Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.5 | ||
Root | \(1.80194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.y.1351.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0.643104i | 0.243071i | 0.992587 | + | 0.121535i | \(0.0387817\pi\) | ||||
−0.992587 | + | 0.121535i | \(0.961218\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 4.40581i | 1.32840i | 0.747554 | + | 0.664201i | \(0.231228\pi\) | ||||
−0.747554 | + | 0.664201i | \(0.768772\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.643104 | −0.171877 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.939001 | −0.227741 | −0.113871 | − | 0.993496i | \(-0.536325\pi\) | ||||
−0.113871 | + | 0.993496i | \(0.536325\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | − 2.75302i | − 0.631586i | −0.948828 | − | 0.315793i | \(-0.897729\pi\) | ||||
0.948828 | − | 0.315793i | \(-0.102271\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 0.643104i | 0.140337i | ||||||||
\(22\) | −4.40581 | −0.939323 | ||||||||
\(23\) | 2.04892 | 0.427229 | 0.213614 | − | 0.976918i | \(-0.431476\pi\) | ||||
0.213614 | + | 0.976918i | \(0.431476\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 0.643104i | − 0.121535i | ||||||||
\(29\) | −0.149145 | −0.0276955 | −0.0138478 | − | 0.999904i | \(-0.504408\pi\) | ||||
−0.0138478 | + | 0.999904i | \(0.504408\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 2.08815i | − 0.375042i | −0.982261 | − | 0.187521i | \(-0.939955\pi\) | ||||
0.982261 | − | 0.187521i | \(-0.0600453\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 4.40581i | 0.766954i | ||||||||
\(34\) | − 0.939001i | − 0.161037i | ||||||||
\(35\) | 0.643104 | 0.108704 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 6.07069i | 0.998015i | 0.866598 | + | 0.499007i | \(0.166302\pi\) | ||||
−0.866598 | + | 0.499007i | \(0.833698\pi\) | |||||||
\(38\) | 2.75302 | 0.446599 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 5.74094i | 0.896584i | 0.893887 | + | 0.448292i | \(0.147968\pi\) | ||||
−0.893887 | + | 0.448292i | \(0.852032\pi\) | |||||||
\(42\) | −0.643104 | −0.0992331 | ||||||||
\(43\) | −4.69202 | −0.715527 | −0.357763 | − | 0.933812i | \(-0.616461\pi\) | ||||
−0.357763 | + | 0.933812i | \(0.616461\pi\) | |||||||
\(44\) | − 4.40581i | − 0.664201i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | 2.04892i | 0.302096i | ||||||||
\(47\) | 7.00000i | 1.02105i | 0.859861 | + | 0.510527i | \(0.170550\pi\) | ||||
−0.859861 | + | 0.510527i | \(0.829450\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 6.58642 | 0.940917 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | −0.939001 | −0.131486 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.68664 | 0.231678 | 0.115839 | − | 0.993268i | \(-0.463044\pi\) | ||||
0.115839 | + | 0.993268i | \(0.463044\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 4.40581 | 0.594080 | ||||||||
\(56\) | 0.643104 | 0.0859384 | ||||||||
\(57\) | − 2.75302i | − 0.364646i | ||||||||
\(58\) | − 0.149145i | − 0.0195837i | ||||||||
\(59\) | 7.85623i | 1.02279i | 0.859344 | + | 0.511397i | \(0.170872\pi\) | ||||
−0.859344 | + | 0.511397i | \(0.829128\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −12.0761 | −1.54618 | −0.773091 | − | 0.634295i | \(-0.781290\pi\) | ||||
−0.773091 | + | 0.634295i | \(0.781290\pi\) | |||||||
\(62\) | 2.08815 | 0.265195 | ||||||||
\(63\) | 0.643104i | 0.0810235i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.40581 | −0.542318 | ||||||||
\(67\) | − 1.45712i | − 0.178016i | −0.996031 | − | 0.0890080i | \(-0.971630\pi\) | ||||
0.996031 | − | 0.0890080i | \(-0.0283697\pi\) | |||||||
\(68\) | 0.939001 | 0.113871 | ||||||||
\(69\) | 2.04892 | 0.246661 | ||||||||
\(70\) | 0.643104i | 0.0768656i | ||||||||
\(71\) | 7.03684i | 0.835119i | 0.908650 | + | 0.417559i | \(0.137114\pi\) | ||||
−0.908650 | + | 0.417559i | \(0.862886\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 14.8605i | 1.73930i | 0.493673 | + | 0.869648i | \(0.335654\pi\) | ||||
−0.493673 | + | 0.869648i | \(0.664346\pi\) | |||||||
\(74\) | −6.07069 | −0.705703 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.75302i | 0.315793i | ||||||||
\(77\) | −2.83340 | −0.322896 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.929312 | 0.104556 | 0.0522779 | − | 0.998633i | \(-0.483352\pi\) | ||||
0.0522779 | + | 0.998633i | \(0.483352\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.74094 | −0.633981 | ||||||||
\(83\) | − 11.2959i | − 1.23989i | −0.784647 | − | 0.619943i | \(-0.787156\pi\) | ||||
0.784647 | − | 0.619943i | \(-0.212844\pi\) | |||||||
\(84\) | − 0.643104i | − 0.0701684i | ||||||||
\(85\) | 0.939001i | 0.101849i | ||||||||
\(86\) | − 4.69202i | − 0.505954i | ||||||||
\(87\) | −0.149145 | −0.0159900 | ||||||||
\(88\) | 4.40581 | 0.469661 | ||||||||
\(89\) | − 7.47650i | − 0.792508i | −0.918141 | − | 0.396254i | \(-0.870310\pi\) | ||||
0.918141 | − | 0.396254i | \(-0.129690\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.04892 | −0.213614 | ||||||||
\(93\) | − 2.08815i | − 0.216531i | ||||||||
\(94\) | −7.00000 | −0.721995 | ||||||||
\(95\) | −2.75302 | −0.282454 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 5.05861i | 0.513624i | 0.966461 | + | 0.256812i | \(0.0826721\pi\) | ||||
−0.966461 | + | 0.256812i | \(0.917328\pi\) | |||||||
\(98\) | 6.58642i | 0.665329i | ||||||||
\(99\) | 4.40581i | 0.442801i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 6.81163 | 0.677782 | 0.338891 | − | 0.940826i | \(-0.389948\pi\) | ||||
0.338891 | + | 0.940826i | \(0.389948\pi\) | |||||||
\(102\) | − 0.939001i | − 0.0929750i | ||||||||
\(103\) | 12.0858 | 1.19084 | 0.595422 | − | 0.803413i | \(-0.296985\pi\) | ||||
0.595422 | + | 0.803413i | \(0.296985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.643104 | 0.0627605 | ||||||||
\(106\) | 1.68664i | 0.163821i | ||||||||
\(107\) | −14.6679 | −1.41800 | −0.708998 | − | 0.705211i | \(-0.750852\pi\) | ||||
−0.708998 | + | 0.705211i | \(0.750852\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | − 8.15883i | − 0.781475i | −0.920502 | − | 0.390737i | \(-0.872220\pi\) | ||||
0.920502 | − | 0.390737i | \(-0.127780\pi\) | |||||||
\(110\) | 4.40581i | 0.420078i | ||||||||
\(111\) | 6.07069i | 0.576204i | ||||||||
\(112\) | 0.643104i | 0.0607676i | ||||||||
\(113\) | 16.8442 | 1.58456 | 0.792282 | − | 0.610155i | \(-0.208893\pi\) | ||||
0.792282 | + | 0.610155i | \(0.208893\pi\) | |||||||
\(114\) | 2.75302 | 0.257844 | ||||||||
\(115\) | − 2.04892i | − 0.191063i | ||||||||
\(116\) | 0.149145 | 0.0138478 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.85623 | −0.723225 | ||||||||
\(119\) | − 0.603875i | − 0.0553572i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −8.41119 | −0.764654 | ||||||||
\(122\) | − 12.0761i | − 1.09332i | ||||||||
\(123\) | 5.74094i | 0.517643i | ||||||||
\(124\) | 2.08815i | 0.187521i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −0.643104 | −0.0572923 | ||||||||
\(127\) | −4.85086 | −0.430444 | −0.215222 | − | 0.976565i | \(-0.569047\pi\) | ||||
−0.215222 | + | 0.976565i | \(0.569047\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −4.69202 | −0.413109 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.52781 | 0.133485 | 0.0667427 | − | 0.997770i | \(-0.478739\pi\) | ||||
0.0667427 | + | 0.997770i | \(0.478739\pi\) | |||||||
\(132\) | − 4.40581i | − 0.383477i | ||||||||
\(133\) | 1.77048 | 0.153520 | ||||||||
\(134\) | 1.45712 | 0.125876 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | 0.939001i | 0.0805187i | ||||||||
\(137\) | − 6.41119i | − 0.547745i | −0.961766 | − | 0.273872i | \(-0.911695\pi\) | ||||
0.961766 | − | 0.273872i | \(-0.0883046\pi\) | |||||||
\(138\) | 2.04892i | 0.174415i | ||||||||
\(139\) | −8.78017 | −0.744724 | −0.372362 | − | 0.928088i | \(-0.621452\pi\) | ||||
−0.372362 | + | 0.928088i | \(0.621452\pi\) | |||||||
\(140\) | −0.643104 | −0.0543522 | ||||||||
\(141\) | 7.00000i | 0.589506i | ||||||||
\(142\) | −7.03684 | −0.590518 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.149145i | 0.0123858i | ||||||||
\(146\) | −14.8605 | −1.22987 | ||||||||
\(147\) | 6.58642 | 0.543239 | ||||||||
\(148\) | − 6.07069i | − 0.499007i | ||||||||
\(149\) | 22.6504i | 1.85559i | 0.373087 | + | 0.927797i | \(0.378299\pi\) | ||||
−0.373087 | + | 0.927797i | \(0.621701\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | 10.2959i | 0.837868i | 0.908017 | + | 0.418934i | \(0.137596\pi\) | ||||
−0.908017 | + | 0.418934i | \(0.862404\pi\) | |||||||
\(152\) | −2.75302 | −0.223299 | ||||||||
\(153\) | −0.939001 | −0.0759137 | ||||||||
\(154\) | − 2.83340i | − 0.228322i | ||||||||
\(155\) | −2.08815 | −0.167724 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.994623 | 0.0793796 | 0.0396898 | − | 0.999212i | \(-0.487363\pi\) | ||||
0.0396898 | + | 0.999212i | \(0.487363\pi\) | |||||||
\(158\) | 0.929312i | 0.0739321i | ||||||||
\(159\) | 1.68664 | 0.133760 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.31767i | 0.103847i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 21.6015i | 1.69196i | 0.533216 | + | 0.845979i | \(0.320983\pi\) | ||||
−0.533216 | + | 0.845979i | \(0.679017\pi\) | |||||||
\(164\) | − 5.74094i | − 0.448292i | ||||||||
\(165\) | 4.40581 | 0.342992 | ||||||||
\(166\) | 11.2959 | 0.876732 | ||||||||
\(167\) | 7.96615i | 0.616439i | 0.951315 | + | 0.308220i | \(0.0997331\pi\) | ||||
−0.951315 | + | 0.308220i | \(0.900267\pi\) | |||||||
\(168\) | 0.643104 | 0.0496166 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.939001 | −0.0720181 | ||||||||
\(171\) | − 2.75302i | − 0.210529i | ||||||||
\(172\) | 4.69202 | 0.357763 | ||||||||
\(173\) | −4.11960 | −0.313208 | −0.156604 | − | 0.987661i | \(-0.550055\pi\) | ||||
−0.156604 | + | 0.987661i | \(0.550055\pi\) | |||||||
\(174\) | − 0.149145i | − 0.0113066i | ||||||||
\(175\) | − 0.643104i | − 0.0486141i | ||||||||
\(176\) | 4.40581i | 0.332101i | ||||||||
\(177\) | 7.85623i | 0.590511i | ||||||||
\(178\) | 7.47650 | 0.560387 | ||||||||
\(179\) | 8.78017 | 0.656261 | 0.328130 | − | 0.944632i | \(-0.393582\pi\) | ||||
0.328130 | + | 0.944632i | \(0.393582\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | −19.4741 | −1.44750 | −0.723750 | − | 0.690063i | \(-0.757583\pi\) | ||||
−0.723750 | + | 0.690063i | \(0.757583\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.0761 | −0.892688 | ||||||||
\(184\) | − 2.04892i | − 0.151048i | ||||||||
\(185\) | 6.07069 | 0.446326 | ||||||||
\(186\) | 2.08815 | 0.153110 | ||||||||
\(187\) | − 4.13706i | − 0.302532i | ||||||||
\(188\) | − 7.00000i | − 0.510527i | ||||||||
\(189\) | 0.643104i | 0.0467789i | ||||||||
\(190\) | − 2.75302i | − 0.199725i | ||||||||
\(191\) | 0.753020 | 0.0544866 | 0.0272433 | − | 0.999629i | \(-0.491327\pi\) | ||||
0.0272433 | + | 0.999629i | \(0.491327\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − 7.84117i | − 0.564420i | −0.959353 | − | 0.282210i | \(-0.908933\pi\) | ||||
0.959353 | − | 0.282210i | \(-0.0910674\pi\) | |||||||
\(194\) | −5.05861 | −0.363187 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.58642 | −0.470458 | ||||||||
\(197\) | − 10.2010i | − 0.726794i | −0.931634 | − | 0.363397i | \(-0.881617\pi\) | ||||
0.931634 | − | 0.363397i | \(-0.118383\pi\) | |||||||
\(198\) | −4.40581 | −0.313108 | ||||||||
\(199\) | −1.65279 | −0.117163 | −0.0585817 | − | 0.998283i | \(-0.518658\pi\) | ||||
−0.0585817 | + | 0.998283i | \(0.518658\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | − 1.45712i | − 0.102778i | ||||||||
\(202\) | 6.81163i | 0.479264i | ||||||||
\(203\) | − 0.0959157i | − 0.00673196i | ||||||||
\(204\) | 0.939001 | 0.0657432 | ||||||||
\(205\) | 5.74094 | 0.400965 | ||||||||
\(206\) | 12.0858i | 0.842054i | ||||||||
\(207\) | 2.04892 | 0.142410 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.1293 | 0.839001 | ||||||||
\(210\) | 0.643104i | 0.0443784i | ||||||||
\(211\) | 11.7453 | 0.808576 | 0.404288 | − | 0.914632i | \(-0.367519\pi\) | ||||
0.404288 | + | 0.914632i | \(0.367519\pi\) | |||||||
\(212\) | −1.68664 | −0.115839 | ||||||||
\(213\) | 7.03684i | 0.482156i | ||||||||
\(214\) | − 14.6679i | − 1.00267i | ||||||||
\(215\) | 4.69202i | 0.319993i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | 1.34290 | 0.0911617 | ||||||||
\(218\) | 8.15883 | 0.552586 | ||||||||
\(219\) | 14.8605i | 1.00418i | ||||||||
\(220\) | −4.40581 | −0.297040 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.07069 | −0.407438 | ||||||||
\(223\) | 9.73855i | 0.652141i | 0.945345 | + | 0.326071i | \(0.105725\pi\) | ||||
−0.945345 | + | 0.326071i | \(0.894275\pi\) | |||||||
\(224\) | −0.643104 | −0.0429692 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 16.8442i | 1.12046i | ||||||||
\(227\) | 25.2500i | 1.67590i | 0.545748 | + | 0.837949i | \(0.316246\pi\) | ||||
−0.545748 | + | 0.837949i | \(0.683754\pi\) | |||||||
\(228\) | 2.75302i | 0.182323i | ||||||||
\(229\) | 23.7845i | 1.57172i | 0.618403 | + | 0.785861i | \(0.287780\pi\) | ||||
−0.618403 | + | 0.785861i | \(0.712220\pi\) | |||||||
\(230\) | 2.04892 | 0.135102 | ||||||||
\(231\) | −2.83340 | −0.186424 | ||||||||
\(232\) | 0.149145i | 0.00979184i | ||||||||
\(233\) | −0.603875 | −0.0395612 | −0.0197806 | − | 0.999804i | \(-0.506297\pi\) | ||||
−0.0197806 | + | 0.999804i | \(0.506297\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00000 | 0.456630 | ||||||||
\(236\) | − 7.85623i | − 0.511397i | ||||||||
\(237\) | 0.929312 | 0.0603653 | ||||||||
\(238\) | 0.603875 | 0.0391434 | ||||||||
\(239\) | 28.5579i | 1.84726i | 0.383286 | + | 0.923630i | \(0.374792\pi\) | ||||
−0.383286 | + | 0.923630i | \(0.625208\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | 6.31096i | 0.406525i | 0.979124 | + | 0.203262i | \(0.0651545\pi\) | ||||
−0.979124 | + | 0.203262i | \(0.934846\pi\) | |||||||
\(242\) | − 8.41119i | − 0.540692i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.0761 | 0.773091 | ||||||||
\(245\) | − 6.58642i | − 0.420791i | ||||||||
\(246\) | −5.74094 | −0.366029 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.08815 | −0.132597 | ||||||||
\(249\) | − 11.2959i | − 0.715848i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −24.5972 | −1.55256 | −0.776280 | − | 0.630388i | \(-0.782896\pi\) | ||||
−0.776280 | + | 0.630388i | \(0.782896\pi\) | |||||||
\(252\) | − 0.643104i | − 0.0405118i | ||||||||
\(253\) | 9.02715i | 0.567532i | ||||||||
\(254\) | − 4.85086i | − 0.304370i | ||||||||
\(255\) | 0.939001i | 0.0588025i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.9463 | 1.68086 | 0.840432 | − | 0.541917i | \(-0.182301\pi\) | ||||
0.840432 | + | 0.541917i | \(0.182301\pi\) | |||||||
\(258\) | − 4.69202i | − 0.292112i | ||||||||
\(259\) | −3.90408 | −0.242588 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.149145 | −0.00923184 | ||||||||
\(262\) | 1.52781i | 0.0943885i | ||||||||
\(263\) | −24.0465 | −1.48277 | −0.741386 | − | 0.671079i | \(-0.765831\pi\) | ||||
−0.741386 | + | 0.671079i | \(0.765831\pi\) | |||||||
\(264\) | 4.40581 | 0.271159 | ||||||||
\(265\) | − 1.68664i | − 0.103610i | ||||||||
\(266\) | 1.77048i | 0.108555i | ||||||||
\(267\) | − 7.47650i | − 0.457554i | ||||||||
\(268\) | 1.45712i | 0.0890080i | ||||||||
\(269\) | −7.17523 | −0.437481 | −0.218741 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218741 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 10.9825i | 0.667142i | 0.942725 | + | 0.333571i | \(0.108254\pi\) | ||||
−0.942725 | + | 0.333571i | \(0.891746\pi\) | |||||||
\(272\) | −0.939001 | −0.0569353 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.41119 | 0.387314 | ||||||||
\(275\) | − 4.40581i | − 0.265681i | ||||||||
\(276\) | −2.04892 | −0.123330 | ||||||||
\(277\) | −16.2107 | −0.974009 | −0.487004 | − | 0.873400i | \(-0.661910\pi\) | ||||
−0.487004 | + | 0.873400i | \(0.661910\pi\) | |||||||
\(278\) | − 8.78017i | − 0.526599i | ||||||||
\(279\) | − 2.08815i | − 0.125014i | ||||||||
\(280\) | − 0.643104i | − 0.0384328i | ||||||||
\(281\) | − 12.9584i | − 0.773032i | −0.922283 | − | 0.386516i | \(-0.873678\pi\) | ||||
0.922283 | − | 0.386516i | \(-0.126322\pi\) | |||||||
\(282\) | −7.00000 | −0.416844 | ||||||||
\(283\) | −21.5415 | −1.28051 | −0.640256 | − | 0.768162i | \(-0.721172\pi\) | ||||
−0.640256 | + | 0.768162i | \(0.721172\pi\) | |||||||
\(284\) | − 7.03684i | − 0.417559i | ||||||||
\(285\) | −2.75302 | −0.163075 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.69202 | −0.217933 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −16.1183 | −0.948134 | ||||||||
\(290\) | −0.149145 | −0.00875809 | ||||||||
\(291\) | 5.05861i | 0.296541i | ||||||||
\(292\) | − 14.8605i | − 0.869648i | ||||||||
\(293\) | 9.57971i | 0.559653i | 0.960051 | + | 0.279826i | \(0.0902769\pi\) | ||||
−0.960051 | + | 0.279826i | \(0.909723\pi\) | |||||||
\(294\) | 6.58642i | 0.384128i | ||||||||
\(295\) | 7.85623 | 0.457408 | ||||||||
\(296\) | 6.07069 | 0.352852 | ||||||||
\(297\) | 4.40581i | 0.255651i | ||||||||
\(298\) | −22.6504 | −1.31210 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | − 3.01746i | − 0.173923i | ||||||||
\(302\) | −10.2959 | −0.592462 | ||||||||
\(303\) | 6.81163 | 0.391318 | ||||||||
\(304\) | − 2.75302i | − 0.157897i | ||||||||
\(305\) | 12.0761i | 0.691473i | ||||||||
\(306\) | − 0.939001i | − 0.0536791i | ||||||||
\(307\) | 19.0140i | 1.08519i | 0.839996 | + | 0.542593i | \(0.182557\pi\) | ||||
−0.839996 | + | 0.542593i | \(0.817443\pi\) | |||||||
\(308\) | 2.83340 | 0.161448 | ||||||||
\(309\) | 12.0858 | 0.687534 | ||||||||
\(310\) | − 2.08815i | − 0.118599i | ||||||||
\(311\) | 3.74764 | 0.212509 | 0.106255 | − | 0.994339i | \(-0.466114\pi\) | ||||
0.106255 | + | 0.994339i | \(0.466114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.1196 | 1.41984 | 0.709922 | − | 0.704280i | \(-0.248730\pi\) | ||||
0.709922 | + | 0.704280i | \(0.248730\pi\) | |||||||
\(314\) | 0.994623i | 0.0561298i | ||||||||
\(315\) | 0.643104 | 0.0362348 | ||||||||
\(316\) | −0.929312 | −0.0522779 | ||||||||
\(317\) | − 12.6679i | − 0.711498i | −0.934582 | − | 0.355749i | \(-0.884226\pi\) | ||||
0.934582 | − | 0.355749i | \(-0.115774\pi\) | |||||||
\(318\) | 1.68664i | 0.0945823i | ||||||||
\(319\) | − 0.657105i | − 0.0367908i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −14.6679 | −0.818680 | ||||||||
\(322\) | −1.31767 | −0.0734307 | ||||||||
\(323\) | 2.58509i | 0.143838i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.6015 | −1.19640 | ||||||||
\(327\) | − 8.15883i | − 0.451185i | ||||||||
\(328\) | 5.74094 | 0.316990 | ||||||||
\(329\) | −4.50173 | −0.248188 | ||||||||
\(330\) | 4.40581i | 0.242532i | ||||||||
\(331\) | 6.43057i | 0.353456i | 0.984260 | + | 0.176728i | \(0.0565513\pi\) | ||||
−0.984260 | + | 0.176728i | \(0.943449\pi\) | |||||||
\(332\) | 11.2959i | 0.619943i | ||||||||
\(333\) | 6.07069i | 0.332672i | ||||||||
\(334\) | −7.96615 | −0.435888 | ||||||||
\(335\) | −1.45712 | −0.0796112 | ||||||||
\(336\) | 0.643104i | 0.0350842i | ||||||||
\(337\) | −10.5496 | −0.574672 | −0.287336 | − | 0.957830i | \(-0.592770\pi\) | ||||
−0.287336 | + | 0.957830i | \(0.592770\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.8442 | 0.914849 | ||||||||
\(340\) | − 0.939001i | − 0.0509245i | ||||||||
\(341\) | 9.19998 | 0.498207 | ||||||||
\(342\) | 2.75302 | 0.148866 | ||||||||
\(343\) | 8.73748i | 0.471780i | ||||||||
\(344\) | 4.69202i | 0.252977i | ||||||||
\(345\) | − 2.04892i | − 0.110310i | ||||||||
\(346\) | − 4.11960i | − 0.221471i | ||||||||
\(347\) | 9.87130 | 0.529919 | 0.264960 | − | 0.964260i | \(-0.414641\pi\) | ||||
0.264960 | + | 0.964260i | \(0.414641\pi\) | |||||||
\(348\) | 0.149145 | 0.00799501 | ||||||||
\(349\) | − 30.5338i | − 1.63444i | −0.576329 | − | 0.817218i | \(-0.695515\pi\) | ||||
0.576329 | − | 0.817218i | \(-0.304485\pi\) | |||||||
\(350\) | 0.643104 | 0.0343754 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.40581 | −0.234831 | ||||||||
\(353\) | 24.7047i | 1.31490i | 0.753499 | + | 0.657449i | \(0.228365\pi\) | ||||
−0.753499 | + | 0.657449i | \(0.771635\pi\) | |||||||
\(354\) | −7.85623 | −0.417554 | ||||||||
\(355\) | 7.03684 | 0.373476 | ||||||||
\(356\) | 7.47650i | 0.396254i | ||||||||
\(357\) | − 0.603875i | − 0.0319605i | ||||||||
\(358\) | 8.78017i | 0.464046i | ||||||||
\(359\) | − 11.5888i | − 0.611634i | −0.952090 | − | 0.305817i | \(-0.901070\pi\) | ||||
0.952090 | − | 0.305817i | \(-0.0989296\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 11.4209 | 0.601099 | ||||||||
\(362\) | − 19.4741i | − 1.02354i | ||||||||
\(363\) | −8.41119 | −0.441473 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.8605 | 0.777836 | ||||||||
\(366\) | − 12.0761i | − 0.631226i | ||||||||
\(367\) | −20.5579 | −1.07312 | −0.536558 | − | 0.843863i | \(-0.680276\pi\) | ||||
−0.536558 | + | 0.843863i | \(0.680276\pi\) | |||||||
\(368\) | 2.04892 | 0.106807 | ||||||||
\(369\) | 5.74094i | 0.298861i | ||||||||
\(370\) | 6.07069i | 0.315600i | ||||||||
\(371\) | 1.08469i | 0.0563142i | ||||||||
\(372\) | 2.08815i | 0.108265i | ||||||||
\(373\) | 1.31037 | 0.0678485 | 0.0339242 | − | 0.999424i | \(-0.489200\pi\) | ||||
0.0339242 | + | 0.999424i | \(0.489200\pi\) | |||||||
\(374\) | 4.13706 | 0.213922 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.643104 | −0.0330777 | ||||||||
\(379\) | − 28.1551i | − 1.44623i | −0.690727 | − | 0.723115i | \(-0.742709\pi\) | ||||
0.690727 | − | 0.723115i | \(-0.257291\pi\) | |||||||
\(380\) | 2.75302 | 0.141227 | ||||||||
\(381\) | −4.85086 | −0.248517 | ||||||||
\(382\) | 0.753020i | 0.0385279i | ||||||||
\(383\) | 18.6679i | 0.953883i | 0.878935 | + | 0.476941i | \(0.158255\pi\) | ||||
−0.878935 | + | 0.476941i | \(0.841745\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | 2.83340i | 0.144403i | ||||||||
\(386\) | 7.84117 | 0.399105 | ||||||||
\(387\) | −4.69202 | −0.238509 | ||||||||
\(388\) | − 5.05861i | − 0.256812i | ||||||||
\(389\) | 29.6752 | 1.50459 | 0.752295 | − | 0.658826i | \(-0.228947\pi\) | ||||
0.752295 | + | 0.658826i | \(0.228947\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.92394 | −0.0972976 | ||||||||
\(392\) | − 6.58642i | − 0.332664i | ||||||||
\(393\) | 1.52781 | 0.0770679 | ||||||||
\(394\) | 10.2010 | 0.513921 | ||||||||
\(395\) | − 0.929312i | − 0.0467588i | ||||||||
\(396\) | − 4.40581i | − 0.221400i | ||||||||
\(397\) | − 28.7536i | − 1.44310i | −0.692361 | − | 0.721551i | \(-0.743429\pi\) | ||||
0.692361 | − | 0.721551i | \(-0.256571\pi\) | |||||||
\(398\) | − 1.65279i | − 0.0828470i | ||||||||
\(399\) | 1.77048 | 0.0886348 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 18.6993i | 0.933799i | 0.884310 | + | 0.466900i | \(0.154629\pi\) | ||||
−0.884310 | + | 0.466900i | \(0.845371\pi\) | |||||||
\(402\) | 1.45712 | 0.0726747 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.81163 | −0.338891 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | 0.0959157 | 0.00476022 | ||||||||
\(407\) | −26.7463 | −1.32577 | ||||||||
\(408\) | 0.939001i | 0.0464875i | ||||||||
\(409\) | − 10.6233i | − 0.525286i | −0.964893 | − | 0.262643i | \(-0.915406\pi\) | ||||
0.964893 | − | 0.262643i | \(-0.0845942\pi\) | |||||||
\(410\) | 5.74094i | 0.283525i | ||||||||
\(411\) | − 6.41119i | − 0.316241i | ||||||||
\(412\) | −12.0858 | −0.595422 | ||||||||
\(413\) | −5.05238 | −0.248611 | ||||||||
\(414\) | 2.04892i | 0.100699i | ||||||||
\(415\) | −11.2959 | −0.554494 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.78017 | −0.429967 | ||||||||
\(418\) | 12.1293i | 0.593263i | ||||||||
\(419\) | 19.4198 | 0.948720 | 0.474360 | − | 0.880331i | \(-0.342680\pi\) | ||||
0.474360 | + | 0.880331i | \(0.342680\pi\) | |||||||
\(420\) | −0.643104 | −0.0313803 | ||||||||
\(421\) | − 20.5719i | − 1.00262i | −0.865269 | − | 0.501308i | \(-0.832853\pi\) | ||||
0.865269 | − | 0.501308i | \(-0.167147\pi\) | |||||||
\(422\) | 11.7453i | 0.571750i | ||||||||
\(423\) | 7.00000i | 0.340352i | ||||||||
\(424\) | − 1.68664i | − 0.0819107i | ||||||||
\(425\) | 0.939001 | 0.0455482 | ||||||||
\(426\) | −7.03684 | −0.340936 | ||||||||
\(427\) | − 7.76617i | − 0.375831i | ||||||||
\(428\) | 14.6679 | 0.708998 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.69202 | −0.226269 | ||||||||
\(431\) | − 33.8079i | − 1.62847i | −0.580536 | − | 0.814235i | \(-0.697157\pi\) | ||||
0.580536 | − | 0.814235i | \(-0.302843\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −27.2838 | −1.31118 | −0.655588 | − | 0.755119i | \(-0.727579\pi\) | ||||
−0.655588 | + | 0.755119i | \(0.727579\pi\) | |||||||
\(434\) | 1.34290i | 0.0644610i | ||||||||
\(435\) | 0.149145i | 0.00715095i | ||||||||
\(436\) | 8.15883i | 0.390737i | ||||||||
\(437\) | − 5.64071i | − 0.269832i | ||||||||
\(438\) | −14.8605 | −0.710064 | ||||||||
\(439\) | 1.56943 | 0.0749049 | 0.0374525 | − | 0.999298i | \(-0.488076\pi\) | ||||
0.0374525 | + | 0.999298i | \(0.488076\pi\) | |||||||
\(440\) | − 4.40581i | − 0.210039i | ||||||||
\(441\) | 6.58642 | 0.313639 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.0489 | 1.80776 | 0.903879 | − | 0.427788i | \(-0.140707\pi\) | ||||
0.903879 | + | 0.427788i | \(0.140707\pi\) | |||||||
\(444\) | − 6.07069i | − 0.288102i | ||||||||
\(445\) | −7.47650 | −0.354420 | ||||||||
\(446\) | −9.73855 | −0.461134 | ||||||||
\(447\) | 22.6504i | 1.07133i | ||||||||
\(448\) | − 0.643104i | − 0.0303838i | ||||||||
\(449\) | − 24.2373i | − 1.14383i | −0.820313 | − | 0.571914i | \(-0.806201\pi\) | ||||
0.820313 | − | 0.571914i | \(-0.193799\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | −25.2935 | −1.19102 | ||||||||
\(452\) | −16.8442 | −0.792282 | ||||||||
\(453\) | 10.2959i | 0.483743i | ||||||||
\(454\) | −25.2500 | −1.18504 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.75302 | −0.128922 | ||||||||
\(457\) | − 9.75063i | − 0.456115i | −0.973648 | − | 0.228058i | \(-0.926763\pi\) | ||||
0.973648 | − | 0.228058i | \(-0.0732374\pi\) | |||||||
\(458\) | −23.7845 | −1.11138 | ||||||||
\(459\) | −0.939001 | −0.0438288 | ||||||||
\(460\) | 2.04892i | 0.0955313i | ||||||||
\(461\) | − 31.0358i | − 1.44548i | −0.691120 | − | 0.722740i | \(-0.742882\pi\) | ||||
0.691120 | − | 0.722740i | \(-0.257118\pi\) | |||||||
\(462\) | − 2.83340i | − 0.131822i | ||||||||
\(463\) | 33.1618i | 1.54116i | 0.637343 | + | 0.770580i | \(0.280033\pi\) | ||||
−0.637343 | + | 0.770580i | \(0.719967\pi\) | |||||||
\(464\) | −0.149145 | −0.00692388 | ||||||||
\(465\) | −2.08815 | −0.0968355 | ||||||||
\(466\) | − 0.603875i | − 0.0279740i | ||||||||
\(467\) | 16.1153 | 0.745727 | 0.372863 | − | 0.927886i | \(-0.378376\pi\) | ||||
0.372863 | + | 0.927886i | \(0.378376\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.937082 | 0.0432704 | ||||||||
\(470\) | 7.00000i | 0.322886i | ||||||||
\(471\) | 0.994623 | 0.0458298 | ||||||||
\(472\) | 7.85623 | 0.361612 | ||||||||
\(473\) | − 20.6722i | − 0.950507i | ||||||||
\(474\) | 0.929312i | 0.0426847i | ||||||||
\(475\) | 2.75302i | 0.126317i | ||||||||
\(476\) | 0.603875i | 0.0276786i | ||||||||
\(477\) | 1.68664 | 0.0772262 | ||||||||
\(478\) | −28.5579 | −1.30621 | ||||||||
\(479\) | − 30.6474i | − 1.40032i | −0.713988 | − | 0.700158i | \(-0.753113\pi\) | ||||
0.713988 | − | 0.700158i | \(-0.246887\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −6.31096 | −0.287456 | ||||||||
\(483\) | 1.31767i | 0.0599559i | ||||||||
\(484\) | 8.41119 | 0.382327 | ||||||||
\(485\) | 5.05861 | 0.229699 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | − 17.6829i | − 0.801290i | −0.916233 | − | 0.400645i | \(-0.868786\pi\) | ||||
0.916233 | − | 0.400645i | \(-0.131214\pi\) | |||||||
\(488\) | 12.0761i | 0.546658i | ||||||||
\(489\) | 21.6015i | 0.976853i | ||||||||
\(490\) | 6.58642 | 0.297544 | ||||||||
\(491\) | 28.5435 | 1.28815 | 0.644074 | − | 0.764963i | \(-0.277243\pi\) | ||||
0.644074 | + | 0.764963i | \(0.277243\pi\) | |||||||
\(492\) | − 5.74094i | − 0.258822i | ||||||||
\(493\) | 0.140047 | 0.00630741 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.40581 | 0.198027 | ||||||||
\(496\) | − 2.08815i | − 0.0937605i | ||||||||
\(497\) | −4.52542 | −0.202993 | ||||||||
\(498\) | 11.2959 | 0.506181 | ||||||||
\(499\) | 27.9409i | 1.25081i | 0.780301 | + | 0.625404i | \(0.215066\pi\) | ||||
−0.780301 | + | 0.625404i | \(0.784934\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | 7.96615i | 0.355901i | ||||||||
\(502\) | − 24.5972i | − 1.09783i | ||||||||
\(503\) | 31.0901 | 1.38624 | 0.693119 | − | 0.720823i | \(-0.256236\pi\) | ||||
0.693119 | + | 0.720823i | \(0.256236\pi\) | |||||||
\(504\) | 0.643104 | 0.0286461 | ||||||||
\(505\) | − 6.81163i | − 0.303113i | ||||||||
\(506\) | −9.02715 | −0.401306 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.85086 | 0.215222 | ||||||||
\(509\) | − 0.0217703i | 0 0.000964950i | −1.00000 | 0.000482475i | \(-0.999846\pi\) | |||||
1.00000 | 0.000482475i | \(-0.000153577\pi\) | ||||||||
\(510\) | −0.939001 | −0.0415797 | ||||||||
\(511\) | −9.55688 | −0.422771 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 2.75302i | − 0.121549i | ||||||||
\(514\) | 26.9463i | 1.18855i | ||||||||
\(515\) | − 12.0858i | − 0.532562i | ||||||||
\(516\) | 4.69202 | 0.206555 | ||||||||
\(517\) | −30.8407 | −1.35637 | ||||||||
\(518\) | − 3.90408i | − 0.171536i | ||||||||
\(519\) | −4.11960 | −0.180831 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0747 | 0.791869 | 0.395934 | − | 0.918279i | \(-0.370421\pi\) | ||||
0.395934 | + | 0.918279i | \(0.370421\pi\) | |||||||
\(522\) | − 0.149145i | − 0.00652790i | ||||||||
\(523\) | −15.3793 | −0.672488 | −0.336244 | − | 0.941775i | \(-0.609157\pi\) | ||||
−0.336244 | + | 0.941775i | \(0.609157\pi\) | |||||||
\(524\) | −1.52781 | −0.0667427 | ||||||||
\(525\) | − 0.643104i | − 0.0280674i | ||||||||
\(526\) | − 24.0465i | − 1.04848i | ||||||||
\(527\) | 1.96077i | 0.0854125i | ||||||||
\(528\) | 4.40581i | 0.191738i | ||||||||
\(529\) | −18.8019 | −0.817476 | ||||||||
\(530\) | 1.68664 | 0.0732632 | ||||||||
\(531\) | 7.85623i | 0.340931i | ||||||||
\(532\) | −1.77048 | −0.0767600 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 7.47650 | 0.323540 | ||||||||
\(535\) | 14.6679i | 0.634147i | ||||||||
\(536\) | −1.45712 | −0.0629381 | ||||||||
\(537\) | 8.78017 | 0.378892 | ||||||||
\(538\) | − 7.17523i | − 0.309346i | ||||||||
\(539\) | 29.0185i | 1.24992i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 5.06339i | 0.217692i | 0.994059 | + | 0.108846i | \(0.0347156\pi\) | ||||
−0.994059 | + | 0.108846i | \(0.965284\pi\) | |||||||
\(542\) | −10.9825 | −0.471741 | ||||||||
\(543\) | −19.4741 | −0.835714 | ||||||||
\(544\) | − 0.939001i | − 0.0402593i | ||||||||
\(545\) | −8.15883 | −0.349486 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.77107 | 0.375024 | 0.187512 | − | 0.982262i | \(-0.439958\pi\) | ||||
0.187512 | + | 0.982262i | \(0.439958\pi\) | |||||||
\(548\) | 6.41119i | 0.273872i | ||||||||
\(549\) | −12.0761 | −0.515394 | ||||||||
\(550\) | 4.40581 | 0.187865 | ||||||||
\(551\) | 0.410599i | 0.0174921i | ||||||||
\(552\) | − 2.04892i | − 0.0872077i | ||||||||
\(553\) | 0.597645i | 0.0254144i | ||||||||
\(554\) | − 16.2107i | − 0.688728i | ||||||||
\(555\) | 6.07069 | 0.257686 | ||||||||
\(556\) | 8.78017 | 0.372362 | ||||||||
\(557\) | − 8.10215i | − 0.343299i | −0.985158 | − | 0.171649i | \(-0.945090\pi\) | ||||
0.985158 | − | 0.171649i | \(-0.0549097\pi\) | |||||||
\(558\) | 2.08815 | 0.0883983 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.643104 | 0.0271761 | ||||||||
\(561\) | − 4.13706i | − 0.174667i | ||||||||
\(562\) | 12.9584 | 0.546616 | ||||||||
\(563\) | 6.86699 | 0.289409 | 0.144704 | − | 0.989475i | \(-0.453777\pi\) | ||||
0.144704 | + | 0.989475i | \(0.453777\pi\) | |||||||
\(564\) | − 7.00000i | − 0.294753i | ||||||||
\(565\) | − 16.8442i | − 0.708639i | ||||||||
\(566\) | − 21.5415i | − 0.905459i | ||||||||
\(567\) | 0.643104i | 0.0270078i | ||||||||
\(568\) | 7.03684 | 0.295259 | ||||||||
\(569\) | −6.93171 | −0.290592 | −0.145296 | − | 0.989388i | \(-0.546413\pi\) | ||||
−0.145296 | + | 0.989388i | \(0.546413\pi\) | |||||||
\(570\) | − 2.75302i | − 0.115311i | ||||||||
\(571\) | 24.2760 | 1.01592 | 0.507960 | − | 0.861380i | \(-0.330400\pi\) | ||||
0.507960 | + | 0.861380i | \(0.330400\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.753020 | 0.0314579 | ||||||||
\(574\) | − 3.69202i | − 0.154102i | ||||||||
\(575\) | −2.04892 | −0.0854458 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 13.8189i | − 0.575289i | −0.957737 | − | 0.287645i | \(-0.907128\pi\) | ||||
0.957737 | − | 0.287645i | \(-0.0928722\pi\) | |||||||
\(578\) | − 16.1183i | − 0.670432i | ||||||||
\(579\) | − 7.84117i | − 0.325868i | ||||||||
\(580\) | − 0.149145i | − 0.00619291i | ||||||||
\(581\) | 7.26444 | 0.301380 | ||||||||
\(582\) | −5.05861 | −0.209686 | ||||||||
\(583\) | 7.43104i | 0.307762i | ||||||||
\(584\) | 14.8605 | 0.614934 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.57971 | −0.395734 | ||||||||
\(587\) | − 27.6165i | − 1.13986i | −0.821694 | − | 0.569928i | \(-0.806971\pi\) | ||||
0.821694 | − | 0.569928i | \(-0.193029\pi\) | |||||||
\(588\) | −6.58642 | −0.271619 | ||||||||
\(589\) | −5.74871 | −0.236871 | ||||||||
\(590\) | 7.85623i | 0.323436i | ||||||||
\(591\) | − 10.2010i | − 0.419615i | ||||||||
\(592\) | 6.07069i | 0.249504i | ||||||||
\(593\) | − 30.3913i | − 1.24802i | −0.781415 | − | 0.624011i | \(-0.785502\pi\) | ||||
0.781415 | − | 0.624011i | \(-0.214498\pi\) | |||||||
\(594\) | −4.40581 | −0.180773 | ||||||||
\(595\) | −0.603875 | −0.0247565 | ||||||||
\(596\) | − 22.6504i | − 0.927797i | ||||||||
\(597\) | −1.65279 | −0.0676443 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.6480 | 0.435066 | 0.217533 | − | 0.976053i | \(-0.430199\pi\) | ||||
0.217533 | + | 0.976053i | \(0.430199\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | 42.2495 | 1.72339 | 0.861696 | − | 0.507424i | \(-0.169402\pi\) | ||||
0.861696 | + | 0.507424i | \(0.169402\pi\) | |||||||
\(602\) | 3.01746 | 0.122982 | ||||||||
\(603\) | − 1.45712i | − 0.0593387i | ||||||||
\(604\) | − 10.2959i | − 0.418934i | ||||||||
\(605\) | 8.41119i | 0.341964i | ||||||||
\(606\) | 6.81163i | 0.276703i | ||||||||
\(607\) | −17.6209 | −0.715209 | −0.357604 | − | 0.933873i | \(-0.616406\pi\) | ||||
−0.357604 | + | 0.933873i | \(0.616406\pi\) | |||||||
\(608\) | 2.75302 | 0.111650 | ||||||||
\(609\) | − 0.0959157i | − 0.00388670i | ||||||||
\(610\) | −12.0761 | −0.488946 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.939001 | 0.0379569 | ||||||||
\(613\) | 27.9527i | 1.12900i | 0.825433 | + | 0.564500i | \(0.190931\pi\) | ||||
−0.825433 | + | 0.564500i | \(0.809069\pi\) | |||||||
\(614\) | −19.0140 | −0.767343 | ||||||||
\(615\) | 5.74094 | 0.231497 | ||||||||
\(616\) | 2.83340i | 0.114161i | ||||||||
\(617\) | − 14.9065i | − 0.600112i | −0.953922 | − | 0.300056i | \(-0.902995\pi\) | ||||
0.953922 | − | 0.300056i | \(-0.0970054\pi\) | |||||||
\(618\) | 12.0858i | 0.486160i | ||||||||
\(619\) | − 33.7493i | − 1.35650i | −0.734832 | − | 0.678249i | \(-0.762739\pi\) | ||||
0.734832 | − | 0.678249i | \(-0.237261\pi\) | |||||||
\(620\) | 2.08815 | 0.0838620 | ||||||||
\(621\) | 2.04892 | 0.0822202 | ||||||||
\(622\) | 3.74764i | 0.150267i | ||||||||
\(623\) | 4.80817 | 0.192635 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 25.1196i | 1.00398i | ||||||||
\(627\) | 12.1293 | 0.484397 | ||||||||
\(628\) | −0.994623 | −0.0396898 | ||||||||
\(629\) | − 5.70038i | − 0.227289i | ||||||||
\(630\) | 0.643104i | 0.0256219i | ||||||||
\(631\) | − 37.2519i | − 1.48297i | −0.670967 | − | 0.741487i | \(-0.734121\pi\) | ||||
0.670967 | − | 0.741487i | \(-0.265879\pi\) | |||||||
\(632\) | − 0.929312i | − 0.0369661i | ||||||||
\(633\) | 11.7453 | 0.466832 | ||||||||
\(634\) | 12.6679 | 0.503105 | ||||||||
\(635\) | 4.85086i | 0.192500i | ||||||||
\(636\) | −1.68664 | −0.0668798 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.657105 | 0.0260150 | ||||||||
\(639\) | 7.03684i | 0.278373i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −24.8203 | −0.980341 | −0.490170 | − | 0.871627i | \(-0.663065\pi\) | ||||
−0.490170 | + | 0.871627i | \(0.663065\pi\) | |||||||
\(642\) | − 14.6679i | − 0.578894i | ||||||||
\(643\) | 5.66248i | 0.223306i | 0.993747 | + | 0.111653i | \(0.0356146\pi\) | ||||
−0.993747 | + | 0.111653i | \(0.964385\pi\) | |||||||
\(644\) | − 1.31767i | − 0.0519234i | ||||||||
\(645\) | 4.69202i | 0.184748i | ||||||||
\(646\) | −2.58509 | −0.101709 | ||||||||
\(647\) | 27.0465 | 1.06331 | 0.531654 | − | 0.846961i | \(-0.321571\pi\) | ||||
0.531654 | + | 0.846961i | \(0.321571\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | −34.6131 | −1.35868 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.34290 | 0.0526322 | ||||||||
\(652\) | − 21.6015i | − 0.845979i | ||||||||
\(653\) | 42.7741 | 1.67388 | 0.836939 | − | 0.547296i | \(-0.184343\pi\) | ||||
0.836939 | + | 0.547296i | \(0.184343\pi\) | |||||||
\(654\) | 8.15883 | 0.319036 | ||||||||
\(655\) | − 1.52781i | − 0.0596965i | ||||||||
\(656\) | 5.74094i | 0.224146i | ||||||||
\(657\) | 14.8605i | 0.579765i | ||||||||
\(658\) | − 4.50173i | − 0.175496i | ||||||||
\(659\) | 21.5623 | 0.839946 | 0.419973 | − | 0.907537i | \(-0.362040\pi\) | ||||
0.419973 | + | 0.907537i | \(0.362040\pi\) | |||||||
\(660\) | −4.40581 | −0.171496 | ||||||||
\(661\) | 48.5002i | 1.88644i | 0.332170 | + | 0.943219i | \(0.392219\pi\) | ||||
−0.332170 | + | 0.943219i | \(0.607781\pi\) | |||||||
\(662\) | −6.43057 | −0.249931 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.2959 | −0.438366 | ||||||||
\(665\) | − 1.77048i | − 0.0686562i | ||||||||
\(666\) | −6.07069 | −0.235234 | ||||||||
\(667\) | −0.305586 | −0.0118323 | ||||||||
\(668\) | − 7.96615i | − 0.308220i | ||||||||
\(669\) | 9.73855i | 0.376514i | ||||||||
\(670\) | − 1.45712i | − 0.0562936i | ||||||||
\(671\) | − 53.2049i | − 2.05395i | ||||||||
\(672\) | −0.643104 | −0.0248083 | ||||||||
\(673\) | −30.4711 | −1.17458 | −0.587288 | − | 0.809378i | \(-0.699804\pi\) | ||||
−0.587288 | + | 0.809378i | \(0.699804\pi\) | |||||||
\(674\) | − 10.5496i | − 0.406355i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.57971 | −0.329745 | −0.164873 | − | 0.986315i | \(-0.552721\pi\) | ||||
−0.164873 | + | 0.986315i | \(0.552721\pi\) | |||||||
\(678\) | 16.8442i | 0.646896i | ||||||||
\(679\) | −3.25321 | −0.124847 | ||||||||
\(680\) | 0.939001 | 0.0360090 | ||||||||
\(681\) | 25.2500i | 0.967581i | ||||||||
\(682\) | 9.19998i | 0.352285i | ||||||||
\(683\) | 27.8890i | 1.06714i | 0.845755 | + | 0.533572i | \(0.179151\pi\) | ||||
−0.845755 | + | 0.533572i | \(0.820849\pi\) | |||||||
\(684\) | 2.75302i | 0.105264i | ||||||||
\(685\) | −6.41119 | −0.244959 | ||||||||
\(686\) | −8.73748 | −0.333599 | ||||||||
\(687\) | 23.7845i | 0.907434i | ||||||||
\(688\) | −4.69202 | −0.178882 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 2.04892 | 0.0780010 | ||||||||
\(691\) | − 39.4198i | − 1.49960i | −0.661664 | − | 0.749800i | \(-0.730150\pi\) | ||||
0.661664 | − | 0.749800i | \(-0.269850\pi\) | |||||||
\(692\) | 4.11960 | 0.156604 | ||||||||
\(693\) | −2.83340 | −0.107632 | ||||||||
\(694\) | 9.87130i | 0.374709i | ||||||||
\(695\) | 8.78017i | 0.333051i | ||||||||
\(696\) | 0.149145i | 0.00565332i | ||||||||
\(697\) | − 5.39075i | − 0.204189i | ||||||||
\(698\) | 30.5338 | 1.15572 | ||||||||
\(699\) | −0.603875 | −0.0228407 | ||||||||
\(700\) | 0.643104i | 0.0243071i | ||||||||
\(701\) | 51.7101 | 1.95306 | 0.976531 | − | 0.215376i | \(-0.0690977\pi\) | ||||
0.976531 | + | 0.215376i | \(0.0690977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7127 | 0.630332 | ||||||||
\(704\) | − 4.40581i | − 0.166050i | ||||||||
\(705\) | 7.00000 | 0.263635 | ||||||||
\(706\) | −24.7047 | −0.929773 | ||||||||
\(707\) | 4.38059i | 0.164749i | ||||||||
\(708\) | − 7.85623i | − 0.295255i | ||||||||
\(709\) | − 12.7278i | − 0.478002i | −0.971019 | − | 0.239001i | \(-0.923180\pi\) | ||||
0.971019 | − | 0.239001i | \(-0.0768200\pi\) | |||||||
\(710\) | 7.03684i | 0.264088i | ||||||||
\(711\) | 0.929312 | 0.0348519 | ||||||||
\(712\) | −7.47650 | −0.280194 | ||||||||
\(713\) | − 4.27844i | − 0.160229i | ||||||||
\(714\) | 0.603875 | 0.0225995 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.78017 | −0.328130 | ||||||||
\(717\) | 28.5579i | 1.06652i | ||||||||
\(718\) | 11.5888 | 0.432491 | ||||||||
\(719\) | 11.7342 | 0.437613 | 0.218807 | − | 0.975768i | \(-0.429784\pi\) | ||||
0.218807 | + | 0.975768i | \(0.429784\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | 7.77240i | 0.289459i | ||||||||
\(722\) | 11.4209i | 0.425041i | ||||||||
\(723\) | 6.31096i | 0.234707i | ||||||||
\(724\) | 19.4741 | 0.723750 | ||||||||
\(725\) | 0.149145 | 0.00553910 | ||||||||
\(726\) | − 8.41119i | − 0.312169i | ||||||||
\(727\) | 6.84979 | 0.254045 | 0.127022 | − | 0.991900i | \(-0.459458\pi\) | ||||
0.127022 | + | 0.991900i | \(0.459458\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.8605i | 0.550013i | ||||||||
\(731\) | 4.40581 | 0.162955 | ||||||||
\(732\) | 12.0761 | 0.446344 | ||||||||
\(733\) | 0.224144i | 0.00827896i | 0.999991 | + | 0.00413948i | \(0.00131764\pi\) | ||||
−0.999991 | + | 0.00413948i | \(0.998682\pi\) | |||||||
\(734\) | − 20.5579i | − 0.758807i | ||||||||
\(735\) | − 6.58642i | − 0.242944i | ||||||||
\(736\) | 2.04892i | 0.0755241i | ||||||||
\(737\) | 6.41981 | 0.236477 | ||||||||
\(738\) | −5.74094 | −0.211327 | ||||||||
\(739\) | − 2.39075i | − 0.0879451i | −0.999033 | − | 0.0439725i | \(-0.985999\pi\) | ||||
0.999033 | − | 0.0439725i | \(-0.0140014\pi\) | |||||||
\(740\) | −6.07069 | −0.223163 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.08469 | −0.0398202 | ||||||||
\(743\) | 25.5144i | 0.936033i | 0.883720 | + | 0.468016i | \(0.155031\pi\) | ||||
−0.883720 | + | 0.468016i | \(0.844969\pi\) | |||||||
\(744\) | −2.08815 | −0.0765551 | ||||||||
\(745\) | 22.6504 | 0.829846 | ||||||||
\(746\) | 1.31037i | 0.0479761i | ||||||||
\(747\) | − 11.2959i | − 0.413295i | ||||||||
\(748\) | 4.13706i | 0.151266i | ||||||||
\(749\) | − 9.43296i | − 0.344673i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −18.2755 | −0.666881 | −0.333440 | − | 0.942771i | \(-0.608210\pi\) | ||||
−0.333440 | + | 0.942771i | \(0.608210\pi\) | |||||||
\(752\) | 7.00000i | 0.255264i | ||||||||
\(753\) | −24.5972 | −0.896371 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.2959 | 0.374706 | ||||||||
\(756\) | − 0.643104i | − 0.0233895i | ||||||||
\(757\) | −20.2301 | −0.735276 | −0.367638 | − | 0.929969i | \(-0.619833\pi\) | ||||
−0.367638 | + | 0.929969i | \(0.619833\pi\) | |||||||
\(758\) | 28.1551 | 1.02264 | ||||||||
\(759\) | 9.02715i | 0.327665i | ||||||||
\(760\) | 2.75302i | 0.0998625i | ||||||||
\(761\) | − 0.217440i | − 0.00788218i | −0.999992 | − | 0.00394109i | \(-0.998746\pi\) | ||||
0.999992 | − | 0.00394109i | \(-0.00125449\pi\) | |||||||
\(762\) | − 4.85086i | − 0.175728i | ||||||||
\(763\) | 5.24698 | 0.189953 | ||||||||
\(764\) | −0.753020 | −0.0272433 | ||||||||
\(765\) | 0.939001i | 0.0339497i | ||||||||
\(766\) | −18.6679 | −0.674497 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | − 0.124982i | − 0.00450696i | −0.999997 | − | 0.00225348i | \(-0.999283\pi\) | ||||
0.999997 | − | 0.00225348i | \(-0.000717305\pi\) | |||||||
\(770\) | −2.83340 | −0.102109 | ||||||||
\(771\) | 26.9463 | 0.970447 | ||||||||
\(772\) | 7.84117i | 0.282210i | ||||||||
\(773\) | − 11.7028i | − 0.420920i | −0.977603 | − | 0.210460i | \(-0.932504\pi\) | ||||
0.977603 | − | 0.210460i | \(-0.0674961\pi\) | |||||||
\(774\) | − 4.69202i | − 0.168651i | ||||||||
\(775\) | 2.08815i | 0.0750084i | ||||||||
\(776\) | 5.05861 | 0.181593 | ||||||||
\(777\) | −3.90408 | −0.140058 | ||||||||
\(778\) | 29.6752i | 1.06391i | ||||||||
\(779\) | 15.8049 | 0.566270 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.0030 | −1.10937 | ||||||||
\(782\) | − 1.92394i | − 0.0687998i | ||||||||
\(783\) | −0.149145 | −0.00533000 | ||||||||
\(784\) | 6.58642 | 0.235229 | ||||||||
\(785\) | − 0.994623i | − 0.0354996i | ||||||||
\(786\) | 1.52781i | 0.0544952i | ||||||||
\(787\) | − 50.6926i | − 1.80700i | −0.428592 | − | 0.903498i | \(-0.640990\pi\) | ||||
0.428592 | − | 0.903498i | \(-0.359010\pi\) | |||||||
\(788\) | 10.2010i | 0.363397i | ||||||||
\(789\) | −24.0465 | −0.856079 | ||||||||
\(790\) | 0.929312 | 0.0330635 | ||||||||
\(791\) | 10.8325i | 0.385161i | ||||||||
\(792\) | 4.40581 | 0.156554 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 28.7536 | 1.02043 | ||||||||
\(795\) | − 1.68664i | − 0.0598191i | ||||||||
\(796\) | 1.65279 | 0.0585817 | ||||||||
\(797\) | −45.7977 | −1.62224 | −0.811120 | − | 0.584880i | \(-0.801141\pi\) | ||||
−0.811120 | + | 0.584880i | \(0.801141\pi\) | |||||||
\(798\) | 1.77048i | 0.0626743i | ||||||||
\(799\) | − 6.57301i | − 0.232536i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | − 7.47650i | − 0.264169i | ||||||||
\(802\) | −18.6993 | −0.660296 | ||||||||
\(803\) | −65.4728 | −2.31048 | ||||||||
\(804\) | 1.45712i | 0.0513888i | ||||||||
\(805\) | 1.31767 | 0.0464417 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.17523 | −0.252580 | ||||||||
\(808\) | − 6.81163i | − 0.239632i | ||||||||
\(809\) | 22.5579 | 0.793095 | 0.396548 | − | 0.918014i | \(-0.370208\pi\) | ||||
0.396548 | + | 0.918014i | \(0.370208\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | − 19.2728i | − 0.676759i | −0.941010 | − | 0.338380i | \(-0.890121\pi\) | ||||
0.941010 | − | 0.338380i | \(-0.109879\pi\) | |||||||
\(812\) | 0.0959157i | 0.00336598i | ||||||||
\(813\) | 10.9825i | 0.385175i | ||||||||
\(814\) | − 26.7463i | − 0.937458i | ||||||||
\(815\) | 21.6015 | 0.756667 | ||||||||
\(816\) | −0.939001 | −0.0328716 | ||||||||
\(817\) | 12.9172i | 0.451917i | ||||||||
\(818\) | 10.6233 | 0.371433 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.74094 | −0.200482 | ||||||||
\(821\) | − 11.5036i | − 0.401480i | −0.979645 | − | 0.200740i | \(-0.935665\pi\) | ||||
0.979645 | − | 0.200740i | \(-0.0643347\pi\) | |||||||
\(822\) | 6.41119 | 0.223616 | ||||||||
\(823\) | 25.2610 | 0.880542 | 0.440271 | − | 0.897865i | \(-0.354882\pi\) | ||||
0.440271 | + | 0.897865i | \(0.354882\pi\) | |||||||
\(824\) | − 12.0858i | − 0.421027i | ||||||||
\(825\) | − 4.40581i | − 0.153391i | ||||||||
\(826\) | − 5.05238i | − 0.175795i | ||||||||
\(827\) | − 7.09677i | − 0.246779i | −0.992358 | − | 0.123389i | \(-0.960624\pi\) | ||||
0.992358 | − | 0.123389i | \(-0.0393764\pi\) | |||||||
\(828\) | −2.04892 | −0.0712048 | ||||||||
\(829\) | −10.1226 | −0.351572 | −0.175786 | − | 0.984428i | \(-0.556247\pi\) | ||||
−0.175786 | + | 0.984428i | \(0.556247\pi\) | |||||||
\(830\) | − 11.2959i | − 0.392086i | ||||||||
\(831\) | −16.2107 | −0.562344 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.18465 | −0.214286 | ||||||||
\(834\) | − 8.78017i | − 0.304032i | ||||||||
\(835\) | 7.96615 | 0.275680 | ||||||||
\(836\) | −12.1293 | −0.419500 | ||||||||
\(837\) | − 2.08815i | − 0.0721769i | ||||||||
\(838\) | 19.4198i | 0.670846i | ||||||||
\(839\) | − 43.0844i | − 1.48744i | −0.668492 | − | 0.743720i | \(-0.733060\pi\) | ||||
0.668492 | − | 0.743720i | \(-0.266940\pi\) | |||||||
\(840\) | − 0.643104i | − 0.0221892i | ||||||||
\(841\) | −28.9778 | −0.999233 | ||||||||
\(842\) | 20.5719 | 0.708956 | ||||||||
\(843\) | − 12.9584i | − 0.446310i | ||||||||
\(844\) | −11.7453 | −0.404288 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.00000 | −0.240665 | ||||||||
\(847\) | − 5.40927i | − 0.185865i | ||||||||
\(848\) | 1.68664 | 0.0579196 | ||||||||
\(849\) | −21.5415 | −0.739304 | ||||||||
\(850\) | 0.939001i | 0.0322075i | ||||||||
\(851\) | 12.4383i | 0.426381i | ||||||||
\(852\) | − 7.03684i | − 0.241078i | ||||||||
\(853\) | 43.7837i | 1.49913i | 0.661933 | + | 0.749563i | \(0.269737\pi\) | ||||
−0.661933 | + | 0.749563i | \(0.730263\pi\) | |||||||
\(854\) | 7.76617 | 0.265753 | ||||||||
\(855\) | −2.75302 | −0.0941513 | ||||||||
\(856\) | 14.6679i | 0.501337i | ||||||||
\(857\) | 16.3067 | 0.557025 | 0.278512 | − | 0.960433i | \(-0.410159\pi\) | ||||
0.278512 | + | 0.960433i | \(0.410159\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.8629 | −1.08715 | −0.543575 | − | 0.839361i | \(-0.682930\pi\) | ||||
−0.543575 | + | 0.839361i | \(0.682930\pi\) | |||||||
\(860\) | − 4.69202i | − 0.159997i | ||||||||
\(861\) | −3.69202 | −0.125824 | ||||||||
\(862\) | 33.8079 | 1.15150 | ||||||||
\(863\) | 0.511418i | 0.0174089i | 0.999962 | + | 0.00870443i | \(0.00277074\pi\) | ||||
−0.999962 | + | 0.00870443i | \(0.997229\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 4.11960i | 0.140071i | ||||||||
\(866\) | − 27.2838i | − 0.927142i | ||||||||
\(867\) | −16.1183 | −0.547405 | ||||||||
\(868\) | −1.34290 | −0.0455808 | ||||||||
\(869\) | 4.09438i | 0.138892i | ||||||||
\(870\) | −0.149145 | −0.00505649 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.15883 | −0.276293 | ||||||||
\(873\) | 5.05861i | 0.171208i | ||||||||
\(874\) | 5.64071 | 0.190800 | ||||||||
\(875\) | −0.643104 | −0.0217409 | ||||||||
\(876\) | − 14.8605i | − 0.502091i | ||||||||
\(877\) | − 3.83638i | − 0.129545i | −0.997900 | − | 0.0647727i | \(-0.979368\pi\) | ||||
0.997900 | − | 0.0647727i | \(-0.0206322\pi\) | |||||||
\(878\) | 1.56943i | 0.0529658i | ||||||||
\(879\) | 9.57971i | 0.323116i | ||||||||
\(880\) | 4.40581 | 0.148520 | ||||||||
\(881\) | 0.499336 | 0.0168231 | 0.00841153 | − | 0.999965i | \(-0.497322\pi\) | ||||
0.00841153 | + | 0.999965i | \(0.497322\pi\) | |||||||
\(882\) | 6.58642i | 0.221776i | ||||||||
\(883\) | 38.8993 | 1.30907 | 0.654533 | − | 0.756034i | \(-0.272865\pi\) | ||||
0.654533 | + | 0.756034i | \(0.272865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.85623 | 0.264084 | ||||||||
\(886\) | 38.0489i | 1.27828i | ||||||||
\(887\) | −8.32245 | −0.279441 | −0.139720 | − | 0.990191i | \(-0.544620\pi\) | ||||
−0.139720 | + | 0.990191i | \(0.544620\pi\) | |||||||
\(888\) | 6.07069 | 0.203719 | ||||||||
\(889\) | − 3.11960i | − 0.104628i | ||||||||
\(890\) | − 7.47650i | − 0.250613i | ||||||||
\(891\) | 4.40581i | 0.147600i | ||||||||
\(892\) | − 9.73855i | − 0.326071i | ||||||||
\(893\) | 19.2711 | 0.644884 | ||||||||
\(894\) | −22.6504 | −0.757543 | ||||||||
\(895\) | − 8.78017i | − 0.293489i | ||||||||
\(896\) | 0.643104 | 0.0214846 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.2373 | 0.808809 | ||||||||
\(899\) | 0.311436i | 0.0103870i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −1.58376 | −0.0527627 | ||||||||
\(902\) | − 25.2935i | − 0.842182i | ||||||||
\(903\) | − 3.01746i | − 0.100415i | ||||||||
\(904\) | − 16.8442i | − 0.560228i | ||||||||
\(905\) | 19.4741i | 0.647341i | ||||||||
\(906\) | −10.2959 | −0.342058 | ||||||||
\(907\) | −27.4566 | −0.911683 | −0.455842 | − | 0.890061i | \(-0.650662\pi\) | ||||
−0.455842 | + | 0.890061i | \(0.650662\pi\) | |||||||
\(908\) | − 25.2500i | − 0.837949i | ||||||||
\(909\) | 6.81163 | 0.225927 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.7224 | −0.984748 | −0.492374 | − | 0.870384i | \(-0.663871\pi\) | ||||
−0.492374 | + | 0.870384i | \(0.663871\pi\) | |||||||
\(912\) | − 2.75302i | − 0.0911616i | ||||||||
\(913\) | 49.7676 | 1.64707 | ||||||||
\(914\) | 9.75063 | 0.322522 | ||||||||
\(915\) | 12.0761i | 0.399222i | ||||||||
\(916\) | − 23.7845i | − 0.785861i | ||||||||
\(917\) | 0.982542i | 0.0324464i | ||||||||
\(918\) | − 0.939001i | − 0.0309917i | ||||||||
\(919\) | −2.02954 | −0.0669483 | −0.0334742 | − | 0.999440i | \(-0.510657\pi\) | ||||
−0.0334742 | + | 0.999440i | \(0.510657\pi\) | |||||||
\(920\) | −2.04892 | −0.0675508 | ||||||||
\(921\) | 19.0140i | 0.626533i | ||||||||
\(922\) | 31.0358 | 1.02211 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.83340 | 0.0932119 | ||||||||
\(925\) | − 6.07069i | − 0.199603i | ||||||||
\(926\) | −33.1618 | −1.08976 | ||||||||
\(927\) | 12.0858 | 0.396948 | ||||||||
\(928\) | − 0.149145i | − 0.00489592i | ||||||||
\(929\) | − 0.815938i | − 0.0267701i | −0.999910 | − | 0.0133850i | \(-0.995739\pi\) | ||||
0.999910 | − | 0.0133850i | \(-0.00426072\pi\) | |||||||
\(930\) | − 2.08815i | − 0.0684730i | ||||||||
\(931\) | − 18.1325i | − 0.594270i | ||||||||
\(932\) | 0.603875 | 0.0197806 | ||||||||
\(933\) | 3.74764 | 0.122692 | ||||||||
\(934\) | 16.1153i | 0.527308i | ||||||||
\(935\) | −4.13706 | −0.135296 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.5864 | −0.966546 | −0.483273 | − | 0.875470i | \(-0.660552\pi\) | ||||
−0.483273 | + | 0.875470i | \(0.660552\pi\) | |||||||
\(938\) | 0.937082i | 0.0305968i | ||||||||
\(939\) | 25.1196 | 0.819747 | ||||||||
\(940\) | −7.00000 | −0.228315 | ||||||||
\(941\) | − 30.2573i | − 0.986358i | −0.869928 | − | 0.493179i | \(-0.835835\pi\) | ||||
0.869928 | − | 0.493179i | \(-0.164165\pi\) | |||||||
\(942\) | 0.994623i | 0.0324066i | ||||||||
\(943\) | 11.7627i | 0.383047i | ||||||||
\(944\) | 7.85623i | 0.255699i | ||||||||
\(945\) | 0.643104 | 0.0209202 | ||||||||
\(946\) | 20.6722 | 0.672110 | ||||||||
\(947\) | 7.12152i | 0.231418i | 0.993283 | + | 0.115709i | \(0.0369141\pi\) | ||||
−0.993283 | + | 0.115709i | \(0.963086\pi\) | |||||||
\(948\) | −0.929312 | −0.0301827 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.75302 | −0.0893198 | ||||||||
\(951\) | − 12.6679i | − 0.410783i | ||||||||
\(952\) | −0.603875 | −0.0195717 | ||||||||
\(953\) | 38.3279 | 1.24156 | 0.620782 | − | 0.783983i | \(-0.286815\pi\) | ||||
0.620782 | + | 0.783983i | \(0.286815\pi\) | |||||||
\(954\) | 1.68664i | 0.0546071i | ||||||||
\(955\) | − 0.753020i | − 0.0243672i | ||||||||
\(956\) | − 28.5579i | − 0.923630i | ||||||||
\(957\) | − 0.657105i | − 0.0212412i | ||||||||
\(958\) | 30.6474 | 0.990173 | ||||||||
\(959\) | 4.12306 | 0.133141 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 26.6396 | 0.859343 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.6679 | −0.472665 | ||||||||
\(964\) | − 6.31096i | − 0.203262i | ||||||||
\(965\) | −7.84117 | −0.252416 | ||||||||
\(966\) | −1.31767 | −0.0423952 | ||||||||
\(967\) | 50.6015i | 1.62723i | 0.581401 | + | 0.813617i | \(0.302505\pi\) | ||||
−0.581401 | + | 0.813617i | \(0.697495\pi\) | |||||||
\(968\) | 8.41119i | 0.270346i | ||||||||
\(969\) | 2.58509i | 0.0830450i | ||||||||
\(970\) | 5.05861i | 0.162422i | ||||||||
\(971\) | −27.3026 | −0.876182 | −0.438091 | − | 0.898931i | \(-0.644345\pi\) | ||||
−0.438091 | + | 0.898931i | \(0.644345\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | − 5.64656i | − 0.181020i | ||||||||
\(974\) | 17.6829 | 0.566597 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0761 | −0.386545 | ||||||||
\(977\) | 46.5491i | 1.48924i | 0.667490 | + | 0.744619i | \(0.267369\pi\) | ||||
−0.667490 | + | 0.744619i | \(0.732631\pi\) | |||||||
\(978\) | −21.6015 | −0.690739 | ||||||||
\(979\) | 32.9401 | 1.05277 | ||||||||
\(980\) | 6.58642i | 0.210395i | ||||||||
\(981\) | − 8.15883i | − 0.260492i | ||||||||
\(982\) | 28.5435i | 0.910859i | ||||||||
\(983\) | 1.10321i | 0.0351870i | 0.999845 | + | 0.0175935i | \(0.00560047\pi\) | ||||
−0.999845 | + | 0.0175935i | \(0.994400\pi\) | |||||||
\(984\) | 5.74094 | 0.183014 | ||||||||
\(985\) | −10.2010 | −0.325032 | ||||||||
\(986\) | 0.140047i | 0.00446001i | ||||||||
\(987\) | −4.50173 | −0.143292 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.61356 | −0.305694 | ||||||||
\(990\) | 4.40581i | 0.140026i | ||||||||
\(991\) | −51.4752 | −1.63516 | −0.817581 | − | 0.575813i | \(-0.804686\pi\) | ||||
−0.817581 | + | 0.575813i | \(0.804686\pi\) | |||||||
\(992\) | 2.08815 | 0.0662987 | ||||||||
\(993\) | 6.43057i | 0.204068i | ||||||||
\(994\) | − 4.52542i | − 0.143538i | ||||||||
\(995\) | 1.65279i | 0.0523971i | ||||||||
\(996\) | 11.2959i | 0.357924i | ||||||||
\(997\) | −28.9715 | −0.917537 | −0.458769 | − | 0.888556i | \(-0.651709\pi\) | ||||
−0.458769 | + | 0.888556i | \(0.651709\pi\) | |||||||
\(998\) | −27.9409 | −0.884454 | ||||||||
\(999\) | 6.07069i | 0.192068i |
(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 | 5070.2.b.y.1351.5 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bv.1.2 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bq.1.2 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.y.1351.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bq.1.2 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.bv.1.2 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.y.1351.2 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.y.1351.5 | 6 | 1.1 | even | 1 | trivial |