Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 15x^{7} + 45x^{6} + 64x^{5} - 201x^{4} - 63x^{3} + 282x^{2} + 3x - 116 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.00639\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00639 | −1.73574 | −0.867870 | − | 0.496791i | \(-0.834512\pi\) | ||||
−0.867870 | + | 0.496791i | \(0.834512\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.62191 | 1.17255 | 0.586277 | − | 0.810110i | \(-0.300593\pi\) | ||||
0.586277 | + | 0.810110i | \(0.300593\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.03838 | 2.01279 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.88249 | −2.03525 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.640640 | −0.155378 | −0.0776890 | − | 0.996978i | \(-0.524754\pi\) | ||||
−0.0776890 | + | 0.996978i | \(0.524754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.26451 | −1.20776 | −0.603881 | − | 0.797075i | \(-0.706380\pi\) | ||||
−0.603881 | + | 0.797075i | \(0.706380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00639 | 0.656048 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.73795 | 0.779416 | 0.389708 | − | 0.920939i | \(-0.372576\pi\) | ||||
0.389708 | + | 0.920939i | \(0.372576\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.87442 | 0.374884 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.13457 | −1.75795 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.10721 | −0.391300 | −0.195650 | − | 0.980674i | \(-0.562682\pi\) | ||||
−0.195650 | + | 0.980674i | \(0.562682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.8285 | −1.94485 | −0.972427 | − | 0.233210i | \(-0.925077\pi\) | ||||
−0.972427 | + | 0.233210i | \(0.925077\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00639 | −0.523345 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.62191 | −0.443184 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.89549 | −0.969213 | −0.484607 | − | 0.874732i | \(-0.661037\pi\) | ||||
−0.484607 | + | 0.874732i | \(0.661037\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.00639 | 0.481408 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7215 | 1.67442 | 0.837212 | − | 0.546879i | \(-0.184184\pi\) | ||||
0.837212 | + | 0.546879i | \(0.184184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.17775 | 0.332104 | 0.166052 | − | 0.986117i | \(-0.446898\pi\) | ||||
0.166052 | + | 0.986117i | \(0.446898\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 15.8321 | 2.36011 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.39933 | 0.495843 | 0.247921 | − | 0.968780i | \(-0.420253\pi\) | ||||
0.247921 | + | 0.968780i | \(0.420253\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.92601 | 0.269696 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.38742 | 0.465298 | 0.232649 | − | 0.972561i | \(-0.425261\pi\) | ||||
0.232649 | + | 0.972561i | \(0.425261\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.62191 | 0.353539 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.8272 | 2.09636 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.21236 | −0.418213 | −0.209107 | − | 0.977893i | \(-0.567056\pi\) | ||||
−0.209107 | + | 0.977893i | \(0.567056\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.8242 | 1.89805 | 0.949024 | − | 0.315203i | \(-0.102073\pi\) | ||||
0.949024 | + | 0.315203i | \(0.102073\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.03838 | −0.760765 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.62191 | −0.325208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.51329 | 0.917895 | 0.458947 | − | 0.888463i | \(-0.348227\pi\) | ||||
0.458947 | + | 0.888463i | \(0.348227\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.2377 | −1.35286 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.60540 | −0.309205 | −0.154602 | − | 0.987977i | \(-0.549410\pi\) | ||||
−0.154602 | + | 0.987977i | \(0.549410\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.811910 | −0.0950269 | −0.0475135 | − | 0.998871i | \(-0.515130\pi\) | ||||
−0.0475135 | + | 0.998871i | \(0.515130\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.63524 | −0.650702 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.43761 | 1.06181 | 0.530907 | − | 0.847430i | \(-0.321851\pi\) | ||||
0.530907 | + | 0.847430i | \(0.321851\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.34693 | 1.03855 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.0593 | −1.76273 | −0.881367 | − | 0.472432i | \(-0.843376\pi\) | ||||
−0.881367 | + | 0.472432i | \(0.843376\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.67970 | −0.182189 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.33511 | 0.679195 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.41905 | −0.892417 | −0.446209 | − | 0.894929i | \(-0.647226\pi\) | ||||
−0.446209 | + | 0.894929i | \(0.647226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 32.5546 | 3.37576 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.8031 | −1.41617 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.56933 | 0.870084 | 0.435042 | − | 0.900410i | \(-0.356734\pi\) | ||||
0.435042 | + | 0.900410i | \(0.356734\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.03838 | 0.606880 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.7195 | −1.66365 | −0.831827 | − | 0.555034i | \(-0.812705\pi\) | ||||
−0.831827 | + | 0.555034i | \(0.812705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.15665 | 0.409567 | 0.204784 | − | 0.978807i | \(-0.434351\pi\) | ||||
0.204784 | + | 0.978807i | \(0.434351\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.88249 | 0.769252 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.7552 | 1.13642 | 0.568209 | − | 0.822884i | \(-0.307636\pi\) | ||||
0.568209 | + | 0.822884i | \(0.307636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0693 | 1.73073 | 0.865363 | − | 0.501145i | \(-0.167088\pi\) | ||||
0.865363 | + | 0.501145i | \(0.167088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.7242 | 1.68230 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.147481 | 0.0138739 | 0.00693694 | − | 0.999976i | \(-0.497792\pi\) | ||||
0.00693694 | + | 0.999976i | \(0.497792\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.80057 | 0.913908 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.03838 | −0.558249 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.640640 | 0.0587273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −32.2331 | −2.90636 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.19499 | −0.732982 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.12294 | −0.809530 | −0.404765 | − | 0.914421i | \(-0.632647\pi\) | ||||
−0.404765 | + | 0.914421i | \(0.632647\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.54718 | −0.576447 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.635495 | 0.0555235 | 0.0277617 | − | 0.999615i | \(-0.491162\pi\) | ||||
0.0277617 | + | 0.999615i | \(0.491162\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.26451 | 0.456491 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −23.9500 | −2.06129 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.6993 | 1.42672 | 0.713358 | − | 0.700799i | \(-0.247173\pi\) | ||||
0.713358 | + | 0.700799i | \(0.247173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.98332 | −0.253042 | −0.126521 | − | 0.991964i | \(-0.540381\pi\) | ||||
−0.126521 | + | 0.991964i | \(0.540381\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.2197 | −0.860654 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.52493 | −0.458821 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.00639 | −0.247963 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.1030 | −0.827671 | −0.413835 | − | 0.910352i | \(-0.635811\pi\) | ||||
−0.413835 | + | 0.910352i | \(0.635811\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.67817 | −0.787598 | −0.393799 | − | 0.919196i | \(-0.628839\pi\) | ||||
−0.393799 | + | 0.919196i | \(0.628839\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.86843 | −0.312744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −28.3913 | −2.28045 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.82238 | −0.704102 | −0.352051 | − | 0.935981i | \(-0.614516\pi\) | ||||
−0.352051 | + | 0.935981i | \(0.614516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.1839 | −0.807637 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.73795 | −0.294591 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.41996 | 0.267872 | 0.133936 | − | 0.990990i | \(-0.457238\pi\) | ||||
0.133936 | + | 0.990990i | \(0.457238\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.88249 | −0.613651 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.94831 | 0.150764 | 0.0753822 | − | 0.997155i | \(-0.475982\pi\) | ||||
0.0753822 | + | 0.997155i | \(0.475982\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −31.7891 | −2.43098 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.9934 | 1.90022 | 0.950108 | − | 0.311922i | \(-0.100973\pi\) | ||||
0.950108 | + | 0.311922i | \(0.100973\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.87442 | −0.141693 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.65760 | 0.725910 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4326 | 0.779766 | 0.389883 | − | 0.920864i | \(-0.372515\pi\) | ||||
0.389883 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.34840 | −0.248884 | −0.124442 | − | 0.992227i | \(-0.539714\pi\) | ||||
−0.124442 | + | 0.992227i | \(0.539714\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −44.5674 | −3.29452 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.4575 | −1.13646 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.640640 | −0.0468482 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.13457 | 0.664442 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0717404 | 0.00519096 | 0.00259548 | − | 0.999997i | \(-0.499174\pi\) | ||||
0.00259548 | + | 0.999997i | \(0.499174\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7086 | 0.986768 | 0.493384 | − | 0.869812i | \(-0.335760\pi\) | ||||
0.493384 | + | 0.869812i | \(0.335760\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.88249 | 0.564477 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.9890 | −0.782934 | −0.391467 | − | 0.920192i | \(-0.628032\pi\) | ||||
−0.391467 | + | 0.920192i | \(0.628032\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.7225 | 1.89431 | 0.947154 | − | 0.320779i | \(-0.103945\pi\) | ||||
0.947154 | + | 0.320779i | \(0.103945\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.5879 | −1.59323 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.10721 | 0.147897 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.1109 | 1.96335 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.5712 | 1.56880 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.26451 | −0.364154 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8725 | −1.23040 | −0.615198 | − | 0.788373i | \(-0.710924\pi\) | ||||
−0.615198 | + | 0.788373i | \(0.710924\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.83286 | 0.536699 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.70988 | 0.389411 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.8285 | 0.735085 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.44092 | 0.164942 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.640640 | 0.0430941 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.5819 | 1.91399 | 0.956993 | − | 0.290110i | \(-0.0936920\pi\) | ||||
0.956993 | + | 0.290110i | \(0.0936920\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.3185 | 0.754565 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.63926 | 0.507036 | 0.253518 | − | 0.967331i | \(-0.418412\pi\) | ||||
0.253518 | + | 0.967331i | \(0.418412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.03493 | −0.464881 | −0.232441 | − | 0.972611i | \(-0.574671\pi\) | ||||
−0.232441 | + | 0.972611i | \(0.574671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.00639 | 0.197806 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.8395 | −0.775630 | −0.387815 | − | 0.921737i | \(-0.626770\pi\) | ||||
−0.387815 | + | 0.921737i | \(0.626770\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.91273 | 0.581402 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.3732 | −1.84303 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.04360 | 0.196874 | 0.0984370 | − | 0.995143i | \(-0.468616\pi\) | ||||
0.0984370 | + | 0.995143i | \(0.468616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.3595 | 0.989394 | 0.494697 | − | 0.869066i | \(-0.335279\pi\) | ||||
0.494697 | + | 0.869066i | \(0.335279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.696807 | −0.0447002 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.62191 | 0.167508 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.26451 | 0.334973 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 48.2804 | 3.05965 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.1777 | −1.46297 | −0.731483 | − | 0.681859i | \(-0.761172\pi\) | ||||
−0.731483 | + | 0.681859i | \(0.761172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.73795 | 0.235003 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.04984 | 0.316233 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.4778 | −0.715964 | −0.357982 | − | 0.933728i | \(-0.616535\pi\) | ||||
−0.357982 | + | 0.933728i | \(0.616535\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.89549 | 0.366328 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.7242 | −0.787606 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.2082 | −1.12277 | −0.561383 | − | 0.827556i | \(-0.689730\pi\) | ||||
−0.561383 | + | 0.827556i | \(0.689730\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.88152 | 0.545587 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.3109 | 1.54900 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.10349 | −0.494078 | −0.247039 | − | 0.969005i | \(-0.579458\pi\) | ||||
−0.247039 | + | 0.969005i | \(0.579458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4840 | 1.00133 | 0.500667 | − | 0.865640i | \(-0.333088\pi\) | ||||
0.500667 | + | 0.865640i | \(0.333088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.00639 | −0.181955 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.87442 | 0.113032 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.0211 | 1.74371 | 0.871855 | − | 0.489764i | \(-0.162917\pi\) | ||||
0.871855 | + | 0.489764i | \(0.162917\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −65.3865 | −3.91459 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4263 | −0.741293 | −0.370646 | − | 0.928774i | \(-0.620864\pi\) | ||||
−0.370646 | + | 0.928774i | \(0.620864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1671 | −0.901593 | −0.450796 | − | 0.892627i | \(-0.648860\pi\) | ||||
−0.450796 | + | 0.892627i | \(0.648860\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 41.4975 | 2.45810 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7215 | −0.632873 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5896 | −0.975858 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25.7628 | −1.51024 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.6503 | 0.797456 | 0.398728 | − | 0.917069i | \(-0.369452\pi\) | ||||
0.398728 | + | 0.917069i | \(0.369452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.42252 | −0.490378 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.13457 | −0.530041 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.73795 | −0.216171 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.17775 | −0.125524 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 50.2654 | 2.88767 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 38.8678 | 2.22557 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.36347 | −0.477328 | −0.238664 | − | 0.971102i | \(-0.576710\pi\) | ||||
−0.238664 | + | 0.971102i | \(0.576710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4965 | −0.710902 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0374 | 0.569169 | 0.284585 | − | 0.958651i | \(-0.408144\pi\) | ||||
0.284585 | + | 0.958651i | \(0.408144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2185 | 0.577583 | 0.288792 | − | 0.957392i | \(-0.406747\pi\) | ||||
0.288792 | + | 0.957392i | \(0.406747\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.8321 | −0.892038 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.0912 | 1.12844 | 0.564218 | − | 0.825626i | \(-0.309178\pi\) | ||||
0.564218 | + | 0.825626i | \(0.309178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.10721 | −0.117981 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.3407 | −1.97253 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.37265 | 0.187660 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.87442 | −0.103974 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −54.3234 | −3.00409 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.39933 | −0.187411 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.159166 | −0.00874854 | −0.00437427 | − | 0.999990i | \(-0.501392\pi\) | ||||
−0.00437427 | + | 0.999990i | \(0.501392\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −35.5993 | −1.95083 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.6992 | 1.07628 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1801 | −0.935858 | −0.467929 | − | 0.883766i | \(-0.655000\pi\) | ||||
−0.467929 | + | 0.883766i | \(0.655000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.443387 | −0.0240815 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.8285 | −0.586395 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29.4643 | −1.58631 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.3482 | 1.19971 | 0.599857 | − | 0.800107i | \(-0.295224\pi\) | ||||
0.599857 | + | 0.800107i | \(0.295224\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.6192 | −1.21078 | −0.605389 | − | 0.795930i | \(-0.706982\pi\) | ||||
−0.605389 | + | 0.795930i | \(0.706982\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.13457 | 0.487567 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.6490 | −0.566788 | −0.283394 | − | 0.959004i | \(-0.591460\pi\) | ||||
−0.283394 | + | 0.959004i | \(0.591460\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.83114 | −0.362559 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.92601 | −0.101935 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.2862 | 0.912332 | 0.456166 | − | 0.889895i | \(-0.349222\pi\) | ||||
0.456166 | + | 0.889895i | \(0.349222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.71508 | 0.458688 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.00639 | −0.157795 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.12876 | −0.111424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.6465 | −0.816739 | −0.408370 | − | 0.912817i | \(-0.633903\pi\) | ||||
−0.408370 | + | 0.912817i | \(0.633903\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 64.7408 | 3.37027 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.38742 | −0.175866 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.8567 | 1.44236 | 0.721182 | − | 0.692746i | \(-0.243599\pi\) | ||||
0.721182 | + | 0.692746i | \(0.243599\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.6373 | 1.27227 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.10721 | 0.108527 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8132 | 1.48004 | 0.740019 | − | 0.672586i | \(-0.234817\pi\) | ||||
0.740019 | + | 0.672586i | \(0.234817\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.4271 | 1.40513 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.23069 | 0.267276 | 0.133638 | − | 0.991030i | \(-0.457334\pi\) | ||||
0.133638 | + | 0.991030i | \(0.457334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.62191 | −0.133625 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.1501 | 0.668458 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.6693 | −0.895868 | −0.447934 | − | 0.894067i | \(-0.647840\pi\) | ||||
−0.447934 | + | 0.894067i | \(0.647840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.39468 | −0.121104 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.91055 | −0.0963743 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.7446 | 1.24504 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.47696 | −0.124315 | −0.0621575 | − | 0.998066i | \(-0.519798\pi\) | ||||
−0.0621575 | + | 0.998066i | \(0.519798\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.8272 | −0.792350 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.0987 | 1.95250 | 0.976248 | − | 0.216656i | \(-0.0695151\pi\) | ||||
0.976248 | + | 0.216656i | \(0.0695151\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.8285 | 0.539405 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.5068 | 1.21775 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.89549 | −0.292229 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.61951 | −0.178973 | −0.0894866 | − | 0.995988i | \(-0.528523\pi\) | ||||
−0.0894866 | + | 0.995988i | \(0.528523\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −50.2046 | −2.47641 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.21236 | 0.158070 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.1060 | −2.06690 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.96903 | 0.439215 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.4317 | −1.04701 | −0.523503 | − | 0.852024i | \(-0.675375\pi\) | ||||
−0.523503 | + | 0.852024i | \(0.675375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.84175 | 0.0897614 | 0.0448807 | − | 0.998992i | \(-0.485709\pi\) | ||||
0.0448807 | + | 0.998992i | \(0.485709\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.5264 | 0.998029 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.20083 | −0.0582488 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.8242 | −0.717395 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.00639 | 0.145150 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.4834 | 1.70918 | 0.854589 | − | 0.519306i | \(-0.173809\pi\) | ||||
0.854589 | + | 0.519306i | \(0.173809\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.68908 | −0.129229 | −0.0646144 | − | 0.997910i | \(-0.520582\pi\) | ||||
−0.0646144 | + | 0.997910i | \(0.520582\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.6101 | 0.796393 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.6785 | −0.941349 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.3807 | −1.21135 | −0.605677 | − | 0.795710i | \(-0.707098\pi\) | ||||
−0.605677 | + | 0.795710i | \(0.707098\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.03838 | 0.287542 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.24993 | −0.154409 | −0.0772044 | − | 0.997015i | \(-0.524599\pi\) | ||||
−0.0772044 | + | 0.997015i | \(0.524599\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.0740 | −1.04641 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.3736 | 1.43662 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.7838 | 1.45278 | 0.726390 | − | 0.687283i | \(-0.241197\pi\) | ||||
0.726390 | + | 0.687283i | \(0.241197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.7215 | 0.504858 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29.0964 | 1.36707 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.62191 | 0.122917 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.91634 | 0.276755 | 0.138377 | − | 0.990380i | \(-0.455811\pi\) | ||||
0.138377 | + | 0.990380i | \(0.455811\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.85197 | 0.273146 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.223628 | −0.0104154 | −0.00520771 | − | 0.999986i | \(-0.501658\pi\) | ||||
−0.00520771 | + | 0.999986i | \(0.501658\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.64416 | −0.122885 | −0.0614423 | − | 0.998111i | \(-0.519570\pi\) | ||||
−0.0614423 | + | 0.998111i | \(0.519570\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 85.3554 | 3.95826 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.9325 | 0.876093 | 0.438046 | − | 0.898952i | \(-0.355671\pi\) | ||||
0.438046 | + | 0.898952i | \(0.355671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.51329 | −0.346932 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.5235 | 1.22214 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.17775 | 0.100133 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.86792 | −0.452771 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.4546 | 0.936550 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.3722 | 1.20498 | 0.602488 | − | 0.798128i | \(-0.294176\pi\) | ||||
0.602488 | + | 0.798128i | \(0.294176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.89549 | 0.268811 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.2377 | 0.511334 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.4680 | 1.02022 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.2556 | 0.872553 | 0.436276 | − | 0.899813i | \(-0.356297\pi\) | ||||
0.436276 | + | 0.899813i | \(0.356297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.2817 | −0.464956 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.3647 | 1.05443 | 0.527217 | − | 0.849731i | \(-0.323236\pi\) | ||||
0.527217 | + | 0.849731i | \(0.323236\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.34997 | 0.0607994 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.8321 | 0.711600 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.60540 | 0.116868 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.8930 | −1.15913 | −0.579565 | − | 0.814926i | \(-0.696777\pi\) | ||||
−0.579565 | + | 0.814926i | \(0.696777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.85737 | −0.261688 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.4397 | 1.71394 | 0.856972 | − | 0.515363i | \(-0.172343\pi\) | ||||
0.856972 | + | 0.515363i | \(0.172343\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −43.8371 | −1.95073 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.00639 | −0.133518 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.0129086 | −0.000572166 0 | −0.000286083 | − | 1.00000i | \(-0.500091\pi\) | ||||
−0.000286083 | 1.00000i | \(0.500091\pi\) | ||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.811910 | 0.0359168 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 48.0890 | 2.12318 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.8984 | 0.480240 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.39933 | 0.149502 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −75.1400 | −3.29828 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.5988 | −0.551965 | −0.275983 | − | 0.961163i | \(-0.589003\pi\) | ||||
−0.275983 | + | 0.961163i | \(0.589003\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.5723 | 1.38056 | 0.690280 | − | 0.723542i | \(-0.257487\pi\) | ||||
0.690280 | + | 0.723542i | \(0.257487\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.63524 | 0.245942 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.93715 | 0.302187 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.02775 | −0.392511 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.3975 | −0.841778 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.7215 | −0.464402 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.8211 | 1.33251 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.3643 | −1.35347 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.7034 | 1.53501 | 0.767504 | − | 0.641045i | \(-0.221499\pi\) | ||||
0.767504 | + | 0.641045i | \(0.221499\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0666 | 0.431998 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 47.3762 | 2.02937 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.6308 | 1.22416 | 0.612082 | − | 0.790794i | \(-0.290332\pi\) | ||||
0.612082 | + | 0.790794i | \(0.290332\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 89.5144 | 3.82038 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.0935 | 0.472597 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.43761 | −0.401328 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 46.4712 | 1.97259 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.4323 | 0.992860 | 0.496430 | − | 0.868077i | \(-0.334644\pi\) | ||||
0.496430 | + | 0.868077i | \(0.334644\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.17775 | −0.0921092 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.92601 | 0.0813163 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.8530 | 1.17386 | 0.586932 | − | 0.809636i | \(-0.300336\pi\) | ||||
0.586932 | + | 0.809636i | \(0.300336\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.386683 | 0.0162679 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.34693 | −0.392534 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.2369 | 0.848374 | 0.424187 | − | 0.905575i | \(-0.360560\pi\) | ||||
0.424187 | + | 0.905575i | \(0.360560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7462 | −0.449716 | −0.224858 | − | 0.974392i | \(-0.572192\pi\) | ||||
−0.224858 | + | 0.974392i | \(0.572192\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.215680 | −0.00901015 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.00649 | 0.292191 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.2497 | 1.67561 | 0.837807 | − | 0.545966i | \(-0.183837\pi\) | ||||
0.837807 | + | 0.545966i | \(0.183837\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −41.2135 | −1.71277 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.0593 | 0.666251 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.38742 | 0.140293 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.8321 | −0.654577 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.0025 | 1.32088 | 0.660442 | − | 0.750877i | \(-0.270369\pi\) | ||||
0.660442 | + | 0.750877i | \(0.270369\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.0067 | 2.34892 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.0372 | 1.35897 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.1994 | −0.829491 | −0.414746 | − | 0.909937i | \(-0.636129\pi\) | ||||
−0.414746 | + | 0.909937i | \(0.636129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.67970 | 0.0688610 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −80.3383 | −3.28803 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.86763 | 0.117168 | 0.0585840 | − | 0.998282i | \(-0.481341\pi\) | ||||
0.0585840 | + | 0.998282i | \(0.481341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.3415 | 0.952119 | 0.476059 | − | 0.879413i | \(-0.342065\pi\) | ||||
0.476059 | + | 0.879413i | \(0.342065\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.3682 | 1.84753 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.62191 | 0.106596 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.78759 | 0.113145 | 0.0565724 | − | 0.998398i | \(-0.481983\pi\) | ||||
0.0565724 | + | 0.998398i | \(0.481983\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.33511 | −0.256712 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.39933 | −0.137522 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.0657 | −0.972004 | −0.486002 | − | 0.873958i | \(-0.661545\pi\) | ||||
−0.486002 | + | 0.873958i | \(0.661545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −84.5125 | −3.40787 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.5876 | 0.466501 | 0.233250 | − | 0.972417i | \(-0.425064\pi\) | ||||
0.233250 | + | 0.972417i | \(0.425064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.4011 | 1.14154 | 0.570768 | − | 0.821111i | \(-0.306645\pi\) | ||||
0.570768 | + | 0.821111i | \(0.306645\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −34.1445 | −1.37017 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.41905 | 0.337302 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8587 | −1.23435 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.8272 | 0.632077 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.77689 | 0.150594 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.5351 | 1.57387 | 0.786934 | − | 0.617037i | \(-0.211667\pi\) | ||||
0.786934 | + | 0.617037i | \(0.211667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 53.7318 | 2.13565 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.9195 | −0.949218 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.7324 | −0.622365 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.5690 | −1.04941 | −0.524706 | − | 0.851284i | \(-0.675825\pi\) | ||||
−0.524706 | + | 0.851284i | \(0.675825\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.30572 | −0.0909287 | −0.0454644 | − | 0.998966i | \(-0.514477\pi\) | ||||
−0.0454644 | + | 0.998966i | \(0.514477\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.1661 | −0.675916 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.403023 | −0.0158445 | −0.00792223 | − | 0.999969i | \(-0.502522\pi\) | ||||
−0.00792223 | + | 0.999969i | \(0.502522\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.21236 | −0.126096 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.5546 | −1.27592 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.2173 | −0.986829 | −0.493415 | − | 0.869794i | \(-0.664251\pi\) | ||||
−0.493415 | + | 0.869794i | \(0.664251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.66621 | 0.0651043 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.90263 | −0.191270 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.45316 | −0.329289 | −0.164644 | − | 0.986353i | \(-0.552648\pi\) | ||||
−0.164644 | + | 0.986353i | \(0.552648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.9491 | 1.47605 | 0.738025 | − | 0.674773i | \(-0.235758\pi\) | ||||
0.738025 | + | 0.674773i | \(0.235758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.92601 | −0.0748001 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.8031 | 0.535261 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.87666 | −0.304985 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −85.9284 | −3.32218 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.8242 | 0.572283 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.9745 | 1.61800 | 0.808998 | − | 0.587811i | \(-0.200010\pi\) | ||||
0.808998 | + | 0.587811i | \(0.200010\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.1220 | −0.659027 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.75283 | 0.259532 | 0.129766 | − | 0.991545i | \(-0.458577\pi\) | ||||
0.129766 | + | 0.991545i | \(0.458577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.56933 | −0.328861 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.9666 | −0.880082 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.11326 | 0.119126 | 0.0595628 | − | 0.998225i | \(-0.481029\pi\) | ||||
0.0595628 | + | 0.998225i | \(0.481029\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.7841 | 1.67290 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.1498 | 0.806913 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.38742 | −0.129050 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.14985 | −0.0817842 | −0.0408921 | − | 0.999164i | \(-0.513020\pi\) | ||||
−0.0408921 | + | 0.999164i | \(0.513020\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.03838 | −0.229379 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.82201 | −0.296706 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.86864 | −0.260168 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.5941 | 1.34629 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.5343 | −1.30434 | −0.652171 | − | 0.758072i | \(-0.726142\pi\) | ||||
−0.652171 | + | 0.758072i | \(0.726142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.0369 | 1.17058 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −26.7951 | −1.00916 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.7195 | 0.628802 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.2520 | 0.798135 | 0.399068 | − | 0.916922i | \(-0.369334\pi\) | ||||
0.399068 | + | 0.916922i | \(0.369334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 56.9879 | 2.13721 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40.4763 | −1.51585 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.62191 | −0.0980539 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.15024 | −0.341722 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.0739 | −1.56909 | −0.784546 | − | 0.620070i | \(-0.787104\pi\) | ||||
−0.784546 | + | 0.620070i | \(0.787104\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.15665 | −0.154802 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.1767 | −1.71733 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.94981 | −0.146692 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6948 | 0.433735 | 0.216868 | − | 0.976201i | \(-0.430416\pi\) | ||||
0.216868 | + | 0.976201i | \(0.430416\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.9459 | −0.960959 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.39516 | −0.0516017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.01427 | −0.332950 | −0.166475 | − | 0.986046i | \(-0.553238\pi\) | ||||
−0.166475 | + | 0.986046i | \(0.553238\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.88249 | −0.290750 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.51329 | 0.276756 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.8353 | −0.472153 | −0.236077 | − | 0.971734i | \(-0.575862\pi\) | ||||
−0.236077 | + | 0.971734i | \(0.575862\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.8272 | −0.581426 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.8116 | 1.02031 | 0.510154 | − | 0.860083i | \(-0.329588\pi\) | ||||
0.510154 | + | 0.860083i | \(0.329588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.4892 | −0.970489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −96.9721 | −3.54802 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.7552 | −0.429526 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.1453 | 0.589149 | 0.294574 | − | 0.955629i | \(-0.404822\pi\) | ||||
0.294574 | + | 0.955629i | \(0.404822\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 69.6814 | 2.53933 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.3753 | −0.923502 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.449041 | 0.0163207 | 0.00816033 | − | 0.999967i | \(-0.497402\pi\) | ||||
0.00816033 | + | 0.999967i | \(0.497402\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.2377 | −0.407904 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.6952 | 1.40270 | 0.701351 | − | 0.712816i | \(-0.252581\pi\) | ||||
0.701351 | + | 0.712816i | \(0.252581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0693 | −0.654153 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.1427 | −0.366709 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.21236 | 0.115992 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.9355 | −0.718891 | −0.359446 | − | 0.933166i | \(-0.617034\pi\) | ||||
−0.359446 | + | 0.933166i | \(0.617034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.5067 | 1.24273 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.0010 | −1.22293 | −0.611466 | − | 0.791270i | \(-0.709420\pi\) | ||||
−0.611466 | + | 0.791270i | \(0.709420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.2971 | −0.729095 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.7242 | −0.635851 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −56.4437 | −2.02230 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.60540 | −0.0932287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.2485 | 0.687885 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.1315 | −0.825599 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.6131 | 1.69722 | 0.848612 | − | 0.529016i | \(-0.177439\pi\) | ||||
0.848612 | + | 0.529016i | \(0.177439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 54.7409 | 1.94883 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.147481 | −0.00524384 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.8242 | −0.526424 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.7013 | −0.946998 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.4579 | 0.724657 | 0.362328 | − | 0.932050i | \(-0.381982\pi\) | ||||
0.362328 | + | 0.932050i | \(0.381982\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.17774 | −0.0770430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −50.8374 | −1.79625 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.811910 | −0.0286517 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.80057 | −0.345425 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.3622 | 0.857592 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.2328 | 1.16840 | 0.584201 | − | 0.811609i | \(-0.301408\pi\) | ||||
0.584201 | + | 0.811609i | \(0.301408\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.2418 | −0.394752 | −0.197376 | − | 0.980328i | \(-0.563242\pi\) | ||||
−0.197376 | + | 0.980328i | \(0.563242\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −49.5574 | −1.73805 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.96683 | 0.314094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.4648 | −0.401103 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.03838 | 0.210998 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.9929 | −1.04676 | −0.523379 | − | 0.852100i | \(-0.675329\pi\) | ||||
−0.523379 | + | 0.852100i | \(0.675329\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.9024 | 0.658897 | 0.329448 | − | 0.944174i | \(-0.393137\pi\) | ||||
0.329448 | + | 0.944174i | \(0.393137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.63524 | −0.196194 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.44487 | 0.119790 | 0.0598949 | − | 0.998205i | \(-0.480923\pi\) | ||||
0.0598949 | + | 0.998205i | \(0.480923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.7370 | −0.928616 | −0.464308 | − | 0.885674i | \(-0.653697\pi\) | ||||
−0.464308 | + | 0.885674i | \(0.653697\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −87.2488 | −3.02663 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.640640 | −0.0221968 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.10829 | 0.176780 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 98.9135 | 3.41895 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.3535 | −0.426491 | −0.213246 | − | 0.976999i | \(-0.568403\pi\) | ||||
−0.213246 | + | 0.976999i | \(0.568403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.5596 | −0.846884 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.3584 | 1.28669 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.62191 | 0.0901965 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 45.5983 | 1.56493 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.0370 | −0.755420 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.6873 | −1.73550 | −0.867750 | − | 0.497002i | \(-0.834434\pi\) | ||||
−0.867750 | + | 0.497002i | \(0.834434\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −83.3483 | −2.85045 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.4844 | −0.460620 | −0.230310 | − | 0.973117i | \(-0.573974\pi\) | ||||
−0.230310 | + | 0.973117i | \(0.573974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.09174 | 0.139608 | 0.0698041 | − | 0.997561i | \(-0.477763\pi\) | ||||
0.0698041 | + | 0.997561i | \(0.477763\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 32.2331 | 1.09850 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.6753 | 1.52077 | 0.760383 | − | 0.649475i | \(-0.225011\pi\) | ||||
0.760383 | + | 0.649475i | \(0.225011\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 65.5306 | 2.22811 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 49.8748 | 1.69384 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.43761 | 0.320149 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.51329 | −0.254578 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 51.7449 | 1.75130 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.19499 | 0.277041 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.5232 | −1.19953 | −0.599767 | − | 0.800175i | \(-0.704740\pi\) | ||||
−0.599767 | + | 0.800175i | \(0.704740\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.0380 | −1.38418 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.1895 | −0.511748 | −0.255874 | − | 0.966710i | \(-0.582363\pi\) | ||||
−0.255874 | + | 0.966710i | \(0.582363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.51926 | −0.118433 | −0.0592163 | − | 0.998245i | \(-0.518860\pi\) | ||||
−0.0592163 | + | 0.998245i | \(0.518860\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.3214 | 0.851169 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.4868 | −0.620726 | −0.310363 | − | 0.950618i | \(-0.600451\pi\) | ||||
−0.310363 | + | 0.950618i | \(0.600451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.12294 | 0.305974 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.34693 | 0.313134 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.8958 | −0.598860 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.3533 | 0.914318 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.2377 | 0.375217 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.8179 | 0.761021 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.17012 | −0.0722971 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.54718 | 0.217877 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.77920 | −0.291830 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.1041 | −1.36484 | −0.682419 | − | 0.730961i | \(-0.739072\pi\) | ||||
−0.682419 | + | 0.730961i | \(0.739072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −100.959 | −3.34860 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.6347 | −0.783051 | −0.391525 | − | 0.920167i | \(-0.628053\pi\) | ||||
−0.391525 | + | 0.920167i | \(0.628053\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.0593 | −0.531484 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −116.852 | −3.86300 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.635495 | −0.0209859 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.3341 | −0.340890 | −0.170445 | − | 0.985367i | \(-0.554520\pi\) | ||||
−0.170445 | + | 0.985367i | \(0.554520\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.1439 | 0.828518 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.60540 | 0.0857579 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0506 | −0.363343 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.0995 | 0.824374 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.88488 | 0.160268 | 0.0801338 | − | 0.996784i | \(-0.474465\pi\) | ||||
0.0801338 | + | 0.996784i | \(0.474465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.26451 | −0.172537 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.1764 | −0.987930 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.67970 | −0.0549321 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.6863 | −0.349106 | −0.174553 | − | 0.984648i | \(-0.555848\pi\) | ||||
−0.174553 | + | 0.984648i | \(0.555848\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.7208 | −1.00253 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.59053 | −0.149647 | −0.0748234 | − | 0.997197i | \(-0.523839\pi\) | ||||
−0.0748234 | + | 0.997197i | \(0.523839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.0766 | 1.30507 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 23.9500 | 0.779095 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.8670 | 1.71795 | 0.858973 | − | 0.512021i | \(-0.171103\pi\) | ||||
0.858973 | + | 0.512021i | \(0.171103\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.811910 | 0.0263557 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −60.4021 | −1.95867 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.8607 | 1.74472 | 0.872359 | − | 0.488865i | \(-0.162589\pi\) | ||||
0.872359 | + | 0.488865i | \(0.162589\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.188097 | 0.00608668 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.33511 | 0.204785 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.6993 | −0.539248 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 86.2560 | 2.78245 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 70.9824 | 2.28738 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.9428 | 1.15704 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.9767 | −0.449462 | −0.224731 | − | 0.974421i | \(-0.572150\pi\) | ||||
−0.224731 | + | 0.974421i | \(0.572150\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.1395 | −0.325728 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.1830 | −0.904436 | −0.452218 | − | 0.891908i | \(-0.649367\pi\) | ||||
−0.452218 | + | 0.891908i | \(0.649367\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.98332 | 0.0956409 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.63524 | 0.180472 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 61.0613 | 1.95352 | 0.976762 | − | 0.214329i | \(-0.0687564\pi\) | ||||
0.976762 | + | 0.214329i | \(0.0687564\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.41905 | −0.269074 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 109.109 | 3.48360 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.2785 | −1.50795 | −0.753975 | − | 0.656904i | \(-0.771866\pi\) | ||||
−0.753975 | + | 0.656904i | \(0.771866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.8122 | −0.918033 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.2197 | 0.325297 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.14033 | 0.258847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9842 | −0.539522 | −0.269761 | − | 0.962927i | \(-0.586945\pi\) | ||||
−0.269761 | + | 0.962927i | \(0.586945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.478515 | 0.0151852 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 70.0641 | 2.22118 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.1064 | 0.668447 | 0.334224 | − | 0.942494i | \(-0.391526\pi\) | ||||
0.334224 | + | 0.942494i | \(0.391526\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 53.8528 | 1.70383 |
(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 | 8008.2.a.n.1.2 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.n.1.2 | ✓ | 9 | 1.1 | even | 1 | trivial |