Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1338,2,Mod(1,1338)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1338, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1338.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1338 = 2 \cdot 3 \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1338.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: | \(10.6839837904\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.356173.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 7x^{3} + 9x^{2} + 14x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.38363\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1338.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.35484 | 1.94754 | 0.973772 | − | 0.227528i | \(-0.0730644\pi\) | ||||
0.973772 | + | 0.227528i | \(0.0730644\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.05676 | 1.15535 | 0.577674 | − | 0.816268i | \(-0.303961\pi\) | ||||
0.577674 | + | 0.816268i | \(0.303961\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.35484 | −1.37712 | ||||||||
\(11\) | −0.734963 | −0.221600 | −0.110800 | − | 0.993843i | \(-0.535341\pi\) | ||||
−0.110800 | + | 0.993843i | \(0.535341\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.43689 | −0.675871 | −0.337935 | − | 0.941169i | \(-0.609728\pi\) | ||||
−0.337935 | + | 0.941169i | \(0.609728\pi\) | |||||||
\(14\) | −3.05676 | −0.816954 | ||||||||
\(15\) | 4.35484 | 1.12441 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.681711 | −0.165339 | −0.0826696 | − | 0.996577i | \(-0.526345\pi\) | ||||
−0.0826696 | + | 0.996577i | \(0.526345\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.87811 | −0.430868 | −0.215434 | − | 0.976518i | \(-0.569117\pi\) | ||||
−0.215434 | + | 0.976518i | \(0.569117\pi\) | |||||||
\(20\) | 4.35484 | 0.973772 | ||||||||
\(21\) | 3.05676 | 0.667040 | ||||||||
\(22\) | 0.734963 | 0.156695 | ||||||||
\(23\) | 6.91115 | 1.44107 | 0.720537 | − | 0.693416i | \(-0.243895\pi\) | ||||
0.720537 | + | 0.693416i | \(0.243895\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 13.9646 | 2.79292 | ||||||||
\(26\) | 2.43689 | 0.477913 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.05676 | 0.577674 | ||||||||
\(29\) | 0.113306 | 0.0210404 | 0.0105202 | − | 0.999945i | \(-0.496651\pi\) | ||||
0.0105202 | + | 0.999945i | \(0.496651\pi\) | |||||||
\(30\) | −4.35484 | −0.795081 | ||||||||
\(31\) | 1.56736 | 0.281506 | 0.140753 | − | 0.990045i | \(-0.455048\pi\) | ||||
0.140753 | + | 0.990045i | \(0.455048\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.734963 | −0.127941 | ||||||||
\(34\) | 0.681711 | 0.116912 | ||||||||
\(35\) | 13.3117 | 2.25009 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.71884 | −0.611374 | −0.305687 | − | 0.952132i | \(-0.598886\pi\) | ||||
−0.305687 | + | 0.952132i | \(0.598886\pi\) | |||||||
\(38\) | 1.87811 | 0.304670 | ||||||||
\(39\) | −2.43689 | −0.390214 | ||||||||
\(40\) | −4.35484 | −0.688560 | ||||||||
\(41\) | −11.1102 | −1.73513 | −0.867563 | − | 0.497327i | \(-0.834315\pi\) | ||||
−0.867563 | + | 0.497327i | \(0.834315\pi\) | |||||||
\(42\) | −3.05676 | −0.471669 | ||||||||
\(43\) | −10.9512 | −1.67004 | −0.835022 | − | 0.550217i | \(-0.814545\pi\) | ||||
−0.835022 | + | 0.550217i | \(0.814545\pi\) | |||||||
\(44\) | −0.734963 | −0.110800 | ||||||||
\(45\) | 4.35484 | 0.649181 | ||||||||
\(46\) | −6.91115 | −1.01899 | ||||||||
\(47\) | −6.22966 | −0.908689 | −0.454344 | − | 0.890826i | \(-0.650126\pi\) | ||||
−0.454344 | + | 0.890826i | \(0.650126\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 2.34379 | 0.334827 | ||||||||
\(50\) | −13.9646 | −1.97490 | ||||||||
\(51\) | −0.681711 | −0.0954586 | ||||||||
\(52\) | −2.43689 | −0.337935 | ||||||||
\(53\) | 6.47426 | 0.889309 | 0.444654 | − | 0.895702i | \(-0.353327\pi\) | ||||
0.444654 | + | 0.895702i | \(0.353327\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.20064 | −0.431575 | ||||||||
\(56\) | −3.05676 | −0.408477 | ||||||||
\(57\) | −1.87811 | −0.248762 | ||||||||
\(58\) | −0.113306 | −0.0148778 | ||||||||
\(59\) | 7.94099 | 1.03383 | 0.516915 | − | 0.856037i | \(-0.327080\pi\) | ||||
0.516915 | + | 0.856037i | \(0.327080\pi\) | |||||||
\(60\) | 4.35484 | 0.562207 | ||||||||
\(61\) | −4.54537 | −0.581974 | −0.290987 | − | 0.956727i | \(-0.593984\pi\) | ||||
−0.290987 | + | 0.956727i | \(0.593984\pi\) | |||||||
\(62\) | −1.56736 | −0.199055 | ||||||||
\(63\) | 3.05676 | 0.385116 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.6122 | −1.31629 | ||||||||
\(66\) | 0.734963 | 0.0904677 | ||||||||
\(67\) | −2.23117 | −0.272581 | −0.136290 | − | 0.990669i | \(-0.543518\pi\) | ||||
−0.136290 | + | 0.990669i | \(0.543518\pi\) | |||||||
\(68\) | −0.681711 | −0.0826696 | ||||||||
\(69\) | 6.91115 | 0.832005 | ||||||||
\(70\) | −13.3117 | −1.59105 | ||||||||
\(71\) | 10.5641 | 1.25372 | 0.626862 | − | 0.779130i | \(-0.284339\pi\) | ||||
0.626862 | + | 0.779130i | \(0.284339\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −3.30232 | −0.386507 | −0.193254 | − | 0.981149i | \(-0.561904\pi\) | ||||
−0.193254 | + | 0.981149i | \(0.561904\pi\) | |||||||
\(74\) | 3.71884 | 0.432307 | ||||||||
\(75\) | 13.9646 | 1.61250 | ||||||||
\(76\) | −1.87811 | −0.215434 | ||||||||
\(77\) | −2.24661 | −0.256024 | ||||||||
\(78\) | 2.43689 | 0.275923 | ||||||||
\(79\) | −3.98486 | −0.448332 | −0.224166 | − | 0.974551i | \(-0.571966\pi\) | ||||
−0.224166 | + | 0.974551i | \(0.571966\pi\) | |||||||
\(80\) | 4.35484 | 0.486886 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.1102 | 1.22692 | ||||||||
\(83\) | −9.77231 | −1.07265 | −0.536325 | − | 0.844011i | \(-0.680188\pi\) | ||||
−0.536325 | + | 0.844011i | \(0.680188\pi\) | |||||||
\(84\) | 3.05676 | 0.333520 | ||||||||
\(85\) | −2.96874 | −0.322005 | ||||||||
\(86\) | 10.9512 | 1.18090 | ||||||||
\(87\) | 0.113306 | 0.0121477 | ||||||||
\(88\) | 0.734963 | 0.0783473 | ||||||||
\(89\) | −3.23802 | −0.343230 | −0.171615 | − | 0.985164i | \(-0.554898\pi\) | ||||
−0.171615 | + | 0.985164i | \(0.554898\pi\) | |||||||
\(90\) | −4.35484 | −0.459040 | ||||||||
\(91\) | −7.44898 | −0.780865 | ||||||||
\(92\) | 6.91115 | 0.720537 | ||||||||
\(93\) | 1.56736 | 0.162528 | ||||||||
\(94\) | 6.22966 | 0.642540 | ||||||||
\(95\) | −8.17887 | −0.839134 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −11.1019 | −1.12723 | −0.563613 | − | 0.826039i | \(-0.690589\pi\) | ||||
−0.563613 | + | 0.826039i | \(0.690589\pi\) | |||||||
\(98\) | −2.34379 | −0.236759 | ||||||||
\(99\) | −0.734963 | −0.0738665 | ||||||||
\(100\) | 13.9646 | 1.39646 | ||||||||
\(101\) | 19.8419 | 1.97434 | 0.987171 | − | 0.159664i | \(-0.0510410\pi\) | ||||
0.987171 | + | 0.159664i | \(0.0510410\pi\) | |||||||
\(102\) | 0.681711 | 0.0674994 | ||||||||
\(103\) | −4.42428 | −0.435937 | −0.217968 | − | 0.975956i | \(-0.569943\pi\) | ||||
−0.217968 | + | 0.975956i | \(0.569943\pi\) | |||||||
\(104\) | 2.43689 | 0.238956 | ||||||||
\(105\) | 13.3117 | 1.29909 | ||||||||
\(106\) | −6.47426 | −0.628836 | ||||||||
\(107\) | 11.4126 | 1.10330 | 0.551651 | − | 0.834075i | \(-0.313998\pi\) | ||||
0.551651 | + | 0.834075i | \(0.313998\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −15.1912 | −1.45506 | −0.727528 | − | 0.686078i | \(-0.759331\pi\) | ||||
−0.727528 | + | 0.686078i | \(0.759331\pi\) | |||||||
\(110\) | 3.20064 | 0.305169 | ||||||||
\(111\) | −3.71884 | −0.352977 | ||||||||
\(112\) | 3.05676 | 0.288837 | ||||||||
\(113\) | −0.723916 | −0.0681003 | −0.0340501 | − | 0.999420i | \(-0.510841\pi\) | ||||
−0.0340501 | + | 0.999420i | \(0.510841\pi\) | |||||||
\(114\) | 1.87811 | 0.175901 | ||||||||
\(115\) | 30.0969 | 2.80655 | ||||||||
\(116\) | 0.113306 | 0.0105202 | ||||||||
\(117\) | −2.43689 | −0.225290 | ||||||||
\(118\) | −7.94099 | −0.731028 | ||||||||
\(119\) | −2.08383 | −0.191024 | ||||||||
\(120\) | −4.35484 | −0.397541 | ||||||||
\(121\) | −10.4598 | −0.950894 | ||||||||
\(122\) | 4.54537 | 0.411518 | ||||||||
\(123\) | −11.1102 | −1.00178 | ||||||||
\(124\) | 1.56736 | 0.140753 | ||||||||
\(125\) | 39.0395 | 3.49180 | ||||||||
\(126\) | −3.05676 | −0.272318 | ||||||||
\(127\) | 17.7134 | 1.57181 | 0.785905 | − | 0.618347i | \(-0.212197\pi\) | ||||
0.785905 | + | 0.618347i | \(0.212197\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.9512 | −0.964200 | ||||||||
\(130\) | 10.6122 | 0.930755 | ||||||||
\(131\) | −4.62868 | −0.404409 | −0.202205 | − | 0.979343i | \(-0.564811\pi\) | ||||
−0.202205 | + | 0.979343i | \(0.564811\pi\) | |||||||
\(132\) | −0.734963 | −0.0639703 | ||||||||
\(133\) | −5.74094 | −0.497802 | ||||||||
\(134\) | 2.23117 | 0.192744 | ||||||||
\(135\) | 4.35484 | 0.374805 | ||||||||
\(136\) | 0.681711 | 0.0584562 | ||||||||
\(137\) | −6.95121 | −0.593882 | −0.296941 | − | 0.954896i | \(-0.595966\pi\) | ||||
−0.296941 | + | 0.954896i | \(0.595966\pi\) | |||||||
\(138\) | −6.91115 | −0.588316 | ||||||||
\(139\) | 23.4964 | 1.99294 | 0.996468 | − | 0.0839681i | \(-0.0267594\pi\) | ||||
0.996468 | + | 0.0839681i | \(0.0267594\pi\) | |||||||
\(140\) | 13.3117 | 1.12504 | ||||||||
\(141\) | −6.22966 | −0.524632 | ||||||||
\(142\) | −10.5641 | −0.886517 | ||||||||
\(143\) | 1.79102 | 0.149773 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.493430 | 0.0409772 | ||||||||
\(146\) | 3.30232 | 0.273302 | ||||||||
\(147\) | 2.34379 | 0.193313 | ||||||||
\(148\) | −3.71884 | −0.305687 | ||||||||
\(149\) | −8.25494 | −0.676271 | −0.338136 | − | 0.941097i | \(-0.609796\pi\) | ||||
−0.338136 | + | 0.941097i | \(0.609796\pi\) | |||||||
\(150\) | −13.9646 | −1.14021 | ||||||||
\(151\) | −15.3701 | −1.25080 | −0.625402 | − | 0.780303i | \(-0.715065\pi\) | ||||
−0.625402 | + | 0.780303i | \(0.715065\pi\) | |||||||
\(152\) | 1.87811 | 0.152335 | ||||||||
\(153\) | −0.681711 | −0.0551131 | ||||||||
\(154\) | 2.24661 | 0.181037 | ||||||||
\(155\) | 6.82559 | 0.548245 | ||||||||
\(156\) | −2.43689 | −0.195107 | ||||||||
\(157\) | 5.70675 | 0.455448 | 0.227724 | − | 0.973726i | \(-0.426872\pi\) | ||||
0.227724 | + | 0.973726i | \(0.426872\pi\) | |||||||
\(158\) | 3.98486 | 0.317019 | ||||||||
\(159\) | 6.47426 | 0.513443 | ||||||||
\(160\) | −4.35484 | −0.344280 | ||||||||
\(161\) | 21.1257 | 1.66494 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 1.46144 | 0.114469 | 0.0572343 | − | 0.998361i | \(-0.481772\pi\) | ||||
0.0572343 | + | 0.998361i | \(0.481772\pi\) | |||||||
\(164\) | −11.1102 | −0.867563 | ||||||||
\(165\) | −3.20064 | −0.249170 | ||||||||
\(166\) | 9.77231 | 0.758478 | ||||||||
\(167\) | −0.335943 | −0.0259960 | −0.0129980 | − | 0.999916i | \(-0.504138\pi\) | ||||
−0.0129980 | + | 0.999916i | \(0.504138\pi\) | |||||||
\(168\) | −3.05676 | −0.235834 | ||||||||
\(169\) | −7.06159 | −0.543199 | ||||||||
\(170\) | 2.96874 | 0.227692 | ||||||||
\(171\) | −1.87811 | −0.143623 | ||||||||
\(172\) | −10.9512 | −0.835022 | ||||||||
\(173\) | 3.25577 | 0.247532 | 0.123766 | − | 0.992311i | \(-0.460503\pi\) | ||||
0.123766 | + | 0.992311i | \(0.460503\pi\) | |||||||
\(174\) | −0.113306 | −0.00858972 | ||||||||
\(175\) | 42.6865 | 3.22680 | ||||||||
\(176\) | −0.734963 | −0.0553999 | ||||||||
\(177\) | 7.94099 | 0.596881 | ||||||||
\(178\) | 3.23802 | 0.242700 | ||||||||
\(179\) | 2.01680 | 0.150743 | 0.0753715 | − | 0.997156i | \(-0.475986\pi\) | ||||
0.0753715 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(180\) | 4.35484 | 0.324591 | ||||||||
\(181\) | −0.718726 | −0.0534225 | −0.0267113 | − | 0.999643i | \(-0.508503\pi\) | ||||
−0.0267113 | + | 0.999643i | \(0.508503\pi\) | |||||||
\(182\) | 7.44898 | 0.552155 | ||||||||
\(183\) | −4.54537 | −0.336003 | ||||||||
\(184\) | −6.91115 | −0.509497 | ||||||||
\(185\) | −16.1950 | −1.19068 | ||||||||
\(186\) | −1.56736 | −0.114924 | ||||||||
\(187\) | 0.501032 | 0.0366391 | ||||||||
\(188\) | −6.22966 | −0.454344 | ||||||||
\(189\) | 3.05676 | 0.222347 | ||||||||
\(190\) | 8.17887 | 0.593357 | ||||||||
\(191\) | 4.95760 | 0.358719 | 0.179360 | − | 0.983784i | \(-0.442597\pi\) | ||||
0.179360 | + | 0.983784i | \(0.442597\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −8.59130 | −0.618415 | −0.309208 | − | 0.950995i | \(-0.600064\pi\) | ||||
−0.309208 | + | 0.950995i | \(0.600064\pi\) | |||||||
\(194\) | 11.1019 | 0.797070 | ||||||||
\(195\) | −10.6122 | −0.759959 | ||||||||
\(196\) | 2.34379 | 0.167414 | ||||||||
\(197\) | 17.0864 | 1.21736 | 0.608678 | − | 0.793417i | \(-0.291700\pi\) | ||||
0.608678 | + | 0.793417i | \(0.291700\pi\) | |||||||
\(198\) | 0.734963 | 0.0522315 | ||||||||
\(199\) | −0.350646 | −0.0248566 | −0.0124283 | − | 0.999923i | \(-0.503956\pi\) | ||||
−0.0124283 | + | 0.999923i | \(0.503956\pi\) | |||||||
\(200\) | −13.9646 | −0.987448 | ||||||||
\(201\) | −2.23117 | −0.157374 | ||||||||
\(202\) | −19.8419 | −1.39607 | ||||||||
\(203\) | 0.346350 | 0.0243090 | ||||||||
\(204\) | −0.681711 | −0.0477293 | ||||||||
\(205\) | −48.3833 | −3.37923 | ||||||||
\(206\) | 4.42428 | 0.308254 | ||||||||
\(207\) | 6.91115 | 0.480358 | ||||||||
\(208\) | −2.43689 | −0.168968 | ||||||||
\(209\) | 1.38034 | 0.0954802 | ||||||||
\(210\) | −13.3117 | −0.918595 | ||||||||
\(211\) | −12.3103 | −0.847475 | −0.423738 | − | 0.905785i | \(-0.639282\pi\) | ||||
−0.423738 | + | 0.905785i | \(0.639282\pi\) | |||||||
\(212\) | 6.47426 | 0.444654 | ||||||||
\(213\) | 10.5641 | 0.723838 | ||||||||
\(214\) | −11.4126 | −0.780152 | ||||||||
\(215\) | −47.6907 | −3.25248 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 4.79104 | 0.325237 | ||||||||
\(218\) | 15.1912 | 1.02888 | ||||||||
\(219\) | −3.30232 | −0.223150 | ||||||||
\(220\) | −3.20064 | −0.215787 | ||||||||
\(221\) | 1.66125 | 0.111748 | ||||||||
\(222\) | 3.71884 | 0.249592 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | −3.05676 | −0.204238 | ||||||||
\(225\) | 13.9646 | 0.930975 | ||||||||
\(226\) | 0.723916 | 0.0481542 | ||||||||
\(227\) | 11.9814 | 0.795233 | 0.397616 | − | 0.917552i | \(-0.369838\pi\) | ||||
0.397616 | + | 0.917552i | \(0.369838\pi\) | |||||||
\(228\) | −1.87811 | −0.124381 | ||||||||
\(229\) | −0.278694 | −0.0184166 | −0.00920831 | − | 0.999958i | \(-0.502931\pi\) | ||||
−0.00920831 | + | 0.999958i | \(0.502931\pi\) | |||||||
\(230\) | −30.0969 | −1.98453 | ||||||||
\(231\) | −2.24661 | −0.147816 | ||||||||
\(232\) | −0.113306 | −0.00743892 | ||||||||
\(233\) | −12.2226 | −0.800732 | −0.400366 | − | 0.916355i | \(-0.631117\pi\) | ||||
−0.400366 | + | 0.916355i | \(0.631117\pi\) | |||||||
\(234\) | 2.43689 | 0.159304 | ||||||||
\(235\) | −27.1291 | −1.76971 | ||||||||
\(236\) | 7.94099 | 0.516915 | ||||||||
\(237\) | −3.98486 | −0.258845 | ||||||||
\(238\) | 2.08383 | 0.135074 | ||||||||
\(239\) | 22.2407 | 1.43863 | 0.719316 | − | 0.694683i | \(-0.244455\pi\) | ||||
0.719316 | + | 0.694683i | \(0.244455\pi\) | |||||||
\(240\) | 4.35484 | 0.281104 | ||||||||
\(241\) | −22.3491 | −1.43963 | −0.719814 | − | 0.694166i | \(-0.755773\pi\) | ||||
−0.719814 | + | 0.694166i | \(0.755773\pi\) | |||||||
\(242\) | 10.4598 | 0.672383 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.54537 | −0.290987 | ||||||||
\(245\) | 10.2068 | 0.652091 | ||||||||
\(246\) | 11.1102 | 0.708362 | ||||||||
\(247\) | 4.57674 | 0.291211 | ||||||||
\(248\) | −1.56736 | −0.0995274 | ||||||||
\(249\) | −9.77231 | −0.619295 | ||||||||
\(250\) | −39.0395 | −2.46907 | ||||||||
\(251\) | 19.7825 | 1.24866 | 0.624331 | − | 0.781160i | \(-0.285372\pi\) | ||||
0.624331 | + | 0.781160i | \(0.285372\pi\) | |||||||
\(252\) | 3.05676 | 0.192558 | ||||||||
\(253\) | −5.07944 | −0.319341 | ||||||||
\(254\) | −17.7134 | −1.11144 | ||||||||
\(255\) | −2.96874 | −0.185910 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.4401 | −0.713617 | −0.356808 | − | 0.934178i | \(-0.616135\pi\) | ||||
−0.356808 | + | 0.934178i | \(0.616135\pi\) | |||||||
\(258\) | 10.9512 | 0.681793 | ||||||||
\(259\) | −11.3676 | −0.706349 | ||||||||
\(260\) | −10.6122 | −0.658143 | ||||||||
\(261\) | 0.113306 | 0.00701348 | ||||||||
\(262\) | 4.62868 | 0.285961 | ||||||||
\(263\) | 13.3295 | 0.821929 | 0.410965 | − | 0.911651i | \(-0.365192\pi\) | ||||
0.410965 | + | 0.911651i | \(0.365192\pi\) | |||||||
\(264\) | 0.734963 | 0.0452338 | ||||||||
\(265\) | 28.1944 | 1.73197 | ||||||||
\(266\) | 5.74094 | 0.351999 | ||||||||
\(267\) | −3.23802 | −0.198164 | ||||||||
\(268\) | −2.23117 | −0.136290 | ||||||||
\(269\) | 3.03055 | 0.184776 | 0.0923878 | − | 0.995723i | \(-0.470550\pi\) | ||||
0.0923878 | + | 0.995723i | \(0.470550\pi\) | |||||||
\(270\) | −4.35484 | −0.265027 | ||||||||
\(271\) | 21.4604 | 1.30362 | 0.651812 | − | 0.758381i | \(-0.274009\pi\) | ||||
0.651812 | + | 0.758381i | \(0.274009\pi\) | |||||||
\(272\) | −0.681711 | −0.0413348 | ||||||||
\(273\) | −7.44898 | −0.450833 | ||||||||
\(274\) | 6.95121 | 0.419938 | ||||||||
\(275\) | −10.2635 | −0.618911 | ||||||||
\(276\) | 6.91115 | 0.416002 | ||||||||
\(277\) | 28.2695 | 1.69855 | 0.849276 | − | 0.527950i | \(-0.177039\pi\) | ||||
0.849276 | + | 0.527950i | \(0.177039\pi\) | |||||||
\(278\) | −23.4964 | −1.40922 | ||||||||
\(279\) | 1.56736 | 0.0938353 | ||||||||
\(280\) | −13.3117 | −0.795526 | ||||||||
\(281\) | −12.7637 | −0.761420 | −0.380710 | − | 0.924694i | \(-0.624320\pi\) | ||||
−0.380710 | + | 0.924694i | \(0.624320\pi\) | |||||||
\(282\) | 6.22966 | 0.370971 | ||||||||
\(283\) | 32.5585 | 1.93540 | 0.967702 | − | 0.252098i | \(-0.0811205\pi\) | ||||
0.967702 | + | 0.252098i | \(0.0811205\pi\) | |||||||
\(284\) | 10.5641 | 0.626862 | ||||||||
\(285\) | −8.17887 | −0.484474 | ||||||||
\(286\) | −1.79102 | −0.105905 | ||||||||
\(287\) | −33.9613 | −2.00467 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.5353 | −0.972663 | ||||||||
\(290\) | −0.493430 | −0.0289752 | ||||||||
\(291\) | −11.1019 | −0.650805 | ||||||||
\(292\) | −3.30232 | −0.193254 | ||||||||
\(293\) | 28.3976 | 1.65901 | 0.829503 | − | 0.558503i | \(-0.188624\pi\) | ||||
0.829503 | + | 0.558503i | \(0.188624\pi\) | |||||||
\(294\) | −2.34379 | −0.136693 | ||||||||
\(295\) | 34.5817 | 2.01343 | ||||||||
\(296\) | 3.71884 | 0.216153 | ||||||||
\(297\) | −0.734963 | −0.0426469 | ||||||||
\(298\) | 8.25494 | 0.478196 | ||||||||
\(299\) | −16.8417 | −0.973980 | ||||||||
\(300\) | 13.9646 | 0.806248 | ||||||||
\(301\) | −33.4752 | −1.92948 | ||||||||
\(302\) | 15.3701 | 0.884452 | ||||||||
\(303\) | 19.8419 | 1.13989 | ||||||||
\(304\) | −1.87811 | −0.107717 | ||||||||
\(305\) | −19.7943 | −1.13342 | ||||||||
\(306\) | 0.681711 | 0.0389708 | ||||||||
\(307\) | −27.9578 | −1.59563 | −0.797817 | − | 0.602900i | \(-0.794012\pi\) | ||||
−0.797817 | + | 0.602900i | \(0.794012\pi\) | |||||||
\(308\) | −2.24661 | −0.128012 | ||||||||
\(309\) | −4.42428 | −0.251688 | ||||||||
\(310\) | −6.82559 | −0.387668 | ||||||||
\(311\) | −3.59459 | −0.203831 | −0.101915 | − | 0.994793i | \(-0.532497\pi\) | ||||
−0.101915 | + | 0.994793i | \(0.532497\pi\) | |||||||
\(312\) | 2.43689 | 0.137961 | ||||||||
\(313\) | 11.4643 | 0.647998 | 0.323999 | − | 0.946057i | \(-0.394972\pi\) | ||||
0.323999 | + | 0.946057i | \(0.394972\pi\) | |||||||
\(314\) | −5.70675 | −0.322050 | ||||||||
\(315\) | 13.3117 | 0.750030 | ||||||||
\(316\) | −3.98486 | −0.224166 | ||||||||
\(317\) | −33.3632 | −1.87386 | −0.936931 | − | 0.349514i | \(-0.886347\pi\) | ||||
−0.936931 | + | 0.349514i | \(0.886347\pi\) | |||||||
\(318\) | −6.47426 | −0.363059 | ||||||||
\(319\) | −0.0832759 | −0.00466255 | ||||||||
\(320\) | 4.35484 | 0.243443 | ||||||||
\(321\) | 11.4126 | 0.636992 | ||||||||
\(322\) | −21.1257 | −1.17729 | ||||||||
\(323\) | 1.28033 | 0.0712394 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −34.0302 | −1.88765 | ||||||||
\(326\) | −1.46144 | −0.0809415 | ||||||||
\(327\) | −15.1912 | −0.840077 | ||||||||
\(328\) | 11.1102 | 0.613460 | ||||||||
\(329\) | −19.0426 | −1.04985 | ||||||||
\(330\) | 3.20064 | 0.176190 | ||||||||
\(331\) | −11.6186 | −0.638615 | −0.319308 | − | 0.947651i | \(-0.603450\pi\) | ||||
−0.319308 | + | 0.947651i | \(0.603450\pi\) | |||||||
\(332\) | −9.77231 | −0.536325 | ||||||||
\(333\) | −3.71884 | −0.203791 | ||||||||
\(334\) | 0.335943 | 0.0183820 | ||||||||
\(335\) | −9.71638 | −0.530862 | ||||||||
\(336\) | 3.05676 | 0.166760 | ||||||||
\(337\) | −7.91263 | −0.431029 | −0.215514 | − | 0.976501i | \(-0.569143\pi\) | ||||
−0.215514 | + | 0.976501i | \(0.569143\pi\) | |||||||
\(338\) | 7.06159 | 0.384100 | ||||||||
\(339\) | −0.723916 | −0.0393177 | ||||||||
\(340\) | −2.96874 | −0.161003 | ||||||||
\(341\) | −1.15195 | −0.0623816 | ||||||||
\(342\) | 1.87811 | 0.101557 | ||||||||
\(343\) | −14.2329 | −0.768505 | ||||||||
\(344\) | 10.9512 | 0.590450 | ||||||||
\(345\) | 30.0969 | 1.62036 | ||||||||
\(346\) | −3.25577 | −0.175031 | ||||||||
\(347\) | −21.1718 | −1.13656 | −0.568280 | − | 0.822835i | \(-0.692391\pi\) | ||||
−0.568280 | + | 0.822835i | \(0.692391\pi\) | |||||||
\(348\) | 0.113306 | 0.00607385 | ||||||||
\(349\) | −11.3838 | −0.609360 | −0.304680 | − | 0.952455i | \(-0.598550\pi\) | ||||
−0.304680 | + | 0.952455i | \(0.598550\pi\) | |||||||
\(350\) | −42.6865 | −2.28169 | ||||||||
\(351\) | −2.43689 | −0.130071 | ||||||||
\(352\) | 0.734963 | 0.0391736 | ||||||||
\(353\) | −20.6961 | −1.10154 | −0.550772 | − | 0.834656i | \(-0.685667\pi\) | ||||
−0.550772 | + | 0.834656i | \(0.685667\pi\) | |||||||
\(354\) | −7.94099 | −0.422059 | ||||||||
\(355\) | 46.0048 | 2.44168 | ||||||||
\(356\) | −3.23802 | −0.171615 | ||||||||
\(357\) | −2.08383 | −0.110288 | ||||||||
\(358\) | −2.01680 | −0.106591 | ||||||||
\(359\) | −13.4560 | −0.710183 | −0.355092 | − | 0.934832i | \(-0.615550\pi\) | ||||
−0.355092 | + | 0.934832i | \(0.615550\pi\) | |||||||
\(360\) | −4.35484 | −0.229520 | ||||||||
\(361\) | −15.4727 | −0.814353 | ||||||||
\(362\) | 0.718726 | 0.0377754 | ||||||||
\(363\) | −10.4598 | −0.548999 | ||||||||
\(364\) | −7.44898 | −0.390433 | ||||||||
\(365\) | −14.3811 | −0.752740 | ||||||||
\(366\) | 4.54537 | 0.237590 | ||||||||
\(367\) | 8.80612 | 0.459675 | 0.229838 | − | 0.973229i | \(-0.426180\pi\) | ||||
0.229838 | + | 0.973229i | \(0.426180\pi\) | |||||||
\(368\) | 6.91115 | 0.360269 | ||||||||
\(369\) | −11.1102 | −0.578375 | ||||||||
\(370\) | 16.1950 | 0.841936 | ||||||||
\(371\) | 19.7903 | 1.02746 | ||||||||
\(372\) | 1.56736 | 0.0812638 | ||||||||
\(373\) | 5.86346 | 0.303598 | 0.151799 | − | 0.988411i | \(-0.451493\pi\) | ||||
0.151799 | + | 0.988411i | \(0.451493\pi\) | |||||||
\(374\) | −0.501032 | −0.0259078 | ||||||||
\(375\) | 39.0395 | 2.01599 | ||||||||
\(376\) | 6.22966 | 0.321270 | ||||||||
\(377\) | −0.276114 | −0.0142206 | ||||||||
\(378\) | −3.05676 | −0.157223 | ||||||||
\(379\) | −20.7423 | −1.06546 | −0.532729 | − | 0.846286i | \(-0.678833\pi\) | ||||
−0.532729 | + | 0.846286i | \(0.678833\pi\) | |||||||
\(380\) | −8.17887 | −0.419567 | ||||||||
\(381\) | 17.7134 | 0.907485 | ||||||||
\(382\) | −4.95760 | −0.253653 | ||||||||
\(383\) | 25.8637 | 1.32158 | 0.660788 | − | 0.750573i | \(-0.270222\pi\) | ||||
0.660788 | + | 0.750573i | \(0.270222\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −9.78361 | −0.498619 | ||||||||
\(386\) | 8.59130 | 0.437286 | ||||||||
\(387\) | −10.9512 | −0.556681 | ||||||||
\(388\) | −11.1019 | −0.563613 | ||||||||
\(389\) | 2.44929 | 0.124184 | 0.0620920 | − | 0.998070i | \(-0.480223\pi\) | ||||
0.0620920 | + | 0.998070i | \(0.480223\pi\) | |||||||
\(390\) | 10.6122 | 0.537372 | ||||||||
\(391\) | −4.71141 | −0.238266 | ||||||||
\(392\) | −2.34379 | −0.118379 | ||||||||
\(393\) | −4.62868 | −0.233486 | ||||||||
\(394\) | −17.0864 | −0.860801 | ||||||||
\(395\) | −17.3534 | −0.873146 | ||||||||
\(396\) | −0.734963 | −0.0369333 | ||||||||
\(397\) | 19.7131 | 0.989370 | 0.494685 | − | 0.869072i | \(-0.335283\pi\) | ||||
0.494685 | + | 0.869072i | \(0.335283\pi\) | |||||||
\(398\) | 0.350646 | 0.0175763 | ||||||||
\(399\) | −5.74094 | −0.287406 | ||||||||
\(400\) | 13.9646 | 0.698231 | ||||||||
\(401\) | 11.7643 | 0.587483 | 0.293742 | − | 0.955885i | \(-0.405100\pi\) | ||||
0.293742 | + | 0.955885i | \(0.405100\pi\) | |||||||
\(402\) | 2.23117 | 0.111281 | ||||||||
\(403\) | −3.81947 | −0.190262 | ||||||||
\(404\) | 19.8419 | 0.987171 | ||||||||
\(405\) | 4.35484 | 0.216394 | ||||||||
\(406\) | −0.346350 | −0.0171891 | ||||||||
\(407\) | 2.73321 | 0.135480 | ||||||||
\(408\) | 0.681711 | 0.0337497 | ||||||||
\(409\) | 29.9196 | 1.47943 | 0.739715 | − | 0.672920i | \(-0.234960\pi\) | ||||
0.739715 | + | 0.672920i | \(0.234960\pi\) | |||||||
\(410\) | 48.3833 | 2.38948 | ||||||||
\(411\) | −6.95121 | −0.342878 | ||||||||
\(412\) | −4.42428 | −0.217968 | ||||||||
\(413\) | 24.2737 | 1.19443 | ||||||||
\(414\) | −6.91115 | −0.339664 | ||||||||
\(415\) | −42.5568 | −2.08903 | ||||||||
\(416\) | 2.43689 | 0.119478 | ||||||||
\(417\) | 23.4964 | 1.15062 | ||||||||
\(418\) | −1.38034 | −0.0675147 | ||||||||
\(419\) | −36.6787 | −1.79187 | −0.895935 | − | 0.444185i | \(-0.853493\pi\) | ||||
−0.895935 | + | 0.444185i | \(0.853493\pi\) | |||||||
\(420\) | 13.3117 | 0.649545 | ||||||||
\(421\) | 30.9616 | 1.50898 | 0.754488 | − | 0.656313i | \(-0.227885\pi\) | ||||
0.754488 | + | 0.656313i | \(0.227885\pi\) | |||||||
\(422\) | 12.3103 | 0.599255 | ||||||||
\(423\) | −6.22966 | −0.302896 | ||||||||
\(424\) | −6.47426 | −0.314418 | ||||||||
\(425\) | −9.51983 | −0.461780 | ||||||||
\(426\) | −10.5641 | −0.511831 | ||||||||
\(427\) | −13.8941 | −0.672383 | ||||||||
\(428\) | 11.4126 | 0.551651 | ||||||||
\(429\) | 1.79102 | 0.0864713 | ||||||||
\(430\) | 47.6907 | 2.29985 | ||||||||
\(431\) | −32.4852 | −1.56476 | −0.782378 | − | 0.622804i | \(-0.785994\pi\) | ||||
−0.782378 | + | 0.622804i | \(0.785994\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −24.9126 | −1.19722 | −0.598612 | − | 0.801039i | \(-0.704281\pi\) | ||||
−0.598612 | + | 0.801039i | \(0.704281\pi\) | |||||||
\(434\) | −4.79104 | −0.229977 | ||||||||
\(435\) | 0.493430 | 0.0236582 | ||||||||
\(436\) | −15.1912 | −0.727528 | ||||||||
\(437\) | −12.9799 | −0.620913 | ||||||||
\(438\) | 3.30232 | 0.157791 | ||||||||
\(439\) | 31.8189 | 1.51863 | 0.759317 | − | 0.650721i | \(-0.225533\pi\) | ||||
0.759317 | + | 0.650721i | \(0.225533\pi\) | |||||||
\(440\) | 3.20064 | 0.152585 | ||||||||
\(441\) | 2.34379 | 0.111609 | ||||||||
\(442\) | −1.66125 | −0.0790177 | ||||||||
\(443\) | −22.4064 | −1.06456 | −0.532281 | − | 0.846568i | \(-0.678665\pi\) | ||||
−0.532281 | + | 0.846568i | \(0.678665\pi\) | |||||||
\(444\) | −3.71884 | −0.176488 | ||||||||
\(445\) | −14.1011 | −0.668455 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | −8.25494 | −0.390445 | ||||||||
\(448\) | 3.05676 | 0.144418 | ||||||||
\(449\) | 27.5968 | 1.30237 | 0.651187 | − | 0.758917i | \(-0.274271\pi\) | ||||
0.651187 | + | 0.758917i | \(0.274271\pi\) | |||||||
\(450\) | −13.9646 | −0.658298 | ||||||||
\(451\) | 8.16560 | 0.384503 | ||||||||
\(452\) | −0.723916 | −0.0340501 | ||||||||
\(453\) | −15.3701 | −0.722152 | ||||||||
\(454\) | −11.9814 | −0.562314 | ||||||||
\(455\) | −32.4391 | −1.52077 | ||||||||
\(456\) | 1.87811 | 0.0879506 | ||||||||
\(457\) | 6.26270 | 0.292957 | 0.146478 | − | 0.989214i | \(-0.453206\pi\) | ||||
0.146478 | + | 0.989214i | \(0.453206\pi\) | |||||||
\(458\) | 0.278694 | 0.0130225 | ||||||||
\(459\) | −0.681711 | −0.0318195 | ||||||||
\(460\) | 30.0969 | 1.40328 | ||||||||
\(461\) | −24.4624 | −1.13933 | −0.569664 | − | 0.821878i | \(-0.692926\pi\) | ||||
−0.569664 | + | 0.821878i | \(0.692926\pi\) | |||||||
\(462\) | 2.24661 | 0.104522 | ||||||||
\(463\) | −10.5467 | −0.490146 | −0.245073 | − | 0.969505i | \(-0.578812\pi\) | ||||
−0.245073 | + | 0.969505i | \(0.578812\pi\) | |||||||
\(464\) | 0.113306 | 0.00526011 | ||||||||
\(465\) | 6.82559 | 0.316529 | ||||||||
\(466\) | 12.2226 | 0.566203 | ||||||||
\(467\) | −27.0318 | −1.25088 | −0.625442 | − | 0.780271i | \(-0.715081\pi\) | ||||
−0.625442 | + | 0.780271i | \(0.715081\pi\) | |||||||
\(468\) | −2.43689 | −0.112645 | ||||||||
\(469\) | −6.82015 | −0.314925 | ||||||||
\(470\) | 27.1291 | 1.25137 | ||||||||
\(471\) | 5.70675 | 0.262953 | ||||||||
\(472\) | −7.94099 | −0.365514 | ||||||||
\(473\) | 8.04873 | 0.370081 | ||||||||
\(474\) | 3.98486 | 0.183031 | ||||||||
\(475\) | −26.2271 | −1.20338 | ||||||||
\(476\) | −2.08383 | −0.0955121 | ||||||||
\(477\) | 6.47426 | 0.296436 | ||||||||
\(478\) | −22.2407 | −1.01727 | ||||||||
\(479\) | 23.9419 | 1.09393 | 0.546967 | − | 0.837154i | \(-0.315782\pi\) | ||||
0.546967 | + | 0.837154i | \(0.315782\pi\) | |||||||
\(480\) | −4.35484 | −0.198770 | ||||||||
\(481\) | 9.06239 | 0.413210 | ||||||||
\(482\) | 22.3491 | 1.01797 | ||||||||
\(483\) | 21.1257 | 0.961254 | ||||||||
\(484\) | −10.4598 | −0.475447 | ||||||||
\(485\) | −48.3470 | −2.19532 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −2.04679 | −0.0927490 | −0.0463745 | − | 0.998924i | \(-0.514767\pi\) | ||||
−0.0463745 | + | 0.998924i | \(0.514767\pi\) | |||||||
\(488\) | 4.54537 | 0.205759 | ||||||||
\(489\) | 1.46144 | 0.0660885 | ||||||||
\(490\) | −10.2068 | −0.461098 | ||||||||
\(491\) | −30.6746 | −1.38433 | −0.692163 | − | 0.721741i | \(-0.743342\pi\) | ||||
−0.692163 | + | 0.721741i | \(0.743342\pi\) | |||||||
\(492\) | −11.1102 | −0.500888 | ||||||||
\(493\) | −0.0772421 | −0.00347881 | ||||||||
\(494\) | −4.57674 | −0.205917 | ||||||||
\(495\) | −3.20064 | −0.143858 | ||||||||
\(496\) | 1.56736 | 0.0703765 | ||||||||
\(497\) | 32.2918 | 1.44849 | ||||||||
\(498\) | 9.77231 | 0.437908 | ||||||||
\(499\) | 29.0813 | 1.30186 | 0.650929 | − | 0.759138i | \(-0.274379\pi\) | ||||
0.650929 | + | 0.759138i | \(0.274379\pi\) | |||||||
\(500\) | 39.0395 | 1.74590 | ||||||||
\(501\) | −0.335943 | −0.0150088 | ||||||||
\(502\) | −19.7825 | −0.882937 | ||||||||
\(503\) | 32.4064 | 1.44493 | 0.722466 | − | 0.691407i | \(-0.243009\pi\) | ||||
0.722466 | + | 0.691407i | \(0.243009\pi\) | |||||||
\(504\) | −3.05676 | −0.136159 | ||||||||
\(505\) | 86.4083 | 3.84512 | ||||||||
\(506\) | 5.07944 | 0.225809 | ||||||||
\(507\) | −7.06159 | −0.313616 | ||||||||
\(508\) | 17.7134 | 0.785905 | ||||||||
\(509\) | −20.3134 | −0.900376 | −0.450188 | − | 0.892934i | \(-0.648643\pi\) | ||||
−0.450188 | + | 0.892934i | \(0.648643\pi\) | |||||||
\(510\) | 2.96874 | 0.131458 | ||||||||
\(511\) | −10.0944 | −0.446550 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.87811 | −0.0829206 | ||||||||
\(514\) | 11.4401 | 0.504603 | ||||||||
\(515\) | −19.2670 | −0.849006 | ||||||||
\(516\) | −10.9512 | −0.482100 | ||||||||
\(517\) | 4.57856 | 0.201365 | ||||||||
\(518\) | 11.3676 | 0.499464 | ||||||||
\(519\) | 3.25577 | 0.142912 | ||||||||
\(520\) | 10.6122 | 0.465378 | ||||||||
\(521\) | −23.8912 | −1.04669 | −0.523346 | − | 0.852120i | \(-0.675317\pi\) | ||||
−0.523346 | + | 0.852120i | \(0.675317\pi\) | |||||||
\(522\) | −0.113306 | −0.00495928 | ||||||||
\(523\) | 26.0276 | 1.13811 | 0.569054 | − | 0.822300i | \(-0.307309\pi\) | ||||
0.569054 | + | 0.822300i | \(0.307309\pi\) | |||||||
\(524\) | −4.62868 | −0.202205 | ||||||||
\(525\) | 42.6865 | 1.86299 | ||||||||
\(526\) | −13.3295 | −0.581192 | ||||||||
\(527\) | −1.06849 | −0.0465440 | ||||||||
\(528\) | −0.734963 | −0.0319851 | ||||||||
\(529\) | 24.7640 | 1.07670 | ||||||||
\(530\) | −28.1944 | −1.22469 | ||||||||
\(531\) | 7.94099 | 0.344610 | ||||||||
\(532\) | −5.74094 | −0.248901 | ||||||||
\(533\) | 27.0744 | 1.17272 | ||||||||
\(534\) | 3.23802 | 0.140123 | ||||||||
\(535\) | 49.7002 | 2.14873 | ||||||||
\(536\) | 2.23117 | 0.0963718 | ||||||||
\(537\) | 2.01680 | 0.0870315 | ||||||||
\(538\) | −3.03055 | −0.130656 | ||||||||
\(539\) | −1.72260 | −0.0741976 | ||||||||
\(540\) | 4.35484 | 0.187402 | ||||||||
\(541\) | −5.46873 | −0.235119 | −0.117559 | − | 0.993066i | \(-0.537507\pi\) | ||||
−0.117559 | + | 0.993066i | \(0.537507\pi\) | |||||||
\(542\) | −21.4604 | −0.921801 | ||||||||
\(543\) | −0.718726 | −0.0308435 | ||||||||
\(544\) | 0.681711 | 0.0292281 | ||||||||
\(545\) | −66.1554 | −2.83378 | ||||||||
\(546\) | 7.44898 | 0.318787 | ||||||||
\(547\) | 0.600980 | 0.0256961 | 0.0128480 | − | 0.999917i | \(-0.495910\pi\) | ||||
0.0128480 | + | 0.999917i | \(0.495910\pi\) | |||||||
\(548\) | −6.95121 | −0.296941 | ||||||||
\(549\) | −4.54537 | −0.193991 | ||||||||
\(550\) | 10.2635 | 0.437636 | ||||||||
\(551\) | −0.212802 | −0.00906565 | ||||||||
\(552\) | −6.91115 | −0.294158 | ||||||||
\(553\) | −12.1808 | −0.517979 | ||||||||
\(554\) | −28.2695 | −1.20106 | ||||||||
\(555\) | −16.1950 | −0.687438 | ||||||||
\(556\) | 23.4964 | 0.996468 | ||||||||
\(557\) | −33.5046 | −1.41963 | −0.709817 | − | 0.704386i | \(-0.751222\pi\) | ||||
−0.709817 | + | 0.704386i | \(0.751222\pi\) | |||||||
\(558\) | −1.56736 | −0.0663516 | ||||||||
\(559\) | 26.6868 | 1.12873 | ||||||||
\(560\) | 13.3117 | 0.562522 | ||||||||
\(561\) | 0.501032 | 0.0211536 | ||||||||
\(562\) | 12.7637 | 0.538405 | ||||||||
\(563\) | −0.0190630 | −0.000803411 0 | −0.000401705 | − | 1.00000i | \(-0.500128\pi\) | ||||
−0.000401705 | 1.00000i | \(0.500128\pi\) | ||||||||
\(564\) | −6.22966 | −0.262316 | ||||||||
\(565\) | −3.15254 | −0.132628 | ||||||||
\(566\) | −32.5585 | −1.36854 | ||||||||
\(567\) | 3.05676 | 0.128372 | ||||||||
\(568\) | −10.5641 | −0.443258 | ||||||||
\(569\) | 17.4587 | 0.731908 | 0.365954 | − | 0.930633i | \(-0.380743\pi\) | ||||
0.365954 | + | 0.930633i | \(0.380743\pi\) | |||||||
\(570\) | 8.17887 | 0.342575 | ||||||||
\(571\) | 18.0879 | 0.756955 | 0.378477 | − | 0.925611i | \(-0.376448\pi\) | ||||
0.378477 | + | 0.925611i | \(0.376448\pi\) | |||||||
\(572\) | 1.79102 | 0.0748863 | ||||||||
\(573\) | 4.95760 | 0.207107 | ||||||||
\(574\) | 33.9613 | 1.41752 | ||||||||
\(575\) | 96.5116 | 4.02481 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 35.8487 | 1.49240 | 0.746200 | − | 0.665722i | \(-0.231876\pi\) | ||||
0.746200 | + | 0.665722i | \(0.231876\pi\) | |||||||
\(578\) | 16.5353 | 0.687777 | ||||||||
\(579\) | −8.59130 | −0.357042 | ||||||||
\(580\) | 0.493430 | 0.0204886 | ||||||||
\(581\) | −29.8716 | −1.23928 | ||||||||
\(582\) | 11.1019 | 0.460188 | ||||||||
\(583\) | −4.75834 | −0.197070 | ||||||||
\(584\) | 3.30232 | 0.136651 | ||||||||
\(585\) | −10.6122 | −0.438762 | ||||||||
\(586\) | −28.3976 | −1.17309 | ||||||||
\(587\) | 2.69524 | 0.111244 | 0.0556222 | − | 0.998452i | \(-0.482286\pi\) | ||||
0.0556222 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(588\) | 2.34379 | 0.0966563 | ||||||||
\(589\) | −2.94367 | −0.121292 | ||||||||
\(590\) | −34.5817 | −1.42371 | ||||||||
\(591\) | 17.0864 | 0.702841 | ||||||||
\(592\) | −3.71884 | −0.152843 | ||||||||
\(593\) | −31.1847 | −1.28060 | −0.640302 | − | 0.768124i | \(-0.721191\pi\) | ||||
−0.640302 | + | 0.768124i | \(0.721191\pi\) | |||||||
\(594\) | 0.734963 | 0.0301559 | ||||||||
\(595\) | −9.07473 | −0.372028 | ||||||||
\(596\) | −8.25494 | −0.338136 | ||||||||
\(597\) | −0.350646 | −0.0143510 | ||||||||
\(598\) | 16.8417 | 0.688708 | ||||||||
\(599\) | −5.49303 | −0.224439 | −0.112220 | − | 0.993683i | \(-0.535796\pi\) | ||||
−0.112220 | + | 0.993683i | \(0.535796\pi\) | |||||||
\(600\) | −13.9646 | −0.570103 | ||||||||
\(601\) | −25.3653 | −1.03467 | −0.517335 | − | 0.855783i | \(-0.673076\pi\) | ||||
−0.517335 | + | 0.855783i | \(0.673076\pi\) | |||||||
\(602\) | 33.4752 | 1.36435 | ||||||||
\(603\) | −2.23117 | −0.0908602 | ||||||||
\(604\) | −15.3701 | −0.625402 | ||||||||
\(605\) | −45.5509 | −1.85191 | ||||||||
\(606\) | −19.8419 | −0.806022 | ||||||||
\(607\) | −12.3964 | −0.503154 | −0.251577 | − | 0.967837i | \(-0.580949\pi\) | ||||
−0.251577 | + | 0.967837i | \(0.580949\pi\) | |||||||
\(608\) | 1.87811 | 0.0761674 | ||||||||
\(609\) | 0.346350 | 0.0140348 | ||||||||
\(610\) | 19.7943 | 0.801449 | ||||||||
\(611\) | 15.1810 | 0.614156 | ||||||||
\(612\) | −0.681711 | −0.0275565 | ||||||||
\(613\) | 11.0514 | 0.446363 | 0.223181 | − | 0.974777i | \(-0.428356\pi\) | ||||
0.223181 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(614\) | 27.9578 | 1.12828 | ||||||||
\(615\) | −48.3833 | −1.95100 | ||||||||
\(616\) | 2.24661 | 0.0905183 | ||||||||
\(617\) | 24.7403 | 0.996006 | 0.498003 | − | 0.867175i | \(-0.334067\pi\) | ||||
0.498003 | + | 0.867175i | \(0.334067\pi\) | |||||||
\(618\) | 4.42428 | 0.177970 | ||||||||
\(619\) | −4.37667 | −0.175913 | −0.0879566 | − | 0.996124i | \(-0.528034\pi\) | ||||
−0.0879566 | + | 0.996124i | \(0.528034\pi\) | |||||||
\(620\) | 6.82559 | 0.274122 | ||||||||
\(621\) | 6.91115 | 0.277335 | ||||||||
\(622\) | 3.59459 | 0.144130 | ||||||||
\(623\) | −9.89786 | −0.396550 | ||||||||
\(624\) | −2.43689 | −0.0975535 | ||||||||
\(625\) | 100.187 | 4.00750 | ||||||||
\(626\) | −11.4643 | −0.458204 | ||||||||
\(627\) | 1.38034 | 0.0551255 | ||||||||
\(628\) | 5.70675 | 0.227724 | ||||||||
\(629\) | 2.53518 | 0.101084 | ||||||||
\(630\) | −13.3117 | −0.530351 | ||||||||
\(631\) | −39.8325 | −1.58571 | −0.792854 | − | 0.609411i | \(-0.791406\pi\) | ||||
−0.792854 | + | 0.609411i | \(0.791406\pi\) | |||||||
\(632\) | 3.98486 | 0.158509 | ||||||||
\(633\) | −12.3103 | −0.489290 | ||||||||
\(634\) | 33.3632 | 1.32502 | ||||||||
\(635\) | 77.1390 | 3.06117 | ||||||||
\(636\) | 6.47426 | 0.256721 | ||||||||
\(637\) | −5.71155 | −0.226300 | ||||||||
\(638\) | 0.0832759 | 0.00329692 | ||||||||
\(639\) | 10.5641 | 0.417908 | ||||||||
\(640\) | −4.35484 | −0.172140 | ||||||||
\(641\) | −44.5598 | −1.76000 | −0.880002 | − | 0.474969i | \(-0.842459\pi\) | ||||
−0.880002 | + | 0.474969i | \(0.842459\pi\) | |||||||
\(642\) | −11.4126 | −0.450421 | ||||||||
\(643\) | 33.6455 | 1.32685 | 0.663425 | − | 0.748243i | \(-0.269102\pi\) | ||||
0.663425 | + | 0.748243i | \(0.269102\pi\) | |||||||
\(644\) | 21.1257 | 0.832471 | ||||||||
\(645\) | −47.6907 | −1.87782 | ||||||||
\(646\) | −1.28033 | −0.0503738 | ||||||||
\(647\) | −7.69538 | −0.302537 | −0.151268 | − | 0.988493i | \(-0.548336\pi\) | ||||
−0.151268 | + | 0.988493i | \(0.548336\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −5.83633 | −0.229096 | ||||||||
\(650\) | 34.0302 | 1.33477 | ||||||||
\(651\) | 4.79104 | 0.187776 | ||||||||
\(652\) | 1.46144 | 0.0572343 | ||||||||
\(653\) | 11.4671 | 0.448742 | 0.224371 | − | 0.974504i | \(-0.427967\pi\) | ||||
0.224371 | + | 0.974504i | \(0.427967\pi\) | |||||||
\(654\) | 15.1912 | 0.594024 | ||||||||
\(655\) | −20.1571 | −0.787605 | ||||||||
\(656\) | −11.1102 | −0.433782 | ||||||||
\(657\) | −3.30232 | −0.128836 | ||||||||
\(658\) | 19.0426 | 0.742357 | ||||||||
\(659\) | 35.9351 | 1.39983 | 0.699916 | − | 0.714225i | \(-0.253221\pi\) | ||||
0.699916 | + | 0.714225i | \(0.253221\pi\) | |||||||
\(660\) | −3.20064 | −0.124585 | ||||||||
\(661\) | −45.1850 | −1.75749 | −0.878747 | − | 0.477288i | \(-0.841620\pi\) | ||||
−0.878747 | + | 0.477288i | \(0.841620\pi\) | |||||||
\(662\) | 11.6186 | 0.451569 | ||||||||
\(663\) | 1.66125 | 0.0645177 | ||||||||
\(664\) | 9.77231 | 0.379239 | ||||||||
\(665\) | −25.0009 | −0.969491 | ||||||||
\(666\) | 3.71884 | 0.144102 | ||||||||
\(667\) | 0.783076 | 0.0303208 | ||||||||
\(668\) | −0.335943 | −0.0129980 | ||||||||
\(669\) | −1.00000 | −0.0386622 | ||||||||
\(670\) | 9.71638 | 0.375376 | ||||||||
\(671\) | 3.34067 | 0.128965 | ||||||||
\(672\) | −3.05676 | −0.117917 | ||||||||
\(673\) | 1.54949 | 0.0597284 | 0.0298642 | − | 0.999554i | \(-0.490493\pi\) | ||||
0.0298642 | + | 0.999554i | \(0.490493\pi\) | |||||||
\(674\) | 7.91263 | 0.304783 | ||||||||
\(675\) | 13.9646 | 0.537498 | ||||||||
\(676\) | −7.06159 | −0.271600 | ||||||||
\(677\) | −18.2028 | −0.699590 | −0.349795 | − | 0.936826i | \(-0.613749\pi\) | ||||
−0.349795 | + | 0.936826i | \(0.613749\pi\) | |||||||
\(678\) | 0.723916 | 0.0278018 | ||||||||
\(679\) | −33.9358 | −1.30234 | ||||||||
\(680\) | 2.96874 | 0.113846 | ||||||||
\(681\) | 11.9814 | 0.459128 | ||||||||
\(682\) | 1.15195 | 0.0441104 | ||||||||
\(683\) | 32.0454 | 1.22618 | 0.613092 | − | 0.790012i | \(-0.289926\pi\) | ||||
0.613092 | + | 0.790012i | \(0.289926\pi\) | |||||||
\(684\) | −1.87811 | −0.0718114 | ||||||||
\(685\) | −30.2714 | −1.15661 | ||||||||
\(686\) | 14.2329 | 0.543415 | ||||||||
\(687\) | −0.278694 | −0.0106328 | ||||||||
\(688\) | −10.9512 | −0.417511 | ||||||||
\(689\) | −15.7770 | −0.601057 | ||||||||
\(690\) | −30.0969 | −1.14577 | ||||||||
\(691\) | 8.17206 | 0.310880 | 0.155440 | − | 0.987845i | \(-0.450321\pi\) | ||||
0.155440 | + | 0.987845i | \(0.450321\pi\) | |||||||
\(692\) | 3.25577 | 0.123766 | ||||||||
\(693\) | −2.24661 | −0.0853415 | ||||||||
\(694\) | 21.1718 | 0.803669 | ||||||||
\(695\) | 102.323 | 3.88133 | ||||||||
\(696\) | −0.113306 | −0.00429486 | ||||||||
\(697\) | 7.57397 | 0.286884 | ||||||||
\(698\) | 11.3838 | 0.430883 | ||||||||
\(699\) | −12.2226 | −0.462303 | ||||||||
\(700\) | 42.6865 | 1.61340 | ||||||||
\(701\) | −25.3718 | −0.958281 | −0.479140 | − | 0.877738i | \(-0.659052\pi\) | ||||
−0.479140 | + | 0.877738i | \(0.659052\pi\) | |||||||
\(702\) | 2.43689 | 0.0919743 | ||||||||
\(703\) | 6.98440 | 0.263422 | ||||||||
\(704\) | −0.734963 | −0.0276999 | ||||||||
\(705\) | −27.1291 | −1.02174 | ||||||||
\(706\) | 20.6961 | 0.778910 | ||||||||
\(707\) | 60.6520 | 2.28105 | ||||||||
\(708\) | 7.94099 | 0.298441 | ||||||||
\(709\) | 7.95024 | 0.298578 | 0.149289 | − | 0.988794i | \(-0.452302\pi\) | ||||
0.149289 | + | 0.988794i | \(0.452302\pi\) | |||||||
\(710\) | −46.0048 | −1.72653 | ||||||||
\(711\) | −3.98486 | −0.149444 | ||||||||
\(712\) | 3.23802 | 0.121350 | ||||||||
\(713\) | 10.8322 | 0.405671 | ||||||||
\(714\) | 2.08383 | 0.0779853 | ||||||||
\(715\) | 7.79960 | 0.291689 | ||||||||
\(716\) | 2.01680 | 0.0753715 | ||||||||
\(717\) | 22.2407 | 0.830595 | ||||||||
\(718\) | 13.4560 | 0.502175 | ||||||||
\(719\) | −31.5123 | −1.17521 | −0.587606 | − | 0.809147i | \(-0.699929\pi\) | ||||
−0.587606 | + | 0.809147i | \(0.699929\pi\) | |||||||
\(720\) | 4.35484 | 0.162295 | ||||||||
\(721\) | −13.5240 | −0.503658 | ||||||||
\(722\) | 15.4727 | 0.575834 | ||||||||
\(723\) | −22.3491 | −0.831170 | ||||||||
\(724\) | −0.718726 | −0.0267113 | ||||||||
\(725\) | 1.58228 | 0.0587643 | ||||||||
\(726\) | 10.4598 | 0.388201 | ||||||||
\(727\) | −41.5993 | −1.54283 | −0.771416 | − | 0.636332i | \(-0.780451\pi\) | ||||
−0.771416 | + | 0.636332i | \(0.780451\pi\) | |||||||
\(728\) | 7.44898 | 0.276078 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.3811 | 0.532267 | ||||||||
\(731\) | 7.46556 | 0.276124 | ||||||||
\(732\) | −4.54537 | −0.168002 | ||||||||
\(733\) | −0.280816 | −0.0103722 | −0.00518608 | − | 0.999987i | \(-0.501651\pi\) | ||||
−0.00518608 | + | 0.999987i | \(0.501651\pi\) | |||||||
\(734\) | −8.80612 | −0.325040 | ||||||||
\(735\) | 10.2068 | 0.376485 | ||||||||
\(736\) | −6.91115 | −0.254748 | ||||||||
\(737\) | 1.63983 | 0.0604038 | ||||||||
\(738\) | 11.1102 | 0.408973 | ||||||||
\(739\) | 30.0973 | 1.10715 | 0.553574 | − | 0.832800i | \(-0.313264\pi\) | ||||
0.553574 | + | 0.832800i | \(0.313264\pi\) | |||||||
\(740\) | −16.1950 | −0.595339 | ||||||||
\(741\) | 4.57674 | 0.168131 | ||||||||
\(742\) | −19.7903 | −0.726524 | ||||||||
\(743\) | 1.49835 | 0.0549692 | 0.0274846 | − | 0.999622i | \(-0.491250\pi\) | ||||
0.0274846 | + | 0.999622i | \(0.491250\pi\) | |||||||
\(744\) | −1.56736 | −0.0574621 | ||||||||
\(745\) | −35.9489 | −1.31707 | ||||||||
\(746\) | −5.86346 | −0.214676 | ||||||||
\(747\) | −9.77231 | −0.357550 | ||||||||
\(748\) | 0.501032 | 0.0183195 | ||||||||
\(749\) | 34.8857 | 1.27470 | ||||||||
\(750\) | −39.0395 | −1.42552 | ||||||||
\(751\) | 19.0975 | 0.696878 | 0.348439 | − | 0.937331i | \(-0.386712\pi\) | ||||
0.348439 | + | 0.937331i | \(0.386712\pi\) | |||||||
\(752\) | −6.22966 | −0.227172 | ||||||||
\(753\) | 19.7825 | 0.720915 | ||||||||
\(754\) | 0.276114 | 0.0100555 | ||||||||
\(755\) | −66.9344 | −2.43599 | ||||||||
\(756\) | 3.05676 | 0.111173 | ||||||||
\(757\) | −29.6151 | −1.07638 | −0.538189 | − | 0.842824i | \(-0.680891\pi\) | ||||
−0.538189 | + | 0.842824i | \(0.680891\pi\) | |||||||
\(758\) | 20.7423 | 0.753392 | ||||||||
\(759\) | −5.07944 | −0.184372 | ||||||||
\(760\) | 8.17887 | 0.296679 | ||||||||
\(761\) | 14.8382 | 0.537886 | 0.268943 | − | 0.963156i | \(-0.413326\pi\) | ||||
0.268943 | + | 0.963156i | \(0.413326\pi\) | |||||||
\(762\) | −17.7134 | −0.641689 | ||||||||
\(763\) | −46.4360 | −1.68110 | ||||||||
\(764\) | 4.95760 | 0.179360 | ||||||||
\(765\) | −2.96874 | −0.107335 | ||||||||
\(766\) | −25.8637 | −0.934495 | ||||||||
\(767\) | −19.3513 | −0.698735 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −23.8346 | −0.859498 | −0.429749 | − | 0.902948i | \(-0.641398\pi\) | ||||
−0.429749 | + | 0.902948i | \(0.641398\pi\) | |||||||
\(770\) | 9.78361 | 0.352577 | ||||||||
\(771\) | −11.4401 | −0.412007 | ||||||||
\(772\) | −8.59130 | −0.309208 | ||||||||
\(773\) | 55.4521 | 1.99447 | 0.997237 | − | 0.0742897i | \(-0.0236690\pi\) | ||||
0.997237 | + | 0.0742897i | \(0.0236690\pi\) | |||||||
\(774\) | 10.9512 | 0.393633 | ||||||||
\(775\) | 21.8876 | 0.786224 | ||||||||
\(776\) | 11.1019 | 0.398535 | ||||||||
\(777\) | −11.3676 | −0.407811 | ||||||||
\(778\) | −2.44929 | −0.0878113 | ||||||||
\(779\) | 20.8662 | 0.747611 | ||||||||
\(780\) | −10.6122 | −0.379979 | ||||||||
\(781\) | −7.76419 | −0.277825 | ||||||||
\(782\) | 4.71141 | 0.168480 | ||||||||
\(783\) | 0.113306 | 0.00404923 | ||||||||
\(784\) | 2.34379 | 0.0837068 | ||||||||
\(785\) | 24.8520 | 0.887005 | ||||||||
\(786\) | 4.62868 | 0.165099 | ||||||||
\(787\) | 33.1602 | 1.18203 | 0.591017 | − | 0.806659i | \(-0.298726\pi\) | ||||
0.591017 | + | 0.806659i | \(0.298726\pi\) | |||||||
\(788\) | 17.0864 | 0.608678 | ||||||||
\(789\) | 13.3295 | 0.474541 | ||||||||
\(790\) | 17.3534 | 0.617407 | ||||||||
\(791\) | −2.21284 | −0.0786795 | ||||||||
\(792\) | 0.734963 | 0.0261158 | ||||||||
\(793\) | 11.0765 | 0.393339 | ||||||||
\(794\) | −19.7131 | −0.699590 | ||||||||
\(795\) | 28.1944 | 0.999951 | ||||||||
\(796\) | −0.350646 | −0.0124283 | ||||||||
\(797\) | 15.2713 | 0.540936 | 0.270468 | − | 0.962729i | \(-0.412821\pi\) | ||||
0.270468 | + | 0.962729i | \(0.412821\pi\) | |||||||
\(798\) | 5.74094 | 0.203227 | ||||||||
\(799\) | 4.24682 | 0.150242 | ||||||||
\(800\) | −13.9646 | −0.493724 | ||||||||
\(801\) | −3.23802 | −0.114410 | ||||||||
\(802\) | −11.7643 | −0.415413 | ||||||||
\(803\) | 2.42708 | 0.0856499 | ||||||||
\(804\) | −2.23117 | −0.0786872 | ||||||||
\(805\) | 91.9992 | 3.24255 | ||||||||
\(806\) | 3.81947 | 0.134535 | ||||||||
\(807\) | 3.03055 | 0.106680 | ||||||||
\(808\) | −19.8419 | −0.698036 | ||||||||
\(809\) | 39.8830 | 1.40221 | 0.701106 | − | 0.713057i | \(-0.252690\pi\) | ||||
0.701106 | + | 0.713057i | \(0.252690\pi\) | |||||||
\(810\) | −4.35484 | −0.153013 | ||||||||
\(811\) | −21.4838 | −0.754400 | −0.377200 | − | 0.926132i | \(-0.623113\pi\) | ||||
−0.377200 | + | 0.926132i | \(0.623113\pi\) | |||||||
\(812\) | 0.346350 | 0.0121545 | ||||||||
\(813\) | 21.4604 | 0.752648 | ||||||||
\(814\) | −2.73321 | −0.0957990 | ||||||||
\(815\) | 6.36432 | 0.222932 | ||||||||
\(816\) | −0.681711 | −0.0238647 | ||||||||
\(817\) | 20.5676 | 0.719569 | ||||||||
\(818\) | −29.9196 | −1.04611 | ||||||||
\(819\) | −7.44898 | −0.260288 | ||||||||
\(820\) | −48.3833 | −1.68962 | ||||||||
\(821\) | 14.5566 | 0.508029 | 0.254014 | − | 0.967200i | \(-0.418249\pi\) | ||||
0.254014 | + | 0.967200i | \(0.418249\pi\) | |||||||
\(822\) | 6.95121 | 0.242451 | ||||||||
\(823\) | 3.79452 | 0.132269 | 0.0661344 | − | 0.997811i | \(-0.478933\pi\) | ||||
0.0661344 | + | 0.997811i | \(0.478933\pi\) | |||||||
\(824\) | 4.42428 | 0.154127 | ||||||||
\(825\) | −10.2635 | −0.357328 | ||||||||
\(826\) | −24.2737 | −0.844591 | ||||||||
\(827\) | 56.9287 | 1.97960 | 0.989802 | − | 0.142452i | \(-0.0454986\pi\) | ||||
0.989802 | + | 0.142452i | \(0.0454986\pi\) | |||||||
\(828\) | 6.91115 | 0.240179 | ||||||||
\(829\) | −44.0562 | −1.53013 | −0.765067 | − | 0.643951i | \(-0.777294\pi\) | ||||
−0.765067 | + | 0.643951i | \(0.777294\pi\) | |||||||
\(830\) | 42.5568 | 1.47717 | ||||||||
\(831\) | 28.2695 | 0.980659 | ||||||||
\(832\) | −2.43689 | −0.0844838 | ||||||||
\(833\) | −1.59779 | −0.0553601 | ||||||||
\(834\) | −23.4964 | −0.813613 | ||||||||
\(835\) | −1.46298 | −0.0506284 | ||||||||
\(836\) | 1.38034 | 0.0477401 | ||||||||
\(837\) | 1.56736 | 0.0541758 | ||||||||
\(838\) | 36.6787 | 1.26704 | ||||||||
\(839\) | 2.03615 | 0.0702957 | 0.0351479 | − | 0.999382i | \(-0.488810\pi\) | ||||
0.0351479 | + | 0.999382i | \(0.488810\pi\) | |||||||
\(840\) | −13.3117 | −0.459297 | ||||||||
\(841\) | −28.9872 | −0.999557 | ||||||||
\(842\) | −30.9616 | −1.06701 | ||||||||
\(843\) | −12.7637 | −0.439606 | ||||||||
\(844\) | −12.3103 | −0.423738 | ||||||||
\(845\) | −30.7521 | −1.05790 | ||||||||
\(846\) | 6.22966 | 0.214180 | ||||||||
\(847\) | −31.9732 | −1.09861 | ||||||||
\(848\) | 6.47426 | 0.222327 | ||||||||
\(849\) | 32.5585 | 1.11741 | ||||||||
\(850\) | 9.51983 | 0.326528 | ||||||||
\(851\) | −25.7015 | −0.881035 | ||||||||
\(852\) | 10.5641 | 0.361919 | ||||||||
\(853\) | 45.1825 | 1.54702 | 0.773510 | − | 0.633785i | \(-0.218499\pi\) | ||||
0.773510 | + | 0.633785i | \(0.218499\pi\) | |||||||
\(854\) | 13.8941 | 0.475446 | ||||||||
\(855\) | −8.17887 | −0.279711 | ||||||||
\(856\) | −11.4126 | −0.390076 | ||||||||
\(857\) | −13.9020 | −0.474883 | −0.237442 | − | 0.971402i | \(-0.576309\pi\) | ||||
−0.237442 | + | 0.971402i | \(0.576309\pi\) | |||||||
\(858\) | −1.79102 | −0.0611444 | ||||||||
\(859\) | 25.9715 | 0.886134 | 0.443067 | − | 0.896488i | \(-0.353890\pi\) | ||||
0.443067 | + | 0.896488i | \(0.353890\pi\) | |||||||
\(860\) | −47.6907 | −1.62624 | ||||||||
\(861\) | −33.9613 | −1.15740 | ||||||||
\(862\) | 32.4852 | 1.10645 | ||||||||
\(863\) | 24.8717 | 0.846642 | 0.423321 | − | 0.905980i | \(-0.360864\pi\) | ||||
0.423321 | + | 0.905980i | \(0.360864\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 14.1784 | 0.482079 | ||||||||
\(866\) | 24.9126 | 0.846566 | ||||||||
\(867\) | −16.5353 | −0.561567 | ||||||||
\(868\) | 4.79104 | 0.162619 | ||||||||
\(869\) | 2.92872 | 0.0993502 | ||||||||
\(870\) | −0.493430 | −0.0167289 | ||||||||
\(871\) | 5.43710 | 0.184229 | ||||||||
\(872\) | 15.1912 | 0.514440 | ||||||||
\(873\) | −11.1019 | −0.375742 | ||||||||
\(874\) | 12.9799 | 0.439052 | ||||||||
\(875\) | 119.334 | 4.03424 | ||||||||
\(876\) | −3.30232 | −0.111575 | ||||||||
\(877\) | −41.9092 | −1.41517 | −0.707586 | − | 0.706627i | \(-0.750216\pi\) | ||||
−0.707586 | + | 0.706627i | \(0.750216\pi\) | |||||||
\(878\) | −31.8189 | −1.07384 | ||||||||
\(879\) | 28.3976 | 0.957827 | ||||||||
\(880\) | −3.20064 | −0.107894 | ||||||||
\(881\) | 0.208232 | 0.00701552 | 0.00350776 | − | 0.999994i | \(-0.498883\pi\) | ||||
0.00350776 | + | 0.999994i | \(0.498883\pi\) | |||||||
\(882\) | −2.34379 | −0.0789196 | ||||||||
\(883\) | −4.62099 | −0.155509 | −0.0777544 | − | 0.996973i | \(-0.524775\pi\) | ||||
−0.0777544 | + | 0.996973i | \(0.524775\pi\) | |||||||
\(884\) | 1.66125 | 0.0558739 | ||||||||
\(885\) | 34.5817 | 1.16245 | ||||||||
\(886\) | 22.4064 | 0.752759 | ||||||||
\(887\) | −11.1644 | −0.374865 | −0.187433 | − | 0.982277i | \(-0.560017\pi\) | ||||
−0.187433 | + | 0.982277i | \(0.560017\pi\) | |||||||
\(888\) | 3.71884 | 0.124796 | ||||||||
\(889\) | 54.1457 | 1.81599 | ||||||||
\(890\) | 14.1011 | 0.472669 | ||||||||
\(891\) | −0.734963 | −0.0246222 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 11.7000 | 0.391525 | ||||||||
\(894\) | 8.25494 | 0.276087 | ||||||||
\(895\) | 8.78285 | 0.293578 | ||||||||
\(896\) | −3.05676 | −0.102119 | ||||||||
\(897\) | −16.8417 | −0.562327 | ||||||||
\(898\) | −27.5968 | −0.920918 | ||||||||
\(899\) | 0.177591 | 0.00592301 | ||||||||
\(900\) | 13.9646 | 0.465487 | ||||||||
\(901\) | −4.41358 | −0.147038 | ||||||||
\(902\) | −8.16560 | −0.271885 | ||||||||
\(903\) | −33.4752 | −1.11399 | ||||||||
\(904\) | 0.723916 | 0.0240771 | ||||||||
\(905\) | −3.12994 | −0.104043 | ||||||||
\(906\) | 15.3701 | 0.510638 | ||||||||
\(907\) | 0.749208 | 0.0248770 | 0.0124385 | − | 0.999923i | \(-0.496041\pi\) | ||||
0.0124385 | + | 0.999923i | \(0.496041\pi\) | |||||||
\(908\) | 11.9814 | 0.397616 | ||||||||
\(909\) | 19.8419 | 0.658114 | ||||||||
\(910\) | 32.4391 | 1.07535 | ||||||||
\(911\) | −45.7170 | −1.51467 | −0.757336 | − | 0.653026i | \(-0.773499\pi\) | ||||
−0.757336 | + | 0.653026i | \(0.773499\pi\) | |||||||
\(912\) | −1.87811 | −0.0621905 | ||||||||
\(913\) | 7.18228 | 0.237699 | ||||||||
\(914\) | −6.26270 | −0.207152 | ||||||||
\(915\) | −19.7943 | −0.654380 | ||||||||
\(916\) | −0.278694 | −0.00920831 | ||||||||
\(917\) | −14.1488 | −0.467233 | ||||||||
\(918\) | 0.681711 | 0.0224998 | ||||||||
\(919\) | −4.43703 | −0.146364 | −0.0731821 | − | 0.997319i | \(-0.523315\pi\) | ||||
−0.0731821 | + | 0.997319i | \(0.523315\pi\) | |||||||
\(920\) | −30.0969 | −0.992267 | ||||||||
\(921\) | −27.9578 | −0.921240 | ||||||||
\(922\) | 24.4624 | 0.805626 | ||||||||
\(923\) | −25.7434 | −0.847355 | ||||||||
\(924\) | −2.24661 | −0.0739079 | ||||||||
\(925\) | −51.9322 | −1.70752 | ||||||||
\(926\) | 10.5467 | 0.346585 | ||||||||
\(927\) | −4.42428 | −0.145312 | ||||||||
\(928\) | −0.113306 | −0.00371946 | ||||||||
\(929\) | 0.789965 | 0.0259179 | 0.0129590 | − | 0.999916i | \(-0.495875\pi\) | ||||
0.0129590 | + | 0.999916i | \(0.495875\pi\) | |||||||
\(930\) | −6.82559 | −0.223820 | ||||||||
\(931\) | −4.40190 | −0.144266 | ||||||||
\(932\) | −12.2226 | −0.400366 | ||||||||
\(933\) | −3.59459 | −0.117682 | ||||||||
\(934\) | 27.0318 | 0.884508 | ||||||||
\(935\) | 2.18191 | 0.0713562 | ||||||||
\(936\) | 2.43689 | 0.0796521 | ||||||||
\(937\) | 11.0887 | 0.362252 | 0.181126 | − | 0.983460i | \(-0.442026\pi\) | ||||
0.181126 | + | 0.983460i | \(0.442026\pi\) | |||||||
\(938\) | 6.82015 | 0.222686 | ||||||||
\(939\) | 11.4643 | 0.374122 | ||||||||
\(940\) | −27.1291 | −0.884855 | ||||||||
\(941\) | −49.8346 | −1.62456 | −0.812281 | − | 0.583267i | \(-0.801774\pi\) | ||||
−0.812281 | + | 0.583267i | \(0.801774\pi\) | |||||||
\(942\) | −5.70675 | −0.185936 | ||||||||
\(943\) | −76.7845 | −2.50045 | ||||||||
\(944\) | 7.94099 | 0.258457 | ||||||||
\(945\) | 13.3117 | 0.433030 | ||||||||
\(946\) | −8.04873 | −0.261687 | ||||||||
\(947\) | 3.22300 | 0.104733 | 0.0523667 | − | 0.998628i | \(-0.483324\pi\) | ||||
0.0523667 | + | 0.998628i | \(0.483324\pi\) | |||||||
\(948\) | −3.98486 | −0.129422 | ||||||||
\(949\) | 8.04738 | 0.261229 | ||||||||
\(950\) | 26.2271 | 0.850919 | ||||||||
\(951\) | −33.3632 | −1.08188 | ||||||||
\(952\) | 2.08383 | 0.0675372 | ||||||||
\(953\) | 35.4866 | 1.14952 | 0.574762 | − | 0.818320i | \(-0.305095\pi\) | ||||
0.574762 | + | 0.818320i | \(0.305095\pi\) | |||||||
\(954\) | −6.47426 | −0.209612 | ||||||||
\(955\) | 21.5895 | 0.698621 | ||||||||
\(956\) | 22.2407 | 0.719316 | ||||||||
\(957\) | −0.0832759 | −0.00269193 | ||||||||
\(958\) | −23.9419 | −0.773528 | ||||||||
\(959\) | −21.2482 | −0.686140 | ||||||||
\(960\) | 4.35484 | 0.140552 | ||||||||
\(961\) | −28.5434 | −0.920754 | ||||||||
\(962\) | −9.06239 | −0.292183 | ||||||||
\(963\) | 11.4126 | 0.367767 | ||||||||
\(964\) | −22.3491 | −0.719814 | ||||||||
\(965\) | −37.4137 | −1.20439 | ||||||||
\(966\) | −21.1257 | −0.679709 | ||||||||
\(967\) | −4.41806 | −0.142075 | −0.0710376 | − | 0.997474i | \(-0.522631\pi\) | ||||
−0.0710376 | + | 0.997474i | \(0.522631\pi\) | |||||||
\(968\) | 10.4598 | 0.336192 | ||||||||
\(969\) | 1.28033 | 0.0411301 | ||||||||
\(970\) | 48.3470 | 1.55233 | ||||||||
\(971\) | 12.8435 | 0.412169 | 0.206084 | − | 0.978534i | \(-0.433928\pi\) | ||||
0.206084 | + | 0.978534i | \(0.433928\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 71.8228 | 2.30253 | ||||||||
\(974\) | 2.04679 | 0.0655834 | ||||||||
\(975\) | −34.0302 | −1.08984 | ||||||||
\(976\) | −4.54537 | −0.145494 | ||||||||
\(977\) | 14.9739 | 0.479057 | 0.239528 | − | 0.970889i | \(-0.423007\pi\) | ||||
0.239528 | + | 0.970889i | \(0.423007\pi\) | |||||||
\(978\) | −1.46144 | −0.0467316 | ||||||||
\(979\) | 2.37983 | 0.0760596 | ||||||||
\(980\) | 10.2068 | 0.326045 | ||||||||
\(981\) | −15.1912 | −0.485019 | ||||||||
\(982\) | 30.6746 | 0.978866 | ||||||||
\(983\) | −22.0615 | −0.703652 | −0.351826 | − | 0.936065i | \(-0.614439\pi\) | ||||
−0.351826 | + | 0.936065i | \(0.614439\pi\) | |||||||
\(984\) | 11.1102 | 0.354181 | ||||||||
\(985\) | 74.4086 | 2.37085 | ||||||||
\(986\) | 0.0772421 | 0.00245989 | ||||||||
\(987\) | −19.0426 | −0.606132 | ||||||||
\(988\) | 4.57674 | 0.145606 | ||||||||
\(989\) | −75.6855 | −2.40666 | ||||||||
\(990\) | 3.20064 | 0.101723 | ||||||||
\(991\) | −8.96101 | −0.284656 | −0.142328 | − | 0.989820i | \(-0.545459\pi\) | ||||
−0.142328 | + | 0.989820i | \(0.545459\pi\) | |||||||
\(992\) | −1.56736 | −0.0497637 | ||||||||
\(993\) | −11.6186 | −0.368705 | ||||||||
\(994\) | −32.2918 | −1.02423 | ||||||||
\(995\) | −1.52701 | −0.0484093 | ||||||||
\(996\) | −9.77231 | −0.309648 | ||||||||
\(997\) | 51.5423 | 1.63236 | 0.816180 | − | 0.577798i | \(-0.196088\pi\) | ||||
0.816180 | + | 0.577798i | \(0.196088\pi\) | |||||||
\(998\) | −29.0813 | −0.920553 | ||||||||
\(999\) | −3.71884 | −0.117659 |
(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 | 1338.2.a.h.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 4014.2.a.r.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1338.2.a.h.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4014.2.a.r.1.1 | 5 | 3.2 | odd | 2 |