Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9680,2,Mod(1,9680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9680.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(77.2951891566\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.25903625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 7x^{4} + 17x^{3} + 16x^{2} - 20x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(3.29288\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9680.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.29288 | 1.90115 | 0.950573 | − | 0.310501i | \(-0.100497\pi\) | ||||
0.950573 | + | 0.310501i | \(0.100497\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.51508 | −1.32857 | −0.664287 | − | 0.747477i | \(-0.731265\pi\) | ||||
−0.664287 | + | 0.747477i | \(0.731265\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.84307 | 2.61436 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.27118 | −1.18461 | −0.592306 | − | 0.805713i | \(-0.701782\pi\) | ||||
−0.592306 | + | 0.805713i | \(0.701782\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.29288 | −0.850218 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.58998 | 0.385626 | 0.192813 | − | 0.981236i | \(-0.438239\pi\) | ||||
0.192813 | + | 0.981236i | \(0.438239\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.55094 | −1.27347 | −0.636736 | − | 0.771082i | \(-0.719716\pi\) | ||||
−0.636736 | + | 0.771082i | \(0.719716\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.5747 | −2.52581 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.39042 | 1.33249 | 0.666247 | − | 0.745731i | \(-0.267900\pi\) | ||||
0.666247 | + | 0.745731i | \(0.267900\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.9477 | 3.06913 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.381220 | −0.0707908 | −0.0353954 | − | 0.999373i | \(-0.511269\pi\) | ||||
−0.0353954 | + | 0.999373i | \(0.511269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.760465 | 0.136584 | 0.0682918 | − | 0.997665i | \(-0.478245\pi\) | ||||
0.0682918 | + | 0.997665i | \(0.478245\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.51508 | 0.594156 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.45191 | −0.238692 | −0.119346 | − | 0.992853i | \(-0.538080\pi\) | ||||
−0.119346 | + | 0.992853i | \(0.538080\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.0645 | −2.25212 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.12208 | −0.956108 | −0.478054 | − | 0.878330i | \(-0.658658\pi\) | ||||
−0.478054 | + | 0.878330i | \(0.658658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.19067 | 1.09657 | 0.548284 | − | 0.836293i | \(-0.315281\pi\) | ||||
0.548284 | + | 0.836293i | \(0.315281\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.84307 | −1.16918 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.32164 | −0.630376 | −0.315188 | − | 0.949029i | \(-0.602068\pi\) | ||||
−0.315188 | + | 0.949029i | \(0.602068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.35577 | 0.765110 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.23561 | 0.733132 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.94904 | −0.954523 | −0.477262 | − | 0.878761i | \(-0.658371\pi\) | ||||
−0.477262 | + | 0.878761i | \(0.658371\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.2786 | −2.42106 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.7110 | −1.65484 | −0.827419 | − | 0.561586i | \(-0.810192\pi\) | ||||
−0.827419 | + | 0.561586i | \(0.810192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.89599 | −1.13901 | −0.569507 | − | 0.821986i | \(-0.692866\pi\) | ||||
−0.569507 | + | 0.821986i | \(0.692866\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −27.5690 | −3.47337 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.27118 | 0.529775 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5135 | −1.52877 | −0.764383 | − | 0.644763i | \(-0.776956\pi\) | ||||
−0.764383 | + | 0.644763i | \(0.776956\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.0429 | 2.53327 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.35890 | −0.873340 | −0.436670 | − | 0.899622i | \(-0.643842\pi\) | ||||
−0.436670 | + | 0.899622i | \(0.643842\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.03210 | 0.823045 | 0.411523 | − | 0.911399i | \(-0.364997\pi\) | ||||
0.411523 | + | 0.911399i | \(0.364997\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.29288 | 0.380229 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.99381 | 0.786865 | 0.393432 | − | 0.919354i | \(-0.371288\pi\) | ||||
0.393432 | + | 0.919354i | \(0.371288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 28.9846 | 3.22051 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.7509 | 1.18007 | 0.590034 | − | 0.807379i | \(-0.299114\pi\) | ||||
0.590034 | + | 0.807379i | \(0.299114\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.58998 | −0.172457 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.25531 | −0.134584 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.451594 | 0.0478689 | 0.0239344 | − | 0.999714i | \(-0.492381\pi\) | ||||
0.0239344 | + | 0.999714i | \(0.492381\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.0135 | 1.57385 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.50412 | 0.259665 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.55094 | 0.569514 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.77956 | −0.282222 | −0.141111 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141111 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.33731 | 0.531082 | 0.265541 | − | 0.964100i | \(-0.414449\pi\) | ||||
0.265541 | + | 0.964100i | \(0.414449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.3817 | −1.71267 | −0.856334 | − | 0.516422i | \(-0.827263\pi\) | ||||
−0.856334 | + | 0.516422i | \(0.827263\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.5747 | 1.12958 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.49783 | −0.338148 | −0.169074 | − | 0.985603i | \(-0.554078\pi\) | ||||
−0.169074 | + | 0.985603i | \(0.554078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.91209 | 0.470493 | 0.235247 | − | 0.971936i | \(-0.424410\pi\) | ||||
0.235247 | + | 0.971936i | \(0.424410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.78096 | −0.453789 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.1718 | −1.61539 | −0.807694 | − | 0.589602i | \(-0.799285\pi\) | ||||
−0.807694 | + | 0.589602i | \(0.799285\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.39042 | −0.595910 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −33.4992 | −3.09700 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.58889 | −0.512333 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −20.1593 | −1.81770 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4883 | −1.37437 | −0.687183 | − | 0.726484i | \(-0.741153\pi\) | ||||
−0.687183 | + | 0.726484i | \(0.741153\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.6780 | 2.08473 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.64734 | 0.318670 | 0.159335 | − | 0.987225i | \(-0.449065\pi\) | ||||
0.159335 | + | 0.987225i | \(0.449065\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.5120 | 1.69190 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.9477 | −1.37256 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2579 | −1.38901 | −0.694503 | − | 0.719490i | \(-0.744376\pi\) | ||||
−0.694503 | + | 0.719490i | \(0.744376\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.49232 | 0.635490 | 0.317745 | − | 0.948176i | \(-0.397074\pi\) | ||||
0.317745 | + | 0.948176i | \(0.397074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.2306 | −1.19844 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.381220 | 0.0316586 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.6359 | 1.45459 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.7025 | −0.958708 | −0.479354 | − | 0.877622i | \(-0.659129\pi\) | ||||
−0.479354 | + | 0.877622i | \(0.659129\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6007 | −1.02543 | −0.512715 | − | 0.858559i | \(-0.671360\pi\) | ||||
−0.512715 | + | 0.858559i | \(0.671360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.4703 | 1.00816 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.760465 | −0.0610820 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.47653 | −0.516883 | −0.258441 | − | 0.966027i | \(-0.583209\pi\) | ||||
−0.258441 | + | 0.966027i | \(0.583209\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.8824 | −1.81469 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.4628 | −1.77032 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.7737 | 1.70545 | 0.852724 | − | 0.522361i | \(-0.174949\pi\) | ||||
0.852724 | + | 0.522361i | \(0.174949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.0881 | −1.47708 | −0.738541 | − | 0.674208i | \(-0.764485\pi\) | ||||
−0.738541 | + | 0.674208i | \(0.764485\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.24299 | 0.403307 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −43.5364 | −3.32931 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.44630 | −0.109960 | −0.0549800 | − | 0.998487i | \(-0.517509\pi\) | ||||
−0.0549800 | + | 0.998487i | \(0.517509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.51508 | −0.265715 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −41.8560 | −3.14609 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.02979 | 0.674918 | 0.337459 | − | 0.941340i | \(-0.390433\pi\) | ||||
0.337459 | + | 0.941340i | \(0.390433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.14725 | −0.0852744 | −0.0426372 | − | 0.999091i | \(-0.513576\pi\) | ||||
−0.0426372 | + | 0.999091i | \(0.513576\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.2934 | −2.16543 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.45191 | 0.106746 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −56.0573 | −4.07757 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9868 | 1.08440 | 0.542202 | − | 0.840248i | \(-0.317591\pi\) | ||||
0.542202 | + | 0.840248i | \(0.317591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.1821 | −1.09283 | −0.546414 | − | 0.837515i | \(-0.684007\pi\) | ||||
−0.546414 | + | 0.837515i | \(0.684007\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.0645 | 1.00718 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.95776 | −0.210731 | −0.105366 | − | 0.994434i | \(-0.533601\pi\) | ||||
−0.105366 | + | 0.994434i | \(0.533601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.07974 | 0.360093 | 0.180046 | − | 0.983658i | \(-0.442375\pi\) | ||||
0.180046 | + | 0.983658i | \(0.442375\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −41.2054 | −2.90641 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.34002 | 0.0940509 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.12208 | 0.427585 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 50.1205 | 3.48362 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.50814 | 0.585724 | 0.292862 | − | 0.956155i | \(-0.405392\pi\) | ||||
0.292862 | + | 0.956155i | \(0.405392\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.2320 | −1.66035 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.19067 | −0.490400 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.67309 | −0.181461 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.1559 | 1.56473 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.79108 | −0.456817 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.0443 | −1.00744 | −0.503719 | − | 0.863867i | \(-0.668035\pi\) | ||||
−0.503719 | + | 0.863867i | \(0.668035\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.84307 | 0.522871 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.7035 | 1.04228 | 0.521138 | − | 0.853473i | \(-0.325508\pi\) | ||||
0.521138 | + | 0.853473i | \(0.325508\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.4760 | 1.41918 | 0.709588 | − | 0.704617i | \(-0.248881\pi\) | ||||
0.709588 | + | 0.704617i | \(0.248881\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.07615 | −0.463574 | −0.231787 | − | 0.972767i | \(-0.574457\pi\) | ||||
−0.231787 | + | 0.972767i | \(0.574457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.32164 | 0.281913 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.0298 | 1.49595 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.9846 | −0.839905 | −0.419952 | − | 0.907546i | \(-0.637953\pi\) | ||||
−0.419952 | + | 0.907546i | \(0.637953\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.91442 | 0.316565 | 0.158283 | − | 0.987394i | \(-0.449404\pi\) | ||||
0.158283 | + | 0.987394i | \(0.449404\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 47.5998 | 3.05353 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.35577 | −0.342167 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.7091 | 1.50857 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35.4015 | 2.24348 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.68561 | −0.295753 | −0.147877 | − | 0.989006i | \(-0.547244\pi\) | ||||
−0.147877 | + | 0.989006i | \(0.547244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.23561 | −0.327866 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.92457 | 0.120051 | 0.0600255 | − | 0.998197i | \(-0.480882\pi\) | ||||
0.0600255 | + | 0.998197i | \(0.480882\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.10357 | 0.317120 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.98994 | −0.185072 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.6865 | 1.02894 | 0.514468 | − | 0.857510i | \(-0.327990\pi\) | ||||
0.514468 | + | 0.857510i | \(0.327990\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.94904 | 0.426876 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.48705 | 0.0910058 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.58774 | −0.279719 | −0.139860 | − | 0.990171i | \(-0.544665\pi\) | ||||
−0.139860 | + | 0.990171i | \(0.544665\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.2427 | −1.22966 | −0.614829 | − | 0.788660i | \(-0.710775\pi\) | ||||
−0.614829 | + | 0.788660i | \(0.710775\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 49.4378 | 2.99211 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.79906 | 0.288348 | 0.144174 | − | 0.989552i | \(-0.453948\pi\) | ||||
0.144174 | + | 0.989552i | \(0.453948\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.96438 | 0.357078 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.5980 | −1.28843 | −0.644214 | − | 0.764845i | \(-0.722815\pi\) | ||||
−0.644214 | + | 0.764845i | \(0.722815\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.2540 | 0.728422 | 0.364211 | − | 0.931316i | \(-0.381339\pi\) | ||||
0.364211 | + | 0.931316i | \(0.381339\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.2786 | 1.08273 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.5196 | 1.27026 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.4720 | −0.851293 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.15277 | −0.536545 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.3193 | 0.836544 | 0.418272 | − | 0.908322i | \(-0.362636\pi\) | ||||
0.418272 | + | 0.908322i | \(0.362636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.7110 | 0.740066 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.2946 | −1.57849 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.2758 | −1.45687 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.5751 | 1.00967 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.89599 | 0.509383 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.568487 | −0.0324453 | −0.0162226 | − | 0.999868i | \(-0.505164\pi\) | ||||
−0.0162226 | + | 0.999868i | \(0.505164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −57.2358 | −3.25603 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.2047 | −0.578654 | −0.289327 | − | 0.957230i | \(-0.593432\pi\) | ||||
−0.289327 | + | 0.957230i | \(0.593432\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.33625 | −0.527716 | −0.263858 | − | 0.964561i | \(-0.584995\pi\) | ||||
−0.263858 | + | 0.964561i | \(0.584995\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 27.5690 | 1.55334 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.2884 | −1.58884 | −0.794418 | − | 0.607372i | \(-0.792224\pi\) | ||||
−0.794418 | + | 0.607372i | \(0.792224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.5179 | −0.642869 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.82586 | −0.491084 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.27118 | −0.236922 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.1749 | 0.894476 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.1909 | 0.837501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.31846 | 0.292329 | 0.146164 | − | 0.989260i | \(-0.453307\pi\) | ||||
0.146164 | + | 0.989260i | \(0.453307\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.3874 | −0.624026 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.5135 | 0.683685 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.6340 | −0.960584 | −0.480292 | − | 0.877109i | \(-0.659469\pi\) | ||||
−0.480292 | + | 0.877109i | \(0.659469\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −56.5448 | −3.07109 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.77961 | 0.312069 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −21.0429 | −1.13291 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.8289 | 0.635006 | 0.317503 | − | 0.948257i | \(-0.397156\pi\) | ||||
0.317503 | + | 0.948257i | \(0.397156\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.35132 | −0.500565 | −0.250282 | − | 0.968173i | \(-0.580523\pi\) | ||||
−0.250282 | + | 0.968173i | \(0.580523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −68.1154 | −3.63573 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.7336 | −0.943863 | −0.471932 | − | 0.881635i | \(-0.656443\pi\) | ||||
−0.471932 | + | 0.881635i | \(0.656443\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.35890 | 0.390570 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.4036 | −0.974020 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.8840 | 0.996658 | 0.498329 | − | 0.866988i | \(-0.333947\pi\) | ||||
0.498329 | + | 0.866988i | \(0.333947\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.8129 | 0.621731 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.03210 | −0.368077 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.3936 | 1.37773 | 0.688867 | − | 0.724887i | \(-0.258108\pi\) | ||||
0.688867 | + | 0.724887i | \(0.258108\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −48.0159 | −2.49961 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.4264 | 1.26816 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.2368 | −0.996043 | −0.498022 | − | 0.867165i | \(-0.665940\pi\) | ||||
−0.498022 | + | 0.867165i | \(0.665940\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.29288 | −0.170044 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.62826 | 0.0838597 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.4665 | 1.77042 | 0.885212 | − | 0.465189i | \(-0.154014\pi\) | ||||
0.885212 | + | 0.465189i | \(0.154014\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −51.0012 | −2.61287 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.3171 | 1.14035 | 0.570176 | − | 0.821523i | \(-0.306875\pi\) | ||||
0.570176 | + | 0.821523i | \(0.306875\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 56.3970 | 2.86682 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.1067 | −0.816644 | −0.408322 | − | 0.912838i | \(-0.633886\pi\) | ||||
−0.408322 | + | 0.912838i | \(0.633886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.1606 | 0.513845 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0103 | 0.605838 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.99381 | −0.351897 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.8311 | 0.844731 | 0.422365 | − | 0.906426i | \(-0.361200\pi\) | ||||
0.422365 | + | 0.906426i | \(0.361200\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 64.2506 | 3.21655 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.26721 | 0.263032 | 0.131516 | − | 0.991314i | \(-0.458016\pi\) | ||||
0.131516 | + | 0.991314i | \(0.458016\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.24808 | −0.161799 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −28.9846 | −1.44025 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.3376 | 1.15397 | 0.576985 | − | 0.816755i | \(-0.304229\pi\) | ||||
0.576985 | + | 0.816755i | \(0.304229\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −53.5353 | −2.64070 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 44.6803 | 2.19857 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.7509 | −0.527742 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.6713 | 1.20816 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.21755 | −0.450307 | −0.225153 | − | 0.974323i | \(-0.572288\pi\) | ||||
−0.225153 | + | 0.974323i | \(0.572288\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.9901 | 1.02299 | 0.511496 | − | 0.859285i | \(-0.329091\pi\) | ||||
0.511496 | + | 0.859285i | \(0.329091\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −33.8949 | −1.64803 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.58998 | 0.0771252 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.2701 | 1.51327 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.8179 | −1.77346 | −0.886729 | − | 0.462290i | \(-0.847028\pi\) | ||||
−0.886729 | + | 0.462290i | \(0.847028\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.6339 | 0.559087 | 0.279544 | − | 0.960133i | \(-0.409817\pi\) | ||||
0.279544 | + | 0.960133i | \(0.409817\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.25531 | 0.0601877 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −35.4728 | −1.69689 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.4765 | 0.595471 | 0.297735 | − | 0.954648i | \(-0.403769\pi\) | ||||
0.297735 | + | 0.954648i | \(0.403769\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 42.0057 | 2.00027 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.22715 | −0.390884 | −0.195442 | − | 0.980715i | \(-0.562614\pi\) | ||||
−0.195442 | + | 0.980715i | \(0.562614\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.451594 | −0.0214076 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −38.5350 | −1.82264 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.2395 | −1.61586 | −0.807930 | − | 0.589278i | \(-0.799412\pi\) | ||||
−0.807930 | + | 0.589278i | \(0.799412\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −41.4926 | −1.94949 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.0135 | −0.703845 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.4317 | 1.14287 | 0.571434 | − | 0.820648i | \(-0.306387\pi\) | ||||
0.571434 | + | 0.820648i | \(0.306387\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.3564 | 1.18354 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.4406 | −0.719141 | −0.359571 | − | 0.933118i | \(-0.617077\pi\) | ||||
−0.359571 | + | 0.933118i | \(0.617077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.6507 | 1.19209 | 0.596046 | − | 0.802951i | \(-0.296738\pi\) | ||||
0.596046 | + | 0.802951i | \(0.296738\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.50412 | −0.116126 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.80052 | 0.360965 | 0.180482 | − | 0.983578i | \(-0.442234\pi\) | ||||
0.180482 | + | 0.983578i | \(0.442234\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 43.9859 | 2.03108 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.3264 | −0.982670 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.55094 | −0.254694 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −54.5018 | −2.49547 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.9353 | 1.77900 | 0.889501 | − | 0.456934i | \(-0.151052\pi\) | ||||
0.889501 | + | 0.456934i | \(0.151052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.20136 | 0.282758 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −73.9674 | −3.36563 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.77956 | 0.126213 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.8252 | 0.807737 | 0.403869 | − | 0.914817i | \(-0.367665\pi\) | ||||
0.403869 | + | 0.914817i | \(0.367665\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 71.6983 | 3.24231 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.37606 | −0.197489 | −0.0987443 | − | 0.995113i | \(-0.531483\pi\) | ||||
−0.0987443 | + | 0.995113i | \(0.531483\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.606131 | −0.0272988 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.8671 | 1.16030 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.6175 | −1.81829 | −0.909145 | − | 0.416479i | \(-0.863264\pi\) | ||||
−0.909145 | + | 0.416479i | \(0.863264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −62.8549 | −2.80815 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.32076 | −0.281829 | −0.140914 | − | 0.990022i | \(-0.545004\pi\) | ||||
−0.140914 | + | 0.990022i | \(0.545004\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.33731 | −0.237507 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.2645 | 0.766745 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.9331 | −0.573250 | −0.286625 | − | 0.958043i | \(-0.592533\pi\) | ||||
−0.286625 | + | 0.958043i | \(0.592533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.7184 | −1.09348 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −88.5245 | −3.90845 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.3817 | 0.765928 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.76249 | −0.209050 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.4286 | −0.719748 | −0.359874 | − | 0.933001i | \(-0.617180\pi\) | ||||
−0.359874 | + | 0.933001i | \(0.617180\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3601 | 0.934012 | 0.467006 | − | 0.884254i | \(-0.345333\pi\) | ||||
0.467006 | + | 0.884254i | \(0.345333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.5747 | −0.505163 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.20912 | 0.0526702 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8375 | 0.775542 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −99.6937 | −4.32634 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.1485 | 1.13262 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.49783 | 0.151224 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.7340 | 1.28312 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.1003 | 1.03615 | 0.518076 | − | 0.855334i | \(-0.326648\pi\) | ||||
0.518076 | + | 0.855334i | \(0.326648\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.77776 | −0.162119 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.91209 | −0.210411 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.1889 | −0.948727 | −0.474364 | − | 0.880329i | \(-0.657322\pi\) | ||||
−0.474364 | + | 0.880329i | \(0.657322\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −69.7719 | −2.97779 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.11613 | 0.0901501 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.5838 | −1.04541 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.78096 | 0.202940 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.3751 | 1.49889 | 0.749445 | − | 0.662067i | \(-0.230321\pi\) | ||||
0.749445 | + | 0.662067i | \(0.230321\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.7127 | −1.29901 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.79389 | 0.286328 | 0.143164 | − | 0.989699i | \(-0.454272\pi\) | ||||
0.143164 | + | 0.989699i | \(0.454272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.1718 | 0.722424 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −101.883 | −4.27868 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.5320 | 1.53150 | 0.765750 | − | 0.643139i | \(-0.222368\pi\) | ||||
0.765750 | + | 0.643139i | \(0.222368\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.4606 | −1.27474 | −0.637369 | − | 0.770559i | \(-0.719977\pi\) | ||||
−0.637369 | + | 0.770559i | \(0.719977\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 49.3496 | 2.06161 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.39042 | 0.266499 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5075 | 0.437434 | 0.218717 | − | 0.975788i | \(-0.429813\pi\) | ||||
0.218717 | + | 0.975788i | \(0.429813\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −49.9927 | −2.07763 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.7903 | −1.56781 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 33.4992 | 1.38502 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.9284 | 0.905083 | 0.452542 | − | 0.891743i | \(-0.350517\pi\) | ||||
0.452542 | + | 0.891743i | \(0.350517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.22129 | −0.173935 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.73955 | −0.400631 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.6482 | −0.888987 | −0.444493 | − | 0.895782i | \(-0.646616\pi\) | ||||
−0.444493 | + | 0.895782i | \(0.646616\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.58889 | 0.229122 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.7270 | 0.684589 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.7105 | 1.78596 | 0.892982 | − | 0.450092i | \(-0.148609\pi\) | ||||
0.892982 | + | 0.450092i | \(0.148609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.09877 | 0.167192 | 0.0835962 | − | 0.996500i | \(-0.473359\pi\) | ||||
0.0835962 | + | 0.996500i | \(0.473359\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −98.1442 | −3.99674 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.1631 | −1.71135 | −0.855674 | − | 0.517515i | \(-0.826857\pi\) | ||||
−0.855674 | + | 0.517515i | \(0.826857\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.41252 | 0.178804 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.4585 | 0.746751 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6572 | −0.430441 | −0.215220 | − | 0.976565i | \(-0.569047\pi\) | ||||
−0.215220 | + | 0.976565i | \(0.569047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.1593 | 0.812901 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.71898 | 0.270496 | 0.135248 | − | 0.990812i | \(-0.456817\pi\) | ||||
0.135248 | + | 0.990812i | \(0.456817\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.3204 | 1.37945 | 0.689727 | − | 0.724069i | \(-0.257730\pi\) | ||||
0.689727 | + | 0.724069i | \(0.257730\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 101.912 | 4.08960 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.58739 | −0.0635974 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.30850 | −0.0920459 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.0326 | −0.439201 | −0.219601 | − | 0.975590i | \(-0.570475\pi\) | ||||
−0.219601 | + | 0.975590i | \(0.570475\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.0163 | 1.11355 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.4883 | 0.614636 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.8755 | −0.906358 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −57.7163 | −2.28322 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.2836 | −0.998644 | −0.499322 | − | 0.866417i | \(-0.666417\pi\) | ||||
−0.499322 | + | 0.866417i | \(0.666417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.33932 | 0.210562 | 0.105281 | − | 0.994442i | \(-0.466426\pi\) | ||||
0.105281 | + | 0.994442i | \(0.466426\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.6780 | −0.932322 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.45155 | −0.135694 | −0.0678471 | − | 0.997696i | \(-0.521613\pi\) | ||||
−0.0678471 | + | 0.997696i | \(0.521613\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.80218 | −0.344985 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3245 | 0.443161 | 0.221580 | − | 0.975142i | \(-0.428878\pi\) | ||||
0.221580 | + | 0.975142i | \(0.428878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.64734 | −0.142513 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 55.1533 | 2.15174 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0511 | −0.469444 | −0.234722 | − | 0.972063i | \(-0.575418\pi\) | ||||
−0.234722 | + | 0.972063i | \(0.575418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.9301 | −0.464027 | −0.232013 | − | 0.972713i | \(-0.574531\pi\) | ||||
−0.232013 | + | 0.972713i | \(0.574531\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.3622 | −0.868477 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.5120 | −0.756642 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.43616 | −0.0943284 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −49.5390 | −1.91529 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.3541 | −1.28571 | −0.642854 | − | 0.765989i | \(-0.722250\pi\) | ||||
−0.642854 | + | 0.765989i | \(0.722250\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.9477 | 0.613826 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.9924 | 1.15270 | 0.576351 | − | 0.817202i | \(-0.304476\pi\) | ||||
0.576351 | + | 0.817202i | \(0.304476\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.77038 | 0.374953 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 51.7096 | 1.98152 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.1505 | −0.503190 | −0.251595 | − | 0.967833i | \(-0.580955\pi\) | ||||
−0.251595 | + | 0.967833i | \(0.580955\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.2579 | 0.621182 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 70.7180 | 2.69806 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.6806 | 1.13074 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.1763 | 0.995792 | 0.497896 | − | 0.867237i | \(-0.334106\pi\) | ||||
0.497896 | + | 0.867237i | \(0.334106\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.49232 | −0.284200 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.73397 | −0.368700 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.3009 | −0.881322 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.41481 | 0.0534368 | 0.0267184 | − | 0.999643i | \(-0.491494\pi\) | ||||
0.0267184 | + | 0.999643i | \(0.491494\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.05944 | 0.303968 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.2306 | 0.535957 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.7611 | −0.705582 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.68174 | 0.138271 | 0.0691353 | − | 0.997607i | \(-0.477976\pi\) | ||||
0.0691353 | + | 0.997607i | \(0.477976\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 54.8529 | 2.05715 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.85969 | 0.181997 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −42.7568 | −1.59678 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.95387 | 0.296629 | 0.148315 | − | 0.988940i | \(-0.452615\pi\) | ||||
0.148315 | + | 0.988940i | \(0.452615\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 61.0980 | 2.27541 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.1826 | 0.601837 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.381220 | −0.0141582 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.6495 | 1.32217 | 0.661083 | − | 0.750313i | \(-0.270097\pi\) | ||||
0.661083 | + | 0.750313i | \(0.270097\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 69.7867 | 2.58469 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.4330 | 0.422865 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.54263 | 0.352465 | 0.176233 | − | 0.984349i | \(-0.443609\pi\) | ||||
0.176233 | + | 0.984349i | \(0.443609\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.6359 | −0.650510 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.9555 | −1.28586 | −0.642929 | − | 0.765926i | \(-0.722281\pi\) | ||||
−0.642929 | + | 0.765926i | \(0.722281\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 78.0711 | 2.86801 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.7663 | −1.23876 | −0.619382 | − | 0.785089i | \(-0.712617\pi\) | ||||
−0.619382 | + | 0.785089i | \(0.712617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7025 | 0.428747 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 84.3203 | 3.08512 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.2951 | 0.449255 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.2772 | 0.484491 | 0.242246 | − | 0.970215i | \(-0.422116\pi\) | ||||
0.242246 | + | 0.970215i | \(0.422116\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.4292 | −0.562270 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.6007 | 0.458586 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.3056 | 0.592636 | 0.296318 | − | 0.955089i | \(-0.404241\pi\) | ||||
0.296318 | + | 0.955089i | \(0.404241\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.2704 | −0.771053 | −0.385526 | − | 0.922697i | \(-0.625980\pi\) | ||||
−0.385526 | + | 0.922697i | \(0.625980\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.2664 | −0.625085 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.4703 | −0.450865 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 54.2912 | 1.96034 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.81494 | −0.209692 | −0.104846 | − | 0.994488i | \(-0.533435\pi\) | ||||
−0.104846 | + | 0.994488i | \(0.533435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.33737 | 0.228235 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.6709 | 0.671544 | 0.335772 | − | 0.941943i | \(-0.391003\pi\) | ||||
0.335772 | + | 0.941943i | \(0.391003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.760465 | 0.0273167 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.8054 | 0.602892 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.9833 | 1.21758 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.07957 | −0.217266 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.47653 | 0.231157 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.3213 | 1.65118 | 0.825588 | − | 0.564274i | \(-0.190844\pi\) | ||||
0.825588 | + | 0.564274i | \(0.190844\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 54.9468 | 1.95616 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 60.3602 | 2.14616 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.9964 | 1.34929 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.8824 | 0.811553 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.11777 | −0.216702 | −0.108351 | − | 0.994113i | \(-0.534557\pi\) | ||||
−0.108351 | + | 0.994113i | \(0.534557\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.87131 | −0.243089 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.54189 | 0.125146 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.4628 | 0.791710 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.1069 | −0.531788 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.2124 | 0.499682 | 0.249841 | − | 0.968287i | \(-0.419622\pi\) | ||||
0.249841 | + | 0.968287i | \(0.419622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.6405 | −1.07593 | −0.537967 | − | 0.842966i | \(-0.680807\pi\) | ||||
−0.537967 | + | 0.842966i | \(0.680807\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −66.6570 | −2.33776 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.7737 | −0.762700 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.9150 | −1.39645 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 117.752 | 4.11460 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.53169 | −0.123257 | −0.0616285 | − | 0.998099i | \(-0.519629\pi\) | ||||
−0.0616285 | + | 0.998099i | \(0.519629\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.7928 | −1.03851 | −0.519256 | − | 0.854619i | \(-0.673791\pi\) | ||||
−0.519256 | + | 0.854619i | \(0.673791\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.4631 | 1.75477 | 0.877386 | − | 0.479785i | \(-0.159285\pi\) | ||||
0.877386 | + | 0.479785i | \(0.159285\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.2980 | −0.670246 | −0.335123 | − | 0.942174i | \(-0.608778\pi\) | ||||
−0.335123 | + | 0.942174i | \(0.608778\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.8027 | 0.548191 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.51555 | 0.295046 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.0881 | 0.660572 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.1276 | 0.419193 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.8989 | 0.583414 | 0.291707 | − | 0.956508i | \(-0.405777\pi\) | ||||
0.291707 | + | 0.956508i | \(0.405777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8547 | −0.994989 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −71.1197 | −2.44949 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.24299 | −0.180364 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.3508 | 1.38484 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.27830 | −0.318056 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.5816 | −1.62916 | −0.814582 | − | 0.580048i | \(-0.803034\pi\) | ||||
−0.814582 | + | 0.580048i | \(0.803034\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 43.5364 | 1.48891 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.8041 | 0.744813 | 0.372406 | − | 0.928070i | \(-0.378533\pi\) | ||||
0.372406 | + | 0.928070i | \(0.378533\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.3331 | 0.796116 | 0.398058 | − | 0.917360i | \(-0.369684\pi\) | ||||
0.398058 | + | 0.917360i | \(0.369684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 70.8615 | 2.41495 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.9086 | 0.745777 | 0.372889 | − | 0.927876i | \(-0.378367\pi\) | ||||
0.372889 | + | 0.927876i | \(0.378367\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.44630 | 0.0491756 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −47.6545 | −1.61843 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53.4474 | 1.81099 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.8003 | −0.737829 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.51508 | 0.118831 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.7358 | 1.78076 | 0.890381 | − | 0.455216i | \(-0.150438\pi\) | ||||
0.890381 | + | 0.455216i | \(0.150438\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 47.1518 | 1.59039 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3244 | 1.15642 | 0.578210 | − | 0.815888i | \(-0.303752\pi\) | ||||
0.578210 | + | 0.815888i | \(0.303752\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.7184 | −1.67316 | −0.836579 | − | 0.547846i | \(-0.815448\pi\) | ||||
−0.836579 | + | 0.547846i | \(0.815448\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 41.8560 | 1.40697 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.9815 | 0.402300 | 0.201150 | − | 0.979560i | \(-0.435532\pi\) | ||||
0.201150 | + | 0.979560i | \(0.435532\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.4427 | 1.82595 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.9891 | 0.802766 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.02979 | −0.301833 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −89.8780 | −3.00094 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.289905 | −0.00966886 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0488 | −0.368089 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −83.2301 | −2.76972 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.14725 | 0.0381359 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.2674 | −1.56949 | −0.784744 | − | 0.619820i | \(-0.787206\pi\) | ||||
−0.784744 | + | 0.619820i | \(0.787206\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41.8609 | 1.38844 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.85300 | 0.293313 | 0.146656 | − | 0.989187i | \(-0.453149\pi\) | ||||
0.146656 | + | 0.989187i | \(0.453149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.2934 | 0.968411 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.8207 | −0.423376 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.5141 | 0.544750 | 0.272375 | − | 0.962191i | \(-0.412191\pi\) | ||||
0.272375 | + | 0.962191i | \(0.412191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.87196 | −0.0616832 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.4312 | 1.03457 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.45191 | −0.0477384 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −136.326 | −4.47753 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.2898 | −0.370408 | −0.185204 | − | 0.982700i | \(-0.559295\pi\) | ||||
−0.185204 | + | 0.982700i | \(0.559295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.7295 | −0.974346 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.6028 | −1.10011 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.5727 | −0.704748 | −0.352374 | − | 0.935859i | \(-0.614626\pi\) | ||||
−0.352374 | + | 0.935859i | \(0.614626\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.7432 | −1.00327 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.3062 | 1.63994 | 0.819968 | − | 0.572409i | \(-0.193991\pi\) | ||||
0.819968 | + | 0.572409i | \(0.193991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.1227 | −1.27401 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 56.0573 | 1.82354 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.7335 | 1.35615 | 0.678077 | − | 0.734990i | \(-0.262813\pi\) | ||||
0.678077 | + | 0.734990i | \(0.262813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.0354 | −0.974990 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −93.1504 | −3.02061 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.2481 | −1.14180 | −0.570899 | − | 0.821021i | \(-0.693405\pi\) | ||||
−0.570899 | + | 0.821021i | \(0.693405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.9868 | −0.484960 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 57.1477 | 1.84540 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4217 | −0.981345 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.4337 | −0.884039 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.1821 | 0.488728 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.6156 | 0.695111 | 0.347556 | − | 0.937659i | \(-0.387012\pi\) | ||||
0.347556 | + | 0.937659i | \(0.387012\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.0625 | −0.933623 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.8335 | 0.379755 | 0.189878 | − | 0.981808i | \(-0.439191\pi\) | ||||
0.189878 | + | 0.981808i | \(0.439191\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.3361 | −0.844296 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.0645 | −0.450424 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.6998 | −1.65402 | −0.827011 | − | 0.562185i | \(-0.809961\pi\) | ||||
−0.827011 | + | 0.562185i | \(0.809961\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.5259 | 1.23004 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.1243 | 1.63061 | 0.815306 | − | 0.579030i | \(-0.196569\pi\) | ||||
0.815306 | + | 0.579030i | \(0.196569\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.95776 | 0.0942420 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 50.0218 | 1.59221 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45.9514 | 1.46117 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.16402 | −0.100508 | −0.0502542 | − | 0.998736i | \(-0.516003\pi\) | ||||
−0.0502542 | + | 0.998736i | \(0.516003\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.5130 | 0.555760 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.07974 | −0.161038 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.68777 | −0.180133 | −0.0900667 | − | 0.995936i | \(-0.528708\pi\) | ||||
−0.0900667 | + | 0.995936i | \(0.528708\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.1545 | −0.732577 |
(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 | 9680.2.a.dc.1.6 | 6 | ||
4.3 | odd | 2 | 4840.2.a.bb.1.1 | 6 | |||
11.5 | even | 5 | 880.2.bo.i.641.3 | 12 | |||
11.9 | even | 5 | 880.2.bo.i.81.3 | 12 | |||
11.10 | odd | 2 | 9680.2.a.dd.1.6 | 6 | |||
44.27 | odd | 10 | 440.2.y.c.201.1 | yes | 12 | ||
44.31 | odd | 10 | 440.2.y.c.81.1 | ✓ | 12 | ||
44.43 | even | 2 | 4840.2.a.ba.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.c.81.1 | ✓ | 12 | 44.31 | odd | 10 | ||
440.2.y.c.201.1 | yes | 12 | 44.27 | odd | 10 | ||
880.2.bo.i.81.3 | 12 | 11.9 | even | 5 | |||
880.2.bo.i.641.3 | 12 | 11.5 | even | 5 | |||
4840.2.a.ba.1.1 | 6 | 44.43 | even | 2 | |||
4840.2.a.bb.1.1 | 6 | 4.3 | odd | 2 | |||
9680.2.a.dc.1.6 | 6 | 1.1 | even | 1 | trivial | ||
9680.2.a.dd.1.6 | 6 | 11.10 | odd | 2 |