Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4704,2,Mod(1,4704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4704, 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("4704.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4704.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: | \(37.5616291108\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.22833\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4704.1 |
$q$-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 | ||||||||
\(5\) | −3.04244 | −1.36062 | −0.680311 | − | 0.732924i | \(-0.738155\pi\) | ||||
−0.680311 | + | 0.732924i | \(0.738155\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.93089 | −1.18521 | −0.592604 | − | 0.805494i | \(-0.701900\pi\) | ||||
−0.592604 | + | 0.805494i | \(0.701900\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.88845 | −1.35581 | −0.677906 | − | 0.735149i | \(-0.737112\pi\) | ||||
−0.677906 | + | 0.735149i | \(0.737112\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.04244 | 0.785555 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.34511 | 1.29638 | 0.648189 | − | 0.761479i | \(-0.275526\pi\) | ||||
0.648189 | + | 0.761479i | \(0.275526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.30266 | 0.528267 | 0.264134 | − | 0.964486i | \(-0.414914\pi\) | ||||
0.264134 | + | 0.964486i | \(0.414914\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.93089 | 1.65371 | 0.826853 | − | 0.562418i | \(-0.190129\pi\) | ||||
0.826853 | + | 0.562418i | \(0.190129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.25646 | 0.851292 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.55912 | 1.03230 | 0.516152 | − | 0.856497i | \(-0.327364\pi\) | ||||
0.516152 | + | 0.856497i | \(0.327364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.645810 | 0.115991 | 0.0579954 | − | 0.998317i | \(-0.481529\pi\) | ||||
0.0579954 | + | 0.998317i | \(0.481529\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.93089 | 0.684281 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.65685 | 0.929981 | 0.464991 | − | 0.885316i | \(-0.346058\pi\) | ||||
0.464991 | + | 0.885316i | \(0.346058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.88845 | 0.782779 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0886 | −1.57558 | −0.787791 | − | 0.615943i | \(-0.788775\pi\) | ||||
−0.787791 | + | 0.615943i | \(0.788775\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.91331 | −1.35927 | −0.679634 | − | 0.733552i | \(-0.737861\pi\) | ||||
−0.679634 | + | 0.733552i | \(0.737861\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.04244 | −0.453541 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.61065 | 0.964262 | 0.482131 | − | 0.876099i | \(-0.339863\pi\) | ||||
0.482131 | + | 0.876099i | \(0.339863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.34511 | −0.748465 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.25646 | 0.172588 | 0.0862939 | − | 0.996270i | \(-0.472498\pi\) | ||||
0.0862939 | + | 0.996270i | \(0.472498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.9595 | 1.61262 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.30266 | −0.304995 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.04621 | −0.396582 | −0.198291 | − | 0.980143i | \(-0.563539\pi\) | ||||
−0.198291 | + | 0.980143i | \(0.563539\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.97334 | 0.380697 | 0.190348 | − | 0.981717i | \(-0.439038\pi\) | ||||
0.190348 | + | 0.981717i | \(0.439038\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.8728 | 1.84475 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5186 | 1.65156 | 0.825782 | − | 0.563989i | \(-0.190734\pi\) | ||||
0.825782 | + | 0.563989i | \(0.190734\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.93089 | −0.954767 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5877 | 1.61257 | 0.806284 | − | 0.591528i | \(-0.201475\pi\) | ||||
0.806284 | + | 0.591528i | \(0.201475\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.67067 | −0.546661 | −0.273330 | − | 0.961920i | \(-0.588125\pi\) | ||||
−0.273330 | + | 0.961920i | \(0.588125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.25646 | −0.491494 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.05153 | 0.118306 | 0.0591530 | − | 0.998249i | \(-0.481160\pi\) | ||||
0.0591530 | + | 0.998249i | \(0.481160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.60533 | −0.944557 | −0.472279 | − | 0.881449i | \(-0.656568\pi\) | ||||
−0.472279 | + | 0.881449i | \(0.656568\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.2622 | −1.76388 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.55912 | −0.596001 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.85983 | −0.515140 | −0.257570 | − | 0.966260i | \(-0.582922\pi\) | ||||
−0.257570 | + | 0.966260i | \(0.582922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.645810 | −0.0669673 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.00572 | −0.718772 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.3275 | −1.86088 | −0.930439 | − | 0.366446i | \(-0.880574\pi\) | ||||
−0.930439 | + | 0.366446i | \(0.880574\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.93089 | −0.395070 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.87087 | −0.584173 | −0.292087 | − | 0.956392i | \(-0.594350\pi\) | ||||
−0.292087 | + | 0.956392i | \(0.594350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0778 | −1.48566 | −0.742828 | − | 0.669482i | \(-0.766516\pi\) | ||||
−0.742828 | + | 0.669482i | \(0.766516\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.238878 | −0.0230932 | −0.0115466 | − | 0.999933i | \(-0.503675\pi\) | ||||
−0.0115466 | + | 0.999933i | \(0.503675\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.9133 | −1.23687 | −0.618436 | − | 0.785836i | \(-0.712233\pi\) | ||||
−0.618436 | + | 0.785836i | \(0.712233\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.65685 | −0.536925 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.3137 | −1.25245 | −0.626224 | − | 0.779643i | \(-0.715401\pi\) | ||||
−0.626224 | + | 0.779643i | \(0.715401\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.1293 | −2.25007 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.88845 | −0.451937 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.45192 | 0.404720 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.0886 | 0.909663 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.26218 | 0.202336 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.69202 | −0.327613 | −0.163807 | − | 0.986492i | \(-0.552377\pi\) | ||||
−0.163807 | + | 0.986492i | \(0.552377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.91331 | 0.784773 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.4320 | 1.61041 | 0.805204 | − | 0.592998i | \(-0.202056\pi\) | ||||
0.805204 | + | 0.592998i | \(0.202056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.04244 | 0.261852 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.26750 | −0.364597 | −0.182299 | − | 0.983243i | \(-0.558354\pi\) | ||||
−0.182299 | + | 0.983243i | \(0.558354\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.31371 | 0.620341 | 0.310170 | − | 0.950681i | \(-0.399614\pi\) | ||||
0.310170 | + | 0.950681i | \(0.399614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.61065 | −0.556717 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.2160 | 1.60692 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.9133 | −1.40457 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.0572 | 1.15161 | 0.575807 | − | 0.817585i | \(-0.304688\pi\) | ||||
0.575807 | + | 0.817585i | \(0.304688\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.5702 | −1.83673 | −0.918367 | − | 0.395730i | \(-0.870492\pi\) | ||||
−0.918367 | + | 0.395730i | \(0.870492\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.34511 | 0.432126 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.96484 | −0.157820 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3147 | 0.982818 | 0.491409 | − | 0.870929i | \(-0.336482\pi\) | ||||
0.491409 | + | 0.870929i | \(0.336482\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.25646 | −0.0996436 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.45192 | −0.270375 | −0.135188 | − | 0.990820i | \(-0.543164\pi\) | ||||
−0.135188 | + | 0.990820i | \(0.543164\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.9595 | −0.931047 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.5076 | 0.967867 | 0.483933 | − | 0.875105i | \(-0.339208\pi\) | ||||
0.483933 | + | 0.875105i | \(0.339208\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8969 | 0.838227 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.30266 | 0.176089 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.0997 | −1.45212 | −0.726061 | − | 0.687630i | \(-0.758651\pi\) | ||||
−0.726061 | + | 0.687630i | \(0.758651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.04621 | 0.228967 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.6908 | 0.873811 | 0.436906 | − | 0.899507i | \(-0.356074\pi\) | ||||
0.436906 | + | 0.899507i | \(0.356074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.3204 | 0.841439 | 0.420720 | − | 0.907191i | \(-0.361778\pi\) | ||||
0.420720 | + | 0.907191i | \(0.361778\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.97334 | −0.219795 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.2107 | −1.26535 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.0110 | −1.53648 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9015 | 1.22295 | 0.611473 | − | 0.791265i | \(-0.290577\pi\) | ||||
0.611473 | + | 0.791265i | \(0.290577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.6884 | −1.70513 | −0.852565 | − | 0.522622i | \(-0.824954\pi\) | ||||
−0.852565 | + | 0.522622i | \(0.824954\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.8728 | −1.06507 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0831 | −0.789637 | −0.394819 | − | 0.918759i | \(-0.629193\pi\) | ||||
−0.394819 | + | 0.918759i | \(0.629193\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.51292 | 0.461688 | 0.230844 | − | 0.972991i | \(-0.425851\pi\) | ||||
0.230844 | + | 0.972991i | \(0.425851\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.5186 | −0.953531 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.6941 | 2.14377 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.93089 | 0.551235 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.05153 | −0.626107 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.83023 | −0.263684 | −0.131842 | − | 0.991271i | \(-0.542089\pi\) | ||||
−0.131842 | + | 0.991271i | \(0.542089\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.5877 | −0.931017 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.1182 | 1.84945 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.67067 | 0.315615 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.1293 | −1.75765 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4099 | −0.831026 | −0.415513 | − | 0.909587i | \(-0.636398\pi\) | ||||
−0.415513 | + | 0.909587i | \(0.636398\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.25646 | 0.283764 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.4782 | 1.16007 | 0.580033 | − | 0.814593i | \(-0.303040\pi\) | ||||
0.580033 | + | 0.814593i | \(0.303040\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.1783 | −1.39950 | −0.699750 | − | 0.714388i | \(-0.746705\pi\) | ||||
−0.699750 | + | 0.714388i | \(0.746705\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.75459 | 0.376995 | 0.188498 | − | 0.982074i | \(-0.439638\pi\) | ||||
0.188498 | + | 0.982074i | \(0.439638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.1125 | −1.31200 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.05153 | −0.0683040 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.93089 | 0.513007 | 0.256503 | − | 0.966543i | \(-0.417430\pi\) | ||||
0.256503 | + | 0.966543i | \(0.417430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.9605 | −1.35018 | −0.675092 | − | 0.737734i | \(-0.735896\pi\) | ||||
−0.675092 | + | 0.737734i | \(0.735896\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.2565 | −0.716231 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.60533 | 0.545340 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.45607 | 0.470623 | 0.235311 | − | 0.971920i | \(-0.424389\pi\) | ||||
0.235311 | + | 0.971920i | \(0.424389\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.1755 | −1.95999 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.2622 | 1.01838 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.3433 | 0.769954 | 0.384977 | − | 0.922926i | \(-0.374209\pi\) | ||||
0.384977 | + | 0.922926i | \(0.374209\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.55912 | 0.344101 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.4144 | −1.44379 | −0.721896 | − | 0.692002i | \(-0.756729\pi\) | ||||
−0.721896 | + | 0.692002i | \(0.756729\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.82270 | −0.234827 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.85983 | 0.297416 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.81362 | −0.354463 | −0.177231 | − | 0.984169i | \(-0.556714\pi\) | ||||
−0.177231 | + | 0.984169i | \(0.556714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.3694 | 1.48033 | 0.740167 | − | 0.672423i | \(-0.234746\pi\) | ||||
0.740167 | + | 0.672423i | \(0.234746\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.7317 | −1.00896 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7587 | 0.946851 | 0.473425 | − | 0.880834i | \(-0.343017\pi\) | ||||
0.473425 | + | 0.880834i | \(0.343017\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.645810 | 0.0386636 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.7698 | −1.83557 | −0.917786 | − | 0.397076i | \(-0.870025\pi\) | ||||
−0.917786 | + | 0.397076i | \(0.870025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.9080 | −1.36174 | −0.680869 | − | 0.732405i | \(-0.738398\pi\) | ||||
−0.680869 | + | 0.732405i | \(0.738398\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.00572 | 0.414983 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.5702 | 0.680598 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.3275 | 1.07438 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.3323 | −1.12940 | −0.564701 | − | 0.825295i | \(-0.691009\pi\) | ||||
−0.564701 | + | 0.825295i | \(0.691009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.26791 | 0.539598 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.93089 | 0.228094 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38.7698 | −2.24211 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.87087 | 0.337273 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.04621 | −0.517984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.8377 | 1.53171 | 0.765853 | − | 0.643015i | \(-0.222317\pi\) | ||||
0.765853 | + | 0.643015i | \(0.222317\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0778 | 0.857744 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.49240 | 0.198036 | 0.0990180 | − | 0.995086i | \(-0.468430\pi\) | ||||
0.0990180 | + | 0.995086i | \(0.468430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.75556 | 0.155753 | 0.0778767 | − | 0.996963i | \(-0.475186\pi\) | ||||
0.0778767 | + | 0.996963i | \(0.475186\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.15341 | −0.401775 | −0.200888 | − | 0.979614i | \(-0.564383\pi\) | ||||
−0.200888 | + | 0.979614i | \(0.564383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.8523 | −1.22349 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.238878 | 0.0133329 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.3080 | 0.684835 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.8075 | −1.15419 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.9133 | 0.714108 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.7236 | −1.74369 | −0.871843 | − | 0.489786i | \(-0.837075\pi\) | ||||
−0.871843 | + | 0.489786i | \(0.837075\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.65685 | 0.309994 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −41.1297 | −2.24716 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6053 | 0.686656 | 0.343328 | − | 0.939216i | \(-0.388446\pi\) | ||||
0.343328 | + | 0.939216i | \(0.388446\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.3137 | 0.723101 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.53861 | −0.137473 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.1293 | 1.29908 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.1064 | 1.66988 | 0.834939 | − | 0.550342i | \(-0.185503\pi\) | ||||
0.834939 | + | 0.550342i | \(0.185503\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.7741 | −0.844370 | −0.422185 | − | 0.906510i | \(-0.638737\pi\) | ||||
−0.422185 | + | 0.906510i | \(0.638737\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.88845 | 0.260926 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.3785 | 0.978187 | 0.489094 | − | 0.872231i | \(-0.337328\pi\) | ||||
0.489094 | + | 0.872231i | \(0.337328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −41.3399 | −2.19410 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.7575 | −0.937206 | −0.468603 | − | 0.883409i | \(-0.655243\pi\) | ||||
−0.468603 | + | 0.883409i | \(0.655243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.6977 | −0.720934 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.45192 | −0.233665 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.2103 | 0.743799 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.9449 | −1.09331 | −0.546657 | − | 0.837357i | \(-0.684100\pi\) | ||||
−0.546657 | + | 0.837357i | \(0.684100\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.0886 | −0.525194 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.2365 | −1.04781 | −0.523903 | − | 0.851778i | \(-0.675525\pi\) | ||||
−0.523903 | + | 0.851778i | \(0.675525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.26218 | −0.116819 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.1755 | −1.39961 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.5244 | −1.87613 | −0.938065 | − | 0.346459i | \(-0.887384\pi\) | ||||
−0.938065 | + | 0.346459i | \(0.887384\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.69202 | 0.189148 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.97417 | 0.151973 | 0.0759864 | − | 0.997109i | \(-0.475789\pi\) | ||||
0.0759864 | + | 0.997109i | \(0.475789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.91331 | −0.453089 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.16445 | −0.109742 | −0.0548710 | − | 0.998493i | \(-0.517475\pi\) | ||||
−0.0548710 | + | 0.998493i | \(0.517475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.3915 | 2.14383 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.4320 | −0.929769 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.19921 | −0.160970 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0249 | 0.603511 | 0.301755 | − | 0.953385i | \(-0.402427\pi\) | ||||
0.301755 | + | 0.953385i | \(0.402427\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.5591 | −1.07661 | −0.538306 | − | 0.842750i | \(-0.680935\pi\) | ||||
−0.538306 | + | 0.842750i | \(0.680935\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.15701 | −0.157262 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.04244 | −0.151180 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.2365 | −1.10222 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.5143 | 1.21215 | 0.606077 | − | 0.795406i | \(-0.292742\pi\) | ||||
0.606077 | + | 0.795406i | \(0.292742\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.26750 | 0.210500 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.1812 | 1.28519 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.31371 | −0.358154 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.3048 | −1.72475 | −0.862376 | − | 0.506269i | \(-0.831024\pi\) | ||||
−0.862376 | + | 0.506269i | \(0.831024\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.47776 | 0.120758 | 0.0603792 | − | 0.998176i | \(-0.480769\pi\) | ||||
0.0603792 | + | 0.998176i | \(0.480769\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.61065 | 0.321421 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.7512 | 1.10360 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.2160 | −0.927756 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.3408 | 0.979780 | 0.489890 | − | 0.871784i | \(-0.337037\pi\) | ||||
0.489890 | + | 0.871784i | \(0.337037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.7964 | −0.759129 | −0.379564 | − | 0.925165i | \(-0.623926\pi\) | ||||
−0.379564 | + | 0.925165i | \(0.623926\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.9133 | 0.810931 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.2622 | 0.873599 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6863 | 0.605484 | 0.302742 | − | 0.953073i | \(-0.402098\pi\) | ||||
0.302742 | + | 0.953073i | \(0.402098\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.9273 | 1.23184 | 0.615921 | − | 0.787808i | \(-0.288784\pi\) | ||||
0.615921 | + | 0.787808i | \(0.288784\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.7857 | 0.700911 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.0572 | −0.664885 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.6574 | 1.86739 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.5702 | 1.06044 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.7236 | 1.39041 | 0.695205 | − | 0.718811i | \(-0.255314\pi\) | ||||
0.695205 | + | 0.718811i | \(0.255314\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.34511 | −0.249488 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.6314 | −0.588303 | −0.294152 | − | 0.955759i | \(-0.595037\pi\) | ||||
−0.294152 | + | 0.955759i | \(0.595037\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.6884 | −1.56563 | −0.782817 | − | 0.622252i | \(-0.786218\pi\) | ||||
−0.782817 | + | 0.622252i | \(0.786218\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.96484 | 0.0911172 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.0941 | −1.57769 | −0.788844 | − | 0.614593i | \(-0.789320\pi\) | ||||
−0.788844 | + | 0.614593i | \(0.789320\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.3147 | −0.567431 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.0373 | 1.61102 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.80119 | 0.449710 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.25646 | 0.0575293 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.0977317 | 0.00446547 | 0.00223274 | − | 0.999998i | \(-0.499289\pi\) | ||||
0.00223274 | + | 0.999998i | \(0.499289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.6533 | −1.26088 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 55.7605 | 2.53195 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.5702 | −1.74778 | −0.873891 | − | 0.486123i | \(-0.838411\pi\) | ||||
−0.873891 | + | 0.486123i | \(0.838411\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.45192 | 0.156101 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0748 | −0.860835 | −0.430418 | − | 0.902630i | \(-0.641634\pi\) | ||||
−0.430418 | + | 0.902630i | \(0.641634\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.7141 | 1.33826 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.9595 | 0.537540 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.05725 | −0.360692 | −0.180346 | − | 0.983603i | \(-0.557722\pi\) | ||||
−0.180346 | + | 0.983603i | \(0.557722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.5076 | −0.558798 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.94487 | −0.220481 | −0.110240 | − | 0.993905i | \(-0.535162\pi\) | ||||
−0.110240 | + | 0.993905i | \(0.535162\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.8618 | 0.794839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.8969 | −0.483950 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.2161 | −1.64958 | −0.824788 | − | 0.565442i | \(-0.808706\pi\) | ||||
−0.824788 | + | 0.565442i | \(0.808706\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.30266 | −0.101665 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 45.8732 | 2.02142 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.9858 | −1.14285 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.0997 | 0.838383 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.1050 | −0.574141 | −0.287071 | − | 0.957909i | \(-0.592681\pi\) | ||||
−0.287071 | + | 0.957909i | \(0.592681\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.5795 | −0.856151 | −0.428076 | − | 0.903743i | \(-0.640808\pi\) | ||||
−0.428076 | + | 0.903743i | \(0.640808\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.45192 | 0.150368 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.8991 | 1.73474 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.04621 | −0.132194 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.3179 | 2.13619 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.726773 | 0.0314211 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.6908 | −0.504495 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9648 | −0.514409 | −0.257204 | − | 0.966357i | \(-0.582801\pi\) | ||||
−0.257204 | + | 0.966357i | \(0.582801\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.3204 | −0.485805 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.2880 | 1.68291 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.8827 | 1.70526 | 0.852631 | − | 0.522514i | \(-0.175006\pi\) | ||||
0.852631 | + | 0.522514i | \(0.175006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.97334 | 0.126899 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.8008 | 0.545332 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.2107 | 0.730552 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.9800 | 1.22792 | 0.613962 | − | 0.789336i | \(-0.289575\pi\) | ||||
0.613962 | + | 0.789336i | \(0.289575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.5723 | 1.84291 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.0110 | 0.887087 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.3857 | −1.15417 | −0.577086 | − | 0.816683i | \(-0.695810\pi\) | ||||
−0.577086 | + | 0.816683i | \(0.695810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.5062 | 1.70411 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.37056 | −0.267068 | −0.133534 | − | 0.991044i | \(-0.542632\pi\) | ||||
−0.133534 | + | 0.991044i | \(0.542632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.9485 | −0.625574 | −0.312787 | − | 0.949823i | \(-0.601263\pi\) | ||||
−0.312787 | + | 0.949823i | \(0.601263\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.9015 | −0.706068 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.7575 | 1.40779 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.21500 | 0.258734 | 0.129367 | − | 0.991597i | \(-0.458705\pi\) | ||||
0.129367 | + | 0.991597i | \(0.458705\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.6884 | 0.984457 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.93900 | −0.204553 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.8728 | 0.614916 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.0462 | −1.11632 | −0.558158 | − | 0.829735i | \(-0.688492\pi\) | ||||
−0.558158 | + | 0.829735i | \(0.688492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.48708 | 0.0612742 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0831 | 0.455897 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.8837 | 0.652266 | 0.326133 | − | 0.945324i | \(-0.394254\pi\) | ||||
0.326133 | + | 0.945324i | \(0.394254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.51292 | −0.266556 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.24820 | 0.214436 | 0.107218 | − | 0.994236i | \(-0.465806\pi\) | ||||
0.107218 | + | 0.994236i | \(0.465806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.3830 | 1.36172 | 0.680860 | − | 0.732414i | \(-0.261606\pi\) | ||||
0.680860 | + | 0.732414i | \(0.261606\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.5186 | 0.550522 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.5447 | −0.550671 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.9228 | 0.768052 | 0.384026 | − | 0.923322i | \(-0.374537\pi\) | ||||
0.384026 | + | 0.923322i | \(0.374537\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.3158 | −1.30736 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4928 | 0.504580 | 0.252290 | − | 0.967652i | \(-0.418816\pi\) | ||||
0.252290 | + | 0.967652i | \(0.418816\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −30.6941 | −1.23771 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.4230 | 1.38582 | 0.692910 | − | 0.721025i | \(-0.256329\pi\) | ||||
0.692910 | + | 0.721025i | \(0.256329\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6381 | −0.909900 | −0.454950 | − | 0.890517i | \(-0.650343\pi\) | ||||
−0.454950 | + | 0.890517i | \(0.650343\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.93089 | −0.318256 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.1649 | −1.12659 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.05153 | 0.361483 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.2365 | 1.20561 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.3489 | −1.00912 | −0.504561 | − | 0.863376i | \(-0.668346\pi\) | ||||
−0.504561 | + | 0.863376i | \(0.668346\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.83023 | 0.152238 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.2327 | 0.445758 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.5877 | 0.537523 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2196 | −0.522142 | −0.261071 | − | 0.965320i | \(-0.584076\pi\) | ||||
−0.261071 | + | 0.965320i | \(0.584076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.7194 | 0.935403 | 0.467701 | − | 0.883887i | \(-0.345082\pi\) | ||||
0.467701 | + | 0.883887i | \(0.345082\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.1182 | −1.06778 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.8213 | 0.622000 | 0.311000 | − | 0.950410i | \(-0.399336\pi\) | ||||
0.311000 | + | 0.950410i | \(0.399336\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.9743 | 0.470033 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4561 | 0.761375 | 0.380687 | − | 0.924704i | \(-0.375687\pi\) | ||||
0.380687 | + | 0.924704i | \(0.375687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −56.0782 | −2.19116 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.67067 | −0.182220 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5820 | 0.412217 | 0.206109 | − | 0.978529i | \(-0.433920\pi\) | ||||
0.206109 | + | 0.978529i | \(0.433920\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.95814 | −0.387327 | −0.193663 | − | 0.981068i | \(-0.562037\pi\) | ||||
−0.193663 | + | 0.981068i | \(0.562037\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.1293 | 1.01478 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.0888 | 1.70713 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.4099 | 0.479793 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.6879 | −0.451205 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0724 | −0.812283 | −0.406141 | − | 0.913810i | \(-0.633126\pi\) | ||||
−0.406141 | + | 0.913810i | \(0.633126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.25646 | −0.163831 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.66021 | 0.179107 | 0.0895533 | − | 0.995982i | \(-0.471456\pi\) | ||||
0.0895533 | + | 0.995982i | \(0.471456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.4782 | −0.669765 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.24820 | 0.353873 | 0.176936 | − | 0.984222i | \(-0.443381\pi\) | ||||
0.176936 | + | 0.984222i | \(0.443381\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9836 | 0.496079 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.1783 | 0.808001 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.14214 | −0.233997 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0924 | 0.383933 | 0.191967 | − | 0.981401i | \(-0.438513\pi\) | ||||
0.191967 | + | 0.981401i | \(0.438513\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.2515 | −0.844049 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53.9249 | −2.04255 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.75459 | −0.217658 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.0683 | 0.644661 | 0.322330 | − | 0.946627i | \(-0.395534\pi\) | ||||
0.322330 | + | 0.946627i | \(0.395534\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.0258 | 0.491279 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.1125 | 0.757481 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.2012 | −1.02156 | −0.510781 | − | 0.859711i | \(-0.670644\pi\) | ||||
−0.510781 | + | 0.859711i | \(0.670644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.05153 | 0.0394353 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.12185 | 0.191815 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −58.4635 | −2.18641 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.93089 | −0.296185 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.5350 | −0.915001 | −0.457501 | − | 0.889209i | \(-0.651255\pi\) | ||||
−0.457501 | + | 0.889209i | \(0.651255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.9605 | 0.779529 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.6622 | 0.878791 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.7603 | 1.51172 | 0.755858 | − | 0.654735i | \(-0.227220\pi\) | ||||
0.755858 | + | 0.654735i | \(0.227220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.6426 | −1.76213 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.1318 | 1.03907 | 0.519537 | − | 0.854448i | \(-0.326105\pi\) | ||||
0.519537 | + | 0.854448i | \(0.326105\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −53.1403 | −1.95745 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.6626 | 0.465800 | 0.232900 | − | 0.972501i | \(-0.425178\pi\) | ||||
0.232900 | + | 0.972501i | \(0.425178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.2565 | 0.413516 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.3477 | 0.489678 | 0.244839 | − | 0.969564i | \(-0.421265\pi\) | ||||
0.244839 | + | 0.969564i | \(0.421265\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −42.7684 | −1.56691 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.60533 | −0.314852 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2843 | 1.03211 | 0.516054 | − | 0.856556i | \(-0.327400\pi\) | ||||
0.516054 | + | 0.856556i | \(0.327400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.45607 | −0.271714 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 68.6684 | 2.49910 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.71410 | 0.353065 | 0.176533 | − | 0.984295i | \(-0.443512\pi\) | ||||
0.176533 | + | 0.984295i | \(0.443512\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 31.1755 | 1.13160 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.5569 | 0.600188 | 0.300094 | − | 0.953910i | \(-0.402982\pi\) | ||||
0.300094 | + | 0.953910i | \(0.402982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.2622 | −0.587960 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.8912 | 0.537691 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.3884 | 0.446736 | 0.223368 | − | 0.974734i | \(-0.428295\pi\) | ||||
0.223368 | + | 0.974734i | \(0.428295\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.3433 | −0.444533 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 55.4211 | 1.99336 | 0.996679 | − | 0.0814351i | \(-0.0259503\pi\) | ||||
0.996679 | + | 0.0814351i | \(0.0259503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.74886 | 0.0987421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.2308 | −0.832329 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.4120 | −1.91123 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.55912 | −0.198667 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.4667 | −1.33724 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.4061 | −0.477877 | −0.238938 | − | 0.971035i | \(-0.576799\pi\) | ||||
−0.238938 | + | 0.971035i | \(0.576799\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.4144 | 0.833574 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.5350 | −0.516153 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.82270 | 0.135577 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.4837 | 0.938102 | 0.469051 | − | 0.883171i | \(-0.344596\pi\) | ||||
0.469051 | + | 0.883171i | \(0.344596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.3346 | 1.25005 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.85983 | −0.171713 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.3599 | 0.647907 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.81362 | 0.204649 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.5760 | −1.28594 | −0.642972 | − | 0.765889i | \(-0.722299\pi\) | ||||
−0.642972 | + | 0.765889i | \(0.722299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.67565 | −0.164184 | −0.0820921 | − | 0.996625i | \(-0.526160\pi\) | ||||
−0.0820921 | + | 0.996625i | \(0.526160\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.3694 | −0.854672 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5023 | 0.367879 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.5244 | −0.718057 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.9212 | −1.49796 | −0.748979 | − | 0.662593i | \(-0.769456\pi\) | ||||
−0.748979 | + | 0.662593i | \(0.769456\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0888 | 0.421389 | 0.210695 | − | 0.977552i | \(-0.432427\pi\) | ||||
0.210695 | + | 0.977552i | \(0.432427\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.7317 | 0.582522 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.23676 | 0.112553 | 0.0562765 | − | 0.998415i | \(-0.482077\pi\) | ||||
0.0562765 | + | 0.998415i | \(0.482077\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.06002 | 0.0715476 | 0.0357738 | − | 0.999360i | \(-0.488610\pi\) | ||||
0.0357738 | + | 0.999360i | \(0.488610\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.7587 | −0.546664 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.0536 | −1.31690 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.645810 | −0.0223224 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.99468 | 0.206959 | 0.103480 | − | 0.994632i | \(-0.467002\pi\) | ||||
0.103480 | + | 0.994632i | \(0.467002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.90384 | 0.0656498 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.7698 | 1.05977 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33.1533 | −1.14051 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.9080 | 0.786200 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.8639 | 1.53791 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.3040 | 1.37998 | 0.689992 | − | 0.723817i | \(-0.257614\pi\) | ||||
0.689992 | + | 0.723817i | \(0.257614\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.00572 | −0.239591 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.1735 | −0.825752 | −0.412876 | − | 0.910787i | \(-0.635476\pi\) | ||||
−0.412876 | + | 0.910787i | \(0.635476\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6316 | 0.772179 | 0.386090 | − | 0.922461i | \(-0.373826\pi\) | ||||
0.386090 | + | 0.922461i | \(0.373826\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.9015 | 1.66462 | 0.832312 | − | 0.554307i | \(-0.187017\pi\) | ||||
0.832312 | + | 0.554307i | \(0.187017\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.1097 | 1.97579 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.5702 | −0.392943 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.13344 | −0.140217 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −66.0852 | −2.23921 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.3275 | −0.620293 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.1461 | −1.08550 | −0.542748 | − | 0.839896i | \(-0.682616\pi\) | ||||
−0.542748 | + | 0.839896i | \(0.682616\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.3323 | 0.652061 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.94291 | −0.0654583 | −0.0327291 | − | 0.999464i | \(-0.510420\pi\) | ||||
−0.0327291 | + | 0.999464i | \(0.510420\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.8770 | −1.64484 | −0.822421 | − | 0.568880i | \(-0.807377\pi\) | ||||
−0.822421 | + | 0.568880i | \(0.807377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.26791 | −0.311537 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.59546 | 0.187877 | 0.0939385 | − | 0.995578i | \(-0.470054\pi\) | ||||
0.0939385 | + | 0.995578i | \(0.470054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.93089 | −0.131690 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.2221 | 0.509388 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.5686 | −1.18893 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 38.7698 | 1.29449 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.59014 | 0.119738 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.71591 | 0.223739 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −34.4417 | −1.14488 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.0945 | −1.69657 | −0.848283 | − | 0.529543i | \(-0.822363\pi\) | ||||
−0.848283 | + | 0.529543i | \(0.822363\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.87087 | −0.194724 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6965 | −0.751969 | −0.375985 | − | 0.926626i | \(-0.622695\pi\) | ||||
−0.375985 | + | 0.926626i | \(0.622695\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.8266 | 1.11950 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.04621 | 0.299058 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9836 | 0.428291 | 0.214145 | − | 0.976802i | \(-0.431303\pi\) | ||||
0.214145 | + | 0.976802i | \(0.431303\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.8377 | −0.884331 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −66.4230 | −2.18634 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.0782 | 0.791685 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.0778 | −0.495219 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.84856 | 0.0606491 | 0.0303246 | − | 0.999540i | \(-0.490346\pi\) | ||||
0.0303246 | + | 0.999540i | \(0.490346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.49240 | −0.114336 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 63.9249 | 2.09057 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.0177 | 1.73201 | 0.866007 | − | 0.500032i | \(-0.166678\pi\) | ||||
0.866007 | + | 0.500032i | \(0.166678\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.75556 | −0.0899242 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.9615 | 0.357334 | 0.178667 | − | 0.983910i | \(-0.442822\pi\) | ||||
0.178667 | + | 0.983910i | \(0.442822\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −80.0120 | −2.60555 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.61718 | 0.280021 | 0.140010 | − | 0.990150i | \(-0.455286\pi\) | ||||
0.140010 | + | 0.990150i | \(0.455286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.8323 | 0.741169 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.15341 | 0.231965 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.40986 | 0.207636 | 0.103818 | − | 0.994596i | \(-0.466894\pi\) | ||||
0.103818 | + | 0.994596i | \(0.466894\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −51.4217 | −1.66397 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.8523 | 0.706385 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5829 | −0.986546 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.238878 | −0.00769774 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 72.0706 | 2.32004 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.2749 | 1.39163 | 0.695814 | − | 0.718222i | \(-0.255044\pi\) | ||||
0.695814 | + | 0.718222i | \(0.255044\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.3080 | −0.395389 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.8266 | −0.700450 | −0.350225 | − | 0.936666i | \(-0.613895\pi\) | ||||
−0.350225 | + | 0.936666i | \(0.613895\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.8075 | 0.666373 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −58.5040 | −1.87171 | −0.935854 | − | 0.352387i | \(-0.885370\pi\) | ||||
−0.935854 | + | 0.352387i | \(0.885370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.1035 | 0.610549 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.9133 | −0.412290 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.17337 | 0.196900 | 0.0984500 | − | 0.995142i | \(-0.468612\pi\) | ||||
0.0984500 | + | 0.995142i | \(0.468612\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.7197 | 1.07440 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −70.6905 | −2.24783 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.11942 | −0.162624 | −0.0813118 | − | 0.996689i | \(-0.525911\pi\) | ||||
−0.0813118 | + | 0.996689i | \(0.525911\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.7236 | 1.00672 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.8152 | −0.628183 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.7448 | −1.57543 | −0.787717 | − | 0.616037i | \(-0.788737\pi\) | ||||
−0.787717 | + | 0.616037i | \(0.788737\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.65685 | −0.178975 |
(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 | 4704.2.a.bw.1.2 | ✓ | 4 | |
4.3 | odd | 2 | 4704.2.a.by.1.2 | yes | 4 | ||
7.6 | odd | 2 | 4704.2.a.bz.1.3 | yes | 4 | ||
8.3 | odd | 2 | 9408.2.a.el.1.3 | 4 | |||
8.5 | even | 2 | 9408.2.a.en.1.3 | 4 | |||
28.27 | even | 2 | 4704.2.a.bx.1.3 | yes | 4 | ||
56.13 | odd | 2 | 9408.2.a.ek.1.2 | 4 | |||
56.27 | even | 2 | 9408.2.a.em.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4704.2.a.bw.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4704.2.a.bx.1.3 | yes | 4 | 28.27 | even | 2 | ||
4704.2.a.by.1.2 | yes | 4 | 4.3 | odd | 2 | ||
4704.2.a.bz.1.3 | yes | 4 | 7.6 | odd | 2 | ||
9408.2.a.ek.1.2 | 4 | 56.13 | odd | 2 | |||
9408.2.a.el.1.3 | 4 | 8.3 | odd | 2 | |||
9408.2.a.em.1.2 | 4 | 56.27 | even | 2 | |||
9408.2.a.en.1.3 | 4 | 8.5 | even | 2 |