Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} - 137 x^{8} - 121665 x^{7} + 60168 x^{6} + 172218 x^{5} - 138024 x^{4} + \cdots - 208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.144883\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.144883 | 0.0647938 | 0.0323969 | − | 0.999475i | \(-0.489686\pi\) | ||||
0.0323969 | + | 0.999475i | \(0.489686\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.05535 | −0.776848 | −0.388424 | − | 0.921481i | \(-0.626980\pi\) | ||||
−0.388424 | + | 0.921481i | \(0.626980\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.70628 | −1.72051 | −0.860254 | − | 0.509866i | \(-0.829695\pi\) | ||||
−0.860254 | + | 0.509866i | \(0.829695\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.46851 | −1.23934 | −0.619671 | − | 0.784861i | \(-0.712734\pi\) | ||||
−0.619671 | + | 0.784861i | \(0.712734\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.144883 | −0.0374087 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.26133 | 1.03352 | 0.516762 | − | 0.856129i | \(-0.327137\pi\) | ||||
0.516762 | + | 0.856129i | \(0.327137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.58278 | 0.821946 | 0.410973 | − | 0.911648i | \(-0.365189\pi\) | ||||
0.410973 | + | 0.911648i | \(0.365189\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.05535 | 0.448513 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97901 | −0.995802 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.14680 | −1.10400 | −0.551999 | − | 0.833845i | \(-0.686135\pi\) | ||||
−0.551999 | + | 0.833845i | \(0.686135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.70628 | 0.993336 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.297786 | −0.0503350 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.53672 | 1.56783 | 0.783913 | − | 0.620870i | \(-0.213221\pi\) | ||||
0.783913 | + | 0.620870i | \(0.213221\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.46851 | 0.715535 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.46765 | −1.16625 | −0.583125 | − | 0.812382i | \(-0.698170\pi\) | ||||
−0.583125 | + | 0.812382i | \(0.698170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.12219 | −0.323630 | −0.161815 | − | 0.986821i | \(-0.551735\pi\) | ||||
−0.161815 | + | 0.986821i | \(0.551735\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.144883 | 0.0215979 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1076 | −1.76608 | −0.883040 | − | 0.469298i | \(-0.844507\pi\) | ||||
−0.883040 | + | 0.469298i | \(0.844507\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.77555 | −0.396507 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.26133 | −0.596705 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.19264 | 0.850625 | 0.425313 | − | 0.905047i | \(-0.360164\pi\) | ||||
0.425313 | + | 0.905047i | \(0.360164\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.826745 | −0.111478 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.58278 | −0.474551 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.2421 | −1.72397 | −0.861987 | − | 0.506931i | \(-0.830780\pi\) | ||||
−0.861987 | + | 0.506931i | \(0.830780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.14159 | 0.658313 | 0.329157 | − | 0.944275i | \(-0.393236\pi\) | ||||
0.329157 | + | 0.944275i | \(0.393236\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.05535 | −0.258949 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.647414 | −0.0803018 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.811030 | −0.0990831 | −0.0495415 | − | 0.998772i | \(-0.515776\pi\) | ||||
−0.0495415 | + | 0.998772i | \(0.515776\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4670 | 1.36088 | 0.680442 | − | 0.732802i | \(-0.261788\pi\) | ||||
0.680442 | + | 0.732802i | \(0.261788\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.7114 | −1.60480 | −0.802398 | − | 0.596790i | \(-0.796443\pi\) | ||||
−0.802398 | + | 0.596790i | \(0.796443\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.97901 | 0.574926 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.7284 | 1.33657 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.51002 | 0.169891 | 0.0849455 | − | 0.996386i | \(-0.472928\pi\) | ||||
0.0849455 | + | 0.996386i | \(0.472928\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.5147 | −1.48343 | −0.741715 | − | 0.670715i | \(-0.765988\pi\) | ||||
−0.741715 | + | 0.670715i | \(0.765988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.617396 | 0.0669660 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.10880 | 0.435532 | 0.217766 | − | 0.976001i | \(-0.430123\pi\) | ||||
0.217766 | + | 0.976001i | \(0.430123\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.18435 | 0.962781 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.14680 | 0.637393 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.519085 | 0.0532570 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.29931 | −0.436529 | −0.218264 | − | 0.975890i | \(-0.570040\pi\) | ||||
−0.218264 | + | 0.975890i | \(0.570040\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.70628 | −0.573503 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.47026 | −0.842822 | −0.421411 | − | 0.906870i | \(-0.638465\pi\) | ||||
−0.421411 | + | 0.906870i | \(0.638465\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.06353 | 0.597458 | 0.298729 | − | 0.954338i | \(-0.403437\pi\) | ||||
0.298729 | + | 0.954338i | \(0.403437\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.297786 | 0.0290609 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.86602 | −0.277069 | −0.138534 | − | 0.990358i | \(-0.544239\pi\) | ||||
−0.138534 | + | 0.990358i | \(0.544239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.68092 | −0.927264 | −0.463632 | − | 0.886028i | \(-0.653454\pi\) | ||||
−0.463632 | + | 0.886028i | \(0.653454\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.53672 | −0.905185 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.96674 | 0.843520 | 0.421760 | − | 0.906708i | \(-0.361413\pi\) | ||||
0.421760 | + | 0.906708i | \(0.361413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.144883 | 0.0135104 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.46851 | −0.413114 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.75851 | −0.802891 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.5616 | 1.96015 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.46765 | 0.673335 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.44579 | −0.129316 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.8240 | 1.67036 | 0.835181 | − | 0.549976i | \(-0.185363\pi\) | ||||
0.835181 | + | 0.549976i | \(0.185363\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.12219 | 0.186848 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.84666 | 0.161344 | 0.0806719 | − | 0.996741i | \(-0.474293\pi\) | ||||
0.0806719 | + | 0.996741i | \(0.474293\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.36385 | −0.638527 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.144883 | −0.0124696 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.78041 | 0.408418 | 0.204209 | − | 0.978927i | \(-0.434538\pi\) | ||||
0.204209 | + | 0.978927i | \(0.434538\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1294 | −0.943985 | −0.471993 | − | 0.881602i | \(-0.656465\pi\) | ||||
−0.471993 | + | 0.881602i | \(0.656465\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1076 | 1.01965 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.4986 | 2.13230 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.144883 | 0.0120319 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.77555 | 0.228923 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6153 | 0.951564 | 0.475782 | − | 0.879563i | \(-0.342165\pi\) | ||||
0.475782 | + | 0.879563i | \(0.342165\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1230 | 1.06793 | 0.533966 | − | 0.845506i | \(-0.320701\pi\) | ||||
0.533966 | + | 0.845506i | \(0.320701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.26133 | 0.344508 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.890569 | −0.0715322 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2659 | 0.819309 | 0.409655 | − | 0.912241i | \(-0.365649\pi\) | ||||
0.409655 | + | 0.912241i | \(0.365649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.19264 | −0.491109 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.05535 | −0.161984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.89039 | −0.226393 | −0.113197 | − | 0.993573i | \(-0.536109\pi\) | ||||
−0.113197 | + | 0.993573i | \(0.536109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.826745 | 0.0643620 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.8680 | −1.30528 | −0.652641 | − | 0.757667i | \(-0.726339\pi\) | ||||
−0.652641 | + | 0.757667i | \(0.726339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.96762 | 0.535970 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.58278 | 0.273982 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.1674 | 1.76138 | 0.880692 | − | 0.473689i | \(-0.157078\pi\) | ||||
0.880692 | + | 0.473689i | \(0.157078\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.2336 | 0.773587 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.2421 | 0.995337 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.8434 | 1.55791 | 0.778954 | − | 0.627081i | \(-0.215750\pi\) | ||||
0.778954 | + | 0.627081i | \(0.215750\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6412 | −0.939612 | −0.469806 | − | 0.882770i | \(-0.655676\pi\) | ||||
−0.469806 | + | 0.882770i | \(0.655676\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.14159 | −0.380077 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.38171 | 0.101585 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.3163 | −1.77819 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.05535 | 0.149504 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1359 | 1.09520 | 0.547599 | − | 0.836741i | \(-0.315542\pi\) | ||||
0.547599 | + | 0.836741i | \(0.315542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.714971 | 0.0514647 | 0.0257324 | − | 0.999669i | \(-0.491808\pi\) | ||||
0.0257324 | + | 0.999669i | \(0.491808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.647414 | 0.0463623 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.61412 | −0.471237 | −0.235618 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235618 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.7823 | 1.40233 | 0.701164 | − | 0.713000i | \(-0.252664\pi\) | ||||
0.701164 | + | 0.713000i | \(0.252664\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.811030 | 0.0572056 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.05535 | −0.144257 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.08194 | −0.0755659 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.4443 | −1.41416 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.00743211 | 0.000511647 0 | 0.000255824 | − | 1.00000i | \(-0.499919\pi\) | ||||
0.000255824 | 1.00000i | \(0.499919\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4670 | −0.785707 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.307470 | −0.0209692 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.6338 | 0.857638 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.7114 | 0.926529 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.0418 | −1.28089 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.8140 | −1.05898 | −0.529492 | − | 0.848315i | \(-0.677618\pi\) | ||||
−0.529492 | + | 0.848315i | \(0.677618\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.97901 | −0.331934 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.8842 | 1.12064 | 0.560321 | − | 0.828276i | \(-0.310678\pi\) | ||||
0.560321 | + | 0.828276i | \(0.310678\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.8250 | 1.97089 | 0.985445 | − | 0.169996i | \(-0.0543756\pi\) | ||||
0.985445 | + | 0.169996i | \(0.0543756\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.7284 | −0.771671 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.2967 | 1.91929 | 0.959644 | − | 0.281216i | \(-0.0907378\pi\) | ||||
0.959644 | + | 0.281216i | \(0.0907378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.75420 | −0.114431 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.51002 | −0.0980867 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.7957 | −1.15111 | −0.575553 | − | 0.817764i | \(-0.695213\pi\) | ||||
−0.575553 | + | 0.817764i | \(0.695213\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.01052 | −0.193925 | −0.0969623 | − | 0.995288i | \(-0.530913\pi\) | ||||
−0.0969623 | + | 0.995288i | \(0.530913\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.402131 | −0.0256912 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.0097 | −1.01867 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.5147 | 0.856459 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.62166 | 0.102358 | 0.0511791 | − | 0.998689i | \(-0.483702\pi\) | ||||
0.0511791 | + | 0.998689i | \(0.483702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.70628 | −0.358751 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.617396 | −0.0386628 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.82055 | −0.363076 | −0.181538 | − | 0.983384i | \(-0.558108\pi\) | ||||
−0.181538 | + | 0.983384i | \(0.558108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.6013 | −1.21796 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.13534 | 0.439984 | 0.219992 | − | 0.975502i | \(-0.429397\pi\) | ||||
0.219992 | + | 0.975502i | \(0.429397\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.897212 | 0.0551153 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.10880 | −0.251454 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.1410 | 1.47191 | 0.735953 | − | 0.677033i | \(-0.236735\pi\) | ||||
0.735953 | + | 0.677033i | \(0.236735\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.19676 | 0.133444 | 0.0667218 | − | 0.997772i | \(-0.478746\pi\) | ||||
0.0667218 | + | 0.997772i | \(0.478746\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.18435 | −0.555862 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.4116 | 1.71329 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.32361 | 0.440033 | 0.220017 | − | 0.975496i | \(-0.429389\pi\) | ||||
0.220017 | + | 0.975496i | \(0.429389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.14680 | −0.367999 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9450 | 1.13016 | 0.565082 | − | 0.825035i | \(-0.308844\pi\) | ||||
0.565082 | + | 0.825035i | \(0.308844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.58396 | 0.510263 | 0.255132 | − | 0.966906i | \(-0.417881\pi\) | ||||
0.255132 | + | 0.966906i | \(0.417881\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.519085 | −0.0307480 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.3486 | 0.906000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.15893 | 0.0681723 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.29931 | 0.252030 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.1079 | 1.17471 | 0.587357 | − | 0.809328i | \(-0.300169\pi\) | ||||
0.587357 | + | 0.809328i | \(0.300169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.91856 | −0.111703 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.70628 | 0.331112 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.46851 | −0.258421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.36183 | 0.251412 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.47026 | 0.486603 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.744931 | 0.0426546 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3268 | −0.703526 | −0.351763 | − | 0.936089i | \(-0.614418\pi\) | ||||
−0.351763 | + | 0.936089i | \(0.614418\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.06353 | −0.344942 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.4348 | −1.32887 | −0.664433 | − | 0.747348i | \(-0.731327\pi\) | ||||
−0.664433 | + | 0.747348i | \(0.731327\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.71056 | −0.379303 | −0.189652 | − | 0.981851i | \(-0.560736\pi\) | ||||
−0.189652 | + | 0.981851i | \(0.560736\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.297786 | −0.0167783 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.8933 | −0.948822 | −0.474411 | − | 0.880303i | \(-0.657339\pi\) | ||||
−0.474411 | + | 0.880303i | \(0.657339\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.70628 | −0.319490 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.86602 | 0.159966 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.2674 | 0.849501 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.2488 | 1.23414 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.68092 | 0.535356 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.8854 | 1.37198 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.5980 | −1.84671 | −0.923356 | − | 0.383944i | \(-0.874566\pi\) | ||||
−0.923356 | + | 0.383944i | \(0.874566\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.53672 | 0.522609 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.117505 | −0.00641997 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8324 | −0.807971 | −0.403986 | − | 0.914765i | \(-0.632375\pi\) | ||||
−0.403986 | + | 0.914765i | \(0.632375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.96674 | −0.487006 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.0753 | 1.89944 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0921 | 1.08487 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.144883 | −0.00780026 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.55077 | 0.512712 | 0.256356 | − | 0.966582i | \(-0.417478\pi\) | ||||
0.256356 | + | 0.966582i | \(0.417478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.9806 | −1.28365 | −0.641827 | − | 0.766850i | \(-0.721823\pi\) | ||||
−0.641827 | + | 0.766850i | \(0.721823\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.46851 | 0.238512 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.1127 | 1.33662 | 0.668308 | − | 0.743884i | \(-0.267019\pi\) | ||||
0.668308 | + | 0.743884i | \(0.267019\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.66138 | 0.0881769 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.75851 | 0.463549 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.3475 | −1.44335 | −0.721674 | − | 0.692233i | \(-0.756627\pi\) | ||||
−0.721674 | + | 0.692233i | \(0.756627\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.16369 | −0.324405 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.5616 | −1.13169 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.98655 | −0.103981 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.3332 | −0.956988 | −0.478494 | − | 0.878091i | \(-0.658817\pi\) | ||||
−0.478494 | + | 0.878091i | \(0.658817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.46765 | −0.388750 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.7280 | −0.660806 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00140 | −0.0518504 | −0.0259252 | − | 0.999664i | \(-0.508253\pi\) | ||||
−0.0259252 | + | 0.999664i | \(0.508253\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.44579 | 0.0746604 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.46851 | −0.230140 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.2117 | 1.60324 | 0.801618 | − | 0.597837i | \(-0.203973\pi\) | ||||
0.801618 | + | 0.597837i | \(0.203973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.8240 | −0.964383 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.9277 | −1.47813 | −0.739067 | − | 0.673632i | \(-0.764734\pi\) | ||||
−0.739067 | + | 0.673632i | \(0.764734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.69925 | 0.0866017 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.12219 | −0.107877 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.77323 | 0.0899065 | 0.0449532 | − | 0.998989i | \(-0.485686\pi\) | ||||
0.0449532 | + | 0.998989i | \(0.485686\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.26133 | 0.215505 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.84666 | −0.0931519 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.218778 | 0.0110079 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.7682 | −1.24308 | −0.621540 | − | 0.783382i | \(-0.713493\pi\) | ||||
−0.621540 | + | 0.783382i | \(0.713493\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.36385 | 0.368654 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.6678 | 0.832351 | 0.416176 | − | 0.909284i | \(-0.363370\pi\) | ||||
0.416176 | + | 0.909284i | \(0.363370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.4670 | 1.36823 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.144883 | 0.00719932 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −54.4192 | −2.69746 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3335 | 1.30211 | 0.651054 | − | 0.759032i | \(-0.274327\pi\) | ||||
0.651054 | + | 0.759032i | \(0.274327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.78041 | −0.235800 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.2171 | 1.33927 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.95806 | −0.0961172 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.1294 | 0.545010 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.9933 | 1.22100 | 0.610501 | − | 0.792016i | \(-0.290968\pi\) | ||||
0.610501 | + | 0.792016i | \(0.290968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.22862 | −0.206090 | −0.103045 | − | 0.994677i | \(-0.532859\pi\) | ||||
−0.103045 | + | 0.994677i | \(0.532859\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1076 | −0.588693 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.2172 | −1.02919 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.5678 | −0.511409 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25.4986 | −1.23108 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.7606 | −1.14451 | −0.572255 | − | 0.820076i | \(-0.693931\pi\) | ||||
−0.572255 | + | 0.820076i | \(0.693931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.3647 | 1.69952 | 0.849760 | − | 0.527171i | \(-0.176747\pi\) | ||||
0.849760 | + | 0.527171i | \(0.176747\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.144883 | −0.00694663 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.58278 | 0.171388 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.1935 | −1.01151 | −0.505756 | − | 0.862677i | \(-0.668786\pi\) | ||||
−0.505756 | + | 0.862677i | \(0.668786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.77555 | −0.132169 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.0327 | 0.761738 | 0.380869 | − | 0.924629i | \(-0.375625\pi\) | ||||
0.380869 | + | 0.924629i | \(0.375625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.595297 | 0.0282198 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.6153 | −0.549386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.1698 | −0.527136 | −0.263568 | − | 0.964641i | \(-0.584899\pi\) | ||||
−0.263568 | + | 0.964641i | \(0.584899\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.6125 | 2.00654 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.1230 | −0.616571 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.33066 | 0.0623823 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.94861 | −0.325042 | −0.162521 | − | 0.986705i | \(-0.551963\pi\) | ||||
−0.162521 | + | 0.986705i | \(0.551963\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.26133 | −0.198902 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.55364 | −0.398383 | −0.199191 | − | 0.979961i | \(-0.563832\pi\) | ||||
−0.199191 | + | 0.979961i | \(0.563832\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2774 | 0.617052 | 0.308526 | − | 0.951216i | \(-0.400164\pi\) | ||||
0.308526 | + | 0.951216i | \(0.400164\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.890569 | 0.0412992 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.6994 | −0.587658 | −0.293829 | − | 0.955858i | \(-0.594930\pi\) | ||||
−0.293829 | + | 0.955858i | \(0.594930\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.66695 | 0.0769725 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.2659 | −0.473028 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.1098 | 0.556809 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.8387 | −0.818495 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.19264 | 0.283542 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.81769 | −0.311508 | −0.155754 | − | 0.987796i | \(-0.549781\pi\) | ||||
−0.155754 | + | 0.987796i | \(0.549781\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.6149 | −1.94307 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.05535 | 0.0935215 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.622899 | −0.0282844 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.77935 | −0.216573 | −0.108287 | − | 0.994120i | \(-0.534536\pi\) | ||||
−0.108287 | + | 0.994120i | \(0.534536\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.89039 | 0.130708 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.1826 | 1.31699 | 0.658496 | − | 0.752585i | \(-0.271193\pi\) | ||||
0.658496 | + | 0.752585i | \(0.271193\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.26133 | 0.191921 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.826745 | −0.0371594 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.5687 | −1.05720 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.7998 | 1.51309 | 0.756544 | − | 0.653943i | \(-0.226886\pi\) | ||||
0.756544 | + | 0.653943i | \(0.226886\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.8680 | 0.753605 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.4418 | 0.510164 | 0.255082 | − | 0.966919i | \(-0.417898\pi\) | ||||
0.255082 | + | 0.966919i | \(0.417898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.22720 | −0.0546097 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.96762 | −0.309443 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.3677 | 1.47900 | 0.739498 | − | 0.673158i | \(-0.235063\pi\) | ||||
0.739498 | + | 0.673158i | \(0.235063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.1816 | 1.24668 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.58278 | −0.158184 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.878505 | 0.0387116 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 69.0896 | 3.03856 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.1674 | −1.01694 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.0119 | −1.53390 | −0.766949 | − | 0.641708i | \(-0.778226\pi\) | ||||
−0.766949 | + | 0.641708i | \(0.778226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.52408 | 0.0666436 | 0.0333218 | − | 0.999445i | \(-0.489391\pi\) | ||||
0.0333218 | + | 0.999445i | \(0.489391\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.2336 | −0.446630 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.1935 | −1.14101 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.2421 | −0.574658 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.3693 | 1.44538 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.415239 | −0.0179523 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.8434 | −0.899459 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.8381 | 0.682194 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.523796 | 0.0225197 | 0.0112599 | − | 0.999937i | \(-0.496416\pi\) | ||||
0.0112599 | + | 0.999937i | \(0.496416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6412 | 0.542485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.40261 | −0.0600810 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.2220 | −1.20668 | −0.603342 | − | 0.797483i | \(-0.706165\pi\) | ||||
−0.603342 | + | 0.797483i | \(0.706165\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.14159 | 0.219438 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.58278 | 0.152632 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.10362 | −0.131980 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.38171 | −0.0586504 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.1829 | −1.44838 | −0.724188 | − | 0.689602i | \(-0.757785\pi\) | ||||
−0.724188 | + | 0.689602i | \(0.757785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.48302 | 0.401089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.3163 | 1.02664 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.3468 | 0.983951 | 0.491976 | − | 0.870609i | \(-0.336275\pi\) | ||||
0.491976 | + | 0.870609i | \(0.336275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.29913 | 0.0546549 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.05535 | −0.0863165 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.9873 | 1.08945 | 0.544723 | − | 0.838616i | \(-0.316635\pi\) | ||||
0.544723 | + | 0.838616i | \(0.316635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.4492 | 1.65090 | 0.825448 | − | 0.564478i | \(-0.190922\pi\) | ||||
0.825448 | + | 0.564478i | \(0.190922\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.1359 | −0.632313 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.97901 | −0.207639 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.44605 | −0.185091 | −0.0925457 | − | 0.995708i | \(-0.529500\pi\) | ||||
−0.0925457 | + | 0.995708i | \(0.529500\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.714971 | −0.0297132 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.7774 | 1.15240 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.3370 | −1.46351 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.647414 | −0.0267673 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.7877 | 1.18819 | 0.594097 | − | 0.804393i | \(-0.297509\pi\) | ||||
0.594097 | + | 0.804393i | \(0.297509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.0226 | −0.907426 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.61412 | 0.272069 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.2194 | 0.624985 | 0.312493 | − | 0.949920i | \(-0.398836\pi\) | ||||
0.312493 | + | 0.949920i | \(0.398836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.26896 | −0.0520224 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.7823 | −0.809635 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.0977 | −1.02546 | −0.512732 | − | 0.858549i | \(-0.671367\pi\) | ||||
−0.512732 | + | 0.858549i | \(0.671367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8712 | 0.606607 | 0.303304 | − | 0.952894i | \(-0.401910\pi\) | ||||
0.303304 | + | 0.952894i | \(0.401910\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.811030 | −0.0330277 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.12392 | 0.127006 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.01004 | −0.0815852 | −0.0407926 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407926 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.05535 | 0.0832869 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 54.1031 | 2.18878 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.1099 | 1.09496 | 0.547479 | − | 0.836819i | \(-0.315588\pi\) | ||||
0.547479 | + | 0.836819i | \(0.315588\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.08194 | 0.0436280 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.4508 | 1.54797 | 0.773986 | − | 0.633202i | \(-0.218260\pi\) | ||||
0.773986 | + | 0.633202i | \(0.218260\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.1717 | 1.61464 | 0.807319 | − | 0.590115i | \(-0.200918\pi\) | ||||
0.807319 | + | 0.590115i | \(0.200918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.44500 | −0.338342 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.6856 | 0.987423 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.4443 | 0.816468 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 40.6391 | 1.62039 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.82352 | −0.0725932 | −0.0362966 | − | 0.999341i | \(-0.511556\pi\) | ||||
−0.0362966 | + | 0.999341i | \(0.511556\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.00743211 | −0.000295400 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.72729 | 0.108229 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.4026 | 0.491408 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.4670 | 0.453628 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.12386 | 0.0443900 | 0.0221950 | − | 0.999754i | \(-0.492935\pi\) | ||||
0.0221950 | + | 0.999754i | \(0.492935\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.8557 | −0.783032 | −0.391516 | − | 0.920171i | \(-0.628049\pi\) | ||||
−0.391516 | + | 0.920171i | \(0.628049\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.307470 | 0.0121066 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.5287 | 1.86855 | 0.934274 | − | 0.356557i | \(-0.116049\pi\) | ||||
0.934274 | + | 0.356557i | \(0.116049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 75.5631 | 2.96611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.6338 | −0.495158 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.1825 | 0.750668 | 0.375334 | − | 0.926890i | \(-0.377528\pi\) | ||||
0.375334 | + | 0.926890i | \(0.377528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.267551 | 0.0104541 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.7114 | −0.534932 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.3549 | 1.14350 | 0.571752 | − | 0.820427i | \(-0.306264\pi\) | ||||
0.571752 | + | 0.820427i | \(0.306264\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.8387 | −1.47175 | −0.735877 | − | 0.677115i | \(-0.763230\pi\) | ||||
−0.735877 | + | 0.677115i | \(0.763230\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.0418 | 0.739523 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.06690 | −0.0413726 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.8140 | 0.611405 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.3394 | −1.13263 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.4296 | −0.864597 | −0.432298 | − | 0.901731i | \(-0.642297\pi\) | ||||
−0.432298 | + | 0.901731i | \(0.642297\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.97901 | 0.191642 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.1866 | 1.54450 | 0.772249 | − | 0.635320i | \(-0.219132\pi\) | ||||
0.772249 | + | 0.635320i | \(0.219132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.83657 | 0.339117 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.8842 | −0.647003 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.397782 | 0.0152207 | 0.00761035 | − | 0.999971i | \(-0.497578\pi\) | ||||
0.00761035 | + | 0.999971i | \(0.497578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.692602 | 0.0264630 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.8250 | −1.13789 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.6719 | −1.05422 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.7272 | 1.35913 | 0.679564 | − | 0.733617i | \(-0.262169\pi\) | ||||
0.679564 | + | 0.733617i | \(0.262169\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.7284 | 0.445524 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.61247 | −0.0611644 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.8221 | −1.20535 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.2967 | −1.10810 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.4728 | −0.924325 | −0.462163 | − | 0.886795i | \(-0.652926\pi\) | ||||
−0.462163 | + | 0.886795i | \(0.652926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.1679 | 1.28867 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.75420 | 0.0660668 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.4093 | 0.654745 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.6182 | 0.473888 | 0.236944 | − | 0.971523i | \(-0.423854\pi\) | ||||
0.236944 | + | 0.971523i | \(0.423854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.51002 | 0.0566304 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.14680 | −0.230199 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.69432 | 0.138160 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.7957 | 0.664592 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.7271 | 1.40698 | 0.703492 | − | 0.710704i | \(-0.251623\pi\) | ||||
0.703492 | + | 0.710704i | \(0.251623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.4627 | −0.464134 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.01052 | 0.111962 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.97901 | −0.184916 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.91752 | −0.367820 | −0.183910 | − | 0.982943i | \(-0.558876\pi\) | ||||
−0.183910 | + | 0.982943i | \(0.558876\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.04333 | −0.334480 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.9733 | −1.21790 | −0.608949 | − | 0.793209i | \(-0.708409\pi\) | ||||
−0.608949 | + | 0.793209i | \(0.708409\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.402131 | 0.0148328 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.62796 | 0.170473 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.1806 | −1.55164 | −0.775819 | − | 0.630956i | \(-0.782663\pi\) | ||||
−0.775819 | + | 0.630956i | \(0.782663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0097 | 0.588131 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.7038 | −0.502745 | −0.251373 | − | 0.967890i | \(-0.580882\pi\) | ||||
−0.251373 | + | 0.967890i | \(0.580882\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.68287 | 0.0616555 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.5147 | −0.494477 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.89066 | 0.215240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.36385 | 0.268711 | 0.134355 | − | 0.990933i | \(-0.457104\pi\) | ||||
0.134355 | + | 0.990933i | \(0.457104\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.62166 | −0.0590965 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.90130 | 0.0691954 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.9064 | 1.41408 | 0.707039 | − | 0.707174i | \(-0.250030\pi\) | ||||
0.707039 | + | 0.707174i | \(0.250030\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.70628 | 0.207125 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.0038 | 1.55889 | 0.779444 | − | 0.626472i | \(-0.215502\pi\) | ||||
0.779444 | + | 0.626472i | \(0.215502\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.8976 | 0.720343 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.617396 | 0.0223220 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 59.1725 | 2.13659 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.9722 | −0.972641 | −0.486320 | − | 0.873781i | \(-0.661661\pi\) | ||||
−0.486320 | + | 0.873781i | \(0.661661\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.82055 | 0.209622 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.21412 | 0.331409 | 0.165704 | − | 0.986175i | \(-0.447010\pi\) | ||||
0.165704 | + | 0.986175i | \(0.447010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.6050 | 1.09936 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.6013 | 0.703191 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.7549 | −0.958595 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −65.4340 | −2.34141 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.48736 | 0.0530862 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.9823 | 1.06875 | 0.534377 | − | 0.845246i | \(-0.320546\pi\) | ||||
0.534377 | + | 0.845246i | \(0.320546\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.13534 | −0.254025 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.4298 | −0.655287 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.9753 | −0.815876 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.897212 | −0.0318208 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.1582 | −0.961992 | −0.480996 | − | 0.876723i | \(-0.659725\pi\) | ||||
−0.480996 | + | 0.876723i | \(0.659725\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.5946 | −1.82529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.10880 | 0.145177 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 78.2410 | 2.76106 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.297786 | −0.0104956 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.1410 | −0.849805 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.80455 | −0.344710 | −0.172355 | − | 0.985035i | \(-0.555138\pi\) | ||||
−0.172355 | + | 0.985035i | \(0.555138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.3639 | −1.48760 | −0.743799 | − | 0.668404i | \(-0.766978\pi\) | ||||
−0.743799 | + | 0.668404i | \(0.766978\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.19676 | −0.0770437 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.418770 | −0.0146689 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.60332 | −0.266007 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.18435 | 0.320927 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.6899 | 0.861685 | 0.430842 | − | 0.902427i | \(-0.358216\pi\) | ||||
0.430842 | + | 0.902427i | \(0.358216\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.7338 | −0.513586 | −0.256793 | − | 0.966466i | \(-0.582666\pi\) | ||||
−0.256793 | + | 0.966466i | \(0.582666\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −28.4116 | −0.989166 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.7964 | −0.375429 | −0.187714 | − | 0.982224i | \(-0.560108\pi\) | ||||
−0.187714 | + | 0.982224i | \(0.560108\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.5085 | −0.434439 | −0.217220 | − | 0.976123i | \(-0.569699\pi\) | ||||
−0.217220 | + | 0.976123i | \(0.569699\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.32361 | −0.254053 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.8275 | −0.409800 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.44389 | −0.0845743 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.14680 | 0.212464 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.8777 | 0.444588 | 0.222294 | − | 0.974980i | \(-0.428646\pi\) | ||||
0.222294 | + | 0.974980i | \(0.428646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.9450 | −0.652501 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00949 | 0.0347276 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.3166 | −1.52274 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.58396 | −0.294601 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.53672 | 0.326914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.3317 | −0.559186 | −0.279593 | − | 0.960119i | \(-0.590200\pi\) | ||||
−0.279593 | + | 0.960119i | \(0.590200\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.519085 | 0.0177523 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.4820 | −1.34868 | −0.674340 | − | 0.738421i | \(-0.735572\pi\) | ||||
−0.674340 | + | 0.738421i | \(0.735572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.0864 | −1.33361 | −0.666806 | − | 0.745231i | \(-0.732339\pi\) | ||||
−0.666806 | + | 0.745231i | \(0.732339\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.3486 | −0.523079 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.0938 | −0.718041 | −0.359021 | − | 0.933330i | \(-0.616889\pi\) | ||||
−0.359021 | + | 0.933330i | \(0.616889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.35657 | 0.114127 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.15893 | −0.0393593 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.61662 | −0.292299 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.62410 | 0.122798 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.29931 | −0.145510 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.97161 | 0.100459 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.5956 | −0.492858 | −0.246429 | − | 0.969161i | \(-0.579257\pi\) | ||||
−0.246429 | + | 0.969161i | \(0.579257\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.1079 | −0.678221 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.4253 | 1.49673 | 0.748363 | − | 0.663289i | \(-0.230840\pi\) | ||||
0.748363 | + | 0.663289i | \(0.230840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.5763 | −0.490532 | −0.245266 | − | 0.969456i | \(-0.578875\pi\) | ||||
−0.245266 | + | 0.969456i | \(0.578875\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.91856 | 0.0644917 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.36549 | −0.113002 | −0.0565010 | − | 0.998403i | \(-0.517994\pi\) | ||||
−0.0565010 | + | 0.998403i | \(0.517994\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.6899 | −1.29762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.70628 | −0.191168 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43.3790 | −1.45162 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.01986 | 0.100943 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.46851 | 0.149199 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.14680 | −0.205007 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.3889 | 0.879142 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.36183 | −0.145153 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.83150 | −0.0608811 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.65151 | −0.187655 | −0.0938276 | − | 0.995588i | \(-0.529910\pi\) | ||||
−0.0938276 | + | 0.995588i | \(0.529910\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.47026 | −0.280941 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.39906 | 0.178879 | 0.0894394 | − | 0.995992i | \(-0.471492\pi\) | ||||
0.0894394 | + | 0.995992i | \(0.471492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 77.1187 | 2.55225 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.744931 | −0.0246267 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.79554 | −0.125340 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2548 | 0.470224 | 0.235112 | − | 0.971968i | \(-0.424454\pi\) | ||||
0.235112 | + | 0.971968i | \(0.424454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.3268 | 0.406181 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −51.2405 | −1.68660 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.4834 | −1.56124 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.06353 | 0.199153 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.8621 | 0.356374 | 0.178187 | − | 0.983997i | \(-0.442977\pi\) | ||||
0.178187 | + | 0.983997i | \(0.442977\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.94418 | −0.325907 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.4348 | 0.767221 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.52303 | −0.115216 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.1322 | −0.755697 | −0.377848 | − | 0.925868i | \(-0.623336\pi\) | ||||
−0.377848 | + | 0.925868i | \(0.623336\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.71056 | 0.218991 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.86711 | −0.289060 | −0.144530 | − | 0.989500i | \(-0.546167\pi\) | ||||
−0.144530 | + | 0.989500i | \(0.546167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.46765 | −0.243180 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.297786 | 0.00968697 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.341452 | 0.0110957 | 0.00554784 | − | 0.999985i | \(-0.498234\pi\) | ||||
0.00554784 | + | 0.999985i | \(0.498234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61.2695 | 1.98889 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.8933 | 0.547803 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.70632 | −0.0876662 | −0.0438331 | − | 0.999039i | \(-0.513957\pi\) | ||||
−0.0438331 | + | 0.999039i | \(0.513957\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.19295 | 0.0709621 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.70628 | 0.184458 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.82539 | −0.317279 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.78312 | 0.218810 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.86602 | −0.0923562 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.103587 | 0.00333460 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.6891 | −1.27631 | −0.638157 | − | 0.769906i | \(-0.720303\pi\) | ||||
−0.638157 | + | 0.769906i | \(0.720303\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.2674 | −0.490460 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.1509 | 1.09596 | 0.547978 | − | 0.836493i | \(-0.315398\pi\) | ||||
0.547978 | + | 0.836493i | \(0.315398\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.8748 | 0.733333 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.2488 | −0.712531 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.9568 | −1.08637 | −0.543187 | − | 0.839612i | \(-0.682782\pi\) | ||||
−0.543187 | + | 0.839612i | \(0.682782\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.4460 | −0.749336 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.68092 | −0.309088 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.7522 | −1.33169 | −0.665844 | − | 0.746091i | \(-0.731928\pi\) | ||||
−0.665844 | + | 0.746091i | \(0.731928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.958276 | −0.0305332 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.8854 | −0.792111 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.12219 | −0.0674816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.93753 | −0.125080 | −0.0625398 | − | 0.998042i | \(-0.519920\pi\) | ||||
−0.0625398 | + | 0.998042i | \(0.519920\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.5980 | 1.06620 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.86612 | 0.0908622 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.45768 | −0.141176 | −0.0705880 | − | 0.997506i | \(-0.522488\pi\) | ||||
−0.0705880 | + | 0.997506i | \(0.522488\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.53672 | −0.301728 |
(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 | 8004.2.a.i.1.8 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.i.1.8 | ✓ | 16 | 1.1 | even | 1 | trivial |