Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 7x^{5} + 11x^{4} + 12x^{3} - 14x^{2} - 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.05123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.597616 | −0.267262 | −0.133631 | − | 0.991031i | \(-0.542664\pi\) | ||||
−0.133631 | + | 0.991031i | \(0.542664\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60994 | −0.986465 | −0.493233 | − | 0.869897i | \(-0.664185\pi\) | ||||
−0.493233 | + | 0.869897i | \(0.664185\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.70008 | 1.41713 | 0.708564 | − | 0.705646i | \(-0.249343\pi\) | ||||
0.708564 | + | 0.705646i | \(0.249343\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.30432 | −1.19380 | −0.596902 | − | 0.802314i | \(-0.703602\pi\) | ||||
−0.596902 | + | 0.802314i | \(0.703602\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.597616 | −0.154304 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.94088 | 0.713269 | 0.356635 | − | 0.934244i | \(-0.383924\pi\) | ||||
0.356635 | + | 0.934244i | \(0.383924\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.08825 | 0.937910 | 0.468955 | − | 0.883222i | \(-0.344631\pi\) | ||||
0.468955 | + | 0.883222i | \(0.344631\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.60994 | −0.569536 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.33094 | −0.486035 | −0.243018 | − | 0.970022i | \(-0.578137\pi\) | ||||
−0.243018 | + | 0.970022i | \(0.578137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.64285 | −0.928571 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00408 | −0.372148 | −0.186074 | − | 0.982536i | \(-0.559576\pi\) | ||||
−0.186074 | + | 0.982536i | \(0.559576\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.83579 | −1.04814 | −0.524070 | − | 0.851675i | \(-0.675587\pi\) | ||||
−0.524070 | + | 0.851675i | \(0.675587\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.70008 | 0.818179 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.55974 | 0.263645 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.82343 | −0.299770 | −0.149885 | − | 0.988703i | \(-0.547890\pi\) | ||||
−0.149885 | + | 0.988703i | \(0.547890\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.30432 | −0.689243 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.73365 | 1.36397 | 0.681984 | − | 0.731367i | \(-0.261118\pi\) | ||||
0.681984 | + | 0.731367i | \(0.261118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.8623 | −1.80898 | −0.904489 | − | 0.426496i | \(-0.859748\pi\) | ||||
−0.904489 | + | 0.426496i | \(0.859748\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.597616 | −0.0890874 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.91468 | 0.425150 | 0.212575 | − | 0.977145i | \(-0.431815\pi\) | ||||
0.212575 | + | 0.977145i | \(0.431815\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.188202 | −0.0268860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.94088 | 0.411806 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.63168 | 1.32301 | 0.661507 | − | 0.749939i | \(-0.269917\pi\) | ||||
0.661507 | + | 0.749939i | \(0.269917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.80885 | −0.378745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.08825 | 0.541502 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.28216 | −0.817867 | −0.408934 | − | 0.912564i | \(-0.634099\pi\) | ||||
−0.408934 | + | 0.912564i | \(0.634099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.58971 | −1.09980 | −0.549900 | − | 0.835231i | \(-0.685334\pi\) | ||||
−0.549900 | + | 0.835231i | \(0.685334\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.60994 | −0.328822 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.57233 | 0.319059 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.46847 | 0.668080 | 0.334040 | − | 0.942559i | \(-0.391588\pi\) | ||||
0.334040 | + | 0.942559i | \(0.391588\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.33094 | −0.280612 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.16011 | −1.08711 | −0.543553 | − | 0.839375i | \(-0.682921\pi\) | ||||
−0.543553 | + | 0.839375i | \(0.682921\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.56015 | −0.299643 | −0.149822 | − | 0.988713i | \(-0.547870\pi\) | ||||
−0.149822 | + | 0.988713i | \(0.547870\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.64285 | −0.536111 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.2669 | −1.39795 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.32690 | −0.486815 | −0.243407 | − | 0.969924i | \(-0.578265\pi\) | ||||
−0.243407 | + | 0.969924i | \(0.578265\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.40318 | 0.922369 | 0.461185 | − | 0.887304i | \(-0.347425\pi\) | ||||
0.461185 | + | 0.887304i | \(0.347425\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.75752 | −0.190630 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00408 | −0.214860 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.59052 | 0.910593 | 0.455297 | − | 0.890340i | \(-0.349533\pi\) | ||||
0.455297 | + | 0.890340i | \(0.349533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.2340 | 1.17765 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.83579 | −0.605144 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.44321 | −0.250668 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.10370 | 0.619737 | 0.309868 | − | 0.950779i | \(-0.399715\pi\) | ||||
0.309868 | + | 0.950779i | \(0.399715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.70008 | 0.472376 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.97986 | 0.396011 | 0.198005 | − | 0.980201i | \(-0.436554\pi\) | ||||
0.198005 | + | 0.980201i | \(0.436554\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.527144 | 0.0519410 | 0.0259705 | − | 0.999663i | \(-0.491732\pi\) | ||||
0.0259705 | + | 0.999663i | \(0.491732\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.55974 | 0.152215 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.5907 | −1.70056 | −0.850279 | − | 0.526332i | \(-0.823567\pi\) | ||||
−0.850279 | + | 0.526332i | \(0.823567\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.62048 | −0.346779 | −0.173389 | − | 0.984853i | \(-0.555472\pi\) | ||||
−0.173389 | + | 0.984853i | \(0.555472\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.82343 | −0.173072 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.2414 | −1.24564 | −0.622822 | − | 0.782364i | \(-0.714014\pi\) | ||||
−0.622822 | + | 0.782364i | \(0.714014\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.39301 | 0.129899 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.30432 | −0.397935 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.67554 | −0.703615 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0908 | 1.00825 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.73365 | 0.787487 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.76273 | 0.515434 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7823 | 1.04551 | 0.522756 | − | 0.852483i | \(-0.324904\pi\) | ||||
0.522756 | + | 0.852483i | \(0.324904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.8623 | −1.04441 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.718799 | −0.0628018 | −0.0314009 | − | 0.999507i | \(-0.509997\pi\) | ||||
−0.0314009 | + | 0.999507i | \(0.509997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.6701 | −0.925215 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.597616 | −0.0514346 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.6668 | 1.50937 | 0.754687 | − | 0.656086i | \(-0.227789\pi\) | ||||
0.754687 | + | 0.656086i | \(0.227789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.9527 | −1.86200 | −0.931002 | − | 0.365013i | \(-0.881064\pi\) | ||||
−0.931002 | + | 0.365013i | \(0.881064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.91468 | 0.245460 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.2307 | −1.69177 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.19767 | 0.0994611 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.188202 | −0.0155227 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.43757 | −0.445463 | −0.222731 | − | 0.974880i | \(-0.571497\pi\) | ||||
−0.222731 | + | 0.974880i | \(0.571497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.821226 | −0.0668304 | −0.0334152 | − | 0.999442i | \(-0.510638\pi\) | ||||
−0.0334152 | + | 0.999442i | \(0.510638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.94088 | 0.237756 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.48757 | 0.280128 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.50629 | −0.758685 | −0.379342 | − | 0.925256i | \(-0.623850\pi\) | ||||
−0.379342 | + | 0.925256i | \(0.623850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.63168 | 0.763842 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.08362 | 0.479457 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2885 | 0.962506 | 0.481253 | − | 0.876582i | \(-0.340182\pi\) | ||||
0.481253 | + | 0.876582i | \(0.340182\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.80885 | −0.218668 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.52719 | 0.425169 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.08825 | 0.312637 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.7951 | 1.65705 | 0.828525 | − | 0.559952i | \(-0.189180\pi\) | ||||
0.828525 | + | 0.559952i | \(0.189180\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.1176 | 0.916003 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.28216 | −0.472196 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.7053 | −1.24861 | −0.624307 | − | 0.781179i | \(-0.714619\pi\) | ||||
−0.624307 | + | 0.781179i | \(0.714619\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.62717 | 0.269606 | 0.134803 | − | 0.990872i | \(-0.456960\pi\) | ||||
0.134803 | + | 0.990872i | \(0.456960\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.58971 | −0.634969 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.08971 | 0.0801171 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.8224 | 1.01079 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.60994 | −0.189845 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.6156 | −1.41933 | −0.709667 | − | 0.704537i | \(-0.751154\pi\) | ||||
−0.709667 | + | 0.704537i | \(0.751154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.10177 | −0.295252 | −0.147626 | − | 0.989043i | \(-0.547163\pi\) | ||||
−0.147626 | + | 0.989043i | \(0.547163\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.57233 | 0.184209 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.5624 | −1.03753 | −0.518763 | − | 0.854918i | \(-0.673607\pi\) | ||||
−0.518763 | + | 0.854918i | \(0.673607\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.9202 | −1.34122 | −0.670608 | − | 0.741812i | \(-0.733967\pi\) | ||||
−0.670608 | + | 0.741812i | \(0.733967\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.46847 | 0.385716 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.23053 | 0.367111 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.21937 | −0.364537 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.33094 | −0.162012 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.2151 | 1.32914 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7857 | −1.01789 | −0.508944 | − | 0.860800i | \(-0.669964\pi\) | ||||
−0.508944 | + | 0.860800i | \(0.669964\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.16011 | −0.627641 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.08908 | 0.483472 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.2311 | 1.03395 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.56015 | −0.172999 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.6585 | −0.851504 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.1986 | −0.883844 | −0.441922 | − | 0.897054i | \(-0.645703\pi\) | ||||
−0.441922 | + | 0.897054i | \(0.645703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.64285 | −0.309524 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.0436562 | −0.00289756 | −0.00144878 | − | 0.999999i | \(-0.500461\pi\) | ||||
−0.00144878 | + | 0.999999i | \(0.500461\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2711 | −1.14131 | −0.570654 | − | 0.821190i | \(-0.693310\pi\) | ||||
−0.570654 | + | 0.821190i | \(0.693310\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.2669 | −0.807106 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.50687 | −0.295255 | −0.147627 | − | 0.989043i | \(-0.547164\pi\) | ||||
−0.147627 | + | 0.989043i | \(0.547164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.74186 | −0.113626 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.32690 | −0.281063 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.31017 | −0.343486 | −0.171743 | − | 0.985142i | \(-0.554940\pi\) | ||||
−0.171743 | + | 0.985142i | \(0.554940\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0415 | −0.646830 | −0.323415 | − | 0.946257i | \(-0.604831\pi\) | ||||
−0.323415 | + | 0.946257i | \(0.604831\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.112473 | 0.00718562 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.5972 | −1.11968 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.40318 | 0.532530 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.4734 | −0.850436 | −0.425218 | − | 0.905091i | \(-0.639802\pi\) | ||||
−0.425218 | + | 0.905091i | \(0.639802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.9556 | −0.688774 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.75752 | −0.110060 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.27420 | −0.516130 | −0.258065 | − | 0.966127i | \(-0.583085\pi\) | ||||
−0.258065 | + | 0.966127i | \(0.583085\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.75904 | 0.295712 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00408 | −0.124049 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.94503 | 0.181598 | 0.0907990 | − | 0.995869i | \(-0.471058\pi\) | ||||
0.0907990 | + | 0.995869i | \(0.471058\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.75605 | −0.353591 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.59052 | 0.525731 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.30723 | 0.140675 | 0.0703373 | − | 0.997523i | \(-0.477592\pi\) | ||||
0.0703373 | + | 0.997523i | \(0.477592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.9041 | −1.08759 | −0.543797 | − | 0.839217i | \(-0.683014\pi\) | ||||
−0.543797 | + | 0.839217i | \(0.683014\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.2340 | 0.679915 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.8218 | −1.31590 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.7020 | 1.12369 | 0.561846 | − | 0.827242i | \(-0.310091\pi\) | ||||
0.561846 | + | 0.827242i | \(0.310091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.83579 | −0.349380 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.7088 | −0.758144 | −0.379072 | − | 0.925367i | \(-0.623757\pi\) | ||||
−0.379072 | + | 0.925367i | \(0.623757\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.7962 | −1.89009 | −0.945044 | − | 0.326944i | \(-0.893981\pi\) | ||||
−0.945044 | + | 0.326944i | \(0.893981\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.44321 | −0.144723 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.7943 | −1.34551 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.35120 | −0.491247 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.10370 | 0.357805 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.5156 | 0.614327 | 0.307164 | − | 0.951657i | \(-0.400620\pi\) | ||||
0.307164 | + | 0.951657i | \(0.400620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.75432 | 0.218585 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.70008 | 0.272726 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.0331 | 0.580231 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.9598 | 1.78449 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.97986 | 0.228637 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.13335 | 0.293935 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.2239 | −1.61082 | −0.805412 | − | 0.592716i | \(-0.798056\pi\) | ||||
−0.805412 | + | 0.592716i | \(0.798056\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.527144 | 0.0299882 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.06229 | 0.287056 | 0.143528 | − | 0.989646i | \(-0.454155\pi\) | ||||
0.143528 | + | 0.989646i | \(0.454155\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.34882 | 0.245810 | 0.122905 | − | 0.992418i | \(-0.460779\pi\) | ||||
0.122905 | + | 0.992418i | \(0.460779\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.55974 | 0.0878816 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.2380 | 1.02435 | 0.512175 | − | 0.858881i | \(-0.328840\pi\) | ||||
0.512175 | + | 0.858881i | \(0.328840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.41934 | −0.527382 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.5907 | −0.981818 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0231 | 0.668982 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.9843 | 1.10853 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.62048 | −0.200213 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.60715 | −0.419396 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.31296 | −0.346992 | −0.173496 | − | 0.984835i | \(-0.555506\pi\) | ||||
−0.173496 | + | 0.984835i | \(0.555506\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.82343 | −0.0999232 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.26805 | −0.178553 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.2585 | 0.558815 | 0.279407 | − | 0.960173i | \(-0.409862\pi\) | ||||
0.279407 | + | 0.960173i | \(0.409862\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.2414 | −0.719173 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.4287 | −1.48535 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.7608 | 1.01299 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.39301 | 0.0749971 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.2848 | −1.35736 | −0.678680 | − | 0.734434i | \(-0.737448\pi\) | ||||
−0.678680 | + | 0.734434i | \(0.737448\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.7879 | 0.952165 | 0.476083 | − | 0.879401i | \(-0.342056\pi\) | ||||
0.476083 | + | 0.879401i | \(0.342056\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.30432 | −0.229748 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.9434 | −1.16793 | −0.583964 | − | 0.811780i | \(-0.698499\pi\) | ||||
−0.583964 | + | 0.811780i | \(0.698499\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.47423 | 0.290542 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.67554 | −0.406233 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.6414 | 0.719967 | 0.359983 | − | 0.932959i | \(-0.382782\pi\) | ||||
0.359983 | + | 0.932959i | \(0.382782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.28618 | −0.120325 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.0908 | 0.582115 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.52999 | 0.0800833 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.32286 | −0.330051 | −0.165025 | − | 0.986289i | \(-0.552771\pi\) | ||||
−0.165025 | + | 0.986289i | \(0.552771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.73365 | 0.454656 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.1381 | −1.30511 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.51797 | 0.0785974 | 0.0392987 | − | 0.999228i | \(-0.487488\pi\) | ||||
0.0392987 | + | 0.999228i | \(0.487488\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.76273 | 0.297586 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.62620 | 0.444272 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.06679 | 0.0547973 | 0.0273986 | − | 0.999625i | \(-0.491278\pi\) | ||||
0.0273986 | + | 0.999625i | \(0.491278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7823 | 0.603626 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.8956 | −0.607837 | −0.303919 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303919 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.33093 | 0.373619 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.8623 | −0.602993 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.6928 | −1.09987 | −0.549935 | − | 0.835207i | \(-0.685348\pi\) | ||||
−0.549935 | + | 0.835207i | \(0.685348\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.85503 | −0.346674 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.718799 | −0.0362586 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.58583 | 0.130107 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.338020 | −0.0169648 | −0.00848238 | − | 0.999964i | \(-0.502700\pi\) | ||||
−0.00848238 | + | 0.999964i | \(0.502700\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.6701 | −0.534173 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.5413 | 1.17560 | 0.587798 | − | 0.809008i | \(-0.299995\pi\) | ||||
0.587798 | + | 0.809008i | \(0.299995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.1191 | 1.25127 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.597616 | −0.0296958 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.57026 | −0.424812 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.86567 | −0.487826 | −0.243913 | − | 0.969797i | \(-0.578431\pi\) | ||||
−0.243913 | + | 0.969797i | \(0.578431\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.6668 | 0.871437 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.3961 | 0.806798 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.02188 | −0.246514 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.9527 | −1.07503 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.01568 | −0.196179 | −0.0980895 | − | 0.995178i | \(-0.531273\pi\) | ||||
−0.0980895 | + | 0.995178i | \(0.531273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6265 | 0.664116 | 0.332058 | − | 0.943259i | \(-0.392257\pi\) | ||||
0.332058 | + | 0.943259i | \(0.392257\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.91468 | 0.141717 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.6541 | −0.662321 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.4186 | 1.08491 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.2307 | −0.976746 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.0798 | −1.64157 | −0.820783 | − | 0.571241i | \(-0.806462\pi\) | ||||
−0.820783 | + | 0.571241i | \(0.806462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.6902 | −0.609853 | −0.304926 | − | 0.952376i | \(-0.598632\pi\) | ||||
−0.304926 | + | 0.952376i | \(0.598632\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.19767 | 0.0574239 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.52948 | −0.455857 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.2168 | 0.773985 | 0.386993 | − | 0.922083i | \(-0.373514\pi\) | ||||
0.386993 | + | 0.922083i | \(0.373514\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.188202 | −0.00896202 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.51185 | 0.404410 | 0.202205 | − | 0.979343i | \(-0.435189\pi\) | ||||
0.202205 | + | 0.979343i | \(0.435189\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.13384 | −0.243367 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.43757 | −0.257188 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.0909 | −0.806568 | −0.403284 | − | 0.915075i | \(-0.632131\pi\) | ||||
−0.403284 | + | 0.915075i | \(0.632131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.0489 | 1.93292 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.821226 | −0.0385846 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.71364 | −0.314740 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.6512 | −1.01280 | −0.506400 | − | 0.862299i | \(-0.669024\pi\) | ||||
−0.506400 | + | 0.862299i | \(0.669024\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.94088 | 0.137269 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.243769 | −0.0113534 | −0.00567672 | − | 0.999984i | \(-0.501807\pi\) | ||||
−0.00567672 | + | 0.999984i | \(0.501807\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.8493 | 1.38721 | 0.693606 | − | 0.720354i | \(-0.256021\pi\) | ||||
0.693606 | + | 0.720354i | \(0.256021\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.48757 | 0.161732 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.9645 | −1.01640 | −0.508198 | − | 0.861240i | \(-0.669688\pi\) | ||||
−0.508198 | + | 0.861240i | \(0.669688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.2724 | −0.659038 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.50629 | −0.438027 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −55.7536 | −2.56355 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.9812 | −0.870916 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.63168 | 0.441004 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.4694 | 1.16372 | 0.581862 | − | 0.813287i | \(-0.302324\pi\) | ||||
0.581862 | + | 0.813287i | \(0.302324\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.84862 | 0.357866 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.08362 | 0.276814 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.64767 | −0.165632 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.6138 | −0.480959 | −0.240480 | − | 0.970654i | \(-0.577305\pi\) | ||||
−0.240480 | + | 0.970654i | \(0.577305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.2885 | 0.555703 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.3302 | −0.962617 | −0.481308 | − | 0.876551i | \(-0.659838\pi\) | ||||
−0.481308 | + | 0.876551i | \(0.659838\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.89376 | −0.265442 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.80885 | −0.126248 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.9074 | 1.07239 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.09710 | 0.0491129 | 0.0245565 | − | 0.999698i | \(-0.492183\pi\) | ||||
0.0245565 | + | 0.999698i | \(0.492183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.3037 | 1.44035 | 0.720175 | − | 0.693793i | \(-0.244062\pi\) | ||||
0.720175 | + | 0.693793i | \(0.244062\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.37843 | −0.105839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.52719 | 0.245471 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.6050 | −1.35654 | −0.678271 | − | 0.734812i | \(-0.737270\pi\) | ||||
−0.678271 | + | 0.734812i | \(0.737270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.68185 | 0.295588 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.08825 | 0.180501 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.315030 | −0.0138819 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6992 | 0.602492 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.7951 | 0.956699 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.2872 | 1.58977 | 0.794885 | − | 0.606759i | \(-0.207531\pi\) | ||||
0.794885 | + | 0.606759i | \(0.207531\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.5672 | 1.42406 | 0.712031 | − | 0.702148i | \(-0.247775\pi\) | ||||
0.712031 | + | 0.702148i | \(0.247775\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.1176 | 0.528855 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.1624 | −0.747605 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5667 | −0.763770 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.28216 | −0.272622 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.5925 | −1.62831 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.5125 | 0.454495 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.7053 | −0.720887 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.884567 | −0.0381010 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6189 | −0.456541 | −0.228270 | − | 0.973598i | \(-0.573307\pi\) | ||||
−0.228270 | + | 0.973598i | \(0.573307\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.62717 | 0.155657 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.16366 | 0.0926808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.13950 | 0.134235 | 0.0671177 | − | 0.997745i | \(-0.478620\pi\) | ||||
0.0671177 | + | 0.997745i | \(0.478620\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.58971 | −0.366600 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.19318 | −0.349041 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.2930 | 0.480226 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.08971 | 0.0462556 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.4739 | 1.16411 | 0.582053 | − | 0.813151i | \(-0.302250\pi\) | ||||
0.582053 | + | 0.813151i | \(0.302250\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.0590 | 2.15957 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.8224 | 0.583582 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.0913 | 0.678169 | 0.339084 | − | 0.940756i | \(-0.389883\pi\) | ||||
0.339084 | + | 0.940756i | \(0.389883\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.91326 | 0.332913 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.60994 | −0.109607 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.40907 | −0.394449 | −0.197224 | − | 0.980358i | \(-0.563193\pi\) | ||||
−0.197224 | + | 0.980358i | \(0.563193\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.6950 | 1.61934 | 0.809668 | − | 0.586888i | \(-0.199647\pi\) | ||||
0.809668 | + | 0.586888i | \(0.199647\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.6156 | −0.819453 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8222 | 0.451318 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.8472 | 1.11767 | 0.558833 | − | 0.829280i | \(-0.311249\pi\) | ||||
0.558833 | + | 0.829280i | \(0.311249\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.10177 | −0.170464 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.9318 | −0.909885 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.2697 | 1.87488 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.57233 | 0.106353 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.0850 | 1.53066 | 0.765332 | − | 0.643636i | \(-0.222575\pi\) | ||||
0.765332 | + | 0.643636i | \(0.222575\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.8582 | −0.983060 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.5624 | −0.599016 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.0629 | −0.988145 | −0.494072 | − | 0.869421i | \(-0.664492\pi\) | ||||
−0.494072 | + | 0.869421i | \(0.664492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.58703 | 0.188050 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.9202 | −0.774352 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.7712 | −1.54329 | −0.771644 | − | 0.636054i | \(-0.780565\pi\) | ||||
−0.771644 | + | 0.636054i | \(0.780565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.0915 | −0.697175 | −0.348588 | − | 0.937276i | \(-0.613339\pi\) | ||||
−0.348588 | + | 0.937276i | \(0.613339\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.46847 | 0.222693 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.62803 | −0.269468 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.5907 | 0.592217 | 0.296109 | − | 0.955154i | \(-0.404311\pi\) | ||||
0.296109 | + | 0.955154i | \(0.404311\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.23053 | 0.211952 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.5457 | −0.507546 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.1169 | 1.45875 | 0.729375 | − | 0.684115i | \(-0.239811\pi\) | ||||
0.729375 | + | 0.684115i | \(0.239811\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.21937 | −0.210465 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.4728 | 1.18653 | 0.593265 | − | 0.805007i | \(-0.297838\pi\) | ||||
0.593265 | + | 0.805007i | \(0.297838\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.6128 | −0.828497 | −0.414249 | − | 0.910164i | \(-0.635956\pi\) | ||||
−0.414249 | + | 0.910164i | \(0.635956\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.33094 | −0.0935375 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.4208 | −0.898269 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.7704 | 0.790815 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.2151 | 0.767378 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.36249 | −0.213816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.1872 | 0.843450 | 0.421725 | − | 0.906724i | \(-0.361425\pi\) | ||||
0.421725 | + | 0.906724i | \(0.361425\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.7857 | −0.587678 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.04130 | −0.279426 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.810084 | 0.0320967 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.16011 | −0.362368 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0393 | −0.436025 | −0.218012 | − | 0.975946i | \(-0.569957\pi\) | ||||
−0.218012 | + | 0.975946i | \(0.569957\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.4130 | −1.15994 | −0.579968 | − | 0.814639i | \(-0.696935\pi\) | ||||
−0.579968 | + | 0.814639i | \(0.696935\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.08908 | 0.279132 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.6968 | −1.32476 | −0.662378 | − | 0.749169i | \(-0.730453\pi\) | ||||
−0.662378 | + | 0.749169i | \(0.730453\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.5267 | −1.15902 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.2311 | 0.596953 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.89310 | −0.152349 | −0.0761745 | − | 0.997095i | \(-0.524271\pi\) | ||||
−0.0761745 | + | 0.997095i | \(0.524271\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.429566 | 0.0167845 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.56015 | −0.0998810 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.8140 | 1.90152 | 0.950761 | − | 0.309926i | \(-0.100304\pi\) | ||||
0.950761 | + | 0.309926i | \(0.100304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.28000 | −0.244264 | −0.122132 | − | 0.992514i | \(-0.538973\pi\) | ||||
−0.122132 | + | 0.992514i | \(0.538973\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.6585 | −0.491616 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.37663 | 0.247275 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.67139 | 0.180877 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.1986 | −0.510287 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.3723 | −1.55856 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.2666 | −0.973954 | −0.486977 | − | 0.873415i | \(-0.661901\pi\) | ||||
−0.486977 | + | 0.873415i | \(0.661901\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.64285 | −0.178704 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.38840 | 0.322392 | 0.161196 | − | 0.986922i | \(-0.448465\pi\) | ||||
0.161196 | + | 0.986922i | \(0.448465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.9303 | −0.611349 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0436562 | −0.00167291 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.1864 | −1.53769 | −0.768844 | − | 0.639436i | \(-0.779168\pi\) | ||||
−0.768844 | + | 0.639436i | \(0.779168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.5579 | −0.403398 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.2711 | −0.658935 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.4579 | −1.57942 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.9709 | 1.44448 | 0.722240 | − | 0.691642i | \(-0.243112\pi\) | ||||
0.722240 | + | 0.691642i | \(0.243112\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.2669 | −0.465983 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.1193 | 0.497643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.6847 | 0.972876 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.50687 | −0.170465 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.1397 | −0.382972 | −0.191486 | − | 0.981495i | \(-0.561331\pi\) | ||||
−0.191486 | + | 0.981495i | \(0.561331\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.45463 | −0.281157 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.74186 | −0.0656023 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.3872 | −0.390651 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.7876 | 0.517804 | 0.258902 | − | 0.965904i | \(-0.416639\pi\) | ||||
0.258902 | + | 0.965904i | \(0.416639\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.32690 | −0.162272 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.6029 | 0.509432 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0902 | 0.452147 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.31017 | −0.198312 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.1050 | 0.712496 | 0.356248 | − | 0.934391i | \(-0.384056\pi\) | ||||
0.356248 | + | 0.934391i | \(0.384056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.37581 | −0.0512380 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.0415 | −0.373447 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.30465 | 0.345566 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52.7736 | 1.95726 | 0.978632 | − | 0.205618i | \(-0.0659203\pi\) | ||||
0.978632 | + | 0.205618i | \(0.0659203\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.8856 | −1.29029 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.1372 | 1.88880 | 0.944399 | − | 0.328803i | \(-0.106645\pi\) | ||||
0.944399 | + | 0.328803i | \(0.106645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.112473 | 0.00414862 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.7023 | 0.946756 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.74479 | −0.321682 | −0.160841 | − | 0.986980i | \(-0.551421\pi\) | ||||
−0.160841 | + | 0.986980i | \(0.551421\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.5972 | −0.646448 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.4343 | −1.04315 | −0.521576 | − | 0.853205i | \(-0.674656\pi\) | ||||
−0.521576 | + | 0.853205i | \(0.674656\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.24958 | 0.119055 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.40318 | 0.307456 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.9107 | 1.67754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.7346 | −1.08503 | −0.542515 | − | 0.840046i | \(-0.682528\pi\) | ||||
−0.542515 | + | 0.840046i | \(0.682528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.4734 | −0.490999 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.490778 | 0.0178612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8251 | 0.466135 | 0.233067 | − | 0.972461i | \(-0.425124\pi\) | ||||
0.233067 | + | 0.972461i | \(0.425124\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.9556 | −0.397664 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 50.6844 | 1.83731 | 0.918653 | − | 0.395065i | \(-0.129278\pi\) | ||||
0.918653 | + | 0.395065i | \(0.129278\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.44923 | 0.342085 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.75752 | −0.0635433 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.0404 | 0.976374 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.47689 | −0.305684 | −0.152842 | − | 0.988251i | \(-0.548843\pi\) | ||||
−0.152842 | + | 0.988251i | \(0.548843\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.27420 | −0.297988 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.4837 | 1.13239 | 0.566195 | − | 0.824272i | \(-0.308415\pi\) | ||||
0.566195 | + | 0.824272i | \(0.308415\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.0947 | 0.973272 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.75904 | 0.170730 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.7054 | 1.27928 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.0533 | −1.54057 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00408 | −0.0716199 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.68111 | 0.202768 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4579 | 0.907475 | 0.453738 | − | 0.891135i | \(-0.350090\pi\) | ||||
0.453738 | + | 0.891135i | \(0.350090\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.94503 | 0.104846 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.5592 | 1.22878 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.9729 | 1.31294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.75605 | −0.204146 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.5432 | 0.621413 | 0.310707 | − | 0.950506i | \(-0.399434\pi\) | ||||
0.310707 | + | 0.950506i | \(0.399434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.57174 | 0.303246 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.59052 | 0.303531 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0329 | −0.424633 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.63567 | −0.128141 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.30723 | 0.0812185 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.8265 | 1.04865 | 0.524323 | − | 0.851520i | \(-0.324319\pi\) | ||||
0.524323 | + | 0.851520i | \(0.324319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.08561 | 0.319039 | 0.159519 | − | 0.987195i | \(-0.449006\pi\) | ||||
0.159519 | + | 0.987195i | \(0.449006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.9041 | −0.627923 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.34378 | −0.257241 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48.4960 | −1.69666 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.2340 | 0.392549 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.2210 | 0.740618 | 0.370309 | − | 0.928909i | \(-0.379252\pi\) | ||||
0.370309 | + | 0.928909i | \(0.379252\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.12448 | 0.0740547 | 0.0370273 | − | 0.999314i | \(-0.488211\pi\) | ||||
0.0370273 | + | 0.999314i | \(0.488211\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.8218 | −0.759738 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.6543 | 0.579127 | 0.289564 | − | 0.957159i | \(-0.406490\pi\) | ||||
0.289564 | + | 0.957159i | \(0.406490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.1703 | −1.53410 | −0.767049 | − | 0.641588i | \(-0.778276\pi\) | ||||
−0.767049 | + | 0.641588i | \(0.778276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.7020 | 0.648764 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.553481 | −0.0191770 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.597616 | −0.0206814 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.83579 | −0.201715 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.2467 | 0.457328 | 0.228664 | − | 0.973505i | \(-0.426564\pi\) | ||||
0.228664 | + | 0.973505i | \(0.426564\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.9837 | −0.861506 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.7088 | −0.437714 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.30314 | −0.113631 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.9463 | −0.994607 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.7962 | −1.09124 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.25030 | 0.145699 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.557679 | −0.0190946 | −0.00954728 | − | 0.999954i | \(-0.503039\pi\) | ||||
−0.00954728 | + | 0.999954i | \(0.503039\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.44321 | −0.0835559 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.2809 | −0.692784 | −0.346392 | − | 0.938090i | \(-0.612593\pi\) | ||||
−0.346392 | + | 0.938090i | \(0.612593\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.5678 | −1.82771 | −0.913855 | − | 0.406040i | \(-0.866909\pi\) | ||||
−0.913855 | + | 0.406040i | \(0.866909\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.7943 | −0.776829 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.0933 | 1.63711 | 0.818557 | − | 0.574425i | \(-0.194774\pi\) | ||||
0.818557 | + | 0.574425i | \(0.194774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.0251 | −0.442867 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.35120 | −0.283622 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.3368 | −0.689879 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.5381 | −0.797557 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.10370 | 0.206579 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.0404 | −0.508458 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.7094 | 1.91494 | 0.957470 | − | 0.288532i | \(-0.0931670\pi\) | ||||
0.957470 | + | 0.288532i | \(0.0931670\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.5156 | 0.354682 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.31381 | 0.0442635 | 0.0221318 | − | 0.999755i | \(-0.492955\pi\) | ||||
0.0221318 | + | 0.999755i | \(0.492955\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.3942 | 0.686321 | 0.343160 | − | 0.939277i | \(-0.388503\pi\) | ||||
0.343160 | + | 0.939277i | \(0.388503\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.75432 | 0.126200 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.2392 | 0.545260 | 0.272630 | − | 0.962119i | \(-0.412106\pi\) | ||||
0.272630 | + | 0.962119i | \(0.412106\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.7512 | −1.03136 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.70008 | 0.157459 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.9160 | 0.398752 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.98337 | 0.333707 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.0331 | 0.334996 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.6954 | 0.390063 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.3257 | 0.943664 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.9598 | 1.03028 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.16766 | −0.0720553 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.6423 | 1.24989 | 0.624946 | − | 0.780668i | \(-0.285121\pi\) | ||||
0.624946 | + | 0.780668i | \(0.285121\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.97986 | 0.132004 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.1491 | −0.336254 | −0.168127 | − | 0.985765i | \(-0.553772\pi\) | ||||
−0.168127 | + | 0.985765i | \(0.553772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.4957 | 1.30712 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.13335 | 0.169703 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.87602 | 0.0619518 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.3876 | −0.573563 | −0.286781 | − | 0.957996i | \(-0.592585\pi\) | ||||
−0.286781 | + | 0.957996i | \(0.592585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.2239 | −0.930009 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.4281 | 1.29779 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.46591 | 0.278357 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.527144 | 0.0173137 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.3989 | −0.898930 | −0.449465 | − | 0.893298i | \(-0.648385\pi\) | ||||
−0.449465 | + | 0.893298i | \(0.648385\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.769419 | −0.0252167 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.06229 | 0.165732 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.26049 | −0.270147 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.8491 | 0.354424 | 0.177212 | − | 0.984173i | \(-0.443292\pi\) | ||||
0.177212 | + | 0.984173i | \(0.443292\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.34882 | 0.141918 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.6872 | −0.609184 | −0.304592 | − | 0.952483i | \(-0.598520\pi\) | ||||
−0.304592 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.3576 | −0.662936 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.55974 | 0.0507385 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.23655 | 0.105174 | 0.0525869 | − | 0.998616i | \(-0.483253\pi\) | ||||
0.0525869 | + | 0.998616i | \(0.483253\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.0197 | 0.357715 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.2380 | 0.591409 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.3359 | −0.626350 | −0.313175 | − | 0.949695i | \(-0.601393\pi\) | ||||
−0.313175 | + | 0.949695i | \(0.601393\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.7226 | 0.379334 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.41934 | −0.304484 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.1092 | −1.48894 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.05648 | 0.0985960 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.5907 | −0.566853 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.45129 | 0.0789097 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.8874 | 0.768166 | 0.384083 | − | 0.923299i | \(-0.374518\pi\) | ||||
0.384083 | + | 0.923299i | \(0.374518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.0231 | 0.386237 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.7505 | −0.377092 | −0.188546 | − | 0.982064i | \(-0.560377\pi\) | ||||
−0.188546 | + | 0.982064i | \(0.560377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57.2953 | 1.83680 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.9843 | 0.640011 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.6651 | −0.341207 | −0.170604 | − | 0.985340i | \(-0.554572\pi\) | ||||
−0.170604 | + | 0.985340i | \(0.554572\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.3762 | 1.29043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.62048 | −0.115593 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.1379 | 0.610403 | 0.305201 | − | 0.952288i | \(-0.401276\pi\) | ||||
0.305201 | + | 0.952288i | \(0.401276\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.70272 | 0.277292 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.60715 | −0.242138 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.6503 | 0.879227 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.4631 | 0.777097 | 0.388549 | − | 0.921428i | \(-0.372977\pi\) | ||||
0.388549 | + | 0.921428i | \(0.372977\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.31296 | −0.200336 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3070 | 0.358456 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5133 | 0.839685 | 0.419842 | − | 0.907597i | \(-0.362085\pi\) | ||||
0.419842 | + | 0.907597i | \(0.362085\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.82343 | −0.0576907 |
(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 | 8016.2.a.w.1.4 | 7 | ||
4.3 | odd | 2 | 4008.2.a.g.1.4 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.g.1.4 | ✓ | 7 | 4.3 | odd | 2 | ||
8016.2.a.w.1.4 | 7 | 1.1 | even | 1 | trivial |