Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,4,Mod(1,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("960.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.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: | \(56.6418336055\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 480) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.80625 | −0.367503 | −0.183751 | − | 0.982973i | \(-0.558824\pi\) | ||||
−0.183751 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.2250 | −1.07516 | −0.537581 | − | 0.843212i | \(-0.680662\pi\) | ||||
−0.537581 | + | 0.843212i | \(0.680662\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −78.4187 | −1.67303 | −0.836517 | − | 0.547941i | \(-0.815412\pi\) | ||||
−0.836517 | + | 0.547941i | \(0.815412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −95.2562 | −1.35900 | −0.679501 | − | 0.733675i | \(-0.737804\pi\) | ||||
−0.679501 | + | 0.733675i | \(0.737804\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 133.256 | 1.60900 | 0.804502 | − | 0.593950i | \(-0.202432\pi\) | ||||
0.804502 | + | 0.593950i | \(0.202432\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 20.4187 | 0.212178 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 66.8062 | 0.605655 | 0.302828 | − | 0.953045i | \(-0.402069\pi\) | ||||
0.302828 | + | 0.953045i | \(0.402069\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −99.6750 | −0.638248 | −0.319124 | − | 0.947713i | \(-0.603389\pi\) | ||||
−0.319124 | + | 0.947713i | \(0.603389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 322.031 | 1.86576 | 0.932879 | − | 0.360189i | \(-0.117288\pi\) | ||||
0.932879 | + | 0.360189i | \(0.117288\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 117.675 | 0.620745 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −34.0312 | −0.164352 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −108.744 | −0.483172 | −0.241586 | − | 0.970379i | \(-0.577668\pi\) | ||||
−0.241586 | + | 0.970379i | \(0.577668\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 235.256 | 0.965927 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 278.187 | 1.05965 | 0.529824 | − | 0.848108i | \(-0.322258\pi\) | ||||
0.529824 | + | 0.848108i | \(0.322258\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −381.675 | −1.35360 | −0.676801 | − | 0.736166i | \(-0.736634\pi\) | ||||
−0.676801 | + | 0.736166i | \(0.736634\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 211.519 | 0.656451 | 0.328225 | − | 0.944599i | \(-0.393549\pi\) | ||||
0.328225 | + | 0.944599i | \(0.393549\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −296.675 | −0.864942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 285.769 | 0.784620 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 411.862 | 1.06743 | 0.533714 | − | 0.845665i | \(-0.320796\pi\) | ||||
0.533714 | + | 0.845665i | \(0.320796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −196.125 | −0.480827 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −399.769 | −0.928959 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −447.225 | −0.986843 | −0.493421 | − | 0.869790i | \(-0.664254\pi\) | ||||
−0.493421 | + | 0.869790i | \(0.664254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −158.837 | −0.333394 | −0.166697 | − | 0.986008i | \(-0.553310\pi\) | ||||
−0.166697 | + | 0.986008i | \(0.553310\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −61.2562 | −0.122501 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −392.094 | −0.748204 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −455.475 | −0.830524 | −0.415262 | − | 0.909702i | \(-0.636310\pi\) | ||||
−0.415262 | + | 0.909702i | \(0.636310\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −200.419 | −0.349675 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 630.450 | 1.05381 | 0.526906 | − | 0.849924i | \(-0.323352\pi\) | ||||
0.526906 | + | 0.849924i | \(0.323352\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58.8375 | 0.0943343 | 0.0471672 | − | 0.998887i | \(-0.484981\pi\) | ||||
0.0471672 | + | 0.998887i | \(0.484981\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 266.975 | 0.395125 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1257.32 | 1.79063 | 0.895313 | − | 0.445438i | \(-0.146952\pi\) | ||||
0.895313 | + | 0.445438i | \(0.146952\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 229.800 | 0.303901 | 0.151951 | − | 0.988388i | \(-0.451444\pi\) | ||||
0.151951 | + | 0.988388i | \(0.451444\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −476.281 | −0.607764 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 299.025 | 0.368492 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1178.19 | −1.40323 | −0.701616 | − | 0.712555i | \(-0.747538\pi\) | ||||
−0.701616 | + | 0.712555i | \(0.747538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 533.737 | 0.614845 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −966.094 | −1.07720 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 666.281 | 0.719568 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1692.05 | 1.77115 | 0.885575 | − | 0.464496i | \(-0.153764\pi\) | ||||
0.885575 | + | 0.464496i | \(0.153764\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −353.025 | −0.358387 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 791.675 | 0.779947 | 0.389973 | − | 0.920826i | \(-0.372484\pi\) | ||||
0.389973 | + | 0.920826i | \(0.372484\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 362.494 | 0.346773 | 0.173386 | − | 0.984854i | \(-0.444529\pi\) | ||||
0.173386 | + | 0.984854i | \(0.444529\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 102.094 | 0.0948888 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2114.36 | 1.91031 | 0.955155 | − | 0.296107i | \(-0.0956885\pi\) | ||||
0.955155 | + | 0.296107i | \(0.0956885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2149.72 | 1.88905 | 0.944524 | − | 0.328442i | \(-0.106523\pi\) | ||||
0.944524 | + | 0.328442i | \(0.106523\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 326.231 | 0.278959 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 577.119 | 0.480449 | 0.240225 | − | 0.970717i | \(-0.422779\pi\) | ||||
0.240225 | + | 0.970717i | \(0.422779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 334.031 | 0.270857 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −705.769 | −0.557678 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 648.338 | 0.499437 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 207.600 | 0.155973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −834.562 | −0.611788 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 55.5188 | 0.0387913 | 0.0193956 | − | 0.999812i | \(-0.493826\pi\) | ||||
0.0193956 | + | 0.999812i | \(0.493826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1145.02 | 0.781503 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1577.06 | −1.05182 | −0.525911 | − | 0.850540i | \(-0.676275\pi\) | ||||
−0.525911 | + | 0.850540i | \(0.676275\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −906.975 | −0.591314 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1133.12 | −0.706634 | −0.353317 | − | 0.935504i | \(-0.614946\pi\) | ||||
−0.353317 | + | 0.935504i | \(0.614946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 425.194 | 0.259457 | 0.129728 | − | 0.991550i | \(-0.458589\pi\) | ||||
0.129728 | + | 0.991550i | \(0.458589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −634.556 | −0.379002 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3075.97 | 1.79878 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −498.375 | −0.285433 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 890.025 | 0.499374 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 136.975 | 0.0753116 | 0.0376558 | − | 0.999291i | \(-0.488011\pi\) | ||||
0.0376558 | + | 0.999291i | \(0.488011\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 493.631 | 0.266034 | 0.133017 | − | 0.991114i | \(-0.457534\pi\) | ||||
0.133017 | + | 0.991114i | \(0.457534\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −857.306 | −0.453001 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1610.16 | 0.834393 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 597.394 | 0.303677 | 0.151838 | − | 0.988405i | \(-0.451481\pi\) | ||||
0.151838 | + | 0.988405i | \(0.451481\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1235.59 | −0.616280 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −454.700 | −0.222580 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2272.35 | 1.09193 | 0.545964 | − | 0.837809i | \(-0.316164\pi\) | ||||
0.545964 | + | 0.837809i | \(0.316164\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 588.375 | 0.277606 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2092.82 | −0.969744 | −0.484872 | − | 0.874585i | \(-0.661134\pi\) | ||||
−0.484872 | + | 0.874585i | \(0.661134\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3952.50 | 1.79904 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1199.31 | 0.536335 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −58.7498 | −0.0258189 | −0.0129094 | − | 0.999917i | \(-0.504109\pi\) | ||||
−0.0129094 | + | 0.999917i | \(0.504109\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −170.156 | −0.0735006 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1341.67 | 0.569754 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2348.96 | 0.980836 | 0.490418 | − | 0.871487i | \(-0.336844\pi\) | ||||
0.490418 | + | 0.871487i | \(0.336844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2103.12 | −0.863669 | −0.431834 | − | 0.901953i | \(-0.642133\pi\) | ||||
−0.431834 | + | 0.901953i | \(0.642133\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 476.512 | 0.192485 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −543.719 | −0.216081 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3736.43 | 1.46115 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 183.769 | 0.0707260 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3203.17 | −1.21347 | −0.606737 | − | 0.794903i | \(-0.707522\pi\) | ||||
−0.606737 | + | 0.794903i | \(0.707522\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 471.113 | 0.175707 | 0.0878534 | − | 0.996133i | \(-0.471999\pi\) | ||||
0.0878534 | + | 0.996133i | \(0.471999\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1176.28 | 0.431976 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1535.21 | 0.555225 | 0.277613 | − | 0.960693i | \(-0.410457\pi\) | ||||
0.277613 | + | 0.960693i | \(0.410457\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4361.98 | 1.55383 | 0.776916 | − | 0.629604i | \(-0.216783\pi\) | ||||
0.776916 | + | 0.629604i | \(0.216783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1366.42 | 0.479503 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 678.413 | 0.234558 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1390.94 | 0.473889 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 601.256 | 0.201885 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5226.98 | −1.72994 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 385.444 | 0.125758 | 0.0628792 | − | 0.998021i | \(-0.479972\pi\) | ||||
0.0628792 | + | 0.998021i | \(0.479972\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1891.35 | −0.608419 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1908.37 | −0.605349 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2191.82 | −0.685672 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −176.512 | −0.0544640 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7469.87 | 2.27366 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −922.744 | −0.277092 | −0.138546 | − | 0.990356i | \(-0.544243\pi\) | ||||
−0.138546 | + | 0.990356i | \(0.544243\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1390.35 | 0.406523 | 0.203262 | − | 0.979124i | \(-0.434846\pi\) | ||||
0.203262 | + | 0.979124i | \(0.434846\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −750.837 | −0.216667 | −0.108333 | − | 0.994115i | \(-0.534551\pi\) | ||||
−0.108333 | + | 0.994115i | \(0.534551\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −800.925 | −0.228126 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4457.39 | −1.25328 | −0.626639 | − | 0.779310i | \(-0.715570\pi\) | ||||
−0.626639 | + | 0.779310i | \(0.715570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1057.59 | 0.293574 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3771.96 | −1.03382 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6388.69 | 1.72908 | 0.864539 | − | 0.502565i | \(-0.167610\pi\) | ||||
0.864539 | + | 0.502565i | \(0.167610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5719.02 | 1.52861 | 0.764305 | − | 0.644855i | \(-0.223082\pi\) | ||||
0.764305 | + | 0.644855i | \(0.223082\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1483.37 | −0.386814 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10449.8 | −2.69192 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −689.400 | −0.175458 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3449.44 | 0.867436 | 0.433718 | − | 0.901049i | \(-0.357201\pi\) | ||||
0.433718 | + | 0.901049i | \(0.357201\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2620.47 | −0.651177 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1428.84 | 0.350893 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1012.83 | −0.245831 | −0.122916 | − | 0.992417i | \(-0.539224\pi\) | ||||
−0.122916 | + | 0.992417i | \(0.539224\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 740.137 | 0.177567 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −897.075 | −0.212749 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6716.31 | −1.57470 | −0.787348 | − | 0.616509i | \(-0.788547\pi\) | ||||
−0.787348 | + | 0.616509i | \(0.788547\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2059.31 | 0.477368 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3534.56 | 0.810156 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1299.67 | −0.294582 | −0.147291 | − | 0.989093i | \(-0.547055\pi\) | ||||
−0.147291 | + | 0.989093i | \(0.547055\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1690.11 | 0.378844 | 0.189422 | − | 0.981896i | \(-0.439339\pi\) | ||||
0.189422 | + | 0.981896i | \(0.439339\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1601.21 | −0.354981 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −980.625 | −0.215032 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6230.89 | 1.35155 | 0.675773 | − | 0.737110i | \(-0.263810\pi\) | ||||
0.675773 | + | 0.737110i | \(0.263810\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2898.28 | 0.621920 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4759.76 | −1.01048 | −0.505238 | − | 0.862980i | \(-0.668595\pi\) | ||||
−0.505238 | + | 0.862980i | \(0.668595\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2665.95 | −0.559980 | −0.279990 | − | 0.960003i | \(-0.590331\pi\) | ||||
−0.279990 | + | 0.960003i | \(0.590331\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1998.84 | −0.415443 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1893.41 | −0.389424 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4160.75 | 0.846886 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5076.15 | −1.02257 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −517.063 | −0.103096 | −0.0515480 | − | 0.998671i | \(-0.516416\pi\) | ||||
−0.0515480 | + | 0.998671i | \(0.516416\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2236.12 | −0.441330 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1059.07 | 0.206915 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5238.86 | −1.01328 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2597.77 | 0.497453 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2375.02 | −0.450302 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −794.187 | −0.149098 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 123.038 | 0.0228734 | 0.0114367 | − | 0.999935i | \(-0.496360\pi\) | ||||
0.0114367 | + | 0.999935i | \(0.496360\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1087.48 | −0.200209 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 699.938 | 0.127620 | 0.0638100 | − | 0.997962i | \(-0.479675\pi\) | ||||
0.0638100 | + | 0.997962i | \(0.479675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1268.89 | 0.229143 | 0.114571 | − | 0.993415i | \(-0.463450\pi\) | ||||
0.114571 | + | 0.993415i | \(0.463450\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −306.281 | −0.0547841 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2507.21 | −0.444224 | −0.222112 | − | 0.975021i | \(-0.571295\pi\) | ||||
−0.222112 | + | 0.975021i | \(0.571295\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3909.75 | 0.686219 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6343.09 | −1.10292 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12693.5 | −2.18664 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1960.47 | −0.334607 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6449.17 | −1.09064 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1439.65 | −0.241248 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4639.26 | −0.770382 | −0.385191 | − | 0.922837i | \(-0.625864\pi\) | ||||
−0.385191 | + | 0.922837i | \(0.625864\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −978.694 | −0.161057 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2277.37 | −0.371422 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5643.79 | 0.912275 | 0.456137 | − | 0.889909i | \(-0.349233\pi\) | ||||
0.456137 | + | 0.889909i | \(0.349233\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1731.36 | −0.277387 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12631.7 | −2.00599 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4353.79 | 0.685371 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1002.09 | −0.156379 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11753.5 | 1.81833 | 0.909167 | − | 0.416433i | \(-0.136720\pi\) | ||||
0.909167 | + | 0.416433i | \(0.136720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −476.812 | −0.0731322 | −0.0365661 | − | 0.999331i | \(-0.511642\pi\) | ||||
−0.0365661 | + | 0.999331i | \(0.511642\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2117.31 | 0.321976 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11743.4 | −1.77064 | −0.885321 | − | 0.464981i | \(-0.846061\pi\) | ||||
−0.885321 | + | 0.464981i | \(0.846061\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3152.25 | 0.471279 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1945.01 | −0.288350 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4552.87 | 0.669336 | 0.334668 | − | 0.942336i | \(-0.391376\pi\) | ||||
0.334668 | + | 0.942336i | \(0.391376\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10898.2 | 1.58889 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −622.800 | −0.0900511 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 294.187 | 0.0421876 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 792.056 | 0.112657 | 0.0563283 | − | 0.998412i | \(-0.482061\pi\) | ||||
0.0563283 | + | 0.998412i | \(0.482061\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2503.69 | 0.353216 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2803.24 | −0.392283 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10232.0 | 1.42036 | 0.710179 | − | 0.704021i | \(-0.248614\pi\) | ||||
0.710179 | + | 0.704021i | \(0.248614\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7816.39 | 1.06781 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2064.39 | −0.279791 | −0.139895 | − | 0.990166i | \(-0.544677\pi\) | ||||
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −166.556 | −0.0223962 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2202.51 | −0.293845 | −0.146923 | − | 0.989148i | \(-0.546937\pi\) | ||||
−0.146923 | + | 0.989148i | \(0.546937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1334.88 | 0.176705 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3435.07 | −0.451201 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1898.55 | −0.247456 | −0.123728 | − | 0.992316i | \(-0.539485\pi\) | ||||
−0.123728 | + | 0.992316i | \(0.539485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6363.71 | −0.823086 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4731.19 | 0.607269 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6286.59 | 0.800792 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5070.61 | 0.641024 | 0.320512 | − | 0.947244i | \(-0.396145\pi\) | ||||
0.320512 | + | 0.947244i | \(0.396145\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2720.93 | 0.341395 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4768.98 | −0.593893 | −0.296947 | − | 0.954894i | \(-0.595968\pi\) | ||||
−0.296947 | + | 0.954894i | \(0.595968\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25253.3 | −3.12148 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4265.47 | 0.519488 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7003.60 | −0.846713 | −0.423357 | − | 0.905963i | \(-0.639148\pi\) | ||||
−0.423357 | + | 0.905963i | \(0.639148\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3399.36 | 0.407975 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3043.92 | 0.362668 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1149.00 | 0.135909 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1275.58 | −0.149797 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6643.09 | −0.774549 | −0.387275 | − | 0.921964i | \(-0.626583\pi\) | ||||
−0.387275 | + | 0.921964i | \(0.626583\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13952.5 | 1.61521 | 0.807603 | − | 0.589727i | \(-0.200765\pi\) | ||||
0.807603 | + | 0.589727i | \(0.200765\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1903.67 | 0.218817 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2381.41 | −0.271800 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1081.09 | 0.122523 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9227.92 | −1.03853 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1549.27 | 0.173146 | 0.0865730 | − | 0.996246i | \(-0.472408\pi\) | ||||
0.0865730 | + | 0.996246i | \(0.472408\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7022.39 | 0.779387 | 0.389693 | − | 0.920945i | \(-0.372581\pi\) | ||||
0.389693 | + | 0.920945i | \(0.372581\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1495.12 | 0.164795 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8902.35 | 0.974501 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3107.31 | 0.337822 | 0.168911 | − | 0.985631i | \(-0.445975\pi\) | ||||
0.168911 | + | 0.985631i | \(0.445975\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2670.07 | −0.288314 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15463.8 | −1.65848 | −0.829241 | − | 0.558892i | \(-0.811227\pi\) | ||||
−0.829241 | + | 0.558892i | \(0.811227\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5890.94 | −0.627544 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −410.925 | −0.0434812 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14043.0 | 1.47601 | 0.738005 | − | 0.674795i | \(-0.235768\pi\) | ||||
0.738005 | + | 0.674795i | \(0.235768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10911.9 | −1.13929 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1480.89 | −0.153595 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2668.69 | 0.274967 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13860.5 | −1.41875 | −0.709375 | − | 0.704831i | \(-0.751023\pi\) | ||||
−0.709375 | + | 0.704831i | \(0.751023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2571.92 | 0.261540 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7593.75 | 0.767193 | 0.383597 | − | 0.923501i | \(-0.374685\pi\) | ||||
0.383597 | + | 0.923501i | \(0.374685\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6630.96 | −0.665587 | −0.332793 | − | 0.943000i | \(-0.607991\pi\) | ||||
−0.332793 | + | 0.943000i | \(0.607991\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4830.47 | −0.481737 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6699.79 | −0.663874 | −0.331937 | − | 0.943302i | \(-0.607702\pi\) | ||||
−0.331937 | + | 0.943302i | \(0.607702\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3100.08 | 0.305220 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1792.18 | −0.175328 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14971.2 | 1.45534 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3331.41 | 0.321801 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3706.76 | 0.355809 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19984.2 | 1.90627 | 0.953133 | − | 0.302552i | \(-0.0978385\pi\) | ||||
0.953133 | + | 0.302552i | \(0.0978385\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8527.55 | 0.808363 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1364.10 | 0.128507 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8460.25 | 0.792083 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20569.1 | −1.91392 | −0.956958 | − | 0.290227i | \(-0.906269\pi\) | ||||
−0.956958 | + | 0.290227i | \(0.906269\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6817.05 | −0.630425 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19131.8 | −1.75847 | −0.879233 | − | 0.476391i | \(-0.841945\pi\) | ||||
−0.879233 | + | 0.476391i | \(0.841945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9494.66 | 0.867380 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1765.12 | −0.160276 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4291.00 | −0.387279 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16396.9 | −1.47100 | −0.735498 | − | 0.677526i | \(-0.763052\pi\) | ||||
−0.735498 | + | 0.677526i | \(0.763052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6278.46 | 0.559882 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7013.16 | −0.621672 | −0.310836 | − | 0.950464i | \(-0.600609\pi\) | ||||
−0.310836 | + | 0.950464i | \(0.600609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3958.37 | 0.348803 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11857.5 | −1.03868 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12431.8 | −1.08257 | −0.541287 | − | 0.840838i | \(-0.682063\pi\) | ||||
−0.541287 | + | 0.840838i | \(0.682063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −400.463 | −0.0346681 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3597.92 | −0.309653 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1812.47 | 0.155081 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8296.82 | −0.705791 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 176.249 | 0.0149065 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6707.07 | −0.563997 | −0.281998 | − | 0.959415i | \(-0.590997\pi\) | ||||
−0.281998 | + | 0.959415i | \(0.590997\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16645.5 | 1.39169 | 0.695846 | − | 0.718191i | \(-0.255030\pi\) | ||||
0.695846 | + | 0.718191i | \(0.255030\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 510.469 | 0.0424356 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30675.5 | −2.53557 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7703.93 | −0.633182 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4025.02 | −0.328948 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21815.1 | −1.77283 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10571.8 | 0.854316 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7046.89 | −0.566286 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11637.1 | 0.929952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15644.5 | −1.24327 | −0.621636 | − | 0.783306i | \(-0.713532\pi\) | ||||
−0.621636 | + | 0.783306i | \(0.713532\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6309.37 | 0.498639 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10748.6 | 0.844808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11548.0 | 0.902667 | 0.451334 | − | 0.892355i | \(-0.350948\pi\) | ||||
0.451334 | + | 0.892355i | \(0.350948\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1429.54 | −0.111131 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13282.3 | −1.02694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8557.62 | −0.658060 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1631.16 | 0.124754 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25455.4 | −1.93641 | −0.968206 | − | 0.250156i | \(-0.919518\pi\) | ||||
−0.968206 | + | 0.250156i | \(0.919518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29930.5 | 2.26462 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11209.3 | −0.843594 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9573.34 | 0.716639 | 0.358320 | − | 0.933599i | \(-0.383350\pi\) | ||||
0.358320 | + | 0.933599i | \(0.383350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2885.59 | 0.214863 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −551.306 | −0.0408337 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13986.4 | 1.03048 | 0.515238 | − | 0.857047i | \(-0.327704\pi\) | ||||
0.515238 | + | 0.857047i | \(0.327704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7881.02 | 0.577601 | 0.288801 | − | 0.957389i | \(-0.406744\pi\) | ||||
0.288801 | + | 0.957389i | \(0.406744\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9609.52 | 0.700600 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1670.16 | 0.121131 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9304.52 | 0.671321 | 0.335661 | − | 0.941983i | \(-0.391040\pi\) | ||||
0.335661 | + | 0.941983i | \(0.391040\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1413.34 | −0.101444 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1564.08 | −0.111685 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16155.3 | −1.14766 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3528.84 | −0.249401 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3335.66 | −0.234544 | −0.117272 | − | 0.993100i | \(-0.537415\pi\) | ||||
−0.117272 | + | 0.993100i | \(0.537415\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42912.7 | 3.00201 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4605.64 | −0.320559 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14241.4 | −0.986210 | −0.493105 | − | 0.869970i | \(-0.664138\pi\) | ||||
−0.493105 | + | 0.869970i | \(0.664138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3241.69 | 0.223355 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13085.9 | −0.897105 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13333.6 | −0.909508 | −0.454754 | − | 0.890617i | \(-0.650273\pi\) | ||||
−0.454754 | + | 0.890617i | \(0.650273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13080.5 | 0.887795 | 0.443897 | − | 0.896078i | \(-0.353595\pi\) | ||||
0.443897 | + | 0.896078i | \(0.353595\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4099.27 | −0.276841 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1038.00 | 0.0697533 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20502.2 | 1.37094 | 0.685469 | − | 0.728102i | \(-0.259597\pi\) | ||||
0.685469 | + | 0.728102i | \(0.259597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2035.24 | −0.135422 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16587.0 | −1.09826 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11003.5 | 0.725004 | 0.362502 | − | 0.931983i | \(-0.381923\pi\) | ||||
0.362502 | + | 0.931983i | \(0.381923\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4172.81 | −0.273600 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13387.8 | 0.873538 | 0.436769 | − | 0.899574i | \(-0.356123\pi\) | ||||
0.436769 | + | 0.899574i | \(0.356123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25240.6 | 1.63894 | 0.819471 | − | 0.573121i | \(-0.194267\pi\) | ||||
0.819471 | + | 0.573121i | \(0.194267\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1803.77 | −0.116558 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8019.04 | 0.515692 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15680.9 | 0.998781 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10358.5 | 0.656632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23458.3 | −1.47997 | −0.739985 | − | 0.672623i | \(-0.765168\pi\) | ||||
−0.739985 | + | 0.672623i | \(0.765168\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1156.33 | −0.0726067 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 277.594 | 0.0173480 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23264.9 | 1.44708 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5674.05 | 0.351271 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1962.14 | 0.120904 | 0.0604522 | − | 0.998171i | \(-0.480746\pi\) | ||||
0.0604522 | + | 0.998171i | \(0.480746\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30832.4 | −1.89100 | −0.945499 | − | 0.325624i | \(-0.894426\pi\) | ||||
−0.945499 | + | 0.325624i | \(0.894426\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5725.12 | 0.349499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19561.1 | −1.18861 | −0.594303 | − | 0.804241i | \(-0.702572\pi\) | ||||
−0.594303 | + | 0.804241i | \(0.702572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17542.4 | 1.06102 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6575.47 | 0.395873 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32695.6 | −1.95939 | −0.979693 | − | 0.200505i | \(-0.935742\pi\) | ||||
−0.979693 | + | 0.200505i | \(0.935742\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7885.31 | −0.470389 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 529.537 | 0.0314448 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29419.3 | 1.73902 | 0.869509 | − | 0.493918i | \(-0.164436\pi\) | ||||
0.869509 | + | 0.493918i | \(0.164436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25674.1 | −1.51075 | −0.755375 | − | 0.655293i | \(-0.772545\pi\) | ||||
−0.755375 | + | 0.655293i | \(0.772545\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22409.6 | −1.31270 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4534.88 | −0.264443 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6658.91 | −0.386558 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2768.23 | 0.159979 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6230.40 | 0.358453 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19112.3 | 1.09469 | 0.547343 | − | 0.836908i | \(-0.315639\pi\) | ||||
0.547343 | + | 0.836908i | \(0.315639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3091.32 | −0.175494 | −0.0877469 | − | 0.996143i | \(-0.527967\pi\) | ||||
−0.0877469 | + | 0.996143i | \(0.527967\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11516.5 | −0.650903 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4171.05 | −0.234706 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13351.7 | 0.748006 | 0.374003 | − | 0.927427i | \(-0.377985\pi\) | ||||
0.374003 | + | 0.927427i | \(0.377985\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5665.59 | −0.316016 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2252.51 | 0.125093 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32297.7 | −1.78584 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10622.7 | 0.584815 | 0.292408 | − | 0.956294i | \(-0.405544\pi\) | ||||
0.292408 | + | 0.956294i | \(0.405544\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2402.78 | 0.131708 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2125.97 | 0.116033 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26499.1 | −1.44006 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13372.2 | 0.723580 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18023.4 | −0.971092 | −0.485546 | − | 0.874211i | \(-0.661379\pi\) | ||||
−0.485546 | + | 0.874211i | \(0.661379\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14490.8 | −0.777426 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3172.78 | −0.169495 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5388.34 | −0.286633 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14437.1 | −0.764732 | −0.382366 | − | 0.924011i | \(-0.624891\pi\) | ||||
−0.382366 | + | 0.924011i | \(0.624891\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11315.9 | 0.596875 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21513.7 | 1.13001 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15379.9 | 0.804440 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19166.1 | −0.998284 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31328.7 | 1.62498 | 0.812491 | − | 0.582974i | \(-0.198111\pi\) | ||||
0.812491 | + | 0.582974i | \(0.198111\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2467.22 | −0.127440 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17157.1 | −0.882543 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2491.87 | −0.127650 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19209.6 | 0.979978 | 0.489989 | − | 0.871729i | \(-0.337001\pi\) | ||||
0.489989 | + | 0.871729i | \(0.337001\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36356.9 | 1.83955 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14683.0 | 0.739874 | 0.369937 | − | 0.929057i | \(-0.379379\pi\) | ||||
0.369937 | + | 0.929057i | \(0.379379\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4450.12 | 0.223327 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17866.0 | 0.892948 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25001.5 | 1.24451 | 0.622256 | − | 0.782814i | \(-0.286216\pi\) | ||||
0.622256 | + | 0.782814i | \(0.286216\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31349.4 | 1.55418 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5512.07 | −0.272165 | −0.136082 | − | 0.990698i | \(-0.543451\pi\) | ||||
−0.136082 | + | 0.990698i | \(0.543451\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 684.875 | 0.0336804 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2068.20 | 0.101300 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14390.9 | −0.702044 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9405.13 | 0.456988 | 0.228494 | − | 0.973545i | \(-0.426620\pi\) | ||||
0.228494 | + | 0.973545i | \(0.426620\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10348.3 | −0.500815 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2468.16 | 0.118974 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37411.5 | 1.79623 | 0.898113 | − | 0.439765i | \(-0.144938\pi\) | ||||
0.898113 | + | 0.439765i | \(0.144938\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7861.42 | 0.375957 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23465.7 | −1.11778 | −0.558891 | − | 0.829241i | \(-0.688773\pi\) | ||||
−0.558891 | + | 0.829241i | \(0.688773\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14631.6 | −0.694231 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4286.53 | −0.202588 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35070.8 | 1.65102 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25677.3 | −1.20409 | −0.602046 | − | 0.798461i | \(-0.705648\pi\) | ||||
−0.602046 | + | 0.798461i | \(0.705648\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3038.49 | 0.141931 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24591.8 | 1.14425 | 0.572125 | − | 0.820167i | \(-0.306119\pi\) | ||||
0.572125 | + | 0.820167i | \(0.306119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8050.78 | 0.373152 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2220.41 | −0.102518 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37070.2 | 1.70498 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24729.4 | −1.13302 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2691.22 | 0.122831 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2986.97 | 0.135808 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35055.7 | 1.58780 | 0.793902 | − | 0.608046i | \(-0.208046\pi\) | ||||
0.793902 | + | 0.608046i | \(0.208046\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20148.9 | 0.909151 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3928.01 | −0.176566 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12455.8 | 0.557780 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6177.94 | −0.275609 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15901.1 | −0.706709 | −0.353354 | − | 0.935490i | \(-0.614959\pi\) | ||||
−0.353354 | + | 0.935490i | \(0.614959\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20148.5 | −0.892118 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10603.7 | −0.467744 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2307.90 | −0.101425 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2273.50 | −0.0995408 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3899.02 | 0.170077 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14097.0 | 0.612640 | 0.306320 | − | 0.951929i | \(-0.400902\pi\) | ||||
0.306320 | + | 0.951929i | \(0.400902\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6846.50 | −0.296441 | −0.148220 | − | 0.988954i | \(-0.547354\pi\) | ||||
−0.148220 | + | 0.988954i | \(0.547354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5070.32 | −0.218725 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11361.7 | 0.488325 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −50860.6 | −2.17795 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4803.64 | 0.204948 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3531.25 | 0.150111 | 0.0750557 | − | 0.997179i | \(-0.476087\pi\) | ||||
0.0750557 | + | 0.997179i | \(0.476087\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20412.7 | −0.864572 | −0.432286 | − | 0.901736i | \(-0.642293\pi\) | ||||
−0.432286 | + | 0.901736i | \(0.642293\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2941.87 | 0.124149 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6429.97 | 0.270365 | 0.135183 | − | 0.990821i | \(-0.456838\pi\) | ||||
0.135183 | + | 0.990821i | \(0.456838\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15491.8 | 0.649039 | 0.324520 | − | 0.945879i | \(-0.394797\pi\) | ||||
0.324520 | + | 0.945879i | \(0.394797\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18692.7 | −0.780315 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28260.1 | 1.17546 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10464.1 | −0.433683 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8694.84 | −0.359065 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8101.80 | 0.333379 | 0.166690 | − | 0.986009i | \(-0.446692\pi\) | ||||
0.166690 | + | 0.986009i | \(0.446692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14453.9 | −0.592640 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14279.3 | 0.583398 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19762.5 | 0.804557 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1412.98 | −0.0573205 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7997.85 | 0.323304 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7264.76 | −0.292636 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18343.8 | −0.736317 | −0.368159 | − | 0.929763i | \(-0.620012\pi\) | ||||
−0.368159 | + | 0.929763i | \(0.620012\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5996.53 | 0.239856 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34069.4 | 1.35798 | 0.678991 | − | 0.734147i | \(-0.262418\pi\) | ||||
0.678991 | + | 0.734147i | \(0.262418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22555.2 | 0.895894 | 0.447947 | − | 0.894060i | \(-0.352155\pi\) | ||||
0.447947 | + | 0.894060i | \(0.352155\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5680.24 | 0.224834 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26094.0 | −1.02926 | −0.514630 | − | 0.857413i | \(-0.672071\pi\) | ||||
−0.514630 | + | 0.857413i | \(0.672071\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −293.749 | −0.0115466 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12482.3 | −0.488950 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49318.3 | −1.92521 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35717.8 | 1.38950 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15228.4 | 0.590384 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −850.781 | −0.0328705 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32275.2 | 1.24271 | 0.621355 | − | 0.783530i | \(-0.286583\pi\) | ||||
0.621355 | + | 0.783530i | \(0.286583\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1551.19 | 0.0595225 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32969.3 | 1.26080 | 0.630399 | − | 0.776271i | \(-0.282891\pi\) | ||||
0.630399 | + | 0.776271i | \(0.282891\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19708.7 | 0.751134 | 0.375567 | − | 0.926795i | \(-0.377448\pi\) | ||||
0.375567 | + | 0.926795i | \(0.377448\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6708.37 | 0.254802 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29868.2 | 1.13064 | 0.565319 | − | 0.824872i | \(-0.308753\pi\) | ||||
0.565319 | + | 0.824872i | \(0.308753\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −377.875 | −0.0142559 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3177.22 | −0.119462 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28186.2 | 1.05623 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11744.8 | 0.438643 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15716.6 | 0.585018 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32098.5 | −1.19082 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39232.5 | −1.45064 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7793.32 | −0.287204 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10515.6 | −0.386244 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25106.4 | −0.919124 | −0.459562 | − | 0.888146i | \(-0.651994\pi\) | ||||
−0.459562 | + | 0.888146i | \(0.651994\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7125.07 | 0.259982 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17411.2 | −0.633215 | −0.316608 | − | 0.948557i | \(-0.602544\pi\) | ||||
−0.316608 | + | 0.948557i | \(0.602544\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9013.90 | −0.326743 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2382.56 | 0.0860821 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10733.9 | 0.386547 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38193.1 | 1.37092 | 0.685460 | − | 0.728111i | \(-0.259601\pi\) | ||||
0.685460 | + | 0.728111i | \(0.259601\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −369.113 | −0.0132059 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49439.1 | −1.76306 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2718.59 | −0.0966344 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3262.44 | 0.115591 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36084.2 | −1.27437 | −0.637183 | − | 0.770713i | \(-0.719900\pi\) | ||||
−0.637183 | + | 0.770713i | \(0.719900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39533.8 | −1.39169 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2099.81 | −0.0736814 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18682.1 | 0.653445 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12854.3 | −0.448166 | −0.224083 | − | 0.974570i | \(-0.571939\pi\) | ||||
−0.224083 | + | 0.974570i | \(0.571939\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3806.66 | −0.132296 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40368.6 | 1.39849 | 0.699245 | − | 0.714882i | \(-0.253520\pi\) | ||||
0.699245 | + | 0.714882i | \(0.253520\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18584.7 | 0.641781 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 918.844 | 0.0316296 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18858.1 | −0.647103 | −0.323551 | − | 0.946211i | \(-0.604877\pi\) | ||||
−0.323551 | + | 0.946211i | \(0.604877\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4613.96 | −0.157825 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7521.64 | 0.256473 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37267.2 | −1.26674 | −0.633370 | − | 0.773849i | \(-0.718329\pi\) | ||||
−0.633370 | + | 0.773849i | \(0.718329\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16015.9 | −0.542682 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11729.3 | −0.396189 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7712.29 | 0.259690 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73913.1 | 2.48106 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19029.3 | 0.636770 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2355.56 | 0.0785785 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33833.4 | 1.12514 | 0.562569 | − | 0.826750i | \(-0.309813\pi\) | ||||
0.562569 | + | 0.826750i | \(0.309813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 38080.5 | 1.26246 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42354.0 | 1.39980 | 0.699899 | − | 0.714242i | \(-0.253228\pi\) | ||||
0.699899 | + | 0.714242i | \(0.253228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2893.97 | −0.0953510 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5881.41 | 0.193185 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26051.8 | 0.853092 | 0.426546 | − | 0.904466i | \(-0.359730\pi\) | ||||
0.426546 | + | 0.904466i | \(0.359730\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46214.4 | 1.50870 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19347.5 | 0.629683 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34810.4 | −1.12948 | −0.564740 | − | 0.825269i | \(-0.691023\pi\) | ||||
−0.564740 | + | 0.825269i | \(0.691023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7676.06 | 0.248304 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4318.95 | 0.139284 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25498.3 | −0.819816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15896.1 | −0.509542 | −0.254771 | − | 0.967001i | \(-0.582000\pi\) | ||||
−0.254771 | + | 0.967001i | \(0.582000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13917.8 | 0.444780 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21809.9 | 0.694895 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43981.7 | −1.39711 | −0.698553 | − | 0.715559i | \(-0.746172\pi\) | ||||
−0.698553 | + | 0.715559i | \(0.746172\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2936.08 | 0.0929865 |
(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 | 960.4.a.bm.1.1 | 2 | ||
4.3 | odd | 2 | 960.4.a.bo.1.2 | 2 | |||
8.3 | odd | 2 | 480.4.a.m.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 480.4.a.q.1.1 | yes | 2 | ||
24.5 | odd | 2 | 1440.4.a.bg.1.1 | 2 | |||
24.11 | even | 2 | 1440.4.a.z.1.2 | 2 | |||
40.19 | odd | 2 | 2400.4.a.bc.1.1 | 2 | |||
40.29 | even | 2 | 2400.4.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.4.a.m.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
480.4.a.q.1.1 | yes | 2 | 8.5 | even | 2 | ||
960.4.a.bm.1.1 | 2 | 1.1 | even | 1 | trivial | ||
960.4.a.bo.1.2 | 2 | 4.3 | odd | 2 | |||
1440.4.a.z.1.2 | 2 | 24.11 | even | 2 | |||
1440.4.a.bg.1.1 | 2 | 24.5 | odd | 2 | |||
2400.4.a.x.1.2 | 2 | 40.29 | even | 2 | |||
2400.4.a.bc.1.1 | 2 | 40.19 | odd | 2 |