Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.136768.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 23x^{2} + 18x + 119 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 588) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(4.93153\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(5\) | 19.1403 | 1.71196 | 0.855982 | − | 0.517006i | \(-0.172954\pi\) | ||||
0.855982 | + | 0.517006i | \(0.172954\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −40.5951 | −1.11272 | −0.556359 | − | 0.830942i | \(-0.687802\pi\) | ||||
−0.556359 | + | 0.830942i | \(0.687802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −50.4776 | −1.07692 | −0.538460 | − | 0.842651i | \(-0.680994\pi\) | ||||
−0.538460 | + | 0.842651i | \(0.680994\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −57.4210 | −0.988402 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 51.9195 | 0.740725 | 0.370362 | − | 0.928887i | \(-0.379234\pi\) | ||||
0.370362 | + | 0.928887i | \(0.379234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −33.1331 | −0.400066 | −0.200033 | − | 0.979789i | \(-0.564105\pi\) | ||||
−0.200033 | + | 0.979789i | \(0.564105\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −62.8499 | −0.569787 | −0.284894 | − | 0.958559i | \(-0.591958\pi\) | ||||
−0.284894 | + | 0.958559i | \(0.591958\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 241.352 | 1.93082 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 129.921 | 0.831924 | 0.415962 | − | 0.909382i | \(-0.363445\pi\) | ||||
0.415962 | + | 0.909382i | \(0.363445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 242.415 | 1.40448 | 0.702242 | − | 0.711938i | \(-0.252182\pi\) | ||||
0.702242 | + | 0.711938i | \(0.252182\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 121.785 | 0.642428 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −389.385 | −1.73012 | −0.865061 | − | 0.501667i | \(-0.832720\pi\) | ||||
−0.865061 | + | 0.501667i | \(0.832720\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 151.433 | 0.621761 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 470.110 | 1.79071 | 0.895353 | − | 0.445358i | \(-0.146924\pi\) | ||||
0.895353 | + | 0.445358i | \(0.146924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 125.003 | 0.443321 | 0.221661 | − | 0.975124i | \(-0.428852\pi\) | ||||
0.221661 | + | 0.975124i | \(0.428852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 172.263 | 0.570654 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −386.624 | −1.19989 | −0.599946 | − | 0.800040i | \(-0.704811\pi\) | ||||
−0.599946 | + | 0.800040i | \(0.704811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −155.758 | −0.427658 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −611.436 | −1.58466 | −0.792332 | − | 0.610091i | \(-0.791133\pi\) | ||||
−0.792332 | + | 0.610091i | \(0.791133\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −777.004 | −1.90493 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 99.3994 | 0.230978 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 226.432 | 0.499644 | 0.249822 | − | 0.968292i | \(-0.419628\pi\) | ||||
0.249822 | + | 0.968292i | \(0.419628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −725.191 | −1.52215 | −0.761075 | − | 0.648664i | \(-0.775328\pi\) | ||||
−0.761075 | + | 0.648664i | \(0.775328\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −966.158 | −1.84365 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1045.11 | −1.90568 | −0.952840 | − | 0.303474i | \(-0.901853\pi\) | ||||
−0.952840 | + | 0.303474i | \(0.901853\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 188.550 | 0.328967 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −169.839 | −0.283889 | −0.141945 | − | 0.989875i | \(-0.545336\pi\) | ||||
−0.141945 | + | 0.989875i | \(0.545336\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 381.731 | 0.612031 | 0.306015 | − | 0.952027i | \(-0.401004\pi\) | ||||
0.306015 | + | 0.952027i | \(0.401004\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −724.057 | −1.11476 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1161.12 | 1.65362 | 0.826812 | − | 0.562479i | \(-0.190152\pi\) | ||||
0.826812 | + | 0.562479i | \(0.190152\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −808.448 | −1.06914 | −0.534570 | − | 0.845124i | \(-0.679527\pi\) | ||||
−0.534570 | + | 0.845124i | \(0.679527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 993.756 | 1.26809 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −389.764 | −0.480311 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 319.867 | 0.380964 | 0.190482 | − | 0.981691i | \(-0.438995\pi\) | ||||
0.190482 | + | 0.981691i | \(0.438995\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −727.245 | −0.810880 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −634.179 | −0.684899 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1133.24 | −1.18622 | −0.593110 | − | 0.805121i | \(-0.702100\pi\) | ||||
−0.593110 | + | 0.805121i | \(0.702100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −365.356 | −0.370906 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1045.74 | 1.03025 | 0.515126 | − | 0.857115i | \(-0.327745\pi\) | ||||
0.515126 | + | 0.857115i | \(0.327745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1898.21 | −1.81589 | −0.907943 | − | 0.419093i | \(-0.862348\pi\) | ||||
−0.907943 | + | 0.419093i | \(0.862348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 868.785 | 0.784940 | 0.392470 | − | 0.919765i | \(-0.371621\pi\) | ||||
0.392470 | + | 0.919765i | \(0.371621\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 227.649 | 0.200044 | 0.100022 | − | 0.994985i | \(-0.468109\pi\) | ||||
0.100022 | + | 0.994985i | \(0.468109\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1168.16 | 0.998886 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 581.462 | 0.484065 | 0.242032 | − | 0.970268i | \(-0.422186\pi\) | ||||
0.242032 | + | 0.970268i | \(0.422186\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1202.97 | −0.975455 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −454.299 | −0.358974 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 316.963 | 0.238139 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1410.33 | −1.03386 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2227.02 | 1.59353 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1129.10 | −0.788908 | −0.394454 | − | 0.918916i | \(-0.629066\pi\) | ||||
−0.394454 | + | 0.918916i | \(0.629066\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −375.010 | −0.255952 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 879.662 | 0.586690 | 0.293345 | − | 0.956007i | \(-0.405231\pi\) | ||||
0.293345 | + | 0.956007i | \(0.405231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −516.789 | −0.329467 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −323.300 | −0.201616 | −0.100808 | − | 0.994906i | \(-0.532143\pi\) | ||||
−0.100808 | + | 0.994906i | \(0.532143\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1710.64 | −1.04385 | −0.521923 | − | 0.852993i | \(-0.674785\pi\) | ||||
−0.521923 | + | 0.852993i | \(0.674785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1159.87 | 0.692758 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2049.14 | 1.19831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2486.74 | 1.42422 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −959.778 | −0.527705 | −0.263853 | − | 0.964563i | \(-0.584993\pi\) | ||||
−0.263853 | + | 0.964563i | \(0.584993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1618.84 | 0.872449 | 0.436224 | − | 0.899838i | \(-0.356315\pi\) | ||||
0.436224 | + | 0.899838i | \(0.356315\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 467.275 | 0.246908 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4639.90 | 2.40443 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −557.333 | −0.283312 | −0.141656 | − | 0.989916i | \(-0.545243\pi\) | ||||
−0.141656 | + | 0.989916i | \(0.545243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1834.31 | 0.914906 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 366.034 | 0.175889 | 0.0879447 | − | 0.996125i | \(-0.471970\pi\) | ||||
0.0879447 | + | 0.996125i | \(0.471970\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2331.01 | 1.09981 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2834.00 | −1.31318 | −0.656591 | − | 0.754247i | \(-0.728002\pi\) | ||||
−0.656591 | + | 0.754247i | \(0.728002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 350.990 | 0.159759 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −298.198 | −0.133355 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3570.39 | −1.56909 | −0.784543 | − | 0.620074i | \(-0.787102\pi\) | ||||
−0.784543 | + | 0.620074i | \(0.787102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −679.297 | −0.288470 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3677.38 | 1.53553 | 0.767767 | − | 0.640729i | \(-0.221368\pi\) | ||||
0.767767 | + | 0.640729i | \(0.221368\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1718.18 | −0.705588 | −0.352794 | − | 0.935701i | \(-0.614768\pi\) | ||||
−0.352794 | + | 0.935701i | \(0.614768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2175.57 | 0.878814 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7452.96 | −2.96191 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2107.68 | −0.824217 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1959.05 | −0.742155 | −0.371077 | − | 0.928602i | \(-0.621012\pi\) | ||||
−0.371077 | + | 0.928602i | \(0.621012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2492.46 | −0.929591 | −0.464795 | − | 0.885418i | \(-0.653872\pi\) | ||||
−0.464795 | + | 0.885418i | \(0.653872\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2898.47 | 1.06443 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2174.45 | 0.786410 | 0.393205 | − | 0.919451i | \(-0.371366\pi\) | ||||
0.393205 | + | 0.919451i | \(0.371366\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3864.61 | −1.37666 | −0.688329 | − | 0.725399i | \(-0.741655\pi\) | ||||
−0.688329 | + | 0.725399i | \(0.741655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3135.33 | 1.10024 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8998.07 | 3.06562 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −565.649 | −0.189929 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1345.04 | 0.445161 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 127.267 | 0.0415233 | 0.0207616 | − | 0.999784i | \(-0.493391\pi\) | ||||
0.0207616 | + | 0.999784i | \(0.493391\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 509.516 | 0.163904 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2392.60 | 0.758950 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1145.19 | −0.353356 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2620.77 | −0.797702 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4071.36 | 1.22259 | 0.611297 | − | 0.791401i | \(-0.290648\pi\) | ||||
0.611297 | + | 0.791401i | \(0.290648\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2172.17 | 0.643606 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5282.36 | −1.54450 | −0.772252 | − | 0.635316i | \(-0.780870\pi\) | ||||
−0.772252 | + | 0.635316i | \(0.780870\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4580.19 | −1.32169 | −0.660846 | − | 0.750522i | \(-0.729802\pi\) | ||||
−0.660846 | + | 0.750522i | \(0.729802\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2156.51 | −0.606343 | −0.303171 | − | 0.952936i | \(-0.598045\pi\) | ||||
−0.303171 | + | 0.952936i | \(0.598045\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7400.11 | −2.05417 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3483.36 | −0.954720 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5755.76 | 1.55778 | 0.778889 | − | 0.627162i | \(-0.215783\pi\) | ||||
0.778889 | + | 0.627162i | \(0.215783\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2591.55 | −0.692683 | −0.346342 | − | 0.938108i | \(-0.612576\pi\) | ||||
−0.346342 | + | 0.938108i | \(0.612576\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1672.48 | 0.430840 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2425.34 | 0.617269 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3809.47 | 0.957974 | 0.478987 | − | 0.877822i | \(-0.341004\pi\) | ||||
0.478987 | + | 0.877822i | \(0.341004\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2551.40 | 0.634012 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2981.27 | −0.732134 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1357.69 | 0.329534 | 0.164767 | − | 0.986333i | \(-0.447313\pi\) | ||||
0.164767 | + | 0.986333i | \(0.447313\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1169.29 | 0.277308 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4417.73 | 1.03578 | 0.517888 | − | 0.855448i | \(-0.326718\pi\) | ||||
0.517888 | + | 0.855448i | \(0.326718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11703.1 | −2.71289 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −959.600 | −0.219950 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3627.32 | −0.822162 | −0.411081 | − | 0.911599i | \(-0.634849\pi\) | ||||
−0.411081 | + | 0.911599i | \(0.634849\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5171.03 | 1.15911 | 0.579553 | − | 0.814935i | \(-0.303227\pi\) | ||||
0.579553 | + | 0.814935i | \(0.303227\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9797.72 | −2.14845 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1794.63 | 0.389274 | 0.194637 | − | 0.980875i | \(-0.437647\pi\) | ||||
0.194637 | + | 0.980875i | \(0.437647\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2181.74 | 0.468162 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9118.63 | −1.93584 | −0.967921 | − | 0.251254i | \(-0.919157\pi\) | ||||
−0.967921 | + | 0.251254i | \(0.919157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5804.72 | −1.21927 | −0.609637 | − | 0.792681i | \(-0.708685\pi\) | ||||
−0.609637 | + | 0.792681i | \(0.708685\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1902.54 | 0.395426 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2217.37 | −0.451327 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3399.73 | 0.684865 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1384.21 | 0.275995 | 0.137997 | − | 0.990433i | \(-0.455933\pi\) | ||||
0.137997 | + | 0.990433i | \(0.455933\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4333.99 | 0.855372 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1096.07 | 0.214143 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3172.51 | 0.613616 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3137.23 | −0.594816 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13880.4 | −2.60587 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 337.112 | 0.0626709 | 0.0313355 | − | 0.999509i | \(-0.490024\pi\) | ||||
0.0313355 | + | 0.999509i | \(0.490024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5694.63 | 1.04840 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1964.69 | 0.358224 | 0.179112 | − | 0.983829i | \(-0.442678\pi\) | ||||
0.179112 | + | 0.983829i | \(0.442678\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3596.98 | −0.649563 | −0.324781 | − | 0.945789i | \(-0.605291\pi\) | ||||
−0.324781 | + | 0.945789i | \(0.605291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −215.450 | −0.0381731 | −0.0190865 | − | 0.999818i | \(-0.506076\pi\) | ||||
−0.0190865 | + | 0.999818i | \(0.506076\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5274.17 | −0.925696 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2606.35 | −0.453185 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1720.25 | −0.296339 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12182.9 | −2.07934 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −682.947 | −0.115496 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1685.35 | 0.279865 | 0.139933 | − | 0.990161i | \(-0.455311\pi\) | ||||
0.139933 | + | 0.990161i | \(0.455311\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3504.47 | −0.576707 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20003.7 | −3.26245 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7497.87 | −1.21197 | −0.605987 | − | 0.795475i | \(-0.707222\pi\) | ||||
−0.605987 | + | 0.795475i | \(0.707222\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1744.38 | −0.279475 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9840.87 | −1.56279 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3608.90 | 0.563179 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6038.83 | 0.934241 | 0.467120 | − | 0.884194i | \(-0.345291\pi\) | ||||
0.467120 | + | 0.884194i | \(0.345291\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1992.86 | −0.305659 | −0.152830 | − | 0.988253i | \(-0.548839\pi\) | ||||
−0.152830 | + | 0.988253i | \(0.548839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1362.90 | 0.207254 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6336.08 | 0.955342 | 0.477671 | − | 0.878539i | \(-0.341481\pi\) | ||||
0.477671 | + | 0.878539i | \(0.341481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3250.77 | −0.486008 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −904.510 | −0.132975 | −0.0664877 | − | 0.997787i | \(-0.521179\pi\) | ||||
−0.0664877 | + | 0.997787i | \(0.521179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5761.20 | −0.839947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −950.890 | −0.137490 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7306.46 | 1.04777 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1252.76 | 0.178184 | 0.0890920 | − | 0.996023i | \(-0.471603\pi\) | ||||
0.0890920 | + | 0.996023i | \(0.471603\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4230.99 | 0.596902 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2565.91 | −0.356187 | −0.178094 | − | 0.984014i | \(-0.556993\pi\) | ||||
−0.178094 | + | 0.984014i | \(0.556993\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6681.06 | −0.920022 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6558.12 | −0.895916 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3900.45 | 0.528634 | 0.264317 | − | 0.964436i | \(-0.414853\pi\) | ||||
0.264317 | + | 0.964436i | \(0.414853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3387.29 | 0.455476 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1669.11 | −0.222683 | −0.111342 | − | 0.993782i | \(-0.535515\pi\) | ||||
−0.111342 | + | 0.993782i | \(0.535515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1125.03 | 0.147774 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1189.74 | 0.155070 | 0.0775351 | − | 0.996990i | \(-0.475295\pi\) | ||||
0.0775351 | + | 0.996990i | \(0.475295\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3263.13 | −0.422056 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2638.99 | −0.338726 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22224.2 | 2.83094 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 802.190 | 0.101412 | 0.0507062 | − | 0.998714i | \(-0.483853\pi\) | ||||
0.0507062 | + | 0.998714i | \(0.483853\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10532.2 | −1.31161 | −0.655803 | − | 0.754932i | \(-0.727670\pi\) | ||||
−0.655803 | + | 0.754932i | \(0.727670\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12236.5 | −1.51252 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1550.37 | 0.190218 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15807.1 | 1.92514 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3671.52 | 0.443875 | 0.221937 | − | 0.975061i | \(-0.428762\pi\) | ||||
0.221937 | + | 0.975061i | \(0.428762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 969.899 | 0.116403 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15474.0 | −1.83033 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5131.92 | 0.602664 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1668.29 | −0.194514 | −0.0972569 | − | 0.995259i | \(-0.531007\pi\) | ||||
−0.0972569 | + | 0.995259i | \(0.531007\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16043.7 | 1.85730 | 0.928649 | − | 0.370961i | \(-0.120972\pi\) | ||||
0.928649 | + | 0.370961i | \(0.120972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3479.62 | −0.399964 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12530.9 | 1.43020 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6147.43 | −0.691844 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12986.7 | −1.45138 | −0.725692 | − | 0.688020i | \(-0.758480\pi\) | ||||
−0.725692 | + | 0.688020i | \(0.758480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −943.959 | −0.104766 | −0.0523831 | − | 0.998627i | \(-0.516682\pi\) | ||||
−0.0523831 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7460.21 | −0.822275 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2082.41 | 0.227953 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6427.32 | −0.698769 | −0.349384 | − | 0.936980i | \(-0.613609\pi\) | ||||
−0.349384 | + | 0.936980i | \(0.613609\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7254.91 | −0.778084 | −0.389042 | − | 0.921220i | \(-0.627194\pi\) | ||||
−0.389042 | + | 0.921220i | \(0.627194\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6122.35 | 0.652196 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2879.34 | 0.304671 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17381.9 | 1.82696 | 0.913478 | − | 0.406887i | \(-0.133386\pi\) | ||||
0.913478 | + | 0.406887i | \(0.133386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19084.2 | −1.99255 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4856.53 | −0.503708 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13800.8 | −1.41264 | −0.706319 | − | 0.707894i | \(-0.749645\pi\) | ||||
−0.706319 | + | 0.707894i | \(0.749645\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1401.83 | −0.142553 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.6989 | −0.00138400 | −0.000691998 | − | 1.00000i | \(-0.500220\pi\) | ||||
−0.000691998 | 1.00000i | \(0.500220\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13910.8 | −1.39631 | −0.698153 | − | 0.715949i | \(-0.745994\pi\) | ||||
−0.698153 | + | 0.715949i | \(0.745994\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13919.7 | −1.38820 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7818.53 | −0.774729 | −0.387364 | − | 0.921927i | \(-0.626614\pi\) | ||||
−0.387364 | + | 0.921927i | \(0.626614\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1672.00 | 0.163570 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5074.52 | −0.493291 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7996.75 | −0.772455 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5502.92 | −0.528221 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18025.4 | −1.71942 | −0.859709 | − | 0.510784i | \(-0.829355\pi\) | ||||
−0.859709 | + | 0.510784i | \(0.829355\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19655.2 | 1.86320 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21690.6 | −2.03077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17431.4 | 1.62195 | 0.810977 | − | 0.585078i | \(-0.198936\pi\) | ||||
0.810977 | + | 0.585078i | \(0.198936\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1098.10 | −0.101550 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7107.17 | −0.653243 | −0.326621 | − | 0.945155i | \(-0.605910\pi\) | ||||
−0.326621 | + | 0.945155i | \(0.605910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6745.45 | 0.616226 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6993.03 | −0.634977 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3499.61 | −0.313956 | −0.156978 | − | 0.987602i | \(-0.550175\pi\) | ||||
−0.156978 | + | 0.987602i | \(0.550175\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8501.99 | 0.758166 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9115.24 | −0.808009 | −0.404005 | − | 0.914757i | \(-0.632382\pi\) | ||||
−0.404005 | + | 0.914757i | \(0.632382\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20015.9 | 1.76375 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1052.97 | −0.0922367 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16049.7 | −1.39762 | −0.698811 | − | 0.715306i | \(-0.746287\pi\) | ||||
−0.698811 | + | 0.715306i | \(0.746287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 894.594 | 0.0769928 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36332.4 | −3.10873 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15695.1 | 1.33514 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10711.2 | 0.905912 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5574.48 | −0.468757 | −0.234379 | − | 0.972145i | \(-0.575306\pi\) | ||||
−0.234379 | + | 0.972145i | \(0.575306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 458.890 | 0.0383669 | 0.0191834 | − | 0.999816i | \(-0.493893\pi\) | ||||
0.0191834 | + | 0.999816i | \(0.493893\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12586.1 | 1.04034 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8216.89 | −0.675342 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2037.89 | 0.166548 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23730.1 | −1.92845 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16628.8 | 1.34379 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11032.1 | −0.886541 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10972.7 | −0.871999 | −0.436000 | − | 0.899947i | \(-0.643605\pi\) | ||||
−0.436000 | + | 0.899947i | \(0.643605\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5154.54 | 0.407371 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4357.28 | 0.342468 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19276.8 | 1.50679 | 0.753396 | − | 0.657567i | \(-0.228414\pi\) | ||||
0.753396 | + | 0.657567i | \(0.228414\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6526.72 | −0.507383 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4304.70 | −0.332825 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22358.9 | 1.71006 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12191.4 | −0.927410 | −0.463705 | − | 0.885990i | \(-0.653480\pi\) | ||||
−0.463705 | + | 0.885990i | \(0.653480\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6309.87 | −0.477422 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6323.03 | 0.475862 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3236.06 | −0.242244 | −0.121122 | − | 0.992638i | \(-0.538649\pi\) | ||||
−0.121122 | + | 0.992638i | \(0.538649\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11129.4 | 0.828701 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12167.8 | 0.896488 | 0.448244 | − | 0.893911i | \(-0.352050\pi\) | ||||
0.448244 | + | 0.893911i | \(0.352050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24412.3 | 1.78918 | 0.894592 | − | 0.446884i | \(-0.147466\pi\) | ||||
0.894592 | + | 0.446884i | \(0.147466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5877.14 | 0.428483 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15169.0 | −1.10016 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4346.85 | 0.313625 | 0.156812 | − | 0.987628i | \(-0.449878\pi\) | ||||
0.156812 | + | 0.987628i | \(0.449878\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7477.37 | 0.536700 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24821.3 | 1.76328 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8695.42 | −0.614550 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8752.61 | −0.615432 | −0.307716 | − | 0.951478i | \(-0.599565\pi\) | ||||
−0.307716 | + | 0.951478i | \(0.599565\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8031.97 | −0.561887 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6523.34 | −0.454034 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7788.77 | −0.539370 | −0.269685 | − | 0.962949i | \(-0.586920\pi\) | ||||
−0.269685 | + | 0.962949i | \(0.586920\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11593.8 | 0.794814 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1144.02 | 0.0780354 | 0.0390177 | − | 0.999239i | \(-0.487577\pi\) | ||||
0.0390177 | + | 0.999239i | \(0.487577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24673.4 | 1.67463 | 0.837314 | − | 0.546723i | \(-0.184125\pi\) | ||||
0.837314 | + | 0.546723i | \(0.184125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9405.99 | −0.635226 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6066.78 | 0.407686 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6325.62 | 0.422980 | 0.211490 | − | 0.977380i | \(-0.432168\pi\) | ||||
0.211490 | + | 0.977380i | \(0.432168\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19515.9 | 1.29219 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22976.2 | 1.51387 | 0.756935 | − | 0.653491i | \(-0.226696\pi\) | ||||
0.756935 | + | 0.653491i | \(0.226696\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −26994.2 | −1.76994 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8229.26 | 0.536949 | 0.268475 | − | 0.963287i | \(-0.413480\pi\) | ||||
0.268475 | + | 0.963287i | \(0.413480\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16852.8 | −1.09430 | −0.547150 | − | 0.837035i | \(-0.684287\pi\) | ||||
−0.547150 | + | 0.837035i | \(0.684287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1696.95 | 0.109656 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12456.9 | 0.797239 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4035.13 | −0.257014 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20216.7 | −1.28154 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8408.46 | 0.530484 | 0.265242 | − | 0.964182i | \(-0.414548\pi\) | ||||
0.265242 | + | 0.964182i | \(0.414548\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −381.801 | −0.0239735 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21611.3 | −1.35058 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1528.55 | −0.0946298 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9122.52 | 0.562118 | 0.281059 | − | 0.959690i | \(-0.409314\pi\) | ||||
0.281059 | + | 0.959690i | \(0.409314\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19279.4 | 1.18243 | 0.591217 | − | 0.806513i | \(-0.298648\pi\) | ||||
0.591217 | + | 0.806513i | \(0.298648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7177.81 | −0.438180 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2177.86 | 0.132335 | 0.0661673 | − | 0.997809i | \(-0.478923\pi\) | ||||
0.0661673 | + | 0.997809i | \(0.478923\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9192.05 | −0.555962 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6288.85 | −0.376879 | −0.188439 | − | 0.982085i | \(-0.560343\pi\) | ||||
−0.188439 | + | 0.982085i | \(0.560343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16837.0 | 1.00439 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3435.58 | 0.204010 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20346.5 | −1.20271 | −0.601357 | − | 0.798980i | \(-0.705373\pi\) | ||||
−0.601357 | + | 0.798980i | \(0.705373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27669.2 | −1.62815 | −0.814074 | − | 0.580761i | \(-0.802755\pi\) | ||||
−0.814074 | + | 0.580761i | \(0.802755\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7862.31 | 0.460553 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8165.54 | −0.474020 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12214.1 | −0.705865 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29439.2 | 1.69372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11862.6 | 0.679450 | 0.339725 | − | 0.940525i | \(-0.389666\pi\) | ||||
0.339725 | + | 0.940525i | \(0.389666\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6516.51 | −0.371586 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13526.6 | 0.767901 | 0.383950 | − | 0.923354i | \(-0.374563\pi\) | ||||
0.383950 | + | 0.923354i | \(0.374563\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15847.1 | 0.891720 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 713.863 | 0.0399930 | 0.0199965 | − | 0.999800i | \(-0.493634\pi\) | ||||
0.0199965 | + | 0.999800i | \(0.493634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6188.06 | −0.345159 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13740.6 | 0.763079 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30863.8 | 1.70656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15816.1 | 0.870727 | 0.435364 | − | 0.900255i | \(-0.356620\pi\) | ||||
0.435364 | + | 0.900255i | \(0.356620\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32742.2 | −1.78702 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24407.9 | 1.32642 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6469.54 | 0.350072 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28556.9 | 1.53863 | 0.769314 | − | 0.638871i | \(-0.220598\pi\) | ||||
0.769314 | + | 0.638871i | \(0.220598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12901.5 | 0.692163 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22200.3 | 1.18598 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1934.72 | −0.102482 | −0.0512411 | − | 0.998686i | \(-0.516318\pi\) | ||||
−0.0512411 | + | 0.998686i | \(0.516318\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10450.1 | 0.551208 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15235.8 | −0.800258 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39221.3 | 2.05146 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17267.3 | −0.899384 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18666.7 | −0.968218 | −0.484109 | − | 0.875008i | \(-0.660856\pi\) | ||||
−0.484109 | + | 0.875008i | \(0.660856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7774.66 | 0.399921 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31356.8 | 1.60629 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25955.3 | 1.32411 | 0.662055 | − | 0.749455i | \(-0.269685\pi\) | ||||
0.662055 | + | 0.749455i | \(0.269685\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6490.10 | 0.328379 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2083.79 | −0.105002 | −0.0525010 | − | 0.998621i | \(-0.516719\pi\) | ||||
−0.0525010 | + | 0.998621i | \(0.516719\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42426.4 | 2.12048 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28857.3 | −1.43645 | −0.718223 | − | 0.695813i | \(-0.755044\pi\) | ||||
−0.718223 | + | 0.695813i | \(0.755044\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5017.44 | −0.248745 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 899.017 | 0.0443900 | 0.0221950 | − | 0.999754i | \(-0.492935\pi\) | ||||
0.0221950 | + | 0.999754i | \(0.492935\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18370.5 | −0.903412 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7276.03 | −0.356380 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29009.3 | 1.40954 | 0.704770 | − | 0.709436i | \(-0.251050\pi\) | ||||
0.704770 | + | 0.709436i | \(0.251050\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11428.4 | −0.553087 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30985.2 | 1.49360 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10932.4 | −0.524892 | −0.262446 | − | 0.964947i | \(-0.584529\pi\) | ||||
−0.262446 | + | 0.964947i | \(0.584529\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7654.20 | −0.366047 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13212.8 | −0.629387 | −0.314693 | − | 0.949193i | \(-0.601902\pi\) | ||||
−0.314693 | + | 0.949193i | \(0.601902\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8943.80 | 0.422698 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11429.8 | −0.538077 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30129.7 | 1.41288 | 0.706440 | − | 0.707773i | \(-0.250300\pi\) | ||||
0.706440 | + | 0.707773i | \(0.250300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4073.06 | −0.190257 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11840.7 | 0.550947 | 0.275474 | − | 0.961309i | \(-0.411165\pi\) | ||||
0.275474 | + | 0.961309i | \(0.411165\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 58507.4 | 2.71180 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15576.2 | −0.716401 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6894.62 | 0.315889 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3507.88 | −0.160104 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10667.5 | −0.485020 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6529.10 | −0.295727 | −0.147863 | − | 0.989008i | \(-0.547240\pi\) | ||||
−0.147863 | + | 0.989008i | \(0.547240\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13253.2 | −0.598006 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36605.9 | 1.63924 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35109.2 | 1.56628 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41987.6 | −1.86609 | −0.933046 | − | 0.359757i | \(-0.882860\pi\) | ||||
−0.933046 | + | 0.359757i | \(0.882860\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20073.3 | −0.888790 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2878.80 | 0.126988 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15496.4 | −0.681017 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10882.0 | 0.474676 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13634.1 | −0.592522 | −0.296261 | − | 0.955107i | \(-0.595740\pi\) | ||||
−0.296261 | + | 0.955107i | \(0.595740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20093.9 | −0.870025 | −0.435013 | − | 0.900424i | \(-0.643256\pi\) | ||||
−0.435013 | + | 0.900424i | \(0.643256\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15513.1 | −0.669210 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7006.01 | 0.301116 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4141.75 | −0.177358 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7636.29 | −0.324615 | −0.162307 | − | 0.986740i | \(-0.551894\pi\) | ||||
−0.162307 | + | 0.986740i | \(0.551894\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28788.4 | 1.21932 | 0.609660 | − | 0.792663i | \(-0.291306\pi\) | ||||
0.609660 | + | 0.792663i | \(0.291306\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29393.2 | 1.24041 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20515.4 | 0.862623 | 0.431312 | − | 0.902203i | \(-0.358051\pi\) | ||||
0.431312 | + | 0.902203i | \(0.358051\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16264.4 | −0.681407 | −0.340704 | − | 0.940171i | \(-0.610665\pi\) | ||||
−0.340704 | + | 0.940171i | \(0.610665\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5383.89 | −0.224748 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54243.7 | −2.24812 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6545.21 | −0.270293 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13770.2 | −0.566629 | −0.283314 | − | 0.959027i | \(-0.591434\pi\) | ||||
−0.283314 | + | 0.959027i | \(0.591434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7509.45 | −0.307903 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27355.9 | 1.11766 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6718.06 | 0.273501 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17414.2 | 0.703948 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24472.8 | 0.985802 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8031.48 | 0.322383 | 0.161191 | − | 0.986923i | \(-0.448466\pi\) | ||||
0.161191 | + | 0.986923i | \(0.448466\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5707.61 | −0.228300 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42764.0 | 1.70454 | 0.852270 | − | 0.523102i | \(-0.175225\pi\) | ||||
0.852270 | + | 0.523102i | \(0.175225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8155.05 | 0.323919 | 0.161960 | − | 0.986797i | \(-0.448219\pi\) | ||||
0.161960 | + | 0.986797i | \(0.448219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40660.0 | −1.60380 | −0.801901 | − | 0.597457i | \(-0.796178\pi\) | ||||
−0.801901 | + | 0.597457i | \(0.796178\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −68338.5 | −2.68622 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6652.11 | 0.260574 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47135.8 | −1.84002 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52754.7 | 2.05227 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10199.2 | −0.395407 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28260.6 | −1.08813 | −0.544067 | − | 0.839042i | \(-0.683116\pi\) | ||||
−0.544067 | + | 0.839042i | \(0.683116\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4152.64 | −0.159346 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15951.2 | −0.609998 | −0.304999 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304999 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1750.48 | 0.0667137 | 0.0333569 | − | 0.999444i | \(-0.489380\pi\) | ||||
0.0333569 | + | 0.999444i | \(0.489380\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13002.0 | −0.493849 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2007.02 | 0.0759741 | 0.0379871 | − | 0.999278i | \(-0.487905\pi\) | ||||
0.0379871 | + | 0.999278i | \(0.487905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3288.20 | −0.123635 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12810.1 | 0.480036 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 70386.3 | 2.62878 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9517.54 | −0.354271 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31494.9 | 1.16842 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31745.4 | −1.17380 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −32886.6 | −1.20794 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12069.7 | 0.441861 | 0.220930 | − | 0.975290i | \(-0.429091\pi\) | ||||
0.220930 | + | 0.975290i | \(0.429091\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9411.69 | 0.343417 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40167.1 | −1.46081 | −0.730404 | − | 0.683016i | \(-0.760668\pi\) | ||||
−0.730404 | + | 0.683016i | \(0.760668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32819.0 | 1.18965 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 41641.2 | 1.50450 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13503.5 | 0.484699 | 0.242349 | − | 0.970189i | \(-0.422082\pi\) | ||||
0.242349 | + | 0.970189i | \(0.422082\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1011.33 | −0.0361831 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8573.05 | 0.305726 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −93978.9 | −3.34055 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17083.9 | −0.605295 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31001.9 | −1.09488 | −0.547438 | − | 0.836846i | \(-0.684397\pi\) | ||||
−0.547438 | + | 0.836846i | \(0.684397\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5894.08 | −0.206821 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40341.6 | −1.41103 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34998.0 | 1.22021 | 0.610104 | − | 0.792322i | \(-0.291128\pi\) | ||||
0.610104 | + | 0.792322i | \(0.291128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10790.9 | 0.375025 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11652.5 | 0.403679 | 0.201839 | − | 0.979419i | \(-0.435308\pi\) | ||||
0.201839 | + | 0.979419i | \(0.435308\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29546.4 | −1.02032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2921.85 | −0.100261 | −0.0501306 | − | 0.998743i | \(-0.515964\pi\) | ||||
−0.0501306 | + | 0.998743i | \(0.515964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19268.9 | −0.659109 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 646.350 | 0.0220392 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24262.5 | 0.824702 | 0.412351 | − | 0.911025i | \(-0.364708\pi\) | ||||
0.412351 | + | 0.911025i | \(0.364708\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37496.8 | −1.27054 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15822.5 | 0.534451 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28974.1 | 0.972577 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7819.06 | 0.261647 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −47706.5 | −1.59143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10258.0 | −0.341131 | −0.170565 | − | 0.985346i | \(-0.554559\pi\) | ||||
−0.170565 | + | 0.985346i | \(0.554559\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5160.76 | 0.171091 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16635.7 | 0.549809 | 0.274905 | − | 0.961472i | \(-0.411354\pi\) | ||||
0.274905 | + | 0.961472i | \(0.411354\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 36548.7 | 1.20051 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12850.2 | 0.420791 | 0.210395 | − | 0.977616i | \(-0.432525\pi\) | ||||
0.210395 | + | 0.977616i | \(0.432525\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12985.0 | −0.423905 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2048.84 | 0.0666814 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42272.8 | 1.37161 | 0.685805 | − | 0.727785i | \(-0.259450\pi\) | ||||
0.685805 | + | 0.727785i | \(0.259450\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41619.6 | 1.34631 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7856.44 | −0.252599 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11504.2 | 0.368761 | 0.184380 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184380 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5056.06 | −0.161580 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −73969.9 | −2.35679 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17180.9 | 0.545763 | 0.272881 | − | 0.962048i | \(-0.412023\pi\) | ||||
0.272881 | + | 0.962048i | \(0.412023\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10513.4 | 0.332962 |
(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 | 2352.4.a.cl.1.4 | 4 | ||
4.3 | odd | 2 | 588.4.a.k.1.4 | yes | 4 | ||
7.6 | odd | 2 | 2352.4.a.cq.1.1 | 4 | |||
12.11 | even | 2 | 1764.4.a.ba.1.1 | 4 | |||
28.3 | even | 6 | 588.4.i.l.373.4 | 8 | |||
28.11 | odd | 6 | 588.4.i.k.373.1 | 8 | |||
28.19 | even | 6 | 588.4.i.l.361.4 | 8 | |||
28.23 | odd | 6 | 588.4.i.k.361.1 | 8 | |||
28.27 | even | 2 | 588.4.a.j.1.1 | ✓ | 4 | ||
84.11 | even | 6 | 1764.4.k.bd.1549.4 | 8 | |||
84.23 | even | 6 | 1764.4.k.bd.361.4 | 8 | |||
84.47 | odd | 6 | 1764.4.k.bb.361.1 | 8 | |||
84.59 | odd | 6 | 1764.4.k.bb.1549.1 | 8 | |||
84.83 | odd | 2 | 1764.4.a.bc.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.j.1.1 | ✓ | 4 | 28.27 | even | 2 | ||
588.4.a.k.1.4 | yes | 4 | 4.3 | odd | 2 | ||
588.4.i.k.361.1 | 8 | 28.23 | odd | 6 | |||
588.4.i.k.373.1 | 8 | 28.11 | odd | 6 | |||
588.4.i.l.361.4 | 8 | 28.19 | even | 6 | |||
588.4.i.l.373.4 | 8 | 28.3 | even | 6 | |||
1764.4.a.ba.1.1 | 4 | 12.11 | even | 2 | |||
1764.4.a.bc.1.4 | 4 | 84.83 | odd | 2 | |||
1764.4.k.bb.361.1 | 8 | 84.47 | odd | 6 | |||
1764.4.k.bb.1549.1 | 8 | 84.59 | odd | 6 | |||
1764.4.k.bd.361.4 | 8 | 84.23 | even | 6 | |||
1764.4.k.bd.1549.4 | 8 | 84.11 | even | 6 | |||
2352.4.a.cl.1.4 | 4 | 1.1 | even | 1 | trivial | ||
2352.4.a.cq.1.1 | 4 | 7.6 | odd | 2 |