Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 49 x^{14} + 130 x^{13} + 932 x^{12} - 2028 x^{11} - 8965 x^{10} + 14400 x^{9} + 46229 x^{8} - 47547 x^{7} - 122604 x^{6} + 65278 x^{5} + 151028 x^{4} + \cdots + 3888 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.900032\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.900032 | −0.402506 | −0.201253 | − | 0.979539i | \(-0.564501\pi\) | ||||
−0.201253 | + | 0.979539i | \(0.564501\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.226627 | 0.0856570 | 0.0428285 | − | 0.999082i | \(-0.486363\pi\) | ||||
0.0428285 | + | 0.999082i | \(0.486363\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.23685 | −0.975945 | −0.487973 | − | 0.872859i | \(-0.662263\pi\) | ||||
−0.487973 | + | 0.872859i | \(0.662263\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.29181 | −1.74503 | −0.872517 | − | 0.488583i | \(-0.837514\pi\) | ||||
−0.872517 | + | 0.488583i | \(0.837514\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.900032 | −0.232387 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.102835 | 0.0249411 | 0.0124705 | − | 0.999922i | \(-0.496030\pi\) | ||||
0.0124705 | + | 0.999922i | \(0.496030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.74323 | 1.54700 | 0.773502 | − | 0.633794i | \(-0.218503\pi\) | ||||
0.773502 | + | 0.633794i | \(0.218503\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.226627 | 0.0494541 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.18994 | −0.837989 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.708382 | −0.127229 | −0.0636146 | − | 0.997975i | \(-0.520263\pi\) | ||||
−0.0636146 | + | 0.997975i | \(0.520263\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.23685 | −0.563462 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.203972 | −0.0344775 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.94929 | 0.320461 | 0.160230 | − | 0.987080i | \(-0.448776\pi\) | ||||
0.160230 | + | 0.987080i | \(0.448776\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.29181 | −1.00750 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.13468 | −0.489555 | −0.244777 | − | 0.969579i | \(-0.578715\pi\) | ||||
−0.244777 | + | 0.969579i | \(0.578715\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.38054 | 0.668026 | 0.334013 | − | 0.942568i | \(-0.391597\pi\) | ||||
0.334013 | + | 0.942568i | \(0.391597\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.900032 | −0.134169 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.47641 | 0.944682 | 0.472341 | − | 0.881416i | \(-0.343409\pi\) | ||||
0.472341 | + | 0.881416i | \(0.343409\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.94864 | −0.992663 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.102835 | 0.0143997 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.91308 | −1.08694 | −0.543472 | − | 0.839427i | \(-0.682891\pi\) | ||||
−0.543472 | + | 0.839427i | \(0.682891\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.91326 | 0.392824 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.74323 | 0.893163 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.52648 | 1.11005 | 0.555027 | − | 0.831832i | \(-0.312708\pi\) | ||||
0.555027 | + | 0.831832i | \(0.312708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.66345 | 0.981205 | 0.490602 | − | 0.871384i | \(-0.336777\pi\) | ||||
0.490602 | + | 0.871384i | \(0.336777\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.226627 | 0.0285523 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.66283 | 0.702387 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4119 | 1.51636 | 0.758180 | − | 0.652045i | \(-0.226089\pi\) | ||||
0.758180 | + | 0.652045i | \(0.226089\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.53670 | 1.01312 | 0.506560 | − | 0.862205i | \(-0.330917\pi\) | ||||
0.506560 | + | 0.862205i | \(0.330917\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.34060 | 0.508029 | 0.254015 | − | 0.967200i | \(-0.418249\pi\) | ||||
0.254015 | + | 0.967200i | \(0.418249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.18994 | −0.483813 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.733557 | −0.0835965 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.86789 | −0.885207 | −0.442604 | − | 0.896717i | \(-0.645945\pi\) | ||||
−0.442604 | + | 0.896717i | \(0.645945\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.62194 | 0.726853 | 0.363426 | − | 0.931623i | \(-0.381607\pi\) | ||||
0.363426 | + | 0.931623i | \(0.381607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0925544 | −0.0100389 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.363565 | 0.0385378 | 0.0192689 | − | 0.999814i | \(-0.493866\pi\) | ||||
0.0192689 | + | 0.999814i | \(0.493866\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.42589 | −0.149474 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.708382 | −0.0734558 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.06912 | −0.622679 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.11380 | 0.925367 | 0.462683 | − | 0.886524i | \(-0.346887\pi\) | ||||
0.462683 | + | 0.886524i | \(0.346887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.23685 | −0.325315 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.0896 | −1.50147 | −0.750736 | − | 0.660603i | \(-0.770301\pi\) | ||||
−0.750736 | + | 0.660603i | \(0.770301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.89634 | 0.975115 | 0.487557 | − | 0.873091i | \(-0.337888\pi\) | ||||
0.487557 | + | 0.873091i | \(0.337888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.203972 | −0.0199056 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.93286 | −0.670225 | −0.335113 | − | 0.942178i | \(-0.608774\pi\) | ||||
−0.335113 | + | 0.942178i | \(0.608774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.80062 | 0.268251 | 0.134125 | − | 0.990964i | \(-0.457177\pi\) | ||||
0.134125 | + | 0.990964i | \(0.457177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.94929 | 0.185018 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.152376 | 0.0143344 | 0.00716718 | − | 0.999974i | \(-0.497719\pi\) | ||||
0.00716718 | + | 0.999974i | \(0.497719\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.900032 | −0.0839284 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.29181 | −0.581678 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0233051 | 0.00213638 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.522834 | −0.0475304 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.13468 | −0.282645 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.27124 | 0.739802 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.4073 | −0.923500 | −0.461750 | − | 0.887010i | \(-0.652778\pi\) | ||||
−0.461750 | + | 0.887010i | \(0.652778\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.38054 | 0.385685 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3477 | 0.991455 | 0.495727 | − | 0.868478i | \(-0.334902\pi\) | ||||
0.495727 | + | 0.868478i | \(0.334902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.52820 | 0.132512 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.900032 | −0.0774624 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.481635 | 0.0411488 | 0.0205744 | − | 0.999788i | \(-0.493450\pi\) | ||||
0.0205744 | + | 0.999788i | \(0.493450\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.40085 | −0.458094 | −0.229047 | − | 0.973415i | \(-0.573561\pi\) | ||||
−0.229047 | + | 0.973415i | \(0.573561\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.47641 | 0.545412 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.3656 | 1.70306 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.900032 | 0.0747436 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.94864 | −0.573114 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.66802 | 0.300496 | 0.150248 | − | 0.988648i | \(-0.451993\pi\) | ||||
0.150248 | + | 0.988648i | \(0.451993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.4106 | 1.41685 | 0.708427 | − | 0.705784i | \(-0.249405\pi\) | ||||
0.708427 | + | 0.705784i | \(0.249405\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.102835 | 0.00831369 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.637566 | 0.0512105 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.8723 | 1.42637 | 0.713184 | − | 0.700976i | \(-0.247252\pi\) | ||||
0.713184 | + | 0.700976i | \(0.247252\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.91308 | −0.627548 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.226627 | 0.0178607 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6475 | 1.06895 | 0.534477 | − | 0.845183i | \(-0.320509\pi\) | ||||
0.534477 | + | 0.845183i | \(0.320509\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.91326 | 0.226797 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0938 | −0.935847 | −0.467924 | − | 0.883769i | \(-0.654998\pi\) | ||||
−0.467924 | + | 0.883769i | \(0.654998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.5869 | 2.04515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.74323 | 0.515668 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5174 | 0.875649 | 0.437825 | − | 0.899060i | \(-0.355749\pi\) | ||||
0.437825 | + | 0.899060i | \(0.355749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.949555 | −0.0717796 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.52648 | 0.640890 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.23450 | −0.167014 | −0.0835072 | − | 0.996507i | \(-0.526612\pi\) | ||||
−0.0835072 | + | 0.996507i | \(0.526612\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.7251 | −1.46616 | −0.733078 | − | 0.680145i | \(-0.761917\pi\) | ||||
−0.733078 | + | 0.680145i | \(0.761917\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.66345 | 0.566499 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.75442 | −0.128987 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.332860 | −0.0243411 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.226627 | 0.0164847 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.6235 | 1.49227 | 0.746133 | − | 0.665797i | \(-0.231908\pi\) | ||||
0.746133 | + | 0.665797i | \(0.231908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.9362 | 1.00315 | 0.501576 | − | 0.865113i | \(-0.332754\pi\) | ||||
0.501576 | + | 0.865113i | \(0.332754\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.66283 | 0.405524 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.12354 | 0.436284 | 0.218142 | − | 0.975917i | \(-0.430000\pi\) | ||||
0.218142 | + | 0.975917i | \(0.430000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.1948 | 0.793576 | 0.396788 | − | 0.917910i | \(-0.370125\pi\) | ||||
0.396788 | + | 0.917910i | \(0.370125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4119 | 0.875471 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.226627 | −0.0159061 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.82131 | 0.197049 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.8268 | −1.50979 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3704 | 0.782770 | 0.391385 | − | 0.920227i | \(-0.371996\pi\) | ||||
0.391385 | + | 0.920227i | \(0.371996\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.53670 | 0.584925 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.94262 | −0.268885 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.160538 | −0.0108981 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.34060 | 0.293311 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.647016 | −0.0435230 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9124 | 0.797713 | 0.398856 | − | 0.917013i | \(-0.369407\pi\) | ||||
0.398856 | + | 0.917013i | \(0.369407\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.18994 | −0.279330 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.71622 | −0.578516 | −0.289258 | − | 0.957251i | \(-0.593409\pi\) | ||||
−0.289258 | + | 0.957251i | \(0.593409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.984405 | −0.0650513 | −0.0325256 | − | 0.999471i | \(-0.510355\pi\) | ||||
−0.0325256 | + | 0.999471i | \(0.510355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.733557 | −0.0482645 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.418820 | 0.0274378 | 0.0137189 | − | 0.999906i | \(-0.495633\pi\) | ||||
0.0137189 | + | 0.999906i | \(0.495633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.82898 | −0.380240 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.86789 | −0.511075 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.9016 | −0.769853 | −0.384927 | − | 0.922947i | \(-0.625773\pi\) | ||||
−0.384927 | + | 0.922947i | \(0.625773\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.4060 | 1.57213 | 0.786063 | − | 0.618146i | \(-0.212116\pi\) | ||||
0.786063 | + | 0.618146i | \(0.212116\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.25400 | 0.399553 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −42.4271 | −2.69957 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.62194 | 0.419649 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.2426 | 0.646504 | 0.323252 | − | 0.946313i | \(-0.395224\pi\) | ||||
0.323252 | + | 0.946313i | \(0.395224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.23685 | −0.203499 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0925544 | −0.00579598 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30.7464 | 1.91791 | 0.958955 | − | 0.283558i | \(-0.0915150\pi\) | ||||
0.958955 | + | 0.283558i | \(0.0915150\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.441761 | 0.0274497 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.2721 | 1.25003 | 0.625016 | − | 0.780612i | \(-0.285093\pi\) | ||||
0.625016 | + | 0.780612i | \(0.285093\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.12202 | 0.437502 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.363565 | 0.0222498 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.9148 | −1.82394 | −0.911970 | − | 0.410257i | \(-0.865439\pi\) | ||||
−0.911970 | + | 0.410257i | \(0.865439\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.3436 | −1.72175 | −0.860876 | − | 0.508814i | \(-0.830084\pi\) | ||||
−0.860876 | + | 0.508814i | \(0.830084\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.42589 | −0.0862991 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.5622 | 0.817831 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.98371 | 0.539779 | 0.269889 | − | 0.962891i | \(-0.413013\pi\) | ||||
0.269889 | + | 0.962891i | \(0.413013\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.708382 | −0.0424097 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.54304 | −0.330670 | −0.165335 | − | 0.986237i | \(-0.552871\pi\) | ||||
−0.165335 | + | 0.986237i | \(0.552871\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.89295 | 0.290856 | 0.145428 | − | 0.989369i | \(-0.453544\pi\) | ||||
0.145428 | + | 0.989369i | \(0.453544\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.06912 | −0.359504 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.710403 | −0.0419338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9894 | −0.999378 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.11380 | 0.534261 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.6786 | −1.61700 | −0.808502 | − | 0.588494i | \(-0.799721\pi\) | ||||
−0.808502 | + | 0.588494i | \(0.799721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.67410 | −0.446804 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.23685 | −0.187821 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.29181 | −0.363865 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.992749 | 0.0572211 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.0896 | −0.866875 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.89735 | −0.394941 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.47911 | 0.198563 | 0.0992817 | − | 0.995059i | \(-0.468346\pi\) | ||||
0.0992817 | + | 0.995059i | \(0.468346\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.89634 | 0.562983 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.6058 | 1.56538 | 0.782690 | − | 0.622412i | \(-0.213847\pi\) | ||||
0.782690 | + | 0.622412i | \(0.213847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0525 | 1.02039 | 0.510193 | − | 0.860060i | \(-0.329574\pi\) | ||||
0.510193 | + | 0.860060i | \(0.329574\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.203972 | −0.0114925 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.5432 | −0.985326 | −0.492663 | − | 0.870220i | \(-0.663976\pi\) | ||||
−0.492663 | + | 0.870220i | \(0.663976\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.23685 | 0.181229 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.93286 | −0.386955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.693438 | 0.0385839 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.3623 | 1.46232 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.80062 | 0.154875 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.46773 | 0.0809186 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.2002 | 1.11030 | 0.555152 | − | 0.831749i | \(-0.312660\pi\) | ||||
0.555152 | + | 0.831749i | \(0.312660\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.94929 | 0.106820 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.1711 | −0.610345 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.8573 | −1.78985 | −0.894926 | − | 0.446214i | \(-0.852772\pi\) | ||||
−0.894926 | + | 0.446214i | \(0.852772\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.152376 | 0.00827594 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.29292 | 0.124169 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.16114 | −0.170685 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.900032 | −0.0484561 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.9662 | −1.23289 | −0.616446 | − | 0.787397i | \(-0.711428\pi\) | ||||
−0.616446 | + | 0.787397i | \(0.711428\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.1157 | 1.87970 | 0.939851 | − | 0.341586i | \(-0.110964\pi\) | ||||
0.939851 | + | 0.341586i | \(0.110964\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.29181 | −0.335832 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.3890 | −0.552951 | −0.276475 | − | 0.961021i | \(-0.589166\pi\) | ||||
−0.276475 | + | 0.961021i | \(0.589166\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.68330 | −0.407787 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0233051 | 0.00123344 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.3495 | −1.54901 | −0.774504 | − | 0.632569i | \(-0.782000\pi\) | ||||
−0.774504 | + | 0.632569i | \(0.782000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.4712 | 1.39322 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.522834 | −0.0274417 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.90668 | −0.204485 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.2527 | 1.21378 | 0.606890 | − | 0.794786i | \(-0.292417\pi\) | ||||
0.606890 | + | 0.794786i | \(0.292417\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.13468 | −0.163185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.79332 | −0.0931044 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.204094 | −0.0105676 | −0.00528379 | − | 0.999986i | \(-0.501682\pi\) | ||||
−0.00528379 | + | 0.999986i | \(0.501682\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.27124 | 0.427125 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.29181 | 0.324045 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.2755 | −1.09285 | −0.546424 | − | 0.837508i | \(-0.684011\pi\) | ||||
−0.546424 | + | 0.837508i | \(0.684011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4073 | −0.533183 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.23847 | 0.216576 | 0.108288 | − | 0.994120i | \(-0.465463\pi\) | ||||
0.108288 | + | 0.994120i | \(0.465463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.660224 | 0.0336481 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.38054 | 0.222675 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.45435 | −0.0737385 | −0.0368693 | − | 0.999320i | \(-0.511739\pi\) | ||||
−0.0368693 | + | 0.999320i | \(0.511739\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.102835 | 0.00520057 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.3477 | 0.572417 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.08135 | 0.356302 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.88004 | 0.445677 | 0.222838 | − | 0.974855i | \(-0.428468\pi\) | ||||
0.222838 | + | 0.974855i | \(0.428468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.52820 | 0.0765056 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.93855 | −0.196682 | −0.0983409 | − | 0.995153i | \(-0.531354\pi\) | ||||
−0.0983409 | + | 0.995153i | \(0.531354\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.45700 | 0.222019 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.900032 | −0.0447229 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.30954 | −0.312752 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.6982 | −0.627886 | −0.313943 | − | 0.949442i | \(-0.601650\pi\) | ||||
−0.313943 | + | 0.949442i | \(0.601650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.481635 | 0.0237573 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.93233 | 0.0950838 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.95996 | −0.292563 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.40085 | −0.264481 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.97848 | 0.0966551 | 0.0483275 | − | 0.998832i | \(-0.484611\pi\) | ||||
0.0483275 | + | 0.998832i | \(0.484611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4852 | 0.803441 | 0.401721 | − | 0.915762i | \(-0.368412\pi\) | ||||
0.401721 | + | 0.915762i | \(0.368412\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.47641 | 0.314894 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.430871 | −0.0209003 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.73675 | 0.0840470 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.3656 | 0.983261 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.14755 | −0.151612 | −0.0758062 | − | 0.997123i | \(-0.524153\pi\) | ||||
−0.0758062 | + | 0.997123i | \(0.524153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7163 | −0.563050 | −0.281525 | − | 0.959554i | \(-0.590840\pi\) | ||||
−0.281525 | + | 0.959554i | \(0.590840\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.900032 | 0.0431532 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.74323 | 0.322573 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.20247 | −0.296028 | −0.148014 | − | 0.988985i | \(-0.547288\pi\) | ||||
−0.148014 | + | 0.988985i | \(0.547288\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.94864 | −0.330888 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.5271 | −1.11780 | −0.558902 | − | 0.829234i | \(-0.688777\pi\) | ||||
−0.558902 | + | 0.829234i | \(0.688777\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.327220 | −0.0155117 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.66802 | 0.173492 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.9587 | 1.46103 | 0.730517 | − | 0.682895i | \(-0.239279\pi\) | ||||
0.730517 | + | 0.682895i | \(0.239279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.1465 | 0.477779 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.4106 | 0.818021 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.28335 | 0.0601644 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.6330 | −1.10551 | −0.552753 | − | 0.833345i | \(-0.686423\pi\) | ||||
−0.552753 | + | 0.833345i | \(0.686423\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.102835 | 0.00479991 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.3619 | −1.13465 | −0.567324 | − | 0.823495i | \(-0.692021\pi\) | ||||
−0.567324 | + | 0.823495i | \(0.692021\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.140581 | −0.00653333 | −0.00326667 | − | 0.999995i | \(-0.501040\pi\) | ||||
−0.00326667 | + | 0.999995i | \(0.501040\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.637566 | 0.0295664 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.8526 | 0.964943 | 0.482471 | − | 0.875912i | \(-0.339739\pi\) | ||||
0.482471 | + | 0.875912i | \(0.339739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.81288 | 0.129887 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.8723 | 0.823514 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.1791 | −0.651957 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.2538 | −1.29637 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.91308 | −0.362315 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.5333 | 0.755426 | 0.377713 | − | 0.925923i | \(-0.376711\pi\) | ||||
0.377713 | + | 0.925923i | \(0.376711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.2645 | −0.559215 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.226627 | 0.0103119 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.20271 | −0.372466 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.8004 | −0.670671 | −0.335335 | − | 0.942099i | \(-0.608850\pi\) | ||||
−0.335335 | + | 0.942099i | \(0.608850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.6475 | 0.617161 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.0837 | −1.04175 | −0.520877 | − | 0.853632i | \(-0.674395\pi\) | ||||
−0.520877 | + | 0.853632i | \(0.674395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.102835 | −0.00463144 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.91326 | 0.130941 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.93465 | 0.0867808 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.57973 | −0.160251 | −0.0801254 | − | 0.996785i | \(-0.525532\pi\) | ||||
−0.0801254 | + | 0.996785i | \(0.525532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.0938 | −0.540312 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.8915 | −1.77867 | −0.889337 | − | 0.457252i | \(-0.848834\pi\) | ||||
−0.889337 | + | 0.457252i | \(0.848834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5811 | 0.604352 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.5869 | 1.18077 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.9187 | 1.06018 | 0.530089 | − | 0.847942i | \(-0.322159\pi\) | ||||
0.530089 | + | 0.847942i | \(0.322159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.983698 | 0.0435162 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.74323 | 0.297721 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.90701 | −0.392490 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.9631 | −0.921958 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.5174 | 0.505556 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.1944 | −0.709489 | −0.354745 | − | 0.934963i | \(-0.615432\pi\) | ||||
−0.354745 | + | 0.934963i | \(0.615432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.0996 | 1.79716 | 0.898580 | − | 0.438810i | \(-0.144600\pi\) | ||||
0.898580 | + | 0.438810i | \(0.144600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.949555 | −0.0414420 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.0728462 | −0.00317323 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.52648 | 0.370018 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.7228 | 0.854290 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.23979 | 0.269770 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.23450 | −0.0964258 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.4917 | 0.968785 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.4291 | 1.78118 | 0.890588 | − | 0.454811i | \(-0.150293\pi\) | ||||
0.890588 | + | 0.454811i | \(0.150293\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.7251 | −0.846485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.52065 | −0.107973 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.9184 | 0.766134 | 0.383067 | − | 0.923721i | \(-0.374868\pi\) | ||||
0.383067 | + | 0.923721i | \(0.374868\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.66345 | 0.327068 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.74323 | −0.287271 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.78308 | −0.0758242 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.75442 | −0.0744709 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.8199 | 1.00928 | 0.504640 | − | 0.863330i | \(-0.331625\pi\) | ||||
0.504640 | + | 0.863330i | \(0.331625\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.5615 | −1.16573 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.332860 | −0.0140534 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.58477 | 0.361805 | 0.180902 | − | 0.983501i | \(-0.442098\pi\) | ||||
0.180902 | + | 0.983501i | \(0.442098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.137143 | −0.00576967 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.226627 | 0.00951744 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.0076 | 1.42567 | 0.712836 | − | 0.701330i | \(-0.247410\pi\) | ||||
0.712836 | + | 0.701330i | \(0.247410\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.0231 | 1.04718 | 0.523591 | − | 0.851970i | \(-0.324592\pi\) | ||||
0.523591 | + | 0.851970i | \(0.324592\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.6235 | 0.861560 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.18994 | −0.174733 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.8134 | −0.949735 | −0.474868 | − | 0.880057i | \(-0.657504\pi\) | ||||
−0.474868 | + | 0.880057i | \(0.657504\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.9362 | 0.579170 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.50071 | 0.0622600 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.6134 | 1.06080 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.66283 | 0.234129 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.3056 | 0.590456 | 0.295228 | − | 0.955427i | \(-0.404604\pi\) | ||||
0.295228 | + | 0.955427i | \(0.404604\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.77678 | −0.196824 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.12354 | 0.251889 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.1392 | 0.744889 | 0.372445 | − | 0.928054i | \(-0.378520\pi\) | ||||
0.372445 | + | 0.928054i | \(0.378520\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0209753 | −0.000859905 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.1948 | 0.458171 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.3863 | 0.873820 | 0.436910 | − | 0.899505i | \(-0.356073\pi\) | ||||
0.436910 | + | 0.899505i | \(0.356073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.7899 | 1.29674 | 0.648368 | − | 0.761327i | \(-0.275452\pi\) | ||||
0.648368 | + | 0.761327i | \(0.275452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.4119 | 0.505453 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.470567 | 0.0191313 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.8911 | −0.847944 | −0.423972 | − | 0.905675i | \(-0.639365\pi\) | ||||
−0.423972 | + | 0.905675i | \(0.639365\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.226627 | −0.00918339 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.7484 | −1.64850 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.82497 | −0.235268 | −0.117634 | − | 0.993057i | \(-0.537531\pi\) | ||||
−0.117634 | + | 0.993057i | \(0.537531\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.82131 | 0.113766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.5710 | −1.67358 | −0.836792 | − | 0.547521i | \(-0.815572\pi\) | ||||
−0.836792 | + | 0.547521i | \(0.815572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.58491 | −0.184283 | −0.0921416 | − | 0.995746i | \(-0.529371\pi\) | ||||
−0.0921416 | + | 0.995746i | \(0.529371\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.0823937 | 0.00330103 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.5053 | 0.540214 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.8268 | −0.871678 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.200454 | 0.00799263 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.2896 | −0.728096 | −0.364048 | − | 0.931380i | \(-0.618606\pi\) | ||||
−0.364048 | + | 0.931380i | \(0.618606\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.3704 | 0.451933 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.36691 | 0.371715 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.7195 | 1.73223 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.53670 | 0.337707 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.2822 | 1.67005 | 0.835024 | − | 0.550213i | \(-0.185454\pi\) | ||||
0.835024 | + | 0.550213i | \(0.185454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0222 | 0.868471 | 0.434235 | − | 0.900799i | \(-0.357019\pi\) | ||||
0.434235 | + | 0.900799i | \(0.357019\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.94262 | −0.155241 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.98336 | −0.117288 | −0.0586439 | − | 0.998279i | \(-0.518678\pi\) | ||||
−0.0586439 | + | 0.998279i | \(0.518678\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.5989 | −1.08335 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.160538 | −0.00629200 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −38.5647 | −1.50915 | −0.754576 | − | 0.656213i | \(-0.772157\pi\) | ||||
−0.754576 | + | 0.656213i | \(0.772157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.2133 | −0.399067 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.34060 | 0.169343 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.04166 | −0.0795316 | −0.0397658 | − | 0.999209i | \(-0.512661\pi\) | ||||
−0.0397658 | + | 0.999209i | \(0.512661\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.3912 | 1.22098 | 0.610488 | − | 0.792025i | \(-0.290973\pi\) | ||||
0.610488 | + | 0.792025i | \(0.290973\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.647016 | −0.0251280 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.37543 | −0.0533368 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.9124 | 0.460560 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.8054 | −0.957602 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.8206 | 1.45788 | 0.728938 | − | 0.684579i | \(-0.240014\pi\) | ||||
0.728938 | + | 0.684579i | \(0.240014\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.18994 | −0.161271 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.7393 | 0.451177 | 0.225588 | − | 0.974223i | \(-0.427570\pi\) | ||||
0.225588 | + | 0.974223i | \(0.427570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.06543 | 0.0792641 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.71622 | −0.334006 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.03624 | −0.192706 | −0.0963531 | − | 0.995347i | \(-0.530718\pi\) | ||||
−0.0963531 | + | 0.995347i | \(0.530718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.433487 | −0.0165627 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.984405 | −0.0375574 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 49.7876 | 1.89676 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.4007 | 1.53691 | 0.768457 | − | 0.639902i | \(-0.221025\pi\) | ||||
0.768457 | + | 0.639902i | \(0.221025\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.733557 | −0.0278655 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.86094 | 0.184386 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.322354 | −0.0122100 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.418820 | 0.0158412 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.1231 | −0.986656 | −0.493328 | − | 0.869843i | \(-0.664220\pi\) | ||||
−0.493328 | + | 0.869843i | \(0.664220\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1445 | 0.495754 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.82898 | −0.219532 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.41971 | −0.128612 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.7522 | 0.854477 | 0.427239 | − | 0.904139i | \(-0.359486\pi\) | ||||
0.427239 | + | 0.904139i | \(0.359486\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.86789 | −0.295069 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.708382 | −0.0265291 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.3297 | −0.685492 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.9016 | −0.444475 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.1973 | −1.01429 | −0.507144 | − | 0.861861i | \(-0.669299\pi\) | ||||
−0.507144 | + | 0.861861i | \(0.669299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.24278 | 0.0835254 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.4060 | 0.907667 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.18994 | 0.155611 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.2288 | −0.898595 | −0.449298 | − | 0.893382i | \(-0.648326\pi\) | ||||
−0.449298 | + | 0.893382i | \(0.648326\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.450471 | 0.0166613 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.3863 | −1.52864 | −0.764320 | − | 0.644838i | \(-0.776925\pi\) | ||||
−0.764320 | + | 0.644838i | \(0.776925\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.25400 | 0.230682 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40.1755 | −1.47988 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.5874 | 1.45625 | 0.728124 | − | 0.685446i | \(-0.240393\pi\) | ||||
0.728124 | + | 0.685446i | \(0.240393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −42.4271 | −1.55860 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.4928 | 1.37548 | 0.687739 | − | 0.725958i | \(-0.258603\pi\) | ||||
0.687739 | + | 0.725958i | \(0.258603\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.30134 | −0.120952 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.62194 | 0.242284 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.57117 | −0.0574095 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.7428 | −0.756914 | −0.378457 | − | 0.925619i | \(-0.623545\pi\) | ||||
−0.378457 | + | 0.925619i | \(0.623545\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.2426 | 0.373260 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.6701 | −0.570293 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.5865 | −1.72956 | −0.864781 | − | 0.502149i | \(-0.832543\pi\) | ||||
−0.864781 | + | 0.502149i | \(0.832543\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.23685 | −0.117490 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.8468 | −1.19069 | −0.595347 | − | 0.803468i | \(-0.702986\pi\) | ||||
−0.595347 | + | 0.803468i | \(0.702986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.634697 | 0.0229776 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0925544 | −0.00334631 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −53.6470 | −1.93708 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.7101 | 1.21562 | 0.607809 | − | 0.794083i | \(-0.292049\pi\) | ||||
0.607809 | + | 0.794083i | \(0.292049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.7464 | 1.10731 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.8623 | −0.966171 | −0.483086 | − | 0.875573i | \(-0.660484\pi\) | ||||
−0.483086 | + | 0.875573i | \(0.660484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.96808 | 0.106617 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.441761 | 0.0158481 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.1379 | −0.757343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.6320 | −0.988750 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0857 | −0.574122 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.9018 | 1.42235 | 0.711173 | − | 0.703017i | \(-0.248164\pi\) | ||||
0.711173 | + | 0.703017i | \(0.248164\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.2721 | 0.721706 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.0345326 | 0.00122784 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.2170 | −1.71224 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.12202 | 0.252592 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.9592 | −0.459039 | −0.229519 | − | 0.973304i | \(-0.573715\pi\) | ||||
−0.229519 | + | 0.973304i | \(0.573715\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.666000 | 0.0235614 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.363565 | 0.0128459 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.0499 | −0.495809 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.203972 | −0.00718905 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.9148 | −1.05305 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.4405 | −1.10539 | −0.552695 | − | 0.833384i | \(-0.686400\pi\) | ||||
−0.552695 | + | 0.833384i | \(0.686400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.3379 | 1.20577 | 0.602884 | − | 0.797829i | \(-0.294018\pi\) | ||||
0.602884 | + | 0.797829i | \(0.294018\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.3436 | −0.994054 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.2832 | −0.430261 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.5390 | 1.03344 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.42589 | −0.0498248 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.9730 | 1.91857 | 0.959285 | − | 0.282439i | \(-0.0911436\pi\) | ||||
0.959285 | + | 0.282439i | \(0.0911436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.2273 | −1.36738 | −0.683688 | − | 0.729774i | \(-0.739625\pi\) | ||||
−0.683688 | + | 0.729774i | \(0.739625\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.5622 | 0.472175 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.8397 | 1.38536 | 0.692681 | − | 0.721245i | \(-0.256430\pi\) | ||||
0.692681 | + | 0.721245i | \(0.256430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.7285 | −0.824126 | −0.412063 | − | 0.911155i | \(-0.635192\pi\) | ||||
−0.412063 | + | 0.911155i | \(0.635192\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.98371 | 0.311641 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.714561 | −0.0247581 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.8848 | 0.376684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.708382 | −0.0244853 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.7974 | 0.579909 | 0.289955 | − | 0.957040i | \(-0.406360\pi\) | ||||
0.289955 | + | 0.957040i | \(0.406360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.54304 | −0.190912 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.9290 | −0.823184 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.118488 | −0.00407131 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.89295 | 0.167926 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.94929 | 0.0668206 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.47058 | 0.187309 | 0.0936546 | − | 0.995605i | \(-0.470145\pi\) | ||||
0.0936546 | + | 0.995605i | \(0.470145\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.06912 | −0.207560 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.0918 | −1.47199 | −0.735994 | − | 0.676988i | \(-0.763285\pi\) | ||||
−0.735994 | + | 0.676988i | \(0.763285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.2963 | 0.794859 | 0.397429 | − | 0.917633i | \(-0.369902\pi\) | ||||
0.397429 | + | 0.917633i | \(0.369902\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.710403 | −0.0242105 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.4776 | −0.969390 | −0.484695 | − | 0.874683i | \(-0.661069\pi\) | ||||
−0.484695 | + | 0.874683i | \(0.661069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.3660 | −0.352454 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9894 | −0.576991 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.4672 | 0.863914 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −78.0936 | −2.64610 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.11380 | 0.308456 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.87449 | 0.0633692 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.2552 | −1.08918 | −0.544590 | − | 0.838703i | \(-0.683315\pi\) | ||||
−0.544590 | + | 0.838703i | \(0.683315\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.6786 | −0.933577 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.0988 | −0.778218 | −0.389109 | − | 0.921192i | \(-0.627217\pi\) | ||||
−0.389109 | + | 0.921192i | \(0.627217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.3781 | 0.382904 | 0.191452 | − | 0.981502i | \(-0.438680\pi\) | ||||
0.191452 | + | 0.981502i | \(0.438680\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.67410 | −0.257962 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.1079 | 1.48100 | 0.740500 | − | 0.672056i | \(-0.234589\pi\) | ||||
0.740500 | + | 0.672056i | \(0.234589\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.35858 | −0.0791042 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.23685 | −0.108438 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43.6720 | 1.46143 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.01112 | 0.0672244 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.29181 | −0.210077 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.708382 | 0.0236259 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.813738 | −0.0271096 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.992749 | 0.0330366 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.7532 | 0.590137 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.9837 | 0.431116 | 0.215558 | − | 0.976491i | \(-0.430843\pi\) | ||||
0.215558 | + | 0.976491i | \(0.430843\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.0896 | −0.500490 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.39043 | 0.0791984 | 0.0395992 | − | 0.999216i | \(-0.487392\pi\) | ||||
0.0395992 | + | 0.999216i | \(0.487392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.4342 | −0.709369 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.89735 | −0.228019 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.57170 | 0.0849250 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.0414 | 0.463184 | 0.231592 | − | 0.972813i | \(-0.425607\pi\) | ||||
0.231592 | + | 0.972813i | \(0.425607\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.47911 | 0.114641 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −53.7113 | −1.76793 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.16740 | −0.268542 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.89634 | 0.325038 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.2034 | 1.05656 | 0.528280 | − | 0.849070i | \(-0.322837\pi\) | ||||
0.528280 | + | 0.849070i | \(0.322837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.8563 | −1.53565 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.6058 | 0.903773 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.299584 | 0.00979745 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.2319 | −1.28165 | −0.640826 | − | 0.767686i | \(-0.721408\pi\) | ||||
−0.640826 | + | 0.767686i | \(0.721408\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.0525 | 0.589121 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.0865 | 1.40458 | 0.702289 | − | 0.711892i | \(-0.252161\pi\) | ||||
0.702289 | + | 0.711892i | \(0.252161\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.13468 | −0.102079 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.203972 | −0.00663519 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.01457 | 0.162952 | 0.0814758 | − | 0.996675i | \(-0.474037\pi\) | ||||
0.0814758 | + | 0.996675i | \(0.474037\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.3103 | −0.886528 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.5432 | −0.568878 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.9570 | −0.387326 | −0.193663 | − | 0.981068i | \(-0.562037\pi\) | ||||
−0.193663 | + | 0.981068i | \(0.562037\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.5618 | −0.600647 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.23685 | 0.104632 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.109151 | 0.00352468 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4982 | −0.983813 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.93286 | −0.223408 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.5431 | −0.403775 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.19874 | 0.135022 | 0.0675112 | − | 0.997719i | \(-0.478494\pi\) | ||||
0.0675112 | + | 0.997719i | \(0.478494\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.693438 | 0.0222764 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.0968 | 0.805396 | 0.402698 | − | 0.915333i | \(-0.368073\pi\) | ||||
0.402698 | + | 0.915333i | \(0.368073\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.22398 | −0.0392390 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.3623 | 0.844270 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.68006 | −0.149728 | −0.0748642 | − | 0.997194i | \(-0.523852\pi\) | ||||
−0.0748642 | + | 0.997194i | \(0.523852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.17680 | −0.0376108 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.80062 | 0.0894170 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.5713 | −1.38971 | −0.694854 | − | 0.719151i | \(-0.744531\pi\) | ||||
−0.694854 | + | 0.719151i | \(0.744531\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.51138 | −0.175607 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.46773 | 0.0467184 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.38054 | 0.139293 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.3492 | −0.328752 | −0.164376 | − | 0.986398i | \(-0.552561\pi\) | ||||
−0.164376 | + | 0.986398i | \(0.552561\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.2002 | 0.641034 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.0756 | −0.319419 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.8284 | 0.722984 | 0.361492 | − | 0.932375i | \(-0.382268\pi\) | ||||
0.361492 | + | 0.932375i | \(0.382268\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.94929 | 0.0616727 |
(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 | 8004.2.a.j.1.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.j.1.6 | ✓ | 16 | 1.1 | even | 1 | trivial |