Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,4,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(57.9988775356\) |
Analytic rank: | \(1\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.46204 | −1.57757 | −0.788785 | − | 0.614670i | \(-0.789289\pi\) | ||||
−0.788785 | + | 0.614670i | \(0.789289\pi\) | |||||||
\(3\) | −5.70729 | −1.09837 | −0.549185 | − | 0.835701i | \(-0.685062\pi\) | ||||
−0.549185 | + | 0.835701i | \(0.685062\pi\) | |||||||
\(4\) | 11.9098 | 1.48872 | ||||||||
\(5\) | −10.3218 | −0.923208 | −0.461604 | − | 0.887086i | \(-0.652726\pi\) | ||||
−0.461604 | + | 0.887086i | \(0.652726\pi\) | |||||||
\(6\) | 25.4662 | 1.73275 | ||||||||
\(7\) | 32.8198 | 1.77210 | 0.886052 | − | 0.463586i | \(-0.153438\pi\) | ||||
0.886052 | + | 0.463586i | \(0.153438\pi\) | |||||||
\(8\) | −17.4456 | −0.770996 | ||||||||
\(9\) | 5.57321 | 0.206415 | ||||||||
\(10\) | 46.0562 | 1.45642 | ||||||||
\(11\) | 55.2787 | 1.51520 | 0.757599 | − | 0.652721i | \(-0.226372\pi\) | ||||
0.757599 | + | 0.652721i | \(0.226372\pi\) | |||||||
\(12\) | −67.9727 | −1.63517 | ||||||||
\(13\) | −2.90988 | −0.0620812 | −0.0310406 | − | 0.999518i | \(-0.509882\pi\) | ||||
−0.0310406 | + | 0.999518i | \(0.509882\pi\) | |||||||
\(14\) | −146.443 | −2.79562 | ||||||||
\(15\) | 58.9094 | 1.01402 | ||||||||
\(16\) | −17.4352 | −0.272425 | ||||||||
\(17\) | 9.44318 | 0.134724 | 0.0673620 | − | 0.997729i | \(-0.478542\pi\) | ||||
0.0673620 | + | 0.997729i | \(0.478542\pi\) | |||||||
\(18\) | −24.8679 | −0.325634 | ||||||||
\(19\) | −110.722 | −1.33692 | −0.668459 | − | 0.743749i | \(-0.733046\pi\) | ||||
−0.668459 | + | 0.743749i | \(0.733046\pi\) | |||||||
\(20\) | −122.930 | −1.37440 | ||||||||
\(21\) | −187.312 | −1.94642 | ||||||||
\(22\) | −246.656 | −2.39033 | ||||||||
\(23\) | 51.7607 | 0.469255 | 0.234627 | − | 0.972085i | \(-0.424613\pi\) | ||||
0.234627 | + | 0.972085i | \(0.424613\pi\) | |||||||
\(24\) | 99.5674 | 0.846838 | ||||||||
\(25\) | −18.4608 | −0.147687 | ||||||||
\(26\) | 12.9840 | 0.0979373 | ||||||||
\(27\) | 122.289 | 0.871649 | ||||||||
\(28\) | 390.877 | 2.63817 | ||||||||
\(29\) | −161.889 | −1.03662 | −0.518309 | − | 0.855193i | \(-0.673438\pi\) | ||||
−0.518309 | + | 0.855193i | \(0.673438\pi\) | |||||||
\(30\) | −262.856 | −1.59969 | ||||||||
\(31\) | −54.7937 | −0.317459 | −0.158730 | − | 0.987322i | \(-0.550740\pi\) | ||||
−0.158730 | + | 0.987322i | \(0.550740\pi\) | |||||||
\(32\) | 217.362 | 1.20076 | ||||||||
\(33\) | −315.492 | −1.66425 | ||||||||
\(34\) | −42.1358 | −0.212536 | ||||||||
\(35\) | −338.759 | −1.63602 | ||||||||
\(36\) | 66.3757 | 0.307295 | ||||||||
\(37\) | −314.623 | −1.39794 | −0.698968 | − | 0.715153i | \(-0.746357\pi\) | ||||
−0.698968 | + | 0.715153i | \(0.746357\pi\) | |||||||
\(38\) | 494.048 | 2.10908 | ||||||||
\(39\) | 16.6075 | 0.0681881 | ||||||||
\(40\) | 180.070 | 0.711790 | ||||||||
\(41\) | 379.325 | 1.44489 | 0.722446 | − | 0.691427i | \(-0.243018\pi\) | ||||
0.722446 | + | 0.691427i | \(0.243018\pi\) | |||||||
\(42\) | 835.795 | 3.07062 | ||||||||
\(43\) | 104.190 | 0.369508 | 0.184754 | − | 0.982785i | \(-0.440851\pi\) | ||||
0.184754 | + | 0.982785i | \(0.440851\pi\) | |||||||
\(44\) | 658.358 | 2.25571 | ||||||||
\(45\) | −57.5254 | −0.190564 | ||||||||
\(46\) | −230.958 | −0.740282 | ||||||||
\(47\) | −467.077 | −1.44958 | −0.724789 | − | 0.688971i | \(-0.758063\pi\) | ||||
−0.724789 | + | 0.688971i | \(0.758063\pi\) | |||||||
\(48\) | 99.5077 | 0.299223 | ||||||||
\(49\) | 734.140 | 2.14035 | ||||||||
\(50\) | 82.3730 | 0.232986 | ||||||||
\(51\) | −53.8950 | −0.147977 | ||||||||
\(52\) | −34.6561 | −0.0924217 | ||||||||
\(53\) | 285.530 | 0.740012 | 0.370006 | − | 0.929029i | \(-0.379356\pi\) | ||||
0.370006 | + | 0.929029i | \(0.379356\pi\) | |||||||
\(54\) | −545.658 | −1.37509 | ||||||||
\(55\) | −570.575 | −1.39884 | ||||||||
\(56\) | −572.563 | −1.36628 | ||||||||
\(57\) | 631.925 | 1.46843 | ||||||||
\(58\) | 722.353 | 1.63534 | ||||||||
\(59\) | 123.325 | 0.272127 | 0.136064 | − | 0.990700i | \(-0.456555\pi\) | ||||
0.136064 | + | 0.990700i | \(0.456555\pi\) | |||||||
\(60\) | 701.599 | 1.50960 | ||||||||
\(61\) | −19.8015 | −0.0415628 | −0.0207814 | − | 0.999784i | \(-0.506615\pi\) | ||||
−0.0207814 | + | 0.999784i | \(0.506615\pi\) | |||||||
\(62\) | 244.492 | 0.500814 | ||||||||
\(63\) | 182.912 | 0.365789 | ||||||||
\(64\) | −830.395 | −1.62186 | ||||||||
\(65\) | 30.0351 | 0.0573138 | ||||||||
\(66\) | 1407.74 | 2.62546 | ||||||||
\(67\) | 875.121 | 1.59572 | 0.797859 | − | 0.602844i | \(-0.205966\pi\) | ||||
0.797859 | + | 0.602844i | \(0.205966\pi\) | |||||||
\(68\) | 112.466 | 0.200567 | ||||||||
\(69\) | −295.414 | −0.515415 | ||||||||
\(70\) | 1511.56 | 2.58094 | ||||||||
\(71\) | −613.162 | −1.02491 | −0.512457 | − | 0.858713i | \(-0.671265\pi\) | ||||
−0.512457 | + | 0.858713i | \(0.671265\pi\) | |||||||
\(72\) | −97.2282 | −0.159145 | ||||||||
\(73\) | −710.907 | −1.13980 | −0.569900 | − | 0.821714i | \(-0.693018\pi\) | ||||
−0.569900 | + | 0.821714i | \(0.693018\pi\) | |||||||
\(74\) | 1403.86 | 2.20534 | ||||||||
\(75\) | 105.361 | 0.162215 | ||||||||
\(76\) | −1318.68 | −1.99030 | ||||||||
\(77\) | 1814.24 | 2.68509 | ||||||||
\(78\) | −74.1035 | −0.107571 | ||||||||
\(79\) | −536.451 | −0.763993 | −0.381997 | − | 0.924164i | \(-0.624763\pi\) | ||||
−0.381997 | + | 0.924164i | \(0.624763\pi\) | |||||||
\(80\) | 179.962 | 0.251505 | ||||||||
\(81\) | −848.416 | −1.16381 | ||||||||
\(82\) | −1692.56 | −2.27942 | ||||||||
\(83\) | −455.726 | −0.602680 | −0.301340 | − | 0.953517i | \(-0.597434\pi\) | ||||
−0.301340 | + | 0.953517i | \(0.597434\pi\) | |||||||
\(84\) | −2230.85 | −2.89769 | ||||||||
\(85\) | −97.4704 | −0.124378 | ||||||||
\(86\) | −464.900 | −0.582924 | ||||||||
\(87\) | 923.946 | 1.13859 | ||||||||
\(88\) | −964.373 | −1.16821 | ||||||||
\(89\) | −316.018 | −0.376380 | −0.188190 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188190 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(90\) | 256.681 | 0.300628 | ||||||||
\(91\) | −95.5017 | −0.110014 | ||||||||
\(92\) | 616.460 | 0.698591 | ||||||||
\(93\) | 312.724 | 0.348687 | ||||||||
\(94\) | 2084.11 | 2.28681 | ||||||||
\(95\) | 1142.85 | 1.23425 | ||||||||
\(96\) | −1240.55 | −1.31888 | ||||||||
\(97\) | −70.8410 | −0.0741527 | −0.0370763 | − | 0.999312i | \(-0.511804\pi\) | ||||
−0.0370763 | + | 0.999312i | \(0.511804\pi\) | |||||||
\(98\) | −3275.76 | −3.37655 | ||||||||
\(99\) | 308.080 | 0.312759 | ||||||||
\(100\) | −219.865 | −0.219865 | ||||||||
\(101\) | 1474.56 | 1.45271 | 0.726355 | − | 0.687319i | \(-0.241213\pi\) | ||||
0.726355 | + | 0.687319i | \(0.241213\pi\) | |||||||
\(102\) | 240.482 | 0.233443 | ||||||||
\(103\) | 169.964 | 0.162592 | 0.0812962 | − | 0.996690i | \(-0.474094\pi\) | ||||
0.0812962 | + | 0.996690i | \(0.474094\pi\) | |||||||
\(104\) | 50.7647 | 0.0478643 | ||||||||
\(105\) | 1933.40 | 1.79695 | ||||||||
\(106\) | −1274.05 | −1.16742 | ||||||||
\(107\) | 546.128 | 0.493422 | 0.246711 | − | 0.969089i | \(-0.420650\pi\) | ||||
0.246711 | + | 0.969089i | \(0.420650\pi\) | |||||||
\(108\) | 1456.44 | 1.29765 | ||||||||
\(109\) | 1144.59 | 1.00579 | 0.502897 | − | 0.864346i | \(-0.332267\pi\) | ||||
0.502897 | + | 0.864346i | \(0.332267\pi\) | |||||||
\(110\) | 2545.93 | 2.20677 | ||||||||
\(111\) | 1795.64 | 1.53545 | ||||||||
\(112\) | −572.220 | −0.482765 | ||||||||
\(113\) | 1946.72 | 1.62064 | 0.810318 | − | 0.585990i | \(-0.199294\pi\) | ||||
0.810318 | + | 0.585990i | \(0.199294\pi\) | |||||||
\(114\) | −2819.67 | −2.31655 | ||||||||
\(115\) | −534.263 | −0.433220 | ||||||||
\(116\) | −1928.06 | −1.54324 | ||||||||
\(117\) | −16.2174 | −0.0128145 | ||||||||
\(118\) | −550.279 | −0.429299 | ||||||||
\(119\) | 309.923 | 0.238745 | ||||||||
\(120\) | −1027.71 | −0.781808 | ||||||||
\(121\) | 1724.74 | 1.29582 | ||||||||
\(122\) | 88.3553 | 0.0655681 | ||||||||
\(123\) | −2164.92 | −1.58702 | ||||||||
\(124\) | −652.581 | −0.472609 | ||||||||
\(125\) | 1480.77 | 1.05955 | ||||||||
\(126\) | −816.159 | −0.577057 | ||||||||
\(127\) | −1825.93 | −1.27579 | −0.637895 | − | 0.770124i | \(-0.720194\pi\) | ||||
−0.637895 | + | 0.770124i | \(0.720194\pi\) | |||||||
\(128\) | 1966.36 | 1.35784 | ||||||||
\(129\) | −594.643 | −0.405856 | ||||||||
\(130\) | −134.018 | −0.0904166 | ||||||||
\(131\) | 1231.13 | 0.821103 | 0.410552 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410552 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(132\) | −3757.45 | −2.47760 | ||||||||
\(133\) | −3633.89 | −2.36916 | ||||||||
\(134\) | −3904.83 | −2.51736 | ||||||||
\(135\) | −1262.24 | −0.804714 | ||||||||
\(136\) | −164.742 | −0.103872 | ||||||||
\(137\) | −1951.87 | −1.21722 | −0.608611 | − | 0.793469i | \(-0.708273\pi\) | ||||
−0.608611 | + | 0.793469i | \(0.708273\pi\) | |||||||
\(138\) | 1318.15 | 0.813103 | ||||||||
\(139\) | −2330.95 | −1.42237 | −0.711183 | − | 0.703006i | \(-0.751840\pi\) | ||||
−0.711183 | + | 0.703006i | \(0.751840\pi\) | |||||||
\(140\) | −4034.55 | −2.43558 | ||||||||
\(141\) | 2665.74 | 1.59217 | ||||||||
\(142\) | 2735.95 | 1.61687 | ||||||||
\(143\) | −160.854 | −0.0940652 | ||||||||
\(144\) | −97.1699 | −0.0562326 | ||||||||
\(145\) | 1670.98 | 0.957015 | ||||||||
\(146\) | 3172.09 | 1.79811 | ||||||||
\(147\) | −4189.95 | −2.35090 | ||||||||
\(148\) | −3747.09 | −2.08114 | ||||||||
\(149\) | 11.3137 | 0.00622048 | 0.00311024 | − | 0.999995i | \(-0.499010\pi\) | ||||
0.00311024 | + | 0.999995i | \(0.499010\pi\) | |||||||
\(150\) | −470.127 | −0.255905 | ||||||||
\(151\) | −2168.65 | −1.16876 | −0.584379 | − | 0.811481i | \(-0.698662\pi\) | ||||
−0.584379 | + | 0.811481i | \(0.698662\pi\) | |||||||
\(152\) | 1931.62 | 1.03076 | ||||||||
\(153\) | 52.6288 | 0.0278090 | ||||||||
\(154\) | −8095.20 | −4.23591 | ||||||||
\(155\) | 565.568 | 0.293081 | ||||||||
\(156\) | 197.792 | 0.101513 | ||||||||
\(157\) | 1774.82 | 0.902203 | 0.451102 | − | 0.892473i | \(-0.351031\pi\) | ||||
0.451102 | + | 0.892473i | \(0.351031\pi\) | |||||||
\(158\) | 2393.67 | 1.20525 | ||||||||
\(159\) | −1629.61 | −0.812806 | ||||||||
\(160\) | −2243.56 | −1.10856 | ||||||||
\(161\) | 1698.78 | 0.831568 | ||||||||
\(162\) | 3785.66 | 1.83599 | ||||||||
\(163\) | −2842.13 | −1.36572 | −0.682862 | − | 0.730547i | \(-0.739265\pi\) | ||||
−0.682862 | + | 0.730547i | \(0.739265\pi\) | |||||||
\(164\) | 4517.68 | 2.15105 | ||||||||
\(165\) | 3256.44 | 1.53645 | ||||||||
\(166\) | 2033.47 | 0.950769 | ||||||||
\(167\) | −2508.14 | −1.16219 | −0.581095 | − | 0.813835i | \(-0.697376\pi\) | ||||
−0.581095 | + | 0.813835i | \(0.697376\pi\) | |||||||
\(168\) | 3267.78 | 1.50068 | ||||||||
\(169\) | −2188.53 | −0.996146 | ||||||||
\(170\) | 434.917 | 0.196215 | ||||||||
\(171\) | −617.079 | −0.275960 | ||||||||
\(172\) | 1240.88 | 0.550095 | ||||||||
\(173\) | 2493.75 | 1.09593 | 0.547967 | − | 0.836500i | \(-0.315402\pi\) | ||||
0.547967 | + | 0.836500i | \(0.315402\pi\) | |||||||
\(174\) | −4122.68 | −1.79620 | ||||||||
\(175\) | −605.881 | −0.261716 | ||||||||
\(176\) | −963.795 | −0.412777 | ||||||||
\(177\) | −703.850 | −0.298896 | ||||||||
\(178\) | 1410.08 | 0.593766 | ||||||||
\(179\) | 308.665 | 0.128887 | 0.0644433 | − | 0.997921i | \(-0.479473\pi\) | ||||
0.0644433 | + | 0.997921i | \(0.479473\pi\) | |||||||
\(180\) | −685.116 | −0.283697 | ||||||||
\(181\) | 2425.01 | 0.995853 | 0.497927 | − | 0.867219i | \(-0.334095\pi\) | ||||
0.497927 | + | 0.867219i | \(0.334095\pi\) | |||||||
\(182\) | 426.132 | 0.173555 | ||||||||
\(183\) | 113.013 | 0.0456513 | ||||||||
\(184\) | −903.000 | −0.361794 | ||||||||
\(185\) | 3247.47 | 1.29059 | ||||||||
\(186\) | −1395.39 | −0.550078 | ||||||||
\(187\) | 522.007 | 0.204133 | ||||||||
\(188\) | −5562.79 | −2.15802 | ||||||||
\(189\) | 4013.50 | 1.54465 | ||||||||
\(190\) | −5099.45 | −1.94712 | ||||||||
\(191\) | 4540.17 | 1.71997 | 0.859987 | − | 0.510317i | \(-0.170472\pi\) | ||||
0.859987 | + | 0.510317i | \(0.170472\pi\) | |||||||
\(192\) | 4739.31 | 1.78141 | ||||||||
\(193\) | −4857.77 | −1.81176 | −0.905880 | − | 0.423535i | \(-0.860789\pi\) | ||||
−0.905880 | + | 0.423535i | \(0.860789\pi\) | |||||||
\(194\) | 316.095 | 0.116981 | ||||||||
\(195\) | −171.419 | −0.0629518 | ||||||||
\(196\) | 8743.46 | 3.18639 | ||||||||
\(197\) | −3490.97 | −1.26255 | −0.631273 | − | 0.775561i | \(-0.717467\pi\) | ||||
−0.631273 | + | 0.775561i | \(0.717467\pi\) | |||||||
\(198\) | −1374.66 | −0.493400 | ||||||||
\(199\) | 2241.97 | 0.798638 | 0.399319 | − | 0.916812i | \(-0.369247\pi\) | ||||
0.399319 | + | 0.916812i | \(0.369247\pi\) | |||||||
\(200\) | 322.061 | 0.113866 | ||||||||
\(201\) | −4994.58 | −1.75269 | ||||||||
\(202\) | −6579.53 | −2.29175 | ||||||||
\(203\) | −5313.15 | −1.83700 | ||||||||
\(204\) | −641.878 | −0.220296 | ||||||||
\(205\) | −3915.31 | −1.33394 | ||||||||
\(206\) | −758.385 | −0.256501 | ||||||||
\(207\) | 288.473 | 0.0968612 | ||||||||
\(208\) | 50.7343 | 0.0169125 | ||||||||
\(209\) | −6120.59 | −2.02570 | ||||||||
\(210\) | −8626.89 | −2.83482 | ||||||||
\(211\) | −4948.13 | −1.61442 | −0.807211 | − | 0.590263i | \(-0.799024\pi\) | ||||
−0.807211 | + | 0.590263i | \(0.799024\pi\) | |||||||
\(212\) | 3400.61 | 1.10167 | ||||||||
\(213\) | 3499.49 | 1.12573 | ||||||||
\(214\) | −2436.84 | −0.778407 | ||||||||
\(215\) | −1075.43 | −0.341133 | ||||||||
\(216\) | −2133.41 | −0.672038 | ||||||||
\(217\) | −1798.32 | −0.562571 | ||||||||
\(218\) | −5107.19 | −1.58671 | ||||||||
\(219\) | 4057.36 | 1.25192 | ||||||||
\(220\) | −6795.43 | −2.08249 | ||||||||
\(221\) | −27.4785 | −0.00836382 | ||||||||
\(222\) | −8012.24 | −2.42228 | ||||||||
\(223\) | 4344.05 | 1.30448 | 0.652241 | − | 0.758012i | \(-0.273829\pi\) | ||||
0.652241 | + | 0.758012i | \(0.273829\pi\) | |||||||
\(224\) | 7133.77 | 2.12788 | ||||||||
\(225\) | −102.886 | −0.0304848 | ||||||||
\(226\) | −8686.33 | −2.55667 | ||||||||
\(227\) | 362.635 | 0.106030 | 0.0530152 | − | 0.998594i | \(-0.483117\pi\) | ||||
0.0530152 | + | 0.998594i | \(0.483117\pi\) | |||||||
\(228\) | 7526.10 | 2.18609 | ||||||||
\(229\) | −2714.36 | −0.783274 | −0.391637 | − | 0.920120i | \(-0.628091\pi\) | ||||
−0.391637 | + | 0.920120i | \(0.628091\pi\) | |||||||
\(230\) | 2383.90 | 0.683434 | ||||||||
\(231\) | −10354.4 | −2.94922 | ||||||||
\(232\) | 2824.25 | 0.799229 | ||||||||
\(233\) | −5462.36 | −1.53584 | −0.767921 | − | 0.640545i | \(-0.778709\pi\) | ||||
−0.767921 | + | 0.640545i | \(0.778709\pi\) | |||||||
\(234\) | 72.3625 | 0.0202157 | ||||||||
\(235\) | 4821.06 | 1.33826 | ||||||||
\(236\) | 1468.77 | 0.405122 | ||||||||
\(237\) | 3061.68 | 0.839147 | ||||||||
\(238\) | −1382.89 | −0.376636 | ||||||||
\(239\) | 3940.13 | 1.06638 | 0.533192 | − | 0.845994i | \(-0.320992\pi\) | ||||
0.533192 | + | 0.845994i | \(0.320992\pi\) | |||||||
\(240\) | −1027.10 | −0.276245 | ||||||||
\(241\) | 6500.63 | 1.73752 | 0.868761 | − | 0.495232i | \(-0.164917\pi\) | ||||
0.868761 | + | 0.495232i | \(0.164917\pi\) | |||||||
\(242\) | −7695.86 | −2.04425 | ||||||||
\(243\) | 1540.36 | 0.406641 | ||||||||
\(244\) | −235.832 | −0.0618755 | ||||||||
\(245\) | −7577.64 | −1.97599 | ||||||||
\(246\) | 9659.95 | 2.50364 | ||||||||
\(247\) | 322.189 | 0.0829975 | ||||||||
\(248\) | 955.911 | 0.244760 | ||||||||
\(249\) | 2600.96 | 0.661965 | ||||||||
\(250\) | −6607.26 | −1.67152 | ||||||||
\(251\) | 4533.97 | 1.14017 | 0.570083 | − | 0.821587i | \(-0.306911\pi\) | ||||
0.570083 | + | 0.821587i | \(0.306911\pi\) | |||||||
\(252\) | 2178.44 | 0.544559 | ||||||||
\(253\) | 2861.27 | 0.711014 | ||||||||
\(254\) | 8147.38 | 2.01265 | ||||||||
\(255\) | 556.292 | 0.136613 | ||||||||
\(256\) | −2130.82 | −0.520219 | ||||||||
\(257\) | −3205.52 | −0.778034 | −0.389017 | − | 0.921231i | \(-0.627185\pi\) | ||||
−0.389017 | + | 0.921231i | \(0.627185\pi\) | |||||||
\(258\) | 2653.32 | 0.640266 | ||||||||
\(259\) | −10325.9 | −2.47729 | ||||||||
\(260\) | 357.712 | 0.0853245 | ||||||||
\(261\) | −902.238 | −0.213974 | ||||||||
\(262\) | −5493.36 | −1.29535 | ||||||||
\(263\) | −4733.83 | −1.10989 | −0.554944 | − | 0.831888i | \(-0.687260\pi\) | ||||
−0.554944 | + | 0.831888i | \(0.687260\pi\) | |||||||
\(264\) | 5503.96 | 1.28313 | ||||||||
\(265\) | −2947.18 | −0.683185 | ||||||||
\(266\) | 16214.6 | 3.73751 | ||||||||
\(267\) | 1803.61 | 0.413404 | ||||||||
\(268\) | 10422.5 | 2.37558 | ||||||||
\(269\) | −3865.37 | −0.876119 | −0.438059 | − | 0.898946i | \(-0.644334\pi\) | ||||
−0.438059 | + | 0.898946i | \(0.644334\pi\) | |||||||
\(270\) | 5632.17 | 1.26949 | ||||||||
\(271\) | −5315.53 | −1.19150 | −0.595748 | − | 0.803172i | \(-0.703144\pi\) | ||||
−0.595748 | + | 0.803172i | \(0.703144\pi\) | |||||||
\(272\) | −164.644 | −0.0367021 | ||||||||
\(273\) | 545.056 | 0.120836 | ||||||||
\(274\) | 8709.31 | 1.92025 | ||||||||
\(275\) | −1020.49 | −0.223775 | ||||||||
\(276\) | −3518.32 | −0.767311 | ||||||||
\(277\) | 3472.55 | 0.753232 | 0.376616 | − | 0.926369i | \(-0.377088\pi\) | ||||
0.376616 | + | 0.926369i | \(0.377088\pi\) | |||||||
\(278\) | 10400.8 | 2.24388 | ||||||||
\(279\) | −305.376 | −0.0655283 | ||||||||
\(280\) | 5909.87 | 1.26136 | ||||||||
\(281\) | −2590.79 | −0.550012 | −0.275006 | − | 0.961443i | \(-0.588680\pi\) | ||||
−0.275006 | + | 0.961443i | \(0.588680\pi\) | |||||||
\(282\) | −11894.7 | −2.51176 | ||||||||
\(283\) | −1478.51 | −0.310558 | −0.155279 | − | 0.987871i | \(-0.549628\pi\) | ||||
−0.155279 | + | 0.987871i | \(0.549628\pi\) | |||||||
\(284\) | −7302.63 | −1.52581 | ||||||||
\(285\) | −6522.59 | −1.35567 | ||||||||
\(286\) | 717.739 | 0.148394 | ||||||||
\(287\) | 12449.4 | 2.56050 | ||||||||
\(288\) | 1211.40 | 0.247856 | ||||||||
\(289\) | −4823.83 | −0.981849 | ||||||||
\(290\) | −7455.97 | −1.50976 | ||||||||
\(291\) | 404.310 | 0.0814470 | ||||||||
\(292\) | −8466.75 | −1.69685 | ||||||||
\(293\) | 7475.57 | 1.49054 | 0.745269 | − | 0.666764i | \(-0.232321\pi\) | ||||
0.745269 | + | 0.666764i | \(0.232321\pi\) | |||||||
\(294\) | 18695.7 | 3.70870 | ||||||||
\(295\) | −1272.93 | −0.251230 | ||||||||
\(296\) | 5488.80 | 1.07780 | ||||||||
\(297\) | 6759.98 | 1.32072 | ||||||||
\(298\) | −50.4820 | −0.00981324 | ||||||||
\(299\) | −150.618 | −0.0291319 | ||||||||
\(300\) | 1254.83 | 0.241493 | ||||||||
\(301\) | 3419.50 | 0.654806 | ||||||||
\(302\) | 9676.62 | 1.84380 | ||||||||
\(303\) | −8415.72 | −1.59561 | ||||||||
\(304\) | 1930.47 | 0.364210 | ||||||||
\(305\) | 204.387 | 0.0383711 | ||||||||
\(306\) | −234.832 | −0.0438707 | ||||||||
\(307\) | −1414.23 | −0.262913 | −0.131457 | − | 0.991322i | \(-0.541965\pi\) | ||||
−0.131457 | + | 0.991322i | \(0.541965\pi\) | |||||||
\(308\) | 21607.2 | 3.99735 | ||||||||
\(309\) | −970.033 | −0.178587 | ||||||||
\(310\) | −2523.59 | −0.462355 | ||||||||
\(311\) | 4721.68 | 0.860906 | 0.430453 | − | 0.902613i | \(-0.358354\pi\) | ||||
0.430453 | + | 0.902613i | \(0.358354\pi\) | |||||||
\(312\) | −289.729 | −0.0525727 | ||||||||
\(313\) | −8664.43 | −1.56467 | −0.782336 | − | 0.622857i | \(-0.785972\pi\) | ||||
−0.782336 | + | 0.622857i | \(0.785972\pi\) | |||||||
\(314\) | −7919.31 | −1.42329 | ||||||||
\(315\) | −1887.97 | −0.337699 | ||||||||
\(316\) | −6389.02 | −1.13738 | ||||||||
\(317\) | −5273.97 | −0.934434 | −0.467217 | − | 0.884143i | \(-0.654743\pi\) | ||||
−0.467217 | + | 0.884143i | \(0.654743\pi\) | |||||||
\(318\) | 7271.37 | 1.28226 | ||||||||
\(319\) | −8949.00 | −1.57068 | ||||||||
\(320\) | 8571.15 | 1.49732 | ||||||||
\(321\) | −3116.91 | −0.541960 | ||||||||
\(322\) | −7580.01 | −1.31186 | ||||||||
\(323\) | −1045.57 | −0.180115 | ||||||||
\(324\) | −10104.5 | −1.73259 | ||||||||
\(325\) | 53.7188 | 0.00916857 | ||||||||
\(326\) | 12681.7 | 2.15452 | ||||||||
\(327\) | −6532.50 | −1.10473 | ||||||||
\(328\) | −6617.56 | −1.11401 | ||||||||
\(329\) | −15329.4 | −2.56880 | ||||||||
\(330\) | −14530.4 | −2.42385 | ||||||||
\(331\) | 7529.36 | 1.25030 | 0.625152 | − | 0.780503i | \(-0.285037\pi\) | ||||
0.625152 | + | 0.780503i | \(0.285037\pi\) | |||||||
\(332\) | −5427.60 | −0.897224 | ||||||||
\(333\) | −1753.46 | −0.288555 | ||||||||
\(334\) | 11191.4 | 1.83344 | ||||||||
\(335\) | −9032.81 | −1.47318 | ||||||||
\(336\) | 3265.83 | 0.530254 | ||||||||
\(337\) | 1521.00 | 0.245858 | 0.122929 | − | 0.992415i | \(-0.460771\pi\) | ||||
0.122929 | + | 0.992415i | \(0.460771\pi\) | |||||||
\(338\) | 9765.32 | 1.57149 | ||||||||
\(339\) | −11110.5 | −1.78006 | ||||||||
\(340\) | −1160.85 | −0.185165 | ||||||||
\(341\) | −3028.93 | −0.481013 | ||||||||
\(342\) | 2753.43 | 0.435346 | ||||||||
\(343\) | 12837.2 | 2.02082 | ||||||||
\(344\) | −1817.66 | −0.284889 | ||||||||
\(345\) | 3049.20 | 0.475835 | ||||||||
\(346\) | −11127.2 | −1.72891 | ||||||||
\(347\) | 8682.94 | 1.34330 | 0.671649 | − | 0.740870i | \(-0.265586\pi\) | ||||
0.671649 | + | 0.740870i | \(0.265586\pi\) | |||||||
\(348\) | 11004.0 | 1.69505 | ||||||||
\(349\) | 8438.80 | 1.29432 | 0.647161 | − | 0.762353i | \(-0.275956\pi\) | ||||
0.647161 | + | 0.762353i | \(0.275956\pi\) | |||||||
\(350\) | 2703.47 | 0.412875 | ||||||||
\(351\) | −355.846 | −0.0541130 | ||||||||
\(352\) | 12015.5 | 1.81940 | ||||||||
\(353\) | −171.504 | −0.0258591 | −0.0129295 | − | 0.999916i | \(-0.504116\pi\) | ||||
−0.0129295 | + | 0.999916i | \(0.504116\pi\) | |||||||
\(354\) | 3140.61 | 0.471529 | ||||||||
\(355\) | 6328.92 | 0.946209 | ||||||||
\(356\) | −3763.71 | −0.560326 | ||||||||
\(357\) | −1768.82 | −0.262230 | ||||||||
\(358\) | −1377.27 | −0.203327 | ||||||||
\(359\) | 2031.61 | 0.298674 | 0.149337 | − | 0.988786i | \(-0.452286\pi\) | ||||
0.149337 | + | 0.988786i | \(0.452286\pi\) | |||||||
\(360\) | 1003.57 | 0.146924 | ||||||||
\(361\) | 5400.45 | 0.787352 | ||||||||
\(362\) | −10820.5 | −1.57103 | ||||||||
\(363\) | −9843.60 | −1.42329 | ||||||||
\(364\) | −1137.41 | −0.163781 | ||||||||
\(365\) | 7337.83 | 1.05227 | ||||||||
\(366\) | −504.270 | −0.0720180 | ||||||||
\(367\) | −10114.4 | −1.43860 | −0.719301 | − | 0.694698i | \(-0.755538\pi\) | ||||
−0.719301 | + | 0.694698i | \(0.755538\pi\) | |||||||
\(368\) | −902.458 | −0.127837 | ||||||||
\(369\) | 2114.05 | 0.298247 | ||||||||
\(370\) | −14490.3 | −2.03599 | ||||||||
\(371\) | 9371.06 | 1.31138 | ||||||||
\(372\) | 3724.47 | 0.519099 | ||||||||
\(373\) | 1596.82 | 0.221663 | 0.110832 | − | 0.993839i | \(-0.464649\pi\) | ||||
0.110832 | + | 0.993839i | \(0.464649\pi\) | |||||||
\(374\) | −2329.22 | −0.322034 | ||||||||
\(375\) | −8451.20 | −1.16378 | ||||||||
\(376\) | 8148.46 | 1.11762 | ||||||||
\(377\) | 471.076 | 0.0643545 | ||||||||
\(378\) | −17908.4 | −2.43680 | ||||||||
\(379\) | −206.933 | −0.0280460 | −0.0140230 | − | 0.999902i | \(-0.504464\pi\) | ||||
−0.0140230 | + | 0.999902i | \(0.504464\pi\) | |||||||
\(380\) | 13611.1 | 1.83746 | ||||||||
\(381\) | 10421.1 | 1.40129 | ||||||||
\(382\) | −20258.4 | −2.71338 | ||||||||
\(383\) | −2868.55 | −0.382705 | −0.191353 | − | 0.981521i | \(-0.561287\pi\) | ||||
−0.191353 | + | 0.981521i | \(0.561287\pi\) | |||||||
\(384\) | −11222.6 | −1.49141 | ||||||||
\(385\) | −18726.2 | −2.47889 | ||||||||
\(386\) | 21675.5 | 2.85818 | ||||||||
\(387\) | 580.673 | 0.0762720 | ||||||||
\(388\) | −843.701 | −0.110393 | ||||||||
\(389\) | −2260.86 | −0.294680 | −0.147340 | − | 0.989086i | \(-0.547071\pi\) | ||||
−0.147340 | + | 0.989086i | \(0.547071\pi\) | |||||||
\(390\) | 764.880 | 0.0993108 | ||||||||
\(391\) | 488.786 | 0.0632199 | ||||||||
\(392\) | −12807.6 | −1.65020 | ||||||||
\(393\) | −7026.43 | −0.901874 | ||||||||
\(394\) | 15576.9 | 1.99175 | ||||||||
\(395\) | 5537.13 | 0.705325 | ||||||||
\(396\) | 3669.17 | 0.465613 | ||||||||
\(397\) | −7366.58 | −0.931280 | −0.465640 | − | 0.884974i | \(-0.654176\pi\) | ||||
−0.465640 | + | 0.884974i | \(0.654176\pi\) | |||||||
\(398\) | −10003.8 | −1.25991 | ||||||||
\(399\) | 20739.7 | 2.60221 | ||||||||
\(400\) | 321.868 | 0.0402335 | ||||||||
\(401\) | 650.496 | 0.0810080 | 0.0405040 | − | 0.999179i | \(-0.487104\pi\) | ||||
0.0405040 | + | 0.999179i | \(0.487104\pi\) | |||||||
\(402\) | 22286.0 | 2.76499 | ||||||||
\(403\) | 159.443 | 0.0197082 | ||||||||
\(404\) | 17561.7 | 2.16269 | ||||||||
\(405\) | 8757.16 | 1.07444 | ||||||||
\(406\) | 23707.5 | 2.89799 | ||||||||
\(407\) | −17392.0 | −2.11815 | ||||||||
\(408\) | 940.233 | 0.114089 | ||||||||
\(409\) | 1953.99 | 0.236232 | 0.118116 | − | 0.993000i | \(-0.462315\pi\) | ||||
0.118116 | + | 0.993000i | \(0.462315\pi\) | |||||||
\(410\) | 17470.3 | 2.10438 | ||||||||
\(411\) | 11139.9 | 1.33696 | ||||||||
\(412\) | 2024.23 | 0.242055 | ||||||||
\(413\) | 4047.49 | 0.482237 | ||||||||
\(414\) | −1287.18 | −0.152805 | ||||||||
\(415\) | 4703.90 | 0.556399 | ||||||||
\(416\) | −632.496 | −0.0745449 | ||||||||
\(417\) | 13303.4 | 1.56228 | ||||||||
\(418\) | 27310.3 | 3.19567 | ||||||||
\(419\) | −3118.76 | −0.363632 | −0.181816 | − | 0.983333i | \(-0.558197\pi\) | ||||
−0.181816 | + | 0.983333i | \(0.558197\pi\) | |||||||
\(420\) | 23026.4 | 2.67517 | ||||||||
\(421\) | 9337.44 | 1.08095 | 0.540474 | − | 0.841361i | \(-0.318245\pi\) | ||||
0.540474 | + | 0.841361i | \(0.318245\pi\) | |||||||
\(422\) | 22078.7 | 2.54686 | ||||||||
\(423\) | −2603.11 | −0.299215 | ||||||||
\(424\) | −4981.26 | −0.570546 | ||||||||
\(425\) | −174.329 | −0.0198969 | ||||||||
\(426\) | −15614.9 | −1.77592 | ||||||||
\(427\) | −649.883 | −0.0736535 | ||||||||
\(428\) | 6504.27 | 0.734569 | ||||||||
\(429\) | 918.044 | 0.103318 | ||||||||
\(430\) | 4798.60 | 0.538160 | ||||||||
\(431\) | −15124.7 | −1.69033 | −0.845166 | − | 0.534504i | \(-0.820498\pi\) | ||||
−0.845166 | + | 0.534504i | \(0.820498\pi\) | |||||||
\(432\) | −2132.13 | −0.237459 | ||||||||
\(433\) | 16011.8 | 1.77709 | 0.888544 | − | 0.458792i | \(-0.151718\pi\) | ||||
0.888544 | + | 0.458792i | \(0.151718\pi\) | |||||||
\(434\) | 8024.17 | 0.887494 | ||||||||
\(435\) | −9536.76 | −1.05116 | ||||||||
\(436\) | 13631.8 | 1.49735 | ||||||||
\(437\) | −5731.07 | −0.627356 | ||||||||
\(438\) | −18104.1 | −1.97499 | ||||||||
\(439\) | −10062.7 | −1.09400 | −0.547001 | − | 0.837132i | \(-0.684231\pi\) | ||||
−0.547001 | + | 0.837132i | \(0.684231\pi\) | |||||||
\(440\) | 9954.05 | 1.07850 | ||||||||
\(441\) | 4091.52 | 0.441801 | ||||||||
\(442\) | 122.610 | 0.0131945 | ||||||||
\(443\) | −3931.79 | −0.421682 | −0.210841 | − | 0.977520i | \(-0.567620\pi\) | ||||
−0.210841 | + | 0.977520i | \(0.567620\pi\) | |||||||
\(444\) | 21385.8 | 2.28586 | ||||||||
\(445\) | 3261.87 | 0.347477 | ||||||||
\(446\) | −19383.3 | −2.05791 | ||||||||
\(447\) | −64.5704 | −0.00683239 | ||||||||
\(448\) | −27253.4 | −2.87411 | ||||||||
\(449\) | 1101.21 | 0.115745 | 0.0578724 | − | 0.998324i | \(-0.481568\pi\) | ||||
0.0578724 | + | 0.998324i | \(0.481568\pi\) | |||||||
\(450\) | 459.082 | 0.0480918 | ||||||||
\(451\) | 20968.6 | 2.18930 | ||||||||
\(452\) | 23185.0 | 2.41268 | ||||||||
\(453\) | 12377.1 | 1.28373 | ||||||||
\(454\) | −1618.09 | −0.167270 | ||||||||
\(455\) | 985.748 | 0.101566 | ||||||||
\(456\) | −11024.3 | −1.13215 | ||||||||
\(457\) | −9927.88 | −1.01621 | −0.508104 | − | 0.861296i | \(-0.669653\pi\) | ||||
−0.508104 | + | 0.861296i | \(0.669653\pi\) | |||||||
\(458\) | 12111.6 | 1.23567 | ||||||||
\(459\) | 1154.80 | 0.117432 | ||||||||
\(460\) | −6362.96 | −0.644945 | ||||||||
\(461\) | −1512.55 | −0.152812 | −0.0764061 | − | 0.997077i | \(-0.524345\pi\) | ||||
−0.0764061 | + | 0.997077i | \(0.524345\pi\) | |||||||
\(462\) | 46201.7 | 4.65259 | ||||||||
\(463\) | 8571.68 | 0.860389 | 0.430194 | − | 0.902736i | \(-0.358445\pi\) | ||||
0.430194 | + | 0.902736i | \(0.358445\pi\) | |||||||
\(464\) | 2822.56 | 0.282401 | ||||||||
\(465\) | −3227.86 | −0.321911 | ||||||||
\(466\) | 24373.3 | 2.42290 | ||||||||
\(467\) | −14778.5 | −1.46439 | −0.732194 | − | 0.681096i | \(-0.761503\pi\) | ||||
−0.732194 | + | 0.681096i | \(0.761503\pi\) | |||||||
\(468\) | −193.145 | −0.0190772 | ||||||||
\(469\) | 28721.3 | 2.82778 | ||||||||
\(470\) | −21511.8 | −2.11120 | ||||||||
\(471\) | −10129.4 | −0.990952 | ||||||||
\(472\) | −2151.48 | −0.209809 | ||||||||
\(473\) | 5759.50 | 0.559877 | ||||||||
\(474\) | −13661.4 | −1.32381 | ||||||||
\(475\) | 2044.03 | 0.197445 | ||||||||
\(476\) | 3691.12 | 0.355425 | ||||||||
\(477\) | 1591.32 | 0.152750 | ||||||||
\(478\) | −17581.0 | −1.68230 | ||||||||
\(479\) | −8114.31 | −0.774013 | −0.387006 | − | 0.922077i | \(-0.626491\pi\) | ||||
−0.387006 | + | 0.922077i | \(0.626491\pi\) | |||||||
\(480\) | 12804.7 | 1.21760 | ||||||||
\(481\) | 915.514 | 0.0867856 | ||||||||
\(482\) | −29006.1 | −2.74106 | ||||||||
\(483\) | −9695.43 | −0.913369 | ||||||||
\(484\) | 20541.3 | 1.92912 | ||||||||
\(485\) | 731.205 | 0.0684583 | ||||||||
\(486\) | −6873.13 | −0.641505 | ||||||||
\(487\) | −8615.16 | −0.801623 | −0.400811 | − | 0.916161i | \(-0.631272\pi\) | ||||
−0.400811 | + | 0.916161i | \(0.631272\pi\) | |||||||
\(488\) | 345.451 | 0.0320447 | ||||||||
\(489\) | 16220.9 | 1.50007 | ||||||||
\(490\) | 33811.7 | 3.11726 | ||||||||
\(491\) | −5196.70 | −0.477646 | −0.238823 | − | 0.971063i | \(-0.576762\pi\) | ||||
−0.238823 | + | 0.971063i | \(0.576762\pi\) | |||||||
\(492\) | −25783.7 | −2.36264 | ||||||||
\(493\) | −1528.74 | −0.139657 | ||||||||
\(494\) | −1437.62 | −0.130934 | ||||||||
\(495\) | −3179.93 | −0.288742 | ||||||||
\(496\) | 955.338 | 0.0864838 | ||||||||
\(497\) | −20123.8 | −1.81625 | ||||||||
\(498\) | −11605.6 | −1.04430 | ||||||||
\(499\) | 8312.20 | 0.745702 | 0.372851 | − | 0.927891i | \(-0.378380\pi\) | ||||
0.372851 | + | 0.927891i | \(0.378380\pi\) | |||||||
\(500\) | 17635.7 | 1.57738 | ||||||||
\(501\) | 14314.7 | 1.27651 | ||||||||
\(502\) | −20230.8 | −1.79869 | ||||||||
\(503\) | 10199.2 | 0.904092 | 0.452046 | − | 0.891995i | \(-0.350694\pi\) | ||||
0.452046 | + | 0.891995i | \(0.350694\pi\) | |||||||
\(504\) | −3191.01 | −0.282022 | ||||||||
\(505\) | −15220.0 | −1.34115 | ||||||||
\(506\) | −12767.1 | −1.12167 | ||||||||
\(507\) | 12490.6 | 1.09414 | ||||||||
\(508\) | −21746.5 | −1.89930 | ||||||||
\(509\) | −9301.01 | −0.809941 | −0.404970 | − | 0.914330i | \(-0.632718\pi\) | ||||
−0.404970 | + | 0.914330i | \(0.632718\pi\) | |||||||
\(510\) | −2482.20 | −0.215517 | ||||||||
\(511\) | −23331.8 | −2.01984 | ||||||||
\(512\) | −6223.09 | −0.537157 | ||||||||
\(513\) | −13540.1 | −1.16532 | ||||||||
\(514\) | 14303.1 | 1.22740 | ||||||||
\(515\) | −1754.33 | −0.150107 | ||||||||
\(516\) | −7082.08 | −0.604208 | ||||||||
\(517\) | −25819.4 | −2.19640 | ||||||||
\(518\) | 46074.4 | 3.90809 | ||||||||
\(519\) | −14232.6 | −1.20374 | ||||||||
\(520\) | −523.982 | −0.0441887 | ||||||||
\(521\) | 14584.6 | 1.22641 | 0.613207 | − | 0.789922i | \(-0.289879\pi\) | ||||
0.613207 | + | 0.789922i | \(0.289879\pi\) | |||||||
\(522\) | 4025.82 | 0.337558 | ||||||||
\(523\) | 7276.77 | 0.608395 | 0.304198 | − | 0.952609i | \(-0.401612\pi\) | ||||
0.304198 | + | 0.952609i | \(0.401612\pi\) | |||||||
\(524\) | 14662.5 | 1.22240 | ||||||||
\(525\) | 3457.94 | 0.287461 | ||||||||
\(526\) | 21122.5 | 1.75092 | ||||||||
\(527\) | −517.426 | −0.0427694 | ||||||||
\(528\) | 5500.66 | 0.453382 | ||||||||
\(529\) | −9487.83 | −0.779800 | ||||||||
\(530\) | 13150.4 | 1.07777 | ||||||||
\(531\) | 687.314 | 0.0561711 | ||||||||
\(532\) | −43278.9 | −3.52702 | ||||||||
\(533\) | −1103.79 | −0.0897006 | ||||||||
\(534\) | −8047.77 | −0.652174 | ||||||||
\(535\) | −5637.01 | −0.455531 | ||||||||
\(536\) | −15267.1 | −1.23029 | ||||||||
\(537\) | −1761.64 | −0.141565 | ||||||||
\(538\) | 17247.4 | 1.38214 | ||||||||
\(539\) | 40582.4 | 3.24305 | ||||||||
\(540\) | −15033.0 | −1.19800 | ||||||||
\(541\) | 7177.23 | 0.570375 | 0.285188 | − | 0.958472i | \(-0.407944\pi\) | ||||
0.285188 | + | 0.958472i | \(0.407944\pi\) | |||||||
\(542\) | 23718.1 | 1.87967 | ||||||||
\(543\) | −13840.2 | −1.09381 | ||||||||
\(544\) | 2052.58 | 0.161772 | ||||||||
\(545\) | −11814.2 | −0.928558 | ||||||||
\(546\) | −2432.06 | −0.190628 | ||||||||
\(547\) | −20588.7 | −1.60934 | −0.804669 | − | 0.593723i | \(-0.797657\pi\) | ||||
−0.804669 | + | 0.593723i | \(0.797657\pi\) | |||||||
\(548\) | −23246.3 | −1.81211 | ||||||||
\(549\) | −110.358 | −0.00857918 | ||||||||
\(550\) | 4553.48 | 0.353020 | ||||||||
\(551\) | 17924.7 | 1.38588 | ||||||||
\(552\) | 5153.68 | 0.397383 | ||||||||
\(553\) | −17606.2 | −1.35388 | ||||||||
\(554\) | −15494.6 | −1.18828 | ||||||||
\(555\) | −18534.2 | −1.41754 | ||||||||
\(556\) | −27761.2 | −2.11751 | ||||||||
\(557\) | 5138.84 | 0.390915 | 0.195457 | − | 0.980712i | \(-0.437381\pi\) | ||||
0.195457 | + | 0.980712i | \(0.437381\pi\) | |||||||
\(558\) | 1362.60 | 0.103375 | ||||||||
\(559\) | −303.181 | −0.0229395 | ||||||||
\(560\) | 5906.33 | 0.445693 | ||||||||
\(561\) | −2979.25 | −0.224214 | ||||||||
\(562\) | 11560.2 | 0.867681 | ||||||||
\(563\) | −17090.4 | −1.27935 | −0.639677 | − | 0.768644i | \(-0.720932\pi\) | ||||
−0.639677 | + | 0.768644i | \(0.720932\pi\) | |||||||
\(564\) | 31748.5 | 2.37030 | ||||||||
\(565\) | −20093.6 | −1.49618 | ||||||||
\(566\) | 6597.15 | 0.489927 | ||||||||
\(567\) | −27844.9 | −2.06239 | ||||||||
\(568\) | 10697.0 | 0.790204 | ||||||||
\(569\) | 4519.31 | 0.332969 | 0.166484 | − | 0.986044i | \(-0.446758\pi\) | ||||
0.166484 | + | 0.986044i | \(0.446758\pi\) | |||||||
\(570\) | 29104.1 | 2.13866 | ||||||||
\(571\) | −4982.15 | −0.365142 | −0.182571 | − | 0.983193i | \(-0.558442\pi\) | ||||
−0.182571 | + | 0.983193i | \(0.558442\pi\) | |||||||
\(572\) | −1915.74 | −0.140037 | ||||||||
\(573\) | −25912.1 | −1.88917 | ||||||||
\(574\) | −55549.6 | −4.03936 | ||||||||
\(575\) | −955.547 | −0.0693027 | ||||||||
\(576\) | −4627.96 | −0.334777 | ||||||||
\(577\) | −14799.9 | −1.06781 | −0.533907 | − | 0.845543i | \(-0.679277\pi\) | ||||
−0.533907 | + | 0.845543i | \(0.679277\pi\) | |||||||
\(578\) | 21524.1 | 1.54894 | ||||||||
\(579\) | 27724.7 | 1.98998 | ||||||||
\(580\) | 19901.0 | 1.42473 | ||||||||
\(581\) | −14956.8 | −1.06801 | ||||||||
\(582\) | −1804.05 | −0.128488 | ||||||||
\(583\) | 15783.8 | 1.12126 | ||||||||
\(584\) | 12402.2 | 0.878781 | ||||||||
\(585\) | 167.392 | 0.0118304 | ||||||||
\(586\) | −33356.3 | −2.35143 | ||||||||
\(587\) | −8229.83 | −0.578673 | −0.289337 | − | 0.957227i | \(-0.593435\pi\) | ||||
−0.289337 | + | 0.957227i | \(0.593435\pi\) | |||||||
\(588\) | −49901.5 | −3.49983 | ||||||||
\(589\) | 6066.89 | 0.424417 | ||||||||
\(590\) | 5679.86 | 0.396333 | ||||||||
\(591\) | 19924.0 | 1.38674 | ||||||||
\(592\) | 5485.51 | 0.380833 | ||||||||
\(593\) | −8334.86 | −0.577186 | −0.288593 | − | 0.957452i | \(-0.593188\pi\) | ||||
−0.288593 | + | 0.957452i | \(0.593188\pi\) | |||||||
\(594\) | −30163.3 | −2.08353 | ||||||||
\(595\) | −3198.96 | −0.220411 | ||||||||
\(596\) | 134.743 | 0.00926058 | ||||||||
\(597\) | −12795.6 | −0.877200 | ||||||||
\(598\) | 672.061 | 0.0459576 | ||||||||
\(599\) | −21695.8 | −1.47991 | −0.739954 | − | 0.672658i | \(-0.765153\pi\) | ||||
−0.739954 | + | 0.672658i | \(0.765153\pi\) | |||||||
\(600\) | −1838.10 | −0.125067 | ||||||||
\(601\) | −15732.6 | −1.06780 | −0.533899 | − | 0.845548i | \(-0.679274\pi\) | ||||
−0.533899 | + | 0.845548i | \(0.679274\pi\) | |||||||
\(602\) | −15257.9 | −1.03300 | ||||||||
\(603\) | 4877.23 | 0.329380 | ||||||||
\(604\) | −25828.2 | −1.73996 | ||||||||
\(605\) | −17802.4 | −1.19631 | ||||||||
\(606\) | 37551.3 | 2.51719 | ||||||||
\(607\) | −17808.5 | −1.19082 | −0.595409 | − | 0.803423i | \(-0.703010\pi\) | ||||
−0.595409 | + | 0.803423i | \(0.703010\pi\) | |||||||
\(608\) | −24066.8 | −1.60533 | ||||||||
\(609\) | 30323.7 | 2.01770 | ||||||||
\(610\) | −911.984 | −0.0605330 | ||||||||
\(611\) | 1359.14 | 0.0899915 | ||||||||
\(612\) | 626.798 | 0.0414000 | ||||||||
\(613\) | −19461.6 | −1.28229 | −0.641146 | − | 0.767419i | \(-0.721541\pi\) | ||||
−0.641146 | + | 0.767419i | \(0.721541\pi\) | |||||||
\(614\) | 6310.35 | 0.414764 | ||||||||
\(615\) | 22345.8 | 1.46515 | ||||||||
\(616\) | −31650.6 | −2.07019 | ||||||||
\(617\) | −25712.2 | −1.67769 | −0.838843 | − | 0.544373i | \(-0.816768\pi\) | ||||
−0.838843 | + | 0.544373i | \(0.816768\pi\) | |||||||
\(618\) | 4328.33 | 0.281733 | ||||||||
\(619\) | −3376.81 | −0.219266 | −0.109633 | − | 0.993972i | \(-0.534968\pi\) | ||||
−0.109633 | + | 0.993972i | \(0.534968\pi\) | |||||||
\(620\) | 6735.80 | 0.436317 | ||||||||
\(621\) | 6329.77 | 0.409026 | ||||||||
\(622\) | −21068.3 | −1.35814 | ||||||||
\(623\) | −10371.7 | −0.666985 | ||||||||
\(624\) | −289.556 | −0.0185761 | ||||||||
\(625\) | −12976.6 | −0.830502 | ||||||||
\(626\) | 38661.0 | 2.46838 | ||||||||
\(627\) | 34932.0 | 2.22496 | ||||||||
\(628\) | 21137.7 | 1.34313 | ||||||||
\(629\) | −2971.04 | −0.188336 | ||||||||
\(630\) | 8424.21 | 0.532744 | ||||||||
\(631\) | −8779.27 | −0.553878 | −0.276939 | − | 0.960887i | \(-0.589320\pi\) | ||||
−0.276939 | + | 0.960887i | \(0.589320\pi\) | |||||||
\(632\) | 9358.74 | 0.589036 | ||||||||
\(633\) | 28240.4 | 1.77323 | ||||||||
\(634\) | 23532.6 | 1.47413 | ||||||||
\(635\) | 18846.9 | 1.17782 | ||||||||
\(636\) | −19408.3 | −1.21004 | ||||||||
\(637\) | −2136.26 | −0.132876 | ||||||||
\(638\) | 39930.8 | 2.47786 | ||||||||
\(639\) | −3417.28 | −0.211558 | ||||||||
\(640\) | −20296.3 | −1.25357 | ||||||||
\(641\) | 4999.03 | 0.308034 | 0.154017 | − | 0.988068i | \(-0.450779\pi\) | ||||
0.154017 | + | 0.988068i | \(0.450779\pi\) | |||||||
\(642\) | 13907.8 | 0.854979 | ||||||||
\(643\) | −19683.6 | −1.20722 | −0.603611 | − | 0.797279i | \(-0.706272\pi\) | ||||
−0.603611 | + | 0.797279i | \(0.706272\pi\) | |||||||
\(644\) | 20232.1 | 1.23798 | ||||||||
\(645\) | 6137.78 | 0.374690 | ||||||||
\(646\) | 4665.38 | 0.284144 | ||||||||
\(647\) | 8213.13 | 0.499059 | 0.249530 | − | 0.968367i | \(-0.419724\pi\) | ||||
0.249530 | + | 0.968367i | \(0.419724\pi\) | |||||||
\(648\) | 14801.2 | 0.897291 | ||||||||
\(649\) | 6817.23 | 0.412326 | ||||||||
\(650\) | −239.696 | −0.0144640 | ||||||||
\(651\) | 10263.5 | 0.617910 | ||||||||
\(652\) | −33849.2 | −2.03319 | ||||||||
\(653\) | −30188.1 | −1.80911 | −0.904556 | − | 0.426355i | \(-0.859797\pi\) | ||||
−0.904556 | + | 0.426355i | \(0.859797\pi\) | |||||||
\(654\) | 29148.3 | 1.74279 | ||||||||
\(655\) | −12707.5 | −0.758049 | ||||||||
\(656\) | −6613.60 | −0.393624 | ||||||||
\(657\) | −3962.03 | −0.235272 | ||||||||
\(658\) | 68400.3 | 4.05246 | ||||||||
\(659\) | 4719.39 | 0.278970 | 0.139485 | − | 0.990224i | \(-0.455455\pi\) | ||||
0.139485 | + | 0.990224i | \(0.455455\pi\) | |||||||
\(660\) | 38783.5 | 2.28734 | ||||||||
\(661\) | 6750.25 | 0.397208 | 0.198604 | − | 0.980080i | \(-0.436359\pi\) | ||||
0.198604 | + | 0.980080i | \(0.436359\pi\) | |||||||
\(662\) | −33596.3 | −1.97244 | ||||||||
\(663\) | 156.828 | 0.00918656 | ||||||||
\(664\) | 7950.43 | 0.464663 | ||||||||
\(665\) | 37508.2 | 2.18723 | ||||||||
\(666\) | 7823.99 | 0.455216 | ||||||||
\(667\) | −8379.47 | −0.486438 | ||||||||
\(668\) | −29871.4 | −1.73018 | ||||||||
\(669\) | −24792.8 | −1.43280 | ||||||||
\(670\) | 40304.8 | 2.32404 | ||||||||
\(671\) | −1094.60 | −0.0629758 | ||||||||
\(672\) | −40714.5 | −2.33720 | ||||||||
\(673\) | 8623.30 | 0.493913 | 0.246957 | − | 0.969027i | \(-0.420569\pi\) | ||||
0.246957 | + | 0.969027i | \(0.420569\pi\) | |||||||
\(674\) | −6786.75 | −0.387857 | ||||||||
\(675\) | −2257.56 | −0.128731 | ||||||||
\(676\) | −26065.0 | −1.48299 | ||||||||
\(677\) | 922.397 | 0.0523643 | 0.0261821 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261821 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(678\) | 49575.5 | 2.80816 | ||||||||
\(679\) | −2324.99 | −0.131406 | ||||||||
\(680\) | 1700.43 | 0.0958951 | ||||||||
\(681\) | −2069.66 | −0.116461 | ||||||||
\(682\) | 13515.2 | 0.758832 | ||||||||
\(683\) | −15531.3 | −0.870116 | −0.435058 | − | 0.900402i | \(-0.643272\pi\) | ||||
−0.435058 | + | 0.900402i | \(0.643272\pi\) | |||||||
\(684\) | −7349.28 | −0.410828 | ||||||||
\(685\) | 20146.7 | 1.12375 | ||||||||
\(686\) | −57279.9 | −3.18798 | ||||||||
\(687\) | 15491.6 | 0.860324 | ||||||||
\(688\) | −1816.57 | −0.100663 | ||||||||
\(689\) | −830.859 | −0.0459408 | ||||||||
\(690\) | −13605.6 | −0.750663 | ||||||||
\(691\) | 25847.6 | 1.42299 | 0.711496 | − | 0.702690i | \(-0.248018\pi\) | ||||
0.711496 | + | 0.702690i | \(0.248018\pi\) | |||||||
\(692\) | 29700.1 | 1.63154 | ||||||||
\(693\) | 10111.1 | 0.554242 | ||||||||
\(694\) | −38743.6 | −2.11915 | ||||||||
\(695\) | 24059.6 | 1.31314 | ||||||||
\(696\) | −16118.8 | −0.877848 | ||||||||
\(697\) | 3582.03 | 0.194662 | ||||||||
\(698\) | −37654.2 | −2.04188 | ||||||||
\(699\) | 31175.3 | 1.68692 | ||||||||
\(700\) | −7215.92 | −0.389623 | ||||||||
\(701\) | −22664.4 | −1.22115 | −0.610573 | − | 0.791960i | \(-0.709061\pi\) | ||||
−0.610573 | + | 0.791960i | \(0.709061\pi\) | |||||||
\(702\) | 1587.80 | 0.0853670 | ||||||||
\(703\) | 34835.8 | 1.86893 | ||||||||
\(704\) | −45903.2 | −2.45744 | ||||||||
\(705\) | −27515.2 | −1.46991 | ||||||||
\(706\) | 765.259 | 0.0407945 | ||||||||
\(707\) | 48394.7 | 2.57435 | ||||||||
\(708\) | −8382.71 | −0.444974 | ||||||||
\(709\) | −19054.9 | −1.00934 | −0.504669 | − | 0.863313i | \(-0.668386\pi\) | ||||
−0.504669 | + | 0.863313i | \(0.668386\pi\) | |||||||
\(710\) | −28239.9 | −1.49271 | ||||||||
\(711\) | −2989.75 | −0.157700 | ||||||||
\(712\) | 5513.14 | 0.290188 | ||||||||
\(713\) | −2836.16 | −0.148969 | ||||||||
\(714\) | 7892.56 | 0.413686 | ||||||||
\(715\) | 1660.30 | 0.0868418 | ||||||||
\(716\) | 3676.13 | 0.191876 | ||||||||
\(717\) | −22487.5 | −1.17128 | ||||||||
\(718\) | −9065.11 | −0.471179 | ||||||||
\(719\) | −14553.9 | −0.754892 | −0.377446 | − | 0.926032i | \(-0.623198\pi\) | ||||
−0.377446 | + | 0.926032i | \(0.623198\pi\) | |||||||
\(720\) | 1002.97 | 0.0519144 | ||||||||
\(721\) | 5578.18 | 0.288131 | ||||||||
\(722\) | −24097.0 | −1.24210 | ||||||||
\(723\) | −37101.0 | −1.90844 | ||||||||
\(724\) | 28881.3 | 1.48255 | ||||||||
\(725\) | 2988.60 | 0.153095 | ||||||||
\(726\) | 43922.5 | 2.24534 | ||||||||
\(727\) | 2583.82 | 0.131814 | 0.0659068 | − | 0.997826i | \(-0.479006\pi\) | ||||
0.0659068 | + | 0.997826i | \(0.479006\pi\) | |||||||
\(728\) | 1666.09 | 0.0848206 | ||||||||
\(729\) | 14116.0 | 0.717165 | ||||||||
\(730\) | −32741.7 | −1.66003 | ||||||||
\(731\) | 983.885 | 0.0497816 | ||||||||
\(732\) | 1345.96 | 0.0679621 | ||||||||
\(733\) | 26552.5 | 1.33798 | 0.668990 | − | 0.743272i | \(-0.266727\pi\) | ||||
0.668990 | + | 0.743272i | \(0.266727\pi\) | |||||||
\(734\) | 45130.8 | 2.26949 | ||||||||
\(735\) | 43247.8 | 2.17037 | ||||||||
\(736\) | 11250.8 | 0.563465 | ||||||||
\(737\) | 48375.6 | 2.41783 | ||||||||
\(738\) | −9432.99 | −0.470506 | ||||||||
\(739\) | 13965.3 | 0.695156 | 0.347578 | − | 0.937651i | \(-0.387004\pi\) | ||||
0.347578 | + | 0.937651i | \(0.387004\pi\) | |||||||
\(740\) | 38676.7 | 1.92133 | ||||||||
\(741\) | −1838.83 | −0.0911619 | ||||||||
\(742\) | −41814.0 | −2.06879 | ||||||||
\(743\) | −7580.87 | −0.374314 | −0.187157 | − | 0.982330i | \(-0.559927\pi\) | ||||
−0.187157 | + | 0.982330i | \(0.559927\pi\) | |||||||
\(744\) | −5455.67 | −0.268837 | ||||||||
\(745\) | −116.777 | −0.00574280 | ||||||||
\(746\) | −7125.09 | −0.349689 | ||||||||
\(747\) | −2539.85 | −0.124402 | ||||||||
\(748\) | 6217.00 | 0.303898 | ||||||||
\(749\) | 17923.8 | 0.874395 | ||||||||
\(750\) | 37709.6 | 1.83595 | ||||||||
\(751\) | −18089.5 | −0.878954 | −0.439477 | − | 0.898254i | \(-0.644836\pi\) | ||||
−0.439477 | + | 0.898254i | \(0.644836\pi\) | |||||||
\(752\) | 8143.57 | 0.394901 | ||||||||
\(753\) | −25876.7 | −1.25232 | ||||||||
\(754\) | −2101.96 | −0.101524 | ||||||||
\(755\) | 22384.4 | 1.07901 | ||||||||
\(756\) | 47800.0 | 2.29956 | ||||||||
\(757\) | −24935.6 | −1.19722 | −0.598612 | − | 0.801039i | \(-0.704281\pi\) | ||||
−0.598612 | + | 0.801039i | \(0.704281\pi\) | |||||||
\(758\) | 923.342 | 0.0442444 | ||||||||
\(759\) | −16330.1 | −0.780955 | ||||||||
\(760\) | −19937.8 | −0.951605 | ||||||||
\(761\) | 1982.92 | 0.0944556 | 0.0472278 | − | 0.998884i | \(-0.484961\pi\) | ||||
0.0472278 | + | 0.998884i | \(0.484961\pi\) | |||||||
\(762\) | −46499.5 | −2.21063 | ||||||||
\(763\) | 37565.2 | 1.78237 | ||||||||
\(764\) | 54072.4 | 2.56057 | ||||||||
\(765\) | −543.223 | −0.0256735 | ||||||||
\(766\) | 12799.6 | 0.603744 | ||||||||
\(767\) | −358.860 | −0.0168940 | ||||||||
\(768\) | 12161.2 | 0.571393 | ||||||||
\(769\) | −8136.59 | −0.381551 | −0.190776 | − | 0.981634i | \(-0.561100\pi\) | ||||
−0.190776 | + | 0.981634i | \(0.561100\pi\) | |||||||
\(770\) | 83556.9 | 3.91063 | ||||||||
\(771\) | 18294.8 | 0.854568 | ||||||||
\(772\) | −57855.0 | −2.69721 | ||||||||
\(773\) | −36988.0 | −1.72104 | −0.860522 | − | 0.509414i | \(-0.829862\pi\) | ||||
−0.860522 | + | 0.509414i | \(0.829862\pi\) | |||||||
\(774\) | −2590.98 | −0.120324 | ||||||||
\(775\) | 1011.54 | 0.0468845 | ||||||||
\(776\) | 1235.87 | 0.0571714 | ||||||||
\(777\) | 58932.7 | 2.72098 | ||||||||
\(778\) | 10088.1 | 0.464878 | ||||||||
\(779\) | −41999.7 | −1.93170 | ||||||||
\(780\) | −2041.57 | −0.0937178 | ||||||||
\(781\) | −33894.8 | −1.55295 | ||||||||
\(782\) | −2180.98 | −0.0997337 | ||||||||
\(783\) | −19797.2 | −0.903568 | ||||||||
\(784\) | −12799.9 | −0.583085 | ||||||||
\(785\) | −18319.3 | −0.832921 | ||||||||
\(786\) | 31352.2 | 1.42277 | ||||||||
\(787\) | −2077.02 | −0.0940759 | −0.0470380 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470380 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(788\) | −41576.8 | −1.87958 | ||||||||
\(789\) | 27017.3 | 1.21907 | ||||||||
\(790\) | −24706.9 | −1.11270 | ||||||||
\(791\) | 63890.9 | 2.87193 | ||||||||
\(792\) | −5374.65 | −0.241136 | ||||||||
\(793\) | 57.6201 | 0.00258026 | ||||||||
\(794\) | 32870.0 | 1.46916 | ||||||||
\(795\) | 16820.4 | 0.750389 | ||||||||
\(796\) | 26701.4 | 1.18895 | ||||||||
\(797\) | −17824.8 | −0.792204 | −0.396102 | − | 0.918206i | \(-0.629637\pi\) | ||||
−0.396102 | + | 0.918206i | \(0.629637\pi\) | |||||||
\(798\) | −92541.2 | −4.10517 | ||||||||
\(799\) | −4410.69 | −0.195293 | ||||||||
\(800\) | −4012.68 | −0.177337 | ||||||||
\(801\) | −1761.23 | −0.0776905 | ||||||||
\(802\) | −2902.54 | −0.127796 | ||||||||
\(803\) | −39298.1 | −1.72702 | ||||||||
\(804\) | −59484.4 | −2.60927 | ||||||||
\(805\) | −17534.4 | −0.767710 | ||||||||
\(806\) | −711.441 | −0.0310911 | ||||||||
\(807\) | 22060.8 | 0.962302 | ||||||||
\(808\) | −25724.6 | −1.12003 | ||||||||
\(809\) | 785.015 | 0.0341158 | 0.0170579 | − | 0.999855i | \(-0.494570\pi\) | ||||
0.0170579 | + | 0.999855i | \(0.494570\pi\) | |||||||
\(810\) | −39074.8 | −1.69500 | ||||||||
\(811\) | −14206.0 | −0.615092 | −0.307546 | − | 0.951533i | \(-0.599508\pi\) | ||||
−0.307546 | + | 0.951533i | \(0.599508\pi\) | |||||||
\(812\) | −63278.5 | −2.73478 | ||||||||
\(813\) | 30337.3 | 1.30870 | ||||||||
\(814\) | 77603.6 | 3.34153 | ||||||||
\(815\) | 29335.9 | 1.26085 | ||||||||
\(816\) | 939.669 | 0.0403125 | ||||||||
\(817\) | −11536.2 | −0.494002 | ||||||||
\(818\) | −8718.80 | −0.372672 | ||||||||
\(819\) | −532.251 | −0.0227086 | ||||||||
\(820\) | −46630.5 | −1.98586 | ||||||||
\(821\) | −17779.1 | −0.755780 | −0.377890 | − | 0.925851i | \(-0.623350\pi\) | ||||
−0.377890 | + | 0.925851i | \(0.623350\pi\) | |||||||
\(822\) | −49706.6 | −2.10914 | ||||||||
\(823\) | 38036.5 | 1.61102 | 0.805510 | − | 0.592583i | \(-0.201892\pi\) | ||||
0.805510 | + | 0.592583i | \(0.201892\pi\) | |||||||
\(824\) | −2965.13 | −0.125358 | ||||||||
\(825\) | 5824.25 | 0.245787 | ||||||||
\(826\) | −18060.1 | −0.760763 | ||||||||
\(827\) | 27945.2 | 1.17503 | 0.587515 | − | 0.809213i | \(-0.300106\pi\) | ||||
0.587515 | + | 0.809213i | \(0.300106\pi\) | |||||||
\(828\) | 3435.66 | 0.144200 | ||||||||
\(829\) | 8714.87 | 0.365115 | 0.182557 | − | 0.983195i | \(-0.441562\pi\) | ||||
0.182557 | + | 0.983195i | \(0.441562\pi\) | |||||||
\(830\) | −20989.0 | −0.877757 | ||||||||
\(831\) | −19818.9 | −0.827327 | ||||||||
\(832\) | 2416.35 | 0.100687 | ||||||||
\(833\) | 6932.62 | 0.288357 | ||||||||
\(834\) | −59360.5 | −2.46461 | ||||||||
\(835\) | 25888.5 | 1.07294 | ||||||||
\(836\) | −72895.0 | −3.01570 | ||||||||
\(837\) | −6700.67 | −0.276713 | ||||||||
\(838\) | 13916.0 | 0.573654 | ||||||||
\(839\) | −17155.4 | −0.705924 | −0.352962 | − | 0.935638i | \(-0.614826\pi\) | ||||
−0.352962 | + | 0.935638i | \(0.614826\pi\) | |||||||
\(840\) | −33729.4 | −1.38544 | ||||||||
\(841\) | 1818.90 | 0.0745787 | ||||||||
\(842\) | −41664.0 | −1.70527 | ||||||||
\(843\) | 14786.4 | 0.604116 | ||||||||
\(844\) | −58931.2 | −2.40343 | ||||||||
\(845\) | 22589.6 | 0.919650 | ||||||||
\(846\) | 11615.2 | 0.472032 | ||||||||
\(847\) | 56605.7 | 2.29633 | ||||||||
\(848\) | −4978.28 | −0.201598 | ||||||||
\(849\) | 8438.26 | 0.341108 | ||||||||
\(850\) | 777.863 | 0.0313888 | ||||||||
\(851\) | −16285.1 | −0.655989 | ||||||||
\(852\) | 41678.2 | 1.67591 | ||||||||
\(853\) | −12274.2 | −0.492685 | −0.246342 | − | 0.969183i | \(-0.579229\pi\) | ||||
−0.246342 | + | 0.969183i | \(0.579229\pi\) | |||||||
\(854\) | 2899.80 | 0.116193 | ||||||||
\(855\) | 6369.35 | 0.254769 | ||||||||
\(856\) | −9527.55 | −0.380426 | ||||||||
\(857\) | −7027.38 | −0.280106 | −0.140053 | − | 0.990144i | \(-0.544727\pi\) | ||||
−0.140053 | + | 0.990144i | \(0.544727\pi\) | |||||||
\(858\) | −4096.35 | −0.162992 | ||||||||
\(859\) | 23043.6 | 0.915292 | 0.457646 | − | 0.889134i | \(-0.348693\pi\) | ||||
0.457646 | + | 0.889134i | \(0.348693\pi\) | |||||||
\(860\) | −12808.1 | −0.507852 | ||||||||
\(861\) | −71052.2 | −2.81237 | ||||||||
\(862\) | 67487.2 | 2.66662 | ||||||||
\(863\) | 15303.3 | 0.603628 | 0.301814 | − | 0.953367i | \(-0.402408\pi\) | ||||
0.301814 | + | 0.953367i | \(0.402408\pi\) | |||||||
\(864\) | 26580.9 | 1.04665 | ||||||||
\(865\) | −25740.0 | −1.01177 | ||||||||
\(866\) | −71445.4 | −2.80348 | ||||||||
\(867\) | 27531.0 | 1.07843 | ||||||||
\(868\) | −21417.6 | −0.837512 | ||||||||
\(869\) | −29654.3 | −1.15760 | ||||||||
\(870\) | 42553.4 | 1.65827 | ||||||||
\(871\) | −2546.50 | −0.0990641 | ||||||||
\(872\) | −19968.1 | −0.775463 | ||||||||
\(873\) | −394.811 | −0.0153062 | ||||||||
\(874\) | 25572.3 | 0.989697 | ||||||||
\(875\) | 48598.6 | 1.87764 | ||||||||
\(876\) | 48322.3 | 1.86376 | ||||||||
\(877\) | 35190.6 | 1.35496 | 0.677480 | − | 0.735541i | \(-0.263072\pi\) | ||||
0.677480 | + | 0.735541i | \(0.263072\pi\) | |||||||
\(878\) | 44900.2 | 1.72586 | ||||||||
\(879\) | −42665.3 | −1.63716 | ||||||||
\(880\) | 9948.08 | 0.381079 | ||||||||
\(881\) | −24727.9 | −0.945635 | −0.472818 | − | 0.881160i | \(-0.656763\pi\) | ||||
−0.472818 | + | 0.881160i | \(0.656763\pi\) | |||||||
\(882\) | −18256.5 | −0.696971 | ||||||||
\(883\) | −20288.2 | −0.773219 | −0.386609 | − | 0.922244i | \(-0.626354\pi\) | ||||
−0.386609 | + | 0.922244i | \(0.626354\pi\) | |||||||
\(884\) | −327.263 | −0.0124514 | ||||||||
\(885\) | 7264.99 | 0.275943 | ||||||||
\(886\) | 17543.8 | 0.665232 | ||||||||
\(887\) | −7075.42 | −0.267835 | −0.133917 | − | 0.990993i | \(-0.542756\pi\) | ||||
−0.133917 | + | 0.990993i | \(0.542756\pi\) | |||||||
\(888\) | −31326.2 | −1.18383 | ||||||||
\(889\) | −59926.7 | −2.26083 | ||||||||
\(890\) | −14554.6 | −0.548169 | ||||||||
\(891\) | −46899.4 | −1.76340 | ||||||||
\(892\) | 51736.8 | 1.94201 | ||||||||
\(893\) | 51715.9 | 1.93797 | ||||||||
\(894\) | 288.116 | 0.0107786 | ||||||||
\(895\) | −3185.97 | −0.118989 | ||||||||
\(896\) | 64535.6 | 2.40623 | ||||||||
\(897\) | 859.618 | 0.0319976 | ||||||||
\(898\) | −4913.65 | −0.182596 | ||||||||
\(899\) | 8870.47 | 0.329084 | ||||||||
\(900\) | −1225.35 | −0.0453834 | ||||||||
\(901\) | 2696.31 | 0.0996973 | ||||||||
\(902\) | −93562.7 | −3.45377 | ||||||||
\(903\) | −19516.1 | −0.719219 | ||||||||
\(904\) | −33961.8 | −1.24950 | ||||||||
\(905\) | −25030.4 | −0.919380 | ||||||||
\(906\) | −55227.3 | −2.02517 | ||||||||
\(907\) | −33322.0 | −1.21989 | −0.609943 | − | 0.792445i | \(-0.708808\pi\) | ||||
−0.609943 | + | 0.792445i | \(0.708808\pi\) | |||||||
\(908\) | 4318.90 | 0.157850 | ||||||||
\(909\) | 8218.00 | 0.299861 | ||||||||
\(910\) | −4398.44 | −0.160227 | ||||||||
\(911\) | 12674.4 | 0.460945 | 0.230472 | − | 0.973079i | \(-0.425973\pi\) | ||||
0.230472 | + | 0.973079i | \(0.425973\pi\) | |||||||
\(912\) | −11017.7 | −0.400037 | ||||||||
\(913\) | −25192.0 | −0.913178 | ||||||||
\(914\) | 44298.6 | 1.60314 | ||||||||
\(915\) | −1166.50 | −0.0421456 | ||||||||
\(916\) | −32327.4 | −1.16608 | ||||||||
\(917\) | 40405.5 | 1.45508 | ||||||||
\(918\) | −5152.75 | −0.185257 | ||||||||
\(919\) | 38442.0 | 1.37985 | 0.689926 | − | 0.723880i | \(-0.257643\pi\) | ||||
0.689926 | + | 0.723880i | \(0.257643\pi\) | |||||||
\(920\) | 9320.56 | 0.334011 | ||||||||
\(921\) | 8071.42 | 0.288776 | ||||||||
\(922\) | 6749.06 | 0.241072 | ||||||||
\(923\) | 1784.23 | 0.0636279 | ||||||||
\(924\) | −123319. | −4.39057 | ||||||||
\(925\) | 5808.20 | 0.206457 | ||||||||
\(926\) | −38247.2 | −1.35732 | ||||||||
\(927\) | 947.243 | 0.0335615 | ||||||||
\(928\) | −35188.4 | −1.24474 | ||||||||
\(929\) | −3869.62 | −0.136661 | −0.0683305 | − | 0.997663i | \(-0.521767\pi\) | ||||
−0.0683305 | + | 0.997663i | \(0.521767\pi\) | |||||||
\(930\) | 14402.9 | 0.507837 | ||||||||
\(931\) | −81285.8 | −2.86148 | ||||||||
\(932\) | −65055.6 | −2.28644 | ||||||||
\(933\) | −26948.0 | −0.945593 | ||||||||
\(934\) | 65942.4 | 2.31017 | ||||||||
\(935\) | −5388.04 | −0.188458 | ||||||||
\(936\) | 282.922 | 0.00987992 | ||||||||
\(937\) | −1018.02 | −0.0354933 | −0.0177467 | − | 0.999843i | \(-0.505649\pi\) | ||||
−0.0177467 | + | 0.999843i | \(0.505649\pi\) | |||||||
\(938\) | −128156. | −4.46101 | ||||||||
\(939\) | 49450.4 | 1.71859 | ||||||||
\(940\) | 57417.9 | 1.99230 | ||||||||
\(941\) | 52160.0 | 1.80698 | 0.903489 | − | 0.428610i | \(-0.140997\pi\) | ||||
0.903489 | + | 0.428610i | \(0.140997\pi\) | |||||||
\(942\) | 45197.8 | 1.56330 | ||||||||
\(943\) | 19634.1 | 0.678022 | ||||||||
\(944\) | −2150.19 | −0.0741342 | ||||||||
\(945\) | −41426.5 | −1.42604 | ||||||||
\(946\) | −25699.1 | −0.883245 | ||||||||
\(947\) | 1706.03 | 0.0585411 | 0.0292705 | − | 0.999572i | \(-0.490682\pi\) | ||||
0.0292705 | + | 0.999572i | \(0.490682\pi\) | |||||||
\(948\) | 36464.0 | 1.24926 | ||||||||
\(949\) | 2068.65 | 0.0707601 | ||||||||
\(950\) | −9120.54 | −0.311483 | ||||||||
\(951\) | 30100.1 | 1.02635 | ||||||||
\(952\) | −5406.81 | −0.184071 | ||||||||
\(953\) | −12115.9 | −0.411829 | −0.205915 | − | 0.978570i | \(-0.566017\pi\) | ||||
−0.205915 | + | 0.978570i | \(0.566017\pi\) | |||||||
\(954\) | −7100.53 | −0.240973 | ||||||||
\(955\) | −46862.6 | −1.58789 | ||||||||
\(956\) | 46926.1 | 1.58755 | ||||||||
\(957\) | 51074.6 | 1.72519 | ||||||||
\(958\) | 36206.4 | 1.22106 | ||||||||
\(959\) | −64059.9 | −2.15704 | ||||||||
\(960\) | −48918.1 | −1.64461 | ||||||||
\(961\) | −26788.7 | −0.899220 | ||||||||
\(962\) | −4085.06 | −0.136910 | ||||||||
\(963\) | 3043.68 | 0.101850 | ||||||||
\(964\) | 77421.2 | 2.58669 | ||||||||
\(965\) | 50140.8 | 1.67263 | ||||||||
\(966\) | 43261.4 | 1.44090 | ||||||||
\(967\) | −24059.0 | −0.800088 | −0.400044 | − | 0.916496i | \(-0.631005\pi\) | ||||
−0.400044 | + | 0.916496i | \(0.631005\pi\) | |||||||
\(968\) | −30089.2 | −0.999074 | ||||||||
\(969\) | 5967.38 | 0.197833 | ||||||||
\(970\) | −3262.66 | −0.107998 | ||||||||
\(971\) | −34143.9 | −1.12846 | −0.564228 | − | 0.825619i | \(-0.690826\pi\) | ||||
−0.564228 | + | 0.825619i | \(0.690826\pi\) | |||||||
\(972\) | 18345.3 | 0.605377 | ||||||||
\(973\) | −76501.5 | −2.52058 | ||||||||
\(974\) | 38441.2 | 1.26462 | ||||||||
\(975\) | −306.589 | −0.0100705 | ||||||||
\(976\) | 345.244 | 0.0113227 | ||||||||
\(977\) | 10022.0 | 0.328181 | 0.164091 | − | 0.986445i | \(-0.447531\pi\) | ||||
0.164091 | + | 0.986445i | \(0.447531\pi\) | |||||||
\(978\) | −72378.2 | −2.36646 | ||||||||
\(979\) | −17469.1 | −0.570290 | ||||||||
\(980\) | −90248.1 | −2.94170 | ||||||||
\(981\) | 6379.02 | 0.207611 | ||||||||
\(982\) | 23187.9 | 0.753519 | ||||||||
\(983\) | 983.000 | 0.0318950 | ||||||||
\(984\) | 37768.4 | 1.22359 | ||||||||
\(985\) | 36033.1 | 1.16559 | ||||||||
\(986\) | 6821.31 | 0.220319 | ||||||||
\(987\) | 87489.2 | 2.82149 | ||||||||
\(988\) | 3837.20 | 0.123560 | ||||||||
\(989\) | 5392.96 | 0.173393 | ||||||||
\(990\) | 14189.0 | 0.455511 | ||||||||
\(991\) | 49079.5 | 1.57322 | 0.786610 | − | 0.617450i | \(-0.211834\pi\) | ||||
0.786610 | + | 0.617450i | \(0.211834\pi\) | |||||||
\(992\) | −11910.0 | −0.381194 | ||||||||
\(993\) | −42972.2 | −1.37330 | ||||||||
\(994\) | 89793.4 | 2.86527 | ||||||||
\(995\) | −23141.1 | −0.737309 | ||||||||
\(996\) | 30976.9 | 0.985483 | ||||||||
\(997\) | −52518.0 | −1.66827 | −0.834134 | − | 0.551563i | \(-0.814032\pi\) | ||||
−0.834134 | + | 0.551563i | \(0.814032\pi\) | |||||||
\(998\) | −37089.4 | −1.17640 | ||||||||
\(999\) | −38474.9 | −1.21851 |
(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 | 983.4.a.a.1.16 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.4.a.a.1.16 | ✓ | 109 | 1.1 | even | 1 | trivial |