Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.46081 | 0.653295 | 0.326647 | − | 0.945146i | \(-0.394081\pi\) | ||||
0.326647 | + | 0.945146i | \(0.394081\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.34017 | 0.884502 | 0.442251 | − | 0.896891i | \(-0.354180\pi\) | ||||
0.442251 | + | 0.896891i | \(0.354180\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.63090 | −0.793245 | −0.396623 | − | 0.917982i | \(-0.629818\pi\) | ||||
−0.396623 | + | 0.917982i | \(0.629818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.46081 | −0.377180 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.61757 | 0.392318 | 0.196159 | − | 0.980572i | \(-0.437153\pi\) | ||||
0.196159 | + | 0.980572i | \(0.437153\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.41855 | −0.784269 | −0.392135 | − | 0.919908i | \(-0.628263\pi\) | ||||
−0.392135 | + | 0.919908i | \(0.628263\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.34017 | −0.510668 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.00000 | −1.66812 | −0.834058 | − | 0.551677i | \(-0.813988\pi\) | ||||
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.86603 | −0.573206 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.26180 | −1.34848 | −0.674241 | − | 0.738512i | \(-0.735529\pi\) | ||||
−0.674241 | + | 0.738512i | \(0.735529\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.41855 | 0.613990 | 0.306995 | − | 0.951711i | \(-0.400677\pi\) | ||||
0.306995 | + | 0.951711i | \(0.400677\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.63090 | 0.457980 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.41855 | 0.577841 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.340173 | 0.0559241 | 0.0279620 | − | 0.999609i | \(-0.491098\pi\) | ||||
0.0279620 | + | 0.999609i | \(0.491098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.63809 | −1.34904 | −0.674521 | − | 0.738256i | \(-0.735650\pi\) | ||||
−0.674521 | + | 0.738256i | \(0.735650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.95774 | −1.21354 | −0.606772 | − | 0.794876i | \(-0.707536\pi\) | ||||
−0.606772 | + | 0.794876i | \(0.707536\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.46081 | 0.217765 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.89269 | −0.567808 | −0.283904 | − | 0.958853i | \(-0.591630\pi\) | ||||
−0.283904 | + | 0.958853i | \(0.591630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.52359 | −0.217656 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.61757 | −0.226505 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.29791 | 0.865085 | 0.432542 | − | 0.901614i | \(-0.357617\pi\) | ||||
0.432542 | + | 0.901614i | \(0.357617\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.84324 | −0.518223 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.41855 | 0.452798 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.26180 | −0.164272 | −0.0821359 | − | 0.996621i | \(-0.526174\pi\) | ||||
−0.0821359 | + | 0.996621i | \(0.526174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5464 | 1.60640 | 0.803199 | − | 0.595710i | \(-0.203129\pi\) | ||||
0.803199 | + | 0.595710i | \(0.203129\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.34017 | 0.294834 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.92162 | 0.362383 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8794 | −1.57346 | −0.786732 | − | 0.617294i | \(-0.788229\pi\) | ||||
−0.786732 | + | 0.617294i | \(0.788229\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.9155 | −1.88882 | −0.944410 | − | 0.328770i | \(-0.893366\pi\) | ||||
−0.944410 | + | 0.328770i | \(0.893366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50307 | 0.175921 | 0.0879606 | − | 0.996124i | \(-0.471965\pi\) | ||||
0.0879606 | + | 0.996124i | \(0.471965\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.86603 | 0.330941 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.15676 | −0.701627 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.35577 | 0.265045 | 0.132522 | − | 0.991180i | \(-0.457692\pi\) | ||||
0.132522 | + | 0.991180i | \(0.457692\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.5958 | 1.82163 | 0.910814 | − | 0.412816i | \(-0.135455\pi\) | ||||
0.910814 | + | 0.412816i | \(0.135455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.36296 | 0.256299 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.26180 | 0.778546 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.9421 | −1.26586 | −0.632932 | − | 0.774207i | \(-0.718149\pi\) | ||||
−0.632932 | + | 0.774207i | \(0.718149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.68035 | 0.490634 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.41855 | −0.354487 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.99386 | −0.512359 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.23513 | −0.125409 | −0.0627044 | − | 0.998032i | \(-0.519973\pi\) | ||||
−0.0627044 | + | 0.998032i | \(0.519973\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.63090 | −0.264415 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.87936 | 0.485515 | 0.242757 | − | 0.970087i | \(-0.421948\pi\) | ||||
0.242757 | + | 0.970087i | \(0.421948\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.12064 | −0.307486 | −0.153743 | − | 0.988111i | \(-0.549133\pi\) | ||||
−0.153743 | + | 0.988111i | \(0.549133\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.41855 | −0.333616 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.04945 | 0.584822 | 0.292411 | − | 0.956293i | \(-0.405542\pi\) | ||||
0.292411 | + | 0.956293i | \(0.405542\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.94214 | 0.760719 | 0.380360 | − | 0.924839i | \(-0.375800\pi\) | ||||
0.380360 | + | 0.924839i | \(0.375800\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.340173 | −0.0322878 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.21953 | 0.679157 | 0.339578 | − | 0.940578i | \(-0.389716\pi\) | ||||
0.339578 | + | 0.940578i | \(0.389716\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.6865 | −1.08977 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.78539 | 0.347006 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.07838 | −0.370762 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.63809 | 0.778870 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.4908 | −1.02777 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.60197 | 0.319623 | 0.159811 | − | 0.987148i | \(-0.448911\pi\) | ||||
0.159811 | + | 0.987148i | \(0.448911\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.95774 | 0.700640 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.183417 | 0.0160253 | 0.00801263 | − | 0.999968i | \(-0.497449\pi\) | ||||
0.00801263 | + | 0.999968i | \(0.497449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.46081 | −0.125727 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.81658 | −0.155201 | −0.0776006 | − | 0.996985i | \(-0.524726\pi\) | ||||
−0.0776006 | + | 0.996985i | \(0.524726\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.4608 | 0.972093 | 0.486047 | − | 0.873933i | \(-0.338439\pi\) | ||||
0.486047 | + | 0.873933i | \(0.338439\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.89269 | 0.327824 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.26180 | −0.440013 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.6081 | −0.880956 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.52359 | 0.125664 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.1929 | −0.916956 | −0.458478 | − | 0.888706i | \(-0.651605\pi\) | ||||
−0.458478 | + | 0.888706i | \(0.651605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.06278 | 0.574761 | 0.287380 | − | 0.957817i | \(-0.407216\pi\) | ||||
0.287380 | + | 0.957817i | \(0.407216\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.61757 | 0.130773 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.99386 | 0.401116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.60197 | 0.127851 | 0.0639255 | − | 0.997955i | \(-0.479638\pi\) | ||||
0.0639255 | + | 0.997955i | \(0.479638\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.29791 | −0.499457 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.7214 | −1.47545 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.4608 | −0.897680 | −0.448840 | − | 0.893612i | \(-0.648163\pi\) | ||||
−0.448840 | + | 0.893612i | \(0.648163\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.84324 | 0.299196 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.41855 | −0.261423 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.8371 | 1.58422 | 0.792108 | − | 0.610381i | \(-0.208984\pi\) | ||||
0.792108 | + | 0.610381i | \(0.208984\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.70701 | −0.507002 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.26180 | 0.0948423 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1568 | −1.05813 | −0.529063 | − | 0.848583i | \(-0.677456\pi\) | ||||
−0.529063 | + | 0.848583i | \(0.677456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.81432 | 0.655163 | 0.327581 | − | 0.944823i | \(-0.393766\pi\) | ||||
0.327581 | + | 0.944823i | \(0.393766\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.5464 | −0.927455 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.496928 | 0.0365349 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.25565 | −0.311204 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.34017 | −0.170223 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.7877 | −1.21471 | −0.607356 | − | 0.794430i | \(-0.707770\pi\) | ||||
−0.607356 | + | 0.794430i | \(0.707770\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.26180 | 0.522715 | 0.261358 | − | 0.965242i | \(-0.415830\pi\) | ||||
0.261358 | + | 0.965242i | \(0.415830\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.92162 | −0.209222 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.114495 | 0.00815744 | 0.00407872 | − | 0.999992i | \(-0.498702\pi\) | ||||
0.00407872 | + | 0.999992i | \(0.498702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.9155 | −0.844666 | −0.422333 | − | 0.906441i | \(-0.638789\pi\) | ||||
−0.422333 | + | 0.906441i | \(0.638789\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.8794 | 0.908440 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.9939 | −1.19273 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.6186 | −0.881322 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.00000 | −0.556038 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.99386 | 0.622118 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2039 | −0.771311 | −0.385655 | − | 0.922643i | \(-0.626025\pi\) | ||||
−0.385655 | + | 0.922643i | \(0.626025\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.9155 | 1.09051 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.6248 | −0.792802 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.50307 | −0.101568 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.23513 | 0.217619 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.34017 | 0.156710 | 0.0783548 | − | 0.996926i | \(-0.475033\pi\) | ||||
0.0783548 | + | 0.996926i | \(0.475033\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.86603 | −0.191069 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.8310 | −1.31623 | −0.658113 | − | 0.752919i | \(-0.728645\pi\) | ||||
−0.658113 | + | 0.752919i | \(0.728645\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7031 | 1.23594 | 0.617969 | − | 0.786203i | \(-0.287956\pi\) | ||||
0.617969 | + | 0.786203i | \(0.287956\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.15676 | 0.405085 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.8638 | −1.49785 | −0.748927 | − | 0.662652i | \(-0.769431\pi\) | ||||
−0.748927 | + | 0.662652i | \(0.769431\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.68649 | −0.370946 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.35577 | −0.153024 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.2534 | 1.11603 | 0.558014 | − | 0.829831i | \(-0.311563\pi\) | ||||
0.558014 | + | 0.829831i | \(0.311563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.8576 | 0.763816 | 0.381908 | − | 0.924200i | \(-0.375267\pi\) | ||||
0.381908 | + | 0.924200i | \(0.375267\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.22568 | −0.142193 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.83710 | −0.435034 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.5958 | −1.05172 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.4908 | −1.10401 | −0.552004 | − | 0.833841i | \(-0.686137\pi\) | ||||
−0.552004 | + | 0.833841i | \(0.686137\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.0472 | 1.32322 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.36296 | −0.147974 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.97826 | 0.310535 | 0.155268 | − | 0.987872i | \(-0.450376\pi\) | ||||
0.155268 | + | 0.987872i | \(0.450376\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.796064 | 0.0494650 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.26180 | −0.449494 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.1711 | 1.61378 | 0.806891 | − | 0.590701i | \(-0.201149\pi\) | ||||
0.806891 | + | 0.590701i | \(0.201149\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.20006 | 0.565155 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.9421 | 0.730847 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.37629 | 0.205856 | 0.102928 | − | 0.994689i | \(-0.467179\pi\) | ||||
0.102928 | + | 0.994689i | \(0.467179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.29791 | 0.504062 | 0.252031 | − | 0.967719i | \(-0.418901\pi\) | ||||
0.252031 | + | 0.967719i | \(0.418901\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.68035 | −0.283267 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.54023 | 0.454693 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3090 | −0.979911 | −0.489956 | − | 0.871747i | \(-0.662987\pi\) | ||||
−0.489956 | + | 0.871747i | \(0.662987\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.41855 | 0.204663 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.8638 | −0.648078 | −0.324039 | − | 0.946044i | \(-0.605041\pi\) | ||||
−0.324039 | + | 0.946044i | \(0.605041\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.8950 | 1.00430 | 0.502151 | − | 0.864780i | \(-0.332542\pi\) | ||||
0.502151 | + | 0.864780i | \(0.332542\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.99386 | 0.295811 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.2146 | −1.19323 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3835 | −0.846087 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.23513 | 0.0724048 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 33.0349 | 1.92992 | 0.964960 | − | 0.262399i | \(-0.0845135\pi\) | ||||
0.964960 | + | 0.262399i | \(0.0845135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.84324 | −0.107318 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.63090 | 0.152660 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.0000 | −0.925304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.6225 | −1.07338 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.87936 | −0.280312 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.3279 | 1.04945 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.21953 | −0.526187 | −0.263093 | − | 0.964770i | \(-0.584743\pi\) | ||||
−0.263093 | + | 0.964770i | \(0.584743\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.12064 | 0.177527 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.8576 | −0.785794 | −0.392897 | − | 0.919583i | \(-0.628527\pi\) | ||||
−0.392897 | + | 0.919583i | \(0.628527\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.8371 | −0.725596 | −0.362798 | − | 0.931868i | \(-0.618178\pi\) | ||||
−0.362798 | + | 0.931868i | \(0.618178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.41855 | 0.192614 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.09890 | −0.342548 | −0.171274 | − | 0.985223i | \(-0.554788\pi\) | ||||
−0.171274 | + | 0.985223i | \(0.554788\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.1050 | 1.06968 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.04945 | −0.337647 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.52973 | −0.307683 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.73206 | −0.317958 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.94214 | −0.439201 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.10957 | −0.502227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8482 | −0.706199 | −0.353100 | − | 0.935586i | \(-0.614872\pi\) | ||||
−0.353100 | + | 0.935586i | \(0.614872\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.340173 | 0.0186414 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.8143 | −1.02794 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.5958 | −1.44877 | −0.724383 | − | 0.689397i | \(-0.757875\pi\) | ||||
−0.724383 | + | 0.689397i | \(0.757875\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.21953 | −0.392111 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.99386 | −0.487045 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9467 | −1.07702 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.6865 | 0.629179 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35.3028 | −1.89516 | −0.947578 | − | 0.319525i | \(-0.896477\pi\) | ||||
−0.947578 | + | 0.319525i | \(0.896477\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.81658 | −0.525470 | −0.262735 | − | 0.964868i | \(-0.584624\pi\) | ||||
−0.262735 | + | 0.964868i | \(0.584624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1834 | 0.754907 | 0.377454 | − | 0.926029i | \(-0.376800\pi\) | ||||
0.377454 | + | 0.926029i | \(0.376800\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.2495 | −1.23396 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.78539 | −0.200344 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.20394 | 0.380209 | 0.190105 | − | 0.981764i | \(-0.439117\pi\) | ||||
0.190105 | + | 0.981764i | \(0.439117\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.31351 | −0.384922 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.07838 | 0.214059 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.19570 | 0.114928 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.4596 | −1.53778 | −0.768889 | − | 0.639382i | \(-0.779190\pi\) | ||||
−0.768889 | + | 0.639382i | \(0.779190\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.63809 | −0.449681 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.7382 | 0.765169 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.3857 | 1.46976 | 0.734879 | − | 0.678198i | \(-0.237239\pi\) | ||||
0.734879 | + | 0.678198i | \(0.237239\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.4908 | 0.593382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.5236 | −0.748003 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.4280 | −0.741117 | −0.370558 | − | 0.928809i | \(-0.620834\pi\) | ||||
−0.370558 | + | 0.928809i | \(0.620834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.60197 | −0.184534 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.7298 | −0.752657 | −0.376329 | − | 0.926486i | \(-0.622814\pi\) | ||||
−0.376329 | + | 0.926486i | \(0.622814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.99386 | −0.458369 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.95774 | −0.404515 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.1145 | −1.42546 | −0.712731 | − | 0.701438i | \(-0.752542\pi\) | ||||
−0.712731 | + | 0.701438i | \(0.752542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.9405 | −0.654431 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.183417 | −0.00925219 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.44134 | 0.173152 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.3256 | 1.67256 | 0.836282 | − | 0.548299i | \(-0.184724\pi\) | ||||
0.836282 | + | 0.548299i | \(0.184724\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.8794 | −0.842915 | −0.421458 | − | 0.906848i | \(-0.638481\pi\) | ||||
−0.421458 | + | 0.906848i | \(0.638481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.83710 | 0.340580 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.46081 | 0.0725883 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.894960 | −0.0443615 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3958 | 0.662378 | 0.331189 | − | 0.943564i | \(-0.392550\pi\) | ||||
0.331189 | + | 0.943564i | \(0.392550\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.81658 | 0.0896054 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.95282 | −0.145299 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.2434 | 1.19006 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.4608 | −0.561238 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8348 | 0.675876 | 0.337938 | − | 0.941168i | \(-0.390271\pi\) | ||||
0.337938 | + | 0.941168i | \(0.390271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.07223 | 0.393417 | 0.196708 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196708 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.89269 | −0.189269 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.63600 | −0.224879 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.3607 | 1.42086 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.26180 | 0.254042 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.7070 | −1.28643 | −0.643216 | − | 0.765685i | \(-0.722400\pi\) | ||||
−0.643216 | + | 0.765685i | \(0.722400\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.5936 | −0.845492 | −0.422746 | − | 0.906248i | \(-0.638934\pi\) | ||||
−0.422746 | + | 0.906248i | \(0.638934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.6081 | 0.508620 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.3484 | 1.30825 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.5741 | 1.69786 | 0.848929 | − | 0.528507i | \(-0.177248\pi\) | ||||
0.848929 | + | 0.528507i | \(0.177248\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.52359 | −0.0725519 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.948284 | −0.0450543 | −0.0225272 | − | 0.999746i | \(-0.507171\pi\) | ||||
−0.0225272 | + | 0.999746i | \(0.507171\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.4452 | −0.826982 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.1929 | 0.529405 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9565 | 0.941806 | 0.470903 | − | 0.882185i | \(-0.343928\pi\) | ||||
0.470903 | + | 0.882185i | \(0.343928\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.7259 | 1.07012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.06278 | −0.331838 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.83710 | 0.320528 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.9155 | 0.650939 | 0.325469 | − | 0.945553i | \(-0.394478\pi\) | ||||
0.325469 | + | 0.945553i | \(0.394478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.61757 | −0.0755015 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.9216 | 1.34701 | 0.673507 | − | 0.739181i | \(-0.264787\pi\) | ||||
0.673507 | + | 0.739181i | \(0.264787\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.396809 | −0.0184413 | −0.00922064 | − | 0.999957i | \(-0.502935\pi\) | ||||
−0.00922064 | + | 0.999957i | \(0.502935\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.99386 | −0.231585 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.5708 | 0.905627 | 0.452814 | − | 0.891605i | \(-0.350420\pi\) | ||||
0.452814 | + | 0.891605i | \(0.350420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.1399 | −1.39173 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.60197 | −0.0738148 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.9360 | 0.962638 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.79767 | 0.449548 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.29791 | 0.288362 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.23513 | 0.330582 | 0.165291 | − | 0.986245i | \(-0.447144\pi\) | ||||
0.165291 | + | 0.986245i | \(0.447144\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.680346 | 0.0310211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.7214 | 0.851852 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.80430 | −0.0819289 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.78661 | −0.171588 | −0.0857938 | − | 0.996313i | \(-0.527343\pi\) | ||||
−0.0857938 | + | 0.996313i | \(0.527343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.4608 | 0.518276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.5669 | −1.51485 | −0.757426 | − | 0.652921i | \(-0.773544\pi\) | ||||
−0.757426 | + | 0.652921i | \(0.773544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.7464 | −0.529033 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.84324 | −0.172741 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.2450 | −1.67067 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.7948 | 1.10997 | 0.554985 | − | 0.831861i | \(-0.312724\pi\) | ||||
0.554985 | + | 0.831861i | \(0.312724\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.6248 | −1.41008 | −0.705039 | − | 0.709168i | \(-0.749071\pi\) | ||||
−0.705039 | + | 0.709168i | \(0.749071\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.12783 | 0.317184 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.6430 | −1.22525 | −0.612627 | − | 0.790372i | \(-0.709887\pi\) | ||||
−0.612627 | + | 0.790372i | \(0.709887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.51745 | 0.155603 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.41855 | 0.150933 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.55866 | −0.200879 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.2413 | 0.450411 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.8371 | −0.914647 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.2667 | 0.975523 | 0.487761 | − | 0.872977i | \(-0.337814\pi\) | ||||
0.487761 | + | 0.872977i | \(0.337814\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5113 | 0.547081 | 0.273541 | − | 0.961860i | \(-0.411805\pi\) | ||||
0.273541 | + | 0.961860i | \(0.411805\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.70701 | 0.292718 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.52973 | 0.240879 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.26180 | −0.0547572 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.2762 | −0.748314 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.83710 | 0.382061 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.1568 | 0.610909 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.00841 | 0.172654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.6270 | 0.456891 | 0.228446 | − | 0.973557i | \(-0.426636\pi\) | ||||
0.228446 | + | 0.973557i | \(0.426636\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.81432 | −0.378258 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.6020 | 0.496974 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9060 | 0.979391 | 0.489695 | − | 0.871894i | \(-0.337108\pi\) | ||||
0.489695 | + | 0.871894i | \(0.337108\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.5464 | 0.535466 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.8248 | 1.05757 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.51291 | 0.234433 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.496928 | −0.0210934 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.3340 | −0.903952 | −0.451976 | − | 0.892030i | \(-0.649281\pi\) | ||||
−0.451976 | + | 0.892030i | \(0.649281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.9155 | −0.673153 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.25565 | 0.179674 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.5441 | 1.24514 | 0.622568 | − | 0.782566i | \(-0.286089\pi\) | ||||
0.622568 | + | 0.782566i | \(0.286089\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.5464 | 0.443689 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.34017 | 0.0982780 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −45.6730 | −1.91471 | −0.957355 | − | 0.288913i | \(-0.906706\pi\) | ||||
−0.957355 | + | 0.288913i | \(0.906706\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.4485 | −1.23238 | −0.616191 | − | 0.787597i | \(-0.711325\pi\) | ||||
−0.616191 | + | 0.787597i | \(0.711325\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.7877 | 0.701314 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.9282 | 0.956174 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.3195 | 1.59526 | 0.797630 | − | 0.603147i | \(-0.206087\pi\) | ||||
0.797630 | + | 0.603147i | \(0.206087\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.26180 | −0.301790 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.8371 | 1.61123 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.5692 | −0.686225 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.92162 | 0.120794 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.9877 | −1.56792 | −0.783960 | − | 0.620811i | \(-0.786803\pi\) | ||||
−0.783960 | + | 0.620811i | \(0.786803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.6865 | −0.481533 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.114495 | −0.00470970 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.9516 | 0.942509 | 0.471255 | − | 0.881997i | \(-0.343801\pi\) | ||||
0.471255 | + | 0.881997i | \(0.343801\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52973 | 0.226697 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.9155 | 0.487668 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.8843 | 0.485579 | 0.242789 | − | 0.970079i | \(-0.421938\pi\) | ||||
0.242789 | + | 0.970079i | \(0.421938\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.1506 | 0.536425 | 0.268212 | − | 0.963360i | \(-0.413567\pi\) | ||||
0.268212 | + | 0.963360i | \(0.413567\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.8794 | −0.524488 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.95774 | −0.242217 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.7226 | 1.16581 | 0.582907 | − | 0.812539i | \(-0.301915\pi\) | ||||
0.582907 | + | 0.812539i | \(0.301915\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.9939 | 0.688626 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.78539 | −0.314963 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.97107 | 0.120000 | 0.0600002 | − | 0.998198i | \(-0.480890\pi\) | ||||
0.0600002 | + | 0.998198i | \(0.480890\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.6186 | 0.508832 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.68035 | −0.268941 | −0.134470 | − | 0.990918i | \(-0.542933\pi\) | ||||
−0.134470 | + | 0.990918i | \(0.542933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.1990 | 1.29419 | 0.647094 | − | 0.762410i | \(-0.275984\pi\) | ||||
0.647094 | + | 0.762410i | \(0.275984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.9467 | −1.11966 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.45571 | −0.0982285 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.99386 | −0.359180 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.550252 | 0.0219400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.9627 | 1.31222 | 0.656111 | − | 0.754664i | \(-0.272200\pi\) | ||||
0.656111 | + | 0.754664i | \(0.272200\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.2039 | 0.445316 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.26180 | 0.208808 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.04718 | −0.120734 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.9155 | −0.629607 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.4547 | −1.20289 | −0.601444 | − | 0.798915i | \(-0.705408\pi\) | ||||
−0.601444 | + | 0.798915i | \(0.705408\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.5490 | 1.44135 | 0.720677 | − | 0.693271i | \(-0.243831\pi\) | ||||
0.720677 | + | 0.693271i | \(0.243831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.6248 | 0.457724 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.1605 | −1.77544 | −0.887720 | − | 0.460383i | \(-0.847712\pi\) | ||||
−0.887720 | + | 0.460383i | \(0.847712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.31965 | 0.130308 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.99386 | −0.273691 | −0.136845 | − | 0.990592i | \(-0.543696\pi\) | ||||
−0.136845 | + | 0.990592i | \(0.543696\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.267938 | 0.0104692 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.50307 | 0.0586404 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.1338 | 1.36862 | 0.684309 | − | 0.729192i | \(-0.260104\pi\) | ||||
0.684309 | + | 0.729192i | \(0.260104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.4846 | −1.88583 | −0.942917 | − | 0.333028i | \(-0.891930\pi\) | ||||
−0.942917 | + | 0.333028i | \(0.891930\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.23513 | −0.125642 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.6865 | −0.453183 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 58.0944 | 2.24942 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.34017 | −0.0904763 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.0082 | −1.27427 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.2101 | 0.624853 | 0.312426 | − | 0.949942i | \(-0.398858\pi\) | ||||
0.312426 | + | 0.949942i | \(0.398858\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.86603 | 0.110314 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.7152 | −1.44951 | −0.724757 | − | 0.689004i | \(-0.758048\pi\) | ||||
−0.724757 | + | 0.689004i | \(0.758048\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.89043 | −0.110924 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.8310 | 0.759924 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.4391 | 0.705551 | 0.352776 | − | 0.935708i | \(-0.385238\pi\) | ||||
0.352776 | + | 0.935708i | \(0.385238\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.65368 | −0.101392 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.7031 | −0.713569 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.5958 | 0.479863 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.86499 | 0.337240 | 0.168620 | − | 0.985681i | \(-0.446069\pi\) | ||||
0.168620 | + | 0.985681i | \(0.446069\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.15676 | −0.233876 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.7421 | 0.635063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.9727 | −0.529253 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.8638 | 0.864787 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.8059 | 1.39014 | 0.695070 | − | 0.718942i | \(-0.255373\pi\) | ||||
0.695070 | + | 0.718942i | \(0.255373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.16290 | −0.0438595 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.68649 | 0.214166 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4186 | 0.429439 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.1978 | 0.833656 | 0.416828 | − | 0.908985i | \(-0.363142\pi\) | ||||
0.416828 | + | 0.908985i | \(0.363142\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.35577 | 0.0883483 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.3484 | −1.02421 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.68649 | −0.287458 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.2534 | −0.644339 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.3919 | 0.797783 | 0.398891 | − | 0.916998i | \(-0.369395\pi\) | ||||
0.398891 | + | 0.916998i | \(0.369395\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.30283 | −0.271972 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.8576 | −0.440990 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.8125 | 0.772958 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.2979 | 1.27204 | 0.636020 | − | 0.771673i | \(-0.280580\pi\) | ||||
0.636020 | + | 0.771673i | \(0.280580\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.8722 | −0.476095 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.5418 | −0.980345 | −0.490173 | − | 0.871625i | \(-0.663066\pi\) | ||||
−0.490173 | + | 0.871625i | \(0.663066\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.22568 | 0.0820954 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.8843 | 1.24814 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.5741 | 1.38219 | 0.691093 | − | 0.722766i | \(-0.257130\pi\) | ||||
0.691093 | + | 0.722766i | \(0.257130\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.83710 | 0.251167 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.3545 | −1.26035 | −0.630173 | − | 0.776455i | \(-0.717016\pi\) | ||||
−0.630173 | + | 0.776455i | \(0.717016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.3507 | −0.599042 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.5958 | 0.607209 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.1568 | 0.517277 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.4403 | 1.03780 | 0.518901 | − | 0.854835i | \(-0.326342\pi\) | ||||
0.518901 | + | 0.854835i | \(0.326342\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.4908 | 0.637400 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.3174 | 0.375488 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.7337 | 0.535504 | 0.267752 | − | 0.963488i | \(-0.413719\pi\) | ||||
0.267752 | + | 0.963488i | \(0.413719\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.0472 | −0.763964 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.6742 | −0.423190 | −0.211595 | − | 0.977357i | \(-0.567866\pi\) | ||||
−0.211595 | + | 0.977357i | \(0.567866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.5860 | 0.672858 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.36296 | 0.0854330 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.52359 | −0.0911216 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.3545 | −0.734004 | −0.367002 | − | 0.930220i | \(-0.619616\pi\) | ||||
−0.367002 | + | 0.930220i | \(0.619616\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.97826 | −0.179288 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.28354 | 0.297938 | 0.148969 | − | 0.988842i | \(-0.452405\pi\) | ||||
0.148969 | + | 0.988842i | \(0.452405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.79767 | −0.351943 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.796064 | −0.0285586 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.5297 | 1.05801 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.8720 | 1.49830 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.26180 | 0.259515 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.34017 | 0.0835244 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.14116 | 0.290201 | 0.145100 | − | 0.989417i | \(-0.453649\pi\) | ||||
0.145100 | + | 0.989417i | \(0.453649\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.1711 | −0.931717 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.8950 | 0.600716 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.0928 | 0.891070 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.20006 | −0.326293 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.8588 | 0.561749 | 0.280875 | − | 0.959744i | \(-0.409376\pi\) | ||||
0.280875 | + | 0.959744i | \(0.409376\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.29669 | −0.222761 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.9421 | −0.421955 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.95443 | −0.139549 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.3484 | −0.963905 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.37629 | −0.118851 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.8043 | 1.11818 | 0.559090 | − | 0.829107i | \(-0.311151\pi\) | ||||
0.559090 | + | 0.829107i | \(0.311151\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.55356 | −0.159897 | −0.0799486 | − | 0.996799i | \(-0.525476\pi\) | ||||
−0.0799486 | + | 0.996799i | \(0.525476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.29791 | −0.291020 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.7421 | −0.586449 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.2039 | 0.951745 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.68035 | 0.163545 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.4235 | 0.573183 | 0.286592 | − | 0.958053i | \(-0.407478\pi\) | ||||
0.286592 | + | 0.958053i | \(0.407478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.46081 | −0.0509207 | −0.0254603 | − | 0.999676i | \(-0.508105\pi\) | ||||
−0.0254603 | + | 0.999676i | \(0.508105\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.54023 | −0.262517 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.0472 | −0.731882 | −0.365941 | − | 0.930638i | \(-0.619253\pi\) | ||||
−0.365941 | + | 0.930638i | \(0.619253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.9421 | −1.10940 | −0.554698 | − | 0.832052i | \(-0.687166\pi\) | ||||
−0.554698 | + | 0.832052i | \(0.687166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.3090 | 0.565752 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.46451 | −0.0853902 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.46081 | 0.0505535 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.41855 | −0.118162 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.3584 | −1.25523 | −0.627616 | − | 0.778523i | \(-0.715969\pi\) | ||||
−0.627616 | + | 0.778523i | \(0.715969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.7337 | 0.818402 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.8638 | 0.374168 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.1473 | −0.452281 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.54411 | −0.327939 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.8950 | −0.579834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.72138 | −0.0932878 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.5464 | −0.429580 | −0.214790 | − | 0.976660i | \(-0.568907\pi\) | ||||
−0.214790 | + | 0.976660i | \(0.568907\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.99386 | −0.170786 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.523590 | −0.0178855 | −0.00894275 | − | 0.999960i | \(-0.502847\pi\) | ||||
−0.00894275 | + | 0.999960i | \(0.502847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.75872 | 0.196485 | 0.0982426 | − | 0.995162i | \(-0.468678\pi\) | ||||
0.0982426 | + | 0.995162i | \(0.468678\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.2146 | 0.688912 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.2868 | −0.758653 | −0.379327 | − | 0.925263i | \(-0.623844\pi\) | ||||
−0.379327 | + | 0.925263i | \(0.623844\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.4391 | 1.03496 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.3835 | 0.488489 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.19779 | −0.210246 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.7587 | −0.872801 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.23513 | −0.0418029 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.8904 | −0.909062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.4801 | −1.16431 | −0.582155 | − | 0.813078i | \(-0.697790\pi\) | ||||
−0.582155 | + | 0.813078i | \(0.697790\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −33.0349 | −1.11424 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.64423 | 0.324922 | 0.162461 | − | 0.986715i | \(-0.448057\pi\) | ||||
0.162461 | + | 0.986715i | \(0.448057\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.68488 | 0.224964 | 0.112482 | − | 0.993654i | \(-0.464120\pi\) | ||||
0.112482 | + | 0.993654i | \(0.464120\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.84324 | 0.0619600 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.9109 | 1.13862 | 0.569309 | − | 0.822124i | \(-0.307211\pi\) | ||||
0.569309 | + | 0.822124i | \(0.307211\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.42923 | 0.282707 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.63090 | −0.0881384 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.3074 | 0.445314 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.6803 | −0.691268 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000 | 0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.8248 | −0.827954 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.1873 | 0.339388 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.6225 | 0.619718 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.8760 | 0.428014 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.72383 | −0.0904433 | −0.0452216 | − | 0.998977i | \(-0.514399\pi\) | ||||
−0.0452216 | + | 0.998977i | \(0.514399\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.87936 | 0.161838 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.9405 | 0.958843 | 0.479421 | − | 0.877585i | \(-0.340847\pi\) | ||||
0.479421 | + | 0.877585i | \(0.340847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.6619 | −1.44500 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.3279 | −0.605901 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.429229 | 0.0141744 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.4740 | 1.10420 | 0.552102 | − | 0.833777i | \(-0.313826\pi\) | ||||
0.552102 | + | 0.833777i | \(0.313826\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.21953 | 0.303794 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.8310 | −1.04773 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.974946 | −0.0320560 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.12064 | −0.102495 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.2663 | −0.435254 | −0.217627 | − | 0.976032i | \(-0.569832\pi\) | ||||
−0.217627 | + | 0.976032i | \(0.569832\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.20847 | 0.170701 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.8576 | 0.453678 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.21670 | −0.203308 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.2679 | −0.335439 | −0.167719 | − | 0.985835i | \(-0.553640\pi\) | ||||
−0.167719 | + | 0.985835i | \(0.553640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.8371 | 0.418923 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.1867 | 1.11446 | 0.557228 | − | 0.830360i | \(-0.311865\pi\) | ||||
0.557228 | + | 0.830360i | \(0.311865\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 69.1047 | 2.25036 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.41855 | −0.111205 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.2185 | −0.332056 | −0.166028 | − | 0.986121i | \(-0.553094\pi\) | ||||
−0.166028 | + | 0.986121i | \(0.553094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.00614 | 0.0975835 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.09890 | 0.197770 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.2257 | −0.590388 | −0.295194 | − | 0.955437i | \(-0.595384\pi\) | ||||
−0.295194 | + | 0.955437i | \(0.595384\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.5236 | −0.793565 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.1050 | −0.617578 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.25112 | −0.137276 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.3135 | −0.623016 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.04945 | 0.194941 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.6081 | 0.341487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.3234 | 1.10376 | 0.551882 | − | 0.833922i | \(-0.313910\pi\) | ||||
0.551882 | + | 0.833922i | \(0.313910\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.52973 | 0.177641 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.8043 | 1.34156 | 0.670782 | − | 0.741655i | \(-0.265959\pi\) | ||||
0.670782 | + | 0.741655i | \(0.265959\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.8203 | 0.859819 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.73206 | 0.183573 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.50638 | −0.240150 | −0.120075 | − | 0.992765i | \(-0.538314\pi\) | ||||
−0.120075 | + | 0.992765i | \(0.538314\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.4186 | 1.00414 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.94214 | 0.253573 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.5441 | 0.814731 | 0.407365 | − | 0.913265i | \(-0.366448\pi\) | ||||
0.407365 | + | 0.913265i | \(0.366448\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.167256 | 0.00532921 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.10957 | 0.289961 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.6619 | 2.02433 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.9926 | −0.793917 | −0.396959 | − | 0.917837i | \(-0.629934\pi\) | ||||
−0.396959 | + | 0.917837i | \(0.629934\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.8482 | 0.407724 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.4063 | −0.551816 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.2846 | −0.990793 | −0.495396 | − | 0.868667i | \(-0.664977\pi\) | ||||
−0.495396 | + | 0.868667i | \(0.664977\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.340173 | −0.0107626 |
(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 | 4008.2.a.e.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 8016.2.a.n.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.e.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
8016.2.a.n.1.2 | 3 | 4.3 | odd | 2 |