Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, 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("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.246302029.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 9x^{4} + 14x^{3} + 15x^{2} - 13x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73486\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-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 | ||||||||
\(3\) | −1.73486 | −1.00162 | −0.500812 | − | 0.865556i | \(-0.666965\pi\) | ||||
−0.500812 | + | 0.865556i | \(0.666965\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.63787 | 0.732477 | 0.366239 | − | 0.930521i | \(-0.380645\pi\) | ||||
0.366239 | + | 0.930521i | \(0.380645\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.00974910 | 0.00324970 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.84148 | −0.733666 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.66359 | 1.13109 | 0.565543 | − | 0.824719i | \(-0.308667\pi\) | ||||
0.565543 | + | 0.824719i | \(0.308667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.13950 | 0.261418 | 0.130709 | − | 0.991421i | \(-0.458275\pi\) | ||||
0.130709 | + | 0.991421i | \(0.458275\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73486 | −0.378578 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.21421 | −1.29575 | −0.647876 | − | 0.761746i | \(-0.724343\pi\) | ||||
−0.647876 | + | 0.761746i | \(0.724343\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.31739 | −0.463477 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.18768 | 0.998369 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.84148 | −1.08474 | −0.542368 | − | 0.840141i | \(-0.682472\pi\) | ||||
−0.542368 | + | 0.840141i | \(0.682472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.87694 | 0.875925 | 0.437962 | − | 0.898993i | \(-0.355700\pi\) | ||||
0.437962 | + | 0.898993i | \(0.355700\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73486 | 0.302001 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.63787 | 0.276850 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.62859 | −1.41853 | −0.709266 | − | 0.704941i | \(-0.750973\pi\) | ||||
−0.709266 | + | 0.704941i | \(0.750973\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.73486 | 0.277800 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.59622 | −0.561635 | −0.280817 | − | 0.959761i | \(-0.590606\pi\) | ||||
−0.280817 | + | 0.959761i | \(0.590606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.28549 | 0.196035 | 0.0980174 | − | 0.995185i | \(-0.468750\pi\) | ||||
0.0980174 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0159677 | 0.00238033 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.07569 | 1.03210 | 0.516048 | − | 0.856560i | \(-0.327403\pi\) | ||||
0.516048 | + | 0.856560i | \(0.327403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.09068 | −1.13292 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.181146 | 0.0248823 | 0.0124411 | − | 0.999923i | \(-0.496040\pi\) | ||||
0.0124411 | + | 0.999923i | \(0.496040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.63787 | −0.220850 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.97687 | −0.261843 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.206703 | 0.0269104 | 0.0134552 | − | 0.999909i | \(-0.495717\pi\) | ||||
0.0134552 | + | 0.999909i | \(0.495717\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.76708 | −0.738398 | −0.369199 | − | 0.929350i | \(-0.620368\pi\) | ||||
−0.369199 | + | 0.929350i | \(0.620368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.00974910 | 0.00122827 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.63787 | −0.203153 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.45947 | −0.544811 | −0.272405 | − | 0.962183i | \(-0.587819\pi\) | ||||
−0.272405 | + | 0.962183i | \(0.587819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.7808 | 1.29786 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.09421 | 0.367215 | 0.183608 | − | 0.983000i | \(-0.441222\pi\) | ||||
0.183608 | + | 0.983000i | \(0.441222\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.97432 | −0.816282 | −0.408141 | − | 0.912919i | \(-0.633823\pi\) | ||||
−0.408141 | + | 0.912919i | \(0.633823\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.02035 | 0.464230 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.52507 | 0.509110 | 0.254555 | − | 0.967058i | \(-0.418071\pi\) | ||||
0.254555 | + | 0.967058i | \(0.418071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.02915 | −1.00324 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.63478 | −0.838026 | −0.419013 | − | 0.907980i | \(-0.637624\pi\) | ||||
−0.419013 | + | 0.907980i | \(0.637624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.63834 | 0.828494 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.1342 | 1.08650 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.284199 | 0.0301250 | 0.0150625 | − | 0.999887i | \(-0.495205\pi\) | ||||
0.0150625 | + | 0.999887i | \(0.495205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.46083 | −0.877347 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.86634 | 0.191483 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.615716 | 0.0625165 | 0.0312583 | − | 0.999511i | \(-0.490049\pi\) | ||||
0.0312583 | + | 0.999511i | \(0.490049\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.00974910 | −0.000979821 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.5796 | −1.15221 | −0.576106 | − | 0.817375i | \(-0.695429\pi\) | ||||
−0.576106 | + | 0.817375i | \(0.695429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.86054 | −0.380390 | −0.190195 | − | 0.981746i | \(-0.560912\pi\) | ||||
−0.190195 | + | 0.981746i | \(0.560912\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.84148 | −0.277300 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4321 | 1.39520 | 0.697602 | − | 0.716485i | \(-0.254250\pi\) | ||||
0.697602 | + | 0.716485i | \(0.254250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.47269 | 0.236841 | 0.118420 | − | 0.992964i | \(-0.462217\pi\) | ||||
0.118420 | + | 0.992964i | \(0.462217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.9694 | 1.42083 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.91686 | −0.932900 | −0.466450 | − | 0.884548i | \(-0.654467\pi\) | ||||
−0.466450 | + | 0.884548i | \(0.654467\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.1781 | −0.949109 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.00974910 | −0.000901304 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.66359 | 0.427510 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.23895 | 0.562547 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.9849 | −1.07196 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.21679 | 0.640387 | 0.320193 | − | 0.947352i | \(-0.396252\pi\) | ||||
0.320193 | + | 0.947352i | \(0.396252\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.23014 | −0.196353 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.52854 | 0.220920 | 0.110460 | − | 0.993881i | \(-0.464768\pi\) | ||||
0.110460 | + | 0.993881i | \(0.464768\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.13950 | 0.0988068 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.49673 | 0.731282 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.5679 | −1.07375 | −0.536875 | − | 0.843662i | \(-0.680395\pi\) | ||||
−0.536875 | + | 0.843662i | \(0.680395\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.68536 | −0.567045 | −0.283522 | − | 0.958966i | \(-0.591503\pi\) | ||||
−0.283522 | + | 0.958966i | \(0.591503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.2754 | −1.03377 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.56757 | −0.794543 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.73486 | −0.143089 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.0016 | 1.22898 | 0.614491 | − | 0.788924i | \(-0.289362\pi\) | ||||
0.614491 | + | 0.788924i | \(0.289362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.570661 | −0.0464397 | −0.0232199 | − | 0.999730i | \(-0.507392\pi\) | ||||
−0.0232199 | + | 0.999730i | \(0.507392\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0454657 | 0.00367569 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.98779 | 0.641595 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.89988 | −0.391053 | −0.195527 | − | 0.980698i | \(-0.562642\pi\) | ||||
−0.195527 | + | 0.980698i | \(0.562642\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.314263 | −0.0249227 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.21421 | −0.489748 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.41863 | −0.581072 | −0.290536 | − | 0.956864i | \(-0.593834\pi\) | ||||
−0.290536 | + | 0.956864i | \(0.593834\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.84148 | 0.221209 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.6073 | −1.13034 | −0.565172 | − | 0.824973i | \(-0.691190\pi\) | ||||
−0.565172 | + | 0.824973i | \(0.691190\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0111090 | 0.000849530 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.4903 | 1.25373 | 0.626865 | − | 0.779128i | \(-0.284338\pi\) | ||||
0.626865 | + | 0.779128i | \(0.284338\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.31739 | −0.175178 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.358601 | −0.0269541 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.7614 | −1.17806 | −0.589031 | − | 0.808110i | \(-0.700490\pi\) | ||||
−0.589031 | + | 0.808110i | \(0.700490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0789 | −1.12081 | −0.560405 | − | 0.828219i | \(-0.689354\pi\) | ||||
−0.560405 | + | 0.828219i | \(0.689354\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0051 | 0.739597 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.1325 | −1.03904 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.66359 | −0.341035 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.18768 | 0.377348 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1683 | 1.16990 | 0.584950 | − | 0.811069i | \(-0.301114\pi\) | ||||
0.584950 | + | 0.811069i | \(0.301114\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.68349 | 0.553070 | 0.276535 | − | 0.961004i | \(-0.410814\pi\) | ||||
0.276535 | + | 0.961004i | \(0.410814\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.84148 | 0.203482 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.07865 | 0.504333 | 0.252167 | − | 0.967684i | \(-0.418857\pi\) | ||||
0.252167 | + | 0.967684i | \(0.418857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3781 | −0.806570 | −0.403285 | − | 0.915075i | \(-0.632132\pi\) | ||||
−0.403285 | + | 0.915075i | \(0.632132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.73656 | 0.545695 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.84148 | −0.409991 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.89013 | −0.411385 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0605829 | −0.00421080 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.13950 | −0.0788205 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6730 | −0.734761 | −0.367381 | − | 0.930071i | \(-0.619745\pi\) | ||||
−0.367381 | + | 0.930071i | \(0.619745\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.36803 | −0.367811 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.10546 | 0.143591 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.87694 | 0.331068 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0995 | 0.817607 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.66359 | −0.313707 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.0941 | −1.14471 | −0.572353 | − | 0.820008i | \(-0.693969\pi\) | ||||
−0.572353 | + | 0.820008i | \(0.693969\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0225924 | −0.00150616 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.53908 | −0.168525 | −0.0842623 | − | 0.996444i | \(-0.526853\pi\) | ||||
−0.0842623 | + | 0.996444i | \(0.526853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.8923 | 1.44668 | 0.723342 | − | 0.690490i | \(-0.242605\pi\) | ||||
0.723342 | + | 0.690490i | \(0.242605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.73486 | 0.114146 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.1460 | −0.861225 | −0.430612 | − | 0.902537i | \(-0.641702\pi\) | ||||
−0.430612 | + | 0.902537i | \(0.641702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.5891 | 0.755987 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.85038 | −0.509937 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.3412 | −1.05702 | −0.528511 | − | 0.848926i | \(-0.677250\pi\) | ||||
−0.528511 | + | 0.848926i | \(0.677250\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.9504 | −1.09187 | −0.545934 | − | 0.837828i | \(-0.683825\pi\) | ||||
−0.545934 | + | 0.837828i | \(0.683825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.101315 | 0.00649937 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.63787 | 0.104640 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.13950 | −0.0725043 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.2453 | 0.839386 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.85366 | −0.558838 | −0.279419 | − | 0.960169i | \(-0.590142\pi\) | ||||
−0.279419 | + | 0.960169i | \(0.590142\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.21421 | 0.390684 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.2515 | −0.829839 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.51481 | −0.406383 | −0.203191 | − | 0.979139i | \(-0.565131\pi\) | ||||
−0.203191 | + | 0.979139i | \(0.565131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.62859 | −0.536154 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0569491 | −0.00352506 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.74465 | 0.354230 | 0.177115 | − | 0.984190i | \(-0.443324\pi\) | ||||
0.177115 | + | 0.984190i | \(0.443324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.296693 | 0.0182257 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.493047 | −0.0301740 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.1717 | −1.47378 | −0.736888 | − | 0.676014i | \(-0.763706\pi\) | ||||
−0.736888 | + | 0.676014i | \(0.763706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.93279 | −0.238900 | −0.119450 | − | 0.992840i | \(-0.538113\pi\) | ||||
−0.119450 | + | 0.992840i | \(0.538113\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73486 | 0.104999 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.31739 | 0.139744 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.0368 | −1.02364 | −0.511820 | − | 0.859093i | \(-0.671028\pi\) | ||||
−0.511820 | + | 0.859093i | \(0.671028\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0475458 | 0.00284649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.71275 | 0.281139 | 0.140569 | − | 0.990071i | \(-0.455107\pi\) | ||||
0.140569 | + | 0.990071i | \(0.455107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.94578 | −0.234552 | −0.117276 | − | 0.993099i | \(-0.537416\pi\) | ||||
−0.117276 | + | 0.993099i | \(0.537416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.23785 | −0.191794 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.59622 | −0.212278 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.74903 | 0.279355 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.06818 | −0.0626180 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.4035 | −0.783042 | −0.391521 | − | 0.920169i | \(-0.628051\pi\) | ||||
−0.391521 | + | 0.920169i | \(0.628051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.338552 | 0.0197113 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.18768 | −0.301019 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.21421 | 0.359377 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.28549 | 0.0740942 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.0890 | 1.15408 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.44571 | −0.540860 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.4474 | −0.938705 | −0.469353 | − | 0.883011i | \(-0.655513\pi\) | ||||
−0.469353 | + | 0.883011i | \(0.655513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.69751 | 0.381008 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.81962 | 0.443410 | 0.221705 | − | 0.975114i | \(-0.428838\pi\) | ||||
0.221705 | + | 0.975114i | \(0.428838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.133838 | 0.00756499 | 0.00378250 | − | 0.999993i | \(-0.498796\pi\) | ||||
0.00378250 | + | 0.999993i | \(0.498796\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0159677 | 0.000899680 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.9340 | −1.56893 | −0.784465 | − | 0.620174i | \(-0.787062\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.84148 | 0.327060 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.0377 | −1.39747 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.31413 | 0.295686 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.31739 | 0.128546 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.28978 | −0.237225 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.07569 | 0.390096 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1098 | −0.940441 | −0.470221 | − | 0.882549i | \(-0.655826\pi\) | ||||
−0.470221 | + | 0.882549i | \(0.655826\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0841209 | −0.00460980 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.30402 | −0.399061 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.2128 | 1.48238 | 0.741189 | − | 0.671296i | \(-0.234262\pi\) | ||||
0.741189 | + | 0.671296i | \(0.234262\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.2044 | 0.934414 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.87694 | −0.264101 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.6575 | 0.950649 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.6097 | −0.999022 | −0.499511 | − | 0.866307i | \(-0.666487\pi\) | ||||
−0.499511 | + | 0.866307i | \(0.666487\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.7942 | −1.54132 | −0.770660 | − | 0.637247i | \(-0.780073\pi\) | ||||
−0.770660 | + | 0.637247i | \(0.780073\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.18768 | −0.276898 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.6656 | −1.79184 | −0.895919 | − | 0.444218i | \(-0.853482\pi\) | ||||
−0.895919 | + | 0.444218i | \(0.853482\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.06791 | 0.268977 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.09068 | −0.428204 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.30618 | −0.280049 | −0.140025 | − | 0.990148i | \(-0.544718\pi\) | ||||
−0.140025 | + | 0.990148i | \(0.544718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7016 | −0.931661 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.73486 | −0.0910567 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.4230 | −0.597908 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.49510 | 0.234642 | 0.117321 | − | 0.993094i | \(-0.462569\pi\) | ||||
0.117321 | + | 0.993094i | \(0.462569\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0350599 | −0.00182514 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.181146 | 0.00940461 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.733587 | 0.0379837 | 0.0189918 | − | 0.999820i | \(-0.493954\pi\) | ||||
0.0189918 | + | 0.999820i | \(0.493954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.7922 | 1.07370 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.84148 | 0.300851 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.425767 | −0.0218702 | −0.0109351 | − | 0.999940i | \(-0.503481\pi\) | ||||
−0.0109351 | + | 0.999940i | \(0.503481\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.5201 | −0.641427 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.69446 | −0.342071 | −0.171036 | − | 0.985265i | \(-0.554711\pi\) | ||||
−0.171036 | + | 0.985265i | \(0.554711\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.63787 | −0.0834735 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0125323 | 0.000637054 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.7103 | −0.897950 | −0.448975 | − | 0.893544i | \(-0.648211\pi\) | ||||
−0.448975 | + | 0.893544i | \(0.648211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.9805 | −1.46561 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.38667 | −0.221278 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.41147 | 0.372911 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.4680 | 1.27820 | 0.639102 | − | 0.769122i | \(-0.279306\pi\) | ||||
0.639102 | + | 0.769122i | \(0.279306\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.97687 | −0.0989672 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.4696 | −0.722577 | −0.361289 | − | 0.932454i | \(-0.617663\pi\) | ||||
−0.361289 | + | 0.932454i | \(0.617663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.87694 | −0.242938 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.7886 | −0.734850 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.62859 | 0.427703 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.37125 | −0.166698 | −0.0833488 | − | 0.996520i | \(-0.526562\pi\) | ||||
−0.0833488 | + | 0.996520i | \(0.526562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.8036 | 1.07549 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.206703 | 0.0101712 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.5048 | −0.613835 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.5982 | 0.567965 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.2787 | 1.43036 | 0.715179 | − | 0.698942i | \(-0.246345\pi\) | ||||
0.715179 | + | 0.698942i | \(0.246345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5789 | −0.515585 | −0.257793 | − | 0.966200i | \(-0.582995\pi\) | ||||
−0.257793 | + | 0.966200i | \(0.582995\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.0689816 | 0.00335400 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.8073 | −0.524233 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.76708 | −0.279088 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.73486 | −0.0837600 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.79215 | 0.278998 | 0.139499 | − | 0.990222i | \(-0.455451\pi\) | ||||
0.139499 | + | 0.990222i | \(0.455451\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.12235 | −0.198108 | −0.0990538 | − | 0.995082i | \(-0.531582\pi\) | ||||
−0.0990538 | + | 0.995082i | \(0.531582\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.5984 | 0.795833 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.08106 | −0.338733 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.71845 | −0.320654 | −0.160327 | − | 0.987064i | \(-0.551255\pi\) | ||||
−0.160327 | + | 0.987064i | \(0.551255\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.00974910 | 0.000464243 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.7031 | 0.841102 | 0.420551 | − | 0.907269i | \(-0.361837\pi\) | ||||
0.420551 | + | 0.907269i | \(0.361837\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.465481 | 0.0220659 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26.0258 | −1.23098 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.0333214 | 0.00157254 | 0.000786268 | − | 1.00000i | \(-0.499750\pi\) | ||||
0.000786268 | 1.00000i | \(0.499750\pi\) | ||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.59622 | 0.169339 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.990018 | 0.0465151 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.63787 | −0.0767845 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.79852 | 0.130909 | 0.0654546 | − | 0.997856i | \(-0.479150\pi\) | ||||
0.0654546 | + | 0.997856i | \(0.479150\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.1932 | 1.12924 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.7320 | −1.05873 | −0.529367 | − | 0.848393i | \(-0.677571\pi\) | ||||
−0.529367 | + | 0.848393i | \(0.677571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.41422 | 0.112198 | 0.0560992 | − | 0.998425i | \(-0.482134\pi\) | ||||
0.0560992 | + | 0.998425i | \(0.482134\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.8577 | −0.642636 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.5247 | 1.08859 | 0.544296 | − | 0.838893i | \(-0.316797\pi\) | ||||
0.544296 | + | 0.838893i | \(0.316797\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.45947 | −0.205919 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.50062 | 0.391688 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.28549 | −0.0591067 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.64065 | −0.121161 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.00176601 | 8.08598e−5 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.7473 | 1.35919 | 0.679594 | − | 0.733589i | \(-0.262156\pi\) | ||||
0.679594 | + | 0.733589i | \(0.262156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.62859 | 0.393430 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.7808 | 0.490543 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.00846 | 0.0457919 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.2523 | 0.872406 | 0.436203 | − | 0.899848i | \(-0.356323\pi\) | ||||
0.436203 | + | 0.899848i | \(0.356323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.8703 | 0.582016 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50585 | −0.338734 | −0.169367 | − | 0.985553i | \(-0.554172\pi\) | ||||
−0.169367 | + | 0.985553i | \(0.554172\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.2422 | −1.22693 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0159677 | −0.000717696 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.09421 | 0.138794 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.7993 | 1.73689 | 0.868447 | − | 0.495783i | \(-0.165119\pi\) | ||||
0.868447 | + | 0.495783i | \(0.165119\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.3416 | 1.13218 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.2814 | 1.17183 | 0.585916 | − | 0.810372i | \(-0.300735\pi\) | ||||
0.585916 | + | 0.810372i | \(0.300735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.9659 | −0.843969 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.73486 | −0.0770480 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.7496 | 1.58457 | 0.792286 | − | 0.610150i | \(-0.208891\pi\) | ||||
0.792286 | + | 0.610150i | \(0.208891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.97432 | −0.308526 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.91133 | 0.260992 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.32305 | −0.278627 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.07569 | −0.311189 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.6083 | −1.25577 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.0441 | 1.36007 | 0.680034 | − | 0.733181i | \(-0.261965\pi\) | ||||
0.680034 | + | 0.733181i | \(0.261965\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.1729 | 1.05701 | 0.528504 | − | 0.848931i | \(-0.322753\pi\) | ||||
0.528504 | + | 0.848931i | \(0.322753\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.02035 | 0.175462 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.7440 | 0.990746 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.6164 | 0.678973 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.00201517 | 8.74508e−5 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.59622 | 0.155769 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.6379 | 1.02196 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.3439 | 1.17997 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.1903 | −1.85690 | −0.928448 | − | 0.371462i | \(-0.878857\pi\) | ||||
−0.928448 | + | 0.371462i | \(0.878857\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.1599 | 1.12263 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.04994 | 0.173480 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7546 | 0.673616 | 0.336808 | − | 0.941573i | \(-0.390653\pi\) | ||||
0.336808 | + | 0.941573i | \(0.390653\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0562238 | −0.00239957 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.65634 | −0.283569 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.52507 | 0.192426 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.5179 | 1.04073 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.825920 | −0.0349953 | −0.0174977 | − | 0.999847i | \(-0.505570\pi\) | ||||
−0.0174977 | + | 0.999847i | \(0.505570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.28549 | −0.0543703 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.09068 | 0.341589 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.60467 | −0.109774 | −0.0548869 | − | 0.998493i | \(-0.517480\pi\) | ||||
−0.0548869 | + | 0.998493i | \(0.517480\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.2425 | −0.683328 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.02915 | −0.379189 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.7400 | 0.743701 | 0.371850 | − | 0.928293i | \(-0.378723\pi\) | ||||
0.371850 | + | 0.928293i | \(0.378723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.3546 | −1.01921 | −0.509604 | − | 0.860409i | \(-0.670208\pi\) | ||||
−0.509604 | + | 0.860409i | \(0.670208\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.0498 | −1.17180 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.4007 | 0.600552 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.2930 | 0.803180 | 0.401590 | − | 0.915820i | \(-0.368458\pi\) | ||||
0.401590 | + | 0.915820i | \(0.368458\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.3298 | −0.553968 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.63478 | −0.316744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.181146 | −0.00750228 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0159677 | −0.000660185 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.4812 | 0.886625 | 0.443312 | − | 0.896367i | \(-0.353803\pi\) | ||||
0.443312 | + | 0.896367i | \(0.353803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.55725 | 0.228983 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.2805 | −0.505152 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.21714 | 0.296373 | 0.148186 | − | 0.988959i | \(-0.452656\pi\) | ||||
0.148186 | + | 0.988959i | \(0.452656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.63834 | 0.313141 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.7394 | 0.807879 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.7141 | −0.887213 | −0.443606 | − | 0.896222i | \(-0.646301\pi\) | ||||
−0.443606 | + | 0.896222i | \(0.646301\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.2351 | 1.19252 | 0.596261 | − | 0.802790i | \(-0.296652\pi\) | ||||
0.596261 | + | 0.802790i | \(0.296652\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0434758 | −0.00177047 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.63787 | 0.0665888 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.0138 | 0.528212 | 0.264106 | − | 0.964494i | \(-0.414923\pi\) | ||||
0.264106 | + | 0.964494i | \(0.414923\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.1342 | 0.410657 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.07569 | −0.286252 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.02218 | −0.122065 | −0.0610323 | − | 0.998136i | \(-0.519439\pi\) | ||||
−0.0610323 | + | 0.998136i | \(0.519439\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.2186 | 0.412053 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.56386 | 0.344768 | 0.172384 | − | 0.985030i | \(-0.444853\pi\) | ||||
0.172384 | + | 0.985030i | \(0.444853\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.6278 | −0.748715 | −0.374357 | − | 0.927284i | \(-0.622137\pi\) | ||||
−0.374357 | + | 0.927284i | \(0.622137\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.2373 | −1.29364 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.284199 | 0.0113862 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.04278 | −0.321711 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.97687 | 0.0789485 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40.2402 | −1.60448 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0341 | −1.35488 | −0.677438 | − | 0.735580i | \(-0.736910\pi\) | ||||
−0.677438 | + | 0.735580i | \(0.736910\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.5162 | 0.735954 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.8202 | 0.469069 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.0301658 | 0.00119334 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.1799 | 1.42902 | 0.714509 | − | 0.699626i | \(-0.246650\pi\) | ||||
0.714509 | + | 0.699626i | \(0.246650\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.2053 | −0.757384 | −0.378692 | − | 0.925523i | \(-0.623626\pi\) | ||||
−0.378692 | + | 0.925523i | \(0.623626\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.65268 | −0.143824 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.9020 | 0.467914 | 0.233957 | − | 0.972247i | \(-0.424832\pi\) | ||||
0.233957 | + | 0.972247i | \(0.424832\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.206703 | −0.00811380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.46083 | −0.331606 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.66683 | −0.0652283 | −0.0326141 | − | 0.999468i | \(-0.510383\pi\) | ||||
−0.0326141 | + | 0.999468i | \(0.510383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.14142 | 0.161819 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.0679933 | −0.00265267 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.02811 | −0.156913 | −0.0784564 | − | 0.996918i | \(-0.524999\pi\) | ||||
−0.0784564 | + | 0.996918i | \(0.524999\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.31714 | −0.323499 | −0.161750 | − | 0.986832i | \(-0.551714\pi\) | ||||
−0.161750 | + | 0.986832i | \(0.551714\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.09068 | 0.314216 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.86634 | 0.0723737 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.3002 | 1.40555 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.6559 | 1.14656 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.76708 | 0.222635 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.4505 | −0.557027 | −0.278513 | − | 0.960432i | \(-0.589842\pi\) | ||||
−0.278513 | + | 0.960432i | \(0.589842\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.0219 | −0.462721 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.9742 | 0.882971 | 0.441485 | − | 0.897268i | \(-0.354452\pi\) | ||||
0.441485 | + | 0.897268i | \(0.354452\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.615716 | 0.0236290 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.40495 | 0.168798 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.4897 | 0.516168 | 0.258084 | − | 0.966122i | \(-0.416909\pi\) | ||||
0.258084 | + | 0.966122i | \(0.416909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.5846 | −0.786497 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37.9801 | −1.44903 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.181146 | −0.00690110 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.54231 | 0.0967141 | 0.0483571 | − | 0.998830i | \(-0.484601\pi\) | ||||
0.0483571 | + | 0.998830i | \(0.484601\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.00974910 | −0.000370337 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.9497 | −0.415347 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.7713 | −0.635257 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.8066 | 0.862623 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.10882 | 0.344035 | 0.172018 | − | 0.985094i | \(-0.444971\pi\) | ||||
0.172018 | + | 0.985094i | \(0.444971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.83224 | −0.370830 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.1054 | −0.757214 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.5796 | −0.435495 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.6986 | 0.927577 | 0.463788 | − | 0.885946i | \(-0.346490\pi\) | ||||
0.463788 | + | 0.885946i | \(0.346490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0441153 | 0.00165445 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.3063 | −1.13498 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63787 | 0.0612528 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.3497 | 1.05874 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.0789 | 1.08446 | 0.542230 | − | 0.840230i | \(-0.317580\pi\) | ||||
0.542230 | + | 0.840230i | \(0.317580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.86054 | −0.143774 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.4066 | 1.09364 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.5370 | 0.502750 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.9744 | 0.889160 | 0.444580 | − | 0.895739i | \(-0.353353\pi\) | ||||
0.444580 | + | 0.895739i | \(0.353353\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9117 | 0.996729 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.99497 | 0.221732 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.4024 | −0.753579 | −0.376789 | − | 0.926299i | \(-0.622972\pi\) | ||||
−0.376789 | + | 0.926299i | \(0.622972\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.84148 | −0.104809 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.45947 | 0.164267 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.9158 | −0.879755 | −0.439878 | − | 0.898058i | \(-0.644978\pi\) | ||||
−0.439878 | + | 0.898058i | \(0.644978\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.97687 | 0.0726221 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.8674 | 1.46259 | 0.731297 | − | 0.682059i | \(-0.238915\pi\) | ||||
0.731297 | + | 0.682059i | \(0.238915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.5707 | 0.900201 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0744322 | −0.00272333 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.4321 | 0.527338 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.01398 | 0.219453 | 0.109727 | − | 0.993962i | \(-0.465002\pi\) | ||||
0.109727 | + | 0.993962i | \(0.465002\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.3599 | 0.559746 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.934667 | −0.0340160 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.7106 | 0.716393 | 0.358196 | − | 0.933646i | \(-0.383392\pi\) | ||||
0.358196 | + | 0.933646i | \(0.383392\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.7808 | −0.391318 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 54.9847 | 1.99319 | 0.996597 | − | 0.0824252i | \(-0.0262665\pi\) | ||||
0.996597 | + | 0.0824252i | \(0.0262665\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.47269 | 0.0895174 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0744669 | 0.00269236 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.206703 | −0.00746361 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.645787 | 0.0232877 | 0.0116438 | − | 0.999932i | \(-0.496294\pi\) | ||||
0.0116438 | + | 0.999932i | \(0.496294\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.3023 | 0.407043 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.1272 | 1.40731 | 0.703653 | − | 0.710543i | \(-0.251551\pi\) | ||||
0.703653 | + | 0.710543i | \(0.251551\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.3018 | −0.405971 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.9694 | 0.537025 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.09787 | −0.146822 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.09421 | −0.110720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −30.3037 | −1.08297 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.02536 | −0.286437 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.8801 | 0.459127 | 0.229564 | − | 0.973294i | \(-0.426270\pi\) | ||||
0.229564 | + | 0.973294i | \(0.426270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.96617 | −0.354805 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.91686 | −0.352603 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.76708 | 0.204795 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.514721 | −0.0182553 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.59881 | −0.162898 | −0.0814491 | − | 0.996677i | \(-0.525955\pi\) | ||||
−0.0814491 | + | 0.996677i | \(0.525955\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.9981 | 1.16739 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.00277068 | 9.78973e−5 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.97432 | 0.246118 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.1781 | −0.358729 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 41.9346 | 1.47617 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.8098 | 1.04806 | 0.524029 | − | 0.851700i | \(-0.324428\pi\) | ||||
0.524029 | + | 0.851700i | \(0.324428\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.8971 | −1.04983 | −0.524915 | − | 0.851155i | \(-0.675903\pi\) | ||||
−0.524915 | + | 0.851155i | \(0.675903\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.82286 | 0.239288 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1507 | −0.425622 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.46481 | 0.0512470 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.00974910 | −0.000340661 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.0115 | −1.01251 | −0.506255 | − | 0.862384i | \(-0.668970\pi\) | ||||
−0.506255 | + | 0.862384i | \(0.668970\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.8663 | 1.11079 | 0.555394 | − | 0.831587i | \(-0.312567\pi\) | ||||
0.555394 | + | 0.831587i | \(0.312567\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.02035 | −0.139971 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.6232 | −1.65602 | −0.828011 | − | 0.560712i | \(-0.810527\pi\) | ||||
−0.828011 | + | 0.560712i | \(0.810527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.1325 | −1.56752 | −0.783758 | − | 0.621067i | \(-0.786700\pi\) | ||||
−0.783758 | + | 0.621067i | \(0.786700\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.5564 | 1.02530 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.66359 | 0.161584 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.9248 | −0.827951 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.3000 | 0.874496 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47.3419 | 1.63443 | 0.817213 | − | 0.576336i | \(-0.195518\pi\) | ||||
0.817213 | + | 0.576336i | \(0.195518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.12285 | 0.176650 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.17597 | −0.281595 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.63787 | 0.0563444 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.84539 | 0.234933 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.6199 | 1.83806 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.1241 | 0.654796 | 0.327398 | − | 0.944887i | \(-0.393828\pi\) | ||||
0.327398 | + | 0.944887i | \(0.393828\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0181952 | 0.000622261 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.5360 | 0.428223 | 0.214111 | − | 0.976809i | \(-0.431314\pi\) | ||||
0.214111 | + | 0.976809i | \(0.431314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.3818 | −0.388342 | −0.194171 | − | 0.980968i | \(-0.562202\pi\) | ||||
−0.194171 | + | 0.980968i | \(0.562202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.23895 | 0.212623 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.0466353 | −0.00158748 | −0.000793741 | − | 1.00000i | \(-0.500253\pi\) | ||||
−0.000793741 | 1.00000i | \(0.500253\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.0089 | 0.918329 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.23891 | −0.279808 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.52507 | −0.153502 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.45947 | 0.151103 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.00600268 | 0.000203160 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.9849 | −0.405164 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.3083 | 1.02344 | 0.511719 | − | 0.859153i | \(-0.329009\pi\) | ||||
0.511719 | + | 0.859153i | \(0.329009\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.2533 | 0.784313 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.9104 | 0.738179 | 0.369089 | − | 0.929394i | \(-0.379670\pi\) | ||||
0.369089 | + | 0.929394i | \(0.379670\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.1127 | 0.845110 | 0.422555 | − | 0.906337i | \(-0.361133\pi\) | ||||
0.422555 | + | 0.906337i | \(0.361133\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.587341 | −0.0197433 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.10949 | −0.171560 | −0.0857799 | − | 0.996314i | \(-0.527338\pi\) | ||||
−0.0857799 | + | 0.996314i | \(0.527338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.21679 | 0.242043 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.02915 | 0.302488 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.06272 | 0.269809 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.8151 | −0.862903 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.7808 | −0.359960 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.4886 | −0.950146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.844788 | 0.0281440 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.23014 | −0.0742145 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.6973 | −0.820967 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.19256 | 0.238825 | 0.119413 | − | 0.992845i | \(-0.461899\pi\) | ||||
0.119413 | + | 0.992845i | \(0.461899\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.112891 | −0.00374434 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.6165 | 1.01437 | 0.507184 | − | 0.861838i | \(-0.330686\pi\) | ||||
0.507184 | + | 0.861838i | \(0.330686\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.63478 | 0.252674 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.3870 | 0.541738 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.52854 | 0.0834997 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.6554 | −1.73694 | −0.868470 | − | 0.495741i | \(-0.834896\pi\) | ||||
−0.868470 | + | 0.495741i | \(0.834896\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.5341 | 0.940229 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.09421 | −0.101847 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.9958 | 0.657457 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0376368 | −0.00123615 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.9958 | −0.590423 | −0.295211 | − | 0.955432i | \(-0.595390\pi\) | ||||
−0.295211 | + | 0.955432i | \(0.595390\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.13950 | 0.0373454 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.5660 | −0.444130 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.63834 | −0.249800 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.1337 | 0.461729 | 0.230865 | − | 0.972986i | \(-0.425845\pi\) | ||||
0.230865 | + | 0.972986i | \(0.425845\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.232191 | −0.00757727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.85933 | −0.158409 | −0.0792047 | − | 0.996858i | \(-0.525238\pi\) | ||||
−0.0792047 | + | 0.996858i | \(0.525238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.3476 | 0.727740 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.49673 | 0.276399 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.4556 | −0.469745 | −0.234873 | − | 0.972026i | \(-0.575467\pi\) | ||||
−0.234873 | + | 0.972026i | \(0.575467\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.97432 | 0.226396 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.4616 | 1.57148 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.115449 | 0.00373975 | 0.00186987 | − | 0.999998i | \(-0.499405\pi\) | ||||
0.00186987 | + | 0.999998i | \(0.499405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.4816 | 0.856925 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.1342 | −0.327591 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.5679 | −0.405839 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.21543 | −0.232756 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.140700 | 0.00453399 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.5846 | 0.405111 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.83521 | −0.219806 | −0.109903 | − | 0.993942i | \(-0.535054\pi\) | ||||
−0.109903 | + | 0.993942i | \(0.535054\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.21929 | −0.296166 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.9294 | 0.607474 | 0.303737 | − | 0.952756i | \(-0.401766\pi\) | ||||
0.303737 | + | 0.952756i | \(0.401766\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.68536 | −0.214323 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.02035 | −0.128754 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.9280 | 0.477591 | 0.238795 | − | 0.971070i | \(-0.423248\pi\) | ||||
0.238795 | + | 0.971070i | \(0.423248\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.284199 | −0.00908304 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0241065 | 0.000769661 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.3488 | −0.840396 | −0.420198 | − | 0.907433i | \(-0.638039\pi\) | ||||
−0.420198 | + | 0.907433i | \(0.638039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5939 | 0.369412 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.2754 | −0.390729 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.98828 | −0.254012 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.7656 | 1.10437 | 0.552184 | − | 0.833723i | \(-0.313795\pi\) | ||||
0.552184 | + | 0.833723i | \(0.313795\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.6832 | 0.941968 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.6358 | −0.590794 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.0505 | −1.42676 | −0.713382 | − | 0.700776i | \(-0.752837\pi\) | ||||
−0.713382 | + | 0.700776i | \(0.752837\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −44.7623 | −1.41622 |
(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 | 4004.2.a.g.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.g.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |