Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3864,2,Mod(1,3864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3864.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: | \(30.8541953410\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.256549.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 12x^{2} + 11x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.73320\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3864.1 |
$q$-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 | ||||||||
\(5\) | 3.73320 | 1.66954 | 0.834768 | − | 0.550601i | \(-0.185602\pi\) | ||||
0.834768 | + | 0.550601i | \(0.185602\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.20357 | −1.26742 | −0.633711 | − | 0.773570i | \(-0.718469\pi\) | ||||
−0.633711 | + | 0.773570i | \(0.718469\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.470368 | 0.130457 | 0.0652283 | − | 0.997870i | \(-0.479222\pi\) | ||||
0.0652283 | + | 0.997870i | \(0.479222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.73320 | 0.963907 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.20357 | −1.01951 | −0.509757 | − | 0.860318i | \(-0.670265\pi\) | ||||
−0.509757 | + | 0.860318i | \(0.670265\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.20357 | 0.964364 | 0.482182 | − | 0.876071i | \(-0.339844\pi\) | ||||
0.482182 | + | 0.876071i | \(0.339844\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.93676 | 1.78735 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.651155 | −0.120916 | −0.0604582 | − | 0.998171i | \(-0.519256\pi\) | ||||
−0.0604582 | + | 0.998171i | \(0.519256\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.20357 | 1.11419 | 0.557097 | − | 0.830448i | \(-0.311915\pi\) | ||||
0.557097 | + | 0.830448i | \(0.311915\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.20357 | −0.731747 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.73320 | 0.631026 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.75598 | −0.946277 | −0.473138 | − | 0.880988i | \(-0.656879\pi\) | ||||
−0.473138 | + | 0.880988i | \(0.656879\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.470368 | 0.0753191 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.75598 | −0.586585 | −0.293292 | − | 0.956023i | \(-0.594751\pi\) | ||||
−0.293292 | + | 0.956023i | \(0.594751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.9368 | 1.82034 | 0.910170 | − | 0.414236i | \(-0.135951\pi\) | ||||
0.910170 | + | 0.414236i | \(0.135951\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.73320 | 0.556512 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.61168 | 0.964412 | 0.482206 | − | 0.876058i | \(-0.339836\pi\) | ||||
0.482206 | + | 0.876058i | \(0.339836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.20357 | −0.588617 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.28561 | −0.451313 | −0.225656 | − | 0.974207i | \(-0.572453\pi\) | ||||
−0.225656 | + | 0.974207i | \(0.572453\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.6927 | −2.11601 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.20357 | 0.556776 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.58792 | 1.11805 | 0.559026 | − | 0.829150i | \(-0.311175\pi\) | ||||
0.559026 | + | 0.829150i | \(0.311175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.08204 | 1.16284 | 0.581418 | − | 0.813605i | \(-0.302498\pi\) | ||||
0.581418 | + | 0.813605i | \(0.302498\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.75598 | 0.217802 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.81921 | 0.710930 | 0.355465 | − | 0.934690i | \(-0.384323\pi\) | ||||
0.355465 | + | 0.934690i | \(0.384323\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.85075 | 1.16907 | 0.584534 | − | 0.811369i | \(-0.301277\pi\) | ||||
0.584534 | + | 0.811369i | \(0.301277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.84199 | 0.449671 | 0.224836 | − | 0.974397i | \(-0.427816\pi\) | ||||
0.224836 | + | 0.974397i | \(0.427816\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.93676 | 1.03193 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.20357 | −0.479041 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.5514 | 1.74967 | 0.874836 | − | 0.484419i | \(-0.160969\pi\) | ||||
0.874836 | + | 0.484419i | \(0.160969\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.3677 | 1.13800 | 0.568999 | − | 0.822338i | \(-0.307331\pi\) | ||||
0.568999 | + | 0.822338i | \(0.307331\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.6927 | −1.70212 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.651155 | −0.0698111 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7915 | 1.35589 | 0.677947 | − | 0.735111i | \(-0.262870\pi\) | ||||
0.677947 | + | 0.735111i | \(0.262870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.470368 | 0.0493079 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.20357 | 0.643280 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.6927 | 1.61004 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.11755 | −0.418074 | −0.209037 | − | 0.977908i | \(-0.567033\pi\) | ||||
−0.209037 | + | 0.977908i | \(0.567033\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.20357 | −0.422474 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6927 | −1.36248 | −0.681239 | − | 0.732061i | \(-0.738559\pi\) | ||||
−0.681239 | + | 0.732061i | \(0.738559\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.3667 | −1.61266 | −0.806328 | − | 0.591469i | \(-0.798548\pi\) | ||||
−0.806328 | + | 0.591469i | \(0.798548\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.73320 | 0.364323 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.27953 | 0.123697 | 0.0618484 | − | 0.998086i | \(-0.480300\pi\) | ||||
0.0618484 | + | 0.998086i | \(0.480300\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.266803 | 0.0255551 | 0.0127775 | − | 0.999918i | \(-0.495933\pi\) | ||||
0.0127775 | + | 0.999918i | \(0.495933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.75598 | −0.546333 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.1996 | −1.61800 | −0.809001 | − | 0.587808i | \(-0.799991\pi\) | ||||
−0.809001 | + | 0.587808i | \(0.799991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.73320 | 0.348122 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.470368 | 0.0434855 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.20357 | −0.385340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.66996 | 0.606360 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.75598 | −0.338665 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14.6967 | 1.31451 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3439 | −0.917872 | −0.458936 | − | 0.888469i | \(-0.651769\pi\) | ||||
−0.458936 | + | 0.888469i | \(0.651769\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.9368 | 1.05097 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.20357 | −0.542008 | −0.271004 | − | 0.962578i | \(-0.587356\pi\) | ||||
−0.271004 | + | 0.962578i | \(0.587356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.20357 | 0.364495 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.73320 | 0.321302 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.23032 | 0.105113 | 0.0525565 | − | 0.998618i | \(-0.483263\pi\) | ||||
0.0525565 | + | 0.998618i | \(0.483263\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5475 | −1.40354 | −0.701769 | − | 0.712405i | \(-0.747606\pi\) | ||||
−0.701769 | + | 0.712405i | \(0.747606\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.61168 | 0.556803 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.97722 | −0.165344 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.43089 | −0.201874 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.04556 | 0.331425 | 0.165712 | − | 0.986174i | \(-0.447008\pi\) | ||||
0.165712 | + | 0.986174i | \(0.447008\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.32111 | −0.677163 | −0.338581 | − | 0.940937i | \(-0.609947\pi\) | ||||
−0.338581 | + | 0.940937i | \(0.609947\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.20357 | −0.339838 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.1591 | 1.86019 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.5712 | −1.16291 | −0.581455 | − | 0.813579i | \(-0.697516\pi\) | ||||
−0.581455 | + | 0.813579i | \(0.697516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.28561 | −0.260566 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.3312 | 1.20083 | 0.600415 | − | 0.799689i | \(-0.295002\pi\) | ||||
0.600415 | + | 0.799689i | \(0.295002\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.6927 | −1.22168 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.7155 | −1.37087 | −0.685434 | − | 0.728135i | \(-0.740387\pi\) | ||||
−0.685434 | + | 0.728135i | \(0.740387\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7788 | −0.982981 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.20357 | 0.321455 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.90126 | −0.220578 | −0.110289 | − | 0.993900i | \(-0.535178\pi\) | ||||
−0.110289 | + | 0.993900i | \(0.535178\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.93676 | 0.675556 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.58792 | 0.645507 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.2589 | −0.766783 | −0.383391 | − | 0.923586i | \(-0.625244\pi\) | ||||
−0.383391 | + | 0.923586i | \(0.625244\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0908 | −0.973031 | −0.486516 | − | 0.873672i | \(-0.661732\pi\) | ||||
−0.486516 | + | 0.873672i | \(0.661732\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.08204 | 0.671364 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.4882 | −1.57984 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.6700 | 1.29216 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.76870 | −0.634481 | −0.317241 | − | 0.948345i | \(-0.602756\pi\) | ||||
−0.317241 | + | 0.948345i | \(0.602756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.3211 | 0.742930 | 0.371465 | − | 0.928447i | \(-0.378856\pi\) | ||||
0.371465 | + | 0.928447i | \(0.378856\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.75598 | 0.125748 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.4032 | −0.812441 | −0.406221 | − | 0.913775i | \(-0.633154\pi\) | ||||
−0.406221 | + | 0.913775i | \(0.633154\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.6660 | −1.03964 | −0.519822 | − | 0.854275i | \(-0.674002\pi\) | ||||
−0.519822 | + | 0.854275i | \(0.674002\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.81921 | 0.410456 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.651155 | −0.0457021 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.0218 | −0.979325 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.6700 | −1.22226 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7155 | −0.944215 | −0.472108 | − | 0.881541i | \(-0.656507\pi\) | ||||
−0.472108 | + | 0.881541i | \(0.656507\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.85075 | 0.674962 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 44.5623 | 3.03912 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.20357 | 0.421125 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.84199 | 0.259618 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.97722 | −0.133002 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.0464 | −1.74419 | −0.872097 | − | 0.489333i | \(-0.837240\pi\) | ||||
−0.872097 | + | 0.489333i | \(0.837240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.93676 | 0.595784 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.3044 | −1.08216 | −0.541081 | − | 0.840971i | \(-0.681985\pi\) | ||||
−0.541081 | + | 0.840971i | \(0.681985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9240 | 0.986208 | 0.493104 | − | 0.869970i | \(-0.335862\pi\) | ||||
0.493104 | + | 0.869970i | \(0.335862\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.20357 | −0.276574 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.172841 | 0.0113232 | 0.00566158 | − | 0.999984i | \(-0.498198\pi\) | ||||
0.00566158 | + | 0.999984i | \(0.498198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.6827 | 1.61012 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.5514 | 1.01017 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.0999 | 1.81763 | 0.908815 | − | 0.417200i | \(-0.136989\pi\) | ||||
0.908815 | + | 0.417200i | \(0.136989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1175 | 1.03822 | 0.519111 | − | 0.854707i | \(-0.326263\pi\) | ||||
0.519111 | + | 0.854707i | \(0.326263\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.73320 | 0.238505 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.97722 | 0.125808 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.3677 | 0.657023 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.4259 | −1.35239 | −0.676197 | − | 0.736721i | \(-0.736373\pi\) | ||||
−0.676197 | + | 0.736721i | \(0.736373\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.20357 | −0.264276 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.6927 | −0.982717 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.3616 | −0.646337 | −0.323169 | − | 0.946341i | \(-0.604748\pi\) | ||||
−0.323169 | + | 0.946341i | \(0.604748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.75598 | −0.357659 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.651155 | −0.0403055 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.487069 | 0.0300340 | 0.0150170 | − | 0.999887i | \(-0.495220\pi\) | ||||
0.0150170 | + | 0.999887i | \(0.495220\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.2658 | −0.753484 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.7915 | 0.782826 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.1869 | 0.621104 | 0.310552 | − | 0.950556i | \(-0.399486\pi\) | ||||
0.310552 | + | 0.950556i | \(0.399486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.26283 | 0.562677 | 0.281338 | − | 0.959609i | \(-0.409222\pi\) | ||||
0.281338 | + | 0.959609i | \(0.409222\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.470368 | 0.0284680 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −37.5663 | −2.26533 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.4220 | 1.58754 | 0.793771 | − | 0.608217i | \(-0.208115\pi\) | ||||
0.793771 | + | 0.608217i | \(0.208115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.20357 | 0.371398 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.3211 | 0.854326 | 0.427163 | − | 0.904175i | \(-0.359513\pi\) | ||||
0.427163 | + | 0.904175i | \(0.359513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.71439 | 0.399129 | 0.199565 | − | 0.979885i | \(-0.436047\pi\) | ||||
0.199565 | + | 0.979885i | \(0.436047\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.6927 | 0.929558 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.75598 | −0.221708 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.669960 | 0.0394094 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.11755 | −0.241375 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.22335 | −0.0714689 | −0.0357344 | − | 0.999361i | \(-0.511377\pi\) | ||||
−0.0357344 | + | 0.999361i | \(0.511377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.0604 | 1.86663 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.20357 | −0.243916 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.470368 | 0.0272021 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.9368 | 0.688024 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.6927 | −0.786627 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 33.9051 | 1.94140 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.9774 | 1.53968 | 0.769840 | − | 0.638237i | \(-0.220336\pi\) | ||||
0.769840 | + | 0.638237i | \(0.220336\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.3667 | −0.931067 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.9100 | −0.732060 | −0.366030 | − | 0.930603i | \(-0.619283\pi\) | ||||
−0.366030 | + | 0.930603i | \(0.619283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.47434 | −0.422475 | −0.211237 | − | 0.977435i | \(-0.567749\pi\) | ||||
−0.211237 | + | 0.977435i | \(0.567749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.73320 | 0.210342 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.7788 | −1.44788 | −0.723940 | − | 0.689863i | \(-0.757671\pi\) | ||||
−0.723940 | + | 0.689863i | \(0.757671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.73717 | 0.153252 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.27953 | 0.0714164 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.6700 | −0.983183 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.20357 | 0.233172 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.266803 | 0.0147542 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.61168 | 0.364513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.1029 | −1.92943 | −0.964714 | − | 0.263300i | \(-0.915189\pi\) | ||||
−0.964714 | + | 0.263300i | \(0.915189\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.75598 | −0.315426 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.7243 | 1.18692 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.8746 | 1.89974 | 0.949872 | − | 0.312640i | \(-0.101213\pi\) | ||||
0.949872 | + | 0.312640i | \(0.101213\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.1996 | −0.934154 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.0771 | −1.41215 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.73320 | 0.200989 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.4575 | −1.15190 | −0.575949 | − | 0.817486i | \(-0.695367\pi\) | ||||
−0.575949 | + | 0.817486i | \(0.695367\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0881 | −0.807649 | −0.403824 | − | 0.914837i | \(-0.632319\pi\) | ||||
−0.403824 | + | 0.914837i | \(0.632319\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.470368 | 0.0251064 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.651155 | −0.0346575 | −0.0173287 | − | 0.999850i | \(-0.505516\pi\) | ||||
−0.0173287 | + | 0.999850i | \(0.505516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.7748 | 1.95180 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.20357 | −0.222476 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.5988 | 1.35105 | 0.675526 | − | 0.737336i | \(-0.263917\pi\) | ||||
0.675526 | + | 0.737336i | \(0.263917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.33004 | −0.0700021 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.66996 | 0.350082 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.3429 | 0.750742 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.5217 | −1.01902 | −0.509512 | − | 0.860464i | \(-0.670174\pi\) | ||||
−0.509512 | + | 0.860464i | \(0.670174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.75598 | −0.195528 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.28561 | −0.170580 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7292 | 0.659094 | 0.329547 | − | 0.944139i | \(-0.393104\pi\) | ||||
0.329547 | + | 0.944139i | \(0.393104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.6967 | 0.758935 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.306282 | −0.0157743 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.250102 | 0.0128469 | 0.00642343 | − | 0.999979i | \(-0.497955\pi\) | ||||
0.00642343 | + | 0.999979i | \(0.497955\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.3439 | −0.529934 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.55143 | −0.385860 | −0.192930 | − | 0.981213i | \(-0.561799\pi\) | ||||
−0.192930 | + | 0.981213i | \(0.561799\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.6927 | −0.799776 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.9368 | 0.606780 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.1937 | −1.83509 | −0.917546 | − | 0.397630i | \(-0.869833\pi\) | ||||
−0.917546 | + | 0.397630i | \(0.869833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.20357 | −0.212583 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.20357 | −0.312928 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 58.0566 | 2.92114 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.3855 | −1.87632 | −0.938162 | − | 0.346198i | \(-0.887473\pi\) | ||||
−0.938162 | + | 0.346198i | \(0.887473\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.20357 | 0.210441 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.19562 | 0.109644 | 0.0548220 | − | 0.998496i | \(-0.482541\pi\) | ||||
0.0548220 | + | 0.998496i | \(0.482541\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.91796 | 0.145354 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.73320 | 0.185504 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.1956 | 1.19933 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.13635 | 0.352870 | 0.176435 | − | 0.984312i | \(-0.443543\pi\) | ||||
0.176435 | + | 0.984312i | \(0.443543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.23032 | 0.0606870 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.58792 | 0.422584 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.7045 | 1.89993 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.5475 | −0.810332 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.81921 | 0.284287 | 0.142144 | − | 0.989846i | \(-0.454601\pi\) | ||||
0.142144 | + | 0.989846i | \(0.454601\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.5535 | 1.39161 | 0.695807 | − | 0.718229i | \(-0.255047\pi\) | ||||
0.695807 | + | 0.718229i | \(0.255047\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.61168 | 0.321471 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37.5663 | −1.82223 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.08204 | 0.439511 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.97722 | −0.0954612 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.6937 | 0.755940 | 0.377970 | − | 0.925818i | \(-0.376622\pi\) | ||||
0.377970 | + | 0.925818i | \(0.376622\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3074 | 0.735627 | 0.367814 | − | 0.929900i | \(-0.380106\pi\) | ||||
0.367814 | + | 0.929900i | \(0.380106\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.43089 | −0.116552 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.20357 | 0.201084 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.8595 | 1.42512 | 0.712558 | − | 0.701613i | \(-0.247536\pi\) | ||||
0.712558 | + | 0.701613i | \(0.247536\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.4715 | 0.545027 | 0.272514 | − | 0.962152i | \(-0.412145\pi\) | ||||
0.272514 | + | 0.962152i | \(0.412145\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47.7531 | 2.26372 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.04556 | 0.191348 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.9358 | −0.940828 | −0.470414 | − | 0.882446i | \(-0.655895\pi\) | ||||
−0.470414 | + | 0.882446i | \(0.655895\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7885 | 0.743451 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.32111 | −0.390960 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.75598 | 0.0823214 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.2263 | −1.60104 | −0.800520 | − | 0.599305i | \(-0.795443\pi\) | ||||
−0.800520 | + | 0.599305i | \(0.795443\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.20357 | −0.196206 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.12152 | 0.331682 | 0.165841 | − | 0.986152i | \(-0.446966\pi\) | ||||
0.165841 | + | 0.986152i | \(0.446966\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2341 | 1.12626 | 0.563128 | − | 0.826370i | \(-0.309598\pi\) | ||||
0.563128 | + | 0.826370i | \(0.309598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23.1591 | 1.07398 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.8666 | −1.10441 | −0.552206 | − | 0.833707i | \(-0.686214\pi\) | ||||
−0.552206 | + | 0.833707i | \(0.686214\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.81921 | 0.268706 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.5712 | −0.671406 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −50.1770 | −2.30714 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.5663 | 1.72366 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.28561 | −0.150438 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.8203 | −1.49960 | −0.749800 | − | 0.661665i | \(-0.769850\pi\) | ||||
−0.749800 | + | 0.661665i | \(0.769850\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.70743 | −0.123448 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.3716 | −0.697989 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.2224 | 1.14293 | 0.571467 | − | 0.820625i | \(-0.306374\pi\) | ||||
0.571467 | + | 0.820625i | \(0.306374\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.3312 | 0.693299 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6612 | −0.797039 | −0.398520 | − | 0.917160i | \(-0.630476\pi\) | ||||
−0.398520 | + | 0.917160i | \(0.630476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.73717 | 0.123276 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.6927 | −0.705336 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.85075 | 0.441866 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.50896 | −0.380913 | −0.190457 | − | 0.981696i | \(-0.560997\pi\) | ||||
−0.190457 | + | 0.981696i | \(0.560997\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.7155 | −0.791471 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.9495 | −0.934092 | −0.467046 | − | 0.884233i | \(-0.654682\pi\) | ||||
−0.467046 | + | 0.884233i | \(0.654682\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −51.1177 | −2.27471 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7788 | −0.567524 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.8853 | 1.45761 | 0.728807 | − | 0.684719i | \(-0.240075\pi\) | ||||
0.728807 | + | 0.684719i | \(0.240075\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.84199 | 0.169960 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.20357 | 0.185592 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −61.1000 | −2.69239 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.7926 | −1.22232 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.90126 | −0.127351 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.27685 | −0.231183 | −0.115592 | − | 0.993297i | \(-0.536876\pi\) | ||||
−0.115592 | + | 0.993297i | \(0.536876\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.9328 | 1.26514 | 0.632571 | − | 0.774502i | \(-0.282000\pi\) | ||||
0.632571 | + | 0.774502i | \(0.282000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.93676 | 0.390032 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.0771 | −1.13594 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.58792 | 0.372684 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.76669 | −0.0765238 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.77674 | 0.206516 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.2589 | −0.442702 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.20357 | −0.181060 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.46639 | 0.0630452 | 0.0315226 | − | 0.999503i | \(-0.489964\pi\) | ||||
0.0315226 | + | 0.999503i | \(0.489964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.0908 | −0.561780 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.996027 | 0.0426651 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.8606 | −1.31951 | −0.659753 | − | 0.751483i | \(-0.729339\pi\) | ||||
−0.659753 | + | 0.751483i | \(0.729339\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.08204 | 0.387612 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.73717 | −0.116607 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.5514 | 0.661314 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.4882 | −0.912123 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.1997 | 1.53383 | 0.766916 | − | 0.641747i | \(-0.221790\pi\) | ||||
0.766916 | + | 0.641747i | \(0.221790\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.61467 | 0.237475 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.6700 | 0.746026 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.41110 | 0.0594709 | 0.0297355 | − | 0.999558i | \(-0.490534\pi\) | ||||
0.0297355 | + | 0.999558i | \(0.490534\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −64.2095 | −2.70131 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.9732 | −0.879244 | −0.439622 | − | 0.898183i | \(-0.644888\pi\) | ||||
−0.439622 | + | 0.898183i | \(0.644888\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.6165 | 0.904621 | 0.452310 | − | 0.891861i | \(-0.350600\pi\) | ||||
0.452310 | + | 0.891861i | \(0.350600\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.76870 | −0.366318 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.93676 | 0.372689 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.6285 | −1.81628 | −0.908140 | − | 0.418668i | \(-0.862497\pi\) | ||||
−0.908140 | + | 0.418668i | \(0.862497\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.3211 | 0.428931 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3677 | 0.430123 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8113 | 0.572004 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.75598 | 0.0726007 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.5701 | −0.725195 | −0.362598 | − | 0.931946i | \(-0.618110\pi\) | ||||
−0.362598 | + | 0.931946i | \(0.618110\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.0771 | 1.07449 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.4032 | −0.469063 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.99335 | 0.122922 | 0.0614611 | − | 0.998109i | \(-0.480424\pi\) | ||||
0.0614611 | + | 0.998109i | \(0.480424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.6927 | −0.643340 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.6660 | −0.600239 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.1314 | −0.740829 | −0.370414 | − | 0.928867i | \(-0.620784\pi\) | ||||
−0.370414 | + | 0.928867i | \(0.620784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.6335 | −0.923239 | −0.461619 | − | 0.887078i | \(-0.652731\pi\) | ||||
−0.461619 | + | 0.887078i | \(0.652731\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.81921 | 0.236977 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.9003 | 1.01234 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.3430 | 1.63747 | 0.818736 | − | 0.574170i | \(-0.194675\pi\) | ||||
0.818736 | + | 0.574170i | \(0.194675\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.651155 | −0.0263861 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.10992 | 0.125814 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.4992 | −0.666397 | −0.333199 | − | 0.942857i | \(-0.608128\pi\) | ||||
−0.333199 | + | 0.942857i | \(0.608128\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.0218 | −0.565413 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.7125 | −0.994889 | −0.497444 | − | 0.867496i | \(-0.665728\pi\) | ||||
−0.497444 | + | 0.867496i | \(0.665728\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.38435 | 0.176222 | 0.0881110 | − | 0.996111i | \(-0.471917\pi\) | ||||
0.0881110 | + | 0.996111i | \(0.471917\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.7915 | 0.512480 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.1819 | 0.407276 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.6700 | −0.705670 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.1956 | 0.964743 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.71552 | −0.227531 | −0.113766 | − | 0.993508i | \(-0.536291\pi\) | ||||
−0.113766 | + | 0.993508i | \(0.536291\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.7155 | −0.545143 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.6158 | −1.53242 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.470368 | 0.0186367 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.85075 | 0.389690 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.35760 | −0.290608 | −0.145304 | − | 0.989387i | \(-0.546416\pi\) | ||||
−0.145304 | + | 0.989387i | \(0.546416\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.1075 | 0.516909 | 0.258455 | − | 0.966023i | \(-0.416787\pi\) | ||||
0.258455 | + | 0.966023i | \(0.416787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 44.5623 | 1.75464 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.3369 | 1.58581 | 0.792904 | − | 0.609346i | \(-0.208568\pi\) | ||||
0.792904 | + | 0.609346i | \(0.208568\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0999 | −1.41704 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.20357 | 0.243137 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.1540 | −0.827821 | −0.413911 | − | 0.910317i | \(-0.635837\pi\) | ||||
−0.413911 | + | 0.910317i | \(0.635837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.1591 | −0.904902 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.84199 | 0.149890 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.7410 | −1.00273 | −0.501363 | − | 0.865237i | \(-0.667168\pi\) | ||||
−0.501363 | + | 0.865237i | \(0.667168\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5377 | 0.798825 | 0.399412 | − | 0.916771i | \(-0.369214\pi\) | ||||
0.399412 | + | 0.916771i | \(0.369214\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.97722 | −0.0767889 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.6927 | 0.608538 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.651155 | −0.0252128 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.0464 | −1.00701 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.1770 | −1.47381 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.6808 | 1.56813 | 0.784065 | − | 0.620679i | \(-0.213143\pi\) | ||||
0.784065 | + | 0.620679i | \(0.213143\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.93676 | 0.343976 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.50092 | −0.172984 | −0.0864922 | − | 0.996253i | \(-0.527566\pi\) | ||||
−0.0864922 | + | 0.996253i | \(0.527566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.11755 | −0.158017 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.3044 | −0.624786 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.0771 | 0.538645 | 0.269322 | − | 0.963050i | \(-0.413200\pi\) | ||||
0.269322 | + | 0.963050i | \(0.413200\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.59301 | 0.175490 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.9240 | 0.569387 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.54544 | −0.0588767 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.5376 | 0.591077 | 0.295539 | − | 0.955331i | \(-0.404501\pi\) | ||||
0.295539 | + | 0.955331i | \(0.404501\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.20357 | −0.159680 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −61.7749 | −2.34326 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7885 | 0.598032 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.172841 | 0.00653743 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.92403 | −0.261517 | −0.130759 | − | 0.991414i | \(-0.541741\pi\) | ||||
−0.130759 | + | 0.991414i | \(0.541741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.1956 | −0.912555 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.6827 | 0.929604 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.6927 | −0.514968 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.0721 | 0.415823 | 0.207911 | − | 0.978148i | \(-0.433333\pi\) | ||||
0.207911 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.5514 | 0.583224 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.20357 | 0.232325 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.38136 | −0.276047 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.0999 | 1.04941 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.2204 | 0.642213 | 0.321106 | − | 0.947043i | \(-0.395945\pi\) | ||||
0.321106 | + | 0.947043i | \(0.395945\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.3667 | −0.609527 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.1175 | 0.599418 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.81921 | −0.216120 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.7273 | 0.620380 | 0.310190 | − | 0.950675i | \(-0.399607\pi\) | ||||
0.310190 | + | 0.950675i | \(0.399607\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −50.1770 | −1.85586 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.3855 | −1.15925 | −0.579625 | − | 0.814884i | \(-0.696801\pi\) | ||||
−0.579625 | + | 0.814884i | \(0.696801\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.73320 | 0.137701 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.4614 | −0.901049 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4645 | 0.936728 | 0.468364 | − | 0.883536i | \(-0.344844\pi\) | ||||
0.468364 | + | 0.883536i | \(0.344844\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.97722 | 0.0726351 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.8568 | −1.24209 | −0.621043 | − | 0.783776i | \(-0.713291\pi\) | ||||
−0.621043 | + | 0.783776i | \(0.713291\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.1029 | 0.553326 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.3677 | 0.379333 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.27953 | 0.0467530 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.37033 | −0.305438 | −0.152719 | − | 0.988270i | \(-0.548803\pi\) | ||||
−0.152719 | + | 0.988270i | \(0.548803\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.4259 | −0.780804 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.0644 | −1.13055 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.12461 | −0.222603 | −0.111301 | − | 0.993787i | \(-0.535502\pi\) | ||||
−0.111301 | + | 0.993787i | \(0.535502\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.20357 | −0.152580 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.4310 | 1.06687 | 0.533437 | − | 0.845840i | \(-0.320900\pi\) | ||||
0.533437 | + | 0.845840i | \(0.320900\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.266803 | 0.00965890 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.6927 | −0.567372 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.03948 | 0.145857 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.4498 | −1.74715 | −0.873573 | − | 0.486693i | \(-0.838203\pi\) | ||||
−0.873573 | + | 0.486693i | \(0.838203\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.3616 | −0.373163 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.6432 | 0.454745 | 0.227372 | − | 0.973808i | \(-0.426987\pi\) | ||||
0.227372 | + | 0.973808i | \(0.426987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.4398 | 1.99146 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.75598 | −0.206494 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.7885 | −0.565681 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41.4083 | −1.48170 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.651155 | −0.0232704 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −54.3972 | −1.94152 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.5207 | −0.767130 | −0.383565 | − | 0.923514i | \(-0.625304\pi\) | ||||
−0.383565 | + | 0.923514i | \(0.625304\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.487069 | 0.0173401 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.1996 | −0.611547 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.27190 | 0.151700 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.2658 | −0.435024 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0071 | 0.425312 | 0.212656 | − | 0.977127i | \(-0.431789\pi\) | ||||
0.212656 | + | 0.977127i | \(0.431789\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.7926 | −0.983232 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.7915 | 0.451965 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.1501 | −0.569923 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.73320 | 0.131578 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.1869 | 0.358595 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.88456 | −0.171732 | −0.0858659 | − | 0.996307i | \(-0.527366\pi\) | ||||
−0.0858659 | + | 0.996307i | \(0.527366\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.65910 | −0.304062 | −0.152031 | − | 0.988376i | \(-0.548581\pi\) | ||||
−0.152031 | + | 0.988376i | \(0.548581\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.26283 | 0.324862 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 57.2343 | 2.00483 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.1770 | 1.75547 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.470368 | 0.0164360 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.5199 | −0.960451 | −0.480226 | − | 0.877145i | \(-0.659445\pi\) | ||||
−0.480226 | + | 0.877145i | \(0.659445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.3617 | 1.44178 | 0.720889 | − | 0.693050i | \(-0.243734\pi\) | ||||
0.720889 | + | 0.693050i | \(0.243734\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −37.5663 | −1.30789 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.2697 | 1.01781 | 0.508904 | − | 0.860823i | \(-0.330051\pi\) | ||||
0.508904 | + | 0.860823i | \(0.330051\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.8340 | 1.86973 | 0.934867 | − | 0.354999i | \(-0.115519\pi\) | ||||
0.934867 | + | 0.354999i | \(0.115519\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.4220 | 0.916568 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.20357 | −0.145645 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −66.1355 | −2.28871 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.20357 | 0.214427 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.5920 | 0.849011 | 0.424506 | − | 0.905425i | \(-0.360448\pi\) | ||||
0.424506 | + | 0.905425i | \(0.360448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5760 | −0.985379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.3211 | 0.493245 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −47.7056 | −1.64112 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.66996 | 0.229183 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.71439 | 0.230437 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.75598 | −0.197312 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.83503 | 0.199787 | 0.0998937 | − | 0.994998i | \(-0.468150\pi\) | ||||
0.0998937 | + | 0.994998i | \(0.468150\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.6927 | 0.536680 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.3450 | 1.13904 | 0.569522 | − | 0.821976i | \(-0.307128\pi\) | ||||
0.569522 | + | 0.821976i | \(0.307128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.26381 | 0.0431206 | 0.0215603 | − | 0.999768i | \(-0.493137\pi\) | ||||
0.0215603 | + | 0.999768i | \(0.493137\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.75598 | −0.128003 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.0179 | −1.39627 | −0.698133 | − | 0.715968i | \(-0.745986\pi\) | ||||
−0.698133 | + | 0.715968i | \(0.745986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.8310 | −0.368264 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.669960 | 0.0227530 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −65.3715 | −2.21757 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.73717 | 0.0927455 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.11755 | −0.139358 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.6967 | 0.496840 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.6031 | 0.729484 | 0.364742 | − | 0.931109i | \(-0.381157\pi\) | ||||
0.364742 | + | 0.931109i | \(0.381157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.22335 | −0.0412626 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.8872 | 0.838472 | 0.419236 | − | 0.907877i | \(-0.362298\pi\) | ||||
0.419236 | + | 0.907877i | \(0.362298\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.7223 | 1.40407 | 0.702034 | − | 0.712144i | \(-0.252276\pi\) | ||||
0.702034 | + | 0.712144i | \(0.252276\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.0604 | 1.07770 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.8370 | 0.632486 | 0.316243 | − | 0.948678i | \(-0.397579\pi\) | ||||
0.316243 | + | 0.948678i | \(0.397579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.3439 | −0.346923 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.20357 | −0.140825 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.7926 | 0.930044 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38.2983 | −1.28017 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.470368 | 0.0157051 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.03948 | −0.134724 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.8113 | 0.460120 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.9368 | 0.397231 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48.8705 | −1.62451 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.72145 | 0.223182 | 0.111591 | − | 0.993754i | \(-0.464405\pi\) | ||||
0.111591 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.6927 | −0.454159 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3587 | 0.343200 | 0.171600 | − | 0.985167i | \(-0.445106\pi\) | ||||
0.171600 | + | 0.985167i | \(0.445106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.5811 | −1.44232 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.9051 | 1.12087 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.20357 | −0.204860 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0041 | 0.791823 | 0.395911 | − | 0.918289i | \(-0.370429\pi\) | ||||
0.395911 | + | 0.918289i | \(0.370429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.9774 | 0.888934 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.63347 | 0.152513 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51.4398 | −1.69133 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.3667 | −0.537552 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.0473 | 0.329640 | 0.164820 | − | 0.986324i | \(-0.447296\pi\) | ||||
0.164820 | + | 0.986324i | \(0.447296\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.20357 | 0.137766 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.9100 | −0.422655 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 65.9654 | 2.15730 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.5304 | −0.964717 | −0.482359 | − | 0.875974i | \(-0.660220\pi\) | ||||
−0.482359 | + | 0.875974i | \(0.660220\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.47434 | −0.243916 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.6333 | 0.509632 | 0.254816 | − | 0.966990i | \(-0.417985\pi\) | ||||
0.254816 | + | 0.966990i | \(0.417985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.75598 | −0.122311 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.73320 | 0.121441 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.66898 | 0.314200 | 0.157100 | − | 0.987583i | \(-0.449786\pi\) | ||||
0.157100 | + | 0.987583i | \(0.449786\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.80715 | 0.0586625 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.7788 | −0.835933 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.3627 | 0.497647 | 0.248823 | − | 0.968549i | \(-0.419956\pi\) | ||||
0.248823 | + | 0.968549i | \(0.419956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.7353 | −1.05929 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.73717 | 0.0884802 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.23032 | 0.0397290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.48422 | 0.241426 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.27953 | 0.0412323 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 38.5308 | 1.24035 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.5929 | 0.372802 | 0.186401 | − | 0.982474i | \(-0.440318\pi\) | ||||
0.186401 | + | 0.982474i | \(0.440318\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.6700 | −0.567641 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.79943 | 0.0898379 | 0.0449190 | − | 0.998991i | \(-0.485697\pi\) | ||||
0.0449190 | + | 0.998991i | \(0.485697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.5475 | −0.530487 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.20357 | 0.134622 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.5137 | −0.880243 | −0.440121 | − | 0.897938i | \(-0.645065\pi\) | ||||
−0.440121 | + | 0.897938i | \(0.645065\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.7698 | −1.71849 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.266803 | 0.00851835 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.9564 | 1.37010 | 0.685048 | − | 0.728498i | \(-0.259781\pi\) | ||||
0.685048 | + | 0.728498i | \(0.259781\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.5702 | −1.35640 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.61168 | 0.210452 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.9368 | 0.379567 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.7698 | −0.818606 | −0.409303 | − | 0.912399i | \(-0.634228\pi\) | ||||
−0.409303 | + | 0.912399i | \(0.634228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.1029 | −1.11396 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −54.7510 | −1.73572 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.1618 | 0.796883 | 0.398441 | − | 0.917194i | \(-0.369551\pi\) | ||||
0.398441 | + | 0.917194i | \(0.369551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.75598 | −0.182111 |
(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 | 3864.2.a.u.1.4 | ✓ | 4 | |
4.3 | odd | 2 | 7728.2.a.ca.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.u.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7728.2.a.ca.1.4 | 4 | 4.3 | odd | 2 |