Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.36147\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(5\) | −2.36147 | −1.05608 | −0.528040 | − | 0.849219i | \(-0.677073\pi\) | ||||
−0.528040 | + | 0.849219i | \(0.677073\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.93800 | −1.79038 | −0.895188 | − | 0.445689i | \(-0.852959\pi\) | ||||
−0.895188 | + | 0.445689i | \(0.852959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.29947 | 1.74716 | 0.873580 | − | 0.486681i | \(-0.161793\pi\) | ||||
0.873580 | + | 0.486681i | \(0.161793\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.36147 | −0.609729 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.784934 | 0.190374 | 0.0951872 | − | 0.995459i | \(-0.469655\pi\) | ||||
0.0951872 | + | 0.995459i | \(0.469655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.93800 | 0.444608 | 0.222304 | − | 0.974977i | \(-0.428642\pi\) | ||||
0.222304 | + | 0.974977i | \(0.428642\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.576535 | 0.115307 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.93800 | −1.42571 | −0.712854 | − | 0.701313i | \(-0.752598\pi\) | ||||
−0.712854 | + | 0.701313i | \(0.752598\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.93800 | −1.03367 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.36147 | 0.399161 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.72294 | −1.26964 | −0.634822 | − | 0.772659i | \(-0.718926\pi\) | ||||
−0.634822 | + | 0.772659i | \(0.718926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.29947 | 1.00872 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.15307 | 0.960948 | 0.480474 | − | 0.877009i | \(-0.340465\pi\) | ||||
0.480474 | + | 0.877009i | \(0.340465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.0224 | 1.98590 | 0.992949 | − | 0.118539i | \(-0.0378210\pi\) | ||||
0.992949 | + | 0.118539i | \(0.0378210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.36147 | −0.352027 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.215066 | −0.0313706 | −0.0156853 | − | 0.999877i | \(-0.504993\pi\) | ||||
−0.0156853 | + | 0.999877i | \(0.504993\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.784934 | 0.109913 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.14640 | 0.294831 | 0.147416 | − | 0.989075i | \(-0.452905\pi\) | ||||
0.147416 | + | 0.989075i | \(0.452905\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.0224 | 1.89078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.93800 | 0.256695 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.7296 | −1.52706 | −0.763532 | − | 0.645770i | \(-0.776537\pi\) | ||||
−0.763532 | + | 0.645770i | \(0.776537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.51454 | −0.578027 | −0.289014 | − | 0.957325i | \(-0.593327\pi\) | ||||
−0.289014 | + | 0.957325i | \(0.593327\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.8760 | −1.84514 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.993333 | −0.121355 | −0.0606775 | − | 0.998157i | \(-0.519326\pi\) | ||||
−0.0606775 | + | 0.998157i | \(0.519326\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.51454 | 0.535777 | 0.267889 | − | 0.963450i | \(-0.413674\pi\) | ||||
0.267889 | + | 0.963450i | \(0.413674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.35480 | −0.275609 | −0.137804 | − | 0.990459i | \(-0.544005\pi\) | ||||
−0.137804 | + | 0.990459i | \(0.544005\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.576535 | 0.0665725 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.93800 | 0.676698 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.492128 | −0.0553688 | −0.0276844 | − | 0.999617i | \(-0.508813\pi\) | ||||
−0.0276844 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.07774 | −0.996411 | −0.498206 | − | 0.867059i | \(-0.666008\pi\) | ||||
−0.498206 | + | 0.867059i | \(0.666008\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.85360 | −0.201051 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.00000 | 0.536056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.51454 | −0.478540 | −0.239270 | − | 0.970953i | \(-0.576908\pi\) | ||||
−0.239270 | + | 0.970953i | \(0.576908\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.29947 | −0.660364 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.93800 | −0.823133 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.57653 | −0.469543 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.59894 | 0.568487 | 0.284243 | − | 0.958752i | \(-0.408258\pi\) | ||||
0.284243 | + | 0.958752i | \(0.408258\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.93800 | −0.596792 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.29947 | −0.129302 | −0.0646512 | − | 0.997908i | \(-0.520593\pi\) | ||||
−0.0646512 | + | 0.997908i | \(0.520593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.38388 | 0.826088 | 0.413044 | − | 0.910711i | \(-0.364466\pi\) | ||||
0.413044 | + | 0.910711i | \(0.364466\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.36147 | 0.230456 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.36147 | −0.905007 | −0.452504 | − | 0.891763i | \(-0.649469\pi\) | ||||
−0.452504 | + | 0.891763i | \(0.649469\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.06866 | −0.198142 | −0.0990710 | − | 0.995080i | \(-0.531587\pi\) | ||||
−0.0990710 | + | 0.995080i | \(0.531587\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.72294 | −0.733029 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.9604 | −1.59550 | −0.797751 | − | 0.602987i | \(-0.793977\pi\) | ||||
−0.797751 | + | 0.602987i | \(0.793977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.36147 | −0.220208 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.29947 | 0.582386 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.784934 | −0.0719548 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.2599 | 2.20544 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.15307 | 0.554804 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4459 | 0.934307 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.5923 | 1.47233 | 0.736163 | − | 0.676804i | \(-0.236636\pi\) | ||||
0.736163 | + | 0.676804i | \(0.236636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.0224 | 1.14656 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.2151 | −1.15461 | −0.577303 | − | 0.816530i | \(-0.695895\pi\) | ||||
−0.577303 | + | 0.816530i | \(0.695895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.93800 | −0.168046 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.36147 | −0.203243 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.0000 | −1.11066 | −0.555332 | − | 0.831628i | \(-0.687409\pi\) | ||||
−0.555332 | + | 0.831628i | \(0.687409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.22173 | −0.103626 | −0.0518130 | − | 0.998657i | \(-0.516500\pi\) | ||||
−0.0518130 | + | 0.998657i | \(0.516500\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.215066 | −0.0181118 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −37.4063 | −3.12807 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.8073 | −0.980547 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.72294 | −0.550765 | −0.275382 | − | 0.961335i | \(-0.588804\pi\) | ||||
−0.275382 | + | 0.961335i | \(0.588804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.2308 | −1.40222 | −0.701112 | − | 0.713051i | \(-0.747313\pi\) | ||||
−0.701112 | + | 0.713051i | \(0.747313\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.784934 | 0.0634582 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.7453 | 1.50566 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.5989 | 1.80359 | 0.901796 | − | 0.432162i | \(-0.142249\pi\) | ||||
0.901796 | + | 0.432162i | \(0.142249\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.14640 | 0.170221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.70053 | −0.368174 | −0.184087 | − | 0.982910i | \(-0.558933\pi\) | ||||
−0.184087 | + | 0.982910i | \(0.558933\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.0224 | 1.09164 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.1068 | −1.71068 | −0.855338 | − | 0.518070i | \(-0.826651\pi\) | ||||
−0.855338 | + | 0.518070i | \(0.826651\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.6834 | 2.05257 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.93800 | 0.148203 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.8007 | 1.35336 | 0.676680 | − | 0.736277i | \(-0.263418\pi\) | ||||
0.676680 | + | 0.736277i | \(0.263418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.576535 | −0.0435819 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.7296 | −0.881651 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.915594 | −0.0684347 | −0.0342173 | − | 0.999414i | \(-0.510894\pi\) | ||||
−0.0342173 | + | 0.999414i | \(0.510894\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9828 | −1.48531 | −0.742656 | − | 0.669673i | \(-0.766434\pi\) | ||||
−0.742656 | + | 0.669673i | \(0.766434\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.51454 | −0.333724 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.2375 | 1.34085 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.66094 | −0.340842 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.0291 | −1.81104 | −0.905520 | − | 0.424303i | \(-0.860519\pi\) | ||||
−0.905520 | + | 0.424303i | \(0.860519\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.78493 | −0.704335 | −0.352167 | − | 0.935937i | \(-0.614555\pi\) | ||||
−0.352167 | + | 0.935937i | \(0.614555\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.8760 | −1.06529 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.8827 | 0.989100 | 0.494550 | − | 0.869149i | \(-0.335333\pi\) | ||||
0.494550 | + | 0.869149i | \(0.335333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.2241 | −0.866546 | −0.433273 | − | 0.901263i | \(-0.642641\pi\) | ||||
−0.433273 | + | 0.901263i | \(0.642641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.993333 | −0.0700643 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.00000 | −0.350931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.5303 | −1.01484 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.5079 | −0.796016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.66094 | −0.320872 | −0.160436 | − | 0.987046i | \(-0.551290\pi\) | ||||
−0.160436 | + | 0.987046i | \(0.551290\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.51454 | 0.309331 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −30.7520 | −2.09727 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.93800 | 0.538867 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.35480 | −0.159123 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.94467 | 0.332615 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8693 | −0.727865 | −0.363932 | − | 0.931425i | \(-0.618566\pi\) | ||||
−0.363932 | + | 0.931425i | \(0.618566\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.576535 | 0.0384356 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2084 | −0.743928 | −0.371964 | − | 0.928247i | \(-0.621315\pi\) | ||||
−0.371964 | + | 0.928247i | \(0.621315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.14640 | 0.406166 | 0.203083 | − | 0.979162i | \(-0.434904\pi\) | ||||
0.203083 | + | 0.979162i | \(0.434904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.93800 | 0.390692 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0224 | −0.787614 | −0.393807 | − | 0.919193i | \(-0.628842\pi\) | ||||
−0.393807 | + | 0.919193i | \(0.628842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.507872 | 0.0331299 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.492128 | −0.0319672 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.5923 | −1.26732 | −0.633660 | − | 0.773612i | \(-0.718448\pi\) | ||||
−0.633660 | + | 0.773612i | \(0.718448\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9051 | −0.766874 | −0.383437 | − | 0.923567i | \(-0.625260\pi\) | ||||
−0.383437 | + | 0.923567i | \(0.625260\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.36147 | −0.150869 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.2084 | 0.776802 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.07774 | −0.575278 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.2151 | −1.40220 | −0.701101 | − | 0.713062i | \(-0.747308\pi\) | ||||
−0.701101 | + | 0.713062i | \(0.747308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.93800 | −0.373319 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.85360 | −0.116077 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.70719 | 0.106492 | 0.0532459 | − | 0.998581i | \(-0.483043\pi\) | ||||
0.0532459 | + | 0.998581i | \(0.483043\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.72294 | 0.479880 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.4750 | 0.954226 | 0.477113 | − | 0.878842i | \(-0.341683\pi\) | ||||
0.477113 | + | 0.878842i | \(0.341683\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.06866 | −0.311366 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.51454 | −0.276285 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.1292 | −1.34924 | −0.674621 | − | 0.738164i | \(-0.735693\pi\) | ||||
−0.674621 | + | 0.738164i | \(0.735693\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.6609 | 1.01208 | 0.506040 | − | 0.862510i | \(-0.331109\pi\) | ||||
0.506040 | + | 0.862510i | \(0.331109\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.29947 | −0.381261 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.42347 | −0.206443 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.5145 | 0.872094 | 0.436047 | − | 0.899924i | \(-0.356378\pi\) | ||||
0.436047 | + | 0.899924i | \(0.356378\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.93800 | −0.475236 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.9671 | −1.07183 | −0.535913 | − | 0.844273i | \(-0.680033\pi\) | ||||
−0.535913 | + | 0.844273i | \(0.680033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.29947 | 0.552796 | 0.276398 | − | 0.961043i | \(-0.410859\pi\) | ||||
0.276398 | + | 0.961043i | \(0.410859\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.57653 | −0.271091 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.15307 | −0.363204 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3839 | −0.963758 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.59894 | 0.328216 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.1821 | −1.41274 | −0.706368 | − | 0.707845i | \(-0.749668\pi\) | ||||
−0.706368 | + | 0.707845i | \(0.749668\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.6991 | 1.61270 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.93800 | −0.344558 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.29947 | 0.364308 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.0224 | −0.750599 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.29947 | −0.0746527 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.6609 | 0.610444 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.4616 | −1.68146 | −0.840732 | − | 0.541452i | \(-0.817875\pi\) | ||||
−0.840732 | + | 0.541452i | \(0.817875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.38388 | 0.476942 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.2666 | 1.48944 | 0.744720 | − | 0.667377i | \(-0.232583\pi\) | ||||
0.744720 | + | 0.667377i | \(0.232583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.4883 | −1.49721 | −0.748603 | − | 0.663018i | \(-0.769275\pi\) | ||||
−0.748603 | + | 0.663018i | \(0.769275\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.36147 | 0.133054 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.51454 | 0.534390 | 0.267195 | − | 0.963643i | \(-0.413903\pi\) | ||||
0.267195 | + | 0.963643i | \(0.413903\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.6900 | −1.66232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.36147 | −0.522506 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.52120 | 0.0846421 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.63186 | 0.201460 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.06866 | −0.114397 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.215066 | 0.0118570 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.87601 | −0.432904 | −0.216452 | − | 0.976293i | \(-0.569449\pi\) | ||||
−0.216452 | + | 0.976293i | \(0.569449\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.72294 | −0.423214 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.34573 | 0.128161 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.39055 | 0.348115 | 0.174058 | − | 0.984735i | \(-0.444312\pi\) | ||||
0.174058 | + | 0.984735i | \(0.444312\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.9604 | −0.921163 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 47.1359 | 2.55255 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.36147 | −0.127137 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.3510 | 1.36091 | 0.680455 | − | 0.732790i | \(-0.261782\pi\) | ||||
0.680455 | + | 0.732790i | \(0.261782\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.3285 | −1.40933 | −0.704667 | − | 0.709538i | \(-0.748904\pi\) | ||||
−0.704667 | + | 0.709538i | \(0.748904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.29947 | 0.336241 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.9208 | −1.32640 | −0.663201 | − | 0.748441i | \(-0.730802\pi\) | ||||
−0.663201 | + | 0.748441i | \(0.730802\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.6609 | −0.565824 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.784934 | −0.0415431 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.37721 | −0.283798 | −0.141899 | − | 0.989881i | \(-0.545321\pi\) | ||||
−0.141899 | + | 0.989881i | \(0.545321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2441 | −0.802323 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.2599 | 1.27331 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.56079 | 0.291065 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.85360 | −0.357755 | −0.178877 | − | 0.983871i | \(-0.557247\pi\) | ||||
−0.178877 | + | 0.983871i | \(0.557247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.15307 | 0.320316 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.14640 | −0.111436 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.2890 | 1.56830 | 0.784152 | − | 0.620569i | \(-0.213098\pi\) | ||||
0.784152 | + | 0.620569i | \(0.213098\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.4459 | 0.539423 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.4974 | 1.62220 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.79827 | 0.400570 | 0.200285 | − | 0.979738i | \(-0.435813\pi\) | ||||
0.200285 | + | 0.979738i | \(0.435813\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.5923 | 0.850048 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.92226 | −0.149321 | −0.0746603 | − | 0.997209i | \(-0.523787\pi\) | ||||
−0.0746603 | + | 0.997209i | \(0.523787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.0224 | −0.714648 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.0224 | 0.661966 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.5369 | 1.75109 | 0.875546 | − | 0.483134i | \(-0.160502\pi\) | ||||
0.875546 | + | 0.483134i | \(0.160502\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.784934 | 0.0396958 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.2151 | −0.666612 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.16215 | 0.0584739 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0448 | 1.30715 | 0.653576 | − | 0.756861i | \(-0.273268\pi\) | ||||
0.653576 | + | 0.756861i | \(0.273268\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.93800 | −0.0970215 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.21507 | 0.0606775 | 0.0303387 | − | 0.999540i | \(-0.490341\pi\) | ||||
0.0303387 | + | 0.999540i | \(0.490341\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −50.0052 | −2.49094 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.36147 | −0.117342 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.8588 | 2.27314 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.10441 | 0.450184 | 0.225092 | − | 0.974338i | \(-0.427732\pi\) | ||||
0.225092 | + | 0.974338i | \(0.427732\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.0000 | −0.641243 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.7296 | 0.577176 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.4368 | 1.05229 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.22173 | −0.0598285 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.8984 | 1.26522 | 0.632610 | − | 0.774470i | \(-0.281984\pi\) | ||||
0.632610 | + | 0.774470i | \(0.281984\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.605611 | 0.0295157 | 0.0147578 | − | 0.999891i | \(-0.495302\pi\) | ||||
0.0147578 | + | 0.999891i | \(0.495302\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.215066 | −0.0104569 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.452542 | 0.0219515 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.51454 | 0.218474 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −37.4063 | −1.80599 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7902 | −1.33861 | −0.669303 | − | 0.742990i | \(-0.733407\pi\) | ||||
−0.669303 | + | 0.742990i | \(0.733407\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.8007 | −0.711275 | −0.355638 | − | 0.934624i | \(-0.615736\pi\) | ||||
−0.355638 | + | 0.934624i | \(0.615736\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.8073 | −0.566119 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.93800 | 0.0927073 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.63186 | −0.268794 | −0.134397 | − | 0.990928i | \(-0.542910\pi\) | ||||
−0.134397 | + | 0.990928i | \(0.542910\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.36814 | −0.160025 | −0.0800125 | − | 0.996794i | \(-0.525496\pi\) | ||||
−0.0800125 | + | 0.996794i | \(0.525496\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.6609 | 0.505377 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.72294 | −0.317984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.11733 | −0.147116 | −0.0735579 | − | 0.997291i | \(-0.523435\pi\) | ||||
−0.0735579 | + | 0.997291i | \(0.523435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.5369 | −1.72046 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.2308 | −0.809574 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.8760 | 0.697398 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.72960 | −0.455132 | −0.227566 | − | 0.973763i | \(-0.573077\pi\) | ||||
−0.227566 | + | 0.973763i | \(0.573077\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.784934 | 0.0366376 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.7587 | 0.594231 | 0.297116 | − | 0.954842i | \(-0.403975\pi\) | ||||
0.297116 | + | 0.954842i | \(0.403975\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.67812 | 0.263885 | 0.131942 | − | 0.991257i | \(-0.457879\pi\) | ||||
0.131942 | + | 0.991257i | \(0.457879\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.7453 | 0.869295 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.7520 | −1.14539 | −0.572693 | − | 0.819770i | \(-0.694101\pi\) | ||||
−0.572693 | + | 0.819770i | \(0.694101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.993333 | 0.0458679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.5989 | 1.04130 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −77.3271 | −3.55550 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.11733 | 0.0512664 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.14640 | 0.0982770 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.9404 | −1.32232 | −0.661161 | − | 0.750244i | \(-0.729936\pi\) | ||||
−0.661161 | + | 0.750244i | \(0.729936\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.6504 | −2.21827 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.2217 | −0.600368 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.0582 | −1.22612 | −0.613061 | − | 0.790036i | \(-0.710062\pi\) | ||||
−0.613061 | + | 0.790036i | \(0.710062\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.70053 | −0.212565 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.0977 | −1.17777 | −0.588887 | − | 0.808215i | \(-0.700434\pi\) | ||||
−0.588887 | + | 0.808215i | \(0.700434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.92467 | 0.176758 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.0224 | 0.630260 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.51454 | −0.202505 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.9933 | 0.671194 | 0.335597 | − | 0.942006i | \(-0.391062\pi\) | ||||
0.335597 | + | 0.942006i | \(0.391062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.1068 | −0.987660 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.74294 | −0.0777137 | −0.0388569 | − | 0.999245i | \(-0.512372\pi\) | ||||
−0.0388569 | + | 0.999245i | \(0.512372\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.06866 | 0.136554 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.6834 | 1.18505 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.7811 | 0.921106 | 0.460553 | − | 0.887632i | \(-0.347651\pi\) | ||||
0.460553 | + | 0.887632i | \(0.347651\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.35480 | 0.104170 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.93800 | 0.0855649 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.7983 | −0.872416 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.27706 | 0.0561651 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.8007 | 0.781363 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.306139 | −0.0134122 | −0.00670610 | − | 0.999978i | \(-0.502135\pi\) | ||||
−0.00670610 | + | 0.999978i | \(0.502135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.7520 | −0.601334 | −0.300667 | − | 0.953729i | \(-0.597209\pi\) | ||||
−0.300667 | + | 0.953729i | \(0.597209\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.576535 | −0.0251620 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.23081 | −0.271418 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.7296 | −0.509021 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.7611 | 1.67893 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.1068 | 0.955761 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.915594 | −0.0395108 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.93800 | −0.255768 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −45.6147 | −1.96113 | −0.980564 | − | 0.196198i | \(-0.937140\pi\) | ||||
−0.980564 | + | 0.196198i | \(0.937140\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.9828 | −0.857545 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.88508 | 0.209254 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.4392 | 1.55803 | 0.779014 | − | 0.627007i | \(-0.215720\pi\) | ||||
0.779014 | + | 0.627007i | \(0.215720\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.51454 | −0.192676 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.69002 | 0.412809 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.492128 | 0.0209274 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.2375 | 0.774138 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.7387 | 1.26007 | 0.630034 | − | 0.776567i | \(-0.283041\pi\) | ||||
0.630034 | + | 0.776567i | \(0.283041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 82.0343 | 3.46968 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.66094 | −0.196785 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.41013 | 0.101575 | 0.0507875 | − | 0.998709i | \(-0.483827\pi\) | ||||
0.0507875 | + | 0.998709i | \(0.483827\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.0515 | 1.68498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.9537 | −1.00419 | −0.502097 | − | 0.864812i | \(-0.667438\pi\) | ||||
−0.502097 | + | 0.864812i | \(0.667438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.5394 | −1.57097 | −0.785487 | − | 0.618879i | \(-0.787587\pi\) | ||||
−0.785487 | + | 0.618879i | \(0.787587\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.0291 | −1.04560 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.576535 | 0.0240432 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.6123 | 1.27441 | 0.637203 | − | 0.770696i | \(-0.280091\pi\) | ||||
0.637203 | + | 0.770696i | \(0.280091\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.78493 | −0.406648 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.07774 | 0.376608 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.7453 | −0.527858 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.8760 | −0.615047 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.5303 | 1.54904 | 0.774520 | − | 0.632549i | \(-0.217991\pi\) | ||||
0.774520 | + | 0.632549i | \(0.217991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.3839 | −0.633882 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.8827 | 0.571057 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.3705 | 0.754388 | 0.377194 | − | 0.926134i | \(-0.376889\pi\) | ||||
0.377194 | + | 0.926134i | \(0.376889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.85360 | 0.0759901 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.2241 | −0.500301 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.9604 | 0.978996 | 0.489498 | − | 0.872004i | \(-0.337180\pi\) | ||||
0.489498 | + | 0.872004i | \(0.337180\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.9142 | 1.17943 | 0.589717 | − | 0.807610i | \(-0.299239\pi\) | ||||
0.589717 | + | 0.807610i | \(0.299239\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.993333 | −0.0404517 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −57.2890 | −2.32913 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.5436 | 1.68620 | 0.843102 | − | 0.537754i | \(-0.180727\pi\) | ||||
0.843102 | + | 0.537754i | \(0.180727\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.00000 | −0.202610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.35480 | −0.0548094 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.0582 | 1.57754 | 0.788772 | − | 0.614686i | \(-0.210717\pi\) | ||||
0.788772 | + | 0.614686i | \(0.210717\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.5303 | −0.585917 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1001 | 0.849460 | 0.424730 | − | 0.905320i | \(-0.360369\pi\) | ||||
0.424730 | + | 0.905320i | \(0.360369\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.2666 | 1.13613 | 0.568064 | − | 0.822984i | \(-0.307692\pi\) | ||||
0.568064 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.51454 | 0.180871 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.5503 | −1.10201 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.5079 | −0.459580 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.06200 | −0.241708 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.9247 | −1.11166 | −0.555832 | − | 0.831295i | \(-0.687600\pi\) | ||||
−0.555832 | + | 0.831295i | \(0.687600\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.66094 | −0.185256 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −39.1821 | −1.55490 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.29947 | 0.249594 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.51454 | 0.178592 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.6371 | −1.68406 | −0.842032 | − | 0.539428i | \(-0.818641\pi\) | ||||
−0.842032 | + | 0.539428i | \(0.818641\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.37721 | −0.251493 | −0.125746 | − | 0.992062i | \(-0.540133\pi\) | ||||
−0.125746 | + | 0.992062i | \(0.540133\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.7520 | −1.21086 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.7611 | −1.09140 | −0.545701 | − | 0.837980i | \(-0.683736\pi\) | ||||
−0.545701 | + | 0.837980i | \(0.683736\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 69.6504 | 2.73402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.93800 | 0.311115 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.1268 | −0.396293 | −0.198146 | − | 0.980172i | \(-0.563492\pi\) | ||||
−0.198146 | + | 0.980172i | \(0.563492\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.2070 | 1.21936 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.35480 | −0.0918696 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.8879 | −1.51486 | −0.757429 | − | 0.652918i | \(-0.773545\pi\) | ||||
−0.757429 | + | 0.652918i | \(0.773545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.98282 | −0.154914 | −0.0774569 | − | 0.996996i | \(-0.524680\pi\) | ||||
−0.0774569 | + | 0.996996i | \(0.524680\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.94467 | 0.192035 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.57653 | 0.177470 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.00000 | 0.193601 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.8693 | −0.420233 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.8073 | 1.03489 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.98426 | −0.230676 | −0.115338 | − | 0.993326i | \(-0.536795\pi\) | ||||
−0.115338 | + | 0.993326i | \(0.536795\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.576535 | 0.0221908 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.3930 | −0.822198 | −0.411099 | − | 0.911591i | \(-0.634855\pi\) | ||||
−0.411099 | + | 0.911591i | \(0.634855\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.59894 | −0.214868 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.2084 | −0.429507 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.3047 | 1.04479 | 0.522393 | − | 0.852705i | \(-0.325040\pi\) | ||||
0.522393 | + | 0.852705i | \(0.325040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.6991 | 1.17295 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.14640 | 0.234500 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.5212 | 0.515117 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4974 | −0.969965 | −0.484983 | − | 0.874524i | \(-0.661174\pi\) | ||||
−0.484983 | + | 0.874524i | \(0.661174\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.93800 | 0.225566 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.88508 | 0.109437 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.82975 | 0.182940 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0224 | −0.454729 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.85360 | 0.372165 | 0.186083 | − | 0.982534i | \(-0.440421\pi\) | ||||
0.186083 | + | 0.982534i | \(0.440421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.9671 | −0.564494 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.507872 | 0.0191275 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.29947 | 0.0488717 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.2980 | 1.28809 | 0.644045 | − | 0.764988i | \(-0.277255\pi\) | ||||
0.644045 | + | 0.764988i | \(0.277255\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.492128 | −0.0184563 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.93800 | −0.297281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 88.3338 | 3.30350 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.5923 | −0.731687 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.3219 | 0.907053 | 0.453527 | − | 0.891243i | \(-0.350166\pi\) | ||||
0.453527 | + | 0.891243i | \(0.350166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.38388 | −0.312232 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.9051 | −0.442755 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.88267 | 0.107060 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.2599 | 1.15936 | 0.579682 | − | 0.814842i | \(-0.303177\pi\) | ||||
0.579682 | + | 0.814842i | \(0.303177\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.2217 | 0.378064 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.95518 | −0.293831 | −0.146916 | − | 0.989149i | \(-0.546935\pi\) | ||||
−0.146916 | + | 0.989149i | \(0.546935\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.36147 | −0.0871041 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.89842 | 0.217271 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.2151 | 0.633266 | 0.316633 | − | 0.948548i | \(-0.397448\pi\) | ||||
0.316633 | + | 0.948548i | \(0.397448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.2084 | 0.448487 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.7453 | −0.467581 | −0.233791 | − | 0.972287i | \(-0.575113\pi\) | ||||
−0.233791 | + | 0.972287i | \(0.575113\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.8760 | 0.581652 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.07774 | −0.332137 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.36147 | 0.342061 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.0357 | 1.60689 | 0.803444 | − | 0.595381i | \(-0.202999\pi\) | ||||
0.803444 | + | 0.595381i | \(0.202999\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.2151 | −0.809562 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.6900 | 1.48086 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.9828 | −0.726288 | −0.363144 | − | 0.931733i | \(-0.618297\pi\) | ||||
−0.363144 | + | 0.931733i | \(0.618297\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.93800 | −0.215536 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.9075 | 1.44665 | 0.723323 | − | 0.690510i | \(-0.242614\pi\) | ||||
0.723323 | + | 0.690510i | \(0.242614\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.06866 | 0.0748906 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.85360 | −0.0670169 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −73.8903 | −2.66802 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.5369 | −1.35362 | −0.676808 | − | 0.736159i | \(-0.736637\pi\) | ||||
−0.676808 | + | 0.736159i | \(0.736637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.70719 | 0.0614831 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.2718 | 1.77218 | 0.886091 | − | 0.463510i | \(-0.153410\pi\) | ||||
0.886091 | + | 0.463510i | \(0.153410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.57653 | −0.164394 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.72294 | 0.277059 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.9247 | 0.427246 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.8073 | −0.959242 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −53.3667 | −1.90474 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.1331 | 0.432497 | 0.216249 | − | 0.976338i | \(-0.430618\pi\) | ||||
0.216249 | + | 0.976338i | \(0.430618\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.4750 | 0.550923 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.9604 | 0.603043 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.4392 | −1.00991 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.06866 | −0.179767 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.8273 | −1.30449 | −0.652246 | − | 0.758008i | \(-0.726173\pi\) | ||||
−0.652246 | + | 0.758008i | \(0.726173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.168813 | −0.00597216 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.51454 | −0.159513 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.9828 | 0.493443 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.36147 | 0.0832308 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.1292 | −0.778986 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.6967 | −1.29019 | −0.645093 | − | 0.764104i | \(-0.723182\pi\) | ||||
−0.645093 | + | 0.764104i | \(0.723182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.5565 | 0.440920 | 0.220460 | − | 0.975396i | \(-0.429244\pi\) | ||||
0.220460 | + | 0.975396i | \(0.429244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.6609 | 0.584325 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.1001 | 0.388821 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.2375 | 0.882948 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.29947 | −0.220121 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.9051 | −0.380590 | −0.190295 | − | 0.981727i | \(-0.560944\pi\) | ||||
−0.190295 | + | 0.981727i | \(0.560944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.8231 | −1.00471 | −0.502355 | − | 0.864662i | \(-0.667533\pi\) | ||||
−0.502355 | + | 0.864662i | \(0.667533\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.42347 | −0.119190 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.27281 | −0.0442598 | −0.0221299 | − | 0.999755i | \(-0.507045\pi\) | ||||
−0.0221299 | + | 0.999755i | \(0.507045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.5236 | 0.434963 | 0.217482 | − | 0.976064i | \(-0.430216\pi\) | ||||
0.217482 | + | 0.976064i | \(0.430216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5145 | 0.503504 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.784934 | 0.0271964 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 52.2046 | 1.80661 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.93800 | −0.274378 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.8073 | −0.580254 | −0.290127 | − | 0.956988i | \(-0.593698\pi\) | ||||
−0.290127 | + | 0.956988i | \(0.593698\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.9671 | −0.618819 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −63.0119 | −2.16768 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.2599 | −0.833580 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.29947 | 0.319157 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.72294 | −0.264739 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.1993 | 0.451936 | 0.225968 | − | 0.974135i | \(-0.427445\pi\) | ||||
0.225968 | + | 0.974135i | \(0.427445\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.57653 | −0.156514 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.924670 | 0.0315861 | 0.0157931 | − | 0.999875i | \(-0.494973\pi\) | ||||
0.0157931 | + | 0.999875i | \(0.494973\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.24414 | −0.247167 | −0.123583 | − | 0.992334i | \(-0.539439\pi\) | ||||
−0.123583 | + | 0.992334i | \(0.539439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.15307 | −0.209696 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.8784 | 0.438386 | 0.219193 | − | 0.975681i | \(-0.429657\pi\) | ||||
0.219193 | + | 0.975681i | \(0.429657\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.0357 | −1.42926 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.3839 | −0.556426 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.92226 | 0.0991309 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.25748 | −0.212026 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.59894 | 0.189496 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.4459 | −0.353135 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.3958 | 1.56667 | 0.783337 | − | 0.621597i | \(-0.213516\pi\) | ||||
0.783337 | + | 0.621597i | \(0.213516\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.1821 | −0.815644 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.07917 | −0.0700491 | −0.0350246 | − | 0.999386i | \(-0.511151\pi\) | ||||
−0.0350246 | + | 0.999386i | \(0.511151\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.8522 | −0.970953 | −0.485476 | − | 0.874250i | \(-0.661354\pi\) | ||||
−0.485476 | + | 0.874250i | \(0.661354\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27.6991 | 0.931095 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.0501 | 1.47906 | 0.739528 | − | 0.673126i | \(-0.235049\pi\) | ||||
0.739528 | + | 0.673126i | \(0.235049\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.5923 | −0.556487 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.93800 | −0.198931 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.416799 | −0.0139476 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.16215 | 0.0722726 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.29947 | 0.210333 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −39.6900 | −1.32374 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.68478 | 0.0561283 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.0224 | −0.433359 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 47.1888 | 1.56861 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.8364 | −0.359817 | −0.179909 | − | 0.983683i | \(-0.557580\pi\) | ||||
−0.179909 | + | 0.983683i | \(0.557580\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.29947 | −0.0431008 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2732 | −1.40057 | −0.700287 | − | 0.713861i | \(-0.746945\pi\) | ||||
−0.700287 | + | 0.713861i | \(0.746945\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 53.9036 | 1.78395 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.6609 | 0.352440 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.2151 | 0.436400 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.1068 | 0.993132 | 0.496566 | − | 0.867999i | \(-0.334594\pi\) | ||||
0.496566 | + | 0.867999i | \(0.334594\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.4616 | −0.970793 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.4392 | 0.936088 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.45254 | −0.146399 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.38388 | 0.275363 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.76252 | −0.320298 | −0.160149 | − | 0.987093i | \(-0.551197\pi\) | ||||
−0.160149 | + | 0.987093i | \(0.551197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.93800 | 0.0635155 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.2666 | 0.859928 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.0067 | 0.359956 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.6438 | −0.903082 | −0.451541 | − | 0.892250i | \(-0.649126\pi\) | ||||
−0.451541 | + | 0.892250i | \(0.649126\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.4883 | −0.864413 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.9223 | 0.975438 | 0.487719 | − | 0.873001i | \(-0.337829\pi\) | ||||
0.487719 | + | 0.873001i | \(0.337829\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.15307 | 0.200372 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.36147 | 0.0768186 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.8140 | 0.611373 | 0.305687 | − | 0.952132i | \(-0.401114\pi\) | ||||
0.305687 | + | 0.952132i | \(0.401114\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.8340 | −0.481532 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.51454 | 0.308530 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.34573 | −0.270345 | −0.135172 | − | 0.990822i | \(-0.543159\pi\) | ||||
−0.135172 | + | 0.990822i | \(0.543159\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 59.1054 | 1.91261 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.6900 | −0.959742 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.0000 | 0.419792 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.0119 | 1.03264 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.36147 | −0.301669 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.1068 | 0.743835 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.5198 | 1.88187 | 0.940934 | − | 0.338589i | \(-0.109950\pi\) | ||||
0.940934 | + | 0.338589i | \(0.109950\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.52120 | 0.0488681 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.8655 | 0.412873 | 0.206437 | − | 0.978460i | \(-0.433813\pi\) | ||||
0.206437 | + | 0.978460i | \(0.433813\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.22173 | 0.0391670 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.63186 | 0.116313 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.16215 | 0.133159 | 0.0665794 | − | 0.997781i | \(-0.478791\pi\) | ||||
0.0665794 | + | 0.997781i | \(0.478791\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.8073 | 0.856766 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.06866 | −0.0660473 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.35239 | −0.106925 | −0.0534624 | − | 0.998570i | \(-0.517026\pi\) | ||||
−0.0534624 | + | 0.998570i | \(0.517026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.7835 | −1.04457 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.215066 | 0.00684563 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.0224 | 0.414089 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.1001 | −1.62325 | −0.811625 | − | 0.584179i | \(-0.801417\pi\) | ||||
−0.811625 | + | 0.584179i | \(0.801417\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.87601 | −0.249938 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.8669 | 0.915143 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.9036 | −1.26376 | −0.631881 | − | 0.775066i | \(-0.717717\pi\) | ||||
−0.631881 | + | 0.775066i | \(0.717717\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.72294 | −0.244343 |
(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 | 7728.2.a.bx.1.1 | 3 | ||
4.3 | odd | 2 | 3864.2.a.m.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.m.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
7728.2.a.bx.1.1 | 3 | 1.1 | even | 1 | trivial |