Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,4,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2166.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(127.798137072\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{313}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 78 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(9.34590\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −16.3459 | −1.46202 | −0.731011 | − | 0.682366i | \(-0.760951\pi\) | ||||
−0.731011 | + | 0.682366i | \(0.760951\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 31.0377 | 1.67588 | 0.837939 | − | 0.545763i | \(-0.183760\pi\) | ||||
0.837939 | + | 0.545763i | \(0.183760\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 32.6918 | 1.03381 | ||||||||
\(11\) | 4.34590 | 0.119122 | 0.0595609 | − | 0.998225i | \(-0.481030\pi\) | ||||
0.0595609 | + | 0.998225i | \(0.481030\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 24.0000 | 0.512031 | 0.256015 | − | 0.966673i | \(-0.417590\pi\) | ||||
0.256015 | + | 0.966673i | \(0.417590\pi\) | |||||||
\(14\) | −62.0754 | −1.18503 | ||||||||
\(15\) | −49.0377 | −0.844099 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −6.42132 | −0.0916117 | −0.0458059 | − | 0.998950i | \(-0.514586\pi\) | ||||
−0.0458059 | + | 0.998950i | \(0.514586\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −65.3836 | −0.731011 | ||||||||
\(21\) | 93.1131 | 0.967569 | ||||||||
\(22\) | −8.69181 | −0.0842318 | ||||||||
\(23\) | −157.459 | −1.42750 | −0.713750 | − | 0.700401i | \(-0.753005\pi\) | ||||
−0.713750 | + | 0.700401i | \(0.753005\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 142.189 | 1.13751 | ||||||||
\(26\) | −48.0000 | −0.362061 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 124.151 | 0.837939 | ||||||||
\(29\) | −248.075 | −1.58850 | −0.794249 | − | 0.607592i | \(-0.792136\pi\) | ||||
−0.794249 | + | 0.607592i | \(0.792136\pi\) | |||||||
\(30\) | 98.0754 | 0.596868 | ||||||||
\(31\) | 308.302 | 1.78621 | 0.893107 | − | 0.449845i | \(-0.148521\pi\) | ||||
0.893107 | + | 0.449845i | \(0.148521\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 13.0377 | 0.0687750 | ||||||||
\(34\) | 12.8426 | 0.0647793 | ||||||||
\(35\) | −507.339 | −2.45017 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −84.0000 | −0.373230 | −0.186615 | − | 0.982433i | \(-0.559752\pi\) | ||||
−0.186615 | + | 0.982433i | \(0.559752\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 72.0000 | 0.295621 | ||||||||
\(40\) | 130.767 | 0.516903 | ||||||||
\(41\) | −152.075 | −0.579273 | −0.289636 | − | 0.957137i | \(-0.593534\pi\) | ||||
−0.289636 | + | 0.957137i | \(0.593534\pi\) | |||||||
\(42\) | −186.226 | −0.684175 | ||||||||
\(43\) | −481.566 | −1.70786 | −0.853931 | − | 0.520386i | \(-0.825788\pi\) | ||||
−0.853931 | + | 0.520386i | \(0.825788\pi\) | |||||||
\(44\) | 17.3836 | 0.0595609 | ||||||||
\(45\) | −147.113 | −0.487341 | ||||||||
\(46\) | 314.918 | 1.00939 | ||||||||
\(47\) | 426.874 | 1.32481 | 0.662404 | − | 0.749147i | \(-0.269536\pi\) | ||||
0.662404 | + | 0.749147i | \(0.269536\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 620.339 | 1.80857 | ||||||||
\(50\) | −284.377 | −0.804340 | ||||||||
\(51\) | −19.2640 | −0.0528920 | ||||||||
\(52\) | 96.0000 | 0.256015 | ||||||||
\(53\) | −184.377 | −0.477852 | −0.238926 | − | 0.971038i | \(-0.576795\pi\) | ||||
−0.238926 | + | 0.971038i | \(0.576795\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −71.0377 | −0.174159 | ||||||||
\(56\) | −248.302 | −0.592513 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 496.151 | 1.12324 | ||||||||
\(59\) | −584.754 | −1.29031 | −0.645157 | − | 0.764050i | \(-0.723208\pi\) | ||||
−0.645157 | + | 0.764050i | \(0.723208\pi\) | |||||||
\(60\) | −196.151 | −0.422049 | ||||||||
\(61\) | −291.566 | −0.611986 | −0.305993 | − | 0.952034i | \(-0.598988\pi\) | ||||
−0.305993 | + | 0.952034i | \(0.598988\pi\) | |||||||
\(62\) | −616.603 | −1.26304 | ||||||||
\(63\) | 279.339 | 0.558626 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −392.302 | −0.748601 | ||||||||
\(66\) | −26.0754 | −0.0486312 | ||||||||
\(67\) | −420.453 | −0.766663 | −0.383332 | − | 0.923611i | \(-0.625223\pi\) | ||||
−0.383332 | + | 0.923611i | \(0.625223\pi\) | |||||||
\(68\) | −25.6853 | −0.0458059 | ||||||||
\(69\) | −472.377 | −0.824167 | ||||||||
\(70\) | 1014.68 | 1.73253 | ||||||||
\(71\) | 1088.30 | 1.81912 | 0.909561 | − | 0.415571i | \(-0.136418\pi\) | ||||
0.909561 | + | 0.415571i | \(0.136418\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −628.887 | −1.00830 | −0.504148 | − | 0.863617i | \(-0.668193\pi\) | ||||
−0.504148 | + | 0.863617i | \(0.668193\pi\) | |||||||
\(74\) | 168.000 | 0.263914 | ||||||||
\(75\) | 426.566 | 0.656741 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 134.887 | 0.199634 | ||||||||
\(78\) | −144.000 | −0.209036 | ||||||||
\(79\) | 197.056 | 0.280639 | 0.140320 | − | 0.990106i | \(-0.455187\pi\) | ||||
0.140320 | + | 0.990106i | \(0.455187\pi\) | |||||||
\(80\) | −261.534 | −0.365506 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 304.151 | 0.409608 | ||||||||
\(83\) | 519.597 | 0.687147 | 0.343573 | − | 0.939126i | \(-0.388363\pi\) | ||||
0.343573 | + | 0.939126i | \(0.388363\pi\) | |||||||
\(84\) | 372.453 | 0.483785 | ||||||||
\(85\) | 104.962 | 0.133938 | ||||||||
\(86\) | 963.131 | 1.20764 | ||||||||
\(87\) | −744.226 | −0.917120 | ||||||||
\(88\) | −34.7672 | −0.0421159 | ||||||||
\(89\) | −992.980 | −1.18265 | −0.591324 | − | 0.806434i | \(-0.701395\pi\) | ||||
−0.591324 | + | 0.806434i | \(0.701395\pi\) | |||||||
\(90\) | 294.226 | 0.344602 | ||||||||
\(91\) | 744.905 | 0.858102 | ||||||||
\(92\) | −629.836 | −0.713750 | ||||||||
\(93\) | 924.905 | 1.03127 | ||||||||
\(94\) | −853.748 | −0.936780 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 1049.06 | 1.09810 | 0.549049 | − | 0.835790i | \(-0.314990\pi\) | ||||
0.549049 | + | 0.835790i | \(0.314990\pi\) | |||||||
\(98\) | −1240.68 | −1.27885 | ||||||||
\(99\) | 39.1131 | 0.0397072 | ||||||||
\(100\) | 568.754 | 0.568754 | ||||||||
\(101\) | −280.767 | −0.276608 | −0.138304 | − | 0.990390i | \(-0.544165\pi\) | ||||
−0.138304 | + | 0.990390i | \(0.544165\pi\) | |||||||
\(102\) | 38.5279 | 0.0374003 | ||||||||
\(103\) | −1546.11 | −1.47906 | −0.739529 | − | 0.673125i | \(-0.764952\pi\) | ||||
−0.739529 | + | 0.673125i | \(0.764952\pi\) | |||||||
\(104\) | −192.000 | −0.181030 | ||||||||
\(105\) | −1522.02 | −1.41461 | ||||||||
\(106\) | 368.754 | 0.337892 | ||||||||
\(107\) | 1584.45 | 1.43154 | 0.715770 | − | 0.698336i | \(-0.246076\pi\) | ||||
0.715770 | + | 0.698336i | \(0.246076\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 603.246 | 0.530096 | 0.265048 | − | 0.964235i | \(-0.414612\pi\) | ||||
0.265048 | + | 0.964235i | \(0.414612\pi\) | |||||||
\(110\) | 142.075 | 0.123149 | ||||||||
\(111\) | −252.000 | −0.215485 | ||||||||
\(112\) | 496.603 | 0.418970 | ||||||||
\(113\) | 770.036 | 0.641052 | 0.320526 | − | 0.947240i | \(-0.396140\pi\) | ||||
0.320526 | + | 0.947240i | \(0.396140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2573.81 | 2.08703 | ||||||||
\(116\) | −992.302 | −0.794249 | ||||||||
\(117\) | 216.000 | 0.170677 | ||||||||
\(118\) | 1169.51 | 0.912390 | ||||||||
\(119\) | −199.303 | −0.153530 | ||||||||
\(120\) | 392.302 | 0.298434 | ||||||||
\(121\) | −1312.11 | −0.985810 | ||||||||
\(122\) | 583.131 | 0.432740 | ||||||||
\(123\) | −456.226 | −0.334443 | ||||||||
\(124\) | 1233.21 | 0.893107 | ||||||||
\(125\) | −280.962 | −0.201040 | ||||||||
\(126\) | −558.679 | −0.395008 | ||||||||
\(127\) | 2734.11 | 1.91034 | 0.955170 | − | 0.296058i | \(-0.0956721\pi\) | ||||
0.955170 | + | 0.296058i | \(0.0956721\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −1444.70 | −0.986035 | ||||||||
\(130\) | 784.603 | 0.529341 | ||||||||
\(131\) | −575.743 | −0.383991 | −0.191996 | − | 0.981396i | \(-0.561496\pi\) | ||||
−0.191996 | + | 0.981396i | \(0.561496\pi\) | |||||||
\(132\) | 52.1508 | 0.0343875 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 840.905 | 0.542113 | ||||||||
\(135\) | −441.339 | −0.281366 | ||||||||
\(136\) | 51.3706 | 0.0323896 | ||||||||
\(137\) | 2126.46 | 1.32610 | 0.663049 | − | 0.748576i | \(-0.269262\pi\) | ||||
0.663049 | + | 0.748576i | \(0.269262\pi\) | |||||||
\(138\) | 944.754 | 0.582774 | ||||||||
\(139\) | −1747.22 | −1.06617 | −0.533085 | − | 0.846062i | \(-0.678967\pi\) | ||||
−0.533085 | + | 0.846062i | \(0.678967\pi\) | |||||||
\(140\) | −2029.36 | −1.22509 | ||||||||
\(141\) | 1280.62 | 0.764878 | ||||||||
\(142\) | −2176.60 | −1.28631 | ||||||||
\(143\) | 104.302 | 0.0609940 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 4055.02 | 2.32242 | ||||||||
\(146\) | 1257.77 | 0.712973 | ||||||||
\(147\) | 1861.02 | 1.04418 | ||||||||
\(148\) | −336.000 | −0.186615 | ||||||||
\(149\) | −1171.20 | −0.643950 | −0.321975 | − | 0.946748i | \(-0.604347\pi\) | ||||
−0.321975 | + | 0.946748i | \(0.604347\pi\) | |||||||
\(150\) | −853.131 | −0.464386 | ||||||||
\(151\) | −985.810 | −0.531285 | −0.265643 | − | 0.964072i | \(-0.585584\pi\) | ||||
−0.265643 | + | 0.964072i | \(0.585584\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −57.7919 | −0.0305372 | ||||||||
\(154\) | −269.774 | −0.141162 | ||||||||
\(155\) | −5039.47 | −2.61148 | ||||||||
\(156\) | 288.000 | 0.147811 | ||||||||
\(157\) | −653.547 | −0.332221 | −0.166111 | − | 0.986107i | \(-0.553121\pi\) | ||||
−0.166111 | + | 0.986107i | \(0.553121\pi\) | |||||||
\(158\) | −394.112 | −0.198442 | ||||||||
\(159\) | −553.131 | −0.275888 | ||||||||
\(160\) | 523.069 | 0.258451 | ||||||||
\(161\) | −4887.17 | −2.39232 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −3450.41 | −1.65802 | −0.829010 | − | 0.559234i | \(-0.811095\pi\) | ||||
−0.829010 | + | 0.559234i | \(0.811095\pi\) | |||||||
\(164\) | −608.302 | −0.289636 | ||||||||
\(165\) | −213.113 | −0.100551 | ||||||||
\(166\) | −1039.19 | −0.485886 | ||||||||
\(167\) | 1589.96 | 0.736736 | 0.368368 | − | 0.929680i | \(-0.379917\pi\) | ||||
0.368368 | + | 0.929680i | \(0.379917\pi\) | |||||||
\(168\) | −744.905 | −0.342087 | ||||||||
\(169\) | −1621.00 | −0.737824 | ||||||||
\(170\) | −209.925 | −0.0947087 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1926.26 | −0.853931 | ||||||||
\(173\) | −2523.47 | −1.10899 | −0.554497 | − | 0.832186i | \(-0.687089\pi\) | ||||
−0.554497 | + | 0.832186i | \(0.687089\pi\) | |||||||
\(174\) | 1488.45 | 0.648502 | ||||||||
\(175\) | 4413.21 | 1.90633 | ||||||||
\(176\) | 69.5344 | 0.0297804 | ||||||||
\(177\) | −1754.26 | −0.744963 | ||||||||
\(178\) | 1985.96 | 0.836259 | ||||||||
\(179\) | −1086.41 | −0.453644 | −0.226822 | − | 0.973936i | \(-0.572834\pi\) | ||||
−0.226822 | + | 0.973936i | \(0.572834\pi\) | |||||||
\(180\) | −588.453 | −0.243670 | ||||||||
\(181\) | −3353.51 | −1.37715 | −0.688575 | − | 0.725165i | \(-0.741764\pi\) | ||||
−0.688575 | + | 0.725165i | \(0.741764\pi\) | |||||||
\(182\) | −1489.81 | −0.606770 | ||||||||
\(183\) | −874.697 | −0.353330 | ||||||||
\(184\) | 1259.67 | 0.504697 | ||||||||
\(185\) | 1373.06 | 0.545671 | ||||||||
\(186\) | −1849.81 | −0.729219 | ||||||||
\(187\) | −27.9064 | −0.0109129 | ||||||||
\(188\) | 1707.50 | 0.662404 | ||||||||
\(189\) | 838.018 | 0.322523 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2644.86 | −1.00197 | −0.500983 | − | 0.865457i | \(-0.667028\pi\) | ||||
−0.500983 | + | 0.865457i | \(0.667028\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 1440.37 | 0.537204 | 0.268602 | − | 0.963251i | \(-0.413438\pi\) | ||||
0.268602 | + | 0.963251i | \(0.413438\pi\) | |||||||
\(194\) | −2098.11 | −0.776472 | ||||||||
\(195\) | −1176.91 | −0.432205 | ||||||||
\(196\) | 2481.36 | 0.904285 | ||||||||
\(197\) | −1197.37 | −0.433041 | −0.216521 | − | 0.976278i | \(-0.569471\pi\) | ||||
−0.216521 | + | 0.976278i | \(0.569471\pi\) | |||||||
\(198\) | −78.2263 | −0.0280773 | ||||||||
\(199\) | −3012.66 | −1.07318 | −0.536588 | − | 0.843845i | \(-0.680287\pi\) | ||||
−0.536588 | + | 0.843845i | \(0.680287\pi\) | |||||||
\(200\) | −1137.51 | −0.402170 | ||||||||
\(201\) | −1261.36 | −0.442633 | ||||||||
\(202\) | 561.534 | 0.195591 | ||||||||
\(203\) | −7699.69 | −2.66213 | ||||||||
\(204\) | −77.0559 | −0.0264460 | ||||||||
\(205\) | 2485.81 | 0.846910 | ||||||||
\(206\) | 3092.22 | 1.04585 | ||||||||
\(207\) | −1417.13 | −0.475833 | ||||||||
\(208\) | 384.000 | 0.128008 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3044.04 | 1.00028 | ||||||||
\(211\) | 5040.91 | 1.64469 | 0.822346 | − | 0.568987i | \(-0.192665\pi\) | ||||
0.822346 | + | 0.568987i | \(0.192665\pi\) | |||||||
\(212\) | −737.508 | −0.238926 | ||||||||
\(213\) | 3264.91 | 1.05027 | ||||||||
\(214\) | −3168.91 | −1.01225 | ||||||||
\(215\) | 7871.63 | 2.49693 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 9568.98 | 2.99348 | ||||||||
\(218\) | −1206.49 | −0.374835 | ||||||||
\(219\) | −1886.66 | −0.582140 | ||||||||
\(220\) | −284.151 | −0.0870793 | ||||||||
\(221\) | −154.112 | −0.0469080 | ||||||||
\(222\) | 504.000 | 0.152371 | ||||||||
\(223\) | 29.0559 | 0.00872522 | 0.00436261 | − | 0.999990i | \(-0.498611\pi\) | ||||
0.00436261 | + | 0.999990i | \(0.498611\pi\) | |||||||
\(224\) | −993.207 | −0.296256 | ||||||||
\(225\) | 1279.70 | 0.379169 | ||||||||
\(226\) | −1540.07 | −0.453292 | ||||||||
\(227\) | −4940.68 | −1.44460 | −0.722300 | − | 0.691580i | \(-0.756915\pi\) | ||||
−0.722300 | + | 0.691580i | \(0.756915\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2852.36 | −0.823096 | −0.411548 | − | 0.911388i | \(-0.635012\pi\) | ||||
−0.411548 | + | 0.911388i | \(0.635012\pi\) | |||||||
\(230\) | −5147.62 | −1.47576 | ||||||||
\(231\) | 404.661 | 0.115259 | ||||||||
\(232\) | 1984.60 | 0.561619 | ||||||||
\(233\) | −4659.44 | −1.31009 | −0.655043 | − | 0.755591i | \(-0.727350\pi\) | ||||
−0.655043 | + | 0.755591i | \(0.727350\pi\) | |||||||
\(234\) | −432.000 | −0.120687 | ||||||||
\(235\) | −6977.64 | −1.93690 | ||||||||
\(236\) | −2339.02 | −0.645157 | ||||||||
\(237\) | 591.168 | 0.162027 | ||||||||
\(238\) | 398.606 | 0.108562 | ||||||||
\(239\) | 3902.83 | 1.05629 | 0.528145 | − | 0.849154i | \(-0.322888\pi\) | ||||
0.528145 | + | 0.849154i | \(0.322888\pi\) | |||||||
\(240\) | −784.603 | −0.211025 | ||||||||
\(241\) | 5584.53 | 1.49266 | 0.746330 | − | 0.665576i | \(-0.231814\pi\) | ||||
0.746330 | + | 0.665576i | \(0.231814\pi\) | |||||||
\(242\) | 2624.23 | 0.697073 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −1166.26 | −0.305993 | ||||||||
\(245\) | −10140.0 | −2.64417 | ||||||||
\(246\) | 912.453 | 0.236487 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2466.41 | −0.631522 | ||||||||
\(249\) | 1558.79 | 0.396724 | ||||||||
\(250\) | 561.925 | 0.142157 | ||||||||
\(251\) | 1943.56 | 0.488750 | 0.244375 | − | 0.969681i | \(-0.421417\pi\) | ||||
0.244375 | + | 0.969681i | \(0.421417\pi\) | |||||||
\(252\) | 1117.36 | 0.279313 | ||||||||
\(253\) | −684.302 | −0.170046 | ||||||||
\(254\) | −5468.22 | −1.35081 | ||||||||
\(255\) | 314.887 | 0.0773293 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2120.45 | 0.514669 | 0.257335 | − | 0.966322i | \(-0.417156\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417156\pi\) | |||||||
\(258\) | 2889.39 | 0.697232 | ||||||||
\(259\) | −2607.17 | −0.625488 | ||||||||
\(260\) | −1569.21 | −0.374300 | ||||||||
\(261\) | −2232.68 | −0.529499 | ||||||||
\(262\) | 1151.49 | 0.271523 | ||||||||
\(263\) | −5039.09 | −1.18146 | −0.590729 | − | 0.806870i | \(-0.701160\pi\) | ||||
−0.590729 | + | 0.806870i | \(0.701160\pi\) | |||||||
\(264\) | −104.302 | −0.0243156 | ||||||||
\(265\) | 3013.81 | 0.698630 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2978.94 | −0.682802 | ||||||||
\(268\) | −1681.81 | −0.383332 | ||||||||
\(269\) | 5587.09 | 1.26636 | 0.633180 | − | 0.774004i | \(-0.281749\pi\) | ||||
0.633180 | + | 0.774004i | \(0.281749\pi\) | |||||||
\(270\) | 882.679 | 0.198956 | ||||||||
\(271\) | −2707.55 | −0.606907 | −0.303454 | − | 0.952846i | \(-0.598140\pi\) | ||||
−0.303454 | + | 0.952846i | \(0.598140\pi\) | |||||||
\(272\) | −102.741 | −0.0229029 | ||||||||
\(273\) | 2234.72 | 0.495425 | ||||||||
\(274\) | −4252.92 | −0.937693 | ||||||||
\(275\) | 617.938 | 0.135502 | ||||||||
\(276\) | −1889.51 | −0.412083 | ||||||||
\(277\) | −2841.87 | −0.616431 | −0.308216 | − | 0.951317i | \(-0.599732\pi\) | ||||
−0.308216 | + | 0.951317i | \(0.599732\pi\) | |||||||
\(278\) | 3494.45 | 0.753896 | ||||||||
\(279\) | 2774.72 | 0.595404 | ||||||||
\(280\) | 4058.72 | 0.866266 | ||||||||
\(281\) | 2365.13 | 0.502106 | 0.251053 | − | 0.967973i | \(-0.419223\pi\) | ||||
0.251053 | + | 0.967973i | \(0.419223\pi\) | |||||||
\(282\) | −2561.24 | −0.540850 | ||||||||
\(283\) | 3582.43 | 0.752486 | 0.376243 | − | 0.926521i | \(-0.377216\pi\) | ||||
0.376243 | + | 0.926521i | \(0.377216\pi\) | |||||||
\(284\) | 4353.21 | 0.909561 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −208.603 | −0.0431293 | ||||||||
\(287\) | −4720.07 | −0.970791 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −4871.77 | −0.991607 | ||||||||
\(290\) | −8110.03 | −1.64220 | ||||||||
\(291\) | 3147.17 | 0.633987 | ||||||||
\(292\) | −2515.55 | −0.504148 | ||||||||
\(293\) | 2840.45 | 0.566351 | 0.283175 | − | 0.959068i | \(-0.408612\pi\) | ||||
0.283175 | + | 0.959068i | \(0.408612\pi\) | |||||||
\(294\) | −3722.04 | −0.738345 | ||||||||
\(295\) | 9558.34 | 1.88647 | ||||||||
\(296\) | 672.000 | 0.131957 | ||||||||
\(297\) | 117.339 | 0.0229250 | ||||||||
\(298\) | 2342.40 | 0.455342 | ||||||||
\(299\) | −3779.02 | −0.730924 | ||||||||
\(300\) | 1706.26 | 0.328370 | ||||||||
\(301\) | −14946.7 | −2.86217 | ||||||||
\(302\) | 1971.62 | 0.375675 | ||||||||
\(303\) | −842.302 | −0.159700 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4765.90 | 0.894737 | ||||||||
\(306\) | 115.584 | 0.0215931 | ||||||||
\(307\) | −9295.16 | −1.72802 | −0.864011 | − | 0.503472i | \(-0.832056\pi\) | ||||
−0.864011 | + | 0.503472i | \(0.832056\pi\) | |||||||
\(308\) | 539.547 | 0.0998168 | ||||||||
\(309\) | −4638.34 | −0.853934 | ||||||||
\(310\) | 10078.9 | 1.84660 | ||||||||
\(311\) | 1866.72 | 0.340360 | 0.170180 | − | 0.985413i | \(-0.445565\pi\) | ||||
0.170180 | + | 0.985413i | \(0.445565\pi\) | |||||||
\(312\) | −576.000 | −0.104518 | ||||||||
\(313\) | −5516.34 | −0.996173 | −0.498086 | − | 0.867127i | \(-0.665964\pi\) | ||||
−0.498086 | + | 0.867127i | \(0.665964\pi\) | |||||||
\(314\) | 1307.09 | 0.234916 | ||||||||
\(315\) | −4566.05 | −0.816724 | ||||||||
\(316\) | 788.223 | 0.140320 | ||||||||
\(317\) | 5247.69 | 0.929778 | 0.464889 | − | 0.885369i | \(-0.346094\pi\) | ||||
0.464889 | + | 0.885369i | \(0.346094\pi\) | |||||||
\(318\) | 1106.26 | 0.195082 | ||||||||
\(319\) | −1078.11 | −0.189225 | ||||||||
\(320\) | −1046.14 | −0.182753 | ||||||||
\(321\) | 4753.36 | 0.826500 | ||||||||
\(322\) | 9774.34 | 1.69162 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 3412.53 | 0.582439 | ||||||||
\(326\) | 6900.83 | 1.17240 | ||||||||
\(327\) | 1809.74 | 0.306051 | ||||||||
\(328\) | 1216.60 | 0.204804 | ||||||||
\(329\) | 13249.2 | 2.22022 | ||||||||
\(330\) | 426.226 | 0.0710999 | ||||||||
\(331\) | 3649.89 | 0.606091 | 0.303045 | − | 0.952976i | \(-0.401997\pi\) | ||||
0.303045 | + | 0.952976i | \(0.401997\pi\) | |||||||
\(332\) | 2078.39 | 0.343573 | ||||||||
\(333\) | −756.000 | −0.124410 | ||||||||
\(334\) | −3179.92 | −0.520951 | ||||||||
\(335\) | 6872.68 | 1.12088 | ||||||||
\(336\) | 1489.81 | 0.241892 | ||||||||
\(337\) | −5598.04 | −0.904880 | −0.452440 | − | 0.891795i | \(-0.649446\pi\) | ||||
−0.452440 | + | 0.891795i | \(0.649446\pi\) | |||||||
\(338\) | 3242.00 | 0.521721 | ||||||||
\(339\) | 2310.11 | 0.370112 | ||||||||
\(340\) | 419.849 | 0.0669692 | ||||||||
\(341\) | 1339.85 | 0.212777 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8607.98 | 1.35506 | ||||||||
\(344\) | 3852.53 | 0.603820 | ||||||||
\(345\) | 7721.43 | 1.20495 | ||||||||
\(346\) | 5046.94 | 0.784177 | ||||||||
\(347\) | −12868.1 | −1.99077 | −0.995386 | − | 0.0959483i | \(-0.969412\pi\) | ||||
−0.995386 | + | 0.0959483i | \(0.969412\pi\) | |||||||
\(348\) | −2976.91 | −0.458560 | ||||||||
\(349\) | −1940.05 | −0.297561 | −0.148780 | − | 0.988870i | \(-0.547535\pi\) | ||||
−0.148780 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(350\) | −8826.41 | −1.34798 | ||||||||
\(351\) | 648.000 | 0.0985404 | ||||||||
\(352\) | −139.069 | −0.0210579 | ||||||||
\(353\) | 596.544 | 0.0899457 | 0.0449728 | − | 0.998988i | \(-0.485680\pi\) | ||||
0.0449728 | + | 0.998988i | \(0.485680\pi\) | |||||||
\(354\) | 3508.53 | 0.526768 | ||||||||
\(355\) | −17789.3 | −2.65960 | ||||||||
\(356\) | −3971.92 | −0.591324 | ||||||||
\(357\) | −597.909 | −0.0886407 | ||||||||
\(358\) | 2172.83 | 0.320775 | ||||||||
\(359\) | −2921.84 | −0.429552 | −0.214776 | − | 0.976663i | \(-0.568902\pi\) | ||||
−0.214776 | + | 0.976663i | \(0.568902\pi\) | |||||||
\(360\) | 1176.91 | 0.172301 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 6707.02 | 0.973793 | ||||||||
\(363\) | −3936.34 | −0.569158 | ||||||||
\(364\) | 2979.62 | 0.429051 | ||||||||
\(365\) | 10279.7 | 1.47415 | ||||||||
\(366\) | 1749.39 | 0.249842 | ||||||||
\(367\) | −4450.79 | −0.633050 | −0.316525 | − | 0.948584i | \(-0.602516\pi\) | ||||
−0.316525 | + | 0.948584i | \(0.602516\pi\) | |||||||
\(368\) | −2519.34 | −0.356875 | ||||||||
\(369\) | −1368.68 | −0.193091 | ||||||||
\(370\) | −2746.11 | −0.385847 | ||||||||
\(371\) | −5722.64 | −0.800822 | ||||||||
\(372\) | 3699.62 | 0.515635 | ||||||||
\(373\) | −12624.1 | −1.75242 | −0.876211 | − | 0.481928i | \(-0.839937\pi\) | ||||
−0.876211 | + | 0.481928i | \(0.839937\pi\) | |||||||
\(374\) | 55.8129 | 0.00771662 | ||||||||
\(375\) | −842.887 | −0.116071 | ||||||||
\(376\) | −3414.99 | −0.468390 | ||||||||
\(377\) | −5953.81 | −0.813360 | ||||||||
\(378\) | −1676.04 | −0.228058 | ||||||||
\(379\) | −11622.9 | −1.57528 | −0.787639 | − | 0.616137i | \(-0.788697\pi\) | ||||
−0.787639 | + | 0.616137i | \(0.788697\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8202.34 | 1.10294 | ||||||||
\(382\) | 5289.72 | 0.708497 | ||||||||
\(383\) | −9928.82 | −1.32465 | −0.662323 | − | 0.749219i | \(-0.730429\pi\) | ||||
−0.662323 | + | 0.749219i | \(0.730429\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | −2204.85 | −0.291869 | ||||||||
\(386\) | −2880.75 | −0.379861 | ||||||||
\(387\) | −4334.09 | −0.569287 | ||||||||
\(388\) | 4196.22 | 0.549049 | ||||||||
\(389\) | 7151.20 | 0.932082 | 0.466041 | − | 0.884763i | \(-0.345680\pi\) | ||||
0.466041 | + | 0.884763i | \(0.345680\pi\) | |||||||
\(390\) | 2353.81 | 0.305615 | ||||||||
\(391\) | 1011.09 | 0.130776 | ||||||||
\(392\) | −4962.72 | −0.639426 | ||||||||
\(393\) | −1727.23 | −0.221697 | ||||||||
\(394\) | 2394.74 | 0.306206 | ||||||||
\(395\) | −3221.06 | −0.410301 | ||||||||
\(396\) | 156.453 | 0.0198536 | ||||||||
\(397\) | 12822.1 | 1.62097 | 0.810483 | − | 0.585762i | \(-0.199205\pi\) | ||||
0.810483 | + | 0.585762i | \(0.199205\pi\) | |||||||
\(398\) | 6025.32 | 0.758849 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2275.02 | 0.284377 | ||||||||
\(401\) | −97.5838 | −0.0121524 | −0.00607619 | − | 0.999982i | \(-0.501934\pi\) | ||||
−0.00607619 | + | 0.999982i | \(0.501934\pi\) | |||||||
\(402\) | 2522.72 | 0.312989 | ||||||||
\(403\) | 7399.24 | 0.914597 | ||||||||
\(404\) | −1123.07 | −0.138304 | ||||||||
\(405\) | −1324.02 | −0.162447 | ||||||||
\(406\) | 15399.4 | 1.88241 | ||||||||
\(407\) | −365.056 | −0.0444598 | ||||||||
\(408\) | 154.112 | 0.0187002 | ||||||||
\(409\) | 2995.55 | 0.362153 | 0.181076 | − | 0.983469i | \(-0.442042\pi\) | ||||
0.181076 | + | 0.983469i | \(0.442042\pi\) | |||||||
\(410\) | −4971.62 | −0.598856 | ||||||||
\(411\) | 6379.37 | 0.765623 | ||||||||
\(412\) | −6184.45 | −0.739529 | ||||||||
\(413\) | −18149.4 | −2.16241 | ||||||||
\(414\) | 2834.26 | 0.336465 | ||||||||
\(415\) | −8493.28 | −1.00462 | ||||||||
\(416\) | −768.000 | −0.0905151 | ||||||||
\(417\) | −5241.67 | −0.615554 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1153.01 | 0.134434 | 0.0672172 | − | 0.997738i | \(-0.478588\pi\) | ||||
0.0672172 | + | 0.997738i | \(0.478588\pi\) | |||||||
\(420\) | −6088.07 | −0.707304 | ||||||||
\(421\) | 3850.49 | 0.445751 | 0.222876 | − | 0.974847i | \(-0.428456\pi\) | ||||
0.222876 | + | 0.974847i | \(0.428456\pi\) | |||||||
\(422\) | −10081.8 | −1.16297 | ||||||||
\(423\) | 3841.86 | 0.441602 | ||||||||
\(424\) | 1475.02 | 0.168946 | ||||||||
\(425\) | −913.038 | −0.104209 | ||||||||
\(426\) | −6529.81 | −0.742653 | ||||||||
\(427\) | −9049.53 | −1.02561 | ||||||||
\(428\) | 6337.81 | 0.715770 | ||||||||
\(429\) | 312.905 | 0.0352149 | ||||||||
\(430\) | −15743.3 | −1.76560 | ||||||||
\(431\) | 5049.96 | 0.564380 | 0.282190 | − | 0.959359i | \(-0.408939\pi\) | ||||
0.282190 | + | 0.959359i | \(0.408939\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | −9340.74 | −1.03669 | −0.518346 | − | 0.855171i | \(-0.673452\pi\) | ||||
−0.518346 | + | 0.855171i | \(0.673452\pi\) | |||||||
\(434\) | −19138.0 | −2.11671 | ||||||||
\(435\) | 12165.1 | 1.34085 | ||||||||
\(436\) | 2412.98 | 0.265048 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 3773.32 | 0.411635 | ||||||||
\(439\) | −6445.04 | −0.700695 | −0.350348 | − | 0.936620i | \(-0.613937\pi\) | ||||
−0.350348 | + | 0.936620i | \(0.613937\pi\) | |||||||
\(440\) | 568.302 | 0.0615744 | ||||||||
\(441\) | 5583.05 | 0.602857 | ||||||||
\(442\) | 308.223 | 0.0331690 | ||||||||
\(443\) | −8463.66 | −0.907721 | −0.453861 | − | 0.891073i | \(-0.649954\pi\) | ||||
−0.453861 | + | 0.891073i | \(0.649954\pi\) | |||||||
\(444\) | −1008.00 | −0.107742 | ||||||||
\(445\) | 16231.2 | 1.72906 | ||||||||
\(446\) | −58.1117 | −0.00616966 | ||||||||
\(447\) | −3513.60 | −0.371785 | ||||||||
\(448\) | 1986.41 | 0.209485 | ||||||||
\(449\) | −1737.96 | −0.182672 | −0.0913358 | − | 0.995820i | \(-0.529114\pi\) | ||||
−0.0913358 | + | 0.995820i | \(0.529114\pi\) | |||||||
\(450\) | −2559.39 | −0.268113 | ||||||||
\(451\) | −660.905 | −0.0690040 | ||||||||
\(452\) | 3080.15 | 0.320526 | ||||||||
\(453\) | −2957.43 | −0.306738 | ||||||||
\(454\) | 9881.35 | 1.02149 | ||||||||
\(455\) | −12176.1 | −1.25456 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17723.3 | 1.81414 | 0.907069 | − | 0.420983i | \(-0.138315\pi\) | ||||
0.907069 | + | 0.420983i | \(0.138315\pi\) | |||||||
\(458\) | 5704.71 | 0.582017 | ||||||||
\(459\) | −173.376 | −0.0176307 | ||||||||
\(460\) | 10295.2 | 1.04352 | ||||||||
\(461\) | 4851.58 | 0.490153 | 0.245077 | − | 0.969504i | \(-0.421187\pi\) | ||||
0.245077 | + | 0.969504i | \(0.421187\pi\) | |||||||
\(462\) | −809.321 | −0.0815001 | ||||||||
\(463\) | −10677.1 | −1.07173 | −0.535863 | − | 0.844305i | \(-0.680014\pi\) | ||||
−0.535863 | + | 0.844305i | \(0.680014\pi\) | |||||||
\(464\) | −3969.21 | −0.397125 | ||||||||
\(465\) | −15118.4 | −1.50774 | ||||||||
\(466\) | 9318.88 | 0.926371 | ||||||||
\(467\) | −8464.27 | −0.838714 | −0.419357 | − | 0.907821i | \(-0.637744\pi\) | ||||
−0.419357 | + | 0.907821i | \(0.637744\pi\) | |||||||
\(468\) | 864.000 | 0.0853385 | ||||||||
\(469\) | −13049.9 | −1.28483 | ||||||||
\(470\) | 13955.3 | 1.36959 | ||||||||
\(471\) | −1960.64 | −0.191808 | ||||||||
\(472\) | 4678.03 | 0.456195 | ||||||||
\(473\) | −2092.84 | −0.203443 | ||||||||
\(474\) | −1182.34 | −0.114571 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −797.212 | −0.0767651 | ||||||||
\(477\) | −1659.39 | −0.159284 | ||||||||
\(478\) | −7805.66 | −0.746910 | ||||||||
\(479\) | −8449.99 | −0.806033 | −0.403017 | − | 0.915193i | \(-0.632038\pi\) | ||||
−0.403017 | + | 0.915193i | \(0.632038\pi\) | |||||||
\(480\) | 1569.21 | 0.149217 | ||||||||
\(481\) | −2016.00 | −0.191105 | ||||||||
\(482\) | −11169.1 | −1.05547 | ||||||||
\(483\) | −14661.5 | −1.38120 | ||||||||
\(484\) | −5248.45 | −0.492905 | ||||||||
\(485\) | −17147.8 | −1.60544 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −7855.10 | −0.730901 | −0.365450 | − | 0.930831i | \(-0.619085\pi\) | ||||
−0.365450 | + | 0.930831i | \(0.619085\pi\) | |||||||
\(488\) | 2332.53 | 0.216370 | ||||||||
\(489\) | −10351.2 | −0.957258 | ||||||||
\(490\) | 20280.0 | 1.86971 | ||||||||
\(491\) | −5341.38 | −0.490943 | −0.245472 | − | 0.969404i | \(-0.578943\pi\) | ||||
−0.245472 | + | 0.969404i | \(0.578943\pi\) | |||||||
\(492\) | −1824.91 | −0.167222 | ||||||||
\(493\) | 1592.97 | 0.145525 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −639.339 | −0.0580529 | ||||||||
\(496\) | 4932.83 | 0.446553 | ||||||||
\(497\) | 33778.4 | 3.04863 | ||||||||
\(498\) | −3117.58 | −0.280526 | ||||||||
\(499\) | −3157.08 | −0.283227 | −0.141613 | − | 0.989922i | \(-0.545229\pi\) | ||||
−0.141613 | + | 0.989922i | \(0.545229\pi\) | |||||||
\(500\) | −1123.85 | −0.100520 | ||||||||
\(501\) | 4769.88 | 0.425355 | ||||||||
\(502\) | −3887.11 | −0.345598 | ||||||||
\(503\) | −16111.5 | −1.42818 | −0.714092 | − | 0.700052i | \(-0.753160\pi\) | ||||
−0.714092 | + | 0.700052i | \(0.753160\pi\) | |||||||
\(504\) | −2234.72 | −0.197504 | ||||||||
\(505\) | 4589.39 | 0.404407 | ||||||||
\(506\) | 1368.60 | 0.120241 | ||||||||
\(507\) | −4863.00 | −0.425983 | ||||||||
\(508\) | 10936.4 | 0.955170 | ||||||||
\(509\) | −15652.4 | −1.36302 | −0.681512 | − | 0.731807i | \(-0.738677\pi\) | ||||
−0.681512 | + | 0.731807i | \(0.738677\pi\) | |||||||
\(510\) | −629.774 | −0.0546801 | ||||||||
\(511\) | −19519.2 | −1.68978 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4240.90 | −0.363926 | ||||||||
\(515\) | 25272.6 | 2.16241 | ||||||||
\(516\) | −5778.79 | −0.493017 | ||||||||
\(517\) | 1855.15 | 0.157813 | ||||||||
\(518\) | 5214.34 | 0.442287 | ||||||||
\(519\) | −7570.42 | −0.640278 | ||||||||
\(520\) | 3138.41 | 0.264670 | ||||||||
\(521\) | 6090.64 | 0.512161 | 0.256080 | − | 0.966655i | \(-0.417569\pi\) | ||||
0.256080 | + | 0.966655i | \(0.417569\pi\) | |||||||
\(522\) | 4465.36 | 0.374413 | ||||||||
\(523\) | −4300.68 | −0.359571 | −0.179786 | − | 0.983706i | \(-0.557540\pi\) | ||||
−0.179786 | + | 0.983706i | \(0.557540\pi\) | |||||||
\(524\) | −2302.97 | −0.191996 | ||||||||
\(525\) | 13239.6 | 1.10062 | ||||||||
\(526\) | 10078.2 | 0.835417 | ||||||||
\(527\) | −1979.70 | −0.163638 | ||||||||
\(528\) | 208.603 | 0.0171937 | ||||||||
\(529\) | 12626.3 | 1.03775 | ||||||||
\(530\) | −6027.62 | −0.494006 | ||||||||
\(531\) | −5262.79 | −0.430105 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3649.81 | −0.296606 | ||||||||
\(534\) | 5957.88 | 0.482814 | ||||||||
\(535\) | −25899.3 | −2.09294 | ||||||||
\(536\) | 3363.62 | 0.271056 | ||||||||
\(537\) | −3259.24 | −0.261912 | ||||||||
\(538\) | −11174.2 | −0.895452 | ||||||||
\(539\) | 2695.93 | 0.215440 | ||||||||
\(540\) | −1765.36 | −0.140683 | ||||||||
\(541\) | −7444.62 | −0.591625 | −0.295812 | − | 0.955246i | \(-0.595590\pi\) | ||||
−0.295812 | + | 0.955246i | \(0.595590\pi\) | |||||||
\(542\) | 5415.09 | 0.429148 | ||||||||
\(543\) | −10060.5 | −0.795098 | ||||||||
\(544\) | 205.482 | 0.0161948 | ||||||||
\(545\) | −9860.60 | −0.775012 | ||||||||
\(546\) | −4469.43 | −0.350319 | ||||||||
\(547\) | 10139.6 | 0.792576 | 0.396288 | − | 0.918126i | \(-0.370298\pi\) | ||||
0.396288 | + | 0.918126i | \(0.370298\pi\) | |||||||
\(548\) | 8505.83 | 0.663049 | ||||||||
\(549\) | −2624.09 | −0.203995 | ||||||||
\(550\) | −1235.88 | −0.0958144 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3779.02 | 0.291387 | ||||||||
\(553\) | 6116.16 | 0.470318 | ||||||||
\(554\) | 5683.74 | 0.435883 | ||||||||
\(555\) | 4119.17 | 0.315043 | ||||||||
\(556\) | −6988.90 | −0.533085 | ||||||||
\(557\) | 17922.0 | 1.36334 | 0.681669 | − | 0.731661i | \(-0.261254\pi\) | ||||
0.681669 | + | 0.731661i | \(0.261254\pi\) | |||||||
\(558\) | −5549.43 | −0.421015 | ||||||||
\(559\) | −11557.6 | −0.874478 | ||||||||
\(560\) | −8117.43 | −0.612543 | ||||||||
\(561\) | −83.7193 | −0.00630059 | ||||||||
\(562\) | −4730.26 | −0.355043 | ||||||||
\(563\) | 1620.91 | 0.121337 | 0.0606687 | − | 0.998158i | \(-0.480677\pi\) | ||||
0.0606687 | + | 0.998158i | \(0.480677\pi\) | |||||||
\(564\) | 5122.49 | 0.382439 | ||||||||
\(565\) | −12586.9 | −0.937233 | ||||||||
\(566\) | −7164.87 | −0.532088 | ||||||||
\(567\) | 2514.05 | 0.186209 | ||||||||
\(568\) | −8706.41 | −0.643157 | ||||||||
\(569\) | 4613.42 | 0.339903 | 0.169951 | − | 0.985452i | \(-0.445639\pi\) | ||||
0.169951 | + | 0.985452i | \(0.445639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6112.45 | 0.447983 | 0.223991 | − | 0.974591i | \(-0.428091\pi\) | ||||
0.223991 | + | 0.974591i | \(0.428091\pi\) | |||||||
\(572\) | 417.207 | 0.0304970 | ||||||||
\(573\) | −7934.58 | −0.578485 | ||||||||
\(574\) | 9440.15 | 0.686453 | ||||||||
\(575\) | −22388.9 | −1.62379 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −9098.80 | −0.656478 | −0.328239 | − | 0.944595i | \(-0.606455\pi\) | ||||
−0.328239 | + | 0.944595i | \(0.606455\pi\) | |||||||
\(578\) | 9743.53 | 0.701172 | ||||||||
\(579\) | 4321.12 | 0.310155 | ||||||||
\(580\) | 16220.1 | 1.16121 | ||||||||
\(581\) | 16127.1 | 1.15157 | ||||||||
\(582\) | −6294.34 | −0.448297 | ||||||||
\(583\) | −801.285 | −0.0569225 | ||||||||
\(584\) | 5031.09 | 0.356487 | ||||||||
\(585\) | −3530.72 | −0.249534 | ||||||||
\(586\) | −5680.90 | −0.400471 | ||||||||
\(587\) | −402.016 | −0.0282675 | −0.0141337 | − | 0.999900i | \(-0.504499\pi\) | ||||
−0.0141337 | + | 0.999900i | \(0.504499\pi\) | |||||||
\(588\) | 7444.07 | 0.522089 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −19116.7 | −1.33393 | ||||||||
\(591\) | −3592.11 | −0.250016 | ||||||||
\(592\) | −1344.00 | −0.0933075 | ||||||||
\(593\) | −11044.5 | −0.764831 | −0.382415 | − | 0.923991i | \(-0.624908\pi\) | ||||
−0.382415 | + | 0.923991i | \(0.624908\pi\) | |||||||
\(594\) | −234.679 | −0.0162104 | ||||||||
\(595\) | 3257.79 | 0.224464 | ||||||||
\(596\) | −4684.81 | −0.321975 | ||||||||
\(597\) | −9037.98 | −0.619598 | ||||||||
\(598\) | 7558.03 | 0.516841 | ||||||||
\(599\) | −12554.3 | −0.856355 | −0.428177 | − | 0.903695i | \(-0.640844\pi\) | ||||
−0.428177 | + | 0.903695i | \(0.640844\pi\) | |||||||
\(600\) | −3412.53 | −0.232193 | ||||||||
\(601\) | 2024.89 | 0.137433 | 0.0687164 | − | 0.997636i | \(-0.478110\pi\) | ||||
0.0687164 | + | 0.997636i | \(0.478110\pi\) | |||||||
\(602\) | 29893.4 | 2.02386 | ||||||||
\(603\) | −3784.07 | −0.255554 | ||||||||
\(604\) | −3943.24 | −0.265643 | ||||||||
\(605\) | 21447.7 | 1.44128 | ||||||||
\(606\) | 1684.60 | 0.112925 | ||||||||
\(607\) | −23449.2 | −1.56800 | −0.783998 | − | 0.620763i | \(-0.786823\pi\) | ||||
−0.783998 | + | 0.620763i | \(0.786823\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23099.1 | −1.53698 | ||||||||
\(610\) | −9531.81 | −0.632675 | ||||||||
\(611\) | 10245.0 | 0.678342 | ||||||||
\(612\) | −231.168 | −0.0152686 | ||||||||
\(613\) | 27561.9 | 1.81601 | 0.908005 | − | 0.418958i | \(-0.137605\pi\) | ||||
0.908005 | + | 0.418958i | \(0.137605\pi\) | |||||||
\(614\) | 18590.3 | 1.22190 | ||||||||
\(615\) | 7457.43 | 0.488964 | ||||||||
\(616\) | −1079.09 | −0.0705811 | ||||||||
\(617\) | 12506.6 | 0.816040 | 0.408020 | − | 0.912973i | \(-0.366219\pi\) | ||||
0.408020 | + | 0.912973i | \(0.366219\pi\) | |||||||
\(618\) | 9276.67 | 0.603823 | ||||||||
\(619\) | 5823.54 | 0.378139 | 0.189069 | − | 0.981964i | \(-0.439453\pi\) | ||||
0.189069 | + | 0.981964i | \(0.439453\pi\) | |||||||
\(620\) | −20157.9 | −1.30574 | ||||||||
\(621\) | −4251.39 | −0.274722 | ||||||||
\(622\) | −3733.43 | −0.240671 | ||||||||
\(623\) | −30819.8 | −1.98198 | ||||||||
\(624\) | 1152.00 | 0.0739053 | ||||||||
\(625\) | −13181.0 | −0.843583 | ||||||||
\(626\) | 11032.7 | 0.704400 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2614.19 | −0.166111 | ||||||||
\(629\) | 539.391 | 0.0341923 | ||||||||
\(630\) | 9132.11 | 0.577511 | ||||||||
\(631\) | −17701.4 | −1.11677 | −0.558385 | − | 0.829582i | \(-0.688579\pi\) | ||||
−0.558385 | + | 0.829582i | \(0.688579\pi\) | |||||||
\(632\) | −1576.45 | −0.0992210 | ||||||||
\(633\) | 15122.7 | 0.949564 | ||||||||
\(634\) | −10495.4 | −0.657452 | ||||||||
\(635\) | −44691.5 | −2.79296 | ||||||||
\(636\) | −2212.53 | −0.137944 | ||||||||
\(637\) | 14888.1 | 0.926044 | ||||||||
\(638\) | 2156.22 | 0.133802 | ||||||||
\(639\) | 9794.72 | 0.606374 | ||||||||
\(640\) | 2092.28 | 0.129226 | ||||||||
\(641\) | −8093.73 | −0.498726 | −0.249363 | − | 0.968410i | \(-0.580221\pi\) | ||||
−0.249363 | + | 0.968410i | \(0.580221\pi\) | |||||||
\(642\) | −9506.72 | −0.584424 | ||||||||
\(643\) | 3232.10 | 0.198229 | 0.0991147 | − | 0.995076i | \(-0.468399\pi\) | ||||
0.0991147 | + | 0.995076i | \(0.468399\pi\) | |||||||
\(644\) | −19548.7 | −1.19616 | ||||||||
\(645\) | 23614.9 | 1.44160 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27741.4 | −1.68567 | −0.842835 | − | 0.538172i | \(-0.819115\pi\) | ||||
−0.842835 | + | 0.538172i | \(0.819115\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | −2541.28 | −0.153704 | ||||||||
\(650\) | −6825.05 | −0.411847 | ||||||||
\(651\) | 28706.9 | 1.72828 | ||||||||
\(652\) | −13801.7 | −0.829010 | ||||||||
\(653\) | −25073.6 | −1.50261 | −0.751307 | − | 0.659953i | \(-0.770576\pi\) | ||||
−0.751307 | + | 0.659953i | \(0.770576\pi\) | |||||||
\(654\) | −3619.47 | −0.216411 | ||||||||
\(655\) | 9411.03 | 0.561404 | ||||||||
\(656\) | −2433.21 | −0.144818 | ||||||||
\(657\) | −5659.98 | −0.336099 | ||||||||
\(658\) | −26498.4 | −1.56993 | ||||||||
\(659\) | 7758.63 | 0.458624 | 0.229312 | − | 0.973353i | \(-0.426352\pi\) | ||||
0.229312 | + | 0.973353i | \(0.426352\pi\) | |||||||
\(660\) | −852.453 | −0.0502753 | ||||||||
\(661\) | 24560.3 | 1.44521 | 0.722605 | − | 0.691261i | \(-0.242944\pi\) | ||||
0.722605 | + | 0.691261i | \(0.242944\pi\) | |||||||
\(662\) | −7299.78 | −0.428571 | ||||||||
\(663\) | −462.335 | −0.0270824 | ||||||||
\(664\) | −4156.77 | −0.242943 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1512.00 | 0.0879712 | ||||||||
\(667\) | 39061.7 | 2.26758 | ||||||||
\(668\) | 6359.84 | 0.368368 | ||||||||
\(669\) | 87.1676 | 0.00503751 | ||||||||
\(670\) | −13745.4 | −0.792581 | ||||||||
\(671\) | −1267.12 | −0.0729008 | ||||||||
\(672\) | −2979.62 | −0.171044 | ||||||||
\(673\) | 24146.9 | 1.38305 | 0.691526 | − | 0.722352i | \(-0.256939\pi\) | ||||
0.691526 | + | 0.722352i | \(0.256939\pi\) | |||||||
\(674\) | 11196.1 | 0.639847 | ||||||||
\(675\) | 3839.09 | 0.218914 | ||||||||
\(676\) | −6484.00 | −0.368912 | ||||||||
\(677\) | 2559.33 | 0.145293 | 0.0726463 | − | 0.997358i | \(-0.476856\pi\) | ||||
0.0726463 | + | 0.997358i | \(0.476856\pi\) | |||||||
\(678\) | −4620.22 | −0.261709 | ||||||||
\(679\) | 32560.3 | 1.84028 | ||||||||
\(680\) | −839.698 | −0.0473544 | ||||||||
\(681\) | −14822.0 | −0.834040 | ||||||||
\(682\) | −2679.70 | −0.150456 | ||||||||
\(683\) | 21797.7 | 1.22118 | 0.610591 | − | 0.791946i | \(-0.290932\pi\) | ||||
0.610591 | + | 0.791946i | \(0.290932\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34758.9 | −1.93879 | ||||||||
\(686\) | −17216.0 | −0.958175 | ||||||||
\(687\) | −8557.07 | −0.475215 | ||||||||
\(688\) | −7705.05 | −0.426966 | ||||||||
\(689\) | −4425.05 | −0.244675 | ||||||||
\(690\) | −15442.9 | −0.852028 | ||||||||
\(691\) | −8254.22 | −0.454421 | −0.227211 | − | 0.973846i | \(-0.572961\pi\) | ||||
−0.227211 | + | 0.973846i | \(0.572961\pi\) | |||||||
\(692\) | −10093.9 | −0.554497 | ||||||||
\(693\) | 1213.98 | 0.0665445 | ||||||||
\(694\) | 25736.3 | 1.40769 | ||||||||
\(695\) | 28560.0 | 1.55876 | ||||||||
\(696\) | 5953.81 | 0.324251 | ||||||||
\(697\) | 976.525 | 0.0530682 | ||||||||
\(698\) | 3880.11 | 0.210407 | ||||||||
\(699\) | −13978.3 | −0.756379 | ||||||||
\(700\) | 17652.8 | 0.953163 | ||||||||
\(701\) | −31060.9 | −1.67354 | −0.836771 | − | 0.547553i | \(-0.815559\pi\) | ||||
−0.836771 | + | 0.547553i | \(0.815559\pi\) | |||||||
\(702\) | −1296.00 | −0.0696786 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 278.138 | 0.0148902 | ||||||||
\(705\) | −20932.9 | −1.11827 | ||||||||
\(706\) | −1193.09 | −0.0636012 | ||||||||
\(707\) | −8714.37 | −0.463561 | ||||||||
\(708\) | −7017.05 | −0.372481 | ||||||||
\(709\) | −15942.7 | −0.844488 | −0.422244 | − | 0.906482i | \(-0.638758\pi\) | ||||
−0.422244 | + | 0.906482i | \(0.638758\pi\) | |||||||
\(710\) | 35578.5 | 1.88062 | ||||||||
\(711\) | 1773.50 | 0.0935465 | ||||||||
\(712\) | 7943.84 | 0.418129 | ||||||||
\(713\) | −48544.9 | −2.54982 | ||||||||
\(714\) | 1195.82 | 0.0626784 | ||||||||
\(715\) | −1704.91 | −0.0891746 | ||||||||
\(716\) | −4345.65 | −0.226822 | ||||||||
\(717\) | 11708.5 | 0.609849 | ||||||||
\(718\) | 5843.69 | 0.303739 | ||||||||
\(719\) | 34289.0 | 1.77853 | 0.889265 | − | 0.457393i | \(-0.151217\pi\) | ||||
0.889265 | + | 0.457393i | \(0.151217\pi\) | |||||||
\(720\) | −2353.81 | −0.121835 | ||||||||
\(721\) | −47987.8 | −2.47872 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16753.6 | 0.861787 | ||||||||
\(724\) | −13414.0 | −0.688575 | ||||||||
\(725\) | −35273.5 | −1.80693 | ||||||||
\(726\) | 7872.68 | 0.402455 | ||||||||
\(727\) | −11249.9 | −0.573914 | −0.286957 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286957 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(728\) | −5959.24 | −0.303385 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −20559.4 | −1.04238 | ||||||||
\(731\) | 3092.29 | 0.156460 | ||||||||
\(732\) | −3498.79 | −0.176665 | ||||||||
\(733\) | 163.883 | 0.00825804 | 0.00412902 | − | 0.999991i | \(-0.498686\pi\) | ||||
0.00412902 | + | 0.999991i | \(0.498686\pi\) | |||||||
\(734\) | 8901.58 | 0.447634 | ||||||||
\(735\) | −30420.0 | −1.52661 | ||||||||
\(736\) | 5038.69 | 0.252349 | ||||||||
\(737\) | −1827.25 | −0.0913263 | ||||||||
\(738\) | 2737.36 | 0.136536 | ||||||||
\(739\) | 21950.5 | 1.09264 | 0.546321 | − | 0.837576i | \(-0.316028\pi\) | ||||
0.546321 | + | 0.837576i | \(0.316028\pi\) | |||||||
\(740\) | 5492.22 | 0.272835 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11445.3 | 0.566266 | ||||||||
\(743\) | 1194.51 | 0.0589802 | 0.0294901 | − | 0.999565i | \(-0.490612\pi\) | ||||
0.0294901 | + | 0.999565i | \(0.490612\pi\) | |||||||
\(744\) | −7399.24 | −0.364609 | ||||||||
\(745\) | 19144.3 | 0.941469 | ||||||||
\(746\) | 25248.3 | 1.23915 | ||||||||
\(747\) | 4676.37 | 0.229049 | ||||||||
\(748\) | −111.626 | −0.00545647 | ||||||||
\(749\) | 49177.8 | 2.39909 | ||||||||
\(750\) | 1685.77 | 0.0820743 | ||||||||
\(751\) | −15628.2 | −0.759363 | −0.379681 | − | 0.925117i | \(-0.623966\pi\) | ||||
−0.379681 | + | 0.925117i | \(0.623966\pi\) | |||||||
\(752\) | 6829.98 | 0.331202 | ||||||||
\(753\) | 5830.67 | 0.282180 | ||||||||
\(754\) | 11907.6 | 0.575133 | ||||||||
\(755\) | 16114.0 | 0.776751 | ||||||||
\(756\) | 3352.07 | 0.161262 | ||||||||
\(757\) | 11865.5 | 0.569695 | 0.284847 | − | 0.958573i | \(-0.408057\pi\) | ||||
0.284847 | + | 0.958573i | \(0.408057\pi\) | |||||||
\(758\) | 23245.9 | 1.11389 | ||||||||
\(759\) | −2052.91 | −0.0981762 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15761.0 | 0.750768 | 0.375384 | − | 0.926869i | \(-0.377511\pi\) | ||||
0.375384 | + | 0.926869i | \(0.377511\pi\) | |||||||
\(762\) | −16404.7 | −0.779893 | ||||||||
\(763\) | 18723.4 | 0.888377 | ||||||||
\(764\) | −10579.4 | −0.500983 | ||||||||
\(765\) | 944.661 | 0.0446461 | ||||||||
\(766\) | 19857.6 | 0.936666 | ||||||||
\(767\) | −14034.1 | −0.660681 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 3067.23 | 0.143833 | 0.0719163 | − | 0.997411i | \(-0.477089\pi\) | ||||
0.0719163 | + | 0.997411i | \(0.477089\pi\) | |||||||
\(770\) | 4409.70 | 0.206382 | ||||||||
\(771\) | 6361.35 | 0.297144 | ||||||||
\(772\) | 5761.50 | 0.268602 | ||||||||
\(773\) | −16600.1 | −0.772401 | −0.386200 | − | 0.922415i | \(-0.626213\pi\) | ||||
−0.386200 | + | 0.922415i | \(0.626213\pi\) | |||||||
\(774\) | 8668.18 | 0.402547 | ||||||||
\(775\) | 43837.0 | 2.03183 | ||||||||
\(776\) | −8392.45 | −0.388236 | ||||||||
\(777\) | −7821.50 | −0.361126 | ||||||||
\(778\) | −14302.4 | −0.659082 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −4707.62 | −0.216102 | ||||||||
\(781\) | 4729.65 | 0.216697 | ||||||||
\(782\) | −2022.19 | −0.0924723 | ||||||||
\(783\) | −6698.04 | −0.305707 | ||||||||
\(784\) | 9925.43 | 0.452142 | ||||||||
\(785\) | 10682.8 | 0.485715 | ||||||||
\(786\) | 3454.46 | 0.156764 | ||||||||
\(787\) | 18271.7 | 0.827594 | 0.413797 | − | 0.910369i | \(-0.364202\pi\) | ||||
0.413797 | + | 0.910369i | \(0.364202\pi\) | |||||||
\(788\) | −4789.48 | −0.216521 | ||||||||
\(789\) | −15117.3 | −0.682115 | ||||||||
\(790\) | 6442.11 | 0.290127 | ||||||||
\(791\) | 23900.2 | 1.07433 | ||||||||
\(792\) | −312.905 | −0.0140386 | ||||||||
\(793\) | −6997.58 | −0.313356 | ||||||||
\(794\) | −25644.2 | −1.14620 | ||||||||
\(795\) | 9041.43 | 0.403354 | ||||||||
\(796\) | −12050.6 | −0.536588 | ||||||||
\(797\) | −11702.7 | −0.520114 | −0.260057 | − | 0.965593i | \(-0.583741\pi\) | ||||
−0.260057 | + | 0.965593i | \(0.583741\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2741.09 | −0.121368 | ||||||||
\(800\) | −4550.03 | −0.201085 | ||||||||
\(801\) | −8936.82 | −0.394216 | ||||||||
\(802\) | 195.168 | 0.00859302 | ||||||||
\(803\) | −2733.08 | −0.120110 | ||||||||
\(804\) | −5045.43 | −0.221317 | ||||||||
\(805\) | 79885.2 | 3.49762 | ||||||||
\(806\) | −14798.5 | −0.646717 | ||||||||
\(807\) | 16761.3 | 0.731134 | ||||||||
\(808\) | 2246.14 | 0.0977956 | ||||||||
\(809\) | −37702.6 | −1.63851 | −0.819254 | − | 0.573431i | \(-0.805612\pi\) | ||||
−0.819254 | + | 0.573431i | \(0.805612\pi\) | |||||||
\(810\) | 2648.04 | 0.114867 | ||||||||
\(811\) | 6225.35 | 0.269546 | 0.134773 | − | 0.990877i | \(-0.456970\pi\) | ||||
0.134773 | + | 0.990877i | \(0.456970\pi\) | |||||||
\(812\) | −30798.8 | −1.33107 | ||||||||
\(813\) | −8122.64 | −0.350398 | ||||||||
\(814\) | 730.112 | 0.0314378 | ||||||||
\(815\) | 56400.1 | 2.42406 | ||||||||
\(816\) | −308.223 | −0.0132230 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −5991.11 | −0.256081 | ||||||||
\(819\) | 6704.15 | 0.286034 | ||||||||
\(820\) | 9943.24 | 0.423455 | ||||||||
\(821\) | −7967.79 | −0.338706 | −0.169353 | − | 0.985555i | \(-0.554168\pi\) | ||||
−0.169353 | + | 0.985555i | \(0.554168\pi\) | |||||||
\(822\) | −12758.7 | −0.541378 | ||||||||
\(823\) | 27328.1 | 1.15747 | 0.578736 | − | 0.815515i | \(-0.303546\pi\) | ||||
0.578736 | + | 0.815515i | \(0.303546\pi\) | |||||||
\(824\) | 12368.9 | 0.522926 | ||||||||
\(825\) | 1853.81 | 0.0782321 | ||||||||
\(826\) | 36298.9 | 1.52905 | ||||||||
\(827\) | 3241.58 | 0.136301 | 0.0681503 | − | 0.997675i | \(-0.478290\pi\) | ||||
0.0681503 | + | 0.997675i | \(0.478290\pi\) | |||||||
\(828\) | −5668.53 | −0.237917 | ||||||||
\(829\) | −16527.9 | −0.692444 | −0.346222 | − | 0.938153i | \(-0.612536\pi\) | ||||
−0.346222 | + | 0.938153i | \(0.612536\pi\) | |||||||
\(830\) | 16986.6 | 0.710376 | ||||||||
\(831\) | −8525.61 | −0.355897 | ||||||||
\(832\) | 1536.00 | 0.0640039 | ||||||||
\(833\) | −3983.40 | −0.165686 | ||||||||
\(834\) | 10483.3 | 0.435262 | ||||||||
\(835\) | −25989.3 | −1.07712 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8324.15 | 0.343757 | ||||||||
\(838\) | −2306.01 | −0.0950595 | ||||||||
\(839\) | −2868.98 | −0.118055 | −0.0590276 | − | 0.998256i | \(-0.518800\pi\) | ||||
−0.0590276 | + | 0.998256i | \(0.518800\pi\) | |||||||
\(840\) | 12176.1 | 0.500139 | ||||||||
\(841\) | 37152.4 | 1.52333 | ||||||||
\(842\) | −7700.97 | −0.315194 | ||||||||
\(843\) | 7095.39 | 0.289891 | ||||||||
\(844\) | 20163.6 | 0.822346 | ||||||||
\(845\) | 26496.7 | 1.07872 | ||||||||
\(846\) | −7683.73 | −0.312260 | ||||||||
\(847\) | −40725.0 | −1.65210 | ||||||||
\(848\) | −2950.03 | −0.119463 | ||||||||
\(849\) | 10747.3 | 0.434448 | ||||||||
\(850\) | 1826.08 | 0.0736870 | ||||||||
\(851\) | 13226.6 | 0.532786 | ||||||||
\(852\) | 13059.6 | 0.525135 | ||||||||
\(853\) | 48181.8 | 1.93401 | 0.967007 | − | 0.254749i | \(-0.0819930\pi\) | ||||
0.967007 | + | 0.254749i | \(0.0819930\pi\) | |||||||
\(854\) | 18099.1 | 0.725219 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12675.6 | −0.506126 | ||||||||
\(857\) | 11377.9 | 0.453516 | 0.226758 | − | 0.973951i | \(-0.427187\pi\) | ||||
0.226758 | + | 0.973951i | \(0.427187\pi\) | |||||||
\(858\) | −625.810 | −0.0249007 | ||||||||
\(859\) | −2197.20 | −0.0872731 | −0.0436365 | − | 0.999047i | \(-0.513894\pi\) | ||||
−0.0436365 | + | 0.999047i | \(0.513894\pi\) | |||||||
\(860\) | 31486.5 | 1.24847 | ||||||||
\(861\) | −14160.2 | −0.560487 | ||||||||
\(862\) | −10099.9 | −0.399077 | ||||||||
\(863\) | 37507.8 | 1.47947 | 0.739734 | − | 0.672899i | \(-0.234951\pi\) | ||||
0.739734 | + | 0.672899i | \(0.234951\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 41248.4 | 1.62137 | ||||||||
\(866\) | 18681.5 | 0.733052 | ||||||||
\(867\) | −14615.3 | −0.572505 | ||||||||
\(868\) | 38275.9 | 1.49674 | ||||||||
\(869\) | 856.386 | 0.0334303 | ||||||||
\(870\) | −24330.1 | −0.948124 | ||||||||
\(871\) | −10090.9 | −0.392555 | ||||||||
\(872\) | −4825.97 | −0.187417 | ||||||||
\(873\) | 9441.50 | 0.366033 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8720.43 | −0.336919 | ||||||||
\(876\) | −7546.64 | −0.291070 | ||||||||
\(877\) | −15932.7 | −0.613464 | −0.306732 | − | 0.951796i | \(-0.599236\pi\) | ||||
−0.306732 | + | 0.951796i | \(0.599236\pi\) | |||||||
\(878\) | 12890.1 | 0.495466 | ||||||||
\(879\) | 8521.35 | 0.326983 | ||||||||
\(880\) | −1136.60 | −0.0435396 | ||||||||
\(881\) | 43405.8 | 1.65991 | 0.829953 | − | 0.557833i | \(-0.188367\pi\) | ||||
0.829953 | + | 0.557833i | \(0.188367\pi\) | |||||||
\(882\) | −11166.1 | −0.426284 | ||||||||
\(883\) | 15528.8 | 0.591829 | 0.295915 | − | 0.955214i | \(-0.404376\pi\) | ||||
0.295915 | + | 0.955214i | \(0.404376\pi\) | |||||||
\(884\) | −616.447 | −0.0234540 | ||||||||
\(885\) | 28675.0 | 1.08915 | ||||||||
\(886\) | 16927.3 | 0.641856 | ||||||||
\(887\) | −36209.0 | −1.37067 | −0.685333 | − | 0.728230i | \(-0.740343\pi\) | ||||
−0.685333 | + | 0.728230i | \(0.740343\pi\) | |||||||
\(888\) | 2016.00 | 0.0761853 | ||||||||
\(889\) | 84860.6 | 3.20150 | ||||||||
\(890\) | −32462.3 | −1.22263 | ||||||||
\(891\) | 352.018 | 0.0132357 | ||||||||
\(892\) | 116.223 | 0.00436261 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 7027.21 | 0.262892 | ||||||||
\(895\) | 17758.4 | 0.663238 | ||||||||
\(896\) | −3972.83 | −0.148128 | ||||||||
\(897\) | −11337.1 | −0.421999 | ||||||||
\(898\) | 3475.93 | 0.129168 | ||||||||
\(899\) | −76482.1 | −2.83740 | ||||||||
\(900\) | 5118.79 | 0.189585 | ||||||||
\(901\) | 1183.94 | 0.0437768 | ||||||||
\(902\) | 1321.81 | 0.0487932 | ||||||||
\(903\) | −44840.1 | −1.65247 | ||||||||
\(904\) | −6160.29 | −0.226646 | ||||||||
\(905\) | 54816.1 | 2.01342 | ||||||||
\(906\) | 5914.86 | 0.216896 | ||||||||
\(907\) | −8592.97 | −0.314581 | −0.157290 | − | 0.987552i | \(-0.550276\pi\) | ||||
−0.157290 | + | 0.987552i | \(0.550276\pi\) | |||||||
\(908\) | −19762.7 | −0.722300 | ||||||||
\(909\) | −2526.91 | −0.0922026 | ||||||||
\(910\) | 24352.3 | 0.887111 | ||||||||
\(911\) | 25963.2 | 0.944235 | 0.472117 | − | 0.881536i | \(-0.343490\pi\) | ||||
0.472117 | + | 0.881536i | \(0.343490\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2258.12 | 0.0818541 | ||||||||
\(914\) | −35446.6 | −1.28279 | ||||||||
\(915\) | 14297.7 | 0.516577 | ||||||||
\(916\) | −11409.4 | −0.411548 | ||||||||
\(917\) | −17869.7 | −0.643523 | ||||||||
\(918\) | 346.751 | 0.0124668 | ||||||||
\(919\) | 2229.83 | 0.0800385 | 0.0400193 | − | 0.999199i | \(-0.487258\pi\) | ||||
0.0400193 | + | 0.999199i | \(0.487258\pi\) | |||||||
\(920\) | −20590.5 | −0.737878 | ||||||||
\(921\) | −27885.5 | −0.997674 | ||||||||
\(922\) | −9703.16 | −0.346591 | ||||||||
\(923\) | 26119.2 | 0.931447 | ||||||||
\(924\) | 1618.64 | 0.0576293 | ||||||||
\(925\) | −11943.8 | −0.424552 | ||||||||
\(926\) | 21354.3 | 0.757825 | ||||||||
\(927\) | −13915.0 | −0.493019 | ||||||||
\(928\) | 7938.41 | 0.280809 | ||||||||
\(929\) | 14164.9 | 0.500253 | 0.250126 | − | 0.968213i | \(-0.419528\pi\) | ||||
0.250126 | + | 0.968213i | \(0.419528\pi\) | |||||||
\(930\) | 30236.8 | 1.06613 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18637.8 | −0.655043 | ||||||||
\(933\) | 5600.15 | 0.196507 | ||||||||
\(934\) | 16928.5 | 0.593061 | ||||||||
\(935\) | 456.156 | 0.0159550 | ||||||||
\(936\) | −1728.00 | −0.0603434 | ||||||||
\(937\) | −42462.9 | −1.48047 | −0.740236 | − | 0.672347i | \(-0.765286\pi\) | ||||
−0.740236 | + | 0.672347i | \(0.765286\pi\) | |||||||
\(938\) | 26099.8 | 0.908516 | ||||||||
\(939\) | −16549.0 | −0.575141 | ||||||||
\(940\) | −27910.6 | −0.968449 | ||||||||
\(941\) | 47645.2 | 1.65057 | 0.825287 | − | 0.564714i | \(-0.191013\pi\) | ||||
0.825287 | + | 0.564714i | \(0.191013\pi\) | |||||||
\(942\) | 3921.28 | 0.135629 | ||||||||
\(943\) | 23945.6 | 0.826912 | ||||||||
\(944\) | −9356.07 | −0.322578 | ||||||||
\(945\) | −13698.2 | −0.471536 | ||||||||
\(946\) | 4185.68 | 0.143856 | ||||||||
\(947\) | 40549.9 | 1.39144 | 0.695721 | − | 0.718312i | \(-0.255085\pi\) | ||||
0.695721 | + | 0.718312i | \(0.255085\pi\) | |||||||
\(948\) | 2364.67 | 0.0810136 | ||||||||
\(949\) | −15093.3 | −0.516279 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15743.1 | 0.536808 | ||||||||
\(952\) | 1594.42 | 0.0542811 | ||||||||
\(953\) | −8636.89 | −0.293574 | −0.146787 | − | 0.989168i | \(-0.546893\pi\) | ||||
−0.146787 | + | 0.989168i | \(0.546893\pi\) | |||||||
\(954\) | 3318.79 | 0.112631 | ||||||||
\(955\) | 43232.6 | 1.46490 | ||||||||
\(956\) | 15611.3 | 0.528145 | ||||||||
\(957\) | −3234.34 | −0.109249 | ||||||||
\(958\) | 16900.0 | 0.569952 | ||||||||
\(959\) | 66000.4 | 2.22238 | ||||||||
\(960\) | −3138.41 | −0.105512 | ||||||||
\(961\) | 65258.9 | 2.19056 | ||||||||
\(962\) | 4032.00 | 0.135132 | ||||||||
\(963\) | 14260.1 | 0.477180 | ||||||||
\(964\) | 22338.1 | 0.746330 | ||||||||
\(965\) | −23544.2 | −0.785404 | ||||||||
\(966\) | 29323.0 | 0.976659 | ||||||||
\(967\) | 32994.5 | 1.09724 | 0.548620 | − | 0.836072i | \(-0.315154\pi\) | ||||
0.548620 | + | 0.836072i | \(0.315154\pi\) | |||||||
\(968\) | 10496.9 | 0.348536 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34295.5 | 1.13522 | ||||||||
\(971\) | −5801.68 | −0.191745 | −0.0958727 | − | 0.995394i | \(-0.530564\pi\) | ||||
−0.0958727 | + | 0.995394i | \(0.530564\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | −54229.9 | −1.78677 | ||||||||
\(974\) | 15710.2 | 0.516825 | ||||||||
\(975\) | 10237.6 | 0.336272 | ||||||||
\(976\) | −4665.05 | −0.152997 | ||||||||
\(977\) | −35449.2 | −1.16082 | −0.580410 | − | 0.814324i | \(-0.697108\pi\) | ||||
−0.580410 | + | 0.814324i | \(0.697108\pi\) | |||||||
\(978\) | 20702.5 | 0.676884 | ||||||||
\(979\) | −4315.40 | −0.140879 | ||||||||
\(980\) | −40560.0 | −1.32208 | ||||||||
\(981\) | 5429.21 | 0.176699 | ||||||||
\(982\) | 10682.8 | 0.347149 | ||||||||
\(983\) | 22860.0 | 0.741732 | 0.370866 | − | 0.928686i | \(-0.379061\pi\) | ||||
0.370866 | + | 0.928686i | \(0.379061\pi\) | |||||||
\(984\) | 3649.81 | 0.118244 | ||||||||
\(985\) | 19572.1 | 0.633116 | ||||||||
\(986\) | −3185.94 | −0.102902 | ||||||||
\(987\) | 39747.6 | 1.28184 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 75826.9 | 2.43797 | ||||||||
\(990\) | 1278.68 | 0.0410496 | ||||||||
\(991\) | −22985.4 | −0.736787 | −0.368394 | − | 0.929670i | \(-0.620092\pi\) | ||||
−0.368394 | + | 0.929670i | \(0.620092\pi\) | |||||||
\(992\) | −9865.65 | −0.315761 | ||||||||
\(993\) | 10949.7 | 0.349927 | ||||||||
\(994\) | −67556.8 | −2.15571 | ||||||||
\(995\) | 49244.7 | 1.56901 | ||||||||
\(996\) | 6235.16 | 0.198362 | ||||||||
\(997\) | 13201.6 | 0.419357 | 0.209678 | − | 0.977770i | \(-0.432758\pi\) | ||||
0.209678 | + | 0.977770i | \(0.432758\pi\) | |||||||
\(998\) | 6314.15 | 0.200272 | ||||||||
\(999\) | −2268.00 | −0.0718282 |
(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 | 2166.4.a.m.1.1 | ✓ | 2 | |
19.18 | odd | 2 | 2166.4.a.o.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2166.4.a.m.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2166.4.a.o.1.1 | yes | 2 | 19.18 | odd | 2 |