Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(1,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2475.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.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: | \(19.7629745003\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56155 | −1.81129 | −0.905646 | − | 0.424035i | \(-0.860613\pi\) | ||||
−0.905646 | + | 0.424035i | \(0.860613\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.56155 | 2.28078 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −6.56155 | −2.31986 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.438447 | −0.121603 | −0.0608017 | − | 0.998150i | \(-0.519366\pi\) | ||||
−0.0608017 | + | 0.998150i | \(0.519366\pi\) | |||||||
\(14\) | −2.56155 | −0.684604 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.68466 | 1.92116 | ||||||||
\(17\) | −1.43845 | −0.348875 | −0.174437 | − | 0.984668i | \(-0.555811\pi\) | ||||
−0.174437 | + | 0.984668i | \(0.555811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | 0.688247 | 0.344124 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344124 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.56155 | −0.546125 | ||||||||
\(23\) | −6.56155 | −1.36818 | −0.684089 | − | 0.729398i | \(-0.739800\pi\) | ||||
−0.684089 | + | 0.729398i | \(0.739800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.12311 | 0.220259 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.56155 | 0.862052 | ||||||||
\(29\) | −5.12311 | −0.951337 | −0.475668 | − | 0.879625i | \(-0.657794\pi\) | ||||
−0.475668 | + | 0.879625i | \(0.657794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.68466 | 0.841389 | 0.420695 | − | 0.907202i | \(-0.361786\pi\) | ||||
0.420695 | + | 0.907202i | \(0.361786\pi\) | |||||||
\(32\) | −6.56155 | −1.15993 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.68466 | 0.631914 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8078 | −1.77679 | −0.888393 | − | 0.459084i | \(-0.848178\pi\) | ||||
−0.888393 | + | 0.459084i | \(0.848178\pi\) | |||||||
\(38\) | −7.68466 | −1.24662 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.68466 | 1.20014 | 0.600071 | − | 0.799947i | \(-0.295139\pi\) | ||||
0.600071 | + | 0.799947i | \(0.295139\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.68466 | 0.714404 | 0.357202 | − | 0.934027i | \(-0.383731\pi\) | ||||
0.357202 | + | 0.934027i | \(0.383731\pi\) | |||||||
\(44\) | 4.56155 | 0.687680 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.8078 | 2.47817 | ||||||||
\(47\) | −5.43845 | −0.793279 | −0.396640 | − | 0.917974i | \(-0.629824\pi\) | ||||
−0.396640 | + | 0.917974i | \(0.629824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | 1.12311 | 0.154270 | 0.0771352 | − | 0.997021i | \(-0.475423\pi\) | ||||
0.0771352 | + | 0.997021i | \(0.475423\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.56155 | −0.876824 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 13.1231 | 1.72315 | ||||||||
\(59\) | −10.5616 | −1.37500 | −0.687499 | − | 0.726186i | \(-0.741291\pi\) | ||||
−0.687499 | + | 0.726186i | \(0.741291\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.56155 | −0.968158 | −0.484079 | − | 0.875024i | \(-0.660845\pi\) | ||||
−0.484079 | + | 0.875024i | \(0.660845\pi\) | |||||||
\(62\) | −12.0000 | −1.52400 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.43845 | 0.179806 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.68466 | −0.816661 | −0.408331 | − | 0.912834i | \(-0.633889\pi\) | ||||
−0.408331 | + | 0.912834i | \(0.633889\pi\) | |||||||
\(68\) | −6.56155 | −0.795705 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.80776 | −1.04529 | −0.522645 | − | 0.852551i | \(-0.675055\pi\) | ||||
−0.522645 | + | 0.852551i | \(0.675055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.2462 | 1.90148 | 0.950738 | − | 0.309997i | \(-0.100328\pi\) | ||||
0.950738 | + | 0.309997i | \(0.100328\pi\) | |||||||
\(74\) | 27.6847 | 3.21828 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.6847 | 1.56974 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.6847 | −1.76466 | −0.882331 | − | 0.470629i | \(-0.844027\pi\) | ||||
−0.882331 | + | 0.470629i | \(0.844027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −19.6847 | −2.17381 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.0000 | −1.29399 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.56155 | −0.699464 | ||||||||
\(89\) | 17.1231 | 1.81505 | 0.907523 | − | 0.420003i | \(-0.137971\pi\) | ||||
0.907523 | + | 0.420003i | \(0.137971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.438447 | −0.0459618 | ||||||||
\(92\) | −29.9309 | −3.12051 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.9309 | 1.43686 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.12311 | 0.215569 | 0.107784 | − | 0.994174i | \(-0.465624\pi\) | ||||
0.107784 | + | 0.994174i | \(0.465624\pi\) | |||||||
\(98\) | 15.3693 | 1.55254 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.43845 | −0.143131 | −0.0715654 | − | 0.997436i | \(-0.522799\pi\) | ||||
−0.0715654 | + | 0.997436i | \(0.522799\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.12311 | −0.898926 | −0.449463 | − | 0.893299i | \(-0.648385\pi\) | ||||
−0.449463 | + | 0.893299i | \(0.648385\pi\) | |||||||
\(104\) | 2.87689 | 0.282103 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.87689 | −0.279429 | ||||||||
\(107\) | 9.12311 | 0.881964 | 0.440982 | − | 0.897516i | \(-0.354630\pi\) | ||||
0.440982 | + | 0.897516i | \(0.354630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.80776 | −0.747848 | −0.373924 | − | 0.927459i | \(-0.621988\pi\) | ||||
−0.373924 | + | 0.927459i | \(0.621988\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.68466 | 0.726132 | ||||||||
\(113\) | 9.12311 | 0.858230 | 0.429115 | − | 0.903250i | \(-0.358826\pi\) | ||||
0.429115 | + | 0.903250i | \(0.358826\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −23.3693 | −2.16979 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 27.0540 | 2.49052 | ||||||||
\(119\) | −1.43845 | −0.131862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 19.3693 | 1.75362 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 21.3693 | 1.91902 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.80776 | −0.426620 | −0.213310 | − | 0.976985i | \(-0.568424\pi\) | ||||
−0.213310 | + | 0.976985i | \(0.568424\pi\) | |||||||
\(128\) | 9.43845 | 0.834249 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4924 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | 0.260133 | ||||||||
\(134\) | 17.1231 | 1.47921 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.43845 | 0.809340 | ||||||||
\(137\) | 3.36932 | 0.287860 | 0.143930 | − | 0.989588i | \(-0.454026\pi\) | ||||
0.143930 | + | 0.989588i | \(0.454026\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 22.5616 | 1.89332 | ||||||||
\(143\) | −0.438447 | −0.0366648 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −41.6155 | −3.44413 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −49.3002 | −4.05245 | ||||||||
\(149\) | −8.80776 | −0.721560 | −0.360780 | − | 0.932651i | \(-0.617490\pi\) | ||||
−0.360780 | + | 0.932651i | \(0.617490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.6847 | −1.35778 | −0.678889 | − | 0.734241i | \(-0.737538\pi\) | ||||
−0.678889 | + | 0.734241i | \(0.737538\pi\) | |||||||
\(152\) | −19.6847 | −1.59664 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.56155 | −0.206416 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.68466 | 0.214259 | 0.107130 | − | 0.994245i | \(-0.465834\pi\) | ||||
0.107130 | + | 0.994245i | \(0.465834\pi\) | |||||||
\(158\) | 40.1771 | 3.19632 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.56155 | −0.517123 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.31534 | −0.416330 | −0.208165 | − | 0.978094i | \(-0.566749\pi\) | ||||
−0.208165 | + | 0.978094i | \(0.566749\pi\) | |||||||
\(164\) | 35.0540 | 2.73726 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3693 | 1.18931 | 0.594657 | − | 0.803980i | \(-0.297288\pi\) | ||||
0.594657 | + | 0.803980i | \(0.297288\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8078 | −0.985213 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 21.3693 | 1.62940 | ||||||||
\(173\) | −13.4384 | −1.02171 | −0.510853 | − | 0.859668i | \(-0.670670\pi\) | ||||
−0.510853 | + | 0.859668i | \(0.670670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.68466 | 0.579253 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −43.8617 | −3.28758 | ||||||||
\(179\) | −14.5616 | −1.08838 | −0.544191 | − | 0.838961i | \(-0.683163\pi\) | ||||
−0.544191 | + | 0.838961i | \(0.683163\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8769 | 0.882803 | 0.441401 | − | 0.897310i | \(-0.354482\pi\) | ||||
0.441401 | + | 0.897310i | \(0.354482\pi\) | |||||||
\(182\) | 1.12311 | 0.0832501 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 43.0540 | 3.17398 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.43845 | −0.105190 | ||||||||
\(188\) | −24.8078 | −1.80929 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.93087 | 0.139713 | 0.0698564 | − | 0.997557i | \(-0.477746\pi\) | ||||
0.0698564 | + | 0.997557i | \(0.477746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.5616 | 1.26411 | 0.632054 | − | 0.774924i | \(-0.282212\pi\) | ||||
0.632054 | + | 0.774924i | \(0.282212\pi\) | |||||||
\(194\) | −5.43845 | −0.390458 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −27.3693 | −1.95495 | ||||||||
\(197\) | −17.9309 | −1.27752 | −0.638761 | − | 0.769405i | \(-0.720553\pi\) | ||||
−0.638761 | + | 0.769405i | \(0.720553\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8078 | −0.978806 | −0.489403 | − | 0.872058i | \(-0.662785\pi\) | ||||
−0.489403 | + | 0.872058i | \(0.662785\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.68466 | 0.259252 | ||||||||
\(203\) | −5.12311 | −0.359572 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 23.3693 | 1.62822 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.36932 | −0.233620 | ||||||||
\(209\) | 3.00000 | 0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.31534 | 0.228238 | 0.114119 | − | 0.993467i | \(-0.463596\pi\) | ||||
0.114119 | + | 0.993467i | \(0.463596\pi\) | |||||||
\(212\) | 5.12311 | 0.351856 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.3693 | −1.59749 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.68466 | 0.318015 | ||||||||
\(218\) | 20.0000 | 1.35457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.630683 | 0.0424243 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.8078 | 1.46036 | 0.730178 | − | 0.683257i | \(-0.239437\pi\) | ||||
0.730178 | + | 0.683257i | \(0.239437\pi\) | |||||||
\(224\) | −6.56155 | −0.438412 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.3693 | −1.55450 | ||||||||
\(227\) | −20.4924 | −1.36013 | −0.680065 | − | 0.733152i | \(-0.738048\pi\) | ||||
−0.680065 | + | 0.733152i | \(0.738048\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.12311 | −0.536790 | −0.268395 | − | 0.963309i | \(-0.586493\pi\) | ||||
−0.268395 | + | 0.963309i | \(0.586493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 33.6155 | 2.20697 | ||||||||
\(233\) | −24.8078 | −1.62521 | −0.812605 | − | 0.582814i | \(-0.801951\pi\) | ||||
−0.812605 | + | 0.582814i | \(0.801951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −48.1771 | −3.13606 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.68466 | 0.238841 | ||||||||
\(239\) | 16.4924 | 1.06681 | 0.533403 | − | 0.845861i | \(-0.320913\pi\) | ||||
0.533403 | + | 0.845861i | \(0.320913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0540 | −0.905296 | −0.452648 | − | 0.891689i | \(-0.649521\pi\) | ||||
−0.452648 | + | 0.891689i | \(0.649521\pi\) | |||||||
\(242\) | −2.56155 | −0.164663 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −34.4924 | −2.20815 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.31534 | −0.0836932 | ||||||||
\(248\) | −30.7386 | −1.95191 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.56155 | −0.412521 | ||||||||
\(254\) | 12.3153 | 0.772733 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.0540 | −1.69087 | ||||||||
\(257\) | −18.2462 | −1.13817 | −0.569084 | − | 0.822280i | \(-0.692702\pi\) | ||||
−0.569084 | + | 0.822280i | \(0.692702\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.8078 | −0.671562 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −42.2462 | −2.60998 | ||||||||
\(263\) | 3.36932 | 0.207761 | 0.103880 | − | 0.994590i | \(-0.466874\pi\) | ||||
0.103880 | + | 0.994590i | \(0.466874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.68466 | −0.471177 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −30.4924 | −1.86262 | ||||||||
\(269\) | −28.4924 | −1.73721 | −0.868607 | − | 0.495502i | \(-0.834984\pi\) | ||||
−0.868607 | + | 0.495502i | \(0.834984\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.1771 | −1.71164 | −0.855818 | − | 0.517277i | \(-0.826946\pi\) | ||||
−0.855818 | + | 0.517277i | \(0.826946\pi\) | |||||||
\(272\) | −11.0540 | −0.670246 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.63068 | −0.521399 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.1771 | −1.39258 | −0.696288 | − | 0.717763i | \(-0.745166\pi\) | ||||
−0.696288 | + | 0.717763i | \(0.745166\pi\) | |||||||
\(278\) | −20.4924 | −1.22905 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.19224 | 0.190433 | 0.0952164 | − | 0.995457i | \(-0.469646\pi\) | ||||
0.0952164 | + | 0.995457i | \(0.469646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.1231 | 1.90952 | 0.954760 | − | 0.297377i | \(-0.0961117\pi\) | ||||
0.954760 | + | 0.297377i | \(0.0961117\pi\) | |||||||
\(284\) | −40.1771 | −2.38407 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.12311 | 0.0664106 | ||||||||
\(287\) | 7.68466 | 0.453611 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9309 | −0.878286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 74.1080 | 4.33684 | ||||||||
\(293\) | −2.06913 | −0.120880 | −0.0604399 | − | 0.998172i | \(-0.519250\pi\) | ||||
−0.0604399 | + | 0.998172i | \(0.519250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 70.9157 | 4.12189 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.5616 | 1.30696 | ||||||||
\(299\) | 2.87689 | 0.166375 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.68466 | 0.270019 | ||||||||
\(302\) | 42.7386 | 2.45933 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 23.0540 | 1.32224 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.9309 | −1.30873 | −0.654367 | − | 0.756177i | \(-0.727065\pi\) | ||||
−0.654367 | + | 0.756177i | \(0.727065\pi\) | |||||||
\(308\) | 4.56155 | 0.259919 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.7538 | 0.779906 | 0.389953 | − | 0.920835i | \(-0.372491\pi\) | ||||
0.389953 | + | 0.920835i | \(0.372491\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.2462 | −1.76614 | −0.883070 | − | 0.469241i | \(-0.844528\pi\) | ||||
−0.883070 | + | 0.469241i | \(0.844528\pi\) | |||||||
\(314\) | −6.87689 | −0.388086 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −71.5464 | −4.02480 | ||||||||
\(317\) | −6.87689 | −0.386245 | −0.193122 | − | 0.981175i | \(-0.561861\pi\) | ||||
−0.193122 | + | 0.981175i | \(0.561861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.12311 | −0.286839 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 16.8078 | 0.936660 | ||||||||
\(323\) | −4.31534 | −0.240112 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.6155 | 0.754094 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −50.4233 | −2.78416 | ||||||||
\(329\) | −5.43845 | −0.299831 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2462 | −0.563183 | −0.281591 | − | 0.959534i | \(-0.590862\pi\) | ||||
−0.281591 | + | 0.959534i | \(0.590862\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −39.3693 | −2.15419 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.6847 | −0.582030 | −0.291015 | − | 0.956718i | \(-0.593993\pi\) | ||||
−0.291015 | + | 0.956718i | \(0.593993\pi\) | |||||||
\(338\) | 32.8078 | 1.78451 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.68466 | 0.253688 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −30.7386 | −1.65732 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 34.4233 | 1.85061 | ||||||||
\(347\) | 27.3693 | 1.46926 | 0.734631 | − | 0.678467i | \(-0.237355\pi\) | ||||
0.734631 | + | 0.678467i | \(0.237355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.63068 | 0.354932 | 0.177466 | − | 0.984127i | \(-0.443210\pi\) | ||||
0.177466 | + | 0.984127i | \(0.443210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.56155 | −0.349732 | ||||||||
\(353\) | −27.8617 | −1.48293 | −0.741465 | − | 0.670991i | \(-0.765869\pi\) | ||||
−0.741465 | + | 0.670991i | \(0.765869\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 78.1080 | 4.13971 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 37.3002 | 1.97138 | ||||||||
\(359\) | −26.2462 | −1.38522 | −0.692611 | − | 0.721311i | \(-0.743540\pi\) | ||||
−0.692611 | + | 0.721311i | \(0.743540\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | −30.4233 | −1.59901 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0540 | 0.733612 | 0.366806 | − | 0.930298i | \(-0.380451\pi\) | ||||
0.366806 | + | 0.930298i | \(0.380451\pi\) | |||||||
\(368\) | −50.4233 | −2.62850 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.12311 | 0.0583087 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8078 | −0.714939 | −0.357469 | − | 0.933925i | \(-0.616360\pi\) | ||||
−0.357469 | + | 0.933925i | \(0.616360\pi\) | |||||||
\(374\) | 3.68466 | 0.190529 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 35.6847 | 1.84030 | ||||||||
\(377\) | 2.24621 | 0.115686 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.3002 | −1.24822 | −0.624108 | − | 0.781338i | \(-0.714538\pi\) | ||||
−0.624108 | + | 0.781338i | \(0.714538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.94602 | −0.253061 | ||||||||
\(383\) | −22.2462 | −1.13673 | −0.568364 | − | 0.822777i | \(-0.692424\pi\) | ||||
−0.568364 | + | 0.822777i | \(0.692424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −44.9848 | −2.28967 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.68466 | 0.491664 | ||||||||
\(389\) | 23.8617 | 1.20984 | 0.604919 | − | 0.796287i | \(-0.293205\pi\) | ||||
0.604919 | + | 0.796287i | \(0.293205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.43845 | 0.477323 | ||||||||
\(392\) | 39.3693 | 1.98845 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 45.9309 | 2.31396 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.4384 | 1.42728 | 0.713642 | − | 0.700510i | \(-0.247044\pi\) | ||||
0.713642 | + | 0.700510i | \(0.247044\pi\) | |||||||
\(398\) | 35.3693 | 1.77290 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.61553 | −0.280426 | −0.140213 | − | 0.990121i | \(-0.544779\pi\) | ||||
−0.140213 | + | 0.990121i | \(0.544779\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.05398 | −0.102316 | ||||||||
\(404\) | −6.56155 | −0.326449 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.1231 | 0.651289 | ||||||||
\(407\) | −10.8078 | −0.535721 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.05398 | 0.398243 | 0.199122 | − | 0.979975i | \(-0.436191\pi\) | ||||
0.199122 | + | 0.979975i | \(0.436191\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −41.6155 | −2.05025 | ||||||||
\(413\) | −10.5616 | −0.519700 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.87689 | 0.141051 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.68466 | −0.375869 | ||||||||
\(419\) | −25.4384 | −1.24275 | −0.621375 | − | 0.783514i | \(-0.713426\pi\) | ||||
−0.621375 | + | 0.783514i | \(0.713426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0540 | −0.831160 | −0.415580 | − | 0.909557i | \(-0.636421\pi\) | ||||
−0.415580 | + | 0.909557i | \(0.636421\pi\) | |||||||
\(422\) | −8.49242 | −0.413405 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.36932 | −0.357886 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.56155 | −0.365929 | ||||||||
\(428\) | 41.6155 | 2.01156 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.7538 | 1.04784 | 0.523922 | − | 0.851767i | \(-0.324468\pi\) | ||||
0.523922 | + | 0.851767i | \(0.324468\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9309 | 0.813646 | 0.406823 | − | 0.913507i | \(-0.366637\pi\) | ||||
0.406823 | + | 0.913507i | \(0.366637\pi\) | |||||||
\(434\) | −12.0000 | −0.576018 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.6155 | −1.70567 | ||||||||
\(437\) | −19.6847 | −0.941645 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.7386 | 0.560254 | 0.280127 | − | 0.959963i | \(-0.409623\pi\) | ||||
0.280127 | + | 0.959963i | \(0.409623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.61553 | −0.0768428 | ||||||||
\(443\) | −25.3002 | −1.20205 | −0.601024 | − | 0.799231i | \(-0.705240\pi\) | ||||
−0.601024 | + | 0.799231i | \(0.705240\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −55.8617 | −2.64513 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.43845 | 0.0679602 | ||||||||
\(449\) | 28.4924 | 1.34464 | 0.672320 | − | 0.740260i | \(-0.265298\pi\) | ||||
0.672320 | + | 0.740260i | \(0.265298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.68466 | 0.361856 | ||||||||
\(452\) | 41.6155 | 1.95743 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 52.4924 | 2.46359 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.3693 | 0.625390 | 0.312695 | − | 0.949854i | \(-0.398768\pi\) | ||||
0.312695 | + | 0.949854i | \(0.398768\pi\) | |||||||
\(458\) | 20.8078 | 0.972283 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.8617 | 0.738755 | 0.369377 | − | 0.929279i | \(-0.379571\pi\) | ||||
0.369377 | + | 0.929279i | \(0.379571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.75379 | −0.0815055 | −0.0407527 | − | 0.999169i | \(-0.512976\pi\) | ||||
−0.0407527 | + | 0.999169i | \(0.512976\pi\) | |||||||
\(464\) | −39.3693 | −1.82767 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 63.5464 | 2.94373 | ||||||||
\(467\) | −2.24621 | −0.103942 | −0.0519711 | − | 0.998649i | \(-0.516550\pi\) | ||||
−0.0519711 | + | 0.998649i | \(0.516550\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.68466 | −0.308669 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 69.3002 | 3.18980 | ||||||||
\(473\) | 4.68466 | 0.215401 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.56155 | −0.300748 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −42.2462 | −1.93230 | ||||||||
\(479\) | −3.36932 | −0.153948 | −0.0769740 | − | 0.997033i | \(-0.524526\pi\) | ||||
−0.0769740 | + | 0.997033i | \(0.524526\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.73863 | 0.216063 | ||||||||
\(482\) | 36.0000 | 1.63976 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.56155 | 0.207343 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.0540 | −0.546218 | −0.273109 | − | 0.961983i | \(-0.588052\pi\) | ||||
−0.273109 | + | 0.961983i | \(0.588052\pi\) | |||||||
\(488\) | 49.6155 | 2.24599 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4924 | −0.744293 | −0.372146 | − | 0.928174i | \(-0.621378\pi\) | ||||
−0.372146 | + | 0.928174i | \(0.621378\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.36932 | 0.331897 | ||||||||
\(494\) | 3.36932 | 0.151593 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.0000 | 1.61645 | ||||||||
\(497\) | −8.80776 | −0.395082 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.80776 | 0.170459 | 0.0852295 | − | 0.996361i | \(-0.472838\pi\) | ||||
0.0852295 | + | 0.996361i | \(0.472838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.7386 | −1.37193 | ||||||||
\(503\) | 16.4924 | 0.735361 | 0.367680 | − | 0.929952i | \(-0.380152\pi\) | ||||
0.367680 | + | 0.929952i | \(0.380152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.8078 | 0.747196 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.9309 | −0.973025 | ||||||||
\(509\) | 17.1231 | 0.758968 | 0.379484 | − | 0.925198i | \(-0.376101\pi\) | ||||
0.379484 | + | 0.925198i | \(0.376101\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.2462 | 0.718690 | ||||||||
\(512\) | 50.4233 | 2.22842 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 46.7386 | 2.06155 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.43845 | −0.239183 | ||||||||
\(518\) | 27.6847 | 1.21639 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.6155 | 1.12224 | 0.561118 | − | 0.827736i | \(-0.310371\pi\) | ||||
0.561118 | + | 0.827736i | \(0.310371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.24621 | 0.404309 | 0.202154 | − | 0.979354i | \(-0.435206\pi\) | ||||
0.202154 | + | 0.979354i | \(0.435206\pi\) | |||||||
\(524\) | 75.2311 | 3.28648 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.63068 | −0.376316 | ||||||||
\(527\) | −6.73863 | −0.293539 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.0540 | 0.871912 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.6847 | 0.593305 | ||||||||
\(533\) | −3.36932 | −0.145941 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 43.8617 | 1.89454 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 72.9848 | 3.14660 | ||||||||
\(539\) | −6.00000 | −0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.31534 | −0.314511 | −0.157256 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157256 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(542\) | 72.1771 | 3.10027 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.43845 | 0.404670 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.68466 | 0.157545 | 0.0787723 | − | 0.996893i | \(-0.474900\pi\) | ||||
0.0787723 | + | 0.996893i | \(0.474900\pi\) | |||||||
\(548\) | 15.3693 | 0.656545 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.3693 | −0.654755 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.6847 | −0.666980 | ||||||||
\(554\) | 59.3693 | 2.52236 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 36.4924 | 1.54762 | ||||||||
\(557\) | −1.12311 | −0.0475875 | −0.0237938 | − | 0.999717i | \(-0.507575\pi\) | ||||
−0.0237938 | + | 0.999717i | \(0.507575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.05398 | −0.0868739 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.17708 | −0.344929 | ||||||||
\(563\) | 10.8769 | 0.458406 | 0.229203 | − | 0.973379i | \(-0.426388\pi\) | ||||
0.229203 | + | 0.973379i | \(0.426388\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −82.2850 | −3.45870 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 57.7926 | 2.42492 | ||||||||
\(569\) | −37.9309 | −1.59014 | −0.795072 | − | 0.606515i | \(-0.792567\pi\) | ||||
−0.795072 | + | 0.606515i | \(0.792567\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.0540 | 1.59251 | 0.796255 | − | 0.604962i | \(-0.206812\pi\) | ||||
0.796255 | + | 0.604962i | \(0.206812\pi\) | |||||||
\(572\) | −2.00000 | −0.0836242 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.6847 | −0.821622 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.3693 | −1.18103 | −0.590515 | − | 0.807027i | \(-0.701075\pi\) | ||||
−0.590515 | + | 0.807027i | \(0.701075\pi\) | |||||||
\(578\) | 38.2462 | 1.59083 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.12311 | 0.0465143 | ||||||||
\(584\) | −106.600 | −4.41115 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.30019 | 0.218949 | ||||||||
\(587\) | 27.1922 | 1.12234 | 0.561172 | − | 0.827699i | \(-0.310351\pi\) | ||||
0.561172 | + | 0.827699i | \(0.310351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.0540 | 0.579084 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −83.0540 | −3.41350 | ||||||||
\(593\) | 34.1080 | 1.40065 | 0.700323 | − | 0.713826i | \(-0.253039\pi\) | ||||
0.700323 | + | 0.713826i | \(0.253039\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −40.1771 | −1.64572 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.36932 | −0.301354 | ||||||||
\(599\) | −24.1771 | −0.987849 | −0.493924 | − | 0.869505i | \(-0.664438\pi\) | ||||
−0.493924 | + | 0.869505i | \(0.664438\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.4233 | 1.52653 | 0.763264 | − | 0.646087i | \(-0.223596\pi\) | ||||
0.763264 | + | 0.646087i | \(0.223596\pi\) | |||||||
\(602\) | −12.0000 | −0.489083 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −76.1080 | −3.09679 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.24621 | 0.253526 | 0.126763 | − | 0.991933i | \(-0.459541\pi\) | ||||
0.126763 | + | 0.991933i | \(0.459541\pi\) | |||||||
\(608\) | −19.6847 | −0.798318 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.38447 | 0.0964654 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.1080 | 1.13527 | 0.567635 | − | 0.823281i | \(-0.307859\pi\) | ||||
0.567635 | + | 0.823281i | \(0.307859\pi\) | |||||||
\(614\) | 58.7386 | 2.37050 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.56155 | −0.264372 | ||||||||
\(617\) | −21.7538 | −0.875775 | −0.437887 | − | 0.899030i | \(-0.644273\pi\) | ||||
−0.437887 | + | 0.899030i | \(0.644273\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.17708 | 0.288471 | 0.144236 | − | 0.989543i | \(-0.453928\pi\) | ||||
0.144236 | + | 0.989543i | \(0.453928\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −35.2311 | −1.41264 | ||||||||
\(623\) | 17.1231 | 0.686023 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 80.0388 | 3.19899 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.2462 | 0.488677 | ||||||||
\(629\) | 15.5464 | 0.619875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.6847 | −0.903062 | −0.451531 | − | 0.892255i | \(-0.649122\pi\) | ||||
−0.451531 | + | 0.892255i | \(0.649122\pi\) | |||||||
\(632\) | 102.916 | 4.09377 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.6155 | 0.699602 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.63068 | 0.104231 | ||||||||
\(638\) | 13.1231 | 0.519549 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.7386 | −1.68807 | −0.844037 | − | 0.536285i | \(-0.819827\pi\) | ||||
−0.844037 | + | 0.536285i | \(0.819827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.3693 | 0.606107 | 0.303053 | − | 0.952974i | \(-0.401994\pi\) | ||||
0.303053 | + | 0.952974i | \(0.401994\pi\) | |||||||
\(644\) | −29.9309 | −1.17944 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.0540 | 0.434913 | ||||||||
\(647\) | 40.8078 | 1.60432 | 0.802159 | − | 0.597110i | \(-0.203684\pi\) | ||||
0.802159 | + | 0.597110i | \(0.203684\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.5616 | −0.414577 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.2462 | −0.949555 | ||||||||
\(653\) | −7.50758 | −0.293794 | −0.146897 | − | 0.989152i | \(-0.546929\pi\) | ||||
−0.146897 | + | 0.989152i | \(0.546929\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 59.0540 | 2.30567 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.9309 | 0.543082 | ||||||||
\(659\) | −8.63068 | −0.336204 | −0.168102 | − | 0.985770i | \(-0.553764\pi\) | ||||
−0.168102 | + | 0.985770i | \(0.553764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.80776 | 0.264791 | 0.132396 | − | 0.991197i | \(-0.457733\pi\) | ||||
0.132396 | + | 0.991197i | \(0.457733\pi\) | |||||||
\(662\) | 26.2462 | 1.02009 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.6155 | 1.30160 | ||||||||
\(668\) | 70.1080 | 2.71256 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.56155 | −0.291911 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.6307 | 0.409783 | 0.204891 | − | 0.978785i | \(-0.434316\pi\) | ||||
0.204891 | + | 0.978785i | \(0.434316\pi\) | |||||||
\(674\) | 27.3693 | 1.05423 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −58.4233 | −2.24705 | ||||||||
\(677\) | −29.1231 | −1.11929 | −0.559646 | − | 0.828732i | \(-0.689063\pi\) | ||||
−0.559646 | + | 0.828732i | \(0.689063\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.12311 | 0.0814773 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | −0.459504 | ||||||||
\(683\) | 20.8078 | 0.796187 | 0.398093 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398093 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 33.3002 | 1.27141 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 36.0000 | 1.37249 | ||||||||
\(689\) | −0.492423 | −0.0187598 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.4924 | 0.475234 | 0.237617 | − | 0.971359i | \(-0.423634\pi\) | ||||
0.237617 | + | 0.971359i | \(0.423634\pi\) | |||||||
\(692\) | −61.3002 | −2.33028 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −70.1080 | −2.66126 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.0540 | −0.418699 | ||||||||
\(698\) | −16.9848 | −0.642886 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.93087 | 0.0729279 | 0.0364640 | − | 0.999335i | \(-0.488391\pi\) | ||||
0.0364640 | + | 0.999335i | \(0.488391\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.4233 | −1.22287 | ||||||||
\(704\) | 1.43845 | 0.0542135 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 71.3693 | 2.68602 | ||||||||
\(707\) | −1.43845 | −0.0540984 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.12311 | 0.229958 | 0.114979 | − | 0.993368i | \(-0.463320\pi\) | ||||
0.114979 | + | 0.993368i | \(0.463320\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −112.354 | −4.21065 | ||||||||
\(713\) | −30.7386 | −1.15117 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −66.4233 | −2.48235 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 67.2311 | 2.50904 | ||||||||
\(719\) | 32.9848 | 1.23013 | 0.615064 | − | 0.788478i | \(-0.289130\pi\) | ||||
0.615064 | + | 0.788478i | \(0.289130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.12311 | −0.339762 | ||||||||
\(722\) | 25.6155 | 0.953311 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 54.1771 | 2.01348 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.0540 | −1.11464 | −0.557320 | − | 0.830298i | \(-0.688170\pi\) | ||||
−0.557320 | + | 0.830298i | \(0.688170\pi\) | |||||||
\(728\) | 2.87689 | 0.106625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.73863 | −0.249237 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.00000 | 0.0738717 | 0.0369358 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369358 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(734\) | −36.0000 | −1.32878 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 43.0540 | 1.58699 | ||||||||
\(737\) | −6.68466 | −0.246233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.6847 | −0.429827 | −0.214914 | − | 0.976633i | \(-0.568947\pi\) | ||||
−0.214914 | + | 0.976633i | \(0.568947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.87689 | −0.105614 | ||||||||
\(743\) | −47.8617 | −1.75588 | −0.877938 | − | 0.478773i | \(-0.841082\pi\) | ||||
−0.877938 | + | 0.478773i | \(0.841082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 35.3693 | 1.29496 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.56155 | −0.239914 | ||||||||
\(749\) | 9.12311 | 0.333351 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.7386 | 0.975707 | 0.487853 | − | 0.872926i | \(-0.337780\pi\) | ||||
0.487853 | + | 0.872926i | \(0.337780\pi\) | |||||||
\(752\) | −41.7926 | −1.52402 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.75379 | −0.209541 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.30019 | 0.228984 | 0.114492 | − | 0.993424i | \(-0.463476\pi\) | ||||
0.114492 | + | 0.993424i | \(0.463476\pi\) | |||||||
\(758\) | 62.2462 | 2.26088 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.6307 | −0.747862 | −0.373931 | − | 0.927457i | \(-0.621990\pi\) | ||||
−0.373931 | + | 0.927457i | \(0.621990\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.80776 | −0.282660 | ||||||||
\(764\) | 8.80776 | 0.318654 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 56.9848 | 2.05895 | ||||||||
\(767\) | 4.63068 | 0.167204 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.05398 | 0.218312 | 0.109156 | − | 0.994025i | \(-0.465185\pi\) | ||||
0.109156 | + | 0.994025i | \(0.465185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 80.1080 | 2.88315 | ||||||||
\(773\) | −48.4924 | −1.74415 | −0.872076 | − | 0.489371i | \(-0.837226\pi\) | ||||
−0.872076 | + | 0.489371i | \(0.837226\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.9309 | −0.500089 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −61.1231 | −2.19137 | ||||||||
\(779\) | 23.0540 | 0.825994 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.80776 | −0.315167 | ||||||||
\(782\) | −24.1771 | −0.864571 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −46.1080 | −1.64671 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.26137 | 0.151901 | 0.0759507 | − | 0.997112i | \(-0.475801\pi\) | ||||
0.0759507 | + | 0.997112i | \(0.475801\pi\) | |||||||
\(788\) | −81.7926 | −2.91374 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.12311 | 0.324380 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.31534 | 0.117731 | ||||||||
\(794\) | −72.8466 | −2.58523 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −62.9848 | −2.23244 | ||||||||
\(797\) | −42.8769 | −1.51878 | −0.759389 | − | 0.650637i | \(-0.774502\pi\) | ||||
−0.759389 | + | 0.650637i | \(0.774502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.82292 | 0.276755 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.3845 | 0.507933 | ||||||||
\(803\) | 16.2462 | 0.573316 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.26137 | 0.185324 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.43845 | 0.332043 | ||||||||
\(809\) | −19.6847 | −0.692076 | −0.346038 | − | 0.938221i | \(-0.612473\pi\) | ||||
−0.346038 | + | 0.938221i | \(0.612473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.00000 | −0.0351147 | −0.0175574 | − | 0.999846i | \(-0.505589\pi\) | ||||
−0.0175574 | + | 0.999846i | \(0.505589\pi\) | |||||||
\(812\) | −23.3693 | −0.820102 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 27.6847 | 0.970347 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.0540 | 0.491686 | ||||||||
\(818\) | −20.6307 | −0.721335 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.1231 | 0.876802 | 0.438401 | − | 0.898779i | \(-0.355545\pi\) | ||||
0.438401 | + | 0.898779i | \(0.355545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0539753 | 0.00188146 | 0.000940731 | − | 1.00000i | \(-0.499701\pi\) | ||||
0.000940731 | 1.00000i | \(0.499701\pi\) | ||||||||
\(824\) | 59.8617 | 2.08538 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.0540 | 0.941328 | ||||||||
\(827\) | −9.75379 | −0.339172 | −0.169586 | − | 0.985515i | \(-0.554243\pi\) | ||||
−0.169586 | + | 0.985515i | \(0.554243\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.7386 | 1.69276 | 0.846381 | − | 0.532577i | \(-0.178776\pi\) | ||||
0.846381 | + | 0.532577i | \(0.178776\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.630683 | −0.0218650 | ||||||||
\(833\) | 8.63068 | 0.299035 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.6847 | 0.473294 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 65.1619 | 2.25098 | ||||||||
\(839\) | −20.4924 | −0.707477 | −0.353738 | − | 0.935344i | \(-0.615090\pi\) | ||||
−0.353738 | + | 0.935344i | \(0.615090\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.75379 | −0.0949582 | ||||||||
\(842\) | 43.6847 | 1.50547 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.1231 | 0.520559 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 8.63068 | 0.296379 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 70.9157 | 2.43096 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.4233 | −1.21287 | −0.606435 | − | 0.795133i | \(-0.707401\pi\) | ||||
−0.606435 | + | 0.795133i | \(0.707401\pi\) | |||||||
\(854\) | 19.3693 | 0.662804 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −59.8617 | −2.04603 | ||||||||
\(857\) | −5.43845 | −0.185774 | −0.0928869 | − | 0.995677i | \(-0.529610\pi\) | ||||
−0.0928869 | + | 0.995677i | \(0.529610\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.3542 | 1.92278 | 0.961390 | − | 0.275191i | \(-0.0887411\pi\) | ||||
0.961390 | + | 0.275191i | \(0.0887411\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −55.7235 | −1.89795 | ||||||||
\(863\) | 2.24621 | 0.0764619 | 0.0382310 | − | 0.999269i | \(-0.487828\pi\) | ||||
0.0382310 | + | 0.999269i | \(0.487828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −43.3693 | −1.47375 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 21.3693 | 0.725322 | ||||||||
\(869\) | −15.6847 | −0.532066 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.93087 | 0.0993087 | ||||||||
\(872\) | 51.2311 | 1.73490 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 50.4233 | 1.70559 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0540 | 0.474569 | 0.237285 | − | 0.971440i | \(-0.423743\pi\) | ||||
0.237285 | + | 0.971440i | \(0.423743\pi\) | |||||||
\(878\) | −30.0691 | −1.01478 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.75379 | 0.328613 | 0.164307 | − | 0.986409i | \(-0.447461\pi\) | ||||
0.164307 | + | 0.986409i | \(0.447461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.9309 | −1.51204 | −0.756022 | − | 0.654546i | \(-0.772860\pi\) | ||||
−0.756022 | + | 0.654546i | \(0.772860\pi\) | |||||||
\(884\) | 2.87689 | 0.0967604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 64.8078 | 2.17726 | ||||||||
\(887\) | −27.8617 | −0.935506 | −0.467753 | − | 0.883859i | \(-0.654936\pi\) | ||||
−0.467753 | + | 0.883859i | \(0.654936\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.80776 | −0.161247 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 99.4773 | 3.33075 | ||||||||
\(893\) | −16.3153 | −0.545972 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 9.43845 | 0.315316 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −72.9848 | −2.43554 | ||||||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.61553 | −0.0538210 | ||||||||
\(902\) | −19.6847 | −0.655427 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −59.8617 | −1.99097 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.1080 | 1.53099 | 0.765495 | − | 0.643442i | \(-0.222494\pi\) | ||||
0.765495 | + | 0.643442i | \(0.222494\pi\) | |||||||
\(908\) | −93.4773 | −3.10215 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.1619 | 1.89386 | 0.946930 | − | 0.321441i | \(-0.104167\pi\) | ||||
0.946930 | + | 0.321441i | \(0.104167\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −34.2462 | −1.13276 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −37.0540 | −1.22430 | ||||||||
\(917\) | 16.4924 | 0.544628 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.1080 | 1.35603 | 0.678013 | − | 0.735050i | \(-0.262841\pi\) | ||||
0.678013 | + | 0.735050i | \(0.262841\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −40.6307 | −1.33810 | ||||||||
\(923\) | 3.86174 | 0.127111 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.49242 | 0.147630 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 33.6155 | 1.10348 | ||||||||
\(929\) | −23.2311 | −0.762186 | −0.381093 | − | 0.924537i | \(-0.624452\pi\) | ||||
−0.381093 | + | 0.924537i | \(0.624452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | −113.162 | −3.70674 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.75379 | 0.188270 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.6847 | 1.13310 | 0.566549 | − | 0.824028i | \(-0.308278\pi\) | ||||
0.566549 | + | 0.824028i | \(0.308278\pi\) | |||||||
\(938\) | 17.1231 | 0.559089 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −60.1771 | −1.96172 | −0.980858 | − | 0.194722i | \(-0.937619\pi\) | ||||
−0.980858 | + | 0.194722i | \(0.937619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50.4233 | −1.64201 | ||||||||
\(944\) | −81.1619 | −2.64160 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | 32.1771 | 1.04561 | 0.522807 | − | 0.852451i | \(-0.324885\pi\) | ||||
0.522807 | + | 0.852451i | \(0.324885\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.12311 | −0.231226 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.43845 | 0.305902 | ||||||||
\(953\) | 4.80776 | 0.155739 | 0.0778694 | − | 0.996964i | \(-0.475188\pi\) | ||||
0.0778694 | + | 0.996964i | \(0.475188\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 75.2311 | 2.43315 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.63068 | 0.278845 | ||||||||
\(959\) | 3.36932 | 0.108801 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.05398 | −0.292064 | ||||||||
\(962\) | −12.1383 | −0.391353 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −64.1080 | −2.06478 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.0000 | 1.41494 | 0.707472 | − | 0.706741i | \(-0.249835\pi\) | ||||
0.707472 | + | 0.706741i | \(0.249835\pi\) | |||||||
\(968\) | −6.56155 | −0.210896 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.17708 | −0.262415 | −0.131208 | − | 0.991355i | \(-0.541885\pi\) | ||||
−0.131208 | + | 0.991355i | \(0.541885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00000 | 0.256468 | ||||||||
\(974\) | 30.8769 | 0.989360 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −58.1080 | −1.85999 | ||||||||
\(977\) | 25.6155 | 0.819513 | 0.409757 | − | 0.912195i | \(-0.365614\pi\) | ||||
0.409757 | + | 0.912195i | \(0.365614\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.1231 | 0.547257 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 42.2462 | 1.34813 | ||||||||
\(983\) | −21.9309 | −0.699486 | −0.349743 | − | 0.936846i | \(-0.613731\pi\) | ||||
−0.349743 | + | 0.936846i | \(0.613731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.8769 | −0.601163 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.00000 | −0.190885 | ||||||||
\(989\) | −30.7386 | −0.977432 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.3153 | 1.18536 | 0.592680 | − | 0.805438i | \(-0.298070\pi\) | ||||
0.592680 | + | 0.805438i | \(0.298070\pi\) | |||||||
\(992\) | −30.7386 | −0.975953 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22.5616 | 0.715609 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.7386 | 0.656799 | 0.328400 | − | 0.944539i | \(-0.393491\pi\) | ||||
0.328400 | + | 0.944539i | \(0.393491\pi\) | |||||||
\(998\) | −9.75379 | −0.308751 | ||||||||
\(999\) | 0 | 0 |
(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 | 2475.2.a.q.1.1 | yes | 2 | |
3.2 | odd | 2 | 2475.2.a.v.1.2 | yes | 2 | ||
5.2 | odd | 4 | 2475.2.c.j.199.1 | 4 | |||
5.3 | odd | 4 | 2475.2.c.j.199.4 | 4 | |||
5.4 | even | 2 | 2475.2.a.u.1.2 | yes | 2 | ||
15.2 | even | 4 | 2475.2.c.i.199.4 | 4 | |||
15.8 | even | 4 | 2475.2.c.i.199.1 | 4 | |||
15.14 | odd | 2 | 2475.2.a.p.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2475.2.a.p.1.1 | ✓ | 2 | 15.14 | odd | 2 | ||
2475.2.a.q.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
2475.2.a.u.1.2 | yes | 2 | 5.4 | even | 2 | ||
2475.2.a.v.1.2 | yes | 2 | 3.2 | odd | 2 | ||
2475.2.c.i.199.1 | 4 | 15.8 | even | 4 | |||
2475.2.c.i.199.4 | 4 | 15.2 | even | 4 | |||
2475.2.c.j.199.1 | 4 | 5.2 | odd | 4 | |||
2475.2.c.j.199.4 | 4 | 5.3 | odd | 4 |