Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + 1860 x^{8} - 5877 x^{7} - 2496 x^{6} + 6612 x^{5} + 1842 x^{4} - 3011 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.445942\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.445942 | −0.315329 | −0.157664 | − | 0.987493i | \(-0.550396\pi\) | ||||
−0.157664 | + | 0.987493i | \(0.550396\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.80114 | −0.900568 | ||||||||
\(5\) | −2.46971 | −1.10449 | −0.552244 | − | 0.833682i | \(-0.686228\pi\) | ||||
−0.552244 | + | 0.833682i | \(0.686228\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.81741 | −1.06488 | −0.532440 | − | 0.846468i | \(-0.678725\pi\) | ||||
−0.532440 | + | 0.846468i | \(0.678725\pi\) | |||||||
\(8\) | 1.69509 | 0.599304 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.10135 | 0.348277 | ||||||||
\(11\) | −4.28934 | −1.29328 | −0.646642 | − | 0.762794i | \(-0.723827\pi\) | ||||
−0.646642 | + | 0.762794i | \(0.723827\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.41981 | 1.22584 | 0.612918 | − | 0.790147i | \(-0.289996\pi\) | ||||
0.612918 | + | 0.790147i | \(0.289996\pi\) | |||||||
\(14\) | 1.25640 | 0.335787 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.84636 | 0.711590 | ||||||||
\(17\) | −6.60695 | −1.60242 | −0.801210 | − | 0.598383i | \(-0.795810\pi\) | ||||
−0.801210 | + | 0.598383i | \(0.795810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.20884 | 0.965574 | 0.482787 | − | 0.875738i | \(-0.339625\pi\) | ||||
0.482787 | + | 0.875738i | \(0.339625\pi\) | |||||||
\(20\) | 4.44829 | 0.994667 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.91280 | 0.407810 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.09948 | 0.219895 | ||||||||
\(26\) | −1.97098 | −0.386541 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.07453 | 0.958996 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00347 | 0.539439 | 0.269719 | − | 0.962939i | \(-0.413069\pi\) | ||||
0.269719 | + | 0.962939i | \(0.413069\pi\) | |||||||
\(32\) | −4.65949 | −0.823689 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.94632 | 0.505289 | ||||||||
\(35\) | 6.95818 | 1.17615 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.401833 | 0.0660609 | 0.0330305 | − | 0.999454i | \(-0.489484\pi\) | ||||
0.0330305 | + | 0.999454i | \(0.489484\pi\) | |||||||
\(38\) | −1.87690 | −0.304473 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.18638 | −0.661924 | ||||||||
\(41\) | 2.84424 | 0.444196 | 0.222098 | − | 0.975024i | \(-0.428709\pi\) | ||||
0.222098 | + | 0.975024i | \(0.428709\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.53651 | 0.386814 | 0.193407 | − | 0.981119i | \(-0.438046\pi\) | ||||
0.193407 | + | 0.981119i | \(0.438046\pi\) | |||||||
\(44\) | 7.72567 | 1.16469 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.445942 | 0.0657506 | ||||||||
\(47\) | 11.7062 | 1.70753 | 0.853763 | − | 0.520662i | \(-0.174315\pi\) | ||||
0.853763 | + | 0.520662i | \(0.174315\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.937778 | 0.133968 | ||||||||
\(50\) | −0.490303 | −0.0693393 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.96068 | −1.10395 | ||||||||
\(53\) | −7.37978 | −1.01369 | −0.506846 | − | 0.862037i | \(-0.669189\pi\) | ||||
−0.506846 | + | 0.862037i | \(0.669189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.5934 | 1.42842 | ||||||||
\(56\) | −4.77575 | −0.638186 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.445942 | −0.0585551 | ||||||||
\(59\) | 1.99814 | 0.260136 | 0.130068 | − | 0.991505i | \(-0.458480\pi\) | ||||
0.130068 | + | 0.991505i | \(0.458480\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6586 | 1.87685 | 0.938423 | − | 0.345488i | \(-0.112287\pi\) | ||||
0.938423 | + | 0.345488i | \(0.112287\pi\) | |||||||
\(62\) | −1.33937 | −0.170101 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.61486 | −0.451857 | ||||||||
\(65\) | −10.9157 | −1.35392 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.4268 | −1.51817 | −0.759085 | − | 0.650992i | \(-0.774353\pi\) | ||||
−0.759085 | + | 0.650992i | \(0.774353\pi\) | |||||||
\(68\) | 11.9000 | 1.44309 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.10295 | −0.370873 | ||||||||
\(71\) | 6.86171 | 0.814335 | 0.407168 | − | 0.913353i | \(-0.366516\pi\) | ||||
0.407168 | + | 0.913353i | \(0.366516\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.98002 | 0.465827 | 0.232913 | − | 0.972498i | \(-0.425174\pi\) | ||||
0.232913 | + | 0.972498i | \(0.425174\pi\) | |||||||
\(74\) | −0.179194 | −0.0208309 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.58069 | −0.869564 | ||||||||
\(77\) | 12.0848 | 1.37719 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.1580 | 1.93042 | 0.965212 | − | 0.261469i | \(-0.0842069\pi\) | ||||
0.965212 | + | 0.261469i | \(0.0842069\pi\) | |||||||
\(80\) | −7.02969 | −0.785943 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.26837 | −0.140068 | ||||||||
\(83\) | −3.57952 | −0.392903 | −0.196452 | − | 0.980514i | \(-0.562942\pi\) | ||||
−0.196452 | + | 0.980514i | \(0.562942\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.3173 | 1.76985 | ||||||||
\(86\) | −1.13114 | −0.121974 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.27080 | −0.775070 | ||||||||
\(89\) | 7.34060 | 0.778102 | 0.389051 | − | 0.921216i | \(-0.372803\pi\) | ||||
0.389051 | + | 0.921216i | \(0.372803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4524 | −1.30537 | ||||||||
\(92\) | 1.80114 | 0.187781 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.22029 | −0.538432 | ||||||||
\(95\) | −10.3946 | −1.06646 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.56673 | 0.768285 | 0.384143 | − | 0.923274i | \(-0.374497\pi\) | ||||
0.384143 | + | 0.923274i | \(0.374497\pi\) | |||||||
\(98\) | −0.418195 | −0.0422441 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.98030 | −0.198030 | ||||||||
\(101\) | 8.93289 | 0.888856 | 0.444428 | − | 0.895815i | \(-0.353407\pi\) | ||||
0.444428 | + | 0.895815i | \(0.353407\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.0586 | −1.68083 | −0.840415 | − | 0.541944i | \(-0.817689\pi\) | ||||
−0.840415 | + | 0.541944i | \(0.817689\pi\) | |||||||
\(104\) | 7.49197 | 0.734648 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.29096 | 0.319646 | ||||||||
\(107\) | −1.72224 | −0.166496 | −0.0832478 | − | 0.996529i | \(-0.526529\pi\) | ||||
−0.0832478 | + | 0.996529i | \(0.526529\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6626 | −1.02129 | −0.510644 | − | 0.859792i | \(-0.670593\pi\) | ||||
−0.510644 | + | 0.859792i | \(0.670593\pi\) | |||||||
\(110\) | −4.72406 | −0.450421 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.01935 | −0.757757 | ||||||||
\(113\) | −16.2113 | −1.52503 | −0.762515 | − | 0.646971i | \(-0.776036\pi\) | ||||
−0.762515 | + | 0.646971i | \(0.776036\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.46971 | 0.230302 | ||||||||
\(116\) | −1.80114 | −0.167231 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.891056 | −0.0820283 | ||||||||
\(119\) | 18.6145 | 1.70638 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.39840 | 0.672582 | ||||||||
\(122\) | −6.53691 | −0.591824 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.40965 | −0.485801 | ||||||||
\(125\) | 9.63317 | 0.861617 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.42264 | 0.569917 | 0.284958 | − | 0.958540i | \(-0.408020\pi\) | ||||
0.284958 | + | 0.958540i | \(0.408020\pi\) | |||||||
\(128\) | 10.9310 | 0.966172 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.86776 | 0.426931 | ||||||||
\(131\) | 14.9726 | 1.30817 | 0.654083 | − | 0.756423i | \(-0.273055\pi\) | ||||
0.654083 | + | 0.756423i | \(0.273055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.8580 | −1.02822 | ||||||||
\(134\) | 5.54162 | 0.478723 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.1994 | −0.960337 | ||||||||
\(137\) | 0.156153 | 0.0133410 | 0.00667052 | − | 0.999978i | \(-0.497877\pi\) | ||||
0.00667052 | + | 0.999978i | \(0.497877\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.5888 | −1.15259 | −0.576295 | − | 0.817241i | \(-0.695502\pi\) | ||||
−0.576295 | + | 0.817241i | \(0.695502\pi\) | |||||||
\(140\) | −12.5326 | −1.05920 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.05993 | −0.256783 | ||||||||
\(143\) | −18.9581 | −1.58535 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.46971 | −0.205098 | ||||||||
\(146\) | −1.77486 | −0.146889 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.723756 | −0.0594924 | ||||||||
\(149\) | −2.15399 | −0.176461 | −0.0882307 | − | 0.996100i | \(-0.528121\pi\) | ||||
−0.0882307 | + | 0.996100i | \(0.528121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.13094 | 0.254792 | 0.127396 | − | 0.991852i | \(-0.459338\pi\) | ||||
0.127396 | + | 0.991852i | \(0.459338\pi\) | |||||||
\(152\) | 7.13435 | 0.578672 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.38913 | −0.434268 | ||||||||
\(155\) | −7.41770 | −0.595804 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.8952 | 1.34838 | 0.674191 | − | 0.738557i | \(-0.264492\pi\) | ||||
0.674191 | + | 0.738557i | \(0.264492\pi\) | |||||||
\(158\) | −7.65147 | −0.608718 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 11.5076 | 0.909755 | ||||||||
\(161\) | 2.81741 | 0.222043 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.1137 | −1.73208 | −0.866038 | − | 0.499978i | \(-0.833342\pi\) | ||||
−0.866038 | + | 0.499978i | \(0.833342\pi\) | |||||||
\(164\) | −5.12287 | −0.400029 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.59626 | 0.123894 | ||||||||
\(167\) | −2.95049 | −0.228316 | −0.114158 | − | 0.993463i | \(-0.536417\pi\) | ||||
−0.114158 | + | 0.993463i | \(0.536417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.53474 | 0.502673 | ||||||||
\(170\) | −7.27656 | −0.558086 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.56860 | −0.348352 | ||||||||
\(173\) | −18.1533 | −1.38017 | −0.690085 | − | 0.723728i | \(-0.742427\pi\) | ||||
−0.690085 | + | 0.723728i | \(0.742427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.09767 | −0.234162 | ||||||||
\(176\) | −12.2090 | −0.920287 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.27348 | −0.245358 | ||||||||
\(179\) | 10.1727 | 0.760346 | 0.380173 | − | 0.924915i | \(-0.375864\pi\) | ||||
0.380173 | + | 0.924915i | \(0.375864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.4731 | 1.59608 | 0.798040 | − | 0.602604i | \(-0.205870\pi\) | ||||
0.798040 | + | 0.602604i | \(0.205870\pi\) | |||||||
\(182\) | 5.55306 | 0.411620 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.69509 | −0.124964 | ||||||||
\(185\) | −0.992412 | −0.0729636 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.3394 | 2.07238 | ||||||||
\(188\) | −21.0845 | −1.53774 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.63540 | 0.336287 | ||||||||
\(191\) | −21.7372 | −1.57285 | −0.786425 | − | 0.617686i | \(-0.788070\pi\) | ||||
−0.786425 | + | 0.617686i | \(0.788070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.77711 | −0.415846 | −0.207923 | − | 0.978145i | \(-0.566670\pi\) | ||||
−0.207923 | + | 0.978145i | \(0.566670\pi\) | |||||||
\(194\) | −3.37433 | −0.242263 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.68906 | −0.120647 | ||||||||
\(197\) | 16.9138 | 1.20506 | 0.602529 | − | 0.798097i | \(-0.294160\pi\) | ||||
0.602529 | + | 0.798097i | \(0.294160\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.4767 | −1.09712 | −0.548559 | − | 0.836112i | \(-0.684823\pi\) | ||||
−0.548559 | + | 0.836112i | \(0.684823\pi\) | |||||||
\(200\) | 1.86371 | 0.131784 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.98355 | −0.280282 | ||||||||
\(203\) | −2.81741 | −0.197743 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.02446 | −0.490610 | ||||||||
\(206\) | 7.60713 | 0.530014 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.5804 | 0.872292 | ||||||||
\(209\) | −18.0531 | −1.24876 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.84718 | 0.402536 | 0.201268 | − | 0.979536i | \(-0.435494\pi\) | ||||
0.201268 | + | 0.979536i | \(0.435494\pi\) | |||||||
\(212\) | 13.2920 | 0.912897 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.768022 | 0.0525009 | ||||||||
\(215\) | −6.26445 | −0.427232 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.46199 | −0.574437 | ||||||||
\(218\) | 4.75489 | 0.322042 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −19.0802 | −1.28639 | ||||||||
\(221\) | −29.2015 | −1.96430 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.7769 | −1.52525 | −0.762625 | − | 0.646840i | \(-0.776090\pi\) | ||||
−0.762625 | + | 0.646840i | \(0.776090\pi\) | |||||||
\(224\) | 13.1277 | 0.877129 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.22930 | 0.480886 | ||||||||
\(227\) | −4.87598 | −0.323630 | −0.161815 | − | 0.986821i | \(-0.551735\pi\) | ||||
−0.161815 | + | 0.986821i | \(0.551735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.9661 | −0.724661 | −0.362330 | − | 0.932050i | \(-0.618019\pi\) | ||||
−0.362330 | + | 0.932050i | \(0.618019\pi\) | |||||||
\(230\) | −1.10135 | −0.0726208 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.69509 | 0.111288 | ||||||||
\(233\) | −29.0404 | −1.90250 | −0.951251 | − | 0.308418i | \(-0.900200\pi\) | ||||
−0.951251 | + | 0.308418i | \(0.900200\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.9109 | −1.88594 | ||||||||
\(236\) | −3.59892 | −0.234270 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.30098 | −0.538072 | ||||||||
\(239\) | −22.0157 | −1.42408 | −0.712039 | − | 0.702140i | \(-0.752228\pi\) | ||||
−0.712039 | + | 0.702140i | \(0.752228\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.2176 | −1.62441 | −0.812206 | − | 0.583371i | \(-0.801733\pi\) | ||||
−0.812206 | + | 0.583371i | \(0.801733\pi\) | |||||||
\(242\) | −3.29926 | −0.212085 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −26.4022 | −1.69023 | ||||||||
\(245\) | −2.31604 | −0.147966 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.6023 | 1.18363 | ||||||||
\(248\) | 5.09114 | 0.323288 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.29584 | −0.271693 | ||||||||
\(251\) | 21.9563 | 1.38587 | 0.692933 | − | 0.721002i | \(-0.256318\pi\) | ||||
0.692933 | + | 0.721002i | \(0.256318\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.28934 | 0.269668 | ||||||||
\(254\) | −2.86413 | −0.179711 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.35512 | 0.147195 | ||||||||
\(257\) | 23.2366 | 1.44946 | 0.724731 | − | 0.689032i | \(-0.241964\pi\) | ||||
0.724731 | + | 0.689032i | \(0.241964\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.13213 | −0.0703469 | ||||||||
\(260\) | 19.6606 | 1.21930 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.67694 | −0.412503 | ||||||||
\(263\) | 7.44609 | 0.459145 | 0.229573 | − | 0.973292i | \(-0.426267\pi\) | ||||
0.229573 | + | 0.973292i | \(0.426267\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.2259 | 1.11961 | ||||||||
\(266\) | 5.28799 | 0.324227 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 22.3823 | 1.36721 | ||||||||
\(269\) | −17.2475 | −1.05160 | −0.525800 | − | 0.850608i | \(-0.676234\pi\) | ||||
−0.525800 | + | 0.850608i | \(0.676234\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.53709 | 0.214863 | 0.107431 | − | 0.994212i | \(-0.465737\pi\) | ||||
0.107431 | + | 0.994212i | \(0.465737\pi\) | |||||||
\(272\) | −18.8057 | −1.14027 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0696352 | −0.00420682 | ||||||||
\(275\) | −4.71602 | −0.284387 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.35010 | −0.321456 | −0.160728 | − | 0.986999i | \(-0.551384\pi\) | ||||
−0.160728 | + | 0.986999i | \(0.551384\pi\) | |||||||
\(278\) | 6.05984 | 0.363445 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.7947 | 0.704870 | ||||||||
\(281\) | −2.43662 | −0.145356 | −0.0726782 | − | 0.997355i | \(-0.523155\pi\) | ||||
−0.0726782 | + | 0.997355i | \(0.523155\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.9942 | −0.891313 | −0.445656 | − | 0.895204i | \(-0.647030\pi\) | ||||
−0.445656 | + | 0.895204i | \(0.647030\pi\) | |||||||
\(284\) | −12.3589 | −0.733364 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.45420 | 0.499908 | ||||||||
\(287\) | −8.01339 | −0.473016 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.6518 | 1.56775 | ||||||||
\(290\) | 1.10135 | 0.0646735 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.16856 | −0.419508 | ||||||||
\(293\) | 9.90190 | 0.578475 | 0.289238 | − | 0.957257i | \(-0.406598\pi\) | ||||
0.289238 | + | 0.957257i | \(0.406598\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.93483 | −0.287317 | ||||||||
\(296\) | 0.681142 | 0.0395906 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.960554 | 0.0556434 | ||||||||
\(299\) | −4.41981 | −0.255604 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.14638 | −0.411910 | ||||||||
\(302\) | −1.39622 | −0.0803433 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.9799 | 0.687092 | ||||||||
\(305\) | −36.2026 | −2.07296 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.06498 | 0.460293 | 0.230146 | − | 0.973156i | \(-0.426079\pi\) | ||||
0.230146 | + | 0.973156i | \(0.426079\pi\) | |||||||
\(308\) | −21.7664 | −1.24025 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.30787 | 0.187874 | ||||||||
\(311\) | 16.9600 | 0.961714 | 0.480857 | − | 0.876799i | \(-0.340326\pi\) | ||||
0.480857 | + | 0.876799i | \(0.340326\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.2949 | 1.71237 | 0.856185 | − | 0.516669i | \(-0.172828\pi\) | ||||
0.856185 | + | 0.516669i | \(0.172828\pi\) | |||||||
\(314\) | −7.53428 | −0.425184 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −30.9038 | −1.73848 | ||||||||
\(317\) | 21.3506 | 1.19917 | 0.599584 | − | 0.800312i | \(-0.295333\pi\) | ||||
0.599584 | + | 0.800312i | \(0.295333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.28934 | −0.240157 | ||||||||
\(320\) | 8.92765 | 0.499071 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.25640 | −0.0700165 | ||||||||
\(323\) | −27.8076 | −1.54725 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.85948 | 0.269555 | ||||||||
\(326\) | 9.86143 | 0.546174 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.82124 | 0.266209 | ||||||||
\(329\) | −32.9811 | −1.81831 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.784375 | 0.0431131 | 0.0215566 | − | 0.999768i | \(-0.493138\pi\) | ||||
0.0215566 | + | 0.999768i | \(0.493138\pi\) | |||||||
\(332\) | 6.44720 | 0.353836 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.31575 | 0.0719946 | ||||||||
\(335\) | 30.6905 | 1.67680 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.2511 | −1.21209 | −0.606047 | − | 0.795429i | \(-0.707246\pi\) | ||||
−0.606047 | + | 0.795429i | \(0.707246\pi\) | |||||||
\(338\) | −2.91412 | −0.158507 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −29.3896 | −1.59387 | ||||||||
\(341\) | −12.8829 | −0.697647 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0797 | 0.922219 | ||||||||
\(344\) | 4.29961 | 0.231819 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.09533 | 0.435207 | ||||||||
\(347\) | −19.0506 | −1.02269 | −0.511344 | − | 0.859376i | \(-0.670852\pi\) | ||||
−0.511344 | + | 0.859376i | \(0.670852\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.1162 | −0.702096 | −0.351048 | − | 0.936357i | \(-0.614175\pi\) | ||||
−0.351048 | + | 0.936357i | \(0.614175\pi\) | |||||||
\(350\) | 1.38138 | 0.0738380 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.9861 | 1.06526 | ||||||||
\(353\) | −17.5345 | −0.933265 | −0.466633 | − | 0.884451i | \(-0.654533\pi\) | ||||
−0.466633 | + | 0.884451i | \(0.654533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.9464 | −0.899424 | ||||||||
\(356\) | −13.2214 | −0.700733 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.53646 | −0.239759 | ||||||||
\(359\) | −21.0184 | −1.10931 | −0.554653 | − | 0.832082i | \(-0.687149\pi\) | ||||
−0.554653 | + | 0.832082i | \(0.687149\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.28569 | −0.0676678 | ||||||||
\(362\) | −9.57575 | −0.503290 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 22.4285 | 1.17557 | ||||||||
\(365\) | −9.82951 | −0.514500 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.5736 | 1.17833 | 0.589165 | − | 0.808013i | \(-0.299457\pi\) | ||||
0.589165 | + | 0.808013i | \(0.299457\pi\) | |||||||
\(368\) | −2.84636 | −0.148377 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.442559 | 0.0230075 | ||||||||
\(371\) | 20.7918 | 1.07946 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.5809 | −1.47986 | −0.739931 | − | 0.672683i | \(-0.765142\pi\) | ||||
−0.739931 | + | 0.672683i | \(0.765142\pi\) | |||||||
\(374\) | −12.6377 | −0.653482 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.8430 | 1.02333 | ||||||||
\(377\) | 4.41981 | 0.227632 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.35998 | −0.429423 | −0.214712 | − | 0.976677i | \(-0.568881\pi\) | ||||
−0.214712 | + | 0.976677i | \(0.568881\pi\) | |||||||
\(380\) | 18.7221 | 0.960424 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.69355 | 0.495965 | ||||||||
\(383\) | 1.67118 | 0.0853932 | 0.0426966 | − | 0.999088i | \(-0.486405\pi\) | ||||
0.0426966 | + | 0.999088i | \(0.486405\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.8460 | −1.52109 | ||||||||
\(386\) | 2.57626 | 0.131128 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.6287 | −0.691893 | ||||||||
\(389\) | 18.1730 | 0.921405 | 0.460703 | − | 0.887554i | \(-0.347597\pi\) | ||||
0.460703 | + | 0.887554i | \(0.347597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.60695 | 0.334128 | ||||||||
\(392\) | 1.58962 | 0.0802877 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.54258 | −0.379990 | ||||||||
\(395\) | −42.3753 | −2.13213 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.1359 | 0.558897 | 0.279449 | − | 0.960161i | \(-0.409848\pi\) | ||||
0.279449 | + | 0.960161i | \(0.409848\pi\) | |||||||
\(398\) | 6.90174 | 0.345953 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.12950 | 0.156475 | ||||||||
\(401\) | −36.0633 | −1.80091 | −0.900457 | − | 0.434945i | \(-0.856768\pi\) | ||||
−0.900457 | + | 0.434945i | \(0.856768\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.2748 | 0.661263 | ||||||||
\(404\) | −16.0893 | −0.800475 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.25640 | 0.0623541 | ||||||||
\(407\) | −1.72360 | −0.0854355 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.09351 | −0.251858 | −0.125929 | − | 0.992039i | \(-0.540191\pi\) | ||||
−0.125929 | + | 0.992039i | \(0.540191\pi\) | |||||||
\(410\) | 3.13251 | 0.154703 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.7248 | 1.51370 | ||||||||
\(413\) | −5.62958 | −0.277013 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.84038 | 0.433957 | ||||||||
\(416\) | −20.5941 | −1.00971 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.05065 | 0.393770 | ||||||||
\(419\) | 18.9896 | 0.927701 | 0.463850 | − | 0.885914i | \(-0.346468\pi\) | ||||
0.463850 | + | 0.885914i | \(0.346468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.9673 | −1.26557 | −0.632784 | − | 0.774328i | \(-0.718088\pi\) | ||||
−0.632784 | + | 0.774328i | \(0.718088\pi\) | |||||||
\(422\) | −2.60750 | −0.126931 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.5094 | −0.607509 | ||||||||
\(425\) | −7.26418 | −0.352364 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −41.2993 | −1.99862 | ||||||||
\(428\) | 3.10200 | 0.149941 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.79358 | 0.134719 | ||||||||
\(431\) | 20.4418 | 0.984648 | 0.492324 | − | 0.870412i | \(-0.336148\pi\) | ||||
0.492324 | + | 0.870412i | \(0.336148\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.43016 | 0.116786 | 0.0583930 | − | 0.998294i | \(-0.481402\pi\) | ||||
0.0583930 | + | 0.998294i | \(0.481402\pi\) | |||||||
\(434\) | 3.77356 | 0.181137 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.2047 | 0.919739 | ||||||||
\(437\) | −4.20884 | −0.201336 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.08175 | 0.433448 | 0.216724 | − | 0.976233i | \(-0.430463\pi\) | ||||
0.216724 | + | 0.976233i | \(0.430463\pi\) | |||||||
\(440\) | 17.9568 | 0.856056 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.0222 | 0.619402 | ||||||||
\(443\) | −26.2999 | −1.24954 | −0.624772 | − | 0.780807i | \(-0.714808\pi\) | ||||
−0.624772 | + | 0.780807i | \(0.714808\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.1292 | −0.859405 | ||||||||
\(446\) | 10.1572 | 0.480956 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.1845 | 0.481173 | ||||||||
\(449\) | 21.0659 | 0.994161 | 0.497081 | − | 0.867704i | \(-0.334405\pi\) | ||||
0.497081 | + | 0.867704i | \(0.334405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.1999 | −0.574472 | ||||||||
\(452\) | 29.1987 | 1.37339 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.17441 | 0.102050 | ||||||||
\(455\) | 30.7539 | 1.44176 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.7132 | −0.547922 | −0.273961 | − | 0.961741i | \(-0.588334\pi\) | ||||
−0.273961 | + | 0.961741i | \(0.588334\pi\) | |||||||
\(458\) | 4.89025 | 0.228506 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.44829 | −0.207402 | ||||||||
\(461\) | 11.7310 | 0.546369 | 0.273184 | − | 0.961962i | \(-0.411923\pi\) | ||||
0.273184 | + | 0.961962i | \(0.411923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.9534 | −0.509049 | −0.254525 | − | 0.967066i | \(-0.581919\pi\) | ||||
−0.254525 | + | 0.967066i | \(0.581919\pi\) | |||||||
\(464\) | 2.84636 | 0.132139 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.9504 | 0.599914 | ||||||||
\(467\) | 3.23636 | 0.149761 | 0.0748804 | − | 0.997193i | \(-0.476143\pi\) | ||||
0.0748804 | + | 0.997193i | \(0.476143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.0112 | 1.61667 | ||||||||
\(470\) | 12.8926 | 0.594692 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.38702 | 0.155900 | ||||||||
\(473\) | −10.8799 | −0.500260 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.62751 | 0.212325 | ||||||||
\(476\) | −33.5272 | −1.53671 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.81773 | 0.449053 | ||||||||
\(479\) | 19.1033 | 0.872854 | 0.436427 | − | 0.899740i | \(-0.356244\pi\) | ||||
0.436427 | + | 0.899740i | \(0.356244\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.77603 | 0.0809799 | ||||||||
\(482\) | 11.2456 | 0.512224 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.3255 | −0.605706 | ||||||||
\(485\) | −18.6877 | −0.848563 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.3407 | −0.468580 | −0.234290 | − | 0.972167i | \(-0.575277\pi\) | ||||
−0.234290 | + | 0.972167i | \(0.575277\pi\) | |||||||
\(488\) | 24.8477 | 1.12480 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.03282 | 0.0466581 | ||||||||
\(491\) | 5.57488 | 0.251591 | 0.125795 | − | 0.992056i | \(-0.459852\pi\) | ||||
0.125795 | + | 0.992056i | \(0.459852\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.60695 | −0.297562 | ||||||||
\(494\) | −8.29554 | −0.373234 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.54895 | 0.383859 | ||||||||
\(497\) | −19.3322 | −0.867169 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.7898 | −0.706847 | −0.353423 | − | 0.935463i | \(-0.614982\pi\) | ||||
−0.353423 | + | 0.935463i | \(0.614982\pi\) | |||||||
\(500\) | −17.3506 | −0.775944 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.79123 | −0.437004 | ||||||||
\(503\) | 33.2833 | 1.48403 | 0.742015 | − | 0.670383i | \(-0.233870\pi\) | ||||
0.742015 | + | 0.670383i | \(0.233870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.0617 | −0.981731 | ||||||||
\(506\) | −1.91280 | −0.0850342 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.5680 | −0.513249 | ||||||||
\(509\) | −21.2303 | −0.941015 | −0.470507 | − | 0.882396i | \(-0.655929\pi\) | ||||
−0.470507 | + | 0.882396i | \(0.655929\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2133 | −0.496049 | ||||||||
\(512\) | −22.9122 | −1.01259 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.3622 | −0.457057 | ||||||||
\(515\) | 42.1297 | 1.85646 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −50.2118 | −2.20831 | ||||||||
\(518\) | 0.504863 | 0.0221824 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.5030 | −0.811410 | ||||||||
\(521\) | 31.4014 | 1.37572 | 0.687860 | − | 0.725843i | \(-0.258550\pi\) | ||||
0.687860 | + | 0.725843i | \(0.258550\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.7232 | 0.774981 | 0.387491 | − | 0.921874i | \(-0.373342\pi\) | ||||
0.387491 | + | 0.921874i | \(0.373342\pi\) | |||||||
\(524\) | −26.9678 | −1.17809 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.32053 | −0.144782 | ||||||||
\(527\) | −19.8437 | −0.864407 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −8.12772 | −0.353046 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 21.3579 | 0.925981 | ||||||||
\(533\) | 12.5710 | 0.544512 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.25345 | 0.183893 | ||||||||
\(536\) | −21.0644 | −0.909845 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.69140 | 0.331600 | ||||||||
\(539\) | −4.02244 | −0.173259 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.4106 | 0.533575 | 0.266788 | − | 0.963755i | \(-0.414038\pi\) | ||||
0.266788 | + | 0.963755i | \(0.414038\pi\) | |||||||
\(542\) | −1.57734 | −0.0677525 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 30.7850 | 1.31990 | ||||||||
\(545\) | 26.3334 | 1.12800 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4806 | 1.08947 | 0.544737 | − | 0.838607i | \(-0.316630\pi\) | ||||
0.544737 | + | 0.838607i | \(0.316630\pi\) | |||||||
\(548\) | −0.281253 | −0.0120145 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.10307 | 0.0896754 | ||||||||
\(551\) | 4.20884 | 0.179302 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −48.3410 | −2.05567 | ||||||||
\(554\) | 2.38584 | 0.101364 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24.4754 | 1.03799 | ||||||||
\(557\) | 3.73579 | 0.158291 | 0.0791453 | − | 0.996863i | \(-0.474781\pi\) | ||||
0.0791453 | + | 0.996863i | \(0.474781\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.2109 | 0.474170 | ||||||||
\(560\) | 19.8055 | 0.836934 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.08659 | 0.0458351 | ||||||||
\(563\) | −25.6826 | −1.08239 | −0.541197 | − | 0.840896i | \(-0.682029\pi\) | ||||
−0.541197 | + | 0.840896i | \(0.682029\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.0372 | 1.68438 | ||||||||
\(566\) | 6.68655 | 0.281057 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.6312 | 0.488034 | ||||||||
\(569\) | −15.4592 | −0.648082 | −0.324041 | − | 0.946043i | \(-0.605042\pi\) | ||||
−0.324041 | + | 0.946043i | \(0.605042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.9487 | −0.960373 | −0.480186 | − | 0.877166i | \(-0.659431\pi\) | ||||
−0.480186 | + | 0.877166i | \(0.659431\pi\) | |||||||
\(572\) | 34.1460 | 1.42772 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.57351 | 0.149156 | ||||||||
\(575\) | −1.09948 | −0.0458513 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.10729 | −0.337511 | −0.168755 | − | 0.985658i | \(-0.553975\pi\) | ||||
−0.168755 | + | 0.985658i | \(0.553975\pi\) | |||||||
\(578\) | −11.8852 | −0.494357 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.44829 | 0.184705 | ||||||||
\(581\) | 10.0850 | 0.418394 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.6544 | 1.31099 | ||||||||
\(584\) | 6.74649 | 0.279172 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.41568 | −0.182410 | ||||||||
\(587\) | 21.2223 | 0.875938 | 0.437969 | − | 0.898990i | \(-0.355698\pi\) | ||||
0.437969 | + | 0.898990i | \(0.355698\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.6411 | 0.520868 | ||||||||
\(590\) | 2.20065 | 0.0905994 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.14376 | 0.0470083 | ||||||||
\(593\) | 4.05015 | 0.166320 | 0.0831599 | − | 0.996536i | \(-0.473499\pi\) | ||||
0.0831599 | + | 0.996536i | \(0.473499\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −45.9723 | −1.88468 | ||||||||
\(596\) | 3.87962 | 0.158915 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.97098 | 0.0805994 | ||||||||
\(599\) | 35.6449 | 1.45641 | 0.728205 | − | 0.685359i | \(-0.240355\pi\) | ||||
0.728205 | + | 0.685359i | \(0.240355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0859 | −1.39039 | −0.695196 | − | 0.718820i | \(-0.744683\pi\) | ||||
−0.695196 | + | 0.718820i | \(0.744683\pi\) | |||||||
\(602\) | 3.18687 | 0.129887 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.63924 | −0.229457 | ||||||||
\(605\) | −18.2719 | −0.742859 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0259 | 0.975183 | 0.487592 | − | 0.873072i | \(-0.337876\pi\) | ||||
0.487592 | + | 0.873072i | \(0.337876\pi\) | |||||||
\(608\) | −19.6110 | −0.795332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.1443 | 0.653663 | ||||||||
\(611\) | 51.7392 | 2.09315 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.2325 | −0.413285 | −0.206643 | − | 0.978417i | \(-0.566254\pi\) | ||||
−0.206643 | + | 0.978417i | \(0.566254\pi\) | |||||||
\(614\) | −3.59652 | −0.145144 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.4848 | 0.825356 | ||||||||
\(617\) | −21.8083 | −0.877969 | −0.438985 | − | 0.898495i | \(-0.644662\pi\) | ||||
−0.438985 | + | 0.898495i | \(0.644662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.64506 | 0.146507 | 0.0732537 | − | 0.997313i | \(-0.476662\pi\) | ||||
0.0732537 | + | 0.997313i | \(0.476662\pi\) | |||||||
\(620\) | 13.3603 | 0.536562 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.56319 | −0.303256 | ||||||||
\(623\) | −20.6815 | −0.828585 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.2885 | −1.17154 | ||||||||
\(626\) | −13.5098 | −0.539960 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30.4305 | −1.21431 | ||||||||
\(629\) | −2.65489 | −0.105857 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.2926 | 1.04669 | 0.523346 | − | 0.852120i | \(-0.324684\pi\) | ||||
0.523346 | + | 0.852120i | \(0.324684\pi\) | |||||||
\(632\) | 29.0843 | 1.15691 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.52112 | −0.378132 | ||||||||
\(635\) | −15.8621 | −0.629467 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.14480 | 0.164223 | ||||||||
\(638\) | 1.91280 | 0.0757284 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26.9964 | −1.06713 | ||||||||
\(641\) | 0.983922 | 0.0388626 | 0.0194313 | − | 0.999811i | \(-0.493814\pi\) | ||||
0.0194313 | + | 0.999811i | \(0.493814\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.65539 | 0.183591 | 0.0917953 | − | 0.995778i | \(-0.470739\pi\) | ||||
0.0917953 | + | 0.995778i | \(0.470739\pi\) | |||||||
\(644\) | −5.07453 | −0.199964 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.4006 | 0.487894 | ||||||||
\(647\) | −28.6978 | −1.12823 | −0.564114 | − | 0.825697i | \(-0.690782\pi\) | ||||
−0.564114 | + | 0.825697i | \(0.690782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.57070 | −0.336429 | ||||||||
\(650\) | −2.16705 | −0.0849986 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 39.8297 | 1.55985 | ||||||||
\(653\) | −9.32695 | −0.364992 | −0.182496 | − | 0.983207i | \(-0.558418\pi\) | ||||
−0.182496 | + | 0.983207i | \(0.558418\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.9781 | −1.44486 | ||||||||
\(656\) | 8.09574 | 0.316086 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.7077 | 0.573365 | ||||||||
\(659\) | 27.8179 | 1.08363 | 0.541816 | − | 0.840497i | \(-0.317737\pi\) | ||||
0.541816 | + | 0.840497i | \(0.317737\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.22069 | −0.164166 | −0.0820828 | − | 0.996626i | \(-0.526157\pi\) | ||||
−0.0820828 | + | 0.996626i | \(0.526157\pi\) | |||||||
\(662\) | −0.349786 | −0.0135948 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.06760 | −0.235468 | ||||||||
\(665\) | 29.2859 | 1.13566 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 5.31424 | 0.205614 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.6862 | −0.528744 | ||||||||
\(671\) | −62.8758 | −2.42729 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7109 | 0.798348 | 0.399174 | − | 0.916875i | \(-0.369297\pi\) | ||||
0.399174 | + | 0.916875i | \(0.369297\pi\) | |||||||
\(674\) | 9.92271 | 0.382208 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.7700 | −0.452691 | ||||||||
\(677\) | −32.4382 | −1.24670 | −0.623350 | − | 0.781943i | \(-0.714229\pi\) | ||||
−0.623350 | + | 0.781943i | \(0.714229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.3186 | −0.818131 | ||||||||
\(680\) | 27.6592 | 1.06068 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.74502 | 0.219988 | ||||||||
\(683\) | 30.2595 | 1.15785 | 0.578923 | − | 0.815382i | \(-0.303473\pi\) | ||||
0.578923 | + | 0.815382i | \(0.303473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.385653 | −0.0147350 | ||||||||
\(686\) | −7.61658 | −0.290802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.21982 | 0.275253 | ||||||||
\(689\) | −32.6173 | −1.24262 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.4824 | 1.23569 | 0.617845 | − | 0.786300i | \(-0.288006\pi\) | ||||
0.617845 | + | 0.786300i | \(0.288006\pi\) | |||||||
\(692\) | 32.6965 | 1.24294 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.49545 | 0.322483 | ||||||||
\(695\) | 33.5605 | 1.27302 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.7918 | −0.711789 | ||||||||
\(698\) | 5.84909 | 0.221391 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.57932 | 0.210879 | ||||||||
\(701\) | −7.93803 | −0.299815 | −0.149908 | − | 0.988700i | \(-0.547898\pi\) | ||||
−0.149908 | + | 0.988700i | \(0.547898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.69125 | 0.0637867 | ||||||||
\(704\) | 15.5053 | 0.584379 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.81936 | 0.294286 | ||||||||
\(707\) | −25.1676 | −0.946524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.4257 | 0.992438 | 0.496219 | − | 0.868197i | \(-0.334721\pi\) | ||||
0.496219 | + | 0.868197i | \(0.334721\pi\) | |||||||
\(710\) | 7.55714 | 0.283614 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.4430 | 0.466320 | ||||||||
\(713\) | −3.00347 | −0.112481 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 46.8209 | 1.75100 | ||||||||
\(716\) | −18.3225 | −0.684743 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.37298 | 0.349796 | ||||||||
\(719\) | 10.2899 | 0.383747 | 0.191873 | − | 0.981420i | \(-0.438544\pi\) | ||||
0.191873 | + | 0.981420i | \(0.438544\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.0609 | 1.78988 | ||||||||
\(722\) | 0.573343 | 0.0213376 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −38.6759 | −1.43738 | ||||||||
\(725\) | 1.09948 | 0.0408335 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.52204 | −0.316065 | −0.158033 | − | 0.987434i | \(-0.550515\pi\) | ||||
−0.158033 | + | 0.987434i | \(0.550515\pi\) | |||||||
\(728\) | −21.1079 | −0.782312 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.38340 | 0.162237 | ||||||||
\(731\) | −16.7586 | −0.619839 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.2153 | −1.63313 | −0.816566 | − | 0.577253i | \(-0.804125\pi\) | ||||
−0.816566 | + | 0.577253i | \(0.804125\pi\) | |||||||
\(734\) | −10.0665 | −0.371562 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.65949 | 0.171751 | ||||||||
\(737\) | 53.3025 | 1.96342 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.5582 | −0.461959 | −0.230980 | − | 0.972959i | \(-0.574193\pi\) | ||||
−0.230980 | + | 0.972959i | \(0.574193\pi\) | |||||||
\(740\) | 1.78747 | 0.0657086 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.27197 | −0.340385 | ||||||||
\(743\) | −22.9126 | −0.840580 | −0.420290 | − | 0.907390i | \(-0.638072\pi\) | ||||
−0.420290 | + | 0.907390i | \(0.638072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.31973 | 0.194900 | ||||||||
\(746\) | 12.7454 | 0.466643 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −51.0431 | −1.86632 | ||||||||
\(749\) | 4.85226 | 0.177298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.20310 | −0.0439018 | −0.0219509 | − | 0.999759i | \(-0.506988\pi\) | ||||
−0.0219509 | + | 0.999759i | \(0.506988\pi\) | |||||||
\(752\) | 33.3201 | 1.21506 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.97098 | −0.0717789 | ||||||||
\(755\) | −7.73251 | −0.281415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.23336 | 0.117518 | 0.0587592 | − | 0.998272i | \(-0.481286\pi\) | ||||
0.0587592 | + | 0.998272i | \(0.481286\pi\) | |||||||
\(758\) | 3.72807 | 0.135410 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.6198 | −0.639137 | ||||||||
\(761\) | 42.3343 | 1.53462 | 0.767308 | − | 0.641279i | \(-0.221596\pi\) | ||||
0.767308 | + | 0.641279i | \(0.221596\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.0408 | 1.08755 | ||||||||
\(764\) | 39.1517 | 1.41646 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.745249 | −0.0269269 | ||||||||
\(767\) | 8.83141 | 0.318884 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.5767 | −1.03050 | −0.515251 | − | 0.857040i | \(-0.672301\pi\) | ||||
−0.515251 | + | 0.857040i | \(0.672301\pi\) | |||||||
\(770\) | 13.3096 | 0.479644 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.4054 | 0.374497 | ||||||||
\(773\) | 14.8823 | 0.535281 | 0.267640 | − | 0.963519i | \(-0.413756\pi\) | ||||
0.267640 | + | 0.963519i | \(0.413756\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.30224 | 0.118620 | ||||||||
\(776\) | 12.8263 | 0.460437 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.10409 | −0.290546 | ||||||||
\(779\) | 11.9710 | 0.428904 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.4322 | −1.05317 | ||||||||
\(782\) | −2.94632 | −0.105360 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.66925 | 0.0953305 | ||||||||
\(785\) | −41.7262 | −1.48927 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.61476 | −0.271437 | −0.135719 | − | 0.990747i | \(-0.543334\pi\) | ||||
−0.135719 | + | 0.990747i | \(0.543334\pi\) | |||||||
\(788\) | −30.4640 | −1.08524 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.8969 | 0.672323 | ||||||||
\(791\) | 45.6738 | 1.62397 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 64.7884 | 2.30070 | ||||||||
\(794\) | −4.96599 | −0.176236 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.8757 | 0.988029 | ||||||||
\(797\) | −31.1708 | −1.10413 | −0.552063 | − | 0.833803i | \(-0.686159\pi\) | ||||
−0.552063 | + | 0.833803i | \(0.686159\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −77.3423 | −2.73617 | ||||||||
\(800\) | −5.12299 | −0.181125 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.0821 | 0.567880 | ||||||||
\(803\) | −17.0717 | −0.602446 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.95818 | −0.245244 | ||||||||
\(806\) | −5.91978 | −0.208515 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.1420 | 0.532695 | ||||||||
\(809\) | 17.5131 | 0.615729 | 0.307864 | − | 0.951430i | \(-0.400386\pi\) | ||||
0.307864 | + | 0.951430i | \(0.400386\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.4490 | 0.893634 | 0.446817 | − | 0.894625i | \(-0.352558\pi\) | ||||
0.446817 | + | 0.894625i | \(0.352558\pi\) | |||||||
\(812\) | 5.07453 | 0.178081 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.768625 | 0.0269403 | ||||||||
\(815\) | 54.6144 | 1.91306 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.6758 | 0.373497 | ||||||||
\(818\) | 2.27141 | 0.0794181 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.6520 | 0.441827 | ||||||||
\(821\) | −46.7718 | −1.63235 | −0.816174 | − | 0.577807i | \(-0.803909\pi\) | ||||
−0.816174 | + | 0.577807i | \(0.803909\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.5789 | −1.13563 | −0.567814 | − | 0.823157i | \(-0.692211\pi\) | ||||
−0.567814 | + | 0.823157i | \(0.692211\pi\) | |||||||
\(824\) | −28.9157 | −1.00733 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.51047 | 0.0873503 | ||||||||
\(827\) | 39.4266 | 1.37100 | 0.685499 | − | 0.728074i | \(-0.259584\pi\) | ||||
0.685499 | + | 0.728074i | \(0.259584\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.3107 | −0.601224 | −0.300612 | − | 0.953746i | \(-0.597191\pi\) | ||||
−0.300612 | + | 0.953746i | \(0.597191\pi\) | |||||||
\(830\) | −3.94230 | −0.136839 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.9770 | −0.553902 | ||||||||
\(833\) | −6.19585 | −0.214673 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.28686 | 0.252172 | ||||||||
\(836\) | 32.5161 | 1.12459 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.46825 | −0.292531 | ||||||||
\(839\) | 44.8932 | 1.54988 | 0.774942 | − | 0.632032i | \(-0.217779\pi\) | ||||
0.774942 | + | 0.632032i | \(0.217779\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 11.5799 | 0.399070 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.5316 | −0.362511 | ||||||||
\(845\) | −16.1389 | −0.555196 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.8443 | −0.716219 | ||||||||
\(848\) | −21.0055 | −0.721332 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.23941 | 0.111111 | ||||||||
\(851\) | −0.401833 | −0.0137747 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6947 | 0.366180 | 0.183090 | − | 0.983096i | \(-0.441390\pi\) | ||||
0.183090 | + | 0.983096i | \(0.441390\pi\) | |||||||
\(854\) | 18.4171 | 0.630221 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.91936 | −0.0997815 | ||||||||
\(857\) | 9.25319 | 0.316083 | 0.158042 | − | 0.987432i | \(-0.449482\pi\) | ||||
0.158042 | + | 0.987432i | \(0.449482\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.609581 | 0.0207986 | 0.0103993 | − | 0.999946i | \(-0.496690\pi\) | ||||
0.0103993 | + | 0.999946i | \(0.496690\pi\) | |||||||
\(860\) | 11.2831 | 0.384751 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.11587 | −0.310488 | ||||||||
\(863\) | −39.0869 | −1.33053 | −0.665267 | − | 0.746605i | \(-0.731682\pi\) | ||||
−0.665267 | + | 0.746605i | \(0.731682\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.8334 | 1.52438 | ||||||||
\(866\) | −1.08371 | −0.0368260 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.2412 | 0.517319 | ||||||||
\(869\) | −73.5963 | −2.49659 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.9239 | −1.86103 | ||||||||
\(872\) | −18.0740 | −0.612062 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.87690 | 0.0634871 | ||||||||
\(875\) | −27.1406 | −0.917518 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.4590 | 0.893456 | 0.446728 | − | 0.894670i | \(-0.352589\pi\) | ||||
0.446728 | + | 0.894670i | \(0.352589\pi\) | |||||||
\(878\) | −4.04994 | −0.136679 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 30.1527 | 1.01645 | ||||||||
\(881\) | −14.3959 | −0.485009 | −0.242504 | − | 0.970150i | \(-0.577969\pi\) | ||||
−0.242504 | + | 0.970150i | \(0.577969\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.2893 | −1.05297 | −0.526485 | − | 0.850184i | \(-0.676490\pi\) | ||||
−0.526485 | + | 0.850184i | \(0.676490\pi\) | |||||||
\(884\) | 52.5958 | 1.76899 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.7282 | 0.394017 | ||||||||
\(887\) | 2.94486 | 0.0988786 | 0.0494393 | − | 0.998777i | \(-0.484257\pi\) | ||||
0.0494393 | + | 0.998777i | \(0.484257\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0952 | −0.606893 | ||||||||
\(890\) | 8.08456 | 0.270995 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41.0242 | 1.37359 | ||||||||
\(893\) | 49.2695 | 1.64874 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.1237 | −0.839794 | ||||||||
\(896\) | −30.7970 | −1.02886 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.39418 | −0.313488 | ||||||||
\(899\) | 3.00347 | 0.100171 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.7578 | 1.62436 | ||||||||
\(902\) | 5.44046 | 0.181148 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27.4796 | −0.913956 | ||||||||
\(905\) | −53.0323 | −1.76285 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.2269 | 1.43533 | 0.717663 | − | 0.696390i | \(-0.245212\pi\) | ||||
0.717663 | + | 0.696390i | \(0.245212\pi\) | |||||||
\(908\) | 8.78230 | 0.291451 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.7144 | −0.454630 | ||||||||
\(911\) | −7.76302 | −0.257200 | −0.128600 | − | 0.991697i | \(-0.541048\pi\) | ||||
−0.128600 | + | 0.991697i | \(0.541048\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3538 | 0.508135 | ||||||||
\(914\) | 5.22343 | 0.172776 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.7514 | 0.652606 | ||||||||
\(917\) | −42.1840 | −1.39304 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.8327 | −0.555258 | −0.277629 | − | 0.960688i | \(-0.589549\pi\) | ||||
−0.277629 | + | 0.960688i | \(0.589549\pi\) | |||||||
\(920\) | 4.18638 | 0.138021 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.23137 | −0.172286 | ||||||||
\(923\) | 30.3275 | 0.998241 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.441806 | 0.0145265 | ||||||||
\(926\) | 4.88460 | 0.160518 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.65949 | −0.152955 | ||||||||
\(929\) | −3.48943 | −0.114485 | −0.0572423 | − | 0.998360i | \(-0.518231\pi\) | ||||
−0.0572423 | + | 0.998360i | \(0.518231\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.94695 | 0.129356 | ||||||||
\(932\) | 52.3057 | 1.71333 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.44323 | −0.0472239 | ||||||||
\(935\) | −69.9902 | −2.28892 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.1417 | −0.396651 | −0.198325 | − | 0.980136i | \(-0.563550\pi\) | ||||
−0.198325 | + | 0.980136i | \(0.563550\pi\) | |||||||
\(938\) | −15.6130 | −0.509782 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 52.0725 | 1.69842 | ||||||||
\(941\) | 0.794187 | 0.0258897 | 0.0129449 | − | 0.999916i | \(-0.495879\pi\) | ||||
0.0129449 | + | 0.999916i | \(0.495879\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.84424 | −0.0926214 | ||||||||
\(944\) | 5.68743 | 0.185110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.85183 | 0.157747 | ||||||||
\(947\) | 4.85051 | 0.157620 | 0.0788102 | − | 0.996890i | \(-0.474888\pi\) | ||||
0.0788102 | + | 0.996890i | \(0.474888\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.5910 | 0.571027 | ||||||||
\(950\) | −2.06361 | −0.0669522 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 31.5531 | 1.02264 | ||||||||
\(953\) | −45.0348 | −1.45882 | −0.729410 | − | 0.684077i | \(-0.760205\pi\) | ||||
−0.729410 | + | 0.684077i | \(0.760205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53.6847 | 1.73720 | ||||||||
\(956\) | 39.6532 | 1.28248 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.51899 | −0.275236 | ||||||||
\(959\) | −0.439946 | −0.0142066 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.9792 | −0.709006 | ||||||||
\(962\) | −0.792006 | −0.0255353 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 45.4204 | 1.46289 | ||||||||
\(965\) | 14.2678 | 0.459297 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.2318 | 0.393348 | 0.196674 | − | 0.980469i | \(-0.436986\pi\) | ||||
0.196674 | + | 0.980469i | \(0.436986\pi\) | |||||||
\(968\) | 12.5409 | 0.403081 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.33362 | 0.267576 | ||||||||
\(971\) | −13.2141 | −0.424062 | −0.212031 | − | 0.977263i | \(-0.568008\pi\) | ||||
−0.212031 | + | 0.977263i | \(0.568008\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.2853 | 1.22737 | ||||||||
\(974\) | 4.61134 | 0.147757 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 41.7238 | 1.33554 | ||||||||
\(977\) | 34.4548 | 1.10231 | 0.551153 | − | 0.834404i | \(-0.314188\pi\) | ||||
0.551153 | + | 0.834404i | \(0.314188\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.4863 | −1.00631 | ||||||||
\(980\) | 4.17150 | 0.133254 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.48607 | −0.0793338 | ||||||||
\(983\) | −6.12679 | −0.195414 | −0.0977071 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977071 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.7722 | −1.33097 | ||||||||
\(986\) | 2.94632 | 0.0938299 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.5052 | −1.06594 | ||||||||
\(989\) | −2.53651 | −0.0806563 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.7917 | −1.64522 | −0.822609 | − | 0.568608i | \(-0.807482\pi\) | ||||
−0.822609 | + | 0.568608i | \(0.807482\pi\) | |||||||
\(992\) | −13.9946 | −0.444329 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.62106 | 0.273443 | ||||||||
\(995\) | 38.2231 | 1.21175 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.0083 | 1.26708 | 0.633538 | − | 0.773711i | \(-0.281602\pi\) | ||||
0.633538 | + | 0.773711i | \(0.281602\pi\) | |||||||
\(998\) | 7.04132 | 0.222889 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.q.1.8 | 16 | ||
3.2 | odd | 2 | 667.2.a.d.1.9 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.d.1.9 | ✓ | 16 | 3.2 | odd | 2 | ||
6003.2.a.q.1.8 | 16 | 1.1 | even | 1 | trivial |