Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(287,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.d (of order \(2\), degree \(1\), 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: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 287.3 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.287 |
Dual form | 624.2.d.g.287.4 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.18614 | − | 1.26217i | 0.684819 | − | 0.728714i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.939764i | 0.420275i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) | ||||
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.52434i | 0.954110i | 0.878873 | + | 0.477055i | \(0.158296\pi\) | ||||
−0.878873 | + | 0.477055i | \(0.841704\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.186141 | − | 2.99422i | −0.0620469 | − | 0.998073i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.18614 | + | 1.11469i | 0.306260 | + | 0.287812i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.10891i | − | 0.996557i | −0.867017 | − | 0.498279i | \(-0.833966\pi\) | ||
0.867017 | − | 0.498279i | \(-0.166034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.18614 | + | 2.99422i | 0.695273 | + | 0.653392i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.74456 | 0.989310 | 0.494655 | − | 0.869090i | \(-0.335294\pi\) | ||||
0.494655 | + | 0.869090i | \(0.335294\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.11684 | 0.823369 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | − | 3.31662i | −0.769800 | − | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.63325i | 1.19137i | 0.803219 | + | 0.595683i | \(0.203119\pi\) | ||||
−0.803219 | + | 0.595683i | \(0.796881\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.74456 | − | 5.04868i | 0.825922 | − | 0.878862i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.37228 | −0.400989 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.372281 | 0.0612027 | 0.0306013 | − | 0.999532i | \(-0.490258\pi\) | ||||
0.0306013 | + | 0.999532i | \(0.490258\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.18614 | − | 1.26217i | 0.189935 | − | 0.202109i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.04868i | − | 0.788471i | −0.919010 | − | 0.394235i | \(-0.871009\pi\) | ||
0.919010 | − | 0.394235i | \(-0.128991\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.644810i | − | 0.0983326i | −0.998791 | − | 0.0491663i | \(-0.984344\pi\) | ||
0.998791 | − | 0.0491663i | \(-0.0156564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.81386 | − | 0.174928i | 0.419465 | − | 0.0260768i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.37228 | −0.929493 | −0.464746 | − | 0.885444i | \(-0.653854\pi\) | ||||
−0.464746 | + | 0.885444i | \(0.653854\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.627719 | 0.0896741 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.18614 | − | 4.87375i | −0.726205 | − | 0.682461i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.9769i | − | 1.64515i | −0.568656 | − | 0.822575i | \(-0.692536\pi\) | ||
0.568656 | − | 0.822575i | \(-0.307464\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.75906i | 0.506871i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.37228 | + | 4.10891i | 0.579123 | + | 0.544239i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.4891 | −1.47103 | −0.735516 | − | 0.677507i | \(-0.763060\pi\) | ||||
−0.735516 | + | 0.677507i | \(0.763060\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.55842 | − | 0.469882i | 0.952272 | − | 0.0591996i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.939764i | 0.116563i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46410i | 0.423207i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.62772 | − | 5.98844i | 0.677498 | − | 0.720923i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1168 | 1.31933 | 0.659663 | − | 0.751561i | \(-0.270699\pi\) | ||||
0.659663 | + | 0.751561i | \(0.270699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7446 | −1.25756 | −0.628778 | − | 0.777585i | \(-0.716445\pi\) | ||||
−0.628778 | + | 0.777585i | \(0.716445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.88316 | − | 5.19615i | 0.563858 | − | 0.600000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.0974i | 1.15070i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.58457i | − | 0.178279i | −0.996019 | − | 0.0891393i | \(-0.971588\pi\) | ||
0.996019 | − | 0.0891393i | \(-0.0284116\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.93070 | + | 1.11469i | −0.992300 | + | 0.123855i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.86141 | 0.418828 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.04868i | 0.535159i | 0.963536 | + | 0.267579i | \(0.0862237\pi\) | ||||
−0.963536 | + | 0.267579i | \(0.913776\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.52434i | 0.264623i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.37228 | + | 7.86797i | 0.868165 | + | 0.815870i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.25544 | −0.334001 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.74456 | −0.278668 | −0.139334 | − | 0.990245i | \(-0.544496\pi\) | ||||
−0.139334 | + | 0.990245i | \(0.544496\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.744563 | − | 11.9769i | −0.0748314 | − | 1.20372i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0974i | 1.00472i | 0.864657 | + | 0.502362i | \(0.167536\pi\) | ||||
−0.864657 | + | 0.502362i | \(0.832464\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.51278i | 0.838789i | 0.907804 | + | 0.419394i | \(0.137758\pi\) | ||||
−0.907804 | + | 0.419394i | \(0.862242\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.81386 | + | 2.99422i | −0.274605 | + | 0.292206i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.4891 | −1.69074 | −0.845369 | − | 0.534183i | \(-0.820619\pi\) | ||||
−0.845369 | + | 0.534183i | \(0.820619\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.3723 | −1.18505 | −0.592525 | − | 0.805552i | \(-0.701869\pi\) | ||||
−0.592525 | + | 0.805552i | \(0.701869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.441578 | − | 0.469882i | 0.0419127 | − | 0.0445992i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.1947i | 1.89976i | 0.312618 | + | 0.949879i | \(0.398794\pi\) | ||||
−0.312618 | + | 0.949879i | \(0.601206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.45877i | 0.415782i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.186141 | − | 2.99422i | −0.0172087 | − | 0.276816i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.3723 | 0.950825 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.37228 | − | 5.98844i | −0.574569 | − | 0.539959i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.56768i | 0.766317i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.63325i | 0.588606i | 0.955712 | + | 0.294303i | \(0.0950874\pi\) | ||||
−0.955712 | + | 0.294303i | \(0.904913\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.813859 | − | 0.764836i | −0.0716563 | − | 0.0673400i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.11684 | −0.621802 | −0.310901 | − | 0.950442i | \(-0.600631\pi\) | ||||
−0.310901 | + | 0.950442i | \(0.600631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.74456 | −0.758250 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.11684 | − | 3.75906i | 0.268255 | − | 0.323528i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.1460i | − | 1.29401i | −0.762485 | − | 0.647006i | \(-0.776021\pi\) | ||
0.762485 | − | 0.647006i | \(-0.223979\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.8395i | − | 1.76758i | −0.467880 | − | 0.883792i | \(-0.654982\pi\) | ||
0.467880 | − | 0.883792i | \(-0.345018\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.55842 | + | 8.04290i | −0.636534 | + | 0.677334i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.744563 | − | 0.792287i | 0.0614105 | − | 0.0653467i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 17.0256i | − | 1.39479i | −0.716688 | − | 0.697394i | \(-0.754343\pi\) | ||
0.716688 | − | 0.697394i | \(-0.245657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.69349i | − | 0.463329i | −0.972796 | − | 0.231665i | \(-0.925583\pi\) | ||
0.972796 | − | 0.231665i | \(-0.0744172\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.3030 | + | 0.764836i | −0.994637 | + | 0.0618333i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.23369 | −0.500702 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.74456 | 0.219040 | 0.109520 | − | 0.993985i | \(-0.465069\pi\) | ||||
0.109520 | + | 0.993985i | \(0.465069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.1168 | − | 14.2063i | −1.19884 | − | 1.12663i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.9769i | 0.943910i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.22316i | 0.565761i | 0.959155 | + | 0.282881i | \(0.0912900\pi\) | ||||
−0.959155 | + | 0.282881i | \(0.908710\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.74456 | + | 4.45877i | 0.369364 | + | 0.347115i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.00000 | 0.309529 | 0.154765 | − | 0.987951i | \(-0.450538\pi\) | ||||
0.154765 | + | 0.987951i | \(0.450538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3723 | − | 0.644810i | 0.793188 | − | 0.0493099i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.33830i | − | 0.481892i | −0.970539 | − | 0.240946i | \(-0.922542\pi\) | ||
0.970539 | − | 0.240946i | \(-0.0774576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.3923i | 0.785584i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.2337 | + | 15.1460i | −1.06987 | + | 1.13845i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.62772 | −0.420635 | −0.210318 | − | 0.977633i | \(-0.567450\pi\) | ||||
−0.210318 | + | 0.977633i | \(0.567450\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.2337 | −1.80128 | −0.900638 | − | 0.434570i | \(-0.856900\pi\) | ||||
−0.900638 | + | 0.434570i | \(0.856900\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.6277 | + | 14.5012i | −1.00739 | + | 1.07196i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.349857i | 0.0257220i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16.4356i | − | 1.20189i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.37228 | − | 10.0974i | 0.608994 | − | 0.734474i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.48913 | −0.107749 | −0.0538747 | − | 0.998548i | \(-0.517157\pi\) | ||||
−0.0538747 | + | 0.998548i | \(0.517157\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.7446 | 1.63719 | 0.818595 | − | 0.574372i | \(-0.194754\pi\) | ||||
0.818595 | + | 0.574372i | \(0.194754\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.18614 | + | 1.11469i | 0.0849413 | + | 0.0798248i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.939764i | 0.0669554i | 0.999439 | + | 0.0334777i | \(0.0106583\pi\) | ||||
−0.999439 | + | 0.0334777i | \(0.989342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7306i | 1.18600i | 0.805202 | + | 0.593000i | \(0.202057\pi\) | ||||
−0.805202 | + | 0.593000i | \(0.797943\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.37228 | + | 4.10891i | 0.308397 | + | 0.289820i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.74456 | 0.331375 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.883156 | − | 14.2063i | −0.0613836 | − | 0.987404i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.8564i | 0.958468i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.28339i | − | 0.432567i | −0.976331 | − | 0.216283i | \(-0.930607\pi\) | ||
0.976331 | − | 0.216283i | \(-0.0693935\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.1861 | − | 14.0313i | 0.903499 | − | 0.961411i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.605969 | 0.0413268 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.7446 | −1.13669 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.7446 | + | 13.5615i | −0.861198 | + | 0.916398i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.10891i | − | 0.276395i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.11425i | − | 0.208545i | −0.994549 | − | 0.104273i | \(-0.966749\pi\) | ||
0.994549 | − | 0.104273i | \(-0.0332515\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.766312 | − | 12.3267i | −0.0510875 | − | 0.821782i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.74456 | −0.580397 | −0.290199 | − | 0.956966i | \(-0.593721\pi\) | ||||
−0.290199 | + | 0.956966i | \(0.593721\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.8614 | −1.97330 | −0.986649 | − | 0.162863i | \(-0.947927\pi\) | ||||
−0.986649 | + | 0.162863i | \(0.947927\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.7446 | + | 11.9769i | 0.838531 | + | 0.788021i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.0858i | − | 1.05382i | −0.849923 | − | 0.526908i | \(-0.823351\pi\) | ||
0.849923 | − | 0.526908i | \(-0.176649\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5.98844i | − | 0.390643i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.00000 | − | 1.87953i | −0.129914 | − | 0.122088i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.86141 | −0.508512 | −0.254256 | − | 0.967137i | \(-0.581831\pi\) | ||||
−0.254256 | + | 0.967137i | \(0.581831\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.18614 | + | 12.5942i | −0.589291 | + | 0.807921i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.589907i | 0.0376878i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.46410i | 0.220416i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.2337 | − | 15.1460i | 0.902023 | − | 0.959840i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0000 | 1.00991 | 0.504956 | − | 0.863145i | \(-0.331509\pi\) | ||||
0.504956 | + | 0.863145i | \(0.331509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.9783 | 1.19315 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.58017 | − | 4.87375i | 0.286821 | − | 0.305206i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.349857i | 0.0218234i | 0.999940 | + | 0.0109117i | \(0.00347338\pi\) | ||||
−0.999940 | + | 0.0109117i | \(0.996527\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.939764i | 0.0583941i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7446 | −0.785863 | −0.392932 | − | 0.919568i | \(-0.628539\pi\) | ||||
−0.392932 | + | 0.919568i | \(0.628539\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.2554 | 0.691416 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.37228 | + | 5.98844i | 0.389977 | + | 0.366487i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.9769i | 0.730243i | 0.930960 | + | 0.365122i | \(0.118973\pi\) | ||||
−0.930960 | + | 0.365122i | \(0.881027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 15.7908i | − | 0.959225i | −0.877480 | − | 0.479613i | \(-0.840777\pi\) | ||
0.877480 | − | 0.479613i | \(-0.159223\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.18614 | + | 2.99422i | 0.192834 | + | 0.181218i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.4674 | 0.993020 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9783 | 1.50080 | 0.750399 | − | 0.660985i | \(-0.229861\pi\) | ||||
0.750399 | + | 0.660985i | \(0.229861\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.8614 | − | 1.23472i | 1.18907 | − | 0.0739206i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.4843i | 1.28165i | 0.767688 | + | 0.640824i | \(0.221407\pi\) | ||||
−0.767688 | + | 0.640824i | \(0.778593\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.1514i | − | 0.841211i | −0.907244 | − | 0.420606i | \(-0.861818\pi\) | ||
0.907244 | − | 0.420606i | \(-0.138182\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.86141 | + | 4.10891i | −0.228730 | + | 0.243391i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.7446 | 0.752288 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.116844 | 0.00687317 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.25544 | + | 3.46410i | −0.190837 | + | 0.203069i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 25.5932i | − | 1.49517i | −0.664165 | − | 0.747586i | \(-0.731213\pi\) | ||
0.664165 | − | 0.747586i | \(-0.268787\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11.2772i | − | 0.656582i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.0000 | − | 13.2665i | −0.928414 | − | 0.769800i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.74456 | 0.274385 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.62772 | 0.0938201 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.7446 | + | 11.9769i | 0.732156 | + | 0.688054i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 10.7971i | − | 0.618238i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.2000i | 1.09580i | 0.836543 | + | 0.547902i | \(0.184573\pi\) | ||||
−0.836543 | + | 0.547902i | \(0.815427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.7446 | + | 10.0974i | 0.611237 | + | 0.574418i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.7446 | 1.17632 | 0.588158 | − | 0.808746i | \(-0.299853\pi\) | ||||
0.588158 | + | 0.808746i | \(0.299853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.3723 | 1.15151 | 0.575755 | − | 0.817622i | \(-0.304708\pi\) | ||||
0.575755 | + | 0.817622i | \(0.304708\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.441578 | + | 7.10313i | 0.0248801 | + | 0.400216i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.0256i | − | 0.956250i | −0.878292 | − | 0.478125i | \(-0.841317\pi\) | ||
0.878292 | − | 0.478125i | \(-0.158683\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.7446 | + | 22.0742i | −1.15785 | + | 1.23206i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.2337 | 0.791984 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.11684 | 0.228361 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.6753 | + | 15.6159i | −0.811544 | + | 0.863562i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 16.0858i | − | 0.886838i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.17448i | − | 0.119520i | −0.998213 | − | 0.0597602i | \(-0.980966\pi\) | ||
0.998213 | − | 0.0597602i | \(-0.0190336\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0692967 | − | 1.11469i | −0.00379744 | − | 0.0610847i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.25544 | −0.177864 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.88316 | 0.157056 | 0.0785278 | − | 0.996912i | \(-0.474978\pi\) | ||||
0.0785278 | + | 0.996912i | \(0.474978\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.4891 | + | 23.9538i | 1.38438 | + | 1.30099i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.5330i | 1.43684i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2549i | 1.03967i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.62772 | + | 5.28873i | 0.302986 | + | 0.284735i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.6060 | −0.891455 | −0.445728 | − | 0.895169i | \(-0.647055\pi\) | ||||
−0.445728 | + | 0.895169i | \(0.647055\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.8832 | 0.796677 | 0.398339 | − | 0.917238i | \(-0.369587\pi\) | ||||
0.398339 | + | 0.917238i | \(0.369587\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | − | 3.31662i | −0.213504 | − | 0.177028i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 33.4612i | − | 1.78096i | −0.455022 | − | 0.890480i | \(-0.650369\pi\) | ||
0.455022 | − | 0.890480i | \(-0.349631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4472i | 0.554480i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.3030 | − | 13.0916i | 0.651143 | − | 0.692879i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.4891 | −1.13415 | −0.567076 | − | 0.823665i | \(-0.691926\pi\) | ||||
−0.567076 | + | 0.823665i | \(0.691926\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.93070 | − | 6.31084i | 0.311281 | − | 0.331233i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 10.0974i | − | 0.528520i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.7562i | − | 1.76206i | −0.473063 | − | 0.881028i | \(-0.656852\pi\) | ||
0.473063 | − | 0.881028i | \(-0.343148\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.1168 | + | 0.939764i | −0.786951 | + | 0.0489222i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.2337 | 1.56965 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.25544 | 0.0650041 | 0.0325020 | − | 0.999472i | \(-0.489652\pi\) | ||||
0.0325020 | + | 0.999472i | \(0.489652\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.8139 | + | 10.1625i | 0.558425 | + | 0.524788i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3205i | 0.889695i | 0.895606 | + | 0.444847i | \(0.146742\pi\) | ||||
−0.895606 | + | 0.444847i | \(0.853258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.37228 | + | 7.86797i | 0.428925 | + | 0.403088i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.88316 | −0.249518 | −0.124759 | − | 0.992187i | \(-0.539816\pi\) | ||||
−0.124759 | + | 0.992187i | \(0.539816\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.48913 | −0.483611 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.93070 | + | 0.120025i | −0.0981432 | + | 0.00610123i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.8102i | 1.91705i | 0.285006 | + | 0.958526i | \(0.408004\pi\) | ||||
−0.285006 | + | 0.958526i | \(0.591996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.4950i | − | 0.985904i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.44158 | + | 8.98266i | −0.425821 | + | 0.453115i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.48913 | 0.0749260 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.51087 | 0.226394 | 0.113197 | − | 0.993573i | \(-0.463891\pi\) | ||||
0.113197 | + | 0.993573i | \(0.463891\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.3723 | + | 11.0371i | −0.519264 | + | 0.552547i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 18.9051i | − | 0.944075i | −0.881579 | − | 0.472037i | \(-0.843519\pi\) | ||
0.881579 | − | 0.472037i | \(-0.156481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.63325i | 0.330426i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.04755 | − | 8.39275i | −0.0520530 | − | 0.417039i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.48913 | 0.0738132 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.9783 | 0.641733 | 0.320867 | − | 0.947124i | \(-0.396026\pi\) | ||||
0.320867 | + | 0.947124i | \(0.396026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.1168 | − | 17.9653i | −0.942964 | − | 0.886164i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 30.2921i | − | 1.49057i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2772i | 0.553574i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.3030 | − | 24.7186i | −1.28806 | − | 1.21047i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.8614 | 1.36112 | 0.680559 | − | 0.732693i | \(-0.261737\pi\) | ||||
0.680559 | + | 0.732693i | \(0.261737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.8832 | −0.530413 | −0.265206 | − | 0.964192i | \(-0.585440\pi\) | ||||
−0.265206 | + | 0.964192i | \(0.585440\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.18614 | + | 19.0800i | 0.0576721 | + | 0.927702i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 16.9157i | − | 0.820534i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 29.0024i | − | 1.40353i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.74456 | − | 5.04868i | 0.229070 | − | 0.243752i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.3505 | −1.60644 | −0.803219 | − | 0.595683i | \(-0.796881\pi\) | ||||
−0.803219 | + | 0.595683i | \(0.796881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.3505 | 1.50661 | 0.753305 | − | 0.657671i | \(-0.228458\pi\) | ||||
0.753305 | + | 0.657671i | \(0.228458\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.4356i | 0.786224i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 28.1176i | − | 1.34198i | −0.741467 | − | 0.670989i | \(-0.765870\pi\) | ||
0.741467 | − | 0.670989i | \(-0.234130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.116844 | − | 1.87953i | −0.00556400 | − | 0.0895013i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.37228 | 0.112710 | 0.0563552 | − | 0.998411i | \(-0.482052\pi\) | ||||
0.0563552 | + | 0.998411i | \(0.482052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.74456 | −0.224914 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.4891 | − | 20.1947i | −1.01640 | − | 0.955177i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.92820i | − | 0.326962i | −0.986546 | − | 0.163481i | \(-0.947728\pi\) | ||
0.986546 | − | 0.163481i | \(-0.0522723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 20.1947i | − | 0.950931i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.18614 | − | 6.75327i | −0.337634 | − | 0.317297i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.37228 | −0.111214 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.9783 | 1.35555 | 0.677773 | − | 0.735271i | \(-0.262945\pi\) | ||||
0.677773 | + | 0.735271i | \(0.262945\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.6277 | + | 16.4356i | −0.636087 | + | 0.767150i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.3754i | 0.809254i | 0.914482 | + | 0.404627i | \(0.132599\pi\) | ||||
−0.914482 | + | 0.404627i | \(0.867401\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 37.5152i | − | 1.74348i | −0.489969 | − | 0.871740i | \(-0.662992\pi\) | ||
0.489969 | − | 0.871740i | \(-0.337008\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.39403 | + | 7.86797i | −0.342890 | + | 0.364868i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.4891 | −1.17950 | −0.589748 | − | 0.807587i | \(-0.700773\pi\) | ||||
−0.589748 | + | 0.807587i | \(0.700773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.74456 | −0.403786 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.25544 | − | 3.46410i | 0.150003 | − | 0.159617i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.57924i | − | 0.118594i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.2612i | 0.654347i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.8614 | + | 2.22938i | −1.64198 | + | 0.102076i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.1168 | −1.23900 | −0.619500 | − | 0.784997i | \(-0.712665\pi\) | ||||
−0.619500 | + | 0.784997i | \(0.712665\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.372281 | 0.0169746 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.1168 | + | 14.2063i | 0.687840 | + | 0.646407i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.57924i | − | 0.117117i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.6844i | 1.84358i | 0.387684 | + | 0.921792i | \(0.373275\pi\) | ||||
−0.387684 | + | 0.921792i | \(0.626725\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.11684 | + | 8.56768i | 0.412278 | + | 0.387444i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.3505 | −1.32457 | −0.662285 | − | 0.749252i | \(-0.730413\pi\) | ||||
−0.662285 | + | 0.749252i | \(0.730413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.2554 | − | 0.699713i | 0.505894 | − | 0.0314498i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.0627i | 1.25878i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.6588i | 1.05911i | 0.848275 | + | 0.529557i | \(0.177642\pi\) | ||||
−0.848275 | + | 0.529557i | \(0.822358\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.74456 | − | 5.04868i | 0.211971 | − | 0.225558i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.23369 | −0.277946 | −0.138973 | − | 0.990296i | \(-0.544380\pi\) | ||||
−0.138973 | + | 0.990296i | \(0.544380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.48913 | −0.422261 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.18614 | − | 1.26217i | 0.0526784 | − | 0.0560549i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.8820i | 1.36882i | 0.729098 | + | 0.684409i | \(0.239940\pi\) | ||||
−0.729098 | + | 0.684409i | \(0.760060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 27.1229i | − | 1.19985i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.4891 | − | 13.8564i | 0.507257 | − | 0.611775i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | −0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.4891 | −1.12101 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.00000 | − | 7.51811i | −0.351161 | − | 0.330008i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.7013i | 1.47648i | 0.674539 | + | 0.738239i | \(0.264342\pi\) | ||||
−0.674539 | + | 0.738239i | \(0.735658\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.9971i | 1.31168i | 0.754899 | + | 0.655841i | \(0.227686\pi\) | ||||
−0.754899 | + | 0.655841i | \(0.772314\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.1168 | + | 12.3267i | 0.572466 | + | 0.537983i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.2554 | 1.18727 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.489125 | −0.0212663 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.23369 | + | 35.9306i | 0.0969338 | + | 1.55926i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.04868i | − | 0.218682i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 16.4356i | − | 0.710575i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.67527 | + | 7.10313i | −0.288059 | + | 0.306523i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.51087 | 0.108151 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.3723 | −1.21982 | −0.609910 | − | 0.792471i | \(-0.708794\pi\) | ||||
−0.609910 | + | 0.792471i | \(0.708794\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28.7446 | + | 30.5870i | −1.23355 | + | 1.31261i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 11.6270i | − | 0.498047i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 33.9962i | − | 1.45357i | −0.686864 | − | 0.726786i | \(-0.741013\pi\) | ||
0.686864 | − | 0.726786i | \(-0.258987\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.13859 | + | 34.4010i | 0.0912729 | + | 1.46820i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.441578 | + | 0.414979i | 0.0187439 | + | 0.0176149i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 20.4348i | − | 0.865848i | −0.901430 | − | 0.432924i | \(-0.857482\pi\) | ||
0.901430 | − | 0.432924i | \(-0.142518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.644810i | − | 0.0272726i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.7446 | − | 19.4950i | −0.875836 | − | 0.823079i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.0951 | 1.43694 | 0.718468 | − | 0.695560i | \(-0.244843\pi\) | ||||
0.718468 | + | 0.695560i | \(0.244843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.9783 | −0.798421 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.81386 | − | 22.5441i | −0.118171 | − | 0.946764i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.349857i | 0.0146667i | 0.999973 | + | 0.00733337i | \(0.00233431\pi\) | ||||
−0.999973 | + | 0.00733337i | \(0.997666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 20.8395i | − | 0.872106i | −0.899921 | − | 0.436053i | \(-0.856376\pi\) | ||
0.899921 | − | 0.436053i | \(-0.143624\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.76631 | + | 1.87953i | −0.0737887 | + | 0.0785184i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.5326 | 0.814567 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.74456 | −0.114258 | −0.0571288 | − | 0.998367i | \(-0.518195\pi\) | ||||
−0.0571288 | + | 0.998367i | \(0.518195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.9783 | − | 28.7075i | 1.12118 | − | 1.19304i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.2921i | 1.25673i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 47.9075i | − | 1.98413i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.81386 | − | 0.174928i | 0.116339 | − | 0.00723239i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.744563 | 0.0307314 | 0.0153657 | − | 0.999882i | \(-0.495109\pi\) | ||||
0.0153657 | + | 0.999882i | \(0.495109\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.9783 | −0.946802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.18614 | + | 1.11469i | 0.0487913 | + | 0.0458523i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.2203i | 1.52845i | 0.644948 | + | 0.764226i | \(0.276879\pi\) | ||||
−0.644948 | + | 0.764226i | \(0.723121\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.74749i | 0.399608i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.1168 | + | 19.8448i | 0.864255 | + | 0.812195i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.48913 | −0.0608440 | −0.0304220 | − | 0.999537i | \(-0.509685\pi\) | ||||
−0.0304220 | + | 0.999537i | \(0.509685\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.8397 | −1.82905 | −0.914524 | − | 0.404532i | \(-0.867434\pi\) | ||||
−0.914524 | + | 0.404532i | \(0.867434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.3723 | − | 0.644810i | 0.422392 | − | 0.0262587i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.69882i | 0.191034i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.5383i | − | 1.03657i | −0.855208 | − | 0.518284i | \(-0.826571\pi\) | ||
0.855208 | − | 0.518284i | \(-0.173429\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.37228 | −0.257795 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.4891 | 0.625600 | 0.312800 | − | 0.949819i | \(-0.398733\pi\) | ||||
0.312800 | + | 0.949819i | \(0.398733\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.62772 | − | 5.98844i | 0.226932 | − | 0.241477i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.8820i | 1.24326i | 0.783311 | + | 0.621630i | \(0.213529\pi\) | ||||
−0.783311 | + | 0.621630i | \(0.786471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.7562i | 1.35677i | 0.734705 | + | 0.678387i | \(0.237321\pi\) | ||||
−0.734705 | + | 0.678387i | \(0.762679\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.9783 | − | 15.7359i | −0.761571 | − | 0.631461i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.7446 | −0.510600 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5326 | 0.501305 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.4891 | + | 16.4356i | 0.698448 | + | 0.656377i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.52967i | − | 0.0609920i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.7422i | 0.427639i | 0.976873 | + | 0.213819i | \(0.0685904\pi\) | ||||
−0.976873 | + | 0.213819i | \(0.931410\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.93070 | − | 7.45299i | −0.315217 | − | 0.296230i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.23369 | −0.247376 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.627719 | 0.0248711 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.06930 | − | 33.2863i | −0.0818601 | − | 1.31678i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 37.8102i | − | 1.49341i | −0.665154 | − | 0.746706i | \(-0.731634\pi\) | ||
0.665154 | − | 0.746706i | \(-0.268366\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.21249i | − | 0.363305i | −0.983363 | − | 0.181653i | \(-0.941855\pi\) | ||
0.983363 | − | 0.181653i | \(-0.0581446\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.718765 | − | 0.764836i | 0.0283013 | − | 0.0301154i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.9783 | 1.37514 | 0.687568 | − | 0.726120i | \(-0.258678\pi\) | ||||
0.687568 | + | 0.726120i | \(0.258678\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.0000 | −1.88416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.8614 | + | 21.1345i | −0.778430 | + | 0.828325i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 6.68815i | − | 0.261328i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | + | 32.1716i | 0.0780274 | + | 1.25513i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.4891 | 0.681280 | 0.340640 | − | 0.940194i | \(-0.389356\pi\) | ||||
0.340640 | + | 0.940194i | \(0.389356\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.510875 | −0.0198707 | −0.00993536 | − | 0.999951i | \(-0.503163\pi\) | ||||
−0.00993536 | + | 0.999951i | \(0.503163\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.18614 | − | 4.87375i | −0.201413 | − | 0.189281i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 8.21782i | − | 0.318674i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.93070 | − | 3.69393i | −0.151970 | − | 0.142816i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −45.9565 | −1.77413 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.1168 | 1.27656 | 0.638280 | − | 0.769804i | \(-0.279646\pi\) | ||||
0.638280 | + | 0.769804i | \(0.279646\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.4674 | − | 13.6540i | −0.633830 | − | 0.525544i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 7.51811i | − | 0.288944i | −0.989509 | − | 0.144472i | \(-0.953852\pi\) | ||
0.989509 | − | 0.144472i | \(-0.0461484\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.92820i | − | 0.265880i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.3723 | + | 11.0371i | −0.397467 | + | 0.422943i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.9783 | 0.879238 | 0.439619 | − | 0.898184i | \(-0.355113\pi\) | ||||
0.439619 | + | 0.898184i | \(0.355113\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.2337 | 0.543841 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.4198 | + | 37.6901i | −1.35135 | + | 1.43797i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 11.9769i | − | 0.456283i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4410i | 0.587403i | 0.955897 | + | 0.293701i | \(0.0948871\pi\) | ||||
−0.955897 | + | 0.293701i | \(0.905113\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 30.2337 | − | 1.87953i | 1.14848 | − | 0.0713974i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.5842 | 0.742872 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.7446 | −0.785756 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.3030 | − | 19.0800i | −0.767929 | − | 0.721672i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.39764i | − | 0.354944i | −0.984126 | − | 0.177472i | \(-0.943208\pi\) | ||
0.984126 | − | 0.177472i | \(-0.0567919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.28962i | 0.0486390i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.55842 | − | 7.10313i | −0.284667 | − | 0.267519i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25.4891 | −0.958617 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.9783 | 0.938078 | 0.469039 | − | 0.883177i | \(-0.344600\pi\) | ||||
0.469039 | + | 0.883177i | \(0.344600\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.74456 | + | 0.294954i | −0.177935 | + | 0.0110616i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.4719i | 1.17863i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.75906i | 0.140581i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.32473 | + | 9.92242i | −0.348239 | + | 0.370560i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.72281 | −0.288012 | −0.144006 | − | 0.989577i | \(-0.545999\pi\) | ||||
−0.144006 | + | 0.989577i | \(0.545999\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.4891 | −0.800297 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.3505 | − | 22.7190i | 0.794035 | − | 0.844930i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.3841i | 1.53485i | 0.641139 | + | 0.767425i | \(0.278462\pi\) | ||||
−0.641139 | + | 0.767425i | \(0.721538\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.64947 | −0.0979941 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.3505 | 0.419241 | 0.209621 | − | 0.977783i | \(-0.432777\pi\) | ||||
0.209621 | + | 0.977783i | \(0.432777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.744563 | + | 0.699713i | 0.0274636 | + | 0.0258093i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.8564i | 0.510407i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.8997i | 0.732024i | 0.930610 | + | 0.366012i | \(0.119277\pi\) | ||||
−0.930610 | + | 0.366012i | \(0.880723\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.37228 | + | 4.10891i | 0.160620 | + | 0.150945i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.62772 | 0.0597152 | 0.0298576 | − | 0.999554i | \(-0.490495\pi\) | ||||
0.0298576 | + | 0.999554i | \(0.490495\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.0000 | 0.586195 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.23369 | − | 35.9306i | −0.0817264 | − | 1.31463i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 44.1485i | − | 1.61315i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 0.884861i | − | 0.0322890i | −0.999870 | − | 0.0161445i | \(-0.994861\pi\) | ||
0.999870 | − | 0.0161445i | \(-0.00513918\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.9783 | − | 20.1947i | 0.691606 | − | 0.735936i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.35053 | 0.194726 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.9783 | −1.05323 | −0.526616 | − | 0.850103i | \(-0.676539\pi\) | ||||
−0.526616 | + | 0.850103i | \(0.676539\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.5109 | − | 23.9538i | 0.817093 | − | 0.869466i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.9793i | 1.48550i | 0.669569 | + | 0.742749i | \(0.266479\pi\) | ||||
−0.669569 | + | 0.742749i | \(0.733521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 31.2318i | − | 1.13067i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.718765 | − | 11.5619i | −0.0259870 | − | 0.418021i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.72281 | 0.350614 | 0.175307 | − | 0.984514i | \(-0.443908\pi\) | ||||
0.175307 | + | 0.984514i | \(0.443908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.441578 | + | 0.414979i | 0.0159030 | + | 0.0149451i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 31.2318i | − | 1.12333i | −0.827365 | − | 0.561665i | \(-0.810161\pi\) | ||
0.827365 | − | 0.561665i | \(-0.189839\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.3081i | 0.980934i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.18614 | + | 1.11469i | 0.0425526 | + | 0.0399894i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.4891 | 0.626613 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.4674 | 1.59117 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.57924i | 0.0920570i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.4179i | 0.977341i | 0.872468 | + | 0.488671i | \(0.162518\pi\) | ||||
−0.872468 | + | 0.488671i | \(0.837482\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.1168 | + | 16.0858i | −0.538174 | + | 0.572669i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −50.9783 | −1.81258 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.4891 | −0.407991 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.3505 | − | 14.2063i | 0.473495 | − | 0.503844i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.8333i | 0.915062i | 0.889194 | + | 0.457531i | \(0.151266\pi\) | ||||
−0.889194 | + | 0.457531i | \(0.848734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.1831i | 0.926293i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.1168 | − | 0.939764i | 0.534127 | − | 0.0332049i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −42.9783 | −1.51667 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.2554 | −0.396702 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.1168 | + | 14.2063i | 0.532138 | + | 0.500084i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 26.1831i | − | 0.920550i | −0.887776 | − | 0.460275i | \(-0.847751\pi\) | ||
0.887776 | − | 0.460275i | \(-0.152249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.0564i | 1.16077i | 0.814343 | + | 0.580384i | \(0.197098\pi\) | ||||
−0.814343 | + | 0.580384i | \(0.802902\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.9307 | − | 18.7302i | −0.699000 | − | 0.656895i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.78806 | −0.237775 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.23369 | 0.0781468 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.55842 | − | 0.469882i | 0.264113 | − | 0.0164190i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 50.7268i | − | 1.77038i | −0.465232 | − | 0.885189i | \(-0.654029\pi\) | ||
0.465232 | − | 0.885189i | \(-0.345971\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.2718i | 0.427769i | 0.976859 | + | 0.213885i | \(0.0686117\pi\) | ||||
−0.976859 | + | 0.213885i | \(0.931388\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19.5326 | − | 20.7846i | 0.680039 | − | 0.723627i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.7446 | 1.41683 | 0.708414 | − | 0.705798i | \(-0.249411\pi\) | ||||
0.708414 | + | 0.705798i | \(0.249411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.00000 | −0.0694629 | −0.0347314 | − | 0.999397i | \(-0.511058\pi\) | ||||
−0.0347314 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.6277 | − | 31.5268i | 1.02777 | − | 1.09365i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.57924i | − | 0.0893654i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.75906i | 0.130087i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.0000 | − | 26.5330i | 0.760431 | − | 0.917115i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.02175 | 0.0352747 | 0.0176374 | − | 0.999844i | \(-0.494386\pi\) | ||||
0.0176374 | + | 0.999844i | \(0.494386\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.1168 | + | 25.4834i | 0.933954 | + | 0.877696i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.939764i | 0.0323289i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.6217i | 0.433686i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.8614 | − | 16.7855i | −0.613002 | − | 0.576077i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.76631 | 0.0605484 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.6060 | 0.500099 | 0.250049 | − | 0.968233i | \(-0.419553\pi\) | ||||
0.250049 | + | 0.968233i | \(0.419553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.605969 | + | 9.74749i | 0.0207237 | + | 0.333357i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0974i | 0.344919i | 0.985017 | + | 0.172459i | \(0.0551714\pi\) | ||||
−0.985017 | + | 0.172459i | \(0.944829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 26.8280i | − | 0.915358i | −0.889118 | − | 0.457679i | \(-0.848681\pi\) | ||
0.889118 | − | 0.457679i | \(-0.151319\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.1168 | − | 16.0858i | 0.515181 | − | 0.548202i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.35053 | 0.318296 | 0.159148 | − | 0.987255i | \(-0.449125\pi\) | ||||
0.159148 | + | 0.987255i | \(0.449125\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.95650 | 0.202527 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.138593 | − | 0.147477i | 0.00470688 | − | 0.00500858i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6.33830i | − | 0.215012i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.46410i | 0.117377i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.510875 | + | 8.21782i | 0.0172905 | + | 0.278131i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.6277 | −0.731150 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.11684 | −0.0377131 | −0.0188566 | − | 0.999822i | \(-0.506003\pi\) | ||||
−0.0188566 | + | 0.999822i | \(0.506003\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.3030 | − | 30.3572i | −1.08955 | − | 1.02392i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.6270i | 0.391724i | 0.980631 | + | 0.195862i | \(0.0627505\pi\) | ||||
−0.980631 | + | 0.195862i | \(0.937249\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.4294i | 0.721157i | 0.932729 | + | 0.360579i | \(0.117421\pi\) | ||||
−0.932729 | + | 0.360579i | \(0.882579\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.2337 | − | 13.3763i | −0.478460 | − | 0.449640i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.2337 | −1.28376 | −0.641881 | − | 0.766804i | \(-0.721846\pi\) | ||||
−0.641881 | + | 0.766804i | \(0.721846\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.7446 | −0.561595 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.7228 | + | 4.45877i | −1.19676 | + | 0.149374i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 22.0742i | − | 0.738686i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.28873i | − | 0.176783i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.62772 | − | 5.98844i | 0.187904 | − | 0.199948i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.2119 | −1.63949 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.93070 | − | 2.05446i | 0.0642498 | − | 0.0683680i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 22.7739i | − | 0.757031i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 16.3807i | − | 0.543914i | −0.962309 | − | 0.271957i | \(-0.912329\pi\) | ||
0.962309 | − | 0.271957i | \(-0.0876708\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.2337 | − | 1.87953i | 1.00279 | − | 0.0623400i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.9783 | 0.363726 | 0.181863 | − | 0.983324i | \(-0.441787\pi\) | ||||
0.181863 | + | 0.983324i | \(0.441787\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.0000 | 1.58857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.6277 | − | 12.8068i | −0.450518 | − | 0.423381i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 17.9653i | − | 0.593267i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.4203i | 1.86113i | 0.366122 | + | 0.930567i | \(0.380685\pi\) | ||||
−0.366122 | + | 0.930567i | \(0.619315\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.2337 | + | 22.7739i | 0.798527 | + | 0.750427i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.1168 | 0.365915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.53262 | 0.0503924 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.4891 | − | 1.58457i | 0.837173 | − | 0.0520442i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 40.9793i | − | 1.34449i | −0.740330 | − | 0.672244i | \(-0.765331\pi\) | ||
0.740330 | − | 0.672244i | \(-0.234669\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.17448i | 0.0712657i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.6060 | − | 26.1831i | 0.805563 | − | 0.857198i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.4456 | 0.505126 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.5109 | −0.408712 | −0.204356 | − | 0.978897i | \(-0.565510\pi\) | ||||
−0.204356 | + | 0.978897i | \(0.565510\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.1644 | − | 25.7133i | 0.788575 | − | 0.839121i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 7.27806i | − | 0.237258i | −0.992939 | − | 0.118629i | \(-0.962150\pi\) | ||
0.992939 | − | 0.118629i | \(-0.0378499\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 23.9538i | − | 0.780042i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.48913 | + | 7.86797i | 0.308681 | + | 0.255945i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.9783 | 0.746693 | 0.373346 | − | 0.927692i | \(-0.378210\pi\) | ||||
0.373346 | + | 0.927692i | \(0.378210\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.7446 | −0.348783 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.4891 | − | 20.1947i | −0.696833 | − | 0.654858i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.40920i | 0.110435i | 0.998474 | + | 0.0552174i | \(0.0175852\pi\) | ||||
−0.998474 | + | 0.0552174i | \(0.982415\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.39943i | − | 0.0452844i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.2337 | 1.23463 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0000 | −0.419355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.25544 | + | 52.3663i | 0.104905 | + | 1.68748i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.3745i | 0.688070i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.5012i | 0.466328i | 0.972437 | + | 0.233164i | \(0.0749078\pi\) | ||||
−0.972437 | + | 0.233164i | \(0.925092\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.8832 | − | 17.9653i | 0.542365 | − | 0.577129i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.8614 | −0.380651 | −0.190325 | − | 0.981721i | \(-0.560954\pi\) | ||||
−0.190325 | + | 0.981721i | \(0.560954\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.6060 | 1.68647 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.88316 | − | 5.19615i | 0.156386 | − | 0.166410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.6641i | 0.725090i | 0.931966 | + | 0.362545i | \(0.118092\pi\) | ||||
−0.931966 | + | 0.362545i | \(0.881908\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.1947i | 0.645425i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.30298 | + | 37.0453i | 0.0735286 | + | 1.18277i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.1168 | 1.63037 | 0.815187 | − | 0.579198i | \(-0.196634\pi\) | ||||
0.815187 | + | 0.579198i | \(0.196634\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.883156 | −0.0281397 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.3030 | − | 19.0800i | −0.646251 | − | 0.607323i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.05934i | − | 0.0972814i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 6.04334i | − | 0.191973i | −0.995383 | − | 0.0959865i | \(-0.969399\pi\) | ||
0.995383 | − | 0.0959865i | \(-0.0306006\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.74456 | − | 2.57924i | −0.0870961 | − | 0.0818497i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.7228 | −0.498447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.7446 | 1.35373 | 0.676867 | − | 0.736105i | \(-0.263337\pi\) | ||||
0.676867 | + | 0.736105i | \(0.263337\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.48913 | − | 1.23472i | −0.0471138 | − | 0.0390647i |
(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 | 624.2.d.g.287.3 | ✓ | 4 | |
3.2 | odd | 2 | 624.2.d.i.287.1 | yes | 4 | ||
4.3 | odd | 2 | 624.2.d.i.287.2 | yes | 4 | ||
8.3 | odd | 2 | 2496.2.d.i.1535.3 | 4 | |||
8.5 | even | 2 | 2496.2.d.l.1535.2 | 4 | |||
12.11 | even | 2 | inner | 624.2.d.g.287.4 | yes | 4 | |
24.5 | odd | 2 | 2496.2.d.i.1535.4 | 4 | |||
24.11 | even | 2 | 2496.2.d.l.1535.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.2.d.g.287.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
624.2.d.g.287.4 | yes | 4 | 12.11 | even | 2 | inner | |
624.2.d.i.287.1 | yes | 4 | 3.2 | odd | 2 | ||
624.2.d.i.287.2 | yes | 4 | 4.3 | odd | 2 | ||
2496.2.d.i.1535.3 | 4 | 8.3 | odd | 2 | |||
2496.2.d.i.1535.4 | 4 | 24.5 | odd | 2 | |||
2496.2.d.l.1535.1 | 4 | 24.11 | even | 2 | |||
2496.2.d.l.1535.2 | 4 | 8.5 | even | 2 |