Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,4,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, 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("1088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.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: | \(64.1940780862\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 67x^{5} - 35x^{4} + 893x^{3} + 595x^{2} - 3064x - 2804 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 544) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.00457\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.24805 | −0.625087 | −0.312543 | − | 0.949903i | \(-0.601181\pi\) | ||||
−0.312543 | + | 0.949903i | \(0.601181\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.51829 | −0.314685 | −0.157343 | − | 0.987544i | \(-0.550293\pi\) | ||||
−0.157343 | + | 0.987544i | \(0.550293\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.9586 | −0.591709 | −0.295854 | − | 0.955233i | \(-0.595604\pi\) | ||||
−0.295854 | + | 0.955233i | \(0.595604\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −16.4502 | −0.609266 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 23.7437 | 0.650818 | 0.325409 | − | 0.945573i | \(-0.394498\pi\) | ||||
0.325409 | + | 0.945573i | \(0.394498\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −47.1585 | −1.00611 | −0.503055 | − | 0.864255i | \(-0.667791\pi\) | ||||
−0.503055 | + | 0.864255i | \(0.667791\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.4276 | 0.196706 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.0000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −67.6749 | −0.817141 | −0.408571 | − | 0.912727i | \(-0.633973\pi\) | ||||
−0.408571 | + | 0.912727i | \(0.633973\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 35.5940 | 0.369869 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −55.1122 | −0.499639 | −0.249820 | − | 0.968292i | \(-0.580371\pi\) | ||||
−0.249820 | + | 0.968292i | \(0.580371\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −112.622 | −0.900973 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 141.128 | 1.00593 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 237.588 | 1.52134 | 0.760672 | − | 0.649137i | \(-0.224870\pi\) | ||||
0.760672 | + | 0.649137i | \(0.224870\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −303.801 | −1.76014 | −0.880069 | − | 0.474846i | \(-0.842504\pi\) | ||||
−0.880069 | + | 0.474846i | \(0.842504\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −77.1206 | −0.406818 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 38.5555 | 0.186202 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −122.719 | −0.545269 | −0.272635 | − | 0.962118i | \(-0.587895\pi\) | ||||
−0.272635 | + | 0.962118i | \(0.587895\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 153.173 | 0.628906 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 435.595 | 1.65923 | 0.829615 | − | 0.558335i | \(-0.188560\pi\) | ||||
0.829615 | + | 0.558335i | \(0.188560\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −232.067 | −0.823020 | −0.411510 | − | 0.911405i | \(-0.634998\pi\) | ||||
−0.411510 | + | 0.911405i | \(0.634998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 57.8765 | 0.191727 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −594.099 | −1.84379 | −0.921897 | − | 0.387435i | \(-0.873361\pi\) | ||||
−0.921897 | + | 0.387435i | \(0.873361\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −222.909 | −0.649881 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 55.2168 | 0.151606 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 392.312 | 1.01676 | 0.508379 | − | 0.861133i | \(-0.330245\pi\) | ||||
0.508379 | + | 0.861133i | \(0.330245\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −83.5372 | −0.204803 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 219.811 | 0.510784 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 174.029 | 0.384012 | 0.192006 | − | 0.981394i | \(-0.438501\pi\) | ||||
0.192006 | + | 0.981394i | \(0.438501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −332.321 | −0.697530 | −0.348765 | − | 0.937210i | \(-0.613399\pi\) | ||||
−0.348765 | + | 0.937210i | \(0.613399\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 180.271 | 0.360508 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 165.917 | 0.316608 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 165.594 | 0.301949 | 0.150974 | − | 0.988538i | \(-0.451759\pi\) | ||||
0.150974 | + | 0.988538i | \(0.451759\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 179.007 | 0.312318 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 76.2120 | 0.127390 | 0.0636951 | − | 0.997969i | \(-0.479711\pi\) | ||||
0.0636951 | + | 0.997969i | \(0.479711\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 559.023 | 0.896284 | 0.448142 | − | 0.893962i | \(-0.352086\pi\) | ||||
0.448142 | + | 0.893962i | \(0.352086\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 365.800 | 0.563187 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −260.198 | −0.385094 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1003.29 | −1.42885 | −0.714423 | − | 0.699714i | \(-0.753311\pi\) | ||||
−0.714423 | + | 0.699714i | \(0.753311\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −14.2359 | −0.0195280 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1333.13 | 1.76301 | 0.881504 | − | 0.472177i | \(-0.156532\pi\) | ||||
0.881504 | + | 0.472177i | \(0.156532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 59.8109 | 0.0763224 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −771.696 | −0.950972 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −31.9895 | −0.0380998 | −0.0190499 | − | 0.999819i | \(-0.506064\pi\) | ||||
−0.0190499 | + | 0.999819i | \(0.506064\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 516.791 | 0.595323 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 986.760 | 1.10024 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 238.100 | 0.257142 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1633.36 | 1.70972 | 0.854859 | − | 0.518860i | \(-0.173643\pi\) | ||||
0.854859 | + | 0.518860i | \(0.173643\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −390.588 | −0.396521 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1019.74 | −1.00463 | −0.502316 | − | 0.864684i | \(-0.667519\pi\) | ||||
−0.502316 | + | 0.864684i | \(0.667519\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −754.337 | −0.721622 | −0.360811 | − | 0.932639i | \(-0.617500\pi\) | ||||
−0.360811 | + | 0.932639i | \(0.617500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −125.230 | −0.116392 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1165.48 | 1.05300 | 0.526501 | − | 0.850175i | \(-0.323504\pi\) | ||||
0.526501 | + | 0.850175i | \(0.323504\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1241.76 | 1.09118 | 0.545592 | − | 0.838051i | \(-0.316305\pi\) | ||||
0.545592 | + | 0.838051i | \(0.316305\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 398.598 | 0.340840 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 262.115 | 0.218209 | 0.109105 | − | 0.994030i | \(-0.465202\pi\) | ||||
0.109105 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 193.901 | 0.157229 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 775.767 | 0.612989 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 186.296 | 0.143510 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −767.237 | −0.576436 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1414.83 | −1.03716 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 836.021 | 0.598208 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −722.607 | −0.504890 | −0.252445 | − | 0.967611i | \(-0.581235\pi\) | ||||
−0.252445 | + | 0.967611i | \(0.581235\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 753.764 | 0.514459 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1673.19 | −1.11593 | −0.557966 | − | 0.829864i | \(-0.688418\pi\) | ||||
−0.557966 | + | 0.829864i | \(0.688418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 741.622 | 0.483509 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −496.530 | −0.316552 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2338.46 | 1.45831 | 0.729154 | − | 0.684349i | \(-0.239914\pi\) | ||||
0.729154 | + | 0.684349i | \(0.239914\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 263.184 | 0.160597 | 0.0802985 | − | 0.996771i | \(-0.474413\pi\) | ||||
0.0802985 | + | 0.996771i | \(0.474413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1929.66 | 1.15253 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1119.72 | −0.654794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −835.902 | −0.478744 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 724.019 | 0.406232 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1430.79 | −0.786676 | −0.393338 | − | 0.919394i | \(-0.628680\pi\) | ||||
−0.393338 | + | 0.919394i | \(0.628680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2818.89 | 1.51919 | 0.759596 | − | 0.650395i | \(-0.225396\pi\) | ||||
0.759596 | + | 0.650395i | \(0.225396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 279.653 | 0.147769 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1068.86 | 0.553890 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2466.38 | 1.25375 | 0.626874 | − | 0.779121i | \(-0.284334\pi\) | ||||
0.626874 | + | 0.779121i | \(0.284334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1274.25 | −0.635562 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 603.953 | 0.295641 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 865.510 | 0.415902 | 0.207951 | − | 0.978139i | \(-0.433321\pi\) | ||||
0.207951 | + | 0.978139i | \(0.433321\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 271.333 | 0.128019 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2024.39 | 0.938036 | 0.469018 | − | 0.883189i | \(-0.344608\pi\) | ||||
0.469018 | + | 0.883189i | \(0.344608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.9258 | 0.0122557 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1113.26 | 0.497857 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 663.819 | 0.291729 | 0.145865 | − | 0.989305i | \(-0.453404\pi\) | ||||
0.145865 | + | 0.989305i | \(0.453404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1234.18 | 0.533114 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −565.256 | −0.240041 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −70.2472 | −0.0293325 | −0.0146663 | − | 0.999892i | \(-0.504669\pi\) | ||||
−0.0146663 | + | 0.999892i | \(0.504669\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −926.748 | −0.380578 | −0.190289 | − | 0.981728i | \(-0.560943\pi\) | ||||
−0.190289 | + | 0.981728i | \(0.560943\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1079.39 | 0.436017 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 431.762 | 0.171588 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −403.643 | −0.157846 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1546.57 | −0.595218 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1970.62 | 0.746540 | 0.373270 | − | 0.927723i | \(-0.378236\pi\) | ||||
0.373270 | + | 0.927723i | \(0.378236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2101.01 | 0.783597 | 0.391799 | − | 0.920051i | \(-0.371853\pi\) | ||||
0.391799 | + | 0.920051i | \(0.371853\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −538.907 | −0.197907 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3671.99 | 1.32801 | 0.664006 | − | 0.747727i | \(-0.268855\pi\) | ||||
0.664006 | + | 0.747727i | \(0.268855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1161.43 | −0.413726 | −0.206863 | − | 0.978370i | \(-0.566325\pi\) | ||||
−0.206863 | + | 0.978370i | \(0.566325\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −537.858 | −0.188744 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2603.63 | −0.900192 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1532.55 | −0.522135 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 906.607 | 0.304413 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1606.85 | −0.531810 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3709.86 | −1.21041 | −0.605207 | − | 0.796068i | \(-0.706910\pi\) | ||||
−0.605207 | + | 0.796068i | \(0.706910\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −247.540 | −0.0796299 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 816.478 | 0.258992 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3329.23 | 1.04149 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1815.73 | −0.560255 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 801.695 | 0.244017 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 397.023 | 0.119223 | 0.0596113 | − | 0.998222i | \(-0.481014\pi\) | ||||
0.0596113 | + | 0.998222i | \(0.481014\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1852.65 | 0.548933 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1730.14 | 0.505875 | 0.252938 | − | 0.967483i | \(-0.418603\pi\) | ||||
0.252938 | + | 0.967483i | \(0.418603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5103.01 | 1.47256 | 0.736280 | − | 0.676677i | \(-0.236581\pi\) | ||||
0.736280 | + | 0.676677i | \(0.236581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 845.134 | 0.240717 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1961.49 | 0.551509 | 0.275755 | − | 0.961228i | \(-0.411072\pi\) | ||||
0.275755 | + | 0.961228i | \(0.411072\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2090.21 | 0.580215 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3258.73 | 0.893153 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5798.95 | 1.56947 | 0.784734 | − | 0.619833i | \(-0.212800\pi\) | ||||
0.784734 | + | 0.619833i | \(0.212800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5483.62 | 1.46569 | 0.732845 | − | 0.680396i | \(-0.238192\pi\) | ||||
0.732845 | + | 0.680396i | \(0.238192\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3764.22 | −0.993725 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 784.259 | 0.204508 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3191.45 | 0.822133 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4330.06 | −1.10203 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3381.15 | 0.850265 | 0.425133 | − | 0.905131i | \(-0.360227\pi\) | ||||
0.425133 | + | 0.905131i | \(0.360227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1308.57 | −0.325174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −194.269 | −0.0477081 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5482.55 | −1.33071 | −0.665355 | − | 0.746527i | \(-0.731720\pi\) | ||||
−0.665355 | + | 0.746527i | \(0.731720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1344.83 | 0.322640 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3908.37 | −0.926903 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −970.197 | −0.227471 | −0.113736 | − | 0.993511i | \(-0.536282\pi\) | ||||
−0.113736 | + | 0.993511i | \(0.536282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1380.27 | −0.319959 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 103.903 | 0.0238157 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3255.29 | −0.737839 | −0.368919 | − | 0.929461i | \(-0.620272\pi\) | ||||
−0.368919 | + | 0.929461i | \(0.620272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4122.65 | −0.924109 | −0.462054 | − | 0.886852i | \(-0.652887\pi\) | ||||
−0.462054 | + | 0.886852i | \(0.652887\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1678.56 | −0.372129 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2674.05 | −0.586369 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6463.78 | −1.40206 | −0.701031 | − | 0.713131i | \(-0.747277\pi\) | ||||
−0.701031 | + | 0.713131i | \(0.747277\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4997.59 | 1.07239 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8077.95 | 1.71491 | 0.857456 | − | 0.514558i | \(-0.172044\pi\) | ||||
0.857456 | + | 0.514558i | \(0.172044\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8426.73 | −1.77003 | −0.885013 | − | 0.465566i | \(-0.845851\pi\) | ||||
−0.885013 | + | 0.465566i | \(0.845851\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −773.359 | −0.160736 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4773.51 | −0.981781 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5305.23 | −1.06872 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1742.82 | −0.347496 | −0.173748 | − | 0.984790i | \(-0.555588\pi\) | ||||
−0.173748 | + | 0.984790i | \(0.555588\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −612.286 | −0.120843 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3350.91 | 0.654678 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2599.01 | 0.502691 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2543.13 | 0.486988 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3312.16 | 0.627983 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1169.20 | 0.219503 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9097.79 | −1.69133 | −0.845665 | − | 0.533714i | \(-0.820796\pi\) | ||||
−0.845665 | + | 0.533714i | \(0.820796\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2450.12 | 0.451076 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8491.06 | −1.54818 | −0.774090 | − | 0.633076i | \(-0.781792\pi\) | ||||
−0.774090 | + | 0.633076i | \(0.781792\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 134.718 | 0.0243282 | 0.0121641 | − | 0.999926i | \(-0.496128\pi\) | ||||
0.0121641 | + | 0.999926i | \(0.496128\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −634.245 | −0.113447 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2901.67 | 0.514113 | 0.257056 | − | 0.966396i | \(-0.417247\pi\) | ||||
0.257056 | + | 0.966396i | \(0.417247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5641.21 | 0.990117 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3785.53 | −0.658218 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1150.47 | 0.198186 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5311.07 | 0.906477 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4033.29 | −0.682085 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6510.50 | 1.09099 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1895.83 | −0.314816 | −0.157408 | − | 0.987534i | \(-0.550314\pi\) | ||||
−0.157408 | + | 0.987534i | \(0.550314\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2018.76 | 0.332214 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −582.609 | −0.0950189 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 93.0976 | 0.0150485 | 0.00752426 | − | 0.999972i | \(-0.497605\pi\) | ||||
0.00752426 | + | 0.999972i | \(0.497605\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −851.360 | −0.136400 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7213.36 | −1.14553 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6201.57 | 0.976249 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −629.799 | −0.0982818 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7925.10 | 1.22606 | 0.613028 | − | 0.790061i | \(-0.289951\pi\) | ||||
0.613028 | + | 0.790061i | \(0.289951\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4721.70 | 0.724202 | 0.362101 | − | 0.932139i | \(-0.382059\pi\) | ||||
0.362101 | + | 0.932139i | \(0.382059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6655.40 | −1.01208 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11711.7 | −1.76586 | −0.882931 | − | 0.469503i | \(-0.844433\pi\) | ||||
−0.882931 | + | 0.469503i | \(0.844433\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −268.136 | −0.0400878 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −605.099 | −0.0897065 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1754.65 | 0.257958 | 0.128979 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128979 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2279.11 | −0.332280 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2492.02 | 0.360323 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1966.80 | −0.282047 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6298.45 | 0.895848 | 0.447924 | − | 0.894072i | \(-0.352164\pi\) | ||||
0.447924 | + | 0.894072i | \(0.352164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7165.62 | −1.01091 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4299.19 | −0.601625 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6682.68 | −0.927657 | −0.463828 | − | 0.885925i | \(-0.653525\pi\) | ||||
−0.463828 | + | 0.885925i | \(0.653525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2715.44 | −0.373932 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11204.3 | −1.53064 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1058.29 | −0.143432 | −0.0717158 | − | 0.997425i | \(-0.522847\pi\) | ||||
−0.0717158 | + | 0.997425i | \(0.522847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2347.06 | 0.315600 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9898.73 | −1.32063 | −0.660315 | − | 0.750989i | \(-0.729577\pi\) | ||||
−0.660315 | + | 0.750989i | \(0.729577\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 915.450 | 0.121184 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3817.54 | 0.501438 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −305.994 | −0.0398831 | −0.0199416 | − | 0.999801i | \(-0.506348\pi\) | ||||
−0.0199416 | + | 0.999801i | \(0.506348\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 936.908 | 0.121180 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5434.59 | 0.697554 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3529.86 | 0.449637 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4705.55 | 0.594874 | 0.297437 | − | 0.954741i | \(-0.403868\pi\) | ||||
0.297437 | + | 0.954741i | \(0.403868\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2408.82 | −0.302235 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7468.90 | −0.930122 | −0.465061 | − | 0.885279i | \(-0.653968\pi\) | ||||
−0.465061 | + | 0.885279i | \(0.653968\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14326.8 | 1.77089 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 50.0861 | 0.00614518 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2913.81 | −0.354871 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9585.99 | 1.15892 | 0.579458 | − | 0.815002i | \(-0.303264\pi\) | ||||
0.579458 | + | 0.815002i | \(0.303264\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7595.43 | −0.911570 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1907.12 | −0.227223 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4690.32 | −0.554793 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −854.834 | −0.100387 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 196.371 | 0.0228958 | 0.0114479 | − | 0.999934i | \(-0.496356\pi\) | ||||
0.0114479 | + | 0.999934i | \(0.496356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12431.5 | −1.43914 | −0.719568 | − | 0.694421i | \(-0.755660\pi\) | ||||
−0.719568 | + | 0.694421i | \(0.755660\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9773.05 | 1.12336 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1914.57 | 0.218518 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3641.77 | 0.412735 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3636.89 | 0.409303 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6717.95 | −0.750794 | −0.375397 | − | 0.926864i | \(-0.622494\pi\) | ||||
−0.375397 | + | 0.926864i | \(0.622494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11135.8 | −1.23592 | −0.617960 | − | 0.786209i | \(-0.712041\pi\) | ||||
−0.617960 | + | 0.786209i | \(0.712041\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2715.05 | 0.299257 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3729.71 | 0.408276 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7516.31 | −0.817162 | −0.408581 | − | 0.912722i | \(-0.633976\pi\) | ||||
−0.408581 | + | 0.912722i | \(0.633976\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3666.90 | 0.395951 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1252.05 | 0.134282 | 0.0671409 | − | 0.997744i | \(-0.478612\pi\) | ||||
0.0671409 | + | 0.997744i | \(0.478612\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 112.548 | 0.0119894 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4647.27 | 0.491741 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5794.88 | −0.609081 | −0.304540 | − | 0.952499i | \(-0.598503\pi\) | ||||
−0.304540 | + | 0.952499i | \(0.598503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10342.6 | 1.07986 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9155.89 | −0.949628 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1818.22 | −0.187340 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1188.56 | −0.121660 | −0.0608298 | − | 0.998148i | \(-0.519375\pi\) | ||||
−0.0608298 | + | 0.998148i | \(0.519375\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2399.18 | −0.243974 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6391.87 | −0.645768 | −0.322884 | − | 0.946439i | \(-0.604652\pi\) | ||||
−0.322884 | + | 0.946439i | \(0.604652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8214.34 | 0.824520 | 0.412260 | − | 0.911066i | \(-0.364740\pi\) | ||||
0.412260 | + | 0.911066i | \(0.364740\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3471.71 | −0.346229 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16444.2 | 1.62944 | 0.814718 | − | 0.579857i | \(-0.196892\pi\) | ||||
0.814718 | + | 0.579857i | \(0.196892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1814.68 | −0.178666 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8010.91 | −0.783701 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5510.12 | −0.535636 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7621.66 | 0.736222 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6453.61 | −0.619477 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10295.6 | −0.982082 | −0.491041 | − | 0.871137i | \(-0.663383\pi\) | ||||
−0.491041 | + | 0.871137i | \(0.663383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5787.27 | 0.548600 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1961.67 | −0.184801 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5746.63 | −0.538023 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 773.861 | 0.0720061 | 0.0360031 | − | 0.999352i | \(-0.488537\pi\) | ||||
0.0360031 | + | 0.999352i | \(0.488537\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2811.22 | −0.259975 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7715.06 | 0.709115 | 0.354558 | − | 0.935034i | \(-0.384631\pi\) | ||||
0.354558 | + | 0.935034i | \(0.384631\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4038.99 | −0.368980 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1374.20 | 0.124779 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −835.177 | −0.0753779 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3926.92 | −0.352291 | −0.176146 | − | 0.984364i | \(-0.556363\pi\) | ||||
−0.176146 | + | 0.984364i | \(0.556363\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6575.31 | −0.586354 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3593.23 | 0.318517 | 0.159258 | − | 0.987237i | \(-0.449090\pi\) | ||||
0.159258 | + | 0.987237i | \(0.449090\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3587.74 | 0.316143 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −87.4563 | −0.00766089 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6533.93 | −0.568981 | −0.284490 | − | 0.958679i | \(-0.591824\pi\) | ||||
−0.284490 | + | 0.958679i | \(0.591824\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6126.11 | −0.530339 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9550.84 | −0.821988 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2653.98 | 0.227084 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14106.1 | −1.19997 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2156.11 | −0.182356 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12512.0 | −1.05213 | −0.526066 | − | 0.850444i | \(-0.676334\pi\) | ||||
−0.526066 | + | 0.850444i | \(0.676334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10715.0 | 0.895863 | 0.447932 | − | 0.894068i | \(-0.352161\pi\) | ||||
0.447932 | + | 0.894068i | \(0.352161\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4008.66 | −0.333242 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5164.62 | 0.426896 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9129.64 | −0.750361 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2862.82 | −0.233966 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20542.0 | −1.66937 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4100.49 | −0.331364 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 228.166 | 0.0183354 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5292.69 | −0.422954 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20006.9 | 1.58995 | 0.794975 | − | 0.606642i | \(-0.207484\pi\) | ||||
0.794975 | + | 0.606642i | \(0.207484\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3010.12 | 0.237894 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4368.87 | −0.343379 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16250.5 | −1.27024 | −0.635121 | − | 0.772413i | \(-0.719050\pi\) | ||||
−0.635121 | + | 0.772413i | \(0.719050\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5466.75 | 0.424982 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16078.7 | −1.24315 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10994.6 | 0.845460 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1402.38 | −0.107257 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8475.62 | 0.644746 | 0.322373 | − | 0.946613i | \(-0.395519\pi\) | ||||
0.322373 | + | 0.946613i | \(0.395519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10943.9 | 0.828048 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1311.05 | 0.0986677 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22563.0 | 1.68902 | 0.844508 | − | 0.535543i | \(-0.179893\pi\) | ||||
0.844508 | + | 0.535543i | \(0.179893\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −922.194 | −0.0686673 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 156.006 | 0.0115549 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1820.31 | 0.134115 | 0.0670576 | − | 0.997749i | \(-0.478639\pi\) | ||||
0.0670576 | + | 0.997749i | \(0.478639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12294.2 | −0.901043 | −0.450522 | − | 0.892766i | \(-0.648762\pi\) | ||||
−0.450522 | + | 0.892766i | \(0.648762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6400.67 | −0.466652 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6206.83 | 0.450161 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10948.3 | −0.789918 | −0.394959 | − | 0.918699i | \(-0.629241\pi\) | ||||
−0.394959 | + | 0.918699i | \(0.629241\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6824.19 | −0.489816 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14609.2 | −1.04319 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9314.94 | 0.661724 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2729.37 | −0.192898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5593.92 | −0.393332 | −0.196666 | − | 0.980471i | \(-0.563011\pi\) | ||||
−0.196666 | + | 0.980471i | \(0.563011\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20559.7 | 1.43828 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11926.8 | −0.830123 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15467.3 | 1.07111 | 0.535554 | − | 0.844501i | \(-0.320103\pi\) | ||||
0.535554 | + | 0.844501i | \(0.320103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −655.443 | −0.0451606 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3772.37 | 0.258615 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20969.4 | −1.43036 | −0.715181 | − | 0.698939i | \(-0.753656\pi\) | ||||
−0.715181 | + | 0.698939i | \(0.753656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10747.5 | −0.729447 | −0.364724 | − | 0.931116i | \(-0.618837\pi\) | ||||
−0.364724 | + | 0.931116i | \(0.618837\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2724.06 | −0.183967 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2699.36 | 0.181396 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12074.0 | 0.807364 | 0.403682 | − | 0.914899i | \(-0.367730\pi\) | ||||
0.403682 | + | 0.914899i | \(0.367730\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8456.71 | 0.562698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28016.9 | 1.85506 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9438.87 | 0.621912 | 0.310956 | − | 0.950424i | \(-0.399351\pi\) | ||||
0.310956 | + | 0.950424i | \(0.399351\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4977.79 | 0.326380 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18221.6 | 1.18893 | 0.594467 | − | 0.804120i | \(-0.297363\pi\) | ||||
0.594467 | + | 0.804120i | \(0.297363\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12655.7 | 0.821772 | 0.410886 | − | 0.911687i | \(-0.365220\pi\) | ||||
0.410886 | + | 0.911687i | \(0.365220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7777.90 | −0.502603 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 350.560 | 0.0225440 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11136.3 | 0.712726 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5219.13 | 0.332427 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2086.23 | 0.132247 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12669.0 | 0.799276 | 0.399638 | − | 0.916673i | \(-0.369136\pi\) | ||||
0.399638 | + | 0.916673i | \(0.369136\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12049.8 | 0.756614 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2542.34 | 0.158881 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10512.1 | 0.653851 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1253.70 | −0.0776145 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11292.9 | −0.695856 | −0.347928 | − | 0.937521i | \(-0.613115\pi\) | ||||
−0.347928 | + | 0.937521i | \(0.613115\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 746.447 | 0.0457807 | 0.0228904 | − | 0.999738i | \(-0.492713\pi\) | ||||
0.0228904 | + | 0.999738i | \(0.492713\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2651.96 | −0.161893 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17692.6 | 1.07507 | 0.537533 | − | 0.843243i | \(-0.319356\pi\) | ||||
0.537533 | + | 0.843243i | \(0.319356\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4132.10 | 0.249922 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10813.5 | −0.651021 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −132.798 | −0.00795833 | −0.00397916 | − | 0.999992i | \(-0.501267\pi\) | ||||
−0.00397916 | + | 0.999992i | \(0.501267\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5886.75 | 0.351167 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9196.04 | −0.546076 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17767.6 | 1.05027 | 0.525136 | − | 0.851018i | \(-0.324015\pi\) | ||||
0.525136 | + | 0.851018i | \(0.324015\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20422.1 | −1.20171 | −0.600854 | − | 0.799359i | \(-0.705173\pi\) | ||||
−0.600854 | + | 0.799359i | \(0.705173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2603.94 | −0.152532 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2609.24 | −0.152153 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13094.0 | −0.760123 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1289.55 | −0.0745245 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7890.53 | −0.453965 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30616.6 | −1.75361 | −0.876807 | − | 0.480842i | \(-0.840331\pi\) | ||||
−0.876807 | + | 0.480842i | \(0.840331\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15894.1 | −0.906317 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18997.9 | 1.07851 | 0.539253 | − | 0.842144i | \(-0.318707\pi\) | ||||
0.539253 | + | 0.842144i | \(0.318707\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17899.3 | −1.01166 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5619.59 | −0.316216 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33428.1 | −1.87275 | −0.936377 | − | 0.350996i | \(-0.885843\pi\) | ||||
−0.936377 | + | 0.350996i | \(0.885843\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8227.38 | −0.458908 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16574.8 | −0.920478 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18500.8 | −1.02297 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26903.4 | −1.48112 | −0.740560 | − | 0.671991i | \(-0.765440\pi\) | ||||
−0.740560 | + | 0.671991i | \(0.765440\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4280.30 | 0.234625 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −925.958 | −0.0505375 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7405.11 | −0.402423 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6371.02 | −0.344741 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26025.9 | 1.40226 | 0.701129 | − | 0.713034i | \(-0.252680\pi\) | ||||
0.701129 | + | 0.713034i | \(0.252680\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8305.02 | 0.445562 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6789.11 | −0.362685 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11174.9 | 0.594450 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1570.27 | −0.0831774 | −0.0415887 | − | 0.999135i | \(-0.513242\pi\) | ||||
−0.0415887 | + | 0.999135i | \(0.513242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16504.3 | 0.870548 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16743.2 | 0.879434 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3939.49 | 0.206054 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18835.2 | −0.981053 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1539.79 | 0.0798669 | 0.0399335 | − | 0.999202i | \(-0.487285\pi\) | ||||
0.0399335 | + | 0.999202i | \(0.487285\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8266.48 | 0.426990 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17811.1 | −0.916183 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26757.5 | −1.37069 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21003.5 | −1.07150 | −0.535748 | − | 0.844378i | \(-0.679970\pi\) | ||||
−0.535748 | + | 0.844378i | \(0.679970\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12610.7 | 0.640692 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3945.14 | 0.199612 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14983.1 | 0.754997 | 0.377498 | − | 0.926010i | \(-0.376784\pi\) | ||||
0.377498 | + | 0.926010i | \(0.376784\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2547.31 | −0.127835 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3931.82 | 0.196514 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2001.07 | 0.0996082 | 0.0498041 | − | 0.998759i | \(-0.484140\pi\) | ||||
0.0498041 | + | 0.998759i | \(0.484140\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10366.0 | −0.513905 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13139.2 | 0.648765 | 0.324382 | − | 0.945926i | \(-0.394844\pi\) | ||||
0.324382 | + | 0.945926i | \(0.394844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5033.92 | 0.247555 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21930.2 | −1.07414 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12772.0 | −0.623070 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27803.1 | 1.35093 | 0.675466 | − | 0.737391i | \(-0.263942\pi\) | ||||
0.675466 | + | 0.737391i | \(0.263942\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10982.1 | −0.531490 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9917.67 | −0.478068 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26943.6 | 1.29364 | 0.646818 | − | 0.762644i | \(-0.276099\pi\) | ||||
0.646818 | + | 0.762644i | \(0.276099\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4250.29 | 0.203262 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8418.10 | 0.400993 | 0.200497 | − | 0.979694i | \(-0.435744\pi\) | ||||
0.200497 | + | 0.979694i | \(0.435744\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13607.9 | −0.645663 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −983.901 | −0.0465007 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8206.97 | −0.386358 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11445.7 | −0.536726 | −0.268363 | − | 0.963318i | \(-0.586483\pi\) | ||||
−0.268363 | + | 0.963318i | \(0.586483\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17807.6 | 0.831809 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13064.8 | 0.607902 | 0.303951 | − | 0.952688i | \(-0.401694\pi\) | ||||
0.303951 | + | 0.952688i | \(0.401694\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34214.6 | 1.58584 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4368.08 | −0.201678 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29478.8 | −1.35583 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1809.55 | 0.0829078 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33530.4 | 1.53037 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8677.43 | −0.394536 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39876.6 | −1.80616 | −0.903080 | − | 0.429473i | \(-0.858700\pi\) | ||||
−0.903080 | + | 0.429473i | \(0.858700\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3151.24 | 0.142189 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2872.41 | −0.129116 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15671.8 | 0.701792 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4483.17 | 0.200002 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27650.2 | 1.22888 | 0.614442 | − | 0.788962i | \(-0.289381\pi\) | ||||
0.614442 | + | 0.788962i | \(0.289381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10099.7 | 0.447186 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 526.234 | 0.0232129 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13273.3 | 0.583317 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2124.88 | −0.0930338 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10573.3 | 0.461213 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4760.40 | 0.206881 | 0.103441 | − | 0.994636i | \(-0.467015\pi\) | ||||
0.103441 | + | 0.994636i | \(0.467015\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34075.5 | 1.47540 | 0.737701 | − | 0.675127i | \(-0.235911\pi\) | ||||
0.737701 | + | 0.675127i | \(0.235911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13390.6 | 0.577648 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3045.12 | −0.130878 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15705.1 | 0.672524 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8501.31 | −0.362711 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2245.59 | −0.0954589 | −0.0477294 | − | 0.998860i | \(-0.515199\pi\) | ||||
−0.0477294 | + | 0.998860i | \(0.515199\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12914.3 | −0.546980 | −0.273490 | − | 0.961875i | \(-0.588178\pi\) | ||||
−0.273490 | + | 0.961875i | \(0.588178\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8685.45 | 0.366532 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40085.3 | 1.68549 | 0.842747 | − | 0.538309i | \(-0.180937\pi\) | ||||
0.842747 | + | 0.538309i | \(0.180937\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3101.91 | −0.129956 | −0.0649782 | − | 0.997887i | \(-0.520698\pi\) | ||||
−0.0649782 | + | 0.997887i | \(0.520698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20994.7 | 0.876410 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3789.46 | 0.157619 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7122.39 | −0.295186 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −42874.9 | −1.77058 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46317.7 | −1.90592 | −0.952958 | − | 0.303103i | \(-0.901978\pi\) | ||||
−0.952958 | + | 0.303103i | \(0.901978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32059.0 | 1.31449 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26237.6 | −1.07197 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −94.7327 | −0.00385669 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8407.84 | 0.341082 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27370.4 | 1.10642 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6763.34 | 0.272438 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32134.3 | 1.28987 | 0.644934 | − | 0.764238i | \(-0.276885\pi\) | ||||
0.644934 | + | 0.764238i | \(0.276885\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3916.79 | −0.156668 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11227.7 | −0.447529 | −0.223765 | − | 0.974643i | \(-0.571835\pi\) | ||||
−0.223765 | + | 0.974643i | \(0.571835\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28714.1 | 1.14053 | 0.570263 | − | 0.821462i | \(-0.306841\pi\) | ||||
0.570263 | + | 0.821462i | \(0.306841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15504.6 | 0.613698 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22544.0 | −0.889229 | −0.444615 | − | 0.895722i | \(-0.646659\pi\) | ||||
−0.444615 | + | 0.895722i | \(0.646659\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2335.50 | −0.0918029 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −938.685 | −0.0367698 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23821.8 | −0.929918 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7809.19 | −0.303794 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26869.1 | −1.04167 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9161.62 | −0.353965 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.8851 | 0.000419114 0 | 0.000209557 | − | 1.00000i | \(-0.499933\pi\) | ||||
0.000209557 | 1.00000i | \(0.499933\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5660.75 | 0.217215 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5955.61 | 0.227752 | 0.113876 | − | 0.993495i | \(-0.463673\pi\) | ||||
0.113876 | + | 0.993495i | \(0.463673\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30192.6 | −1.15069 | −0.575347 | − | 0.817910i | \(-0.695133\pi\) | ||||
−0.575347 | + | 0.817910i | \(0.695133\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1988.73 | 0.0755373 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5404.65 | 0.204589 | 0.102295 | − | 0.994754i | \(-0.467382\pi\) | ||||
0.102295 | + | 0.994754i | \(0.467382\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7918.76 | 0.298748 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −338.013 | −0.0127092 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40205.6 | 1.50664 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 247.150 | 0.00923051 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8441.71 | −0.314226 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −72179.4 | −2.67777 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6669.30 | −0.246600 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8260.19 | −0.304410 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3260.57 | 0.119762 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 594.900 | 0.0217788 | 0.0108894 | − | 0.999941i | \(-0.496534\pi\) | ||||
0.0108894 | + | 0.999941i | \(0.496534\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16774.9 | 0.612089 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16139.5 | 0.586965 | 0.293483 | − | 0.955964i | \(-0.405186\pi\) | ||||
0.293483 | + | 0.955964i | \(0.405186\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31653.4 | 1.14740 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3797.62 | −0.137208 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18335.8 | 0.660306 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54241.0 | 1.94695 | 0.973474 | − | 0.228799i | \(-0.0734798\pi\) | ||||
0.973474 | + | 0.228799i | \(0.0734798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29550.1 | 1.05723 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3594.05 | −0.128168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13820.9 | 0.491273 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12409.0 | 0.439660 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14010.7 | 0.494807 | 0.247404 | − | 0.968913i | \(-0.420423\pi\) | ||||
0.247404 | + | 0.968913i | \(0.420423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15085.4 | 0.531044 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27579.4 | 0.967746 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1420.13 | 0.0496719 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23701.6 | 0.826357 | 0.413178 | − | 0.910650i | \(-0.364419\pi\) | ||||
0.413178 | + | 0.910650i | \(0.364419\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −437.571 | −0.0152072 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1871.24 | −0.0648253 | −0.0324126 | − | 0.999475i | \(-0.510319\pi\) | ||||
−0.0324126 | + | 0.999475i | \(0.510319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24006.6 | −0.829016 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5441.27 | 0.187306 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51077.5 | 1.75269 | 0.876345 | − | 0.481684i | \(-0.159975\pi\) | ||||
0.876345 | + | 0.481684i | \(0.159975\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26362.7 | −0.901759 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9424.75 | −0.321365 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9534.26 | 0.324076 | 0.162038 | − | 0.986784i | \(-0.448193\pi\) | ||||
0.162038 | + | 0.986784i | \(0.448193\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6933.21 | −0.234925 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18322.9 | −0.618909 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25626.3 | −0.862894 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62504.1 | 2.09809 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19172.4 | −0.641559 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7391.97 | −0.246586 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8267.50 | 0.274938 | 0.137469 | − | 0.990506i | \(-0.456103\pi\) | ||||
0.137469 | + | 0.990506i | \(0.456103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3736.79 | −0.123883 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52149.6 | 1.72354 | 0.861771 | − | 0.507297i | \(-0.169355\pi\) | ||||
0.861771 | + | 0.507297i | \(0.169355\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2884.13 | −0.0950266 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17250.6 | −0.566627 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20321.3 | −0.665441 | −0.332721 | − | 0.943025i | \(-0.607967\pi\) | ||||
−0.332721 | + | 0.943025i | \(0.607967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −759.549 | −0.0247960 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20427.2 | −0.664822 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15604.0 | 0.506298 | 0.253149 | − | 0.967427i | \(-0.418534\pi\) | ||||
0.253149 | + | 0.967427i | \(0.418534\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12919.1 | −0.417906 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21146.4 | −0.681963 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12789.7 | 0.411213 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22050.5 | −0.706818 | −0.353409 | − | 0.935469i | \(-0.614978\pi\) | ||||
−0.353409 | + | 0.935469i | \(0.614978\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6157.74 | 0.196787 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4086.24 | 0.130194 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19850.1 | 0.630549 | 0.315275 | − | 0.949000i | \(-0.397903\pi\) | ||||
0.315275 | + | 0.949000i | \(0.397903\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17319.2 | −0.548503 |
(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 | 1088.4.a.bh.1.3 | 7 | ||
4.3 | odd | 2 | 1088.4.a.bg.1.5 | 7 | |||
8.3 | odd | 2 | 544.4.a.k.1.3 | ✓ | 7 | ||
8.5 | even | 2 | 544.4.a.l.1.5 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
544.4.a.k.1.3 | ✓ | 7 | 8.3 | odd | 2 | ||
544.4.a.l.1.5 | yes | 7 | 8.5 | even | 2 | ||
1088.4.a.bg.1.5 | 7 | 4.3 | odd | 2 | |||
1088.4.a.bh.1.3 | 7 | 1.1 | even | 1 | trivial |