Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
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: | \( x^{16} - 22x^{14} + 190x^{12} - 820x^{10} + 1862x^{8} - 2154x^{6} + 1163x^{4} - 256x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1805) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.317290\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.317290 | 0.224358 | 0.112179 | − | 0.993688i | \(-0.464217\pi\) | ||||
0.112179 | + | 0.993688i | \(0.464217\pi\) | |||||||
\(3\) | −2.04300 | −1.17953 | −0.589763 | − | 0.807576i | \(-0.700779\pi\) | ||||
−0.589763 | + | 0.807576i | \(0.700779\pi\) | |||||||
\(4\) | −1.89933 | −0.949664 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.648223 | −0.264636 | ||||||||
\(7\) | −3.69961 | −1.39832 | −0.699161 | − | 0.714964i | \(-0.746443\pi\) | ||||
−0.699161 | + | 0.714964i | \(0.746443\pi\) | |||||||
\(8\) | −1.23722 | −0.437422 | ||||||||
\(9\) | 1.17385 | 0.391283 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.01076 | −1.51080 | −0.755400 | − | 0.655263i | \(-0.772558\pi\) | ||||
−0.755400 | + | 0.655263i | \(0.772558\pi\) | |||||||
\(12\) | 3.88033 | 1.12015 | ||||||||
\(13\) | −4.59159 | −1.27348 | −0.636738 | − | 0.771080i | \(-0.719717\pi\) | ||||
−0.636738 | + | 0.771080i | \(0.719717\pi\) | |||||||
\(14\) | −1.17385 | −0.313724 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.40610 | 0.851525 | ||||||||
\(17\) | 3.21112 | 0.778811 | 0.389405 | − | 0.921066i | \(-0.372681\pi\) | ||||
0.389405 | + | 0.921066i | \(0.372681\pi\) | |||||||
\(18\) | 0.372450 | 0.0877873 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.55831 | 1.64936 | ||||||||
\(22\) | −1.58986 | −0.338960 | ||||||||
\(23\) | −0.220987 | −0.0460789 | −0.0230395 | − | 0.999735i | \(-0.507334\pi\) | ||||
−0.0230395 | + | 0.999735i | \(0.507334\pi\) | |||||||
\(24\) | 2.52763 | 0.515951 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.45686 | −0.285714 | ||||||||
\(27\) | 3.73083 | 0.717998 | ||||||||
\(28\) | 7.02678 | 1.32794 | ||||||||
\(29\) | −3.42114 | −0.635289 | −0.317644 | − | 0.948210i | \(-0.602892\pi\) | ||||
−0.317644 | + | 0.948210i | \(0.602892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.89725 | −1.41839 | −0.709194 | − | 0.705013i | \(-0.750941\pi\) | ||||
−0.709194 | + | 0.705013i | \(0.750941\pi\) | |||||||
\(32\) | 3.55515 | 0.628468 | ||||||||
\(33\) | 10.2370 | 1.78203 | ||||||||
\(34\) | 1.01885 | 0.174732 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.22952 | −0.371587 | ||||||||
\(37\) | 2.98622 | 0.490932 | 0.245466 | − | 0.969405i | \(-0.421059\pi\) | ||||
0.245466 | + | 0.969405i | \(0.421059\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.38061 | 1.50210 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.183247 | 0.0286184 | 0.0143092 | − | 0.999898i | \(-0.495445\pi\) | ||||
0.0143092 | + | 0.999898i | \(0.495445\pi\) | |||||||
\(42\) | 2.39817 | 0.370046 | ||||||||
\(43\) | −7.30424 | −1.11389 | −0.556943 | − | 0.830551i | \(-0.688026\pi\) | ||||
−0.556943 | + | 0.830551i | \(0.688026\pi\) | |||||||
\(44\) | 9.51707 | 1.43475 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0701168 | −0.0103382 | ||||||||
\(47\) | 10.8876 | 1.58812 | 0.794060 | − | 0.607840i | \(-0.207964\pi\) | ||||
0.794060 | + | 0.607840i | \(0.207964\pi\) | |||||||
\(48\) | −6.95866 | −1.00440 | ||||||||
\(49\) | 6.68714 | 0.955306 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.56032 | −0.918628 | ||||||||
\(52\) | 8.72092 | 1.20937 | ||||||||
\(53\) | −1.93670 | −0.266026 | −0.133013 | − | 0.991114i | \(-0.542465\pi\) | ||||
−0.133013 | + | 0.991114i | \(0.542465\pi\) | |||||||
\(54\) | 1.18375 | 0.161088 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.57722 | 0.611657 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.08549 | −0.142532 | ||||||||
\(59\) | 6.15338 | 0.801102 | 0.400551 | − | 0.916275i | \(-0.368819\pi\) | ||||
0.400551 | + | 0.916275i | \(0.368819\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.02293 | 0.643121 | 0.321560 | − | 0.946889i | \(-0.395793\pi\) | ||||
0.321560 | + | 0.946889i | \(0.395793\pi\) | |||||||
\(62\) | −2.50572 | −0.318226 | ||||||||
\(63\) | −4.34279 | −0.547140 | ||||||||
\(64\) | −5.68419 | −0.710523 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.24809 | 0.399812 | ||||||||
\(67\) | 11.2753 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(68\) | −6.09897 | −0.739608 | ||||||||
\(69\) | 0.451476 | 0.0543513 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.851223 | −0.101022 | −0.0505108 | − | 0.998724i | \(-0.516085\pi\) | ||||
−0.0505108 | + | 0.998724i | \(0.516085\pi\) | |||||||
\(72\) | −1.45230 | −0.171156 | ||||||||
\(73\) | 5.15625 | 0.603494 | 0.301747 | − | 0.953388i | \(-0.402430\pi\) | ||||
0.301747 | + | 0.953388i | \(0.402430\pi\) | |||||||
\(74\) | 0.947498 | 0.110144 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.5379 | 2.11259 | ||||||||
\(78\) | 2.97637 | 0.337007 | ||||||||
\(79\) | −9.19657 | −1.03469 | −0.517347 | − | 0.855776i | \(-0.673080\pi\) | ||||
−0.517347 | + | 0.855776i | \(0.673080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1436 | −1.23818 | ||||||||
\(82\) | 0.0581424 | 0.00642076 | ||||||||
\(83\) | 4.53528 | 0.497811 | 0.248906 | − | 0.968528i | \(-0.419929\pi\) | ||||
0.248906 | + | 0.968528i | \(0.419929\pi\) | |||||||
\(84\) | −14.3557 | −1.56634 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.31756 | −0.249909 | ||||||||
\(87\) | 6.98938 | 0.749340 | ||||||||
\(88\) | 6.19939 | 0.660857 | ||||||||
\(89\) | 14.8752 | 1.57677 | 0.788385 | − | 0.615183i | \(-0.210918\pi\) | ||||
0.788385 | + | 0.615183i | \(0.210918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.9871 | 1.78073 | ||||||||
\(92\) | 0.419726 | 0.0437595 | ||||||||
\(93\) | 16.1341 | 1.67303 | ||||||||
\(94\) | 3.45452 | 0.356307 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.26317 | −0.741295 | ||||||||
\(97\) | 1.36602 | 0.138698 | 0.0693490 | − | 0.997592i | \(-0.477908\pi\) | ||||
0.0693490 | + | 0.997592i | \(0.477908\pi\) | |||||||
\(98\) | 2.12176 | 0.214330 | ||||||||
\(99\) | −5.88187 | −0.591151 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.08643 | −0.605622 | −0.302811 | − | 0.953051i | \(-0.597925\pi\) | ||||
−0.302811 | + | 0.953051i | \(0.597925\pi\) | |||||||
\(102\) | −2.08152 | −0.206101 | ||||||||
\(103\) | 13.7063 | 1.35052 | 0.675261 | − | 0.737579i | \(-0.264031\pi\) | ||||
0.675261 | + | 0.737579i | \(0.264031\pi\) | |||||||
\(104\) | 5.68078 | 0.557047 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.614494 | −0.0596850 | ||||||||
\(107\) | 17.3036 | 1.67280 | 0.836400 | − | 0.548119i | \(-0.184656\pi\) | ||||
0.836400 | + | 0.548119i | \(0.184656\pi\) | |||||||
\(108\) | −7.08606 | −0.681857 | ||||||||
\(109\) | −13.7511 | −1.31712 | −0.658561 | − | 0.752528i | \(-0.728834\pi\) | ||||
−0.658561 | + | 0.752528i | \(0.728834\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.10086 | −0.579068 | ||||||||
\(112\) | −12.6012 | −1.19071 | ||||||||
\(113\) | −4.15573 | −0.390938 | −0.195469 | − | 0.980710i | \(-0.562623\pi\) | ||||
−0.195469 | + | 0.980710i | \(0.562623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.49786 | 0.603311 | ||||||||
\(117\) | −5.38983 | −0.498290 | ||||||||
\(118\) | 1.95240 | 0.179733 | ||||||||
\(119\) | −11.8799 | −1.08903 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.1077 | 1.28252 | ||||||||
\(122\) | 1.59372 | 0.144289 | ||||||||
\(123\) | −0.374374 | −0.0337562 | ||||||||
\(124\) | 14.9995 | 1.34699 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.37792 | −0.122755 | ||||||||
\(127\) | −11.9185 | −1.05760 | −0.528799 | − | 0.848747i | \(-0.677357\pi\) | ||||
−0.528799 | + | 0.848747i | \(0.677357\pi\) | |||||||
\(128\) | −8.91384 | −0.787879 | ||||||||
\(129\) | 14.9226 | 1.31386 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.58093 | −0.662349 | −0.331175 | − | 0.943569i | \(-0.607445\pi\) | ||||
−0.331175 | + | 0.943569i | \(0.607445\pi\) | |||||||
\(132\) | −19.4434 | −1.69233 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.57755 | 0.309053 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.97285 | −0.340669 | ||||||||
\(137\) | −7.98581 | −0.682274 | −0.341137 | − | 0.940014i | \(-0.610812\pi\) | ||||
−0.341137 | + | 0.940014i | \(0.610812\pi\) | |||||||
\(138\) | 0.143249 | 0.0121941 | ||||||||
\(139\) | 2.65651 | 0.225322 | 0.112661 | − | 0.993633i | \(-0.464063\pi\) | ||||
0.112661 | + | 0.993633i | \(0.464063\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.2434 | −1.87323 | ||||||||
\(142\) | −0.270084 | −0.0226650 | ||||||||
\(143\) | 23.0073 | 1.92397 | ||||||||
\(144\) | 3.99825 | 0.333187 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.63603 | 0.135398 | ||||||||
\(147\) | −13.6618 | −1.12681 | ||||||||
\(148\) | −5.67182 | −0.466221 | ||||||||
\(149\) | 8.35153 | 0.684184 | 0.342092 | − | 0.939666i | \(-0.388865\pi\) | ||||
0.342092 | + | 0.939666i | \(0.388865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.56471 | −0.696986 | −0.348493 | − | 0.937311i | \(-0.613306\pi\) | ||||
−0.348493 | + | 0.937311i | \(0.613306\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.76937 | 0.304735 | ||||||||
\(154\) | 5.88187 | 0.473975 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −17.8168 | −1.42649 | ||||||||
\(157\) | −11.3335 | −0.904510 | −0.452255 | − | 0.891889i | \(-0.649380\pi\) | ||||
−0.452255 | + | 0.891889i | \(0.649380\pi\) | |||||||
\(158\) | −2.91797 | −0.232142 | ||||||||
\(159\) | 3.95668 | 0.313785 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.817566 | 0.0644332 | ||||||||
\(162\) | −3.53576 | −0.277795 | ||||||||
\(163\) | −4.65048 | −0.364254 | −0.182127 | − | 0.983275i | \(-0.558298\pi\) | ||||
−0.182127 | + | 0.983275i | \(0.558298\pi\) | |||||||
\(164\) | −0.348046 | −0.0271779 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.43900 | 0.111688 | ||||||||
\(167\) | −8.89485 | −0.688304 | −0.344152 | − | 0.938914i | \(-0.611834\pi\) | ||||
−0.344152 | + | 0.938914i | \(0.611834\pi\) | |||||||
\(168\) | −9.35126 | −0.721466 | ||||||||
\(169\) | 8.08265 | 0.621743 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.8731 | 1.05782 | ||||||||
\(173\) | 18.6570 | 1.41847 | 0.709233 | − | 0.704974i | \(-0.249042\pi\) | ||||
0.709233 | + | 0.704974i | \(0.249042\pi\) | |||||||
\(174\) | 2.21766 | 0.168120 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.0671 | −1.28648 | ||||||||
\(177\) | −12.5713 | −0.944921 | ||||||||
\(178\) | 4.71975 | 0.353760 | ||||||||
\(179\) | 0.224791 | 0.0168017 | 0.00840083 | − | 0.999965i | \(-0.497326\pi\) | ||||
0.00840083 | + | 0.999965i | \(0.497326\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8780 | 1.84917 | 0.924583 | − | 0.380981i | \(-0.124414\pi\) | ||||
0.924583 | + | 0.380981i | \(0.124414\pi\) | |||||||
\(182\) | 5.38983 | 0.399521 | ||||||||
\(183\) | −10.2618 | −0.758578 | ||||||||
\(184\) | 0.273408 | 0.0201559 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.11918 | 0.375356 | ||||||||
\(187\) | −16.0901 | −1.17663 | ||||||||
\(188\) | −20.6791 | −1.50818 | ||||||||
\(189\) | −13.8026 | −1.00399 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.43889 | 0.610616 | 0.305308 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305308 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(192\) | 11.6128 | 0.838081 | ||||||||
\(193\) | 1.60346 | 0.115420 | 0.0577098 | − | 0.998333i | \(-0.481620\pi\) | ||||
0.0577098 | + | 0.998333i | \(0.481620\pi\) | |||||||
\(194\) | 0.433423 | 0.0311180 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.7011 | −0.907219 | ||||||||
\(197\) | 2.01284 | 0.143409 | 0.0717043 | − | 0.997426i | \(-0.477156\pi\) | ||||
0.0717043 | + | 0.997426i | \(0.477156\pi\) | |||||||
\(198\) | −1.86626 | −0.132629 | ||||||||
\(199\) | 5.03693 | 0.357059 | 0.178529 | − | 0.983935i | \(-0.442866\pi\) | ||||
0.178529 | + | 0.983935i | \(0.442866\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.0355 | −1.62480 | ||||||||
\(202\) | −1.93116 | −0.135876 | ||||||||
\(203\) | 12.6569 | 0.888339 | ||||||||
\(204\) | 12.4602 | 0.872388 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.34886 | 0.303000 | ||||||||
\(207\) | −0.259405 | −0.0180299 | ||||||||
\(208\) | −15.6394 | −1.08440 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.18849 | −0.288348 | −0.144174 | − | 0.989552i | \(-0.546052\pi\) | ||||
−0.144174 | + | 0.989552i | \(0.546052\pi\) | |||||||
\(212\) | 3.67842 | 0.252635 | ||||||||
\(213\) | 1.73905 | 0.119158 | ||||||||
\(214\) | 5.49025 | 0.375306 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.61584 | −0.314068 | ||||||||
\(217\) | 29.2168 | 1.98336 | ||||||||
\(218\) | −4.36310 | −0.295506 | ||||||||
\(219\) | −10.5342 | −0.711837 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.7441 | −0.991797 | ||||||||
\(222\) | −1.93574 | −0.129918 | ||||||||
\(223\) | −5.32967 | −0.356901 | −0.178451 | − | 0.983949i | \(-0.557108\pi\) | ||||
−0.178451 | + | 0.983949i | \(0.557108\pi\) | |||||||
\(224\) | −13.1527 | −0.878801 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.31857 | −0.0877099 | ||||||||
\(227\) | 5.17899 | 0.343741 | 0.171871 | − | 0.985120i | \(-0.445019\pi\) | ||||
0.171871 | + | 0.985120i | \(0.445019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.0790 | −1.12861 | −0.564306 | − | 0.825566i | \(-0.690856\pi\) | ||||
−0.564306 | + | 0.825566i | \(0.690856\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −37.8729 | −2.49185 | ||||||||
\(232\) | 4.23268 | 0.277889 | ||||||||
\(233\) | 15.8503 | 1.03839 | 0.519195 | − | 0.854656i | \(-0.326232\pi\) | ||||
0.519195 | + | 0.854656i | \(0.326232\pi\) | |||||||
\(234\) | −1.71014 | −0.111795 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.6873 | −0.760777 | ||||||||
\(237\) | 18.7886 | 1.22045 | ||||||||
\(238\) | −3.76937 | −0.244332 | ||||||||
\(239\) | −17.7688 | −1.14937 | −0.574685 | − | 0.818375i | \(-0.694875\pi\) | ||||
−0.574685 | + | 0.818375i | \(0.694875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.3823 | 1.76385 | 0.881925 | − | 0.471390i | \(-0.156247\pi\) | ||||
0.881925 | + | 0.471390i | \(0.156247\pi\) | |||||||
\(242\) | 4.47623 | 0.287743 | ||||||||
\(243\) | 11.5739 | 0.742469 | ||||||||
\(244\) | −9.54019 | −0.610748 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.118785 | −0.00757345 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.77061 | 0.620434 | ||||||||
\(249\) | −9.26557 | −0.587182 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.50216 | −0.536651 | −0.268326 | − | 0.963328i | \(-0.586470\pi\) | ||||
−0.268326 | + | 0.963328i | \(0.586470\pi\) | |||||||
\(252\) | 8.24837 | 0.519599 | ||||||||
\(253\) | 1.10731 | 0.0696161 | ||||||||
\(254\) | −3.78162 | −0.237280 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.54010 | 0.533756 | ||||||||
\(257\) | 20.9865 | 1.30910 | 0.654552 | − | 0.756017i | \(-0.272857\pi\) | ||||
0.654552 | + | 0.756017i | \(0.272857\pi\) | |||||||
\(258\) | 4.73477 | 0.294774 | ||||||||
\(259\) | −11.0479 | −0.686482 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.01590 | −0.248578 | ||||||||
\(262\) | −2.40535 | −0.148603 | ||||||||
\(263\) | −11.7173 | −0.722522 | −0.361261 | − | 0.932465i | \(-0.617654\pi\) | ||||
−0.361261 | + | 0.932465i | \(0.617654\pi\) | |||||||
\(264\) | −12.6654 | −0.779499 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −30.3901 | −1.85984 | ||||||||
\(268\) | −21.4156 | −1.30816 | ||||||||
\(269\) | 13.1743 | 0.803253 | 0.401626 | − | 0.915804i | \(-0.368445\pi\) | ||||
0.401626 | + | 0.915804i | \(0.368445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.7363 | −1.56337 | −0.781683 | − | 0.623676i | \(-0.785639\pi\) | ||||
−0.781683 | + | 0.623676i | \(0.785639\pi\) | |||||||
\(272\) | 10.9374 | 0.663177 | ||||||||
\(273\) | −34.7046 | −2.10042 | ||||||||
\(274\) | −2.53381 | −0.153073 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.857501 | −0.0516155 | ||||||||
\(277\) | −5.11697 | −0.307449 | −0.153724 | − | 0.988114i | \(-0.549127\pi\) | ||||
−0.153724 | + | 0.988114i | \(0.549127\pi\) | |||||||
\(278\) | 0.842882 | 0.0505527 | ||||||||
\(279\) | −9.27018 | −0.554991 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.80790 | 0.107850 | 0.0539251 | − | 0.998545i | \(-0.482827\pi\) | ||||
0.0539251 | + | 0.998545i | \(0.482827\pi\) | |||||||
\(282\) | −7.05759 | −0.420273 | ||||||||
\(283\) | −18.6741 | −1.11006 | −0.555029 | − | 0.831831i | \(-0.687293\pi\) | ||||
−0.555029 | + | 0.831831i | \(0.687293\pi\) | |||||||
\(284\) | 1.61675 | 0.0959366 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.29999 | 0.431657 | ||||||||
\(287\) | −0.677944 | −0.0400178 | ||||||||
\(288\) | 4.17321 | 0.245909 | ||||||||
\(289\) | −6.68871 | −0.393454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.79077 | −0.163598 | ||||||||
\(292\) | −9.79341 | −0.573116 | ||||||||
\(293\) | 0.150745 | 0.00880664 | 0.00440332 | − | 0.999990i | \(-0.498598\pi\) | ||||
0.00440332 | + | 0.999990i | \(0.498598\pi\) | |||||||
\(294\) | −4.33475 | −0.252808 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.69461 | −0.214745 | ||||||||
\(297\) | −18.6943 | −1.08475 | ||||||||
\(298\) | 2.64985 | 0.153502 | ||||||||
\(299\) | 1.01468 | 0.0586804 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.0228 | 1.55757 | ||||||||
\(302\) | −2.71749 | −0.156374 | ||||||||
\(303\) | 12.4346 | 0.714347 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.19598 | 0.0683697 | ||||||||
\(307\) | 4.94936 | 0.282475 | 0.141237 | − | 0.989976i | \(-0.454892\pi\) | ||||
0.141237 | + | 0.989976i | \(0.454892\pi\) | |||||||
\(308\) | −35.2095 | −2.00625 | ||||||||
\(309\) | −28.0020 | −1.59298 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.6262 | −1.33972 | −0.669859 | − | 0.742489i | \(-0.733645\pi\) | ||||
−0.669859 | + | 0.742489i | \(0.733645\pi\) | |||||||
\(312\) | −11.6058 | −0.657051 | ||||||||
\(313\) | 8.89248 | 0.502632 | 0.251316 | − | 0.967905i | \(-0.419137\pi\) | ||||
0.251316 | + | 0.967905i | \(0.419137\pi\) | |||||||
\(314\) | −3.59600 | −0.202934 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.4673 | 0.982612 | ||||||||
\(317\) | 29.5976 | 1.66237 | 0.831185 | − | 0.555996i | \(-0.187663\pi\) | ||||
0.831185 | + | 0.555996i | \(0.187663\pi\) | |||||||
\(318\) | 1.25541 | 0.0704000 | ||||||||
\(319\) | 17.1425 | 0.959795 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.3512 | −1.97311 | ||||||||
\(322\) | 0.259405 | 0.0144561 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 21.1654 | 1.17586 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.47555 | −0.0817232 | ||||||||
\(327\) | 28.0936 | 1.55358 | ||||||||
\(328\) | −0.226716 | −0.0125183 | ||||||||
\(329\) | −40.2799 | −2.22070 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.8866 | −1.42285 | −0.711427 | − | 0.702760i | \(-0.751951\pi\) | ||||
−0.711427 | + | 0.702760i | \(0.751951\pi\) | |||||||
\(332\) | −8.61397 | −0.472753 | ||||||||
\(333\) | 3.50538 | 0.192093 | ||||||||
\(334\) | −2.82224 | −0.154426 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 25.7444 | 1.40447 | ||||||||
\(337\) | 6.08960 | 0.331721 | 0.165861 | − | 0.986149i | \(-0.446960\pi\) | ||||
0.165861 | + | 0.986149i | \(0.446960\pi\) | |||||||
\(338\) | 2.56454 | 0.139493 | ||||||||
\(339\) | 8.49015 | 0.461122 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.5712 | 2.14290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.15747 | 0.0624972 | ||||||||
\(344\) | 9.03692 | 0.487238 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.91967 | 0.318244 | ||||||||
\(347\) | 6.60514 | 0.354582 | 0.177291 | − | 0.984158i | \(-0.443267\pi\) | ||||
0.177291 | + | 0.984158i | \(0.443267\pi\) | |||||||
\(348\) | −13.2751 | −0.711621 | ||||||||
\(349\) | 19.6123 | 1.04982 | 0.524912 | − | 0.851156i | \(-0.324098\pi\) | ||||
0.524912 | + | 0.851156i | \(0.324098\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.1304 | −0.914354 | ||||||||
\(352\) | −17.8140 | −0.949490 | ||||||||
\(353\) | 19.2599 | 1.02510 | 0.512551 | − | 0.858657i | \(-0.328701\pi\) | ||||
0.512551 | + | 0.858657i | \(0.328701\pi\) | |||||||
\(354\) | −3.98876 | −0.212000 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −28.2529 | −1.49740 | ||||||||
\(357\) | 24.2706 | 1.28454 | ||||||||
\(358\) | 0.0713238 | 0.00376958 | ||||||||
\(359\) | −35.7362 | −1.88609 | −0.943043 | − | 0.332671i | \(-0.892050\pi\) | ||||
−0.943043 | + | 0.332671i | \(0.892050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 7.89352 | 0.414874 | ||||||||
\(363\) | −28.8221 | −1.51277 | ||||||||
\(364\) | −32.2640 | −1.69110 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.25598 | −0.170193 | ||||||||
\(367\) | −13.8593 | −0.723450 | −0.361725 | − | 0.932285i | \(-0.617812\pi\) | ||||
−0.361725 | + | 0.932285i | \(0.617812\pi\) | |||||||
\(368\) | −0.752703 | −0.0392373 | ||||||||
\(369\) | 0.215105 | 0.0111979 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.16504 | 0.371990 | ||||||||
\(372\) | −30.6439 | −1.58881 | ||||||||
\(373\) | −23.6819 | −1.22620 | −0.613101 | − | 0.790005i | \(-0.710078\pi\) | ||||
−0.613101 | + | 0.790005i | \(0.710078\pi\) | |||||||
\(374\) | −5.10524 | −0.263985 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.4703 | −0.694678 | ||||||||
\(377\) | 15.7084 | 0.809026 | ||||||||
\(378\) | −4.37943 | −0.225253 | ||||||||
\(379\) | 33.7504 | 1.73364 | 0.866820 | − | 0.498622i | \(-0.166160\pi\) | ||||
0.866820 | + | 0.498622i | \(0.166160\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.3495 | 1.24746 | ||||||||
\(382\) | 2.67757 | 0.136996 | ||||||||
\(383\) | −15.9027 | −0.812588 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(384\) | 18.2110 | 0.929325 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.508761 | 0.0258953 | ||||||||
\(387\) | −8.57407 | −0.435844 | ||||||||
\(388\) | −2.59451 | −0.131716 | ||||||||
\(389\) | −0.715535 | −0.0362791 | −0.0181395 | − | 0.999835i | \(-0.505774\pi\) | ||||
−0.0181395 | + | 0.999835i | \(0.505774\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.709615 | −0.0358868 | ||||||||
\(392\) | −8.27344 | −0.417872 | ||||||||
\(393\) | 15.4878 | 0.781259 | ||||||||
\(394\) | 0.638652 | 0.0321748 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 11.1716 | 0.561394 | ||||||||
\(397\) | 14.3593 | 0.720671 | 0.360336 | − | 0.932823i | \(-0.382662\pi\) | ||||
0.360336 | + | 0.932823i | \(0.382662\pi\) | |||||||
\(398\) | 1.59817 | 0.0801088 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.5791 | 1.72680 | 0.863398 | − | 0.504524i | \(-0.168332\pi\) | ||||
0.863398 | + | 0.504524i | \(0.168332\pi\) | |||||||
\(402\) | −7.30893 | −0.364536 | ||||||||
\(403\) | 36.2609 | 1.80628 | ||||||||
\(404\) | 11.5601 | 0.575137 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.01590 | 0.199306 | ||||||||
\(407\) | −14.9633 | −0.741701 | ||||||||
\(408\) | 8.11653 | 0.401828 | ||||||||
\(409\) | 18.4355 | 0.911575 | 0.455788 | − | 0.890089i | \(-0.349358\pi\) | ||||
0.455788 | + | 0.890089i | \(0.349358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.3150 | 0.804760 | ||||||||
\(412\) | −26.0327 | −1.28254 | ||||||||
\(413\) | −22.7651 | −1.12020 | ||||||||
\(414\) | −0.0823065 | −0.00404514 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.3238 | −0.800339 | ||||||||
\(417\) | −5.42725 | −0.265773 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.3437 | −1.67780 | −0.838901 | − | 0.544285i | \(-0.816801\pi\) | ||||
−0.838901 | + | 0.544285i | \(0.816801\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.225020 | 0.0109668 | 0.00548340 | − | 0.999985i | \(-0.498255\pi\) | ||||
0.00548340 | + | 0.999985i | \(0.498255\pi\) | |||||||
\(422\) | −1.32897 | −0.0646930 | ||||||||
\(423\) | 12.7804 | 0.621404 | ||||||||
\(424\) | 2.39611 | 0.116366 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.551782 | 0.0267339 | ||||||||
\(427\) | −18.5829 | −0.899290 | ||||||||
\(428\) | −32.8652 | −1.58860 | ||||||||
\(429\) | −47.0040 | −2.26937 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.3531 | −0.643198 | −0.321599 | − | 0.946876i | \(-0.604220\pi\) | ||||
−0.321599 | + | 0.946876i | \(0.604220\pi\) | |||||||
\(432\) | 12.7076 | 0.611393 | ||||||||
\(433\) | −21.4161 | −1.02919 | −0.514595 | − | 0.857433i | \(-0.672058\pi\) | ||||
−0.514595 | + | 0.857433i | \(0.672058\pi\) | |||||||
\(434\) | 9.27018 | 0.444983 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.1179 | 1.25082 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.34240 | −0.159706 | ||||||||
\(439\) | 7.21678 | 0.344438 | 0.172219 | − | 0.985059i | \(-0.444906\pi\) | ||||
0.172219 | + | 0.985059i | \(0.444906\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.84969 | 0.373795 | ||||||||
\(442\) | −4.67816 | −0.222517 | ||||||||
\(443\) | 34.6591 | 1.64671 | 0.823353 | − | 0.567530i | \(-0.192101\pi\) | ||||
0.823353 | + | 0.567530i | \(0.192101\pi\) | |||||||
\(444\) | 11.5875 | 0.549920 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.69105 | −0.0800735 | ||||||||
\(447\) | −17.0622 | −0.807013 | ||||||||
\(448\) | 21.0293 | 0.993540 | ||||||||
\(449\) | −5.09006 | −0.240215 | −0.120107 | − | 0.992761i | \(-0.538324\pi\) | ||||
−0.120107 | + | 0.992761i | \(0.538324\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.918208 | −0.0432367 | ||||||||
\(452\) | 7.89309 | 0.371260 | ||||||||
\(453\) | 17.4977 | 0.822113 | ||||||||
\(454\) | 1.64324 | 0.0771210 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.9916 | −1.87073 | −0.935364 | − | 0.353686i | \(-0.884928\pi\) | ||||
−0.935364 | + | 0.353686i | \(0.884928\pi\) | |||||||
\(458\) | −5.41899 | −0.253213 | ||||||||
\(459\) | 11.9801 | 0.559185 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.4955 | 1.23402 | 0.617009 | − | 0.786956i | \(-0.288344\pi\) | ||||
0.617009 | + | 0.786956i | \(0.288344\pi\) | |||||||
\(462\) | −12.0167 | −0.559066 | ||||||||
\(463\) | 9.68844 | 0.450260 | 0.225130 | − | 0.974329i | \(-0.427719\pi\) | ||||
0.225130 | + | 0.974329i | \(0.427719\pi\) | |||||||
\(464\) | −11.6527 | −0.540964 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.02915 | 0.232971 | ||||||||
\(467\) | 5.78310 | 0.267610 | 0.133805 | − | 0.991008i | \(-0.457280\pi\) | ||||
0.133805 | + | 0.991008i | \(0.457280\pi\) | |||||||
\(468\) | 10.2370 | 0.473208 | ||||||||
\(469\) | −41.7144 | −1.92619 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.1543 | 1.06689 | ||||||||
\(472\) | −7.61306 | −0.350419 | ||||||||
\(473\) | 36.5998 | 1.68286 | ||||||||
\(474\) | 5.96142 | 0.273817 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.5638 | 1.03421 | ||||||||
\(477\) | −2.27339 | −0.104091 | ||||||||
\(478\) | −5.63786 | −0.257870 | ||||||||
\(479\) | 1.77194 | 0.0809620 | 0.0404810 | − | 0.999180i | \(-0.487111\pi\) | ||||
0.0404810 | + | 0.999180i | \(0.487111\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7115 | −0.625191 | ||||||||
\(482\) | 8.68812 | 0.395733 | ||||||||
\(483\) | −1.67029 | −0.0760007 | ||||||||
\(484\) | −26.7952 | −1.21796 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.67229 | 0.166579 | ||||||||
\(487\) | −16.2131 | −0.734688 | −0.367344 | − | 0.930085i | \(-0.619733\pi\) | ||||
−0.367344 | + | 0.930085i | \(0.619733\pi\) | |||||||
\(488\) | −6.21445 | −0.281315 | ||||||||
\(489\) | 9.50094 | 0.429647 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4869 | 0.834300 | 0.417150 | − | 0.908838i | \(-0.363029\pi\) | ||||
0.417150 | + | 0.908838i | \(0.363029\pi\) | |||||||
\(492\) | 0.711059 | 0.0320570 | ||||||||
\(493\) | −10.9857 | −0.494770 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −26.8988 | −1.20779 | ||||||||
\(497\) | 3.14920 | 0.141261 | ||||||||
\(498\) | −2.93987 | −0.131739 | ||||||||
\(499\) | −17.2843 | −0.773751 | −0.386875 | − | 0.922132i | \(-0.626446\pi\) | ||||
−0.386875 | + | 0.922132i | \(0.626446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.1722 | 0.811873 | ||||||||
\(502\) | −2.69765 | −0.120402 | ||||||||
\(503\) | −40.7325 | −1.81617 | −0.908087 | − | 0.418782i | \(-0.862457\pi\) | ||||
−0.908087 | + | 0.418782i | \(0.862457\pi\) | |||||||
\(504\) | 5.37297 | 0.239331 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.351338 | 0.0156189 | ||||||||
\(507\) | −16.5129 | −0.733362 | ||||||||
\(508\) | 22.6372 | 1.00436 | ||||||||
\(509\) | −21.2017 | −0.939747 | −0.469873 | − | 0.882734i | \(-0.655700\pi\) | ||||
−0.469873 | + | 0.882734i | \(0.655700\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.0761 | −0.843879 | ||||||||
\(512\) | 20.5374 | 0.907632 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.65881 | 0.293707 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −28.3428 | −1.24772 | ||||||||
\(517\) | −54.5551 | −2.39933 | ||||||||
\(518\) | −3.50538 | −0.154017 | ||||||||
\(519\) | −38.1163 | −1.67312 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.2704 | −0.844251 | −0.422125 | − | 0.906538i | \(-0.638716\pi\) | ||||
−0.422125 | + | 0.906538i | \(0.638716\pi\) | |||||||
\(522\) | −1.27420 | −0.0557703 | ||||||||
\(523\) | 24.4971 | 1.07118 | 0.535591 | − | 0.844477i | \(-0.320089\pi\) | ||||
0.535591 | + | 0.844477i | \(0.320089\pi\) | |||||||
\(524\) | 14.3987 | 0.629009 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.71779 | −0.162103 | ||||||||
\(527\) | −25.3590 | −1.10466 | ||||||||
\(528\) | 34.8682 | 1.51744 | ||||||||
\(529\) | −22.9512 | −0.997877 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.22313 | 0.313457 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.841395 | −0.0364449 | ||||||||
\(534\) | −9.64245 | −0.417270 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.9500 | −0.602550 | ||||||||
\(537\) | −0.459248 | −0.0198180 | ||||||||
\(538\) | 4.18008 | 0.180216 | ||||||||
\(539\) | −33.5076 | −1.44328 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.5029 | 1.31142 | 0.655711 | − | 0.755012i | \(-0.272369\pi\) | ||||
0.655711 | + | 0.755012i | \(0.272369\pi\) | |||||||
\(542\) | −8.16585 | −0.350753 | ||||||||
\(543\) | −50.8257 | −2.18114 | ||||||||
\(544\) | 11.4160 | 0.489458 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.0114 | −0.471245 | ||||||||
\(547\) | 3.16224 | 0.135207 | 0.0676037 | − | 0.997712i | \(-0.478465\pi\) | ||||
0.0676037 | + | 0.997712i | \(0.478465\pi\) | |||||||
\(548\) | 15.1677 | 0.647931 | ||||||||
\(549\) | 5.89616 | 0.251642 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.558573 | −0.0237745 | ||||||||
\(553\) | 34.0237 | 1.44684 | ||||||||
\(554\) | −1.62356 | −0.0689785 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.04558 | −0.213980 | ||||||||
\(557\) | 33.8886 | 1.43591 | 0.717953 | − | 0.696092i | \(-0.245079\pi\) | ||||
0.717953 | + | 0.696092i | \(0.245079\pi\) | |||||||
\(558\) | −2.94133 | −0.124517 | ||||||||
\(559\) | 33.5380 | 1.41851 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.8722 | 1.38786 | ||||||||
\(562\) | 0.573627 | 0.0241970 | ||||||||
\(563\) | 36.5457 | 1.54022 | 0.770110 | − | 0.637911i | \(-0.220201\pi\) | ||||
0.770110 | + | 0.637911i | \(0.220201\pi\) | |||||||
\(564\) | 42.2474 | 1.77894 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.92509 | −0.249050 | ||||||||
\(567\) | 41.2271 | 1.73138 | ||||||||
\(568\) | 1.05315 | 0.0441891 | ||||||||
\(569\) | 1.31802 | 0.0552543 | 0.0276272 | − | 0.999618i | \(-0.491205\pi\) | ||||
0.0276272 | + | 0.999618i | \(0.491205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.0771 | −0.714656 | −0.357328 | − | 0.933979i | \(-0.616312\pi\) | ||||
−0.357328 | + | 0.933979i | \(0.616312\pi\) | |||||||
\(572\) | −43.6985 | −1.82712 | ||||||||
\(573\) | −17.2406 | −0.720238 | ||||||||
\(574\) | −0.215105 | −0.00897829 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.67237 | −0.278016 | ||||||||
\(577\) | 47.2699 | 1.96787 | 0.983937 | − | 0.178517i | \(-0.0571299\pi\) | ||||
0.983937 | + | 0.178517i | \(0.0571299\pi\) | |||||||
\(578\) | −2.12226 | −0.0882744 | ||||||||
\(579\) | −3.27587 | −0.136140 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.7788 | −0.696101 | ||||||||
\(582\) | −0.885483 | −0.0367045 | ||||||||
\(583\) | 9.70433 | 0.401912 | ||||||||
\(584\) | −6.37940 | −0.263981 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.0478300 | 0.00197584 | ||||||||
\(587\) | −0.620087 | −0.0255937 | −0.0127969 | − | 0.999918i | \(-0.504073\pi\) | ||||
−0.0127969 | + | 0.999918i | \(0.504073\pi\) | |||||||
\(588\) | 25.9483 | 1.07009 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.11222 | −0.169154 | ||||||||
\(592\) | 10.1714 | 0.418041 | ||||||||
\(593\) | 8.96071 | 0.367972 | 0.183986 | − | 0.982929i | \(-0.441100\pi\) | ||||
0.183986 | + | 0.982929i | \(0.441100\pi\) | |||||||
\(594\) | −5.93150 | −0.243372 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.8623 | −0.649745 | ||||||||
\(597\) | −10.2905 | −0.421160 | ||||||||
\(598\) | 0.321947 | 0.0131654 | ||||||||
\(599\) | −0.338212 | −0.0138190 | −0.00690948 | − | 0.999976i | \(-0.502199\pi\) | ||||
−0.00690948 | + | 0.999976i | \(0.502199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.7523 | −1.62153 | −0.810766 | − | 0.585370i | \(-0.800949\pi\) | ||||
−0.810766 | + | 0.585370i | \(0.800949\pi\) | |||||||
\(602\) | 8.57407 | 0.349453 | ||||||||
\(603\) | 13.2355 | 0.538993 | ||||||||
\(604\) | 16.2672 | 0.661902 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.94536 | 0.160269 | ||||||||
\(607\) | 22.5614 | 0.915738 | 0.457869 | − | 0.889020i | \(-0.348613\pi\) | ||||
0.457869 | + | 0.889020i | \(0.348613\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.8580 | −1.04782 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.9913 | −2.02243 | ||||||||
\(612\) | −7.15926 | −0.289396 | ||||||||
\(613\) | −32.5953 | −1.31651 | −0.658257 | − | 0.752794i | \(-0.728706\pi\) | ||||
−0.658257 | + | 0.752794i | \(0.728706\pi\) | |||||||
\(614\) | 1.57038 | 0.0633754 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.9354 | −0.924092 | ||||||||
\(617\) | −29.4270 | −1.18469 | −0.592343 | − | 0.805686i | \(-0.701797\pi\) | ||||
−0.592343 | + | 0.805686i | \(0.701797\pi\) | |||||||
\(618\) | −8.88473 | −0.357396 | ||||||||
\(619\) | −24.9940 | −1.00459 | −0.502297 | − | 0.864695i | \(-0.667512\pi\) | ||||
−0.502297 | + | 0.864695i | \(0.667512\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.824463 | −0.0330846 | ||||||||
\(622\) | −7.49634 | −0.300576 | ||||||||
\(623\) | −55.0325 | −2.20483 | ||||||||
\(624\) | 31.9513 | 1.27907 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.82149 | 0.112769 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.5260 | 0.858981 | ||||||||
\(629\) | 9.58912 | 0.382343 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.3101 | −1.12701 | −0.563504 | − | 0.826113i | \(-0.690547\pi\) | ||||
−0.563504 | + | 0.826113i | \(0.690547\pi\) | |||||||
\(632\) | 11.3781 | 0.452598 | ||||||||
\(633\) | 8.55709 | 0.340114 | ||||||||
\(634\) | 9.39103 | 0.372965 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.51502 | −0.297990 | ||||||||
\(637\) | −30.7046 | −1.21656 | ||||||||
\(638\) | 5.43913 | 0.215337 | ||||||||
\(639\) | −0.999208 | −0.0395280 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.7741 | 1.13651 | 0.568254 | − | 0.822853i | \(-0.307619\pi\) | ||||
0.568254 | + | 0.822853i | \(0.307619\pi\) | |||||||
\(642\) | −11.2166 | −0.442683 | ||||||||
\(643\) | 10.0599 | 0.396722 | 0.198361 | − | 0.980129i | \(-0.436438\pi\) | ||||
0.198361 | + | 0.980129i | \(0.436438\pi\) | |||||||
\(644\) | −1.55282 | −0.0611899 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.9903 | 0.746586 | 0.373293 | − | 0.927714i | \(-0.378229\pi\) | ||||
0.373293 | + | 0.927714i | \(0.378229\pi\) | |||||||
\(648\) | 13.7871 | 0.541607 | ||||||||
\(649\) | −30.8331 | −1.21030 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −59.6899 | −2.33943 | ||||||||
\(652\) | 8.83279 | 0.345919 | ||||||||
\(653\) | 42.6940 | 1.67074 | 0.835372 | − | 0.549685i | \(-0.185252\pi\) | ||||
0.835372 | + | 0.549685i | \(0.185252\pi\) | |||||||
\(654\) | 8.91381 | 0.348557 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.624158 | 0.0243693 | ||||||||
\(657\) | 6.05266 | 0.236137 | ||||||||
\(658\) | −12.7804 | −0.498232 | ||||||||
\(659\) | −14.4043 | −0.561111 | −0.280556 | − | 0.959838i | \(-0.590519\pi\) | ||||
−0.280556 | + | 0.959838i | \(0.590519\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.24176 | 0.320567 | 0.160284 | − | 0.987071i | \(-0.448759\pi\) | ||||
0.160284 | + | 0.987071i | \(0.448759\pi\) | |||||||
\(662\) | −8.21354 | −0.319228 | ||||||||
\(663\) | 30.1222 | 1.16985 | ||||||||
\(664\) | −5.61112 | −0.217754 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.11222 | 0.0430976 | ||||||||
\(667\) | 0.756026 | 0.0292734 | ||||||||
\(668\) | 16.8942 | 0.653657 | ||||||||
\(669\) | 10.8885 | 0.420974 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.1687 | −0.971627 | ||||||||
\(672\) | 26.8709 | 1.03657 | ||||||||
\(673\) | −37.9246 | −1.46189 | −0.730944 | − | 0.682438i | \(-0.760920\pi\) | ||||
−0.730944 | + | 0.682438i | \(0.760920\pi\) | |||||||
\(674\) | 1.93217 | 0.0744242 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.3516 | −0.590446 | ||||||||
\(677\) | −8.17207 | −0.314078 | −0.157039 | − | 0.987592i | \(-0.550195\pi\) | ||||
−0.157039 | + | 0.987592i | \(0.550195\pi\) | |||||||
\(678\) | 2.69384 | 0.103456 | ||||||||
\(679\) | −5.05374 | −0.193945 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5807 | −0.405452 | ||||||||
\(682\) | 12.5555 | 0.480777 | ||||||||
\(683\) | 16.4611 | 0.629868 | 0.314934 | − | 0.949114i | \(-0.398018\pi\) | ||||
0.314934 | + | 0.949114i | \(0.398018\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.367252 | 0.0140217 | ||||||||
\(687\) | 34.8924 | 1.33123 | ||||||||
\(688\) | −24.8789 | −0.948501 | ||||||||
\(689\) | 8.89252 | 0.338778 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.9386 | 0.454166 | 0.227083 | − | 0.973875i | \(-0.427081\pi\) | ||||
0.227083 | + | 0.973875i | \(0.427081\pi\) | |||||||
\(692\) | −35.4358 | −1.34707 | ||||||||
\(693\) | 21.7607 | 0.826619 | ||||||||
\(694\) | 2.09574 | 0.0795532 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.64737 | −0.327778 | ||||||||
\(697\) | 0.588429 | 0.0222883 | ||||||||
\(698\) | 6.22279 | 0.235536 | ||||||||
\(699\) | −32.3822 | −1.22481 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.7112 | −0.593404 | −0.296702 | − | 0.954970i | \(-0.595887\pi\) | ||||
−0.296702 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(702\) | −5.43530 | −0.205142 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 28.4821 | 1.07346 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.11097 | 0.229989 | ||||||||
\(707\) | 22.5174 | 0.846855 | ||||||||
\(708\) | 23.8771 | 0.897357 | ||||||||
\(709\) | −0.810620 | −0.0304435 | −0.0152217 | − | 0.999884i | \(-0.504845\pi\) | ||||
−0.0152217 | + | 0.999884i | \(0.504845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.7954 | −0.404858 | ||||||||
\(712\) | −18.4039 | −0.689713 | ||||||||
\(713\) | 1.74519 | 0.0653578 | ||||||||
\(714\) | 7.70082 | 0.288196 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.426951 | −0.0159559 | ||||||||
\(717\) | 36.3017 | 1.35571 | ||||||||
\(718\) | −11.3387 | −0.423158 | ||||||||
\(719\) | −13.4593 | −0.501948 | −0.250974 | − | 0.967994i | \(-0.580751\pi\) | ||||
−0.250974 | + | 0.967994i | \(0.580751\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.7080 | −1.88846 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −55.9421 | −2.08051 | ||||||||
\(724\) | −47.2514 | −1.75609 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.14494 | −0.339401 | ||||||||
\(727\) | 2.13941 | 0.0793464 | 0.0396732 | − | 0.999213i | \(-0.487368\pi\) | ||||
0.0396732 | + | 0.999213i | \(0.487368\pi\) | |||||||
\(728\) | −21.0167 | −0.778931 | ||||||||
\(729\) | 9.78531 | 0.362419 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.4548 | −0.867506 | ||||||||
\(732\) | 19.4906 | 0.720394 | ||||||||
\(733\) | 0.353890 | 0.0130712 | 0.00653561 | − | 0.999979i | \(-0.497920\pi\) | ||||
0.00653561 | + | 0.999979i | \(0.497920\pi\) | |||||||
\(734\) | −4.39741 | −0.162311 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.785641 | −0.0289591 | ||||||||
\(737\) | −56.4980 | −2.08113 | ||||||||
\(738\) | 0.0682504 | 0.00251233 | ||||||||
\(739\) | 0.530279 | 0.0195066 | 0.00975332 | − | 0.999952i | \(-0.496895\pi\) | ||||
0.00975332 | + | 0.999952i | \(0.496895\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.27339 | 0.0834588 | ||||||||
\(743\) | −10.9210 | −0.400654 | −0.200327 | − | 0.979729i | \(-0.564200\pi\) | ||||
−0.200327 | + | 0.979729i | \(0.564200\pi\) | |||||||
\(744\) | −19.9614 | −0.731819 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.51402 | −0.275108 | ||||||||
\(747\) | 5.32373 | 0.194785 | ||||||||
\(748\) | 30.5605 | 1.11740 | ||||||||
\(749\) | −64.0166 | −2.33911 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00460 | 0.292092 | 0.146046 | − | 0.989278i | \(-0.453345\pi\) | ||||
0.146046 | + | 0.989278i | \(0.453345\pi\) | |||||||
\(752\) | 37.0842 | 1.35232 | ||||||||
\(753\) | 17.3699 | 0.632995 | ||||||||
\(754\) | 4.98412 | 0.181511 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 26.2157 | 0.953455 | ||||||||
\(757\) | 30.1904 | 1.09729 | 0.548645 | − | 0.836056i | \(-0.315144\pi\) | ||||
0.548645 | + | 0.836056i | \(0.315144\pi\) | |||||||
\(758\) | 10.7086 | 0.388955 | ||||||||
\(759\) | −2.26224 | −0.0821140 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.399315 | −0.0144751 | −0.00723757 | − | 0.999974i | \(-0.502304\pi\) | ||||
−0.00723757 | + | 0.999974i | \(0.502304\pi\) | |||||||
\(762\) | 7.72585 | 0.279878 | ||||||||
\(763\) | 50.8739 | 1.84176 | ||||||||
\(764\) | −16.0282 | −0.579880 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.04575 | −0.182310 | ||||||||
\(767\) | −28.2538 | −1.02018 | ||||||||
\(768\) | −17.4474 | −0.629580 | ||||||||
\(769\) | −6.52791 | −0.235403 | −0.117701 | − | 0.993049i | \(-0.537553\pi\) | ||||
−0.117701 | + | 0.993049i | \(0.537553\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.8755 | −1.54412 | ||||||||
\(772\) | −3.04550 | −0.109610 | ||||||||
\(773\) | −29.2223 | −1.05105 | −0.525527 | − | 0.850777i | \(-0.676132\pi\) | ||||
−0.525527 | + | 0.850777i | \(0.676132\pi\) | |||||||
\(774\) | −2.72046 | −0.0977850 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.69006 | −0.0606696 | ||||||||
\(777\) | 22.5708 | 0.809723 | ||||||||
\(778\) | −0.227032 | −0.00813949 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.26528 | 0.152624 | ||||||||
\(782\) | −0.225153 | −0.00805147 | ||||||||
\(783\) | −12.7637 | −0.456136 | ||||||||
\(784\) | 22.7771 | 0.813466 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.91413 | 0.175281 | ||||||||
\(787\) | −43.2638 | −1.54219 | −0.771093 | − | 0.636722i | \(-0.780290\pi\) | ||||
−0.771093 | + | 0.636722i | \(0.780290\pi\) | |||||||
\(788\) | −3.82303 | −0.136190 | ||||||||
\(789\) | 23.9385 | 0.852234 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.3746 | 0.546657 | ||||||||
\(792\) | 7.27715 | 0.258582 | ||||||||
\(793\) | −23.0632 | −0.818999 | ||||||||
\(794\) | 4.55605 | 0.161688 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.56678 | −0.339086 | ||||||||
\(797\) | −27.5833 | −0.977050 | −0.488525 | − | 0.872550i | \(-0.662465\pi\) | ||||
−0.488525 | + | 0.872550i | \(0.662465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.9614 | 1.23684 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.4613 | 0.616963 | ||||||||
\(802\) | 10.9716 | 0.387420 | ||||||||
\(803\) | −25.8368 | −0.911759 | ||||||||
\(804\) | 43.7520 | 1.54301 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.5052 | 0.405254 | ||||||||
\(807\) | −26.9151 | −0.947458 | ||||||||
\(808\) | 7.53023 | 0.264912 | ||||||||
\(809\) | 47.2870 | 1.66252 | 0.831262 | − | 0.555881i | \(-0.187619\pi\) | ||||
0.831262 | + | 0.555881i | \(0.187619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.1587 | 1.23459 | 0.617294 | − | 0.786733i | \(-0.288229\pi\) | ||||
0.617294 | + | 0.786733i | \(0.288229\pi\) | |||||||
\(812\) | −24.0396 | −0.843623 | ||||||||
\(813\) | 52.5792 | 1.84403 | ||||||||
\(814\) | −4.74769 | −0.166406 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −22.3451 | −0.782234 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 5.84938 | 0.204519 | ||||||||
\(819\) | 19.9403 | 0.696770 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.1078 | 1.12057 | 0.560285 | − | 0.828300i | \(-0.310692\pi\) | ||||
0.560285 | + | 0.828300i | \(0.310692\pi\) | |||||||
\(822\) | 5.17658 | 0.180554 | ||||||||
\(823\) | −24.6481 | −0.859180 | −0.429590 | − | 0.903024i | \(-0.641342\pi\) | ||||
−0.429590 | + | 0.903024i | \(0.641342\pi\) | |||||||
\(824\) | −16.9576 | −0.590748 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.22313 | −0.251325 | ||||||||
\(827\) | −4.29867 | −0.149479 | −0.0747397 | − | 0.997203i | \(-0.523813\pi\) | ||||
−0.0747397 | + | 0.997203i | \(0.523813\pi\) | |||||||
\(828\) | 0.492695 | 0.0171223 | ||||||||
\(829\) | 11.2729 | 0.391524 | 0.195762 | − | 0.980651i | \(-0.437282\pi\) | ||||
0.195762 | + | 0.980651i | \(0.437282\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.4540 | 0.362644 | ||||||||
\(832\) | 26.0994 | 0.904835 | ||||||||
\(833\) | 21.4732 | 0.744002 | ||||||||
\(834\) | −1.72201 | −0.0596283 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.4633 | −1.01840 | ||||||||
\(838\) | −10.8969 | −0.376427 | ||||||||
\(839\) | 36.5388 | 1.26146 | 0.630730 | − | 0.776003i | \(-0.282756\pi\) | ||||
0.630730 | + | 0.776003i | \(0.282756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.2958 | −0.596408 | ||||||||
\(842\) | 0.0713965 | 0.00246049 | ||||||||
\(843\) | −3.69353 | −0.127212 | ||||||||
\(844\) | 7.95532 | 0.273833 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.05509 | 0.139417 | ||||||||
\(847\) | −52.1931 | −1.79338 | ||||||||
\(848\) | −6.59659 | −0.226528 | ||||||||
\(849\) | 38.1511 | 1.30934 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.659916 | −0.0226216 | ||||||||
\(852\) | −3.30302 | −0.113160 | ||||||||
\(853\) | −13.5898 | −0.465306 | −0.232653 | − | 0.972560i | \(-0.574741\pi\) | ||||
−0.232653 | + | 0.972560i | \(0.574741\pi\) | |||||||
\(854\) | −5.89616 | −0.201763 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.4083 | −0.731720 | ||||||||
\(857\) | 5.85278 | 0.199927 | 0.0999637 | − | 0.994991i | \(-0.468127\pi\) | ||||
0.0999637 | + | 0.994991i | \(0.468127\pi\) | |||||||
\(858\) | −14.9139 | −0.509151 | ||||||||
\(859\) | −20.2569 | −0.691157 | −0.345579 | − | 0.938390i | \(-0.612317\pi\) | ||||
−0.345579 | + | 0.938390i | \(0.612317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.38504 | 0.0472020 | ||||||||
\(862\) | −4.23681 | −0.144306 | ||||||||
\(863\) | 5.65447 | 0.192481 | 0.0962403 | − | 0.995358i | \(-0.469318\pi\) | ||||
0.0962403 | + | 0.995358i | \(0.469318\pi\) | |||||||
\(864\) | 13.2637 | 0.451239 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.79509 | −0.230907 | ||||||||
\(867\) | 13.6650 | 0.464089 | ||||||||
\(868\) | −55.4922 | −1.88353 | ||||||||
\(869\) | 46.0818 | 1.56322 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.7717 | −1.75422 | ||||||||
\(872\) | 17.0131 | 0.576138 | ||||||||
\(873\) | 1.60350 | 0.0542702 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.0079 | 0.676006 | ||||||||
\(877\) | −57.4540 | −1.94008 | −0.970041 | − | 0.242939i | \(-0.921888\pi\) | ||||
−0.970041 | + | 0.242939i | \(0.921888\pi\) | |||||||
\(878\) | 2.28981 | 0.0772773 | ||||||||
\(879\) | −0.307973 | −0.0103877 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.46121 | 0.285065 | 0.142533 | − | 0.989790i | \(-0.454475\pi\) | ||||
0.142533 | + | 0.989790i | \(0.454475\pi\) | |||||||
\(882\) | 2.49063 | 0.0838637 | ||||||||
\(883\) | −12.8839 | −0.433578 | −0.216789 | − | 0.976218i | \(-0.569558\pi\) | ||||
−0.216789 | + | 0.976218i | \(0.569558\pi\) | |||||||
\(884\) | 28.0039 | 0.941874 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.9970 | 0.369451 | ||||||||
\(887\) | 32.9290 | 1.10565 | 0.552823 | − | 0.833298i | \(-0.313550\pi\) | ||||
0.552823 | + | 0.833298i | \(0.313550\pi\) | |||||||
\(888\) | 7.54808 | 0.253297 | ||||||||
\(889\) | 44.0939 | 1.47886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 55.8380 | 1.87064 | ||||||||
\(892\) | 10.1228 | 0.338936 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −5.41365 | −0.181060 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 32.9777 | 1.10171 | ||||||||
\(897\) | −2.07299 | −0.0692151 | ||||||||
\(898\) | −1.61502 | −0.0538940 | ||||||||
\(899\) | 27.0176 | 0.901087 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.21897 | −0.207184 | ||||||||
\(902\) | −0.291338 | −0.00970049 | ||||||||
\(903\) | −55.2077 | −1.83720 | ||||||||
\(904\) | 5.14153 | 0.171005 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.55184 | 0.184447 | ||||||||
\(907\) | −34.1251 | −1.13311 | −0.566553 | − | 0.824025i | \(-0.691723\pi\) | ||||
−0.566553 | + | 0.824025i | \(0.691723\pi\) | |||||||
\(908\) | −9.83659 | −0.326439 | ||||||||
\(909\) | −7.14455 | −0.236970 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.5938 | 0.914222 | 0.457111 | − | 0.889410i | \(-0.348884\pi\) | ||||
0.457111 | + | 0.889410i | \(0.348884\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.7252 | −0.752094 | ||||||||
\(914\) | −12.6889 | −0.419712 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 32.4386 | 1.07180 | ||||||||
\(917\) | 28.0465 | 0.926178 | ||||||||
\(918\) | 3.80117 | 0.125457 | ||||||||
\(919\) | 13.1572 | 0.434017 | 0.217009 | − | 0.976170i | \(-0.430370\pi\) | ||||
0.217009 | + | 0.976170i | \(0.430370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.1115 | −0.333186 | ||||||||
\(922\) | 8.40674 | 0.276861 | ||||||||
\(923\) | 3.90846 | 0.128649 | ||||||||
\(924\) | 71.9330 | 2.36642 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.07404 | 0.101019 | ||||||||
\(927\) | 16.0891 | 0.528436 | ||||||||
\(928\) | −12.1627 | −0.399259 | ||||||||
\(929\) | −23.5599 | −0.772975 | −0.386487 | − | 0.922295i | \(-0.626312\pi\) | ||||
−0.386487 | + | 0.922295i | \(0.626312\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −30.1050 | −0.986121 | ||||||||
\(933\) | 48.2683 | 1.58023 | ||||||||
\(934\) | 1.83492 | 0.0600403 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.66838 | 0.217963 | ||||||||
\(937\) | 35.9997 | 1.17606 | 0.588030 | − | 0.808839i | \(-0.299904\pi\) | ||||
0.588030 | + | 0.808839i | \(0.299904\pi\) | |||||||
\(938\) | −13.2355 | −0.432156 | ||||||||
\(939\) | −18.1673 | −0.592868 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.8515 | −1.36432 | −0.682160 | − | 0.731203i | \(-0.738959\pi\) | ||||
−0.682160 | + | 0.731203i | \(0.738959\pi\) | |||||||
\(942\) | 7.34662 | 0.239366 | ||||||||
\(943\) | −0.0404952 | −0.00131871 | ||||||||
\(944\) | 20.9590 | 0.682158 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.6127 | 0.377562 | ||||||||
\(947\) | −3.63656 | −0.118172 | −0.0590861 | − | 0.998253i | \(-0.518819\pi\) | ||||
−0.0590861 | + | 0.998253i | \(0.518819\pi\) | |||||||
\(948\) | −35.6857 | −1.15902 | ||||||||
\(949\) | −23.6754 | −0.768535 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −60.4680 | −1.96081 | ||||||||
\(952\) | 14.6980 | 0.476365 | ||||||||
\(953\) | −10.7543 | −0.348366 | −0.174183 | − | 0.984713i | \(-0.555728\pi\) | ||||
−0.174183 | + | 0.984713i | \(0.555728\pi\) | |||||||
\(954\) | −0.721324 | −0.0233537 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 33.7488 | 1.09151 | ||||||||
\(957\) | −35.0221 | −1.13210 | ||||||||
\(958\) | 0.562218 | 0.0181644 | ||||||||
\(959\) | 29.5444 | 0.954039 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.3666 | 1.01183 | ||||||||
\(962\) | −4.35052 | −0.140266 | ||||||||
\(963\) | 20.3118 | 0.654538 | ||||||||
\(964\) | −52.0080 | −1.67506 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.529964 | −0.0170513 | ||||||||
\(967\) | −18.7666 | −0.603493 | −0.301747 | − | 0.953388i | \(-0.597570\pi\) | ||||
−0.301747 | + | 0.953388i | \(0.597570\pi\) | |||||||
\(968\) | −17.4543 | −0.561002 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.4930 | 1.23530 | 0.617650 | − | 0.786453i | \(-0.288085\pi\) | ||||
0.617650 | + | 0.786453i | \(0.288085\pi\) | |||||||
\(972\) | −21.9827 | −0.705096 | ||||||||
\(973\) | −9.82805 | −0.315073 | ||||||||
\(974\) | −5.14426 | −0.164833 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.1086 | 0.547633 | ||||||||
\(977\) | 21.7651 | 0.696328 | 0.348164 | − | 0.937434i | \(-0.386805\pi\) | ||||
0.348164 | + | 0.937434i | \(0.386805\pi\) | |||||||
\(978\) | 3.01455 | 0.0963946 | ||||||||
\(979\) | −74.5361 | −2.38218 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.1418 | −0.515367 | ||||||||
\(982\) | 5.86569 | 0.187182 | ||||||||
\(983\) | 32.9796 | 1.05189 | 0.525943 | − | 0.850520i | \(-0.323712\pi\) | ||||
0.525943 | + | 0.850520i | \(0.323712\pi\) | |||||||
\(984\) | 0.463182 | 0.0147657 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.48564 | −0.111005 | ||||||||
\(987\) | 82.2918 | 2.61938 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.61414 | 0.0513266 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.9400 | 1.42757 | 0.713783 | − | 0.700367i | \(-0.246980\pi\) | ||||
0.713783 | + | 0.700367i | \(0.246980\pi\) | |||||||
\(992\) | −28.0759 | −0.891412 | ||||||||
\(993\) | 52.8862 | 1.67829 | ||||||||
\(994\) | 0.999208 | 0.0316929 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.5983 | 0.557625 | ||||||||
\(997\) | −1.52970 | −0.0484462 | −0.0242231 | − | 0.999707i | \(-0.507711\pi\) | ||||
−0.0242231 | + | 0.999707i | \(0.507711\pi\) | |||||||
\(998\) | −5.48412 | −0.173597 | ||||||||
\(999\) | 11.1411 | 0.352488 |
(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 | 9025.2.a.ck.1.9 | 16 | ||
5.2 | odd | 4 | 1805.2.b.j.1084.9 | yes | 16 | ||
5.3 | odd | 4 | 1805.2.b.j.1084.8 | yes | 16 | ||
5.4 | even | 2 | inner | 9025.2.a.ck.1.8 | 16 | ||
19.18 | odd | 2 | 9025.2.a.cl.1.8 | 16 | |||
95.18 | even | 4 | 1805.2.b.i.1084.9 | yes | 16 | ||
95.37 | even | 4 | 1805.2.b.i.1084.8 | ✓ | 16 | ||
95.94 | odd | 2 | 9025.2.a.cl.1.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.b.i.1084.8 | ✓ | 16 | 95.37 | even | 4 | ||
1805.2.b.i.1084.9 | yes | 16 | 95.18 | even | 4 | ||
1805.2.b.j.1084.8 | yes | 16 | 5.3 | odd | 4 | ||
1805.2.b.j.1084.9 | yes | 16 | 5.2 | odd | 4 | ||
9025.2.a.ck.1.8 | 16 | 5.4 | even | 2 | inner | ||
9025.2.a.ck.1.9 | 16 | 1.1 | even | 1 | trivial | ||
9025.2.a.cl.1.8 | 16 | 19.18 | odd | 2 | |||
9025.2.a.cl.1.9 | 16 | 95.94 | odd | 2 |