Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5775,2,Mod(1,5775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5775, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5775.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5775.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: | \(46.1136071673\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5775.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.79129 | −1.26663 | −0.633316 | − | 0.773893i | \(-0.718307\pi\) | ||||
−0.633316 | + | 0.773893i | \(0.718307\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.20871 | 0.604356 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.79129 | −0.731290 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.41742 | 0.501135 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.20871 | 0.348925 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 1.79129 | 0.478742 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.95644 | −1.23911 | ||||||||
\(17\) | −7.58258 | −1.83904 | −0.919522 | − | 0.393038i | \(-0.871424\pi\) | ||||
−0.919522 | + | 0.393038i | \(0.871424\pi\) | |||||||
\(18\) | −1.79129 | −0.422211 | ||||||||
\(19\) | −6.58258 | −1.51015 | −0.755073 | − | 0.655640i | \(-0.772399\pi\) | ||||
−0.755073 | + | 0.655640i | \(0.772399\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.79129 | 0.381904 | ||||||||
\(23\) | 5.58258 | 1.16405 | 0.582024 | − | 0.813172i | \(-0.302261\pi\) | ||||
0.582024 | + | 0.813172i | \(0.302261\pi\) | |||||||
\(24\) | 1.41742 | 0.289331 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.79129 | 0.351300 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.20871 | −0.228425 | ||||||||
\(29\) | −8.16515 | −1.51623 | −0.758115 | − | 0.652121i | \(-0.773880\pi\) | ||||
−0.758115 | + | 0.652121i | \(0.773880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.58258 | 0.643450 | 0.321725 | − | 0.946833i | \(-0.395737\pi\) | ||||
0.321725 | + | 0.946833i | \(0.395737\pi\) | |||||||
\(32\) | 6.04356 | 1.06836 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 13.5826 | 2.32939 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.20871 | 0.201452 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 11.7913 | 1.91280 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.1652 | −1.74370 | −0.871852 | − | 0.489770i | \(-0.837081\pi\) | ||||
−0.871852 | + | 0.489770i | \(0.837081\pi\) | |||||||
\(42\) | 1.79129 | 0.276402 | ||||||||
\(43\) | −1.58258 | −0.241341 | −0.120670 | − | 0.992693i | \(-0.538504\pi\) | ||||
−0.120670 | + | 0.992693i | \(0.538504\pi\) | |||||||
\(44\) | −1.20871 | −0.182220 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.0000 | −1.47442 | ||||||||
\(47\) | −1.41742 | −0.206753 | −0.103376 | − | 0.994642i | \(-0.532965\pi\) | ||||
−0.103376 | + | 0.994642i | \(0.532965\pi\) | |||||||
\(48\) | −4.95644 | −0.715400 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.58258 | −1.06177 | ||||||||
\(52\) | −1.20871 | −0.167618 | ||||||||
\(53\) | 9.58258 | 1.31627 | 0.658134 | − | 0.752901i | \(-0.271346\pi\) | ||||
0.658134 | + | 0.752901i | \(0.271346\pi\) | |||||||
\(54\) | −1.79129 | −0.243763 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.41742 | −0.189411 | ||||||||
\(57\) | −6.58258 | −0.871883 | ||||||||
\(58\) | 14.6261 | 1.92051 | ||||||||
\(59\) | 4.58258 | 0.596601 | 0.298300 | − | 0.954472i | \(-0.403580\pi\) | ||||
0.298300 | + | 0.954472i | \(0.403580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | −6.41742 | −0.815014 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −0.912878 | −0.114110 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.79129 | 0.220492 | ||||||||
\(67\) | −8.58258 | −1.04853 | −0.524264 | − | 0.851556i | \(-0.675660\pi\) | ||||
−0.524264 | + | 0.851556i | \(0.675660\pi\) | |||||||
\(68\) | −9.16515 | −1.11144 | ||||||||
\(69\) | 5.58258 | 0.672063 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1652 | 1.32506 | 0.662530 | − | 0.749036i | \(-0.269483\pi\) | ||||
0.662530 | + | 0.749036i | \(0.269483\pi\) | |||||||
\(72\) | 1.41742 | 0.167045 | ||||||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 1.79129 | 0.208233 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.95644 | −0.912666 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 1.79129 | 0.202823 | ||||||||
\(79\) | 7.16515 | 0.806143 | 0.403071 | − | 0.915169i | \(-0.367943\pi\) | ||||
0.403071 | + | 0.915169i | \(0.367943\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.0000 | 2.20863 | ||||||||
\(83\) | 11.5826 | 1.27135 | 0.635676 | − | 0.771956i | \(-0.280721\pi\) | ||||
0.635676 | + | 0.771956i | \(0.280721\pi\) | |||||||
\(84\) | −1.20871 | −0.131881 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.83485 | 0.305690 | ||||||||
\(87\) | −8.16515 | −0.875396 | ||||||||
\(88\) | −1.41742 | −0.151098 | ||||||||
\(89\) | 9.16515 | 0.971504 | 0.485752 | − | 0.874097i | \(-0.338546\pi\) | ||||
0.485752 | + | 0.874097i | \(0.338546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 6.74773 | 0.703499 | ||||||||
\(93\) | 3.58258 | 0.371496 | ||||||||
\(94\) | 2.53901 | 0.261879 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.04356 | 0.616818 | ||||||||
\(97\) | 2.41742 | 0.245452 | 0.122726 | − | 0.992441i | \(-0.460836\pi\) | ||||
0.122726 | + | 0.992441i | \(0.460836\pi\) | |||||||
\(98\) | −1.79129 | −0.180947 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5826 | 1.15251 | 0.576255 | − | 0.817270i | \(-0.304514\pi\) | ||||
0.576255 | + | 0.817270i | \(0.304514\pi\) | |||||||
\(102\) | 13.5826 | 1.34488 | ||||||||
\(103\) | 1.16515 | 0.114806 | 0.0574029 | − | 0.998351i | \(-0.481718\pi\) | ||||
0.0574029 | + | 0.998351i | \(0.481718\pi\) | |||||||
\(104\) | −1.41742 | −0.138990 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.1652 | −1.66723 | ||||||||
\(107\) | 12.5826 | 1.21640 | 0.608202 | − | 0.793782i | \(-0.291891\pi\) | ||||
0.608202 | + | 0.793782i | \(0.291891\pi\) | |||||||
\(108\) | 1.20871 | 0.116308 | ||||||||
\(109\) | 3.58258 | 0.343149 | 0.171574 | − | 0.985171i | \(-0.445115\pi\) | ||||
0.171574 | + | 0.985171i | \(0.445115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 4.95644 | 0.468339 | ||||||||
\(113\) | −9.16515 | −0.862185 | −0.431092 | − | 0.902308i | \(-0.641872\pi\) | ||||
−0.431092 | + | 0.902308i | \(0.641872\pi\) | |||||||
\(114\) | 11.7913 | 1.10436 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.86932 | −0.916343 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −8.20871 | −0.755673 | ||||||||
\(119\) | 7.58258 | 0.695094 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −17.9129 | −1.62176 | ||||||||
\(123\) | −11.1652 | −1.00673 | ||||||||
\(124\) | 4.33030 | 0.388873 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.79129 | 0.159581 | ||||||||
\(127\) | 11.5826 | 1.02779 | 0.513894 | − | 0.857854i | \(-0.328203\pi\) | ||||
0.513894 | + | 0.857854i | \(0.328203\pi\) | |||||||
\(128\) | −10.4519 | −0.923826 | ||||||||
\(129\) | −1.58258 | −0.139338 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0000 | −1.39793 | −0.698963 | − | 0.715158i | \(-0.746355\pi\) | ||||
−0.698963 | + | 0.715158i | \(0.746355\pi\) | |||||||
\(132\) | −1.20871 | −0.105205 | ||||||||
\(133\) | 6.58258 | 0.570782 | ||||||||
\(134\) | 15.3739 | 1.32810 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.7477 | −0.921610 | ||||||||
\(137\) | 11.5826 | 0.989566 | 0.494783 | − | 0.869016i | \(-0.335248\pi\) | ||||
0.494783 | + | 0.869016i | \(0.335248\pi\) | |||||||
\(138\) | −10.0000 | −0.851257 | ||||||||
\(139\) | 11.1652 | 0.947016 | 0.473508 | − | 0.880790i | \(-0.342988\pi\) | ||||
0.473508 | + | 0.880790i | \(0.342988\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.41742 | −0.119369 | ||||||||
\(142\) | −20.0000 | −1.67836 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | −4.95644 | −0.413037 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.5390 | 1.03774 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −1.20871 | −0.0993555 | ||||||||
\(149\) | 6.16515 | 0.505069 | 0.252534 | − | 0.967588i | \(-0.418736\pi\) | ||||
0.252534 | + | 0.967588i | \(0.418736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.58258 | 0.291546 | 0.145773 | − | 0.989318i | \(-0.453433\pi\) | ||||
0.145773 | + | 0.989318i | \(0.453433\pi\) | |||||||
\(152\) | −9.33030 | −0.756787 | ||||||||
\(153\) | −7.58258 | −0.613015 | ||||||||
\(154\) | −1.79129 | −0.144346 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.20871 | −0.0967744 | ||||||||
\(157\) | −19.1652 | −1.52955 | −0.764773 | − | 0.644300i | \(-0.777149\pi\) | ||||
−0.764773 | + | 0.644300i | \(0.777149\pi\) | |||||||
\(158\) | −12.8348 | −1.02109 | ||||||||
\(159\) | 9.58258 | 0.759948 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.58258 | −0.439969 | ||||||||
\(162\) | −1.79129 | −0.140737 | ||||||||
\(163\) | −8.58258 | −0.672239 | −0.336120 | − | 0.941819i | \(-0.609115\pi\) | ||||
−0.336120 | + | 0.941819i | \(0.609115\pi\) | |||||||
\(164\) | −13.4955 | −1.05382 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.7477 | −1.61034 | ||||||||
\(167\) | 4.74773 | 0.367390 | 0.183695 | − | 0.982983i | \(-0.441194\pi\) | ||||
0.183695 | + | 0.982983i | \(0.441194\pi\) | |||||||
\(168\) | −1.41742 | −0.109357 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.58258 | −0.503382 | ||||||||
\(172\) | −1.91288 | −0.145856 | ||||||||
\(173\) | 7.16515 | 0.544756 | 0.272378 | − | 0.962190i | \(-0.412190\pi\) | ||||
0.272378 | + | 0.962190i | \(0.412190\pi\) | |||||||
\(174\) | 14.6261 | 1.10880 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.95644 | 0.373606 | ||||||||
\(177\) | 4.58258 | 0.344447 | ||||||||
\(178\) | −16.4174 | −1.23054 | ||||||||
\(179\) | 14.3303 | 1.07110 | 0.535549 | − | 0.844504i | \(-0.320105\pi\) | ||||
0.535549 | + | 0.844504i | \(0.320105\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.58258 | −0.414950 | −0.207475 | − | 0.978240i | \(-0.566524\pi\) | ||||
−0.207475 | + | 0.978240i | \(0.566524\pi\) | |||||||
\(182\) | −1.79129 | −0.132779 | ||||||||
\(183\) | 10.0000 | 0.739221 | ||||||||
\(184\) | 7.91288 | 0.583345 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.41742 | −0.470548 | ||||||||
\(187\) | 7.58258 | 0.554493 | ||||||||
\(188\) | −1.71326 | −0.124952 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5826 | 0.838086 | 0.419043 | − | 0.907966i | \(-0.362366\pi\) | ||||
0.419043 | + | 0.907966i | \(0.362366\pi\) | |||||||
\(192\) | −0.912878 | −0.0658813 | ||||||||
\(193\) | 2.41742 | 0.174010 | 0.0870050 | − | 0.996208i | \(-0.472270\pi\) | ||||
0.0870050 | + | 0.996208i | \(0.472270\pi\) | |||||||
\(194\) | −4.33030 | −0.310898 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.20871 | 0.0863366 | ||||||||
\(197\) | −5.16515 | −0.368002 | −0.184001 | − | 0.982926i | \(-0.558905\pi\) | ||||
−0.184001 | + | 0.982926i | \(0.558905\pi\) | |||||||
\(198\) | 1.79129 | 0.127301 | ||||||||
\(199\) | −9.58258 | −0.679291 | −0.339645 | − | 0.940554i | \(-0.610307\pi\) | ||||
−0.339645 | + | 0.940554i | \(0.610307\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.58258 | −0.605368 | ||||||||
\(202\) | −20.7477 | −1.45980 | ||||||||
\(203\) | 8.16515 | 0.573081 | ||||||||
\(204\) | −9.16515 | −0.641689 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.08712 | −0.145417 | ||||||||
\(207\) | 5.58258 | 0.388016 | ||||||||
\(208\) | 4.95644 | 0.343667 | ||||||||
\(209\) | 6.58258 | 0.455326 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1652 | −0.906326 | −0.453163 | − | 0.891428i | \(-0.649705\pi\) | ||||
−0.453163 | + | 0.891428i | \(0.649705\pi\) | |||||||
\(212\) | 11.5826 | 0.795495 | ||||||||
\(213\) | 11.1652 | 0.765024 | ||||||||
\(214\) | −22.5390 | −1.54074 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.41742 | 0.0964435 | ||||||||
\(217\) | −3.58258 | −0.243201 | ||||||||
\(218\) | −6.41742 | −0.434643 | ||||||||
\(219\) | −7.00000 | −0.473016 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.58258 | 0.510059 | ||||||||
\(222\) | 1.79129 | 0.120223 | ||||||||
\(223\) | −6.00000 | −0.401790 | −0.200895 | − | 0.979613i | \(-0.564385\pi\) | ||||
−0.200895 | + | 0.979613i | \(0.564385\pi\) | |||||||
\(224\) | −6.04356 | −0.403802 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.4174 | 1.09207 | ||||||||
\(227\) | 22.0000 | 1.46019 | 0.730096 | − | 0.683345i | \(-0.239475\pi\) | ||||
0.730096 | + | 0.683345i | \(0.239475\pi\) | |||||||
\(228\) | −7.95644 | −0.526928 | ||||||||
\(229\) | 0.747727 | 0.0494112 | 0.0247056 | − | 0.999695i | \(-0.492135\pi\) | ||||
0.0247056 | + | 0.999695i | \(0.492135\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | −11.5735 | −0.759836 | ||||||||
\(233\) | 14.0000 | 0.917170 | 0.458585 | − | 0.888650i | \(-0.348356\pi\) | ||||
0.458585 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(234\) | 1.79129 | 0.117100 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.53901 | 0.360559 | ||||||||
\(237\) | 7.16515 | 0.465427 | ||||||||
\(238\) | −13.5826 | −0.880428 | ||||||||
\(239\) | 16.5826 | 1.07264 | 0.536319 | − | 0.844015i | \(-0.319814\pi\) | ||||
0.536319 | + | 0.844015i | \(0.319814\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1652 | −0.654795 | −0.327397 | − | 0.944887i | \(-0.606172\pi\) | ||||
−0.327397 | + | 0.944887i | \(0.606172\pi\) | |||||||
\(242\) | −1.79129 | −0.115148 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.0871 | 0.773799 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 20.0000 | 1.27515 | ||||||||
\(247\) | 6.58258 | 0.418839 | ||||||||
\(248\) | 5.07803 | 0.322455 | ||||||||
\(249\) | 11.5826 | 0.734016 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.41742 | 0.468184 | 0.234092 | − | 0.972214i | \(-0.424788\pi\) | ||||
0.234092 | + | 0.972214i | \(0.424788\pi\) | |||||||
\(252\) | −1.20871 | −0.0761417 | ||||||||
\(253\) | −5.58258 | −0.350974 | ||||||||
\(254\) | −20.7477 | −1.30183 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.5481 | 1.28426 | ||||||||
\(257\) | −19.0000 | −1.18519 | −0.592594 | − | 0.805502i | \(-0.701896\pi\) | ||||
−0.592594 | + | 0.805502i | \(0.701896\pi\) | |||||||
\(258\) | 2.83485 | 0.176490 | ||||||||
\(259\) | 1.00000 | 0.0621370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.16515 | −0.505410 | ||||||||
\(262\) | 28.6606 | 1.77066 | ||||||||
\(263\) | 22.9129 | 1.41287 | 0.706434 | − | 0.707779i | \(-0.250303\pi\) | ||||
0.706434 | + | 0.707779i | \(0.250303\pi\) | |||||||
\(264\) | −1.41742 | −0.0872364 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −11.7913 | −0.722970 | ||||||||
\(267\) | 9.16515 | 0.560898 | ||||||||
\(268\) | −10.3739 | −0.633685 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.41742 | 0.329085 | 0.164543 | − | 0.986370i | \(-0.447385\pi\) | ||||
0.164543 | + | 0.986370i | \(0.447385\pi\) | |||||||
\(272\) | 37.5826 | 2.27878 | ||||||||
\(273\) | 1.00000 | 0.0605228 | ||||||||
\(274\) | −20.7477 | −1.25342 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.74773 | 0.406165 | ||||||||
\(277\) | 19.1652 | 1.15152 | 0.575761 | − | 0.817618i | \(-0.304706\pi\) | ||||
0.575761 | + | 0.817618i | \(0.304706\pi\) | |||||||
\(278\) | −20.0000 | −1.19952 | ||||||||
\(279\) | 3.58258 | 0.214483 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.3303 | −1.63039 | −0.815195 | − | 0.579187i | \(-0.803370\pi\) | ||||
−0.815195 | + | 0.579187i | \(0.803370\pi\) | |||||||
\(282\) | 2.53901 | 0.151196 | ||||||||
\(283\) | −27.7477 | −1.64943 | −0.824716 | − | 0.565548i | \(-0.808665\pi\) | ||||
−0.824716 | + | 0.565548i | \(0.808665\pi\) | |||||||
\(284\) | 13.4955 | 0.800808 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.79129 | −0.105921 | ||||||||
\(287\) | 11.1652 | 0.659058 | ||||||||
\(288\) | 6.04356 | 0.356120 | ||||||||
\(289\) | 40.4955 | 2.38209 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.41742 | 0.141712 | ||||||||
\(292\) | −8.46099 | −0.495142 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −1.79129 | −0.104470 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.41742 | −0.0823861 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −11.0436 | −0.639736 | ||||||||
\(299\) | −5.58258 | −0.322849 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.58258 | 0.0912181 | ||||||||
\(302\) | −6.41742 | −0.369281 | ||||||||
\(303\) | 11.5826 | 0.665402 | ||||||||
\(304\) | 32.6261 | 1.87124 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.5826 | 0.776464 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 1.20871 | 0.0688728 | ||||||||
\(309\) | 1.16515 | 0.0662831 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.3303 | 0.812597 | 0.406298 | − | 0.913740i | \(-0.366819\pi\) | ||||
0.406298 | + | 0.913740i | \(0.366819\pi\) | |||||||
\(312\) | −1.41742 | −0.0802458 | ||||||||
\(313\) | −19.5826 | −1.10687 | −0.553436 | − | 0.832891i | \(-0.686684\pi\) | ||||
−0.553436 | + | 0.832891i | \(0.686684\pi\) | |||||||
\(314\) | 34.3303 | 1.93737 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.66061 | 0.487197 | ||||||||
\(317\) | 22.4174 | 1.25909 | 0.629544 | − | 0.776965i | \(-0.283242\pi\) | ||||
0.629544 | + | 0.776965i | \(0.283242\pi\) | |||||||
\(318\) | −17.1652 | −0.962574 | ||||||||
\(319\) | 8.16515 | 0.457161 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.5826 | 0.702291 | ||||||||
\(322\) | 10.0000 | 0.557278 | ||||||||
\(323\) | 49.9129 | 2.77723 | ||||||||
\(324\) | 1.20871 | 0.0671507 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.3739 | 0.851480 | ||||||||
\(327\) | 3.58258 | 0.198117 | ||||||||
\(328\) | −15.8258 | −0.873831 | ||||||||
\(329\) | 1.41742 | 0.0781451 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.16515 | −0.173972 | −0.0869862 | − | 0.996210i | \(-0.527724\pi\) | ||||
−0.0869862 | + | 0.996210i | \(0.527724\pi\) | |||||||
\(332\) | 14.0000 | 0.768350 | ||||||||
\(333\) | −1.00000 | −0.0547997 | ||||||||
\(334\) | −8.50455 | −0.465348 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.95644 | 0.270396 | ||||||||
\(337\) | −17.5826 | −0.957784 | −0.478892 | − | 0.877874i | \(-0.658961\pi\) | ||||
−0.478892 | + | 0.877874i | \(0.658961\pi\) | |||||||
\(338\) | 21.4955 | 1.16920 | ||||||||
\(339\) | −9.16515 | −0.497783 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.58258 | −0.194007 | ||||||||
\(342\) | 11.7913 | 0.637600 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.24318 | −0.120944 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.8348 | −0.690006 | ||||||||
\(347\) | −26.3303 | −1.41348 | −0.706742 | − | 0.707471i | \(-0.749836\pi\) | ||||
−0.706742 | + | 0.707471i | \(0.749836\pi\) | |||||||
\(348\) | −9.86932 | −0.529051 | ||||||||
\(349\) | −15.0000 | −0.802932 | −0.401466 | − | 0.915874i | \(-0.631499\pi\) | ||||
−0.401466 | + | 0.915874i | \(0.631499\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −6.04356 | −0.322123 | ||||||||
\(353\) | −24.1652 | −1.28618 | −0.643091 | − | 0.765790i | \(-0.722348\pi\) | ||||
−0.643091 | + | 0.765790i | \(0.722348\pi\) | |||||||
\(354\) | −8.20871 | −0.436288 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.0780 | 0.587134 | ||||||||
\(357\) | 7.58258 | 0.401312 | ||||||||
\(358\) | −25.6697 | −1.35669 | ||||||||
\(359\) | −8.83485 | −0.466285 | −0.233143 | − | 0.972443i | \(-0.574901\pi\) | ||||
−0.233143 | + | 0.972443i | \(0.574901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.3303 | 1.28054 | ||||||||
\(362\) | 10.0000 | 0.525588 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 1.20871 | 0.0633537 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −17.9129 | −0.936321 | ||||||||
\(367\) | −22.0000 | −1.14839 | −0.574195 | − | 0.818718i | \(-0.694685\pi\) | ||||
−0.574195 | + | 0.818718i | \(0.694685\pi\) | |||||||
\(368\) | −27.6697 | −1.44238 | ||||||||
\(369\) | −11.1652 | −0.581235 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.58258 | −0.497503 | ||||||||
\(372\) | 4.33030 | 0.224516 | ||||||||
\(373\) | 34.7477 | 1.79917 | 0.899585 | − | 0.436747i | \(-0.143869\pi\) | ||||
0.899585 | + | 0.436747i | \(0.143869\pi\) | |||||||
\(374\) | −13.5826 | −0.702338 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.00909 | −0.103611 | ||||||||
\(377\) | 8.16515 | 0.420527 | ||||||||
\(378\) | 1.79129 | 0.0921339 | ||||||||
\(379\) | −12.5826 | −0.646323 | −0.323162 | − | 0.946344i | \(-0.604746\pi\) | ||||
−0.323162 | + | 0.946344i | \(0.604746\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.5826 | 0.593393 | ||||||||
\(382\) | −20.7477 | −1.06155 | ||||||||
\(383\) | −10.3303 | −0.527854 | −0.263927 | − | 0.964543i | \(-0.585018\pi\) | ||||
−0.263927 | + | 0.964543i | \(0.585018\pi\) | |||||||
\(384\) | −10.4519 | −0.533371 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.33030 | −0.220407 | ||||||||
\(387\) | −1.58258 | −0.0804468 | ||||||||
\(388\) | 2.92197 | 0.148341 | ||||||||
\(389\) | −26.3303 | −1.33500 | −0.667500 | − | 0.744610i | \(-0.732635\pi\) | ||||
−0.667500 | + | 0.744610i | \(0.732635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.3303 | −2.14074 | ||||||||
\(392\) | 1.41742 | 0.0715907 | ||||||||
\(393\) | −16.0000 | −0.807093 | ||||||||
\(394\) | 9.25227 | 0.466123 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.20871 | −0.0607401 | ||||||||
\(397\) | 31.5826 | 1.58508 | 0.792542 | − | 0.609817i | \(-0.208757\pi\) | ||||
0.792542 | + | 0.609817i | \(0.208757\pi\) | |||||||
\(398\) | 17.1652 | 0.860411 | ||||||||
\(399\) | 6.58258 | 0.329541 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.9129 | 1.59365 | 0.796827 | − | 0.604208i | \(-0.206510\pi\) | ||||
0.796827 | + | 0.604208i | \(0.206510\pi\) | |||||||
\(402\) | 15.3739 | 0.766779 | ||||||||
\(403\) | −3.58258 | −0.178461 | ||||||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.6261 | −0.725883 | ||||||||
\(407\) | 1.00000 | 0.0495682 | ||||||||
\(408\) | −10.7477 | −0.532092 | ||||||||
\(409\) | 8.33030 | 0.411907 | 0.205953 | − | 0.978562i | \(-0.433970\pi\) | ||||
0.205953 | + | 0.978562i | \(0.433970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.5826 | 0.571326 | ||||||||
\(412\) | 1.40833 | 0.0693836 | ||||||||
\(413\) | −4.58258 | −0.225494 | ||||||||
\(414\) | −10.0000 | −0.491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.04356 | −0.296310 | ||||||||
\(417\) | 11.1652 | 0.546760 | ||||||||
\(418\) | −11.7913 | −0.576731 | ||||||||
\(419\) | 2.58258 | 0.126167 | 0.0630835 | − | 0.998008i | \(-0.479907\pi\) | ||||
0.0630835 | + | 0.998008i | \(0.479907\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.6606 | −1.64052 | −0.820259 | − | 0.571993i | \(-0.806171\pi\) | ||||
−0.820259 | + | 0.571993i | \(0.806171\pi\) | |||||||
\(422\) | 23.5826 | 1.14798 | ||||||||
\(423\) | −1.41742 | −0.0689175 | ||||||||
\(424\) | 13.5826 | 0.659628 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −20.0000 | −0.969003 | ||||||||
\(427\) | −10.0000 | −0.483934 | ||||||||
\(428\) | 15.2087 | 0.735141 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7477 | 0.854878 | 0.427439 | − | 0.904044i | \(-0.359416\pi\) | ||||
0.427439 | + | 0.904044i | \(0.359416\pi\) | |||||||
\(432\) | −4.95644 | −0.238467 | ||||||||
\(433\) | 11.1652 | 0.536563 | 0.268281 | − | 0.963341i | \(-0.413544\pi\) | ||||
0.268281 | + | 0.963341i | \(0.413544\pi\) | |||||||
\(434\) | 6.41742 | 0.308046 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.33030 | 0.207384 | ||||||||
\(437\) | −36.7477 | −1.75788 | ||||||||
\(438\) | 12.5390 | 0.599137 | ||||||||
\(439\) | 17.4174 | 0.831288 | 0.415644 | − | 0.909527i | \(-0.363556\pi\) | ||||
0.415644 | + | 0.909527i | \(0.363556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −13.5826 | −0.646057 | ||||||||
\(443\) | 23.1652 | 1.10061 | 0.550305 | − | 0.834964i | \(-0.314512\pi\) | ||||
0.550305 | + | 0.834964i | \(0.314512\pi\) | |||||||
\(444\) | −1.20871 | −0.0573629 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.7477 | 0.508920 | ||||||||
\(447\) | 6.16515 | 0.291602 | ||||||||
\(448\) | 0.912878 | 0.0431295 | ||||||||
\(449\) | −18.3303 | −0.865060 | −0.432530 | − | 0.901619i | \(-0.642379\pi\) | ||||
−0.432530 | + | 0.901619i | \(0.642379\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.1652 | 0.525746 | ||||||||
\(452\) | −11.0780 | −0.521067 | ||||||||
\(453\) | 3.58258 | 0.168324 | ||||||||
\(454\) | −39.4083 | −1.84952 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.33030 | −0.436931 | ||||||||
\(457\) | 19.9129 | 0.931485 | 0.465743 | − | 0.884920i | \(-0.345787\pi\) | ||||
0.465743 | + | 0.884920i | \(0.345787\pi\) | |||||||
\(458\) | −1.33939 | −0.0625858 | ||||||||
\(459\) | −7.58258 | −0.353924 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.3303 | 0.853727 | 0.426864 | − | 0.904316i | \(-0.359618\pi\) | ||||
0.426864 | + | 0.904316i | \(0.359618\pi\) | |||||||
\(462\) | −1.79129 | −0.0833383 | ||||||||
\(463\) | −8.58258 | −0.398866 | −0.199433 | − | 0.979911i | \(-0.563910\pi\) | ||||
−0.199433 | + | 0.979911i | \(0.563910\pi\) | |||||||
\(464\) | 40.4701 | 1.87878 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.0780 | −1.16172 | ||||||||
\(467\) | 38.5826 | 1.78539 | 0.892694 | − | 0.450663i | \(-0.148812\pi\) | ||||
0.892694 | + | 0.450663i | \(0.148812\pi\) | |||||||
\(468\) | −1.20871 | −0.0558727 | ||||||||
\(469\) | 8.58258 | 0.396307 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.1652 | −0.883084 | ||||||||
\(472\) | 6.49545 | 0.298978 | ||||||||
\(473\) | 1.58258 | 0.0727669 | ||||||||
\(474\) | −12.8348 | −0.589524 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.16515 | 0.420084 | ||||||||
\(477\) | 9.58258 | 0.438756 | ||||||||
\(478\) | −29.7042 | −1.35864 | ||||||||
\(479\) | −15.5826 | −0.711986 | −0.355993 | − | 0.934489i | \(-0.615857\pi\) | ||||
−0.355993 | + | 0.934489i | \(0.615857\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.00000 | 0.0455961 | ||||||||
\(482\) | 18.2087 | 0.829384 | ||||||||
\(483\) | −5.58258 | −0.254016 | ||||||||
\(484\) | 1.20871 | 0.0549415 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.79129 | −0.0812545 | ||||||||
\(487\) | −10.3303 | −0.468111 | −0.234055 | − | 0.972223i | \(-0.575200\pi\) | ||||
−0.234055 | + | 0.972223i | \(0.575200\pi\) | |||||||
\(488\) | 14.1742 | 0.641638 | ||||||||
\(489\) | −8.58258 | −0.388117 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.9129 | −1.03404 | −0.517022 | − | 0.855972i | \(-0.672959\pi\) | ||||
−0.517022 | + | 0.855972i | \(0.672959\pi\) | |||||||
\(492\) | −13.4955 | −0.608422 | ||||||||
\(493\) | 61.9129 | 2.78842 | ||||||||
\(494\) | −11.7913 | −0.530515 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.7568 | −0.797305 | ||||||||
\(497\) | −11.1652 | −0.500825 | ||||||||
\(498\) | −20.7477 | −0.929728 | ||||||||
\(499\) | 41.7477 | 1.86888 | 0.934442 | − | 0.356114i | \(-0.115899\pi\) | ||||
0.934442 | + | 0.356114i | \(0.115899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.74773 | 0.212113 | ||||||||
\(502\) | −13.2867 | −0.593016 | ||||||||
\(503\) | 0.747727 | 0.0333395 | 0.0166698 | − | 0.999861i | \(-0.494694\pi\) | ||||
0.0166698 | + | 0.999861i | \(0.494694\pi\) | |||||||
\(504\) | −1.41742 | −0.0631371 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.0000 | 0.444554 | ||||||||
\(507\) | −12.0000 | −0.532939 | ||||||||
\(508\) | 14.0000 | 0.621150 | ||||||||
\(509\) | 6.00000 | 0.265945 | 0.132973 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132973 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.00000 | 0.309662 | ||||||||
\(512\) | −15.9038 | −0.702855 | ||||||||
\(513\) | −6.58258 | −0.290628 | ||||||||
\(514\) | 34.0345 | 1.50120 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.91288 | −0.0842098 | ||||||||
\(517\) | 1.41742 | 0.0623382 | ||||||||
\(518\) | −1.79129 | −0.0787047 | ||||||||
\(519\) | 7.16515 | 0.314515 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.8348 | 0.693737 | 0.346869 | − | 0.937914i | \(-0.387245\pi\) | ||||
0.346869 | + | 0.937914i | \(0.387245\pi\) | |||||||
\(522\) | 14.6261 | 0.640169 | ||||||||
\(523\) | −15.4174 | −0.674157 | −0.337078 | − | 0.941477i | \(-0.609439\pi\) | ||||
−0.337078 | + | 0.941477i | \(0.609439\pi\) | |||||||
\(524\) | −19.3394 | −0.844845 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −41.0436 | −1.78958 | ||||||||
\(527\) | −27.1652 | −1.18333 | ||||||||
\(528\) | 4.95644 | 0.215701 | ||||||||
\(529\) | 8.16515 | 0.355007 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.58258 | 0.198867 | ||||||||
\(532\) | 7.95644 | 0.344955 | ||||||||
\(533\) | 11.1652 | 0.483616 | ||||||||
\(534\) | −16.4174 | −0.710451 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.1652 | −0.525455 | ||||||||
\(537\) | 14.3303 | 0.618398 | ||||||||
\(538\) | −17.9129 | −0.772279 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.3303 | 0.788081 | 0.394041 | − | 0.919093i | \(-0.371077\pi\) | ||||
0.394041 | + | 0.919093i | \(0.371077\pi\) | |||||||
\(542\) | −9.70417 | −0.416830 | ||||||||
\(543\) | −5.58258 | −0.239571 | ||||||||
\(544\) | −45.8258 | −1.96476 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.79129 | −0.0766600 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 14.0000 | 0.598050 | ||||||||
\(549\) | 10.0000 | 0.426790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 53.7477 | 2.28973 | ||||||||
\(552\) | 7.91288 | 0.336794 | ||||||||
\(553\) | −7.16515 | −0.304693 | ||||||||
\(554\) | −34.3303 | −1.45855 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.4955 | 0.572335 | ||||||||
\(557\) | −9.33030 | −0.395338 | −0.197669 | − | 0.980269i | \(-0.563337\pi\) | ||||
−0.197669 | + | 0.980269i | \(0.563337\pi\) | |||||||
\(558\) | −6.41742 | −0.271671 | ||||||||
\(559\) | 1.58258 | 0.0669358 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.58258 | 0.320137 | ||||||||
\(562\) | 48.9564 | 2.06510 | ||||||||
\(563\) | 37.5826 | 1.58392 | 0.791958 | − | 0.610575i | \(-0.209062\pi\) | ||||
0.791958 | + | 0.610575i | \(0.209062\pi\) | |||||||
\(564\) | −1.71326 | −0.0721412 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 49.7042 | 2.08922 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 15.8258 | 0.664034 | ||||||||
\(569\) | −26.6606 | −1.11767 | −0.558835 | − | 0.829279i | \(-0.688752\pi\) | ||||
−0.558835 | + | 0.829279i | \(0.688752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.8348 | 1.20670 | 0.603350 | − | 0.797476i | \(-0.293832\pi\) | ||||
0.603350 | + | 0.797476i | \(0.293832\pi\) | |||||||
\(572\) | 1.20871 | 0.0505388 | ||||||||
\(573\) | 11.5826 | 0.483869 | ||||||||
\(574\) | −20.0000 | −0.834784 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.912878 | −0.0380366 | ||||||||
\(577\) | 21.9129 | 0.912245 | 0.456123 | − | 0.889917i | \(-0.349238\pi\) | ||||
0.456123 | + | 0.889917i | \(0.349238\pi\) | |||||||
\(578\) | −72.5390 | −3.01723 | ||||||||
\(579\) | 2.41742 | 0.100465 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.5826 | −0.480526 | ||||||||
\(582\) | −4.33030 | −0.179497 | ||||||||
\(583\) | −9.58258 | −0.396870 | ||||||||
\(584\) | −9.92197 | −0.410574 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.7477 | −1.55802 | −0.779008 | − | 0.627014i | \(-0.784277\pi\) | ||||
−0.779008 | + | 0.627014i | \(0.784277\pi\) | |||||||
\(588\) | 1.20871 | 0.0498464 | ||||||||
\(589\) | −23.5826 | −0.971703 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.16515 | −0.212466 | ||||||||
\(592\) | 4.95644 | 0.203708 | ||||||||
\(593\) | −16.0000 | −0.657041 | −0.328521 | − | 0.944497i | \(-0.606550\pi\) | ||||
−0.328521 | + | 0.944497i | \(0.606550\pi\) | |||||||
\(594\) | 1.79129 | 0.0734974 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.45189 | 0.305241 | ||||||||
\(597\) | −9.58258 | −0.392189 | ||||||||
\(598\) | 10.0000 | 0.408930 | ||||||||
\(599\) | 7.16515 | 0.292760 | 0.146380 | − | 0.989228i | \(-0.453238\pi\) | ||||
0.146380 | + | 0.989228i | \(0.453238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.4955 | 0.999190 | 0.499595 | − | 0.866259i | \(-0.333482\pi\) | ||||
0.499595 | + | 0.866259i | \(0.333482\pi\) | |||||||
\(602\) | −2.83485 | −0.115540 | ||||||||
\(603\) | −8.58258 | −0.349510 | ||||||||
\(604\) | 4.33030 | 0.176198 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.7477 | −0.842819 | ||||||||
\(607\) | 21.7477 | 0.882713 | 0.441357 | − | 0.897332i | \(-0.354497\pi\) | ||||
0.441357 | + | 0.897332i | \(0.354497\pi\) | |||||||
\(608\) | −39.7822 | −1.61338 | ||||||||
\(609\) | 8.16515 | 0.330869 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.41742 | 0.0573428 | ||||||||
\(612\) | −9.16515 | −0.370479 | ||||||||
\(613\) | 26.7477 | 1.08033 | 0.540165 | − | 0.841559i | \(-0.318362\pi\) | ||||
0.540165 | + | 0.841559i | \(0.318362\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.41742 | 0.0571097 | ||||||||
\(617\) | −2.83485 | −0.114127 | −0.0570634 | − | 0.998371i | \(-0.518174\pi\) | ||||
−0.0570634 | + | 0.998371i | \(0.518174\pi\) | |||||||
\(618\) | −2.08712 | −0.0839563 | ||||||||
\(619\) | −29.0780 | −1.16874 | −0.584372 | − | 0.811486i | \(-0.698659\pi\) | ||||
−0.584372 | + | 0.811486i | \(0.698659\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.58258 | 0.224021 | ||||||||
\(622\) | −25.6697 | −1.02926 | ||||||||
\(623\) | −9.16515 | −0.367194 | ||||||||
\(624\) | 4.95644 | 0.198416 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 35.0780 | 1.40200 | ||||||||
\(627\) | 6.58258 | 0.262883 | ||||||||
\(628\) | −23.1652 | −0.924390 | ||||||||
\(629\) | 7.58258 | 0.302337 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1652 | 0.922190 | 0.461095 | − | 0.887351i | \(-0.347457\pi\) | ||||
0.461095 | + | 0.887351i | \(0.347457\pi\) | |||||||
\(632\) | 10.1561 | 0.403986 | ||||||||
\(633\) | −13.1652 | −0.523268 | ||||||||
\(634\) | −40.1561 | −1.59480 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 11.5826 | 0.459279 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | −14.6261 | −0.579054 | ||||||||
\(639\) | 11.1652 | 0.441687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.5826 | 1.72141 | 0.860704 | − | 0.509106i | \(-0.170024\pi\) | ||||
0.860704 | + | 0.509106i | \(0.170024\pi\) | |||||||
\(642\) | −22.5390 | −0.889544 | ||||||||
\(643\) | −38.2432 | −1.50816 | −0.754082 | − | 0.656780i | \(-0.771918\pi\) | ||||
−0.754082 | + | 0.656780i | \(0.771918\pi\) | |||||||
\(644\) | −6.74773 | −0.265898 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −89.4083 | −3.51772 | ||||||||
\(647\) | 10.9129 | 0.429030 | 0.214515 | − | 0.976721i | \(-0.431183\pi\) | ||||
0.214515 | + | 0.976721i | \(0.431183\pi\) | |||||||
\(648\) | 1.41742 | 0.0556817 | ||||||||
\(649\) | −4.58258 | −0.179882 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.58258 | −0.140412 | ||||||||
\(652\) | −10.3739 | −0.406272 | ||||||||
\(653\) | 30.3303 | 1.18692 | 0.593458 | − | 0.804865i | \(-0.297762\pi\) | ||||
0.593458 | + | 0.804865i | \(0.297762\pi\) | |||||||
\(654\) | −6.41742 | −0.250941 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 55.3394 | 2.16064 | ||||||||
\(657\) | −7.00000 | −0.273096 | ||||||||
\(658\) | −2.53901 | −0.0989811 | ||||||||
\(659\) | −28.5826 | −1.11342 | −0.556710 | − | 0.830707i | \(-0.687936\pi\) | ||||
−0.556710 | + | 0.830707i | \(0.687936\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.0780 | −1.51996 | −0.759980 | − | 0.649947i | \(-0.774791\pi\) | ||||
−0.759980 | + | 0.649947i | \(0.774791\pi\) | |||||||
\(662\) | 5.66970 | 0.220359 | ||||||||
\(663\) | 7.58258 | 0.294483 | ||||||||
\(664\) | 16.4174 | 0.637120 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.79129 | 0.0694110 | ||||||||
\(667\) | −45.5826 | −1.76496 | ||||||||
\(668\) | 5.73864 | 0.222034 | ||||||||
\(669\) | −6.00000 | −0.231973 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0000 | −0.386046 | ||||||||
\(672\) | −6.04356 | −0.233135 | ||||||||
\(673\) | −11.2523 | −0.433743 | −0.216872 | − | 0.976200i | \(-0.569585\pi\) | ||||
−0.216872 | + | 0.976200i | \(0.569585\pi\) | |||||||
\(674\) | 31.4955 | 1.21316 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.5045 | −0.557867 | ||||||||
\(677\) | 45.1652 | 1.73584 | 0.867919 | − | 0.496706i | \(-0.165457\pi\) | ||||
0.867919 | + | 0.496706i | \(0.165457\pi\) | |||||||
\(678\) | 16.4174 | 0.630507 | ||||||||
\(679\) | −2.41742 | −0.0927722 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.0000 | 0.843042 | ||||||||
\(682\) | 6.41742 | 0.245736 | ||||||||
\(683\) | 33.0780 | 1.26570 | 0.632848 | − | 0.774276i | \(-0.281886\pi\) | ||||
0.632848 | + | 0.774276i | \(0.281886\pi\) | |||||||
\(684\) | −7.95644 | −0.304222 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.79129 | 0.0683917 | ||||||||
\(687\) | 0.747727 | 0.0285276 | ||||||||
\(688\) | 7.84394 | 0.299047 | ||||||||
\(689\) | −9.58258 | −0.365067 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | 0.380418 | 0.190209 | − | 0.981744i | \(-0.439083\pi\) | ||||
0.190209 | + | 0.981744i | \(0.439083\pi\) | |||||||
\(692\) | 8.66061 | 0.329227 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 47.1652 | 1.79036 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −11.5735 | −0.438692 | ||||||||
\(697\) | 84.6606 | 3.20675 | ||||||||
\(698\) | 26.8693 | 1.01702 | ||||||||
\(699\) | 14.0000 | 0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0000 | 0.377695 | 0.188847 | − | 0.982006i | \(-0.439525\pi\) | ||||
0.188847 | + | 0.982006i | \(0.439525\pi\) | |||||||
\(702\) | 1.79129 | 0.0676078 | ||||||||
\(703\) | 6.58258 | 0.248267 | ||||||||
\(704\) | 0.912878 | 0.0344054 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 43.2867 | 1.62912 | ||||||||
\(707\) | −11.5826 | −0.435608 | ||||||||
\(708\) | 5.53901 | 0.208169 | ||||||||
\(709\) | 27.6606 | 1.03882 | 0.519408 | − | 0.854526i | \(-0.326153\pi\) | ||||
0.519408 | + | 0.854526i | \(0.326153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.16515 | 0.268714 | ||||||||
\(712\) | 12.9909 | 0.486855 | ||||||||
\(713\) | 20.0000 | 0.749006 | ||||||||
\(714\) | −13.5826 | −0.508315 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17.3212 | 0.647324 | ||||||||
\(717\) | 16.5826 | 0.619288 | ||||||||
\(718\) | 15.8258 | 0.590612 | ||||||||
\(719\) | −14.0780 | −0.525022 | −0.262511 | − | 0.964929i | \(-0.584551\pi\) | ||||
−0.262511 | + | 0.964929i | \(0.584551\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.16515 | −0.0433925 | ||||||||
\(722\) | −43.5826 | −1.62198 | ||||||||
\(723\) | −10.1652 | −0.378046 | ||||||||
\(724\) | −6.74773 | −0.250777 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.79129 | −0.0664809 | ||||||||
\(727\) | 15.9129 | 0.590176 | 0.295088 | − | 0.955470i | \(-0.404651\pi\) | ||||
0.295088 | + | 0.955470i | \(0.404651\pi\) | |||||||
\(728\) | 1.41742 | 0.0525332 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | 0.443836 | ||||||||
\(732\) | 12.0871 | 0.446753 | ||||||||
\(733\) | 34.0000 | 1.25582 | 0.627909 | − | 0.778287i | \(-0.283911\pi\) | ||||
0.627909 | + | 0.778287i | \(0.283911\pi\) | |||||||
\(734\) | 39.4083 | 1.45459 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33.7386 | 1.24362 | ||||||||
\(737\) | 8.58258 | 0.316143 | ||||||||
\(738\) | 20.0000 | 0.736210 | ||||||||
\(739\) | −31.9129 | −1.17393 | −0.586967 | − | 0.809611i | \(-0.699678\pi\) | ||||
−0.586967 | + | 0.809611i | \(0.699678\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.58258 | 0.241817 | ||||||||
\(742\) | 17.1652 | 0.630153 | ||||||||
\(743\) | 53.2432 | 1.95330 | 0.976651 | − | 0.214830i | \(-0.0689198\pi\) | ||||
0.976651 | + | 0.214830i | \(0.0689198\pi\) | |||||||
\(744\) | 5.07803 | 0.186170 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −62.2432 | −2.27888 | ||||||||
\(747\) | 11.5826 | 0.423784 | ||||||||
\(748\) | 9.16515 | 0.335111 | ||||||||
\(749\) | −12.5826 | −0.459757 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.91288 | −0.325236 | −0.162618 | − | 0.986689i | \(-0.551994\pi\) | ||||
−0.162618 | + | 0.986689i | \(0.551994\pi\) | |||||||
\(752\) | 7.02538 | 0.256189 | ||||||||
\(753\) | 7.41742 | 0.270306 | ||||||||
\(754\) | −14.6261 | −0.532652 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.20871 | −0.0439604 | ||||||||
\(757\) | −27.3303 | −0.993337 | −0.496668 | − | 0.867940i | \(-0.665443\pi\) | ||||
−0.496668 | + | 0.867940i | \(0.665443\pi\) | |||||||
\(758\) | 22.5390 | 0.818654 | ||||||||
\(759\) | −5.58258 | −0.202635 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.3303 | 1.53447 | 0.767236 | − | 0.641365i | \(-0.221631\pi\) | ||||
0.767236 | + | 0.641365i | \(0.221631\pi\) | |||||||
\(762\) | −20.7477 | −0.751611 | ||||||||
\(763\) | −3.58258 | −0.129698 | ||||||||
\(764\) | 14.0000 | 0.506502 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.5045 | 0.668596 | ||||||||
\(767\) | −4.58258 | −0.165467 | ||||||||
\(768\) | 20.5481 | 0.741466 | ||||||||
\(769\) | 6.49545 | 0.234232 | 0.117116 | − | 0.993118i | \(-0.462635\pi\) | ||||
0.117116 | + | 0.993118i | \(0.462635\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.0000 | −0.684268 | ||||||||
\(772\) | 2.92197 | 0.105164 | ||||||||
\(773\) | −6.16515 | −0.221745 | −0.110873 | − | 0.993835i | \(-0.535365\pi\) | ||||
−0.110873 | + | 0.993835i | \(0.535365\pi\) | |||||||
\(774\) | 2.83485 | 0.101897 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.42652 | 0.123005 | ||||||||
\(777\) | 1.00000 | 0.0358748 | ||||||||
\(778\) | 47.1652 | 1.69095 | ||||||||
\(779\) | 73.4955 | 2.63325 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1652 | −0.399521 | ||||||||
\(782\) | 75.8258 | 2.71152 | ||||||||
\(783\) | −8.16515 | −0.291799 | ||||||||
\(784\) | −4.95644 | −0.177016 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 28.6606 | 1.02229 | ||||||||
\(787\) | −38.5826 | −1.37532 | −0.687660 | − | 0.726033i | \(-0.741362\pi\) | ||||
−0.687660 | + | 0.726033i | \(0.741362\pi\) | |||||||
\(788\) | −6.24318 | −0.222404 | ||||||||
\(789\) | 22.9129 | 0.815720 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.16515 | 0.325875 | ||||||||
\(792\) | −1.41742 | −0.0503660 | ||||||||
\(793\) | −10.0000 | −0.355110 | ||||||||
\(794\) | −56.5735 | −2.00772 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.5826 | −0.410534 | ||||||||
\(797\) | 52.4955 | 1.85948 | 0.929742 | − | 0.368211i | \(-0.120030\pi\) | ||||
0.929742 | + | 0.368211i | \(0.120030\pi\) | |||||||
\(798\) | −11.7913 | −0.417407 | ||||||||
\(799\) | 10.7477 | 0.380227 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.16515 | 0.323835 | ||||||||
\(802\) | −57.1652 | −2.01857 | ||||||||
\(803\) | 7.00000 | 0.247025 | ||||||||
\(804\) | −10.3739 | −0.365858 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.41742 | 0.226044 | ||||||||
\(807\) | 10.0000 | 0.352017 | ||||||||
\(808\) | 16.4174 | 0.577563 | ||||||||
\(809\) | 9.33030 | 0.328036 | 0.164018 | − | 0.986457i | \(-0.447554\pi\) | ||||
0.164018 | + | 0.986457i | \(0.447554\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.25227 | −0.0790880 | −0.0395440 | − | 0.999218i | \(-0.512591\pi\) | ||||
−0.0395440 | + | 0.999218i | \(0.512591\pi\) | |||||||
\(812\) | 9.86932 | 0.346345 | ||||||||
\(813\) | 5.41742 | 0.189997 | ||||||||
\(814\) | −1.79129 | −0.0627846 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 37.5826 | 1.31565 | ||||||||
\(817\) | 10.4174 | 0.364460 | ||||||||
\(818\) | −14.9220 | −0.521734 | ||||||||
\(819\) | 1.00000 | 0.0349428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.0000 | −1.64031 | −0.820156 | − | 0.572140i | \(-0.806113\pi\) | ||||
−0.820156 | + | 0.572140i | \(0.806113\pi\) | |||||||
\(822\) | −20.7477 | −0.723660 | ||||||||
\(823\) | 30.5826 | 1.06604 | 0.533021 | − | 0.846102i | \(-0.321057\pi\) | ||||
0.533021 | + | 0.846102i | \(0.321057\pi\) | |||||||
\(824\) | 1.65151 | 0.0575332 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.20871 | 0.285618 | ||||||||
\(827\) | −8.91288 | −0.309931 | −0.154966 | − | 0.987920i | \(-0.549527\pi\) | ||||
−0.154966 | + | 0.987920i | \(0.549527\pi\) | |||||||
\(828\) | 6.74773 | 0.234500 | ||||||||
\(829\) | −40.0000 | −1.38926 | −0.694629 | − | 0.719368i | \(-0.744431\pi\) | ||||
−0.694629 | + | 0.719368i | \(0.744431\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.1652 | 0.664832 | ||||||||
\(832\) | 0.912878 | 0.0316484 | ||||||||
\(833\) | −7.58258 | −0.262721 | ||||||||
\(834\) | −20.0000 | −0.692543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.95644 | 0.275179 | ||||||||
\(837\) | 3.58258 | 0.123832 | ||||||||
\(838\) | −4.62614 | −0.159807 | ||||||||
\(839\) | 7.08712 | 0.244675 | 0.122337 | − | 0.992489i | \(-0.460961\pi\) | ||||
0.122337 | + | 0.992489i | \(0.460961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.6697 | 1.29896 | ||||||||
\(842\) | 60.2958 | 2.07793 | ||||||||
\(843\) | −27.3303 | −0.941306 | ||||||||
\(844\) | −15.9129 | −0.547744 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.53901 | 0.0872931 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | −47.4955 | −1.63100 | ||||||||
\(849\) | −27.7477 | −0.952300 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.58258 | −0.191368 | ||||||||
\(852\) | 13.4955 | 0.462347 | ||||||||
\(853\) | −17.1652 | −0.587724 | −0.293862 | − | 0.955848i | \(-0.594941\pi\) | ||||
−0.293862 | + | 0.955848i | \(0.594941\pi\) | |||||||
\(854\) | 17.9129 | 0.612966 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.8348 | 0.609583 | ||||||||
\(857\) | 7.66970 | 0.261992 | 0.130996 | − | 0.991383i | \(-0.458183\pi\) | ||||
0.130996 | + | 0.991383i | \(0.458183\pi\) | |||||||
\(858\) | −1.79129 | −0.0611536 | ||||||||
\(859\) | 12.0000 | 0.409435 | 0.204717 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204717 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.1652 | 0.380507 | ||||||||
\(862\) | −31.7913 | −1.08282 | ||||||||
\(863\) | −14.4174 | −0.490775 | −0.245387 | − | 0.969425i | \(-0.578915\pi\) | ||||
−0.245387 | + | 0.969425i | \(0.578915\pi\) | |||||||
\(864\) | 6.04356 | 0.205606 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.0000 | −0.679628 | ||||||||
\(867\) | 40.4955 | 1.37530 | ||||||||
\(868\) | −4.33030 | −0.146980 | ||||||||
\(869\) | −7.16515 | −0.243061 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.58258 | 0.290809 | ||||||||
\(872\) | 5.07803 | 0.171964 | ||||||||
\(873\) | 2.41742 | 0.0818174 | ||||||||
\(874\) | 65.8258 | 2.22659 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.46099 | −0.285870 | ||||||||
\(877\) | −9.49545 | −0.320639 | −0.160319 | − | 0.987065i | \(-0.551252\pi\) | ||||
−0.160319 | + | 0.987065i | \(0.551252\pi\) | |||||||
\(878\) | −31.1996 | −1.05294 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.6606 | −1.26882 | −0.634409 | − | 0.772998i | \(-0.718756\pi\) | ||||
−0.634409 | + | 0.772998i | \(0.718756\pi\) | |||||||
\(882\) | −1.79129 | −0.0603158 | ||||||||
\(883\) | 55.7477 | 1.87606 | 0.938030 | − | 0.346554i | \(-0.112648\pi\) | ||||
0.938030 | + | 0.346554i | \(0.112648\pi\) | |||||||
\(884\) | 9.16515 | 0.308257 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.4955 | −1.39407 | ||||||||
\(887\) | −38.7477 | −1.30102 | −0.650511 | − | 0.759497i | \(-0.725445\pi\) | ||||
−0.650511 | + | 0.759497i | \(0.725445\pi\) | |||||||
\(888\) | −1.41742 | −0.0475656 | ||||||||
\(889\) | −11.5826 | −0.388467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −7.25227 | −0.242824 | ||||||||
\(893\) | 9.33030 | 0.312227 | ||||||||
\(894\) | −11.0436 | −0.369352 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10.4519 | 0.349173 | ||||||||
\(897\) | −5.58258 | −0.186397 | ||||||||
\(898\) | 32.8348 | 1.09571 | ||||||||
\(899\) | −29.2523 | −0.975618 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −72.6606 | −2.42068 | ||||||||
\(902\) | −20.0000 | −0.665927 | ||||||||
\(903\) | 1.58258 | 0.0526648 | ||||||||
\(904\) | −12.9909 | −0.432071 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.41742 | −0.213205 | ||||||||
\(907\) | −42.3303 | −1.40555 | −0.702777 | − | 0.711410i | \(-0.748057\pi\) | ||||
−0.702777 | + | 0.711410i | \(0.748057\pi\) | |||||||
\(908\) | 26.5917 | 0.882475 | ||||||||
\(909\) | 11.5826 | 0.384170 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.49545 | −0.115810 | −0.0579048 | − | 0.998322i | \(-0.518442\pi\) | ||||
−0.0579048 | + | 0.998322i | \(0.518442\pi\) | |||||||
\(912\) | 32.6261 | 1.08036 | ||||||||
\(913\) | −11.5826 | −0.383327 | ||||||||
\(914\) | −35.6697 | −1.17985 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.903787 | 0.0298620 | ||||||||
\(917\) | 16.0000 | 0.528367 | ||||||||
\(918\) | 13.5826 | 0.448292 | ||||||||
\(919\) | −8.08712 | −0.266770 | −0.133385 | − | 0.991064i | \(-0.542585\pi\) | ||||
−0.133385 | + | 0.991064i | \(0.542585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −32.8348 | −1.08136 | ||||||||
\(923\) | −11.1652 | −0.367505 | ||||||||
\(924\) | 1.20871 | 0.0397637 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.3739 | 0.505217 | ||||||||
\(927\) | 1.16515 | 0.0382686 | ||||||||
\(928\) | −49.3466 | −1.61988 | ||||||||
\(929\) | −21.3303 | −0.699825 | −0.349912 | − | 0.936782i | \(-0.613789\pi\) | ||||
−0.349912 | + | 0.936782i | \(0.613789\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.58258 | −0.215735 | ||||||||
\(932\) | 16.9220 | 0.554298 | ||||||||
\(933\) | 14.3303 | 0.469153 | ||||||||
\(934\) | −69.1125 | −2.26143 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.41742 | −0.0463300 | ||||||||
\(937\) | −10.0000 | −0.326686 | −0.163343 | − | 0.986569i | \(-0.552228\pi\) | ||||
−0.163343 | + | 0.986569i | \(0.552228\pi\) | |||||||
\(938\) | −15.3739 | −0.501974 | ||||||||
\(939\) | −19.5826 | −0.639053 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.1652 | 1.14635 | 0.573176 | − | 0.819433i | \(-0.305711\pi\) | ||||
0.573176 | + | 0.819433i | \(0.305711\pi\) | |||||||
\(942\) | 34.3303 | 1.11854 | ||||||||
\(943\) | −62.3303 | −2.02975 | ||||||||
\(944\) | −22.7133 | −0.739254 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.83485 | −0.0921689 | ||||||||
\(947\) | −45.1652 | −1.46767 | −0.733835 | − | 0.679328i | \(-0.762272\pi\) | ||||
−0.733835 | + | 0.679328i | \(0.762272\pi\) | |||||||
\(948\) | 8.66061 | 0.281283 | ||||||||
\(949\) | 7.00000 | 0.227230 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.4174 | 0.726935 | ||||||||
\(952\) | 10.7477 | 0.348336 | ||||||||
\(953\) | 28.1652 | 0.912359 | 0.456179 | − | 0.889888i | \(-0.349218\pi\) | ||||
0.456179 | + | 0.889888i | \(0.349218\pi\) | |||||||
\(954\) | −17.1652 | −0.555742 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.0436 | 0.648255 | ||||||||
\(957\) | 8.16515 | 0.263942 | ||||||||
\(958\) | 27.9129 | 0.901824 | ||||||||
\(959\) | −11.5826 | −0.374021 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.1652 | −0.585973 | ||||||||
\(962\) | −1.79129 | −0.0577534 | ||||||||
\(963\) | 12.5826 | 0.405468 | ||||||||
\(964\) | −12.2867 | −0.395729 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 10.0000 | 0.321745 | ||||||||
\(967\) | 13.1652 | 0.423363 | 0.211681 | − | 0.977339i | \(-0.432106\pi\) | ||||
0.211681 | + | 0.977339i | \(0.432106\pi\) | |||||||
\(968\) | 1.41742 | 0.0455577 | ||||||||
\(969\) | 49.9129 | 1.60343 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.5826 | −0.403794 | −0.201897 | − | 0.979407i | \(-0.564711\pi\) | ||||
−0.201897 | + | 0.979407i | \(0.564711\pi\) | |||||||
\(972\) | 1.20871 | 0.0387695 | ||||||||
\(973\) | −11.1652 | −0.357938 | ||||||||
\(974\) | 18.5045 | 0.592924 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −49.5644 | −1.58652 | ||||||||
\(977\) | −23.2523 | −0.743906 | −0.371953 | − | 0.928252i | \(-0.621312\pi\) | ||||
−0.371953 | + | 0.928252i | \(0.621312\pi\) | |||||||
\(978\) | 15.3739 | 0.491602 | ||||||||
\(979\) | −9.16515 | −0.292920 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.58258 | 0.114383 | ||||||||
\(982\) | 41.0436 | 1.30975 | ||||||||
\(983\) | 4.83485 | 0.154208 | 0.0771039 | − | 0.997023i | \(-0.475433\pi\) | ||||
0.0771039 | + | 0.997023i | \(0.475433\pi\) | |||||||
\(984\) | −15.8258 | −0.504507 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −110.904 | −3.53190 | ||||||||
\(987\) | 1.41742 | 0.0451171 | ||||||||
\(988\) | 7.95644 | 0.253128 | ||||||||
\(989\) | −8.83485 | −0.280932 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.2523 | −0.643335 | −0.321667 | − | 0.946853i | \(-0.604243\pi\) | ||||
−0.321667 | + | 0.946853i | \(0.604243\pi\) | |||||||
\(992\) | 21.6515 | 0.687436 | ||||||||
\(993\) | −3.16515 | −0.100443 | ||||||||
\(994\) | 20.0000 | 0.634361 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.0000 | 0.443607 | ||||||||
\(997\) | −10.6606 | −0.337625 | −0.168812 | − | 0.985648i | \(-0.553993\pi\) | ||||
−0.168812 | + | 0.985648i | \(0.553993\pi\) | |||||||
\(998\) | −74.7822 | −2.36719 | ||||||||
\(999\) | −1.00000 | −0.0316386 |
(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 | 5775.2.a.bn.1.1 | 2 | ||
5.4 | even | 2 | 231.2.a.b.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 693.2.a.j.1.1 | 2 | |||
20.19 | odd | 2 | 3696.2.a.bl.1.2 | 2 | |||
35.34 | odd | 2 | 1617.2.a.o.1.2 | 2 | |||
55.54 | odd | 2 | 2541.2.a.z.1.1 | 2 | |||
105.104 | even | 2 | 4851.2.a.ba.1.1 | 2 | |||
165.164 | even | 2 | 7623.2.a.bf.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.a.b.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
693.2.a.j.1.1 | 2 | 15.14 | odd | 2 | |||
1617.2.a.o.1.2 | 2 | 35.34 | odd | 2 | |||
2541.2.a.z.1.1 | 2 | 55.54 | odd | 2 | |||
3696.2.a.bl.1.2 | 2 | 20.19 | odd | 2 | |||
4851.2.a.ba.1.1 | 2 | 105.104 | even | 2 | |||
5775.2.a.bn.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7623.2.a.bf.1.2 | 2 | 165.164 | even | 2 |