Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2525.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.46673\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.46673 | −1.74424 | −0.872121 | − | 0.489290i | \(-0.837256\pi\) | ||||
−0.872121 | + | 0.489290i | \(0.837256\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.08477 | 2.04238 | ||||||||
\(5\) | 3.46673 | 1.55037 | 0.775185 | − | 0.631735i | \(-0.217657\pi\) | ||||
0.775185 | + | 0.631735i | \(0.217657\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −5.14256 | −1.81817 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.55150 | −2.70422 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.653752 | −0.181318 | −0.0906590 | − | 0.995882i | \(-0.528897\pi\) | ||||
−0.0906590 | + | 0.995882i | \(0.528897\pi\) | |||||||
\(14\) | 2.46673 | 0.659262 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.51578 | 1.12894 | ||||||||
\(17\) | 1.13715 | 0.275800 | 0.137900 | − | 0.990446i | \(-0.455965\pi\) | ||||
0.137900 | + | 0.990446i | \(0.455965\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.07602 | −1.39393 | −0.696967 | − | 0.717103i | \(-0.745468\pi\) | ||||
−0.696967 | + | 0.717103i | \(0.745468\pi\) | |||||||
\(20\) | 14.1608 | 3.16645 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.66708 | 1.39018 | 0.695091 | − | 0.718921i | \(-0.255364\pi\) | ||||
0.695091 | + | 0.718921i | \(0.255364\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.01823 | 1.40365 | ||||||||
\(26\) | 1.61263 | 0.316263 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.08477 | −0.771948 | ||||||||
\(29\) | 4.57357 | 0.849291 | 0.424646 | − | 0.905360i | \(-0.360399\pi\) | ||||
0.424646 | + | 0.905360i | \(0.360399\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.79631 | 0.502232 | 0.251116 | − | 0.967957i | \(-0.419202\pi\) | ||||
0.251116 | + | 0.967957i | \(0.419202\pi\) | |||||||
\(32\) | −0.854102 | −0.150985 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.80505 | −0.481063 | ||||||||
\(35\) | −3.46673 | −0.585985 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.439758 | −0.0722958 | −0.0361479 | − | 0.999346i | \(-0.511509\pi\) | ||||
−0.0361479 | + | 0.999346i | \(0.511509\pi\) | |||||||
\(38\) | 14.9879 | 2.43136 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −17.8279 | −2.81883 | ||||||||
\(41\) | 5.90315 | 0.921917 | 0.460959 | − | 0.887422i | \(-0.347506\pi\) | ||||
0.460959 | + | 0.887422i | \(0.347506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.70820 | 1.32799 | 0.663994 | − | 0.747738i | \(-0.268860\pi\) | ||||
0.663994 | + | 0.747738i | \(0.268860\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −16.4459 | −2.42482 | ||||||||
\(47\) | 0.604703 | 0.0882051 | 0.0441025 | − | 0.999027i | \(-0.485957\pi\) | ||||
0.0441025 | + | 0.999027i | \(0.485957\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −17.3121 | −2.44830 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.67042 | −0.370321 | ||||||||
\(53\) | −9.82247 | −1.34922 | −0.674610 | − | 0.738175i | \(-0.735688\pi\) | ||||
−0.674610 | + | 0.738175i | \(0.735688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.14256 | 0.687203 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.2818 | −1.48137 | ||||||||
\(59\) | −1.69406 | −0.220547 | −0.110274 | − | 0.993901i | \(-0.535173\pi\) | ||||
−0.110274 | + | 0.993901i | \(0.535173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.85818 | 0.878100 | 0.439050 | − | 0.898463i | \(-0.355315\pi\) | ||||
0.439050 | + | 0.898463i | \(0.355315\pi\) | |||||||
\(62\) | −6.89775 | −0.876015 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.92472 | −0.865590 | ||||||||
\(65\) | −2.26638 | −0.281110 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.17828 | −0.754797 | −0.377398 | − | 0.926051i | \(-0.623181\pi\) | ||||
−0.377398 | + | 0.926051i | \(0.623181\pi\) | |||||||
\(68\) | 4.64501 | 0.563290 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.55150 | 1.02210 | ||||||||
\(71\) | 5.41687 | 0.642864 | 0.321432 | − | 0.946933i | \(-0.395836\pi\) | ||||
0.321432 | + | 0.946933i | \(0.395836\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.70198 | 0.784408 | 0.392204 | − | 0.919878i | \(-0.371713\pi\) | ||||
0.392204 | + | 0.919878i | \(0.371713\pi\) | |||||||
\(74\) | 1.08477 | 0.126101 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −24.8191 | −2.84695 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.65375 | 0.298570 | 0.149285 | − | 0.988794i | \(-0.452303\pi\) | ||||
0.149285 | + | 0.988794i | \(0.452303\pi\) | |||||||
\(80\) | 15.6550 | 1.75028 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.5615 | −1.60805 | ||||||||
\(83\) | −6.69658 | −0.735045 | −0.367522 | − | 0.930015i | \(-0.619794\pi\) | ||||
−0.367522 | + | 0.930015i | \(0.619794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.94221 | 0.427592 | ||||||||
\(86\) | −21.4808 | −2.31633 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.698213 | 0.0740105 | 0.0370052 | − | 0.999315i | \(-0.488218\pi\) | ||||
0.0370052 | + | 0.999315i | \(0.488218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.653752 | 0.0685318 | ||||||||
\(92\) | 27.2335 | 2.83929 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.49164 | −0.153851 | ||||||||
\(95\) | −21.0639 | −2.16111 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.8587 | −1.50867 | −0.754336 | − | 0.656489i | \(-0.772041\pi\) | ||||
−0.754336 | + | 0.656489i | \(0.772041\pi\) | |||||||
\(98\) | −2.46673 | −0.249178 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 28.6678 | 2.86678 | ||||||||
\(101\) | −8.61959 | −0.857682 | −0.428841 | − | 0.903380i | \(-0.641078\pi\) | ||||
−0.428841 | + | 0.903380i | \(0.641078\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.932958 | −0.0919271 | −0.0459636 | − | 0.998943i | \(-0.514636\pi\) | ||||
−0.0459636 | + | 0.998943i | \(0.514636\pi\) | |||||||
\(104\) | 3.36196 | 0.329667 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.2294 | 2.35337 | ||||||||
\(107\) | −6.62212 | −0.640184 | −0.320092 | − | 0.947386i | \(-0.603714\pi\) | ||||
−0.320092 | + | 0.947386i | \(0.603714\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.12507 | −0.395110 | −0.197555 | − | 0.980292i | \(-0.563300\pi\) | ||||
−0.197555 | + | 0.980292i | \(0.563300\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.51578 | −0.426701 | ||||||||
\(113\) | 18.8258 | 1.77098 | 0.885491 | − | 0.464656i | \(-0.153822\pi\) | ||||
0.885491 | + | 0.464656i | \(0.153822\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.1130 | 2.15530 | ||||||||
\(116\) | 18.6820 | 1.73458 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.17878 | 0.384688 | ||||||||
\(119\) | −1.13715 | −0.104243 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −16.9173 | −1.53162 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.4223 | 1.02575 | ||||||||
\(125\) | 6.99666 | 0.625800 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.96635 | −0.706899 | −0.353449 | − | 0.935454i | \(-0.614991\pi\) | ||||
−0.353449 | + | 0.935454i | \(0.614991\pi\) | |||||||
\(128\) | 18.7896 | 1.66078 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.59056 | 0.490324 | ||||||||
\(131\) | 4.80505 | 0.419819 | 0.209910 | − | 0.977721i | \(-0.432683\pi\) | ||||
0.209910 | + | 0.977721i | \(0.432683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.07602 | 0.526858 | ||||||||
\(134\) | 15.2401 | 1.31655 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.84788 | −0.501452 | ||||||||
\(137\) | 21.8777 | 1.86914 | 0.934571 | − | 0.355778i | \(-0.115784\pi\) | ||||
0.934571 | + | 0.355778i | \(0.115784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.8137 | −1.68058 | −0.840289 | − | 0.542139i | \(-0.817615\pi\) | ||||
−0.840289 | + | 0.542139i | \(0.817615\pi\) | |||||||
\(140\) | −14.1608 | −1.19680 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.3620 | −1.12131 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.8553 | 1.31672 | ||||||||
\(146\) | −16.5320 | −1.36820 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.79631 | −0.147656 | ||||||||
\(149\) | −3.16211 | −0.259050 | −0.129525 | − | 0.991576i | \(-0.541345\pi\) | ||||
−0.129525 | + | 0.991576i | \(0.541345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.92806 | 0.726555 | 0.363278 | − | 0.931681i | \(-0.381658\pi\) | ||||
0.363278 | + | 0.931681i | \(0.381658\pi\) | |||||||
\(152\) | 31.2463 | 2.53441 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.69406 | 0.778645 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.13968 | 0.0909561 | 0.0454780 | − | 0.998965i | \(-0.485519\pi\) | ||||
0.0454780 | + | 0.998965i | \(0.485519\pi\) | |||||||
\(158\) | −6.54609 | −0.520779 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.96094 | −0.234083 | ||||||||
\(161\) | −6.66708 | −0.525440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.06728 | −0.396900 | −0.198450 | − | 0.980111i | \(-0.563591\pi\) | ||||
−0.198450 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(164\) | 24.1130 | 1.88291 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.5187 | 1.28210 | ||||||||
\(167\) | 19.7069 | 1.52496 | 0.762482 | − | 0.647009i | \(-0.223981\pi\) | ||||
0.762482 | + | 0.647009i | \(0.223981\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5726 | −0.967124 | ||||||||
\(170\) | −9.72437 | −0.745825 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 35.5710 | 2.71226 | ||||||||
\(173\) | 14.3948 | 1.09442 | 0.547208 | − | 0.836997i | \(-0.315691\pi\) | ||||
0.547208 | + | 0.836997i | \(0.315691\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.01823 | −0.530528 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.72230 | −0.129092 | ||||||||
\(179\) | 4.66420 | 0.348619 | 0.174309 | − | 0.984691i | \(-0.444231\pi\) | ||||
0.174309 | + | 0.984691i | \(0.444231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.90805 | 0.736459 | 0.368230 | − | 0.929735i | \(-0.379964\pi\) | ||||
0.368230 | + | 0.929735i | \(0.379964\pi\) | |||||||
\(182\) | −1.61263 | −0.119536 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −34.2859 | −2.52759 | ||||||||
\(185\) | −1.52452 | −0.112085 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.47007 | 0.180148 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 51.9591 | 3.76951 | ||||||||
\(191\) | −9.94295 | −0.719447 | −0.359723 | − | 0.933059i | \(-0.617129\pi\) | ||||
−0.359723 | + | 0.933059i | \(0.617129\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.70665 | 0.266810 | 0.133405 | − | 0.991062i | \(-0.457409\pi\) | ||||
0.133405 | + | 0.991062i | \(0.457409\pi\) | |||||||
\(194\) | 36.6524 | 2.63149 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.08477 | 0.291769 | ||||||||
\(197\) | −5.91982 | −0.421770 | −0.210885 | − | 0.977511i | \(-0.567635\pi\) | ||||
−0.210885 | + | 0.977511i | \(0.567635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4842 | 0.814095 | 0.407047 | − | 0.913407i | \(-0.366558\pi\) | ||||
0.407047 | + | 0.913407i | \(0.366558\pi\) | |||||||
\(200\) | −36.0917 | −2.55207 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 21.2622 | 1.49600 | ||||||||
\(203\) | −4.57357 | −0.321002 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.4646 | 1.42931 | ||||||||
\(206\) | 2.30136 | 0.160343 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.95220 | −0.204698 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.72487 | 0.600645 | 0.300323 | − | 0.953838i | \(-0.402906\pi\) | ||||
0.300323 | + | 0.953838i | \(0.402906\pi\) | |||||||
\(212\) | −40.1225 | −2.75562 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.3350 | 1.11664 | ||||||||
\(215\) | 30.1890 | 2.05887 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.79631 | −0.189826 | ||||||||
\(218\) | 10.1754 | 0.689168 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.743416 | −0.0500076 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3328 | 0.691938 | 0.345969 | − | 0.938246i | \(-0.387550\pi\) | ||||
0.345969 | + | 0.938246i | \(0.387550\pi\) | |||||||
\(224\) | 0.854102 | 0.0570671 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −46.4382 | −3.08902 | ||||||||
\(227\) | 13.2690 | 0.880691 | 0.440346 | − | 0.897828i | \(-0.354856\pi\) | ||||
0.440346 | + | 0.897828i | \(0.354856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.49623 | −0.164955 | −0.0824777 | − | 0.996593i | \(-0.526283\pi\) | ||||
−0.0824777 | + | 0.996593i | \(0.526283\pi\) | |||||||
\(230\) | −57.0135 | −3.75936 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.5199 | −1.54415 | ||||||||
\(233\) | 9.60389 | 0.629171 | 0.314586 | − | 0.949229i | \(-0.398134\pi\) | ||||
0.314586 | + | 0.949229i | \(0.398134\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.09634 | 0.136750 | ||||||||
\(236\) | −6.91982 | −0.450442 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.80505 | 0.181825 | ||||||||
\(239\) | −5.56327 | −0.359858 | −0.179929 | − | 0.983680i | \(-0.557587\pi\) | ||||
−0.179929 | + | 0.983680i | \(0.557587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0208 | 0.967572 | 0.483786 | − | 0.875186i | \(-0.339261\pi\) | ||||
0.483786 | + | 0.875186i | \(0.339261\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 28.0141 | 1.79342 | ||||||||
\(245\) | 3.46673 | 0.221481 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.97221 | 0.252746 | ||||||||
\(248\) | −14.3802 | −0.913143 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −17.2589 | −1.09155 | ||||||||
\(251\) | −27.6131 | −1.74292 | −0.871460 | − | 0.490466i | \(-0.836827\pi\) | ||||
−0.871460 | + | 0.490466i | \(0.836827\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 19.6508 | 1.23300 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.4995 | −2.03122 | ||||||||
\(257\) | 28.4680 | 1.77578 | 0.887892 | − | 0.460052i | \(-0.152169\pi\) | ||||
0.887892 | + | 0.460052i | \(0.152169\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.439758 | 0.0273253 | ||||||||
\(260\) | −9.25764 | −0.574134 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.8528 | −0.732267 | ||||||||
\(263\) | −14.1803 | −0.874397 | −0.437199 | − | 0.899365i | \(-0.644029\pi\) | ||||
−0.437199 | + | 0.899365i | \(0.644029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.0519 | −2.09179 | ||||||||
\(266\) | −14.9879 | −0.918968 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25.2368 | −1.54158 | ||||||||
\(269\) | 24.1937 | 1.47511 | 0.737557 | − | 0.675285i | \(-0.235979\pi\) | ||||
0.737557 | + | 0.675285i | \(0.235979\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.44975 | 0.452540 | 0.226270 | − | 0.974065i | \(-0.427347\pi\) | ||||
0.226270 | + | 0.974065i | \(0.427347\pi\) | |||||||
\(272\) | 5.13514 | 0.311363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −53.9665 | −3.26024 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.1890 | −1.15296 | −0.576478 | − | 0.817113i | \(-0.695573\pi\) | ||||
−0.576478 | + | 0.817113i | \(0.695573\pi\) | |||||||
\(278\) | 48.8751 | 2.93134 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 17.8279 | 1.06542 | ||||||||
\(281\) | 1.90063 | 0.113382 | 0.0566910 | − | 0.998392i | \(-0.481945\pi\) | ||||
0.0566910 | + | 0.998392i | \(0.481945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.25178 | 0.431073 | 0.215537 | − | 0.976496i | \(-0.430850\pi\) | ||||
0.215537 | + | 0.976496i | \(0.430850\pi\) | |||||||
\(284\) | 22.1266 | 1.31297 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.90315 | −0.348452 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7069 | −0.923934 | ||||||||
\(290\) | −39.1109 | −2.29667 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 27.3760 | 1.60206 | ||||||||
\(293\) | 3.27097 | 0.191092 | 0.0955460 | − | 0.995425i | \(-0.469540\pi\) | ||||
0.0955460 | + | 0.995425i | \(0.469540\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.87284 | −0.341930 | ||||||||
\(296\) | 2.26148 | 0.131446 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.80008 | 0.451846 | ||||||||
\(299\) | −4.35862 | −0.252065 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.70820 | −0.501933 | ||||||||
\(302\) | −22.0231 | −1.26729 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −27.4380 | −1.57368 | ||||||||
\(305\) | 23.7755 | 1.36138 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.6121 | 1.80420 | 0.902099 | − | 0.431530i | \(-0.142026\pi\) | ||||
0.902099 | + | 0.431530i | \(0.142026\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −23.9126 | −1.35815 | ||||||||
\(311\) | 9.03829 | 0.512514 | 0.256257 | − | 0.966609i | \(-0.417511\pi\) | ||||
0.256257 | + | 0.966609i | \(0.417511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4990 | 0.819534 | 0.409767 | − | 0.912190i | \(-0.365610\pi\) | ||||
0.409767 | + | 0.912190i | \(0.365610\pi\) | |||||||
\(314\) | −2.81128 | −0.158649 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.8400 | 0.609795 | ||||||||
\(317\) | 18.4174 | 1.03442 | 0.517211 | − | 0.855858i | \(-0.326970\pi\) | ||||
0.517211 | + | 0.855858i | \(0.326970\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −24.0061 | −1.34198 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 16.4459 | 0.916494 | ||||||||
\(323\) | −6.90937 | −0.384448 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.58818 | −0.254506 | ||||||||
\(326\) | 12.4996 | 0.692290 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −30.3573 | −1.67620 | ||||||||
\(329\) | −0.604703 | −0.0333384 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.47653 | −0.355982 | −0.177991 | − | 0.984032i | \(-0.556960\pi\) | ||||
−0.177991 | + | 0.984032i | \(0.556960\pi\) | |||||||
\(332\) | −27.3540 | −1.50124 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −48.6116 | −2.65991 | ||||||||
\(335\) | −21.4184 | −1.17021 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.25682 | 0.340831 | 0.170415 | − | 0.985372i | \(-0.445489\pi\) | ||||
0.170415 | + | 0.985372i | \(0.445489\pi\) | |||||||
\(338\) | 31.0133 | 1.68690 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.1030 | 0.873308 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −44.7824 | −2.41451 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −35.5081 | −1.90893 | ||||||||
\(347\) | −22.7156 | −1.21944 | −0.609719 | − | 0.792617i | \(-0.708718\pi\) | ||||
−0.609719 | + | 0.792617i | \(0.708718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.6941 | 1.58949 | 0.794743 | − | 0.606946i | \(-0.207606\pi\) | ||||
0.794743 | + | 0.606946i | \(0.207606\pi\) | |||||||
\(350\) | 17.3121 | 0.925370 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.82506 | 0.363262 | 0.181631 | − | 0.983367i | \(-0.441862\pi\) | ||||
0.181631 | + | 0.983367i | \(0.441862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.7788 | 0.996676 | ||||||||
\(356\) | 2.85204 | 0.151158 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.5053 | −0.608076 | ||||||||
\(359\) | 7.25970 | 0.383152 | 0.191576 | − | 0.981478i | \(-0.438640\pi\) | ||||
0.191576 | + | 0.981478i | \(0.438640\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.9180 | 0.943055 | ||||||||
\(362\) | −24.4405 | −1.28456 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.67042 | 0.139968 | ||||||||
\(365\) | 23.2340 | 1.21612 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.3366 | −1.89676 | −0.948378 | − | 0.317143i | \(-0.897277\pi\) | ||||
−0.948378 | + | 0.317143i | \(0.897277\pi\) | |||||||
\(368\) | 30.1071 | 1.56944 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.76059 | 0.195504 | ||||||||
\(371\) | 9.82247 | 0.509957 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.2913 | −0.739977 | −0.369989 | − | 0.929036i | \(-0.620638\pi\) | ||||
−0.369989 | + | 0.929036i | \(0.620638\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.10972 | −0.160372 | ||||||||
\(377\) | −2.98998 | −0.153992 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.54528 | −0.130742 | −0.0653710 | − | 0.997861i | \(-0.520823\pi\) | ||||
−0.0653710 | + | 0.997861i | \(0.520823\pi\) | |||||||
\(380\) | −86.0413 | −4.41382 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.5266 | 1.25489 | ||||||||
\(383\) | 23.1367 | 1.18223 | 0.591115 | − | 0.806587i | \(-0.298688\pi\) | ||||
0.591115 | + | 0.806587i | \(0.298688\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.14330 | −0.465382 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −60.6943 | −3.08128 | ||||||||
\(389\) | −30.2615 | −1.53432 | −0.767158 | − | 0.641458i | \(-0.778330\pi\) | ||||
−0.767158 | + | 0.641458i | \(0.778330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.58150 | 0.383413 | ||||||||
\(392\) | −5.14256 | −0.259738 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.6026 | 0.735669 | ||||||||
\(395\) | 9.19985 | 0.462894 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.6740 | −1.13798 | −0.568989 | − | 0.822345i | \(-0.692665\pi\) | ||||
−0.568989 | + | 0.822345i | \(0.692665\pi\) | |||||||
\(398\) | −28.3285 | −1.41998 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 31.6928 | 1.58464 | ||||||||
\(401\) | 16.2186 | 0.809917 | 0.404959 | − | 0.914335i | \(-0.367286\pi\) | ||||
0.404959 | + | 0.914335i | \(0.367286\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.82809 | −0.0910637 | ||||||||
\(404\) | −35.2090 | −1.75171 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.2818 | 0.559905 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.0614 | −1.73368 | −0.866838 | − | 0.498590i | \(-0.833851\pi\) | ||||
−0.866838 | + | 0.498590i | \(0.833851\pi\) | |||||||
\(410\) | −50.4808 | −2.49307 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.81092 | −0.187750 | ||||||||
\(413\) | 1.69406 | 0.0833590 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.2152 | −1.13959 | ||||||||
\(416\) | 0.558371 | 0.0273764 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.2633 | −1.38075 | −0.690376 | − | 0.723451i | \(-0.742555\pi\) | ||||
−0.690376 | + | 0.723451i | \(0.742555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7947 | −0.672311 | −0.336156 | − | 0.941806i | \(-0.609127\pi\) | ||||
−0.336156 | + | 0.941806i | \(0.609127\pi\) | |||||||
\(422\) | −21.5219 | −1.04767 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 50.5126 | 2.45311 | ||||||||
\(425\) | 7.98081 | 0.387126 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.85818 | −0.331891 | ||||||||
\(428\) | −27.0498 | −1.30750 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −74.4682 | −3.59117 | ||||||||
\(431\) | −28.1700 | −1.35690 | −0.678451 | − | 0.734645i | \(-0.737349\pi\) | ||||
−0.678451 | + | 0.734645i | \(0.737349\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.1793 | 0.681415 | 0.340708 | − | 0.940169i | \(-0.389333\pi\) | ||||
0.340708 | + | 0.940169i | \(0.389333\pi\) | |||||||
\(434\) | 6.89775 | 0.331102 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.8499 | −0.806966 | ||||||||
\(437\) | −40.5093 | −1.93782 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0185 | 1.33725 | 0.668625 | − | 0.743599i | \(-0.266883\pi\) | ||||
0.668625 | + | 0.743599i | \(0.266883\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.83381 | 0.0872254 | ||||||||
\(443\) | −17.3370 | −0.823706 | −0.411853 | − | 0.911250i | \(-0.635118\pi\) | ||||
−0.411853 | + | 0.911250i | \(0.635118\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.42052 | 0.114744 | ||||||||
\(446\) | −25.4883 | −1.20691 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.92472 | 0.327162 | ||||||||
\(449\) | 29.5215 | 1.39321 | 0.696603 | − | 0.717457i | \(-0.254694\pi\) | ||||
0.696603 | + | 0.717457i | \(0.254694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 76.8990 | 3.61702 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −32.7309 | −1.53614 | ||||||||
\(455\) | 2.26638 | 0.106250 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.69725 | 0.453618 | 0.226809 | − | 0.973939i | \(-0.427171\pi\) | ||||
0.226809 | + | 0.973939i | \(0.427171\pi\) | |||||||
\(458\) | 6.15752 | 0.287722 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 94.4111 | 4.40194 | ||||||||
\(461\) | 19.2216 | 0.895240 | 0.447620 | − | 0.894224i | \(-0.352272\pi\) | ||||
0.447620 | + | 0.894224i | \(0.352272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5327 | 0.954235 | 0.477117 | − | 0.878840i | \(-0.341682\pi\) | ||||
0.477117 | + | 0.878840i | \(0.341682\pi\) | |||||||
\(464\) | 20.6532 | 0.958803 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.6902 | −1.09743 | ||||||||
\(467\) | −33.6714 | −1.55813 | −0.779064 | − | 0.626944i | \(-0.784305\pi\) | ||||
−0.779064 | + | 0.626944i | \(0.784305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.17828 | 0.285286 | ||||||||
\(470\) | −5.17112 | −0.238526 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.71178 | 0.400992 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −42.6429 | −1.95659 | ||||||||
\(476\) | −4.64501 | −0.212904 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.7231 | 0.627680 | ||||||||
\(479\) | −14.1708 | −0.647479 | −0.323740 | − | 0.946146i | \(-0.604940\pi\) | ||||
−0.323740 | + | 0.946146i | \(0.604940\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.287493 | 0.0131085 | ||||||||
\(482\) | −37.0522 | −1.68768 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −51.5111 | −2.33900 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.7415 | 1.25709 | 0.628543 | − | 0.777775i | \(-0.283652\pi\) | ||||
0.628543 | + | 0.777775i | \(0.283652\pi\) | |||||||
\(488\) | −35.2686 | −1.59653 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.55150 | −0.386317 | ||||||||
\(491\) | 3.44295 | 0.155378 | 0.0776891 | − | 0.996978i | \(-0.475246\pi\) | ||||
0.0776891 | + | 0.996978i | \(0.475246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.20086 | 0.234235 | ||||||||
\(494\) | −9.79837 | −0.440850 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.6275 | 0.566992 | ||||||||
\(497\) | −5.41687 | −0.242980 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.58923 | −0.115910 | −0.0579550 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579550 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(500\) | 28.5797 | 1.27812 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 68.1140 | 3.04008 | ||||||||
\(503\) | 22.9026 | 1.02118 | 0.510589 | − | 0.859825i | \(-0.329427\pi\) | ||||
0.510589 | + | 0.859825i | \(0.329427\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.8818 | −1.32972 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32.5407 | −1.44376 | ||||||||
\(509\) | 24.0985 | 1.06815 | 0.534074 | − | 0.845438i | \(-0.320660\pi\) | ||||
0.534074 | + | 0.845438i | \(0.320660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.70198 | −0.296478 | ||||||||
\(512\) | 42.5884 | 1.88216 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −70.2229 | −3.09740 | ||||||||
\(515\) | −3.23432 | −0.142521 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.08477 | −0.0476619 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 11.6550 | 0.511105 | ||||||||
\(521\) | 33.5057 | 1.46791 | 0.733956 | − | 0.679197i | \(-0.237672\pi\) | ||||
0.733956 | + | 0.679197i | \(0.237672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.1574 | −1.36242 | −0.681208 | − | 0.732090i | \(-0.738545\pi\) | ||||
−0.681208 | + | 0.732090i | \(0.738545\pi\) | |||||||
\(524\) | 19.6275 | 0.857432 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.9791 | 1.52516 | ||||||||
\(527\) | 3.17983 | 0.138516 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.4500 | 0.932608 | ||||||||
\(530\) | 83.9968 | 3.64859 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.8191 | 1.07605 | ||||||||
\(533\) | −3.85919 | −0.167160 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.9571 | −0.992522 | ||||||||
\(536\) | 31.7721 | 1.37235 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −59.6793 | −2.57296 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.6071 | 0.971957 | 0.485979 | − | 0.873971i | \(-0.338463\pi\) | ||||
0.485979 | + | 0.873971i | \(0.338463\pi\) | |||||||
\(542\) | −18.3765 | −0.789340 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.971245 | −0.0416418 | ||||||||
\(545\) | −14.3005 | −0.612567 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.4442 | −1.17343 | −0.586715 | − | 0.809794i | \(-0.699579\pi\) | ||||
−0.586715 | + | 0.809794i | \(0.699579\pi\) | |||||||
\(548\) | 89.3654 | 3.81750 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.7891 | −1.18386 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.65375 | −0.112849 | ||||||||
\(554\) | 47.3341 | 2.01103 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −80.9344 | −3.43238 | ||||||||
\(557\) | 30.2504 | 1.28175 | 0.640875 | − | 0.767645i | \(-0.278572\pi\) | ||||
0.640875 | + | 0.767645i | \(0.278572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.69300 | −0.240788 | ||||||||
\(560\) | −15.6550 | −0.661544 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.68834 | −0.197766 | ||||||||
\(563\) | −7.46234 | −0.314500 | −0.157250 | − | 0.987559i | \(-0.550263\pi\) | ||||
−0.157250 | + | 0.987559i | \(0.550263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 65.2640 | 2.74568 | ||||||||
\(566\) | −17.8882 | −0.751896 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.8565 | −1.16883 | ||||||||
\(569\) | −35.6483 | −1.49446 | −0.747228 | − | 0.664568i | \(-0.768616\pi\) | ||||
−0.747228 | + | 0.664568i | \(0.768616\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.8902 | 1.08347 | 0.541737 | − | 0.840548i | \(-0.317767\pi\) | ||||
0.541737 | + | 0.840548i | \(0.317767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.5615 | 0.607785 | ||||||||
\(575\) | 46.7911 | 1.95132 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.16382 | 0.339864 | 0.169932 | − | 0.985456i | \(-0.445645\pi\) | ||||
0.169932 | + | 0.985456i | \(0.445645\pi\) | |||||||
\(578\) | 38.7447 | 1.61157 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 64.7654 | 2.68924 | ||||||||
\(581\) | 6.69658 | 0.277821 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −34.4653 | −1.42619 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.06860 | −0.333311 | ||||||||
\(587\) | 12.4634 | 0.514419 | 0.257210 | − | 0.966356i | \(-0.417197\pi\) | ||||
0.257210 | + | 0.966356i | \(0.417197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.9904 | −0.700079 | ||||||||
\(590\) | 14.4867 | 0.596409 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.98585 | −0.0816180 | ||||||||
\(593\) | 23.6707 | 0.972037 | 0.486019 | − | 0.873948i | \(-0.338449\pi\) | ||||
0.486019 | + | 0.873948i | \(0.338449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.94221 | −0.161615 | ||||||||
\(596\) | −12.9165 | −0.529080 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.7515 | 0.439663 | ||||||||
\(599\) | −38.9809 | −1.59272 | −0.796358 | − | 0.604826i | \(-0.793243\pi\) | ||||
−0.796358 | + | 0.604826i | \(0.793243\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.5510 | 1.24620 | 0.623100 | − | 0.782142i | \(-0.285873\pi\) | ||||
0.623100 | + | 0.782142i | \(0.285873\pi\) | |||||||
\(602\) | 21.4808 | 0.875492 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 36.4690 | 1.48390 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.6173 | 1.52684 | 0.763420 | − | 0.645903i | \(-0.223519\pi\) | ||||
0.763420 | + | 0.645903i | \(0.223519\pi\) | |||||||
\(608\) | 5.18954 | 0.210464 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −58.6477 | −2.37458 | ||||||||
\(611\) | −0.395326 | −0.0159932 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.6272 | 0.711956 | 0.355978 | − | 0.934494i | \(-0.384148\pi\) | ||||
0.355978 | + | 0.934494i | \(0.384148\pi\) | |||||||
\(614\) | −77.9786 | −3.14696 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.4849 | 1.79089 | 0.895447 | − | 0.445168i | \(-0.146856\pi\) | ||||
0.895447 | + | 0.445168i | \(0.146856\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.20424 | −0.249369 | −0.124685 | − | 0.992196i | \(-0.539792\pi\) | ||||
−0.124685 | + | 0.992196i | \(0.539792\pi\) | |||||||
\(620\) | 39.5979 | 1.59029 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.2950 | −0.893949 | ||||||||
\(623\) | −0.698213 | −0.0279733 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.8356 | −0.433424 | ||||||||
\(626\) | −35.7652 | −1.42947 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.65531 | 0.185767 | ||||||||
\(629\) | −0.500073 | −0.0199392 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.8057 | 1.78369 | 0.891844 | − | 0.452344i | \(-0.149412\pi\) | ||||
0.891844 | + | 0.452344i | \(0.149412\pi\) | |||||||
\(632\) | −13.6471 | −0.542851 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −45.4307 | −1.80428 | ||||||||
\(635\) | −27.6172 | −1.09595 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.653752 | −0.0259026 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 65.1386 | 2.57483 | ||||||||
\(641\) | 10.2756 | 0.405863 | 0.202932 | − | 0.979193i | \(-0.434953\pi\) | ||||
0.202932 | + | 0.979193i | \(0.434953\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.4446 | −0.648511 | −0.324255 | − | 0.945970i | \(-0.605114\pi\) | ||||
−0.324255 | + | 0.945970i | \(0.605114\pi\) | |||||||
\(644\) | −27.2335 | −1.07315 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.0436 | 0.670570 | ||||||||
\(647\) | 26.9686 | 1.06025 | 0.530123 | − | 0.847920i | \(-0.322146\pi\) | ||||
0.530123 | + | 0.847920i | \(0.322146\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 11.3178 | 0.443921 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.6986 | −0.810621 | ||||||||
\(653\) | −7.10602 | −0.278080 | −0.139040 | − | 0.990287i | \(-0.544402\pi\) | ||||
−0.139040 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.6578 | 0.650875 | ||||||||
\(656\) | 26.6573 | 1.04079 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.49164 | 0.0581502 | ||||||||
\(659\) | 32.6279 | 1.27100 | 0.635502 | − | 0.772099i | \(-0.280793\pi\) | ||||
0.635502 | + | 0.772099i | \(0.280793\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.8165 | −1.31531 | −0.657654 | − | 0.753320i | \(-0.728451\pi\) | ||||
−0.657654 | + | 0.753320i | \(0.728451\pi\) | |||||||
\(662\) | 15.9759 | 0.620919 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 34.4375 | 1.33644 | ||||||||
\(665\) | 21.0639 | 0.816824 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.4924 | 1.18067 | ||||||||
\(668\) | 80.4980 | 3.11456 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 52.8335 | 2.04114 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.7496 | 0.915478 | 0.457739 | − | 0.889087i | \(-0.348659\pi\) | ||||
0.457739 | + | 0.889087i | \(0.348659\pi\) | |||||||
\(674\) | −15.4339 | −0.594491 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −51.3562 | −1.97524 | ||||||||
\(677\) | 45.6311 | 1.75375 | 0.876874 | − | 0.480721i | \(-0.159625\pi\) | ||||
0.876874 | + | 0.480721i | \(0.159625\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.8587 | 0.570224 | ||||||||
\(680\) | −20.2730 | −0.777435 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.8727 | 1.10478 | 0.552392 | − | 0.833585i | \(-0.313715\pi\) | ||||
0.552392 | + | 0.833585i | \(0.313715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 75.8442 | 2.89786 | ||||||||
\(686\) | 2.46673 | 0.0941803 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 39.3243 | 1.49923 | ||||||||
\(689\) | 6.42145 | 0.244638 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0635 | −1.02954 | −0.514772 | − | 0.857327i | \(-0.672123\pi\) | ||||
−0.514772 | + | 0.857327i | \(0.672123\pi\) | |||||||
\(692\) | 58.7994 | 2.23522 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 56.0334 | 2.12700 | ||||||||
\(695\) | −68.6889 | −2.60552 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.71279 | 0.254265 | ||||||||
\(698\) | −73.2473 | −2.77245 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −28.6678 | −1.08354 | ||||||||
\(701\) | −38.5156 | −1.45471 | −0.727357 | − | 0.686259i | \(-0.759252\pi\) | ||||
−0.727357 | + | 0.686259i | \(0.759252\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.67198 | 0.100776 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.8356 | −0.633616 | ||||||||
\(707\) | 8.61959 | 0.324173 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.89464 | −0.0711548 | −0.0355774 | − | 0.999367i | \(-0.511327\pi\) | ||||
−0.0355774 | + | 0.999367i | \(0.511327\pi\) | |||||||
\(710\) | −46.3223 | −1.73845 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.59060 | −0.134564 | ||||||||
\(713\) | 18.6432 | 0.698194 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.0522 | 0.712013 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.9077 | −0.668311 | ||||||||
\(719\) | −14.5772 | −0.543639 | −0.271819 | − | 0.962348i | \(-0.587625\pi\) | ||||
−0.271819 | + | 0.962348i | \(0.587625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.932958 | 0.0347452 | ||||||||
\(722\) | −44.1990 | −1.64492 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 40.4721 | 1.50413 | ||||||||
\(725\) | 32.0984 | 1.19210 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.04780 | 0.150125 | 0.0750623 | − | 0.997179i | \(-0.476084\pi\) | ||||
0.0750623 | + | 0.997179i | \(0.476084\pi\) | |||||||
\(728\) | −3.36196 | −0.124602 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −57.3120 | −2.12121 | ||||||||
\(731\) | 9.90257 | 0.366260 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.5012 | −0.868036 | −0.434018 | − | 0.900904i | \(-0.642905\pi\) | ||||
−0.434018 | + | 0.900904i | \(0.642905\pi\) | |||||||
\(734\) | 89.6327 | 3.30840 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.69437 | −0.209897 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.6786 | −1.20210 | −0.601051 | − | 0.799210i | \(-0.705251\pi\) | ||||
−0.601051 | + | 0.799210i | \(0.705251\pi\) | |||||||
\(740\) | −6.22732 | −0.228921 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24.2294 | −0.889489 | ||||||||
\(743\) | 18.1058 | 0.664237 | 0.332119 | − | 0.943238i | \(-0.392237\pi\) | ||||
0.332119 | + | 0.943238i | \(0.392237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.9622 | −0.401624 | ||||||||
\(746\) | 35.2529 | 1.29070 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.62212 | 0.241967 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.14357 | 0.333654 | 0.166827 | − | 0.985986i | \(-0.446648\pi\) | ||||
0.166827 | + | 0.985986i | \(0.446648\pi\) | |||||||
\(752\) | 2.73071 | 0.0995787 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.37548 | 0.268599 | ||||||||
\(755\) | 30.9512 | 1.12643 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.3509 | 1.72100 | 0.860499 | − | 0.509452i | \(-0.170152\pi\) | ||||
0.860499 | + | 0.509452i | \(0.170152\pi\) | |||||||
\(758\) | 6.27851 | 0.228046 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 108.323 | 3.92927 | ||||||||
\(761\) | −3.44828 | −0.125000 | −0.0625000 | − | 0.998045i | \(-0.519907\pi\) | ||||
−0.0625000 | + | 0.998045i | \(0.519907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.12507 | 0.149338 | ||||||||
\(764\) | −40.6146 | −1.46939 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −57.0720 | −2.06210 | ||||||||
\(767\) | 1.10749 | 0.0399892 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.9787 | 1.26137 | 0.630683 | − | 0.776041i | \(-0.282775\pi\) | ||||
0.630683 | + | 0.776041i | \(0.282775\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.1408 | 0.544928 | ||||||||
\(773\) | −25.3794 | −0.912832 | −0.456416 | − | 0.889766i | \(-0.650867\pi\) | ||||
−0.456416 | + | 0.889766i | \(0.650867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.6251 | 0.704956 | ||||||||
\(776\) | 76.4117 | 2.74302 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 74.6469 | 2.67622 | ||||||||
\(779\) | −35.8677 | −1.28509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.7015 | −0.668765 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.51578 | 0.161278 | ||||||||
\(785\) | 3.95095 | 0.141016 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.7552 | 1.06066 | 0.530329 | − | 0.847792i | \(-0.322068\pi\) | ||||
0.530329 | + | 0.847792i | \(0.322068\pi\) | |||||||
\(788\) | −24.1811 | −0.861415 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.6936 | −0.807400 | ||||||||
\(791\) | −18.8258 | −0.669369 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.48355 | −0.159215 | ||||||||
\(794\) | 55.9308 | 1.98491 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 46.9103 | 1.66269 | ||||||||
\(797\) | 6.24330 | 0.221149 | 0.110575 | − | 0.993868i | \(-0.464731\pi\) | ||||
0.110575 | + | 0.993868i | \(0.464731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.687641 | 0.0243270 | ||||||||
\(800\) | −5.99428 | −0.211930 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −40.0069 | −1.41269 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.1130 | −0.814626 | ||||||||
\(806\) | 4.50941 | 0.158837 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 44.3268 | 1.55941 | ||||||||
\(809\) | −39.1860 | −1.37771 | −0.688854 | − | 0.724900i | \(-0.741886\pi\) | ||||
−0.688854 | + | 0.724900i | \(0.741886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.3809 | −0.434753 | −0.217376 | − | 0.976088i | \(-0.569750\pi\) | ||||
−0.217376 | + | 0.976088i | \(0.569750\pi\) | |||||||
\(812\) | −18.6820 | −0.655609 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.5669 | −0.615341 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −52.9112 | −1.85113 | ||||||||
\(818\) | 86.4871 | 3.02395 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 83.5933 | 2.91920 | ||||||||
\(821\) | −47.6987 | −1.66470 | −0.832349 | − | 0.554252i | \(-0.813004\pi\) | ||||
−0.832349 | + | 0.554252i | \(0.813004\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.5207 | −0.506161 | −0.253080 | − | 0.967445i | \(-0.581444\pi\) | ||||
−0.253080 | + | 0.967445i | \(0.581444\pi\) | |||||||
\(824\) | 4.79779 | 0.167139 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.17878 | −0.145398 | ||||||||
\(827\) | 30.9372 | 1.07579 | 0.537896 | − | 0.843011i | \(-0.319219\pi\) | ||||
0.537896 | + | 0.843011i | \(0.319219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.0858057 | 0.00298015 | 0.00149008 | − | 0.999999i | \(-0.499526\pi\) | ||||
0.00149008 | + | 0.999999i | \(0.499526\pi\) | |||||||
\(830\) | 57.2658 | 1.98772 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.52705 | 0.156947 | ||||||||
\(833\) | 1.13715 | 0.0394000 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 68.3185 | 2.36426 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 69.7179 | 2.40837 | ||||||||
\(839\) | −10.6905 | −0.369078 | −0.184539 | − | 0.982825i | \(-0.559079\pi\) | ||||
−0.184539 | + | 0.982825i | \(0.559079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.08244 | −0.278705 | ||||||||
\(842\) | 34.0278 | 1.17267 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.6391 | 1.22675 | ||||||||
\(845\) | −43.5859 | −1.49940 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −44.3561 | −1.52319 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −19.6865 | −0.675242 | ||||||||
\(851\) | −2.93190 | −0.100504 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.2003 | 0.725884 | 0.362942 | − | 0.931812i | \(-0.381772\pi\) | ||||
0.362942 | + | 0.931812i | \(0.381772\pi\) | |||||||
\(854\) | 16.9173 | 0.578898 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 34.0546 | 1.16396 | ||||||||
\(857\) | 9.45359 | 0.322929 | 0.161464 | − | 0.986879i | \(-0.448378\pi\) | ||||
0.161464 | + | 0.986879i | \(0.448378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.8261 | −1.32473 | −0.662365 | − | 0.749181i | \(-0.730447\pi\) | ||||
−0.662365 | + | 0.749181i | \(0.730447\pi\) | |||||||
\(860\) | 123.315 | 4.20501 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 69.4879 | 2.36677 | ||||||||
\(863\) | 37.6046 | 1.28008 | 0.640038 | − | 0.768343i | \(-0.278919\pi\) | ||||
0.640038 | + | 0.768343i | \(0.278919\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49.9029 | 1.69675 | ||||||||
\(866\) | −34.9766 | −1.18855 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.4223 | −0.387697 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.03906 | 0.136858 | ||||||||
\(872\) | 21.2134 | 0.718377 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 99.9257 | 3.38004 | ||||||||
\(875\) | −6.99666 | −0.236530 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.0086 | 0.743178 | 0.371589 | − | 0.928397i | \(-0.378813\pi\) | ||||
0.371589 | + | 0.928397i | \(0.378813\pi\) | |||||||
\(878\) | −69.1142 | −2.33249 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.92969 | 0.233467 | 0.116734 | − | 0.993163i | \(-0.462758\pi\) | ||||
0.116734 | + | 0.993163i | \(0.462758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.3388 | 1.42481 | 0.712407 | − | 0.701767i | \(-0.247605\pi\) | ||||
0.712407 | + | 0.701767i | \(0.247605\pi\) | |||||||
\(884\) | −3.03668 | −0.102135 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.7657 | 1.43674 | ||||||||
\(887\) | −8.05647 | −0.270510 | −0.135255 | − | 0.990811i | \(-0.543185\pi\) | ||||
−0.135255 | + | 0.990811i | \(0.543185\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.96635 | 0.267183 | ||||||||
\(890\) | −5.97077 | −0.200141 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 42.2072 | 1.41320 | ||||||||
\(893\) | −3.67419 | −0.122952 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.1695 | 0.540488 | ||||||||
\(896\) | −18.7896 | −0.627717 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −72.8216 | −2.43009 | ||||||||
\(899\) | 12.7891 | 0.426541 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.1697 | −0.372115 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −96.8128 | −3.21995 | ||||||||
\(905\) | 34.3485 | 1.14178 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.89429 | 0.0961033 | 0.0480517 | − | 0.998845i | \(-0.484699\pi\) | ||||
0.0480517 | + | 0.998845i | \(0.484699\pi\) | |||||||
\(908\) | 54.2006 | 1.79871 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.59056 | −0.185325 | ||||||||
\(911\) | 20.2500 | 0.670912 | 0.335456 | − | 0.942056i | \(-0.391110\pi\) | ||||
0.335456 | + | 0.942056i | \(0.391110\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −23.9205 | −0.791220 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.1965 | −0.336902 | ||||||||
\(917\) | −4.80505 | −0.158677 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.7261 | 0.617718 | 0.308859 | − | 0.951108i | \(-0.400053\pi\) | ||||
0.308859 | + | 0.951108i | \(0.400053\pi\) | |||||||
\(920\) | −118.860 | −3.91869 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −47.4146 | −1.56152 | ||||||||
\(923\) | −3.54128 | −0.116563 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.08632 | −0.101478 | ||||||||
\(926\) | −50.6486 | −1.66442 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.90630 | −0.128230 | ||||||||
\(929\) | 45.2701 | 1.48526 | 0.742631 | − | 0.669700i | \(-0.233577\pi\) | ||||
0.742631 | + | 0.669700i | \(0.233577\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.07602 | −0.199134 | ||||||||
\(932\) | 39.2296 | 1.28501 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 83.0584 | 2.71775 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4599 | 0.962413 | 0.481207 | − | 0.876607i | \(-0.340199\pi\) | ||||
0.481207 | + | 0.876607i | \(0.340199\pi\) | |||||||
\(938\) | −15.2401 | −0.497609 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.56308 | 0.279297 | ||||||||
\(941\) | −58.2346 | −1.89839 | −0.949197 | − | 0.314683i | \(-0.898102\pi\) | ||||
−0.949197 | + | 0.314683i | \(0.898102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.3568 | 1.28163 | ||||||||
\(944\) | −7.64998 | −0.248986 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.3642 | −1.47414 | −0.737069 | − | 0.675818i | \(-0.763791\pi\) | ||||
−0.737069 | + | 0.675818i | \(0.763791\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.38143 | −0.142227 | ||||||||
\(950\) | 105.189 | 3.41277 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.84788 | 0.189531 | ||||||||
\(953\) | 41.3375 | 1.33905 | 0.669527 | − | 0.742788i | \(-0.266497\pi\) | ||||
0.669527 | + | 0.742788i | \(0.266497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.4695 | −1.11541 | ||||||||
\(956\) | −22.7247 | −0.734968 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34.9555 | 1.12936 | ||||||||
\(959\) | −21.8777 | −0.706469 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.1807 | −0.747763 | ||||||||
\(962\) | −0.709167 | −0.0228645 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 61.3563 | 1.97615 | ||||||||
\(965\) | 12.8499 | 0.413654 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.52818 | −0.209932 | −0.104966 | − | 0.994476i | \(-0.533473\pi\) | ||||
−0.104966 | + | 0.994476i | \(0.533473\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 127.064 | 4.07978 | ||||||||
\(971\) | −28.8587 | −0.926119 | −0.463060 | − | 0.886327i | \(-0.653248\pi\) | ||||
−0.463060 | + | 0.886327i | \(0.653248\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.8137 | 0.635199 | ||||||||
\(974\) | −68.4308 | −2.19266 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.9700 | 0.991327 | ||||||||
\(977\) | 8.98453 | 0.287441 | 0.143720 | − | 0.989618i | \(-0.454093\pi\) | ||||
0.143720 | + | 0.989618i | \(0.454093\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14.1608 | 0.452350 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.49284 | −0.271017 | ||||||||
\(983\) | −36.8819 | −1.17635 | −0.588175 | − | 0.808734i | \(-0.700153\pi\) | ||||
−0.588175 | + | 0.808734i | \(0.700153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.5224 | −0.653899 | ||||||||
\(986\) | −12.8291 | −0.408562 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.2255 | 0.516203 | ||||||||
\(989\) | 58.0583 | 1.84615 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.98352 | −0.0947746 | −0.0473873 | − | 0.998877i | \(-0.515089\pi\) | ||||
−0.0473873 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(992\) | −2.38833 | −0.0758297 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.3620 | 0.423815 | ||||||||
\(995\) | 39.8127 | 1.26215 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 62.8553 | 1.99065 | 0.995324 | − | 0.0965930i | \(-0.0307945\pi\) | ||||
0.995324 | + | 0.0965930i | \(0.0307945\pi\) | |||||||
\(998\) | 6.38694 | 0.202175 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.ch.1.1 | 4 | ||
3.2 | odd | 2 | 847.2.a.l.1.4 | 4 | |||
11.5 | even | 5 | 693.2.m.g.190.2 | 8 | |||
11.9 | even | 5 | 693.2.m.g.631.2 | 8 | |||
11.10 | odd | 2 | 7623.2.a.co.1.4 | 4 | |||
21.20 | even | 2 | 5929.2.a.bi.1.4 | 4 | |||
33.2 | even | 10 | 847.2.f.q.323.2 | 8 | |||
33.5 | odd | 10 | 77.2.f.a.36.1 | yes | 8 | ||
33.8 | even | 10 | 847.2.f.s.372.1 | 8 | |||
33.14 | odd | 10 | 847.2.f.p.372.2 | 8 | |||
33.17 | even | 10 | 847.2.f.q.729.2 | 8 | |||
33.20 | odd | 10 | 77.2.f.a.15.1 | ✓ | 8 | ||
33.26 | odd | 10 | 847.2.f.p.148.2 | 8 | |||
33.29 | even | 10 | 847.2.f.s.148.1 | 8 | |||
33.32 | even | 2 | 847.2.a.k.1.1 | 4 | |||
231.5 | even | 30 | 539.2.q.b.410.2 | 16 | |||
231.20 | even | 10 | 539.2.f.d.246.1 | 8 | |||
231.38 | even | 30 | 539.2.q.b.520.1 | 16 | |||
231.53 | odd | 30 | 539.2.q.c.422.2 | 16 | |||
231.86 | odd | 30 | 539.2.q.c.312.1 | 16 | |||
231.104 | even | 10 | 539.2.f.d.344.1 | 8 | |||
231.137 | odd | 30 | 539.2.q.c.520.1 | 16 | |||
231.152 | even | 30 | 539.2.q.b.312.1 | 16 | |||
231.170 | odd | 30 | 539.2.q.c.410.2 | 16 | |||
231.185 | even | 30 | 539.2.q.b.422.2 | 16 | |||
231.230 | odd | 2 | 5929.2.a.bb.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.15.1 | ✓ | 8 | 33.20 | odd | 10 | ||
77.2.f.a.36.1 | yes | 8 | 33.5 | odd | 10 | ||
539.2.f.d.246.1 | 8 | 231.20 | even | 10 | |||
539.2.f.d.344.1 | 8 | 231.104 | even | 10 | |||
539.2.q.b.312.1 | 16 | 231.152 | even | 30 | |||
539.2.q.b.410.2 | 16 | 231.5 | even | 30 | |||
539.2.q.b.422.2 | 16 | 231.185 | even | 30 | |||
539.2.q.b.520.1 | 16 | 231.38 | even | 30 | |||
539.2.q.c.312.1 | 16 | 231.86 | odd | 30 | |||
539.2.q.c.410.2 | 16 | 231.170 | odd | 30 | |||
539.2.q.c.422.2 | 16 | 231.53 | odd | 30 | |||
539.2.q.c.520.1 | 16 | 231.137 | odd | 30 | |||
693.2.m.g.190.2 | 8 | 11.5 | even | 5 | |||
693.2.m.g.631.2 | 8 | 11.9 | even | 5 | |||
847.2.a.k.1.1 | 4 | 33.32 | even | 2 | |||
847.2.a.l.1.4 | 4 | 3.2 | odd | 2 | |||
847.2.f.p.148.2 | 8 | 33.26 | odd | 10 | |||
847.2.f.p.372.2 | 8 | 33.14 | odd | 10 | |||
847.2.f.q.323.2 | 8 | 33.2 | even | 10 | |||
847.2.f.q.729.2 | 8 | 33.17 | even | 10 | |||
847.2.f.s.148.1 | 8 | 33.29 | even | 10 | |||
847.2.f.s.372.1 | 8 | 33.8 | even | 10 | |||
5929.2.a.bb.1.1 | 4 | 231.230 | odd | 2 | |||
5929.2.a.bi.1.4 | 4 | 21.20 | even | 2 | |||
7623.2.a.ch.1.1 | 4 | 1.1 | even | 1 | trivial | ||
7623.2.a.co.1.4 | 4 | 11.10 | odd | 2 |