Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.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: | \(54.8093159474\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.22676.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 6x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.35449\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.16536 | −0.968379 | −0.484189 | − | 0.874963i | \(-0.660885\pi\) | ||||
−0.484189 | + | 0.874963i | \(0.660885\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.64193 | 1.37652 | 0.688261 | − | 0.725463i | \(-0.258375\pi\) | ||||
0.688261 | + | 0.725463i | \(0.258375\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.16536 | −0.559094 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.80729 | 1.40848 | 0.704238 | − | 0.709964i | \(-0.251289\pi\) | ||||
0.704238 | + | 0.709964i | \(0.251289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.70898 | −0.621482 | −0.310741 | − | 0.950495i | \(-0.600577\pi\) | ||||
−0.310741 | + | 0.950495i | \(0.600577\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.64193 | 0.794735 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.50785 | −1.98252 | −0.991262 | − | 0.131911i | \(-0.957889\pi\) | ||||
−0.991262 | + | 0.131911i | \(0.957889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.311211 | −0.0622422 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.4095 | −1.93300 | −0.966500 | − | 0.256665i | \(-0.917376\pi\) | ||||
−0.966500 | + | 0.256665i | \(0.917376\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.5163 | −1.88878 | −0.944389 | − | 0.328830i | \(-0.893346\pi\) | ||||
−0.944389 | + | 0.328830i | \(0.893346\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.88610 | −1.33299 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.19664 | 1.34752 | 0.673759 | − | 0.738951i | \(-0.264678\pi\) | ||||
0.673759 | + | 0.738951i | \(0.264678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.31121 | −0.829472 | −0.414736 | − | 0.909942i | \(-0.636126\pi\) | ||||
−0.414736 | + | 0.909942i | \(0.636126\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.74025 | 1.33288 | 0.666438 | − | 0.745561i | \(-0.267818\pi\) | ||||
0.666438 | + | 0.745561i | \(0.267818\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.16536 | −0.322793 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.41795 | −0.790290 | −0.395145 | − | 0.918619i | \(-0.629306\pi\) | ||||
−0.395145 | + | 0.918619i | \(0.629306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.26368 | 0.894811 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.80729 | 0.813184 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.16536 | −0.291977 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.70898 | −0.358813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.35091 | −0.826818 | −0.413409 | − | 0.910545i | \(-0.635662\pi\) | ||||
−0.413409 | + | 0.910545i | \(0.635662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.79887 | −1.12658 | −0.563290 | − | 0.826259i | \(-0.690465\pi\) | ||||
−0.563290 | + | 0.826259i | \(0.690465\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.64193 | 0.458840 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.16536 | 0.268580 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.70055 | −0.207755 | −0.103878 | − | 0.994590i | \(-0.533125\pi\) | ||||
−0.103878 | + | 0.994590i | \(0.533125\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.50785 | −1.14461 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.91277 | −0.345682 | −0.172841 | − | 0.984950i | \(-0.555295\pi\) | ||||
−0.172841 | + | 0.984950i | \(0.555295\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.9727 | −1.63538 | −0.817688 | − | 0.575662i | \(-0.804744\pi\) | ||||
−0.817688 | + | 0.575662i | \(0.804744\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.311211 | −0.0359356 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.64193 | 0.415037 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.80729 | 0.428354 | 0.214177 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214177 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.7018 | 1.83326 | 0.916631 | − | 0.399733i | \(-0.130897\pi\) | ||||
0.916631 | + | 0.399733i | \(0.130897\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.5749 | −1.36394 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4095 | −1.11602 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.4290 | −1.21148 | −0.605738 | − | 0.795664i | \(-0.707122\pi\) | ||||
−0.605738 | + | 0.795664i | \(0.707122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.64193 | −0.381778 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.5163 | −1.09049 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.86591 | 0.601830 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.19664 | 0.832242 | 0.416121 | − | 0.909309i | \(-0.363389\pi\) | ||||
0.416121 | + | 0.909309i | \(0.363389\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.89453 | 0.288016 | 0.144008 | − | 0.989577i | \(-0.454001\pi\) | ||||
0.144008 | + | 0.989577i | \(0.454001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.35091 | 0.231642 | 0.115821 | − | 0.993270i | \(-0.463050\pi\) | ||||
0.115821 | + | 0.993270i | \(0.463050\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.88610 | −0.769605 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.06704 | 0.296502 | 0.148251 | − | 0.988950i | \(-0.452636\pi\) | ||||
0.148251 | + | 0.988950i | \(0.452636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4408 | 1.19161 | 0.595806 | − | 0.803128i | \(-0.296833\pi\) | ||||
0.595806 | + | 0.803128i | \(0.296833\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.19664 | 0.777990 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.3431 | −1.63150 | −0.815750 | − | 0.578405i | \(-0.803675\pi\) | ||||
−0.815750 | + | 0.578405i | \(0.803675\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.5879 | 1.91983 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.1498 | 1.93880 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.31121 | −0.478896 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5007 | 1.02865 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.80729 | −0.692785 | −0.346393 | − | 0.938090i | \(-0.612594\pi\) | ||||
−0.346393 | + | 0.938090i | \(0.612594\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.74025 | 0.769536 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.46815 | 0.565125 | 0.282562 | − | 0.959249i | \(-0.408816\pi\) | ||||
0.282562 | + | 0.959249i | \(0.408816\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.86591 | −0.855483 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.16536 | −0.186365 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.7129 | −1.59875 | −0.799376 | − | 0.600831i | \(-0.794836\pi\) | ||||
−0.799376 | + | 0.600831i | \(0.794836\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.13802 | 0.690258 | 0.345129 | − | 0.938555i | \(-0.387835\pi\) | ||||
0.345129 | + | 0.938555i | \(0.387835\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.41795 | −0.456274 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.5404 | 1.87188 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.26368 | 0.516620 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.0554 | 1.64300 | 0.821501 | − | 0.570207i | \(-0.193137\pi\) | ||||
0.821501 | + | 0.570207i | \(0.193137\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.57489 | −0.697815 | −0.348907 | − | 0.937157i | \(-0.613447\pi\) | ||||
−0.348907 | + | 0.937157i | \(0.613447\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.80729 | 0.469492 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.7715 | 1.82905 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9928 | −0.957133 | −0.478567 | − | 0.878051i | \(-0.658843\pi\) | ||||
−0.478567 | + | 0.878051i | \(0.658843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −34.6269 | −2.72899 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.5990 | −1.61344 | −0.806719 | − | 0.590935i | \(-0.798759\pi\) | ||||
−0.806719 | + | 0.590935i | \(0.798759\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.16536 | −0.168573 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.154275 | −0.0119381 | −0.00596907 | − | 0.999982i | \(-0.501900\pi\) | ||||
−0.00596907 | + | 0.999982i | \(0.501900\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.70898 | −0.207161 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.02412 | 0.153891 | 0.0769454 | − | 0.997035i | \(-0.475483\pi\) | ||||
0.0769454 | + | 0.997035i | \(0.475483\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.13341 | −0.0856778 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.35091 | −0.477364 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.7011 | 1.17356 | 0.586779 | − | 0.809747i | \(-0.300396\pi\) | ||||
0.586779 | + | 0.809747i | \(0.300396\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.26102 | 0.316719 | 0.158359 | − | 0.987382i | \(-0.449380\pi\) | ||||
0.158359 | + | 0.987382i | \(0.449380\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.79887 | −0.650431 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.7487 | −1.30491 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.80729 | 0.424671 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.64193 | 0.264912 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.154275 | 0.0111629 | 0.00558147 | − | 0.999984i | \(-0.498223\pi\) | ||||
0.00558147 | + | 0.999984i | \(0.498223\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4108 | 1.25326 | 0.626628 | − | 0.779318i | \(-0.284434\pi\) | ||||
0.626628 | + | 0.779318i | \(0.284434\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.16536 | 0.155065 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.6621 | −1.40087 | −0.700434 | − | 0.713717i | \(-0.747010\pi\) | ||||
−0.700434 | + | 0.713717i | \(0.747010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.42129 | −0.384305 | −0.192153 | − | 0.981365i | \(-0.561547\pi\) | ||||
−0.192153 | + | 0.981365i | \(0.561547\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.70055 | −0.119948 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −37.9108 | −2.66082 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.5007 | 0.803243 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.50785 | −0.660841 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.70898 | −0.187384 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0912 | 1.31429 | 0.657145 | − | 0.753764i | \(-0.271764\pi\) | ||||
0.657145 | + | 0.753764i | \(0.271764\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.91277 | −0.199580 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.9258 | −1.29073 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −38.2996 | −2.59994 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.9727 | −0.944185 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.80729 | −0.390641 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.46942 | −0.0983994 | −0.0491997 | − | 0.998789i | \(-0.515667\pi\) | ||||
−0.0491997 | + | 0.998789i | \(0.515667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.311211 | −0.0207474 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.62175 | −0.373128 | −0.186564 | − | 0.982443i | \(-0.559735\pi\) | ||||
−0.186564 | + | 0.982443i | \(0.559735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.0059 | 1.32203 | 0.661013 | − | 0.750375i | \(-0.270127\pi\) | ||||
0.661013 | + | 0.750375i | \(0.270127\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.64193 | 0.239622 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.18487 | 0.208648 | 0.104324 | − | 0.994543i | \(-0.466732\pi\) | ||||
0.104324 | + | 0.994543i | \(0.466732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.7318 | 0.765300 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.80729 | 0.247310 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.60291 | 0.621161 | 0.310580 | − | 0.950547i | \(-0.399477\pi\) | ||||
0.310580 | + | 0.950547i | \(0.399477\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.07940 | −0.520440 | −0.260220 | − | 0.965549i | \(-0.583795\pi\) | ||||
−0.260220 | + | 0.965549i | \(0.583795\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.5631 | −0.866516 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.70898 | 0.172368 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.7018 | 1.05843 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.01569 | −0.442827 | −0.221413 | − | 0.975180i | \(-0.571067\pi\) | ||||
−0.221413 | + | 0.975180i | \(0.571067\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.50785 | −0.597753 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.5749 | −0.787470 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −31.3262 | −1.95408 | −0.977038 | − | 0.213064i | \(-0.931656\pi\) | ||||
−0.977038 | + | 0.213064i | \(0.931656\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.8516 | 1.85489 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.4095 | −0.644334 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.95314 | −0.428749 | −0.214375 | − | 0.976752i | \(-0.568771\pi\) | ||||
−0.214375 | + | 0.976752i | \(0.568771\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.33072 | 0.266034 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.4290 | −0.699446 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.4101 | −1.00054 | −0.500271 | − | 0.865869i | \(-0.666766\pi\) | ||||
−0.500271 | + | 0.865869i | \(0.666766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.574890 | 0.0349221 | 0.0174610 | − | 0.999848i | \(-0.494442\pi\) | ||||
0.0174610 | + | 0.999848i | \(0.494442\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.64193 | −0.220420 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.311211 | −0.0187667 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8561 | −0.652280 | −0.326140 | − | 0.945322i | \(-0.605748\pi\) | ||||
−0.326140 | + | 0.945322i | \(0.605748\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.5163 | −0.629593 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.3516 | −1.03511 | −0.517554 | − | 0.855650i | \(-0.673158\pi\) | ||||
−0.517554 | + | 0.855650i | \(0.673158\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7871 | 0.819558 | 0.409779 | − | 0.912185i | \(-0.365606\pi\) | ||||
0.409779 | + | 0.912185i | \(0.365606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.86591 | 0.347467 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.3431 | −1.14179 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7247 | 0.983804 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.19664 | 0.480495 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.7962 | −1.03967 | −0.519833 | − | 0.854268i | \(-0.674006\pi\) | ||||
−0.519833 | + | 0.854268i | \(0.674006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.7520 | 0.800673 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.50785 | 0.549853 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.8314 | 1.83473 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.89453 | 0.166286 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.0527 | 1.09096 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.61527 | 0.491699 | 0.245850 | − | 0.969308i | \(-0.420933\pi\) | ||||
0.245850 | + | 0.969308i | \(0.420933\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.35091 | 0.133739 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.03970 | 0.172366 | 0.0861828 | − | 0.996279i | \(-0.472533\pi\) | ||||
0.0861828 | + | 0.996279i | \(0.472533\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.72916 | −0.154262 | −0.0771308 | − | 0.997021i | \(-0.524576\pi\) | ||||
−0.0771308 | + | 0.997021i | \(0.524576\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.88610 | −0.444331 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.7631 | −1.55933 | −0.779666 | − | 0.626196i | \(-0.784611\pi\) | ||||
−0.779666 | + | 0.626196i | \(0.784611\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.4095 | −0.582822 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.06704 | 0.171186 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.7318 | −0.875342 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.311211 | 0.0172629 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.4408 | 0.687978 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.7318 | −1.08785 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.16536 | −0.228949 | −0.114474 | − | 0.993426i | \(-0.536518\pi\) | ||||
−0.114474 | + | 0.993426i | \(0.536518\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.19664 | 0.449173 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.68231 | 0.201186 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.291700 | 0.0158899 | 0.00794495 | − | 0.999968i | \(-0.497471\pi\) | ||||
0.00794495 | + | 0.999968i | \(0.497471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.3431 | −0.941947 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5163 | −0.569488 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.68163 | −0.144795 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.5879 | 1.10842 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.24349 | −0.388851 | −0.194425 | − | 0.980917i | \(-0.562284\pi\) | ||||
−0.194425 | + | 0.980917i | \(0.562284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.7475 | 1.32470 | 0.662352 | − | 0.749193i | \(-0.269558\pi\) | ||||
0.662352 | + | 0.749193i | \(0.269558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.2012 | 1.02198 | 0.510990 | − | 0.859587i | \(-0.329279\pi\) | ||||
0.510990 | + | 0.859587i | \(0.329279\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.30720 | 0.334751 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.1498 | 1.11937 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.2097 | 0.538846 | 0.269423 | − | 0.963022i | \(-0.413167\pi\) | ||||
0.269423 | + | 0.963022i | \(0.413167\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.6614 | −0.613760 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.2558 | 1.58366 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.3933 | 0.646923 | 0.323462 | − | 0.946241i | \(-0.395153\pi\) | ||||
0.323462 | + | 0.946241i | \(0.395153\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.31121 | −0.276491 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.28387 | −0.378160 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.05273 | −0.261620 | −0.130810 | − | 0.991407i | \(-0.541758\pi\) | ||||
−0.130810 | + | 0.991407i | \(0.541758\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.5007 | 0.593893 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.4095 | 0.536118 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.2728 | −0.579044 | −0.289522 | − | 0.957171i | \(-0.593496\pi\) | ||||
−0.289522 | + | 0.957171i | \(0.593496\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.80729 | −0.399980 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.84239 | −0.196337 | −0.0981684 | − | 0.995170i | \(-0.531298\pi\) | ||||
−0.0981684 | + | 0.995170i | \(0.531298\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.88610 | −0.401913 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.74025 | 0.444292 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.85808 | 0.449122 | 0.224561 | − | 0.974460i | \(-0.427905\pi\) | ||||
0.224561 | + | 0.974460i | \(0.427905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −55.2149 | −2.79234 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.46815 | 0.326275 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.24417 | −0.414809 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.9173 | −0.849054 | −0.424527 | − | 0.905415i | \(-0.639560\pi\) | ||||
−0.424527 | + | 0.905415i | \(0.639560\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.86591 | −0.493913 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.11517 | 0.255439 | 0.127720 | − | 0.991810i | \(-0.459234\pi\) | ||||
0.127720 | + | 0.991810i | \(0.459234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.5163 | 0.523853 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.16536 | −0.107598 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.19664 | 0.406292 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.3906 | 1.55217 | 0.776083 | − | 0.630631i | \(-0.217204\pi\) | ||||
0.776083 | + | 0.630631i | \(0.217204\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.7129 | −0.923040 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.1296 | −1.13813 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.1655 | −1.77529 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.13802 | 0.398520 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.7572 | −1.50259 | −0.751294 | − | 0.659968i | \(-0.770570\pi\) | ||||
−0.751294 | + | 0.659968i | \(0.770570\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.9565 | −0.631460 | −0.315730 | − | 0.948849i | \(-0.602249\pi\) | ||||
−0.315730 | + | 0.948849i | \(0.602249\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.41795 | −0.263430 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.80729 | −0.0876667 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.0449 | −1.55076 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00000 | −0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.9857 | 0.577330 | 0.288665 | − | 0.957430i | \(-0.406789\pi\) | ||||
0.288665 | + | 0.957430i | \(0.406789\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.2247 | −1.83696 | −0.918481 | − | 0.395466i | \(-0.870583\pi\) | ||||
−0.918481 | + | 0.395466i | \(0.870583\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22.5404 | 1.08073 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.7565 | 1.23210 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.9414 | −0.856295 | −0.428148 | − | 0.903709i | \(-0.640834\pi\) | ||||
−0.428148 | + | 0.903709i | \(0.640834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.26368 | 0.298270 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.9063 | 1.23084 | 0.615422 | − | 0.788197i | \(-0.288985\pi\) | ||||
0.615422 | + | 0.788197i | \(0.288985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.7480 | 1.17317 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.0554 | 0.948588 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.4838 | −1.72177 | −0.860887 | − | 0.508795i | \(-0.830091\pi\) | ||||
−0.860887 | + | 0.508795i | \(0.830091\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.31121 | −0.250095 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.57489 | −0.402883 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.88610 | 0.369706 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.80535 | 0.0844507 | 0.0422253 | − | 0.999108i | \(-0.486555\pi\) | ||||
0.0422253 | + | 0.999108i | \(0.486555\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.80729 | 0.271061 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.4018 | −1.64883 | −0.824413 | − | 0.565988i | \(-0.808495\pi\) | ||||
−0.824413 | + | 0.565988i | \(0.808495\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.7755 | 1.33731 | 0.668654 | − | 0.743573i | \(-0.266871\pi\) | ||||
0.668654 | + | 0.743573i | \(0.266871\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.7715 | 1.05600 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.2599 | 0.521044 | 0.260522 | − | 0.965468i | \(-0.416105\pi\) | ||||
0.260522 | + | 0.965468i | \(0.416105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.19330 | −0.285980 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.9928 | −0.552601 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.74025 | 0.401877 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.843064 | 0.0386824 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2644 | −0.468990 | −0.234495 | − | 0.972117i | \(-0.575344\pi\) | ||||
−0.234495 | + | 0.972117i | \(0.575344\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.19664 | −0.373734 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −34.6269 | −1.57558 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.7487 | −0.805926 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.6257 | −0.526810 | −0.263405 | − | 0.964685i | \(-0.584845\pi\) | ||||
−0.263405 | + | 0.964685i | \(0.584845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.5990 | −0.931519 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9565 | 0.494459 | 0.247230 | − | 0.968957i | \(-0.420480\pi\) | ||||
0.247230 | + | 0.968957i | \(0.420480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60.4512 | −2.72259 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.16536 | −0.0973257 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.6081 | −0.475839 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.3008 | 1.31169 | 0.655843 | − | 0.754898i | \(-0.272313\pi\) | ||||
0.655843 | + | 0.754898i | \(0.272313\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.154275 | −0.00689249 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.4168 | 1.35622 | 0.678109 | − | 0.734961i | \(-0.262800\pi\) | ||||
0.678109 | + | 0.734961i | \(0.262800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.26769 | −0.278909 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.4929 | −1.83914 | −0.919571 | − | 0.392924i | \(-0.871464\pi\) | ||||
−0.919571 | + | 0.392924i | \(0.871464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −50.8875 | −2.25113 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.70898 | −0.119604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.09057 | −0.224317 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.41795 | −0.238281 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.02412 | 0.0888489 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.67262 | 0.423765 | 0.211883 | − | 0.977295i | \(-0.432041\pi\) | ||||
0.211883 | + | 0.977295i | \(0.432041\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.61849 | 0.376860 | 0.188430 | − | 0.982087i | \(-0.439660\pi\) | ||||
0.188430 | + | 0.982087i | \(0.439660\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.13341 | −0.0494661 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −61.0711 | −2.66030 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 67.3991 | 2.93040 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.35091 | −0.275606 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.31121 | 0.230054 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.64126 | −0.287127 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.7011 | 0.677554 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.26368 | 0.269796 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.51302 | 0.151036 | 0.0755182 | − | 0.997144i | \(-0.475939\pi\) | ||||
0.0755182 | + | 0.997144i | \(0.475939\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.26102 | 0.182858 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.9388 | −1.15393 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.1204 | 1.54440 | 0.772198 | − | 0.635382i | \(-0.219158\pi\) | ||||
0.772198 | + | 0.635382i | \(0.219158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.79887 | −0.375527 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.1992 | 1.20133 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.8659 | 0.589639 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.7487 | −0.753389 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.54235 | −0.404322 | −0.202161 | − | 0.979352i | \(-0.564796\pi\) | ||||
−0.202161 | + | 0.979352i | \(0.564796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.74025 | −0.369673 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.80729 | 0.245184 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.2435 | 0.811016 | 0.405508 | − | 0.914091i | \(-0.367095\pi\) | ||||
0.405508 | + | 0.914091i | \(0.367095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.5540 | 1.57991 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.64193 | 0.152947 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.1694 | 1.51630 | 0.758150 | − | 0.652080i | \(-0.226103\pi\) | ||||
0.758150 | + | 0.652080i | \(0.226103\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.133495 | −0.00558660 | −0.00279330 | − | 0.999996i | \(-0.500889\pi\) | ||||
−0.00279330 | + | 0.999996i | \(0.500889\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.154275 | 0.00644492 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.95895 | 0.123397 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.5977 | 0.649342 | 0.324671 | − | 0.945827i | \(-0.394746\pi\) | ||||
0.324671 | + | 0.945827i | \(0.394746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.4108 | 0.723568 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 60.8269 | 2.52353 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00000 | −0.0828315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.16536 | 0.0895267 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8693 | −0.572445 | −0.286223 | − | 0.958163i | \(-0.592400\pi\) | ||||
−0.286223 | + | 0.958163i | \(0.592400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.4883 | 1.17384 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.6621 | −0.808792 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.5514 | −0.679683 | −0.339842 | − | 0.940483i | \(-0.610373\pi\) | ||||
−0.339842 | + | 0.940483i | \(0.610373\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −45.7969 | −1.87749 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.42129 | −0.221879 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.8561 | 0.525286 | 0.262643 | − | 0.964893i | \(-0.415406\pi\) | ||||
0.262643 | + | 0.964893i | \(0.415406\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.622422 | 0.0253891 | 0.0126946 | − | 0.999919i | \(-0.495959\pi\) | ||||
0.0126946 | + | 0.999919i | \(0.495959\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.70055 | −0.0692518 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.16536 | −0.0880344 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.17704 | 0.0883633 | 0.0441816 | − | 0.999024i | \(-0.485932\pi\) | ||||
0.0441816 | + | 0.999024i | \(0.485932\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −37.9108 | −1.53622 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.41795 | 0.219187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.0085 | −0.929306 | −0.464653 | − | 0.885493i | \(-0.653821\pi\) | ||||
−0.464653 | + | 0.885493i | \(0.653821\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.5007 | 0.463753 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.53194 | 0.262966 | 0.131483 | − | 0.991318i | \(-0.458026\pi\) | ||||
0.131483 | + | 0.991318i | \(0.458026\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0313 | 0.885512 | 0.442756 | − | 0.896642i | \(-0.354001\pi\) | ||||
0.442756 | + | 0.896642i | \(0.354001\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.50785 | −0.381537 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −41.6238 | −1.66762 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.3471 | −0.933884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.70898 | −0.108186 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.6003 | 1.89795 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.4057 | −1.68814 | −0.844072 | − | 0.536229i | \(-0.819848\pi\) | ||||
−0.844072 | + | 0.536229i | \(0.819848\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.0912 | 0.758806 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.9056 | 0.670879 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.26368 | −0.248176 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.91277 | −0.115227 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.5879 | 0.734179 | 0.367089 | − | 0.930186i | \(-0.380354\pi\) | ||||
0.367089 | + | 0.930186i | \(0.380354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −45.4551 | −1.79257 | −0.896287 | − | 0.443474i | \(-0.853746\pi\) | ||||
−0.896287 | + | 0.443474i | \(0.853746\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.9258 | −0.745203 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.4727 | 0.726236 | 0.363118 | − | 0.931743i | \(-0.381712\pi\) | ||||
0.363118 | + | 0.931743i | \(0.381712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.35091 | −0.249295 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.2996 | −1.50108 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.1733 | −1.14164 | −0.570820 | − | 0.821075i | \(-0.693375\pi\) | ||||
−0.570820 | + | 0.821075i | \(0.693375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.0059 | −0.547255 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.9727 | −0.545125 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.3568 | −1.72790 | −0.863948 | − | 0.503582i | \(-0.832015\pi\) | ||||
−0.863948 | + | 0.503582i | \(0.832015\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0079 | −0.700425 | −0.350212 | − | 0.936670i | \(-0.613891\pi\) | ||||
−0.350212 | + | 0.936670i | \(0.613891\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.80729 | −0.225537 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.3633 | 0.828432 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 98.9722 | 3.83222 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.46942 | −0.0568109 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.79887 | −0.339677 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.6875 | 1.49129 | 0.745647 | − | 0.666341i | \(-0.232141\pi\) | ||||
0.745647 | + | 0.666341i | \(0.232141\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.311211 | −0.0119785 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.9271 | 1.07332 | 0.536662 | − | 0.843797i | \(-0.319685\pi\) | ||||
0.536662 | + | 0.843797i | \(0.319685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.8516 | 1.14560 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.62175 | −0.215426 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.28188 | −0.0490499 | −0.0245249 | − | 0.999699i | \(-0.507807\pi\) | ||||
−0.0245249 | + | 0.999699i | \(0.507807\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.5202 | 1.54820 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.0059 | 0.763272 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00000 | 0.0761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.436873 | 0.0166194 | 0.00830972 | − | 0.999965i | \(-0.497355\pi\) | ||||
0.00830972 | + | 0.999965i | \(0.497355\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.64193 | 0.138346 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.6217 | −0.668431 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.8438 | −1.16829 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.18487 | 0.120463 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.7234 | −0.782712 | −0.391356 | − | 0.920239i | \(-0.627994\pi\) | ||||
−0.391356 | + | 0.920239i | \(0.627994\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.2045 | −0.837458 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.7318 | 0.441846 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.5417 | 0.396460 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.9355 | 1.53736 | 0.768682 | − | 0.639631i | \(-0.220913\pi\) | ||||
0.768682 | + | 0.639631i | \(0.220913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.80729 | 0.142785 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 99.9871 | 3.74455 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.16536 | 0.0809799 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.60291 | 0.358627 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.53853 | 0.355727 | 0.177864 | − | 0.984055i | \(-0.443081\pi\) | ||||
0.177864 | + | 0.984055i | \(0.443081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.56186 | 0.318860 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.07940 | −0.300476 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.23956 | 0.120314 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.17195 | 0.340169 | 0.170084 | − | 0.985429i | \(-0.445596\pi\) | ||||
0.170084 | + | 0.985429i | \(0.445596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.7572 | 1.87732 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.2363 | −1.44923 | −0.724614 | − | 0.689155i | \(-0.757982\pi\) | ||||
−0.724614 | + | 0.689155i | \(0.757982\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.5631 | −0.500283 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.70055 | −0.0626406 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.4187 | 1.30290 | 0.651448 | − | 0.758693i | \(-0.274162\pi\) | ||||
0.651448 | + | 0.758693i | \(0.274162\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.70898 | 0.0995168 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.1453 | 1.54616 | 0.773080 | − | 0.634308i | \(-0.218715\pi\) | ||||
0.773080 | + | 0.634308i | \(0.218715\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.4272 | −1.59105 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.7018 | 0.611088 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.1700 | 0.408142 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.3184 | 0.960372 | 0.480186 | − | 0.877167i | \(-0.340569\pi\) | ||||
0.480186 | + | 0.877167i | \(0.340569\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.01569 | −0.255666 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.5677 | 0.675749 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.73898 | 0.281278 | 0.140639 | − | 0.990061i | \(-0.455084\pi\) | ||||
0.140639 | + | 0.990061i | \(0.455084\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.50785 | −0.345113 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.9154 | 0.431934 | 0.215967 | − | 0.976401i | \(-0.430710\pi\) | ||||
0.215967 | + | 0.976401i | \(0.430710\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 45.3086 | 1.64028 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.5749 | −0.454646 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.35091 | 0.229318 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.63224 | −0.203104 | −0.101552 | − | 0.994830i | \(-0.532381\pi\) | ||||
−0.101552 | + | 0.994830i | \(0.532381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.3262 | −1.12819 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.7937 | −1.25144 | −0.625720 | − | 0.780047i | \(-0.715195\pi\) | ||||
−0.625720 | + | 0.780047i | \(0.715195\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.27278 | 0.117562 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.8516 | 1.07092 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.3879 | 0.515502 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.91277 | −0.104227 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.4095 | −0.372006 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.9688 | 0.926868 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.1438 | −0.646756 | −0.323378 | − | 0.946270i | \(-0.604819\pi\) | ||||
−0.323378 | + | 0.946270i | \(0.604819\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.95314 | −0.247538 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −63.1623 | −2.24579 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.79887 | 0.312457 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.33072 | 0.153595 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.4701 | 0.370871 | 0.185436 | − | 0.982656i | \(-0.440630\pi\) | ||||
0.185436 | + | 0.982656i | \(0.440630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.4637 | −1.11310 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.4290 | −0.403825 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.9727 | −0.493084 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 74.9798 | 2.64269 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.4101 | −0.577664 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.4869 | 0.368701 | 0.184351 | − | 0.982861i | \(-0.440982\pi\) | ||||
0.184351 | + | 0.982861i | \(0.440982\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.8027 | −0.625138 | −0.312569 | − | 0.949895i | \(-0.601190\pi\) | ||||
−0.312569 | + | 0.949895i | \(0.601190\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.574890 | 0.0201623 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.6043 | 1.56242 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.6771 | −0.828358 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.64193 | −0.127259 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.6386 | 1.20890 | 0.604448 | − | 0.796645i | \(-0.293394\pi\) | ||||
0.604448 | + | 0.796645i | \(0.293394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.8002 | 1.14334 | 0.571672 | − | 0.820482i | \(-0.306295\pi\) | ||||
0.571672 | + | 0.820482i | \(0.306295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.311211 | −0.0108350 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.6765 | −1.76219 | −0.881097 | − | 0.472936i | \(-0.843194\pi\) | ||||
−0.881097 | + | 0.472936i | \(0.843194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.9767 | 0.520161 | 0.260081 | − | 0.965587i | \(-0.416251\pi\) | ||||
0.260081 | + | 0.965587i | \(0.416251\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.8561 | −0.376594 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.3750 | 1.26032 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.334061 | 0.0115606 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.5163 | −0.363496 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.60811 | 0.228137 | 0.114069 | − | 0.993473i | \(-0.463612\pi\) | ||||
0.114069 | + | 0.993473i | \(0.463612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 79.3583 | 2.73649 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.3516 | −0.597620 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.16536 | −0.0744907 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.64193 | 0.125138 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.7871 | 0.473172 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −77.9324 | −2.67149 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.51834 | 0.0519870 | 0.0259935 | − | 0.999662i | \(-0.491725\pi\) | ||||
0.0259935 | + | 0.999662i | \(0.491725\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.86591 | 0.200610 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.9806 | 0.716684 | 0.358342 | − | 0.933590i | \(-0.383342\pi\) | ||||
0.358342 | + | 0.933590i | \(0.383342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.4011 | −1.51495 | −0.757474 | − | 0.652866i | \(-0.773567\pi\) | ||||
−0.757474 | + | 0.652866i | \(0.773567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.3431 | −0.659210 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.6953 | −0.398114 | −0.199057 | − | 0.979988i | \(-0.563788\pi\) | ||||
−0.199057 | + | 0.979988i | \(0.563788\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.38295 | −0.149025 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.7247 | 0.568000 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.80729 | 0.129154 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.70055 | 0.0576210 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.19664 | 0.277414 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.8847 | 1.41596 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.89060 | 0.165144 | 0.0825718 | − | 0.996585i | \(-0.473687\pi\) | ||||
0.0825718 | + | 0.996585i | \(0.473687\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.7962 | −0.600251 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.5032 | −1.60042 | −0.800212 | − | 0.599717i | \(-0.795280\pi\) | ||||
−0.800212 | + | 0.599717i | \(0.795280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.9779 | −1.37901 | −0.689507 | − | 0.724279i | \(-0.742173\pi\) | ||||
−0.689507 | + | 0.724279i | \(0.742173\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.7520 | 0.462269 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.09391 | −0.305344 | −0.152672 | − | 0.988277i | \(-0.548788\pi\) | ||||
−0.152672 | + | 0.988277i | \(0.548788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.4336 | −0.953634 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.6771 | 0.491151 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.9986 | −1.13645 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.50785 | 0.317458 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 109.469 | 3.65101 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.6146 | −0.386938 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.8314 | 1.05928 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.22664 | −0.306704 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.4036 | 0.710696 | 0.355348 | − | 0.934734i | \(-0.384362\pi\) | ||||
0.355348 | + | 0.934734i | \(0.384362\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.89453 | 0.0960054 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.77984 | −0.125232 | −0.0626158 | − | 0.998038i | \(-0.519944\pi\) | ||||
−0.0626158 | + | 0.998038i | \(0.519944\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.7018 | 0.552750 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.0527 | 0.629864 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.5566 | 0.777906 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.8230 | −1.41260 | −0.706300 | − | 0.707913i | \(-0.749637\pi\) | ||||
−0.706300 | + | 0.707913i | \(0.749637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.61527 | 0.283883 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.91277 | 0.0958749 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.55088 | −0.0838725 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.35091 | 0.0772140 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.6817 | 1.85967 | 0.929834 | − | 0.367980i | \(-0.119950\pi\) | ||||
0.929834 | + | 0.367980i | \(0.119950\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.9682 | −0.556109 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.03970 | 0.0995153 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.5749 | −0.411243 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.0937 | −1.08113 | −0.540563 | − | 0.841304i | \(-0.681789\pi\) | ||||
−0.540563 | + | 0.841304i | \(0.681789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.72916 | −0.0890629 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.1830 | −1.60332 | −0.801660 | − | 0.597780i | \(-0.796050\pi\) | ||||
−0.801660 | + | 0.597780i | \(0.796050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.4982 | 1.64445 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.88610 | −0.256535 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.3152 | 0.530174 | 0.265087 | − | 0.964225i | \(-0.414599\pi\) | ||||
0.265087 | + | 0.964225i | \(0.414599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.9727 | 0.453572 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.7631 | −0.900280 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.3686 | 1.82596 | 0.912979 | − | 0.408007i | \(-0.133776\pi\) | ||||
0.912979 | + | 0.408007i | \(0.133776\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.334061 | −0.0108099 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.4095 | −0.336492 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −68.1512 | −2.20072 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79.5920 | 2.56748 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.06704 | 0.0988341 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −37.7007 | −1.21363 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.89444 | −0.0609211 | −0.0304606 | − | 0.999536i | \(-0.509697\pi\) | ||||
−0.0304606 | + | 0.999536i | \(0.509697\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.7318 | −0.505379 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.4030 | 1.42496 | 0.712479 | − | 0.701693i | \(-0.247572\pi\) | ||||
0.712479 | + | 0.701693i | \(0.247572\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.6381 | 0.950154 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.311211 | 0.00996673 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.34964 | 0.0431789 | 0.0215894 | − | 0.999767i | \(-0.493127\pi\) | ||||
0.0215894 | + | 0.999767i | \(0.493127\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.4290 | −0.365274 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.4408 | 0.397204 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.2202 | 1.69746 | 0.848730 | − | 0.528826i | \(-0.177368\pi\) | ||||
0.848730 | + | 0.528826i | \(0.177368\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.5756 | 1.35657 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.7318 | −0.628071 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −83.1010 | −2.64246 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.7832 | −0.787264 | −0.393632 | − | 0.919268i | \(-0.628782\pi\) | ||||
−0.393632 | + | 0.919268i | \(0.628782\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.16536 | −0.132184 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.7391 | 0.372153 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.00703 | 0.221915 | 0.110957 | − | 0.993825i | \(-0.464608\pi\) | ||||
0.110957 | + | 0.993825i | \(0.464608\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.19664 | 0.259330 |
(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 | 6864.2.a.by.1.2 | 4 | ||
4.3 | odd | 2 | 3432.2.a.q.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.q.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
6864.2.a.by.1.2 | 4 | 1.1 | even | 1 | trivial |