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: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 19x^{5} + 19x^{4} - 35x^{3} - 10x^{2} + 18x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.55127\) 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 | ||||||||
\(5\) | −1.29538 | −0.579309 | −0.289655 | − | 0.957131i | \(-0.593540\pi\) | ||||
−0.289655 | + | 0.957131i | \(0.593540\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.07218 | 0.783210 | 0.391605 | − | 0.920133i | \(-0.371920\pi\) | ||||
0.391605 | + | 0.920133i | \(0.371920\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.34522 | −1.00862 | −0.504312 | − | 0.863522i | \(-0.668254\pi\) | ||||
−0.504312 | + | 0.863522i | \(0.668254\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.39646 | 0.664657 | 0.332329 | − | 0.943164i | \(-0.392166\pi\) | ||||
0.332329 | + | 0.943164i | \(0.392166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.29538 | −0.334464 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.56989 | 1.10836 | 0.554180 | − | 0.832397i | \(-0.313032\pi\) | ||||
0.554180 | + | 0.832397i | \(0.313032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.47664 | −0.568181 | −0.284091 | − | 0.958797i | \(-0.591692\pi\) | ||||
−0.284091 | + | 0.958797i | \(0.591692\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.07218 | 0.452187 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.32200 | −0.664401 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.5344 | −1.89204 | −0.946018 | − | 0.324113i | \(-0.894934\pi\) | ||||
−0.946018 | + | 0.324113i | \(0.894934\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.34522 | −0.582329 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.68425 | −0.453721 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.207606 | −0.0341302 | −0.0170651 | − | 0.999854i | \(-0.505432\pi\) | ||||
−0.0170651 | + | 0.999854i | \(0.505432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.39646 | 0.383740 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.96963 | −1.40082 | −0.700410 | − | 0.713740i | \(-0.747000\pi\) | ||||
−0.700410 | + | 0.713740i | \(0.747000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.63588 | −1.16446 | −0.582230 | − | 0.813024i | \(-0.697820\pi\) | ||||
−0.582230 | + | 0.813024i | \(0.697820\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.29538 | −0.193103 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.402401 | −0.0586962 | −0.0293481 | − | 0.999569i | \(-0.509343\pi\) | ||||
−0.0293481 | + | 0.999569i | \(0.509343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.70607 | −0.386581 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.56989 | 0.639912 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.7012 | −1.60728 | −0.803639 | − | 0.595117i | \(-0.797106\pi\) | ||||
−0.803639 | + | 0.595117i | \(0.797106\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.33332 | 0.584305 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.47664 | −0.328040 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.18505 | 0.414658 | 0.207329 | − | 0.978271i | \(-0.433523\pi\) | ||||
0.207329 | + | 0.978271i | \(0.433523\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.69207 | −0.472721 | −0.236360 | − | 0.971665i | \(-0.575955\pi\) | ||||
−0.236360 | + | 0.971665i | \(0.575955\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.07218 | 0.261070 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.10431 | −0.385042 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.52007 | 0.307875 | 0.153938 | − | 0.988081i | \(-0.450805\pi\) | ||||
0.153938 | + | 0.988081i | \(0.450805\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.77089 | 1.04091 | 0.520457 | − | 0.853888i | \(-0.325762\pi\) | ||||
0.520457 | + | 0.853888i | \(0.325762\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.10000 | 0.245786 | 0.122893 | − | 0.992420i | \(-0.460783\pi\) | ||||
0.122893 | + | 0.992420i | \(0.460783\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.32200 | −0.383592 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.93191 | −0.789964 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.54874 | −0.286756 | −0.143378 | − | 0.989668i | \(-0.545796\pi\) | ||||
−0.143378 | + | 0.989668i | \(0.545796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.26686 | 0.468349 | 0.234174 | − | 0.972195i | \(-0.424761\pi\) | ||||
0.234174 | + | 0.972195i | \(0.424761\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.91972 | −0.642084 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4643 | 1.21522 | 0.607609 | − | 0.794236i | \(-0.292129\pi\) | ||||
0.607609 | + | 0.794236i | \(0.292129\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.96589 | 0.520566 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.5344 | −1.09237 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.20818 | 0.329153 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.13627 | −0.318440 | −0.159220 | − | 0.987243i | \(-0.550898\pi\) | ||||
−0.159220 | + | 0.987243i | \(0.550898\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.34522 | −0.336208 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.99330 | −0.695860 | −0.347930 | − | 0.937521i | \(-0.613115\pi\) | ||||
−0.347930 | + | 0.937521i | \(0.613115\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.242322 | 0.0238767 | 0.0119383 | − | 0.999929i | \(-0.496200\pi\) | ||||
0.0119383 | + | 0.999929i | \(0.496200\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.68425 | −0.261956 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.51995 | 0.630307 | 0.315154 | − | 0.949041i | \(-0.397944\pi\) | ||||
0.315154 | + | 0.949041i | \(0.397944\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.31025 | −0.317064 | −0.158532 | − | 0.987354i | \(-0.550676\pi\) | ||||
−0.158532 | + | 0.987354i | \(0.550676\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.207606 | −0.0197051 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.81651 | −0.264955 | −0.132477 | − | 0.991186i | \(-0.542293\pi\) | ||||
−0.132477 | + | 0.991186i | \(0.542293\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.29538 | −0.120794 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.39646 | 0.221552 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.46963 | 0.868080 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.190527 | 0.0173206 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.96963 | −0.808764 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7801 | 0.964203 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.9180 | 1.76744 | 0.883720 | − | 0.468016i | \(-0.155031\pi\) | ||||
0.883720 | + | 0.468016i | \(0.155031\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.63588 | −0.672301 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.0614 | 1.22855 | 0.614274 | − | 0.789093i | \(-0.289449\pi\) | ||||
0.614274 | + | 0.789093i | \(0.289449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.13205 | −0.445006 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.29538 | −0.111488 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.50454 | −0.128542 | −0.0642709 | − | 0.997932i | \(-0.520472\pi\) | ||||
−0.0642709 | + | 0.997932i | \(0.520472\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.952139 | −0.0807594 | −0.0403797 | − | 0.999184i | \(-0.512857\pi\) | ||||
−0.0403797 | + | 0.999184i | \(0.512857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.402401 | −0.0338883 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.01668 | −0.670389 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.29538 | −0.107575 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.70607 | −0.223193 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.9676 | 0.898498 | 0.449249 | − | 0.893407i | \(-0.351692\pi\) | ||||
0.449249 | + | 0.893407i | \(0.351692\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.6627 | −1.60013 | −0.800064 | − | 0.599915i | \(-0.795201\pi\) | ||||
−0.800064 | + | 0.599915i | \(0.795201\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.56989 | 0.369454 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.6460 | 1.09607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.8999 | −0.949713 | −0.474856 | − | 0.880063i | \(-0.657500\pi\) | ||||
−0.474856 | + | 0.880063i | \(0.657500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.7012 | −0.927962 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.07218 | 0.163311 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.26061 | −0.412043 | −0.206021 | − | 0.978547i | \(-0.566052\pi\) | ||||
−0.206021 | + | 0.978547i | \(0.566052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.33332 | 0.337349 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.47097 | 0.578121 | 0.289061 | − | 0.957311i | \(-0.406657\pi\) | ||||
0.289061 | + | 0.957311i | \(0.406657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.25700 | −0.558231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.47664 | −0.189394 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.6123 | −1.33904 | −0.669520 | − | 0.742794i | \(-0.733500\pi\) | ||||
−0.669520 | + | 0.742794i | \(0.733500\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.88379 | −0.520366 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.18505 | 0.239403 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.7861 | −1.92734 | −0.963671 | − | 0.267092i | \(-0.913937\pi\) | ||||
−0.963671 | + | 0.267092i | \(0.913937\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.6428 | −1.83169 | −0.915843 | − | 0.401537i | \(-0.868476\pi\) | ||||
−0.915843 | + | 0.401537i | \(0.868476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.69207 | −0.272925 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.268928 | 0.0197720 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.2873 | −1.11792 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.07218 | 0.150729 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.87144 | −0.424843 | −0.212421 | − | 0.977178i | \(-0.568135\pi\) | ||||
−0.212421 | + | 0.977178i | \(0.568135\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.91160 | 0.713453 | 0.356726 | − | 0.934209i | \(-0.383893\pi\) | ||||
0.356726 | + | 0.934209i | \(0.383893\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.10431 | −0.222304 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.88494 | 0.205543 | 0.102772 | − | 0.994705i | \(-0.467229\pi\) | ||||
0.102772 | + | 0.994705i | \(0.467229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.02405 | −0.214369 | −0.107185 | − | 0.994239i | \(-0.534184\pi\) | ||||
−0.107185 | + | 0.994239i | \(0.534184\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.52007 | 0.177752 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.07218 | 0.145439 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6190 | 0.811509 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.28493 | 0.573081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0518 | −0.760838 | −0.380419 | − | 0.924814i | \(-0.624220\pi\) | ||||
−0.380419 | + | 0.924814i | \(0.624220\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.77089 | 0.600972 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.89132 | 0.674583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.8292 | −1.48186 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.10000 | 0.141905 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.9515 | 0.736680 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.7076 | −1.52062 | −0.760308 | − | 0.649563i | \(-0.774952\pi\) | ||||
−0.760308 | + | 0.649563i | \(0.774952\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.32200 | −0.221467 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.93703 | −0.327682 | −0.163841 | − | 0.986487i | \(-0.552388\pi\) | ||||
−0.163841 | + | 0.986487i | \(0.552388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.626925 | 0.0414284 | 0.0207142 | − | 0.999785i | \(-0.493406\pi\) | ||||
0.0207142 | + | 0.999785i | \(0.493406\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.93191 | −0.456086 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.30837 | −0.151227 | −0.0756133 | − | 0.997137i | \(-0.524091\pi\) | ||||
−0.0756133 | + | 0.997137i | \(0.524091\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.521260 | 0.0340033 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.54874 | −0.165558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.58186 | 0.619799 | 0.309900 | − | 0.950769i | \(-0.399705\pi\) | ||||
0.309900 | + | 0.950769i | \(0.399705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.3502 | −1.43971 | −0.719853 | − | 0.694127i | \(-0.755791\pi\) | ||||
−0.719853 | + | 0.694127i | \(0.755791\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.50538 | 0.223950 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.93517 | −0.377646 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.26686 | 0.270401 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.6196 | 1.42774 | 0.713868 | − | 0.700281i | \(-0.246942\pi\) | ||||
0.713868 | + | 0.700281i | \(0.246942\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.34522 | −0.210312 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.91972 | −0.370707 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.75230 | 0.358818 | 0.179409 | − | 0.983775i | \(-0.442581\pi\) | ||||
0.179409 | + | 0.983775i | \(0.442581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.430197 | −0.0267311 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.8177 | −1.03703 | −0.518513 | − | 0.855070i | \(-0.673514\pi\) | ||||
−0.518513 | + | 0.855070i | \(0.673514\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.1574 | 0.931111 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.4643 | 0.701606 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.31440 | 0.445967 | 0.222983 | − | 0.974822i | \(-0.428420\pi\) | ||||
0.222983 | + | 0.974822i | \(0.428420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.77195 | 0.472113 | 0.236056 | − | 0.971739i | \(-0.424145\pi\) | ||||
0.236056 | + | 0.971739i | \(0.424145\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.96589 | 0.300549 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.1128 | 0.670130 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.9342 | −0.837224 | −0.418612 | − | 0.908165i | \(-0.637483\pi\) | ||||
−0.418612 | + | 0.908165i | \(0.637483\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.5344 | −0.630679 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.2711 | −1.50755 | −0.753774 | − | 0.657134i | \(-0.771769\pi\) | ||||
−0.753774 | + | 0.657134i | \(0.771769\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.83289 | −0.108954 | −0.0544770 | − | 0.998515i | \(-0.517349\pi\) | ||||
−0.0544770 | + | 0.998515i | \(0.517349\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.20818 | 0.190036 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.5867 | −1.09714 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.88388 | 0.228464 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.13627 | −0.183851 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.56600 | −0.325169 | −0.162585 | − | 0.986695i | \(-0.551983\pi\) | ||||
−0.162585 | + | 0.986695i | \(0.551983\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.12583 | −0.240215 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.34522 | −0.194110 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.39646 | 0.138591 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.8229 | −0.912017 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.99330 | −0.401755 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.78261 | 0.273852 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.0931 | −1.26092 | −0.630459 | − | 0.776223i | \(-0.717133\pi\) | ||||
−0.630459 | + | 0.776223i | \(0.717133\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.242322 | 0.0137852 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.65450 | 0.150523 | 0.0752613 | − | 0.997164i | \(-0.476021\pi\) | ||||
0.0752613 | + | 0.997164i | \(0.476021\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0163 | 0.622675 | 0.311338 | − | 0.950299i | \(-0.399223\pi\) | ||||
0.311338 | + | 0.950299i | \(0.399223\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.68425 | −0.151240 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.4677 | 0.868750 | 0.434375 | − | 0.900732i | \(-0.356969\pi\) | ||||
0.434375 | + | 0.900732i | \(0.356969\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.34522 | −0.187297 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.51995 | 0.363908 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.3180 | −0.629750 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.96103 | −0.441599 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.31025 | −0.183057 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.833847 | −0.0459715 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.8710 | 1.36703 | 0.683516 | − | 0.729935i | \(-0.260450\pi\) | ||||
0.683516 | + | 0.729935i | \(0.260450\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.207606 | −0.0113767 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.26443 | −0.178355 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0891 | 1.42116 | 0.710581 | − | 0.703616i | \(-0.248432\pi\) | ||||
0.710581 | + | 0.703616i | \(0.248432\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.81651 | −0.152972 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.2400 | 1.90835 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1127 | −1.08599 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.29538 | −0.0697407 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.7184 | −0.682761 | −0.341381 | − | 0.939925i | \(-0.610895\pi\) | ||||
−0.341381 | + | 0.939925i | \(0.610895\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.30296 | −0.283861 | −0.141930 | − | 0.989877i | \(-0.545331\pi\) | ||||
−0.141930 | + | 0.989877i | \(0.545331\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.39646 | 0.127913 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.486228 | −0.0258793 | −0.0129397 | − | 0.999916i | \(-0.504119\pi\) | ||||
−0.0129397 | + | 0.999916i | \(0.504119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.3616 | −0.603011 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.46963 | 0.501186 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.55410 | −0.293134 | −0.146567 | − | 0.989201i | \(-0.546822\pi\) | ||||
−0.146567 | + | 0.989201i | \(0.546822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8662 | −0.677170 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.190527 | 0.0100001 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.72028 | −0.142386 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.4300 | 1.37963 | 0.689817 | − | 0.723983i | \(-0.257691\pi\) | ||||
0.689817 | + | 0.723983i | \(0.257691\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.96963 | −0.466940 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.2469 | −1.25884 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8677 | −0.718041 | −0.359020 | − | 0.933330i | \(-0.616889\pi\) | ||||
−0.359020 | + | 0.933330i | \(0.616889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.7801 | 0.556683 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.39646 | 0.123424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.75453 | 0.501057 | 0.250528 | − | 0.968109i | \(-0.419396\pi\) | ||||
0.250528 | + | 0.968109i | \(0.419396\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.9180 | 1.02043 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.2399 | −1.69848 | −0.849239 | − | 0.528009i | \(-0.822939\pi\) | ||||
−0.849239 | + | 0.528009i | \(0.822939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.97942 | 0.457634 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.63588 | −0.388153 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.7182 | 1.30397 | 0.651983 | − | 0.758234i | \(-0.273937\pi\) | ||||
0.651983 | + | 0.758234i | \(0.273937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.56989 | 0.231109 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.0614 | 0.709302 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.30157 | 0.166120 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.87415 | 0.445381 | 0.222690 | − | 0.974889i | \(-0.428516\pi\) | ||||
0.222690 | + | 0.974889i | \(0.428516\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.13205 | −0.256924 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.9358 | 0.745860 | 0.372930 | − | 0.927859i | \(-0.378353\pi\) | ||||
0.372930 | + | 0.927859i | \(0.378353\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.2453 | −1.25756 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.29538 | −0.0643677 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.694489 | 0.0344245 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.06303 | 0.349244 | 0.174622 | − | 0.984636i | \(-0.444130\pi\) | ||||
0.174622 | + | 0.984636i | \(0.444130\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50454 | −0.0742136 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.59999 | 0.324764 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.52718 | −0.271319 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.952139 | −0.0466264 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.9202 | −0.582339 | −0.291169 | − | 0.956672i | \(-0.594044\pi\) | ||||
−0.291169 | + | 0.956672i | \(0.594044\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.8575 | −1.01653 | −0.508266 | − | 0.861200i | \(-0.669713\pi\) | ||||
−0.508266 | + | 0.861200i | \(0.669713\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.402401 | −0.0195654 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.1812 | −0.736396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.65063 | −0.370240 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.01668 | −0.387049 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.8354 | 0.714596 | 0.357298 | − | 0.933991i | \(-0.383698\pi\) | ||||
0.357298 | + | 0.933991i | \(0.383698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0717 | −0.676244 | −0.338122 | − | 0.941102i | \(-0.609792\pi\) | ||||
−0.338122 | + | 0.941102i | \(0.609792\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.29538 | −0.0621085 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.47664 | −0.118474 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5612 | 0.694970 | 0.347485 | − | 0.937686i | \(-0.387036\pi\) | ||||
0.347485 | + | 0.937686i | \(0.387036\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.70607 | −0.128860 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.80116 | −0.323133 | −0.161566 | − | 0.986862i | \(-0.551655\pi\) | ||||
−0.161566 | + | 0.986862i | \(0.551655\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.8506 | −0.703987 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.9676 | 0.518748 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.6453 | −1.77659 | −0.888295 | − | 0.459273i | \(-0.848110\pi\) | ||||
−0.888295 | + | 0.459273i | \(0.848110\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.0054 | 1.41290 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.6627 | −0.923834 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.43269 | −0.301569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.7498 | 1.25130 | 0.625651 | − | 0.780103i | \(-0.284833\pi\) | ||||
0.625651 | + | 0.780103i | \(0.284833\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.56989 | 0.213304 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.4003 | −1.64876 | −0.824378 | − | 0.566040i | \(-0.808475\pi\) | ||||
−0.824378 | + | 0.566040i | \(0.808475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.0666 | 0.700205 | 0.350103 | − | 0.936711i | \(-0.386147\pi\) | ||||
0.350103 | + | 0.936711i | \(0.386147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.6460 | 0.632819 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.1976 | −1.76757 | −0.883787 | − | 0.467890i | \(-0.845014\pi\) | ||||
−0.883787 | + | 0.467890i | \(0.845014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.22203 | 0.241131 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.8999 | −0.548317 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.5437 | 1.17450 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.22742 | 0.377500 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.7012 | −0.535759 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.2228 | 1.19815 | 0.599074 | − | 0.800693i | \(-0.295535\pi\) | ||||
0.599074 | + | 0.800693i | \(0.295535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.497519 | −0.0226849 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.07218 | 0.0942875 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.06265 | 0.184475 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2431 | 1.05324 | 0.526622 | − | 0.850099i | \(-0.323458\pi\) | ||||
0.526622 | + | 0.850099i | \(0.323458\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.26061 | −0.237893 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.8054 | 0.803546 | 0.401773 | − | 0.915739i | \(-0.368394\pi\) | ||||
0.401773 | + | 0.915739i | \(0.368394\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.56989 | 0.205817 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.33332 | 0.194768 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.1749 | 0.815254 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.04536 | −0.0915628 | −0.0457814 | − | 0.998951i | \(-0.514578\pi\) | ||||
−0.0457814 | + | 0.998951i | \(0.514578\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.47097 | 0.333778 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.43371 | 0.0639258 | 0.0319629 | − | 0.999489i | \(-0.489824\pi\) | ||||
0.0319629 | + | 0.999489i | \(0.489824\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.05895 | 0.403118 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.25700 | −0.322295 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.0972 | −1.86593 | −0.932963 | − | 0.359973i | \(-0.882786\pi\) | ||||
−0.932963 | + | 0.359973i | \(0.882786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.35157 | 0.192502 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.47664 | −0.109347 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.313897 | −0.0138320 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.34612 | 0.0592024 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.6123 | −0.773095 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8944 | 1.26588 | 0.632942 | − | 0.774199i | \(-0.281847\pi\) | ||||
0.632942 | + | 0.774199i | \(0.281847\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.6066 | −1.20715 | −0.603576 | − | 0.797305i | \(-0.706258\pi\) | ||||
−0.603576 | + | 0.797305i | \(0.706258\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.88379 | −0.300433 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −48.1411 | −2.09706 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.18505 | 0.138219 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.4953 | −0.931065 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.44578 | −0.365143 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.7861 | −1.11275 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.05241 | 0.389915 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.1781 | 1.29746 | 0.648728 | − | 0.761020i | \(-0.275301\pi\) | ||||
0.648728 | + | 0.761020i | \(0.275301\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.6428 | −1.05752 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.28801 | 0.183678 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.1654 | −1.41805 | −0.709026 | − | 0.705183i | \(-0.750865\pi\) | ||||
−0.709026 | + | 0.705183i | \(0.750865\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.69207 | −0.157574 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.47664 | −0.105509 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.28145 | −0.224590 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.268928 | 0.0114153 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.76297 | −0.159442 | −0.0797212 | − | 0.996817i | \(-0.525403\pi\) | ||||
−0.0797212 | + | 0.996817i | \(0.525403\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.2990 | −0.773967 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.2873 | −0.645430 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.4214 | 0.439209 | 0.219605 | − | 0.975589i | \(-0.429523\pi\) | ||||
0.219605 | + | 0.975589i | \(0.429523\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.64843 | 0.153491 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.07218 | 0.0870234 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.75895 | −0.241428 | −0.120714 | − | 0.992687i | \(-0.538518\pi\) | ||||
−0.120714 | + | 0.992687i | \(0.538518\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.5956 | 1.15484 | 0.577420 | − | 0.816447i | \(-0.304060\pi\) | ||||
0.577420 | + | 0.816447i | \(0.304060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.87144 | −0.245283 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.32200 | −0.138537 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.1518 | −0.880563 | −0.440281 | − | 0.897860i | \(-0.645121\pi\) | ||||
−0.440281 | + | 0.897860i | \(0.645121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.91160 | 0.411912 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.84170 | 0.366815 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.1430 | 1.62114 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.10431 | −0.128347 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.77333 | 0.403388 | 0.201694 | − | 0.979449i | \(-0.435355\pi\) | ||||
0.201694 | + | 0.979449i | \(0.435355\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.0900 | 1.07502 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.88494 | 0.118671 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.8530 | 0.733134 | 0.366567 | − | 0.930392i | \(-0.380533\pi\) | ||||
0.366567 | + | 0.930392i | \(0.380533\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.2667 | −0.502887 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.02405 | −0.123766 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.3672 | 1.44506 | 0.722532 | − | 0.691337i | \(-0.242978\pi\) | ||||
0.722532 | + | 0.691337i | \(0.242978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.06551 | 0.0842540 | 0.0421270 | − | 0.999112i | \(-0.486587\pi\) | ||||
0.0421270 | + | 0.999112i | \(0.486587\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.52007 | 0.102625 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.246804 | −0.0100340 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.6383 | −0.512974 | −0.256487 | − | 0.966548i | \(-0.582565\pi\) | ||||
−0.256487 | + | 0.966548i | \(0.582565\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.07218 | 0.0839690 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.964336 | −0.0390129 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.2427 | −1.58500 | −0.792498 | − | 0.609874i | \(-0.791220\pi\) | ||||
−0.792498 | + | 0.609874i | \(0.791220\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.6190 | 0.468525 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.1575 | −0.892027 | −0.446013 | − | 0.895026i | \(-0.647157\pi\) | ||||
−0.446013 | + | 0.895026i | \(0.647157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.8696 | 1.40153 | 0.700765 | − | 0.713392i | \(-0.252842\pi\) | ||||
0.700765 | + | 0.713392i | \(0.252842\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.7562 | 0.951771 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.64572 | 0.105829 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.28493 | 0.330868 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.948736 | −0.0378286 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.841411 | 0.0334960 | 0.0167480 | − | 0.999860i | \(-0.494669\pi\) | ||||
0.0167480 | + | 0.999860i | \(0.494669\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.0518 | −0.439270 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.8013 | −1.02389 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.48497 | −0.256944 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.77089 | 0.346971 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.96517 | 0.117117 | 0.0585586 | − | 0.998284i | \(-0.481350\pi\) | ||||
0.0585586 | + | 0.998284i | \(0.481350\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.7424 | −1.25180 | −0.625900 | − | 0.779903i | \(-0.715268\pi\) | ||||
−0.625900 | + | 0.779903i | \(0.715268\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.89132 | 0.389470 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.2960 | −0.837233 | −0.418616 | − | 0.908163i | \(-0.637485\pi\) | ||||
−0.418616 | + | 0.908163i | \(0.637485\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.6547 | −0.418233 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.8292 | −0.855554 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.17578 | 0.163411 | 0.0817055 | − | 0.996657i | \(-0.473963\pi\) | ||||
0.0817055 | + | 0.996657i | \(0.473963\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.2147 | −0.711709 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.10000 | 0.0819287 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.2473 | 0.866634 | 0.433317 | − | 0.901242i | \(-0.357343\pi\) | ||||
0.433317 | + | 0.901242i | \(0.357343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.3765 | −0.481389 | −0.240694 | − | 0.970601i | \(-0.577375\pi\) | ||||
−0.240694 | + | 0.970601i | \(0.577375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.9515 | 0.425322 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.64794 | 0.257796 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.7076 | −0.877928 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.3508 | 0.476797 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.79407 | −0.261892 | −0.130946 | − | 0.991390i | \(-0.541801\pi\) | ||||
−0.130946 | + | 0.991390i | \(0.541801\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.32200 | −0.127864 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.2863 | 0.625932 | 0.312966 | − | 0.949764i | \(-0.398677\pi\) | ||||
0.312966 | + | 0.949764i | \(0.398677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.49892 | −0.249406 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.93703 | −0.189187 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.8757 | −0.990104 | −0.495052 | − | 0.868863i | \(-0.664851\pi\) | ||||
−0.495052 | + | 0.868863i | \(0.664851\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.94895 | 0.0744655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.626925 | 0.0239187 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.0413 | −1.06829 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7317 | −1.16909 | −0.584544 | − | 0.811362i | \(-0.698726\pi\) | ||||
−0.584544 | + | 0.811362i | \(0.698726\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.93191 | −0.263321 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.23338 | 0.0467847 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40.9902 | −1.55261 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.30837 | −0.0873107 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.3829 | 1.07201 | 0.536003 | − | 0.844216i | \(-0.319933\pi\) | ||||
0.536003 | + | 0.844216i | \(0.319933\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.514166 | 0.0193922 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.521260 | 0.0196318 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.4914 | −0.545005 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.0589 | 1.09133 | 0.545666 | − | 0.838003i | \(-0.316277\pi\) | ||||
0.545666 | + | 0.838003i | \(0.316277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.54874 | −0.0955852 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.5344 | −0.394517 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.3846 | 0.388362 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.58186 | 0.357841 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.4207 | 1.84308 | 0.921540 | − | 0.388283i | \(-0.126932\pi\) | ||||
0.921540 | + | 0.388283i | \(0.126932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.502134 | 0.0187004 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.3502 | −0.831215 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.32200 | −0.123376 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.8099 | 0.845972 | 0.422986 | − | 0.906136i | \(-0.360982\pi\) | ||||
0.422986 | + | 0.906136i | \(0.360982\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.8951 | −1.29064 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.89556 | 0.143886 | 0.0719429 | − | 0.997409i | \(-0.477080\pi\) | ||||
0.0719429 | + | 0.997409i | \(0.477080\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.50538 | 0.129298 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.43019 | −0.310530 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.4058 | −0.529925 | −0.264963 | − | 0.964259i | \(-0.585360\pi\) | ||||
−0.264963 | + | 0.964259i | \(0.585360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.93517 | −0.218034 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.33015 | −0.195544 | −0.0977722 | − | 0.995209i | \(-0.531172\pi\) | ||||
−0.0977722 | + | 0.995209i | \(0.531172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.2071 | −0.520508 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.26686 | 0.156116 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.5105 | 0.493663 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.7768 | 0.758157 | 0.379079 | − | 0.925364i | \(-0.376241\pi\) | ||||
0.379079 | + | 0.925364i | \(0.376241\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.6196 | 0.824303 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.4706 | 0.926969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.5790 | 1.94736 | 0.973680 | − | 0.227918i | \(-0.0731917\pi\) | ||||
0.973680 | + | 0.227918i | \(0.0731917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.34522 | −0.121424 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.1972 | 0.985896 | 0.492948 | − | 0.870059i | \(-0.335919\pi\) | ||||
0.492948 | + | 0.870059i | \(0.335919\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.85943 | −0.248328 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.91972 | −0.214028 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.63282 | 0.275605 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.1185 | 1.51883 | 0.759417 | − | 0.650605i | \(-0.225485\pi\) | ||||
0.759417 | + | 0.650605i | \(0.225485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.75230 | 0.207164 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.3920 | −0.697483 | −0.348742 | − | 0.937219i | \(-0.613391\pi\) | ||||
−0.348742 | + | 0.937219i | \(0.613391\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.9954 | 1.25707 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.430197 | −0.0154332 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.2146 | 0.795920 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.3406 | −1.04989 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.4148 | 0.550178 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.62566 | 0.129241 | 0.0646204 | − | 0.997910i | \(-0.479416\pi\) | ||||
0.0646204 | + | 0.997910i | \(0.479416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.8177 | −0.598727 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.83631 | −0.207515 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.84787 | −0.314197 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.1574 | 0.537577 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.63466 | −0.0579026 | −0.0289513 | − | 0.999581i | \(-0.509217\pi\) | ||||
−0.0289513 | + | 0.999581i | \(0.509217\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.83893 | −0.0650566 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.4643 | 0.405073 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.02496 | −0.247905 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.68425 | −0.0946074 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.31440 | 0.257479 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.0528 | −0.494069 | −0.247034 | − | 0.969007i | \(-0.579456\pi\) | ||||
−0.247034 | + | 0.969007i | \(0.579456\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.5614 | −0.405976 | −0.202988 | − | 0.979181i | \(-0.565065\pi\) | ||||
−0.202988 | + | 0.979181i | \(0.565065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.77195 | 0.272574 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.81446 | 0.238700 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.9114 | 0.661624 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.96589 | 0.173522 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.6772 | −0.896141 | −0.448070 | − | 0.893998i | \(-0.647889\pi\) | ||||
−0.448070 | + | 0.893998i | \(0.647889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.6775 | 1.31336 | 0.656678 | − | 0.754171i | \(-0.271961\pi\) | ||||
0.656678 | + | 0.754171i | \(0.271961\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.1128 | 0.386900 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.8022 | −0.410404 | −0.205202 | − | 0.978720i | \(-0.565785\pi\) | ||||
−0.205202 | + | 0.978720i | \(0.565785\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.4581 | 1.12731 | 0.563657 | − | 0.826009i | \(-0.309394\pi\) | ||||
0.563657 | + | 0.826009i | \(0.309394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.9342 | −0.483372 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.3664 | −0.428472 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.67771 | −0.334911 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.5344 | −0.364123 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.7743 | 0.958874 | 0.479437 | − | 0.877576i | \(-0.340841\pi\) | ||||
0.479437 | + | 0.877576i | \(0.340841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.2711 | −0.870383 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.40054 | 0.323388 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.394806 | 0.0135657 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.83289 | −0.0629046 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.207606 | −0.00711664 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.3405 | −1.51819 | −0.759095 | − | 0.650980i | \(-0.774358\pi\) | ||||
−0.759095 | + | 0.650980i | \(0.774358\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.20818 | 0.109718 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.1959 | −0.894833 | −0.447417 | − | 0.894326i | \(-0.647656\pi\) | ||||
−0.447417 | + | 0.894326i | \(0.647656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.69695 | 0.0920186 | 0.0460093 | − | 0.998941i | \(-0.485350\pi\) | ||||
0.0460093 | + | 0.998941i | \(0.485350\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.5867 | −0.633433 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.2978 | 1.09943 | 0.549715 | − | 0.835352i | \(-0.314736\pi\) | ||||
0.549715 | + | 0.835352i | \(0.314736\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.8146 | 0.775718 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.88388 | 0.131904 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.52610 | 0.289228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.03923 | 0.204631 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.13627 | −0.106147 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.3383 | 0.755174 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −58.3784 | −1.97130 | −0.985649 | − | 0.168807i | \(-0.946009\pi\) | ||||
−0.985649 | + | 0.168807i | \(0.946009\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.56600 | −0.187736 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.7270 | 1.13629 | 0.568145 | − | 0.822928i | \(-0.307661\pi\) | ||||
0.568145 | + | 0.822928i | \(0.307661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.7213 | −0.831939 | −0.415969 | − | 0.909379i | \(-0.636558\pi\) | ||||
−0.415969 | + | 0.909379i | \(0.636558\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.12583 | −0.138688 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.8477 | 0.464961 | 0.232480 | − | 0.972601i | \(-0.425316\pi\) | ||||
0.232480 | + | 0.972601i | \(0.425316\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.2738 | 1.38428 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.34522 | −0.112069 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.996604 | 0.0333501 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.4026 | 1.11653 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.39646 | 0.0800153 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.5344 | −0.351342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.4730 | −1.78144 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.8229 | −0.526553 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31.9217 | 1.06111 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.7772 | −1.52001 | −0.760004 | − | 0.649918i | \(-0.774803\pi\) | ||||
−0.760004 | + | 0.649918i | \(0.774803\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.99330 | −0.231953 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.0176 | −1.02766 | −0.513829 | − | 0.857892i | \(-0.671774\pi\) | ||||
−0.513829 | + | 0.857892i | \(0.671774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.2736 | −0.472387 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.78261 | 0.158108 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.1377 | 0.962211 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6585 | −0.384579 | −0.192289 | − | 0.981338i | \(-0.561591\pi\) | ||||
−0.192289 | + | 0.981338i | \(0.561591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.0931 | −0.727991 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.0191 | 0.691851 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.689668 | 0.0226761 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.242322 | 0.00795889 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.1735 | −0.432210 | −0.216105 | − | 0.976370i | \(-0.569335\pi\) | ||||
−0.216105 | + | 0.976370i | \(0.569335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.70197 | 0.219648 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.65450 | 0.0869043 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.8028 | 0.647621 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.4194 | −0.863084 | −0.431542 | − | 0.902093i | \(-0.642030\pi\) | ||||
−0.431542 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.0163 | 0.359502 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.9867 | 1.85771 | 0.928857 | − | 0.370439i | \(-0.120793\pi\) | ||||
0.928857 | + | 0.370439i | \(0.120793\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.96963 | −0.292091 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.68425 | −0.0873187 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.07399 | 0.229874 | 0.114937 | − | 0.993373i | \(-0.463333\pi\) | ||||
0.114937 | + | 0.993373i | \(0.463333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.03255 | 0.163363 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.4677 | 0.501573 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.22561 | 0.169274 | 0.0846370 | − | 0.996412i | \(-0.473027\pi\) | ||||
0.0846370 | + | 0.996412i | \(0.473027\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.60572 | 0.246115 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.34522 | −0.108136 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.11768 | −0.100675 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79.9739 | 2.57980 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.51995 | 0.210102 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.8392 | −0.413310 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.8964 | −0.607668 | −0.303834 | − | 0.952725i | \(-0.598267\pi\) | ||||
−0.303834 | + | 0.952725i | \(0.598267\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.3180 | −0.363586 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.1467 | 1.32046 | 0.660230 | − | 0.751063i | \(-0.270459\pi\) | ||||
0.660230 | + | 0.751063i | \(0.270459\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.97300 | −0.0632516 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.96103 | −0.254957 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.6384 | −0.852238 | −0.426119 | − | 0.904667i | \(-0.640119\pi\) | ||||
−0.426119 | + | 0.904667i | \(0.640119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38.3508 | −1.22570 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.31025 | −0.105688 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.8376 | 1.49389 | 0.746944 | − | 0.664887i | \(-0.231520\pi\) | ||||
0.746944 | + | 0.664887i | \(0.231520\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.73708 | −0.119073 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.833847 | −0.0265417 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.63588 | −0.242807 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.7917 | −1.83582 | −0.917908 | − | 0.396794i | \(-0.870123\pi\) | ||||
−0.917908 | + | 0.396794i | \(0.870123\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.8710 | 0.789256 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.91728 | 0.124186 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.0535 | 1.52187 | 0.760935 | − | 0.648828i | \(-0.224740\pi\) | ||||
0.760935 | + | 0.648828i | \(0.224740\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.207606 | −0.00656836 |
(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.d.1.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.d.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial |