Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,4,Mod(1,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.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: | \(104.079369250\) |
Analytic rank: | \(0\) |
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 | 1.3 | ||
Root | \(2.89590\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.16940 | 0.730694 | 0.365347 | − | 0.930871i | \(-0.380950\pi\) | ||||
0.365347 | + | 0.930871i | \(0.380950\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −37.8189 | −1.03662 | −0.518310 | − | 0.855193i | \(-0.673439\pi\) | ||||
−0.518310 | + | 0.855193i | \(0.673439\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −39.9319 | −0.851933 | −0.425966 | − | 0.904739i | \(-0.640066\pi\) | ||||
−0.425966 | + | 0.904739i | \(0.640066\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.93596 | 0.141754 | 0.0708772 | − | 0.997485i | \(-0.477420\pi\) | ||||
0.0708772 | + | 0.997485i | \(0.477420\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 90.4458 | 1.09209 | 0.546045 | − | 0.837756i | \(-0.316133\pi\) | ||||
0.546045 | + | 0.837756i | \(0.316133\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −118.595 | −1.07516 | −0.537580 | − | 0.843213i | \(-0.680661\pi\) | ||||
−0.537580 | + | 0.843213i | \(0.680661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −58.2608 | −0.466087 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 78.4061 | 0.502057 | 0.251028 | − | 0.967980i | \(-0.419231\pi\) | ||||
0.251028 | + | 0.967980i | \(0.419231\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −92.0110 | −0.533086 | −0.266543 | − | 0.963823i | \(-0.585881\pi\) | ||||
−0.266543 | + | 0.963823i | \(0.585881\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 332.435 | 1.47708 | 0.738541 | − | 0.674209i | \(-0.235515\pi\) | ||||
0.738541 | + | 0.674209i | \(0.235515\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 71.7451 | 0.273285 | 0.136643 | − | 0.990620i | \(-0.456369\pi\) | ||||
0.136643 | + | 0.990620i | \(0.456369\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −115.947 | −0.411202 | −0.205601 | − | 0.978636i | \(-0.565915\pi\) | ||||
−0.205601 | + | 0.978636i | \(0.565915\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 307.927 | 0.955656 | 0.477828 | − | 0.878453i | \(-0.341424\pi\) | ||||
0.477828 | + | 0.878453i | \(0.341424\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 403.150 | 1.04485 | 0.522424 | − | 0.852686i | \(-0.325028\pi\) | ||||
0.522424 | + | 0.852686i | \(0.325028\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −308.958 | −0.757451 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 593.710 | 1.31008 | 0.655038 | − | 0.755596i | \(-0.272653\pi\) | ||||
0.655038 | + | 0.755596i | \(0.272653\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −333.170 | −0.699313 | −0.349657 | − | 0.936878i | \(-0.613702\pi\) | ||||
−0.349657 | + | 0.936878i | \(0.613702\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −326.220 | −0.622502 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −743.511 | −1.35574 | −0.677869 | − | 0.735183i | \(-0.737096\pi\) | ||||
−0.677869 | + | 0.735183i | \(0.737096\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 728.272 | 1.21732 | 0.608662 | − | 0.793429i | \(-0.291706\pi\) | ||||
0.608662 | + | 0.793429i | \(0.291706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 801.749 | 1.28545 | 0.642723 | − | 0.766098i | \(-0.277804\pi\) | ||||
0.642723 | + | 0.766098i | \(0.277804\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1067.91 | 1.52087 | 0.760435 | − | 0.649414i | \(-0.224986\pi\) | ||||
0.760435 | + | 0.649414i | \(0.224986\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 906.756 | 1.19915 | 0.599575 | − | 0.800319i | \(-0.295336\pi\) | ||||
0.599575 | + | 0.800319i | \(0.295336\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 81.1709 | 0.103579 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1113.27 | 1.32591 | 0.662957 | − | 0.748658i | \(-0.269301\pi\) | ||||
0.662957 | + | 0.748658i | \(0.269301\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 738.889 | 0.797983 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1480.94 | −1.55017 | −0.775084 | − | 0.631858i | \(-0.782293\pi\) | ||||
−0.775084 | + | 0.631858i | \(0.782293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −556.316 | −0.548075 | −0.274037 | − | 0.961719i | \(-0.588359\pi\) | ||||
−0.274037 | + | 0.961719i | \(0.588359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −552.435 | −0.528476 | −0.264238 | − | 0.964458i | \(-0.585120\pi\) | ||||
−0.264238 | + | 0.964458i | \(0.585120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −533.804 | −0.482288 | −0.241144 | − | 0.970489i | \(-0.577523\pi\) | ||||
−0.241144 | + | 0.970489i | \(0.577523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1094.63 | 0.961894 | 0.480947 | − | 0.876750i | \(-0.340293\pi\) | ||||
0.480947 | + | 0.876750i | \(0.340293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1425.18 | 1.18646 | 0.593228 | − | 0.805035i | \(-0.297853\pi\) | ||||
0.593228 | + | 0.805035i | \(0.297853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −968.847 | −0.785612 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 99.2659 | 0.0745800 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1497.13 | −1.07126 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −786.485 | −0.549522 | −0.274761 | − | 0.961513i | \(-0.588599\pi\) | ||||
−0.274761 | + | 0.961513i | \(0.588599\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −27.7303 | −0.0184947 | −0.00924735 | − | 0.999957i | \(-0.502944\pi\) | ||||
−0.00924735 | + | 0.999957i | \(0.502944\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2362.98 | 1.47360 | 0.736798 | − | 0.676113i | \(-0.236337\pi\) | ||||
0.736798 | + | 0.676113i | \(0.236337\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2513.28 | −1.53362 | −0.766811 | − | 0.641873i | \(-0.778158\pi\) | ||||
−0.766811 | + | 0.641873i | \(0.778158\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1510.18 | 0.883130 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 640.531 | 0.366850 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2265.83 | −1.24580 | −0.622900 | − | 0.782302i | \(-0.714045\pi\) | ||||
−0.622900 | + | 0.782302i | \(0.714045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 283.146 | 0.152597 | 0.0762984 | − | 0.997085i | \(-0.475690\pi\) | ||||
0.0762984 | + | 0.997085i | \(0.475690\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −751.675 | −0.389522 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −192.581 | −0.0978956 | −0.0489478 | − | 0.998801i | \(-0.515587\pi\) | ||||
−0.0489478 | + | 0.998801i | \(0.515587\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −842.833 | −0.405005 | −0.202502 | − | 0.979282i | \(-0.564907\pi\) | ||||
−0.202502 | + | 0.979282i | \(0.564907\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3859.21 | −1.78823 | −0.894116 | − | 0.447836i | \(-0.852195\pi\) | ||||
−0.894116 | + | 0.447836i | \(0.852195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −602.441 | −0.274211 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1510.66 | 0.663891 | 0.331946 | − | 0.943298i | \(-0.392295\pi\) | ||||
0.331946 | + | 0.943298i | \(0.392295\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2464.63 | 1.02913 | 0.514566 | − | 0.857451i | \(-0.327953\pi\) | ||||
0.514566 | + | 0.857451i | \(0.327953\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3297.36 | 1.35409 | 0.677047 | − | 0.735940i | \(-0.263259\pi\) | ||||
0.677047 | + | 0.735940i | \(0.263259\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2715.80 | 1.07929 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −375.767 | −0.146945 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4729.71 | 1.79178 | 0.895889 | − | 0.444278i | \(-0.146540\pi\) | ||||
0.895889 | + | 0.444278i | \(0.146540\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4553.18 | 1.69816 | 0.849080 | − | 0.528264i | \(-0.177157\pi\) | ||||
0.849080 | + | 0.528264i | \(0.177157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3109.06 | 1.12442 | 0.562212 | − | 0.826993i | \(-0.309950\pi\) | ||||
0.562212 | + | 0.826993i | \(0.309950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 443.512 | 0.157989 | 0.0789943 | − | 0.996875i | \(-0.474829\pi\) | ||||
0.0789943 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 586.114 | 0.199688 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3420.56 | −1.13208 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4653.28 | 1.51822 | 0.759112 | − | 0.650960i | \(-0.225633\pi\) | ||||
0.759112 | + | 0.650960i | \(0.225633\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −947.214 | −0.300463 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −396.762 | −0.120765 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2778.90 | −0.834481 | −0.417240 | − | 0.908796i | \(-0.637003\pi\) | ||||
−0.417240 | + | 0.908796i | \(0.637003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3217.22 | 0.940681 | 0.470340 | − | 0.882485i | \(-0.344131\pi\) | ||||
0.470340 | + | 0.882485i | \(0.344131\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3728.01 | 1.07578 | 0.537891 | − | 0.843014i | \(-0.319221\pi\) | ||||
0.537891 | + | 0.843014i | \(0.319221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3603.51 | 1.01319 | 0.506596 | − | 0.862183i | \(-0.330903\pi\) | ||||
0.506596 | + | 0.862183i | \(0.330903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2515.58 | 0.698292 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2348.76 | −0.635684 | −0.317842 | − | 0.948144i | \(-0.602958\pi\) | ||||
−0.317842 | + | 0.948144i | \(0.602958\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5093.39 | 1.36139 | 0.680693 | − | 0.732569i | \(-0.261679\pi\) | ||||
0.680693 | + | 0.732569i | \(0.261679\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3611.68 | −0.930386 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5939.02 | −1.49350 | −0.746749 | − | 0.665106i | \(-0.768386\pi\) | ||||
−0.746749 | + | 0.665106i | \(0.768386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4485.11 | 1.11453 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1515.89 | −0.367932 | −0.183966 | − | 0.982933i | \(-0.558894\pi\) | ||||
−0.183966 | + | 0.982933i | \(0.558894\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6433.92 | 1.50849 | 0.754244 | − | 0.656594i | \(-0.228003\pi\) | ||||
0.754244 | + | 0.656594i | \(0.228003\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3293.50 | 0.763464 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6949.79 | −1.57523 | −0.787614 | − | 0.616169i | \(-0.788684\pi\) | ||||
−0.787614 | + | 0.616169i | \(0.788684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 961.994 | 0.215635 | 0.107817 | − | 0.994171i | \(-0.465614\pi\) | ||||
0.107817 | + | 0.994171i | \(0.465614\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2203.36 | 0.483154 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 760.010 | 0.164854 | 0.0824271 | − | 0.996597i | \(-0.473733\pi\) | ||||
0.0824271 | + | 0.996597i | \(0.473733\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4412.07 | 0.936662 | 0.468331 | − | 0.883553i | \(-0.344855\pi\) | ||||
0.468331 | + | 0.883553i | \(0.344855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2602.15 | 0.546578 | 0.273289 | − | 0.961932i | \(-0.411888\pi\) | ||||
0.273289 | + | 0.961932i | \(0.411888\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4814.28 | −0.979906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9332.18 | −1.86072 | −0.930361 | − | 0.366644i | \(-0.880507\pi\) | ||||
−0.930361 | + | 0.366644i | \(0.880507\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4850.26 | 0.957264 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4735.71 | 0.915964 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2721.80 | −0.510984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4895.51 | −0.910103 | −0.455051 | − | 0.890465i | \(-0.650379\pi\) | ||||
−0.455051 | + | 0.890465i | \(0.650379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7505.28 | 1.36844 | 0.684221 | − | 0.729275i | \(-0.260142\pi\) | ||||
0.684221 | + | 0.729275i | \(0.260142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6349.27 | 1.14659 | 0.573294 | − | 0.819350i | \(-0.305665\pi\) | ||||
0.573294 | + | 0.819350i | \(0.305665\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7999.60 | 1.41736 | 0.708679 | − | 0.705531i | \(-0.249292\pi\) | ||||
0.708679 | + | 0.705531i | \(0.249292\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2965.23 | −0.520442 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 898.666 | 0.154808 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2326.47 | 0.397074 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2121.56 | −0.352300 | −0.176150 | − | 0.984363i | \(-0.556364\pi\) | ||||
−0.176150 | + | 0.984363i | \(0.556364\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6074.05 | −0.990629 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9114.19 | −1.47324 | −0.736620 | − | 0.676307i | \(-0.763579\pi\) | ||||
−0.736620 | + | 0.676307i | \(0.763579\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3479.75 | 0.552607 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1673.07 | 0.258833 | 0.129416 | − | 0.991590i | \(-0.458690\pi\) | ||||
0.129416 | + | 0.991590i | \(0.458690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3467.56 | 0.531845 | 0.265923 | − | 0.963994i | \(-0.414323\pi\) | ||||
0.265923 | + | 0.963994i | \(0.414323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3984.24 | 0.600736 | 0.300368 | − | 0.953823i | \(-0.402891\pi\) | ||||
0.300368 | + | 0.953823i | \(0.402891\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5949.55 | 0.889491 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2170.93 | −0.319157 | −0.159579 | − | 0.987185i | \(-0.551014\pi\) | ||||
−0.159579 | + | 0.987185i | \(0.551014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1321.45 | 0.192659 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6549.81 | 0.939268 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3592.12 | −0.510918 | −0.255459 | − | 0.966820i | \(-0.582227\pi\) | ||||
−0.255459 | + | 0.966820i | \(0.582227\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7439.80 | 1.03276 | 0.516378 | − | 0.856361i | \(-0.327280\pi\) | ||||
0.516378 | + | 0.856361i | \(0.327280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3130.91 | −0.427719 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11243.9 | 1.52390 | 0.761951 | − | 0.647635i | \(-0.224242\pi\) | ||||
0.761951 | + | 0.647635i | \(0.224242\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3541.25 | 0.472452 | 0.236226 | − | 0.971698i | \(-0.424089\pi\) | ||||
0.236226 | + | 0.971698i | \(0.424089\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10558.2 | 1.37615 | 0.688074 | − | 0.725640i | \(-0.258456\pi\) | ||||
0.688074 | + | 0.725640i | \(0.258456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1178.35 | −0.152409 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8724.15 | 1.11129 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 540.574 | 0.0683391 | 0.0341696 | − | 0.999416i | \(-0.489121\pi\) | ||||
0.0341696 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2167.03 | −0.269866 | −0.134933 | − | 0.990855i | \(-0.543082\pi\) | ||||
−0.134933 | + | 0.990855i | \(0.543082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3674.17 | 0.454153 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12572.3 | −1.53117 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 957.690 | 0.115782 | 0.0578908 | − | 0.998323i | \(-0.481562\pi\) | ||||
0.0578908 | + | 0.998323i | \(0.481562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7407.66 | 0.876211 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6464.42 | 0.753718 | 0.376859 | − | 0.926271i | \(-0.377004\pi\) | ||||
0.376859 | + | 0.926271i | \(0.377004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6201.23 | −0.717885 | −0.358943 | − | 0.933360i | \(-0.616863\pi\) | ||||
−0.358943 | + | 0.933360i | \(0.616863\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −578.877 | −0.0660698 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1415.59 | −0.158206 | −0.0791029 | − | 0.996866i | \(-0.525206\pi\) | ||||
−0.0791029 | + | 0.996866i | \(0.525206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8905.73 | −0.988411 | −0.494206 | − | 0.869345i | \(-0.664541\pi\) | ||||
−0.494206 | + | 0.869345i | \(0.664541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10726.4 | −1.17417 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10876.5 | −1.18248 | −0.591238 | − | 0.806497i | \(-0.701361\pi\) | ||||
−0.591238 | + | 0.806497i | \(0.701361\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11403.0 | −1.22296 | −0.611479 | − | 0.791260i | \(-0.709425\pi\) | ||||
−0.611479 | + | 0.791260i | \(0.709425\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9094.74 | 0.968837 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12689.0 | 1.33370 | 0.666852 | − | 0.745190i | \(-0.267641\pi\) | ||||
0.666852 | + | 0.745190i | \(0.267641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2713.32 | −0.283293 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2270.05 | 0.232360 | 0.116180 | − | 0.993228i | \(-0.462935\pi\) | ||||
0.116180 | + | 0.993228i | \(0.462935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10731.2 | 1.08417 | 0.542085 | − | 0.840324i | \(-0.317635\pi\) | ||||
0.542085 | + | 0.840324i | \(0.317635\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3307.74 | −0.332017 | −0.166008 | − | 0.986124i | \(-0.553088\pi\) | ||||
−0.166008 | + | 0.986124i | \(0.553088\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9246.69 | −0.916244 | −0.458122 | − | 0.888889i | \(-0.651478\pi\) | ||||
−0.458122 | + | 0.888889i | \(0.651478\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4384.96 | 0.426260 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5269.45 | −0.509008 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15223.3 | 1.45213 | 0.726066 | − | 0.687625i | \(-0.241347\pi\) | ||||
0.726066 | + | 0.687625i | \(0.241347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13274.8 | −1.25837 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12098.4 | −1.13270 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7758.72 | −0.721933 | −0.360966 | − | 0.932579i | \(-0.617553\pi\) | ||||
−0.360966 | + | 0.932579i | \(0.617553\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8342.30 | 0.766767 | 0.383384 | − | 0.923589i | \(-0.374759\pi\) | ||||
0.383384 | + | 0.923589i | \(0.374759\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 779.040 | 0.0711688 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2586.95 | −0.232079 | −0.116040 | − | 0.993245i | \(-0.537020\pi\) | ||||
−0.116040 | + | 0.993245i | \(0.537020\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 409.682 | 0.0363157 | 0.0181578 | − | 0.999835i | \(-0.494220\pi\) | ||||
0.0181578 | + | 0.999835i | \(0.494220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4544.77 | −0.400475 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4390.51 | 0.382330 | 0.191165 | − | 0.981558i | \(-0.438774\pi\) | ||||
0.191165 | + | 0.981558i | \(0.438774\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4513.06 | −0.386154 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11645.5 | −0.990652 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19429.5 | −1.63382 | −0.816912 | − | 0.576762i | \(-0.804316\pi\) | ||||
−0.816912 | + | 0.576762i | \(0.804316\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17948.7 | −1.50065 | −0.750326 | − | 0.661067i | \(-0.770104\pi\) | ||||
−0.750326 | + | 0.661067i | \(0.770104\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −914.217 | −0.0755672 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1897.67 | 0.155968 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2864.92 | −0.232821 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4360.86 | −0.352405 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23094.0 | 1.83528 | 0.917641 | − | 0.397411i | \(-0.130091\pi\) | ||||
0.917641 | + | 0.397411i | \(0.130091\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8942.47 | 0.702850 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2266.68 | −0.177178 | −0.0885889 | − | 0.996068i | \(-0.528236\pi\) | ||||
−0.0885889 | + | 0.996068i | \(0.528236\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7091.50 | 0.548291 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11038.5 | 0.839709 | 0.419854 | − | 0.907592i | \(-0.362081\pi\) | ||||
0.419854 | + | 0.907592i | \(0.362081\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4629.97 | 0.350316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7059.36 | −0.528448 | −0.264224 | − | 0.964461i | \(-0.585116\pi\) | ||||
−0.264224 | + | 0.964461i | \(0.585116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11642.9 | 0.866936 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1352.81 | 0.0996706 | 0.0498353 | − | 0.998757i | \(-0.484130\pi\) | ||||
0.0498353 | + | 0.998757i | \(0.484130\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20839.2 | −1.52731 | −0.763655 | − | 0.645625i | \(-0.776597\pi\) | ||||
−0.763655 | + | 0.645625i | \(0.776597\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6909.42 | 0.501117 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10014.6 | −0.722556 | −0.361278 | − | 0.932458i | \(-0.617659\pi\) | ||||
−0.361278 | + | 0.932458i | \(0.617659\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15246.7 | −1.08311 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20864.8 | 1.46709 | 0.733546 | − | 0.679640i | \(-0.237864\pi\) | ||||
0.733546 | + | 0.679640i | \(0.237864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8322.01 | −0.582177 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17547.7 | 1.21517 | 0.607586 | − | 0.794254i | \(-0.292138\pi\) | ||||
0.607586 | + | 0.794254i | \(0.292138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 130.682 | 0.00891405 | 0.00445703 | − | 0.999990i | \(-0.498581\pi\) | ||||
0.00445703 | + | 0.999990i | \(0.498581\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5964.47 | 0.404818 | 0.202409 | − | 0.979301i | \(-0.435123\pi\) | ||||
0.202409 | + | 0.979301i | \(0.435123\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 810.944 | 0.0544951 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9911.63 | 0.662769 | 0.331384 | − | 0.943496i | \(-0.392484\pi\) | ||||
0.331384 | + | 0.943496i | \(0.392484\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12296.1 | −0.814155 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6482.53 | −0.427124 | −0.213562 | − | 0.976930i | \(-0.568506\pi\) | ||||
−0.213562 | + | 0.976930i | \(0.568506\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7189.36 | −0.469097 | −0.234548 | − | 0.972104i | \(-0.575361\pi\) | ||||
−0.234548 | + | 0.972104i | \(0.575361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1861.39 | −0.120865 | −0.0604327 | − | 0.998172i | \(-0.519248\pi\) | ||||
−0.0604327 | + | 0.998172i | \(0.519248\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4948.07 | −0.316677 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3303.06 | 0.209383 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29032.0 | −1.83161 | −0.915803 | − | 0.401627i | \(-0.868445\pi\) | ||||
−0.915803 | + | 0.401627i | \(0.868445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6425.12 | −0.401532 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24457.7 | −1.50705 | −0.753527 | − | 0.657417i | \(-0.771649\pi\) | ||||
−0.753527 | + | 0.657417i | \(0.771649\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10968.2 | −0.672695 | −0.336348 | − | 0.941738i | \(-0.609192\pi\) | ||||
−0.336348 | + | 0.941738i | \(0.609192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5484.74 | 0.333272 | 0.166636 | − | 0.986018i | \(-0.446709\pi\) | ||||
0.166636 | + | 0.986018i | \(0.446709\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22453.4 | −1.35805 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10330.0 | 0.619055 | 0.309527 | − | 0.950891i | \(-0.399829\pi\) | ||||
0.309527 | + | 0.950891i | \(0.399829\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −226.540 | −0.0135140 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26822.2 | −1.58550 | −0.792751 | − | 0.609546i | \(-0.791352\pi\) | ||||
−0.792751 | + | 0.609546i | \(0.791352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2498.76 | −0.147035 | −0.0735177 | − | 0.997294i | \(-0.523423\pi\) | ||||
−0.0735177 | + | 0.997294i | \(0.523423\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9298.54 | −0.539791 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12600.1 | 0.724922 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10092.1 | 0.578044 | 0.289022 | − | 0.957322i | \(-0.406670\pi\) | ||||
0.289022 | + | 0.957322i | \(0.406670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26366.4 | −1.49681 | −0.748406 | − | 0.663241i | \(-0.769180\pi\) | ||||
−0.748406 | + | 0.663241i | \(0.769180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22570.8 | −1.26449 | −0.632245 | − | 0.774769i | \(-0.717866\pi\) | ||||
−0.632245 | + | 0.774769i | \(0.717866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19304.1 | 1.07675 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16098.6 | −0.890140 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11931.5 | 0.656867 | 0.328434 | − | 0.944527i | \(-0.393479\pi\) | ||||
0.328434 | + | 0.944527i | \(0.393479\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20532.0 | −1.12061 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 712.856 | 0.0387394 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16592.6 | −0.893997 | −0.446999 | − | 0.894535i | \(-0.647507\pi\) | ||||
−0.446999 | + | 0.894535i | \(0.647507\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30067.4 | 1.61311 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18714.0 | 0.991283 | 0.495641 | − | 0.868527i | \(-0.334933\pi\) | ||||
0.495641 | + | 0.868527i | \(0.334933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10912.0 | 0.573152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12337.3 | 0.645298 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24854.8 | −1.28919 | −0.644594 | − | 0.764525i | \(-0.722974\pi\) | ||||
−0.644594 | + | 0.764525i | \(0.722974\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4568.00 | −0.234002 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22506.0 | 1.14814 | 0.574071 | − | 0.818805i | \(-0.305363\pi\) | ||||
0.574071 | + | 0.818805i | \(0.305363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1152.04 | −0.0582897 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23792.0 | 1.19888 | 0.599440 | − | 0.800420i | \(-0.295390\pi\) | ||||
0.599440 | + | 0.800420i | \(0.295390\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28118.8 | 1.40538 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4803.24 | 0.239093 | 0.119547 | − | 0.992829i | \(-0.461856\pi\) | ||||
0.119547 | + | 0.992829i | \(0.461856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5076.10 | −0.250638 | −0.125319 | − | 0.992116i | \(-0.539995\pi\) | ||||
−0.125319 | + | 0.992116i | \(0.539995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18510.5 | −0.910298 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9158.72 | −0.445015 | −0.222508 | − | 0.974931i | \(-0.571424\pi\) | ||||
−0.222508 | + | 0.974931i | \(0.571424\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2313.14 | 0.111502 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33682.2 | 1.61717 | 0.808587 | − | 0.588377i | \(-0.200233\pi\) | ||||
0.808587 | + | 0.588377i | \(0.200233\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13346.3 | 0.635745 | 0.317873 | − | 0.948133i | \(-0.397032\pi\) | ||||
0.317873 | + | 0.948133i | \(0.397032\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23708.0 | −1.11610 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15530.6 | 0.728281 | 0.364140 | − | 0.931344i | \(-0.381363\pi\) | ||||
0.364140 | + | 0.931344i | \(0.381363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11015.2 | −0.512536 | −0.256268 | − | 0.966606i | \(-0.582493\pi\) | ||||
−0.256268 | + | 0.966606i | \(0.582493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5360.63 | 0.248464 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6489.04 | 0.298452 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27542.4 | −1.26190 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1573.27 | −0.0715317 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21192.6 | −0.959892 | −0.479946 | − | 0.877298i | \(-0.659344\pi\) | ||||
−0.479946 | + | 0.877298i | \(0.659344\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13304.1 | 0.595768 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18189.9 | 0.808432 | 0.404216 | − | 0.914663i | \(-0.367544\pi\) | ||||
0.404216 | + | 0.914663i | \(0.367544\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3059.56 | 0.135468 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30321.2 | −1.33252 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45516.5 | −1.97809 | −0.989045 | − | 0.147611i | \(-0.952842\pi\) | ||||
−0.989045 | + | 0.147611i | \(0.952842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42099.9 | 1.82285 | 0.911423 | − | 0.411472i | \(-0.134985\pi\) | ||||
0.911423 | + | 0.411472i | \(0.134985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6885.45 | −0.295935 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10486.9 | −0.449069 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26555.9 | 1.12888 | 0.564439 | − | 0.825475i | \(-0.309093\pi\) | ||||
0.564439 | + | 0.825475i | \(0.309093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1554.25 | −0.0658295 | −0.0329147 | − | 0.999458i | \(-0.510479\pi\) | ||||
−0.0329147 | + | 0.999458i | \(0.510479\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10548.3 | 0.443531 | 0.221766 | − | 0.975100i | \(-0.428818\pi\) | ||||
0.221766 | + | 0.975100i | \(0.428818\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4331.26 | −0.181461 | −0.0907303 | − | 0.995875i | \(-0.528920\pi\) | ||||
−0.0907303 | + | 0.995875i | \(0.528920\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31527.5 | −1.30665 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23557.7 | −0.969369 | −0.484685 | − | 0.874689i | \(-0.661066\pi\) | ||||
−0.484685 | + | 0.874689i | \(0.661066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18241.5 | −0.747939 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4921.59 | −0.200364 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39425.0 | −1.58810 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11493.6 | 0.461350 | 0.230675 | − | 0.973031i | \(-0.425907\pi\) | ||||
0.230675 | + | 0.973031i | \(0.425907\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2534.23 | −0.101012 | −0.0505062 | − | 0.998724i | \(-0.516083\pi\) | ||||
−0.0505062 | + | 0.998724i | \(0.516083\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3127.09 | −0.124208 | −0.0621041 | − | 0.998070i | \(-0.519781\pi\) | ||||
−0.0621041 | + | 0.998070i | \(0.519781\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15309.9 | −0.603887 | −0.301943 | − | 0.953326i | \(-0.597635\pi\) | ||||
−0.301943 | + | 0.953326i | \(0.597635\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12341.2 | 0.485101 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40387.0 | −1.57656 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29689.8 | 1.15500 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42420.7 | −1.63335 | −0.816673 | − | 0.577100i | \(-0.804184\pi\) | ||||
−0.816673 | + | 0.577100i | \(0.804184\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10060.8 | 0.384740 | 0.192370 | − | 0.981322i | \(-0.438383\pi\) | ||||
0.192370 | + | 0.981322i | \(0.438383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17437.8 | 0.664585 | 0.332293 | − | 0.943176i | \(-0.392178\pi\) | ||||
0.332293 | + | 0.943176i | \(0.392178\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16016.7 | −0.606299 | −0.303149 | − | 0.952943i | \(-0.598038\pi\) | ||||
−0.303149 | + | 0.952943i | \(0.598038\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27850.8 | 1.04366 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20134.5 | 0.751981 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7214.22 | −0.267639 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4005.69 | 0.148112 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26937.5 | 0.989428 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10131.0 | −0.370887 | −0.185443 | − | 0.982655i | \(-0.559372\pi\) | ||||
−0.185443 | + | 0.982655i | \(0.559372\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1320.58 | −0.0480273 | −0.0240137 | − | 0.999712i | \(-0.507645\pi\) | ||||
−0.0240137 | + | 0.999712i | \(0.507645\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34292.5 | −1.24306 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7285.76 | −0.261518 | −0.130759 | − | 0.991414i | \(-0.541741\pi\) | ||||
−0.130759 | + | 0.991414i | \(0.541741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29081.3 | −1.03708 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19368.0 | −0.688448 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23708.0 | 0.837280 | 0.418640 | − | 0.908152i | \(-0.362507\pi\) | ||||
0.418640 | + | 0.908152i | \(0.362507\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3069.79 | −0.107372 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8853.60 | 0.308682 | 0.154341 | − | 0.988018i | \(-0.450675\pi\) | ||||
0.154341 | + | 0.988018i | \(0.450675\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53971.6 | −1.86974 | −0.934869 | − | 0.354994i | \(-0.884483\pi\) | ||||
−0.934869 | + | 0.354994i | \(0.884483\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8508.57 | −0.293825 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8019.80 | −0.275194 | −0.137597 | − | 0.990488i | \(-0.543938\pi\) | ||||
−0.137597 | + | 0.990488i | \(0.543938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32015.4 | −1.09511 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42628.0 | −1.44896 | −0.724479 | − | 0.689297i | \(-0.757920\pi\) | ||||
−0.724479 | + | 0.689297i | \(0.757920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38638.9 | 1.30924 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21325.0 | −0.715820 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37196.8 | 1.24084 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43161.7 | −1.43535 | −0.717676 | − | 0.696377i | \(-0.754794\pi\) | ||||
−0.717676 | + | 0.696377i | \(0.754794\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39775.4 | −1.31458 | −0.657288 | − | 0.753640i | \(-0.728296\pi\) | ||||
−0.657288 | + | 0.753640i | \(0.728296\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26658.1 | 0.872945 | 0.436472 | − | 0.899718i | \(-0.356228\pi\) | ||||
0.436472 | + | 0.899718i | \(0.356228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42102.6 | −1.37447 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2942.43 | −0.0954719 | −0.0477359 | − | 0.998860i | \(-0.515201\pi\) | ||||
−0.0477359 | + | 0.998860i | \(0.515201\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25399.2 | 0.821610 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13750.6 | 0.442108 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44969.8 | 1.44149 | 0.720743 | − | 0.693203i | \(-0.243801\pi\) | ||||
0.720743 | + | 0.693203i | \(0.243801\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3623.23 | 0.115441 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27116.4 | −0.861370 | −0.430685 | − | 0.902502i | \(-0.641728\pi\) | ||||
−0.430685 | + | 0.902502i | \(0.641728\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.4.a.bc.1.3 | 4 | ||
3.2 | odd | 2 | 588.4.a.j.1.2 | ✓ | 4 | ||
7.2 | even | 3 | 1764.4.k.bb.361.2 | 8 | |||
7.3 | odd | 6 | 1764.4.k.bd.1549.3 | 8 | |||
7.4 | even | 3 | 1764.4.k.bb.1549.2 | 8 | |||
7.5 | odd | 6 | 1764.4.k.bd.361.3 | 8 | |||
7.6 | odd | 2 | 1764.4.a.ba.1.2 | 4 | |||
12.11 | even | 2 | 2352.4.a.cq.1.2 | 4 | |||
21.2 | odd | 6 | 588.4.i.l.361.3 | 8 | |||
21.5 | even | 6 | 588.4.i.k.361.2 | 8 | |||
21.11 | odd | 6 | 588.4.i.l.373.3 | 8 | |||
21.17 | even | 6 | 588.4.i.k.373.2 | 8 | |||
21.20 | even | 2 | 588.4.a.k.1.3 | yes | 4 | ||
84.83 | odd | 2 | 2352.4.a.cl.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.j.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
588.4.a.k.1.3 | yes | 4 | 21.20 | even | 2 | ||
588.4.i.k.361.2 | 8 | 21.5 | even | 6 | |||
588.4.i.k.373.2 | 8 | 21.17 | even | 6 | |||
588.4.i.l.361.3 | 8 | 21.2 | odd | 6 | |||
588.4.i.l.373.3 | 8 | 21.11 | odd | 6 | |||
1764.4.a.ba.1.2 | 4 | 7.6 | odd | 2 | |||
1764.4.a.bc.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1764.4.k.bb.361.2 | 8 | 7.2 | even | 3 | |||
1764.4.k.bb.1549.2 | 8 | 7.4 | even | 3 | |||
1764.4.k.bd.361.3 | 8 | 7.5 | odd | 6 | |||
1764.4.k.bd.1549.3 | 8 | 7.3 | odd | 6 | |||
2352.4.a.cl.1.3 | 4 | 84.83 | odd | 2 | |||
2352.4.a.cq.1.2 | 4 | 12.11 | even | 2 |