Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3030748.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 21x^{2} + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.19617\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19617 | 0.422910 | 0.211455 | − | 0.977388i | \(-0.432180\pi\) | ||||
0.211455 | + | 0.977388i | \(0.432180\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.56918 | −0.821147 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −17.4272 | −0.770181 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.52701 | −0.124086 | −0.0620430 | − | 0.998073i | \(-0.519762\pi\) | ||||
−0.0620430 | + | 0.998073i | \(0.519762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.5692 | 0.310828 | 0.155414 | − | 0.987849i | \(-0.450329\pi\) | ||||
0.155414 | + | 0.987849i | \(0.450329\pi\) | |||||||
\(14\) | −8.37319 | −0.159845 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 31.7075 | 0.495430 | ||||||||
\(17\) | −15.5502 | −0.221852 | −0.110926 | − | 0.993829i | \(-0.535382\pi\) | ||||
−0.110926 | + | 0.993829i | \(0.535382\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.8616 | −0.179447 | −0.0897235 | − | 0.995967i | \(-0.528598\pi\) | ||||
−0.0897235 | + | 0.995967i | \(0.528598\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.41507 | −0.0524771 | ||||||||
\(23\) | 166.672 | 1.51102 | 0.755511 | − | 0.655136i | \(-0.227389\pi\) | ||||
0.755511 | + | 0.655136i | \(0.227389\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 17.4272 | 0.131452 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 45.9843 | 0.310365 | ||||||||
\(29\) | 194.865 | 1.24777 | 0.623887 | − | 0.781514i | \(-0.285553\pi\) | ||||
0.623887 | + | 0.781514i | \(0.285553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 104.538 | 0.605662 | 0.302831 | − | 0.953044i | \(-0.402068\pi\) | ||||
0.302831 | + | 0.953044i | \(0.402068\pi\) | |||||||
\(32\) | 177.345 | 0.979703 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −18.6007 | −0.0938232 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −47.5377 | −0.211220 | −0.105610 | − | 0.994408i | \(-0.533680\pi\) | ||||
−0.105610 | + | 0.994408i | \(0.533680\pi\) | |||||||
\(38\) | −17.7770 | −0.0758899 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −378.633 | −1.44226 | −0.721128 | − | 0.692802i | \(-0.756376\pi\) | ||||
−0.721128 | + | 0.692802i | \(0.756376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 194.969 | 0.691452 | 0.345726 | − | 0.938336i | \(-0.387633\pi\) | ||||
0.345726 | + | 0.938336i | \(0.387633\pi\) | |||||||
\(44\) | 29.7387 | 0.101893 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 199.368 | 0.639026 | ||||||||
\(47\) | −488.661 | −1.51657 | −0.758283 | − | 0.651926i | \(-0.773961\pi\) | ||||
−0.758283 | + | 0.651926i | \(0.773961\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −95.7075 | −0.255236 | ||||||||
\(53\) | −316.432 | −0.820099 | −0.410050 | − | 0.912063i | \(-0.634489\pi\) | ||||
−0.410050 | + | 0.912063i | \(0.634489\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 121.990 | 0.291101 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 233.091 | 0.527696 | ||||||||
\(59\) | −350.256 | −0.772871 | −0.386436 | − | 0.922316i | \(-0.626294\pi\) | ||||
−0.386436 | + | 0.922316i | \(0.626294\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 115.613 | 0.242668 | 0.121334 | − | 0.992612i | \(-0.461283\pi\) | ||||
0.121334 | + | 0.992612i | \(0.461283\pi\) | |||||||
\(62\) | 125.045 | 0.256140 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −41.5253 | −0.0811041 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −434.890 | −0.792989 | −0.396494 | − | 0.918037i | \(-0.629773\pi\) | ||||
−0.396494 | + | 0.918037i | \(0.629773\pi\) | |||||||
\(68\) | 102.152 | 0.182173 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 410.119 | 0.685523 | 0.342761 | − | 0.939422i | \(-0.388638\pi\) | ||||
0.342761 | + | 0.939422i | \(0.388638\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 464.182 | 0.744225 | 0.372112 | − | 0.928188i | \(-0.378634\pi\) | ||||
0.372112 | + | 0.928188i | \(0.378634\pi\) | |||||||
\(74\) | −56.8631 | −0.0893271 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 97.6288 | 0.147352 | ||||||||
\(77\) | 31.6891 | 0.0469001 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −290.399 | −0.413576 | −0.206788 | − | 0.978386i | \(-0.566301\pi\) | ||||
−0.206788 | + | 0.978386i | \(0.566301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −452.909 | −0.609944 | ||||||||
\(83\) | −578.005 | −0.764390 | −0.382195 | − | 0.924082i | \(-0.624832\pi\) | ||||
−0.382195 | + | 0.924082i | \(0.624832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 233.215 | 0.292422 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 78.8931 | 0.0955686 | ||||||||
\(89\) | 937.022 | 1.11600 | 0.558001 | − | 0.829841i | \(-0.311569\pi\) | ||||
0.558001 | + | 0.829841i | \(0.311569\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −101.984 | −0.117482 | ||||||||
\(92\) | −1094.90 | −1.24077 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −584.522 | −0.641371 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −839.629 | −0.878880 | −0.439440 | − | 0.898272i | \(-0.644823\pi\) | ||||
−0.439440 | + | 0.898272i | \(0.644823\pi\) | |||||||
\(98\) | 58.6123 | 0.0604157 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1012.69 | −0.997690 | −0.498845 | − | 0.866691i | \(-0.666242\pi\) | ||||
−0.498845 | + | 0.866691i | \(0.666242\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 758.506 | 0.725610 | 0.362805 | − | 0.931865i | \(-0.381819\pi\) | ||||
0.362805 | + | 0.931865i | \(0.381819\pi\) | |||||||
\(104\) | −253.900 | −0.239394 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −378.506 | −0.346828 | ||||||||
\(107\) | −264.372 | −0.238858 | −0.119429 | − | 0.992843i | \(-0.538106\pi\) | ||||
−0.119429 | + | 0.992843i | \(0.538106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −775.538 | −0.681496 | −0.340748 | − | 0.940155i | \(-0.610680\pi\) | ||||
−0.340748 | + | 0.940155i | \(0.610680\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −221.953 | −0.187255 | ||||||||
\(113\) | 437.649 | 0.364341 | 0.182171 | − | 0.983267i | \(-0.441688\pi\) | ||||
0.182171 | + | 0.983267i | \(0.441688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1280.10 | −1.02461 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −418.965 | −0.326855 | ||||||||
\(119\) | 108.851 | 0.0838520 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1310.51 | −0.984603 | ||||||||
\(122\) | 138.293 | 0.102627 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −686.727 | −0.497338 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −991.412 | −0.692705 | −0.346353 | − | 0.938104i | \(-0.612580\pi\) | ||||
−0.346353 | + | 0.938104i | \(0.612580\pi\) | |||||||
\(128\) | −1468.43 | −1.01400 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1529.62 | 1.02018 | 0.510089 | − | 0.860122i | \(-0.329612\pi\) | ||||
0.510089 | + | 0.860122i | \(0.329612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 104.031 | 0.0678246 | ||||||||
\(134\) | −520.202 | −0.335363 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 270.997 | 0.170866 | ||||||||
\(137\) | −220.095 | −0.137255 | −0.0686277 | − | 0.997642i | \(-0.521862\pi\) | ||||
−0.0686277 | + | 0.997642i | \(0.521862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2041.16 | −1.24553 | −0.622767 | − | 0.782407i | \(-0.713991\pi\) | ||||
−0.622767 | + | 0.782407i | \(0.713991\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 490.571 | 0.289914 | ||||||||
\(143\) | −65.9548 | −0.0385694 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 555.241 | 0.314740 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 312.283 | 0.173443 | ||||||||
\(149\) | 591.993 | 0.325490 | 0.162745 | − | 0.986668i | \(-0.447965\pi\) | ||||
0.162745 | + | 0.986668i | \(0.447965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1962.54 | −1.05768 | −0.528839 | − | 0.848722i | \(-0.677373\pi\) | ||||
−0.528839 | + | 0.848722i | \(0.677373\pi\) | |||||||
\(152\) | 258.997 | 0.138207 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 37.9055 | 0.0198345 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 684.081 | 0.347743 | 0.173871 | − | 0.984768i | \(-0.444372\pi\) | ||||
0.173871 | + | 0.984768i | \(0.444372\pi\) | |||||||
\(158\) | −347.367 | −0.174905 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1166.70 | −0.571112 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1199.68 | 0.576478 | 0.288239 | − | 0.957559i | \(-0.406930\pi\) | ||||
0.288239 | + | 0.957559i | \(0.406930\pi\) | |||||||
\(164\) | 2487.31 | 1.18430 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −691.393 | −0.323268 | ||||||||
\(167\) | −2211.33 | −1.02466 | −0.512328 | − | 0.858790i | \(-0.671217\pi\) | ||||
−0.512328 | + | 0.858790i | \(0.671217\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1984.74 | −0.903386 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1280.78 | −0.567784 | ||||||||
\(173\) | 1973.01 | 0.867082 | 0.433541 | − | 0.901134i | \(-0.357264\pi\) | ||||
0.433541 | + | 0.901134i | \(0.357264\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −143.540 | −0.0614759 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1120.84 | 0.471968 | ||||||||
\(179\) | −30.8784 | −0.0128936 | −0.00644681 | − | 0.999979i | \(-0.502052\pi\) | ||||
−0.00644681 | + | 0.999979i | \(0.502052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2459.16 | −1.00988 | −0.504938 | − | 0.863155i | \(-0.668485\pi\) | ||||
−0.504938 | + | 0.863155i | \(0.668485\pi\) | |||||||
\(182\) | −121.990 | −0.0496843 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2904.63 | −1.16376 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 70.3959 | 0.0275287 | ||||||||
\(188\) | 3210.10 | 1.24532 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4163.26 | −1.57719 | −0.788595 | − | 0.614913i | \(-0.789191\pi\) | ||||
−0.788595 | + | 0.614913i | \(0.789191\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2057.39 | 0.767326 | 0.383663 | − | 0.923473i | \(-0.374662\pi\) | ||||
0.383663 | + | 0.923473i | \(0.374662\pi\) | |||||||
\(194\) | −1004.34 | −0.371687 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −321.890 | −0.117307 | ||||||||
\(197\) | 2431.48 | 0.879368 | 0.439684 | − | 0.898153i | \(-0.355090\pi\) | ||||
0.439684 | + | 0.898153i | \(0.355090\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5291.18 | −1.88483 | −0.942417 | − | 0.334441i | \(-0.891453\pi\) | ||||
−0.942417 | + | 0.334441i | \(0.891453\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1211.35 | −0.421933 | ||||||||
\(203\) | −1364.05 | −0.471614 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 907.302 | 0.306868 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 461.953 | 0.153994 | ||||||||
\(209\) | 67.2788 | 0.0222669 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3586.37 | −1.17012 | −0.585061 | − | 0.810989i | \(-0.698929\pi\) | ||||
−0.585061 | + | 0.810989i | \(0.698929\pi\) | |||||||
\(212\) | 2078.70 | 0.673422 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −316.234 | −0.101015 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −731.764 | −0.228919 | ||||||||
\(218\) | −927.675 | −0.288211 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −226.554 | −0.0689577 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1127.13 | 0.338467 | 0.169234 | − | 0.985576i | \(-0.445871\pi\) | ||||
0.169234 | + | 0.985576i | \(0.445871\pi\) | |||||||
\(224\) | −1241.42 | −0.370293 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 523.503 | 0.154084 | ||||||||
\(227\) | −674.839 | −0.197315 | −0.0986577 | − | 0.995121i | \(-0.531455\pi\) | ||||
−0.0986577 | + | 0.995121i | \(0.531455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5906.65 | −1.70447 | −0.852233 | − | 0.523163i | \(-0.824752\pi\) | ||||
−0.852233 | + | 0.523163i | \(0.824752\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3395.95 | −0.961012 | ||||||||
\(233\) | 305.559 | 0.0859136 | 0.0429568 | − | 0.999077i | \(-0.486322\pi\) | ||||
0.0429568 | + | 0.999077i | \(0.486322\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2300.89 | 0.634641 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 130.205 | 0.0354619 | ||||||||
\(239\) | 3268.07 | 0.884494 | 0.442247 | − | 0.896893i | \(-0.354181\pi\) | ||||
0.442247 | + | 0.896893i | \(0.354181\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 477.426 | 0.127609 | 0.0638044 | − | 0.997962i | \(-0.479677\pi\) | ||||
0.0638044 | + | 0.997962i | \(0.479677\pi\) | |||||||
\(242\) | −1567.59 | −0.416398 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −759.483 | −0.199266 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −216.522 | −0.0557772 | ||||||||
\(248\) | −1821.80 | −0.466469 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4439.63 | 1.11644 | 0.558221 | − | 0.829692i | \(-0.311484\pi\) | ||||
0.558221 | + | 0.829692i | \(0.311484\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −754.525 | −0.187496 | ||||||||
\(254\) | −1185.90 | −0.292952 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1424.29 | −0.347728 | ||||||||
\(257\) | −2125.51 | −0.515897 | −0.257949 | − | 0.966159i | \(-0.583047\pi\) | ||||
−0.257949 | + | 0.966159i | \(0.583047\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 332.764 | 0.0798337 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1829.68 | 0.431443 | ||||||||
\(263\) | −993.198 | −0.232864 | −0.116432 | − | 0.993199i | \(-0.537146\pi\) | ||||
−0.116432 | + | 0.993199i | \(0.537146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 124.439 | 0.0286837 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2856.87 | 0.651161 | ||||||||
\(269\) | −6458.23 | −1.46381 | −0.731905 | − | 0.681406i | \(-0.761369\pi\) | ||||
−0.731905 | + | 0.681406i | \(0.761369\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 417.093 | 0.0934930 | 0.0467465 | − | 0.998907i | \(-0.485115\pi\) | ||||
0.0467465 | + | 0.998907i | \(0.485115\pi\) | |||||||
\(272\) | −493.059 | −0.109912 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −263.271 | −0.0580467 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4862.87 | −1.05481 | −0.527404 | − | 0.849615i | \(-0.676834\pi\) | ||||
−0.527404 | + | 0.849615i | \(0.676834\pi\) | |||||||
\(278\) | −2441.58 | −0.526748 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2026.16 | 0.430144 | 0.215072 | − | 0.976598i | \(-0.431001\pi\) | ||||
0.215072 | + | 0.976598i | \(0.431001\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6445.96 | 1.35397 | 0.676983 | − | 0.735998i | \(-0.263287\pi\) | ||||
0.676983 | + | 0.735998i | \(0.263287\pi\) | |||||||
\(284\) | −2694.14 | −0.562915 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −78.8931 | −0.0163114 | ||||||||
\(287\) | 2650.43 | 0.545122 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4671.19 | −0.950782 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3049.30 | −0.611118 | ||||||||
\(293\) | 541.850 | 0.108038 | 0.0540191 | − | 0.998540i | \(-0.482797\pi\) | ||||
0.0540191 | + | 0.998540i | \(0.482797\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 828.449 | 0.162678 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 708.124 | 0.137653 | ||||||||
\(299\) | 2428.27 | 0.469668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1364.78 | −0.261344 | ||||||||
\(302\) | −2347.53 | −0.447303 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −471.226 | −0.0889035 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4494.53 | −0.835558 | −0.417779 | − | 0.908549i | \(-0.637191\pi\) | ||||
−0.417779 | + | 0.908549i | \(0.637191\pi\) | |||||||
\(308\) | −208.171 | −0.0385119 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2869.51 | −0.523199 | −0.261599 | − | 0.965177i | \(-0.584250\pi\) | ||||
−0.261599 | + | 0.965177i | \(0.584250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1653.23 | −0.298550 | −0.149275 | − | 0.988796i | \(-0.547694\pi\) | ||||
−0.149275 | + | 0.988796i | \(0.547694\pi\) | |||||||
\(314\) | 818.277 | 0.147064 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1907.69 | 0.339607 | ||||||||
\(317\) | 3953.00 | 0.700387 | 0.350194 | − | 0.936677i | \(-0.386116\pi\) | ||||
0.350194 | + | 0.936677i | \(0.386116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −882.154 | −0.154831 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1395.57 | −0.241529 | ||||||||
\(323\) | 231.102 | 0.0398106 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1435.02 | 0.243798 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6598.51 | 1.11080 | ||||||||
\(329\) | 3420.63 | 0.573208 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2464.07 | 0.409177 | 0.204589 | − | 0.978848i | \(-0.434414\pi\) | ||||
0.204589 | + | 0.978848i | \(0.434414\pi\) | |||||||
\(332\) | 3797.02 | 0.627677 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2645.12 | −0.433337 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10587.0 | −1.71131 | −0.855656 | − | 0.517545i | \(-0.826846\pi\) | ||||
−0.855656 | + | 0.517545i | \(0.826846\pi\) | |||||||
\(338\) | −2374.08 | −0.382051 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −473.243 | −0.0751541 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −3397.76 | −0.532543 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2360.05 | 0.366697 | ||||||||
\(347\) | 8188.81 | 1.26685 | 0.633427 | − | 0.773803i | \(-0.281648\pi\) | ||||
0.633427 | + | 0.773803i | \(0.281648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2023.68 | 0.310387 | 0.155194 | − | 0.987884i | \(-0.450400\pi\) | ||||
0.155194 | + | 0.987884i | \(0.450400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −802.844 | −0.121567 | ||||||||
\(353\) | 6824.30 | 1.02895 | 0.514477 | − | 0.857504i | \(-0.327986\pi\) | ||||
0.514477 | + | 0.857504i | \(0.327986\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6155.46 | −0.916401 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −36.9358 | −0.00545284 | ||||||||
\(359\) | −1034.05 | −0.152020 | −0.0760100 | − | 0.997107i | \(-0.524218\pi\) | ||||
−0.0760100 | + | 0.997107i | \(0.524218\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6638.13 | −0.967799 | ||||||||
\(362\) | −2941.57 | −0.427087 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 669.953 | 0.0964700 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9573.55 | 1.36168 | 0.680838 | − | 0.732434i | \(-0.261616\pi\) | ||||
0.680838 | + | 0.732434i | \(0.261616\pi\) | |||||||
\(368\) | 5284.75 | 0.748606 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2215.02 | 0.309968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5540.42 | 0.769094 | 0.384547 | − | 0.923105i | \(-0.374358\pi\) | ||||
0.384547 | + | 0.923105i | \(0.374358\pi\) | |||||||
\(374\) | 84.2055 | 0.0116421 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8516.00 | 1.16803 | ||||||||
\(377\) | 2839.02 | 0.387843 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1601.43 | −0.217045 | −0.108522 | − | 0.994094i | \(-0.534612\pi\) | ||||
−0.108522 | + | 0.994094i | \(0.534612\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4979.97 | −0.667009 | ||||||||
\(383\) | 5034.28 | 0.671644 | 0.335822 | − | 0.941926i | \(-0.390986\pi\) | ||||
0.335822 | + | 0.941926i | \(0.390986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2460.98 | 0.324510 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5515.67 | 0.721690 | ||||||||
\(389\) | −4065.87 | −0.529943 | −0.264971 | − | 0.964256i | \(-0.585362\pi\) | ||||
−0.264971 | + | 0.964256i | \(0.585362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2591.78 | −0.335223 | ||||||||
\(392\) | −853.933 | −0.110026 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2908.46 | 0.371893 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −285.834 | −0.0361349 | −0.0180675 | − | 0.999837i | \(-0.505751\pi\) | ||||
−0.0180675 | + | 0.999837i | \(0.505751\pi\) | |||||||
\(398\) | −6329.15 | −0.797115 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12459.4 | 1.55160 | 0.775800 | − | 0.630979i | \(-0.217346\pi\) | ||||
0.775800 | + | 0.630979i | \(0.217346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1523.03 | 0.188257 | ||||||||
\(404\) | 6652.56 | 0.819250 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1631.64 | −0.199450 | ||||||||
\(407\) | 215.204 | 0.0262094 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8756.93 | −1.05868 | −0.529342 | − | 0.848408i | \(-0.677561\pi\) | ||||
−0.529342 | + | 0.848408i | \(0.677561\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4982.76 | −0.595833 | ||||||||
\(413\) | 2451.79 | 0.292118 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2583.77 | 0.304519 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 80.4769 | 0.00941687 | ||||||||
\(419\) | −12419.7 | −1.44807 | −0.724033 | − | 0.689765i | \(-0.757714\pi\) | ||||
−0.724033 | + | 0.689765i | \(0.757714\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −793.783 | −0.0918922 | −0.0459461 | − | 0.998944i | \(-0.514630\pi\) | ||||
−0.0459461 | + | 0.998944i | \(0.514630\pi\) | |||||||
\(422\) | −4289.90 | −0.494856 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5514.52 | 0.631625 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −809.291 | −0.0917198 | ||||||||
\(428\) | 1736.71 | 0.196138 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8485.37 | −0.948320 | −0.474160 | − | 0.880439i | \(-0.657248\pi\) | ||||
−0.474160 | + | 0.880439i | \(0.657248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9098.11 | −1.00976 | −0.504881 | − | 0.863189i | \(-0.668464\pi\) | ||||
−0.504881 | + | 0.863189i | \(0.668464\pi\) | |||||||
\(434\) | −875.313 | −0.0968120 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5094.65 | 0.559608 | ||||||||
\(437\) | −2477.02 | −0.271148 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4232.27 | −0.460126 | −0.230063 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230063 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −270.997 | −0.0291629 | ||||||||
\(443\) | 2348.20 | 0.251843 | 0.125922 | − | 0.992040i | \(-0.459811\pi\) | ||||
0.125922 | + | 0.992040i | \(0.459811\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1348.24 | 0.143141 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 290.677 | 0.0306545 | ||||||||
\(449\) | 10423.7 | 1.09560 | 0.547798 | − | 0.836610i | \(-0.315466\pi\) | ||||
0.547798 | + | 0.836610i | \(0.315466\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1714.07 | 0.178964 | ||||||||
\(452\) | −2875.00 | −0.299178 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −807.221 | −0.0834467 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10221.8 | 1.04630 | 0.523148 | − | 0.852242i | \(-0.324758\pi\) | ||||
0.523148 | + | 0.852242i | \(0.324758\pi\) | |||||||
\(458\) | −7065.36 | −0.720835 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13341.4 | −1.34788 | −0.673941 | − | 0.738786i | \(-0.735400\pi\) | ||||
−0.673941 | + | 0.738786i | \(0.735400\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9155.72 | −0.919012 | −0.459506 | − | 0.888175i | \(-0.651973\pi\) | ||||
−0.459506 | + | 0.888175i | \(0.651973\pi\) | |||||||
\(464\) | 6178.68 | 0.618185 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 365.501 | 0.0363337 | ||||||||
\(467\) | 13759.6 | 1.36342 | 0.681710 | − | 0.731623i | \(-0.261237\pi\) | ||||
0.681710 | + | 0.731623i | \(0.261237\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3044.23 | 0.299722 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6103.98 | 0.595251 | ||||||||
\(473\) | −882.624 | −0.0857994 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −715.064 | −0.0688549 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3909.17 | 0.374061 | ||||||||
\(479\) | 7423.91 | 0.708157 | 0.354079 | − | 0.935216i | \(-0.384795\pi\) | ||||
0.354079 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −692.585 | −0.0656531 | ||||||||
\(482\) | 571.083 | 0.0539670 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8608.95 | 0.808504 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7663.90 | 0.713110 | 0.356555 | − | 0.934274i | \(-0.383951\pi\) | ||||
0.356555 | + | 0.934274i | \(0.383951\pi\) | |||||||
\(488\) | −2014.81 | −0.186898 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1257.19 | 0.115552 | 0.0577760 | − | 0.998330i | \(-0.481599\pi\) | ||||
0.0577760 | + | 0.998330i | \(0.481599\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3030.18 | −0.276821 | ||||||||
\(494\) | −258.997 | −0.0235887 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3314.63 | 0.300063 | ||||||||
\(497\) | −2870.83 | −0.259103 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 402.799 | 0.0361358 | 0.0180679 | − | 0.999837i | \(-0.494248\pi\) | ||||
0.0180679 | + | 0.999837i | \(0.494248\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5310.55 | 0.472154 | ||||||||
\(503\) | 15462.0 | 1.37061 | 0.685304 | − | 0.728257i | \(-0.259669\pi\) | ||||
0.685304 | + | 0.728257i | \(0.259669\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −902.540 | −0.0792941 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6512.76 | 0.568813 | ||||||||
\(509\) | −12974.1 | −1.12980 | −0.564899 | − | 0.825160i | \(-0.691085\pi\) | ||||
−0.564899 | + | 0.825160i | \(0.691085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3249.28 | −0.281291 | ||||||||
\(512\) | 10043.8 | 0.866946 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2542.47 | −0.218178 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2212.18 | 0.188184 | ||||||||
\(518\) | 398.042 | 0.0337625 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4290.85 | 0.360817 | 0.180409 | − | 0.983592i | \(-0.442258\pi\) | ||||
0.180409 | + | 0.983592i | \(0.442258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23233.7 | −1.94252 | −0.971261 | − | 0.238018i | \(-0.923502\pi\) | ||||
−0.971261 | + | 0.238018i | \(0.923502\pi\) | |||||||
\(524\) | −10048.3 | −0.837717 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1188.03 | −0.0984804 | ||||||||
\(527\) | −1625.58 | −0.134367 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15612.5 | 1.28319 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −683.402 | −0.0556940 | ||||||||
\(533\) | −5516.37 | −0.448293 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7578.91 | 0.610745 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7725.13 | −0.619060 | ||||||||
\(539\) | −221.823 | −0.0177266 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10788.7 | −0.857378 | −0.428689 | − | 0.903452i | \(-0.641024\pi\) | ||||
−0.428689 | + | 0.903452i | \(0.641024\pi\) | |||||||
\(542\) | 498.914 | 0.0395391 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2757.75 | −0.217349 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4512.07 | 0.352691 | 0.176346 | − | 0.984328i | \(-0.443572\pi\) | ||||
0.176346 | + | 0.984328i | \(0.443572\pi\) | |||||||
\(548\) | 1445.84 | 0.112707 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2896.01 | −0.223909 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2032.80 | 0.156317 | ||||||||
\(554\) | −5816.82 | −0.446088 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13408.8 | 1.02277 | ||||||||
\(557\) | −22436.2 | −1.70674 | −0.853370 | − | 0.521306i | \(-0.825445\pi\) | ||||
−0.853370 | + | 0.521306i | \(0.825445\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2840.53 | 0.214922 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2423.63 | 0.181912 | ||||||||
\(563\) | −4773.27 | −0.357317 | −0.178658 | − | 0.983911i | \(-0.557176\pi\) | ||||
−0.178658 | + | 0.983911i | \(0.557176\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7710.46 | 0.572606 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7147.22 | −0.527977 | ||||||||
\(569\) | 21212.5 | 1.56287 | 0.781435 | − | 0.623987i | \(-0.214488\pi\) | ||||
0.781435 | + | 0.623987i | \(0.214488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16931.8 | −1.24093 | −0.620467 | − | 0.784232i | \(-0.713057\pi\) | ||||
−0.620467 | + | 0.784232i | \(0.713057\pi\) | |||||||
\(572\) | 433.269 | 0.0316711 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3170.36 | 0.230537 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21721.5 | 1.56721 | 0.783604 | − | 0.621261i | \(-0.213379\pi\) | ||||
0.783604 | + | 0.621261i | \(0.213379\pi\) | |||||||
\(578\) | −5587.54 | −0.402095 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4046.04 | 0.288912 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1432.49 | 0.101763 | ||||||||
\(584\) | −8089.40 | −0.573188 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 648.144 | 0.0456904 | ||||||||
\(587\) | −12620.8 | −0.887421 | −0.443710 | − | 0.896170i | \(-0.646338\pi\) | ||||
−0.443710 | + | 0.896170i | \(0.646338\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1553.60 | −0.108684 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1507.30 | −0.104645 | ||||||||
\(593\) | −25590.5 | −1.77214 | −0.886069 | − | 0.463554i | \(-0.846574\pi\) | ||||
−0.886069 | + | 0.463554i | \(0.846574\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3888.91 | −0.267275 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2904.63 | 0.198627 | ||||||||
\(599\) | 8933.79 | 0.609390 | 0.304695 | − | 0.952450i | \(-0.401445\pi\) | ||||
0.304695 | + | 0.952450i | \(0.401445\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2249.31 | 0.152665 | 0.0763323 | − | 0.997082i | \(-0.475679\pi\) | ||||
0.0763323 | + | 0.997082i | \(0.475679\pi\) | |||||||
\(602\) | −1632.51 | −0.110525 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12892.3 | 0.868510 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5437.17 | 0.363572 | 0.181786 | − | 0.983338i | \(-0.441812\pi\) | ||||
0.181786 | + | 0.983338i | \(0.441812\pi\) | |||||||
\(608\) | −2635.64 | −0.175805 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7119.40 | −0.471391 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7432.72 | −0.489731 | −0.244865 | − | 0.969557i | \(-0.578744\pi\) | ||||
−0.244865 | + | 0.969557i | \(0.578744\pi\) | |||||||
\(614\) | −5376.22 | −0.353365 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −552.252 | −0.0361215 | ||||||||
\(617\) | 5304.71 | 0.346126 | 0.173063 | − | 0.984911i | \(-0.444634\pi\) | ||||
0.173063 | + | 0.984911i | \(0.444634\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16716.9 | 1.08548 | 0.542738 | − | 0.839902i | \(-0.317388\pi\) | ||||
0.542738 | + | 0.839902i | \(0.317388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3432.42 | −0.221266 | ||||||||
\(623\) | −6559.15 | −0.421809 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1977.55 | −0.126260 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4493.85 | −0.285548 | ||||||||
\(629\) | 739.221 | 0.0468595 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7013.44 | −0.442473 | −0.221237 | − | 0.975220i | \(-0.571009\pi\) | ||||
−0.221237 | + | 0.975220i | \(0.571009\pi\) | |||||||
\(632\) | 5060.85 | 0.318528 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4728.46 | 0.296201 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 713.890 | 0.0444040 | ||||||||
\(638\) | −1055.21 | −0.0654796 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9981.90 | 0.615072 | 0.307536 | − | 0.951536i | \(-0.400496\pi\) | ||||
0.307536 | + | 0.951536i | \(0.400496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24635.5 | −1.51093 | −0.755465 | − | 0.655188i | \(-0.772589\pi\) | ||||
−0.755465 | + | 0.655188i | \(0.772589\pi\) | |||||||
\(644\) | 7664.28 | 0.468967 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 276.437 | 0.0168363 | ||||||||
\(647\) | −18252.3 | −1.10908 | −0.554538 | − | 0.832158i | \(-0.687105\pi\) | ||||
−0.554538 | + | 0.832158i | \(0.687105\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1585.61 | 0.0959024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7880.89 | −0.473373 | ||||||||
\(653\) | −11455.4 | −0.686501 | −0.343251 | − | 0.939244i | \(-0.611528\pi\) | ||||
−0.343251 | + | 0.939244i | \(0.611528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12005.5 | −0.714537 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4091.65 | 0.242415 | ||||||||
\(659\) | −4647.50 | −0.274721 | −0.137360 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137360 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11966.6 | −0.704158 | −0.352079 | − | 0.935970i | \(-0.614525\pi\) | ||||
−0.352079 | + | 0.935970i | \(0.614525\pi\) | |||||||
\(662\) | 2947.45 | 0.173045 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10073.0 | 0.588718 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32478.5 | 1.88541 | ||||||||
\(668\) | 14526.6 | 0.841393 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −523.381 | −0.0301116 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17972.2 | −1.02939 | −0.514693 | − | 0.857374i | \(-0.672094\pi\) | ||||
−0.514693 | + | 0.857374i | \(0.672094\pi\) | |||||||
\(674\) | −12663.9 | −0.723731 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13038.1 | 0.741813 | ||||||||
\(677\) | 16225.6 | 0.921125 | 0.460562 | − | 0.887627i | \(-0.347648\pi\) | ||||
0.460562 | + | 0.887627i | \(0.347648\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5877.40 | 0.332186 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −566.079 | −0.0317834 | ||||||||
\(683\) | 32680.3 | 1.83086 | 0.915430 | − | 0.402478i | \(-0.131851\pi\) | ||||
0.915430 | + | 0.402478i | \(0.131851\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −410.286 | −0.0228350 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6181.97 | 0.342566 | ||||||||
\(689\) | −4610.15 | −0.254910 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30421.0 | 1.67477 | 0.837386 | − | 0.546611i | \(-0.184083\pi\) | ||||
0.837386 | + | 0.546611i | \(0.184083\pi\) | |||||||
\(692\) | −12961.1 | −0.712002 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9795.20 | 0.535765 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5887.82 | 0.319967 | ||||||||
\(698\) | 2420.66 | 0.131266 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24865.9 | −1.33976 | −0.669881 | − | 0.742469i | \(-0.733655\pi\) | ||||
−0.669881 | + | 0.742469i | \(0.733655\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 706.488 | 0.0379028 | ||||||||
\(704\) | 187.986 | 0.0100639 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8163.02 | 0.435155 | ||||||||
\(707\) | 7088.85 | 0.377091 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22833.5 | 1.20949 | 0.604746 | − | 0.796418i | \(-0.293275\pi\) | ||||
0.604746 | + | 0.796418i | \(0.293275\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16329.7 | −0.859523 | ||||||||
\(713\) | 17423.5 | 0.915168 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 202.846 | 0.0105876 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1236.90 | −0.0642907 | ||||||||
\(719\) | 32998.1 | 1.71157 | 0.855786 | − | 0.517329i | \(-0.173074\pi\) | ||||
0.855786 | + | 0.517329i | \(0.173074\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5309.54 | −0.274255 | ||||||||
\(722\) | −7940.33 | −0.409292 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16154.6 | 0.829257 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13769.6 | 0.702455 | 0.351228 | − | 0.936290i | \(-0.385764\pi\) | ||||
0.351228 | + | 0.936290i | \(0.385764\pi\) | |||||||
\(728\) | 1777.30 | 0.0904823 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3031.80 | −0.153400 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33872.8 | −1.70685 | −0.853425 | − | 0.521216i | \(-0.825479\pi\) | ||||
−0.853425 | + | 0.521216i | \(0.825479\pi\) | |||||||
\(734\) | 11451.6 | 0.575866 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29558.5 | 1.48035 | ||||||||
\(737\) | 1968.75 | 0.0983987 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19929.6 | 0.992048 | 0.496024 | − | 0.868309i | \(-0.334793\pi\) | ||||
0.496024 | + | 0.868309i | \(0.334793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2649.54 | 0.131089 | ||||||||
\(743\) | −22285.3 | −1.10036 | −0.550182 | − | 0.835045i | \(-0.685442\pi\) | ||||
−0.550182 | + | 0.835045i | \(0.685442\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6627.28 | 0.325257 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −462.443 | −0.0226051 | ||||||||
\(749\) | 1850.61 | 0.0902799 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9443.37 | −0.458846 | −0.229423 | − | 0.973327i | \(-0.573684\pi\) | ||||
−0.229423 | + | 0.973327i | \(0.573684\pi\) | |||||||
\(752\) | −15494.3 | −0.751353 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3395.95 | 0.164023 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9430.33 | 0.452776 | 0.226388 | − | 0.974037i | \(-0.427308\pi\) | ||||
0.226388 | + | 0.974037i | \(0.427308\pi\) | |||||||
\(758\) | −1915.58 | −0.0917903 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24810.4 | −1.18184 | −0.590918 | − | 0.806732i | \(-0.701234\pi\) | ||||
−0.590918 | + | 0.806732i | \(0.701234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5428.76 | 0.257581 | ||||||||
\(764\) | 27349.2 | 1.29510 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6021.85 | 0.284045 | ||||||||
\(767\) | −5102.94 | −0.240230 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4174.16 | 0.195740 | 0.0978699 | − | 0.995199i | \(-0.468797\pi\) | ||||
0.0978699 | + | 0.995199i | \(0.468797\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13515.3 | −0.630088 | ||||||||
\(773\) | 25457.8 | 1.18455 | 0.592274 | − | 0.805737i | \(-0.298230\pi\) | ||||
0.592274 | + | 0.805737i | \(0.298230\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14632.4 | 0.676897 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4863.47 | −0.224118 | ||||||||
\(779\) | 5627.10 | 0.258809 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1856.61 | −0.0850637 | ||||||||
\(782\) | −3100.21 | −0.141769 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1553.67 | 0.0707757 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5696.75 | 0.258027 | 0.129013 | − | 0.991643i | \(-0.458819\pi\) | ||||
0.129013 | + | 0.991643i | \(0.458819\pi\) | |||||||
\(788\) | −15972.8 | −0.722091 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3063.55 | −0.137708 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1684.39 | 0.0754279 | ||||||||
\(794\) | −341.905 | −0.0152818 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34758.7 | 1.54773 | ||||||||
\(797\) | −13044.2 | −0.579736 | −0.289868 | − | 0.957067i | \(-0.593611\pi\) | ||||
−0.289868 | + | 0.957067i | \(0.593611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7598.79 | 0.336453 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14903.5 | 0.656187 | ||||||||
\(803\) | −2101.36 | −0.0923478 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1821.80 | 0.0796156 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17648.4 | 0.768402 | ||||||||
\(809\) | −20548.8 | −0.893026 | −0.446513 | − | 0.894777i | \(-0.647334\pi\) | ||||
−0.446513 | + | 0.894777i | \(0.647334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1266.15 | −0.0548220 | −0.0274110 | − | 0.999624i | \(-0.508726\pi\) | ||||
−0.0274110 | + | 0.999624i | \(0.508726\pi\) | |||||||
\(812\) | 8960.70 | 0.387265 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 257.420 | 0.0110842 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2897.55 | −0.124079 | ||||||||
\(818\) | −10474.8 | −0.447728 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29978.9 | 1.27439 | 0.637193 | − | 0.770704i | \(-0.280095\pi\) | ||||
0.637193 | + | 0.770704i | \(0.280095\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19172.5 | 0.812043 | 0.406021 | − | 0.913864i | \(-0.366916\pi\) | ||||
0.406021 | + | 0.913864i | \(0.366916\pi\) | |||||||
\(824\) | −13218.6 | −0.558851 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2932.76 | 0.123539 | ||||||||
\(827\) | 13488.9 | 0.567175 | 0.283588 | − | 0.958946i | \(-0.408475\pi\) | ||||
0.283588 | + | 0.958946i | \(0.408475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16585.9 | 0.694876 | 0.347438 | − | 0.937703i | \(-0.387052\pi\) | ||||
0.347438 | + | 0.937703i | \(0.387052\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −604.990 | −0.0252094 | ||||||||
\(833\) | −761.960 | −0.0316931 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −441.967 | −0.0182844 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14856.0 | −0.612401 | ||||||||
\(839\) | −37812.6 | −1.55594 | −0.777971 | − | 0.628301i | \(-0.783751\pi\) | ||||
−0.777971 | + | 0.628301i | \(0.783751\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13583.2 | 0.556940 | ||||||||
\(842\) | −949.499 | −0.0388621 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23559.5 | 0.960842 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9173.54 | 0.372145 | ||||||||
\(848\) | −10033.3 | −0.406302 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7923.19 | −0.319158 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5118.65 | 0.205462 | 0.102731 | − | 0.994709i | \(-0.467242\pi\) | ||||
0.102731 | + | 0.994709i | \(0.467242\pi\) | |||||||
\(854\) | −968.049 | −0.0387892 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4607.27 | 0.183964 | ||||||||
\(857\) | 34615.7 | 1.37975 | 0.689877 | − | 0.723927i | \(-0.257665\pi\) | ||||
0.689877 | + | 0.723927i | \(0.257665\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24854.2 | −0.987210 | −0.493605 | − | 0.869686i | \(-0.664321\pi\) | ||||
−0.493605 | + | 0.869686i | \(0.664321\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10149.9 | −0.401054 | ||||||||
\(863\) | −9637.52 | −0.380145 | −0.190072 | − | 0.981770i | \(-0.560872\pi\) | ||||
−0.190072 | + | 0.981770i | \(0.560872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10882.9 | −0.427038 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4807.09 | 0.187976 | ||||||||
\(869\) | 1314.64 | 0.0513189 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6335.99 | −0.246483 | ||||||||
\(872\) | 13515.5 | 0.524875 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2962.93 | −0.114671 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13503.3 | 0.519924 | 0.259962 | − | 0.965619i | \(-0.416290\pi\) | ||||
0.259962 | + | 0.965619i | \(0.416290\pi\) | |||||||
\(878\) | −5062.52 | −0.194592 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43808.4 | −1.67530 | −0.837652 | − | 0.546205i | \(-0.816072\pi\) | ||||
−0.837652 | + | 0.546205i | \(0.816072\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24875.4 | −0.948044 | −0.474022 | − | 0.880513i | \(-0.657198\pi\) | ||||
−0.474022 | + | 0.880513i | \(0.657198\pi\) | |||||||
\(884\) | 1488.27 | 0.0566244 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2808.85 | 0.106507 | ||||||||
\(887\) | −39120.3 | −1.48087 | −0.740435 | − | 0.672128i | \(-0.765381\pi\) | ||||
−0.740435 | + | 0.672128i | \(0.765381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6939.88 | 0.261818 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7404.31 | −0.277931 | ||||||||
\(893\) | 7262.31 | 0.272143 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10279.0 | 0.383257 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12468.5 | 0.463338 | ||||||||
\(899\) | 20370.7 | 0.755729 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4920.58 | 0.181940 | ||||||||
\(902\) | 2050.32 | 0.0756855 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7627.01 | −0.280609 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19658.5 | 0.719681 | 0.359840 | − | 0.933014i | \(-0.382831\pi\) | ||||
0.359840 | + | 0.933014i | \(0.382831\pi\) | |||||||
\(908\) | 4433.14 | 0.162025 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39577.9 | 1.43938 | 0.719690 | − | 0.694295i | \(-0.244284\pi\) | ||||
0.719690 | + | 0.694295i | \(0.244284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2616.64 | 0.0948500 | ||||||||
\(914\) | 12227.0 | 0.442489 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 38801.9 | 1.39962 | ||||||||
\(917\) | −10707.3 | −0.385591 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24855.9 | 0.892188 | 0.446094 | − | 0.894986i | \(-0.352815\pi\) | ||||
0.446094 | + | 0.894986i | \(0.352815\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15958.6 | −0.570032 | ||||||||
\(923\) | 5975.09 | 0.213080 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10951.8 | −0.388659 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 34558.3 | 1.22245 | ||||||||
\(929\) | 4466.02 | 0.157724 | 0.0788619 | − | 0.996886i | \(-0.474871\pi\) | ||||
0.0788619 | + | 0.996886i | \(0.474871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −728.220 | −0.0256353 | ||||||||
\(932\) | −2007.27 | −0.0705477 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16458.8 | 0.576604 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3768.86 | 0.131402 | 0.0657009 | − | 0.997839i | \(-0.479072\pi\) | ||||
0.0657009 | + | 0.997839i | \(0.479072\pi\) | |||||||
\(938\) | 3641.41 | 0.126755 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15423.4 | 0.534312 | 0.267156 | − | 0.963653i | \(-0.413916\pi\) | ||||
0.267156 | + | 0.963653i | \(0.413916\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −63107.4 | −2.17928 | ||||||||
\(944\) | −11105.7 | −0.382904 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1055.77 | −0.0362854 | ||||||||
\(947\) | 11755.0 | 0.403365 | 0.201682 | − | 0.979451i | \(-0.435359\pi\) | ||||
0.201682 | + | 0.979451i | \(0.435359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6762.75 | 0.231326 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1896.98 | −0.0645813 | ||||||||
\(953\) | 7321.10 | 0.248850 | 0.124425 | − | 0.992229i | \(-0.460291\pi\) | ||||
0.124425 | + | 0.992229i | \(0.460291\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21468.6 | −0.726300 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8880.26 | 0.299487 | ||||||||
\(959\) | 1540.67 | 0.0518777 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18862.9 | −0.633174 | ||||||||
\(962\) | −828.449 | −0.0277653 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3136.30 | −0.104786 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21155.8 | 0.703542 | 0.351771 | − | 0.936086i | \(-0.385580\pi\) | ||||
0.351771 | + | 0.936086i | \(0.385580\pi\) | |||||||
\(968\) | 22838.5 | 0.758322 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59824.6 | 1.97720 | 0.988600 | − | 0.150566i | \(-0.0481095\pi\) | ||||
0.988600 | + | 0.150566i | \(0.0481095\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14288.1 | 0.470768 | ||||||||
\(974\) | 9167.33 | 0.301581 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3665.80 | 0.120225 | ||||||||
\(977\) | −19245.9 | −0.630227 | −0.315113 | − | 0.949054i | \(-0.602043\pi\) | ||||
−0.315113 | + | 0.949054i | \(0.602043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4241.91 | −0.138480 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1503.81 | 0.0488681 | ||||||||
\(983\) | −52661.2 | −1.70868 | −0.854339 | − | 0.519716i | \(-0.826038\pi\) | ||||
−0.854339 | + | 0.519716i | \(0.826038\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3624.61 | −0.117070 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1422.37 | 0.0458013 | ||||||||
\(989\) | 32495.8 | 1.04480 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39065.5 | −1.25223 | −0.626114 | − | 0.779732i | \(-0.715356\pi\) | ||||
−0.626114 | + | 0.779732i | \(0.715356\pi\) | |||||||
\(992\) | 18539.3 | 0.593369 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3434.00 | −0.109577 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31074.5 | −0.987099 | −0.493550 | − | 0.869718i | \(-0.664301\pi\) | ||||
−0.493550 | + | 0.869718i | \(0.664301\pi\) | |||||||
\(998\) | 481.816 | 0.0152822 | ||||||||
\(999\) | 0 | 0 |
(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 | 1575.4.a.bh.1.3 | yes | 4 | |
3.2 | odd | 2 | inner | 1575.4.a.bh.1.2 | ✓ | 4 | |
5.4 | even | 2 | 1575.4.a.bi.1.2 | yes | 4 | ||
15.14 | odd | 2 | 1575.4.a.bi.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1575.4.a.bh.1.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
1575.4.a.bh.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
1575.4.a.bi.1.2 | yes | 4 | 5.4 | even | 2 | ||
1575.4.a.bi.1.3 | yes | 4 | 15.14 | odd | 2 |