Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5148,2,Mod(1,5148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5148.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: | \(41.1069869606\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.815952.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 9x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.201024\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5148.1 |
$q$-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 | ||||||||
\(5\) | 1.10258 | 0.493091 | 0.246545 | − | 0.969131i | \(-0.420705\pi\) | ||||
0.246545 | + | 0.969131i | \(0.420705\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32423 | 0.500512 | 0.250256 | − | 0.968180i | \(-0.419485\pi\) | ||||
0.250256 | + | 0.968180i | \(0.419485\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.88689 | 0.942710 | 0.471355 | − | 0.881944i | \(-0.343765\pi\) | ||||
0.471355 | + | 0.881944i | \(0.343765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.25267 | 1.89329 | 0.946647 | − | 0.322273i | \(-0.104447\pi\) | ||||
0.946647 | + | 0.322273i | \(0.104447\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.18538 | 1.70677 | 0.853385 | − | 0.521281i | \(-0.174546\pi\) | ||||
0.853385 | + | 0.521281i | \(0.174546\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.78431 | −0.756861 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.09958 | −0.761273 | −0.380637 | − | 0.924725i | \(-0.624295\pi\) | ||||
−0.380637 | + | 0.924725i | \(0.624295\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.46506 | −1.69997 | −0.849987 | − | 0.526804i | \(-0.823390\pi\) | ||||
−0.849987 | + | 0.526804i | \(0.823390\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.46008 | 0.246798 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.58442 | 1.57567 | 0.787835 | − | 0.615887i | \(-0.211202\pi\) | ||||
0.787835 | + | 0.615887i | \(0.211202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.36547 | 0.837946 | 0.418973 | − | 0.907999i | \(-0.362390\pi\) | ||||
0.418973 | + | 0.907999i | \(0.362390\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35952 | 0.359824 | 0.179912 | − | 0.983683i | \(-0.442419\pi\) | ||||
0.179912 | + | 0.983683i | \(0.442419\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2329 | −1.49262 | −0.746310 | − | 0.665599i | \(-0.768176\pi\) | ||||
−0.746310 | + | 0.665599i | \(0.768176\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.24641 | −0.749488 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.9284 | 1.50114 | 0.750569 | − | 0.660793i | \(-0.229780\pi\) | ||||
0.750569 | + | 0.660793i | \(0.229780\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.10258 | −0.148672 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.12532 | −0.146504 | −0.0732522 | − | 0.997313i | \(-0.523338\pi\) | ||||
−0.0732522 | + | 0.997313i | \(0.523338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.78130 | −0.996294 | −0.498147 | − | 0.867093i | \(-0.665986\pi\) | ||||
−0.498147 | + | 0.867093i | \(0.665986\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.10258 | −0.136759 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.02176 | −0.613506 | −0.306753 | − | 0.951789i | \(-0.599243\pi\) | ||||
−0.306753 | + | 0.951789i | \(0.599243\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3793 | 1.58783 | 0.793913 | − | 0.608032i | \(-0.208041\pi\) | ||||
0.793913 | + | 0.608032i | \(0.208041\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.73457 | 0.905263 | 0.452631 | − | 0.891698i | \(-0.350485\pi\) | ||||
0.452631 | + | 0.891698i | \(0.350485\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.32423 | −0.150910 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.04155 | 0.342201 | 0.171101 | − | 0.985254i | \(-0.445268\pi\) | ||||
0.171101 | + | 0.985254i | \(0.445268\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.5466 | −1.81622 | −0.908112 | − | 0.418727i | \(-0.862476\pi\) | ||||
−0.908112 | + | 0.418727i | \(0.862476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.28563 | 0.464842 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.5710 | 1.12052 | 0.560259 | − | 0.828317i | \(-0.310701\pi\) | ||||
0.560259 | + | 0.828317i | \(0.310701\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.32423 | −0.138817 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.09927 | 0.933566 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.27246 | −0.433803 | −0.216901 | − | 0.976194i | \(-0.569595\pi\) | ||||
−0.216901 | + | 0.976194i | \(0.569595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.09206 | 0.606183 | 0.303091 | − | 0.952962i | \(-0.401981\pi\) | ||||
0.303091 | + | 0.952962i | \(0.401981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.80312 | 0.177667 | 0.0888334 | − | 0.996046i | \(-0.471686\pi\) | ||||
0.0888334 | + | 0.996046i | \(0.471686\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.96042 | −0.382869 | −0.191434 | − | 0.981505i | \(-0.561314\pi\) | ||||
−0.191434 | + | 0.981505i | \(0.561314\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.10980 | 0.202082 | 0.101041 | − | 0.994882i | \(-0.467783\pi\) | ||||
0.101041 | + | 0.994882i | \(0.467783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.61648 | 0.152066 | 0.0760329 | − | 0.997105i | \(-0.475775\pi\) | ||||
0.0760329 | + | 0.997105i | \(0.475775\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.02508 | 0.841593 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.14714 | 0.471838 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.68544 | −0.866292 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.36704 | −0.387512 | −0.193756 | − | 0.981050i | \(-0.562067\pi\) | ||||
−0.193756 | + | 0.981050i | \(0.562067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.6517 | 1.71698 | 0.858489 | − | 0.512831i | \(-0.171403\pi\) | ||||
0.858489 | + | 0.512831i | \(0.171403\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.9284 | 0.947616 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.26741 | 0.450025 | 0.225012 | − | 0.974356i | \(-0.427758\pi\) | ||||
0.225012 | + | 0.974356i | \(0.427758\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3460 | 0.877536 | 0.438768 | − | 0.898600i | \(-0.355415\pi\) | ||||
0.438768 | + | 0.898600i | \(0.355415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.52013 | −0.375377 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.211430 | −0.0173211 | −0.00866053 | − | 0.999962i | \(-0.502757\pi\) | ||||
−0.00866053 | + | 0.999962i | \(0.502757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.4275 | 1.74375 | 0.871874 | − | 0.489730i | \(-0.162905\pi\) | ||||
0.871874 | + | 0.489730i | \(0.162905\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.4360 | −0.838242 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.5990 | −1.88340 | −0.941702 | − | 0.336449i | \(-0.890774\pi\) | ||||
−0.941702 | + | 0.336449i | \(0.890774\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.8393 | 0.854259 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.767831 | −0.0601411 | −0.0300706 | − | 0.999548i | \(-0.509573\pi\) | ||||
−0.0300706 | + | 0.999548i | \(0.509573\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6610 | 1.44403 | 0.722015 | − | 0.691877i | \(-0.243216\pi\) | ||||
0.722015 | + | 0.691877i | \(0.243216\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.4133 | 0.791708 | 0.395854 | − | 0.918314i | \(-0.370449\pi\) | ||||
0.395854 | + | 0.918314i | \(0.370449\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.01130 | −0.378818 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.64469 | 0.571391 | 0.285695 | − | 0.958321i | \(-0.407775\pi\) | ||||
0.285695 | + | 0.958321i | \(0.407775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0390 | −0.820523 | −0.410262 | − | 0.911968i | \(-0.634563\pi\) | ||||
−0.410262 | + | 0.911968i | \(0.634563\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.5676 | 0.776948 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.88689 | −0.284238 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.9812 | 1.73522 | 0.867611 | − | 0.497244i | \(-0.165655\pi\) | ||||
0.867611 | + | 0.497244i | \(0.165655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.4166 | −0.893766 | −0.446883 | − | 0.894592i | \(-0.647466\pi\) | ||||
−0.446883 | + | 0.894592i | \(0.647466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.04425 | 0.644376 | 0.322188 | − | 0.946676i | \(-0.395582\pi\) | ||||
0.322188 | + | 0.946676i | \(0.395582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.50884 | 0.532288 | 0.266144 | − | 0.963933i | \(-0.414250\pi\) | ||||
0.266144 | + | 0.963933i | \(0.414250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.42879 | −0.381026 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.91589 | 0.413184 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.25267 | −0.570849 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.16687 | 0.286859 | 0.143430 | − | 0.989661i | \(-0.454187\pi\) | ||||
0.143430 | + | 0.989661i | \(0.454187\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.60157 | 0.177426 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5339 | −0.850858 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.88689 | −0.261461 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.7929 | −0.923641 | −0.461821 | − | 0.886973i | \(-0.652804\pi\) | ||||
−0.461821 | + | 0.886973i | \(0.652804\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.92316 | 0.525878 | 0.262939 | − | 0.964812i | \(-0.415308\pi\) | ||||
0.262939 | + | 0.964812i | \(0.415308\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0277 | 0.926978 | 0.463489 | − | 0.886103i | \(-0.346597\pi\) | ||||
0.463489 | + | 0.886103i | \(0.346597\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.1946 | −1.06094 | −0.530471 | − | 0.847703i | \(-0.677985\pi\) | ||||
−0.530471 | + | 0.847703i | \(0.677985\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2826 | −0.735997 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.6832 | −0.949778 | −0.474889 | − | 0.880046i | \(-0.657512\pi\) | ||||
−0.474889 | + | 0.880046i | \(0.657512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.9384 | −1.34876 | −0.674381 | − | 0.738384i | \(-0.735589\pi\) | ||||
−0.674381 | + | 0.738384i | \(0.735589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.78462 | −0.369566 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.25267 | −0.525105 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.77882 | 0.427875 | 0.213938 | − | 0.976847i | \(-0.431371\pi\) | ||||
0.213938 | + | 0.976847i | \(0.431371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.18538 | −0.514610 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.1177 | −1.13015 | −0.565076 | − | 0.825039i | \(-0.691153\pi\) | ||||
−0.565076 | + | 0.825039i | \(0.691153\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.6920 | 0.788642 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.5533 | 1.02072 | 0.510361 | − | 0.859960i | \(-0.329512\pi\) | ||||
0.510361 | + | 0.859960i | \(0.329512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0495 | 0.740197 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.1781 | −1.10834 | −0.554170 | − | 0.832404i | \(-0.686964\pi\) | ||||
−0.554170 | + | 0.832404i | \(0.686964\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.43703 | 0.148039 | 0.0740195 | − | 0.997257i | \(-0.476417\pi\) | ||||
0.0740195 | + | 0.997257i | \(0.476417\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.78431 | 0.228202 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.9427 | −0.657486 | −0.328743 | − | 0.944419i | \(-0.606625\pi\) | ||||
−0.328743 | + | 0.944419i | \(0.606625\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.24174 | −0.0740762 | −0.0370381 | − | 0.999314i | \(-0.511792\pi\) | ||||
−0.0370381 | + | 0.999314i | \(0.511792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.19292 | −0.487019 | −0.243509 | − | 0.969899i | \(-0.578299\pi\) | ||||
−0.243509 | + | 0.969899i | \(0.578299\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.10513 | 0.419402 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.89207 | −0.111298 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.9414 | −1.39867 | −0.699336 | − | 0.714793i | \(-0.746521\pi\) | ||||
−0.699336 | + | 0.714793i | \(0.746521\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.24076 | −0.0722400 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.18538 | −0.473373 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.12455 | 0.180096 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.57955 | −0.491263 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.37210 | 0.0783098 | 0.0391549 | − | 0.999233i | \(-0.487533\pi\) | ||||
0.0391549 | + | 0.999233i | \(0.487533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.8953 | 1.63850 | 0.819251 | − | 0.573436i | \(-0.194390\pi\) | ||||
0.819251 | + | 0.573436i | \(0.194390\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.01568 | −0.396550 | −0.198275 | − | 0.980146i | \(-0.563534\pi\) | ||||
−0.198275 | + | 0.980146i | \(0.563534\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.3025 | 1.08414 | 0.542069 | − | 0.840334i | \(-0.317641\pi\) | ||||
0.542069 | + | 0.840334i | \(0.317641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.09958 | 0.229532 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.0773 | 1.78483 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.78431 | 0.209916 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.5507 | −0.747074 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0830 | −0.609179 | −0.304590 | − | 0.952484i | \(-0.598519\pi\) | ||||
−0.304590 | + | 0.952484i | \(0.598519\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.53692 | −0.302514 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.40107 | −0.185268 | −0.0926341 | − | 0.995700i | \(-0.529529\pi\) | ||||
−0.0926341 | + | 0.995700i | \(0.529529\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.46506 | 0.512561 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.2171 | −0.875640 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.8468 | 1.49489 | 0.747447 | − | 0.664321i | \(-0.231279\pi\) | ||||
0.747447 | + | 0.664321i | \(0.231279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.211918 | −0.0113437 | −0.00567185 | − | 0.999984i | \(-0.501805\pi\) | ||||
−0.00567185 | + | 0.999984i | \(0.501805\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.1765 | 1.23356 | 0.616782 | − | 0.787134i | \(-0.288436\pi\) | ||||
0.616782 | + | 0.787134i | \(0.288436\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.7518 | 0.782942 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.6605 | 0.932085 | 0.466043 | − | 0.884762i | \(-0.345679\pi\) | ||||
0.466043 | + | 0.884762i | \(0.345679\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 49.1066 | 2.58456 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.52802 | 0.446377 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.4153 | −1.32667 | −0.663333 | − | 0.748324i | \(-0.730859\pi\) | ||||
−0.663333 | + | 0.748324i | \(0.730859\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.4718 | 0.751337 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.43464 | 0.488507 | 0.244254 | − | 0.969711i | \(-0.421457\pi\) | ||||
0.244254 | + | 0.969711i | \(0.421457\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.09958 | 0.211139 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5560 | 0.747693 | 0.373847 | − | 0.927491i | \(-0.378039\pi\) | ||||
0.373847 | + | 0.927491i | \(0.378039\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.8629 | 1.01495 | 0.507473 | − | 0.861667i | \(-0.330580\pi\) | ||||
0.507473 | + | 0.861667i | \(0.330580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.46008 | −0.0744124 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.2456 | 1.12789 | 0.563947 | − | 0.825811i | \(-0.309282\pi\) | ||||
0.563947 | + | 0.825811i | \(0.309282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.8157 | 1.60899 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.35357 | 0.168736 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.1470 | 1.46285 | 0.731424 | − | 0.681923i | \(-0.238856\pi\) | ||||
0.731424 | + | 0.681923i | \(0.238856\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.65929 | −0.432424 | −0.216212 | − | 0.976346i | \(-0.569370\pi\) | ||||
−0.216212 | + | 0.976346i | \(0.569370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.46506 | 0.471488 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.58442 | −0.475082 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.93242 | −0.441680 | −0.220840 | − | 0.975310i | \(-0.570880\pi\) | ||||
−0.220840 | + | 0.975310i | \(0.570880\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.49019 | −0.0733273 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2440 | −0.895564 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.16205 | 0.203329 | 0.101665 | − | 0.994819i | \(-0.467583\pi\) | ||||
0.101665 | + | 0.994819i | \(0.467583\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.2153 | 1.52134 | 0.760669 | − | 0.649140i | \(-0.224871\pi\) | ||||
0.760669 | + | 0.649140i | \(0.224871\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.7092 | −0.713501 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.3042 | −0.498657 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5114 | 0.698987 | 0.349494 | − | 0.936939i | \(-0.386354\pi\) | ||||
0.349494 | + | 0.936939i | \(0.386354\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.58771 | −0.172414 | −0.0862072 | − | 0.996277i | \(-0.527475\pi\) | ||||
−0.0862072 | + | 0.996277i | \(0.527475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 67.5513 | 3.23142 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.3469 | −0.589285 | −0.294642 | − | 0.955608i | \(-0.595201\pi\) | ||||
−0.294642 | + | 0.955608i | \(0.595201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.2487 | 1.34214 | 0.671068 | − | 0.741396i | \(-0.265836\pi\) | ||||
0.671068 | + | 0.741396i | \(0.265836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6554 | 0.552518 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.0579 | −1.56010 | −0.780050 | − | 0.625717i | \(-0.784806\pi\) | ||||
−0.780050 | + | 0.625717i | \(0.784806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.36547 | −0.252650 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.46008 | −0.0684494 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.3999 | 1.23493 | 0.617467 | − | 0.786597i | \(-0.288159\pi\) | ||||
0.617467 | + | 0.786597i | \(0.288159\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.7092 | −1.75629 | −0.878146 | − | 0.478393i | \(-0.841219\pi\) | ||||
−0.878146 | + | 0.478393i | \(0.841219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.5759 | −0.909768 | −0.454884 | − | 0.890551i | \(-0.650319\pi\) | ||||
−0.454884 | + | 0.890551i | \(0.650319\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.58779 | 0.443670 | 0.221835 | − | 0.975084i | \(-0.428795\pi\) | ||||
0.221835 | + | 0.975084i | \(0.428795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.64997 | −0.307067 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.35952 | −0.108491 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −31.2307 | −1.43296 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.59654 | 0.347095 | 0.173547 | − | 0.984826i | \(-0.444477\pi\) | ||||
0.173547 | + | 0.984826i | \(0.444477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.58442 | −0.437012 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.71075 | −0.213904 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.6332 | −0.572467 | −0.286233 | − | 0.958160i | \(-0.592403\pi\) | ||||
−0.286233 | + | 0.958160i | \(0.592403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.4330 | −1.14778 | −0.573888 | − | 0.818934i | \(-0.694566\pi\) | ||||
−0.573888 | + | 0.818934i | \(0.694566\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.9346 | −0.717659 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.7172 | 0.794726 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.08331 | −0.227560 | −0.113780 | − | 0.993506i | \(-0.536296\pi\) | ||||
−0.113780 | + | 0.993506i | \(0.536296\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.1657 | −1.47879 | −0.739393 | − | 0.673274i | \(-0.764887\pi\) | ||||
−0.739393 | + | 0.673274i | \(0.764887\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.71701 | 0.298903 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.5979 | 0.912986 | 0.456493 | − | 0.889727i | \(-0.349105\pi\) | ||||
0.456493 | + | 0.889727i | \(0.349105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2424 | 0.453095 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.98809 | 0.0876059 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.2329 | 0.450042 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.5456 | −0.768688 | −0.384344 | − | 0.923190i | \(-0.625572\pi\) | ||||
−0.384344 | + | 0.923190i | \(0.625572\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.2014 | 0.533529 | 0.266764 | − | 0.963762i | \(-0.414045\pi\) | ||||
0.266764 | + | 0.963762i | \(0.414045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.7896 | −1.60258 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.0005 | 1.91306 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.36547 | −0.232405 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.36670 | −0.188789 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.24641 | 0.225979 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.0641 | −1.50752 | −0.753761 | − | 0.657148i | \(-0.771763\pi\) | ||||
−0.753761 | + | 0.657148i | \(0.771763\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.32623 | 0.0996447 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.21661 | 0.394074 | 0.197037 | − | 0.980396i | \(-0.436868\pi\) | ||||
0.197037 | + | 0.980396i | \(0.436868\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.8325 | −1.44131 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.02772 | 0.171276 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.0137 | −0.932750 | −0.466375 | − | 0.884587i | \(-0.654440\pi\) | ||||
−0.466375 | + | 0.884587i | \(0.654440\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.35952 | −0.0997971 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.2362 | 0.684273 | 0.342137 | − | 0.939650i | \(-0.388849\pi\) | ||||
0.342137 | + | 0.939650i | \(0.388849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.78231 | 0.0749823 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.4270 | −0.479046 | −0.239523 | − | 0.970891i | \(-0.576991\pi\) | ||||
−0.239523 | + | 0.970891i | \(0.576991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.6051 | 1.36448 | 0.682240 | − | 0.731128i | \(-0.261006\pi\) | ||||
0.682240 | + | 0.731128i | \(0.261006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.9760 | −1.29179 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0059 | −0.416551 | −0.208275 | − | 0.978070i | \(-0.566785\pi\) | ||||
−0.208275 | + | 0.978070i | \(0.566785\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.9115 | −0.909042 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9284 | −0.452610 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0065 | −0.578111 | −0.289055 | − | 0.957312i | \(-0.593341\pi\) | ||||
−0.289055 | + | 0.957312i | \(0.593341\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −78.1120 | −3.21855 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.14263 | −0.170117 | −0.0850586 | − | 0.996376i | \(-0.527108\pi\) | ||||
−0.0850586 | + | 0.996376i | \(0.527108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.67516 | 0.232659 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.0382 | −1.79935 | −0.899676 | − | 0.436558i | \(-0.856197\pi\) | ||||
−0.899676 | + | 0.436558i | \(0.856197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.6222 | 0.637243 | 0.318622 | − | 0.947882i | \(-0.396780\pi\) | ||||
0.318622 | + | 0.947882i | \(0.396780\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.10258 | 0.0448264 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.5704 | 0.794337 | 0.397169 | − | 0.917746i | \(-0.369993\pi\) | ||||
0.397169 | + | 0.917746i | \(0.369993\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2329 | 0.413978 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.3975 | −0.662289 | −0.331144 | − | 0.943580i | \(-0.607435\pi\) | ||||
−0.331144 | + | 0.943580i | \(0.607435\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.50618 | 0.100895 | 0.0504474 | − | 0.998727i | \(-0.483935\pi\) | ||||
0.0504474 | + | 0.998727i | \(0.483935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.2218 | 1.05394 | 0.526972 | − | 0.849883i | \(-0.323327\pi\) | ||||
0.526972 | + | 0.849883i | \(0.323327\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.9984 | 0.560833 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.24251 | 0.329701 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37.2536 | 1.48540 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.3550 | −0.651081 | −0.325541 | − | 0.945528i | \(-0.605546\pi\) | ||||
−0.325541 | + | 0.945528i | \(0.605546\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.81503 | −0.191079 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.24641 | 0.207870 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.3964 | −1.24008 | −0.620042 | − | 0.784569i | \(-0.712884\pi\) | ||||
−0.620042 | + | 0.784569i | \(0.712884\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.8416 | 1.05853 | 0.529265 | − | 0.848456i | \(-0.322468\pi\) | ||||
0.529265 | + | 0.848456i | \(0.322468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.44232 | 0.213960 | 0.106980 | − | 0.994261i | \(-0.465882\pi\) | ||||
0.106980 | + | 0.994261i | \(0.465882\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.12532 | 0.0441728 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.16523 | 0.358663 | 0.179332 | − | 0.983789i | \(-0.442606\pi\) | ||||
0.179332 | + | 0.983789i | \(0.442606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.6677 | 0.846626 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.8455 | −0.656207 | −0.328104 | − | 0.944642i | \(-0.606410\pi\) | ||||
−0.328104 | + | 0.944642i | \(0.606410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.1775 | −0.551441 | −0.275720 | − | 0.961238i | \(-0.588916\pi\) | ||||
−0.275720 | + | 0.961238i | \(0.588916\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0495 | 0.467261 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.5566 | −1.29932 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.78130 | 0.300394 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −49.1337 | −1.89396 | −0.946982 | − | 0.321288i | \(-0.895884\pi\) | ||||
−0.946982 | + | 0.321288i | \(0.895884\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.7935 | 0.876026 | 0.438013 | − | 0.898969i | \(-0.355682\pi\) | ||||
0.438013 | + | 0.898969i | \(0.355682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.65773 | −0.217124 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.3344 | 1.23724 | 0.618621 | − | 0.785690i | \(-0.287692\pi\) | ||||
0.618621 | + | 0.785690i | \(0.287692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.80776 | 0.221903 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.9284 | −0.416341 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.0679 | 1.86663 | 0.933315 | − | 0.359058i | \(-0.116902\pi\) | ||||
0.933315 | + | 0.359058i | \(0.116902\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.4073 | 0.432705 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.8550 | 0.789940 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.51682 | 0.321676 | 0.160838 | − | 0.986981i | \(-0.448580\pi\) | ||||
0.160838 | + | 0.986981i | \(0.448580\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 79.0971 | 2.98320 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.06729 | 0.303402 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.1294 | −0.530639 | −0.265319 | − | 0.964161i | \(-0.585477\pi\) | ||||
−0.265319 | + | 0.964161i | \(0.585477\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −77.4751 | −2.90146 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.10258 | 0.0412343 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5799 | −1.51337 | −0.756687 | − | 0.653777i | \(-0.773183\pi\) | ||||
−0.756687 | + | 0.653777i | \(0.773183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.38775 | 0.0889244 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.5141 | 0.576178 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.2421 | 1.49250 | 0.746248 | − | 0.665668i | \(-0.231853\pi\) | ||||
0.746248 | + | 0.665668i | \(0.231853\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.17121 | 0.339209 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.30724 | −0.343771 | −0.171885 | − | 0.985117i | \(-0.554986\pi\) | ||||
−0.171885 | + | 0.985117i | \(0.554986\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.02176 | 0.184979 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.9562 | −1.69053 | −0.845263 | − | 0.534350i | \(-0.820556\pi\) | ||||
−0.845263 | + | 0.534350i | \(0.820556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.4726 | 0.384204 | 0.192102 | − | 0.981375i | \(-0.438470\pi\) | ||||
0.192102 | + | 0.981375i | \(0.438470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.233120 | −0.00854085 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.24451 | −0.191630 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.7511 | −0.501784 | −0.250892 | − | 0.968015i | \(-0.580724\pi\) | ||||
−0.250892 | + | 0.968015i | \(0.580724\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.6257 | 0.859826 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.4242 | 0.924060 | 0.462030 | − | 0.886864i | \(-0.347121\pi\) | ||||
0.462030 | + | 0.886864i | \(0.347121\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.6491 | −1.29228 | −0.646139 | − | 0.763220i | \(-0.723617\pi\) | ||||
−0.646139 | + | 0.763220i | \(0.723617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.79386 | 0.101144 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.12532 | 0.0406330 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.24231 | −0.116921 | −0.0584603 | − | 0.998290i | \(-0.518619\pi\) | ||||
−0.0584603 | + | 0.998290i | \(0.518619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.71989 | 0.349600 | 0.174800 | − | 0.984604i | \(-0.444072\pi\) | ||||
0.174800 | + | 0.984604i | \(0.444072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.8187 | 1.28664 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.2795 | 1.58648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.3793 | −0.478747 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.0199 | −0.928689 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.6830 | −1.48584 | −0.742919 | − | 0.669382i | \(-0.766559\pi\) | ||||
−0.742919 | + | 0.669382i | \(0.766559\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.14060 | 0.0761108 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.78130 | 0.276322 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.2473 | −1.00057 | −0.500286 | − | 0.865860i | \(-0.666772\pi\) | ||||
−0.500286 | + | 0.865860i | \(0.666772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.7741 | −1.40711 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.73457 | −0.272947 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.9513 | 0.421227 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.8947 | −1.43778 | −0.718891 | − | 0.695123i | \(-0.755350\pi\) | ||||
−0.718891 | + | 0.695123i | \(0.755350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.4263 | −1.70048 | −0.850238 | − | 0.526398i | \(-0.823542\pi\) | ||||
−0.850238 | + | 0.526398i | \(0.823542\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.846598 | −0.0296550 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.4724 | 0.681252 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.0195 | −1.08259 | −0.541294 | − | 0.840834i | \(-0.682065\pi\) | ||||
−0.541294 | + | 0.840834i | \(0.682065\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.0332 | −1.70919 | −0.854595 | − | 0.519296i | \(-0.826194\pi\) | ||||
−0.854595 | + | 0.519296i | \(0.826194\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.72194 | −0.129424 | −0.0647122 | − | 0.997904i | \(-0.520613\pi\) | ||||
−0.0647122 | + | 0.997904i | \(0.520613\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.3682 | −0.776881 | −0.388441 | − | 0.921474i | \(-0.626986\pi\) | ||||
−0.388441 | + | 0.921474i | \(0.626986\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.3922 | −0.706549 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.5753 | 0.712038 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.2968 | −0.355487 | −0.177743 | − | 0.984077i | \(-0.556880\pi\) | ||||
−0.177743 | + | 0.984077i | \(0.556880\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.1934 | −0.420463 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.10258 | 0.0379301 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.32423 | 0.0455011 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 78.4522 | 2.68931 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.3841 | −1.86208 | −0.931038 | − | 0.364922i | \(-0.881096\pi\) | ||||
−0.931038 | + | 0.364922i | \(0.881096\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.04679 | −0.240714 | −0.120357 | − | 0.992731i | \(-0.538404\pi\) | ||||
−0.120357 | + | 0.992731i | \(0.538404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.6623 | −0.602630 | −0.301315 | − | 0.953525i | \(-0.597426\pi\) | ||||
−0.301315 | + | 0.953525i | \(0.597426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.6583 | 1.38402 | 0.692012 | − | 0.721886i | \(-0.256724\pi\) | ||||
0.692012 | + | 0.721886i | \(0.256724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.4815 | 0.390384 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.04155 | −0.103178 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.02176 | 0.170156 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.8258 | −0.433590 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.2002 | 0.547042 | 0.273521 | − | 0.961866i | \(-0.411812\pi\) | ||||
0.273521 | + | 0.961866i | \(0.411812\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.2262 | −1.52371 | −0.761855 | − | 0.647747i | \(-0.775711\pi\) | ||||
−0.761855 | + | 0.647747i | \(0.775711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.8672 | −1.44260 | −0.721298 | − | 0.692625i | \(-0.756454\pi\) | ||||
−0.721298 | + | 0.692625i | \(0.756454\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.2010 | −1.08120 | −0.540602 | − | 0.841278i | \(-0.681804\pi\) | ||||
−0.540602 | + | 0.841278i | \(0.681804\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.78297 | −0.193955 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −84.4487 | −2.82597 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.42891 | 0.281748 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.8028 | 1.29414 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.4777 | 1.41514 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.1714 | −0.404593 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.7097 | −0.886880 | −0.443440 | − | 0.896304i | \(-0.646242\pi\) | ||||
−0.443440 | + | 0.896304i | \(0.646242\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.5096 | −0.414461 | −0.207230 | − | 0.978292i | \(-0.566445\pi\) | ||||
−0.207230 | + | 0.978292i | \(0.566445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.5466 | 0.547612 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.0234 | 0.859369 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.8589 | −0.358203 | −0.179102 | − | 0.983831i | \(-0.557319\pi\) | ||||
−0.179102 | + | 0.983831i | \(0.557319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.3793 | −0.440384 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.2704 | −1.19256 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.1441 | 0.923379 | 0.461690 | − | 0.887042i | \(-0.347243\pi\) | ||||
0.461690 | + | 0.887042i | \(0.347243\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.2969 | −1.41900 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.28563 | −0.140155 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.4153 | −1.05896 | −0.529482 | − | 0.848321i | \(-0.677613\pi\) | ||||
−0.529482 | + | 0.848321i | \(0.677613\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55.1473 | −1.79775 | −0.898875 | − | 0.438206i | \(-0.855614\pi\) | ||||
−0.898875 | + | 0.438206i | \(0.855614\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.9185 | 1.43018 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.85366 | 0.0602359 | 0.0301180 | − | 0.999546i | \(-0.490412\pi\) | ||||
0.0301180 | + | 0.999546i | \(0.490412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.73457 | −0.251075 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.8227 | 1.09562 | 0.547812 | − | 0.836601i | \(-0.315461\pi\) | ||||
0.547812 | + | 0.836601i | \(0.315461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.4413 | 0.855622 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.97526 | 0.225243 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58.5873 | 1.88991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.6904 | −0.440708 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.0634 | 1.48130 | 0.740649 | − | 0.671892i | \(-0.234518\pi\) | ||||
0.740649 | + | 0.671892i | \(0.234518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.1617 | −1.25676 | −0.628379 | − | 0.777907i | \(-0.716281\pi\) | ||||
−0.628379 | + | 0.777907i | \(0.716281\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.7005 | 0.439217 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.60139 | −0.211197 | −0.105599 | − | 0.994409i | \(-0.533676\pi\) | ||||
−0.105599 | + | 0.994409i | \(0.533676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5710 | −0.337849 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.9253 | 1.05016 | 0.525078 | − | 0.851054i | \(-0.324036\pi\) | ||||
0.525078 | + | 0.851054i | \(0.324036\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.97205 | 0.317736 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.3136 | 0.614136 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.8409 | 0.757332 | 0.378666 | − | 0.925533i | \(-0.376383\pi\) | ||||
0.378666 | + | 0.925533i | \(0.376383\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.27913 | 0.262466 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.6716 | 1.09806 | 0.549030 | − | 0.835803i | \(-0.314997\pi\) | ||||
0.549030 | + | 0.835803i | \(0.314997\pi\) | |||||||
\(998\) | 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 | 5148.2.a.t.1.4 | yes | 5 | |
3.2 | odd | 2 | 5148.2.a.s.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5148.2.a.s.1.2 | ✓ | 5 | 3.2 | odd | 2 | ||
5148.2.a.t.1.4 | yes | 5 | 1.1 | even | 1 | trivial |