Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("525.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(30.9760027530\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 13x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.18296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.18296 | −1.12535 | −0.562673 | − | 0.826680i | \(-0.690227\pi\) | ||||
−0.562673 | + | 0.826680i | \(0.690227\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 2.13122 | 0.266402 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 9.54887 | 0.649718 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 18.6801 | 0.825551 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −68.7204 | −1.88363 | −0.941817 | − | 0.336127i | \(-0.890883\pi\) | ||||
−0.941817 | + | 0.336127i | \(0.890883\pi\) | |||||||
\(12\) | −6.39365 | −0.153807 | ||||||||
\(13\) | 56.2290 | 1.19962 | 0.599812 | − | 0.800141i | \(-0.295242\pi\) | ||||
0.599812 | + | 0.800141i | \(0.295242\pi\) | |||||||
\(14\) | 22.2807 | 0.425341 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −76.5076 | −1.19543 | ||||||||
\(17\) | 37.9780 | 0.541825 | 0.270912 | − | 0.962604i | \(-0.412675\pi\) | ||||
0.270912 | + | 0.962604i | \(0.412675\pi\) | |||||||
\(18\) | −28.6466 | −0.375115 | ||||||||
\(19\) | −26.0335 | −0.314341 | −0.157171 | − | 0.987571i | \(-0.550237\pi\) | ||||
−0.157171 | + | 0.987571i | \(0.550237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 218.734 | 2.11974 | ||||||||
\(23\) | 25.5222 | 0.231380 | 0.115690 | − | 0.993285i | \(-0.463092\pi\) | ||||
0.115690 | + | 0.993285i | \(0.463092\pi\) | |||||||
\(24\) | −56.0403 | −0.476632 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −178.974 | −1.34999 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −14.9185 | −0.100690 | ||||||||
\(29\) | 148.336 | 0.949835 | 0.474917 | − | 0.880030i | \(-0.342478\pi\) | ||||
0.474917 | + | 0.880030i | \(0.342478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 75.7982 | 0.439153 | 0.219577 | − | 0.975595i | \(-0.429532\pi\) | ||||
0.219577 | + | 0.975595i | \(0.429532\pi\) | |||||||
\(32\) | 94.0799 | 0.519723 | ||||||||
\(33\) | 206.161 | 1.08752 | ||||||||
\(34\) | −120.882 | −0.609740 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 19.1809 | 0.0888007 | ||||||||
\(37\) | 120.199 | 0.534070 | 0.267035 | − | 0.963687i | \(-0.413956\pi\) | ||||
0.267035 | + | 0.963687i | \(0.413956\pi\) | |||||||
\(38\) | 82.8634 | 0.353743 | ||||||||
\(39\) | −168.687 | −0.692603 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 345.670 | 1.31670 | 0.658348 | − | 0.752713i | \(-0.271255\pi\) | ||||
0.658348 | + | 0.752713i | \(0.271255\pi\) | |||||||
\(42\) | −66.8421 | −0.245570 | ||||||||
\(43\) | 287.989 | 1.02135 | 0.510674 | − | 0.859774i | \(-0.329396\pi\) | ||||
0.510674 | + | 0.859774i | \(0.329396\pi\) | |||||||
\(44\) | −146.458 | −0.501804 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −81.2360 | −0.260383 | ||||||||
\(47\) | −528.711 | −1.64086 | −0.820430 | − | 0.571747i | \(-0.806266\pi\) | ||||
−0.820430 | + | 0.571747i | \(0.806266\pi\) | |||||||
\(48\) | 229.523 | 0.690183 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −113.934 | −0.312823 | ||||||||
\(52\) | 119.836 | 0.319582 | ||||||||
\(53\) | 361.728 | 0.937493 | 0.468747 | − | 0.883333i | \(-0.344706\pi\) | ||||
0.468747 | + | 0.883333i | \(0.344706\pi\) | |||||||
\(54\) | 85.9398 | 0.216573 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −130.761 | −0.312029 | ||||||||
\(57\) | 78.1004 | 0.181485 | ||||||||
\(58\) | −472.146 | −1.06889 | ||||||||
\(59\) | −705.748 | −1.55730 | −0.778649 | − | 0.627460i | \(-0.784095\pi\) | ||||
−0.778649 | + | 0.627460i | \(0.784095\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −393.171 | −0.825253 | −0.412627 | − | 0.910900i | \(-0.635389\pi\) | ||||
−0.412627 | + | 0.910900i | \(0.635389\pi\) | |||||||
\(62\) | −241.262 | −0.494199 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 312.609 | 0.610564 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −656.202 | −1.22383 | ||||||||
\(67\) | 591.202 | 1.07801 | 0.539006 | − | 0.842302i | \(-0.318800\pi\) | ||||
0.539006 | + | 0.842302i | \(0.318800\pi\) | |||||||
\(68\) | 80.9393 | 0.144343 | ||||||||
\(69\) | −76.5666 | −0.133587 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −668.829 | −1.11796 | −0.558981 | − | 0.829180i | \(-0.688808\pi\) | ||||
−0.558981 | + | 0.829180i | \(0.688808\pi\) | |||||||
\(72\) | 168.121 | 0.275184 | ||||||||
\(73\) | −251.755 | −0.403639 | −0.201819 | − | 0.979423i | \(-0.564685\pi\) | ||||
−0.201819 | + | 0.979423i | \(0.564685\pi\) | |||||||
\(74\) | −382.588 | −0.601013 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −55.4830 | −0.0837412 | ||||||||
\(77\) | 481.042 | 0.711946 | ||||||||
\(78\) | 536.923 | 0.779418 | ||||||||
\(79\) | 295.651 | 0.421054 | 0.210527 | − | 0.977588i | \(-0.432482\pi\) | ||||
0.210527 | + | 0.977588i | \(0.432482\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1100.25 | −1.48174 | ||||||||
\(83\) | −916.511 | −1.21205 | −0.606025 | − | 0.795445i | \(-0.707237\pi\) | ||||
−0.606025 | + | 0.795445i | \(0.707237\pi\) | |||||||
\(84\) | 44.7555 | 0.0581337 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −916.658 | −1.14937 | ||||||||
\(87\) | −445.007 | −0.548387 | ||||||||
\(88\) | −1283.70 | −1.55504 | ||||||||
\(89\) | −736.838 | −0.877580 | −0.438790 | − | 0.898590i | \(-0.644593\pi\) | ||||
−0.438790 | + | 0.898590i | \(0.644593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −393.603 | −0.453415 | ||||||||
\(92\) | 54.3933 | 0.0616401 | ||||||||
\(93\) | −227.395 | −0.253545 | ||||||||
\(94\) | 1682.86 | 1.84653 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −282.240 | −0.300062 | ||||||||
\(97\) | −142.964 | −0.149647 | −0.0748236 | − | 0.997197i | \(-0.523839\pi\) | ||||
−0.0748236 | + | 0.997197i | \(0.523839\pi\) | |||||||
\(98\) | −155.965 | −0.160764 | ||||||||
\(99\) | −618.483 | −0.627878 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −566.067 | −0.557681 | −0.278840 | − | 0.960337i | \(-0.589950\pi\) | ||||
−0.278840 | + | 0.960337i | \(0.589950\pi\) | |||||||
\(102\) | 362.647 | 0.352033 | ||||||||
\(103\) | 1340.79 | 1.28264 | 0.641318 | − | 0.767275i | \(-0.278388\pi\) | ||||
0.641318 | + | 0.767275i | \(0.278388\pi\) | |||||||
\(104\) | 1050.36 | 0.990351 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1151.36 | −1.05500 | ||||||||
\(107\) | −1637.85 | −1.47978 | −0.739891 | − | 0.672727i | \(-0.765123\pi\) | ||||
−0.739891 | + | 0.672727i | \(0.765123\pi\) | |||||||
\(108\) | −57.5428 | −0.0512691 | ||||||||
\(109\) | −586.693 | −0.515550 | −0.257775 | − | 0.966205i | \(-0.582989\pi\) | ||||
−0.257775 | + | 0.966205i | \(0.582989\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −360.597 | −0.308345 | ||||||||
\(112\) | 535.554 | 0.451831 | ||||||||
\(113\) | −1617.17 | −1.34629 | −0.673146 | − | 0.739509i | \(-0.735058\pi\) | ||||
−0.673146 | + | 0.739509i | \(0.735058\pi\) | |||||||
\(114\) | −248.590 | −0.204233 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 316.135 | 0.253038 | ||||||||
\(117\) | 506.061 | 0.399875 | ||||||||
\(118\) | 2246.37 | 1.75250 | ||||||||
\(119\) | −265.846 | −0.204790 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3391.49 | 2.54807 | ||||||||
\(122\) | 1251.45 | 0.928695 | ||||||||
\(123\) | −1037.01 | −0.760195 | ||||||||
\(124\) | 161.542 | 0.116991 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 200.526 | 0.141780 | ||||||||
\(127\) | −2042.94 | −1.42741 | −0.713706 | − | 0.700446i | \(-0.752985\pi\) | ||||
−0.713706 | + | 0.700446i | \(0.752985\pi\) | |||||||
\(128\) | −1747.66 | −1.20682 | ||||||||
\(129\) | −863.968 | −0.589675 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2631.04 | −1.75477 | −0.877384 | − | 0.479788i | \(-0.840714\pi\) | ||||
−0.877384 | + | 0.479788i | \(0.840714\pi\) | |||||||
\(132\) | 439.374 | 0.289716 | ||||||||
\(133\) | 182.234 | 0.118810 | ||||||||
\(134\) | −1881.77 | −1.21314 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 709.432 | 0.447304 | ||||||||
\(137\) | −1588.54 | −0.990641 | −0.495320 | − | 0.868710i | \(-0.664949\pi\) | ||||
−0.495320 | + | 0.868710i | \(0.664949\pi\) | |||||||
\(138\) | 243.708 | 0.150332 | ||||||||
\(139\) | 1733.49 | 1.05779 | 0.528894 | − | 0.848688i | \(-0.322607\pi\) | ||||
0.528894 | + | 0.848688i | \(0.322607\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1586.13 | 0.947351 | ||||||||
\(142\) | 2128.85 | 1.25809 | ||||||||
\(143\) | −3864.07 | −2.25965 | ||||||||
\(144\) | −688.569 | −0.398477 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 801.324 | 0.454233 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 256.170 | 0.142277 | ||||||||
\(149\) | −1370.68 | −0.753629 | −0.376815 | − | 0.926289i | \(-0.622981\pi\) | ||||
−0.376815 | + | 0.926289i | \(0.622981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3694.08 | −1.99086 | −0.995429 | − | 0.0955015i | \(-0.969555\pi\) | ||||
−0.995429 | + | 0.0955015i | \(0.969555\pi\) | |||||||
\(152\) | −486.308 | −0.259505 | ||||||||
\(153\) | 341.802 | 0.180608 | ||||||||
\(154\) | −1531.14 | −0.801186 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −359.508 | −0.184511 | ||||||||
\(157\) | −1054.56 | −0.536071 | −0.268036 | − | 0.963409i | \(-0.586374\pi\) | ||||
−0.268036 | + | 0.963409i | \(0.586374\pi\) | |||||||
\(158\) | −941.044 | −0.473832 | ||||||||
\(159\) | −1085.18 | −0.541262 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −178.655 | −0.0874535 | ||||||||
\(162\) | −257.820 | −0.125038 | ||||||||
\(163\) | 1380.12 | 0.663185 | 0.331593 | − | 0.943423i | \(-0.392414\pi\) | ||||
0.331593 | + | 0.943423i | \(0.392414\pi\) | |||||||
\(164\) | 736.697 | 0.350771 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2917.22 | 1.36398 | ||||||||
\(167\) | 3143.10 | 1.45641 | 0.728205 | − | 0.685359i | \(-0.240355\pi\) | ||||
0.728205 | + | 0.685359i | \(0.240355\pi\) | |||||||
\(168\) | 392.282 | 0.180150 | ||||||||
\(169\) | 964.696 | 0.439097 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −234.301 | −0.104780 | ||||||||
\(172\) | 613.767 | 0.272089 | ||||||||
\(173\) | 3306.12 | 1.45295 | 0.726473 | − | 0.687195i | \(-0.241158\pi\) | ||||
0.726473 | + | 0.687195i | \(0.241158\pi\) | |||||||
\(174\) | 1416.44 | 0.617125 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5257.63 | 2.25176 | ||||||||
\(177\) | 2117.24 | 0.899106 | ||||||||
\(178\) | 2345.32 | 0.987581 | ||||||||
\(179\) | 2839.60 | 1.18571 | 0.592854 | − | 0.805310i | \(-0.298001\pi\) | ||||
0.592854 | + | 0.805310i | \(0.298001\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 741.522 | 0.304513 | 0.152257 | − | 0.988341i | \(-0.451346\pi\) | ||||
0.152257 | + | 0.988341i | \(0.451346\pi\) | |||||||
\(182\) | 1252.82 | 0.510249 | ||||||||
\(183\) | 1179.51 | 0.476460 | ||||||||
\(184\) | 476.757 | 0.191016 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 723.787 | 0.285326 | ||||||||
\(187\) | −2609.86 | −1.02060 | ||||||||
\(188\) | −1126.80 | −0.437129 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4428.76 | 1.67777 | 0.838885 | − | 0.544309i | \(-0.183208\pi\) | ||||
0.838885 | + | 0.544309i | \(0.183208\pi\) | |||||||
\(192\) | −937.827 | −0.352510 | ||||||||
\(193\) | 815.034 | 0.303976 | 0.151988 | − | 0.988382i | \(-0.451432\pi\) | ||||
0.151988 | + | 0.988382i | \(0.451432\pi\) | |||||||
\(194\) | 455.048 | 0.168405 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 104.430 | 0.0380574 | ||||||||
\(197\) | −1609.61 | −0.582133 | −0.291067 | − | 0.956703i | \(-0.594010\pi\) | ||||
−0.291067 | + | 0.956703i | \(0.594010\pi\) | |||||||
\(198\) | 1968.61 | 0.706579 | ||||||||
\(199\) | −273.622 | −0.0974700 | −0.0487350 | − | 0.998812i | \(-0.515519\pi\) | ||||
−0.0487350 | + | 0.998812i | \(0.515519\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1773.60 | −0.622390 | ||||||||
\(202\) | 1801.77 | 0.627584 | ||||||||
\(203\) | −1038.35 | −0.359004 | ||||||||
\(204\) | −242.818 | −0.0833366 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4267.66 | −1.44341 | ||||||||
\(207\) | 229.700 | 0.0771267 | ||||||||
\(208\) | −4301.95 | −1.43407 | ||||||||
\(209\) | 1789.03 | 0.592104 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5157.70 | −1.68280 | −0.841399 | − | 0.540414i | \(-0.818267\pi\) | ||||
−0.841399 | + | 0.540414i | \(0.818267\pi\) | |||||||
\(212\) | 770.920 | 0.249750 | ||||||||
\(213\) | 2006.49 | 0.645456 | ||||||||
\(214\) | 5213.20 | 1.66527 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −504.362 | −0.158877 | ||||||||
\(217\) | −530.587 | −0.165984 | ||||||||
\(218\) | 1867.42 | 0.580172 | ||||||||
\(219\) | 755.264 | 0.233041 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2135.46 | 0.649986 | ||||||||
\(222\) | 1147.76 | 0.346995 | ||||||||
\(223\) | 1444.38 | 0.433733 | 0.216867 | − | 0.976201i | \(-0.430416\pi\) | ||||
0.216867 | + | 0.976201i | \(0.430416\pi\) | |||||||
\(224\) | −658.559 | −0.196437 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5147.40 | 1.51504 | ||||||||
\(227\) | 1635.20 | 0.478114 | 0.239057 | − | 0.971006i | \(-0.423162\pi\) | ||||
0.239057 | + | 0.971006i | \(0.423162\pi\) | |||||||
\(228\) | 166.449 | 0.0483480 | ||||||||
\(229\) | −2807.34 | −0.810105 | −0.405052 | − | 0.914293i | \(-0.632747\pi\) | ||||
−0.405052 | + | 0.914293i | \(0.632747\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1443.13 | −0.411042 | ||||||||
\(232\) | 2770.92 | 0.784137 | ||||||||
\(233\) | 579.805 | 0.163023 | 0.0815113 | − | 0.996672i | \(-0.474025\pi\) | ||||
0.0815113 | + | 0.996672i | \(0.474025\pi\) | |||||||
\(234\) | −1610.77 | −0.449997 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1504.10 | −0.414867 | ||||||||
\(237\) | −886.952 | −0.243096 | ||||||||
\(238\) | 846.177 | 0.230460 | ||||||||
\(239\) | −1695.51 | −0.458886 | −0.229443 | − | 0.973322i | \(-0.573690\pi\) | ||||
−0.229443 | + | 0.973322i | \(0.573690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1182.39 | −0.316035 | −0.158018 | − | 0.987436i | \(-0.550510\pi\) | ||||
−0.158018 | + | 0.987436i | \(0.550510\pi\) | |||||||
\(242\) | −10795.0 | −2.86746 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −837.933 | −0.219849 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3300.76 | 0.855482 | ||||||||
\(247\) | −1463.84 | −0.377091 | ||||||||
\(248\) | 1415.92 | 0.362544 | ||||||||
\(249\) | 2749.53 | 0.699778 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2411.68 | 0.606469 | 0.303234 | − | 0.952916i | \(-0.401934\pi\) | ||||
0.303234 | + | 0.952916i | \(0.401934\pi\) | |||||||
\(252\) | −134.267 | −0.0335635 | ||||||||
\(253\) | −1753.89 | −0.435835 | ||||||||
\(254\) | 6502.58 | 1.60633 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3061.85 | 0.747523 | ||||||||
\(257\) | 1054.74 | 0.256003 | 0.128002 | − | 0.991774i | \(-0.459144\pi\) | ||||
0.128002 | + | 0.991774i | \(0.459144\pi\) | |||||||
\(258\) | 2749.97 | 0.663588 | ||||||||
\(259\) | −841.392 | −0.201859 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1335.02 | 0.316612 | ||||||||
\(262\) | 8374.48 | 1.97472 | ||||||||
\(263\) | −3390.76 | −0.794993 | −0.397496 | − | 0.917604i | \(-0.630121\pi\) | ||||
−0.397496 | + | 0.917604i | \(0.630121\pi\) | |||||||
\(264\) | 3851.11 | 0.897800 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −580.044 | −0.133702 | ||||||||
\(267\) | 2210.51 | 0.506671 | ||||||||
\(268\) | 1259.98 | 0.287184 | ||||||||
\(269\) | −8792.06 | −1.99279 | −0.996397 | − | 0.0848151i | \(-0.972970\pi\) | ||||
−0.996397 | + | 0.0848151i | \(0.972970\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1593.15 | 0.357111 | 0.178556 | − | 0.983930i | \(-0.442858\pi\) | ||||
0.178556 | + | 0.983930i | \(0.442858\pi\) | |||||||
\(272\) | −2905.61 | −0.647715 | ||||||||
\(273\) | 1180.81 | 0.261779 | ||||||||
\(274\) | 5056.24 | 1.11481 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −163.180 | −0.0355880 | ||||||||
\(277\) | −208.765 | −0.0452833 | −0.0226417 | − | 0.999744i | \(-0.507208\pi\) | ||||
−0.0226417 | + | 0.999744i | \(0.507208\pi\) | |||||||
\(278\) | −5517.62 | −1.19038 | ||||||||
\(279\) | 682.184 | 0.146384 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2445.06 | 0.519075 | 0.259538 | − | 0.965733i | \(-0.416430\pi\) | ||||
0.259538 | + | 0.965733i | \(0.416430\pi\) | |||||||
\(282\) | −5048.59 | −1.06610 | ||||||||
\(283\) | 3894.53 | 0.818042 | 0.409021 | − | 0.912525i | \(-0.365870\pi\) | ||||
0.409021 | + | 0.912525i | \(0.365870\pi\) | |||||||
\(284\) | −1425.42 | −0.297828 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12299.2 | 2.54289 | ||||||||
\(287\) | −2419.69 | −0.497665 | ||||||||
\(288\) | 846.719 | 0.173241 | ||||||||
\(289\) | −3470.67 | −0.706426 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 428.892 | 0.0863988 | ||||||||
\(292\) | −536.543 | −0.107530 | ||||||||
\(293\) | −5746.21 | −1.14572 | −0.572862 | − | 0.819652i | \(-0.694167\pi\) | ||||
−0.572862 | + | 0.819652i | \(0.694167\pi\) | |||||||
\(294\) | 467.895 | 0.0928169 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2245.33 | 0.440902 | ||||||||
\(297\) | 1855.45 | 0.362505 | ||||||||
\(298\) | 4362.83 | 0.848093 | ||||||||
\(299\) | 1435.09 | 0.277569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2015.93 | −0.386033 | ||||||||
\(302\) | 11758.1 | 2.24040 | ||||||||
\(303\) | 1698.20 | 0.321977 | ||||||||
\(304\) | 1991.76 | 0.375774 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1087.94 | −0.203247 | ||||||||
\(307\) | 1979.55 | 0.368008 | 0.184004 | − | 0.982925i | \(-0.441094\pi\) | ||||
0.184004 | + | 0.982925i | \(0.441094\pi\) | |||||||
\(308\) | 1025.21 | 0.189664 | ||||||||
\(309\) | −4022.36 | −0.740531 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3495.57 | 0.637348 | 0.318674 | − | 0.947864i | \(-0.396762\pi\) | ||||
0.318674 | + | 0.947864i | \(0.396762\pi\) | |||||||
\(312\) | −3151.09 | −0.571779 | ||||||||
\(313\) | −1448.68 | −0.261611 | −0.130805 | − | 0.991408i | \(-0.541756\pi\) | ||||
−0.130805 | + | 0.991408i | \(0.541756\pi\) | |||||||
\(314\) | 3356.62 | 0.603265 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 630.096 | 0.112170 | ||||||||
\(317\) | −9453.34 | −1.67493 | −0.837465 | − | 0.546492i | \(-0.815963\pi\) | ||||
−0.837465 | + | 0.546492i | \(0.815963\pi\) | |||||||
\(318\) | 3454.09 | 0.609107 | ||||||||
\(319\) | −10193.7 | −1.78914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4913.54 | 0.854353 | ||||||||
\(322\) | 568.652 | 0.0984154 | ||||||||
\(323\) | −988.699 | −0.170318 | ||||||||
\(324\) | 172.629 | 0.0296002 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4392.86 | −0.746313 | ||||||||
\(327\) | 1760.08 | 0.297653 | ||||||||
\(328\) | 6457.14 | 1.08700 | ||||||||
\(329\) | 3700.98 | 0.620187 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −791.305 | −0.131402 | −0.0657010 | − | 0.997839i | \(-0.520928\pi\) | ||||
−0.0657010 | + | 0.997839i | \(0.520928\pi\) | |||||||
\(332\) | −1953.28 | −0.322893 | ||||||||
\(333\) | 1081.79 | 0.178023 | ||||||||
\(334\) | −10004.4 | −1.63896 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1606.66 | −0.260865 | ||||||||
\(337\) | 5959.06 | 0.963237 | 0.481618 | − | 0.876381i | \(-0.340049\pi\) | ||||
0.481618 | + | 0.876381i | \(0.340049\pi\) | |||||||
\(338\) | −3070.59 | −0.494136 | ||||||||
\(339\) | 4851.52 | 0.777282 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5208.88 | −0.827204 | ||||||||
\(342\) | 745.771 | 0.117914 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 5379.67 | 0.843175 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10523.2 | −1.63507 | ||||||||
\(347\) | −4560.34 | −0.705509 | −0.352755 | − | 0.935716i | \(-0.614755\pi\) | ||||
−0.352755 | + | 0.935716i | \(0.614755\pi\) | |||||||
\(348\) | −948.405 | −0.146092 | ||||||||
\(349\) | −9404.92 | −1.44250 | −0.721252 | − | 0.692673i | \(-0.756433\pi\) | ||||
−0.721252 | + | 0.692673i | \(0.756433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1518.18 | −0.230868 | ||||||||
\(352\) | −6465.20 | −0.978967 | ||||||||
\(353\) | 1391.37 | 0.209788 | 0.104894 | − | 0.994483i | \(-0.466550\pi\) | ||||
0.104894 | + | 0.994483i | \(0.466550\pi\) | |||||||
\(354\) | −6739.10 | −1.01180 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1570.36 | −0.233789 | ||||||||
\(357\) | 797.538 | 0.118236 | ||||||||
\(358\) | −9038.32 | −1.33433 | ||||||||
\(359\) | 4306.80 | 0.633159 | 0.316579 | − | 0.948566i | \(-0.397466\pi\) | ||||
0.316579 | + | 0.948566i | \(0.397466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6181.26 | −0.901189 | ||||||||
\(362\) | −2360.23 | −0.342682 | ||||||||
\(363\) | −10174.5 | −1.47113 | ||||||||
\(364\) | −838.852 | −0.120791 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3754.34 | −0.536182 | ||||||||
\(367\) | 6405.46 | 0.911069 | 0.455534 | − | 0.890218i | \(-0.349448\pi\) | ||||
0.455534 | + | 0.890218i | \(0.349448\pi\) | |||||||
\(368\) | −1952.64 | −0.276599 | ||||||||
\(369\) | 3111.03 | 0.438899 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2532.09 | −0.354339 | ||||||||
\(372\) | −484.627 | −0.0675450 | ||||||||
\(373\) | −10293.2 | −1.42885 | −0.714425 | − | 0.699712i | \(-0.753312\pi\) | ||||
−0.714425 | + | 0.699712i | \(0.753312\pi\) | |||||||
\(374\) | 8307.08 | 1.14853 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9876.37 | −1.35461 | ||||||||
\(377\) | 8340.75 | 1.13944 | ||||||||
\(378\) | −601.579 | −0.0818568 | ||||||||
\(379\) | 3832.35 | 0.519405 | 0.259702 | − | 0.965689i | \(-0.416375\pi\) | ||||
0.259702 | + | 0.965689i | \(0.416375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6128.81 | 0.824116 | ||||||||
\(382\) | −14096.6 | −1.88807 | ||||||||
\(383\) | −13514.8 | −1.80307 | −0.901536 | − | 0.432705i | \(-0.857559\pi\) | ||||
−0.901536 | + | 0.432705i | \(0.857559\pi\) | |||||||
\(384\) | 5242.98 | 0.696757 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2594.22 | −0.342078 | ||||||||
\(387\) | 2591.90 | 0.340449 | ||||||||
\(388\) | −304.687 | −0.0398663 | ||||||||
\(389\) | −6444.44 | −0.839965 | −0.419982 | − | 0.907532i | \(-0.637964\pi\) | ||||
−0.419982 | + | 0.907532i | \(0.637964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 969.282 | 0.125367 | ||||||||
\(392\) | 915.324 | 0.117936 | ||||||||
\(393\) | 7893.11 | 1.01312 | ||||||||
\(394\) | 5123.33 | 0.655101 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1318.12 | −0.167268 | ||||||||
\(397\) | 2811.16 | 0.355386 | 0.177693 | − | 0.984086i | \(-0.443137\pi\) | ||||
0.177693 | + | 0.984086i | \(0.443137\pi\) | |||||||
\(398\) | 870.926 | 0.109687 | ||||||||
\(399\) | −546.703 | −0.0685949 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9918.99 | 1.23524 | 0.617619 | − | 0.786477i | \(-0.288097\pi\) | ||||
0.617619 | + | 0.786477i | \(0.288097\pi\) | |||||||
\(402\) | 5645.31 | 0.700404 | ||||||||
\(403\) | 4262.05 | 0.526819 | ||||||||
\(404\) | −1206.41 | −0.148567 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3305.02 | 0.404003 | ||||||||
\(407\) | −8260.11 | −1.00599 | ||||||||
\(408\) | −2128.30 | −0.258251 | ||||||||
\(409\) | −562.052 | −0.0679504 | −0.0339752 | − | 0.999423i | \(-0.510817\pi\) | ||||
−0.0339752 | + | 0.999423i | \(0.510817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4765.61 | 0.571947 | ||||||||
\(412\) | 2857.50 | 0.341697 | ||||||||
\(413\) | 4940.24 | 0.588603 | ||||||||
\(414\) | −731.124 | −0.0867942 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5290.01 | 0.623472 | ||||||||
\(417\) | −5200.46 | −0.610714 | ||||||||
\(418\) | −5694.40 | −0.666322 | ||||||||
\(419\) | 354.260 | 0.0413049 | 0.0206525 | − | 0.999787i | \(-0.493426\pi\) | ||||
0.0206525 | + | 0.999787i | \(0.493426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2969.20 | −0.343729 | −0.171864 | − | 0.985121i | \(-0.554979\pi\) | ||||
−0.171864 | + | 0.985121i | \(0.554979\pi\) | |||||||
\(422\) | 16416.7 | 1.89373 | ||||||||
\(423\) | −4758.40 | −0.546954 | ||||||||
\(424\) | 6757.11 | 0.773948 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6386.56 | −0.726361 | ||||||||
\(427\) | 2752.20 | 0.311916 | ||||||||
\(428\) | −3490.61 | −0.394217 | ||||||||
\(429\) | 11592.2 | 1.30461 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4583.08 | −0.512202 | −0.256101 | − | 0.966650i | \(-0.582438\pi\) | ||||
−0.256101 | + | 0.966650i | \(0.582438\pi\) | |||||||
\(432\) | 2065.71 | 0.230061 | ||||||||
\(433\) | −247.808 | −0.0275033 | −0.0137516 | − | 0.999905i | \(-0.504377\pi\) | ||||
−0.0137516 | + | 0.999905i | \(0.504377\pi\) | |||||||
\(434\) | 1688.84 | 0.186790 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1250.37 | −0.137344 | ||||||||
\(437\) | −664.431 | −0.0727324 | ||||||||
\(438\) | −2403.97 | −0.262252 | ||||||||
\(439\) | −3793.19 | −0.412390 | −0.206195 | − | 0.978511i | \(-0.566108\pi\) | ||||
−0.206195 | + | 0.978511i | \(0.566108\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −6797.09 | −0.731458 | ||||||||
\(443\) | 13157.7 | 1.41115 | 0.705575 | − | 0.708635i | \(-0.250689\pi\) | ||||
0.705575 | + | 0.708635i | \(0.250689\pi\) | |||||||
\(444\) | −768.510 | −0.0821438 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4597.38 | −0.488100 | ||||||||
\(447\) | 4112.05 | 0.435108 | ||||||||
\(448\) | −2188.26 | −0.230772 | ||||||||
\(449\) | −8705.75 | −0.915033 | −0.457517 | − | 0.889201i | \(-0.651261\pi\) | ||||
−0.457517 | + | 0.889201i | \(0.651261\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23754.6 | −2.48017 | ||||||||
\(452\) | −3446.55 | −0.358655 | ||||||||
\(453\) | 11082.2 | 1.14942 | ||||||||
\(454\) | −5204.76 | −0.538043 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1458.92 | 0.149825 | ||||||||
\(457\) | −11239.4 | −1.15045 | −0.575227 | − | 0.817994i | \(-0.695086\pi\) | ||||
−0.575227 | + | 0.817994i | \(0.695086\pi\) | |||||||
\(458\) | 8935.63 | 0.911648 | ||||||||
\(459\) | −1025.41 | −0.104274 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12534.3 | −1.26633 | −0.633167 | − | 0.774015i | \(-0.718246\pi\) | ||||
−0.633167 | + | 0.774015i | \(0.718246\pi\) | |||||||
\(462\) | 4593.41 | 0.462565 | ||||||||
\(463\) | 12563.8 | 1.26110 | 0.630549 | − | 0.776150i | \(-0.282830\pi\) | ||||
0.630549 | + | 0.776150i | \(0.282830\pi\) | |||||||
\(464\) | −11348.8 | −1.13546 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1845.49 | −0.183457 | ||||||||
\(467\) | −4817.97 | −0.477407 | −0.238703 | − | 0.971093i | \(-0.576722\pi\) | ||||
−0.238703 | + | 0.971093i | \(0.576722\pi\) | |||||||
\(468\) | 1078.52 | 0.106527 | ||||||||
\(469\) | −4138.41 | −0.407450 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3163.68 | 0.309501 | ||||||||
\(472\) | −13183.4 | −1.28563 | ||||||||
\(473\) | −19790.7 | −1.92384 | ||||||||
\(474\) | 2823.13 | 0.273567 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −566.575 | −0.0545566 | ||||||||
\(477\) | 3255.55 | 0.312498 | ||||||||
\(478\) | 5396.75 | 0.516405 | ||||||||
\(479\) | −7088.81 | −0.676192 | −0.338096 | − | 0.941112i | \(-0.609783\pi\) | ||||
−0.338096 | + | 0.941112i | \(0.609783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6758.66 | 0.640683 | ||||||||
\(482\) | 3763.50 | 0.355649 | ||||||||
\(483\) | 535.966 | 0.0504913 | ||||||||
\(484\) | 7227.99 | 0.678812 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 773.459 | 0.0721909 | ||||||||
\(487\) | −16131.5 | −1.50101 | −0.750503 | − | 0.660867i | \(-0.770189\pi\) | ||||
−0.750503 | + | 0.660867i | \(0.770189\pi\) | |||||||
\(488\) | −7344.48 | −0.681289 | ||||||||
\(489\) | −4140.36 | −0.382890 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3961.20 | −0.364087 | −0.182043 | − | 0.983290i | \(-0.558271\pi\) | ||||
−0.182043 | + | 0.983290i | \(0.558271\pi\) | |||||||
\(492\) | −2210.09 | −0.202518 | ||||||||
\(493\) | 5633.49 | 0.514644 | ||||||||
\(494\) | 4659.32 | 0.424358 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5799.14 | −0.524978 | ||||||||
\(497\) | 4681.80 | 0.422550 | ||||||||
\(498\) | −8751.65 | −0.787492 | ||||||||
\(499\) | −12981.0 | −1.16455 | −0.582274 | − | 0.812992i | \(-0.697837\pi\) | ||||
−0.582274 | + | 0.812992i | \(0.697837\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9429.30 | −0.840859 | ||||||||
\(502\) | −7676.26 | −0.682486 | ||||||||
\(503\) | 9611.24 | 0.851976 | 0.425988 | − | 0.904729i | \(-0.359927\pi\) | ||||
0.425988 | + | 0.904729i | \(0.359927\pi\) | |||||||
\(504\) | −1176.85 | −0.104010 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5582.57 | 0.490465 | ||||||||
\(507\) | −2894.09 | −0.253513 | ||||||||
\(508\) | −4353.94 | −0.380265 | ||||||||
\(509\) | −2605.16 | −0.226860 | −0.113430 | − | 0.993546i | \(-0.536184\pi\) | ||||
−0.113430 | + | 0.993546i | \(0.536184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1762.28 | 0.152561 | ||||||||
\(512\) | 4235.53 | 0.365597 | ||||||||
\(513\) | 702.904 | 0.0604950 | ||||||||
\(514\) | −3357.19 | −0.288092 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1841.30 | −0.157091 | ||||||||
\(517\) | 36333.2 | 3.09078 | ||||||||
\(518\) | 2678.12 | 0.227162 | ||||||||
\(519\) | −9918.36 | −0.838858 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −342.674 | −0.0288154 | −0.0144077 | − | 0.999896i | \(-0.504586\pi\) | ||||
−0.0144077 | + | 0.999896i | \(0.504586\pi\) | |||||||
\(522\) | −4249.31 | −0.356297 | ||||||||
\(523\) | 10494.7 | 0.877441 | 0.438720 | − | 0.898624i | \(-0.355432\pi\) | ||||
0.438720 | + | 0.898624i | \(0.355432\pi\) | |||||||
\(524\) | −5607.31 | −0.467474 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10792.6 | 0.894642 | ||||||||
\(527\) | 2878.66 | 0.237944 | ||||||||
\(528\) | −15772.9 | −1.30005 | ||||||||
\(529\) | −11515.6 | −0.946463 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6351.73 | −0.519099 | ||||||||
\(532\) | 388.381 | 0.0316512 | ||||||||
\(533\) | 19436.7 | 1.57954 | ||||||||
\(534\) | −7035.97 | −0.570180 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11043.7 | 0.889953 | ||||||||
\(537\) | −8518.80 | −0.684568 | ||||||||
\(538\) | 27984.8 | 2.24258 | ||||||||
\(539\) | −3367.30 | −0.269090 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4026.52 | −0.319988 | −0.159994 | − | 0.987118i | \(-0.551148\pi\) | ||||
−0.159994 | + | 0.987118i | \(0.551148\pi\) | |||||||
\(542\) | −5070.93 | −0.401873 | ||||||||
\(543\) | −2224.57 | −0.175811 | ||||||||
\(544\) | 3572.97 | 0.281599 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3758.46 | −0.294592 | ||||||||
\(547\) | 16182.8 | 1.26495 | 0.632475 | − | 0.774581i | \(-0.282039\pi\) | ||||
0.632475 | + | 0.774581i | \(0.282039\pi\) | |||||||
\(548\) | −3385.51 | −0.263909 | ||||||||
\(549\) | −3538.54 | −0.275084 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3861.69 | −0.298573 | ||||||||
\(552\) | −1430.27 | −0.110283 | ||||||||
\(553\) | −2069.55 | −0.159144 | ||||||||
\(554\) | 664.491 | 0.0509594 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3694.44 | 0.281797 | ||||||||
\(557\) | 10934.3 | 0.831779 | 0.415890 | − | 0.909415i | \(-0.363470\pi\) | ||||
0.415890 | + | 0.909415i | \(0.363470\pi\) | |||||||
\(558\) | −2171.36 | −0.164733 | ||||||||
\(559\) | 16193.3 | 1.22523 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7829.59 | 0.589243 | ||||||||
\(562\) | −7782.52 | −0.584139 | ||||||||
\(563\) | −164.542 | −0.0123173 | −0.00615863 | − | 0.999981i | \(-0.501960\pi\) | ||||
−0.00615863 | + | 0.999981i | \(0.501960\pi\) | |||||||
\(564\) | 3380.39 | 0.252376 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12396.1 | −0.920579 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | −12493.8 | −0.922935 | ||||||||
\(569\) | 21924.4 | 1.61532 | 0.807660 | − | 0.589648i | \(-0.200734\pi\) | ||||
0.807660 | + | 0.589648i | \(0.200734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6765.55 | −0.495848 | −0.247924 | − | 0.968779i | \(-0.579748\pi\) | ||||
−0.247924 | + | 0.968779i | \(0.579748\pi\) | |||||||
\(572\) | −8235.18 | −0.601976 | ||||||||
\(573\) | −13286.3 | −0.968661 | ||||||||
\(574\) | 7701.77 | 0.560044 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2813.48 | 0.203521 | ||||||||
\(577\) | 26134.4 | 1.88560 | 0.942798 | − | 0.333365i | \(-0.108184\pi\) | ||||
0.942798 | + | 0.333365i | \(0.108184\pi\) | |||||||
\(578\) | 11047.0 | 0.794973 | ||||||||
\(579\) | −2445.10 | −0.175501 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6415.58 | 0.458112 | ||||||||
\(582\) | −1365.14 | −0.0972285 | ||||||||
\(583\) | −24858.1 | −1.76589 | ||||||||
\(584\) | −4702.80 | −0.333225 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18289.9 | 1.28933 | ||||||||
\(587\) | −6342.06 | −0.445937 | −0.222968 | − | 0.974826i | \(-0.571575\pi\) | ||||
−0.222968 | + | 0.974826i | \(0.571575\pi\) | |||||||
\(588\) | −313.289 | −0.0219725 | ||||||||
\(589\) | −1973.29 | −0.138044 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4828.84 | 0.336095 | ||||||||
\(592\) | −9196.14 | −0.638444 | ||||||||
\(593\) | 24801.2 | 1.71748 | 0.858739 | − | 0.512413i | \(-0.171248\pi\) | ||||
0.858739 | + | 0.512413i | \(0.171248\pi\) | |||||||
\(594\) | −5905.82 | −0.407944 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2921.22 | −0.200768 | ||||||||
\(597\) | 820.865 | 0.0562743 | ||||||||
\(598\) | −4567.82 | −0.312361 | ||||||||
\(599\) | 12339.2 | 0.841681 | 0.420841 | − | 0.907135i | \(-0.361735\pi\) | ||||
0.420841 | + | 0.907135i | \(0.361735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3221.02 | 0.218616 | 0.109308 | − | 0.994008i | \(-0.465137\pi\) | ||||
0.109308 | + | 0.994008i | \(0.465137\pi\) | |||||||
\(602\) | 6416.60 | 0.434421 | ||||||||
\(603\) | 5320.81 | 0.359337 | ||||||||
\(604\) | −7872.87 | −0.530369 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5405.30 | −0.362336 | ||||||||
\(607\) | −20076.6 | −1.34248 | −0.671239 | − | 0.741241i | \(-0.734238\pi\) | ||||
−0.671239 | + | 0.741241i | \(0.734238\pi\) | |||||||
\(608\) | −2449.23 | −0.163370 | ||||||||
\(609\) | 3115.05 | 0.207271 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29728.9 | −1.96842 | ||||||||
\(612\) | 728.454 | 0.0481144 | ||||||||
\(613\) | −7428.07 | −0.489424 | −0.244712 | − | 0.969596i | \(-0.578693\pi\) | ||||
−0.244712 | + | 0.969596i | \(0.578693\pi\) | |||||||
\(614\) | −6300.81 | −0.414137 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8985.92 | 0.587748 | ||||||||
\(617\) | −2200.68 | −0.143592 | −0.0717959 | − | 0.997419i | \(-0.522873\pi\) | ||||
−0.0717959 | + | 0.997419i | \(0.522873\pi\) | |||||||
\(618\) | 12803.0 | 0.833353 | ||||||||
\(619\) | −5674.34 | −0.368451 | −0.184225 | − | 0.982884i | \(-0.558978\pi\) | ||||
−0.184225 | + | 0.982884i | \(0.558978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −689.099 | −0.0445291 | ||||||||
\(622\) | −11126.2 | −0.717237 | ||||||||
\(623\) | 5157.86 | 0.331694 | ||||||||
\(624\) | 12905.8 | 0.827960 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4611.08 | 0.294403 | ||||||||
\(627\) | −5367.09 | −0.341851 | ||||||||
\(628\) | −2247.50 | −0.142810 | ||||||||
\(629\) | 4564.92 | 0.289372 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4650.60 | −0.293403 | −0.146701 | − | 0.989181i | \(-0.546866\pi\) | ||||
−0.146701 | + | 0.989181i | \(0.546866\pi\) | |||||||
\(632\) | 5522.78 | 0.347602 | ||||||||
\(633\) | 15473.1 | 0.971564 | ||||||||
\(634\) | 30089.6 | 1.88487 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2312.76 | −0.144193 | ||||||||
\(637\) | 2755.22 | 0.171375 | ||||||||
\(638\) | 32446.0 | 2.01340 | ||||||||
\(639\) | −6019.46 | −0.372654 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15808.8 | 0.974119 | 0.487060 | − | 0.873369i | \(-0.338069\pi\) | ||||
0.487060 | + | 0.873369i | \(0.338069\pi\) | |||||||
\(642\) | −15639.6 | −0.961442 | ||||||||
\(643\) | 18829.6 | 1.15485 | 0.577424 | − | 0.816444i | \(-0.304058\pi\) | ||||
0.577424 | + | 0.816444i | \(0.304058\pi\) | |||||||
\(644\) | −380.753 | −0.0232978 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3146.99 | 0.191667 | ||||||||
\(647\) | 21519.7 | 1.30761 | 0.653807 | − | 0.756661i | \(-0.273171\pi\) | ||||
0.653807 | + | 0.756661i | \(0.273171\pi\) | |||||||
\(648\) | 1513.09 | 0.0917279 | ||||||||
\(649\) | 48499.2 | 2.93338 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1591.76 | 0.0958311 | ||||||||
\(652\) | 2941.33 | 0.176674 | ||||||||
\(653\) | 4298.98 | 0.257629 | 0.128815 | − | 0.991669i | \(-0.458883\pi\) | ||||
0.128815 | + | 0.991669i | \(0.458883\pi\) | |||||||
\(654\) | −5602.25 | −0.334962 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −26446.4 | −1.57402 | ||||||||
\(657\) | −2265.79 | −0.134546 | ||||||||
\(658\) | −11780.1 | −0.697925 | ||||||||
\(659\) | −1199.37 | −0.0708964 | −0.0354482 | − | 0.999372i | \(-0.511286\pi\) | ||||
−0.0354482 | + | 0.999372i | \(0.511286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14967.5 | 0.880739 | 0.440369 | − | 0.897817i | \(-0.354847\pi\) | ||||
0.440369 | + | 0.897817i | \(0.354847\pi\) | |||||||
\(662\) | 2518.69 | 0.147873 | ||||||||
\(663\) | −6406.39 | −0.375269 | ||||||||
\(664\) | −17120.5 | −1.00061 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3443.29 | −0.200338 | ||||||||
\(667\) | 3785.85 | 0.219773 | ||||||||
\(668\) | 6698.63 | 0.387991 | ||||||||
\(669\) | −4333.13 | −0.250416 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27018.9 | 1.55447 | ||||||||
\(672\) | 1975.68 | 0.113413 | ||||||||
\(673\) | −23664.3 | −1.35541 | −0.677706 | − | 0.735333i | \(-0.737026\pi\) | ||||
−0.677706 | + | 0.735333i | \(0.737026\pi\) | |||||||
\(674\) | −18967.4 | −1.08397 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2055.98 | 0.116976 | ||||||||
\(677\) | −4413.97 | −0.250580 | −0.125290 | − | 0.992120i | \(-0.539986\pi\) | ||||
−0.125290 | + | 0.992120i | \(0.539986\pi\) | |||||||
\(678\) | −15442.2 | −0.874711 | ||||||||
\(679\) | 1000.75 | 0.0565613 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4905.59 | −0.276039 | ||||||||
\(682\) | 16579.6 | 0.930890 | ||||||||
\(683\) | −26357.7 | −1.47664 | −0.738322 | − | 0.674449i | \(-0.764381\pi\) | ||||
−0.738322 | + | 0.674449i | \(0.764381\pi\) | |||||||
\(684\) | −499.347 | −0.0279137 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1091.75 | 0.0607629 | ||||||||
\(687\) | 8422.01 | 0.467714 | ||||||||
\(688\) | −22033.4 | −1.22095 | ||||||||
\(689\) | 20339.6 | 1.12464 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19098.2 | 1.05142 | 0.525708 | − | 0.850665i | \(-0.323800\pi\) | ||||
0.525708 | + | 0.850665i | \(0.323800\pi\) | |||||||
\(692\) | 7046.05 | 0.387068 | ||||||||
\(693\) | 4329.38 | 0.237315 | ||||||||
\(694\) | 14515.4 | 0.793942 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8312.76 | −0.452722 | ||||||||
\(697\) | 13127.9 | 0.713419 | ||||||||
\(698\) | 29935.4 | 1.62331 | ||||||||
\(699\) | −1739.41 | −0.0941211 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7008.54 | −0.377616 | −0.188808 | − | 0.982014i | \(-0.560462\pi\) | ||||
−0.188808 | + | 0.982014i | \(0.560462\pi\) | |||||||
\(702\) | 4832.31 | 0.259806 | ||||||||
\(703\) | −3129.20 | −0.167880 | ||||||||
\(704\) | −21482.6 | −1.15008 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4428.67 | −0.236084 | ||||||||
\(707\) | 3962.47 | 0.210784 | ||||||||
\(708\) | 4512.30 | 0.239524 | ||||||||
\(709\) | 31728.6 | 1.68066 | 0.840332 | − | 0.542071i | \(-0.182360\pi\) | ||||
0.840332 | + | 0.542071i | \(0.182360\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2660.86 | 0.140351 | ||||||||
\(712\) | −13764.2 | −0.724487 | ||||||||
\(713\) | 1934.54 | 0.101611 | ||||||||
\(714\) | −2538.53 | −0.133056 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6051.80 | 0.315875 | ||||||||
\(717\) | 5086.54 | 0.264938 | ||||||||
\(718\) | −13708.4 | −0.712522 | ||||||||
\(719\) | −8033.78 | −0.416703 | −0.208352 | − | 0.978054i | \(-0.566810\pi\) | ||||
−0.208352 | + | 0.978054i | \(0.566810\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9385.50 | −0.484791 | ||||||||
\(722\) | 19674.7 | 1.01415 | ||||||||
\(723\) | 3547.17 | 0.182463 | ||||||||
\(724\) | 1580.34 | 0.0811229 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 32384.9 | 1.65553 | ||||||||
\(727\) | 20514.4 | 1.04654 | 0.523272 | − | 0.852166i | \(-0.324711\pi\) | ||||
0.523272 | + | 0.852166i | \(0.324711\pi\) | |||||||
\(728\) | −7352.53 | −0.374317 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10937.3 | 0.553391 | ||||||||
\(732\) | 2513.80 | 0.126930 | ||||||||
\(733\) | −39200.4 | −1.97531 | −0.987654 | − | 0.156653i | \(-0.949930\pi\) | ||||
−0.987654 | + | 0.156653i | \(0.949930\pi\) | |||||||
\(734\) | −20388.3 | −1.02527 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2401.12 | 0.120254 | ||||||||
\(737\) | −40627.6 | −2.03058 | ||||||||
\(738\) | −9902.27 | −0.493913 | ||||||||
\(739\) | −18386.2 | −0.915221 | −0.457611 | − | 0.889153i | \(-0.651295\pi\) | ||||
−0.457611 | + | 0.889153i | \(0.651295\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4391.51 | 0.217714 | ||||||||
\(742\) | 8059.55 | 0.398754 | ||||||||
\(743\) | 10118.8 | 0.499628 | 0.249814 | − | 0.968294i | \(-0.419631\pi\) | ||||
0.249814 | + | 0.968294i | \(0.419631\pi\) | |||||||
\(744\) | −4247.75 | −0.209315 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32762.8 | 1.60795 | ||||||||
\(747\) | −8248.60 | −0.404017 | ||||||||
\(748\) | −5562.18 | −0.271890 | ||||||||
\(749\) | 11464.9 | 0.559305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16116.3 | −0.783077 | −0.391538 | − | 0.920162i | \(-0.628057\pi\) | ||||
−0.391538 | + | 0.920162i | \(0.628057\pi\) | |||||||
\(752\) | 40450.4 | 1.96154 | ||||||||
\(753\) | −7235.03 | −0.350145 | ||||||||
\(754\) | −26548.3 | −1.28227 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 402.800 | 0.0193779 | ||||||||
\(757\) | −16856.5 | −0.809324 | −0.404662 | − | 0.914466i | \(-0.632611\pi\) | ||||
−0.404662 | + | 0.914466i | \(0.632611\pi\) | |||||||
\(758\) | −12198.2 | −0.584510 | ||||||||
\(759\) | 5261.68 | 0.251630 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19917.5 | 0.948765 | 0.474383 | − | 0.880319i | \(-0.342671\pi\) | ||||
0.474383 | + | 0.880319i | \(0.342671\pi\) | |||||||
\(762\) | −19507.7 | −0.927415 | ||||||||
\(763\) | 4106.85 | 0.194860 | ||||||||
\(764\) | 9438.65 | 0.446961 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43017.2 | 2.02908 | ||||||||
\(767\) | −39683.5 | −1.86817 | ||||||||
\(768\) | −9185.56 | −0.431583 | ||||||||
\(769\) | 2378.22 | 0.111523 | 0.0557613 | − | 0.998444i | \(-0.482241\pi\) | ||||
0.0557613 | + | 0.998444i | \(0.482241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3164.22 | −0.147803 | ||||||||
\(772\) | 1737.01 | 0.0809799 | ||||||||
\(773\) | −7153.02 | −0.332828 | −0.166414 | − | 0.986056i | \(-0.553219\pi\) | ||||
−0.166414 | + | 0.986056i | \(0.553219\pi\) | |||||||
\(774\) | −8249.92 | −0.383123 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2670.58 | −0.123541 | ||||||||
\(777\) | 2524.18 | 0.116544 | ||||||||
\(778\) | 20512.4 | 0.945250 | ||||||||
\(779\) | −8998.99 | −0.413892 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45962.1 | 2.10583 | ||||||||
\(782\) | −3085.18 | −0.141082 | ||||||||
\(783\) | −4005.06 | −0.182796 | ||||||||
\(784\) | −3748.87 | −0.170776 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25123.4 | −1.14011 | ||||||||
\(787\) | −28137.0 | −1.27443 | −0.637214 | − | 0.770687i | \(-0.719913\pi\) | ||||
−0.637214 | + | 0.770687i | \(0.719913\pi\) | |||||||
\(788\) | −3430.44 | −0.155082 | ||||||||
\(789\) | 10172.3 | 0.458989 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11320.2 | 0.508851 | ||||||||
\(792\) | −11553.3 | −0.518345 | ||||||||
\(793\) | −22107.6 | −0.989993 | ||||||||
\(794\) | −8947.81 | −0.399932 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −583.147 | −0.0259662 | ||||||||
\(797\) | −40807.1 | −1.81363 | −0.906815 | − | 0.421530i | \(-0.861493\pi\) | ||||
−0.906815 | + | 0.421530i | \(0.861493\pi\) | |||||||
\(798\) | 1740.13 | 0.0771930 | ||||||||
\(799\) | −20079.4 | −0.889059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6631.54 | −0.292527 | ||||||||
\(802\) | −31571.7 | −1.39007 | ||||||||
\(803\) | 17300.7 | 0.760308 | ||||||||
\(804\) | −3779.93 | −0.165806 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13565.9 | −0.592853 | ||||||||
\(807\) | 26376.2 | 1.15054 | ||||||||
\(808\) | −10574.2 | −0.460394 | ||||||||
\(809\) | 15233.3 | 0.662020 | 0.331010 | − | 0.943627i | \(-0.392611\pi\) | ||||
0.331010 | + | 0.943627i | \(0.392611\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26847.5 | −1.16245 | −0.581223 | − | 0.813744i | \(-0.697426\pi\) | ||||
−0.581223 | + | 0.813744i | \(0.697426\pi\) | |||||||
\(812\) | −2212.95 | −0.0956393 | ||||||||
\(813\) | −4779.46 | −0.206178 | ||||||||
\(814\) | 26291.6 | 1.13209 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8716.82 | 0.373958 | ||||||||
\(817\) | −7497.36 | −0.321052 | ||||||||
\(818\) | 1788.99 | 0.0764676 | ||||||||
\(819\) | −3542.42 | −0.151138 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23640.8 | 1.00496 | 0.502479 | − | 0.864590i | \(-0.332422\pi\) | ||||
0.502479 | + | 0.864590i | \(0.332422\pi\) | |||||||
\(822\) | −15168.7 | −0.643638 | ||||||||
\(823\) | 21191.6 | 0.897562 | 0.448781 | − | 0.893642i | \(-0.351858\pi\) | ||||
0.448781 | + | 0.893642i | \(0.351858\pi\) | |||||||
\(824\) | 25046.0 | 1.05888 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15724.6 | −0.662382 | ||||||||
\(827\) | 8177.77 | 0.343856 | 0.171928 | − | 0.985110i | \(-0.445000\pi\) | ||||
0.171928 | + | 0.985110i | \(0.445000\pi\) | |||||||
\(828\) | 489.540 | 0.0205467 | ||||||||
\(829\) | 28931.0 | 1.21208 | 0.606040 | − | 0.795434i | \(-0.292757\pi\) | ||||
0.606040 | + | 0.795434i | \(0.292757\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 626.296 | 0.0261443 | ||||||||
\(832\) | 17577.7 | 0.732448 | ||||||||
\(833\) | 1860.92 | 0.0774035 | ||||||||
\(834\) | 16552.9 | 0.687264 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3812.81 | 0.157738 | ||||||||
\(837\) | −2046.55 | −0.0845151 | ||||||||
\(838\) | −1127.60 | −0.0464823 | ||||||||
\(839\) | −41631.2 | −1.71307 | −0.856537 | − | 0.516085i | \(-0.827389\pi\) | ||||
−0.856537 | + | 0.516085i | \(0.827389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2385.58 | −0.0978137 | ||||||||
\(842\) | 9450.83 | 0.386814 | ||||||||
\(843\) | −7335.18 | −0.299688 | ||||||||
\(844\) | −10992.2 | −0.448301 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15145.8 | 0.615512 | ||||||||
\(847\) | −23740.4 | −0.963081 | ||||||||
\(848\) | −27674.9 | −1.12071 | ||||||||
\(849\) | −11683.6 | −0.472297 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3067.74 | 0.123573 | ||||||||
\(852\) | 4276.26 | 0.171951 | ||||||||
\(853\) | 38242.1 | 1.53503 | 0.767517 | − | 0.641029i | \(-0.221492\pi\) | ||||
0.767517 | + | 0.641029i | \(0.221492\pi\) | |||||||
\(854\) | −8760.13 | −0.351014 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30595.1 | −1.22164 | ||||||||
\(857\) | −1118.45 | −0.0445805 | −0.0222903 | − | 0.999752i | \(-0.507096\pi\) | ||||
−0.0222903 | + | 0.999752i | \(0.507096\pi\) | |||||||
\(858\) | −36897.5 | −1.46814 | ||||||||
\(859\) | 34103.0 | 1.35458 | 0.677288 | − | 0.735718i | \(-0.263155\pi\) | ||||
0.677288 | + | 0.735718i | \(0.263155\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7259.07 | 0.287327 | ||||||||
\(862\) | 14587.7 | 0.576405 | ||||||||
\(863\) | 12332.6 | 0.486450 | 0.243225 | − | 0.969970i | \(-0.421795\pi\) | ||||
0.243225 | + | 0.969970i | \(0.421795\pi\) | |||||||
\(864\) | −2540.16 | −0.100021 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 788.764 | 0.0309507 | ||||||||
\(867\) | 10412.0 | 0.407855 | ||||||||
\(868\) | −1130.80 | −0.0442186 | ||||||||
\(869\) | −20317.2 | −0.793112 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33242.6 | 1.29321 | ||||||||
\(872\) | −10959.5 | −0.425613 | ||||||||
\(873\) | −1286.67 | −0.0498824 | ||||||||
\(874\) | 2114.86 | 0.0818491 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1609.63 | 0.0620826 | ||||||||
\(877\) | −17287.9 | −0.665644 | −0.332822 | − | 0.942990i | \(-0.608001\pi\) | ||||
−0.332822 | + | 0.942990i | \(0.608001\pi\) | |||||||
\(878\) | 12073.6 | 0.464081 | ||||||||
\(879\) | 17238.6 | 0.661484 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15797.0 | −0.604103 | −0.302052 | − | 0.953292i | \(-0.597671\pi\) | ||||
−0.302052 | + | 0.953292i | \(0.597671\pi\) | |||||||
\(882\) | −1403.68 | −0.0535879 | ||||||||
\(883\) | −40601.9 | −1.54741 | −0.773706 | − | 0.633545i | \(-0.781599\pi\) | ||||
−0.773706 | + | 0.633545i | \(0.781599\pi\) | |||||||
\(884\) | 4551.13 | 0.173157 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41880.3 | −1.58803 | ||||||||
\(887\) | 3654.03 | 0.138320 | 0.0691602 | − | 0.997606i | \(-0.477968\pi\) | ||||
0.0691602 | + | 0.997606i | \(0.477968\pi\) | |||||||
\(888\) | −6735.98 | −0.254555 | ||||||||
\(889\) | 14300.6 | 0.539511 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5566.35 | −0.209293 | ||||||||
\(892\) | 3078.28 | 0.115547 | ||||||||
\(893\) | 13764.2 | 0.515791 | ||||||||
\(894\) | −13088.5 | −0.489647 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12233.6 | 0.456135 | ||||||||
\(897\) | −4305.26 | −0.160255 | ||||||||
\(898\) | 27710.0 | 1.02973 | ||||||||
\(899\) | 11243.6 | 0.417123 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13737.7 | 0.507957 | ||||||||
\(902\) | 75609.7 | 2.79105 | ||||||||
\(903\) | 6047.78 | 0.222876 | ||||||||
\(904\) | −30209.0 | −1.11143 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −35274.3 | −1.29350 | ||||||||
\(907\) | 8732.15 | 0.319676 | 0.159838 | − | 0.987143i | \(-0.448903\pi\) | ||||
0.159838 | + | 0.987143i | \(0.448903\pi\) | |||||||
\(908\) | 3484.96 | 0.127370 | ||||||||
\(909\) | −5094.60 | −0.185894 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29118.5 | −1.05899 | −0.529495 | − | 0.848313i | \(-0.677619\pi\) | ||||
−0.529495 | + | 0.848313i | \(0.677619\pi\) | |||||||
\(912\) | −5975.28 | −0.216953 | ||||||||
\(913\) | 62983.0 | 2.28306 | ||||||||
\(914\) | 35774.6 | 1.29466 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5983.04 | −0.215814 | ||||||||
\(917\) | 18417.3 | 0.663240 | ||||||||
\(918\) | 3263.82 | 0.117344 | ||||||||
\(919\) | −36147.4 | −1.29749 | −0.648745 | − | 0.761006i | \(-0.724706\pi\) | ||||
−0.648745 | + | 0.761006i | \(0.724706\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5938.64 | −0.212470 | ||||||||
\(922\) | 39896.1 | 1.42506 | ||||||||
\(923\) | −37607.5 | −1.34113 | ||||||||
\(924\) | −3075.62 | −0.109503 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −39990.0 | −1.41917 | ||||||||
\(927\) | 12067.1 | 0.427546 | ||||||||
\(928\) | 13955.4 | 0.493651 | ||||||||
\(929\) | −380.568 | −0.0134403 | −0.00672015 | − | 0.999977i | \(-0.502139\pi\) | ||||
−0.00672015 | + | 0.999977i | \(0.502139\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1275.64 | −0.0449059 | ||||||||
\(932\) | 1235.69 | 0.0434295 | ||||||||
\(933\) | −10486.7 | −0.367973 | ||||||||
\(934\) | 15335.4 | 0.537247 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9453.26 | 0.330117 | ||||||||
\(937\) | −11577.5 | −0.403650 | −0.201825 | − | 0.979422i | \(-0.564687\pi\) | ||||
−0.201825 | + | 0.979422i | \(0.564687\pi\) | |||||||
\(938\) | 13172.4 | 0.458522 | ||||||||
\(939\) | 4346.04 | 0.151041 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37835.3 | 1.31073 | 0.655364 | − | 0.755313i | \(-0.272515\pi\) | ||||
0.655364 | + | 0.755313i | \(0.272515\pi\) | |||||||
\(942\) | −10069.9 | −0.348295 | ||||||||
\(943\) | 8822.25 | 0.304657 | ||||||||
\(944\) | 53995.1 | 1.86164 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 62993.0 | 2.16499 | ||||||||
\(947\) | 32719.8 | 1.12276 | 0.561379 | − | 0.827559i | \(-0.310271\pi\) | ||||
0.561379 | + | 0.827559i | \(0.310271\pi\) | |||||||
\(948\) | −1890.29 | −0.0647612 | ||||||||
\(949\) | −14155.9 | −0.484215 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28360.0 | 0.967021 | ||||||||
\(952\) | −4966.03 | −0.169065 | ||||||||
\(953\) | −42719.5 | −1.45207 | −0.726033 | − | 0.687659i | \(-0.758638\pi\) | ||||
−0.726033 | + | 0.687659i | \(0.758638\pi\) | |||||||
\(954\) | −10362.3 | −0.351668 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3613.51 | −0.122248 | ||||||||
\(957\) | 30581.0 | 1.03296 | ||||||||
\(958\) | 22563.4 | 0.760949 | ||||||||
\(959\) | 11119.8 | 0.374427 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24045.6 | −0.807144 | ||||||||
\(962\) | −21512.5 | −0.720989 | ||||||||
\(963\) | −14740.6 | −0.493261 | ||||||||
\(964\) | −2519.93 | −0.0841924 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1705.96 | −0.0568201 | ||||||||
\(967\) | −56616.7 | −1.88280 | −0.941402 | − | 0.337286i | \(-0.890491\pi\) | ||||
−0.941402 | + | 0.337286i | \(0.890491\pi\) | |||||||
\(968\) | 63353.3 | 2.10357 | ||||||||
\(969\) | 2966.10 | 0.0983331 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26230.8 | −0.866927 | −0.433463 | − | 0.901171i | \(-0.642709\pi\) | ||||
−0.433463 | + | 0.901171i | \(0.642709\pi\) | |||||||
\(972\) | −517.886 | −0.0170897 | ||||||||
\(973\) | −12134.4 | −0.399806 | ||||||||
\(974\) | 51346.0 | 1.68915 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30080.6 | 0.986534 | ||||||||
\(977\) | −35339.9 | −1.15724 | −0.578620 | − | 0.815597i | \(-0.696409\pi\) | ||||
−0.578620 | + | 0.815597i | \(0.696409\pi\) | |||||||
\(978\) | 13178.6 | 0.430884 | ||||||||
\(979\) | 50635.8 | 1.65304 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5280.23 | −0.171850 | ||||||||
\(982\) | 12608.3 | 0.409723 | ||||||||
\(983\) | −25377.6 | −0.823419 | −0.411710 | − | 0.911315i | \(-0.635068\pi\) | ||||
−0.411710 | + | 0.911315i | \(0.635068\pi\) | |||||||
\(984\) | −19371.4 | −0.627580 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −17931.1 | −0.579152 | ||||||||
\(987\) | −11102.9 | −0.358065 | ||||||||
\(988\) | −3119.75 | −0.100458 | ||||||||
\(989\) | 7350.12 | 0.236320 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15086.3 | −0.483585 | −0.241792 | − | 0.970328i | \(-0.577735\pi\) | ||||
−0.241792 | + | 0.970328i | \(0.577735\pi\) | |||||||
\(992\) | 7131.08 | 0.228238 | ||||||||
\(993\) | 2373.91 | 0.0758649 | ||||||||
\(994\) | −14902.0 | −0.475515 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5859.85 | 0.186422 | ||||||||
\(997\) | −1393.06 | −0.0442513 | −0.0221256 | − | 0.999755i | \(-0.507043\pi\) | ||||
−0.0221256 | + | 0.999755i | \(0.507043\pi\) | |||||||
\(998\) | 41318.0 | 1.31052 | ||||||||
\(999\) | −3245.37 | −0.102782 |
(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 | 525.4.a.r.1.1 | 3 | ||
3.2 | odd | 2 | 1575.4.a.bc.1.3 | 3 | |||
5.2 | odd | 4 | 105.4.d.a.64.2 | ✓ | 6 | ||
5.3 | odd | 4 | 105.4.d.a.64.5 | yes | 6 | ||
5.4 | even | 2 | 525.4.a.q.1.3 | 3 | |||
15.2 | even | 4 | 315.4.d.a.64.5 | 6 | |||
15.8 | even | 4 | 315.4.d.a.64.2 | 6 | |||
15.14 | odd | 2 | 1575.4.a.bd.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.d.a.64.2 | ✓ | 6 | 5.2 | odd | 4 | ||
105.4.d.a.64.5 | yes | 6 | 5.3 | odd | 4 | ||
315.4.d.a.64.2 | 6 | 15.8 | even | 4 | |||
315.4.d.a.64.5 | 6 | 15.2 | even | 4 | |||
525.4.a.q.1.3 | 3 | 5.4 | even | 2 | |||
525.4.a.r.1.1 | 3 | 1.1 | even | 1 | trivial | ||
1575.4.a.bc.1.3 | 3 | 3.2 | odd | 2 | |||
1575.4.a.bd.1.1 | 3 | 15.14 | odd | 2 |