Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(109.684550701\) |
Analytic rank: | \(1\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + 941923 x^{9} - 2799440 x^{8} - 6021311 x^{7} + 15765187 x^{6} + \cdots + 2596992 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.79502\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79502 | −0.988189 | −0.494094 | − | 0.869408i | \(-0.664500\pi\) | ||||
−0.494094 | + | 0.869408i | \(0.664500\pi\) | |||||||
\(3\) | 10.1456 | 1.95252 | 0.976261 | − | 0.216598i | \(-0.0694960\pi\) | ||||
0.976261 | + | 0.216598i | \(0.0694960\pi\) | |||||||
\(4\) | −0.187860 | −0.0234825 | ||||||||
\(5\) | −5.45712 | −0.488099 | −0.244050 | − | 0.969763i | \(-0.578476\pi\) | ||||
−0.244050 | + | 0.969763i | \(0.578476\pi\) | |||||||
\(6\) | −28.3572 | −1.92946 | ||||||||
\(7\) | −7.73594 | −0.417702 | −0.208851 | − | 0.977948i | \(-0.566972\pi\) | ||||
−0.208851 | + | 0.977948i | \(0.566972\pi\) | |||||||
\(8\) | 22.8852 | 1.01139 | ||||||||
\(9\) | 75.9332 | 2.81234 | ||||||||
\(10\) | 15.2528 | 0.482334 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −1.90595 | −0.0458501 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 21.6221 | 0.412768 | ||||||||
\(15\) | −55.3657 | −0.953025 | ||||||||
\(16\) | −62.4618 | −0.975966 | ||||||||
\(17\) | −18.5218 | −0.264246 | −0.132123 | − | 0.991233i | \(-0.542179\pi\) | ||||
−0.132123 | + | 0.991233i | \(0.542179\pi\) | |||||||
\(18\) | −212.235 | −2.77912 | ||||||||
\(19\) | −65.8223 | −0.794773 | −0.397386 | − | 0.917651i | \(-0.630083\pi\) | ||||
−0.397386 | + | 0.917651i | \(0.630083\pi\) | |||||||
\(20\) | 1.02517 | 0.0114618 | ||||||||
\(21\) | −78.4858 | −0.815572 | ||||||||
\(22\) | −30.7452 | −0.297950 | ||||||||
\(23\) | 38.8477 | 0.352188 | 0.176094 | − | 0.984373i | \(-0.443654\pi\) | ||||
0.176094 | + | 0.984373i | \(0.443654\pi\) | |||||||
\(24\) | 232.184 | 1.97477 | ||||||||
\(25\) | −95.2199 | −0.761759 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 496.457 | 3.53864 | ||||||||
\(28\) | 1.45328 | 0.00980868 | ||||||||
\(29\) | 16.1969 | 0.103714 | 0.0518568 | − | 0.998655i | \(-0.483486\pi\) | ||||
0.0518568 | + | 0.998655i | \(0.483486\pi\) | |||||||
\(30\) | 154.748 | 0.941768 | ||||||||
\(31\) | −100.762 | −0.583788 | −0.291894 | − | 0.956451i | \(-0.594285\pi\) | ||||
−0.291894 | + | 0.956451i | \(0.594285\pi\) | |||||||
\(32\) | −8.49981 | −0.0469552 | ||||||||
\(33\) | 111.602 | 0.588707 | ||||||||
\(34\) | 51.7687 | 0.261125 | ||||||||
\(35\) | 42.2159 | 0.203880 | ||||||||
\(36\) | −14.2648 | −0.0660408 | ||||||||
\(37\) | −327.545 | −1.45536 | −0.727678 | − | 0.685919i | \(-0.759400\pi\) | ||||
−0.727678 | + | 0.685919i | \(0.759400\pi\) | |||||||
\(38\) | 183.975 | 0.785385 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −124.887 | −0.493661 | ||||||||
\(41\) | −460.876 | −1.75553 | −0.877765 | − | 0.479092i | \(-0.840966\pi\) | ||||
−0.877765 | + | 0.479092i | \(0.840966\pi\) | |||||||
\(42\) | 219.369 | 0.805939 | ||||||||
\(43\) | 346.386 | 1.22845 | 0.614225 | − | 0.789131i | \(-0.289469\pi\) | ||||
0.614225 | + | 0.789131i | \(0.289469\pi\) | |||||||
\(44\) | −2.06646 | −0.00708024 | ||||||||
\(45\) | −414.376 | −1.37270 | ||||||||
\(46\) | −108.580 | −0.348028 | ||||||||
\(47\) | −318.457 | −0.988334 | −0.494167 | − | 0.869367i | \(-0.664527\pi\) | ||||
−0.494167 | + | 0.869367i | \(0.664527\pi\) | |||||||
\(48\) | −633.713 | −1.90560 | ||||||||
\(49\) | −283.155 | −0.825525 | ||||||||
\(50\) | 266.142 | 0.752762 | ||||||||
\(51\) | −187.914 | −0.515947 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −387.521 | −1.00434 | −0.502170 | − | 0.864769i | \(-0.667465\pi\) | ||||
−0.502170 | + | 0.864769i | \(0.667465\pi\) | |||||||
\(54\) | −1387.61 | −3.49684 | ||||||||
\(55\) | −60.0283 | −0.147167 | ||||||||
\(56\) | −177.039 | −0.422461 | ||||||||
\(57\) | −667.807 | −1.55181 | ||||||||
\(58\) | −45.2707 | −0.102489 | ||||||||
\(59\) | 93.9545 | 0.207319 | 0.103660 | − | 0.994613i | \(-0.466945\pi\) | ||||
0.103660 | + | 0.994613i | \(0.466945\pi\) | |||||||
\(60\) | 10.4010 | 0.0223794 | ||||||||
\(61\) | 801.303 | 1.68191 | 0.840954 | − | 0.541107i | \(-0.181994\pi\) | ||||
0.840954 | + | 0.541107i | \(0.181994\pi\) | |||||||
\(62\) | 281.632 | 0.576893 | ||||||||
\(63\) | −587.415 | −1.17472 | ||||||||
\(64\) | 523.452 | 1.02237 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −311.929 | −0.581754 | ||||||||
\(67\) | 344.235 | 0.627687 | 0.313843 | − | 0.949475i | \(-0.398383\pi\) | ||||
0.313843 | + | 0.949475i | \(0.398383\pi\) | |||||||
\(68\) | 3.47950 | 0.00620517 | ||||||||
\(69\) | 394.134 | 0.687654 | ||||||||
\(70\) | −117.994 | −0.201472 | ||||||||
\(71\) | −186.939 | −0.312473 | −0.156237 | − | 0.987720i | \(-0.549936\pi\) | ||||
−0.156237 | + | 0.987720i | \(0.549936\pi\) | |||||||
\(72\) | 1737.75 | 2.84439 | ||||||||
\(73\) | 820.160 | 1.31497 | 0.657483 | − | 0.753469i | \(-0.271621\pi\) | ||||
0.657483 | + | 0.753469i | \(0.271621\pi\) | |||||||
\(74\) | 915.496 | 1.43817 | ||||||||
\(75\) | −966.063 | −1.48735 | ||||||||
\(76\) | 12.3654 | 0.0186633 | ||||||||
\(77\) | −85.0954 | −0.125942 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −502.726 | −0.715963 | −0.357981 | − | 0.933729i | \(-0.616535\pi\) | ||||
−0.357981 | + | 0.933729i | \(0.616535\pi\) | |||||||
\(80\) | 340.861 | 0.476368 | ||||||||
\(81\) | 2986.66 | 4.09692 | ||||||||
\(82\) | 1288.16 | 1.73479 | ||||||||
\(83\) | −199.772 | −0.264191 | −0.132096 | − | 0.991237i | \(-0.542171\pi\) | ||||
−0.132096 | + | 0.991237i | \(0.542171\pi\) | |||||||
\(84\) | 14.7443 | 0.0191517 | ||||||||
\(85\) | 101.075 | 0.128978 | ||||||||
\(86\) | −968.156 | −1.21394 | ||||||||
\(87\) | 164.327 | 0.202503 | ||||||||
\(88\) | 251.738 | 0.304947 | ||||||||
\(89\) | −535.708 | −0.638033 | −0.319017 | − | 0.947749i | \(-0.603353\pi\) | ||||
−0.319017 | + | 0.947749i | \(0.603353\pi\) | |||||||
\(90\) | 1158.19 | 1.35649 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.29794 | −0.00827025 | ||||||||
\(93\) | −1022.29 | −1.13986 | ||||||||
\(94\) | 890.093 | 0.976660 | ||||||||
\(95\) | 359.200 | 0.387928 | ||||||||
\(96\) | −86.2356 | −0.0916811 | ||||||||
\(97\) | 462.280 | 0.483891 | 0.241945 | − | 0.970290i | \(-0.422214\pi\) | ||||
0.241945 | + | 0.970290i | \(0.422214\pi\) | |||||||
\(98\) | 791.425 | 0.815775 | ||||||||
\(99\) | 835.265 | 0.847953 | ||||||||
\(100\) | 17.8880 | 0.0178880 | ||||||||
\(101\) | −1430.27 | −1.40908 | −0.704541 | − | 0.709663i | \(-0.748847\pi\) | ||||
−0.704541 | + | 0.709663i | \(0.748847\pi\) | |||||||
\(102\) | 525.225 | 0.509853 | ||||||||
\(103\) | −170.160 | −0.162780 | −0.0813901 | − | 0.996682i | \(-0.525936\pi\) | ||||
−0.0813901 | + | 0.996682i | \(0.525936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 428.306 | 0.398080 | ||||||||
\(106\) | 1083.13 | 0.992478 | ||||||||
\(107\) | 47.2612 | 0.0427002 | 0.0213501 | − | 0.999772i | \(-0.493204\pi\) | ||||
0.0213501 | + | 0.999772i | \(0.493204\pi\) | |||||||
\(108\) | −93.2645 | −0.0830961 | ||||||||
\(109\) | 1320.38 | 1.16027 | 0.580136 | − | 0.814520i | \(-0.303000\pi\) | ||||
0.580136 | + | 0.814520i | \(0.303000\pi\) | |||||||
\(110\) | 167.780 | 0.145429 | ||||||||
\(111\) | −3323.15 | −2.84161 | ||||||||
\(112\) | 483.201 | 0.407663 | ||||||||
\(113\) | −1997.52 | −1.66293 | −0.831465 | − | 0.555577i | \(-0.812497\pi\) | ||||
−0.831465 | + | 0.555577i | \(0.812497\pi\) | |||||||
\(114\) | 1866.53 | 1.53348 | ||||||||
\(115\) | −211.997 | −0.171903 | ||||||||
\(116\) | −3.04275 | −0.00243545 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −262.605 | −0.204870 | ||||||||
\(119\) | 143.283 | 0.110376 | ||||||||
\(120\) | −1267.06 | −0.963884 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −2239.66 | −1.66204 | ||||||||
\(123\) | −4675.86 | −3.42771 | ||||||||
\(124\) | 18.9292 | 0.0137088 | ||||||||
\(125\) | 1201.77 | 0.859913 | ||||||||
\(126\) | 1641.84 | 1.16084 | ||||||||
\(127\) | −1184.44 | −0.827576 | −0.413788 | − | 0.910373i | \(-0.635795\pi\) | ||||
−0.413788 | + | 0.910373i | \(0.635795\pi\) | |||||||
\(128\) | −1395.06 | −0.963336 | ||||||||
\(129\) | 3514.29 | 2.39858 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 499.167 | 0.332919 | 0.166460 | − | 0.986048i | \(-0.446766\pi\) | ||||
0.166460 | + | 0.986048i | \(0.446766\pi\) | |||||||
\(132\) | −20.9655 | −0.0138243 | ||||||||
\(133\) | 509.198 | 0.331978 | ||||||||
\(134\) | −962.144 | −0.620273 | ||||||||
\(135\) | −2709.22 | −1.72721 | ||||||||
\(136\) | −423.875 | −0.267257 | ||||||||
\(137\) | 2929.03 | 1.82660 | 0.913299 | − | 0.407290i | \(-0.133526\pi\) | ||||
0.913299 | + | 0.407290i | \(0.133526\pi\) | |||||||
\(138\) | −1101.61 | −0.679532 | ||||||||
\(139\) | −1710.17 | −1.04356 | −0.521780 | − | 0.853080i | \(-0.674732\pi\) | ||||
−0.521780 | + | 0.853080i | \(0.674732\pi\) | |||||||
\(140\) | −7.93069 | −0.00478761 | ||||||||
\(141\) | −3230.93 | −1.92974 | ||||||||
\(142\) | 522.499 | 0.308783 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4742.93 | −2.74475 | ||||||||
\(145\) | −88.3885 | −0.0506225 | ||||||||
\(146\) | −2292.36 | −1.29943 | ||||||||
\(147\) | −2872.78 | −1.61186 | ||||||||
\(148\) | 61.5327 | 0.0341754 | ||||||||
\(149\) | 8.91668 | 0.00490257 | 0.00245128 | − | 0.999997i | \(-0.499220\pi\) | ||||
0.00245128 | + | 0.999997i | \(0.499220\pi\) | |||||||
\(150\) | 2700.17 | 1.46978 | ||||||||
\(151\) | 1112.51 | 0.599568 | 0.299784 | − | 0.954007i | \(-0.403085\pi\) | ||||
0.299784 | + | 0.954007i | \(0.403085\pi\) | |||||||
\(152\) | −1506.36 | −0.803828 | ||||||||
\(153\) | −1406.42 | −0.743151 | ||||||||
\(154\) | 237.843 | 0.124454 | ||||||||
\(155\) | 549.871 | 0.284946 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2750.70 | −1.39828 | −0.699140 | − | 0.714985i | \(-0.746434\pi\) | ||||
−0.699140 | + | 0.714985i | \(0.746434\pi\) | |||||||
\(158\) | 1405.13 | 0.707506 | ||||||||
\(159\) | −3931.63 | −1.96100 | ||||||||
\(160\) | 46.3844 | 0.0229188 | ||||||||
\(161\) | −300.524 | −0.147109 | ||||||||
\(162\) | −8347.77 | −4.04853 | ||||||||
\(163\) | −3606.84 | −1.73319 | −0.866593 | − | 0.499016i | \(-0.833695\pi\) | ||||
−0.866593 | + | 0.499016i | \(0.833695\pi\) | |||||||
\(164\) | 86.5802 | 0.0412242 | ||||||||
\(165\) | −609.023 | −0.287348 | ||||||||
\(166\) | 558.368 | 0.261071 | ||||||||
\(167\) | −2248.35 | −1.04181 | −0.520906 | − | 0.853614i | \(-0.674406\pi\) | ||||
−0.520906 | + | 0.853614i | \(0.674406\pi\) | |||||||
\(168\) | −1796.17 | −0.824864 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −282.508 | −0.127455 | ||||||||
\(171\) | −4998.10 | −2.23517 | ||||||||
\(172\) | −65.0721 | −0.0288471 | ||||||||
\(173\) | 226.145 | 0.0993843 | 0.0496922 | − | 0.998765i | \(-0.484176\pi\) | ||||
0.0496922 | + | 0.998765i | \(0.484176\pi\) | |||||||
\(174\) | −459.299 | −0.200111 | ||||||||
\(175\) | 736.616 | 0.318188 | ||||||||
\(176\) | −687.080 | −0.294265 | ||||||||
\(177\) | 953.224 | 0.404795 | ||||||||
\(178\) | 1497.32 | 0.630497 | ||||||||
\(179\) | 3424.30 | 1.42986 | 0.714929 | − | 0.699197i | \(-0.246459\pi\) | ||||
0.714929 | + | 0.699197i | \(0.246459\pi\) | |||||||
\(180\) | 77.8448 | 0.0322345 | ||||||||
\(181\) | −2211.50 | −0.908173 | −0.454087 | − | 0.890958i | \(-0.650034\pi\) | ||||
−0.454087 | + | 0.890958i | \(0.650034\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8129.70 | 3.28396 | ||||||||
\(184\) | 889.040 | 0.356200 | ||||||||
\(185\) | 1787.45 | 0.710358 | ||||||||
\(186\) | 2857.33 | 1.12640 | ||||||||
\(187\) | −203.739 | −0.0796733 | ||||||||
\(188\) | 59.8253 | 0.0232086 | ||||||||
\(189\) | −3840.56 | −1.47809 | ||||||||
\(190\) | −1003.97 | −0.383346 | ||||||||
\(191\) | −2358.91 | −0.893636 | −0.446818 | − | 0.894625i | \(-0.647443\pi\) | ||||
−0.446818 | + | 0.894625i | \(0.647443\pi\) | |||||||
\(192\) | 5310.73 | 1.99619 | ||||||||
\(193\) | −2383.69 | −0.889025 | −0.444512 | − | 0.895773i | \(-0.646623\pi\) | ||||
−0.444512 | + | 0.895773i | \(0.646623\pi\) | |||||||
\(194\) | −1292.08 | −0.478176 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 53.1936 | 0.0193854 | ||||||||
\(197\) | 407.461 | 0.147363 | 0.0736813 | − | 0.997282i | \(-0.476525\pi\) | ||||
0.0736813 | + | 0.997282i | \(0.476525\pi\) | |||||||
\(198\) | −2334.58 | −0.837938 | ||||||||
\(199\) | −3844.74 | −1.36958 | −0.684790 | − | 0.728740i | \(-0.740106\pi\) | ||||
−0.684790 | + | 0.728740i | \(0.740106\pi\) | |||||||
\(200\) | −2179.13 | −0.770439 | ||||||||
\(201\) | 3492.47 | 1.22557 | ||||||||
\(202\) | 3997.64 | 1.39244 | ||||||||
\(203\) | −125.298 | −0.0433213 | ||||||||
\(204\) | 35.3016 | 0.0121157 | ||||||||
\(205\) | 2515.05 | 0.856873 | ||||||||
\(206\) | 475.600 | 0.160858 | ||||||||
\(207\) | 2949.83 | 0.990472 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −724.046 | −0.239633 | ||||||||
\(210\) | −1197.12 | −0.393378 | ||||||||
\(211\) | 4758.95 | 1.55270 | 0.776349 | − | 0.630303i | \(-0.217069\pi\) | ||||
0.776349 | + | 0.630303i | \(0.217069\pi\) | |||||||
\(212\) | 72.7997 | 0.0235844 | ||||||||
\(213\) | −1896.61 | −0.610111 | ||||||||
\(214\) | −132.096 | −0.0421958 | ||||||||
\(215\) | −1890.27 | −0.599606 | ||||||||
\(216\) | 11361.5 | 3.57896 | ||||||||
\(217\) | 779.491 | 0.243849 | ||||||||
\(218\) | −3690.49 | −1.14657 | ||||||||
\(219\) | 8321.02 | 2.56750 | ||||||||
\(220\) | 11.2769 | 0.00345586 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9288.26 | 2.80805 | ||||||||
\(223\) | −3483.52 | −1.04607 | −0.523035 | − | 0.852311i | \(-0.675200\pi\) | ||||
−0.523035 | + | 0.852311i | \(0.675200\pi\) | |||||||
\(224\) | 65.7540 | 0.0196133 | ||||||||
\(225\) | −7230.35 | −2.14233 | ||||||||
\(226\) | 5583.12 | 1.64329 | ||||||||
\(227\) | −2480.99 | −0.725414 | −0.362707 | − | 0.931903i | \(-0.618147\pi\) | ||||
−0.362707 | + | 0.931903i | \(0.618147\pi\) | |||||||
\(228\) | 125.454 | 0.0364404 | ||||||||
\(229\) | −4432.17 | −1.27898 | −0.639490 | − | 0.768800i | \(-0.720854\pi\) | ||||
−0.639490 | + | 0.768800i | \(0.720854\pi\) | |||||||
\(230\) | 592.535 | 0.169872 | ||||||||
\(231\) | −863.344 | −0.245904 | ||||||||
\(232\) | 370.670 | 0.104895 | ||||||||
\(233\) | 634.737 | 0.178468 | 0.0892338 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892338 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1737.86 | 0.482405 | ||||||||
\(236\) | −17.6503 | −0.00486837 | ||||||||
\(237\) | −5100.45 | −1.39793 | ||||||||
\(238\) | −400.480 | −0.109072 | ||||||||
\(239\) | 3562.16 | 0.964086 | 0.482043 | − | 0.876147i | \(-0.339895\pi\) | ||||
0.482043 | + | 0.876147i | \(0.339895\pi\) | |||||||
\(240\) | 3458.24 | 0.930120 | ||||||||
\(241\) | −2783.75 | −0.744055 | −0.372027 | − | 0.928222i | \(-0.621337\pi\) | ||||
−0.372027 | + | 0.928222i | \(0.621337\pi\) | |||||||
\(242\) | −338.197 | −0.0898354 | ||||||||
\(243\) | 16897.1 | 4.46070 | ||||||||
\(244\) | −150.533 | −0.0394954 | ||||||||
\(245\) | 1545.21 | 0.402938 | ||||||||
\(246\) | 13069.1 | 3.38722 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2305.97 | −0.590440 | ||||||||
\(249\) | −2026.81 | −0.515839 | ||||||||
\(250\) | −3358.96 | −0.849757 | ||||||||
\(251\) | −5789.65 | −1.45593 | −0.727967 | − | 0.685613i | \(-0.759534\pi\) | ||||
−0.727967 | + | 0.685613i | \(0.759534\pi\) | |||||||
\(252\) | 110.352 | 0.0275854 | ||||||||
\(253\) | 427.325 | 0.106189 | ||||||||
\(254\) | 3310.54 | 0.817802 | ||||||||
\(255\) | 1025.47 | 0.251833 | ||||||||
\(256\) | −288.393 | −0.0704084 | ||||||||
\(257\) | −4982.51 | −1.20934 | −0.604670 | − | 0.796476i | \(-0.706695\pi\) | ||||
−0.604670 | + | 0.796476i | \(0.706695\pi\) | |||||||
\(258\) | −9822.53 | −2.37025 | ||||||||
\(259\) | 2533.87 | 0.607904 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1229.88 | 0.291678 | ||||||||
\(262\) | −1395.18 | −0.328987 | ||||||||
\(263\) | −2717.14 | −0.637057 | −0.318529 | − | 0.947913i | \(-0.603189\pi\) | ||||
−0.318529 | + | 0.947913i | \(0.603189\pi\) | |||||||
\(264\) | 2554.03 | 0.595415 | ||||||||
\(265\) | 2114.75 | 0.490218 | ||||||||
\(266\) | −1423.22 | −0.328057 | ||||||||
\(267\) | −5435.08 | −1.24577 | ||||||||
\(268\) | −64.6680 | −0.0147397 | ||||||||
\(269\) | 4736.82 | 1.07364 | 0.536820 | − | 0.843697i | \(-0.319625\pi\) | ||||
0.536820 | + | 0.843697i | \(0.319625\pi\) | |||||||
\(270\) | 7572.33 | 1.70681 | ||||||||
\(271\) | −2289.85 | −0.513279 | −0.256640 | − | 0.966507i | \(-0.582615\pi\) | ||||
−0.256640 | + | 0.966507i | \(0.582615\pi\) | |||||||
\(272\) | 1156.90 | 0.257895 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8186.70 | −1.80502 | ||||||||
\(275\) | −1047.42 | −0.229679 | ||||||||
\(276\) | −74.0420 | −0.0161478 | ||||||||
\(277\) | 1780.05 | 0.386111 | 0.193055 | − | 0.981188i | \(-0.438160\pi\) | ||||
0.193055 | + | 0.981188i | \(0.438160\pi\) | |||||||
\(278\) | 4779.96 | 1.03123 | ||||||||
\(279\) | −7651.20 | −1.64181 | ||||||||
\(280\) | 966.122 | 0.206203 | ||||||||
\(281\) | 3675.35 | 0.780261 | 0.390130 | − | 0.920760i | \(-0.372430\pi\) | ||||
0.390130 | + | 0.920760i | \(0.372430\pi\) | |||||||
\(282\) | 9030.53 | 1.90695 | ||||||||
\(283\) | −3837.92 | −0.806150 | −0.403075 | − | 0.915167i | \(-0.632059\pi\) | ||||
−0.403075 | + | 0.915167i | \(0.632059\pi\) | |||||||
\(284\) | 35.1184 | 0.00733766 | ||||||||
\(285\) | 3644.30 | 0.757438 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3565.31 | 0.733287 | ||||||||
\(288\) | −645.418 | −0.132054 | ||||||||
\(289\) | −4569.94 | −0.930174 | ||||||||
\(290\) | 247.048 | 0.0500246 | ||||||||
\(291\) | 4690.11 | 0.944808 | ||||||||
\(292\) | −154.075 | −0.0308787 | ||||||||
\(293\) | 7896.16 | 1.57440 | 0.787199 | − | 0.616699i | \(-0.211531\pi\) | ||||
0.787199 | + | 0.616699i | \(0.211531\pi\) | |||||||
\(294\) | 8029.48 | 1.59282 | ||||||||
\(295\) | −512.720 | −0.101192 | ||||||||
\(296\) | −7495.96 | −1.47194 | ||||||||
\(297\) | 5461.03 | 1.06694 | ||||||||
\(298\) | −24.9223 | −0.00484466 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 181.485 | 0.0349267 | ||||||||
\(301\) | −2679.62 | −0.513126 | ||||||||
\(302\) | −3109.49 | −0.592487 | ||||||||
\(303\) | −14511.0 | −2.75126 | ||||||||
\(304\) | 4111.38 | 0.775671 | ||||||||
\(305\) | −4372.81 | −0.820938 | ||||||||
\(306\) | 3930.96 | 0.734373 | ||||||||
\(307\) | 1002.68 | 0.186405 | 0.0932023 | − | 0.995647i | \(-0.470290\pi\) | ||||
0.0932023 | + | 0.995647i | \(0.470290\pi\) | |||||||
\(308\) | 15.9860 | 0.00295743 | ||||||||
\(309\) | −1726.37 | −0.317832 | ||||||||
\(310\) | −1536.90 | −0.281581 | ||||||||
\(311\) | −5246.74 | −0.956641 | −0.478321 | − | 0.878185i | \(-0.658754\pi\) | ||||
−0.478321 | + | 0.878185i | \(0.658754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1548.16 | −0.279576 | −0.139788 | − | 0.990181i | \(-0.544642\pi\) | ||||
−0.139788 | + | 0.990181i | \(0.544642\pi\) | |||||||
\(314\) | 7688.27 | 1.38176 | ||||||||
\(315\) | 3205.59 | 0.573380 | ||||||||
\(316\) | 94.4421 | 0.0168126 | ||||||||
\(317\) | 8289.92 | 1.46880 | 0.734398 | − | 0.678719i | \(-0.237465\pi\) | ||||
0.734398 | + | 0.678719i | \(0.237465\pi\) | |||||||
\(318\) | 10989.0 | 1.93784 | ||||||||
\(319\) | 178.166 | 0.0312708 | ||||||||
\(320\) | −2856.54 | −0.499017 | ||||||||
\(321\) | 479.494 | 0.0833730 | ||||||||
\(322\) | 839.970 | 0.145372 | ||||||||
\(323\) | 1219.15 | 0.210016 | ||||||||
\(324\) | −561.074 | −0.0962061 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10081.2 | 1.71271 | ||||||||
\(327\) | 13396.1 | 2.26545 | ||||||||
\(328\) | −10547.3 | −1.77553 | ||||||||
\(329\) | 2463.56 | 0.412829 | ||||||||
\(330\) | 1702.23 | 0.283954 | ||||||||
\(331\) | 6815.21 | 1.13172 | 0.565858 | − | 0.824503i | \(-0.308545\pi\) | ||||
0.565858 | + | 0.824503i | \(0.308545\pi\) | |||||||
\(332\) | 37.5293 | 0.00620387 | ||||||||
\(333\) | −24871.6 | −4.09296 | ||||||||
\(334\) | 6284.19 | 1.02951 | ||||||||
\(335\) | −1878.53 | −0.306373 | ||||||||
\(336\) | 4902.37 | 0.795970 | ||||||||
\(337\) | 11413.6 | 1.84492 | 0.922460 | − | 0.386094i | \(-0.126176\pi\) | ||||
0.922460 | + | 0.386094i | \(0.126176\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20266.1 | −3.24691 | ||||||||
\(340\) | −18.9880 | −0.00302874 | ||||||||
\(341\) | −1108.38 | −0.176019 | ||||||||
\(342\) | 13969.8 | 2.20877 | ||||||||
\(343\) | 4843.90 | 0.762525 | ||||||||
\(344\) | 7927.13 | 1.24245 | ||||||||
\(345\) | −2150.83 | −0.335643 | ||||||||
\(346\) | −632.080 | −0.0982105 | ||||||||
\(347\) | 7866.47 | 1.21699 | 0.608493 | − | 0.793559i | \(-0.291774\pi\) | ||||
0.608493 | + | 0.793559i | \(0.291774\pi\) | |||||||
\(348\) | −30.8706 | −0.00475528 | ||||||||
\(349\) | −2589.45 | −0.397164 | −0.198582 | − | 0.980084i | \(-0.563634\pi\) | ||||
−0.198582 | + | 0.980084i | \(0.563634\pi\) | |||||||
\(350\) | −2058.86 | −0.314430 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −93.4979 | −0.0141575 | ||||||||
\(353\) | −5349.76 | −0.806626 | −0.403313 | − | 0.915062i | \(-0.632141\pi\) | ||||
−0.403313 | + | 0.915062i | \(0.632141\pi\) | |||||||
\(354\) | −2664.28 | −0.400014 | ||||||||
\(355\) | 1020.15 | 0.152518 | ||||||||
\(356\) | 100.638 | 0.0149826 | ||||||||
\(357\) | 1453.70 | 0.215512 | ||||||||
\(358\) | −9571.00 | −1.41297 | ||||||||
\(359\) | −7919.96 | −1.16434 | −0.582172 | − | 0.813066i | \(-0.697797\pi\) | ||||
−0.582172 | + | 0.813066i | \(0.697797\pi\) | |||||||
\(360\) | −9483.10 | −1.38834 | ||||||||
\(361\) | −2526.42 | −0.368337 | ||||||||
\(362\) | 6181.18 | 0.897447 | ||||||||
\(363\) | 1227.62 | 0.177502 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4475.71 | −0.641834 | ||||||||
\(366\) | −22722.7 | −3.24517 | ||||||||
\(367\) | 8311.54 | 1.18218 | 0.591089 | − | 0.806607i | \(-0.298698\pi\) | ||||
0.591089 | + | 0.806607i | \(0.298698\pi\) | |||||||
\(368\) | −2426.50 | −0.343723 | ||||||||
\(369\) | −34995.8 | −4.93715 | ||||||||
\(370\) | −4995.97 | −0.701968 | ||||||||
\(371\) | 2997.84 | 0.419515 | ||||||||
\(372\) | 192.048 | 0.0267667 | ||||||||
\(373\) | −13584.3 | −1.88570 | −0.942851 | − | 0.333214i | \(-0.891867\pi\) | ||||
−0.942851 | + | 0.333214i | \(0.891867\pi\) | |||||||
\(374\) | 569.456 | 0.0787322 | ||||||||
\(375\) | 12192.6 | 1.67900 | ||||||||
\(376\) | −7287.96 | −0.999595 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 10734.5 | 1.46064 | ||||||||
\(379\) | 13192.4 | 1.78798 | 0.893992 | − | 0.448083i | \(-0.147893\pi\) | ||||
0.893992 | + | 0.448083i | \(0.147893\pi\) | |||||||
\(380\) | −67.4794 | −0.00910952 | ||||||||
\(381\) | −12016.9 | −1.61586 | ||||||||
\(382\) | 6593.20 | 0.883082 | ||||||||
\(383\) | −1397.19 | −0.186405 | −0.0932024 | − | 0.995647i | \(-0.529710\pi\) | ||||
−0.0932024 | + | 0.995647i | \(0.529710\pi\) | |||||||
\(384\) | −14153.7 | −1.88094 | ||||||||
\(385\) | 464.375 | 0.0614721 | ||||||||
\(386\) | 6662.46 | 0.878524 | ||||||||
\(387\) | 26302.2 | 3.45482 | ||||||||
\(388\) | −86.8440 | −0.0113630 | ||||||||
\(389\) | 3634.88 | 0.473768 | 0.236884 | − | 0.971538i | \(-0.423874\pi\) | ||||
0.236884 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −719.529 | −0.0930643 | ||||||||
\(392\) | −6480.07 | −0.834932 | ||||||||
\(393\) | 5064.35 | 0.650032 | ||||||||
\(394\) | −1138.86 | −0.145622 | ||||||||
\(395\) | 2743.43 | 0.349461 | ||||||||
\(396\) | −156.913 | −0.0199121 | ||||||||
\(397\) | 4666.40 | 0.589924 | 0.294962 | − | 0.955509i | \(-0.404693\pi\) | ||||
0.294962 | + | 0.955509i | \(0.404693\pi\) | |||||||
\(398\) | 10746.1 | 1.35340 | ||||||||
\(399\) | 5166.12 | 0.648194 | ||||||||
\(400\) | 5947.61 | 0.743451 | ||||||||
\(401\) | −6638.07 | −0.826657 | −0.413329 | − | 0.910582i | \(-0.635634\pi\) | ||||
−0.413329 | + | 0.910582i | \(0.635634\pi\) | |||||||
\(402\) | −9761.53 | −1.21110 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 268.691 | 0.0330888 | ||||||||
\(405\) | −16298.5 | −1.99971 | ||||||||
\(406\) | 350.212 | 0.0428096 | ||||||||
\(407\) | −3603.00 | −0.438806 | ||||||||
\(408\) | −4300.47 | −0.521825 | ||||||||
\(409\) | −9754.31 | −1.17927 | −0.589633 | − | 0.807672i | \(-0.700727\pi\) | ||||
−0.589633 | + | 0.807672i | \(0.700727\pi\) | |||||||
\(410\) | −7029.62 | −0.846752 | ||||||||
\(411\) | 29716.8 | 3.56647 | ||||||||
\(412\) | 31.9663 | 0.00382249 | ||||||||
\(413\) | −726.826 | −0.0865975 | ||||||||
\(414\) | −8244.85 | −0.978773 | ||||||||
\(415\) | 1090.18 | 0.128952 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17350.7 | −2.03757 | ||||||||
\(418\) | 2023.72 | 0.236803 | ||||||||
\(419\) | −3199.32 | −0.373024 | −0.186512 | − | 0.982453i | \(-0.559718\pi\) | ||||
−0.186512 | + | 0.982453i | \(0.559718\pi\) | |||||||
\(420\) | −80.4616 | −0.00934792 | ||||||||
\(421\) | −7448.14 | −0.862233 | −0.431116 | − | 0.902296i | \(-0.641880\pi\) | ||||
−0.431116 | + | 0.902296i | \(0.641880\pi\) | |||||||
\(422\) | −13301.4 | −1.53436 | ||||||||
\(423\) | −24181.4 | −2.77953 | ||||||||
\(424\) | −8868.50 | −1.01578 | ||||||||
\(425\) | 1763.64 | 0.201292 | ||||||||
\(426\) | 5301.07 | 0.602905 | ||||||||
\(427\) | −6198.84 | −0.702536 | ||||||||
\(428\) | −8.87850 | −0.00100271 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5283.34 | 0.592524 | ||||||||
\(431\) | −935.516 | −0.104553 | −0.0522763 | − | 0.998633i | \(-0.516648\pi\) | ||||
−0.0522763 | + | 0.998633i | \(0.516648\pi\) | |||||||
\(432\) | −31009.6 | −3.45359 | ||||||||
\(433\) | 5279.36 | 0.585935 | 0.292967 | − | 0.956122i | \(-0.405357\pi\) | ||||
0.292967 | + | 0.956122i | \(0.405357\pi\) | |||||||
\(434\) | −2178.69 | −0.240969 | ||||||||
\(435\) | −896.754 | −0.0988415 | ||||||||
\(436\) | −248.047 | −0.0272461 | ||||||||
\(437\) | −2557.05 | −0.279909 | ||||||||
\(438\) | −23257.4 | −2.53717 | ||||||||
\(439\) | 375.139 | 0.0407845 | 0.0203923 | − | 0.999792i | \(-0.493508\pi\) | ||||
0.0203923 | + | 0.999792i | \(0.493508\pi\) | |||||||
\(440\) | −1373.76 | −0.148844 | ||||||||
\(441\) | −21500.9 | −2.32166 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16515.4 | −1.77126 | −0.885631 | − | 0.464389i | \(-0.846274\pi\) | ||||
−0.885631 | + | 0.464389i | \(0.846274\pi\) | |||||||
\(444\) | 624.287 | 0.0667282 | ||||||||
\(445\) | 2923.42 | 0.311424 | ||||||||
\(446\) | 9736.51 | 1.03372 | ||||||||
\(447\) | 90.4651 | 0.00957237 | ||||||||
\(448\) | −4049.39 | −0.427044 | ||||||||
\(449\) | 6135.87 | 0.644921 | 0.322461 | − | 0.946583i | \(-0.395490\pi\) | ||||
0.322461 | + | 0.946583i | \(0.395490\pi\) | |||||||
\(450\) | 20209.0 | 2.11702 | ||||||||
\(451\) | −5069.63 | −0.529312 | ||||||||
\(452\) | 375.255 | 0.0390498 | ||||||||
\(453\) | 11287.1 | 1.17067 | ||||||||
\(454\) | 6934.42 | 0.716846 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15282.9 | −1.56949 | ||||||||
\(457\) | −2609.05 | −0.267059 | −0.133530 | − | 0.991045i | \(-0.542631\pi\) | ||||
−0.133530 | + | 0.991045i | \(0.542631\pi\) | |||||||
\(458\) | 12388.0 | 1.26387 | ||||||||
\(459\) | −9195.26 | −0.935072 | ||||||||
\(460\) | 39.8257 | 0.00403670 | ||||||||
\(461\) | 8234.09 | 0.831887 | 0.415943 | − | 0.909391i | \(-0.363451\pi\) | ||||
0.415943 | + | 0.909391i | \(0.363451\pi\) | |||||||
\(462\) | 2413.06 | 0.243000 | ||||||||
\(463\) | −15472.8 | −1.55309 | −0.776546 | − | 0.630060i | \(-0.783030\pi\) | ||||
−0.776546 | + | 0.630060i | \(0.783030\pi\) | |||||||
\(464\) | −1011.69 | −0.101221 | ||||||||
\(465\) | 5578.77 | 0.556364 | ||||||||
\(466\) | −1774.10 | −0.176360 | ||||||||
\(467\) | 6389.68 | 0.633146 | 0.316573 | − | 0.948568i | \(-0.397468\pi\) | ||||
0.316573 | + | 0.948568i | \(0.397468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2662.98 | −0.262186 | ||||||||
\(470\) | −4857.34 | −0.476707 | ||||||||
\(471\) | −27907.5 | −2.73017 | ||||||||
\(472\) | 2150.17 | 0.209681 | ||||||||
\(473\) | 3810.25 | 0.370392 | ||||||||
\(474\) | 14255.9 | 1.38142 | ||||||||
\(475\) | 6267.59 | 0.605425 | ||||||||
\(476\) | −26.9172 | −0.00259191 | ||||||||
\(477\) | −29425.7 | −2.82455 | ||||||||
\(478\) | −9956.30 | −0.952700 | ||||||||
\(479\) | −14490.9 | −1.38227 | −0.691134 | − | 0.722726i | \(-0.742889\pi\) | ||||
−0.691134 | + | 0.722726i | \(0.742889\pi\) | |||||||
\(480\) | 470.598 | 0.0447495 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7780.64 | 0.735267 | ||||||||
\(483\) | −3049.00 | −0.287234 | ||||||||
\(484\) | −22.7311 | −0.00213477 | ||||||||
\(485\) | −2522.72 | −0.236187 | ||||||||
\(486\) | −47227.7 | −4.40801 | ||||||||
\(487\) | 7754.32 | 0.721524 | 0.360762 | − | 0.932658i | \(-0.382517\pi\) | ||||
0.360762 | + | 0.932658i | \(0.382517\pi\) | |||||||
\(488\) | 18338.0 | 1.70107 | ||||||||
\(489\) | −36593.5 | −3.38408 | ||||||||
\(490\) | −4318.90 | −0.398179 | ||||||||
\(491\) | −7089.28 | −0.651599 | −0.325799 | − | 0.945439i | \(-0.605633\pi\) | ||||
−0.325799 | + | 0.945439i | \(0.605633\pi\) | |||||||
\(492\) | 878.408 | 0.0804912 | ||||||||
\(493\) | −299.995 | −0.0274059 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4558.14 | −0.413885 | ||||||||
\(496\) | 6293.79 | 0.569757 | ||||||||
\(497\) | 1446.15 | 0.130521 | ||||||||
\(498\) | 5664.98 | 0.509746 | ||||||||
\(499\) | 8769.38 | 0.786716 | 0.393358 | − | 0.919385i | \(-0.371313\pi\) | ||||
0.393358 | + | 0.919385i | \(0.371313\pi\) | |||||||
\(500\) | −225.764 | −0.0201929 | ||||||||
\(501\) | −22810.9 | −2.03416 | ||||||||
\(502\) | 16182.2 | 1.43874 | ||||||||
\(503\) | −5128.57 | −0.454616 | −0.227308 | − | 0.973823i | \(-0.572992\pi\) | ||||
−0.227308 | + | 0.973823i | \(0.572992\pi\) | |||||||
\(504\) | −13443.1 | −1.18810 | ||||||||
\(505\) | 7805.15 | 0.687772 | ||||||||
\(506\) | −1194.38 | −0.104934 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 222.509 | 0.0194336 | ||||||||
\(509\) | 13058.9 | 1.13718 | 0.568589 | − | 0.822622i | \(-0.307489\pi\) | ||||
0.568589 | + | 0.822622i | \(0.307489\pi\) | |||||||
\(510\) | −2866.21 | −0.248859 | ||||||||
\(511\) | −6344.71 | −0.549263 | ||||||||
\(512\) | 11966.5 | 1.03291 | ||||||||
\(513\) | −32678.0 | −2.81241 | ||||||||
\(514\) | 13926.2 | 1.19506 | ||||||||
\(515\) | 928.582 | 0.0794529 | ||||||||
\(516\) | −660.196 | −0.0563246 | ||||||||
\(517\) | −3503.02 | −0.297994 | ||||||||
\(518\) | −7082.23 | −0.600724 | ||||||||
\(519\) | 2294.38 | 0.194050 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2189.22 | −0.184091 | −0.0920457 | − | 0.995755i | \(-0.529341\pi\) | ||||
−0.0920457 | + | 0.995755i | \(0.529341\pi\) | |||||||
\(522\) | −3437.55 | −0.288233 | ||||||||
\(523\) | −6183.03 | −0.516950 | −0.258475 | − | 0.966018i | \(-0.583220\pi\) | ||||
−0.258475 | + | 0.966018i | \(0.583220\pi\) | |||||||
\(524\) | −93.7735 | −0.00781778 | ||||||||
\(525\) | 7473.41 | 0.621269 | ||||||||
\(526\) | 7594.46 | 0.629533 | ||||||||
\(527\) | 1866.29 | 0.154264 | ||||||||
\(528\) | −6970.84 | −0.574559 | ||||||||
\(529\) | −10657.9 | −0.875964 | ||||||||
\(530\) | −5910.76 | −0.484428 | ||||||||
\(531\) | 7134.26 | 0.583052 | ||||||||
\(532\) | −95.6580 | −0.00779567 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 15191.2 | 1.23106 | ||||||||
\(535\) | −257.910 | −0.0208419 | ||||||||
\(536\) | 7877.90 | 0.634839 | ||||||||
\(537\) | 34741.6 | 2.79183 | ||||||||
\(538\) | −13239.5 | −1.06096 | ||||||||
\(539\) | −3114.71 | −0.248905 | ||||||||
\(540\) | 508.955 | 0.0405591 | ||||||||
\(541\) | −2056.64 | −0.163442 | −0.0817208 | − | 0.996655i | \(-0.526042\pi\) | ||||
−0.0817208 | + | 0.996655i | \(0.526042\pi\) | |||||||
\(542\) | 6400.19 | 0.507217 | ||||||||
\(543\) | −22437.0 | −1.77323 | ||||||||
\(544\) | 157.431 | 0.0124077 | ||||||||
\(545\) | −7205.47 | −0.566328 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14278.7 | −1.11611 | −0.558055 | − | 0.829804i | \(-0.688452\pi\) | ||||
−0.558055 | + | 0.829804i | \(0.688452\pi\) | |||||||
\(548\) | −550.248 | −0.0428931 | ||||||||
\(549\) | 60845.5 | 4.73010 | ||||||||
\(550\) | 2927.56 | 0.226966 | ||||||||
\(551\) | −1066.12 | −0.0824287 | ||||||||
\(552\) | 9019.84 | 0.695489 | ||||||||
\(553\) | 3889.06 | 0.299059 | ||||||||
\(554\) | −4975.27 | −0.381550 | ||||||||
\(555\) | 18134.8 | 1.38699 | ||||||||
\(556\) | 321.273 | 0.0245054 | ||||||||
\(557\) | −3547.29 | −0.269845 | −0.134922 | − | 0.990856i | \(-0.543078\pi\) | ||||
−0.134922 | + | 0.990856i | \(0.543078\pi\) | |||||||
\(558\) | 21385.3 | 1.62242 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2636.88 | −0.198980 | ||||||||
\(561\) | −2067.06 | −0.155564 | ||||||||
\(562\) | −10272.7 | −0.771045 | ||||||||
\(563\) | −7881.91 | −0.590023 | −0.295011 | − | 0.955494i | \(-0.595323\pi\) | ||||
−0.295011 | + | 0.955494i | \(0.595323\pi\) | |||||||
\(564\) | 606.964 | 0.0453152 | ||||||||
\(565\) | 10900.7 | 0.811675 | ||||||||
\(566\) | 10727.1 | 0.796628 | ||||||||
\(567\) | −23104.6 | −1.71129 | ||||||||
\(568\) | −4278.15 | −0.316034 | ||||||||
\(569\) | −10336.6 | −0.761567 | −0.380784 | − | 0.924664i | \(-0.624346\pi\) | ||||
−0.380784 | + | 0.924664i | \(0.624346\pi\) | |||||||
\(570\) | −10185.9 | −0.748492 | ||||||||
\(571\) | 25104.0 | 1.83988 | 0.919940 | − | 0.392059i | \(-0.128237\pi\) | ||||
0.919940 | + | 0.392059i | \(0.128237\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23932.5 | −1.74484 | ||||||||
\(574\) | −9965.11 | −0.724627 | ||||||||
\(575\) | −3699.08 | −0.268282 | ||||||||
\(576\) | 39747.4 | 2.87524 | ||||||||
\(577\) | −5486.30 | −0.395836 | −0.197918 | − | 0.980219i | \(-0.563418\pi\) | ||||
−0.197918 | + | 0.980219i | \(0.563418\pi\) | |||||||
\(578\) | 12773.1 | 0.919188 | ||||||||
\(579\) | −24184.0 | −1.73584 | ||||||||
\(580\) | 16.6047 | 0.00118874 | ||||||||
\(581\) | 1545.43 | 0.110353 | ||||||||
\(582\) | −13108.9 | −0.933648 | ||||||||
\(583\) | −4262.73 | −0.302820 | ||||||||
\(584\) | 18769.6 | 1.32995 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22069.9 | −1.55580 | ||||||||
\(587\) | −4796.54 | −0.337265 | −0.168632 | − | 0.985679i | \(-0.553935\pi\) | ||||
−0.168632 | + | 0.985679i | \(0.553935\pi\) | |||||||
\(588\) | 539.681 | 0.0378504 | ||||||||
\(589\) | 6632.40 | 0.463979 | ||||||||
\(590\) | 1433.06 | 0.0999971 | ||||||||
\(591\) | 4133.94 | 0.287729 | ||||||||
\(592\) | 20459.1 | 1.42038 | ||||||||
\(593\) | 5888.68 | 0.407790 | 0.203895 | − | 0.978993i | \(-0.434640\pi\) | ||||
0.203895 | + | 0.978993i | \(0.434640\pi\) | |||||||
\(594\) | −15263.7 | −1.05434 | ||||||||
\(595\) | −781.914 | −0.0538745 | ||||||||
\(596\) | −1.67509 | −0.000115125 0 | ||||||||
\(597\) | −39007.2 | −2.67414 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16087.2 | 1.09734 | 0.548668 | − | 0.836041i | \(-0.315135\pi\) | ||||
0.548668 | + | 0.836041i | \(0.315135\pi\) | |||||||
\(600\) | −22108.6 | −1.50430 | ||||||||
\(601\) | 1577.34 | 0.107057 | 0.0535283 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535283 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(602\) | 7489.60 | 0.507065 | ||||||||
\(603\) | 26138.9 | 1.76527 | ||||||||
\(604\) | −208.996 | −0.0140794 | ||||||||
\(605\) | −660.311 | −0.0443727 | ||||||||
\(606\) | 40558.4 | 2.71877 | ||||||||
\(607\) | 29401.1 | 1.96599 | 0.982993 | − | 0.183641i | \(-0.0587884\pi\) | ||||
0.982993 | + | 0.183641i | \(0.0587884\pi\) | |||||||
\(608\) | 559.477 | 0.0373187 | ||||||||
\(609\) | −1271.23 | −0.0845858 | ||||||||
\(610\) | 12222.1 | 0.811242 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 264.210 | 0.0174511 | ||||||||
\(613\) | −21093.0 | −1.38978 | −0.694891 | − | 0.719115i | \(-0.744547\pi\) | ||||
−0.694891 | + | 0.719115i | \(0.744547\pi\) | |||||||
\(614\) | −2802.52 | −0.184203 | ||||||||
\(615\) | 25516.7 | 1.67306 | ||||||||
\(616\) | −1947.43 | −0.127377 | ||||||||
\(617\) | 17937.2 | 1.17038 | 0.585189 | − | 0.810897i | \(-0.301020\pi\) | ||||
0.585189 | + | 0.810897i | \(0.301020\pi\) | |||||||
\(618\) | 4825.25 | 0.314078 | ||||||||
\(619\) | −18166.1 | −1.17958 | −0.589789 | − | 0.807557i | \(-0.700789\pi\) | ||||
−0.589789 | + | 0.807557i | \(0.700789\pi\) | |||||||
\(620\) | −103.299 | −0.00669126 | ||||||||
\(621\) | 19286.2 | 1.24626 | ||||||||
\(622\) | 14664.7 | 0.945342 | ||||||||
\(623\) | 4144.21 | 0.266508 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5344.31 | 0.342036 | ||||||||
\(626\) | 4327.15 | 0.276274 | ||||||||
\(627\) | −7345.88 | −0.467889 | ||||||||
\(628\) | 516.747 | 0.0328351 | ||||||||
\(629\) | 6066.72 | 0.384572 | ||||||||
\(630\) | −8959.70 | −0.566608 | ||||||||
\(631\) | −8878.70 | −0.560151 | −0.280076 | − | 0.959978i | \(-0.590360\pi\) | ||||
−0.280076 | + | 0.959978i | \(0.590360\pi\) | |||||||
\(632\) | −11505.0 | −0.724120 | ||||||||
\(633\) | 48282.4 | 3.03168 | ||||||||
\(634\) | −23170.5 | −1.45145 | ||||||||
\(635\) | 6463.63 | 0.403939 | ||||||||
\(636\) | 738.596 | 0.0460491 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −497.978 | −0.0309015 | ||||||||
\(639\) | −14194.9 | −0.878781 | ||||||||
\(640\) | 7613.00 | 0.470204 | ||||||||
\(641\) | −2369.01 | −0.145975 | −0.0729876 | − | 0.997333i | \(-0.523253\pi\) | ||||
−0.0729876 | + | 0.997333i | \(0.523253\pi\) | |||||||
\(642\) | −1340.19 | −0.0823883 | ||||||||
\(643\) | 5914.40 | 0.362739 | 0.181369 | − | 0.983415i | \(-0.441947\pi\) | ||||
0.181369 | + | 0.983415i | \(0.441947\pi\) | |||||||
\(644\) | 56.4565 | 0.00345450 | ||||||||
\(645\) | −19177.9 | −1.17074 | ||||||||
\(646\) | −3407.54 | −0.207535 | ||||||||
\(647\) | 2640.30 | 0.160434 | 0.0802170 | − | 0.996777i | \(-0.474439\pi\) | ||||
0.0802170 | + | 0.996777i | \(0.474439\pi\) | |||||||
\(648\) | 68350.3 | 4.14360 | ||||||||
\(649\) | 1033.50 | 0.0625091 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7908.40 | 0.476121 | ||||||||
\(652\) | 677.581 | 0.0406996 | ||||||||
\(653\) | 13149.0 | 0.787993 | 0.393997 | − | 0.919112i | \(-0.371092\pi\) | ||||
0.393997 | + | 0.919112i | \(0.371092\pi\) | |||||||
\(654\) | −37442.3 | −2.23870 | ||||||||
\(655\) | −2724.01 | −0.162498 | ||||||||
\(656\) | 28787.1 | 1.71334 | ||||||||
\(657\) | 62277.4 | 3.69813 | ||||||||
\(658\) | −6885.71 | −0.407953 | ||||||||
\(659\) | 18288.3 | 1.08105 | 0.540525 | − | 0.841328i | \(-0.318226\pi\) | ||||
0.540525 | + | 0.841328i | \(0.318226\pi\) | |||||||
\(660\) | 114.411 | 0.00674765 | ||||||||
\(661\) | −6578.84 | −0.387122 | −0.193561 | − | 0.981088i | \(-0.562004\pi\) | ||||
−0.193561 | + | 0.981088i | \(0.562004\pi\) | |||||||
\(662\) | −19048.7 | −1.11835 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4571.84 | −0.267201 | ||||||||
\(665\) | −2778.75 | −0.162038 | ||||||||
\(666\) | 69516.6 | 4.04461 | ||||||||
\(667\) | 629.214 | 0.0365266 | ||||||||
\(668\) | 422.376 | 0.0244644 | ||||||||
\(669\) | −35342.4 | −2.04248 | ||||||||
\(670\) | 5250.53 | 0.302755 | ||||||||
\(671\) | 8814.34 | 0.507114 | ||||||||
\(672\) | 667.114 | 0.0382954 | ||||||||
\(673\) | 13014.3 | 0.745417 | 0.372709 | − | 0.927948i | \(-0.378429\pi\) | ||||
0.372709 | + | 0.927948i | \(0.378429\pi\) | |||||||
\(674\) | −31901.2 | −1.82313 | ||||||||
\(675\) | −47272.6 | −2.69559 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15153.5 | 0.860261 | 0.430131 | − | 0.902767i | \(-0.358468\pi\) | ||||
0.430131 | + | 0.902767i | \(0.358468\pi\) | |||||||
\(678\) | 56644.1 | 3.20856 | ||||||||
\(679\) | −3576.17 | −0.202122 | ||||||||
\(680\) | 2313.13 | 0.130448 | ||||||||
\(681\) | −25171.1 | −1.41639 | ||||||||
\(682\) | 3097.96 | 0.173940 | ||||||||
\(683\) | 5526.04 | 0.309587 | 0.154794 | − | 0.987947i | \(-0.450529\pi\) | ||||
0.154794 | + | 0.987947i | \(0.450529\pi\) | |||||||
\(684\) | 938.944 | 0.0524875 | ||||||||
\(685\) | −15984.1 | −0.891561 | ||||||||
\(686\) | −13538.8 | −0.753519 | ||||||||
\(687\) | −44967.1 | −2.49724 | ||||||||
\(688\) | −21635.9 | −1.19893 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 6011.62 | 0.331679 | ||||||||
\(691\) | 12665.8 | 0.697295 | 0.348648 | − | 0.937254i | \(-0.386641\pi\) | ||||
0.348648 | + | 0.937254i | \(0.386641\pi\) | |||||||
\(692\) | −42.4836 | −0.00233379 | ||||||||
\(693\) | −6461.57 | −0.354191 | ||||||||
\(694\) | −21986.9 | −1.20261 | ||||||||
\(695\) | 9332.60 | 0.509361 | ||||||||
\(696\) | 3760.67 | 0.204810 | ||||||||
\(697\) | 8536.23 | 0.463892 | ||||||||
\(698\) | 7237.57 | 0.392473 | ||||||||
\(699\) | 6439.78 | 0.348462 | ||||||||
\(700\) | −138.381 | −0.00747185 | ||||||||
\(701\) | 31069.9 | 1.67403 | 0.837013 | − | 0.547182i | \(-0.184300\pi\) | ||||
0.837013 | + | 0.547182i | \(0.184300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21559.8 | 1.15668 | ||||||||
\(704\) | 5757.97 | 0.308255 | ||||||||
\(705\) | 17631.6 | 0.941906 | ||||||||
\(706\) | 14952.7 | 0.797099 | ||||||||
\(707\) | 11064.5 | 0.588576 | ||||||||
\(708\) | −179.073 | −0.00950561 | ||||||||
\(709\) | −3060.38 | −0.162108 | −0.0810542 | − | 0.996710i | \(-0.525829\pi\) | ||||
−0.0810542 | + | 0.996710i | \(0.525829\pi\) | |||||||
\(710\) | −2851.34 | −0.150717 | ||||||||
\(711\) | −38173.6 | −2.01353 | ||||||||
\(712\) | −12259.8 | −0.645303 | ||||||||
\(713\) | −3914.38 | −0.205603 | ||||||||
\(714\) | −4063.11 | −0.212966 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −643.290 | −0.0335767 | ||||||||
\(717\) | 36140.2 | 1.88240 | ||||||||
\(718\) | 22136.5 | 1.15059 | ||||||||
\(719\) | 5162.79 | 0.267788 | 0.133894 | − | 0.990996i | \(-0.457252\pi\) | ||||
0.133894 | + | 0.990996i | \(0.457252\pi\) | |||||||
\(720\) | 25882.7 | 1.33971 | ||||||||
\(721\) | 1316.35 | 0.0679935 | ||||||||
\(722\) | 7061.40 | 0.363986 | ||||||||
\(723\) | −28242.8 | −1.45278 | ||||||||
\(724\) | 415.452 | 0.0213262 | ||||||||
\(725\) | −1542.27 | −0.0790047 | ||||||||
\(726\) | −3431.22 | −0.175406 | ||||||||
\(727\) | −19866.9 | −1.01351 | −0.506756 | − | 0.862089i | \(-0.669156\pi\) | ||||
−0.506756 | + | 0.862089i | \(0.669156\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 90791.4 | 4.61268 | ||||||||
\(730\) | 12509.7 | 0.634253 | ||||||||
\(731\) | −6415.68 | −0.324614 | ||||||||
\(732\) | −1527.25 | −0.0771157 | ||||||||
\(733\) | 22311.4 | 1.12427 | 0.562135 | − | 0.827046i | \(-0.309980\pi\) | ||||
0.562135 | + | 0.827046i | \(0.309980\pi\) | |||||||
\(734\) | −23230.9 | −1.16821 | ||||||||
\(735\) | 15677.1 | 0.786746 | ||||||||
\(736\) | −330.198 | −0.0165371 | ||||||||
\(737\) | 3786.59 | 0.189255 | ||||||||
\(738\) | 97813.9 | 4.87883 | ||||||||
\(739\) | 2637.38 | 0.131283 | 0.0656413 | − | 0.997843i | \(-0.479091\pi\) | ||||
0.0656413 | + | 0.997843i | \(0.479091\pi\) | |||||||
\(740\) | −335.791 | −0.0166810 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8379.02 | −0.414560 | ||||||||
\(743\) | −19802.1 | −0.977752 | −0.488876 | − | 0.872353i | \(-0.662593\pi\) | ||||
−0.488876 | + | 0.872353i | \(0.662593\pi\) | |||||||
\(744\) | −23395.4 | −1.15285 | ||||||||
\(745\) | −48.6593 | −0.00239294 | ||||||||
\(746\) | 37968.3 | 1.86343 | ||||||||
\(747\) | −15169.4 | −0.742996 | ||||||||
\(748\) | 38.2745 | 0.00187093 | ||||||||
\(749\) | −365.610 | −0.0178359 | ||||||||
\(750\) | −34078.7 | −1.65917 | ||||||||
\(751\) | −19359.7 | −0.940673 | −0.470337 | − | 0.882487i | \(-0.655867\pi\) | ||||
−0.470337 | + | 0.882487i | \(0.655867\pi\) | |||||||
\(752\) | 19891.4 | 0.964580 | ||||||||
\(753\) | −58739.4 | −2.84274 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6071.10 | −0.292649 | ||||||||
\(756\) | 721.488 | 0.0347094 | ||||||||
\(757\) | −15668.4 | −0.752281 | −0.376140 | − | 0.926563i | \(-0.622749\pi\) | ||||
−0.376140 | + | 0.926563i | \(0.622749\pi\) | |||||||
\(758\) | −36872.9 | −1.76687 | ||||||||
\(759\) | 4335.47 | 0.207335 | ||||||||
\(760\) | 8220.38 | 0.392348 | ||||||||
\(761\) | −9040.74 | −0.430653 | −0.215326 | − | 0.976542i | \(-0.569082\pi\) | ||||
−0.215326 | + | 0.976542i | \(0.569082\pi\) | |||||||
\(762\) | 33587.4 | 1.59678 | ||||||||
\(763\) | −10214.4 | −0.484647 | ||||||||
\(764\) | 443.145 | 0.0209848 | ||||||||
\(765\) | 7674.98 | 0.362731 | ||||||||
\(766\) | 3905.17 | 0.184203 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2925.92 | −0.137474 | ||||||||
\(769\) | 19880.2 | 0.932248 | 0.466124 | − | 0.884719i | \(-0.345650\pi\) | ||||
0.466124 | + | 0.884719i | \(0.345650\pi\) | |||||||
\(770\) | −1297.94 | −0.0607461 | ||||||||
\(771\) | −50550.6 | −2.36126 | ||||||||
\(772\) | 447.800 | 0.0208765 | ||||||||
\(773\) | −26775.9 | −1.24588 | −0.622938 | − | 0.782271i | \(-0.714061\pi\) | ||||
−0.622938 | + | 0.782271i | \(0.714061\pi\) | |||||||
\(774\) | −73515.2 | −3.41402 | ||||||||
\(775\) | 9594.56 | 0.444706 | ||||||||
\(776\) | 10579.4 | 0.489404 | ||||||||
\(777\) | 25707.7 | 1.18695 | ||||||||
\(778\) | −10159.6 | −0.468173 | ||||||||
\(779\) | 30335.9 | 1.39525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2056.33 | −0.0942142 | ||||||||
\(782\) | 2011.10 | 0.0919651 | ||||||||
\(783\) | 8041.07 | 0.367004 | ||||||||
\(784\) | 17686.4 | 0.805685 | ||||||||
\(785\) | 15010.9 | 0.682500 | ||||||||
\(786\) | −14155.0 | −0.642354 | ||||||||
\(787\) | 15119.7 | 0.684825 | 0.342413 | − | 0.939550i | \(-0.388756\pi\) | ||||
0.342413 | + | 0.939550i | \(0.388756\pi\) | |||||||
\(788\) | −76.5457 | −0.00346044 | ||||||||
\(789\) | −27567.0 | −1.24387 | ||||||||
\(790\) | −7667.95 | −0.345333 | ||||||||
\(791\) | 15452.7 | 0.694609 | ||||||||
\(792\) | 19115.2 | 0.857615 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −13042.7 | −0.582957 | ||||||||
\(795\) | 21455.4 | 0.957161 | ||||||||
\(796\) | 722.273 | 0.0321612 | ||||||||
\(797\) | 25759.8 | 1.14487 | 0.572434 | − | 0.819951i | \(-0.305999\pi\) | ||||
0.572434 | + | 0.819951i | \(0.305999\pi\) | |||||||
\(798\) | −14439.4 | −0.640538 | ||||||||
\(799\) | 5898.38 | 0.261164 | ||||||||
\(800\) | 809.351 | 0.0357686 | ||||||||
\(801\) | −40678.0 | −1.79437 | ||||||||
\(802\) | 18553.5 | 0.816893 | ||||||||
\(803\) | 9021.76 | 0.396477 | ||||||||
\(804\) | −656.096 | −0.0287795 | ||||||||
\(805\) | 1639.99 | 0.0718040 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48057.9 | 2.09631 | ||||||||
\(808\) | −32732.1 | −1.42514 | ||||||||
\(809\) | 13250.8 | 0.575864 | 0.287932 | − | 0.957651i | \(-0.407032\pi\) | ||||
0.287932 | + | 0.957651i | \(0.407032\pi\) | |||||||
\(810\) | 45554.7 | 1.97609 | ||||||||
\(811\) | 14548.1 | 0.629903 | 0.314952 | − | 0.949108i | \(-0.398012\pi\) | ||||
0.314952 | + | 0.949108i | \(0.398012\pi\) | |||||||
\(812\) | 23.5386 | 0.00101729 | ||||||||
\(813\) | −23231.9 | −1.00219 | ||||||||
\(814\) | 10070.5 | 0.433623 | ||||||||
\(815\) | 19682.9 | 0.845967 | ||||||||
\(816\) | 11737.5 | 0.503546 | ||||||||
\(817\) | −22799.9 | −0.976339 | ||||||||
\(818\) | 27263.5 | 1.16534 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −472.478 | −0.0201215 | ||||||||
\(821\) | −15581.7 | −0.662369 | −0.331184 | − | 0.943566i | \(-0.607448\pi\) | ||||
−0.331184 | + | 0.943566i | \(0.607448\pi\) | |||||||
\(822\) | −83059.0 | −3.52435 | ||||||||
\(823\) | −38875.7 | −1.64656 | −0.823282 | − | 0.567632i | \(-0.807860\pi\) | ||||
−0.823282 | + | 0.567632i | \(0.807860\pi\) | |||||||
\(824\) | −3894.15 | −0.164635 | ||||||||
\(825\) | −10626.7 | −0.448453 | ||||||||
\(826\) | 2031.49 | 0.0855747 | ||||||||
\(827\) | 12788.7 | 0.537734 | 0.268867 | − | 0.963177i | \(-0.413351\pi\) | ||||
0.268867 | + | 0.963177i | \(0.413351\pi\) | |||||||
\(828\) | −554.156 | −0.0232588 | ||||||||
\(829\) | −19014.4 | −0.796620 | −0.398310 | − | 0.917251i | \(-0.630403\pi\) | ||||
−0.398310 | + | 0.917251i | \(0.630403\pi\) | |||||||
\(830\) | −3047.08 | −0.127428 | ||||||||
\(831\) | 18059.6 | 0.753890 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5244.53 | 0.218142 | ||||||||
\(834\) | 48495.6 | 2.01351 | ||||||||
\(835\) | 12269.5 | 0.508508 | ||||||||
\(836\) | 136.019 | 0.00562718 | ||||||||
\(837\) | −50024.1 | −2.06581 | ||||||||
\(838\) | 8942.17 | 0.368618 | ||||||||
\(839\) | −16563.8 | −0.681581 | −0.340790 | − | 0.940139i | \(-0.610695\pi\) | ||||
−0.340790 | + | 0.940139i | \(0.610695\pi\) | |||||||
\(840\) | 9801.89 | 0.402616 | ||||||||
\(841\) | −24126.7 | −0.989244 | ||||||||
\(842\) | 20817.7 | 0.852049 | ||||||||
\(843\) | 37288.7 | 1.52348 | ||||||||
\(844\) | −894.017 | −0.0364613 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 67587.6 | 2.74670 | ||||||||
\(847\) | −936.049 | −0.0379729 | ||||||||
\(848\) | 24205.2 | 0.980202 | ||||||||
\(849\) | −38938.0 | −1.57403 | ||||||||
\(850\) | −4929.41 | −0.198915 | ||||||||
\(851\) | −12724.4 | −0.512558 | ||||||||
\(852\) | 356.297 | 0.0143269 | ||||||||
\(853\) | 28302.9 | 1.13608 | 0.568038 | − | 0.823002i | \(-0.307703\pi\) | ||||
0.568038 | + | 0.823002i | \(0.307703\pi\) | |||||||
\(854\) | 17325.9 | 0.694238 | ||||||||
\(855\) | 27275.2 | 1.09099 | ||||||||
\(856\) | 1081.58 | 0.0431867 | ||||||||
\(857\) | −33103.8 | −1.31949 | −0.659746 | − | 0.751489i | \(-0.729336\pi\) | ||||
−0.659746 | + | 0.751489i | \(0.729336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −80.2138 | −0.00318610 | −0.00159305 | − | 0.999999i | \(-0.500507\pi\) | ||||
−0.00159305 | + | 0.999999i | \(0.500507\pi\) | |||||||
\(860\) | 355.106 | 0.0140803 | ||||||||
\(861\) | 36172.2 | 1.43176 | ||||||||
\(862\) | 2614.79 | 0.103318 | ||||||||
\(863\) | −6866.87 | −0.270859 | −0.135429 | − | 0.990787i | \(-0.543241\pi\) | ||||
−0.135429 | + | 0.990787i | \(0.543241\pi\) | |||||||
\(864\) | −4219.79 | −0.166158 | ||||||||
\(865\) | −1234.10 | −0.0485094 | ||||||||
\(866\) | −14755.9 | −0.579014 | ||||||||
\(867\) | −46364.8 | −1.81618 | ||||||||
\(868\) | −146.435 | −0.00572619 | ||||||||
\(869\) | −5529.98 | −0.215871 | ||||||||
\(870\) | 2506.45 | 0.0976741 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 30217.2 | 1.17349 | ||||||||
\(873\) | 35102.4 | 1.36087 | ||||||||
\(874\) | 7147.00 | 0.276603 | ||||||||
\(875\) | −9296.79 | −0.359187 | ||||||||
\(876\) | −1563.19 | −0.0602913 | ||||||||
\(877\) | 35907.6 | 1.38257 | 0.691285 | − | 0.722582i | \(-0.257045\pi\) | ||||
0.691285 | + | 0.722582i | \(0.257045\pi\) | |||||||
\(878\) | −1048.52 | −0.0403028 | ||||||||
\(879\) | 80111.3 | 3.07405 | ||||||||
\(880\) | 3749.48 | 0.143630 | ||||||||
\(881\) | −19063.6 | −0.729021 | −0.364511 | − | 0.931199i | \(-0.618764\pi\) | ||||
−0.364511 | + | 0.931199i | \(0.618764\pi\) | |||||||
\(882\) | 60095.4 | 2.29424 | ||||||||
\(883\) | −18097.1 | −0.689711 | −0.344855 | − | 0.938656i | \(-0.612072\pi\) | ||||
−0.344855 | + | 0.938656i | \(0.612072\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5201.86 | −0.197580 | ||||||||
\(886\) | 46160.8 | 1.75034 | ||||||||
\(887\) | −49133.2 | −1.85990 | −0.929949 | − | 0.367687i | \(-0.880150\pi\) | ||||
−0.929949 | + | 0.367687i | \(0.880150\pi\) | |||||||
\(888\) | −76051.0 | −2.87399 | ||||||||
\(889\) | 9162.77 | 0.345680 | ||||||||
\(890\) | −8171.02 | −0.307745 | ||||||||
\(891\) | 32853.2 | 1.23527 | ||||||||
\(892\) | 654.414 | 0.0245644 | ||||||||
\(893\) | 20961.6 | 0.785500 | ||||||||
\(894\) | −252.852 | −0.00945931 | ||||||||
\(895\) | −18686.8 | −0.697913 | ||||||||
\(896\) | 10792.1 | 0.402387 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17149.9 | −0.637304 | ||||||||
\(899\) | −1632.04 | −0.0605467 | ||||||||
\(900\) | 1358.29 | 0.0503072 | ||||||||
\(901\) | 7177.57 | 0.265393 | ||||||||
\(902\) | 14169.7 | 0.523060 | ||||||||
\(903\) | −27186.4 | −1.00189 | ||||||||
\(904\) | −45713.8 | −1.68188 | ||||||||
\(905\) | 12068.4 | 0.443279 | ||||||||
\(906\) | −31547.6 | −1.15684 | ||||||||
\(907\) | 6772.16 | 0.247923 | 0.123961 | − | 0.992287i | \(-0.460440\pi\) | ||||
0.123961 | + | 0.992287i | \(0.460440\pi\) | |||||||
\(908\) | 466.079 | 0.0170346 | ||||||||
\(909\) | −108605. | −3.96282 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16679.9 | 0.606620 | 0.303310 | − | 0.952892i | \(-0.401908\pi\) | ||||
0.303310 | + | 0.952892i | \(0.401908\pi\) | |||||||
\(912\) | 41712.5 | 1.51451 | ||||||||
\(913\) | −2197.50 | −0.0796566 | ||||||||
\(914\) | 7292.34 | 0.263905 | ||||||||
\(915\) | −44364.7 | −1.60290 | ||||||||
\(916\) | 832.629 | 0.0300337 | ||||||||
\(917\) | −3861.52 | −0.139061 | ||||||||
\(918\) | 25700.9 | 0.924027 | ||||||||
\(919\) | 8903.13 | 0.319572 | 0.159786 | − | 0.987152i | \(-0.448920\pi\) | ||||
0.159786 | + | 0.987152i | \(0.448920\pi\) | |||||||
\(920\) | −4851.59 | −0.173861 | ||||||||
\(921\) | 10172.8 | 0.363959 | ||||||||
\(922\) | −23014.4 | −0.822061 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 162.188 | 0.00577445 | ||||||||
\(925\) | 31188.8 | 1.10863 | ||||||||
\(926\) | 43246.8 | 1.53475 | ||||||||
\(927\) | −12920.8 | −0.457793 | ||||||||
\(928\) | −137.671 | −0.00486989 | ||||||||
\(929\) | 42394.0 | 1.49720 | 0.748601 | − | 0.663020i | \(-0.230726\pi\) | ||||
0.748601 | + | 0.663020i | \(0.230726\pi\) | |||||||
\(930\) | −15592.8 | −0.549793 | ||||||||
\(931\) | 18637.9 | 0.656105 | ||||||||
\(932\) | −119.242 | −0.00419087 | ||||||||
\(933\) | −53231.3 | −1.86786 | ||||||||
\(934\) | −17859.3 | −0.625668 | ||||||||
\(935\) | 1111.83 | 0.0388885 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36138.5 | −1.25997 | −0.629986 | − | 0.776607i | \(-0.716939\pi\) | ||||
−0.629986 | + | 0.776607i | \(0.716939\pi\) | |||||||
\(938\) | 7443.09 | 0.259089 | ||||||||
\(939\) | −15707.0 | −0.545878 | ||||||||
\(940\) | −326.474 | −0.0113281 | ||||||||
\(941\) | 20360.0 | 0.705331 | 0.352665 | − | 0.935750i | \(-0.385275\pi\) | ||||
0.352665 | + | 0.935750i | \(0.385275\pi\) | |||||||
\(942\) | 78002.1 | 2.69793 | ||||||||
\(943\) | −17904.0 | −0.618276 | ||||||||
\(944\) | −5868.57 | −0.202336 | ||||||||
\(945\) | 20958.4 | 0.721457 | ||||||||
\(946\) | −10649.7 | −0.366017 | ||||||||
\(947\) | 55852.7 | 1.91655 | 0.958274 | − | 0.285853i | \(-0.0922769\pi\) | ||||
0.958274 | + | 0.285853i | \(0.0922769\pi\) | |||||||
\(948\) | 958.172 | 0.0328270 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −17518.1 | −0.598274 | ||||||||
\(951\) | 84106.2 | 2.86786 | ||||||||
\(952\) | 3279.07 | 0.111634 | ||||||||
\(953\) | 38154.0 | 1.29688 | 0.648441 | − | 0.761265i | \(-0.275421\pi\) | ||||
0.648441 | + | 0.761265i | \(0.275421\pi\) | |||||||
\(954\) | 82245.4 | 2.79119 | ||||||||
\(955\) | 12872.8 | 0.436183 | ||||||||
\(956\) | −669.187 | −0.0226392 | ||||||||
\(957\) | 1807.60 | 0.0610569 | ||||||||
\(958\) | 40502.4 | 1.36594 | ||||||||
\(959\) | −22658.8 | −0.762973 | ||||||||
\(960\) | −28981.3 | −0.974341 | ||||||||
\(961\) | −19638.0 | −0.659192 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3588.70 | 0.120087 | ||||||||
\(964\) | 522.956 | 0.0174723 | ||||||||
\(965\) | 13008.1 | 0.433932 | ||||||||
\(966\) | 8522.01 | 0.283842 | ||||||||
\(967\) | −47950.6 | −1.59461 | −0.797304 | − | 0.603577i | \(-0.793741\pi\) | ||||
−0.797304 | + | 0.603577i | \(0.793741\pi\) | |||||||
\(968\) | 2769.11 | 0.0919449 | ||||||||
\(969\) | 12369.0 | 0.410060 | ||||||||
\(970\) | 7051.04 | 0.233397 | ||||||||
\(971\) | 46410.1 | 1.53385 | 0.766926 | − | 0.641736i | \(-0.221785\pi\) | ||||
0.766926 | + | 0.641736i | \(0.221785\pi\) | |||||||
\(972\) | −3174.29 | −0.104748 | ||||||||
\(973\) | 13229.8 | 0.435896 | ||||||||
\(974\) | −21673.5 | −0.713002 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −50050.9 | −1.64149 | ||||||||
\(977\) | 18690.8 | 0.612050 | 0.306025 | − | 0.952023i | \(-0.401001\pi\) | ||||
0.306025 | + | 0.952023i | \(0.401001\pi\) | |||||||
\(978\) | 102280. | 3.34411 | ||||||||
\(979\) | −5892.79 | −0.192374 | ||||||||
\(980\) | −290.283 | −0.00946201 | ||||||||
\(981\) | 100261. | 3.26308 | ||||||||
\(982\) | 19814.7 | 0.643903 | ||||||||
\(983\) | −44536.0 | −1.44504 | −0.722521 | − | 0.691349i | \(-0.757017\pi\) | ||||
−0.722521 | + | 0.691349i | \(0.757017\pi\) | |||||||
\(984\) | −107008. | −3.46676 | ||||||||
\(985\) | −2223.56 | −0.0719276 | ||||||||
\(986\) | 838.493 | 0.0270822 | ||||||||
\(987\) | 24994.3 | 0.806057 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13456.3 | 0.432645 | ||||||||
\(990\) | 12740.1 | 0.408997 | ||||||||
\(991\) | 30003.5 | 0.961748 | 0.480874 | − | 0.876790i | \(-0.340319\pi\) | ||||
0.480874 | + | 0.876790i | \(0.340319\pi\) | |||||||
\(992\) | 856.459 | 0.0274119 | ||||||||
\(993\) | 69144.4 | 2.20970 | ||||||||
\(994\) | −4042.02 | −0.128979 | ||||||||
\(995\) | 20981.2 | 0.668491 | ||||||||
\(996\) | 380.757 | 0.0121132 | ||||||||
\(997\) | 38357.3 | 1.21844 | 0.609221 | − | 0.793000i | \(-0.291482\pi\) | ||||
0.609221 | + | 0.793000i | \(0.291482\pi\) | |||||||
\(998\) | −24510.6 | −0.777424 | ||||||||
\(999\) | −162612. | −5.14997 |
(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 | 1859.4.a.f.1.5 | 17 | ||
13.4 | even | 6 | 143.4.e.a.133.5 | yes | 34 | ||
13.10 | even | 6 | 143.4.e.a.100.5 | ✓ | 34 | ||
13.12 | even | 2 | 1859.4.a.i.1.13 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.e.a.100.5 | ✓ | 34 | 13.10 | even | 6 | ||
143.4.e.a.133.5 | yes | 34 | 13.4 | even | 6 | ||
1859.4.a.f.1.5 | 17 | 1.1 | even | 1 | trivial | ||
1859.4.a.i.1.13 | 17 | 13.12 | even | 2 |