Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7280,2,Mod(1,7280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7280.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: | \(58.1310926715\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3640) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.13856\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7280.1 |
$q$-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 | ||||||||
\(3\) | 1.13856 | 0.657350 | 0.328675 | − | 0.944443i | \(-0.393398\pi\) | ||||
0.328675 | + | 0.944443i | \(0.393398\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.70367 | −0.567890 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | 0.975711 | 0.487856 | − | 0.872924i | \(-0.337779\pi\) | ||||
0.487856 | + | 0.872924i | \(0.337779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.13856 | 0.293976 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.98080 | 0.722950 | 0.361475 | − | 0.932382i | \(-0.382273\pi\) | ||||
0.361475 | + | 0.932382i | \(0.382273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.93974 | −0.445007 | −0.222503 | − | 0.974932i | \(-0.571423\pi\) | ||||
−0.222503 | + | 0.974932i | \(0.571423\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.13856 | 0.248455 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.17127 | 0.452742 | 0.226371 | − | 0.974041i | \(-0.427314\pi\) | ||||
0.226371 | + | 0.974041i | \(0.427314\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.35543 | −1.03065 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.58697 | 0.666083 | 0.333042 | − | 0.942912i | \(-0.391925\pi\) | ||||
0.333042 | + | 0.942912i | \(0.391925\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.29517 | −1.31025 | −0.655126 | − | 0.755520i | \(-0.727384\pi\) | ||||
−0.655126 | + | 0.755520i | \(0.727384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.68447 | 0.641384 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.37463 | 0.390387 | 0.195194 | − | 0.980765i | \(-0.437466\pi\) | ||||
0.195194 | + | 0.980765i | \(0.437466\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.13856 | 0.182316 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.76846 | 0.276188 | 0.138094 | − | 0.990419i | \(-0.455902\pi\) | ||||
0.138094 | + | 0.990419i | \(0.455902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.51320 | 0.840755 | 0.420377 | − | 0.907349i | \(-0.361898\pi\) | ||||
0.420377 | + | 0.907349i | \(0.361898\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.70367 | −0.253968 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.53693 | 1.09937 | 0.549687 | − | 0.835371i | \(-0.314747\pi\) | ||||
0.549687 | + | 0.835371i | \(0.314747\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.39383 | 0.475232 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.40734 | −0.468035 | −0.234017 | − | 0.972232i | \(-0.575187\pi\) | ||||
−0.234017 | + | 0.972232i | \(0.575187\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.23607 | 0.436351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.20852 | −0.292525 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6377 | 1.51510 | 0.757551 | − | 0.652776i | \(-0.226396\pi\) | ||||
0.757551 | + | 0.652776i | \(0.226396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.68447 | −0.727822 | −0.363911 | − | 0.931434i | \(-0.618559\pi\) | ||||
−0.363911 | + | 0.931434i | \(0.618559\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.70367 | −0.214642 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.04559 | −0.249909 | −0.124954 | − | 0.992162i | \(-0.539878\pi\) | ||||
−0.124954 | + | 0.992162i | \(0.539878\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.47214 | 0.297610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9205 | 1.29603 | 0.648015 | − | 0.761628i | \(-0.275599\pi\) | ||||
0.648015 | + | 0.761628i | \(0.275599\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.09181 | −0.830034 | −0.415017 | − | 0.909814i | \(-0.636224\pi\) | ||||
−0.415017 | + | 0.909814i | \(0.636224\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.13856 | 0.131470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.23607 | 0.368784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7949 | 1.66455 | 0.832276 | − | 0.554362i | \(-0.187038\pi\) | ||||
0.832276 | + | 0.554362i | \(0.187038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.986489 | −0.109610 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.61968 | −0.287547 | −0.143774 | − | 0.989611i | \(-0.545924\pi\) | ||||
−0.143774 | + | 0.989611i | \(0.545924\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.98080 | 0.323313 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.08399 | 0.437850 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.92952 | 0.416528 | 0.208264 | − | 0.978073i | \(-0.433219\pi\) | ||||
0.208264 | + | 0.978073i | \(0.433219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.30602 | −0.861294 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.93974 | −0.199013 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.34192 | −0.136252 | −0.0681258 | − | 0.997677i | \(-0.521702\pi\) | ||||
−0.0681258 | + | 0.997677i | \(0.521702\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.51320 | −0.554097 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.49853 | 0.746132 | 0.373066 | − | 0.927805i | \(-0.378307\pi\) | ||||
0.373066 | + | 0.927805i | \(0.378307\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5685 | −1.43548 | −0.717738 | − | 0.696314i | \(-0.754822\pi\) | ||||
−0.717738 | + | 0.696314i | \(0.754822\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.13856 | 0.111112 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.7736 | 1.13820 | 0.569100 | − | 0.822269i | \(-0.307292\pi\) | ||||
0.569100 | + | 0.822269i | \(0.307292\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.787665 | 0.0754446 | 0.0377223 | − | 0.999288i | \(-0.487990\pi\) | ||||
0.0377223 | + | 0.999288i | \(0.487990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.70367 | 0.256621 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.96160 | −0.748964 | −0.374482 | − | 0.927234i | \(-0.622180\pi\) | ||||
−0.374482 | + | 0.927234i | \(0.622180\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.17127 | 0.202472 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.70367 | −0.157504 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.98080 | 0.273249 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.01351 | 0.181552 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.23607 | 0.287155 | 0.143577 | − | 0.989639i | \(-0.454139\pi\) | ||||
0.143577 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.27713 | 0.552670 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.42467 | 0.561326 | 0.280663 | − | 0.959806i | \(-0.409446\pi\) | ||||
0.280663 | + | 0.959806i | \(0.409446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.93974 | −0.168197 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.35543 | −0.460922 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.83708 | 0.156952 | 0.0784760 | − | 0.996916i | \(-0.474995\pi\) | ||||
0.0784760 | + | 0.996916i | \(0.474995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.62874 | −0.731880 | −0.365940 | − | 0.930638i | \(-0.619253\pi\) | ||||
−0.365940 | + | 0.930638i | \(0.619253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.58128 | 0.722674 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.23607 | 0.270614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.58697 | 0.297881 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.13856 | 0.0939072 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.8405 | −1.54347 | −0.771735 | − | 0.635944i | \(-0.780611\pi\) | ||||
−0.771735 | + | 0.635944i | \(0.780611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6704 | 1.03111 | 0.515553 | − | 0.856858i | \(-0.327587\pi\) | ||||
0.515553 | + | 0.856858i | \(0.327587\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.07830 | −0.410557 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.29517 | −0.585962 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.32717 | 0.185728 | 0.0928641 | − | 0.995679i | \(-0.470398\pi\) | ||||
0.0928641 | + | 0.995679i | \(0.470398\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.87948 | −0.307663 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.17127 | 0.171120 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.1623 | 0.874299 | 0.437149 | − | 0.899389i | \(-0.355988\pi\) | ||||
0.437149 | + | 0.899389i | \(0.355988\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.68447 | 0.286836 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.58128 | 0.664039 | 0.332020 | − | 0.943272i | \(-0.392270\pi\) | ||||
0.332020 | + | 0.943272i | \(0.392270\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.30468 | 0.252715 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.4010 | −1.01886 | −0.509431 | − | 0.860512i | \(-0.670144\pi\) | ||||
−0.509431 | + | 0.860512i | \(0.670144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.2503 | 0.995953 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.45356 | −0.631849 | −0.315925 | − | 0.948784i | \(-0.602315\pi\) | ||||
−0.315925 | + | 0.948784i | \(0.602315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.6989 | −1.61286 | −0.806432 | − | 0.591327i | \(-0.798604\pi\) | ||||
−0.806432 | + | 0.591327i | \(0.798604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.47214 | −0.478434 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.37463 | 0.174586 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.64607 | 0.705391 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.35543 | −0.389550 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.0975 | 1.02006 | 0.510030 | − | 0.860157i | \(-0.329634\pi\) | ||||
0.510030 | + | 0.860157i | \(0.329634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9077 | 1.07308 | 0.536541 | − | 0.843874i | \(-0.319731\pi\) | ||||
0.536541 | + | 0.843874i | \(0.319731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.13856 | 0.0815343 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.1503 | 1.29315 | 0.646577 | − | 0.762848i | \(-0.276200\pi\) | ||||
0.646577 | + | 0.762848i | \(0.276200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.6070 | 1.88612 | 0.943062 | − | 0.332618i | \(-0.107932\pi\) | ||||
0.943062 | + | 0.332618i | \(0.107932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.32904 | −0.164278 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.58697 | 0.251756 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.76846 | 0.123515 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.69914 | −0.257108 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.27713 | −0.434198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.28432 | −0.432631 | −0.216315 | − | 0.976324i | \(-0.569404\pi\) | ||||
−0.216315 | + | 0.976324i | \(0.569404\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.4337 | 0.851946 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.51320 | 0.375997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.29517 | −0.495229 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.07449 | −0.545623 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.98080 | 0.200510 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8885 | −1.19791 | −0.598953 | − | 0.800784i | \(-0.704416\pi\) | ||||
−0.598953 | + | 0.800784i | \(0.704416\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.70367 | −0.113578 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.77566 | −0.516089 | −0.258044 | − | 0.966133i | \(-0.583078\pi\) | ||||
−0.258044 | + | 0.966133i | \(0.583078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.60048 | −0.370090 | −0.185045 | − | 0.982730i | \(-0.559243\pi\) | ||||
−0.185045 | + | 0.982730i | \(0.559243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.68447 | 0.242420 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.88011 | 0.450731 | 0.225365 | − | 0.974274i | \(-0.427642\pi\) | ||||
0.225365 | + | 0.974274i | \(0.427642\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.53693 | 0.491655 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.8449 | 1.09419 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.2722 | −1.37598 | −0.687991 | − | 0.725720i | \(-0.741507\pi\) | ||||
−0.687991 | + | 0.725720i | \(0.741507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.89805 | −0.508758 | −0.254379 | − | 0.967105i | \(-0.581871\pi\) | ||||
−0.254379 | + | 0.967105i | \(0.581871\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.9431 | 0.958601 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.93974 | −0.123423 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.98267 | −0.189019 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.0792 | 1.83546 | 0.917731 | − | 0.397203i | \(-0.130019\pi\) | ||||
0.917731 | + | 0.397203i | \(0.130019\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.02639 | 0.441746 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.39383 | 0.212530 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.12959 | 0.507110 | 0.253555 | − | 0.967321i | \(-0.418400\pi\) | ||||
0.253555 | + | 0.967321i | \(0.418400\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.37463 | 0.147552 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.11101 | −0.378262 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.0416886 | −0.00257063 | −0.00128531 | − | 0.999999i | \(-0.500409\pi\) | ||||
−0.00128531 | + | 0.999999i | \(0.500409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.40734 | −0.209311 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.47401 | 0.273805 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.0068 | 1.46372 | 0.731859 | − | 0.681456i | \(-0.238653\pi\) | ||||
0.731859 | + | 0.681456i | \(0.238653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.8815 | 1.45070 | 0.725349 | − | 0.688381i | \(-0.241678\pi\) | ||||
0.725349 | + | 0.688381i | \(0.241678\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.13856 | 0.0689090 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.23607 | 0.195142 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.5256 | 1.41351 | 0.706757 | − | 0.707457i | \(-0.250158\pi\) | ||||
0.706757 | + | 0.707457i | \(0.250158\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.4286 | 0.744079 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.8405 | −1.12393 | −0.561964 | − | 0.827162i | \(-0.689954\pi\) | ||||
−0.561964 | + | 0.827162i | \(0.689954\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.11742 | 0.541974 | 0.270987 | − | 0.962583i | \(-0.412650\pi\) | ||||
0.270987 | + | 0.962583i | \(0.412650\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.20852 | −0.130821 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.76846 | 0.104389 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.11483 | −0.477343 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.52786 | −0.0895650 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.2387 | −0.598153 | −0.299076 | − | 0.954229i | \(-0.596679\pi\) | ||||
−0.299076 | + | 0.954229i | \(0.596679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6377 | 0.677574 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.3305 | −1.00562 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.17127 | 0.125568 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.51320 | 0.317775 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.53756 | 0.490470 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.68447 | −0.325492 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.9059 | −1.07902 | −0.539508 | − | 0.841981i | \(-0.681390\pi\) | ||||
−0.539508 | + | 0.841981i | \(0.681390\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.5872 | −0.943610 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7499 | 1.00650 | 0.503252 | − | 0.864140i | \(-0.332137\pi\) | ||||
0.503252 | + | 0.864140i | \(0.332137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.53187 | 0.312680 | 0.156340 | − | 0.987703i | \(-0.450031\pi\) | ||||
0.156340 | + | 0.987703i | \(0.450031\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.70367 | −0.0959910 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.13491 | −0.119908 | −0.0599542 | − | 0.998201i | \(-0.519095\pi\) | ||||
−0.0599542 | + | 0.998201i | \(0.519095\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.6077 | 0.649905 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.4050 | 0.748196 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.78198 | −0.321718 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.896807 | 0.0495935 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.53693 | 0.415524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8528 | −0.706454 | −0.353227 | − | 0.935538i | \(-0.614916\pi\) | ||||
−0.353227 | + | 0.935538i | \(0.614916\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.04559 | −0.221697 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.04559 | −0.111763 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.8147 | 1.13385 | 0.566924 | − | 0.823770i | \(-0.308133\pi\) | ||||
0.566924 | + | 0.823770i | \(0.308133\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.06479 | −0.492332 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.6077 | −1.27843 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.47214 | 0.133095 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.2889 | −0.928114 | −0.464057 | − | 0.885805i | \(-0.653607\pi\) | ||||
−0.464057 | + | 0.885805i | \(0.653607\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.9920 | −1.55191 | −0.775953 | − | 0.630791i | \(-0.782731\pi\) | ||||
−0.775953 | + | 0.630791i | \(0.782731\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.35543 | −0.285852 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.9149 | −1.64544 | −0.822718 | − | 0.568450i | \(-0.807543\pi\) | ||||
−0.822718 | + | 0.568450i | \(0.807543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.9205 | 0.579602 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.39383 | 0.179621 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.6584 | 1.35420 | 0.677100 | − | 0.735891i | \(-0.263236\pi\) | ||||
0.677100 | + | 0.735891i | \(0.263236\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2374 | −0.801969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.601007 | −0.0315447 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.09181 | −0.371203 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.4317 | 0.648930 | 0.324465 | − | 0.945898i | \(-0.394816\pi\) | ||||
0.324465 | + | 0.945898i | \(0.394816\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.01288 | −0.156844 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.40734 | −0.176900 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.1613 | −1.50991 | −0.754957 | − | 0.655774i | \(-0.772343\pi\) | ||||
−0.754957 | + | 0.655774i | \(0.772343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.13856 | 0.0587952 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.58697 | 0.184738 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.4921 | −0.641677 | −0.320839 | − | 0.947134i | \(-0.603965\pi\) | ||||
−0.320839 | + | 0.947134i | \(0.603965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.68447 | 0.188761 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.7012 | 0.597902 | 0.298951 | − | 0.954268i | \(-0.403363\pi\) | ||||
0.298951 | + | 0.954268i | \(0.403363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.23607 | 0.164925 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.39268 | −0.477457 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.1758 | 0.769444 | 0.384722 | − | 0.923032i | \(-0.374297\pi\) | ||||
0.384722 | + | 0.923032i | \(0.374297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.47214 | 0.327310 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.31490 | 0.368988 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.7949 | 0.744410 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.0150 | 1.75735 | 0.878677 | − | 0.477417i | \(-0.158427\pi\) | ||||
0.878677 | + | 0.477417i | \(0.158427\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.20852 | −0.110564 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.0059 | −0.849237 | −0.424618 | − | 0.905372i | \(-0.639592\pi\) | ||||
−0.424618 | + | 0.905372i | \(0.639592\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.29517 | −0.363398 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.986489 | −0.0490191 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.68447 | 0.380905 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.05279 | 0.200397 | 0.100199 | − | 0.994967i | \(-0.468052\pi\) | ||||
0.100199 | + | 0.994967i | \(0.468052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.09163 | 0.103172 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.6377 | 0.572655 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.61968 | −0.128595 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.82438 | −0.481102 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.73256 | 0.426614 | 0.213307 | − | 0.976985i | \(-0.431577\pi\) | ||||
0.213307 | + | 0.976985i | \(0.431577\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.8405 | −0.624324 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.98080 | 0.144590 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.68447 | −0.275091 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.68447 | 0.177888 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.20530 | −0.154394 | −0.0771970 | − | 0.997016i | \(-0.524597\pi\) | ||||
−0.0771970 | + | 0.997016i | \(0.524597\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.4199 | −1.60606 | −0.803028 | − | 0.595941i | \(-0.796779\pi\) | ||||
−0.803028 | + | 0.595941i | \(0.796779\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.08399 | 0.195812 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.21171 | −0.201473 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.6551 | −1.12900 | −0.564499 | − | 0.825434i | \(-0.690931\pi\) | ||||
−0.564499 | + | 0.825434i | \(0.690931\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.70367 | −0.0811272 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.15864 | −0.292606 | −0.146303 | − | 0.989240i | \(-0.546737\pi\) | ||||
−0.146303 | + | 0.989240i | \(0.546737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.92952 | 0.186277 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.4511 | −1.01460 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.4073 | 0.727117 | 0.363559 | − | 0.931571i | \(-0.381562\pi\) | ||||
0.363559 | + | 0.931571i | \(0.381562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.72287 | 0.269479 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.4261 | 0.677797 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.6518 | 0.591824 | 0.295912 | − | 0.955215i | \(-0.404376\pi\) | ||||
0.295912 | + | 0.955215i | \(0.404376\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.9635 | −0.745111 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.19838 | 0.335262 | 0.167631 | − | 0.985850i | \(-0.446388\pi\) | ||||
0.167631 | + | 0.985850i | \(0.446388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.2849 | −0.896248 | −0.448124 | − | 0.893972i | \(-0.647908\pi\) | ||||
−0.448124 | + | 0.893972i | \(0.647908\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.30602 | −0.385183 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.59407 | −0.120039 | −0.0600197 | − | 0.998197i | \(-0.519116\pi\) | ||||
−0.0600197 | + | 0.998197i | \(0.519116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.04559 | −0.0944567 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.64963 | 0.122088 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.8411 | 0.820334 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.93974 | −0.0890013 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.80499 | 0.265792 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.6808 | 0.853548 | 0.426774 | − | 0.904358i | \(-0.359650\pi\) | ||||
0.426774 | + | 0.904358i | \(0.359650\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.37463 | 0.108274 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.47214 | 0.112486 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.34192 | −0.0609335 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.27081 | 0.374786 | 0.187393 | − | 0.982285i | \(-0.439996\pi\) | ||||
0.187393 | + | 0.982285i | \(0.439996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.7090 | 0.574720 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.87448 | −0.0845940 | −0.0422970 | − | 0.999105i | \(-0.513468\pi\) | ||||
−0.0422970 | + | 0.999105i | \(0.513468\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.6920 | 0.481545 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.51320 | −0.247800 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.9205 | 0.489853 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.2217 | 1.62151 | 0.810754 | − | 0.585387i | \(-0.199057\pi\) | ||||
0.810754 | + | 0.585387i | \(0.199057\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.77034 | 0.436506 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.53364 | 0.0683817 | 0.0341908 | − | 0.999415i | \(-0.489115\pi\) | ||||
0.0341908 | + | 0.999415i | \(0.489115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.49853 | 0.333680 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.13856 | 0.0505654 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.06229 | 0.357355 | 0.178677 | − | 0.983908i | \(-0.442818\pi\) | ||||
0.178677 | + | 0.983908i | \(0.442818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.09181 | −0.313723 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3881 | 0.458648 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.5685 | −0.641964 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.3900 | 1.07267 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.2579 | −0.669749 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.4835 | −0.459291 | −0.229646 | − | 0.973274i | \(-0.573757\pi\) | ||||
−0.229646 | + | 0.973274i | \(0.573757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.2517 | 1.10418 | 0.552090 | − | 0.833784i | \(-0.313830\pi\) | ||||
0.552090 | + | 0.833784i | \(0.313830\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.13856 | 0.0496910 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.7454 | −0.947247 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.2856 | −0.795025 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.8269 | −0.860412 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.76846 | 0.0766007 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.7736 | 0.509018 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.62493 | −0.415346 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.23607 | 0.139387 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.3947 | −0.661870 | −0.330935 | − | 0.943654i | \(-0.607364\pi\) | ||||
−0.330935 | + | 0.943654i | \(0.607364\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.7055 | −1.06022 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.787665 | 0.0337398 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.9613 | −1.62311 | −0.811554 | − | 0.584277i | \(-0.801378\pi\) | ||||
−0.811554 | + | 0.584277i | \(0.801378\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.68447 | 0.413323 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.95778 | −0.296411 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.7949 | 0.629141 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.70367 | 0.114764 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.5779 | −1.84645 | −0.923227 | − | 0.384254i | \(-0.874459\pi\) | ||||
−0.923227 | + | 0.384254i | \(0.874459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.51320 | 0.233183 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.9827 | 0.463689 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.6423 | −0.912116 | −0.456058 | − | 0.889950i | \(-0.650739\pi\) | ||||
−0.456058 | + | 0.889950i | \(0.650739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.96160 | −0.334947 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.986489 | −0.0414287 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.47845 | −0.103902 | −0.0519511 | − | 0.998650i | \(-0.516544\pi\) | ||||
−0.0519511 | + | 0.998650i | \(0.516544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0040 | 0.418655 | 0.209327 | − | 0.977846i | \(-0.432873\pi\) | ||||
0.209327 | + | 0.977846i | \(0.432873\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0509 | 0.670537 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.17127 | 0.0905484 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2953 | 1.17795 | 0.588974 | − | 0.808152i | \(-0.299532\pi\) | ||||
0.588974 | + | 0.808152i | \(0.299532\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.9734 | 0.705391 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.61968 | −0.108683 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.0264 | −0.456667 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.70367 | −0.0704381 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.614357 | −0.0253572 | −0.0126786 | − | 0.999920i | \(-0.504036\pi\) | ||||
−0.0126786 | + | 0.999920i | \(0.504036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.1507 | 0.583071 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.6653 | 0.850056 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.6227 | −1.42178 | −0.710892 | − | 0.703302i | \(-0.751708\pi\) | ||||
−0.710892 | + | 0.703302i | \(0.751708\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.98080 | 0.122201 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.2938 | 1.23984 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.2311 | −1.56208 | −0.781040 | − | 0.624481i | \(-0.785311\pi\) | ||||
−0.781040 | + | 0.624481i | \(0.785311\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.3390 | −1.48230 | −0.741149 | − | 0.671341i | \(-0.765719\pi\) | ||||
−0.741149 | + | 0.671341i | \(0.765719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.48502 | 0.141921 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.527864 | −0.0214607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.03537 | 0.0826132 | 0.0413066 | − | 0.999147i | \(-0.486848\pi\) | ||||
0.0413066 | + | 0.999147i | \(0.486848\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.08399 | 0.165492 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.53693 | 0.304912 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.8464 | 1.20548 | 0.602742 | − | 0.797936i | \(-0.294075\pi\) | ||||
0.602742 | + | 0.797936i | \(0.294075\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.01351 | 0.0811926 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.72163 | 0.109569 | 0.0547843 | − | 0.998498i | \(-0.482553\pi\) | ||||
0.0547843 | + | 0.998498i | \(0.482553\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.52795 | 0.342767 | 0.171384 | − | 0.985204i | \(-0.445176\pi\) | ||||
0.171384 | + | 0.985204i | \(0.445176\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.6281 | −0.466620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.92952 | 0.157433 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.14691 | −0.285420 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.07830 | 0.282230 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.39268 | 0.0554415 | 0.0277208 | − | 0.999616i | \(-0.491175\pi\) | ||||
0.0277208 | + | 0.999616i | \(0.491175\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.15510 | −0.284390 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.23607 | 0.128419 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.6050 | −0.736003 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.19838 | 0.126329 | 0.0631643 | − | 0.998003i | \(-0.479881\pi\) | ||||
0.0631643 | + | 0.998003i | \(0.479881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.2845 | 0.997124 | 0.498562 | − | 0.866854i | \(-0.333862\pi\) | ||||
0.498562 | + | 0.866854i | \(0.333862\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.27713 | 0.247162 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.414007 | −0.0162763 | −0.00813814 | − | 0.999967i | \(-0.502590\pi\) | ||||
−0.00813814 | + | 0.999967i | \(0.502590\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.6605 | 1.47830 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.30602 | −0.325539 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.4170 | 0.877246 | 0.438623 | − | 0.898671i | \(-0.355466\pi\) | ||||
0.438623 | + | 0.898671i | \(0.355466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.42467 | 0.251033 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0821 | 0.471368 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.8679 | −0.734990 | −0.367495 | − | 0.930026i | \(-0.619784\pi\) | ||||
−0.367495 | + | 0.930026i | \(0.619784\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.8398 | 0.577203 | 0.288601 | − | 0.957449i | \(-0.406810\pi\) | ||||
0.288601 | + | 0.957449i | \(0.406810\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.39383 | 0.131806 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.93974 | −0.0752199 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.78829 | 0.301564 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.3673 | −0.787444 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.3953 | −0.710144 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.488836 | −0.0188432 | −0.00942162 | − | 0.999956i | \(-0.502999\pi\) | ||||
−0.00942162 | + | 0.999956i | \(0.502999\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.35543 | −0.206131 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.5736 | 0.944442 | 0.472221 | − | 0.881480i | \(-0.343452\pi\) | ||||
0.472221 | + | 0.881480i | \(0.343452\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.34192 | −0.0514982 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.85309 | −0.339251 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.8392 | −0.759126 | −0.379563 | − | 0.925166i | \(-0.623926\pi\) | ||||
−0.379563 | + | 0.925166i | \(0.623926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.83708 | 0.0701910 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.37650 | −0.243279 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.40734 | −0.129809 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4788 | −0.969259 | −0.484630 | − | 0.874719i | \(-0.661046\pi\) | ||||
−0.484630 | + | 0.874719i | \(0.661046\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.51320 | −0.209429 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.62874 | −0.327307 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.27144 | 0.199670 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.83344 | 0.296288 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.8981 | 1.05369 | 0.526847 | − | 0.849960i | \(-0.323374\pi\) | ||||
0.526847 | + | 0.849960i | \(0.323374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.60617 | −0.173725 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.58128 | 0.323190 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.49853 | 0.282011 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.7860 | 0.818190 | 0.409095 | − | 0.912492i | \(-0.365845\pi\) | ||||
0.409095 | + | 0.912492i | \(0.365845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.2056 | −0.945283 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.8398 | −0.593206 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.23607 | 0.121022 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.2197 | −0.904502 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.76064 | 0.102955 | 0.0514773 | − | 0.998674i | \(-0.483607\pi\) | ||||
0.0514773 | + | 0.998674i | \(0.483607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.5685 | −0.542559 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.99244 | −0.334432 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.58697 | 0.133217 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.00366 | −0.185575 | −0.0927877 | − | 0.995686i | \(-0.529578\pi\) | ||||
−0.0927877 | + | 0.995686i | \(0.529578\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.9732 | 0.739747 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.4337 | 0.607824 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.26512 | −0.0467283 | −0.0233642 | − | 0.999727i | \(-0.507438\pi\) | ||||
−0.0233642 | + | 0.999727i | \(0.507438\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.13856 | 0.0419966 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.61968 | −0.243839 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.1432 | −1.03526 | −0.517632 | − | 0.855603i | \(-0.673186\pi\) | ||||
−0.517632 | + | 0.855603i | \(0.673186\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.20852 | −0.0811319 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.1298 | 0.481685 | 0.240842 | − | 0.970564i | \(-0.422576\pi\) | ||||
0.240842 | + | 0.970564i | \(0.422576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.8405 | −0.690261 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.46307 | 0.163295 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.7736 | 0.430199 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.3409 | −0.997685 | −0.498842 | − | 0.866693i | \(-0.666241\pi\) | ||||
−0.498842 | + | 0.866693i | \(0.666241\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.1085 | 1.20654 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.6704 | 0.461124 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5640 | 1.07452 | 0.537260 | − | 0.843417i | \(-0.319459\pi\) | ||||
0.537260 | + | 0.843417i | \(0.319459\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.3639 | −0.629440 | −0.314720 | − | 0.949185i | \(-0.601911\pi\) | ||||
−0.314720 | + | 0.949185i | \(0.601911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.787665 | 0.0285154 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.07830 | −0.183606 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.6377 | 0.420214 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.9443 | 0.394661 | 0.197330 | − | 0.980337i | \(-0.436773\pi\) | ||||
0.197330 | + | 0.980337i | \(0.436773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.25606 | 0.333349 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.4003 | −1.38116 | −0.690582 | − | 0.723254i | \(-0.742646\pi\) | ||||
−0.690582 | + | 0.723254i | \(0.742646\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.29517 | −0.262050 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.70367 | 0.0969937 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.43036 | −0.122905 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.3396 | 1.26455 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.2098 | −0.686501 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.32717 | 0.0830602 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.1836 | −0.790761 | −0.395380 | − | 0.918517i | \(-0.629387\pi\) | ||||
−0.395380 | + | 0.918517i | \(0.629387\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.0474651 | −0.00168980 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.96160 | −0.283082 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.68447 | −0.201861 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.87948 | −0.137591 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.2368 | 0.752245 | 0.376123 | − | 0.926570i | \(-0.377257\pi\) | ||||
0.376123 | + | 0.926570i | \(0.377257\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.4661 | 0.794793 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.69461 | −0.236542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.9496 | −0.809874 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.17127 | 0.0765274 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.3332 | 0.962175 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.3677 | −0.716090 | −0.358045 | − | 0.933704i | \(-0.616557\pi\) | ||||
−0.358045 | + | 0.933704i | \(0.616557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.3800 | −1.45305 | −0.726525 | − | 0.687140i | \(-0.758866\pi\) | ||||
−0.726525 | + | 0.687140i | \(0.758866\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.1906 | 0.953617 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.1623 | 0.390998 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.6942 | −0.374141 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.70367 | −0.0595311 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.8328 | −1.00627 | −0.503136 | − | 0.864207i | \(-0.667821\pi\) | ||||
−0.503136 | + | 0.864207i | \(0.667821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.1527 | 0.388758 | 0.194379 | − | 0.980926i | \(-0.437731\pi\) | ||||
0.194379 | + | 0.980926i | \(0.437731\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.68447 | 0.128277 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.0330 | 0.940028 | 0.470014 | − | 0.882659i | \(-0.344249\pi\) | ||||
0.470014 | + | 0.882659i | \(0.344249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.2928 | 0.774260 | 0.387130 | − | 0.922025i | \(-0.373466\pi\) | ||||
0.387130 | + | 0.922025i | \(0.373466\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.7854 | 0.929174 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.98080 | 0.103279 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.58128 | 0.296967 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.0688 | 1.35042 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −50.3602 | −1.73863 | −0.869314 | − | 0.494260i | \(-0.835439\pi\) | ||||
−0.869314 | + | 0.494260i | \(0.835439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.1337 | −0.556333 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.4511 | −0.738814 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.527864 | −0.0181376 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.3808 | 0.356267 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.15598 | 0.176745 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.8989 | 1.22915 | 0.614577 | − | 0.788857i | \(-0.289327\pi\) | ||||
0.614577 | + | 0.788857i | \(0.289327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.30468 | 0.113018 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.48752 | −0.289928 | −0.144964 | − | 0.989437i | \(-0.546307\pi\) | ||||
−0.144964 | + | 0.989437i | \(0.546307\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.8200 | −0.573891 | −0.286946 | − | 0.957947i | \(-0.592640\pi\) | ||||
−0.286946 | + | 0.957947i | \(0.592640\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.01351 | 0.0686203 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.5718 | 0.972594 | 0.486297 | − | 0.873793i | \(-0.338347\pi\) | ||||
0.486297 | + | 0.873793i | \(0.338347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.4010 | −0.455649 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.23926 | −0.313782 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.8772 | 1.62412 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.04559 | −0.0693123 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.28619 | 0.0773759 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.7638 | 0.566072 | 0.283036 | − | 0.959109i | \(-0.408658\pi\) | ||||
0.283036 | + | 0.959109i | \(0.408658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.6575 | −0.393196 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.5933 | −0.997023 | −0.498512 | − | 0.866883i | \(-0.666120\pi\) | ||||
−0.498512 | + | 0.866883i | \(0.666120\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.18203 | −0.107084 | −0.0535418 | − | 0.998566i | \(-0.517051\pi\) | ||||
−0.0535418 | + | 0.998566i | \(0.517051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.2503 | 0.445404 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.31856 | 0.145003 | 0.0725015 | − | 0.997368i | \(-0.476902\pi\) | ||||
0.0725015 | + | 0.997368i | \(0.476902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.23607 | 0.108534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.19235 | −0.106948 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.6197 | −0.489229 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.45356 | −0.282571 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.47214 | 0.0825422 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.1675 | −0.872736 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.1566 | −0.338366 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.27713 | 0.208890 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.6989 | −0.721294 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.46653 | 0.281127 | 0.140563 | − | 0.990072i | \(-0.455109\pi\) | ||||
0.140563 | + | 0.990072i | \(0.455109\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.7750 | −0.423721 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.45356 | −0.147553 | −0.0737766 | − | 0.997275i | \(-0.523505\pi\) | ||||
−0.0737766 | + | 0.997275i | \(0.523505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.47746 | −0.280563 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.47214 | −0.213962 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.42467 | 0.212161 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.310467 | 0.0102414 | 0.00512068 | − | 0.999987i | \(-0.498370\pi\) | ||||
0.00512068 | + | 0.999987i | \(0.498370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.5256 | −0.709291 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.9205 | 0.359454 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.37463 | 0.0780774 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.8199 | 0.815193 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.886424 | −0.0290826 | −0.0145413 | − | 0.999894i | \(-0.504629\pi\) | ||||
−0.0145413 | + | 0.999894i | \(0.504629\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.93974 | −0.0635724 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.2094 | 0.661626 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.64607 | 0.315460 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.3307 | −0.729513 | −0.364757 | − | 0.931103i | \(-0.618848\pi\) | ||||
−0.364757 | + | 0.931103i | \(0.618848\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.29839 | 0.205540 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0673 | −0.328184 | −0.164092 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164092 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.83982 | 0.125042 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.35543 | −0.174212 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.0559 | −0.846703 | −0.423352 | − | 0.905965i | \(-0.639147\pi\) | ||||
−0.423352 | + | 0.905965i | \(0.639147\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.09181 | −0.230210 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.43073 | −0.0788218 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.7206 | 0.379666 | 0.189833 | − | 0.981816i | \(-0.439205\pi\) | ||||
0.189833 | + | 0.981816i | \(0.439205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.0975 | 0.456185 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.2161 | 0.427215 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.83708 | 0.0593222 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.2195 | 0.716759 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.0584 | −0.646373 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.9077 | 0.479897 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0758 | 0.388332 | 0.194166 | − | 0.980969i | \(-0.437800\pi\) | ||||
0.194166 | + | 0.980969i | \(0.437800\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.58315 | −0.211481 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 60.2174 | 1.93247 | 0.966234 | − | 0.257666i | \(-0.0829533\pi\) | ||||
0.966234 | + | 0.257666i | \(0.0829533\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.62874 | −0.276625 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.13856 | 0.0364632 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.1157 | −0.867508 | −0.433754 | − | 0.901031i | \(-0.642811\pi\) | ||||
−0.433754 | + | 0.901031i | \(0.642811\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7162 | 0.406411 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.34192 | −0.0428443 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.4274 | 0.906692 | 0.453346 | − | 0.891335i | \(-0.350230\pi\) | ||||
0.453346 | + | 0.891335i | \(0.350230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.1503 | 0.578316 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.58128 | 0.273145 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.9707 | 0.380645 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.3582 | −0.805529 | −0.402765 | − | 0.915304i | \(-0.631951\pi\) | ||||
−0.402765 | + | 0.915304i | \(0.631951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.6337 | −0.464388 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.6070 | 0.843500 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.7554 | −1.29074 | −0.645368 | − | 0.763872i | \(-0.723296\pi\) | ||||
−0.645368 | + | 0.763872i | \(0.723296\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.7172 | −0.402354 |
(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 | 7280.2.a.ca.1.3 | 4 | ||
4.3 | odd | 2 | 3640.2.a.s.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.s.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
7280.2.a.ca.1.3 | 4 | 1.1 | even | 1 | trivial |