Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(0\) |
Dimension: | \(110\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.20768 | −1.48764 | −0.743819 | − | 0.668381i | \(-0.766988\pi\) | ||||
−0.743819 | + | 0.668381i | \(0.766988\pi\) | |||||||
\(3\) | −0.654616 | −0.125981 | −0.0629905 | − | 0.998014i | \(-0.520064\pi\) | ||||
−0.0629905 | + | 0.998014i | \(0.520064\pi\) | |||||||
\(4\) | 9.70454 | 1.21307 | ||||||||
\(5\) | 13.9092 | 1.24407 | 0.622037 | − | 0.782987i | \(-0.286305\pi\) | ||||
0.622037 | + | 0.782987i | \(0.286305\pi\) | |||||||
\(6\) | 2.75441 | 0.187414 | ||||||||
\(7\) | 32.2423 | 1.74092 | 0.870460 | − | 0.492240i | \(-0.163822\pi\) | ||||
0.870460 | + | 0.492240i | \(0.163822\pi\) | |||||||
\(8\) | −7.17215 | −0.316967 | ||||||||
\(9\) | −26.5715 | −0.984129 | ||||||||
\(10\) | −58.5253 | −1.85073 | ||||||||
\(11\) | 62.9144 | 1.72449 | 0.862246 | − | 0.506490i | \(-0.169057\pi\) | ||||
0.862246 | + | 0.506490i | \(0.169057\pi\) | |||||||
\(12\) | −6.35275 | −0.152823 | ||||||||
\(13\) | 53.0213 | 1.13119 | 0.565594 | − | 0.824684i | \(-0.308647\pi\) | ||||
0.565594 | + | 0.824684i | \(0.308647\pi\) | |||||||
\(14\) | −135.665 | −2.58986 | ||||||||
\(15\) | −9.10518 | −0.156730 | ||||||||
\(16\) | −47.4582 | −0.741535 | ||||||||
\(17\) | −40.5919 | −0.579117 | −0.289559 | − | 0.957160i | \(-0.593509\pi\) | ||||
−0.289559 | + | 0.957160i | \(0.593509\pi\) | |||||||
\(18\) | 111.804 | 1.46403 | ||||||||
\(19\) | 76.2601 | 0.920804 | 0.460402 | − | 0.887711i | \(-0.347705\pi\) | ||||
0.460402 | + | 0.887711i | \(0.347705\pi\) | |||||||
\(20\) | 134.982 | 1.50915 | ||||||||
\(21\) | −21.1063 | −0.219323 | ||||||||
\(22\) | −264.724 | −2.56542 | ||||||||
\(23\) | −103.602 | −0.939241 | −0.469620 | − | 0.882868i | \(-0.655609\pi\) | ||||
−0.469620 | + | 0.882868i | \(0.655609\pi\) | |||||||
\(24\) | 4.69501 | 0.0399318 | ||||||||
\(25\) | 68.4653 | 0.547722 | ||||||||
\(26\) | −223.096 | −1.68280 | ||||||||
\(27\) | 35.0688 | 0.249963 | ||||||||
\(28\) | 312.896 | 2.11185 | ||||||||
\(29\) | 10.3011 | 0.0659611 | 0.0329805 | − | 0.999456i | \(-0.489500\pi\) | ||||
0.0329805 | + | 0.999456i | \(0.489500\pi\) | |||||||
\(30\) | 38.3116 | 0.233157 | ||||||||
\(31\) | 13.7002 | 0.0793752 | 0.0396876 | − | 0.999212i | \(-0.487364\pi\) | ||||
0.0396876 | + | 0.999212i | \(0.487364\pi\) | |||||||
\(32\) | 257.066 | 1.42010 | ||||||||
\(33\) | −41.1848 | −0.217253 | ||||||||
\(34\) | 170.798 | 0.861517 | ||||||||
\(35\) | 448.464 | 2.16583 | ||||||||
\(36\) | −257.864 | −1.19381 | ||||||||
\(37\) | −355.179 | −1.57814 | −0.789068 | − | 0.614305i | \(-0.789436\pi\) | ||||
−0.789068 | + | 0.614305i | \(0.789436\pi\) | |||||||
\(38\) | −320.878 | −1.36982 | ||||||||
\(39\) | −34.7086 | −0.142508 | ||||||||
\(40\) | −99.7587 | −0.394331 | ||||||||
\(41\) | 379.187 | 1.44437 | 0.722184 | − | 0.691701i | \(-0.243138\pi\) | ||||
0.722184 | + | 0.691701i | \(0.243138\pi\) | |||||||
\(42\) | 88.8086 | 0.326273 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 610.555 | 2.09193 | ||||||||
\(45\) | −369.587 | −1.22433 | ||||||||
\(46\) | 435.924 | 1.39725 | ||||||||
\(47\) | 241.252 | 0.748728 | 0.374364 | − | 0.927282i | \(-0.377861\pi\) | ||||
0.374364 | + | 0.927282i | \(0.377861\pi\) | |||||||
\(48\) | 31.0669 | 0.0934193 | ||||||||
\(49\) | 696.564 | 2.03080 | ||||||||
\(50\) | −288.080 | −0.814813 | ||||||||
\(51\) | 26.5722 | 0.0729578 | ||||||||
\(52\) | 514.547 | 1.37221 | ||||||||
\(53\) | −94.7008 | −0.245437 | −0.122718 | − | 0.992442i | \(-0.539161\pi\) | ||||
−0.122718 | + | 0.992442i | \(0.539161\pi\) | |||||||
\(54\) | −147.558 | −0.371854 | ||||||||
\(55\) | 875.088 | 2.14540 | ||||||||
\(56\) | −231.246 | −0.551814 | ||||||||
\(57\) | −49.9211 | −0.116004 | ||||||||
\(58\) | −43.3438 | −0.0981262 | ||||||||
\(59\) | −247.647 | −0.546457 | −0.273228 | − | 0.961949i | \(-0.588091\pi\) | ||||
−0.273228 | + | 0.961949i | \(0.588091\pi\) | |||||||
\(60\) | −88.3616 | −0.190124 | ||||||||
\(61\) | 62.6153 | 0.131427 | 0.0657137 | − | 0.997839i | \(-0.479068\pi\) | ||||
0.0657137 | + | 0.997839i | \(0.479068\pi\) | |||||||
\(62\) | −57.6460 | −0.118082 | ||||||||
\(63\) | −856.725 | −1.71329 | ||||||||
\(64\) | −701.985 | −1.37106 | ||||||||
\(65\) | 737.482 | 1.40728 | ||||||||
\(66\) | 173.292 | 0.323194 | ||||||||
\(67\) | 256.508 | 0.467723 | 0.233861 | − | 0.972270i | \(-0.424864\pi\) | ||||
0.233861 | + | 0.972270i | \(0.424864\pi\) | |||||||
\(68\) | −393.926 | −0.702508 | ||||||||
\(69\) | 67.8196 | 0.118326 | ||||||||
\(70\) | −1886.99 | −3.22198 | ||||||||
\(71\) | −345.573 | −0.577633 | −0.288816 | − | 0.957384i | \(-0.593262\pi\) | ||||
−0.288816 | + | 0.957384i | \(0.593262\pi\) | |||||||
\(72\) | 190.575 | 0.311937 | ||||||||
\(73\) | 270.766 | 0.434121 | 0.217060 | − | 0.976158i | \(-0.430353\pi\) | ||||
0.217060 | + | 0.976158i | \(0.430353\pi\) | |||||||
\(74\) | 1494.48 | 2.34770 | ||||||||
\(75\) | −44.8185 | −0.0690026 | ||||||||
\(76\) | 740.069 | 1.11700 | ||||||||
\(77\) | 2028.50 | 3.00220 | ||||||||
\(78\) | 146.042 | 0.212001 | ||||||||
\(79\) | 1026.68 | 1.46215 | 0.731077 | − | 0.682295i | \(-0.239018\pi\) | ||||
0.731077 | + | 0.682295i | \(0.239018\pi\) | |||||||
\(80\) | −660.105 | −0.922525 | ||||||||
\(81\) | 694.473 | 0.952638 | ||||||||
\(82\) | −1595.50 | −2.14870 | ||||||||
\(83\) | 860.983 | 1.13862 | 0.569308 | − | 0.822124i | \(-0.307211\pi\) | ||||
0.569308 | + | 0.822124i | \(0.307211\pi\) | |||||||
\(84\) | −204.827 | −0.266053 | ||||||||
\(85\) | −564.601 | −0.720465 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.74329 | −0.00830984 | ||||||||
\(88\) | −451.232 | −0.546608 | ||||||||
\(89\) | 511.713 | 0.609455 | 0.304727 | − | 0.952440i | \(-0.401435\pi\) | ||||
0.304727 | + | 0.952440i | \(0.401435\pi\) | |||||||
\(90\) | 1555.10 | 1.82136 | ||||||||
\(91\) | 1709.53 | 1.96931 | ||||||||
\(92\) | −1005.41 | −1.13936 | ||||||||
\(93\) | −8.96838 | −0.00999976 | ||||||||
\(94\) | −1015.11 | −1.11384 | ||||||||
\(95\) | 1060.72 | 1.14555 | ||||||||
\(96\) | −168.280 | −0.178906 | ||||||||
\(97\) | 306.610 | 0.320943 | 0.160472 | − | 0.987040i | \(-0.448698\pi\) | ||||
0.160472 | + | 0.987040i | \(0.448698\pi\) | |||||||
\(98\) | −2930.92 | −3.02109 | ||||||||
\(99\) | −1671.73 | −1.69712 | ||||||||
\(100\) | 664.424 | 0.664424 | ||||||||
\(101\) | 104.607 | 0.103057 | 0.0515286 | − | 0.998672i | \(-0.483591\pi\) | ||||
0.0515286 | + | 0.998672i | \(0.483591\pi\) | |||||||
\(102\) | −111.807 | −0.108535 | ||||||||
\(103\) | −110.014 | −0.105243 | −0.0526215 | − | 0.998615i | \(-0.516758\pi\) | ||||
−0.0526215 | + | 0.998615i | \(0.516758\pi\) | |||||||
\(104\) | −380.276 | −0.358550 | ||||||||
\(105\) | −293.572 | −0.272854 | ||||||||
\(106\) | 398.470 | 0.365121 | ||||||||
\(107\) | 750.436 | 0.678013 | 0.339007 | − | 0.940784i | \(-0.389909\pi\) | ||||
0.339007 | + | 0.940784i | \(0.389909\pi\) | |||||||
\(108\) | 340.326 | 0.303221 | ||||||||
\(109\) | −716.691 | −0.629785 | −0.314893 | − | 0.949127i | \(-0.601968\pi\) | ||||
−0.314893 | + | 0.949127i | \(0.601968\pi\) | |||||||
\(110\) | −3682.09 | −3.19157 | ||||||||
\(111\) | 232.506 | 0.198815 | ||||||||
\(112\) | −1530.16 | −1.29095 | ||||||||
\(113\) | 791.259 | 0.658720 | 0.329360 | − | 0.944204i | \(-0.393167\pi\) | ||||
0.329360 | + | 0.944204i | \(0.393167\pi\) | |||||||
\(114\) | 210.052 | 0.172572 | ||||||||
\(115\) | −1441.02 | −1.16849 | ||||||||
\(116\) | 99.9677 | 0.0800153 | ||||||||
\(117\) | −1408.85 | −1.11324 | ||||||||
\(118\) | 1042.02 | 0.812930 | ||||||||
\(119\) | −1308.78 | −1.00820 | ||||||||
\(120\) | 65.3037 | 0.0496782 | ||||||||
\(121\) | 2627.22 | 1.97387 | ||||||||
\(122\) | −263.465 | −0.195516 | ||||||||
\(123\) | −248.222 | −0.181963 | ||||||||
\(124\) | 132.954 | 0.0962874 | ||||||||
\(125\) | −786.351 | −0.562667 | ||||||||
\(126\) | 3604.82 | 2.54875 | ||||||||
\(127\) | −2092.69 | −1.46217 | −0.731086 | − | 0.682285i | \(-0.760986\pi\) | ||||
−0.731086 | + | 0.682285i | \(0.760986\pi\) | |||||||
\(128\) | 897.197 | 0.619545 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3103.09 | −2.09353 | ||||||||
\(131\) | −2426.04 | −1.61804 | −0.809022 | − | 0.587779i | \(-0.800003\pi\) | ||||
−0.809022 | + | 0.587779i | \(0.800003\pi\) | |||||||
\(132\) | −399.680 | −0.263543 | ||||||||
\(133\) | 2458.80 | 1.60304 | ||||||||
\(134\) | −1079.30 | −0.695803 | ||||||||
\(135\) | 487.778 | 0.310972 | ||||||||
\(136\) | 291.132 | 0.183561 | ||||||||
\(137\) | −36.6355 | −0.0228466 | −0.0114233 | − | 0.999935i | \(-0.503636\pi\) | ||||
−0.0114233 | + | 0.999935i | \(0.503636\pi\) | |||||||
\(138\) | −285.363 | −0.176027 | ||||||||
\(139\) | −697.573 | −0.425665 | −0.212832 | − | 0.977089i | \(-0.568269\pi\) | ||||
−0.212832 | + | 0.977089i | \(0.568269\pi\) | |||||||
\(140\) | 4352.13 | 2.62730 | ||||||||
\(141\) | −157.928 | −0.0943255 | ||||||||
\(142\) | 1454.06 | 0.859309 | ||||||||
\(143\) | 3335.80 | 1.95073 | ||||||||
\(144\) | 1261.04 | 0.729766 | ||||||||
\(145\) | 143.280 | 0.0820605 | ||||||||
\(146\) | −1139.30 | −0.645814 | ||||||||
\(147\) | −455.982 | −0.255842 | ||||||||
\(148\) | −3446.85 | −1.91439 | ||||||||
\(149\) | 1444.54 | 0.794238 | 0.397119 | − | 0.917767i | \(-0.370010\pi\) | ||||
0.397119 | + | 0.917767i | \(0.370010\pi\) | |||||||
\(150\) | 188.582 | 0.102651 | ||||||||
\(151\) | −3298.40 | −1.77761 | −0.888807 | − | 0.458282i | \(-0.848465\pi\) | ||||
−0.888807 | + | 0.458282i | \(0.848465\pi\) | |||||||
\(152\) | −546.949 | −0.291865 | ||||||||
\(153\) | 1078.59 | 0.569926 | ||||||||
\(154\) | −8535.29 | −4.46619 | ||||||||
\(155\) | 190.559 | 0.0987487 | ||||||||
\(156\) | −336.831 | −0.172872 | ||||||||
\(157\) | 1357.08 | 0.689853 | 0.344926 | − | 0.938630i | \(-0.387904\pi\) | ||||
0.344926 | + | 0.938630i | \(0.387904\pi\) | |||||||
\(158\) | −4319.93 | −2.17516 | ||||||||
\(159\) | 61.9927 | 0.0309204 | ||||||||
\(160\) | 3575.58 | 1.76671 | ||||||||
\(161\) | −3340.37 | −1.63514 | ||||||||
\(162\) | −2922.12 | −1.41718 | ||||||||
\(163\) | −762.254 | −0.366284 | −0.183142 | − | 0.983086i | \(-0.558627\pi\) | ||||
−0.183142 | + | 0.983086i | \(0.558627\pi\) | |||||||
\(164\) | 3679.84 | 1.75212 | ||||||||
\(165\) | −572.847 | −0.270279 | ||||||||
\(166\) | −3622.74 | −1.69385 | ||||||||
\(167\) | 865.240 | 0.400924 | 0.200462 | − | 0.979701i | \(-0.435756\pi\) | ||||
0.200462 | + | 0.979701i | \(0.435756\pi\) | |||||||
\(168\) | 151.378 | 0.0695181 | ||||||||
\(169\) | 614.254 | 0.279588 | ||||||||
\(170\) | 2375.66 | 1.07179 | ||||||||
\(171\) | −2026.34 | −0.906189 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2433.22 | 1.06933 | 0.534666 | − | 0.845063i | \(-0.320437\pi\) | ||||
0.534666 | + | 0.845063i | \(0.320437\pi\) | |||||||
\(174\) | 28.3736 | 0.0123620 | ||||||||
\(175\) | 2207.48 | 0.953540 | ||||||||
\(176\) | −2985.81 | −1.27877 | ||||||||
\(177\) | 162.114 | 0.0688431 | ||||||||
\(178\) | −2153.12 | −0.906648 | ||||||||
\(179\) | 175.349 | 0.0732192 | 0.0366096 | − | 0.999330i | \(-0.488344\pi\) | ||||
0.0366096 | + | 0.999330i | \(0.488344\pi\) | |||||||
\(180\) | −3586.68 | −1.48519 | ||||||||
\(181\) | −133.089 | −0.0546542 | −0.0273271 | − | 0.999627i | \(-0.508700\pi\) | ||||
−0.0273271 | + | 0.999627i | \(0.508700\pi\) | |||||||
\(182\) | −7193.13 | −2.92962 | ||||||||
\(183\) | −40.9890 | −0.0165574 | ||||||||
\(184\) | 743.050 | 0.297709 | ||||||||
\(185\) | −4940.25 | −1.96332 | ||||||||
\(186\) | 37.7360 | 0.0148760 | ||||||||
\(187\) | −2553.82 | −0.998683 | ||||||||
\(188\) | 2341.24 | 0.908258 | ||||||||
\(189\) | 1130.70 | 0.435164 | ||||||||
\(190\) | −4463.15 | −1.70416 | ||||||||
\(191\) | −2348.28 | −0.889612 | −0.444806 | − | 0.895627i | \(-0.646727\pi\) | ||||
−0.444806 | + | 0.895627i | \(0.646727\pi\) | |||||||
\(192\) | 459.531 | 0.172728 | ||||||||
\(193\) | −4157.01 | −1.55040 | −0.775202 | − | 0.631714i | \(-0.782352\pi\) | ||||
−0.775202 | + | 0.631714i | \(0.782352\pi\) | |||||||
\(194\) | −1290.11 | −0.477448 | ||||||||
\(195\) | −482.768 | −0.177291 | ||||||||
\(196\) | 6759.83 | 2.46350 | ||||||||
\(197\) | −2234.19 | −0.808017 | −0.404009 | − | 0.914755i | \(-0.632383\pi\) | ||||
−0.404009 | + | 0.914755i | \(0.632383\pi\) | |||||||
\(198\) | 7034.09 | 2.52470 | ||||||||
\(199\) | 2743.66 | 0.977352 | 0.488676 | − | 0.872465i | \(-0.337480\pi\) | ||||
0.488676 | + | 0.872465i | \(0.337480\pi\) | |||||||
\(200\) | −491.043 | −0.173610 | ||||||||
\(201\) | −167.914 | −0.0589242 | ||||||||
\(202\) | −440.152 | −0.153312 | ||||||||
\(203\) | 332.132 | 0.114833 | ||||||||
\(204\) | 257.871 | 0.0885027 | ||||||||
\(205\) | 5274.19 | 1.79690 | ||||||||
\(206\) | 462.905 | 0.156564 | ||||||||
\(207\) | 2752.86 | 0.924334 | ||||||||
\(208\) | −2516.30 | −0.838816 | ||||||||
\(209\) | 4797.86 | 1.58792 | ||||||||
\(210\) | 1235.25 | 0.405908 | ||||||||
\(211\) | 2833.03 | 0.924332 | 0.462166 | − | 0.886793i | \(-0.347072\pi\) | ||||
0.462166 | + | 0.886793i | \(0.347072\pi\) | |||||||
\(212\) | −919.028 | −0.297731 | ||||||||
\(213\) | 226.218 | 0.0727708 | ||||||||
\(214\) | −3157.59 | −1.00864 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −251.518 | −0.0792299 | ||||||||
\(217\) | 441.726 | 0.138186 | ||||||||
\(218\) | 3015.61 | 0.936892 | ||||||||
\(219\) | −177.248 | −0.0546909 | ||||||||
\(220\) | 8492.33 | 2.60251 | ||||||||
\(221\) | −2152.24 | −0.655091 | ||||||||
\(222\) | −978.310 | −0.295765 | ||||||||
\(223\) | 1008.77 | 0.302924 | 0.151462 | − | 0.988463i | \(-0.451602\pi\) | ||||
0.151462 | + | 0.988463i | \(0.451602\pi\) | |||||||
\(224\) | 8288.39 | 2.47228 | ||||||||
\(225\) | −1819.22 | −0.539029 | ||||||||
\(226\) | −3329.36 | −0.979937 | ||||||||
\(227\) | −1858.00 | −0.543259 | −0.271630 | − | 0.962402i | \(-0.587563\pi\) | ||||
−0.271630 | + | 0.962402i | \(0.587563\pi\) | |||||||
\(228\) | −484.461 | −0.140720 | ||||||||
\(229\) | 6638.58 | 1.91568 | 0.957838 | − | 0.287308i | \(-0.0927604\pi\) | ||||
0.957838 | + | 0.287308i | \(0.0927604\pi\) | |||||||
\(230\) | 6063.35 | 1.73828 | ||||||||
\(231\) | −1327.89 | −0.378220 | ||||||||
\(232\) | −73.8813 | −0.0209075 | ||||||||
\(233\) | −1258.53 | −0.353860 | −0.176930 | − | 0.984223i | \(-0.556617\pi\) | ||||
−0.176930 | + | 0.984223i | \(0.556617\pi\) | |||||||
\(234\) | 5928.00 | 1.65609 | ||||||||
\(235\) | 3355.62 | 0.931474 | ||||||||
\(236\) | −2403.30 | −0.662889 | ||||||||
\(237\) | −672.080 | −0.184204 | ||||||||
\(238\) | 5506.91 | 1.49983 | ||||||||
\(239\) | −4792.66 | −1.29712 | −0.648559 | − | 0.761164i | \(-0.724628\pi\) | ||||
−0.648559 | + | 0.761164i | \(0.724628\pi\) | |||||||
\(240\) | 432.116 | 0.116221 | ||||||||
\(241\) | −3314.50 | −0.885915 | −0.442957 | − | 0.896543i | \(-0.646071\pi\) | ||||
−0.442957 | + | 0.896543i | \(0.646071\pi\) | |||||||
\(242\) | −11054.5 | −2.93641 | ||||||||
\(243\) | −1401.47 | −0.369977 | ||||||||
\(244\) | 607.653 | 0.159430 | ||||||||
\(245\) | 9688.64 | 2.52647 | ||||||||
\(246\) | 1044.44 | 0.270695 | ||||||||
\(247\) | 4043.41 | 1.04160 | ||||||||
\(248\) | −98.2600 | −0.0251593 | ||||||||
\(249\) | −563.614 | −0.143444 | ||||||||
\(250\) | 3308.71 | 0.837045 | ||||||||
\(251\) | −7328.40 | −1.84289 | −0.921443 | − | 0.388513i | \(-0.872989\pi\) | ||||
−0.921443 | + | 0.388513i | \(0.872989\pi\) | |||||||
\(252\) | −8314.12 | −2.07833 | ||||||||
\(253\) | −6518.07 | −1.61971 | ||||||||
\(254\) | 8805.35 | 2.17518 | ||||||||
\(255\) | 369.597 | 0.0907649 | ||||||||
\(256\) | 1840.77 | 0.449406 | ||||||||
\(257\) | 7534.47 | 1.82874 | 0.914372 | − | 0.404874i | \(-0.132685\pi\) | ||||
0.914372 | + | 0.404874i | \(0.132685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11451.8 | −2.74741 | ||||||||
\(260\) | 7156.93 | 1.70713 | ||||||||
\(261\) | −273.716 | −0.0649142 | ||||||||
\(262\) | 10208.0 | 2.40706 | ||||||||
\(263\) | 3168.33 | 0.742843 | 0.371422 | − | 0.928464i | \(-0.378870\pi\) | ||||
0.371422 | + | 0.928464i | \(0.378870\pi\) | |||||||
\(264\) | 295.384 | 0.0688622 | ||||||||
\(265\) | −1317.21 | −0.305342 | ||||||||
\(266\) | −10345.8 | −2.38475 | ||||||||
\(267\) | −334.976 | −0.0767797 | ||||||||
\(268\) | 2489.29 | 0.567379 | ||||||||
\(269\) | 3734.70 | 0.846501 | 0.423251 | − | 0.906013i | \(-0.360889\pi\) | ||||
0.423251 | + | 0.906013i | \(0.360889\pi\) | |||||||
\(270\) | −2052.41 | −0.462614 | ||||||||
\(271\) | 2562.20 | 0.574326 | 0.287163 | − | 0.957882i | \(-0.407288\pi\) | ||||
0.287163 | + | 0.957882i | \(0.407288\pi\) | |||||||
\(272\) | 1926.42 | 0.429436 | ||||||||
\(273\) | −1119.08 | −0.248095 | ||||||||
\(274\) | 154.151 | 0.0339875 | ||||||||
\(275\) | 4307.45 | 0.944543 | ||||||||
\(276\) | 658.158 | 0.143538 | ||||||||
\(277\) | −586.811 | −0.127285 | −0.0636427 | − | 0.997973i | \(-0.520272\pi\) | ||||
−0.0636427 | + | 0.997973i | \(0.520272\pi\) | |||||||
\(278\) | 2935.16 | 0.633235 | ||||||||
\(279\) | −364.035 | −0.0781154 | ||||||||
\(280\) | −3216.45 | −0.686498 | ||||||||
\(281\) | 2001.37 | 0.424881 | 0.212441 | − | 0.977174i | \(-0.431859\pi\) | ||||
0.212441 | + | 0.977174i | \(0.431859\pi\) | |||||||
\(282\) | 664.508 | 0.140322 | ||||||||
\(283\) | 2224.86 | 0.467330 | 0.233665 | − | 0.972317i | \(-0.424928\pi\) | ||||
0.233665 | + | 0.972317i | \(0.424928\pi\) | |||||||
\(284\) | −3353.62 | −0.700708 | ||||||||
\(285\) | −694.362 | −0.144317 | ||||||||
\(286\) | −14036.0 | −2.90197 | ||||||||
\(287\) | 12225.9 | 2.51453 | ||||||||
\(288\) | −6830.63 | −1.39756 | ||||||||
\(289\) | −3265.29 | −0.664623 | ||||||||
\(290\) | −602.877 | −0.122076 | ||||||||
\(291\) | −200.712 | −0.0404328 | ||||||||
\(292\) | 2627.66 | 0.526618 | ||||||||
\(293\) | −5130.85 | −1.02303 | −0.511514 | − | 0.859275i | \(-0.670915\pi\) | ||||
−0.511514 | + | 0.859275i | \(0.670915\pi\) | |||||||
\(294\) | 1918.63 | 0.380600 | ||||||||
\(295\) | −3444.57 | −0.679833 | ||||||||
\(296\) | 2547.40 | 0.500218 | ||||||||
\(297\) | 2206.33 | 0.431058 | ||||||||
\(298\) | −6078.16 | −1.18154 | ||||||||
\(299\) | −5493.11 | −1.06246 | ||||||||
\(300\) | −434.943 | −0.0837048 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13878.6 | 2.64445 | ||||||||
\(303\) | −68.4773 | −0.0129832 | ||||||||
\(304\) | −3619.17 | −0.682808 | ||||||||
\(305\) | 870.928 | 0.163506 | ||||||||
\(306\) | −4538.35 | −0.847844 | ||||||||
\(307\) | −1662.64 | −0.309094 | −0.154547 | − | 0.987985i | \(-0.549392\pi\) | ||||
−0.154547 | + | 0.987985i | \(0.549392\pi\) | |||||||
\(308\) | 19685.7 | 3.64187 | ||||||||
\(309\) | 72.0172 | 0.0132586 | ||||||||
\(310\) | −801.809 | −0.146902 | ||||||||
\(311\) | 7499.02 | 1.36730 | 0.683650 | − | 0.729810i | \(-0.260391\pi\) | ||||
0.683650 | + | 0.729810i | \(0.260391\pi\) | |||||||
\(312\) | 248.935 | 0.0451705 | ||||||||
\(313\) | −4871.56 | −0.879734 | −0.439867 | − | 0.898063i | \(-0.644974\pi\) | ||||
−0.439867 | + | 0.898063i | \(0.644974\pi\) | |||||||
\(314\) | −5710.16 | −1.02625 | ||||||||
\(315\) | −11916.3 | −2.13146 | ||||||||
\(316\) | 9963.43 | 1.77369 | ||||||||
\(317\) | 6985.74 | 1.23772 | 0.618862 | − | 0.785500i | \(-0.287594\pi\) | ||||
0.618862 | + | 0.785500i | \(0.287594\pi\) | |||||||
\(318\) | −260.845 | −0.0459983 | ||||||||
\(319\) | 648.090 | 0.113749 | ||||||||
\(320\) | −9764.04 | −1.70571 | ||||||||
\(321\) | −491.248 | −0.0854168 | ||||||||
\(322\) | 14055.2 | 2.43250 | ||||||||
\(323\) | −3095.55 | −0.533253 | ||||||||
\(324\) | 6739.54 | 1.15561 | ||||||||
\(325\) | 3630.12 | 0.619577 | ||||||||
\(326\) | 3207.32 | 0.544899 | ||||||||
\(327\) | 469.158 | 0.0793410 | ||||||||
\(328\) | −2719.59 | −0.457818 | ||||||||
\(329\) | 7778.51 | 1.30348 | ||||||||
\(330\) | 2410.35 | 0.402078 | ||||||||
\(331\) | 370.542 | 0.0615313 | 0.0307656 | − | 0.999527i | \(-0.490205\pi\) | ||||
0.0307656 | + | 0.999527i | \(0.490205\pi\) | |||||||
\(332\) | 8355.45 | 1.38122 | ||||||||
\(333\) | 9437.63 | 1.55309 | ||||||||
\(334\) | −3640.65 | −0.596430 | ||||||||
\(335\) | 3567.82 | 0.581882 | ||||||||
\(336\) | 1001.67 | 0.162635 | ||||||||
\(337\) | 11879.9 | 1.92029 | 0.960147 | − | 0.279496i | \(-0.0901674\pi\) | ||||
0.960147 | + | 0.279496i | \(0.0901674\pi\) | |||||||
\(338\) | −2584.58 | −0.415925 | ||||||||
\(339\) | −517.971 | −0.0829862 | ||||||||
\(340\) | −5479.19 | −0.873973 | ||||||||
\(341\) | 861.941 | 0.136882 | ||||||||
\(342\) | 8526.20 | 1.34808 | ||||||||
\(343\) | 11399.7 | 1.79454 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 943.316 | 0.147207 | ||||||||
\(346\) | −10238.2 | −1.59078 | ||||||||
\(347\) | −303.121 | −0.0468944 | −0.0234472 | − | 0.999725i | \(-0.507464\pi\) | ||||
−0.0234472 | + | 0.999725i | \(0.507464\pi\) | |||||||
\(348\) | −65.4405 | −0.0100804 | ||||||||
\(349\) | −10202.5 | −1.56484 | −0.782420 | − | 0.622752i | \(-0.786015\pi\) | ||||
−0.782420 | + | 0.622752i | \(0.786015\pi\) | |||||||
\(350\) | −9288.35 | −1.41852 | ||||||||
\(351\) | 1859.39 | 0.282755 | ||||||||
\(352\) | 16173.2 | 2.44896 | ||||||||
\(353\) | −3136.89 | −0.472973 | −0.236487 | − | 0.971635i | \(-0.575996\pi\) | ||||
−0.236487 | + | 0.971635i | \(0.575996\pi\) | |||||||
\(354\) | −682.123 | −0.102414 | ||||||||
\(355\) | −4806.63 | −0.718619 | ||||||||
\(356\) | 4965.94 | 0.739310 | ||||||||
\(357\) | 856.747 | 0.127014 | ||||||||
\(358\) | −737.813 | −0.108924 | ||||||||
\(359\) | 10568.7 | 1.55375 | 0.776873 | − | 0.629658i | \(-0.216805\pi\) | ||||
0.776873 | + | 0.629658i | \(0.216805\pi\) | |||||||
\(360\) | 2650.74 | 0.388073 | ||||||||
\(361\) | −1043.40 | −0.152121 | ||||||||
\(362\) | 559.995 | 0.0813057 | ||||||||
\(363\) | −1719.82 | −0.248670 | ||||||||
\(364\) | 16590.2 | 2.38890 | ||||||||
\(365\) | 3766.14 | 0.540079 | ||||||||
\(366\) | 172.469 | 0.0246314 | ||||||||
\(367\) | −9473.38 | −1.34743 | −0.673715 | − | 0.738992i | \(-0.735302\pi\) | ||||
−0.673715 | + | 0.738992i | \(0.735302\pi\) | |||||||
\(368\) | 4916.77 | 0.696480 | ||||||||
\(369\) | −10075.6 | −1.42144 | ||||||||
\(370\) | 20787.0 | 2.92071 | ||||||||
\(371\) | −3053.37 | −0.427286 | ||||||||
\(372\) | −87.0340 | −0.0121304 | ||||||||
\(373\) | −5578.79 | −0.774421 | −0.387210 | − | 0.921991i | \(-0.626561\pi\) | ||||
−0.387210 | + | 0.921991i | \(0.626561\pi\) | |||||||
\(374\) | 10745.6 | 1.48568 | ||||||||
\(375\) | 514.758 | 0.0708854 | ||||||||
\(376\) | −1730.30 | −0.237322 | ||||||||
\(377\) | 546.179 | 0.0746144 | ||||||||
\(378\) | −4757.61 | −0.647367 | ||||||||
\(379\) | 8371.04 | 1.13454 | 0.567271 | − | 0.823531i | \(-0.307999\pi\) | ||||
0.567271 | + | 0.823531i | \(0.307999\pi\) | |||||||
\(380\) | 10293.8 | 1.38963 | ||||||||
\(381\) | 1369.91 | 0.184206 | ||||||||
\(382\) | 9880.82 | 1.32342 | ||||||||
\(383\) | 12121.8 | 1.61721 | 0.808607 | − | 0.588349i | \(-0.200222\pi\) | ||||
0.808607 | + | 0.588349i | \(0.200222\pi\) | |||||||
\(384\) | −587.320 | −0.0780509 | ||||||||
\(385\) | 28214.8 | 3.73496 | ||||||||
\(386\) | 17491.3 | 2.30644 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2975.51 | 0.389326 | ||||||||
\(389\) | 5594.57 | 0.729192 | 0.364596 | − | 0.931166i | \(-0.381207\pi\) | ||||
0.364596 | + | 0.931166i | \(0.381207\pi\) | |||||||
\(390\) | 2031.33 | 0.263745 | ||||||||
\(391\) | 4205.41 | 0.543930 | ||||||||
\(392\) | −4995.86 | −0.643697 | ||||||||
\(393\) | 1588.12 | 0.203843 | ||||||||
\(394\) | 9400.74 | 1.20204 | ||||||||
\(395\) | 14280.2 | 1.81903 | ||||||||
\(396\) | −16223.4 | −2.05872 | ||||||||
\(397\) | 12141.0 | 1.53486 | 0.767428 | − | 0.641135i | \(-0.221536\pi\) | ||||
0.767428 | + | 0.641135i | \(0.221536\pi\) | |||||||
\(398\) | −11544.4 | −1.45395 | ||||||||
\(399\) | −1609.57 | −0.201953 | ||||||||
\(400\) | −3249.24 | −0.406155 | ||||||||
\(401\) | −2199.51 | −0.273910 | −0.136955 | − | 0.990577i | \(-0.543732\pi\) | ||||
−0.136955 | + | 0.990577i | \(0.543732\pi\) | |||||||
\(402\) | 706.529 | 0.0876579 | ||||||||
\(403\) | 726.402 | 0.0897883 | ||||||||
\(404\) | 1015.16 | 0.125015 | ||||||||
\(405\) | 9659.55 | 1.18515 | ||||||||
\(406\) | −1397.50 | −0.170830 | ||||||||
\(407\) | −22345.9 | −2.72148 | ||||||||
\(408\) | −190.579 | −0.0231252 | ||||||||
\(409\) | 3786.14 | 0.457732 | 0.228866 | − | 0.973458i | \(-0.426498\pi\) | ||||
0.228866 | + | 0.973458i | \(0.426498\pi\) | |||||||
\(410\) | −22192.1 | −2.67314 | ||||||||
\(411\) | 23.9822 | 0.00287824 | ||||||||
\(412\) | −1067.64 | −0.127667 | ||||||||
\(413\) | −7984.71 | −0.951337 | ||||||||
\(414\) | −11583.1 | −1.37507 | ||||||||
\(415\) | 11975.6 | 1.41652 | ||||||||
\(416\) | 13630.0 | 1.60640 | ||||||||
\(417\) | 456.643 | 0.0536257 | ||||||||
\(418\) | −20187.8 | −2.36225 | ||||||||
\(419\) | 1056.05 | 0.123130 | 0.0615651 | − | 0.998103i | \(-0.480391\pi\) | ||||
0.0615651 | + | 0.998103i | \(0.480391\pi\) | |||||||
\(420\) | −2848.98 | −0.330990 | ||||||||
\(421\) | −15903.1 | −1.84103 | −0.920513 | − | 0.390712i | \(-0.872229\pi\) | ||||
−0.920513 | + | 0.390712i | \(0.872229\pi\) | |||||||
\(422\) | −11920.5 | −1.37507 | ||||||||
\(423\) | −6410.42 | −0.736845 | ||||||||
\(424\) | 679.208 | 0.0777955 | ||||||||
\(425\) | −2779.14 | −0.317195 | ||||||||
\(426\) | −951.850 | −0.108257 | ||||||||
\(427\) | 2018.86 | 0.228804 | ||||||||
\(428\) | 7282.64 | 0.822476 | ||||||||
\(429\) | −2183.67 | −0.245754 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8420.44 | −0.941064 | −0.470532 | − | 0.882383i | \(-0.655938\pi\) | ||||
−0.470532 | + | 0.882383i | \(0.655938\pi\) | |||||||
\(432\) | −1664.30 | −0.185356 | ||||||||
\(433\) | −14918.0 | −1.65569 | −0.827844 | − | 0.560959i | \(-0.810433\pi\) | ||||
−0.827844 | + | 0.560959i | \(0.810433\pi\) | |||||||
\(434\) | −1858.64 | −0.205570 | ||||||||
\(435\) | −93.7936 | −0.0103381 | ||||||||
\(436\) | −6955.16 | −0.763972 | ||||||||
\(437\) | −7900.71 | −0.864856 | ||||||||
\(438\) | 745.803 | 0.0813603 | ||||||||
\(439\) | −759.012 | −0.0825186 | −0.0412593 | − | 0.999148i | \(-0.513137\pi\) | ||||
−0.0412593 | + | 0.999148i | \(0.513137\pi\) | |||||||
\(440\) | −6276.26 | −0.680021 | ||||||||
\(441\) | −18508.7 | −1.99857 | ||||||||
\(442\) | 9055.91 | 0.974538 | ||||||||
\(443\) | 6067.89 | 0.650777 | 0.325388 | − | 0.945580i | \(-0.394505\pi\) | ||||
0.325388 | + | 0.945580i | \(0.394505\pi\) | |||||||
\(444\) | 2256.36 | 0.241176 | ||||||||
\(445\) | 7117.51 | 0.758208 | ||||||||
\(446\) | −4244.56 | −0.450641 | ||||||||
\(447\) | −945.621 | −0.100059 | ||||||||
\(448\) | −22633.6 | −2.38691 | ||||||||
\(449\) | −1182.72 | −0.124311 | −0.0621557 | − | 0.998066i | \(-0.519798\pi\) | ||||
−0.0621557 | + | 0.998066i | \(0.519798\pi\) | |||||||
\(450\) | 7654.71 | 0.801881 | ||||||||
\(451\) | 23856.4 | 2.49080 | ||||||||
\(452\) | 7678.80 | 0.799072 | ||||||||
\(453\) | 2159.18 | 0.223945 | ||||||||
\(454\) | 7817.86 | 0.808173 | ||||||||
\(455\) | 23778.1 | 2.44997 | ||||||||
\(456\) | 358.042 | 0.0367694 | ||||||||
\(457\) | 14176.7 | 1.45112 | 0.725558 | − | 0.688161i | \(-0.241582\pi\) | ||||
0.725558 | + | 0.688161i | \(0.241582\pi\) | |||||||
\(458\) | −27933.0 | −2.84983 | ||||||||
\(459\) | −1423.51 | −0.144758 | ||||||||
\(460\) | −13984.4 | −1.41745 | ||||||||
\(461\) | −4125.95 | −0.416843 | −0.208422 | − | 0.978039i | \(-0.566833\pi\) | ||||
−0.208422 | + | 0.978039i | \(0.566833\pi\) | |||||||
\(462\) | 5587.34 | 0.562655 | ||||||||
\(463\) | −10697.8 | −1.07380 | −0.536899 | − | 0.843646i | \(-0.680405\pi\) | ||||
−0.536899 | + | 0.843646i | \(0.680405\pi\) | |||||||
\(464\) | −488.873 | −0.0489124 | ||||||||
\(465\) | −124.743 | −0.0124405 | ||||||||
\(466\) | 5295.50 | 0.526415 | ||||||||
\(467\) | −15719.7 | −1.55764 | −0.778821 | − | 0.627246i | \(-0.784182\pi\) | ||||
−0.778821 | + | 0.627246i | \(0.784182\pi\) | |||||||
\(468\) | −13672.3 | −1.35043 | ||||||||
\(469\) | 8270.40 | 0.814268 | ||||||||
\(470\) | −14119.4 | −1.38570 | ||||||||
\(471\) | −888.368 | −0.0869083 | ||||||||
\(472\) | 1776.16 | 0.173209 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2827.89 | 0.274028 | ||||||||
\(475\) | 5221.17 | 0.504345 | ||||||||
\(476\) | −12701.1 | −1.22301 | ||||||||
\(477\) | 2516.34 | 0.241541 | ||||||||
\(478\) | 20165.9 | 1.92964 | ||||||||
\(479\) | −9517.11 | −0.907824 | −0.453912 | − | 0.891046i | \(-0.649972\pi\) | ||||
−0.453912 | + | 0.891046i | \(0.649972\pi\) | |||||||
\(480\) | −2340.63 | −0.222572 | ||||||||
\(481\) | −18832.0 | −1.78517 | ||||||||
\(482\) | 13946.3 | 1.31792 | ||||||||
\(483\) | 2186.66 | 0.205997 | ||||||||
\(484\) | 25496.0 | 2.39444 | ||||||||
\(485\) | 4264.69 | 0.399278 | ||||||||
\(486\) | 5896.93 | 0.550392 | ||||||||
\(487\) | −2176.30 | −0.202500 | −0.101250 | − | 0.994861i | \(-0.532284\pi\) | ||||
−0.101250 | + | 0.994861i | \(0.532284\pi\) | |||||||
\(488\) | −449.087 | −0.0416582 | ||||||||
\(489\) | 498.984 | 0.0461449 | ||||||||
\(490\) | −40766.6 | −3.75847 | ||||||||
\(491\) | 6458.88 | 0.593656 | 0.296828 | − | 0.954931i | \(-0.404071\pi\) | ||||
0.296828 | + | 0.954931i | \(0.404071\pi\) | |||||||
\(492\) | −2408.88 | −0.220733 | ||||||||
\(493\) | −418.143 | −0.0381992 | ||||||||
\(494\) | −17013.3 | −1.54953 | ||||||||
\(495\) | −23252.4 | −2.11135 | ||||||||
\(496\) | −650.188 | −0.0588594 | ||||||||
\(497\) | −11142.0 | −1.00561 | ||||||||
\(498\) | 2371.50 | 0.213393 | ||||||||
\(499\) | 10223.0 | 0.917120 | 0.458560 | − | 0.888664i | \(-0.348365\pi\) | ||||
0.458560 | + | 0.888664i | \(0.348365\pi\) | |||||||
\(500\) | −7631.18 | −0.682553 | ||||||||
\(501\) | −566.400 | −0.0505088 | ||||||||
\(502\) | 30835.5 | 2.74155 | ||||||||
\(503\) | 5795.18 | 0.513707 | 0.256853 | − | 0.966450i | \(-0.417314\pi\) | ||||
0.256853 | + | 0.966450i | \(0.417314\pi\) | |||||||
\(504\) | 6144.56 | 0.543056 | ||||||||
\(505\) | 1455.00 | 0.128211 | ||||||||
\(506\) | 27425.9 | 2.40955 | ||||||||
\(507\) | −402.101 | −0.0352227 | ||||||||
\(508\) | −20308.6 | −1.77371 | ||||||||
\(509\) | 1571.98 | 0.136889 | 0.0684447 | − | 0.997655i | \(-0.478196\pi\) | ||||
0.0684447 | + | 0.997655i | \(0.478196\pi\) | |||||||
\(510\) | −1555.14 | −0.135025 | ||||||||
\(511\) | 8730.12 | 0.755769 | ||||||||
\(512\) | −14922.9 | −1.28810 | ||||||||
\(513\) | 2674.35 | 0.230166 | ||||||||
\(514\) | −31702.6 | −2.72051 | ||||||||
\(515\) | −1530.21 | −0.130930 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15178.2 | 1.29118 | ||||||||
\(518\) | 48185.4 | 4.08715 | ||||||||
\(519\) | −1592.83 | −0.134716 | ||||||||
\(520\) | −5289.33 | −0.446063 | ||||||||
\(521\) | 9189.64 | 0.772755 | 0.386377 | − | 0.922341i | \(-0.373726\pi\) | ||||
0.386377 | + | 0.922341i | \(0.373726\pi\) | |||||||
\(522\) | 1151.71 | 0.0965689 | ||||||||
\(523\) | −9173.46 | −0.766974 | −0.383487 | − | 0.923546i | \(-0.625277\pi\) | ||||
−0.383487 | + | 0.923546i | \(0.625277\pi\) | |||||||
\(524\) | −23543.6 | −1.96280 | ||||||||
\(525\) | −1445.05 | −0.120128 | ||||||||
\(526\) | −13331.3 | −1.10508 | ||||||||
\(527\) | −556.118 | −0.0459675 | ||||||||
\(528\) | 1954.56 | 0.161101 | ||||||||
\(529\) | −1433.60 | −0.117827 | ||||||||
\(530\) | 5542.39 | 0.454238 | ||||||||
\(531\) | 6580.36 | 0.537784 | ||||||||
\(532\) | 23861.5 | 1.94460 | ||||||||
\(533\) | 20105.0 | 1.63385 | ||||||||
\(534\) | 1409.47 | 0.114220 | ||||||||
\(535\) | 10438.0 | 0.843499 | ||||||||
\(536\) | −1839.71 | −0.148253 | ||||||||
\(537\) | −114.787 | −0.00922422 | ||||||||
\(538\) | −15714.4 | −1.25929 | ||||||||
\(539\) | 43823.9 | 3.50210 | ||||||||
\(540\) | 4733.66 | 0.377230 | ||||||||
\(541\) | −5530.27 | −0.439492 | −0.219746 | − | 0.975557i | \(-0.570523\pi\) | ||||
−0.219746 | + | 0.975557i | \(0.570523\pi\) | |||||||
\(542\) | −10780.9 | −0.854389 | ||||||||
\(543\) | 87.1222 | 0.00688539 | ||||||||
\(544\) | −10434.8 | −0.822406 | ||||||||
\(545\) | −9968.59 | −0.783500 | ||||||||
\(546\) | 4708.74 | 0.369076 | ||||||||
\(547\) | −14776.3 | −1.15501 | −0.577504 | − | 0.816388i | \(-0.695973\pi\) | ||||
−0.577504 | + | 0.816388i | \(0.695973\pi\) | |||||||
\(548\) | −355.531 | −0.0277145 | ||||||||
\(549\) | −1663.78 | −0.129341 | ||||||||
\(550\) | −18124.4 | −1.40514 | ||||||||
\(551\) | 785.565 | 0.0607372 | ||||||||
\(552\) | −486.413 | −0.0375056 | ||||||||
\(553\) | 33102.4 | 2.54549 | ||||||||
\(554\) | 2469.11 | 0.189355 | ||||||||
\(555\) | 3233.97 | 0.247341 | ||||||||
\(556\) | −6769.63 | −0.516360 | ||||||||
\(557\) | 25533.5 | 1.94235 | 0.971176 | − | 0.238364i | \(-0.0766111\pi\) | ||||
0.971176 | + | 0.238364i | \(0.0766111\pi\) | |||||||
\(558\) | 1531.74 | 0.116207 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −21283.3 | −1.60604 | ||||||||
\(561\) | 1671.77 | 0.125815 | ||||||||
\(562\) | −8421.11 | −0.632070 | ||||||||
\(563\) | −25508.4 | −1.90950 | −0.954751 | − | 0.297405i | \(-0.903879\pi\) | ||||
−0.954751 | + | 0.297405i | \(0.903879\pi\) | |||||||
\(564\) | −1532.61 | −0.114423 | ||||||||
\(565\) | 11005.8 | 0.819497 | ||||||||
\(566\) | −9361.50 | −0.695218 | ||||||||
\(567\) | 22391.4 | 1.65847 | ||||||||
\(568\) | 2478.50 | 0.183091 | ||||||||
\(569\) | 1770.95 | 0.130478 | 0.0652391 | − | 0.997870i | \(-0.479219\pi\) | ||||
0.0652391 | + | 0.997870i | \(0.479219\pi\) | |||||||
\(570\) | 2921.65 | 0.214692 | ||||||||
\(571\) | −13023.1 | −0.954468 | −0.477234 | − | 0.878776i | \(-0.658361\pi\) | ||||
−0.477234 | + | 0.878776i | \(0.658361\pi\) | |||||||
\(572\) | 32372.4 | 2.36636 | ||||||||
\(573\) | 1537.23 | 0.112074 | ||||||||
\(574\) | −51442.5 | −3.74071 | ||||||||
\(575\) | −7093.15 | −0.514443 | ||||||||
\(576\) | 18652.8 | 1.34930 | ||||||||
\(577\) | −7547.32 | −0.544539 | −0.272270 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272270 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(578\) | 13739.3 | 0.988719 | ||||||||
\(579\) | 2721.24 | 0.195321 | ||||||||
\(580\) | 1390.47 | 0.0995450 | ||||||||
\(581\) | 27760.1 | 1.98224 | ||||||||
\(582\) | 844.530 | 0.0601493 | ||||||||
\(583\) | −5958.05 | −0.423254 | ||||||||
\(584\) | −1941.98 | −0.137602 | ||||||||
\(585\) | −19596.0 | −1.38495 | ||||||||
\(586\) | 21589.0 | 1.52190 | ||||||||
\(587\) | −7727.05 | −0.543321 | −0.271661 | − | 0.962393i | \(-0.587573\pi\) | ||||
−0.271661 | + | 0.962393i | \(0.587573\pi\) | |||||||
\(588\) | −4425.10 | −0.310354 | ||||||||
\(589\) | 1044.78 | 0.0730889 | ||||||||
\(590\) | 14493.6 | 1.01135 | ||||||||
\(591\) | 1462.54 | 0.101795 | ||||||||
\(592\) | 16856.2 | 1.17024 | ||||||||
\(593\) | 12011.5 | 0.831790 | 0.415895 | − | 0.909413i | \(-0.363468\pi\) | ||||
0.415895 | + | 0.909413i | \(0.363468\pi\) | |||||||
\(594\) | −9283.53 | −0.641259 | ||||||||
\(595\) | −18204.0 | −1.25427 | ||||||||
\(596\) | 14018.6 | 0.963464 | ||||||||
\(597\) | −1796.05 | −0.123128 | ||||||||
\(598\) | 23113.2 | 1.58055 | ||||||||
\(599\) | 4737.78 | 0.323172 | 0.161586 | − | 0.986859i | \(-0.448339\pi\) | ||||
0.161586 | + | 0.986859i | \(0.448339\pi\) | |||||||
\(600\) | 321.445 | 0.0218716 | ||||||||
\(601\) | −4096.54 | −0.278039 | −0.139020 | − | 0.990290i | \(-0.544395\pi\) | ||||
−0.139020 | + | 0.990290i | \(0.544395\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6815.80 | −0.460300 | ||||||||
\(604\) | −32009.4 | −2.15636 | ||||||||
\(605\) | 36542.5 | 2.45565 | ||||||||
\(606\) | 288.131 | 0.0193144 | ||||||||
\(607\) | 7628.52 | 0.510102 | 0.255051 | − | 0.966928i | \(-0.417908\pi\) | ||||
0.255051 | + | 0.966928i | \(0.417908\pi\) | |||||||
\(608\) | 19603.9 | 1.30764 | ||||||||
\(609\) | −217.419 | −0.0144668 | ||||||||
\(610\) | −3664.58 | −0.243237 | ||||||||
\(611\) | 12791.5 | 0.846953 | ||||||||
\(612\) | 10467.2 | 0.691359 | ||||||||
\(613\) | 4190.40 | 0.276099 | 0.138049 | − | 0.990425i | \(-0.455917\pi\) | ||||
0.138049 | + | 0.990425i | \(0.455917\pi\) | |||||||
\(614\) | 6995.85 | 0.459820 | ||||||||
\(615\) | −3452.57 | −0.226376 | ||||||||
\(616\) | −14548.7 | −0.951599 | ||||||||
\(617\) | 16915.3 | 1.10370 | 0.551851 | − | 0.833943i | \(-0.313922\pi\) | ||||
0.551851 | + | 0.833943i | \(0.313922\pi\) | |||||||
\(618\) | −303.025 | −0.0197240 | ||||||||
\(619\) | 23926.2 | 1.55359 | 0.776797 | − | 0.629751i | \(-0.216843\pi\) | ||||
0.776797 | + | 0.629751i | \(0.216843\pi\) | |||||||
\(620\) | 1849.28 | 0.119789 | ||||||||
\(621\) | −3633.20 | −0.234775 | ||||||||
\(622\) | −31553.4 | −2.03405 | ||||||||
\(623\) | 16498.8 | 1.06101 | ||||||||
\(624\) | 1647.21 | 0.105675 | ||||||||
\(625\) | −19495.7 | −1.24772 | ||||||||
\(626\) | 20497.9 | 1.30873 | ||||||||
\(627\) | −3140.76 | −0.200048 | ||||||||
\(628\) | 13169.8 | 0.836838 | ||||||||
\(629\) | 14417.4 | 0.913926 | ||||||||
\(630\) | 50140.1 | 3.17084 | ||||||||
\(631\) | −21858.0 | −1.37901 | −0.689503 | − | 0.724283i | \(-0.742171\pi\) | ||||
−0.689503 | + | 0.724283i | \(0.742171\pi\) | |||||||
\(632\) | −7363.48 | −0.463455 | ||||||||
\(633\) | −1854.55 | −0.116448 | ||||||||
\(634\) | −29393.7 | −1.84128 | ||||||||
\(635\) | −29107.5 | −1.81905 | ||||||||
\(636\) | 601.611 | 0.0375085 | ||||||||
\(637\) | 36932.7 | 2.29722 | ||||||||
\(638\) | −2726.95 | −0.169218 | ||||||||
\(639\) | 9182.38 | 0.568465 | ||||||||
\(640\) | 12479.3 | 0.770760 | ||||||||
\(641\) | 31069.9 | 1.91449 | 0.957244 | − | 0.289281i | \(-0.0934161\pi\) | ||||
0.957244 | + | 0.289281i | \(0.0934161\pi\) | |||||||
\(642\) | 2067.01 | 0.127069 | ||||||||
\(643\) | −8457.95 | −0.518739 | −0.259369 | − | 0.965778i | \(-0.583515\pi\) | ||||
−0.259369 | + | 0.965778i | \(0.583515\pi\) | |||||||
\(644\) | −32416.7 | −1.98354 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13025.1 | 0.793288 | ||||||||
\(647\) | −21034.7 | −1.27814 | −0.639072 | − | 0.769147i | \(-0.720682\pi\) | ||||
−0.639072 | + | 0.769147i | \(0.720682\pi\) | |||||||
\(648\) | −4980.87 | −0.301955 | ||||||||
\(649\) | −15580.6 | −0.942360 | ||||||||
\(650\) | −15274.4 | −0.921707 | ||||||||
\(651\) | −289.161 | −0.0174088 | ||||||||
\(652\) | −7397.33 | −0.444328 | ||||||||
\(653\) | 16312.9 | 0.977603 | 0.488802 | − | 0.872395i | \(-0.337434\pi\) | ||||
0.488802 | + | 0.872395i | \(0.337434\pi\) | |||||||
\(654\) | −1974.06 | −0.118031 | ||||||||
\(655\) | −33744.2 | −2.01297 | ||||||||
\(656\) | −17995.6 | −1.07105 | ||||||||
\(657\) | −7194.66 | −0.427231 | ||||||||
\(658\) | −32729.5 | −1.93910 | ||||||||
\(659\) | 13578.7 | 0.802655 | 0.401328 | − | 0.915935i | \(-0.368549\pi\) | ||||
0.401328 | + | 0.915935i | \(0.368549\pi\) | |||||||
\(660\) | −5559.22 | −0.327867 | ||||||||
\(661\) | 20138.0 | 1.18499 | 0.592495 | − | 0.805574i | \(-0.298143\pi\) | ||||
0.592495 | + | 0.805574i | \(0.298143\pi\) | |||||||
\(662\) | −1559.12 | −0.0915363 | ||||||||
\(663\) | 1408.89 | 0.0825290 | ||||||||
\(664\) | −6175.10 | −0.360904 | ||||||||
\(665\) | 34199.9 | 1.99431 | ||||||||
\(666\) | −39710.5 | −2.31044 | ||||||||
\(667\) | −1067.22 | −0.0619533 | ||||||||
\(668\) | 8396.76 | 0.486348 | ||||||||
\(669\) | −660.355 | −0.0381626 | ||||||||
\(670\) | −15012.2 | −0.865630 | ||||||||
\(671\) | 3939.41 | 0.226646 | ||||||||
\(672\) | −5425.72 | −0.311461 | ||||||||
\(673\) | 1613.56 | 0.0924195 | 0.0462098 | − | 0.998932i | \(-0.485286\pi\) | ||||
0.0462098 | + | 0.998932i | \(0.485286\pi\) | |||||||
\(674\) | −49986.7 | −2.85670 | ||||||||
\(675\) | 2400.99 | 0.136910 | ||||||||
\(676\) | 5961.05 | 0.339159 | ||||||||
\(677\) | −10688.3 | −0.606772 | −0.303386 | − | 0.952868i | \(-0.598117\pi\) | ||||
−0.303386 | + | 0.952868i | \(0.598117\pi\) | |||||||
\(678\) | 2179.45 | 0.123453 | ||||||||
\(679\) | 9885.79 | 0.558736 | ||||||||
\(680\) | 4049.40 | 0.228364 | ||||||||
\(681\) | 1216.28 | 0.0684403 | ||||||||
\(682\) | −3626.77 | −0.203631 | ||||||||
\(683\) | −7229.87 | −0.405042 | −0.202521 | − | 0.979278i | \(-0.564913\pi\) | ||||
−0.202521 | + | 0.979278i | \(0.564913\pi\) | |||||||
\(684\) | −19664.7 | −1.09927 | ||||||||
\(685\) | −509.570 | −0.0284229 | ||||||||
\(686\) | −47966.3 | −2.66962 | ||||||||
\(687\) | −4345.73 | −0.241339 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5021.16 | −0.277635 | ||||||||
\(690\) | −3969.17 | −0.218991 | ||||||||
\(691\) | −25962.1 | −1.42930 | −0.714649 | − | 0.699483i | \(-0.753414\pi\) | ||||
−0.714649 | + | 0.699483i | \(0.753414\pi\) | |||||||
\(692\) | 23613.3 | 1.29717 | ||||||||
\(693\) | −53900.3 | −2.95455 | ||||||||
\(694\) | 1275.43 | 0.0697620 | ||||||||
\(695\) | −9702.67 | −0.529559 | ||||||||
\(696\) | 48.3639 | 0.00263395 | ||||||||
\(697\) | −15392.0 | −0.836459 | ||||||||
\(698\) | 42928.9 | 2.32791 | ||||||||
\(699\) | 823.857 | 0.0445796 | ||||||||
\(700\) | 21422.5 | 1.15671 | ||||||||
\(701\) | −6626.06 | −0.357008 | −0.178504 | − | 0.983939i | \(-0.557126\pi\) | ||||
−0.178504 | + | 0.983939i | \(0.557126\pi\) | |||||||
\(702\) | −7823.71 | −0.420637 | ||||||||
\(703\) | −27086.0 | −1.45315 | ||||||||
\(704\) | −44165.0 | −2.36439 | ||||||||
\(705\) | −2196.64 | −0.117348 | ||||||||
\(706\) | 13199.0 | 0.703613 | ||||||||
\(707\) | 3372.76 | 0.179414 | ||||||||
\(708\) | 1573.24 | 0.0835114 | ||||||||
\(709\) | −29713.2 | −1.57391 | −0.786956 | − | 0.617009i | \(-0.788344\pi\) | ||||
−0.786956 | + | 0.617009i | \(0.788344\pi\) | |||||||
\(710\) | 20224.8 | 1.06904 | ||||||||
\(711\) | −27280.3 | −1.43895 | ||||||||
\(712\) | −3670.08 | −0.193177 | ||||||||
\(713\) | −1419.37 | −0.0745524 | ||||||||
\(714\) | −3604.91 | −0.188950 | ||||||||
\(715\) | 46398.3 | 2.42685 | ||||||||
\(716\) | 1701.68 | 0.0888198 | ||||||||
\(717\) | 3137.35 | 0.163412 | ||||||||
\(718\) | −44469.7 | −2.31141 | ||||||||
\(719\) | 24939.1 | 1.29356 | 0.646782 | − | 0.762675i | \(-0.276114\pi\) | ||||
0.646782 | + | 0.762675i | \(0.276114\pi\) | |||||||
\(720\) | 17540.0 | 0.907883 | ||||||||
\(721\) | −3547.11 | −0.183220 | ||||||||
\(722\) | 4390.27 | 0.226301 | ||||||||
\(723\) | 2169.72 | 0.111608 | ||||||||
\(724\) | −1291.57 | −0.0662993 | ||||||||
\(725\) | 705.270 | 0.0361284 | ||||||||
\(726\) | 7236.46 | 0.369932 | ||||||||
\(727\) | −29226.9 | −1.49101 | −0.745507 | − | 0.666498i | \(-0.767793\pi\) | ||||
−0.745507 | + | 0.666498i | \(0.767793\pi\) | |||||||
\(728\) | −12261.0 | −0.624206 | ||||||||
\(729\) | −17833.4 | −0.906028 | ||||||||
\(730\) | −15846.7 | −0.803441 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −397.780 | −0.0200852 | ||||||||
\(733\) | −13372.7 | −0.673849 | −0.336925 | − | 0.941532i | \(-0.609387\pi\) | ||||
−0.336925 | + | 0.941532i | \(0.609387\pi\) | |||||||
\(734\) | 39860.9 | 2.00449 | ||||||||
\(735\) | −6342.34 | −0.318287 | ||||||||
\(736\) | −26632.6 | −1.33382 | ||||||||
\(737\) | 16138.1 | 0.806584 | ||||||||
\(738\) | 42394.7 | 2.11460 | ||||||||
\(739\) | 4818.31 | 0.239843 | 0.119922 | − | 0.992783i | \(-0.461736\pi\) | ||||
0.119922 | + | 0.992783i | \(0.461736\pi\) | |||||||
\(740\) | −47942.8 | −2.38164 | ||||||||
\(741\) | −2646.88 | −0.131222 | ||||||||
\(742\) | 12847.6 | 0.635647 | ||||||||
\(743\) | −15211.9 | −0.751106 | −0.375553 | − | 0.926801i | \(-0.622547\pi\) | ||||
−0.375553 | + | 0.926801i | \(0.622547\pi\) | |||||||
\(744\) | 64.3226 | 0.00316960 | ||||||||
\(745\) | 20092.4 | 0.988091 | ||||||||
\(746\) | 23473.8 | 1.15206 | ||||||||
\(747\) | −22877.6 | −1.12055 | ||||||||
\(748\) | −24783.6 | −1.21147 | ||||||||
\(749\) | 24195.8 | 1.18037 | ||||||||
\(750\) | −2165.94 | −0.105452 | ||||||||
\(751\) | 27003.6 | 1.31208 | 0.656042 | − | 0.754724i | \(-0.272229\pi\) | ||||
0.656042 | + | 0.754724i | \(0.272229\pi\) | |||||||
\(752\) | −11449.4 | −0.555208 | ||||||||
\(753\) | 4797.29 | 0.232169 | ||||||||
\(754\) | −2298.14 | −0.110999 | ||||||||
\(755\) | −45878.0 | −2.21148 | ||||||||
\(756\) | 10972.9 | 0.527884 | ||||||||
\(757\) | −28606.3 | −1.37346 | −0.686732 | − | 0.726910i | \(-0.740956\pi\) | ||||
−0.686732 | + | 0.726910i | \(0.740956\pi\) | |||||||
\(758\) | −35222.6 | −1.68779 | ||||||||
\(759\) | 4266.83 | 0.204053 | ||||||||
\(760\) | −7607.61 | −0.363101 | ||||||||
\(761\) | −11237.8 | −0.535310 | −0.267655 | − | 0.963515i | \(-0.586249\pi\) | ||||
−0.267655 | + | 0.963515i | \(0.586249\pi\) | |||||||
\(762\) | −5764.12 | −0.274032 | ||||||||
\(763\) | −23107.8 | −1.09640 | ||||||||
\(764\) | −22789.0 | −1.07916 | ||||||||
\(765\) | 15002.3 | 0.709031 | ||||||||
\(766\) | −51004.5 | −2.40583 | ||||||||
\(767\) | −13130.6 | −0.618145 | ||||||||
\(768\) | −1205.00 | −0.0566166 | ||||||||
\(769\) | −29016.9 | −1.36070 | −0.680348 | − | 0.732889i | \(-0.738171\pi\) | ||||
−0.680348 | + | 0.732889i | \(0.738171\pi\) | |||||||
\(770\) | −118719. | −5.55627 | ||||||||
\(771\) | −4932.19 | −0.230387 | ||||||||
\(772\) | −40341.8 | −1.88074 | ||||||||
\(773\) | −35838.2 | −1.66754 | −0.833772 | − | 0.552109i | \(-0.813823\pi\) | ||||
−0.833772 | + | 0.552109i | \(0.813823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 937.989 | 0.0434756 | ||||||||
\(776\) | −2199.05 | −0.101729 | ||||||||
\(777\) | 7496.52 | 0.346121 | ||||||||
\(778\) | −23540.1 | −1.08477 | ||||||||
\(779\) | 28916.9 | 1.32998 | ||||||||
\(780\) | −4685.04 | −0.215066 | ||||||||
\(781\) | −21741.5 | −0.996123 | ||||||||
\(782\) | −17695.0 | −0.809172 | ||||||||
\(783\) | 361.248 | 0.0164878 | ||||||||
\(784\) | −33057.7 | −1.50591 | ||||||||
\(785\) | 18875.9 | 0.858228 | ||||||||
\(786\) | −6682.30 | −0.303244 | ||||||||
\(787\) | 19880.4 | 0.900455 | 0.450228 | − | 0.892914i | \(-0.351343\pi\) | ||||
0.450228 | + | 0.892914i | \(0.351343\pi\) | |||||||
\(788\) | −21681.8 | −0.980179 | ||||||||
\(789\) | −2074.04 | −0.0935841 | ||||||||
\(790\) | −60086.6 | −2.70606 | ||||||||
\(791\) | 25512.0 | 1.14678 | ||||||||
\(792\) | 11989.9 | 0.537932 | ||||||||
\(793\) | 3319.94 | 0.148669 | ||||||||
\(794\) | −51085.3 | −2.28331 | ||||||||
\(795\) | 862.268 | 0.0384673 | ||||||||
\(796\) | 26626.0 | 1.18559 | ||||||||
\(797\) | 11240.1 | 0.499555 | 0.249778 | − | 0.968303i | \(-0.419643\pi\) | ||||
0.249778 | + | 0.968303i | \(0.419643\pi\) | |||||||
\(798\) | 6772.55 | 0.300433 | ||||||||
\(799\) | −9792.89 | −0.433601 | ||||||||
\(800\) | 17600.1 | 0.777822 | ||||||||
\(801\) | −13597.0 | −0.599782 | ||||||||
\(802\) | 9254.81 | 0.407480 | ||||||||
\(803\) | 17035.1 | 0.748637 | ||||||||
\(804\) | −1629.53 | −0.0714790 | ||||||||
\(805\) | −46461.8 | −2.03424 | ||||||||
\(806\) | −3056.47 | −0.133572 | ||||||||
\(807\) | −2444.80 | −0.106643 | ||||||||
\(808\) | −750.256 | −0.0326657 | ||||||||
\(809\) | 7574.05 | 0.329159 | 0.164579 | − | 0.986364i | \(-0.447373\pi\) | ||||
0.164579 | + | 0.986364i | \(0.447373\pi\) | |||||||
\(810\) | −40644.3 | −1.76308 | ||||||||
\(811\) | −8976.71 | −0.388674 | −0.194337 | − | 0.980935i | \(-0.562256\pi\) | ||||
−0.194337 | + | 0.980935i | \(0.562256\pi\) | |||||||
\(812\) | 3223.19 | 0.139300 | ||||||||
\(813\) | −1677.26 | −0.0723542 | ||||||||
\(814\) | 94024.2 | 4.04858 | ||||||||
\(815\) | −10602.3 | −0.455685 | ||||||||
\(816\) | −1261.07 | −0.0541007 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −15930.8 | −0.680939 | ||||||||
\(819\) | −45424.6 | −1.93805 | ||||||||
\(820\) | 51183.5 | 2.17976 | ||||||||
\(821\) | 38991.5 | 1.65750 | 0.828752 | − | 0.559616i | \(-0.189051\pi\) | ||||
0.828752 | + | 0.559616i | \(0.189051\pi\) | |||||||
\(822\) | −100.909 | −0.00428178 | ||||||||
\(823\) | −4200.77 | −0.177922 | −0.0889610 | − | 0.996035i | \(-0.528355\pi\) | ||||
−0.0889610 | + | 0.996035i | \(0.528355\pi\) | |||||||
\(824\) | 789.039 | 0.0333586 | ||||||||
\(825\) | −2819.73 | −0.118994 | ||||||||
\(826\) | 33597.1 | 1.41524 | ||||||||
\(827\) | 27413.1 | 1.15266 | 0.576329 | − | 0.817218i | \(-0.304485\pi\) | ||||
0.576329 | + | 0.817218i | \(0.304485\pi\) | |||||||
\(828\) | 26715.3 | 1.12128 | ||||||||
\(829\) | −28260.3 | −1.18398 | −0.591992 | − | 0.805944i | \(-0.701658\pi\) | ||||
−0.591992 | + | 0.805944i | \(0.701658\pi\) | |||||||
\(830\) | −50389.3 | −2.10728 | ||||||||
\(831\) | 384.136 | 0.0160355 | ||||||||
\(832\) | −37220.1 | −1.55093 | ||||||||
\(833\) | −28274.9 | −1.17607 | ||||||||
\(834\) | −1921.41 | −0.0797756 | ||||||||
\(835\) | 12034.8 | 0.498779 | ||||||||
\(836\) | 46561.0 | 1.92625 | ||||||||
\(837\) | 480.449 | 0.0198408 | ||||||||
\(838\) | −4443.53 | −0.183173 | ||||||||
\(839\) | −12924.7 | −0.531837 | −0.265919 | − | 0.963995i | \(-0.585675\pi\) | ||||
−0.265919 | + | 0.963995i | \(0.585675\pi\) | |||||||
\(840\) | 2105.54 | 0.0864857 | ||||||||
\(841\) | −24282.9 | −0.995649 | ||||||||
\(842\) | 66915.3 | 2.73878 | ||||||||
\(843\) | −1310.13 | −0.0535270 | ||||||||
\(844\) | 27493.3 | 1.12128 | ||||||||
\(845\) | 8543.77 | 0.347828 | ||||||||
\(846\) | 26973.0 | 1.09616 | ||||||||
\(847\) | 84707.7 | 3.43635 | ||||||||
\(848\) | 4494.33 | 0.182000 | ||||||||
\(849\) | −1456.43 | −0.0588747 | ||||||||
\(850\) | 11693.7 | 0.471872 | ||||||||
\(851\) | 36797.3 | 1.48225 | ||||||||
\(852\) | 2195.34 | 0.0882758 | ||||||||
\(853\) | 39780.9 | 1.59680 | 0.798401 | − | 0.602126i | \(-0.205680\pi\) | ||||
0.798401 | + | 0.602126i | \(0.205680\pi\) | |||||||
\(854\) | −8494.71 | −0.340378 | ||||||||
\(855\) | −28184.8 | −1.12737 | ||||||||
\(856\) | −5382.24 | −0.214908 | ||||||||
\(857\) | 9841.41 | 0.392271 | 0.196135 | − | 0.980577i | \(-0.437161\pi\) | ||||
0.196135 | + | 0.980577i | \(0.437161\pi\) | |||||||
\(858\) | 9188.18 | 0.365594 | ||||||||
\(859\) | 25413.1 | 1.00941 | 0.504705 | − | 0.863292i | \(-0.331601\pi\) | ||||
0.504705 | + | 0.863292i | \(0.331601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8003.25 | −0.316783 | ||||||||
\(862\) | 35430.5 | 1.39996 | ||||||||
\(863\) | −13442.2 | −0.530219 | −0.265110 | − | 0.964218i | \(-0.585408\pi\) | ||||
−0.265110 | + | 0.964218i | \(0.585408\pi\) | |||||||
\(864\) | 9014.99 | 0.354972 | ||||||||
\(865\) | 33844.1 | 1.33033 | ||||||||
\(866\) | 62770.1 | 2.46306 | ||||||||
\(867\) | 2137.52 | 0.0837299 | ||||||||
\(868\) | 4286.75 | 0.167629 | ||||||||
\(869\) | 64592.8 | 2.52147 | ||||||||
\(870\) | 394.653 | 0.0153793 | ||||||||
\(871\) | 13600.4 | 0.529083 | ||||||||
\(872\) | 5140.22 | 0.199621 | ||||||||
\(873\) | −8147.07 | −0.315850 | ||||||||
\(874\) | 33243.6 | 1.28659 | ||||||||
\(875\) | −25353.8 | −0.979558 | ||||||||
\(876\) | −1720.11 | −0.0663438 | ||||||||
\(877\) | −26400.6 | −1.01652 | −0.508258 | − | 0.861205i | \(-0.669711\pi\) | ||||
−0.508258 | + | 0.861205i | \(0.669711\pi\) | |||||||
\(878\) | 3193.68 | 0.122758 | ||||||||
\(879\) | 3358.74 | 0.128882 | ||||||||
\(880\) | −41530.1 | −1.59089 | ||||||||
\(881\) | 777.294 | 0.0297250 | 0.0148625 | − | 0.999890i | \(-0.495269\pi\) | ||||
0.0148625 | + | 0.999890i | \(0.495269\pi\) | |||||||
\(882\) | 77878.8 | 2.97315 | ||||||||
\(883\) | −27263.3 | −1.03905 | −0.519527 | − | 0.854454i | \(-0.673892\pi\) | ||||
−0.519527 | + | 0.854454i | \(0.673892\pi\) | |||||||
\(884\) | −20886.5 | −0.794669 | ||||||||
\(885\) | 2254.87 | 0.0856460 | ||||||||
\(886\) | −25531.7 | −0.968120 | ||||||||
\(887\) | 12790.6 | 0.484178 | 0.242089 | − | 0.970254i | \(-0.422167\pi\) | ||||
0.242089 | + | 0.970254i | \(0.422167\pi\) | |||||||
\(888\) | −1667.57 | −0.0630179 | ||||||||
\(889\) | −67473.0 | −2.54552 | ||||||||
\(890\) | −29948.2 | −1.12794 | ||||||||
\(891\) | 43692.4 | 1.64282 | ||||||||
\(892\) | 9789.61 | 0.367467 | ||||||||
\(893\) | 18397.9 | 0.689432 | ||||||||
\(894\) | 3978.87 | 0.148851 | ||||||||
\(895\) | 2438.97 | 0.0910901 | ||||||||
\(896\) | 28927.7 | 1.07858 | ||||||||
\(897\) | 3595.88 | 0.133850 | ||||||||
\(898\) | 4976.49 | 0.184930 | ||||||||
\(899\) | 141.128 | 0.00523567 | ||||||||
\(900\) | −17654.7 | −0.653879 | ||||||||
\(901\) | 3844.09 | 0.142137 | ||||||||
\(902\) | −100380. | −3.70541 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5675.03 | −0.208793 | ||||||||
\(905\) | −1851.16 | −0.0679940 | ||||||||
\(906\) | −9085.15 | −0.333150 | ||||||||
\(907\) | −3260.09 | −0.119349 | −0.0596744 | − | 0.998218i | \(-0.519006\pi\) | ||||
−0.0596744 | + | 0.998218i | \(0.519006\pi\) | |||||||
\(908\) | −18031.0 | −0.659010 | ||||||||
\(909\) | −2779.56 | −0.101421 | ||||||||
\(910\) | −100051. | −3.64466 | ||||||||
\(911\) | 19935.7 | 0.725026 | 0.362513 | − | 0.931979i | \(-0.381919\pi\) | ||||
0.362513 | + | 0.931979i | \(0.381919\pi\) | |||||||
\(912\) | 2369.17 | 0.0860208 | ||||||||
\(913\) | 54168.3 | 1.96354 | ||||||||
\(914\) | −59651.1 | −2.15874 | ||||||||
\(915\) | −570.124 | −0.0205986 | ||||||||
\(916\) | 64424.4 | 2.32384 | ||||||||
\(917\) | −78220.9 | −2.81688 | ||||||||
\(918\) | 5989.67 | 0.215347 | ||||||||
\(919\) | 28506.6 | 1.02323 | 0.511614 | − | 0.859216i | \(-0.329048\pi\) | ||||
0.511614 | + | 0.859216i | \(0.329048\pi\) | |||||||
\(920\) | 10335.2 | 0.370372 | ||||||||
\(921\) | 1088.39 | 0.0389400 | ||||||||
\(922\) | 17360.7 | 0.620112 | ||||||||
\(923\) | −18322.7 | −0.653412 | ||||||||
\(924\) | −12886.6 | −0.458807 | ||||||||
\(925\) | −24317.4 | −0.864381 | ||||||||
\(926\) | 45012.9 | 1.59742 | ||||||||
\(927\) | 2923.24 | 0.103573 | ||||||||
\(928\) | 2648.07 | 0.0936715 | ||||||||
\(929\) | −39402.4 | −1.39155 | −0.695775 | − | 0.718260i | \(-0.744939\pi\) | ||||
−0.695775 | + | 0.718260i | \(0.744939\pi\) | |||||||
\(930\) | 524.877 | 0.0185069 | ||||||||
\(931\) | 53120.1 | 1.86997 | ||||||||
\(932\) | −12213.5 | −0.429256 | ||||||||
\(933\) | −4908.98 | −0.172254 | ||||||||
\(934\) | 66143.3 | 2.31721 | ||||||||
\(935\) | −35521.5 | −1.24244 | ||||||||
\(936\) | 10104.5 | 0.352859 | ||||||||
\(937\) | −16653.4 | −0.580621 | −0.290310 | − | 0.956933i | \(-0.593759\pi\) | ||||
−0.290310 | + | 0.956933i | \(0.593759\pi\) | |||||||
\(938\) | −34799.2 | −1.21134 | ||||||||
\(939\) | 3189.00 | 0.110830 | ||||||||
\(940\) | 32564.7 | 1.12994 | ||||||||
\(941\) | 37396.5 | 1.29553 | 0.647764 | − | 0.761841i | \(-0.275704\pi\) | ||||
0.647764 | + | 0.761841i | \(0.275704\pi\) | |||||||
\(942\) | 3737.96 | 0.129288 | ||||||||
\(943\) | −39284.6 | −1.35661 | ||||||||
\(944\) | 11752.9 | 0.405217 | ||||||||
\(945\) | 15727.1 | 0.541377 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30801.6 | 1.05693 | 0.528467 | − | 0.848954i | \(-0.322767\pi\) | ||||
0.528467 | + | 0.848954i | \(0.322767\pi\) | |||||||
\(948\) | −6522.23 | −0.223452 | ||||||||
\(949\) | 14356.4 | 0.491072 | ||||||||
\(950\) | −21969.0 | −0.750283 | ||||||||
\(951\) | −4572.98 | −0.155930 | ||||||||
\(952\) | 9386.74 | 0.319565 | ||||||||
\(953\) | −36744.1 | −1.24896 | −0.624480 | − | 0.781041i | \(-0.714689\pi\) | ||||
−0.624480 | + | 0.781041i | \(0.714689\pi\) | |||||||
\(954\) | −10587.9 | −0.359326 | ||||||||
\(955\) | −32662.7 | −1.10674 | ||||||||
\(956\) | −46510.5 | −1.57349 | ||||||||
\(957\) | −424.250 | −0.0143303 | ||||||||
\(958\) | 40044.9 | 1.35051 | ||||||||
\(959\) | −1181.21 | −0.0397741 | ||||||||
\(960\) | 6391.70 | 0.214887 | ||||||||
\(961\) | −29603.3 | −0.993700 | ||||||||
\(962\) | 79239.1 | 2.65569 | ||||||||
\(963\) | −19940.2 | −0.667252 | ||||||||
\(964\) | −32165.7 | −1.07467 | ||||||||
\(965\) | −57820.6 | −1.92882 | ||||||||
\(966\) | −9200.76 | −0.306449 | ||||||||
\(967\) | 15876.7 | 0.527985 | 0.263992 | − | 0.964525i | \(-0.414961\pi\) | ||||
0.263992 | + | 0.964525i | \(0.414961\pi\) | |||||||
\(968\) | −18842.8 | −0.625653 | ||||||||
\(969\) | 2026.40 | 0.0671798 | ||||||||
\(970\) | −17944.4 | −0.593980 | ||||||||
\(971\) | 18855.2 | 0.623163 | 0.311582 | − | 0.950219i | \(-0.399141\pi\) | ||||
0.311582 | + | 0.950219i | \(0.399141\pi\) | |||||||
\(972\) | −13600.6 | −0.448807 | ||||||||
\(973\) | −22491.4 | −0.741048 | ||||||||
\(974\) | 9157.17 | 0.301247 | ||||||||
\(975\) | −2376.33 | −0.0780550 | ||||||||
\(976\) | −2971.61 | −0.0974580 | ||||||||
\(977\) | −17915.0 | −0.586646 | −0.293323 | − | 0.956013i | \(-0.594761\pi\) | ||||
−0.293323 | + | 0.956013i | \(0.594761\pi\) | |||||||
\(978\) | −2099.56 | −0.0686469 | ||||||||
\(979\) | 32194.1 | 1.05100 | ||||||||
\(980\) | 94023.7 | 3.06477 | ||||||||
\(981\) | 19043.5 | 0.619790 | ||||||||
\(982\) | −27176.9 | −0.883146 | ||||||||
\(983\) | −5064.00 | −0.164310 | −0.0821550 | − | 0.996620i | \(-0.526180\pi\) | ||||
−0.0821550 | + | 0.996620i | \(0.526180\pi\) | |||||||
\(984\) | 1780.29 | 0.0576763 | ||||||||
\(985\) | −31075.7 | −1.00523 | ||||||||
\(986\) | 1759.41 | 0.0568266 | ||||||||
\(987\) | −5091.94 | −0.164213 | ||||||||
\(988\) | 39239.4 | 1.26353 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 97838.5 | 3.14092 | ||||||||
\(991\) | −22909.7 | −0.734361 | −0.367181 | − | 0.930150i | \(-0.619677\pi\) | ||||
−0.367181 | + | 0.930150i | \(0.619677\pi\) | |||||||
\(992\) | 3521.86 | 0.112721 | ||||||||
\(993\) | −242.563 | −0.00775177 | ||||||||
\(994\) | 46882.1 | 1.49599 | ||||||||
\(995\) | 38162.1 | 1.21590 | ||||||||
\(996\) | −5469.61 | −0.174007 | ||||||||
\(997\) | −6909.86 | −0.219496 | −0.109748 | − | 0.993959i | \(-0.535004\pi\) | ||||
−0.109748 | + | 0.993959i | \(0.535004\pi\) | |||||||
\(998\) | −43014.9 | −1.36434 | ||||||||
\(999\) | −12455.7 | −0.394475 |
(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 | 1849.4.a.m.1.19 | ✓ | 110 | |
43.42 | odd | 2 | inner | 1849.4.a.m.1.92 | yes | 110 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.m.1.19 | ✓ | 110 | 1.1 | even | 1 | trivial | |
1849.4.a.m.1.92 | yes | 110 | 43.42 | odd | 2 | inner |