Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3640,2,Mod(1,3640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3640, 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("3640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3640.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: | \(29.0655463357\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4913.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.04948\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3640.1 |
$q$-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 | ||||||||
\(3\) | 3.04948 | 1.76062 | 0.880309 | − | 0.474400i | \(-0.157335\pi\) | ||||
0.880309 | + | 0.474400i | \(0.157335\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.29934 | 2.09978 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.68830 | 0.810553 | 0.405277 | − | 0.914194i | \(-0.367175\pi\) | ||||
0.405277 | + | 0.914194i | \(0.367175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.04948 | −0.787373 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.20037 | 0.776204 | 0.388102 | − | 0.921616i | \(-0.373131\pi\) | ||||
0.388102 | + | 0.921616i | \(0.373131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.48793 | 0.341354 | 0.170677 | − | 0.985327i | \(-0.445405\pi\) | ||||
0.170677 | + | 0.985327i | \(0.445405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.04948 | −0.665451 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.688301 | −0.143521 | −0.0717604 | − | 0.997422i | \(-0.522862\pi\) | ||||
−0.0717604 | + | 0.997422i | \(0.522862\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.0613 | 1.93629 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.361180 | 0.0670694 | 0.0335347 | − | 0.999438i | \(-0.489324\pi\) | ||||
0.0335347 | + | 0.999438i | \(0.489324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.07362 | 0.372434 | 0.186217 | − | 0.982509i | \(-0.440377\pi\) | ||||
0.186217 | + | 0.982509i | \(0.440377\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.19792 | 1.42708 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.88503 | −1.62509 | −0.812545 | − | 0.582899i | \(-0.801918\pi\) | ||||
−0.812545 | + | 0.582899i | \(0.801918\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.04948 | 0.488308 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.24866 | −0.195008 | −0.0975039 | − | 0.995235i | \(-0.531086\pi\) | ||||
−0.0975039 | + | 0.995235i | \(0.531086\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.78726 | 1.34005 | 0.670023 | − | 0.742341i | \(-0.266284\pi\) | ||||
0.670023 | + | 0.742341i | \(0.266284\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.29934 | −0.939049 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.12311 | −0.455552 | −0.227776 | − | 0.973714i | \(-0.573145\pi\) | ||||
−0.227776 | + | 0.973714i | \(0.573145\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.75948 | 1.36660 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.12311 | 0.978434 | 0.489217 | − | 0.872162i | \(-0.337283\pi\) | ||||
0.489217 | + | 0.872162i | \(0.337283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.68830 | −0.362490 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.53741 | 0.600995 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.52505 | −0.849489 | −0.424744 | − | 0.905313i | \(-0.639636\pi\) | ||||
−0.424744 | + | 0.905313i | \(0.639636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.24621 | 1.05582 | 0.527910 | − | 0.849301i | \(-0.322976\pi\) | ||||
0.527910 | + | 0.849301i | \(0.322976\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.29934 | −0.793642 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.10141 | 0.134559 | 0.0672794 | − | 0.997734i | \(-0.478568\pi\) | ||||
0.0672794 | + | 0.997734i | \(0.478568\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.09896 | −0.252685 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.1566 | 1.91743 | 0.958717 | − | 0.284363i | \(-0.0917821\pi\) | ||||
0.958717 | + | 0.284363i | \(0.0917821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.07482 | 0.828045 | 0.414022 | − | 0.910267i | \(-0.364123\pi\) | ||||
0.414022 | + | 0.910267i | \(0.364123\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.04948 | 0.352124 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.68830 | −0.306360 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9221 | −1.45386 | −0.726928 | − | 0.686714i | \(-0.759052\pi\) | ||||
−0.726928 | + | 0.686714i | \(0.759052\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.7836 | 1.30929 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.17139 | −0.128577 | −0.0642885 | − | 0.997931i | \(-0.520478\pi\) | ||||
−0.0642885 | + | 0.997931i | \(0.520478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.20037 | −0.347129 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.10141 | 0.118084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.91156 | −0.732624 | −0.366312 | − | 0.930492i | \(-0.619380\pi\) | ||||
−0.366312 | + | 0.930492i | \(0.619380\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.32348 | 0.655714 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.48793 | −0.152658 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.57214 | 0.971903 | 0.485952 | − | 0.873986i | \(-0.338473\pi\) | ||||
0.485952 | + | 0.873986i | \(0.338473\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.9345 | 1.70198 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.74592 | −0.870252 | −0.435126 | − | 0.900370i | \(-0.643296\pi\) | ||||
−0.435126 | + | 0.900370i | \(0.643296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.562747 | −0.0554492 | −0.0277246 | − | 0.999616i | \(-0.508826\pi\) | ||||
−0.0277246 | + | 0.999616i | \(0.508826\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.04948 | 0.297599 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.28697 | −0.897806 | −0.448903 | − | 0.893581i | \(-0.648185\pi\) | ||||
−0.448903 | + | 0.893581i | \(0.648185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.02653 | 0.289889 | 0.144945 | − | 0.989440i | \(-0.453700\pi\) | ||||
0.144945 | + | 0.989440i | \(0.453700\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −30.1442 | −2.86116 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.4756 | 1.64396 | 0.821981 | − | 0.569514i | \(-0.192869\pi\) | ||||
0.821981 | + | 0.569514i | \(0.192869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.688301 | 0.0641844 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.29934 | 0.582374 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.20037 | −0.293378 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.77304 | −0.343003 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.80776 | −0.343335 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.64001 | 0.589206 | 0.294603 | − | 0.955620i | \(-0.404813\pi\) | ||||
0.294603 | + | 0.955620i | \(0.404813\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 26.7966 | 2.35931 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.876894 | 0.0766146 | 0.0383073 | − | 0.999266i | \(-0.487803\pi\) | ||||
0.0383073 | + | 0.999266i | \(0.487803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.48793 | −0.129020 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.0613 | −0.865936 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.73778 | −0.148469 | −0.0742344 | − | 0.997241i | \(-0.523651\pi\) | ||||
−0.0742344 | + | 0.997241i | \(0.523651\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.5504 | 1.06451 | 0.532255 | − | 0.846584i | \(-0.321345\pi\) | ||||
0.532255 | + | 0.846584i | \(0.321345\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.52385 | −0.802053 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.68830 | 0.224807 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.361180 | −0.0299943 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.04948 | 0.251517 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.12311 | −0.583548 | −0.291774 | − | 0.956487i | \(-0.594245\pi\) | ||||
−0.291774 | + | 0.956487i | \(0.594245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1083 | −1.47363 | −0.736816 | − | 0.676093i | \(-0.763672\pi\) | ||||
−0.736816 | + | 0.676093i | \(0.763672\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.1602 | 1.62986 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.07362 | −0.166558 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.5108 | 1.15809 | 0.579045 | − | 0.815296i | \(-0.303426\pi\) | ||||
0.579045 | + | 0.815296i | \(0.303426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.7218 | 1.72265 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.688301 | 0.0542458 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.76432 | −0.529822 | −0.264911 | − | 0.964273i | \(-0.585343\pi\) | ||||
−0.264911 | + | 0.964273i | \(0.585343\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.19792 | −0.638208 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.94874 | 0.692474 | 0.346237 | − | 0.938147i | \(-0.387459\pi\) | ||||
0.346237 | + | 0.938147i | \(0.387459\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.37296 | 0.716768 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.0347 | 1.21909 | 0.609547 | − | 0.792750i | \(-0.291351\pi\) | ||||
0.609547 | + | 0.792750i | \(0.291351\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.8980 | −1.49563 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.1689 | 1.65698 | 0.828492 | − | 0.560000i | \(-0.189199\pi\) | ||||
0.828492 | + | 0.560000i | \(0.189199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.476148 | −0.0353918 | −0.0176959 | − | 0.999843i | \(-0.505633\pi\) | ||||
−0.0176959 | + | 0.999843i | \(0.505633\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.1467 | 1.85890 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.88503 | 0.726762 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.60357 | 0.629155 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.0613 | −0.731849 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.86089 | 0.207007 | 0.103503 | − | 0.994629i | \(-0.466995\pi\) | ||||
0.103503 | + | 0.994629i | \(0.466995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.7001 | −0.986153 | −0.493077 | − | 0.869986i | \(-0.664128\pi\) | ||||
−0.493077 | + | 0.869986i | \(0.664128\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.04948 | −0.218378 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.868174 | −0.0618549 | −0.0309274 | − | 0.999522i | \(-0.509846\pi\) | ||||
−0.0309274 | + | 0.999522i | \(0.509846\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.2963 | −1.08433 | −0.542163 | − | 0.840273i | \(-0.682395\pi\) | ||||
−0.542163 | + | 0.840273i | \(0.682395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.35873 | 0.236907 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.361180 | −0.0253498 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.24866 | 0.0872102 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.33584 | −0.301362 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.80202 | 0.192899 | 0.0964494 | − | 0.995338i | \(-0.469251\pi\) | ||||
0.0964494 | + | 0.995338i | \(0.469251\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 49.2692 | 3.37587 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.78726 | −0.599286 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.07362 | −0.140767 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.5745 | 1.45787 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.20037 | 0.215280 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0718 | 0.808391 | 0.404195 | − | 0.914673i | \(-0.367552\pi\) | ||||
0.404195 | + | 0.914673i | \(0.367552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.29934 | 0.419956 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.3687 | −1.48467 | −0.742333 | − | 0.670032i | \(-0.766281\pi\) | ||||
−0.742333 | + | 0.670032i | \(0.766281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.5220 | −1.02572 | −0.512861 | − | 0.858472i | \(-0.671414\pi\) | ||||
−0.512861 | + | 0.858472i | \(0.671414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.19792 | −0.539384 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.17139 | −0.469814 | −0.234907 | − | 0.972018i | \(-0.575478\pi\) | ||||
−0.234907 | + | 0.972018i | \(0.575478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.12311 | 0.203729 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −39.4059 | −2.55969 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.8862 | 1.09228 | 0.546140 | − | 0.837694i | \(-0.316097\pi\) | ||||
0.546140 | + | 0.837694i | \(0.316097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5962 | 0.746978 | 0.373489 | − | 0.927635i | \(-0.378161\pi\) | ||||
0.373489 | + | 0.927635i | \(0.378161\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.75015 | 0.368872 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.48793 | 0.0946746 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.57214 | −0.226375 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.2003 | −1.14879 | −0.574397 | − | 0.818577i | \(-0.694763\pi\) | ||||
−0.574397 | + | 0.818577i | \(0.694763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.85036 | −0.116331 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.75948 | −0.611162 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.6155 | −0.724557 | −0.362278 | − | 0.932070i | \(-0.618001\pi\) | ||||
−0.362278 | + | 0.932070i | \(0.618001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.88503 | 0.614226 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.27519 | 0.140831 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.3105 | −1.31406 | −0.657032 | − | 0.753863i | \(-0.728188\pi\) | ||||
−0.657032 | + | 0.753863i | \(0.728188\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.12311 | −0.437569 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.0767 | −1.28987 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.50029 | 0.0914744 | 0.0457372 | − | 0.998954i | \(-0.485436\pi\) | ||||
0.0457372 | + | 0.998954i | \(0.485436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.510206 | −0.0309928 | −0.0154964 | − | 0.999880i | \(-0.504933\pi\) | ||||
−0.0154964 | + | 0.999880i | \(0.504933\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.04948 | −0.184563 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.68830 | 0.162111 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.3476 | −1.34273 | −0.671367 | − | 0.741125i | \(-0.734293\pi\) | ||||
−0.671367 | + | 0.741125i | \(0.734293\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.0625 | 0.782029 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.5021 | −1.46167 | −0.730836 | − | 0.682553i | \(-0.760870\pi\) | ||||
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.88809 | −0.528342 | −0.264171 | − | 0.964476i | \(-0.585098\pi\) | ||||
−0.264171 | + | 0.964476i | \(0.585098\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.53741 | −0.268773 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.24866 | 0.0737060 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.75761 | −0.397507 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.1901 | 1.71115 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.7768 | 1.09695 | 0.548475 | − | 0.836167i | \(-0.315209\pi\) | ||||
0.548475 | + | 0.836167i | \(0.315209\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.52505 | 0.379903 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27.0477 | 1.56947 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.688301 | −0.0398055 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.78726 | −0.506489 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.6705 | −1.53218 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.24621 | −0.472177 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.6976 | −0.724692 | −0.362346 | − | 0.932044i | \(-0.618024\pi\) | ||||
−0.362346 | + | 0.932044i | \(0.618024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.71609 | −0.0976248 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.1394 | −1.42552 | −0.712762 | − | 0.701406i | \(-0.752556\pi\) | ||||
−0.712762 | + | 0.701406i | \(0.752556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5151 | −0.650874 | −0.325437 | − | 0.945564i | \(-0.605511\pi\) | ||||
−0.325437 | + | 0.945564i | \(0.605511\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.29934 | 0.354927 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.8546 | −1.39597 | −0.697986 | − | 0.716112i | \(-0.745920\pi\) | ||||
−0.697986 | + | 0.716112i | \(0.745920\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.970960 | 0.0543633 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28.3204 | −1.58069 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.76193 | 0.264961 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.22935 | 0.510384 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.12311 | 0.172182 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.934513 | −0.0513655 | −0.0256827 | − | 0.999670i | \(-0.508176\pi\) | ||||
−0.0256827 | + | 0.999670i | \(0.508176\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −62.2691 | −3.41233 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.10141 | −0.0601765 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.15022 | −0.171603 | −0.0858017 | − | 0.996312i | \(-0.527345\pi\) | ||||
−0.0858017 | + | 0.996312i | \(0.527345\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 53.2914 | 2.89439 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.57453 | 0.301878 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.09896 | 0.113004 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.63273 | 0.248698 | 0.124349 | − | 0.992239i | \(-0.460316\pi\) | ||||
0.124349 | + | 0.992239i | \(0.460316\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.8367 | −1.70418 | −0.852091 | − | 0.523394i | \(-0.824666\pi\) | ||||
−0.852091 | + | 0.523394i | \(0.824666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.0613 | 0.537030 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.1979 | 1.18148 | 0.590738 | − | 0.806863i | \(-0.298837\pi\) | ||||
0.590738 | + | 0.806863i | \(0.298837\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.1566 | −0.857502 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.75948 | −0.516526 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.8356 | 1.31077 | 0.655385 | − | 0.755295i | \(-0.272506\pi\) | ||||
0.655385 | + | 0.755295i | \(0.272506\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7861 | −0.883477 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.5058 | −0.603898 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.07482 | −0.370313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.4560 | 1.06779 | 0.533897 | − | 0.845550i | \(-0.320727\pi\) | ||||
0.533897 | + | 0.845550i | \(0.320727\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.86573 | −0.409473 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.12311 | −0.369813 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.8455 | −0.613335 | −0.306667 | − | 0.951817i | \(-0.599214\pi\) | ||||
−0.306667 | + | 0.951817i | \(0.599214\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.04948 | −0.157475 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.361180 | 0.0186017 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.76370 | 0.347428 | 0.173714 | − | 0.984796i | \(-0.444423\pi\) | ||||
0.173714 | + | 0.984796i | \(0.444423\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.2486 | 1.03737 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.3234 | −0.680795 | −0.340397 | − | 0.940282i | \(-0.610562\pi\) | ||||
−0.340397 | + | 0.940282i | \(0.610562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.68830 | 0.137009 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 55.3539 | 2.81380 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.3223 | 1.33459 | 0.667297 | − | 0.744792i | \(-0.267451\pi\) | ||||
0.667297 | + | 0.744792i | \(0.267451\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.20282 | −0.111401 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.67407 | 0.134889 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.9221 | 0.650184 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.6179 | −1.18535 | −0.592675 | − | 0.805442i | \(-0.701928\pi\) | ||||
−0.592675 | + | 0.805442i | \(0.701928\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.53741 | −0.227155 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.79776 | −0.139714 | −0.0698568 | − | 0.997557i | \(-0.522254\pi\) | ||||
−0.0698568 | + | 0.997557i | \(0.522254\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.07362 | 0.103295 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.7836 | −0.585533 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.5739 | −1.31722 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.2239 | −1.00001 | −0.500003 | − | 0.866024i | \(-0.666668\pi\) | ||||
−0.500003 | + | 0.866024i | \(0.666668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.29934 | −0.261397 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.52505 | 0.321077 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.17139 | 0.0575014 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 38.2722 | 1.87420 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.6952 | 0.913322 | 0.456661 | − | 0.889641i | \(-0.349045\pi\) | ||||
0.456661 | + | 0.889641i | \(0.349045\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.8135 | −1.94039 | −0.970194 | − | 0.242328i | \(-0.922089\pi\) | ||||
−0.970194 | + | 0.242328i | \(0.922089\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.6735 | −0.956558 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.20037 | 0.155241 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.24621 | −0.399062 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.19792 | 0.395800 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.34254 | 0.0646681 | 0.0323341 | − | 0.999477i | \(-0.489706\pi\) | ||||
0.0323341 | + | 0.999477i | \(0.489706\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.0447 | −1.78025 | −0.890127 | − | 0.455713i | \(-0.849384\pi\) | ||||
−0.890127 | + | 0.455713i | \(0.849384\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.10141 | −0.0528086 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.02414 | −0.0489914 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.3283 | 0.540671 | 0.270336 | − | 0.962766i | \(-0.412865\pi\) | ||||
0.270336 | + | 0.962766i | \(0.412865\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.29934 | 0.299968 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.8789 | −1.08701 | −0.543506 | − | 0.839406i | \(-0.682903\pi\) | ||||
−0.543506 | + | 0.839406i | \(0.682903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.91156 | 0.327640 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.7218 | −1.02740 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.7701 | −1.21616 | −0.608082 | − | 0.793874i | \(-0.708061\pi\) | ||||
−0.608082 | + | 0.793874i | \(0.708061\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.35677 | −0.158064 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −55.2209 | −2.59450 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.65865 | 0.0775884 | 0.0387942 | − | 0.999247i | \(-0.487648\pi\) | ||||
0.0387942 | + | 0.999247i | \(0.487648\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32.1998 | 1.50296 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3123 | −0.713165 | −0.356583 | − | 0.934264i | \(-0.616058\pi\) | ||||
−0.356583 | + | 0.934264i | \(0.616058\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.82616 | 0.363712 | 0.181856 | − | 0.983325i | \(-0.441789\pi\) | ||||
0.181856 | + | 0.983325i | \(0.441789\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.32348 | −0.293244 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.7100 | −0.680697 | −0.340349 | − | 0.940299i | \(-0.610545\pi\) | ||||
−0.340349 | + | 0.940299i | \(0.610545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.10141 | −0.0508584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 44.2505 | 2.03895 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.6228 | 1.08618 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.48793 | 0.0682708 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 44.8708 | 2.05449 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.776154 | −0.0354634 | −0.0177317 | − | 0.999843i | \(-0.505644\pi\) | ||||
−0.0177317 | + | 0.999843i | \(0.505644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.88503 | −0.450719 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.09896 | 0.0955061 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.57214 | −0.434648 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.23807 | −0.146731 | −0.0733656 | − | 0.997305i | \(-0.523374\pi\) | ||||
−0.0733656 | + | 0.997305i | \(0.523374\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.6277 | −0.932815 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.4441 | 1.01289 | 0.506445 | − | 0.862272i | \(-0.330959\pi\) | ||||
0.506445 | + | 0.862272i | \(0.330959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.15591 | 0.0520596 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.9345 | −0.761150 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.1566 | −0.724722 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.2821 | 1.40038 | 0.700189 | − | 0.713958i | \(-0.253099\pi\) | ||||
0.700189 | + | 0.713958i | \(0.253099\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.2890 | 1.21918 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.88681 | 0.0841287 | 0.0420643 | − | 0.999115i | \(-0.486607\pi\) | ||||
0.0420643 | + | 0.999115i | \(0.486607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.74592 | 0.389188 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.04948 | 0.135432 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.4248 | −0.550721 | −0.275360 | − | 0.961341i | \(-0.588797\pi\) | ||||
−0.275360 | + | 0.961341i | \(0.588797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.07482 | −0.312972 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.9704 | 0.660961 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.562747 | 0.0247976 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.39585 | −0.369249 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 48.8974 | 2.14636 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.9735 | 0.831243 | 0.415621 | − | 0.909538i | \(-0.363564\pi\) | ||||
0.415621 | + | 0.909538i | \(0.363564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.76370 | 0.208302 | 0.104151 | − | 0.994561i | \(-0.466787\pi\) | ||||
0.104151 | + | 0.994561i | \(0.466787\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.04948 | −0.133090 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.63637 | 0.289085 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5262 | −0.979402 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −41.1035 | −1.78374 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.24866 | −0.0540855 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.28697 | 0.401511 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 67.6038 | 2.91732 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.68830 | 0.115793 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8726 | −0.768402 | −0.384201 | − | 0.923249i | \(-0.625523\pi\) | ||||
−0.384201 | + | 0.923249i | \(0.625523\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.45200 | −0.0623115 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.02653 | −0.129642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.8597 | −0.678112 | −0.339056 | − | 0.940766i | \(-0.610108\pi\) | ||||
−0.339056 | + | 0.940766i | \(0.610108\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 51.9457 | 2.21699 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.537410 | 0.0228944 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9221 | 0.549506 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 30.1442 | 1.27955 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.5788 | 1.42278 | 0.711389 | − | 0.702798i | \(-0.248066\pi\) | ||||
0.711389 | + | 0.702798i | \(0.248066\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.78726 | 0.371662 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.2364 | 1.10770 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.5586 | 1.83578 | 0.917888 | − | 0.396839i | \(-0.129893\pi\) | ||||
0.917888 | + | 0.396839i | \(0.129893\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.4756 | −0.735203 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.7836 | −0.494866 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.213931 | 0.00896845 | 0.00448422 | − | 0.999990i | \(-0.498573\pi\) | ||||
0.00448422 | + | 0.999990i | \(0.498573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0076 | 0.669895 | 0.334948 | − | 0.942237i | \(-0.391281\pi\) | ||||
0.334948 | + | 0.942237i | \(0.391281\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.72422 | 0.364460 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.688301 | −0.0287042 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.4170 | −0.600188 | −0.300094 | − | 0.953910i | \(-0.597018\pi\) | ||||
−0.300094 | + | 0.953910i | \(0.597018\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −41.7781 | −1.73624 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.17139 | 0.0485975 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.1491 | 0.793073 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.29934 | −0.260445 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.2988 | −0.466352 | −0.233176 | − | 0.972435i | \(-0.574912\pi\) | ||||
−0.233176 | + | 0.972435i | \(0.574912\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.08540 | 0.127132 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.64748 | −0.108903 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.2722 | −0.996738 | −0.498369 | − | 0.866965i | \(-0.666068\pi\) | ||||
−0.498369 | + | 0.866965i | \(0.666068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.20037 | 0.131203 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −46.6458 | −1.90909 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.3953 | −0.710751 | −0.355376 | − | 0.934724i | \(-0.615647\pi\) | ||||
−0.355376 | + | 0.934724i | \(0.615647\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3259 | −0.461994 | −0.230997 | − | 0.972954i | \(-0.574199\pi\) | ||||
−0.230997 | + | 0.972954i | \(0.574199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.93816 | 0.282544 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.77304 | 0.153396 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.2884 | 0.945247 | 0.472624 | − | 0.881264i | \(-0.343307\pi\) | ||||
0.472624 | + | 0.881264i | \(0.343307\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.10141 | −0.0446314 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.12311 | −0.126347 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.8015 | −0.920944 | −0.460472 | − | 0.887674i | \(-0.652320\pi\) | ||||
−0.460472 | + | 0.887674i | \(0.652320\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.80776 | 0.153544 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.03855 | −0.202844 | −0.101422 | − | 0.994843i | \(-0.532339\pi\) | ||||
−0.101422 | + | 0.994843i | \(0.532339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.1701 | 1.37341 | 0.686706 | − | 0.726936i | \(-0.259056\pi\) | ||||
0.686706 | + | 0.726936i | \(0.259056\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.92518 | −0.277898 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.91156 | 0.276906 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.1979 | 0.487138 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.6358 | −1.26140 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.6032 | 0.740583 | 0.370291 | − | 0.928916i | \(-0.379258\pi\) | ||||
0.370291 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.54470 | 0.339621 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.64001 | −0.263501 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 101.776 | 4.02619 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.14581 | 0.163750 | 0.0818749 | − | 0.996643i | \(-0.473909\pi\) | ||||
0.0818749 | + | 0.996643i | \(0.473909\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.0737 | 1.54091 | 0.770457 | − | 0.637492i | \(-0.220028\pi\) | ||||
0.770457 | + | 0.637492i | \(0.220028\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −26.7966 | −1.05511 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.3222 | 1.19209 | 0.596045 | − | 0.802951i | \(-0.296738\pi\) | ||||
0.596045 | + | 0.802951i | \(0.296738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.5413 | −0.688556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.32348 | −0.247837 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.5721 | 0.765917 | 0.382958 | − | 0.923766i | \(-0.374905\pi\) | ||||
0.382958 | + | 0.923766i | \(0.374905\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.876894 | −0.0342631 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 44.5667 | 1.73871 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.1442 | 1.48589 | 0.742944 | − | 0.669354i | \(-0.233429\pi\) | ||||
0.742944 | + | 0.669354i | \(0.233429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.3711 | −1.92031 | −0.960156 | − | 0.279465i | \(-0.909843\pi\) | ||||
−0.960156 | + | 0.279465i | \(0.909843\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.75948 | 0.379027 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.48793 | 0.0576994 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.248601 | −0.00962585 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.8129 | 1.42327 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.1683 | 0.855798 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.66440 | 0.102705 | 0.0513525 | − | 0.998681i | \(-0.483647\pi\) | ||||
0.0513525 | + | 0.998681i | \(0.483647\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0613 | 0.387258 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.7863 | 1.68285 | 0.841423 | − | 0.540377i | \(-0.181718\pi\) | ||||
0.841423 | + | 0.540377i | \(0.181718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.57214 | −0.367345 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −68.2130 | −2.61393 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.42063 | −0.0543591 | −0.0271795 | − | 0.999631i | \(-0.508653\pi\) | ||||
−0.0271795 | + | 0.999631i | \(0.508653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.73778 | 0.0663973 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −47.3340 | −1.80590 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.12311 | 0.271369 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.641449 | 0.0244019 | 0.0122009 | − | 0.999926i | \(-0.496116\pi\) | ||||
0.0122009 | + | 0.999926i | \(0.496116\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.9345 | −0.643289 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.5504 | −0.476063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.99618 | −0.151366 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.8690 | −0.827163 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.2221 | −0.612701 | −0.306351 | − | 0.951919i | \(-0.599108\pi\) | ||||
−0.306351 | + | 0.951919i | \(0.599108\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.7082 | −0.554731 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.52385 | 0.358689 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.74592 | 0.328924 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.99883 | 0.225291 | 0.112645 | − | 0.993635i | \(-0.464068\pi\) | ||||
0.112645 | + | 0.993635i | \(0.464068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −81.4010 | −3.05277 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.42728 | −0.0534520 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.68830 | −0.100537 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 51.4942 | 1.92309 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.5987 | −0.693613 | −0.346807 | − | 0.937937i | \(-0.612734\pi\) | ||||
−0.346807 | + | 0.937937i | \(0.612734\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.562747 | 0.0209578 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 35.3625 | 1.31514 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.361180 | 0.0134139 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.5969 | −1.06060 | −0.530300 | − | 0.847810i | \(-0.677921\pi\) | ||||
−0.530300 | + | 0.847810i | \(0.677921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.8159 | −0.659848 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.1225 | 1.04015 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.5932 | 1.16692 | 0.583461 | − | 0.812141i | \(-0.301698\pi\) | ||||
0.583461 | + | 0.812141i | \(0.301698\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.04948 | −0.112482 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.96092 | 0.109067 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.1892 | −1.88303 | −0.941513 | − | 0.336976i | \(-0.890596\pi\) | ||||
−0.941513 | + | 0.336976i | \(0.890596\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.53741 | 0.166686 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.59919 | 0.315474 | 0.157737 | − | 0.987481i | \(-0.449580\pi\) | ||||
0.157737 | + | 0.987481i | \(0.449580\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.12311 | 0.260970 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.37899 | −0.269983 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.28697 | 0.339339 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.8796 | −1.27277 | −0.636386 | − | 0.771370i | \(-0.719572\pi\) | ||||
−0.636386 | + | 0.771370i | \(0.719572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −55.5015 | −2.02259 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.1083 | 0.659028 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.1702 | 1.13290 | 0.566451 | − | 0.824096i | \(-0.308316\pi\) | ||||
0.566451 | + | 0.824096i | \(0.308316\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.64264 | −0.204815 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.36549 | −0.0494991 | −0.0247496 | − | 0.999694i | \(-0.507879\pi\) | ||||
−0.0247496 | + | 0.999694i | \(0.507879\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.02653 | −0.109568 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20.1602 | −0.728894 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.52505 | −0.235606 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.2245 | −0.981739 | −0.490870 | − | 0.871233i | \(-0.663321\pi\) | ||||
−0.490870 | + | 0.871233i | \(0.663321\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.4213 | −1.27567 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.5745 | 0.704047 | 0.352023 | − | 0.935991i | \(-0.385494\pi\) | ||||
0.352023 | + | 0.935991i | \(0.385494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.07362 | 0.0744868 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.1442 | 1.08142 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.85792 | −0.0665668 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.4338 | 1.55418 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.63392 | 0.129866 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.5108 | −0.517913 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.3132 | −1.57959 | −0.789797 | − | 0.613369i | \(-0.789814\pi\) | ||||
−0.789797 | + | 0.613369i | \(0.789814\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −64.9861 | −2.31357 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.4756 | −0.621360 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.24621 | 0.292832 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.7218 | −0.770392 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −45.7244 | −1.61964 | −0.809821 | − | 0.586677i | \(-0.800436\pi\) | ||||
−0.809821 | + | 0.586677i | \(0.800436\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.99510 | −0.353601 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −43.5383 | −1.53835 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.0192 | 0.671175 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.688301 | −0.0242594 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.57511 | 0.161052 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.0531 | 0.880821 | 0.440410 | − | 0.897797i | \(-0.354833\pi\) | ||||
0.440410 | + | 0.897797i | \(0.354833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.0239 | −0.422216 | −0.211108 | − | 0.977463i | \(-0.567707\pi\) | ||||
−0.211108 | + | 0.977463i | \(0.567707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.55586 | −0.0545665 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.76432 | 0.236944 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.0748 | 0.457430 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.29934 | −0.220117 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.22935 | −0.182506 | −0.0912529 | − | 0.995828i | \(-0.529087\pi\) | ||||
−0.0912529 | + | 0.995828i | \(0.529087\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.5554 | −1.16967 | −0.584834 | − | 0.811153i | \(-0.698840\pi\) | ||||
−0.584834 | + | 0.811153i | \(0.698840\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.19792 | 0.285415 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.6560 | −0.961695 | −0.480848 | − | 0.876804i | \(-0.659671\pi\) | ||||
−0.480848 | + | 0.876804i | \(0.659671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.2576 | 1.81498 | 0.907491 | − | 0.420073i | \(-0.137995\pi\) | ||||
0.907491 | + | 0.420073i | \(0.137995\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −68.1485 | −2.36404 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.20037 | 0.110886 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.94874 | −0.309684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.8633 | 0.721140 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.79024 | −0.0618058 | −0.0309029 | − | 0.999522i | \(-0.509838\pi\) | ||||
−0.0309029 | + | 0.999522i | \(0.509838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8695 | −0.995502 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −74.7187 | −2.57345 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.77304 | 0.129643 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.1041 | −0.930209 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.80388 | 0.233234 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.40255 | 0.253459 | 0.126729 | − | 0.991937i | \(-0.459552\pi\) | ||||
0.126729 | + | 0.991937i | \(0.459552\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.37296 | −0.320548 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.86328 | −0.302764 | −0.151382 | − | 0.988475i | \(-0.548372\pi\) | ||||
−0.151382 | + | 0.988475i | \(0.548372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.6319 | −1.59106 | −0.795530 | − | 0.605914i | \(-0.792807\pi\) | ||||
−0.795530 | + | 0.605914i | \(0.792807\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.80776 | 0.129768 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.6173 | −1.68899 | −0.844496 | − | 0.535562i | \(-0.820100\pi\) | ||||
−0.844496 | + | 0.535562i | \(0.820100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.0347 | −0.545195 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.6072 | −0.699858 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.7386 | −1.17843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.10141 | 0.0373199 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 60.2981 | 2.04078 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.27578 | 0.313221 | 0.156610 | − | 0.987660i | \(-0.449943\pi\) | ||||
0.156610 | + | 0.987660i | \(0.449943\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 57.2594 | 1.93131 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.3102 | 1.79607 | 0.898033 | − | 0.439928i | \(-0.144996\pi\) | ||||
0.898033 | + | 0.439928i | \(0.144996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.7070 | 1.30259 | 0.651297 | − | 0.758823i | \(-0.274225\pi\) | ||||
0.651297 | + | 0.758823i | \(0.274225\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.8980 | 0.668864 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.3560 | 1.11999 | 0.559993 | − | 0.828497i | \(-0.310804\pi\) | ||||
0.559993 | + | 0.828497i | \(0.310804\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.64001 | −0.222699 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.6779 | 1.06125 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.64696 | −0.155505 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.1689 | −0.741026 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.09896 | −0.0700823 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.748951 | 0.0249789 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.7966 | 0.759465 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.7966 | −0.891735 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.476148 | 0.0158277 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.4311 | 1.67454 | 0.837269 | − | 0.546791i | \(-0.184151\pi\) | ||||
0.837269 | + | 0.546791i | \(0.184151\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −55.0935 | −1.82734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.42914 | 0.0473497 | 0.0236748 | − | 0.999720i | \(-0.492463\pi\) | ||||
0.0236748 | + | 0.999720i | \(0.492463\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.14906 | −0.104219 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −25.1467 | −0.831323 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.876894 | −0.0289576 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.53438 | −0.215549 | −0.107775 | − | 0.994175i | \(-0.534372\pi\) | ||||
−0.107775 | + | 0.994175i | \(0.534372\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.7212 | −1.27591 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.1566 | 0.531800 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.88503 | −0.325018 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.54493 | −0.116431 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.7089 | −0.351346 | −0.175673 | − | 0.984449i | \(-0.556210\pi\) | ||||
−0.175673 | + | 0.984449i | \(0.556210\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.48793 | 0.0487649 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −76.6621 | −2.50980 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.60357 | −0.281367 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.1527 | 0.658359 | 0.329180 | − | 0.944267i | \(-0.393228\pi\) | ||||
0.329180 | + | 0.944267i | \(0.393228\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.1152 | −1.14594 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.1678 | 0.983441 | 0.491721 | − | 0.870753i | \(-0.336368\pi\) | ||||
0.491721 | + | 0.870753i | \(0.336368\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.859454 | 0.0279877 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.0613 | 0.327293 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 59.7659 | 1.94213 | 0.971065 | − | 0.238816i | \(-0.0767593\pi\) | ||||
0.971065 | + | 0.238816i | \(0.0767593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.07482 | 0.229658 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −75.7935 | −2.45777 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.2191 | 0.719747 | 0.359874 | − | 0.933001i | \(-0.382820\pi\) | ||||
0.359874 | + | 0.933001i | \(0.382820\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.86089 | −0.0925762 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.96092 | 0.0957131 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.73778 | 0.0561159 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7001 | −0.861293 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −58.5018 | −1.88519 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.7001 | 0.441021 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.81080 | −0.186863 | −0.0934313 | − | 0.995626i | \(-0.529784\pi\) | ||||
−0.0934313 | + | 0.995626i | \(0.529784\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.5214 | 0.466495 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.5692 | −0.467547 | −0.233773 | − | 0.972291i | \(-0.575107\pi\) | ||||
−0.233773 | + | 0.972291i | \(0.575107\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.5504 | −0.402347 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.04948 | 0.0976616 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.1684 | 1.70101 | 0.850503 | − | 0.525970i | \(-0.176297\pi\) | ||||
0.850503 | + | 0.525970i | \(0.176297\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.5804 | −0.593831 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.0651 | 0.608703 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 60.1364 | 1.91805 | 0.959027 | − | 0.283315i | \(-0.0914344\pi\) | ||||
0.959027 | + | 0.283315i | \(0.0914344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.868174 | 0.0276623 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.52385 | 0.303148 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.04829 | −0.192324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.2263 | 0.483680 | 0.241840 | − | 0.970316i | \(-0.422249\pi\) | ||||
0.241840 | + | 0.970316i | \(0.422249\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.84978 | −0.0904350 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.2963 | 0.484925 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.4676 | −1.18661 | −0.593306 | − | 0.804977i | \(-0.702178\pi\) | ||||
−0.593306 | + | 0.804977i | \(0.702178\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −99.4559 | −3.14664 |
(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 | 3640.2.a.x.1.4 | ✓ | 4 | |
4.3 | odd | 2 | 7280.2.a.br.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.x.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7280.2.a.br.1.1 | 4 | 4.3 | odd | 2 |