9443 | −1.72957 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.38197 | −0.413173 | −0.206586 | − | 0.978428i | \(-0.566235\pi\) | ||||
−0.206586 | + | 0.978428i | \(0.566235\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.673762 | −0.0811114 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.9443 | −1.65488 | −0.827440 | − | 0.561554i | \(-0.810204\pi\) | ||||
−0.827440 | + | 0.561554i | \(0.810204\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.85410 | −0.802212 | −0.401106 | − | 0.916032i | \(-0.631374\pi\) | ||||
−0.401106 | + | 0.916032i | \(0.631374\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.85410 | −0.439216 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.47214 | 0.503155 | 0.251577 | − | 0.967837i | \(-0.419051\pi\) | ||||
0.251577 | + | 0.967837i | \(0.419051\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.6180 | −1.49477 | −0.747387 | − | 0.664389i | \(-0.768692\pi\) | ||||
−0.747387 | + | 0.664389i | \(0.768692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.0902 | −1.41983 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.52786 | 0.271015 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.23607 | 0.555022 | 0.277511 | − | 0.960722i | \(-0.410490\pi\) | ||||
0.277511 | + | 0.960722i | \(0.410490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.23607 | −0.653718 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.76393 | 0.182911 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.23607 | 0.229416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.23607 | −0.836246 | −0.418123 | − | 0.908390i | \(-0.637312\pi\) | ||||
−0.418123 | + | 0.908390i | \(0.637312\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.0000 | 1.10554 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.00000 | 0.0995037 | 0.0497519 | − | 0.998762i | \(-0.484157\pi\) | ||||
0.0497519 | + | 0.998762i | \(0.484157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.76393 | 0.370871 | 0.185436 | − | 0.982656i | \(-0.440630\pi\) | ||||
0.185436 | + | 0.982656i | \(0.440630\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.854102 | −0.0833518 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.94427 | −0.381307 | −0.190654 | − | 0.981657i | \(-0.561061\pi\) | ||||
−0.190654 | + | 0.981657i | \(0.561061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.76393 | −0.552085 | −0.276042 | − | 0.961145i | \(-0.589023\pi\) | ||||
−0.276042 | + | 0.961145i | \(0.589023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.85410 | 0.270899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.85410 | −0.832924 | −0.416462 | − | 0.909153i | \(-0.636730\pi\) | ||||
−0.416462 | + | 0.909153i | \(0.636730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.94427 | 0.367805 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.7984 | 1.64546 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.85410 | −0.536645 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.85410 | 0.350373 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.65248 | −0.329333 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.7082 | 1.39388 | 0.696939 | − | 0.717131i | \(-0.254545\pi\) | ||||
0.696939 | + | 0.717131i | \(0.254545\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.18034 | −0.368058 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.7984 | −1.29294 | −0.646470 | − | 0.762939i | \(-0.723755\pi\) | ||||
−0.646470 | + | 0.762939i | \(0.723755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.00000 | 0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.52786 | −0.214411 | −0.107205 | − | 0.994237i | \(-0.534190\pi\) | ||||
−0.107205 | + | 0.994237i | \(0.534190\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.67376 | −0.225171 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.0344 | 2.00986 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.7984 | −1.22894 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.381966 | −0.0315040 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.4721 | 1.75907 | 0.879533 | − | 0.475838i | \(-0.157855\pi\) | ||||
0.879533 | + | 0.475838i | \(0.157855\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.14590 | −0.174631 | −0.0873154 | − | 0.996181i | \(-0.527829\pi\) | ||||
−0.0873154 | + | 0.996181i | \(0.527829\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.7082 | 1.35078 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.3262 | −0.829423 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.85410 | 0.307591 | 0.153795 | − | 0.988103i | \(-0.450850\pi\) | ||||
0.153795 | + | 0.988103i | \(0.450850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.85410 | −0.147040 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.76393 | 0.139017 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.09017 | 0.320367 | 0.160183 | − | 0.987087i | \(-0.448791\pi\) | ||||
0.160183 | + | 0.987087i | \(0.448791\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.29180 | 0.256266 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.4721 | 1.04251 | 0.521253 | − | 0.853402i | \(-0.325465\pi\) | ||||
0.521253 | + | 0.853402i | \(0.325465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.8885 | 1.99143 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.85410 | −0.218259 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.291796 | 0.0221848 | 0.0110924 | − | 0.999938i | \(-0.496469\pi\) | ||||
0.0110924 | + | 0.999938i | \(0.496469\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.03444 | −0.0777534 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.7984 | 1.85352 | 0.926759 | − | 0.375657i | \(-0.122583\pi\) | ||||
0.926759 | + | 0.375657i | \(0.122583\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.6180 | −1.68119 | −0.840593 | − | 0.541668i | \(-0.817793\pi\) | ||||
−0.840593 | + | 0.541668i | \(0.817793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.270510 | −0.0199967 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.7082 | −1.22841 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.5623 | 1.64992 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.23607 | 0.162650 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.03444 | 0.364279 | 0.182140 | − | 0.983273i | \(-0.441698\pi\) | ||||
0.182140 | + | 0.983273i | \(0.441698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.145898 | 0.0105020 | 0.00525099 | − | 0.999986i | \(-0.498329\pi\) | ||||
0.00525099 | + | 0.999986i | \(0.498329\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.32624 | 0.381420 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.56231 | 0.325051 | 0.162525 | − | 0.986704i | \(-0.448036\pi\) | ||||
0.162525 | + | 0.986704i | \(0.448036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.9443 | −1.27204 | −0.636018 | − | 0.771674i | \(-0.719420\pi\) | ||||
−0.636018 | + | 0.771674i | \(0.719420\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.29180 | 0.0911163 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.61803 | −0.464495 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.3820 | 1.49338 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.03444 | −0.349918 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.85410 | −0.266594 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.43769 | −0.0989749 | −0.0494875 | − | 0.998775i | \(-0.515759\pi\) | ||||
−0.0494875 | + | 0.998775i | \(0.515759\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.32624 | 0.364948 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.4721 | 1.66899 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.61803 | −0.313493 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.61803 | 0.176910 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.5066 | 2.45570 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0557 | −0.673381 | −0.336691 | − | 0.941615i | \(-0.609308\pi\) | ||||
−0.336691 | + | 0.941615i | \(0.609308\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.20163 | −0.0797547 | −0.0398774 | − | 0.999205i | \(-0.512697\pi\) | ||||
−0.0398774 | + | 0.999205i | \(0.512697\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.8328 | −1.64100 | −0.820499 | − | 0.571647i | \(-0.806304\pi\) | ||||
−0.820499 | + | 0.571647i | \(0.806304\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.47214 | 0.0968594 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.7984 | 0.707425 | 0.353712 | − | 0.935354i | \(-0.384919\pi\) | ||||
0.353712 | + | 0.935354i | \(0.384919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.6525 | 1.02105 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.70820 | −0.110960 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.29180 | 0.601036 | 0.300518 | − | 0.953776i | \(-0.402840\pi\) | ||||
0.300518 | + | 0.953776i | \(0.402840\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.1246 | −1.61842 | −0.809209 | − | 0.587521i | \(-0.800104\pi\) | ||||
−0.809209 | + | 0.587521i | \(0.800104\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.65248 | −0.619207 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.23607 | 0.142857 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.23607 | −0.396792 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.20163 | 0.329640 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.9787 | −1.19793 | −0.598963 | − | 0.800777i | \(-0.704420\pi\) | ||||
−0.598963 | + | 0.800777i | \(0.704420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.79837 | −0.427410 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.00000 | 0.313112 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.90983 | 0.493402 | 0.246701 | − | 0.969092i | \(-0.420654\pi\) | ||||
0.246701 | + | 0.969092i | \(0.420654\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.47214 | −0.464296 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.8885 | 1.16917 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.3262 | 1.68501 | 0.842504 | − | 0.538690i | \(-0.181081\pi\) | ||||
0.842504 | + | 0.538690i | \(0.181081\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.8541 | 0.666762 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.00000 | −0.122398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.14590 | −0.557635 | −0.278818 | − | 0.960344i | \(-0.589942\pi\) | ||||
−0.278818 | + | 0.960344i | \(0.589942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0344 | 0.731040 | 0.365520 | − | 0.930803i | \(-0.380891\pi\) | ||||
0.365520 | + | 0.930803i | \(0.380891\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.38197 | 0.144163 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.6525 | −0.640045 | −0.320023 | − | 0.947410i | \(-0.603691\pi\) | ||||
−0.320023 | + | 0.947410i | \(0.603691\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.1803 | 0.789086 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.2361 | −0.729943 | −0.364971 | − | 0.931019i | \(-0.618921\pi\) | ||||
−0.364971 | + | 0.931019i | \(0.618921\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.79837 | −0.344678 | −0.172339 | − | 0.985038i | \(-0.555132\pi\) | ||||
−0.172339 | + | 0.985038i | \(0.555132\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.854102 | −0.0505926 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.56231 | 0.564445 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.2705 | 1.01591 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.14590 | 0.184416 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.0000 | −1.34367 | −0.671837 | − | 0.740699i | \(-0.734495\pi\) | ||||
−0.671837 | + | 0.740699i | \(0.734495\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.05573 | 0.352578 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.61803 | −0.500069 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.0000 | −0.636146 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.9443 | 0.630817 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.381966 | −0.0219434 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.58359 | 0.0906762 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.2705 | −1.21397 | −0.606986 | − | 0.794712i | \(-0.707622\pi\) | ||||
−0.606986 | + | 0.794712i | \(0.707622\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.43769 | −0.0817876 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.5066 | 0.709183 | 0.354591 | − | 0.935021i | \(-0.384620\pi\) | ||||
0.354591 | + | 0.935021i | \(0.384620\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.5967 | 1.55986 | 0.779930 | − | 0.625867i | \(-0.215255\pi\) | ||||
0.779930 | + | 0.625867i | \(0.215255\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.38197 | −0.359583 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34.3607 | −1.92989 | −0.964944 | − | 0.262456i | \(-0.915468\pi\) | ||||
−0.964944 | + | 0.262456i | \(0.915468\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.5066 | 1.42809 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.50658 | 0.0840890 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.85410 | −0.325731 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.20163 | 0.121750 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.00000 | 0.385922 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.6180 | −1.84781 | −0.923907 | − | 0.382617i | \(-0.875023\pi\) | ||||
−0.923907 | + | 0.382617i | \(0.875023\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.3262 | 1.16867 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.56231 | −0.413173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.8541 | −1.84415 | −0.922075 | − | 0.387011i | \(-0.873508\pi\) | ||||
−0.922075 | + | 0.387011i | \(0.873508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.38197 | 0.183683 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.7984 | 0.963836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.50658 | −0.0811114 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0344 | −0.807091 | −0.403546 | − | 0.914960i | \(-0.632222\pi\) | ||||
−0.403546 | + | 0.914960i | \(0.632222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.0344 | 1.12595 | 0.562974 | − | 0.826475i | \(-0.309657\pi\) | ||||
0.562974 | + | 0.826475i | \(0.309657\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.9443 | −0.744290 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.9787 | 1.01014 | 0.505068 | − | 0.863080i | \(-0.331468\pi\) | ||||
0.505068 | + | 0.863080i | \(0.331468\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.1803 | −1.65488 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.23607 | 0.118345 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.6180 | 1.61596 | 0.807979 | − | 0.589211i | \(-0.200561\pi\) | ||||
0.807979 | + | 0.589211i | \(0.200561\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.47214 | −0.0772671 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.3262 | −0.802212 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1803 | −1.21000 | −0.605002 | − | 0.796224i | \(-0.706828\pi\) | ||||
−0.605002 | + | 0.796224i | \(0.706828\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.2918 | −1.42075 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.85410 | 0.252012 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0902 | 1.04023 | 0.520115 | − | 0.854096i | \(-0.325889\pi\) | ||||
0.520115 | + | 0.854096i | \(0.325889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.27051 | 0.220528 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.2705 | 2.12554 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6525 | −1.11221 | −0.556106 | − | 0.831111i | \(-0.687705\pi\) | ||||
−0.556106 | + | 0.831111i | \(0.687705\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | −0.307389 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.76393 | −0.192328 | −0.0961640 | − | 0.995366i | \(-0.530657\pi\) | ||||
−0.0961640 | + | 0.995366i | \(0.530657\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.61803 | −0.439216 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −31.2361 | −1.58782 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.32624 | 0.219349 | 0.109674 | − | 0.993968i | \(-0.465019\pi\) | ||||
0.109674 | + | 0.993968i | \(0.465019\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3262 | −0.522220 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.65248 | 0.285130 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.0000 | 0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.7639 | 0.941735 | 0.470867 | − | 0.882204i | \(-0.343941\pi\) | ||||
0.470867 | + | 0.882204i | \(0.343941\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.381966 | −0.0191222 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.506578 | 0.0252973 | 0.0126486 | − | 0.999920i | \(-0.495974\pi\) | ||||
0.0126486 | + | 0.999920i | \(0.495974\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.7984 | 1.43455 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.2361 | 0.856467 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.7984 | 1.42748 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.85410 | −0.437807 | −0.218904 | − | 0.975746i | \(-0.570248\pi\) | ||||
−0.218904 | + | 0.975746i | \(0.570248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.763932 | −0.0376820 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.70820 | 0.133262 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.4508 | −1.49477 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.965558 | 0.0472836 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.3050 | −1.38279 | −0.691394 | − | 0.722478i | \(-0.743003\pi\) | ||||
−0.691394 | + | 0.722478i | \(0.743003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.9443 | −0.679602 | −0.339801 | − | 0.940497i | \(-0.610360\pi\) | ||||
−0.339801 | + | 0.940497i | \(0.610360\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.9787 | −0.971398 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.708204 | 0.0342724 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.18034 | −0.443231 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.8885 | 1.34334 | 0.671672 | − | 0.740849i | \(-0.265576\pi\) | ||||
0.671672 | + | 0.740849i | \(0.265576\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00000 | 0.336399 | 0.168199 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168199 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.65248 | 0.271015 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.76393 | 0.0843803 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.8885 | −1.23559 | −0.617796 | − | 0.786338i | \(-0.711974\pi\) | ||||
−0.617796 | + | 0.786338i | \(0.711974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.85410 | −0.135910 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.2148 | 1.38804 | 0.694018 | − | 0.719958i | \(-0.255839\pi\) | ||||
0.694018 | + | 0.719958i | \(0.255839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.7082 | 0.555022 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.20163 | −0.387924 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.3820 | 0.489955 | 0.244978 | − | 0.969529i | \(-0.421219\pi\) | ||||
0.244978 | + | 0.969529i | \(0.421219\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.8541 | −1.73539 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.819660 | 0.0385110 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.9443 | −0.653718 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.9230 | 1.91430 | 0.957148 | − | 0.289598i | \(-0.0935217\pi\) | ||||
0.957148 | + | 0.289598i | \(0.0935217\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.0902 | −0.610997 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.9787 | −0.744203 | −0.372101 | − | 0.928192i | \(-0.621363\pi\) | ||||
−0.372101 | + | 0.928192i | \(0.621363\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.3607 | −1.08566 | −0.542831 | − | 0.839842i | \(-0.682648\pi\) | ||||
−0.542831 | + | 0.839842i | \(0.682648\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.94427 | 0.182911 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.9098 | −1.29151 | −0.645756 | − | 0.763543i | \(-0.723458\pi\) | ||||
−0.645756 | + | 0.763543i | \(0.723458\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.38197 | −0.156165 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.47214 | −0.0678324 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −42.1803 | −1.93945 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.8541 | −0.634336 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.7426 | 1.63312 | 0.816562 | − | 0.577258i | \(-0.195877\pi\) | ||||
0.816562 | + | 0.577258i | \(0.195877\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 46.5967 | 2.12463 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.673762 | −0.0306572 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.4164 | −0.836246 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.88854 | 0.402778 | 0.201389 | − | 0.979511i | \(-0.435454\pi\) | ||||
0.201389 | + | 0.979511i | \(0.435454\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.56231 | −0.0706499 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.9443 | −0.764684 | −0.382342 | − | 0.924021i | \(-0.624882\pi\) | ||||
−0.382342 | + | 0.924021i | \(0.624882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.7426 | 1.74488 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 24.5967 | 1.10554 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.9443 | −0.625486 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.6180 | −0.699159 | −0.349580 | − | 0.936907i | \(-0.613676\pi\) | ||||
−0.349580 | + | 0.936907i | \(0.613676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.14590 | −0.229902 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.23607 | 0.0995037 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.88854 | −0.439166 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.4721 | 1.43930 | 0.719651 | − | 0.694336i | \(-0.244302\pi\) | ||||
0.719651 | + | 0.694336i | \(0.244302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.85410 | −0.303208 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.23607 | 0.0987248 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.41641 | 0.370871 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.9787 | −1.18652 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.111456 | −0.00489238 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.8885 | 0.915144 | 0.457572 | − | 0.889173i | \(-0.348719\pi\) | ||||
0.457572 | + | 0.889173i | \(0.348719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.94427 | −0.172471 | −0.0862355 | − | 0.996275i | \(-0.527484\pi\) | ||||
−0.0862355 | + | 0.996275i | \(0.527484\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.0344 | 1.17764 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.8885 | −0.864719 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.72949 | −0.335431 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −59.6312 | −2.58291 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.81966 | −0.381307 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.47214 | −0.408753 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.85410 | −0.166008 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.94427 | −0.126584 | −0.0632921 | − | 0.997995i | \(-0.520160\pi\) | ||||
−0.0632921 | + | 0.997995i | \(0.520160\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.63932 | 0.370749 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.8885 | −0.552085 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.03444 | 0.215257 | 0.107629 | − | 0.994191i | \(-0.465674\pi\) | ||||
0.107629 | + | 0.994191i | \(0.465674\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.02129 | −0.0862664 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.61803 | −0.281938 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.47214 | 0.190175 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.38197 | 0.270899 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.0902 | 0.724134 | 0.362067 | − | 0.932152i | \(-0.382071\pi\) | ||||
0.362067 | + | 0.932152i | \(0.382071\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −68.2492 | −2.88663 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.61803 | −0.363854 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2361 | 0.768559 | 0.384279 | − | 0.923217i | \(-0.374450\pi\) | ||||
0.384279 | + | 0.923217i | \(0.374450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.7984 | −0.832924 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.70820 | 0.323714 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.3607 | −1.14702 | −0.573510 | − | 0.819199i | \(-0.694419\pi\) | ||||
−0.573510 | + | 0.819199i | \(0.694419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.0000 | 0.711428 | 0.355714 | − | 0.934595i | \(-0.384238\pi\) | ||||
0.355714 | + | 0.934595i | \(0.384238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.92299 | −0.0803339 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.2148 | −1.54927 | −0.774636 | − | 0.632408i | \(-0.782067\pi\) | ||||
−0.774636 | + | 0.632408i | \(0.782067\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.0557281 | −0.00231598 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.6180 | −0.564971 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.7082 | −0.774815 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 39.7984 | 1.64546 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.472136 | 0.0194871 | 0.00974357 | − | 0.999953i | \(-0.496898\pi\) | ||||
0.00974357 | + | 0.999953i | \(0.496898\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.61803 | −0.190283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.74265 | −0.0716829 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.7771 | 1.75664 | 0.878322 | − | 0.478069i | \(-0.158663\pi\) | ||||
0.878322 | + | 0.478069i | \(0.158663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.0902 | −0.536645 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.85410 | 0.280520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.6869 | −1.13126 | −0.565628 | − | 0.824660i | \(-0.691366\pi\) | ||||
−0.565628 | + | 0.824660i | \(0.691366\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.7426 | −1.33560 | −0.667800 | − | 0.744341i | \(-0.732764\pi\) | ||||
−0.667800 | + | 0.744341i | \(0.732764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.65248 | 0.393079 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.61803 | 0.350373 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.1803 | −0.778506 | −0.389253 | − | 0.921131i | \(-0.627267\pi\) | ||||
−0.389253 | + | 0.921131i | \(0.627267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.52786 | 0.102434 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.6525 | −1.76599 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.3820 | 0.500103 | 0.250051 | − | 0.968233i | \(-0.419552\pi\) | ||||
0.250051 | + | 0.968233i | \(0.419552\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.16718 | −0.329333 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.27051 | 0.131666 | 0.0658329 | − | 0.997831i | \(-0.479030\pi\) | ||||
0.0658329 | + | 0.997831i | \(0.479030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.6869 | 1.19322 | 0.596609 | − | 0.802532i | \(-0.296514\pi\) | ||||
0.596609 | + | 0.802532i | \(0.296514\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.94427 | 0.158278 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.23607 | 0.209779 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.47214 | 0.0587914 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.7426 | 1.74413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.9443 | 1.82901 | 0.914506 | − | 0.404572i | \(-0.132579\pi\) | ||||
0.914506 | + | 0.404572i | \(0.132579\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.549150 | 0.0218268 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.1246 | 1.39388 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.23607 | −0.247082 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 39.7984 | 1.57440 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.6180 | −0.419387 | −0.209694 | − | 0.977767i | \(-0.567247\pi\) | ||||
−0.209694 | + | 0.977767i | \(0.567247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.76393 | 0.0695627 | 0.0347813 | − | 0.999395i | \(-0.488927\pi\) | ||||
0.0347813 | + | 0.999395i | \(0.488927\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.34752 | −0.368058 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.3607 | −0.839775 | −0.419887 | − | 0.907576i | \(-0.637930\pi\) | ||||
−0.419887 | + | 0.907576i | \(0.637930\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.4377 | −0.409715 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.76393 | 0.0691339 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.5967 | 0.962545 | 0.481273 | − | 0.876571i | \(-0.340175\pi\) | ||||
0.481273 | + | 0.876571i | \(0.340175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.0902 | −1.29294 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.5623 | 0.763198 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 51.1591 | 1.99287 | 0.996437 | − | 0.0843417i | \(-0.0268787\pi\) | ||||
0.996437 | + | 0.0843417i | \(0.0268787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.3050 | −0.906458 | −0.453229 | − | 0.891394i | \(-0.649728\pi\) | ||||
−0.453229 | + | 0.891394i | \(0.649728\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.9443 | −0.541551 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.23607 | 0.0867110 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.6738 | −0.452010 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.84095 | 0.148500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.72949 | −0.105371 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5623 | 0.407147 | 0.203573 | − | 0.979060i | \(-0.434744\pi\) | ||||
0.203573 | + | 0.979060i | \(0.434744\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.0344 | −0.577821 | −0.288910 | − | 0.957356i | \(-0.593293\pi\) | ||||
−0.288910 | + | 0.957356i | \(0.593293\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.23607 | −0.316071 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.458980 | 0.0175882 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.7771 | −1.25418 | −0.627090 | − | 0.778947i | \(-0.715754\pi\) | ||||
−0.627090 | + | 0.778947i | \(0.715754\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.47214 | 0.170872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.48529 | 0.361886 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.2705 | −1.15321 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.1803 | −1.07203 | −0.536015 | − | 0.844208i | \(-0.680071\pi\) | ||||
−0.536015 | + | 0.844208i | \(0.680071\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.0000 | 0.417855 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.65248 | −0.214411 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −55.9787 | −2.12034 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.12461 | −0.156007 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.8328 | −1.61777 | −0.808887 | − | 0.587965i | \(-0.799929\pi\) | ||||
−0.808887 | + | 0.587965i | \(0.799929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.47214 | −0.281817 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.97871 | −0.225171 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.00000 | 0.0376089 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.2918 | −1.40052 | −0.700261 | − | 0.713887i | \(-0.746933\pi\) | ||||
−0.700261 | + | 0.713887i | \(0.746933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.7639 | −0.478685 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.14590 | −0.305066 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 53.7426 | 2.00986 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.54915 | −0.132545 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.3050 | −1.09289 | −0.546445 | − | 0.837495i | \(-0.684019\pi\) | ||||
−0.546445 | + | 0.837495i | \(0.684019\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.76393 | 0.140176 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.59675 | 0.356907 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.5410 | 0.947264 | 0.473632 | − | 0.880723i | \(-0.342943\pi\) | ||||
0.473632 | + | 0.880723i | \(0.342943\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −64.0689 | −2.36967 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.3607 | −1.19527 | −0.597634 | − | 0.801769i | \(-0.703893\pi\) | ||||
−0.597634 | + | 0.801769i | \(0.703893\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.854102 | −0.0315040 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.0344 | 0.480130 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.59675 | −0.316236 | −0.158118 | − | 0.987420i | \(-0.550543\pi\) | ||||
−0.158118 | + | 0.987420i | \(0.550543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.38197 | 0.0875037 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.8885 | 1.64680 | 0.823400 | − | 0.567461i | \(-0.192074\pi\) | ||||
0.823400 | + | 0.567461i | \(0.192074\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.0132 | 1.75907 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 38.8673 | 1.42208 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.94427 | −0.144121 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.9098 | −0.872482 | −0.436241 | − | 0.899830i | \(-0.643690\pi\) | ||||
−0.436241 | + | 0.899830i | \(0.643690\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.24922 | 0.264176 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.79837 | −0.174631 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.3607 | 1.83039 | 0.915195 | − | 0.403011i | \(-0.132036\pi\) | ||||
0.915195 | + | 0.403011i | \(0.132036\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.59675 | 0.0942560 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.2361 | 1.09606 | 0.548028 | − | 0.836460i | \(-0.315379\pi\) | ||||
0.548028 | + | 0.836460i | \(0.315379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.76393 | −0.208668 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 37.3607 | 1.35078 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.8885 | −0.609810 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.9443 | −1.04376 | −0.521879 | − | 0.853020i | \(-0.674769\pi\) | ||||
−0.521879 | + | 0.853020i | \(0.674769\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.02129 | −0.108809 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.76393 | 0.315217 | 0.157608 | − | 0.987502i | \(-0.449622\pi\) | ||||
0.157608 | + | 0.987502i | \(0.449622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.85410 | 0.102390 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.56231 | 0.342605 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53.7426 | 1.92306 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.7984 | −0.528851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.61803 | 0.307591 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.7214 | −1.30898 | −0.654488 | − | 0.756073i | \(-0.727116\pi\) | ||||
−0.654488 | + | 0.756073i | \(0.727116\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.4377 | −0.371592 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.85410 | −0.314816 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.41641 | −0.156831 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.14590 | −0.147040 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.7984 | 0.949247 | 0.474624 | − | 0.880189i | \(-0.342584\pi\) | ||||
0.474624 | + | 0.880189i | \(0.342584\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.9787 | −1.44972 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.9443 | −0.528030 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.4164 | 0.932215 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.94427 | 0.139017 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.49342 | 0.122974 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.2361 | −0.781779 | −0.390889 | − | 0.920438i | \(-0.627832\pi\) | ||||
−0.390889 | + | 0.920438i | \(0.627832\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.2492 | 1.13242 | 0.566212 | − | 0.824260i | \(-0.308408\pi\) | ||||
0.566212 | + | 0.824260i | \(0.308408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.59675 | −0.161215 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.14590 | 0.320367 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9443 | 0.382892 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.7984 | 0.621926 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.8328 | 0.517669 | 0.258834 | − | 0.965922i | \(-0.416662\pi\) | ||||
0.258834 | + | 0.965922i | \(0.416662\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.2918 | 0.777043 | 0.388522 | − | 0.921440i | \(-0.372986\pi\) | ||||
0.388522 | + | 0.921440i | \(0.372986\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.3050 | −0.636526 | −0.318263 | − | 0.948003i | \(-0.603099\pi\) | ||||
−0.318263 | + | 0.948003i | \(0.603099\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.4164 | −1.36899 | −0.684494 | − | 0.729018i | \(-0.739977\pi\) | ||||
−0.684494 | + | 0.729018i | \(0.739977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.06888 | 0.141148 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.85410 | −0.202833 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.1246 | 1.04251 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.3262 | −0.356927 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.52786 | 0.0527477 | 0.0263739 | − | 0.999652i | \(-0.491604\pi\) | ||||
0.0263739 | + | 0.999652i | \(0.491604\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.7984 | 0.510289 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.67376 | 0.160973 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 57.8885 | 1.99143 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.85410 | 0.132429 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.21478 | 0.0760111 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.1803 | −0.451816 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.0476 | 1.85055 | 0.925277 | − | 0.379291i | \(-0.123832\pi\) | ||||
0.925277 | + | 0.379291i | \(0.123832\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.38197 | −0.218259 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.8541 | 1.08812 | 0.544058 | − | 0.839048i | \(-0.316887\pi\) | ||||
0.544058 | + | 0.839048i | \(0.316887\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.2148 | −0.485002 | −0.242501 | − | 0.970151i | \(-0.577968\pi\) | ||||
−0.242501 | + | 0.970151i | \(0.577968\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.65248 | −0.124476 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.0344 | 0.716021 | 0.358010 | − | 0.933718i | \(-0.383455\pi\) | ||||
0.358010 | + | 0.933718i | \(0.383455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.652476 | 0.0221848 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.59675 | −0.224037 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.2361 | −0.584694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.0902 | 0.714613 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.5066 | 0.795577 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1803 | −0.377964 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.2918 | 0.550135 | 0.275067 | − | 0.961425i | \(-0.411300\pi\) | ||||
0.275067 | + | 0.961425i | \(0.411300\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.78522 | 0.296318 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.2705 | −0.682931 | −0.341465 | − | 0.939894i | \(-0.610923\pi\) | ||||
−0.341465 | + | 0.939894i | \(0.610923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.1246 | 1.21569 | 0.607845 | − | 0.794056i | \(-0.292034\pi\) | ||||
0.607845 | + | 0.794056i | \(0.292034\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.31308 | −0.0777534 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.5279 | 0.420645 | 0.210322 | − | 0.977632i | \(-0.432549\pi\) | ||||
0.210322 | + | 0.977632i | \(0.432549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.7082 | 0.526836 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.7082 | −0.995262 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.00000 | 0.234246 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55.4508 | 1.85352 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.20163 | 0.140288 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.5623 | 1.01931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.4164 | −0.946688 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.18034 | −0.139113 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −50.5755 | −1.68119 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.8197 | −0.624897 | −0.312448 | − | 0.949935i | \(-0.601149\pi\) | ||||
−0.312448 | + | 0.949935i | \(0.601149\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.85410 | −0.0946646 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5279 | 0.779513 | 0.389756 | − | 0.920918i | \(-0.372559\pi\) | ||||
0.389756 | + | 0.920918i | \(0.372559\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.4853 | 1.73701 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.604878 | −0.0199967 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.7984 | −0.488685 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.1935 | −1.39183 | −0.695917 | − | 0.718122i | \(-0.745002\pi\) | ||||
−0.695917 | + | 0.718122i | \(0.745002\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.12461 | 0.267715 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 86.9574 | 2.86224 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.7426 | −0.352835 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.7426 | −0.746162 | −0.373081 | − | 0.927799i | \(-0.621699\pi\) | ||||
−0.373081 | + | 0.927799i | \(0.621699\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.77709 | −0.156395 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.4508 | 1.64992 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.6738 | 0.773388 | 0.386694 | − | 0.922208i | \(-0.373617\pi\) | ||||
0.386694 | + | 0.922208i | \(0.373617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.5410 | −0.343993 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −58.9443 | −1.92153 | −0.960764 | − | 0.277367i | \(-0.910538\pi\) | ||||
−0.960764 | + | 0.277367i | \(0.910538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.8673 | 0.549273 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.00000 | 0.162650 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.5623 | 1.31810 | 0.659049 | − | 0.752100i | \(-0.270959\pi\) | ||||
0.659049 | + | 0.752100i | \(0.270959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.7426 | 1.38748 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.1246 | 0.425595 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −60.2837 | −1.95278 | −0.976390 | − | 0.216016i | \(-0.930694\pi\) | ||||
−0.976390 | + | 0.216016i | \(0.930694\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.2574 | 0.364279 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.74265 | −0.314935 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.00000 | 0.0645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.67376 | −0.312057 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.2574 | 0.362763 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.326238 | 0.0105020 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.8541 | 1.47457 | 0.737284 | − | 0.675583i | \(-0.236108\pi\) | ||||
0.737284 | + | 0.675583i | \(0.236108\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.23607 | 0.0718329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.2361 | −1.03450 | −0.517252 | − | 0.855833i | \(-0.673045\pi\) | ||||
−0.517252 | + | 0.855833i | \(0.673045\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.52786 | −0.0810396 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.2918 | −1.48101 | −0.740503 | − | 0.672053i | \(-0.765413\pi\) | ||||
−0.740503 | + | 0.672053i | \(0.765413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.1803 | −0.644966 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.4508 | 0.525235 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.1803 | −0.675548 | −0.337774 | − | 0.941227i | \(-0.609674\pi\) | ||||
−0.337774 | + | 0.941227i | \(0.609674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.2016 | 0.325051 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.67376 | −0.0851068 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.3050 | 0.613862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.5967 | 1.00370 | 0.501852 | − | 0.864954i | \(-0.332652\pi\) | ||||
0.501852 | + | 0.864954i | \(0.332652\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.8409 | 0.407495 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.1246 | −1.27204 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.5066 | −0.554439 | −0.277219 | − | 0.960807i | \(-0.589413\pi\) | ||||
−0.277219 | + | 0.960807i | \(0.589413\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.7082 | −0.528624 |
(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 | 1064.2.a.a.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9576.2.a.bm.1.1 | 2 | |||
4.3 | odd | 2 | 2128.2.a.n.1.1 | 2 | |||
7.6 | odd | 2 | 7448.2.a.bc.1.1 | 2 | |||
8.3 | odd | 2 | 8512.2.a.i.1.2 | 2 | |||
8.5 | even | 2 | 8512.2.a.bf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2128.2.a.n.1.1 | 2 | 4.3 | odd | 2 | |||
7448.2.a.bc.1.1 | 2 | 7.6 | odd | 2 | |||
8512.2.a.i.1.2 | 2 | 8.3 | odd | 2 | |||
8512.2.a.bf.1.1 | 2 | 8.5 | even | 2 | |||
9576.2.a.bm.1.1 | 2 | 3.2 | odd | 2 |