Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(1\) |
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: | \( x^{9} - x^{8} - 11x^{7} + 7x^{6} + 40x^{5} - 11x^{4} - 53x^{3} - 2x^{2} + 13x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.0778757\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | −0.0778757 | −0.0449616 | −0.0224808 | − | 0.999747i | \(-0.507156\pi\) | ||||
−0.0224808 | + | 0.999747i | \(0.507156\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.70938 | 0.764459 | 0.382229 | − | 0.924067i | \(-0.375156\pi\) | ||||
0.382229 | + | 0.924067i | \(0.375156\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.05552 | 1.15488 | 0.577438 | − | 0.816434i | \(-0.304052\pi\) | ||||
0.577438 | + | 0.816434i | \(0.304052\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99394 | −0.997978 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.72480 | −0.821557 | −0.410778 | − | 0.911735i | \(-0.634743\pi\) | ||||
−0.410778 | + | 0.911735i | \(0.634743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.571803 | −0.158590 | −0.0792949 | − | 0.996851i | \(-0.525267\pi\) | ||||
−0.0792949 | + | 0.996851i | \(0.525267\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.133119 | −0.0343713 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.03094 | −0.492575 | −0.246287 | − | 0.969197i | \(-0.579211\pi\) | ||||
−0.246287 | + | 0.969197i | \(0.579211\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.65693 | −0.380125 | −0.190062 | − | 0.981772i | \(-0.560869\pi\) | ||||
−0.190062 | + | 0.981772i | \(0.560869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.237951 | −0.0519251 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.92751 | 0.401913 | 0.200956 | − | 0.979600i | \(-0.435595\pi\) | ||||
0.200956 | + | 0.979600i | \(0.435595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.07801 | −0.415603 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.466782 | 0.0898323 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.834774 | −0.155014 | −0.0775068 | − | 0.996992i | \(-0.524696\pi\) | ||||
−0.0775068 | + | 0.996992i | \(0.524696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.56383 | −1.17890 | −0.589449 | − | 0.807805i | \(-0.700655\pi\) | ||||
−0.589449 | + | 0.807805i | \(0.700655\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.212195 | 0.0369385 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.22305 | 0.882856 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.02102 | −1.31865 | −0.659324 | − | 0.751859i | \(-0.729157\pi\) | ||||
−0.659324 | + | 0.751859i | \(0.729157\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0445296 | 0.00713044 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.26496 | −0.353727 | −0.176864 | − | 0.984235i | \(-0.556595\pi\) | ||||
−0.176864 | + | 0.984235i | \(0.556595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.86429 | 1.19929 | 0.599646 | − | 0.800265i | \(-0.295308\pi\) | ||||
0.599646 | + | 0.800265i | \(0.295308\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.11778 | −0.762914 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.38606 | −0.202177 | −0.101089 | − | 0.994877i | \(-0.532233\pi\) | ||||
−0.101089 | + | 0.994877i | \(0.532233\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.33618 | 0.333740 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.158161 | 0.0221469 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7409 | −1.47538 | −0.737690 | − | 0.675140i | \(-0.764083\pi\) | ||||
−0.737690 | + | 0.675140i | \(0.764083\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.65772 | −0.628046 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.129034 | 0.0170910 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.74126 | 0.487070 | 0.243535 | − | 0.969892i | \(-0.421693\pi\) | ||||
0.243535 | + | 0.969892i | \(0.421693\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0554 | −1.41550 | −0.707751 | − | 0.706462i | \(-0.750290\pi\) | ||||
−0.707751 | + | 0.706462i | \(0.750290\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.14802 | −1.15254 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.977430 | −0.121235 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.23468 | 0.517349 | 0.258674 | − | 0.965965i | \(-0.416714\pi\) | ||||
0.258674 | + | 0.965965i | \(0.416714\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.150106 | −0.0180706 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.1893 | −1.80264 | −0.901320 | − | 0.433154i | \(-0.857401\pi\) | ||||
−0.901320 | + | 0.433154i | \(0.857401\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.47586 | −0.406818 | −0.203409 | − | 0.979094i | \(-0.565202\pi\) | ||||
−0.203409 | + | 0.979094i | \(0.565202\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.161827 | 0.0186861 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.32566 | −0.948797 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.59705 | 0.967244 | 0.483622 | − | 0.875277i | \(-0.339321\pi\) | ||||
0.483622 | + | 0.875277i | \(0.339321\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.94546 | 0.993939 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.83230 | 0.859706 | 0.429853 | − | 0.902899i | \(-0.358565\pi\) | ||||
0.429853 | + | 0.902899i | \(0.358565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.47165 | −0.376553 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0650086 | 0.00696966 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.239990 | −0.0254389 | −0.0127195 | − | 0.999919i | \(-0.504049\pi\) | ||||
−0.0127195 | + | 0.999919i | \(0.504049\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.74715 | −0.183152 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.511163 | 0.0530051 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.83232 | −0.290590 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.5490 | −1.57876 | −0.789379 | − | 0.613907i | \(-0.789597\pi\) | ||||
−0.789379 | + | 0.613907i | \(0.789597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.15786 | 0.819896 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.15007 | 0.810962 | 0.405481 | − | 0.914104i | \(-0.367104\pi\) | ||||
0.405481 | + | 0.914104i | \(0.367104\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.00797 | 0.887582 | 0.443791 | − | 0.896130i | \(-0.353633\pi\) | ||||
0.443791 | + | 0.896130i | \(0.353633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.406749 | −0.0396946 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.76227 | −0.943754 | −0.471877 | − | 0.881664i | \(-0.656423\pi\) | ||||
−0.471877 | + | 0.881664i | \(0.656423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.65061 | 0.349665 | 0.174832 | − | 0.984598i | \(-0.444062\pi\) | ||||
0.174832 | + | 0.984598i | \(0.444062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.624643 | 0.0592885 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.78722 | 0.826632 | 0.413316 | − | 0.910588i | \(-0.364370\pi\) | ||||
0.413316 | + | 0.910588i | \(0.364370\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.29484 | 0.307246 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.71194 | 0.158269 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.20556 | −0.568863 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.57549 | −0.325045 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.176385 | 0.0159041 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0990 | −1.08217 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.0108 | −1.50946 | −0.754732 | − | 0.656034i | \(-0.772233\pi\) | ||||
−0.754732 | + | 0.656034i | \(0.772233\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.612437 | −0.0539221 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00757 | −0.262772 | −0.131386 | − | 0.991331i | \(-0.541943\pi\) | ||||
−0.131386 | + | 0.991331i | \(0.541943\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.06276 | −0.438997 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.797909 | 0.0686731 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.58678 | −0.135568 | −0.0677838 | − | 0.997700i | \(-0.521593\pi\) | ||||
−0.0677838 | + | 0.997700i | \(0.521593\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.70602 | 0.483979 | 0.241989 | − | 0.970279i | \(-0.422200\pi\) | ||||
0.241989 | + | 0.970279i | \(0.422200\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.107940 | 0.00909021 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.55805 | 0.130290 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.42695 | −0.118502 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.181932 | −0.0150055 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.4824 | 1.35029 | 0.675145 | − | 0.737685i | \(-0.264081\pi\) | ||||
0.675145 | + | 0.737685i | \(0.264081\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.92705 | 0.400958 | 0.200479 | − | 0.979698i | \(-0.435750\pi\) | ||||
0.200479 | + | 0.979698i | \(0.435750\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.08049 | 0.491579 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.2201 | −0.901220 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3793 | 0.987976 | 0.493988 | − | 0.869469i | \(-0.335539\pi\) | ||||
0.493988 | + | 0.869469i | \(0.335539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.836457 | 0.0663354 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.88952 | 0.464160 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4867 | −0.978033 | −0.489017 | − | 0.872274i | \(-0.662644\pi\) | ||||
−0.489017 | + | 0.872274i | \(0.662644\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.362723 | 0.0282380 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6685 | 1.44461 | 0.722306 | − | 0.691573i | \(-0.243082\pi\) | ||||
0.722306 | + | 0.691573i | \(0.243082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6730 | −0.974849 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.96073 | 0.379356 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.12101 | −0.693458 | −0.346729 | − | 0.937965i | \(-0.612708\pi\) | ||||
−0.346729 | + | 0.937965i | \(0.612708\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.34940 | −0.479970 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.291353 | −0.0218994 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.71249 | 0.651202 | 0.325601 | − | 0.945507i | \(-0.394433\pi\) | ||||
0.325601 | + | 0.945507i | \(0.394433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8288 | 1.02789 | 0.513945 | − | 0.857823i | \(-0.328184\pi\) | ||||
0.513945 | + | 0.857823i | \(0.328184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.860949 | 0.0636432 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.7110 | −1.00805 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.53389 | 0.404678 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.42626 | 0.103745 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0496 | 1.16131 | 0.580655 | − | 0.814150i | \(-0.302796\pi\) | ||||
0.580655 | + | 0.814150i | \(0.302796\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.5061 | −1.26011 | −0.630057 | − | 0.776549i | \(-0.716968\pi\) | ||||
−0.630057 | + | 0.776549i | \(0.716968\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0761181 | 0.00545093 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.8034 | 1.05470 | 0.527351 | − | 0.849648i | \(-0.323185\pi\) | ||||
0.527351 | + | 0.849648i | \(0.323185\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.58294 | −0.183100 | −0.0915500 | − | 0.995800i | \(-0.529182\pi\) | ||||
−0.0915500 | + | 0.995800i | \(0.529182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.329779 | −0.0232608 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.55066 | −0.179022 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.87168 | −0.270410 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.77083 | −0.401100 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.51478 | 0.312294 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.28104 | 0.225876 | 0.112938 | − | 0.993602i | \(-0.463974\pi\) | ||||
0.112938 | + | 0.993602i | \(0.463974\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.18288 | 0.0810495 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.4431 | 0.916810 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.0559 | −1.36148 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.270685 | 0.0182912 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.16130 | 0.0781173 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.34057 | 0.156736 | 0.0783681 | − | 0.996924i | \(-0.475029\pi\) | ||||
0.0783681 | + | 0.996924i | \(0.475029\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.22144 | 0.414762 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.175423 | 0.0116432 | 0.00582162 | − | 0.999983i | \(-0.498147\pi\) | ||||
0.00582162 | + | 0.999983i | \(0.498147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.3240 | −1.80562 | −0.902809 | − | 0.430041i | \(-0.858499\pi\) | ||||
−0.902809 | + | 0.430041i | \(0.858499\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.648367 | 0.0426594 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.48043 | −0.293523 | −0.146761 | − | 0.989172i | \(-0.546885\pi\) | ||||
−0.146761 | + | 0.989172i | \(0.546885\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.36930 | −0.154556 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.669502 | −0.0434888 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.79576 | 0.116158 | 0.0580791 | − | 0.998312i | \(-0.481502\pi\) | ||||
0.0580791 | + | 0.998312i | \(0.481502\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.3951 | 1.82909 | 0.914544 | − | 0.404485i | \(-0.132549\pi\) | ||||
0.914544 | + | 0.404485i | \(0.132549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.09698 | −0.134521 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.99343 | 0.255131 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.947435 | 0.0602839 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.609946 | −0.0386538 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.25206 | −0.330194 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.270357 | 0.0169304 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.17811 | −0.447758 | −0.223879 | − | 0.974617i | \(-0.571872\pi\) | ||||
−0.223879 | + | 0.974617i | \(0.571872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.5084 | −1.52287 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.49926 | 0.154700 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.4933 | −1.57198 | −0.785991 | − | 0.618238i | \(-0.787847\pi\) | ||||
−0.785991 | + | 0.618238i | \(0.787847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.3603 | −1.12787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0186894 | 0.00114377 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.6360 | −1.56305 | −0.781526 | − | 0.623872i | \(-0.785559\pi\) | ||||
−0.781526 | + | 0.623872i | \(0.785559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.8859 | −1.51171 | −0.755857 | − | 0.654737i | \(-0.772779\pi\) | ||||
−0.755857 | + | 0.654737i | \(0.772779\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.136061 | 0.00823478 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.66216 | 0.341441 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.85404 | 0.171483 | 0.0857414 | − | 0.996317i | \(-0.472674\pi\) | ||||
0.0857414 | + | 0.996317i | \(0.472674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.6517 | 1.17652 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0827 | 0.959414 | 0.479707 | − | 0.877429i | \(-0.340743\pi\) | ||||
0.479707 | + | 0.877429i | \(0.340743\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.215076 | 0.0127849 | 0.00639246 | − | 0.999980i | \(-0.497965\pi\) | ||||
0.00639246 | + | 0.999980i | \(0.497965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.220569 | 0.0130654 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.92062 | −0.408511 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8753 | −0.757370 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.21089 | 0.0709834 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.37322 | −0.489169 | −0.244584 | − | 0.969628i | \(-0.578652\pi\) | ||||
−0.244584 | + | 0.969628i | \(0.578652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.39524 | 0.372345 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.27189 | −0.0738023 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.10215 | −0.0637392 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0295 | 1.38503 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.634692 | −0.0364621 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.8979 | −1.08209 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.45372 | −0.482479 | −0.241240 | − | 0.970466i | \(-0.577554\pi\) | ||||
−0.241240 | + | 0.970466i | \(0.577554\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.701503 | −0.0399071 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.13296 | 0.404473 | 0.202237 | − | 0.979337i | \(-0.435179\pi\) | ||||
0.202237 | + | 0.979337i | \(0.435179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.4935 | −1.38445 | −0.692227 | − | 0.721680i | \(-0.743370\pi\) | ||||
−0.692227 | + | 0.721680i | \(0.743370\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.6375 | −0.881071 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.34412 | −0.131659 | −0.0658295 | − | 0.997831i | \(-0.520969\pi\) | ||||
−0.0658295 | + | 0.997831i | \(0.520969\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.27459 | 0.127352 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.760244 | 0.0424327 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.36511 | 0.187240 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.18821 | 0.0659103 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.284294 | −0.0157215 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.23512 | −0.233490 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.1288 | −1.16135 | −0.580673 | − | 0.814137i | \(-0.697210\pi\) | ||||
−0.580673 | + | 0.814137i | \(0.697210\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.0144 | 1.31598 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.23869 | 0.395492 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.2670 | 0.559277 | 0.279638 | − | 0.960105i | \(-0.409785\pi\) | ||||
0.279638 | + | 0.960105i | \(0.409785\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.684311 | −0.0371667 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.8851 | 0.968532 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2504 | −0.769448 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.256588 | −0.0138143 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3461 | 0.984869 | 0.492434 | − | 0.870350i | \(-0.336107\pi\) | ||||
0.492434 | + | 0.870350i | \(0.336107\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.6875 | 1.37502 | 0.687511 | − | 0.726174i | \(-0.258703\pi\) | ||||
0.687511 | + | 0.726174i | \(0.258703\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.266908 | −0.0142465 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.79528 | 0.521350 | 0.260675 | − | 0.965427i | \(-0.416055\pi\) | ||||
0.260675 | + | 0.965427i | \(0.416055\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.9643 | −1.37804 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.483263 | 0.0255770 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.10793 | −0.216808 | −0.108404 | − | 0.994107i | \(-0.534574\pi\) | ||||
−0.108404 | + | 0.994107i | \(0.534574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2546 | −0.855505 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.278444 | 0.0146145 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.94157 | −0.310996 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.2139 | −1.31616 | −0.658078 | − | 0.752950i | \(-0.728630\pi\) | ||||
−0.658078 | + | 0.752950i | \(0.728630\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.78114 | 0.353012 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −32.8191 | −1.70388 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.13770 | −0.369576 | −0.184788 | − | 0.982778i | \(-0.559160\pi\) | ||||
−0.184788 | + | 0.982778i | \(0.559160\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.942221 | 0.0486561 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.477326 | 0.0245836 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.6756 | −1.88390 | −0.941949 | − | 0.335755i | \(-0.891008\pi\) | ||||
−0.941949 | + | 0.335755i | \(0.891008\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.32473 | 0.0678678 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.5767 | −1.66459 | −0.832295 | − | 0.554332i | \(-0.812974\pi\) | ||||
−0.832295 | + | 0.554332i | \(0.812974\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.2317 | −0.725316 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.5452 | −1.19687 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.8625 | −0.550752 | −0.275376 | − | 0.961337i | \(-0.588802\pi\) | ||||
−0.275376 | + | 0.961337i | \(0.588802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.91464 | −0.197972 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.234217 | 0.0118147 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.6957 | 0.739419 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.0798 | 1.25872 | 0.629359 | − | 0.777115i | \(-0.283317\pi\) | ||||
0.629359 | + | 0.777115i | \(0.283317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.394266 | 0.0197380 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.05363 | 0.352241 | 0.176121 | − | 0.984369i | \(-0.443645\pi\) | ||||
0.176121 | + | 0.984369i | \(0.443645\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.75322 | 0.186961 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.2912 | 0.759826 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.8556 | 1.08334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.4077 | 1.10799 | 0.553996 | − | 0.832519i | \(-0.313102\pi\) | ||||
0.553996 | + | 0.832519i | \(0.313102\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.123572 | 0.00609534 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.4315 | 0.562506 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.3884 | 0.657210 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.444361 | −0.0217604 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.9728 | 1.07344 | 0.536721 | − | 0.843760i | \(-0.319663\pi\) | ||||
0.536721 | + | 0.843760i | \(0.319663\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.3286 | 0.942019 | 0.471009 | − | 0.882128i | \(-0.343890\pi\) | ||||
0.471009 | + | 0.882128i | \(0.343890\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.14977 | 0.201768 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.22031 | 0.204715 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.7800 | −1.63473 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.121334 | −0.00585806 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.3393 | −0.787037 | −0.393518 | − | 0.919317i | \(-0.628742\pi\) | ||||
−0.393518 | + | 0.919317i | \(0.628742\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.05445 | −0.290958 | −0.145479 | − | 0.989361i | \(-0.546472\pi\) | ||||
−0.145479 | + | 0.989361i | \(0.546472\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.111125 | 0.00532802 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.19373 | −0.152777 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.447066 | 0.0213373 | 0.0106686 | − | 0.999943i | \(-0.496604\pi\) | ||||
0.0106686 | + | 0.999943i | \(0.496604\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.99438 | −0.333066 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.85194 | −0.135500 | −0.0677498 | − | 0.997702i | \(-0.521582\pi\) | ||||
−0.0677498 | + | 0.997702i | \(0.521582\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.410235 | −0.0194470 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.28358 | −0.0607112 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.54935 | 0.261890 | 0.130945 | − | 0.991390i | \(-0.458199\pi\) | ||||
0.130945 | + | 0.991390i | \(0.458199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.17155 | 0.290607 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.383698 | −0.0180277 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.98655 | −0.140012 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.68251 | 0.172261 | 0.0861303 | − | 0.996284i | \(-0.472550\pi\) | ||||
0.0861303 | + | 0.996284i | \(0.472550\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.948005 | −0.0442491 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.87267 | 0.180368 | 0.0901842 | − | 0.995925i | \(-0.471254\pi\) | ||||
0.0901842 | + | 0.995925i | \(0.471254\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.6014 | −1.37569 | −0.687847 | − | 0.725855i | \(-0.741444\pi\) | ||||
−0.687847 | + | 0.725855i | \(0.741444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.873773 | 0.0405203 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.13850 | −0.330331 | −0.165165 | − | 0.986266i | \(-0.552816\pi\) | ||||
−0.165165 | + | 0.986266i | \(0.552816\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9391 | 0.597474 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.964048 | −0.0444210 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.4286 | −0.985287 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.44311 | 0.157981 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.1576 | 1.47240 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.5680 | −0.802702 | −0.401351 | − | 0.915924i | \(-0.631459\pi\) | ||||
−0.401351 | + | 0.915924i | \(0.631459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.58644 | 0.209124 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.458651 | −0.0208693 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.5791 | −1.20689 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7763 | 0.669578 | 0.334789 | − | 0.942293i | \(-0.391335\pi\) | ||||
0.334789 | + | 0.942293i | \(0.391335\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.972410 | 0.0439739 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.2125 | 1.63425 | 0.817124 | − | 0.576462i | \(-0.195567\pi\) | ||||
0.817124 | + | 0.576462i | \(0.195567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.69537 | 0.0763557 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.9449 | 0.626777 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −46.4112 | −2.08183 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.9435 | 0.937561 | 0.468781 | − | 0.883315i | \(-0.344693\pi\) | ||||
0.468781 | + | 0.883315i | \(0.344693\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.45382 | −0.0649521 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0839 | 0.538793 | 0.269396 | − | 0.963029i | \(-0.413176\pi\) | ||||
0.269396 | + | 0.963029i | \(0.413176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9316 | 0.619947 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.986922 | 0.0438308 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0509 | −0.667119 | −0.333560 | − | 0.942729i | \(-0.608250\pi\) | ||||
−0.333560 | + | 0.942729i | \(0.608250\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.6205 | −0.469825 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.773423 | −0.0341475 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.3981 | 0.678520 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.77672 | 0.166100 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.710306 | 0.0311790 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.29342 | −0.407152 | −0.203576 | − | 0.979059i | \(-0.565256\pi\) | ||||
−0.203576 | + | 0.979059i | \(0.565256\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.5177 | −0.503633 | −0.251817 | − | 0.967775i | \(-0.581028\pi\) | ||||
−0.251817 | + | 0.967775i | \(0.581028\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.494464 | 0.0215802 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.3307 | 0.580695 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2847 | −0.838466 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.2011 | −0.486086 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.29511 | 0.0560975 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.6874 | −0.721461 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.678492 | −0.0292791 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.36562 | −0.274187 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.17430 | 0.265454 | 0.132727 | − | 0.991153i | \(-0.457627\pi\) | ||||
0.132727 | + | 0.991153i | \(0.457627\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.07693 | −0.0462156 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.24028 | 0.267304 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.0123 | 0.770152 | 0.385076 | − | 0.922885i | \(-0.374175\pi\) | ||||
0.385076 | + | 0.922885i | \(0.374175\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.0992 | 1.41264 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.38316 | 0.0589245 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.2684 | 1.11705 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.06775 | 0.0453236 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.8043 | 0.966248 | 0.483124 | − | 0.875552i | \(-0.339502\pi\) | ||||
0.483124 | + | 0.875552i | \(0.339502\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.49682 | −0.190195 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.430956 | −0.0181950 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.0959 | 0.425493 | 0.212746 | − | 0.977107i | \(-0.431759\pi\) | ||||
0.212746 | + | 0.977107i | \(0.431759\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.0207 | 0.631926 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 27.3330 | 1.14788 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.4147 | −0.520451 | −0.260225 | − | 0.965548i | \(-0.583797\pi\) | ||||
−0.260225 | + | 0.965548i | \(0.583797\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.6169 | 1.69976 | 0.849882 | − | 0.526973i | \(-0.176673\pi\) | ||||
0.849882 | + | 0.526973i | \(0.176673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.24988 | −0.0522144 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00538 | −0.167036 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.2850 | 1.13589 | 0.567945 | − | 0.823067i | \(-0.307739\pi\) | ||||
0.567945 | + | 0.823067i | \(0.307739\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.36330 | 0.0566567 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.9317 | 0.992855 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.2668 | 1.21211 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.92636 | 0.120990 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.37884 | 0.0981852 | 0.0490926 | − | 0.998794i | \(-0.484367\pi\) | ||||
0.0490926 | + | 0.998794i | \(0.484367\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.8758 | 0.448128 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.15283 | −0.0474210 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.9090 | −1.10502 | −0.552510 | − | 0.833506i | \(-0.686330\pi\) | ||||
−0.552510 | + | 0.833506i | \(0.686330\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.6077 | −0.434872 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.201149 | 0.00823247 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.8560 | 1.30160 | 0.650801 | − | 0.759248i | \(-0.274433\pi\) | ||||
0.650801 | + | 0.759248i | \(0.274433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.23787 | −0.295239 | −0.147620 | − | 0.989044i | \(-0.547161\pi\) | ||||
−0.147620 | + | 0.989044i | \(0.547161\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.6784 | −0.516303 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.11188 | −0.248483 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.34152 | 0.379161 | 0.189580 | − | 0.981865i | \(-0.439287\pi\) | ||||
0.189580 | + | 0.981865i | \(0.439287\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.198635 | 0.00804909 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.792552 | 0.0320632 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.9349 | 1.28984 | 0.644918 | − | 0.764252i | \(-0.276891\pi\) | ||||
0.644918 | + | 0.764252i | \(0.276891\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.301510 | 0.0121581 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.11548 | 0.326717 | 0.163358 | − | 0.986567i | \(-0.447767\pi\) | ||||
0.163358 | + | 0.986567i | \(0.447767\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0527 | −0.444246 | −0.222123 | − | 0.975019i | \(-0.571299\pi\) | ||||
−0.222123 | + | 0.975019i | \(0.571299\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.899725 | 0.0361047 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.733295 | −0.0293788 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.2918 | −0.411672 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.351592 | −0.0140412 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.2902 | 0.649532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.2530 | 0.527594 | 0.263797 | − | 0.964578i | \(-0.415025\pi\) | ||||
0.263797 | + | 0.964578i | \(0.415025\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.255513 | −0.0101557 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29.0779 | −1.15392 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.33584 | −0.0529278 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 45.4758 | 1.79900 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.287590 | 0.0113591 | 0.00567956 | − | 0.999984i | \(-0.498192\pi\) | ||||
0.00567956 | + | 0.999984i | \(0.498192\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.46321 | −0.373193 | −0.186596 | − | 0.982437i | \(-0.559746\pi\) | ||||
−0.186596 | + | 0.982437i | \(0.559746\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.04689 | −0.0412212 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.4672 | 0.765335 | 0.382668 | − | 0.923886i | \(-0.375005\pi\) | ||||
0.382668 | + | 0.923886i | \(0.375005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.1942 | −0.400156 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.56187 | 0.0612144 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.50880 | 0.372108 | 0.186054 | − | 0.982540i | \(-0.440430\pi\) | ||||
0.186054 | + | 0.982540i | \(0.440430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.14108 | −0.200879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.4065 | 0.405996 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.9280 | −0.698375 | −0.349187 | − | 0.937053i | \(-0.613542\pi\) | ||||
−0.349187 | + | 0.937053i | \(0.613542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5342 | 0.604210 | 0.302105 | − | 0.953275i | \(-0.402311\pi\) | ||||
0.302105 | + | 0.953275i | \(0.402311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0904368 | −0.00351228 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.65420 | −0.335595 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.60903 | −0.0623019 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.182274 | −0.00704711 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.1237 | 1.16291 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.7362 | −0.683682 | −0.341841 | − | 0.939758i | \(-0.611050\pi\) | ||||
−0.341841 | + | 0.939758i | \(0.611050\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.969979 | −0.0373345 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.1083 | −0.542224 | −0.271112 | − | 0.962548i | \(-0.587391\pi\) | ||||
−0.271112 | + | 0.962548i | \(0.587391\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −47.5101 | −1.82327 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0136612 | −0.000523498 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.6593 | 1.13488 | 0.567441 | − | 0.823414i | \(-0.307934\pi\) | ||||
0.567441 | + | 0.823414i | \(0.307934\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.71241 | −0.103636 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.12787 | 0.0811835 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.14170 | 0.233980 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.5743 | 1.58156 | 0.790780 | − | 0.612100i | \(-0.209675\pi\) | ||||
0.790780 | + | 0.612100i | \(0.209675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.9265 | 0.946879 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.75378 | 0.369982 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.59999 | 0.174237 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.348917 | 0.0131972 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2450 | 0.877951 | 0.438975 | − | 0.898499i | \(-0.355342\pi\) | ||||
0.438975 | + | 0.898499i | \(0.355342\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.2902 | 0.501250 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.184511 | 0.00694909 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.9027 | 0.936561 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.5771 | 0.735234 | 0.367617 | − | 0.929977i | \(-0.380174\pi\) | ||||
0.367617 | + | 0.929977i | \(0.380174\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.7390 | −0.965289 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.6518 | −0.473814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.66330 | 0.0996017 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.139846 | −0.00522266 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.1957 | −1.20070 | −0.600349 | − | 0.799738i | \(-0.704972\pi\) | ||||
−0.600349 | + | 0.799738i | \(0.704972\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5240 | 1.02505 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.21129 | −0.0822387 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.73467 | 0.0644240 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.6658 | 0.988979 | 0.494490 | − | 0.869184i | \(-0.335355\pi\) | ||||
0.494490 | + | 0.869184i | \(0.335355\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.6731 | −0.987891 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.9719 | −0.590741 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.38186 | −0.0879760 | −0.0439880 | − | 0.999032i | \(-0.514006\pi\) | ||||
−0.0439880 | + | 0.999032i | \(0.514006\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.310991 | −0.0114711 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.5386 | −0.425031 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.55884 | 0.278056 | 0.139028 | − | 0.990288i | \(-0.455602\pi\) | ||||
0.139028 | + | 0.990288i | \(0.455602\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0737822 | −0.00271046 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.3474 | 1.70032 | 0.850160 | − | 0.526524i | \(-0.176505\pi\) | ||||
0.850160 | + | 0.526524i | \(0.176505\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.1747 | 1.03224 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.4494 | −0.857968 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.8288 | −1.08992 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0561 | −0.804838 | −0.402419 | − | 0.915456i | \(-0.631830\pi\) | ||||
−0.402419 | + | 0.915456i | \(0.631830\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.0778757 | 0.00283795 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.42222 | 0.306516 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.93932 | −0.361251 | −0.180625 | − | 0.983552i | \(-0.557812\pi\) | ||||
−0.180625 | + | 0.983552i | \(0.557812\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.409008 | 0.0148460 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.99238 | −0.180973 | −0.0904867 | − | 0.995898i | \(-0.528842\pi\) | ||||
−0.0904867 | + | 0.995898i | \(0.528842\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.1545 | 0.403820 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.3939 | 0.375792 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.13926 | −0.0772443 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.336906 | −0.0121491 | −0.00607456 | − | 0.999982i | \(-0.501934\pi\) | ||||
−0.00607456 | + | 0.999982i | \(0.501934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.559000 | 0.0201319 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.4451 | 0.627458 | 0.313729 | − | 0.949513i | \(-0.398422\pi\) | ||||
0.313729 | + | 0.949513i | \(0.398422\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.6397 | 0.489953 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.90861 | 0.0684709 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.75287 | 0.134460 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.3878 | 1.48097 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.389657 | −0.0139252 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.1610 | 0.755267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.8946 | −0.923044 | −0.461522 | − | 0.887129i | \(-0.652697\pi\) | ||||
−0.461522 | + | 0.887129i | \(0.652697\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.98531 | 0.0706788 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.8495 | 0.954658 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.32152 | 0.224484 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.42983 | 0.0507107 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.7022 | −1.12295 | −0.561475 | − | 0.827493i | \(-0.689766\pi\) | ||||
−0.561475 | + | 0.827493i | \(0.689766\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.81499 | 0.0995873 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.718516 | 0.0253875 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.47100 | 0.334224 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.0674 | 0.354831 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.99642 | 0.0702773 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.5422 | 0.933174 | 0.466587 | − | 0.884475i | \(-0.345484\pi\) | ||||
0.466587 | + | 0.884475i | \(0.345484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.6485 | 0.584609 | 0.292305 | − | 0.956325i | \(-0.405578\pi\) | ||||
0.292305 | + | 0.956325i | \(0.405578\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.93801 | 0.0679690 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.3445 | −0.747666 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.0305 | −0.455881 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.23087 | 0.182781 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.7418 | 1.56150 | 0.780749 | − | 0.624845i | \(-0.214838\pi\) | ||||
0.780749 | + | 0.624845i | \(0.214838\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −51.9554 | −1.81105 | −0.905525 | − | 0.424293i | \(-0.860523\pi\) | ||||
−0.905525 | + | 0.424293i | \(0.860523\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.440945 | −0.0153517 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.64570 | −0.335414 | −0.167707 | − | 0.985837i | \(-0.553636\pi\) | ||||
−0.167707 | + | 0.985837i | \(0.553636\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.5294 | −1.23399 | −0.616993 | − | 0.786968i | \(-0.711650\pi\) | ||||
−0.616993 | + | 0.786968i | \(0.711650\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.222261 | −0.00771013 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.74464 | −0.164392 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.9116 | 1.10435 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.06388 | −0.105903 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.1025 | −0.659490 | −0.329745 | − | 0.944070i | \(-0.606963\pi\) | ||||
−0.329745 | + | 0.944070i | \(0.606963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3032 | −0.975971 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.25245 | −0.0431368 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.6631 | −0.745232 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9250 | −0.375386 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.0167492 | −0.000574830 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.4606 | −0.529981 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.4326 | −0.870795 | −0.435397 | − | 0.900238i | \(-0.643392\pi\) | ||||
−0.435397 | + | 0.900238i | \(0.643392\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.47978 | 0.290002 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.2512 | −1.44327 | −0.721637 | − | 0.692271i | \(-0.756610\pi\) | ||||
−0.721637 | + | 0.692271i | \(0.756610\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.64578 | −0.158512 | −0.0792560 | − | 0.996854i | \(-0.525254\pi\) | ||||
−0.0792560 | + | 0.996854i | \(0.525254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.538948 | 0.0183673 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.7931 | 0.707804 | 0.353902 | − | 0.935282i | \(-0.384855\pi\) | ||||
0.353902 | + | 0.935282i | \(0.384855\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.5913 | −0.530120 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00267 | 0.0340526 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.4252 | −0.794646 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.42140 | −0.0820462 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.5526 | 1.57557 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −36.9688 | −1.24977 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.97099 | 0.167858 | 0.0839291 | − | 0.996472i | \(-0.473253\pi\) | ||||
0.0839291 | + | 0.996472i | \(0.473253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.652071 | 0.0219938 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.3935 | 1.02398 | 0.511992 | − | 0.858990i | \(-0.328908\pi\) | ||||
0.511992 | + | 0.858990i | \(0.328908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.4333 | 0.923204 | 0.461602 | − | 0.887087i | \(-0.347275\pi\) | ||||
0.461602 | + | 0.887087i | \(0.347275\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.498034 | −0.0167412 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.8209 | 0.665522 | 0.332761 | − | 0.943011i | \(-0.392020\pi\) | ||||
0.332761 | + | 0.943011i | \(0.392020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −51.9767 | −1.74324 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.3745 | −0.816578 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.29659 | 0.0768526 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.8930 | 0.497817 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0858311 | 0.00286582 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.47931 | 0.182745 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.8141 | 0.726734 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.87131 | −0.0622733 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.6388 | 0.785780 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.3531 | 0.476585 | 0.238293 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238293 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.4008 | −0.809322 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.0811 | 0.599054 | 0.299527 | − | 0.954088i | \(-0.403171\pi\) | ||||
0.299527 | + | 0.954088i | \(0.403171\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.3414 | −0.706297 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.47169 | 0.0486526 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.18967 | −0.303470 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.07012 | 0.0353001 | 0.0176500 | − | 0.999844i | \(-0.494382\pi\) | ||||
0.0176500 | + | 0.999844i | \(0.494382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.658340 | 0.0216930 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.68530 | 0.285880 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.6678 | 0.548033 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.9693 | −0.885788 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.0153 | −1.05039 | −0.525193 | − | 0.850983i | \(-0.676007\pi\) | ||||
−0.525193 | + | 0.850983i | \(0.676007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.87088 | −0.126863 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.555484 | −0.0181857 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.45953 | 0.309360 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.6597 | −1.49164 | −0.745818 | − | 0.666149i | \(-0.767941\pi\) | ||||
−0.745818 | + | 0.666149i | \(0.767941\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.90745 | 0.0622472 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.9241 | 1.00810 | 0.504048 | − | 0.863676i | \(-0.331843\pi\) | ||||
0.504048 | + | 0.863676i | \(0.331843\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.36572 | −0.142167 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.43802 | 0.0793089 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.4681 | 1.67249 | 0.836244 | − | 0.548358i | \(-0.184747\pi\) | ||||
0.836244 | + | 0.548358i | \(0.184747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.98751 | 0.0645172 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.182550 | 0.00591960 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.2982 | −1.33778 | −0.668891 | − | 0.743361i | \(-0.733231\pi\) | ||||
−0.668891 | + | 0.743361i | \(0.733231\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.4350 | 0.887774 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.177135 | −0.00572597 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.84843 | −0.156564 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0839 | 0.389802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.2276 | 0.941846 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.9245 | −0.963305 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.8806 | −1.44326 | −0.721632 | − | 0.692277i | \(-0.756608\pi\) | ||||
−0.721632 | + | 0.692277i | \(0.756608\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.262060 | −0.00841860 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.77648 | 0.281651 | 0.140825 | − | 0.990034i | \(-0.455024\pi\) | ||||
0.140825 | + | 0.990034i | \(0.455024\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.4349 | 0.558936 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0925331 | −0.00296343 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.2264 | −0.359165 | −0.179582 | − | 0.983743i | \(-0.557475\pi\) | ||||
−0.179582 | + | 0.983743i | \(0.557475\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.653925 | 0.0208995 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.9297 | −0.348958 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.8297 | 1.04710 | 0.523552 | − | 0.851993i | \(-0.324606\pi\) | ||||
0.523552 | + | 0.851993i | \(0.324606\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.3047 | 0.806276 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.329813 | 0.0104981 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.1585 | 0.482011 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.4687 | −0.904337 | −0.452169 | − | 0.891933i | \(-0.649349\pi\) | ||||
−0.452169 | + | 0.891933i | \(0.649349\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.64542 | 0.0522159 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.41524 | −0.139972 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.2836 | 1.59250 | 0.796249 | − | 0.604969i | \(-0.206814\pi\) | ||||
0.796249 | + | 0.604969i | \(0.206814\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.74407 | −0.118457 |
(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 | 4016.2.a.h.1.5 | 9 | ||
4.3 | odd | 2 | 2008.2.a.a.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.a.1.5 | ✓ | 9 | 4.3 | odd | 2 | ||
4016.2.a.h.1.5 | 9 | 1.1 | even | 1 | trivial |