Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.94581 | −0.687949 | −0.343974 | − | 0.938979i | \(-0.611773\pi\) | ||||
−0.343974 | + | 0.938979i | \(0.611773\pi\) | |||||||
\(3\) | −1.92433 | −0.370337 | −0.185168 | − | 0.982707i | \(-0.559283\pi\) | ||||
−0.185168 | + | 0.982707i | \(0.559283\pi\) | |||||||
\(4\) | −4.21381 | −0.526727 | ||||||||
\(5\) | 20.3652 | 1.82152 | 0.910760 | − | 0.412936i | \(-0.135497\pi\) | ||||
0.910760 | + | 0.412936i | \(0.135497\pi\) | |||||||
\(6\) | 3.74438 | 0.254773 | ||||||||
\(7\) | −13.1013 | −0.707401 | −0.353701 | − | 0.935359i | \(-0.615077\pi\) | ||||
−0.353701 | + | 0.935359i | \(0.615077\pi\) | |||||||
\(8\) | 23.7658 | 1.05031 | ||||||||
\(9\) | −23.2970 | −0.862851 | ||||||||
\(10\) | −39.6269 | −1.25311 | ||||||||
\(11\) | −10.4869 | −0.287448 | −0.143724 | − | 0.989618i | \(-0.545908\pi\) | ||||
−0.143724 | + | 0.989618i | \(0.545908\pi\) | |||||||
\(12\) | 8.10875 | 0.195066 | ||||||||
\(13\) | −22.0421 | −0.470259 | −0.235130 | − | 0.971964i | \(-0.575551\pi\) | ||||
−0.235130 | + | 0.971964i | \(0.575551\pi\) | |||||||
\(14\) | 25.4926 | 0.486656 | ||||||||
\(15\) | −39.1893 | −0.674576 | ||||||||
\(16\) | −12.5333 | −0.195832 | ||||||||
\(17\) | −32.5210 | −0.463970 | −0.231985 | − | 0.972719i | \(-0.574522\pi\) | ||||
−0.231985 | + | 0.972719i | \(0.574522\pi\) | |||||||
\(18\) | 45.3315 | 0.593597 | ||||||||
\(19\) | 81.0332 | 0.978436 | 0.489218 | − | 0.872162i | \(-0.337282\pi\) | ||||
0.489218 | + | 0.872162i | \(0.337282\pi\) | |||||||
\(20\) | −85.8152 | −0.959443 | ||||||||
\(21\) | 25.2111 | 0.261977 | ||||||||
\(22\) | 20.4056 | 0.197749 | ||||||||
\(23\) | −43.2090 | −0.391726 | −0.195863 | − | 0.980631i | \(-0.562751\pi\) | ||||
−0.195863 | + | 0.980631i | \(0.562751\pi\) | |||||||
\(24\) | −45.7331 | −0.388968 | ||||||||
\(25\) | 289.742 | 2.31794 | ||||||||
\(26\) | 42.8897 | 0.323514 | ||||||||
\(27\) | 96.7878 | 0.689882 | ||||||||
\(28\) | 55.2063 | 0.372607 | ||||||||
\(29\) | 263.358 | 1.68636 | 0.843180 | − | 0.537631i | \(-0.180681\pi\) | ||||
0.843180 | + | 0.537631i | \(0.180681\pi\) | |||||||
\(30\) | 76.2551 | 0.464074 | ||||||||
\(31\) | −269.983 | −1.56421 | −0.782103 | − | 0.623149i | \(-0.785853\pi\) | ||||
−0.782103 | + | 0.623149i | \(0.785853\pi\) | |||||||
\(32\) | −165.739 | −0.915587 | ||||||||
\(33\) | 20.1803 | 0.106452 | ||||||||
\(34\) | 63.2797 | 0.319188 | ||||||||
\(35\) | −266.810 | −1.28855 | ||||||||
\(36\) | 98.1691 | 0.454487 | ||||||||
\(37\) | 228.341 | 1.01457 | 0.507285 | − | 0.861778i | \(-0.330649\pi\) | ||||
0.507285 | + | 0.861778i | \(0.330649\pi\) | |||||||
\(38\) | −157.675 | −0.673114 | ||||||||
\(39\) | 42.4161 | 0.174154 | ||||||||
\(40\) | 483.995 | 1.91316 | ||||||||
\(41\) | 23.1758 | 0.0882792 | 0.0441396 | − | 0.999025i | \(-0.485945\pi\) | ||||
0.0441396 | + | 0.999025i | \(0.485945\pi\) | |||||||
\(42\) | −49.0560 | −0.180226 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 44.1899 | 0.151406 | ||||||||
\(45\) | −474.448 | −1.57170 | ||||||||
\(46\) | 84.0766 | 0.269487 | ||||||||
\(47\) | 143.455 | 0.445213 | 0.222606 | − | 0.974908i | \(-0.428544\pi\) | ||||
0.222606 | + | 0.974908i | \(0.428544\pi\) | |||||||
\(48\) | 24.1181 | 0.0725238 | ||||||||
\(49\) | −171.357 | −0.499583 | ||||||||
\(50\) | −563.784 | −1.59462 | ||||||||
\(51\) | 62.5810 | 0.171825 | ||||||||
\(52\) | 92.8812 | 0.247698 | ||||||||
\(53\) | −438.723 | −1.13704 | −0.568521 | − | 0.822669i | \(-0.692484\pi\) | ||||
−0.568521 | + | 0.822669i | \(0.692484\pi\) | |||||||
\(54\) | −188.331 | −0.474603 | ||||||||
\(55\) | −213.568 | −0.523592 | ||||||||
\(56\) | −311.362 | −0.742990 | ||||||||
\(57\) | −155.934 | −0.362351 | ||||||||
\(58\) | −512.446 | −1.16013 | ||||||||
\(59\) | −446.768 | −0.985835 | −0.492917 | − | 0.870076i | \(-0.664069\pi\) | ||||
−0.492917 | + | 0.870076i | \(0.664069\pi\) | |||||||
\(60\) | 165.137 | 0.355317 | ||||||||
\(61\) | 680.512 | 1.42837 | 0.714185 | − | 0.699957i | \(-0.246797\pi\) | ||||
0.714185 | + | 0.699957i | \(0.246797\pi\) | |||||||
\(62\) | 525.336 | 1.07609 | ||||||||
\(63\) | 305.220 | 0.610382 | ||||||||
\(64\) | 422.763 | 0.825709 | ||||||||
\(65\) | −448.892 | −0.856587 | ||||||||
\(66\) | −39.2670 | −0.0732338 | ||||||||
\(67\) | 91.4540 | 0.166759 | 0.0833797 | − | 0.996518i | \(-0.473429\pi\) | ||||
0.0833797 | + | 0.996518i | \(0.473429\pi\) | |||||||
\(68\) | 137.037 | 0.244386 | ||||||||
\(69\) | 83.1482 | 0.145071 | ||||||||
\(70\) | 519.162 | 0.886453 | ||||||||
\(71\) | −1024.93 | −1.71319 | −0.856596 | − | 0.515987i | \(-0.827425\pi\) | ||||
−0.856596 | + | 0.515987i | \(0.827425\pi\) | |||||||
\(72\) | −553.671 | −0.906260 | ||||||||
\(73\) | −342.419 | −0.549002 | −0.274501 | − | 0.961587i | \(-0.588513\pi\) | ||||
−0.274501 | + | 0.961587i | \(0.588513\pi\) | |||||||
\(74\) | −444.310 | −0.697972 | ||||||||
\(75\) | −557.558 | −0.858417 | ||||||||
\(76\) | −341.459 | −0.515368 | ||||||||
\(77\) | 137.392 | 0.203341 | ||||||||
\(78\) | −82.5339 | −0.119809 | ||||||||
\(79\) | 816.013 | 1.16213 | 0.581067 | − | 0.813855i | \(-0.302635\pi\) | ||||
0.581067 | + | 0.813855i | \(0.302635\pi\) | |||||||
\(80\) | −255.242 | −0.356712 | ||||||||
\(81\) | 442.767 | 0.607362 | ||||||||
\(82\) | −45.0957 | −0.0607316 | ||||||||
\(83\) | 1111.95 | 1.47051 | 0.735255 | − | 0.677791i | \(-0.237062\pi\) | ||||
0.735255 | + | 0.677791i | \(0.237062\pi\) | |||||||
\(84\) | −106.235 | −0.137990 | ||||||||
\(85\) | −662.297 | −0.845132 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −506.788 | −0.624521 | ||||||||
\(88\) | −249.230 | −0.301909 | ||||||||
\(89\) | −1266.79 | −1.50876 | −0.754380 | − | 0.656438i | \(-0.772062\pi\) | ||||
−0.754380 | + | 0.656438i | \(0.772062\pi\) | |||||||
\(90\) | 923.186 | 1.08125 | ||||||||
\(91\) | 288.779 | 0.332662 | ||||||||
\(92\) | 182.075 | 0.206333 | ||||||||
\(93\) | 519.535 | 0.579283 | ||||||||
\(94\) | −279.136 | −0.306283 | ||||||||
\(95\) | 1650.26 | 1.78224 | ||||||||
\(96\) | 318.936 | 0.339076 | ||||||||
\(97\) | −632.249 | −0.661806 | −0.330903 | − | 0.943665i | \(-0.607353\pi\) | ||||
−0.330903 | + | 0.943665i | \(0.607353\pi\) | |||||||
\(98\) | 333.429 | 0.343688 | ||||||||
\(99\) | 244.313 | 0.248024 | ||||||||
\(100\) | −1220.92 | −1.22092 | ||||||||
\(101\) | 1812.13 | 1.78529 | 0.892644 | − | 0.450763i | \(-0.148848\pi\) | ||||
0.892644 | + | 0.450763i | \(0.148848\pi\) | |||||||
\(102\) | −121.771 | −0.118207 | ||||||||
\(103\) | 231.655 | 0.221608 | 0.110804 | − | 0.993842i | \(-0.464657\pi\) | ||||
0.110804 | + | 0.993842i | \(0.464657\pi\) | |||||||
\(104\) | −523.847 | −0.493918 | ||||||||
\(105\) | 513.429 | 0.477196 | ||||||||
\(106\) | 853.672 | 0.782226 | ||||||||
\(107\) | −1562.15 | −1.41139 | −0.705697 | − | 0.708514i | \(-0.749366\pi\) | ||||
−0.705697 | + | 0.708514i | \(0.749366\pi\) | |||||||
\(108\) | −407.846 | −0.363379 | ||||||||
\(109\) | 5.29886 | 0.00465632 | 0.00232816 | − | 0.999997i | \(-0.499259\pi\) | ||||
0.00232816 | + | 0.999997i | \(0.499259\pi\) | |||||||
\(110\) | 415.564 | 0.360204 | ||||||||
\(111\) | −439.403 | −0.375733 | ||||||||
\(112\) | 164.201 | 0.138532 | ||||||||
\(113\) | 509.549 | 0.424198 | 0.212099 | − | 0.977248i | \(-0.431970\pi\) | ||||
0.212099 | + | 0.977248i | \(0.431970\pi\) | |||||||
\(114\) | 303.419 | 0.249279 | ||||||||
\(115\) | −879.961 | −0.713537 | ||||||||
\(116\) | −1109.74 | −0.888251 | ||||||||
\(117\) | 513.514 | 0.405764 | ||||||||
\(118\) | 869.327 | 0.678204 | ||||||||
\(119\) | 426.066 | 0.328213 | ||||||||
\(120\) | −931.365 | −0.708513 | ||||||||
\(121\) | −1221.02 | −0.917374 | ||||||||
\(122\) | −1324.15 | −0.982645 | ||||||||
\(123\) | −44.5978 | −0.0326930 | ||||||||
\(124\) | 1137.66 | 0.823909 | ||||||||
\(125\) | 3355.01 | 2.40065 | ||||||||
\(126\) | −593.900 | −0.419911 | ||||||||
\(127\) | 898.096 | 0.627505 | 0.313752 | − | 0.949505i | \(-0.398414\pi\) | ||||
0.313752 | + | 0.949505i | \(0.398414\pi\) | |||||||
\(128\) | 503.294 | 0.347542 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 873.459 | 0.589288 | ||||||||
\(131\) | 1158.48 | 0.772648 | 0.386324 | − | 0.922363i | \(-0.373745\pi\) | ||||
0.386324 | + | 0.922363i | \(0.373745\pi\) | |||||||
\(132\) | −85.0358 | −0.0560714 | ||||||||
\(133\) | −1061.64 | −0.692147 | ||||||||
\(134\) | −177.952 | −0.114722 | ||||||||
\(135\) | 1971.10 | 1.25663 | ||||||||
\(136\) | −772.887 | −0.487313 | ||||||||
\(137\) | 553.843 | 0.345387 | 0.172694 | − | 0.984976i | \(-0.444753\pi\) | ||||
0.172694 | + | 0.984976i | \(0.444753\pi\) | |||||||
\(138\) | −161.791 | −0.0998011 | ||||||||
\(139\) | −2176.41 | −1.32806 | −0.664030 | − | 0.747706i | \(-0.731155\pi\) | ||||
−0.664030 | + | 0.747706i | \(0.731155\pi\) | |||||||
\(140\) | 1124.29 | 0.678712 | ||||||||
\(141\) | −276.053 | −0.164879 | ||||||||
\(142\) | 1994.32 | 1.17859 | ||||||||
\(143\) | 231.153 | 0.135175 | ||||||||
\(144\) | 291.987 | 0.168974 | ||||||||
\(145\) | 5363.35 | 3.07174 | ||||||||
\(146\) | 666.284 | 0.377685 | ||||||||
\(147\) | 329.747 | 0.185014 | ||||||||
\(148\) | −962.188 | −0.534401 | ||||||||
\(149\) | 496.910 | 0.273211 | 0.136606 | − | 0.990626i | \(-0.456381\pi\) | ||||
0.136606 | + | 0.990626i | \(0.456381\pi\) | |||||||
\(150\) | 1084.90 | 0.590547 | ||||||||
\(151\) | −1109.84 | −0.598131 | −0.299065 | − | 0.954233i | \(-0.596675\pi\) | ||||
−0.299065 | + | 0.954233i | \(0.596675\pi\) | |||||||
\(152\) | 1925.82 | 1.02766 | ||||||||
\(153\) | 757.640 | 0.400337 | ||||||||
\(154\) | −267.339 | −0.139888 | ||||||||
\(155\) | −5498.26 | −2.84923 | ||||||||
\(156\) | −178.734 | −0.0917318 | ||||||||
\(157\) | 1707.18 | 0.867821 | 0.433910 | − | 0.900956i | \(-0.357133\pi\) | ||||
0.433910 | + | 0.900956i | \(0.357133\pi\) | |||||||
\(158\) | −1587.81 | −0.799489 | ||||||||
\(159\) | 844.245 | 0.421088 | ||||||||
\(160\) | −3375.31 | −1.66776 | ||||||||
\(161\) | 566.092 | 0.277108 | ||||||||
\(162\) | −861.541 | −0.417834 | ||||||||
\(163\) | −3329.39 | −1.59987 | −0.799933 | − | 0.600089i | \(-0.795132\pi\) | ||||
−0.799933 | + | 0.600089i | \(0.795132\pi\) | |||||||
\(164\) | −97.6584 | −0.0464990 | ||||||||
\(165\) | 410.975 | 0.193905 | ||||||||
\(166\) | −2163.65 | −1.01164 | ||||||||
\(167\) | −271.350 | −0.125735 | −0.0628673 | − | 0.998022i | \(-0.520024\pi\) | ||||
−0.0628673 | + | 0.998022i | \(0.520024\pi\) | |||||||
\(168\) | 599.161 | 0.275157 | ||||||||
\(169\) | −1711.15 | −0.778856 | ||||||||
\(170\) | 1288.71 | 0.581407 | ||||||||
\(171\) | −1887.83 | −0.844244 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 968.753 | 0.425739 | 0.212870 | − | 0.977081i | \(-0.431719\pi\) | ||||
0.212870 | + | 0.977081i | \(0.431719\pi\) | |||||||
\(174\) | 986.114 | 0.429638 | ||||||||
\(175\) | −3795.98 | −1.63971 | ||||||||
\(176\) | 131.435 | 0.0562915 | ||||||||
\(177\) | 859.727 | 0.365091 | ||||||||
\(178\) | 2464.94 | 1.03795 | ||||||||
\(179\) | 3974.82 | 1.65973 | 0.829867 | − | 0.557962i | \(-0.188417\pi\) | ||||
0.829867 | + | 0.557962i | \(0.188417\pi\) | |||||||
\(180\) | 1999.23 | 0.827856 | ||||||||
\(181\) | −612.811 | −0.251657 | −0.125828 | − | 0.992052i | \(-0.540159\pi\) | ||||
−0.125828 | + | 0.992052i | \(0.540159\pi\) | |||||||
\(182\) | −561.909 | −0.228854 | ||||||||
\(183\) | −1309.53 | −0.528978 | ||||||||
\(184\) | −1026.90 | −0.411434 | ||||||||
\(185\) | 4650.22 | 1.84806 | ||||||||
\(186\) | −1010.92 | −0.398517 | ||||||||
\(187\) | 341.045 | 0.133367 | ||||||||
\(188\) | −604.491 | −0.234505 | ||||||||
\(189\) | −1268.04 | −0.488023 | ||||||||
\(190\) | −3211.09 | −1.22609 | ||||||||
\(191\) | −1007.84 | −0.381806 | −0.190903 | − | 0.981609i | \(-0.561142\pi\) | ||||
−0.190903 | + | 0.981609i | \(0.561142\pi\) | |||||||
\(192\) | −813.534 | −0.305790 | ||||||||
\(193\) | −1728.70 | −0.644737 | −0.322369 | − | 0.946614i | \(-0.604479\pi\) | ||||
−0.322369 | + | 0.946614i | \(0.604479\pi\) | |||||||
\(194\) | 1230.24 | 0.455288 | ||||||||
\(195\) | 863.814 | 0.317226 | ||||||||
\(196\) | 722.067 | 0.263144 | ||||||||
\(197\) | 3184.78 | 1.15181 | 0.575903 | − | 0.817518i | \(-0.304650\pi\) | ||||
0.575903 | + | 0.817518i | \(0.304650\pi\) | |||||||
\(198\) | −475.388 | −0.170628 | ||||||||
\(199\) | 339.933 | 0.121091 | 0.0605457 | − | 0.998165i | \(-0.480716\pi\) | ||||
0.0605457 | + | 0.998165i | \(0.480716\pi\) | |||||||
\(200\) | 6885.95 | 2.43455 | ||||||||
\(201\) | −175.987 | −0.0617572 | ||||||||
\(202\) | −3526.07 | −1.22819 | ||||||||
\(203\) | −3450.33 | −1.19293 | ||||||||
\(204\) | −263.705 | −0.0905050 | ||||||||
\(205\) | 471.980 | 0.160802 | ||||||||
\(206\) | −450.757 | −0.152455 | ||||||||
\(207\) | 1006.64 | 0.338001 | ||||||||
\(208\) | 276.259 | 0.0920919 | ||||||||
\(209\) | −849.788 | −0.281249 | ||||||||
\(210\) | −999.037 | −0.328286 | ||||||||
\(211\) | 978.950 | 0.319401 | 0.159701 | − | 0.987165i | \(-0.448947\pi\) | ||||
0.159701 | + | 0.987165i | \(0.448947\pi\) | |||||||
\(212\) | 1848.70 | 0.598910 | ||||||||
\(213\) | 1972.30 | 0.634458 | ||||||||
\(214\) | 3039.66 | 0.970967 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2300.24 | 0.724590 | ||||||||
\(217\) | 3537.12 | 1.10652 | ||||||||
\(218\) | −10.3106 | −0.00320331 | ||||||||
\(219\) | 658.927 | 0.203316 | ||||||||
\(220\) | 899.937 | 0.275790 | ||||||||
\(221\) | 716.830 | 0.218186 | ||||||||
\(222\) | 854.997 | 0.258485 | ||||||||
\(223\) | −3952.31 | −1.18684 | −0.593422 | − | 0.804892i | \(-0.702223\pi\) | ||||
−0.593422 | + | 0.804892i | \(0.702223\pi\) | |||||||
\(224\) | 2171.39 | 0.647687 | ||||||||
\(225\) | −6750.11 | −2.00003 | ||||||||
\(226\) | −991.487 | −0.291826 | ||||||||
\(227\) | −4291.75 | −1.25486 | −0.627431 | − | 0.778672i | \(-0.715893\pi\) | ||||
−0.627431 | + | 0.778672i | \(0.715893\pi\) | |||||||
\(228\) | 657.078 | 0.190860 | ||||||||
\(229\) | −2771.21 | −0.799679 | −0.399839 | − | 0.916585i | \(-0.630934\pi\) | ||||
−0.399839 | + | 0.916585i | \(0.630934\pi\) | |||||||
\(230\) | 1712.24 | 0.490877 | ||||||||
\(231\) | −264.387 | −0.0753046 | ||||||||
\(232\) | 6258.92 | 1.77120 | ||||||||
\(233\) | 879.619 | 0.247321 | 0.123660 | − | 0.992325i | \(-0.460537\pi\) | ||||
0.123660 | + | 0.992325i | \(0.460537\pi\) | |||||||
\(234\) | −999.201 | −0.279144 | ||||||||
\(235\) | 2921.48 | 0.810964 | ||||||||
\(236\) | 1882.60 | 0.519266 | ||||||||
\(237\) | −1570.28 | −0.430381 | ||||||||
\(238\) | −829.044 | −0.225794 | ||||||||
\(239\) | −3245.14 | −0.878286 | −0.439143 | − | 0.898417i | \(-0.644718\pi\) | ||||
−0.439143 | + | 0.898417i | \(0.644718\pi\) | |||||||
\(240\) | 491.170 | 0.132104 | ||||||||
\(241\) | 229.371 | 0.0613074 | 0.0306537 | − | 0.999530i | \(-0.490241\pi\) | ||||
0.0306537 | + | 0.999530i | \(0.490241\pi\) | |||||||
\(242\) | 2375.88 | 0.631106 | ||||||||
\(243\) | −3465.30 | −0.914811 | ||||||||
\(244\) | −2867.55 | −0.752361 | ||||||||
\(245\) | −3489.72 | −0.910001 | ||||||||
\(246\) | 86.7789 | 0.0224911 | ||||||||
\(247\) | −1786.14 | −0.460119 | ||||||||
\(248\) | −6416.36 | −1.64290 | ||||||||
\(249\) | −2139.75 | −0.544584 | ||||||||
\(250\) | −6528.21 | −1.65152 | ||||||||
\(251\) | −578.374 | −0.145445 | −0.0727224 | − | 0.997352i | \(-0.523169\pi\) | ||||
−0.0727224 | + | 0.997352i | \(0.523169\pi\) | |||||||
\(252\) | −1286.14 | −0.321504 | ||||||||
\(253\) | 453.129 | 0.112601 | ||||||||
\(254\) | −1747.53 | −0.431691 | ||||||||
\(255\) | 1274.48 | 0.312983 | ||||||||
\(256\) | −4361.42 | −1.06480 | ||||||||
\(257\) | −6846.67 | −1.66180 | −0.830902 | − | 0.556419i | \(-0.812175\pi\) | ||||
−0.830902 | + | 0.556419i | \(0.812175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2991.56 | −0.717708 | ||||||||
\(260\) | 1891.55 | 0.451187 | ||||||||
\(261\) | −6135.45 | −1.45508 | ||||||||
\(262\) | −2254.18 | −0.531542 | ||||||||
\(263\) | −388.631 | −0.0911179 | −0.0455589 | − | 0.998962i | \(-0.514507\pi\) | ||||
−0.0455589 | + | 0.998962i | \(0.514507\pi\) | |||||||
\(264\) | 479.600 | 0.111808 | ||||||||
\(265\) | −8934.68 | −2.07114 | ||||||||
\(266\) | 2065.74 | 0.476161 | ||||||||
\(267\) | 2437.72 | 0.558749 | ||||||||
\(268\) | −385.370 | −0.0878367 | ||||||||
\(269\) | −5908.90 | −1.33930 | −0.669651 | − | 0.742676i | \(-0.733556\pi\) | ||||
−0.669651 | + | 0.742676i | \(0.733556\pi\) | |||||||
\(270\) | −3835.40 | −0.864500 | ||||||||
\(271\) | 2427.11 | 0.544045 | 0.272023 | − | 0.962291i | \(-0.412307\pi\) | ||||
0.272023 | + | 0.962291i | \(0.412307\pi\) | |||||||
\(272\) | 407.594 | 0.0908603 | ||||||||
\(273\) | −555.705 | −0.123197 | ||||||||
\(274\) | −1077.68 | −0.237609 | ||||||||
\(275\) | −3038.50 | −0.666285 | ||||||||
\(276\) | −350.371 | −0.0764125 | ||||||||
\(277\) | 6618.68 | 1.43566 | 0.717830 | − | 0.696218i | \(-0.245135\pi\) | ||||
0.717830 | + | 0.696218i | \(0.245135\pi\) | |||||||
\(278\) | 4234.88 | 0.913638 | ||||||||
\(279\) | 6289.79 | 1.34968 | ||||||||
\(280\) | −6340.95 | −1.35337 | ||||||||
\(281\) | −6248.79 | −1.32659 | −0.663294 | − | 0.748358i | \(-0.730842\pi\) | ||||
−0.663294 | + | 0.748358i | \(0.730842\pi\) | |||||||
\(282\) | 537.148 | 0.113428 | ||||||||
\(283\) | −6339.90 | −1.33169 | −0.665845 | − | 0.746090i | \(-0.731929\pi\) | ||||
−0.665845 | + | 0.746090i | \(0.731929\pi\) | |||||||
\(284\) | 4318.86 | 0.902385 | ||||||||
\(285\) | −3175.63 | −0.660029 | ||||||||
\(286\) | −449.781 | −0.0929934 | ||||||||
\(287\) | −303.632 | −0.0624488 | ||||||||
\(288\) | 3861.22 | 0.790015 | ||||||||
\(289\) | −3855.39 | −0.784731 | ||||||||
\(290\) | −10436.1 | −2.11320 | ||||||||
\(291\) | 1216.65 | 0.245091 | ||||||||
\(292\) | 1442.89 | 0.289174 | ||||||||
\(293\) | −4848.30 | −0.966691 | −0.483346 | − | 0.875430i | \(-0.660579\pi\) | ||||
−0.483346 | + | 0.875430i | \(0.660579\pi\) | |||||||
\(294\) | −641.626 | −0.127280 | ||||||||
\(295\) | −9098.53 | −1.79572 | ||||||||
\(296\) | 5426.71 | 1.06561 | ||||||||
\(297\) | −1015.01 | −0.198305 | ||||||||
\(298\) | −966.894 | −0.187955 | ||||||||
\(299\) | 952.416 | 0.184213 | ||||||||
\(300\) | 2349.45 | 0.452151 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2159.55 | 0.411483 | ||||||||
\(303\) | −3487.14 | −0.661158 | ||||||||
\(304\) | −1015.61 | −0.191609 | ||||||||
\(305\) | 13858.8 | 2.60181 | ||||||||
\(306\) | −1474.23 | −0.275411 | ||||||||
\(307\) | −9380.78 | −1.74394 | −0.871970 | − | 0.489560i | \(-0.837157\pi\) | ||||
−0.871970 | + | 0.489560i | \(0.837157\pi\) | |||||||
\(308\) | −578.944 | −0.107105 | ||||||||
\(309\) | −445.779 | −0.0820696 | ||||||||
\(310\) | 10698.6 | 1.96013 | ||||||||
\(311\) | −2556.27 | −0.466087 | −0.233043 | − | 0.972466i | \(-0.574868\pi\) | ||||
−0.233043 | + | 0.972466i | \(0.574868\pi\) | |||||||
\(312\) | 1008.05 | 0.182916 | ||||||||
\(313\) | 670.669 | 0.121113 | 0.0605566 | − | 0.998165i | \(-0.480712\pi\) | ||||
0.0605566 | + | 0.998165i | \(0.480712\pi\) | |||||||
\(314\) | −3321.85 | −0.597016 | ||||||||
\(315\) | 6215.86 | 1.11182 | ||||||||
\(316\) | −3438.53 | −0.612127 | ||||||||
\(317\) | −1897.82 | −0.336253 | −0.168126 | − | 0.985765i | \(-0.553772\pi\) | ||||
−0.168126 | + | 0.985765i | \(0.553772\pi\) | |||||||
\(318\) | −1642.74 | −0.289687 | ||||||||
\(319\) | −2761.82 | −0.484740 | ||||||||
\(320\) | 8609.66 | 1.50405 | ||||||||
\(321\) | 3006.10 | 0.522691 | ||||||||
\(322\) | −1101.51 | −0.190636 | ||||||||
\(323\) | −2635.28 | −0.453965 | ||||||||
\(324\) | −1865.74 | −0.319914 | ||||||||
\(325\) | −6386.51 | −1.09003 | ||||||||
\(326\) | 6478.37 | 1.10063 | ||||||||
\(327\) | −10.1967 | −0.00172441 | ||||||||
\(328\) | 550.791 | 0.0927205 | ||||||||
\(329\) | −1879.43 | −0.314944 | ||||||||
\(330\) | −799.681 | −0.133397 | ||||||||
\(331\) | −6332.67 | −1.05159 | −0.525793 | − | 0.850612i | \(-0.676231\pi\) | ||||
−0.525793 | + | 0.850612i | \(0.676231\pi\) | |||||||
\(332\) | −4685.55 | −0.774557 | ||||||||
\(333\) | −5319.66 | −0.875423 | ||||||||
\(334\) | 527.996 | 0.0864990 | ||||||||
\(335\) | 1862.48 | 0.303756 | ||||||||
\(336\) | −315.977 | −0.0513034 | ||||||||
\(337\) | 1125.14 | 0.181870 | 0.0909349 | − | 0.995857i | \(-0.471014\pi\) | ||||
0.0909349 | + | 0.995857i | \(0.471014\pi\) | |||||||
\(338\) | 3329.57 | 0.535813 | ||||||||
\(339\) | −980.539 | −0.157096 | ||||||||
\(340\) | 2790.80 | 0.445153 | ||||||||
\(341\) | 2831.29 | 0.449627 | ||||||||
\(342\) | 3673.36 | 0.580796 | ||||||||
\(343\) | 6738.72 | 1.06081 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1693.33 | 0.264249 | ||||||||
\(346\) | −1885.01 | −0.292887 | ||||||||
\(347\) | 7157.63 | 1.10732 | 0.553662 | − | 0.832741i | \(-0.313230\pi\) | ||||
0.553662 | + | 0.832741i | \(0.313230\pi\) | |||||||
\(348\) | 2135.51 | 0.328952 | ||||||||
\(349\) | −3179.32 | −0.487637 | −0.243818 | − | 0.969821i | \(-0.578400\pi\) | ||||
−0.243818 | + | 0.969821i | \(0.578400\pi\) | |||||||
\(350\) | 7386.27 | 1.12804 | ||||||||
\(351\) | −2133.40 | −0.324424 | ||||||||
\(352\) | 1738.09 | 0.263183 | ||||||||
\(353\) | 4097.11 | 0.617755 | 0.308877 | − | 0.951102i | \(-0.400047\pi\) | ||||
0.308877 | + | 0.951102i | \(0.400047\pi\) | |||||||
\(354\) | −1672.87 | −0.251164 | ||||||||
\(355\) | −20872.9 | −3.12062 | ||||||||
\(356\) | 5338.02 | 0.794704 | ||||||||
\(357\) | −819.889 | −0.121549 | ||||||||
\(358\) | −7734.26 | −1.14181 | ||||||||
\(359\) | 5437.68 | 0.799414 | 0.399707 | − | 0.916643i | \(-0.369112\pi\) | ||||
0.399707 | + | 0.916643i | \(0.369112\pi\) | |||||||
\(360\) | −11275.6 | −1.65077 | ||||||||
\(361\) | −292.627 | −0.0426632 | ||||||||
\(362\) | 1192.41 | 0.173127 | ||||||||
\(363\) | 2349.65 | 0.339737 | ||||||||
\(364\) | −1216.86 | −0.175222 | ||||||||
\(365\) | −6973.44 | −1.00002 | ||||||||
\(366\) | 2548.09 | 0.363910 | ||||||||
\(367\) | −10507.7 | −1.49455 | −0.747274 | − | 0.664516i | \(-0.768638\pi\) | ||||
−0.747274 | + | 0.664516i | \(0.768638\pi\) | |||||||
\(368\) | 541.549 | 0.0767125 | ||||||||
\(369\) | −539.925 | −0.0761718 | ||||||||
\(370\) | −9048.46 | −1.27137 | ||||||||
\(371\) | 5747.82 | 0.804344 | ||||||||
\(372\) | −2189.23 | −0.305124 | ||||||||
\(373\) | −2314.05 | −0.321225 | −0.160613 | − | 0.987018i | \(-0.551347\pi\) | ||||
−0.160613 | + | 0.987018i | \(0.551347\pi\) | |||||||
\(374\) | −663.610 | −0.0917498 | ||||||||
\(375\) | −6456.13 | −0.889048 | ||||||||
\(376\) | 3409.31 | 0.467611 | ||||||||
\(377\) | −5804.97 | −0.793027 | ||||||||
\(378\) | 2467.37 | 0.335735 | ||||||||
\(379\) | −5322.63 | −0.721386 | −0.360693 | − | 0.932685i | \(-0.617460\pi\) | ||||
−0.360693 | + | 0.932685i | \(0.617460\pi\) | |||||||
\(380\) | −6953.88 | −0.938754 | ||||||||
\(381\) | −1728.23 | −0.232388 | ||||||||
\(382\) | 1961.07 | 0.262663 | ||||||||
\(383\) | 974.765 | 0.130047 | 0.0650237 | − | 0.997884i | \(-0.479288\pi\) | ||||
0.0650237 | + | 0.997884i | \(0.479288\pi\) | |||||||
\(384\) | −968.502 | −0.128708 | ||||||||
\(385\) | 2798.01 | 0.370390 | ||||||||
\(386\) | 3363.72 | 0.443546 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2664.18 | 0.348591 | ||||||||
\(389\) | −1161.73 | −0.151419 | −0.0757096 | − | 0.997130i | \(-0.524122\pi\) | ||||
−0.0757096 | + | 0.997130i | \(0.524122\pi\) | |||||||
\(390\) | −1680.82 | −0.218235 | ||||||||
\(391\) | 1405.20 | 0.181749 | ||||||||
\(392\) | −4072.44 | −0.524717 | ||||||||
\(393\) | −2229.29 | −0.286140 | ||||||||
\(394\) | −6196.98 | −0.792384 | ||||||||
\(395\) | 16618.3 | 2.11685 | ||||||||
\(396\) | −1029.49 | −0.130641 | ||||||||
\(397\) | 5403.67 | 0.683129 | 0.341564 | − | 0.939858i | \(-0.389043\pi\) | ||||
0.341564 | + | 0.939858i | \(0.389043\pi\) | |||||||
\(398\) | −661.445 | −0.0833046 | ||||||||
\(399\) | 2042.93 | 0.256327 | ||||||||
\(400\) | −3631.41 | −0.453926 | ||||||||
\(401\) | 6586.98 | 0.820294 | 0.410147 | − | 0.912019i | \(-0.365477\pi\) | ||||
0.410147 | + | 0.912019i | \(0.365477\pi\) | |||||||
\(402\) | 342.438 | 0.0424858 | ||||||||
\(403\) | 5950.99 | 0.735582 | ||||||||
\(404\) | −7635.99 | −0.940359 | ||||||||
\(405\) | 9017.04 | 1.10632 | ||||||||
\(406\) | 6713.69 | 0.820677 | ||||||||
\(407\) | −2394.60 | −0.291636 | ||||||||
\(408\) | 1487.29 | 0.180470 | ||||||||
\(409\) | 3664.02 | 0.442969 | 0.221484 | − | 0.975164i | \(-0.428910\pi\) | ||||
0.221484 | + | 0.975164i | \(0.428910\pi\) | |||||||
\(410\) | −918.384 | −0.110624 | ||||||||
\(411\) | −1065.78 | −0.127910 | ||||||||
\(412\) | −976.150 | −0.116727 | ||||||||
\(413\) | 5853.22 | 0.697381 | ||||||||
\(414\) | −1958.73 | −0.232527 | ||||||||
\(415\) | 22645.1 | 2.67856 | ||||||||
\(416\) | 3653.23 | 0.430563 | ||||||||
\(417\) | 4188.12 | 0.491830 | ||||||||
\(418\) | 1653.53 | 0.193485 | ||||||||
\(419\) | −5113.21 | −0.596173 | −0.298087 | − | 0.954539i | \(-0.596348\pi\) | ||||
−0.298087 | + | 0.954539i | \(0.596348\pi\) | |||||||
\(420\) | −2163.50 | −0.251352 | ||||||||
\(421\) | −10270.3 | −1.18894 | −0.594468 | − | 0.804119i | \(-0.702637\pi\) | ||||
−0.594468 | + | 0.804119i | \(0.702637\pi\) | |||||||
\(422\) | −1904.85 | −0.219732 | ||||||||
\(423\) | −3342.06 | −0.384152 | ||||||||
\(424\) | −10426.6 | −1.19424 | ||||||||
\(425\) | −9422.69 | −1.07545 | ||||||||
\(426\) | −3837.72 | −0.436475 | ||||||||
\(427\) | −8915.56 | −1.01043 | ||||||||
\(428\) | 6582.63 | 0.743419 | ||||||||
\(429\) | −444.815 | −0.0500603 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1086.40 | 0.121415 | 0.0607077 | − | 0.998156i | \(-0.480664\pi\) | ||||
0.0607077 | + | 0.998156i | \(0.480664\pi\) | |||||||
\(432\) | −1213.07 | −0.135101 | ||||||||
\(433\) | −5392.96 | −0.598543 | −0.299272 | − | 0.954168i | \(-0.596744\pi\) | ||||
−0.299272 | + | 0.954168i | \(0.596744\pi\) | |||||||
\(434\) | −6882.56 | −0.761230 | ||||||||
\(435\) | −10320.8 | −1.13758 | ||||||||
\(436\) | −22.3284 | −0.00245261 | ||||||||
\(437\) | −3501.36 | −0.383279 | ||||||||
\(438\) | −1282.15 | −0.139871 | ||||||||
\(439\) | −7125.71 | −0.774696 | −0.387348 | − | 0.921934i | \(-0.626609\pi\) | ||||
−0.387348 | + | 0.921934i | \(0.626609\pi\) | |||||||
\(440\) | −5075.62 | −0.549934 | ||||||||
\(441\) | 3992.10 | 0.431066 | ||||||||
\(442\) | −1394.82 | −0.150101 | ||||||||
\(443\) | 8187.50 | 0.878103 | 0.439052 | − | 0.898462i | \(-0.355315\pi\) | ||||
0.439052 | + | 0.898462i | \(0.355315\pi\) | |||||||
\(444\) | 1851.56 | 0.197908 | ||||||||
\(445\) | −25798.5 | −2.74824 | ||||||||
\(446\) | 7690.45 | 0.816487 | ||||||||
\(447\) | −956.217 | −0.101180 | ||||||||
\(448\) | −5538.73 | −0.584108 | ||||||||
\(449\) | −7136.80 | −0.750125 | −0.375063 | − | 0.926999i | \(-0.622379\pi\) | ||||
−0.375063 | + | 0.926999i | \(0.622379\pi\) | |||||||
\(450\) | 13134.4 | 1.37592 | ||||||||
\(451\) | −243.043 | −0.0253757 | ||||||||
\(452\) | −2147.15 | −0.223436 | ||||||||
\(453\) | 2135.70 | 0.221510 | ||||||||
\(454\) | 8350.94 | 0.863280 | ||||||||
\(455\) | 5881.04 | 0.605951 | ||||||||
\(456\) | −3705.90 | −0.380580 | ||||||||
\(457\) | −5491.92 | −0.562147 | −0.281073 | − | 0.959686i | \(-0.590690\pi\) | ||||
−0.281073 | + | 0.959686i | \(0.590690\pi\) | |||||||
\(458\) | 5392.25 | 0.550138 | ||||||||
\(459\) | −3147.63 | −0.320085 | ||||||||
\(460\) | 3707.99 | 0.375839 | ||||||||
\(461\) | 6867.45 | 0.693815 | 0.346908 | − | 0.937899i | \(-0.387232\pi\) | ||||
0.346908 | + | 0.937899i | \(0.387232\pi\) | |||||||
\(462\) | 514.447 | 0.0518057 | ||||||||
\(463\) | 11786.2 | 1.18305 | 0.591524 | − | 0.806288i | \(-0.298527\pi\) | ||||
0.591524 | + | 0.806288i | \(0.298527\pi\) | |||||||
\(464\) | −3300.74 | −0.330243 | ||||||||
\(465\) | 10580.5 | 1.05518 | ||||||||
\(466\) | −1711.57 | −0.170144 | ||||||||
\(467\) | −4927.74 | −0.488284 | −0.244142 | − | 0.969739i | \(-0.578506\pi\) | ||||
−0.244142 | + | 0.969739i | \(0.578506\pi\) | |||||||
\(468\) | −2163.85 | −0.213727 | ||||||||
\(469\) | −1198.16 | −0.117966 | ||||||||
\(470\) | −5684.66 | −0.557902 | ||||||||
\(471\) | −3285.17 | −0.321386 | ||||||||
\(472\) | −10617.8 | −1.03543 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3055.46 | 0.296080 | ||||||||
\(475\) | 23478.7 | 2.26795 | ||||||||
\(476\) | −1795.36 | −0.172879 | ||||||||
\(477\) | 10220.9 | 0.981097 | ||||||||
\(478\) | 6314.42 | 0.604216 | ||||||||
\(479\) | −2859.41 | −0.272755 | −0.136378 | − | 0.990657i | \(-0.543546\pi\) | ||||
−0.136378 | + | 0.990657i | \(0.543546\pi\) | |||||||
\(480\) | 6495.20 | 0.617633 | ||||||||
\(481\) | −5033.12 | −0.477111 | ||||||||
\(482\) | −446.313 | −0.0421763 | ||||||||
\(483\) | −1089.35 | −0.102623 | ||||||||
\(484\) | 5145.17 | 0.483205 | ||||||||
\(485\) | −12875.9 | −1.20549 | ||||||||
\(486\) | 6742.82 | 0.629343 | ||||||||
\(487\) | −20667.3 | −1.92305 | −0.961525 | − | 0.274716i | \(-0.911416\pi\) | ||||
−0.961525 | + | 0.274716i | \(0.911416\pi\) | |||||||
\(488\) | 16172.9 | 1.50023 | ||||||||
\(489\) | 6406.84 | 0.592489 | ||||||||
\(490\) | 6790.35 | 0.626034 | ||||||||
\(491\) | 754.889 | 0.0693842 | 0.0346921 | − | 0.999398i | \(-0.488955\pi\) | ||||
0.0346921 | + | 0.999398i | \(0.488955\pi\) | |||||||
\(492\) | 187.927 | 0.0172203 | ||||||||
\(493\) | −8564.68 | −0.782421 | ||||||||
\(494\) | 3475.49 | 0.316538 | ||||||||
\(495\) | 4975.50 | 0.451782 | ||||||||
\(496\) | 3383.77 | 0.306322 | ||||||||
\(497\) | 13427.9 | 1.21191 | ||||||||
\(498\) | 4163.56 | 0.374646 | ||||||||
\(499\) | 15119.3 | 1.35638 | 0.678190 | − | 0.734887i | \(-0.262765\pi\) | ||||
0.678190 | + | 0.734887i | \(0.262765\pi\) | |||||||
\(500\) | −14137.4 | −1.26448 | ||||||||
\(501\) | 522.166 | 0.0465642 | ||||||||
\(502\) | 1125.41 | 0.100059 | ||||||||
\(503\) | −5614.73 | −0.497711 | −0.248855 | − | 0.968541i | \(-0.580054\pi\) | ||||
−0.248855 | + | 0.968541i | \(0.580054\pi\) | |||||||
\(504\) | 7253.78 | 0.641090 | ||||||||
\(505\) | 36904.5 | 3.25194 | ||||||||
\(506\) | −881.705 | −0.0774635 | ||||||||
\(507\) | 3292.80 | 0.288439 | ||||||||
\(508\) | −3784.41 | −0.330524 | ||||||||
\(509\) | −3114.06 | −0.271175 | −0.135588 | − | 0.990765i | \(-0.543292\pi\) | ||||
−0.135588 | + | 0.990765i | \(0.543292\pi\) | |||||||
\(510\) | −2479.89 | −0.215316 | ||||||||
\(511\) | 4486.12 | 0.388365 | ||||||||
\(512\) | 4460.15 | 0.384986 | ||||||||
\(513\) | 7843.02 | 0.675005 | ||||||||
\(514\) | 13322.3 | 1.14324 | ||||||||
\(515\) | 4717.70 | 0.403663 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1504.40 | −0.127975 | ||||||||
\(518\) | 5821.01 | 0.493746 | ||||||||
\(519\) | −1864.20 | −0.157667 | ||||||||
\(520\) | −10668.3 | −0.899681 | ||||||||
\(521\) | −8397.20 | −0.706119 | −0.353060 | − | 0.935601i | \(-0.614859\pi\) | ||||
−0.353060 | + | 0.935601i | \(0.614859\pi\) | |||||||
\(522\) | 11938.4 | 1.00102 | ||||||||
\(523\) | 8152.10 | 0.681580 | 0.340790 | − | 0.940139i | \(-0.389306\pi\) | ||||
0.340790 | + | 0.940139i | \(0.389306\pi\) | |||||||
\(524\) | −4881.62 | −0.406974 | ||||||||
\(525\) | 7304.71 | 0.607245 | ||||||||
\(526\) | 756.202 | 0.0626844 | ||||||||
\(527\) | 8780.11 | 0.725745 | ||||||||
\(528\) | −252.924 | −0.0208468 | ||||||||
\(529\) | −10300.0 | −0.846551 | ||||||||
\(530\) | 17385.2 | 1.42484 | ||||||||
\(531\) | 10408.3 | 0.850628 | ||||||||
\(532\) | 4473.54 | 0.364572 | ||||||||
\(533\) | −510.842 | −0.0415141 | ||||||||
\(534\) | −4743.34 | −0.384391 | ||||||||
\(535\) | −31813.6 | −2.57088 | ||||||||
\(536\) | 2173.48 | 0.175149 | ||||||||
\(537\) | −7648.86 | −0.614660 | ||||||||
\(538\) | 11497.6 | 0.921370 | ||||||||
\(539\) | 1797.01 | 0.143604 | ||||||||
\(540\) | −8305.87 | −0.661903 | ||||||||
\(541\) | −15296.5 | −1.21561 | −0.607807 | − | 0.794085i | \(-0.707950\pi\) | ||||
−0.607807 | + | 0.794085i | \(0.707950\pi\) | |||||||
\(542\) | −4722.69 | −0.374275 | ||||||||
\(543\) | 1179.25 | 0.0931977 | ||||||||
\(544\) | 5389.99 | 0.424805 | ||||||||
\(545\) | 107.913 | 0.00848159 | ||||||||
\(546\) | 1081.30 | 0.0847532 | ||||||||
\(547\) | −3667.39 | −0.286666 | −0.143333 | − | 0.989675i | \(-0.545782\pi\) | ||||
−0.143333 | + | 0.989675i | \(0.545782\pi\) | |||||||
\(548\) | −2333.79 | −0.181925 | ||||||||
\(549\) | −15853.9 | −1.23247 | ||||||||
\(550\) | 5912.35 | 0.458370 | ||||||||
\(551\) | 21340.8 | 1.64999 | ||||||||
\(552\) | 1976.08 | 0.152369 | ||||||||
\(553\) | −10690.8 | −0.822096 | ||||||||
\(554\) | −12878.7 | −0.987661 | ||||||||
\(555\) | −8948.55 | −0.684405 | ||||||||
\(556\) | 9170.98 | 0.699525 | ||||||||
\(557\) | 19084.9 | 1.45180 | 0.725900 | − | 0.687800i | \(-0.241424\pi\) | ||||
0.725900 | + | 0.687800i | \(0.241424\pi\) | |||||||
\(558\) | −12238.7 | −0.928508 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3344.00 | 0.252339 | ||||||||
\(561\) | −656.282 | −0.0493908 | ||||||||
\(562\) | 12159.0 | 0.912625 | ||||||||
\(563\) | −21727.6 | −1.62648 | −0.813241 | − | 0.581926i | \(-0.802299\pi\) | ||||
−0.813241 | + | 0.581926i | \(0.802299\pi\) | |||||||
\(564\) | 1163.24 | 0.0868460 | ||||||||
\(565\) | 10377.1 | 0.772685 | ||||||||
\(566\) | 12336.3 | 0.916134 | ||||||||
\(567\) | −5800.80 | −0.429649 | ||||||||
\(568\) | −24358.2 | −1.79938 | ||||||||
\(569\) | 15887.8 | 1.17057 | 0.585283 | − | 0.810829i | \(-0.300984\pi\) | ||||
0.585283 | + | 0.810829i | \(0.300984\pi\) | |||||||
\(570\) | 6179.19 | 0.454066 | ||||||||
\(571\) | −9090.46 | −0.666242 | −0.333121 | − | 0.942884i | \(-0.608102\pi\) | ||||
−0.333121 | + | 0.942884i | \(0.608102\pi\) | |||||||
\(572\) | −974.038 | −0.0712003 | ||||||||
\(573\) | 1939.42 | 0.141397 | ||||||||
\(574\) | 590.810 | 0.0429616 | ||||||||
\(575\) | −12519.5 | −0.907996 | ||||||||
\(576\) | −9849.10 | −0.712463 | ||||||||
\(577\) | −19120.0 | −1.37951 | −0.689755 | − | 0.724043i | \(-0.742282\pi\) | ||||
−0.689755 | + | 0.724043i | \(0.742282\pi\) | |||||||
\(578\) | 7501.86 | 0.539855 | ||||||||
\(579\) | 3326.57 | 0.238770 | ||||||||
\(580\) | −22600.2 | −1.61797 | ||||||||
\(581\) | −14567.9 | −1.04024 | ||||||||
\(582\) | −2367.38 | −0.168610 | ||||||||
\(583\) | 4600.85 | 0.326840 | ||||||||
\(584\) | −8137.87 | −0.576622 | ||||||||
\(585\) | 10457.8 | 0.739107 | ||||||||
\(586\) | 9433.88 | 0.665034 | ||||||||
\(587\) | −15313.7 | −1.07677 | −0.538383 | − | 0.842700i | \(-0.680965\pi\) | ||||
−0.538383 | + | 0.842700i | \(0.680965\pi\) | |||||||
\(588\) | −1389.49 | −0.0974519 | ||||||||
\(589\) | −21877.6 | −1.53048 | ||||||||
\(590\) | 17704.0 | 1.23536 | ||||||||
\(591\) | −6128.55 | −0.426556 | ||||||||
\(592\) | −2861.86 | −0.198685 | ||||||||
\(593\) | −4684.47 | −0.324399 | −0.162199 | − | 0.986758i | \(-0.551859\pi\) | ||||
−0.162199 | + | 0.986758i | \(0.551859\pi\) | |||||||
\(594\) | 1975.01 | 0.136424 | ||||||||
\(595\) | 8676.92 | 0.597847 | ||||||||
\(596\) | −2093.89 | −0.143908 | ||||||||
\(597\) | −654.141 | −0.0448446 | ||||||||
\(598\) | −1853.22 | −0.126729 | ||||||||
\(599\) | −22451.6 | −1.53147 | −0.765734 | − | 0.643157i | \(-0.777624\pi\) | ||||
−0.765734 | + | 0.643157i | \(0.777624\pi\) | |||||||
\(600\) | −13250.8 | −0.901603 | ||||||||
\(601\) | 14772.9 | 1.00266 | 0.501332 | − | 0.865255i | \(-0.332844\pi\) | ||||
0.501332 | + | 0.865255i | \(0.332844\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2130.60 | −0.143889 | ||||||||
\(604\) | 4676.67 | 0.315051 | ||||||||
\(605\) | −24866.4 | −1.67101 | ||||||||
\(606\) | 6785.31 | 0.454842 | ||||||||
\(607\) | 13455.8 | 0.899760 | 0.449880 | − | 0.893089i | \(-0.351467\pi\) | ||||
0.449880 | + | 0.893089i | \(0.351467\pi\) | |||||||
\(608\) | −13430.4 | −0.895843 | ||||||||
\(609\) | 6639.55 | 0.441787 | ||||||||
\(610\) | −26966.6 | −1.78991 | ||||||||
\(611\) | −3162.04 | −0.209365 | ||||||||
\(612\) | −3192.56 | −0.210868 | ||||||||
\(613\) | 17123.4 | 1.12823 | 0.564116 | − | 0.825695i | \(-0.309217\pi\) | ||||
0.564116 | + | 0.825695i | \(0.309217\pi\) | |||||||
\(614\) | 18253.2 | 1.19974 | ||||||||
\(615\) | −908.243 | −0.0595510 | ||||||||
\(616\) | 3265.22 | 0.213571 | ||||||||
\(617\) | −15914.5 | −1.03840 | −0.519201 | − | 0.854652i | \(-0.673770\pi\) | ||||
−0.519201 | + | 0.854652i | \(0.673770\pi\) | |||||||
\(618\) | 867.403 | 0.0564597 | ||||||||
\(619\) | 8669.99 | 0.562967 | 0.281483 | − | 0.959566i | \(-0.409174\pi\) | ||||
0.281483 | + | 0.959566i | \(0.409174\pi\) | |||||||
\(620\) | 23168.7 | 1.50077 | ||||||||
\(621\) | −4182.10 | −0.270245 | ||||||||
\(622\) | 4974.03 | 0.320644 | ||||||||
\(623\) | 16596.6 | 1.06730 | ||||||||
\(624\) | −531.612 | −0.0341050 | ||||||||
\(625\) | 32107.7 | 2.05489 | ||||||||
\(626\) | −1305.00 | −0.0833197 | ||||||||
\(627\) | 1635.27 | 0.104157 | ||||||||
\(628\) | −7193.74 | −0.457105 | ||||||||
\(629\) | −7425.89 | −0.470731 | ||||||||
\(630\) | −12094.9 | −0.764877 | ||||||||
\(631\) | −3419.60 | −0.215740 | −0.107870 | − | 0.994165i | \(-0.534403\pi\) | ||||
−0.107870 | + | 0.994165i | \(0.534403\pi\) | |||||||
\(632\) | 19393.2 | 1.22060 | ||||||||
\(633\) | −1883.82 | −0.118286 | ||||||||
\(634\) | 3692.80 | 0.231325 | ||||||||
\(635\) | 18289.9 | 1.14301 | ||||||||
\(636\) | −3557.49 | −0.221798 | ||||||||
\(637\) | 3777.07 | 0.234934 | ||||||||
\(638\) | 5373.98 | 0.333476 | ||||||||
\(639\) | 23877.7 | 1.47823 | ||||||||
\(640\) | 10249.7 | 0.633054 | ||||||||
\(641\) | 9707.88 | 0.598188 | 0.299094 | − | 0.954224i | \(-0.403316\pi\) | ||||
0.299094 | + | 0.954224i | \(0.403316\pi\) | |||||||
\(642\) | −5849.30 | −0.359585 | ||||||||
\(643\) | −28804.8 | −1.76664 | −0.883321 | − | 0.468768i | \(-0.844698\pi\) | ||||
−0.883321 | + | 0.468768i | \(0.844698\pi\) | |||||||
\(644\) | −2385.41 | −0.145960 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5127.76 | 0.312305 | ||||||||
\(647\) | −30097.3 | −1.82882 | −0.914410 | − | 0.404790i | \(-0.867345\pi\) | ||||
−0.914410 | + | 0.404790i | \(0.867345\pi\) | |||||||
\(648\) | 10522.7 | 0.637918 | ||||||||
\(649\) | 4685.22 | 0.283376 | ||||||||
\(650\) | 12427.0 | 0.749885 | ||||||||
\(651\) | −6806.57 | −0.409785 | ||||||||
\(652\) | 14029.4 | 0.842692 | ||||||||
\(653\) | 26942.7 | 1.61463 | 0.807313 | − | 0.590124i | \(-0.200921\pi\) | ||||
0.807313 | + | 0.590124i | \(0.200921\pi\) | |||||||
\(654\) | 19.8410 | 0.00118630 | ||||||||
\(655\) | 23592.7 | 1.40739 | ||||||||
\(656\) | −290.468 | −0.0172879 | ||||||||
\(657\) | 7977.33 | 0.473707 | ||||||||
\(658\) | 3657.03 | 0.216665 | ||||||||
\(659\) | 5904.52 | 0.349025 | 0.174512 | − | 0.984655i | \(-0.444165\pi\) | ||||
0.174512 | + | 0.984655i | \(0.444165\pi\) | |||||||
\(660\) | −1731.77 | −0.102135 | ||||||||
\(661\) | 18772.0 | 1.10461 | 0.552303 | − | 0.833643i | \(-0.313749\pi\) | ||||
0.552303 | + | 0.833643i | \(0.313749\pi\) | |||||||
\(662\) | 12322.2 | 0.723438 | ||||||||
\(663\) | −1379.41 | −0.0808025 | ||||||||
\(664\) | 26426.4 | 1.54449 | ||||||||
\(665\) | −21620.4 | −1.26076 | ||||||||
\(666\) | 10351.1 | 0.602246 | ||||||||
\(667\) | −11379.5 | −0.660591 | ||||||||
\(668\) | 1143.42 | 0.0662278 | ||||||||
\(669\) | 7605.53 | 0.439532 | ||||||||
\(670\) | −3624.04 | −0.208968 | ||||||||
\(671\) | −7136.47 | −0.410582 | ||||||||
\(672\) | −4178.46 | −0.239862 | ||||||||
\(673\) | −15231.2 | −0.872390 | −0.436195 | − | 0.899852i | \(-0.643674\pi\) | ||||
−0.436195 | + | 0.899852i | \(0.643674\pi\) | |||||||
\(674\) | −2189.31 | −0.125117 | ||||||||
\(675\) | 28043.5 | 1.59910 | ||||||||
\(676\) | 7210.46 | 0.410244 | ||||||||
\(677\) | −18405.3 | −1.04486 | −0.522432 | − | 0.852681i | \(-0.674975\pi\) | ||||
−0.522432 | + | 0.852681i | \(0.674975\pi\) | |||||||
\(678\) | 1907.95 | 0.108074 | ||||||||
\(679\) | 8283.25 | 0.468162 | ||||||||
\(680\) | −15740.0 | −0.887650 | ||||||||
\(681\) | 8258.73 | 0.464721 | ||||||||
\(682\) | −5509.16 | −0.309321 | ||||||||
\(683\) | 16819.0 | 0.942256 | 0.471128 | − | 0.882065i | \(-0.343847\pi\) | ||||
0.471128 | + | 0.882065i | \(0.343847\pi\) | |||||||
\(684\) | 7954.95 | 0.444686 | ||||||||
\(685\) | 11279.1 | 0.629129 | ||||||||
\(686\) | −13112.3 | −0.729781 | ||||||||
\(687\) | 5332.71 | 0.296150 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9670.36 | 0.534704 | ||||||||
\(690\) | −3294.90 | −0.181790 | ||||||||
\(691\) | 24645.7 | 1.35682 | 0.678412 | − | 0.734681i | \(-0.262668\pi\) | ||||
0.678412 | + | 0.734681i | \(0.262668\pi\) | |||||||
\(692\) | −4082.14 | −0.224248 | ||||||||
\(693\) | −3200.81 | −0.175453 | ||||||||
\(694\) | −13927.4 | −0.761783 | ||||||||
\(695\) | −44323.0 | −2.41909 | ||||||||
\(696\) | −12044.2 | −0.655940 | ||||||||
\(697\) | −753.699 | −0.0409590 | ||||||||
\(698\) | 6186.36 | 0.335469 | ||||||||
\(699\) | −1692.67 | −0.0915920 | ||||||||
\(700\) | 15995.6 | 0.863680 | ||||||||
\(701\) | −23686.8 | −1.27623 | −0.638115 | − | 0.769941i | \(-0.720285\pi\) | ||||
−0.638115 | + | 0.769941i | \(0.720285\pi\) | |||||||
\(702\) | 4151.20 | 0.223187 | ||||||||
\(703\) | 18503.2 | 0.992692 | ||||||||
\(704\) | −4433.48 | −0.237348 | ||||||||
\(705\) | −5621.89 | −0.300330 | ||||||||
\(706\) | −7972.22 | −0.424983 | ||||||||
\(707\) | −23741.2 | −1.26291 | ||||||||
\(708\) | −3622.73 | −0.192303 | ||||||||
\(709\) | 481.648 | 0.0255129 | 0.0127565 | − | 0.999919i | \(-0.495939\pi\) | ||||
0.0127565 | + | 0.999919i | \(0.495939\pi\) | |||||||
\(710\) | 40614.7 | 2.14682 | ||||||||
\(711\) | −19010.6 | −1.00275 | ||||||||
\(712\) | −30106.3 | −1.58466 | ||||||||
\(713\) | 11665.7 | 0.612740 | ||||||||
\(714\) | 1595.35 | 0.0836198 | ||||||||
\(715\) | 4707.49 | 0.246224 | ||||||||
\(716\) | −16749.2 | −0.874226 | ||||||||
\(717\) | 6244.70 | 0.325262 | ||||||||
\(718\) | −10580.7 | −0.549956 | ||||||||
\(719\) | −3202.21 | −0.166095 | −0.0830475 | − | 0.996546i | \(-0.526465\pi\) | ||||
−0.0830475 | + | 0.996546i | \(0.526465\pi\) | |||||||
\(720\) | 5946.37 | 0.307789 | ||||||||
\(721\) | −3034.97 | −0.156766 | ||||||||
\(722\) | 569.397 | 0.0293501 | ||||||||
\(723\) | −441.385 | −0.0227044 | ||||||||
\(724\) | 2582.27 | 0.132554 | ||||||||
\(725\) | 76306.0 | 3.90887 | ||||||||
\(726\) | −4571.98 | −0.233722 | ||||||||
\(727\) | 9608.33 | 0.490170 | 0.245085 | − | 0.969502i | \(-0.421184\pi\) | ||||
0.245085 | + | 0.969502i | \(0.421184\pi\) | |||||||
\(728\) | 6863.06 | 0.349398 | ||||||||
\(729\) | −5286.34 | −0.268574 | ||||||||
\(730\) | 13569.0 | 0.687961 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 5518.10 | 0.278627 | ||||||||
\(733\) | −29472.6 | −1.48512 | −0.742562 | − | 0.669777i | \(-0.766390\pi\) | ||||
−0.742562 | + | 0.669777i | \(0.766390\pi\) | |||||||
\(734\) | 20446.1 | 1.02817 | ||||||||
\(735\) | 6715.37 | 0.337007 | ||||||||
\(736\) | 7161.41 | 0.358659 | ||||||||
\(737\) | −959.071 | −0.0479346 | ||||||||
\(738\) | 1050.59 | 0.0524023 | ||||||||
\(739\) | 14639.6 | 0.728725 | 0.364362 | − | 0.931257i | \(-0.381287\pi\) | ||||
0.364362 | + | 0.931257i | \(0.381287\pi\) | |||||||
\(740\) | −19595.2 | −0.973423 | ||||||||
\(741\) | 3437.11 | 0.170399 | ||||||||
\(742\) | −11184.2 | −0.553347 | ||||||||
\(743\) | 2765.18 | 0.136534 | 0.0682669 | − | 0.997667i | \(-0.478253\pi\) | ||||
0.0682669 | + | 0.997667i | \(0.478253\pi\) | |||||||
\(744\) | 12347.2 | 0.608426 | ||||||||
\(745\) | 10119.7 | 0.497660 | ||||||||
\(746\) | 4502.71 | 0.220986 | ||||||||
\(747\) | −25905.1 | −1.26883 | ||||||||
\(748\) | −1437.10 | −0.0702481 | ||||||||
\(749\) | 20466.2 | 0.998422 | ||||||||
\(750\) | 12562.4 | 0.611619 | ||||||||
\(751\) | −35094.8 | −1.70523 | −0.852616 | − | 0.522538i | \(-0.824985\pi\) | ||||
−0.852616 | + | 0.522538i | \(0.824985\pi\) | |||||||
\(752\) | −1797.95 | −0.0871870 | ||||||||
\(753\) | 1112.98 | 0.0538636 | ||||||||
\(754\) | 11295.4 | 0.545561 | ||||||||
\(755\) | −22602.2 | −1.08951 | ||||||||
\(756\) | 5343.29 | 0.257055 | ||||||||
\(757\) | 31615.4 | 1.51794 | 0.758970 | − | 0.651126i | \(-0.225703\pi\) | ||||
0.758970 | + | 0.651126i | \(0.225703\pi\) | |||||||
\(758\) | 10356.8 | 0.496276 | ||||||||
\(759\) | −871.969 | −0.0417002 | ||||||||
\(760\) | 39219.7 | 1.87190 | ||||||||
\(761\) | −7423.91 | −0.353635 | −0.176818 | − | 0.984244i | \(-0.556580\pi\) | ||||
−0.176818 | + | 0.984244i | \(0.556580\pi\) | |||||||
\(762\) | 3362.81 | 0.159871 | ||||||||
\(763\) | −69.4218 | −0.00329389 | ||||||||
\(764\) | 4246.86 | 0.201107 | ||||||||
\(765\) | 15429.5 | 0.729222 | ||||||||
\(766\) | −1896.71 | −0.0894659 | ||||||||
\(767\) | 9847.69 | 0.463598 | ||||||||
\(768\) | 8392.80 | 0.394335 | ||||||||
\(769\) | −11020.6 | −0.516793 | −0.258396 | − | 0.966039i | \(-0.583194\pi\) | ||||
−0.258396 | + | 0.966039i | \(0.583194\pi\) | |||||||
\(770\) | −5444.41 | −0.254809 | ||||||||
\(771\) | 13175.2 | 0.615427 | ||||||||
\(772\) | 7284.40 | 0.339600 | ||||||||
\(773\) | −12846.3 | −0.597735 | −0.298868 | − | 0.954295i | \(-0.596609\pi\) | ||||
−0.298868 | + | 0.954295i | \(0.596609\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −78225.4 | −3.62573 | ||||||||
\(776\) | −15025.9 | −0.695101 | ||||||||
\(777\) | 5756.74 | 0.265794 | ||||||||
\(778\) | 2260.51 | 0.104169 | ||||||||
\(779\) | 1878.01 | 0.0863756 | ||||||||
\(780\) | −3639.95 | −0.167091 | ||||||||
\(781\) | 10748.3 | 0.492453 | ||||||||
\(782\) | −2734.25 | −0.125034 | ||||||||
\(783\) | 25489.9 | 1.16339 | ||||||||
\(784\) | 2147.66 | 0.0978345 | ||||||||
\(785\) | 34767.1 | 1.58075 | ||||||||
\(786\) | 4337.79 | 0.196849 | ||||||||
\(787\) | −6209.95 | −0.281272 | −0.140636 | − | 0.990061i | \(-0.544915\pi\) | ||||
−0.140636 | + | 0.990061i | \(0.544915\pi\) | |||||||
\(788\) | −13420.1 | −0.606687 | ||||||||
\(789\) | 747.852 | 0.0337443 | ||||||||
\(790\) | −32336.1 | −1.45629 | ||||||||
\(791\) | −6675.74 | −0.300078 | ||||||||
\(792\) | 5806.30 | 0.260502 | ||||||||
\(793\) | −14999.9 | −0.671705 | ||||||||
\(794\) | −10514.5 | −0.469958 | ||||||||
\(795\) | 17193.2 | 0.767020 | ||||||||
\(796\) | −1432.41 | −0.0637821 | ||||||||
\(797\) | −4570.33 | −0.203123 | −0.101562 | − | 0.994829i | \(-0.532384\pi\) | ||||
−0.101562 | + | 0.994829i | \(0.532384\pi\) | |||||||
\(798\) | −3975.17 | −0.176340 | ||||||||
\(799\) | −4665.28 | −0.206566 | ||||||||
\(800\) | −48021.5 | −2.12227 | ||||||||
\(801\) | 29512.4 | 1.30183 | ||||||||
\(802\) | −12817.0 | −0.564320 | ||||||||
\(803\) | 3590.92 | 0.157809 | ||||||||
\(804\) | 741.578 | 0.0325292 | ||||||||
\(805\) | 11528.6 | 0.504757 | ||||||||
\(806\) | −11579.5 | −0.506043 | ||||||||
\(807\) | 11370.7 | 0.495992 | ||||||||
\(808\) | 43066.8 | 1.87510 | ||||||||
\(809\) | −11509.3 | −0.500179 | −0.250090 | − | 0.968223i | \(-0.580460\pi\) | ||||
−0.250090 | + | 0.968223i | \(0.580460\pi\) | |||||||
\(810\) | −17545.5 | −0.761093 | ||||||||
\(811\) | 27492.6 | 1.19038 | 0.595189 | − | 0.803585i | \(-0.297077\pi\) | ||||
0.595189 | + | 0.803585i | \(0.297077\pi\) | |||||||
\(812\) | 14539.0 | 0.628350 | ||||||||
\(813\) | −4670.55 | −0.201480 | ||||||||
\(814\) | 4659.44 | 0.200631 | ||||||||
\(815\) | −67803.8 | −2.91419 | ||||||||
\(816\) | −784.343 | −0.0336489 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −7129.50 | −0.304740 | ||||||||
\(819\) | −6727.67 | −0.287038 | ||||||||
\(820\) | −1988.83 | −0.0846989 | ||||||||
\(821\) | 20475.2 | 0.870390 | 0.435195 | − | 0.900336i | \(-0.356679\pi\) | ||||
0.435195 | + | 0.900336i | \(0.356679\pi\) | |||||||
\(822\) | 2073.80 | 0.0879952 | ||||||||
\(823\) | 8523.09 | 0.360992 | 0.180496 | − | 0.983576i | \(-0.442230\pi\) | ||||
0.180496 | + | 0.983576i | \(0.442230\pi\) | |||||||
\(824\) | 5505.46 | 0.232757 | ||||||||
\(825\) | 5847.07 | 0.246750 | ||||||||
\(826\) | −11389.3 | −0.479762 | ||||||||
\(827\) | −44719.4 | −1.88035 | −0.940173 | − | 0.340697i | \(-0.889337\pi\) | ||||
−0.940173 | + | 0.340697i | \(0.889337\pi\) | |||||||
\(828\) | −4241.79 | −0.178034 | ||||||||
\(829\) | 16064.5 | 0.673031 | 0.336515 | − | 0.941678i | \(-0.390752\pi\) | ||||
0.336515 | + | 0.941678i | \(0.390752\pi\) | |||||||
\(830\) | −44063.1 | −1.84271 | ||||||||
\(831\) | −12736.5 | −0.531678 | ||||||||
\(832\) | −9318.57 | −0.388297 | ||||||||
\(833\) | 5572.70 | 0.231792 | ||||||||
\(834\) | −8149.29 | −0.338354 | ||||||||
\(835\) | −5526.10 | −0.229028 | ||||||||
\(836\) | 3580.85 | 0.148141 | ||||||||
\(837\) | −26131.1 | −1.07912 | ||||||||
\(838\) | 9949.34 | 0.410136 | ||||||||
\(839\) | −24208.5 | −0.996150 | −0.498075 | − | 0.867134i | \(-0.665960\pi\) | ||||
−0.498075 | + | 0.867134i | \(0.665960\pi\) | |||||||
\(840\) | 12202.1 | 0.501203 | ||||||||
\(841\) | 44968.7 | 1.84381 | ||||||||
\(842\) | 19984.0 | 0.817927 | ||||||||
\(843\) | 12024.7 | 0.491285 | ||||||||
\(844\) | −4125.11 | −0.168237 | ||||||||
\(845\) | −34847.9 | −1.41870 | ||||||||
\(846\) | 6503.01 | 0.264277 | ||||||||
\(847\) | 15997.0 | 0.648951 | ||||||||
\(848\) | 5498.62 | 0.222669 | ||||||||
\(849\) | 12200.0 | 0.493174 | ||||||||
\(850\) | 18334.8 | 0.739857 | ||||||||
\(851\) | −9866.40 | −0.397434 | ||||||||
\(852\) | −8310.90 | −0.334186 | ||||||||
\(853\) | 27563.0 | 1.10638 | 0.553189 | − | 0.833056i | \(-0.313411\pi\) | ||||
0.553189 | + | 0.833056i | \(0.313411\pi\) | |||||||
\(854\) | 17348.0 | 0.695125 | ||||||||
\(855\) | −38446.0 | −1.53781 | ||||||||
\(856\) | −37125.8 | −1.48240 | ||||||||
\(857\) | −510.284 | −0.0203395 | −0.0101698 | − | 0.999948i | \(-0.503237\pi\) | ||||
−0.0101698 | + | 0.999948i | \(0.503237\pi\) | |||||||
\(858\) | 865.526 | 0.0344389 | ||||||||
\(859\) | −6837.12 | −0.271571 | −0.135786 | − | 0.990738i | \(-0.543356\pi\) | ||||
−0.135786 | + | 0.990738i | \(0.543356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 584.287 | 0.0231271 | ||||||||
\(862\) | −2113.93 | −0.0835275 | ||||||||
\(863\) | 7846.08 | 0.309483 | 0.154741 | − | 0.987955i | \(-0.450546\pi\) | ||||
0.154741 | + | 0.987955i | \(0.450546\pi\) | |||||||
\(864\) | −16041.5 | −0.631647 | ||||||||
\(865\) | 19728.9 | 0.775493 | ||||||||
\(866\) | 10493.7 | 0.411767 | ||||||||
\(867\) | 7419.02 | 0.290615 | ||||||||
\(868\) | −14904.8 | −0.582834 | ||||||||
\(869\) | −8557.46 | −0.334053 | ||||||||
\(870\) | 20082.4 | 0.782595 | ||||||||
\(871\) | −2015.84 | −0.0784202 | ||||||||
\(872\) | 125.932 | 0.00489058 | ||||||||
\(873\) | 14729.5 | 0.571040 | ||||||||
\(874\) | 6812.99 | 0.263676 | ||||||||
\(875\) | −43954.8 | −1.69822 | ||||||||
\(876\) | −2776.59 | −0.107092 | ||||||||
\(877\) | 20448.0 | 0.787320 | 0.393660 | − | 0.919256i | \(-0.371209\pi\) | ||||
0.393660 | + | 0.919256i | \(0.371209\pi\) | |||||||
\(878\) | 13865.3 | 0.532951 | ||||||||
\(879\) | 9329.70 | 0.358001 | ||||||||
\(880\) | 2676.71 | 0.102536 | ||||||||
\(881\) | −1249.19 | −0.0477709 | −0.0238854 | − | 0.999715i | \(-0.507604\pi\) | ||||
−0.0238854 | + | 0.999715i | \(0.507604\pi\) | |||||||
\(882\) | −7767.88 | −0.296551 | ||||||||
\(883\) | 17831.9 | 0.679606 | 0.339803 | − | 0.940497i | \(-0.389640\pi\) | ||||
0.339803 | + | 0.940497i | \(0.389640\pi\) | |||||||
\(884\) | −3020.59 | −0.114925 | ||||||||
\(885\) | 17508.5 | 0.665020 | ||||||||
\(886\) | −15931.3 | −0.604090 | ||||||||
\(887\) | −3260.32 | −0.123417 | −0.0617086 | − | 0.998094i | \(-0.519655\pi\) | ||||
−0.0617086 | + | 0.998094i | \(0.519655\pi\) | |||||||
\(888\) | −10442.8 | −0.394636 | ||||||||
\(889\) | −11766.2 | −0.443898 | ||||||||
\(890\) | 50199.0 | 1.89064 | ||||||||
\(891\) | −4643.26 | −0.174585 | ||||||||
\(892\) | 16654.3 | 0.625142 | ||||||||
\(893\) | 11624.6 | 0.435612 | ||||||||
\(894\) | 1860.62 | 0.0696067 | ||||||||
\(895\) | 80948.1 | 3.02324 | ||||||||
\(896\) | −6593.79 | −0.245852 | ||||||||
\(897\) | −1832.76 | −0.0682208 | ||||||||
\(898\) | 13886.9 | 0.516048 | ||||||||
\(899\) | −71102.3 | −2.63781 | ||||||||
\(900\) | 28443.7 | 1.05347 | ||||||||
\(901\) | 14267.7 | 0.527553 | ||||||||
\(902\) | 472.915 | 0.0174572 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12109.8 | 0.445539 | ||||||||
\(905\) | −12480.0 | −0.458398 | ||||||||
\(906\) | −4155.67 | −0.152387 | ||||||||
\(907\) | −52697.3 | −1.92920 | −0.964601 | − | 0.263713i | \(-0.915053\pi\) | ||||
−0.964601 | + | 0.263713i | \(0.915053\pi\) | |||||||
\(908\) | 18084.6 | 0.660969 | ||||||||
\(909\) | −42217.2 | −1.54044 | ||||||||
\(910\) | −11443.4 | −0.416863 | ||||||||
\(911\) | −23392.6 | −0.850749 | −0.425374 | − | 0.905017i | \(-0.639858\pi\) | ||||
−0.425374 | + | 0.905017i | \(0.639858\pi\) | |||||||
\(912\) | 1954.36 | 0.0709599 | ||||||||
\(913\) | −11660.9 | −0.422695 | ||||||||
\(914\) | 10686.2 | 0.386728 | ||||||||
\(915\) | −26668.8 | −0.963544 | ||||||||
\(916\) | 11677.3 | 0.421212 | ||||||||
\(917\) | −15177.5 | −0.546572 | ||||||||
\(918\) | 6124.71 | 0.220202 | ||||||||
\(919\) | 6550.12 | 0.235113 | 0.117556 | − | 0.993066i | \(-0.462494\pi\) | ||||
0.117556 | + | 0.993066i | \(0.462494\pi\) | |||||||
\(920\) | −20913.0 | −0.749435 | ||||||||
\(921\) | 18051.7 | 0.645845 | ||||||||
\(922\) | −13362.8 | −0.477309 | ||||||||
\(923\) | 22591.6 | 0.805645 | ||||||||
\(924\) | 1114.08 | 0.0396650 | ||||||||
\(925\) | 66160.1 | 2.35171 | ||||||||
\(926\) | −22933.7 | −0.813875 | ||||||||
\(927\) | −5396.85 | −0.191215 | ||||||||
\(928\) | −43648.8 | −1.54401 | ||||||||
\(929\) | 51999.4 | 1.83643 | 0.918217 | − | 0.396079i | \(-0.129629\pi\) | ||||
0.918217 | + | 0.396079i | \(0.129629\pi\) | |||||||
\(930\) | −20587.6 | −0.725906 | ||||||||
\(931\) | −13885.6 | −0.488810 | ||||||||
\(932\) | −3706.55 | −0.130270 | ||||||||
\(933\) | 4919.10 | 0.172609 | ||||||||
\(934\) | 9588.46 | 0.335914 | ||||||||
\(935\) | 6945.45 | 0.242931 | ||||||||
\(936\) | 12204.1 | 0.426177 | ||||||||
\(937\) | −10652.6 | −0.371402 | −0.185701 | − | 0.982606i | \(-0.559456\pi\) | ||||
−0.185701 | + | 0.982606i | \(0.559456\pi\) | |||||||
\(938\) | 2331.40 | 0.0811544 | ||||||||
\(939\) | −1290.59 | −0.0448527 | ||||||||
\(940\) | −12310.6 | −0.427156 | ||||||||
\(941\) | 8065.38 | 0.279409 | 0.139705 | − | 0.990193i | \(-0.455385\pi\) | ||||
0.139705 | + | 0.990193i | \(0.455385\pi\) | |||||||
\(942\) | 6392.33 | 0.221097 | ||||||||
\(943\) | −1001.40 | −0.0345813 | ||||||||
\(944\) | 5599.46 | 0.193058 | ||||||||
\(945\) | −25823.9 | −0.888945 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31142.2 | −1.06862 | −0.534312 | − | 0.845287i | \(-0.679429\pi\) | ||||
−0.534312 | + | 0.845287i | \(0.679429\pi\) | |||||||
\(948\) | 6616.85 | 0.226693 | ||||||||
\(949\) | 7547.63 | 0.258173 | ||||||||
\(950\) | −45685.2 | −1.56023 | ||||||||
\(951\) | 3652.02 | 0.124527 | ||||||||
\(952\) | 10125.8 | 0.344726 | ||||||||
\(953\) | 20888.2 | 0.710005 | 0.355002 | − | 0.934865i | \(-0.384480\pi\) | ||||
0.355002 | + | 0.934865i | \(0.384480\pi\) | |||||||
\(954\) | −19888.0 | −0.674944 | ||||||||
\(955\) | −20524.9 | −0.695467 | ||||||||
\(956\) | 13674.4 | 0.462617 | ||||||||
\(957\) | 5314.64 | 0.179517 | ||||||||
\(958\) | 5563.88 | 0.187642 | ||||||||
\(959\) | −7256.04 | −0.244327 | ||||||||
\(960\) | −16567.8 | −0.557003 | ||||||||
\(961\) | 43099.8 | 1.44674 | ||||||||
\(962\) | 9793.51 | 0.328228 | ||||||||
\(963\) | 36393.5 | 1.21782 | ||||||||
\(964\) | −966.527 | −0.0322922 | ||||||||
\(965\) | −35205.3 | −1.17440 | ||||||||
\(966\) | 2119.66 | 0.0705994 | ||||||||
\(967\) | 24446.5 | 0.812975 | 0.406487 | − | 0.913656i | \(-0.366754\pi\) | ||||
0.406487 | + | 0.913656i | \(0.366754\pi\) | |||||||
\(968\) | −29018.6 | −0.963526 | ||||||||
\(969\) | 5071.14 | 0.168120 | ||||||||
\(970\) | 25054.1 | 0.829317 | ||||||||
\(971\) | −22613.9 | −0.747389 | −0.373695 | − | 0.927552i | \(-0.621909\pi\) | ||||
−0.373695 | + | 0.927552i | \(0.621909\pi\) | |||||||
\(972\) | 14602.1 | 0.481855 | ||||||||
\(973\) | 28513.7 | 0.939472 | ||||||||
\(974\) | 40214.7 | 1.32296 | ||||||||
\(975\) | 12289.7 | 0.403679 | ||||||||
\(976\) | −8529.03 | −0.279721 | ||||||||
\(977\) | 31715.2 | 1.03855 | 0.519273 | − | 0.854608i | \(-0.326203\pi\) | ||||
0.519273 | + | 0.854608i | \(0.326203\pi\) | |||||||
\(978\) | −12466.5 | −0.407602 | ||||||||
\(979\) | 13284.7 | 0.433690 | ||||||||
\(980\) | 14705.1 | 0.479322 | ||||||||
\(981\) | −123.447 | −0.00401771 | ||||||||
\(982\) | −1468.87 | −0.0477328 | ||||||||
\(983\) | 33948.3 | 1.10151 | 0.550754 | − | 0.834668i | \(-0.314340\pi\) | ||||
0.550754 | + | 0.834668i | \(0.314340\pi\) | |||||||
\(984\) | −1059.90 | −0.0343378 | ||||||||
\(985\) | 64858.7 | 2.09804 | ||||||||
\(986\) | 16665.3 | 0.538265 | ||||||||
\(987\) | 3616.65 | 0.116635 | ||||||||
\(988\) | 7526.46 | 0.242357 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −9681.38 | −0.310803 | ||||||||
\(991\) | 33659.2 | 1.07893 | 0.539465 | − | 0.842008i | \(-0.318627\pi\) | ||||
0.539465 | + | 0.842008i | \(0.318627\pi\) | |||||||
\(992\) | 44746.7 | 1.43217 | ||||||||
\(993\) | 12186.1 | 0.389441 | ||||||||
\(994\) | −26128.1 | −0.833735 | ||||||||
\(995\) | 6922.80 | 0.220570 | ||||||||
\(996\) | 9016.52 | 0.286847 | ||||||||
\(997\) | −3785.19 | −0.120239 | −0.0601195 | − | 0.998191i | \(-0.519148\pi\) | ||||
−0.0601195 | + | 0.998191i | \(0.519148\pi\) | |||||||
\(998\) | −29419.3 | −0.933119 | ||||||||
\(999\) | 22100.7 | 0.699934 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1849.4.a.g.1.11 | 30 | ||
43.8 | odd | 14 | 43.4.e.a.21.4 | ✓ | 60 | ||
43.27 | odd | 14 | 43.4.e.a.41.4 | yes | 60 | ||
43.42 | odd | 2 | 1849.4.a.h.1.20 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.21.4 | ✓ | 60 | 43.8 | odd | 14 | ||
43.4.e.a.41.4 | yes | 60 | 43.27 | odd | 14 | ||
1849.4.a.g.1.11 | 30 | 1.1 | even | 1 | trivial | ||
1849.4.a.h.1.20 | 30 | 43.42 | odd | 2 |