Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3720,2,Mod(1,3720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3720.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3720 = 2^{3} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3720.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: | \(29.7043495519\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 3x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3720.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.48119 | −0.937803 | −0.468902 | − | 0.883250i | \(-0.655350\pi\) | ||||
−0.468902 | + | 0.883250i | \(0.655350\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.387873 | −0.116948 | −0.0584741 | − | 0.998289i | \(-0.518623\pi\) | ||||
−0.0584741 | + | 0.998289i | \(0.518623\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.48119 | 0.688159 | 0.344080 | − | 0.938940i | \(-0.388191\pi\) | ||||
0.344080 | + | 0.938940i | \(0.388191\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.418190 | −0.101426 | −0.0507130 | − | 0.998713i | \(-0.516149\pi\) | ||||
−0.0507130 | + | 0.998713i | \(0.516149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.48119 | −0.541441 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.11871 | 1.06733 | 0.533663 | − | 0.845697i | \(-0.320815\pi\) | ||||
0.533663 | + | 0.845697i | \(0.320815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24965 | −0.789140 | −0.394570 | − | 0.918866i | \(-0.629106\pi\) | ||||
−0.394570 | + | 0.918866i | \(0.629106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.387873 | −0.0675200 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.48119 | 0.419398 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.83146 | 0.629887 | 0.314944 | − | 0.949110i | \(-0.398014\pi\) | ||||
0.314944 | + | 0.949110i | \(0.398014\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.48119 | 0.397309 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.31265 | 0.673523 | 0.336761 | − | 0.941590i | \(-0.390668\pi\) | ||||
0.336761 | + | 0.941590i | \(0.390668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.8568 | −1.58363 | −0.791817 | − | 0.610758i | \(-0.790865\pi\) | ||||
−0.791817 | + | 0.610758i | \(0.790865\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.843675 | −0.120525 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.418190 | −0.0585584 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.85685 | −1.21658 | −0.608291 | − | 0.793714i | \(-0.708145\pi\) | ||||
−0.608291 | + | 0.793714i | \(0.708145\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.387873 | 0.0523008 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.86177 | −0.502760 | −0.251380 | − | 0.967888i | \(-0.580884\pi\) | ||||
−0.251380 | + | 0.967888i | \(0.580884\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2374 | 1.56684 | 0.783421 | − | 0.621491i | \(-0.213473\pi\) | ||||
0.783421 | + | 0.621491i | \(0.213473\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.48119 | −0.312601 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.48119 | −0.307754 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.2193 | −1.73717 | −0.868584 | − | 0.495542i | \(-0.834969\pi\) | ||||
−0.868584 | + | 0.495542i | \(0.834969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.11871 | 0.616221 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.59991 | 0.901943 | 0.450972 | − | 0.892538i | \(-0.351078\pi\) | ||||
0.450972 | + | 0.892538i | \(0.351078\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.60720 | −0.539232 | −0.269616 | − | 0.962968i | \(-0.586897\pi\) | ||||
−0.269616 | + | 0.962968i | \(0.586897\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.962389 | 0.109674 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.38058 | −0.605362 | −0.302681 | − | 0.953092i | \(-0.597882\pi\) | ||||
−0.302681 | + | 0.953092i | \(0.597882\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.89446 | −0.647001 | −0.323501 | − | 0.946228i | \(-0.604860\pi\) | ||||
−0.323501 | + | 0.946228i | \(0.604860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.418190 | 0.0453591 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.24965 | −0.455610 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.93700 | −0.629320 | −0.314660 | − | 0.949204i | \(-0.601891\pi\) | ||||
−0.314660 | + | 0.949204i | \(0.601891\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.15633 | −0.645358 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.3127 | −1.25016 | −0.625080 | − | 0.780561i | \(-0.714934\pi\) | ||||
−0.625080 | + | 0.780561i | \(0.714934\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.387873 | −0.0389827 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.05571 | 0.695220 | 0.347610 | − | 0.937639i | \(-0.386993\pi\) | ||||
0.347610 | + | 0.937639i | \(0.386993\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.48119 | 0.242140 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.0435 | 1.06761 | 0.533807 | − | 0.845606i | \(-0.320761\pi\) | ||||
0.533807 | + | 0.845606i | \(0.320761\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.5950 | −1.97264 | −0.986321 | − | 0.164837i | \(-0.947290\pi\) | ||||
−0.986321 | + | 0.164837i | \(0.947290\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.83146 | 0.363666 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0508 | 1.13364 | 0.566821 | − | 0.823841i | \(-0.308173\pi\) | ||||
0.566821 | + | 0.823841i | \(0.308173\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.11871 | −0.477323 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.48119 | 0.229386 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.03761 | 0.0951177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8496 | −0.986323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.31265 | 0.388859 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.66291 | 0.325031 | 0.162515 | − | 0.986706i | \(-0.448039\pi\) | ||||
0.162515 | + | 0.986706i | \(0.448039\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | −0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.24965 | −0.546034 | −0.273017 | − | 0.962009i | \(-0.588022\pi\) | ||||
−0.273017 | + | 0.962009i | \(0.588022\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.92478 | 0.860587 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.73084 | −0.745926 | −0.372963 | − | 0.927846i | \(-0.621658\pi\) | ||||
−0.372963 | + | 0.927846i | \(0.621658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0376 | −0.936198 | −0.468099 | − | 0.883676i | \(-0.655061\pi\) | ||||
−0.468099 | + | 0.883676i | \(0.655061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.8568 | −0.914312 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.962389 | −0.0804790 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.24965 | 0.352914 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.843675 | −0.0695851 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.53690 | −0.617447 | −0.308724 | − | 0.951152i | \(-0.599902\pi\) | ||||
−0.308724 | + | 0.951152i | \(0.599902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9683 | −1.54362 | −0.771808 | − | 0.635856i | \(-0.780647\pi\) | ||||
−0.771808 | + | 0.635856i | \(0.780647\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.418190 | −0.0338087 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.77575 | 0.381146 | 0.190573 | − | 0.981673i | \(-0.438965\pi\) | ||||
0.190573 | + | 0.981673i | \(0.438965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.85685 | −0.702394 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.7005 | −1.00094 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.56959 | 0.122940 | 0.0614699 | − | 0.998109i | \(-0.480421\pi\) | ||||
0.0614699 | + | 0.998109i | \(0.480421\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.387873 | 0.0301959 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.87399 | −0.299779 | −0.149889 | − | 0.988703i | \(-0.547892\pi\) | ||||
−0.149889 | + | 0.988703i | \(0.547892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.84367 | −0.526437 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.05079 | −0.612090 | −0.306045 | − | 0.952017i | \(-0.599006\pi\) | ||||
−0.306045 | + | 0.952017i | \(0.599006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.48119 | −0.187561 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.86177 | −0.290269 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.3879 | −0.776426 | −0.388213 | − | 0.921570i | \(-0.626908\pi\) | ||||
−0.388213 | + | 0.921570i | \(0.626908\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.31265 | 0.171898 | 0.0859490 | − | 0.996300i | \(-0.472608\pi\) | ||||
0.0859490 | + | 0.996300i | \(0.472608\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.2374 | 0.904617 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.83146 | −0.281694 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.162205 | 0.0118616 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.48119 | −0.180480 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.18901 | 0.447821 | 0.223911 | − | 0.974610i | \(-0.428118\pi\) | ||||
0.223911 | + | 0.974610i | \(0.428118\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.55149 | 0.111679 | 0.0558394 | − | 0.998440i | \(-0.482217\pi\) | ||||
0.0558394 | + | 0.998440i | \(0.482217\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.48119 | −0.177682 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1793 | 1.08148 | 0.540742 | − | 0.841189i | \(-0.318144\pi\) | ||||
0.540742 | + | 0.841189i | \(0.318144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.730841 | 0.0518079 | 0.0259040 | − | 0.999664i | \(-0.491754\pi\) | ||||
0.0259040 | + | 0.999664i | \(0.491754\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.2193 | −1.00295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.5442 | 0.740058 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.31265 | −0.301209 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.11871 | 0.355775 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.55149 | 0.107319 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.27504 | 0.363149 | 0.181574 | − | 0.983377i | \(-0.441881\pi\) | ||||
0.181574 | + | 0.983377i | \(0.441881\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.59991 | 0.520737 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.00000 | 0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.48119 | 0.168434 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.60720 | −0.311326 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.03761 | −0.0697973 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.5125 | −1.97630 | −0.988150 | − | 0.153488i | \(-0.950949\pi\) | ||||
−0.988150 | + | 0.153488i | \(0.950949\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.67021 | −0.442717 | −0.221359 | − | 0.975192i | \(-0.571049\pi\) | ||||
−0.221359 | + | 0.975192i | \(0.571049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.27504 | 0.480748 | 0.240374 | − | 0.970680i | \(-0.422730\pi\) | ||||
0.240374 | + | 0.970680i | \(0.422730\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.962389 | 0.0633205 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.0943 | 1.51296 | 0.756478 | − | 0.654019i | \(-0.226918\pi\) | ||||
0.756478 | + | 0.654019i | \(0.226918\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8568 | 0.708223 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.38058 | −0.349506 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.8872 | 0.833601 | 0.416801 | − | 0.908998i | \(-0.363151\pi\) | ||||
0.416801 | + | 0.908998i | \(0.363151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.3634 | 1.31172 | 0.655862 | − | 0.754881i | \(-0.272305\pi\) | ||||
0.655862 | + | 0.754881i | \(0.272305\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.843675 | 0.0539004 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.92478 | −0.631498 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.89446 | −0.373546 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.2374 | −1.15114 | −0.575568 | − | 0.817754i | \(-0.695219\pi\) | ||||
−0.575568 | + | 0.817754i | \(0.695219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.98541 | −0.124822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.418190 | 0.0261881 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.16950 | −0.322464 | −0.161232 | − | 0.986916i | \(-0.551547\pi\) | ||||
−0.161232 | + | 0.986916i | \(0.551547\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.50659 | −0.590711 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.24965 | −0.263047 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.58769 | −0.591202 | −0.295601 | − | 0.955311i | \(-0.595520\pi\) | ||||
−0.295601 | + | 0.955311i | \(0.595520\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.85685 | 0.544072 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.93700 | −0.363338 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.4495 | 1.67362 | 0.836812 | − | 0.547491i | \(-0.184417\pi\) | ||||
0.836812 | + | 0.547491i | \(0.184417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.3634 | −0.629534 | −0.314767 | − | 0.949169i | \(-0.601926\pi\) | ||||
−0.314767 | + | 0.949169i | \(0.601926\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.15633 | −0.372598 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.387873 | −0.0233896 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8691 | 0.893396 | 0.446698 | − | 0.894685i | \(-0.352600\pi\) | ||||
0.446698 | + | 0.894685i | \(0.352600\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.71037 | 0.161687 | 0.0808436 | − | 0.996727i | \(-0.474239\pi\) | ||||
0.0808436 | + | 0.996727i | \(0.474239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3077 | 1.02884 | 0.514419 | − | 0.857539i | \(-0.328008\pi\) | ||||
0.514419 | + | 0.857539i | \(0.328008\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7005 | −0.631632 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8251 | −0.989713 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.3127 | −0.721780 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.1563 | 1.06070 | 0.530352 | − | 0.847778i | \(-0.322060\pi\) | ||||
0.530352 | + | 0.847778i | \(0.322060\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.86177 | 0.224841 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.387873 | −0.0225067 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.7005 | 0.734490 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.8872 | 0.858082 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.2374 | −0.700713 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.9199 | −0.851521 | −0.425760 | − | 0.904836i | \(-0.639993\pi\) | ||||
−0.425760 | + | 0.904836i | \(0.639993\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.05571 | 0.401385 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.86177 | 0.332391 | 0.166195 | − | 0.986093i | \(-0.446852\pi\) | ||||
0.166195 | + | 0.986093i | \(0.446852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.5828 | −1.27645 | −0.638227 | − | 0.769849i | \(-0.720332\pi\) | ||||
−0.638227 | + | 0.769849i | \(0.720332\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.48119 | 0.139799 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.7948 | 1.67344 | 0.836721 | − | 0.547629i | \(-0.184469\pi\) | ||||
0.836721 | + | 0.547629i | \(0.184469\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.64832 | 0.0922884 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.0435 | 0.616388 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.67276 | 0.0930749 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.48119 | 0.137632 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.5950 | −1.13891 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.9380 | 1.48514 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.91890 | −0.435262 | −0.217631 | − | 0.976031i | \(-0.569833\pi\) | ||||
−0.217631 | + | 0.976031i | \(0.569833\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.83146 | 0.209962 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.2193 | 0.776885 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7562 | 0.749350 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.0508 | 0.654509 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.387873 | 0.0210045 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4617 | 1.05083 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.11871 | −0.275582 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35.1998 | −1.88963 | −0.944813 | − | 0.327611i | \(-0.893756\pi\) | ||||
−0.944813 | + | 0.327611i | \(0.893756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.2071 | −0.974604 | −0.487302 | − | 0.873233i | \(-0.662019\pi\) | ||||
−0.487302 | + | 0.873233i | \(0.662019\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.48119 | 0.132436 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.478825 | 0.0254853 | 0.0127426 | − | 0.999919i | \(-0.495944\pi\) | ||||
0.0127426 | + | 0.999919i | \(0.495944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.59991 | −0.403361 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.03761 | 0.0549162 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.9502 | 1.10571 | 0.552854 | − | 0.833278i | \(-0.313539\pi\) | ||||
0.552854 | + | 0.833278i | \(0.313539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.8496 | −0.569454 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.60720 | 0.241152 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.8773 | 1.08979 | 0.544894 | − | 0.838505i | \(-0.316570\pi\) | ||||
0.544894 | + | 0.838505i | \(0.316570\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.31265 | 0.224508 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.9756 | 1.14091 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.20123 | 0.424644 | 0.212322 | − | 0.977200i | \(-0.431897\pi\) | ||||
0.212322 | + | 0.977200i | \(0.431897\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.5442 | −0.543054 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.9234 | −1.79389 | −0.896946 | − | 0.442139i | \(-0.854220\pi\) | ||||
−0.896946 | + | 0.442139i | \(0.854220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.66291 | 0.187657 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.7586 | 1.41840 | 0.709199 | − | 0.705008i | \(-0.249057\pi\) | ||||
0.709199 | + | 0.705008i | \(0.249057\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.962389 | −0.0490479 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.00000 | −0.304997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.1989 | 0.821315 | 0.410657 | − | 0.911790i | \(-0.365299\pi\) | ||||
0.410657 | + | 0.911790i | \(0.365299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.14060 | −0.108255 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.24965 | −0.315253 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.38058 | 0.270726 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.2374 | 1.41720 | 0.708598 | − | 0.705612i | \(-0.249328\pi\) | ||||
0.708598 | + | 0.705612i | \(0.249328\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.92478 | 0.496860 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.83734 | −0.391378 | −0.195689 | − | 0.980666i | \(-0.562694\pi\) | ||||
−0.195689 | + | 0.980666i | \(0.562694\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.48119 | −0.123597 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.48612 | −0.0736642 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0132 | 0.841247 | 0.420624 | − | 0.907235i | \(-0.361811\pi\) | ||||
0.420624 | + | 0.907235i | \(0.361811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.73084 | −0.430661 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.58181 | 0.471490 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.89446 | 0.289348 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.0376 | −0.540514 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.1382 | −0.886110 | −0.443055 | − | 0.896494i | \(-0.646105\pi\) | ||||
−0.443055 | + | 0.896494i | \(0.646105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.1695 | −1.32416 | −0.662080 | − | 0.749433i | \(-0.730326\pi\) | ||||
−0.662080 | + | 0.749433i | \(0.730326\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.8568 | −0.527878 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.418190 | −0.0202852 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.3634 | −1.46939 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.962389 | −0.0464646 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.6375 | 0.705065 | 0.352532 | − | 0.935800i | \(-0.385321\pi\) | ||||
0.352532 | + | 0.935800i | \(0.385321\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.2424 | 1.11696 | 0.558478 | − | 0.829519i | \(-0.311385\pi\) | ||||
0.558478 | + | 0.829519i | \(0.311385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.24965 | 0.203755 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.4749 | −0.979445 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.5501 | −1.26717 | −0.633583 | − | 0.773675i | \(-0.718417\pi\) | ||||
−0.633583 | + | 0.773675i | \(0.718417\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.843675 | −0.0401750 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.6702 | 0.697003 | 0.348501 | − | 0.937308i | \(-0.386691\pi\) | ||||
0.348501 | + | 0.937308i | \(0.386691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.93700 | 0.281441 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.53690 | −0.356483 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.6883 | −0.504412 | −0.252206 | − | 0.967674i | \(-0.581156\pi\) | ||||
−0.252206 | + | 0.967674i | \(0.581156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.67276 | −0.0787672 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.9683 | −0.891207 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.15633 | 0.288613 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.2931 | −0.808939 | −0.404469 | − | 0.914552i | \(-0.632544\pi\) | ||||
−0.404469 | + | 0.914552i | \(0.632544\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.418190 | −0.0195195 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.52610 | −0.397100 | −0.198550 | − | 0.980091i | \(-0.563623\pi\) | ||||
−0.198550 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.53690 | −0.443218 | −0.221609 | − | 0.975136i | \(-0.571131\pi\) | ||||
−0.221609 | + | 0.975136i | \(0.571131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.15633 | 0.192332 | 0.0961659 | − | 0.995365i | \(-0.469342\pi\) | ||||
0.0961659 | + | 0.995365i | \(0.469342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.2809 | 1.62912 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.77575 | 0.220055 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.32724 | 0.107007 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.85685 | −0.405527 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.5867 | 0.575103 | 0.287551 | − | 0.957765i | \(-0.407159\pi\) | ||||
0.287551 | + | 0.957765i | \(0.407159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.50659 | 0.433463 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.7005 | −0.577894 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.3127 | 0.559089 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.3503 | −1.78313 | −0.891565 | − | 0.452892i | \(-0.850392\pi\) | ||||
−0.891565 | + | 0.452892i | \(0.850392\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.56959 | 0.0709794 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.0494 | −1.58176 | −0.790878 | − | 0.611974i | \(-0.790376\pi\) | ||||
−0.790878 | + | 0.611974i | \(0.790376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.77716 | 0.0800393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.387873 | 0.0174336 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.8568 | −0.845845 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.2243 | −1.03966 | −0.519830 | − | 0.854270i | \(-0.674005\pi\) | ||||
−0.519830 | + | 0.854270i | \(0.674005\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.87399 | −0.173077 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.367405 | 0.0163818 | 0.00819089 | − | 0.999966i | \(-0.497393\pi\) | ||||
0.00819089 | + | 0.999966i | \(0.497393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.84367 | −0.303938 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.0484156 | −0.00214598 | −0.00107299 | − | 0.999999i | \(-0.500342\pi\) | ||||
−0.00107299 | + | 0.999999i | \(0.500342\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4314 | 0.505694 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.05571 | −0.310912 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.21108 | 0.185203 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.05079 | −0.353390 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.93795 | −0.216336 | −0.108168 | − | 0.994133i | \(-0.534498\pi\) | ||||
−0.108168 | + | 0.994133i | \(0.534498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.5745 | 0.812207 | 0.406103 | − | 0.913827i | \(-0.366887\pi\) | ||||
0.406103 | + | 0.913827i | \(0.366887\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.48119 | −0.108288 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.418190 | 0.0182167 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.20123 | 0.139184 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.86177 | −0.167587 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.7005 | 0.463491 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.0435 | −0.477452 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.3879 | −0.448270 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.327239 | 0.0140952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.2922 | −0.614469 | −0.307234 | − | 0.951634i | \(-0.599404\pi\) | ||||
−0.307234 | + | 0.951634i | \(0.599404\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.31265 | 0.0992453 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.5950 | 0.882192 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3439 | 0.485031 | 0.242516 | − | 0.970148i | \(-0.422027\pi\) | ||||
0.242516 | + | 0.970148i | \(0.422027\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.2374 | 0.522281 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9986 | 0.724164 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3503 | 0.567711 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.83146 | −0.162636 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.5672 | 1.08332 | 0.541659 | − | 0.840598i | \(-0.317796\pi\) | ||||
0.541659 | + | 0.840598i | \(0.317796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.8872 | −0.629660 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.162205 | 0.00684829 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.6820 | 1.63025 | 0.815125 | − | 0.579285i | \(-0.196668\pi\) | ||||
0.815125 | + | 0.579285i | \(0.196668\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0508 | −0.506980 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.48119 | −0.104200 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.0122 | 0.922800 | 0.461400 | − | 0.887192i | \(-0.347347\pi\) | ||||
0.461400 | + | 0.887192i | \(0.347347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.18664 | 0.175206 | 0.0876028 | − | 0.996155i | \(-0.472079\pi\) | ||||
0.0876028 | + | 0.996155i | \(0.472079\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.18901 | 0.258550 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.11871 | 0.213465 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.8251 | 1.65794 | 0.828971 | − | 0.559292i | \(-0.188927\pi\) | ||||
0.828971 | + | 0.559292i | \(0.188927\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.55149 | 0.0644778 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.6253 | 0.606760 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.43533 | 0.142277 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.48119 | −0.102585 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.85940 | −0.406941 | −0.203471 | − | 0.979081i | \(-0.565222\pi\) | ||||
−0.203471 | + | 0.979081i | \(0.565222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.1793 | 0.624395 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.1114 | 0.497356 | 0.248678 | − | 0.968586i | \(-0.420004\pi\) | ||||
0.248678 | + | 0.968586i | \(0.420004\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.03761 | −0.0425379 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.730841 | 0.0299113 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.8764 | 0.812126 | 0.406063 | − | 0.913845i | \(-0.366901\pi\) | ||||
0.406063 | + | 0.913845i | \(0.366901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.2130 | −1.15083 | −0.575416 | − | 0.817861i | \(-0.695160\pi\) | ||||
−0.575416 | + | 0.817861i | \(0.695160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.2193 | −0.579056 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.8496 | 0.441097 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.7464 | −0.963836 | −0.481918 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481918 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.5442 | 0.427272 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.9380 | −1.08979 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.9560 | −0.765628 | −0.382814 | − | 0.923826i | \(-0.625045\pi\) | ||||
−0.382814 | + | 0.923826i | \(0.625045\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.31265 | −0.173903 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.7255 | 1.92135 | 0.960677 | − | 0.277667i | \(-0.0895613\pi\) | ||||
0.960677 | + | 0.277667i | \(0.0895613\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.9307 | −0.640307 | −0.320154 | − | 0.947366i | \(-0.603735\pi\) | ||||
−0.320154 | + | 0.947366i | \(0.603735\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.11871 | 0.205407 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.7308 | 0.590179 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.55149 | 0.0619606 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.60228 | −0.0638870 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.92478 | 0.395099 | 0.197550 | − | 0.980293i | \(-0.436702\pi\) | ||||
0.197550 | + | 0.980293i | \(0.436702\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.27504 | 0.209664 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.66291 | −0.145358 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.09332 | −0.0829404 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.59991 | 0.300648 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.6639 | 0.816174 | 0.408087 | − | 0.912943i | \(-0.366196\pi\) | ||||
0.408087 | + | 0.912943i | \(0.366196\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5745 | 0.732507 | 0.366254 | − | 0.930515i | \(-0.380640\pi\) | ||||
0.366254 | + | 0.930515i | \(0.380640\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.7889 | 0.463470 | 0.231735 | − | 0.972779i | \(-0.425560\pi\) | ||||
0.231735 | + | 0.972779i | \(0.425560\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.49788 | 0.0587969 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.48119 | 0.0972457 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.2579 | −0.401422 | −0.200711 | − | 0.979650i | \(-0.564325\pi\) | ||||
−0.200711 | + | 0.979650i | \(0.564325\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.24965 | 0.244194 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.60720 | −0.179744 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.5477 | 0.878334 | 0.439167 | − | 0.898405i | \(-0.355274\pi\) | ||||
0.439167 | + | 0.898405i | \(0.355274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.3780 | −1.02599 | −0.512993 | − | 0.858393i | \(-0.671463\pi\) | ||||
−0.512993 | + | 0.858393i | \(0.671463\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.03761 | −0.0402975 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.92478 | −0.384866 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.7527 | −0.842269 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.5125 | −1.14102 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.74657 | −0.183239 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.6156 | 0.833222 | 0.416611 | − | 0.909085i | \(-0.363218\pi\) | ||||
0.416611 | + | 0.909085i | \(0.363218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.31994 | 0.358195 | 0.179097 | − | 0.983831i | \(-0.442682\pi\) | ||||
0.179097 | + | 0.983831i | \(0.442682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.5501 | 1.17240 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.67021 | −0.255603 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.5329 | −1.58921 | −0.794607 | − | 0.607124i | \(-0.792323\pi\) | ||||
−0.794607 | + | 0.607124i | \(0.792323\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.73084 | 0.333588 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.27504 | 0.277560 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.9756 | −0.837202 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.80018 | −0.334775 | −0.167387 | − | 0.985891i | \(-0.553533\pi\) | ||||
−0.167387 | + | 0.985891i | \(0.553533\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.962389 | 0.0365581 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.0376 | 0.418680 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.80351 | −0.0683128 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.0943 | 0.873506 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.3488 | −0.919643 | −0.459822 | − | 0.888011i | \(-0.652087\pi\) | ||||
−0.459822 | + | 0.888011i | \(0.652087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.3258 | −0.578024 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.8568 | 0.408893 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.40105 | 0.127729 | 0.0638645 | − | 0.997959i | \(-0.479657\pi\) | ||||
0.0638645 | + | 0.997959i | \(0.479657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.38058 | −0.201787 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.11871 | −0.191697 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.962389 | 0.0359913 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.8872 | 0.481280 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.6385 | −0.508629 | −0.254315 | − | 0.967122i | \(-0.581850\pi\) | ||||
−0.254315 | + | 0.967122i | \(0.581850\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5066 | −0.651979 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.3634 | 0.757324 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.24965 | −0.157828 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.41582 | −0.312126 | −0.156063 | − | 0.987747i | \(-0.549880\pi\) | ||||
−0.156063 | + | 0.987747i | \(0.549880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.50914 | 0.0928040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.8496 | 1.25026 | 0.625131 | − | 0.780520i | \(-0.285046\pi\) | ||||
0.625131 | + | 0.780520i | \(0.285046\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.843675 | 0.0311194 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.51530 | 0.203159 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.86811 | −0.215862 | −0.107931 | − | 0.994158i | \(-0.534423\pi\) | ||||
−0.107931 | + | 0.994158i | \(0.534423\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.92478 | −0.364596 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.9887 | −0.843375 | −0.421687 | − | 0.906741i | \(-0.638562\pi\) | ||||
−0.421687 | + | 0.906741i | \(0.638562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.53690 | 0.276131 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.89446 | −0.215667 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.4010 | −1.00121 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.2144 | 1.35797 | 0.678986 | − | 0.734151i | \(-0.262419\pi\) | ||||
0.678986 | + | 0.734151i | \(0.262419\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.2374 | −0.664609 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.9683 | 0.690326 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.53198 | −0.310100 | −0.155050 | − | 0.987907i | \(-0.549554\pi\) | ||||
−0.155050 | + | 0.987907i | \(0.549554\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.98541 | −0.0720659 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.2266 | −0.696965 | −0.348482 | − | 0.937315i | \(-0.613303\pi\) | ||||
−0.348482 | + | 0.937315i | \(0.613303\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.1002 | 1.84995 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.418190 | 0.0151197 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.58181 | −0.345979 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.2071 | 1.52203 | 0.761014 | − | 0.648736i | \(-0.224702\pi\) | ||||
0.761014 | + | 0.648736i | \(0.224702\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.16950 | −0.186175 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.609572 | 0.0219248 | 0.0109624 | − | 0.999940i | \(-0.496510\pi\) | ||||
0.0109624 | + | 0.999940i | \(0.496510\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.50659 | −0.341047 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.2506 | −0.618067 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.94780 | −0.105481 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.24965 | −0.151870 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.77575 | −0.170454 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.3225 | 0.439250 | 0.219625 | − | 0.975584i | \(-0.429517\pi\) | ||||
0.219625 | + | 0.975584i | \(0.429517\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.58769 | −0.341331 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.9003 | −1.06313 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.3634 | 1.07824 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.85685 | 0.314120 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.0289 | −0.815726 | −0.407863 | − | 0.913043i | \(-0.633726\pi\) | ||||
−0.407863 | + | 0.913043i | \(0.633726\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.54023 | 0.160622 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.93700 | −0.209773 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.78701 | 0.0630622 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.7005 | 0.447635 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.4495 | 0.966267 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.4250 | 0.612631 | 0.306316 | − | 0.951930i | \(-0.400904\pi\) | ||||
0.306316 | + | 0.951930i | \(0.400904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.8134 | −0.555282 | −0.277641 | − | 0.960685i | \(-0.589553\pi\) | ||||
−0.277641 | + | 0.960685i | \(0.589553\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.3634 | −0.363462 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.56959 | −0.0549804 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.0000 | 0.839654 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.15633 | −0.215119 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.0729 | −0.560946 | −0.280473 | − | 0.959862i | \(-0.590491\pi\) | ||||
−0.280473 | + | 0.959862i | \(0.590491\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.11616 | 0.282912 | 0.141456 | − | 0.989945i | \(-0.454822\pi\) | ||||
0.141456 | + | 0.989945i | \(0.454822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.387873 | −0.0135040 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.5658 | −1.27152 | −0.635759 | − | 0.771888i | \(-0.719313\pi\) | ||||
−0.635759 | + | 0.771888i | \(0.719313\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.7974 | −1.41695 | −0.708475 | − | 0.705736i | \(-0.750617\pi\) | ||||
−0.708475 | + | 0.705736i | \(0.750617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.8691 | 0.515802 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.352817 | 0.0122244 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.87399 | 0.134065 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.5477 | 1.26177 | 0.630884 | − | 0.775878i | \(-0.282693\pi\) | ||||
0.630884 | + | 0.775878i | \(0.282693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.9405 | −0.377259 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.71037 | 0.0933502 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.84367 | 0.235430 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.9199 | 0.924977 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.3077 | 0.594000 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.6121 | 0.672295 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.3343 | 1.72341 | 0.861706 | − | 0.507408i | \(-0.169396\pi\) | ||||
0.861706 | + | 0.507408i | \(0.169396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0982 | 0.720702 | 0.360351 | − | 0.932817i | \(-0.382657\pi\) | ||||
0.360351 | + | 0.932817i | \(0.382657\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0738 | 0.377833 | 0.188917 | − | 0.981993i | \(-0.439502\pi\) | ||||
0.188917 | + | 0.981993i | \(0.439502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.7005 | −0.364673 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.1002 | 1.12674 | 0.563371 | − | 0.826204i | \(-0.309504\pi\) | ||||
0.563371 | + | 0.826204i | \(0.309504\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.05079 | 0.273735 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8251 | −0.571411 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.08698 | 0.0707960 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.2809 | −1.19545 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.3127 | −0.416720 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.48119 | 0.0838797 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.6775 | 0.596927 | 0.298463 | − | 0.954421i | \(-0.403526\pi\) | ||||
0.298463 | + | 0.954421i | \(0.403526\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.1563 | 0.612398 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.4772 | 1.43109 | 0.715547 | − | 0.698565i | \(-0.246178\pi\) | ||||
0.715547 | + | 0.698565i | \(0.246178\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.7499 | −1.60691 | −0.803456 | − | 0.595364i | \(-0.797008\pi\) | ||||
−0.803456 | + | 0.595364i | \(0.797008\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.86177 | 0.129812 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.9452 | −0.669696 | −0.334848 | − | 0.942272i | \(-0.608685\pi\) | ||||
−0.334848 | + | 0.942272i | \(0.608685\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.08840 | −0.304815 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.387873 | −0.0129942 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43.4274 | 1.45324 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.3879 | 0.347228 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.7005 | 0.424058 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.24965 | 0.141734 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.70385 | 0.123393 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.8872 | 0.495414 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.31265 | −0.0768751 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.79526 | 0.325246 | 0.162623 | − | 0.986688i | \(-0.448005\pi\) | ||||
0.162623 | + | 0.986688i | \(0.448005\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.38646 | −0.178461 | −0.0892307 | − | 0.996011i | \(-0.528441\pi\) | ||||
−0.0892307 | + | 0.996011i | \(0.528441\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.28630 | 0.0756656 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.2374 | −0.404557 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.5066 | 0.512073 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.3865 | 1.03534 | 0.517672 | − | 0.855579i | \(-0.326799\pi\) | ||||
0.517672 | + | 0.855579i | \(0.326799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.9199 | −0.491626 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.8568 | 0.620681 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.83146 | 0.125977 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.05571 | 0.231740 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.1236 | 0.397764 | 0.198882 | − | 0.980023i | \(-0.436269\pi\) | ||||
0.198882 | + | 0.980023i | \(0.436269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.37470 | 0.110601 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.86177 | 0.191906 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.162205 | −0.00530466 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.4880 | −1.42069 | −0.710346 | − | 0.703853i | \(-0.751462\pi\) | ||||
−0.710346 | + | 0.703853i | \(0.751462\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.5828 | −0.736961 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.28726 | 0.302756 | 0.151378 | − | 0.988476i | \(-0.451629\pi\) | ||||
0.151378 | + | 0.988476i | \(0.451629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.0752 | 0.718868 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.48119 | 0.0807133 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.2071 | −0.591652 | −0.295826 | − | 0.955242i | \(-0.595595\pi\) | ||||
−0.295826 | + | 0.955242i | \(0.595595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.4314 | −0.371078 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.7948 | 0.966163 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.5936 | −1.54171 | −0.770853 | − | 0.637013i | \(-0.780170\pi\) | ||||
−0.770853 | + | 0.637013i | \(0.780170\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.18901 | −0.200272 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.64832 | 0.0532827 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.6629 | 0.699532 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.0435 | 0.355872 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.55149 | −0.0499443 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0917 | 1.03200 | 0.516000 | − | 0.856589i | \(-0.327420\pi\) | ||||
0.516000 | + | 0.856589i | \(0.327420\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.67276 | 0.0537368 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.0503 | 1.54201 | 0.771004 | − | 0.636830i | \(-0.219755\pi\) | ||||
0.771004 | + | 0.636830i | \(0.219755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.3865 | 0.877970 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.48119 | 0.0794618 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.3272 | 0.394383 | 0.197192 | − | 0.980365i | \(-0.436818\pi\) | ||||
0.197192 | + | 0.980365i | \(0.436818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.30280 | 0.0735978 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.5950 | −0.657547 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.0132 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.1793 | −0.483654 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.9380 | 0.857444 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.7123 | −0.976594 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.9887 | 0.857325 | 0.428663 | − | 0.903465i | \(-0.358985\pi\) | ||||
0.428663 | + | 0.903465i | \(0.358985\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.91890 | −0.251299 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.730841 | −0.0231692 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.32250 | −0.136895 | −0.0684475 | − | 0.997655i | \(-0.521805\pi\) | ||||
−0.0684475 | + | 0.997655i | \(0.521805\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.83146 | 0.121222 |
(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 | 3720.2.a.o.1.1 | ✓ | 3 | |
4.3 | odd | 2 | 7440.2.a.bo.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3720.2.a.o.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7440.2.a.bo.1.3 | 3 | 4.3 | odd | 2 |