Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(1,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(8.17668116698\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 512) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.84776\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.1 |
$q$-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 | ||||||||
\(3\) | −2.61313 | −1.50869 | −0.754344 | − | 0.656479i | \(-0.772045\pi\) | ||||
−0.754344 | + | 0.656479i | \(0.772045\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.41421 | −1.52688 | −0.763441 | − | 0.645877i | \(-0.776492\pi\) | ||||
−0.763441 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.53073 | 0.578563 | 0.289281 | − | 0.957244i | \(-0.406584\pi\) | ||||
0.289281 | + | 0.957244i | \(0.406584\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.82843 | 1.27614 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.77791 | 1.44059 | 0.720297 | − | 0.693666i | \(-0.244005\pi\) | ||||
0.720297 | + | 0.693666i | \(0.244005\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.585786 | −0.162468 | −0.0812340 | − | 0.996695i | \(-0.525886\pi\) | ||||
−0.0812340 | + | 0.996695i | \(0.525886\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.92177 | 2.30359 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | −0.685994 | −0.342997 | − | 0.939336i | \(-0.611442\pi\) | ||||
−0.342997 | + | 0.939336i | \(0.611442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.448342 | 0.102857 | 0.0514283 | − | 0.998677i | \(-0.483623\pi\) | ||||
0.0514283 | + | 0.998677i | \(0.483623\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | −0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.86030 | 1.22196 | 0.610979 | − | 0.791647i | \(-0.290776\pi\) | ||||
0.610979 | + | 0.791647i | \(0.290776\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.16478 | −0.416613 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.58579 | −0.851559 | −0.425780 | − | 0.904827i | \(-0.640000\pi\) | ||||
−0.425780 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.39104 | −1.32747 | −0.663735 | − | 0.747968i | \(-0.731030\pi\) | ||||
−0.663735 | + | 0.747968i | \(0.731030\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.4853 | −2.17341 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.22625 | −0.883398 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.07107 | 0.833678 | 0.416839 | − | 0.908980i | \(-0.363138\pi\) | ||||
0.416839 | + | 0.908980i | \(0.363138\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.53073 | 0.245114 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.61313 | 0.398498 | 0.199249 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199249 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.0711 | −1.94852 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.39104 | −1.07809 | −0.539047 | − | 0.842276i | \(-0.681215\pi\) | ||||
−0.539047 | + | 0.842276i | \(0.681215\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.65685 | −0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.39104 | 1.03495 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.41421 | −1.01842 | −0.509210 | − | 0.860642i | \(-0.670062\pi\) | ||||
−0.509210 | + | 0.860642i | \(0.670062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.3128 | −2.19962 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.17157 | −0.155179 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.61313 | −0.340200 | −0.170100 | − | 0.985427i | \(-0.554409\pi\) | ||||
−0.170100 | + | 0.985427i | \(0.554409\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0711 | −1.67358 | −0.836789 | − | 0.547525i | \(-0.815570\pi\) | ||||
−0.836789 | + | 0.547525i | \(0.815570\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.86030 | 0.738329 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0042 | 1.22220 | 0.611101 | − | 0.791552i | \(-0.290727\pi\) | ||||
0.611101 | + | 0.791552i | \(0.290727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.3137 | −1.84355 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9832 | −1.42215 | −0.711074 | − | 0.703117i | \(-0.751791\pi\) | ||||
−0.711074 | + | 0.703117i | \(0.751791\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4853 | 1.22721 | 0.613605 | − | 0.789613i | \(-0.289719\pi\) | ||||
0.613605 | + | 0.789613i | \(0.289719\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.3952 | −2.00862 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.31371 | 0.833474 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.12293 | −0.688884 | −0.344442 | − | 0.938808i | \(-0.611932\pi\) | ||||
−0.344442 | + | 0.938808i | \(0.611932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.82843 | −0.647603 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.50981 | −0.385252 | −0.192626 | − | 0.981272i | \(-0.561700\pi\) | ||||
−0.192626 | + | 0.981272i | \(0.561700\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.65685 | 1.04743 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.9832 | 1.28474 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.828427 | −0.0878131 | −0.0439065 | − | 0.999036i | \(-0.513980\pi\) | ||||
−0.0439065 | + | 0.999036i | \(0.513980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.896683 | −0.0939979 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.3137 | 2.00274 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.53073 | −0.157050 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8284 | 1.09946 | 0.549730 | − | 0.835342i | \(-0.314731\pi\) | ||||
0.549730 | + | 0.835342i | \(0.314731\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.2919 | 1.83840 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.92893 | −0.291440 | −0.145720 | − | 0.989326i | \(-0.546550\pi\) | ||||
−0.145720 | + | 0.989326i | \(0.546550\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.79884 | 0.275777 | 0.137889 | − | 0.990448i | \(-0.455968\pi\) | ||||
0.137889 | + | 0.990448i | \(0.455968\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.6569 | 1.33277 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0042 | −0.967139 | −0.483569 | − | 0.875306i | \(-0.660660\pi\) | ||||
−0.483569 | + | 0.875306i | \(0.660660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.07107 | −0.102590 | −0.0512948 | − | 0.998684i | \(-0.516335\pi\) | ||||
−0.0512948 | + | 0.998684i | \(0.516335\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.2513 | −1.25776 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.65685 | 0.344008 | 0.172004 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172004 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.0083 | −1.86579 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.24264 | −0.207332 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.32957 | −0.396891 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8284 | 1.07531 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.4525 | 0.942471 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.5140 | 1.19917 | 0.599586 | − | 0.800311i | \(-0.295332\pi\) | ||||
0.599586 | + | 0.800311i | \(0.295332\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.82843 | −0.601209 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.10748 | −0.795724 | −0.397862 | − | 0.917445i | \(-0.630248\pi\) | ||||
−0.397862 | + | 0.917445i | \(0.630248\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.686292 | 0.0595090 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.39104 | 0.636119 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.9706 | −1.79164 | −0.895818 | − | 0.444421i | \(-0.853409\pi\) | ||||
−0.895818 | + | 0.444421i | \(0.853409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.1886 | 1.62755 | 0.813776 | − | 0.581178i | \(-0.197408\pi\) | ||||
0.813776 | + | 0.581178i | \(0.197408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.3137 | 1.62651 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.79884 | −0.234050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.6569 | 1.30023 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.1689 | 1.00368 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.2426 | −0.839110 | −0.419555 | − | 0.907730i | \(-0.637814\pi\) | ||||
−0.419555 | + | 0.907730i | \(0.637814\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.92177 | −0.726043 | −0.363022 | − | 0.931781i | \(-0.618255\pi\) | ||||
−0.363022 | + | 0.931781i | \(0.618255\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.8284 | −0.875426 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.2346 | 2.02689 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.24264 | 0.498217 | 0.249108 | − | 0.968476i | \(-0.419862\pi\) | ||||
0.249108 | + | 0.968476i | \(0.419862\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.3743 | 1.53648 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.97056 | 0.706979 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.0656 | −1.02338 | −0.511690 | − | 0.859170i | \(-0.670980\pi\) | ||||
−0.511690 | + | 0.859170i | \(0.670980\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 42.6274 | 3.31854 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.53073 | 0.118452 | 0.0592259 | − | 0.998245i | \(-0.481137\pi\) | ||||
0.0592259 | + | 0.998245i | \(0.481137\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.71644 | 0.131260 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.2132 | −1.76487 | −0.882434 | − | 0.470437i | \(-0.844096\pi\) | ||||
−0.882434 | + | 0.470437i | \(0.844096\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.1899 | 0.770282 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.82843 | 0.513256 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.71644 | −0.128293 | −0.0641465 | − | 0.997940i | \(-0.520432\pi\) | ||||
−0.0641465 | + | 0.997940i | \(0.520432\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.75736 | 0.427941 | 0.213971 | − | 0.976840i | \(-0.431360\pi\) | ||||
0.213971 | + | 0.976840i | \(0.431360\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 34.1563 | 2.52491 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.3137 | −1.27293 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.5140 | −0.988239 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.31371 | −0.241037 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5140 | −0.977837 | −0.488918 | − | 0.872330i | \(-0.662608\pi\) | ||||
−0.488918 | + | 0.872330i | \(0.662608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4853 | −1.18664 | −0.593318 | − | 0.804968i | \(-0.702182\pi\) | ||||
−0.593318 | + | 0.804968i | \(0.702182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.22625 | −0.374260 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.7279 | −1.04932 | −0.524660 | − | 0.851312i | \(-0.675808\pi\) | ||||
−0.524660 | + | 0.851312i | \(0.675808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4357 | 1.59043 | 0.795214 | − | 0.606329i | \(-0.207359\pi\) | ||||
0.795214 | + | 0.606329i | \(0.207359\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.1421 | −1.84392 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.01962 | −0.492681 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.6569 | 0.953836 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.4357 | 1.55939 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.14214 | 0.148175 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.9510 | −1.85538 | −0.927692 | − | 0.373346i | \(-0.878211\pi\) | ||||
−0.927692 | + | 0.373346i | \(0.878211\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 31.3137 | 2.14558 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.92177 | −0.608460 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3137 | −0.768025 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.3994 | −1.85148 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.65685 | 0.111452 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.39104 | −0.494940 | −0.247470 | − | 0.968896i | \(-0.579599\pi\) | ||||
−0.247470 | + | 0.968896i | \(0.579599\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 25.4853 | 1.69902 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.61313 | −0.173439 | −0.0867196 | − | 0.996233i | \(-0.527638\pi\) | ||||
−0.0867196 | + | 0.996233i | \(0.527638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8995 | 1.05067 | 0.525334 | − | 0.850896i | \(-0.323940\pi\) | ||||
0.525334 | + | 0.850896i | \(0.323940\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.1116 | −1.25745 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1716 | 0.993923 | 0.496961 | − | 0.867773i | \(-0.334449\pi\) | ||||
0.496961 | + | 0.867773i | \(0.334449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.2346 | 1.64612 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.0000 | 1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.5641 | 1.91235 | 0.956173 | − | 0.292803i | \(-0.0945880\pi\) | ||||
0.956173 | + | 0.292803i | \(0.0945880\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.8284 | −1.21285 | −0.606423 | − | 0.795142i | \(-0.707396\pi\) | ||||
−0.606423 | + | 0.795142i | \(0.707396\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.7248 | 1.39364 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.8995 | 1.01578 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.262632 | −0.0167109 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.17157 | 0.581225 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.9623 | 0.881293 | 0.440647 | − | 0.897681i | \(-0.354749\pi\) | ||||
0.440647 | + | 0.897681i | \(0.354749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.0000 | 1.76034 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −25.2346 | −1.58025 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.9706 | 1.18335 | 0.591676 | − | 0.806176i | \(-0.298467\pi\) | ||||
0.591676 | + | 0.806176i | \(0.298467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.76245 | 0.482335 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.5563 | −1.08671 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.6424 | −1.27286 | −0.636432 | − | 0.771333i | \(-0.719590\pi\) | ||||
−0.636432 | + | 0.771333i | \(0.719590\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.3137 | 1.55501 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.16478 | 0.132483 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.55635 | 0.338777 | 0.169388 | − | 0.985549i | \(-0.445821\pi\) | ||||
0.169388 | + | 0.985549i | \(0.445821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.2960 | −1.71886 | −0.859431 | − | 0.511252i | \(-0.829182\pi\) | ||||
−0.859431 | + | 0.511252i | \(0.829182\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.34315 | 0.141814 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 31.8059 | 1.91797 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.585786 | 0.0351965 | 0.0175982 | − | 0.999845i | \(-0.494398\pi\) | ||||
0.0175982 | + | 0.999845i | \(0.494398\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −28.2960 | −1.69404 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.7990 | −1.30042 | −0.650209 | − | 0.759755i | \(-0.725319\pi\) | ||||
−0.650209 | + | 0.759755i | \(0.725319\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.10748 | −0.541383 | −0.270692 | − | 0.962666i | \(-0.587252\pi\) | ||||
−0.270692 | + | 0.962666i | \(0.587252\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.12293 | −0.361425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.2960 | −1.65874 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.41421 | −0.199460 | −0.0997302 | − | 0.995015i | \(-0.531798\pi\) | ||||
−0.0997302 | + | 0.995015i | \(0.531798\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.92177 | 0.519446 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.3431 | −0.600170 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.43289 | −0.198529 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.65367 | 0.439692 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 44.6274 | 2.55536 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.6829 | 1.46580 | 0.732901 | − | 0.680336i | \(-0.238166\pi\) | ||||
0.732901 | + | 0.680336i | \(0.238166\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.31371 | −0.416062 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.12840 | 0.404215 | 0.202107 | − | 0.979363i | \(-0.435221\pi\) | ||||
0.202107 | + | 0.979363i | \(0.435221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.68629 | −0.490978 | −0.245489 | − | 0.969399i | \(-0.578949\pi\) | ||||
−0.245489 | + | 0.969399i | \(0.578949\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20.0083 | −1.12734 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.5858 | −0.706888 | −0.353444 | − | 0.935456i | \(-0.614990\pi\) | ||||
−0.353444 | + | 0.935456i | \(0.614990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.9105 | −1.22675 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.1421 | 1.45911 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.26810 | −0.0705590 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.89949 | −0.216305 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.79884 | 0.154776 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3137 | −0.623745 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.67459 | −0.311904 | −0.155952 | − | 0.987765i | \(-0.549844\pi\) | ||||
−0.155952 | + | 0.987765i | \(0.549844\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.4142 | 1.06389 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −34.1563 | −1.86616 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.55582 | −0.519001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.3137 | −1.91234 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8435 | −0.963461 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 52.2843 | 2.81489 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.7248 | −1.16625 | −0.583123 | − | 0.812384i | \(-0.698170\pi\) | ||||
−0.583123 | + | 0.812384i | \(0.698170\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.7279 | 1.21660 | 0.608299 | − | 0.793708i | \(-0.291852\pi\) | ||||
0.608299 | + | 0.793708i | \(0.291852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.26810 | 0.0676862 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.9706 | −0.583904 | −0.291952 | − | 0.956433i | \(-0.594305\pi\) | ||||
−0.291952 | + | 0.956433i | \(0.594305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 40.9133 | 2.17145 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.3137 | 0.598785 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.92177 | 0.470873 | 0.235437 | − | 0.971890i | \(-0.424348\pi\) | ||||
0.235437 | + | 0.971890i | \(0.424348\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7990 | −0.989421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.9092 | −1.62231 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −35.7990 | −1.87380 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.1731 | 1.15743 | 0.578713 | − | 0.815531i | \(-0.303555\pi\) | ||||
0.578713 | + | 0.815531i | \(0.303555\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.3137 | −0.797200 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3492 | −0.589220 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.7279 | −0.969695 | −0.484848 | − | 0.874599i | \(-0.661125\pi\) | ||||
−0.484848 | + | 0.874599i | \(0.661125\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.7821 | 0.763343 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.68629 | 0.138351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.40649 | −0.226346 | −0.113173 | − | 0.993575i | \(-0.536101\pi\) | ||||
−0.113173 | + | 0.993575i | \(0.536101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.3137 | −1.80918 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.65914 | 0.442461 | 0.221231 | − | 0.975222i | \(-0.428993\pi\) | ||||
0.221231 | + | 0.975222i | \(0.428993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.9706 | −1.27262 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.0042 | 0.508540 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.3848 | 0.830741 | 0.415371 | − | 0.909652i | \(-0.363652\pi\) | ||||
0.415371 | + | 0.909652i | \(0.363652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.5754 | −0.838256 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.7990 | 1.20050 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.9050 | 1.05185 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.07107 | −0.455264 | −0.227632 | − | 0.973747i | \(-0.573098\pi\) | ||||
−0.227632 | + | 0.973747i | \(0.573098\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.79337 | −0.0897806 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.4853 | 1.22274 | 0.611368 | − | 0.791346i | \(-0.290619\pi\) | ||||
0.611368 | + | 0.791346i | \(0.290619\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.32957 | 0.215671 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.8995 | 0.988814 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.2291 | 1.20099 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.68629 | −0.429509 | −0.214755 | − | 0.976668i | \(-0.568895\pi\) | ||||
−0.214755 | + | 0.976668i | \(0.568895\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 54.7987 | 2.70302 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.9832 | 0.588234 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −50.1421 | −2.45547 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.3337 | 0.700249 | 0.350124 | − | 0.936703i | \(-0.386139\pi\) | ||||
0.350124 | + | 0.936703i | \(0.386139\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4142 | −0.556295 | −0.278147 | − | 0.960538i | \(-0.589720\pi\) | ||||
−0.278147 | + | 0.960538i | \(0.589720\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.2960 | −1.37580 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.8284 | −0.913313 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.0083 | −0.968271 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.31371 | 0.353109 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.4558 | −1.22333 | −0.611665 | − | 0.791117i | \(-0.709500\pi\) | ||||
−0.611665 | + | 0.791117i | \(0.709500\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −40.9133 | −1.96164 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.62742 | 0.125686 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8490 | −0.899614 | −0.449807 | − | 0.893126i | \(-0.648507\pi\) | ||||
−0.449807 | + | 0.893126i | \(0.648507\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.8284 | −0.848973 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0042 | 0.475312 | 0.237656 | − | 0.971349i | \(-0.423621\pi\) | ||||
0.237656 | + | 0.971349i | \(0.423621\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.82843 | 0.134080 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.7653 | 1.26596 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.1421 | 1.04495 | 0.522476 | − | 0.852654i | \(-0.325008\pi\) | ||||
0.522476 | + | 0.852654i | \(0.325008\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.1116 | −0.899932 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.3137 | 1.09537 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.06147 | 0.143524 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6274 | 0.871354 | 0.435677 | − | 0.900103i | \(-0.356509\pi\) | ||||
0.435677 | + | 0.900103i | \(0.356509\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.12293 | 0.285794 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.7574 | −1.38594 | −0.692969 | − | 0.720967i | \(-0.743698\pi\) | ||||
−0.692969 | + | 0.720967i | \(0.743698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.53620 | −0.117867 | −0.0589337 | − | 0.998262i | \(-0.518770\pi\) | ||||
−0.0589337 | + | 0.998262i | \(0.518770\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −65.9411 | −3.05795 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.9205 | −0.829260 | −0.414630 | − | 0.909990i | \(-0.636089\pi\) | ||||
−0.414630 | + | 0.909990i | \(0.636089\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.3137 | 0.707121 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.3128 | −0.751654 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.4853 | 0.574074 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.98454 | 0.136940 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.3848 | −1.29965 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.5419 | 1.85241 | 0.926204 | − | 0.377024i | \(-0.123052\pi\) | ||||
0.926204 | + | 0.377024i | \(0.123052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.97056 | −0.135446 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23.4412 | −1.06661 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −36.9706 | −1.67875 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.2178 | 1.68650 | 0.843250 | − | 0.537521i | \(-0.180639\pi\) | ||||
0.843250 | + | 0.537521i | \(0.180639\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.1421 | 1.54396 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3952 | 0.785034 | 0.392517 | − | 0.919745i | \(-0.371604\pi\) | ||||
0.392517 | + | 0.919745i | \(0.371604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.9706 | 0.584165 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −62.4524 | −2.80703 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.3431 | −0.822803 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.4985 | −0.738575 | −0.369287 | − | 0.929315i | \(-0.620398\pi\) | ||||
−0.369287 | + | 0.929315i | \(0.620398\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.00000 | −0.178707 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.1062 | 0.807314 | 0.403657 | − | 0.914910i | \(-0.367739\pi\) | ||||
0.403657 | + | 0.914910i | \(0.367739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.0740 | 1.46887 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.7574 | −0.787081 | −0.393541 | − | 0.919307i | \(-0.628750\pi\) | ||||
−0.393541 | + | 0.919307i | \(0.628750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0502 | 0.710018 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.970563 | −0.0428514 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.55582 | −0.421080 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −35.3137 | −1.55310 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 60.6590 | 2.66264 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.6569 | 0.773561 | 0.386780 | − | 0.922172i | \(-0.373587\pi\) | ||||
0.386780 | + | 0.922172i | \(0.373587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.5683 | −1.73020 | −0.865101 | − | 0.501598i | \(-0.832746\pi\) | ||||
−0.865101 | + | 0.501598i | \(0.832746\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −26.6274 | −1.16212 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.9050 | 0.910636 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3431 | 0.493180 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0042 | −0.434144 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.34315 | 0.101493 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.1563 | 1.47671 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.48528 | 0.193554 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.2500 | −0.958377 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.75736 | −0.0755548 | −0.0377774 | − | 0.999286i | \(-0.512028\pi\) | ||||
−0.0377774 | + | 0.999286i | \(0.512028\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.0447 | −0.645630 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.65685 | 0.156642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.34502 | 0.0575091 | 0.0287545 | − | 0.999587i | \(-0.490846\pi\) | ||||
0.0287545 | + | 0.999587i | \(0.490846\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −50.0416 | −2.13572 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.05600 | −0.0875885 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.37258 | −0.398563 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 45.2429 | 1.92045 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.58579 | −0.363791 | −0.181896 | − | 0.983318i | \(-0.558223\pi\) | ||||
−0.181896 | + | 0.983318i | \(0.558223\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.53073 | −0.0647431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.3137 | 1.49095 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.3533 | 0.899936 | 0.449968 | − | 0.893045i | \(-0.351435\pi\) | ||||
0.449968 | + | 0.893045i | \(0.351435\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.4853 | −0.525260 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.92177 | −0.374679 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.3431 | −0.601296 | −0.300648 | − | 0.953735i | \(-0.597203\pi\) | ||||
−0.300648 | + | 0.953735i | \(0.597203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.2500 | 0.931135 | 0.465567 | − | 0.885012i | \(-0.345850\pi\) | ||||
0.465567 | + | 0.885012i | \(0.345850\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 35.3137 | 1.47525 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 39.0112 | 1.62688 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.31371 | −0.221213 | −0.110606 | − | 0.993864i | \(-0.535279\pi\) | ||||
−0.110606 | + | 0.993864i | \(0.535279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 43.0781 | 1.79027 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.37258 | −0.222892 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.4244 | −1.46713 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.65685 | 0.316572 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.1158 | −1.20174 | −0.600869 | − | 0.799348i | \(-0.705179\pi\) | ||||
−0.600869 | + | 0.799348i | \(0.705179\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.31371 | −0.136539 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38.4859 | 1.58310 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.3137 | −0.546728 | −0.273364 | − | 0.961911i | \(-0.588136\pi\) | ||||
−0.273364 | + | 0.961911i | \(0.588136\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.7821 | 0.606006 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −58.6274 | −2.39946 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.7875 | 0.645061 | 0.322531 | − | 0.946559i | \(-0.395466\pi\) | ||||
0.322531 | + | 0.946559i | \(0.395466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.1716 | 0.618861 | 0.309431 | − | 0.950922i | \(-0.399862\pi\) | ||||
0.309431 | + | 0.950922i | \(0.399862\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.3002 | 1.55970 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40.3848 | −1.64187 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.3431 | 0.743302 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.32957 | 0.175156 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.5858 | 1.47769 | 0.738843 | − | 0.673878i | \(-0.235373\pi\) | ||||
0.738843 | + | 0.673878i | \(0.235373\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −35.6871 | −1.43904 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.5147 | 0.866150 | 0.433075 | − | 0.901358i | \(-0.357429\pi\) | ||||
0.433075 | + | 0.901358i | \(0.357429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.77791 | 0.192040 | 0.0960202 | − | 0.995379i | \(-0.469389\pi\) | ||||
0.0960202 | + | 0.995379i | \(0.469389\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.6863 | −0.509083 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.26810 | −0.0508054 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.59767 | −0.223549 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.3431 | −0.571899 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.79884 | −0.111420 | −0.0557099 | − | 0.998447i | \(-0.517742\pi\) | ||||
−0.0557099 | + | 0.998447i | \(0.517742\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 70.4264 | 2.79920 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.1396 | −1.83099 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.72792 | 0.108084 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.8770 | −1.81486 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.85786 | −0.389362 | −0.194681 | − | 0.980867i | \(-0.562367\pi\) | ||||
−0.194681 | + | 0.980867i | \(0.562367\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.34502 | 0.0530426 | 0.0265213 | − | 0.999648i | \(-0.491557\pi\) | ||||
0.0265213 | + | 0.999648i | \(0.491557\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.3137 | 0.917976 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.262632 | 0.0103251 | 0.00516257 | − | 0.999987i | \(-0.498357\pi\) | ||||
0.00516257 | + | 0.999987i | \(0.498357\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.4853 | −0.490090 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.5641 | 1.15871 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.5563 | 1.46969 | 0.734847 | − | 0.678233i | \(-0.237254\pi\) | ||||
0.734847 | + | 0.678233i | \(0.237254\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.0949 | 1.21498 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 40.1421 | 1.56609 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.0740 | −1.28838 | −0.644189 | − | 0.764866i | \(-0.722805\pi\) | ||||
−0.644189 | + | 0.764866i | \(0.722805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9289 | −0.580668 | −0.290334 | − | 0.956925i | \(-0.593766\pi\) | ||||
−0.290334 | + | 0.956925i | \(0.593766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.32957 | −0.168147 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.34315 | −0.0908633 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.8741 | −1.04057 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.3137 | 0.746711 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −62.4524 | −2.41095 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.1716 | −0.816104 | −0.408052 | − | 0.912959i | \(-0.633792\pi\) | ||||
−0.408052 | + | 0.912959i | \(0.633792\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.4107 | −0.554666 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.5563 | −0.674745 | −0.337373 | − | 0.941371i | \(-0.609538\pi\) | ||||
−0.337373 | + | 0.941371i | \(0.609538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.5754 | 0.636107 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.82843 | 0.261666 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.0852 | −0.768541 | −0.384270 | − | 0.923221i | \(-0.625547\pi\) | ||||
−0.384270 | + | 0.923221i | \(0.625547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 71.5980 | 2.73562 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41.5474 | −1.58513 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.34315 | 0.165461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9314 | 0.758226 | 0.379113 | − | 0.925350i | \(-0.376229\pi\) | ||||
0.379113 | + | 0.925350i | \(0.376229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.0000 | 1.06363 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −65.5139 | −2.48508 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.3137 | 0.428537 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −39.6452 | −1.49952 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.8701 | 1.09041 | 0.545204 | − | 0.838304i | \(-0.316452\pi\) | ||||
0.545204 | + | 0.838304i | \(0.316452\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.27357 | 0.0857493 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −65.9411 | −2.48349 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.48342 | −0.168616 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.6985 | 1.34068 | 0.670342 | − | 0.742052i | \(-0.266147\pi\) | ||||
0.670342 | + | 0.742052i | \(0.266147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.4412 | −0.879114 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.3137 | −1.62211 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.55582 | 0.357367 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −77.2548 | −2.88513 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.2459 | −0.456694 | −0.228347 | − | 0.973580i | \(-0.573332\pi\) | ||||
−0.228347 | + | 0.973580i | \(0.573332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.28427 | 0.159555 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 49.2011 | 1.82981 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.5269 | −1.13374 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.8155 | 1.58794 | 0.793969 | − | 0.607958i | \(-0.208011\pi\) | ||||
0.793969 | + | 0.607958i | \(0.208011\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.2843 | −1.45497 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.39104 | −0.273367 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.5269 | −1.71851 | −0.859255 | − | 0.511547i | \(-0.829073\pi\) | ||||
−0.859255 | + | 0.511547i | \(0.829073\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −41.5474 | −1.53250 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 47.7990 | 1.76070 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.4344 | −1.15633 | −0.578167 | − | 0.815918i | \(-0.696232\pi\) | ||||
−0.578167 | + | 0.815918i | \(0.696232\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.686292 | 0.0252115 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.5587 | 1.04772 | 0.523858 | − | 0.851806i | \(-0.324492\pi\) | ||||
0.523858 | + | 0.851806i | \(0.324492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.9706 | 1.28122 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.4370 | −0.491636 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.3137 | −0.559551 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.12293 | 0.223429 | 0.111715 | − | 0.993740i | \(-0.464366\pi\) | ||||
0.111715 | + | 0.993740i | \(0.464366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.4853 | −1.32960 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.4608 | 1.10858 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.0711 | 1.20199 | 0.600994 | − | 0.799253i | \(-0.294771\pi\) | ||||
0.600994 | + | 0.799253i | \(0.294771\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −73.1675 | −2.65581 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.6274 | −0.385244 | −0.192622 | − | 0.981273i | \(-0.561699\pi\) | ||||
−0.192622 | + | 0.981273i | \(0.561699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.63952 | −0.0593546 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 36.9706 | 1.33667 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.53073 | 0.0552716 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8284 | 0.390483 | 0.195242 | − | 0.980755i | \(-0.437451\pi\) | ||||
0.195242 | + | 0.980755i | \(0.437451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.5725 | −1.78531 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.6985 | 0.708505 | 0.354253 | − | 0.935150i | \(-0.384735\pi\) | ||||
0.354253 | + | 0.935150i | \(0.384735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −49.2011 | −1.76735 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.2843 | −0.727694 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.79337 | −0.0642540 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57.2548 | −2.04874 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.92724 | 0.354771 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3137 | −0.760719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.7527 | 1.73785 | 0.868923 | − | 0.494947i | \(-0.164813\pi\) | ||||
0.868923 | + | 0.494947i | \(0.164813\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 53.9411 | 1.92035 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.59767 | 0.199030 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.65685 | 0.271903 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −66.1479 | −2.34602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.6985 | −0.697756 | −0.348878 | − | 0.937168i | \(-0.613437\pi\) | ||||
−0.348878 | + | 0.937168i | \(0.613437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9050 | 0.739566 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.17157 | −0.112062 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.0977 | 1.76791 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.6274 | −1.07947 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.5194 | −0.511108 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.3137 | −1.66346 | −0.831731 | − | 0.555179i | \(-0.812650\pi\) | ||||
−0.831731 | + | 0.555179i | \(0.812650\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.4567 | −0.718331 | −0.359165 | − | 0.933274i | \(-0.616939\pi\) | ||||
−0.359165 | + | 0.933274i | \(0.616939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 73.9411 | 2.59323 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.6088 | 1.56258 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.17157 | 0.0409881 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.43289 | −0.119955 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.5269 | 0.925796 | 0.462898 | − | 0.886412i | \(-0.346810\pi\) | ||||
0.462898 | + | 0.886412i | \(0.346810\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.8155 | 1.49245 | 0.746227 | − | 0.665692i | \(-0.231863\pi\) | ||||
0.746227 | + | 0.665692i | \(0.231863\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −83.1127 | −2.89361 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.1158 | 1.01246 | 0.506228 | − | 0.862400i | \(-0.331039\pi\) | ||||
0.506228 | + | 0.862400i | \(0.331039\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.3848 | −0.846918 | −0.423459 | − | 0.905915i | \(-0.639184\pi\) | ||||
−0.423459 | + | 0.905915i | \(0.639184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.53073 | −0.0531006 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.1716 | 0.456368 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.22625 | −0.180862 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0000 | 0.553041 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.7540 | 1.37246 | 0.686231 | − | 0.727384i | \(-0.259264\pi\) | ||||
0.686231 | + | 0.727384i | \(0.259264\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.97056 | −0.274847 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 56.9635 | 1.96193 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 43.2132 | 1.48658 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.1062 | 0.622135 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.7990 | 0.816779 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.7180 | 1.01872 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.8995 | 1.77700 | 0.888502 | − | 0.458872i | \(-0.151746\pi\) | ||||
0.888502 | + | 0.458872i | \(0.151746\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.86030 | −0.200418 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.2843 | −1.10281 | −0.551405 | − | 0.834238i | \(-0.685908\pi\) | ||||
−0.551405 | + | 0.834238i | \(0.685908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.7444 | 0.980746 | 0.490373 | − | 0.871513i | \(-0.336861\pi\) | ||||
0.490373 | + | 0.871513i | \(0.336861\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.0000 | 0.545279 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.0781 | −1.46640 | −0.733198 | − | 0.680015i | \(-0.761973\pi\) | ||||
−0.733198 | + | 0.680015i | \(0.761973\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 79.2548 | 2.69475 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.5181 | 0.798718 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.2548 | −0.992402 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.86030 | −0.198569 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 41.4558 | 1.40307 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.65914 | −0.292732 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.4437 | −0.622798 | −0.311399 | − | 0.950279i | \(-0.600798\pi\) | ||||
−0.311399 | + | 0.950279i | \(0.600798\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.92177 | 0.300924 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.9411 | 0.941360 | 0.470680 | − | 0.882304i | \(-0.344009\pi\) | ||||
0.470680 | + | 0.882304i | \(0.344009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.98454 | 0.100438 | 0.0502190 | − | 0.998738i | \(-0.484008\pi\) | ||||
0.0502190 | + | 0.998738i | \(0.484008\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.3137 | −0.783682 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.1899 | −0.342142 | −0.171071 | − | 0.985259i | \(-0.554723\pi\) | ||||
−0.171071 | + | 0.985259i | \(0.554723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.6863 | 0.693796 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.8477 | −0.932933 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.31371 | −0.110889 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.86030 | 0.195888 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.97056 | 0.299518 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.8937 | 1.13042 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.9706 | 0.698631 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.4525 | −0.347838 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.6569 | −0.653416 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.47890 | 0.314742 | 0.157371 | − | 0.987540i | \(-0.449698\pi\) | ||||
0.157371 | + | 0.987540i | \(0.449698\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.2132 | −0.371918 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0502 | −0.531766 | −0.265883 | − | 0.964005i | \(-0.585663\pi\) | ||||
−0.265883 | + | 0.964005i | \(0.585663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.7696 | −0.554991 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −116.617 | −3.85524 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.9411 | −0.460377 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4244 | 1.16854 | 0.584272 | − | 0.811558i | \(-0.301380\pi\) | ||||
0.584272 | + | 0.811558i | \(0.301380\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −67.1127 | −2.21144 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.01962 | 0.231054 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.7574 | 1.10994 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.7151 | 0.351931 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.1716 | −1.21956 | −0.609780 | − | 0.792571i | \(-0.708742\pi\) | ||||
−0.609780 | + | 0.792571i | \(0.708742\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.08786 | −0.0684269 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.6274 | −0.609834 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.1396 | 1.50893 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.45584 | −0.243572 | −0.121786 | − | 0.992556i | \(-0.538862\pi\) | ||||
−0.121786 | + | 0.992556i | \(0.538862\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.6984 | 0.740733 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.0711 | −0.556501 | −0.278250 | − | 0.960509i | \(-0.589755\pi\) | ||||
−0.278250 | + | 0.960509i | \(0.589755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.4412 | −0.763351 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.3137 | 0.368035 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.0321 | −1.20338 | −0.601691 | − | 0.798729i | \(-0.705506\pi\) | ||||
−0.601691 | + | 0.798729i | \(0.705506\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.14214 | −0.199382 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.8882 | 1.06647 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.9706 | 1.45674 | 0.728370 | − | 0.685184i | \(-0.240278\pi\) | ||||
0.728370 | + | 0.685184i | \(0.240278\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.1396 | 1.49304 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 57.2548 | 1.85079 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.1003 | −1.03657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.6274 | 0.762175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.3002 | −1.23421 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 56.2843 | 1.81185 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.59220 | −0.147675 | −0.0738376 | − | 0.997270i | \(-0.523525\pi\) | ||||
−0.0738376 | + | 0.997270i | \(0.523525\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.31371 | 0.106452 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.58221 | −0.275416 | −0.137708 | − | 0.990473i | \(-0.543974\pi\) | ||||
−0.137708 | + | 0.990473i | \(0.543974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.3726 | 0.941642 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.1899 | 0.326337 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.1127 | 0.483498 | 0.241749 | − | 0.970339i | \(-0.422279\pi\) | ||||
0.241749 | + | 0.970339i | \(0.422279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.95815 | −0.126503 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.10051 | −0.130919 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.05600 | 0.0655762 | 0.0327881 | − | 0.999462i | \(-0.489561\pi\) | ||||
0.0327881 | + | 0.999462i | \(0.489561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 50.2843 | 1.60219 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.5641 | 0.941037 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.3137 | 0.486948 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.4412 | 0.744635 | 0.372317 | − | 0.928106i | \(-0.378563\pi\) | ||||
0.372317 | + | 0.928106i | \(0.378563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.8284 | 0.470566 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −76.6004 | −2.42840 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.38478 | 0.265549 | 0.132774 | − | 0.991146i | \(-0.457611\pi\) | ||||
0.132774 | + | 0.991146i | \(0.457611\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.9778 | −0.347321 |
(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 | 1024.2.a.h.1.1 | 4 | ||
3.2 | odd | 2 | 9216.2.a.bp.1.4 | 4 | |||
4.3 | odd | 2 | inner | 1024.2.a.h.1.4 | 4 | ||
8.3 | odd | 2 | 1024.2.a.i.1.1 | 4 | |||
8.5 | even | 2 | 1024.2.a.i.1.4 | 4 | |||
12.11 | even | 2 | 9216.2.a.bp.1.3 | 4 | |||
16.3 | odd | 4 | 1024.2.b.g.513.8 | 8 | |||
16.5 | even | 4 | 1024.2.b.g.513.7 | 8 | |||
16.11 | odd | 4 | 1024.2.b.g.513.1 | 8 | |||
16.13 | even | 4 | 1024.2.b.g.513.2 | 8 | |||
24.5 | odd | 2 | 9216.2.a.w.1.2 | 4 | |||
24.11 | even | 2 | 9216.2.a.w.1.1 | 4 | |||
32.3 | odd | 8 | 512.2.e.j.129.4 | yes | 8 | ||
32.5 | even | 8 | 512.2.e.i.385.4 | yes | 8 | ||
32.11 | odd | 8 | 512.2.e.j.385.4 | yes | 8 | ||
32.13 | even | 8 | 512.2.e.i.129.4 | yes | 8 | ||
32.19 | odd | 8 | 512.2.e.i.129.1 | ✓ | 8 | ||
32.21 | even | 8 | 512.2.e.j.385.1 | yes | 8 | ||
32.27 | odd | 8 | 512.2.e.i.385.1 | yes | 8 | ||
32.29 | even | 8 | 512.2.e.j.129.1 | yes | 8 | ||
96.5 | odd | 8 | 4608.2.k.bi.3457.4 | 8 | |||
96.11 | even | 8 | 4608.2.k.bd.3457.1 | 8 | |||
96.29 | odd | 8 | 4608.2.k.bd.1153.1 | 8 | |||
96.35 | even | 8 | 4608.2.k.bd.1153.2 | 8 | |||
96.53 | odd | 8 | 4608.2.k.bd.3457.2 | 8 | |||
96.59 | even | 8 | 4608.2.k.bi.3457.3 | 8 | |||
96.77 | odd | 8 | 4608.2.k.bi.1153.3 | 8 | |||
96.83 | even | 8 | 4608.2.k.bi.1153.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
512.2.e.i.129.1 | ✓ | 8 | 32.19 | odd | 8 | ||
512.2.e.i.129.4 | yes | 8 | 32.13 | even | 8 | ||
512.2.e.i.385.1 | yes | 8 | 32.27 | odd | 8 | ||
512.2.e.i.385.4 | yes | 8 | 32.5 | even | 8 | ||
512.2.e.j.129.1 | yes | 8 | 32.29 | even | 8 | ||
512.2.e.j.129.4 | yes | 8 | 32.3 | odd | 8 | ||
512.2.e.j.385.1 | yes | 8 | 32.21 | even | 8 | ||
512.2.e.j.385.4 | yes | 8 | 32.11 | odd | 8 | ||
1024.2.a.h.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1024.2.a.h.1.4 | 4 | 4.3 | odd | 2 | inner | ||
1024.2.a.i.1.1 | 4 | 8.3 | odd | 2 | |||
1024.2.a.i.1.4 | 4 | 8.5 | even | 2 | |||
1024.2.b.g.513.1 | 8 | 16.11 | odd | 4 | |||
1024.2.b.g.513.2 | 8 | 16.13 | even | 4 | |||
1024.2.b.g.513.7 | 8 | 16.5 | even | 4 | |||
1024.2.b.g.513.8 | 8 | 16.3 | odd | 4 | |||
4608.2.k.bd.1153.1 | 8 | 96.29 | odd | 8 | |||
4608.2.k.bd.1153.2 | 8 | 96.35 | even | 8 | |||
4608.2.k.bd.3457.1 | 8 | 96.11 | even | 8 | |||
4608.2.k.bd.3457.2 | 8 | 96.53 | odd | 8 | |||
4608.2.k.bi.1153.3 | 8 | 96.77 | odd | 8 | |||
4608.2.k.bi.1153.4 | 8 | 96.83 | even | 8 | |||
4608.2.k.bi.3457.3 | 8 | 96.59 | even | 8 | |||
4608.2.k.bi.3457.4 | 8 | 96.5 | odd | 8 | |||
9216.2.a.w.1.1 | 4 | 24.11 | even | 2 | |||
9216.2.a.w.1.2 | 4 | 24.5 | odd | 2 | |||
9216.2.a.bp.1.3 | 4 | 12.11 | even | 2 | |||
9216.2.a.bp.1.4 | 4 | 3.2 | odd | 2 |