Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, 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("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 84x^{2} - 11x + 1242 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-7.92791\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | ||||||||
\(3\) | −8.92791 | −1.71818 | −0.859088 | − | 0.511828i | \(-0.828969\pi\) | ||||
−0.859088 | + | 0.511828i | \(0.828969\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −23.5524 | −1.27171 | −0.635855 | − | 0.771809i | \(-0.719352\pi\) | ||||
−0.635855 | + | 0.771809i | \(0.719352\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 52.7075 | 1.95213 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.63537 | −0.0448257 | −0.0224129 | − | 0.999749i | \(-0.507135\pi\) | ||||
−0.0224129 | + | 0.999749i | \(0.507135\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −88.6599 | −1.89152 | −0.945762 | − | 0.324860i | \(-0.894683\pi\) | ||||
−0.945762 | + | 0.324860i | \(0.894683\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 44.6395 | 0.768392 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.31435 | −0.104352 | −0.0521762 | − | 0.998638i | \(-0.516616\pi\) | ||||
−0.0521762 | + | 0.998638i | \(0.516616\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.53738 | 0.0789357 | 0.0394678 | − | 0.999221i | \(-0.487434\pi\) | ||||
0.0394678 | + | 0.999221i | \(0.487434\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 210.274 | 2.18502 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −229.514 | −1.63593 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 119.240 | 0.763530 | 0.381765 | − | 0.924259i | \(-0.375316\pi\) | ||||
0.381765 | + | 0.924259i | \(0.375316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 156.456 | 0.906462 | 0.453231 | − | 0.891393i | \(-0.350271\pi\) | ||||
0.453231 | + | 0.891393i | \(0.350271\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.6004 | 0.0770185 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 117.762 | 0.568726 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −293.173 | −1.30263 | −0.651315 | − | 0.758807i | \(-0.725782\pi\) | ||||
−0.651315 | + | 0.758807i | \(0.725782\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 791.547 | 3.24997 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 74.3404 | 0.283171 | 0.141586 | − | 0.989926i | \(-0.454780\pi\) | ||||
0.141586 | + | 0.989926i | \(0.454780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −468.081 | −1.66004 | −0.830020 | − | 0.557733i | \(-0.811671\pi\) | ||||
−0.830020 | + | 0.557733i | \(0.811671\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −263.538 | −0.873019 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 393.971 | 1.22269 | 0.611346 | − | 0.791363i | \(-0.290628\pi\) | ||||
0.611346 | + | 0.791363i | \(0.290628\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 211.715 | 0.617245 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 65.3018 | 0.179296 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 233.171 | 0.604311 | 0.302155 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302155 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.17685 | 0.0200467 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −58.3651 | −0.135625 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 766.648 | 1.69168 | 0.845840 | − | 0.533437i | \(-0.179100\pi\) | ||||
0.845840 | + | 0.533437i | \(0.179100\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 178.365 | 0.374383 | 0.187191 | − | 0.982323i | \(-0.440062\pi\) | ||||
0.187191 | + | 0.982323i | \(0.440062\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1241.39 | −2.48254 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 443.299 | 0.845915 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −246.904 | −0.450211 | −0.225105 | − | 0.974334i | \(-0.572273\pi\) | ||||
−0.225105 | + | 0.974334i | \(0.572273\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 205.342 | 0.358265 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 650.678 | 1.08762 | 0.543812 | − | 0.839207i | \(-0.316980\pi\) | ||||
0.543812 | + | 0.839207i | \(0.316980\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 695.444 | 1.11501 | 0.557504 | − | 0.830174i | \(-0.311759\pi\) | ||||
0.557504 | + | 0.830174i | \(0.311759\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −223.198 | −0.343635 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 38.5169 | 0.0570053 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −660.717 | −0.940967 | −0.470484 | − | 0.882409i | \(-0.655921\pi\) | ||||
−0.470484 | + | 0.882409i | \(0.655921\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 625.978 | 0.858681 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1328.39 | 1.75674 | 0.878372 | − | 0.477977i | \(-0.158630\pi\) | ||||
0.878372 | + | 0.477977i | \(0.158630\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 36.5718 | 0.0466678 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1064.57 | −1.31188 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −824.702 | −0.982227 | −0.491113 | − | 0.871096i | \(-0.663410\pi\) | ||||
−0.491113 | + | 0.871096i | \(0.663410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2088.15 | 2.40547 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1396.82 | −1.55746 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −32.6869 | −0.0353011 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 383.833 | 0.401776 | 0.200888 | − | 0.979614i | \(-0.435617\pi\) | ||||
0.200888 | + | 0.979614i | \(0.435617\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −86.1963 | −0.0875056 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −674.579 | −0.664586 | −0.332293 | − | 0.943176i | \(-0.607822\pi\) | ||||
−0.332293 | + | 0.943176i | \(0.607822\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −169.297 | −0.161955 | −0.0809773 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809773 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1051.37 | −0.977171 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1533.31 | 1.38533 | 0.692665 | − | 0.721259i | \(-0.256436\pi\) | ||||
0.692665 | + | 0.721259i | \(0.256436\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1239.75 | 1.08941 | 0.544707 | − | 0.838626i | \(-0.316641\pi\) | ||||
0.544707 | + | 0.838626i | \(0.316641\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2617.42 | 2.23815 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2299.49 | 1.91432 | 0.957159 | − | 0.289561i | \(-0.0935094\pi\) | ||||
0.957159 | + | 0.289561i | \(0.0935094\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4673.04 | −3.69250 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 172.270 | 0.132706 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1328.33 | −0.997991 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −663.704 | −0.486538 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1177.82 | 0.822948 | 0.411474 | − | 0.911422i | \(-0.365014\pi\) | ||||
0.411474 | + | 0.911422i | \(0.365014\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4178.99 | 2.85224 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2385.56 | −1.59105 | −0.795525 | − | 0.605921i | \(-0.792805\pi\) | ||||
−0.795525 | + | 0.605921i | \(0.792805\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −153.971 | −0.100383 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1147.57 | 0.731609 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1123.22 | 0.700460 | 0.350230 | − | 0.936664i | \(-0.386103\pi\) | ||||
0.350230 | + | 0.936664i | \(0.386103\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1801.75 | 1.09944 | 0.549721 | − | 0.835348i | \(-0.314734\pi\) | ||||
0.549721 | + | 0.835348i | \(0.314734\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3517.33 | −2.10080 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 144.992 | 0.0847889 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −596.202 | −0.341461 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1890.17 | −1.06054 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 663.138 | 0.364607 | 0.182303 | − | 0.983242i | \(-0.441645\pi\) | ||||
0.182303 | + | 0.983242i | \(0.441645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1617.66 | −0.871808 | −0.435904 | − | 0.899993i | \(-0.643571\pi\) | ||||
−0.435904 | + | 0.899993i | \(0.643571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −385.521 | −0.203709 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −782.280 | −0.405382 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 875.080 | 0.444834 | 0.222417 | − | 0.974952i | \(-0.428605\pi\) | ||||
0.222417 | + | 0.974952i | \(0.428605\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2081.73 | −1.03831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 541.705 | 0.265170 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2532.39 | −1.21689 | −0.608443 | − | 0.793597i | \(-0.708206\pi\) | ||||
−0.608443 | + | 0.793597i | \(0.708206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −73.0022 | −0.0344437 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1131.65 | 0.524371 | 0.262186 | − | 0.965017i | \(-0.415557\pi\) | ||||
0.262186 | + | 0.965017i | \(0.415557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5663.57 | 2.57786 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 344.569 | 0.154093 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3186.23 | −1.40026 | −0.700128 | − | 0.714017i | \(-0.746874\pi\) | ||||
−0.700128 | + | 0.714017i | \(0.746874\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −588.810 | −0.254342 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6844.56 | −2.90660 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1663.48 | −0.694606 | −0.347303 | − | 0.937753i | \(-0.612902\pi\) | ||||
−0.347303 | + | 0.937753i | \(0.612902\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3747.35 | −1.53889 | −0.769443 | − | 0.638716i | \(-0.779466\pi\) | ||||
−0.769443 | + | 0.638716i | \(0.779466\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1592.43 | −0.643256 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1465.86 | 0.582554 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.9617 | 0.00467767 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5405.61 | 2.08042 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2262.97 | −0.857291 | −0.428645 | − | 0.903473i | \(-0.641009\pi\) | ||||
−0.428645 | + | 0.903473i | \(0.641009\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2001.25 | −0.746390 | −0.373195 | − | 0.927753i | \(-0.621738\pi\) | ||||
−0.373195 | + | 0.927753i | \(0.621738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3957.73 | −1.45343 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4804.08 | −1.73744 | −0.868722 | − | 0.495300i | \(-0.835058\pi\) | ||||
−0.868722 | + | 0.495300i | \(0.835058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3885.03 | −1.38393 | −0.691967 | − | 0.721929i | \(-0.743256\pi\) | ||||
−0.691967 | + | 0.721929i | \(0.743256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2204.34 | 0.773542 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2808.39 | −0.970989 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −371.702 | −0.126638 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1212.27 | −0.407047 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.6910 | −0.00353835 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4568.39 | −1.49052 | −0.745262 | − | 0.666772i | \(-0.767676\pi\) | ||||
−0.745262 | + | 0.666772i | \(0.767676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5809.20 | −1.86873 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2340.41 | 0.742393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3684.91 | −1.15276 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6208.86 | −1.91578 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 648.489 | 0.197385 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3081.07 | −0.925218 | −0.462609 | − | 0.886563i | \(-0.653087\pi\) | ||||
−0.462609 | + | 0.886563i | \(0.653087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1317.69 | 0.390426 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −678.971 | −0.198524 | −0.0992618 | − | 0.995061i | \(-0.531648\pi\) | ||||
−0.0992618 | + | 0.995061i | \(0.531648\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6399.27 | 1.84662 | 0.923310 | − | 0.384056i | \(-0.125473\pi\) | ||||
0.923310 | + | 0.384056i | \(0.125473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −343.875 | −0.0979451 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6083.30 | 1.71043 | 0.855215 | − | 0.518274i | \(-0.173425\pi\) | ||||
0.855215 | + | 0.518274i | \(0.173425\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1969.85 | −0.546805 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5898.82 | 1.61675 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −438.313 | −0.118628 | −0.0593140 | − | 0.998239i | \(-0.518891\pi\) | ||||
−0.0593140 | + | 0.998239i | \(0.518891\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2854.41 | 0.762941 | 0.381471 | − | 0.924381i | \(-0.375418\pi\) | ||||
0.381471 | + | 0.924381i | \(0.375418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 608.207 | 0.160562 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1058.57 | −0.276040 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −579.603 | −0.149309 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11859.7 | −3.01840 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2292.93 | 0.576607 | 0.288303 | − | 0.957539i | \(-0.406909\pi\) | ||||
0.288303 | + | 0.957539i | \(0.406909\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.6135 | 0.00934681 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −326.509 | −0.0801835 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3547.59 | 0.861060 | 0.430530 | − | 0.902576i | \(-0.358327\pi\) | ||||
0.430530 | + | 0.902576i | \(0.358327\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6904.92 | 1.65657 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6284.86 | 1.49051 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2278.35 | 0.534178 | 0.267089 | − | 0.963672i | \(-0.413938\pi\) | ||||
0.267089 | + | 0.963672i | \(0.413938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1165.85 | −0.270256 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7362.86 | 1.68764 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3915.36 | 0.887450 | 0.443725 | − | 0.896163i | \(-0.353657\pi\) | ||||
0.443725 | + | 0.896163i | \(0.353657\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6252.71 | −1.40157 | −0.700784 | − | 0.713374i | \(-0.747166\pi\) | ||||
−0.700784 | + | 0.713374i | \(0.747166\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18642.8 | −4.13302 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −40.8843 | −0.00896514 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4700.53 | −1.01959 | −0.509797 | − | 0.860295i | \(-0.670279\pi\) | ||||
−0.509797 | + | 0.860295i | \(0.670279\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8246.40 | 1.76953 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5508.07 | 1.16934 | 0.584669 | − | 0.811272i | \(-0.301224\pi\) | ||||
0.584669 | + | 0.811272i | \(0.301224\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6639.20 | −1.39456 | −0.697278 | − | 0.716801i | \(-0.745606\pi\) | ||||
−0.697278 | + | 0.716801i | \(0.745606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 291.826 | 0.0606535 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1750.89 | −0.360111 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4859.50 | −0.989111 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3426.82 | −0.690323 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2120.85 | −0.422872 | −0.211436 | − | 0.977392i | \(-0.567814\pi\) | ||||
−0.211436 | + | 0.977392i | \(0.567814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3833.24 | −0.756542 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 375.341 | 0.0733316 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2039.18 | 0.394410 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11024.4 | 2.11109 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6022.58 | 1.14188 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −891.827 | −0.167429 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7422.87 | −1.37995 | −0.689977 | − | 0.723832i | \(-0.742379\pi\) | ||||
−0.689977 | + | 0.723832i | \(0.742379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1511.47 | 0.278266 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2563.97 | 0.467490 | 0.233745 | − | 0.972298i | \(-0.424902\pi\) | ||||
0.233745 | + | 0.972298i | \(0.424902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9403.53 | 1.69814 | 0.849072 | − | 0.528277i | \(-0.177162\pi\) | ||||
0.849072 | + | 0.528277i | \(0.177162\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6206.94 | 1.11023 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 407.110 | 0.0721312 | 0.0360656 | − | 0.999349i | \(-0.488517\pi\) | ||||
0.0360656 | + | 0.999349i | \(0.488517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −195.002 | −0.0342258 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13689.2 | −2.38024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −47.8167 | −0.00823713 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2216.50 | −0.378305 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11068.3 | −1.87180 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9278.95 | −1.55491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7122.33 | 1.18272 | 0.591358 | − | 0.806409i | \(-0.298592\pi\) | ||||
0.591358 | + | 0.806409i | \(0.298592\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15452.4 | −2.54290 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1234.52 | 0.201340 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8267.78 | −1.33642 | −0.668212 | − | 0.743971i | \(-0.732940\pi\) | ||||
−0.668212 | + | 0.743971i | \(0.732940\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20529.7 | −3.28914 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −255.864 | −0.0406328 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3092.08 | 0.486753 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1026.71 | −0.160221 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1048.83 | −0.162260 | −0.0811302 | − | 0.996704i | \(-0.525853\pi\) | ||||
−0.0811302 | + | 0.996704i | \(0.525853\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9135.87 | −1.40124 | −0.700619 | − | 0.713535i | \(-0.747093\pi\) | ||||
−0.700619 | + | 0.713535i | \(0.747093\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20348.7 | 3.09440 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5253.06 | 0.792046 | 0.396023 | − | 0.918240i | \(-0.370390\pi\) | ||||
0.396023 | + | 0.918240i | \(0.370390\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3253.39 | −0.486400 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1538.01 | −0.228012 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11269.7 | 1.65680 | 0.828400 | − | 0.560137i | \(-0.189252\pi\) | ||||
0.828400 | + | 0.560137i | \(0.189252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6816.26 | −0.993769 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11859.2 | 1.71472 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3477.22 | −0.498646 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5675.46 | 0.807238 | 0.403619 | − | 0.914927i | \(-0.367752\pi\) | ||||
0.403619 | + | 0.914927i | \(0.367752\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3918.29 | 0.552787 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5491.73 | −0.768508 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3662.20 | 0.508369 | 0.254185 | − | 0.967156i | \(-0.418193\pi\) | ||||
0.254185 | + | 0.967156i | \(0.418193\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1115.99 | 0.153678 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10571.8 | −1.44424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5520.89 | −0.748256 | −0.374128 | − | 0.927377i | \(-0.622058\pi\) | ||||
−0.374128 | + | 0.927377i | \(0.622058\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10515.4 | −1.41397 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2309.13 | 0.308071 | 0.154036 | − | 0.988065i | \(-0.450773\pi\) | ||||
0.154036 | + | 0.988065i | \(0.450773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −192.584 | −0.0254935 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24671.4 | −3.24061 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8194.51 | −1.06807 | −0.534034 | − | 0.845463i | \(-0.679324\pi\) | ||||
−0.534034 | + | 0.845463i | \(0.679324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 168.230 | 0.0217590 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21298.1 | 2.73370 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3303.58 | 0.420813 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7273.90 | 0.919564 | 0.459782 | − | 0.888032i | \(-0.347928\pi\) | ||||
0.459782 | + | 0.888032i | \(0.347928\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1374.64 | 0.172476 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1835.81 | −0.228618 | −0.114309 | − | 0.993445i | \(-0.536465\pi\) | ||||
−0.114309 | + | 0.993445i | \(0.536465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13871.4 | −1.71460 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3129.89 | −0.384014 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 479.446 | 0.0583914 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2865.80 | −0.346466 | −0.173233 | − | 0.984881i | \(-0.555421\pi\) | ||||
−0.173233 | + | 0.984881i | \(0.555421\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10028.0 | −1.20351 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18056.4 | −2.15132 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6641.95 | −0.785640 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16085.9 | −1.88904 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11044.0 | −1.28767 | −0.643836 | − | 0.765164i | \(-0.722658\pi\) | ||||
−0.643836 | + | 0.765164i | \(0.722658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6343.24 | 0.734324 | 0.367162 | − | 0.930157i | \(-0.380329\pi\) | ||||
0.367162 | + | 0.930157i | \(0.380329\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20765.2 | 2.38685 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −182.859 | −0.0208705 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4200.93 | −0.476106 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1294.47 | −0.145682 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4117.01 | 0.460115 | 0.230058 | − | 0.973177i | \(-0.426109\pi\) | ||||
0.230058 | + | 0.973177i | \(0.426109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −758.791 | −0.0842151 | −0.0421076 | − | 0.999113i | \(-0.513407\pi\) | ||||
−0.0421076 | + | 0.999113i | \(0.513407\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5322.83 | 0.586690 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −150.360 | −0.0164592 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4150.10 | −0.451193 | −0.225596 | − | 0.974221i | \(-0.572433\pi\) | ||||
−0.225596 | + | 0.974221i | \(0.572433\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11159.0 | 1.20494 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4597.24 | 0.493051 | 0.246525 | − | 0.969136i | \(-0.420711\pi\) | ||||
0.246525 | + | 0.969136i | \(0.420711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4123.51 | 0.439265 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5920.43 | −0.626458 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6402.58 | 0.672954 | 0.336477 | − | 0.941692i | \(-0.390765\pi\) | ||||
0.336477 | + | 0.941692i | \(0.390765\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −121.574 | −0.0126933 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14442.3 | 1.49792 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10440.8 | −1.07576 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 551.499 | 0.0564508 | 0.0282254 | − | 0.999602i | \(-0.491014\pi\) | ||||
0.0282254 | + | 0.999602i | \(0.491014\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1678.75 | 0.170713 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3901.96 | −0.394213 | −0.197107 | − | 0.980382i | \(-0.563154\pi\) | ||||
−0.197107 | + | 0.980382i | \(0.563154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4828.15 | −0.484628 | −0.242314 | − | 0.970198i | \(-0.577906\pi\) | ||||
−0.242314 | + | 0.970198i | \(0.577906\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6984.12 | 0.696518 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14136.3 | 1.40075 | 0.700375 | − | 0.713775i | \(-0.253016\pi\) | ||||
0.700375 | + | 0.713775i | \(0.253016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5815.18 | 0.572538 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7812.63 | −0.764303 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 765.487 | 0.0744125 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 163.434 | 0.0157871 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12289.8 | 1.17969 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15246.1 | −1.45430 | −0.727152 | − | 0.686476i | \(-0.759157\pi\) | ||||
−0.727152 | + | 0.686476i | \(0.759157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25992.7 | 2.46396 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4836.29 | −0.455608 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1919.16 | −0.179680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3876.39 | −0.360690 | −0.180345 | − | 0.983603i | \(-0.557721\pi\) | ||||
−0.180345 | + | 0.983603i | \(0.557721\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22609.0 | 2.09083 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5027.14 | 0.462061 | 0.231030 | − | 0.972947i | \(-0.425790\pi\) | ||||
0.231030 | + | 0.972947i | \(0.425790\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −872.166 | −0.0796762 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 430.982 | 0.0391337 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15325.0 | −1.38314 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7178.10 | −0.643960 | −0.321980 | − | 0.946747i | \(-0.604348\pi\) | ||||
−0.321980 | + | 0.946747i | \(0.604348\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10103.3 | −0.900962 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18169.6 | 1.61063 | 0.805313 | − | 0.592850i | \(-0.201997\pi\) | ||||
0.805313 | + | 0.592850i | \(0.201997\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3372.90 | 0.297212 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −50563.8 | −4.42923 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2296.14 | 0.199950 | 0.0999750 | − | 0.994990i | \(-0.468124\pi\) | ||||
0.0999750 | + | 0.994990i | \(0.468124\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16379.4 | −1.41797 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1500.42 | −0.129133 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 846.484 | 0.0724283 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −644.288 | −0.0548081 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 28446.3 | 2.40589 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12945.5 | 1.08859 | 0.544293 | − | 0.838895i | \(-0.316798\pi\) | ||||
0.544293 | + | 0.838895i | \(0.316798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16093.6 | 1.34555 | 0.672775 | − | 0.739847i | \(-0.265102\pi\) | ||||
0.672775 | + | 0.739847i | \(0.265102\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5256.84 | 0.437004 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1144.37 | −0.0945915 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40408.1 | 3.30238 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6591.01 | −0.535625 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7666.53 | −0.619538 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14851.4 | 1.19346 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −346.232 | −0.0276684 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15424.7 | −1.22580 | −0.612900 | − | 0.790161i | \(-0.709997\pi\) | ||||
−0.612900 | + | 0.790161i | \(0.709997\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33456.0 | 2.64408 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6198.73 | −0.487201 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5307.37 | −0.414857 | −0.207428 | − | 0.978250i | \(-0.566509\pi\) | ||||
−0.207428 | + | 0.978250i | \(0.566509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9401.20 | 0.730844 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 779.519 | 0.0602698 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15561.5 | 1.19664 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13087.1 | −1.00093 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13530.9 | −1.02930 | −0.514651 | − | 0.857400i | \(-0.672079\pi\) | ||||
−0.514651 | + | 0.857400i | \(0.672079\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41500.0 | 3.14001 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −106.793 | −0.00803706 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18109.0 | 1.35560 | 0.677799 | − | 0.735248i | \(-0.262934\pi\) | ||||
0.677799 | + | 0.735248i | \(0.262934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11497.5 | −0.856109 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14743.3 | −1.09199 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −908.991 | −0.0669717 | −0.0334858 | − | 0.999439i | \(-0.510661\pi\) | ||||
−0.0334858 | + | 0.999439i | \(0.510661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8894.71 | 0.651895 | 0.325948 | − | 0.945388i | \(-0.394317\pi\) | ||||
0.325948 | + | 0.945388i | \(0.394317\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20203.6 | 1.47298 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12947.3 | −0.934148 | −0.467074 | − | 0.884218i | \(-0.654692\pi\) | ||||
−0.467074 | + | 0.884218i | \(0.654692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17867.0 | 1.28243 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31286.8 | −2.23407 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −381.321 | −0.0270887 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23365.2 | 1.65134 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19404.1 | 1.36438 | 0.682190 | − | 0.731175i | \(-0.261028\pi\) | ||||
0.682190 | + | 0.731175i | \(0.261028\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1022.81 | 0.0715522 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 42890.4 | 2.98524 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13633.9 | −0.944141 | −0.472070 | − | 0.881561i | \(-0.656493\pi\) | ||||
−0.472070 | + | 0.881561i | \(0.656493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −861.352 | −0.0593479 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34685.2 | 2.37784 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11276.5 | −0.769191 | −0.384595 | − | 0.923085i | \(-0.625659\pi\) | ||||
−0.384595 | + | 0.923085i | \(0.625659\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −380.766 | −0.0258432 | −0.0129216 | − | 0.999917i | \(-0.504113\pi\) | ||||
−0.0129216 | + | 0.999917i | \(0.504113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13013.7 | −0.878870 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6641.63 | 0.446315 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21669.2 | 1.44897 | 0.724485 | − | 0.689290i | \(-0.242077\pi\) | ||||
0.724485 | + | 0.689290i | \(0.242077\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25073.1 | 1.66833 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34929.4 | −2.31275 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −936.980 | −0.0617362 | −0.0308681 | − | 0.999523i | \(-0.509827\pi\) | ||||
−0.0308681 | + | 0.999523i | \(0.509827\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3318.52 | 0.217586 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17539.2 | −1.14441 | −0.572205 | − | 0.820111i | \(-0.693912\pi\) | ||||
−0.572205 | + | 0.820111i | \(0.693912\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4740.20 | 0.307794 | 0.153897 | − | 0.988087i | \(-0.450818\pi\) | ||||
0.153897 | + | 0.988087i | \(0.450818\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5278.83 | 0.341114 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19423.7 | 1.24911 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 95.4486 | 0.00607950 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2144.37 | 0.135933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18505.6 | 1.16751 | 0.583754 | − | 0.811930i | \(-0.301583\pi\) | ||||
0.583754 | + | 0.811930i | \(0.301583\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 40786.1 | 2.56098 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5889.09 | −0.368033 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18770.6 | −1.16753 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34295.6 | 2.12318 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10163.6 | 0.626266 | 0.313133 | − | 0.949709i | \(-0.398621\pi\) | ||||
0.313133 | + | 0.949709i | \(0.398621\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7132.33 | −0.437436 | −0.218718 | − | 0.975788i | \(-0.570188\pi\) | ||||
−0.218718 | + | 0.975788i | \(0.570188\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20894.9 | −1.27556 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14536.9 | −0.883315 | −0.441657 | − | 0.897184i | \(-0.645609\pi\) | ||||
−0.441657 | + | 0.897184i | \(0.645609\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1253.75 | −0.0758307 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32898.5 | 1.98064 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3318.33 | 0.198861 | 0.0994305 | − | 0.995045i | \(-0.468298\pi\) | ||||
0.0994305 | + | 0.995045i | \(0.468298\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11927.8 | 0.711539 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36655.1 | 2.17664 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3088.17 | −0.182546 | −0.0912730 | − | 0.995826i | \(-0.529094\pi\) | ||||
−0.0912730 | + | 0.995826i | \(0.529094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27602.0 | 1.62420 | 0.812098 | − | 0.583521i | \(-0.198325\pi\) | ||||
0.812098 | + | 0.583521i | \(0.198325\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5789.65 | −0.339142 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 769.854 | 0.0448927 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2742.53 | −0.159207 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27507.5 | 1.58969 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −291.694 | −0.0167820 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8091.33 | 0.463444 | 0.231722 | − | 0.972782i | \(-0.425564\pi\) | ||||
0.231722 | + | 0.972782i | \(0.425564\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5737.85 | −0.327185 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9515.37 | −0.540185 | −0.270093 | − | 0.962834i | \(-0.587054\pi\) | ||||
−0.270093 | + | 0.962834i | \(0.587054\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9040.18 | −0.510943 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6061.79 | 0.341099 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 630.346 | 0.0353141 | 0.0176570 | − | 0.999844i | \(-0.494379\pi\) | ||||
0.0176570 | + | 0.999844i | \(0.494379\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5616.09 | −0.313255 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −57132.1 | −3.17282 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20672.9 | −1.14307 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6515.92 | 0.358723 | 0.179361 | − | 0.983783i | \(-0.442597\pi\) | ||||
0.179361 | + | 0.983783i | \(0.442597\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2030.13 | 0.111282 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9008.76 | −0.491686 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −543.751 | −0.0295496 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −54311.1 | −2.93882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32850.2 | −1.76995 | −0.884975 | − | 0.465638i | \(-0.845825\pi\) | ||||
−0.884975 | + | 0.465638i | \(0.845825\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1916.58 | −0.102824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17586.7 | 0.939507 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15888.0 | 0.845160 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21841.2 | −1.15693 | −0.578466 | − | 0.815707i | \(-0.696348\pi\) | ||||
−0.578466 | + | 0.815707i | \(0.696348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34824.7 | −1.83689 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3598.49 | −0.189010 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −724.959 | −0.0379188 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3913.22 | 0.203824 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25807.3 | −1.33859 | −0.669296 | − | 0.742996i | \(-0.733404\pi\) | ||||
−0.669296 | + | 0.742996i | \(0.733404\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3987.34 | 0.205959 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25483.9 | −1.31087 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2981.01 | 0.152706 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14264.0 | −0.727679 | −0.363839 | − | 0.931462i | \(-0.618534\pi\) | ||||
−0.363839 | + | 0.931462i | \(0.618534\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22331.4 | −1.13455 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3423.71 | 0.173229 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 811.706 | 0.0409018 | 0.0204509 | − | 0.999791i | \(-0.493490\pi\) | ||||
0.0204509 | + | 0.999791i | \(0.493490\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9450.86 | 0.474286 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 403.780 | 0.0201810 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30696.9 | 1.52802 | 0.764008 | − | 0.645207i | \(-0.223229\pi\) | ||||
0.764008 | + | 0.645207i | \(0.223229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5174.64 | 0.256539 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26935.6 | 1.32998 | 0.664988 | − | 0.746854i | \(-0.268437\pi\) | ||||
0.664988 | + | 0.746854i | \(0.268437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3315.69 | −0.163057 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 70016.2 | 3.42939 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36113.0 | −1.76174 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22371.2 | −1.08700 | −0.543501 | − | 0.839409i | \(-0.682902\pi\) | ||||
−0.543501 | + | 0.839409i | \(0.682902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20471.0 | −0.990712 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8088.28 | 0.389884 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 697.182 | 0.0334736 | 0.0167368 | − | 0.999860i | \(-0.494672\pi\) | ||||
0.0167368 | + | 0.999860i | \(0.494672\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −335.810 | −0.0160595 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39756.9 | 1.89380 | 0.946902 | − | 0.321522i | \(-0.104194\pi\) | ||||
0.946902 | + | 0.321522i | \(0.104194\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29199.0 | −1.38542 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1927.61 | 0.0911016 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −67970.9 | −3.19985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12574.8 | −0.589673 | −0.294836 | − | 0.955548i | \(-0.595265\pi\) | ||||
−0.294836 | + | 0.955548i | \(0.595265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31672.5 | −1.47945 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2478.65 | 0.115331 | 0.0576654 | − | 0.998336i | \(-0.481634\pi\) | ||||
0.0576654 | + | 0.998336i | \(0.481634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3911.40 | 0.181292 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −61646.5 | −2.84628 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 485.991 | 0.0223523 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1064.10 | −0.0487535 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27367.3 | −1.24908 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4375.40 | −0.198936 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7716.40 | 0.349504 | 0.174752 | − | 0.984612i | \(-0.444088\pi\) | ||||
0.174752 | + | 0.984612i | \(0.444088\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20340.9 | −0.917812 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −54158.5 | −2.43446 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15813.9 | −0.708154 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10408.6 | 0.464347 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26798.1 | −1.19101 | −0.595507 | − | 0.803350i | \(-0.703049\pi\) | ||||
−0.595507 | + | 0.803350i | \(0.703049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2881.64 | −0.127591 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −43468.0 | −1.91743 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1137.31 | −0.0499810 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2708.52 | −0.118588 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34956.0 | −1.52479 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45278.0 | 1.96772 | 0.983862 | − | 0.178927i | \(-0.0572625\pi\) | ||||
0.983862 | + | 0.178927i | \(0.0572625\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24889.6 | 1.07767 | 0.538836 | − | 0.842411i | \(-0.318864\pi\) | ||||
0.538836 | + | 0.842411i | \(0.318864\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 55823.6 | 2.40814 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12662.0 | 0.544208 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3060.03 | −0.131036 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 110061. | 4.69579 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19274.0 | 0.819326 | 0.409663 | − | 0.912237i | \(-0.365646\pi\) | ||||
0.409663 | + | 0.912237i | \(0.365646\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21620.8 | 0.915740 | 0.457870 | − | 0.889019i | \(-0.348613\pi\) | ||||
0.457870 | + | 0.889019i | \(0.348613\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 365.011 | 0.0154037 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9012.81 | 0.378967 | 0.189484 | − | 0.981884i | \(-0.439319\pi\) | ||||
0.189484 | + | 0.981884i | \(0.439319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26574.7 | 1.11336 | 0.556682 | − | 0.830726i | \(-0.312074\pi\) | ||||
0.556682 | + | 0.830726i | \(0.312074\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41965.9 | 1.75184 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1548.56 | −0.0644110 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5658.27 | −0.234506 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −35908.9 | −1.48291 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1261.30 | 0.0519009 | 0.0259504 | − | 0.999663i | \(-0.491739\pi\) | ||||
0.0259504 | + | 0.999663i | \(0.491739\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10170.7 | −0.417022 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −49175.6 | −2.00913 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28317.8 | −1.15286 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31285.2 | 1.26915 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 59274.1 | 2.39609 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6742.98 | 0.271617 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32765.1 | 1.31519 | 0.657594 | − | 0.753373i | \(-0.271574\pi\) | ||||
0.657594 | + | 0.753373i | \(0.271574\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1722.84 | −0.0689123 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 722.029 | 0.0287795 | 0.0143898 | − | 0.999896i | \(-0.495419\pi\) | ||||
0.0143898 | + | 0.999896i | \(0.495419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36626.9 | 1.45482 | 0.727411 | − | 0.686202i | \(-0.240723\pi\) | ||||
0.727411 | + | 0.686202i | \(0.240723\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15631.8 | 0.618735 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33207.9 | 1.30986 | 0.654931 | − | 0.755688i | \(-0.272698\pi\) | ||||
0.654931 | + | 0.755688i | \(0.272698\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15931.1 | 0.626214 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 43385.2 | 1.69947 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1080.52 | 0.0421795 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21890.5 | 0.851585 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20230.9 | 0.784320 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2944.05 | 0.113745 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39507.6 | −1.52118 | −0.760592 | − | 0.649230i | \(-0.775091\pi\) | ||||
−0.760592 | + | 0.649230i | \(0.775091\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18934.8 | 0.726569 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47928.6 | 1.83287 | 0.916434 | − | 0.400187i | \(-0.131055\pi\) | ||||
0.916434 | + | 0.400187i | \(0.131055\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48176.2 | −1.83608 | −0.918040 | − | 0.396488i | \(-0.870229\pi\) | ||||
−0.918040 | + | 0.396488i | \(0.870229\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 34222.8 | 1.29987 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31421.7 | −1.18944 | −0.594722 | − | 0.803932i | \(-0.702738\pi\) | ||||
−0.594722 | + | 0.803932i | \(0.702738\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27740.4 | −1.04655 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1023.71 | −0.0384910 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2575.54 | 0.0965141 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8317.41 | 0.310637 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18205.6 | −0.677666 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18655.9 | 0.692111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1705.49 | −0.0630613 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −98425.1 | −3.62722 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18736.7 | 0.688211 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27694.1 | −1.01385 | −0.506927 | − | 0.861989i | \(-0.669219\pi\) | ||||
−0.506927 | + | 0.861989i | \(0.669219\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35555.4 | −1.29736 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27325.1 | 0.993764 | 0.496882 | − | 0.867818i | \(-0.334478\pi\) | ||||
0.496882 | + | 0.867818i | \(0.334478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2172.41 | −0.0787473 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7962.15 | 0.287673 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 56185.7 | 2.02335 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28135.6 | −1.00991 | −0.504956 | − | 0.863145i | \(-0.668491\pi\) | ||||
−0.504956 | + | 0.863145i | \(0.668491\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 66270.7 | 2.37100 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −57689.1 | −2.05727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7329.32 | −0.260526 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8923.21 | −0.316156 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32497.6 | 1.14770 | 0.573850 | − | 0.818961i | \(-0.305449\pi\) | ||||
0.573850 | + | 0.818961i | \(0.305449\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1384.06 | 0.0487226 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22890.9 | −0.803230 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −59.8084 | −0.00209192 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12209.3 | −0.425678 | −0.212839 | − | 0.977087i | \(-0.568271\pi\) | ||||
−0.212839 | + | 0.977087i | \(0.568271\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −83953.8 | −2.91771 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1317.78 | −0.0456518 | −0.0228259 | − | 0.999739i | \(-0.507266\pi\) | ||||
−0.0228259 | + | 0.999739i | \(0.507266\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1709.83 | −0.0590453 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −27028.0 | −0.930394 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11954.8 | 0.410219 | 0.205110 | − | 0.978739i | \(-0.434245\pi\) | ||||
0.205110 | + | 0.978739i | \(0.434245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −61657.9 | −2.10906 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3634.64 | −0.123934 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19658.8 | −0.668216 | −0.334108 | − | 0.942535i | \(-0.608435\pi\) | ||||
−0.334108 | + | 0.942535i | \(0.608435\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11314.8 | 0.383392 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1740.96 | 0.0588059 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26454.5 | −0.890782 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5312.52 | −0.178326 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 80816.8 | 2.70434 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10006.3 | 0.333796 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7604.58 | 0.252892 | 0.126446 | − | 0.991973i | \(-0.459643\pi\) | ||||
0.126446 | + | 0.991973i | \(0.459643\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 426.903 | 0.0141528 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14731.2 | 0.486866 | 0.243433 | − | 0.969918i | \(-0.421726\pi\) | ||||
0.243433 | + | 0.969918i | \(0.421726\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42435.5 | −1.39817 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19788.7 | 0.649995 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50584.6 | −1.65644 | −0.828222 | − | 0.560400i | \(-0.810647\pi\) | ||||
−0.828222 | + | 0.560400i | \(0.810647\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1348.69 | 0.0440290 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 65343.9 | 2.12668 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15625.9 | −0.507007 | −0.253503 | − | 0.967334i | \(-0.581583\pi\) | ||||
−0.253503 | + | 0.967334i | \(0.581583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24020.4 | 0.777009 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 82841.6 | 2.67161 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10765.9 | 0.346142 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18267.8 | −0.585567 | −0.292783 | − | 0.956179i | \(-0.594581\pi\) | ||||
−0.292783 | + | 0.956179i | \(0.594581\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −63587.5 | −2.03211 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19425.2 | 0.618914 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21580.5 | 0.685519 | 0.342760 | − | 0.939423i | \(-0.388638\pi\) | ||||
0.342760 | + | 0.939423i | \(0.388638\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 67287.3 | 2.13101 |
(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 | 1840.4.a.l.1.1 | 4 | ||
4.3 | odd | 2 | 230.4.a.i.1.4 | ✓ | 4 | ||
12.11 | even | 2 | 2070.4.a.bi.1.3 | 4 | |||
20.3 | even | 4 | 1150.4.b.m.599.4 | 8 | |||
20.7 | even | 4 | 1150.4.b.m.599.5 | 8 | |||
20.19 | odd | 2 | 1150.4.a.o.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.i.1.4 | ✓ | 4 | 4.3 | odd | 2 | ||
1150.4.a.o.1.1 | 4 | 20.19 | odd | 2 | |||
1150.4.b.m.599.4 | 8 | 20.3 | even | 4 | |||
1150.4.b.m.599.5 | 8 | 20.7 | even | 4 | |||
1840.4.a.l.1.1 | 4 | 1.1 | even | 1 | trivial | ||
2070.4.a.bi.1.3 | 4 | 12.11 | even | 2 |