Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(1,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("975.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.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: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.08613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.08613 | −1.47512 | −0.737558 | − | 0.675283i | \(-0.764021\pi\) | ||||
−0.737558 | + | 0.675283i | \(0.764021\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.35194 | 1.17597 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.08613 | −0.851659 | ||||||||
\(7\) | 4.08613 | 1.54441 | 0.772206 | − | 0.635372i | \(-0.219153\pi\) | ||||
0.772206 | + | 0.635372i | \(0.219153\pi\) | |||||||
\(8\) | −0.734191 | −0.259576 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.43807 | −1.03662 | −0.518308 | − | 0.855194i | \(-0.673438\pi\) | ||||
−0.518308 | + | 0.855194i | \(0.673438\pi\) | |||||||
\(12\) | 2.35194 | 0.678946 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −8.52420 | −2.27819 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.17226 | −0.793065 | ||||||||
\(17\) | 7.17226 | 1.73953 | 0.869764 | − | 0.493467i | \(-0.164271\pi\) | ||||
0.869764 | + | 0.493467i | \(0.164271\pi\) | |||||||
\(18\) | −2.08613 | −0.491706 | ||||||||
\(19\) | 7.52420 | 1.72617 | 0.863085 | − | 0.505059i | \(-0.168529\pi\) | ||||
0.863085 | + | 0.505059i | \(0.168529\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.08613 | 0.891667 | ||||||||
\(22\) | 7.17226 | 1.52913 | ||||||||
\(23\) | −2.82032 | −0.588078 | −0.294039 | − | 0.955793i | \(-0.594999\pi\) | ||||
−0.294039 | + | 0.955793i | \(0.594999\pi\) | |||||||
\(24\) | −0.734191 | −0.149866 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.08613 | −0.409124 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 9.61033 | 1.81618 | ||||||||
\(29\) | −5.70388 | −1.05918 | −0.529592 | − | 0.848253i | \(-0.677655\pi\) | ||||
−0.529592 | + | 0.848253i | \(0.677655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.61033 | −1.00764 | −0.503822 | − | 0.863807i | \(-0.668073\pi\) | ||||
−0.503822 | + | 0.863807i | \(0.668073\pi\) | |||||||
\(32\) | 8.08613 | 1.42944 | ||||||||
\(33\) | −3.43807 | −0.598491 | ||||||||
\(34\) | −14.9623 | −2.56601 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.35194 | 0.391990 | ||||||||
\(37\) | 4.82032 | 0.792456 | 0.396228 | − | 0.918152i | \(-0.370319\pi\) | ||||
0.396228 | + | 0.918152i | \(0.370319\pi\) | |||||||
\(38\) | −15.6965 | −2.54630 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.52420 | 0.862735 | 0.431368 | − | 0.902176i | \(-0.358031\pi\) | ||||
0.431368 | + | 0.902176i | \(0.358031\pi\) | |||||||
\(42\) | −8.52420 | −1.31531 | ||||||||
\(43\) | −2.05582 | −0.313509 | −0.156755 | − | 0.987638i | \(-0.550103\pi\) | ||||
−0.156755 | + | 0.987638i | \(0.550103\pi\) | |||||||
\(44\) | −8.08613 | −1.21903 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.88356 | 0.867483 | ||||||||
\(47\) | −7.49389 | −1.09310 | −0.546548 | − | 0.837428i | \(-0.684058\pi\) | ||||
−0.546548 | + | 0.837428i | \(0.684058\pi\) | |||||||
\(48\) | −3.17226 | −0.457876 | ||||||||
\(49\) | 9.69646 | 1.38521 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.17226 | 1.00432 | ||||||||
\(52\) | 2.35194 | 0.326155 | ||||||||
\(53\) | −2.52420 | −0.346725 | −0.173363 | − | 0.984858i | \(-0.555463\pi\) | ||||
−0.173363 | + | 0.984858i | \(0.555463\pi\) | |||||||
\(54\) | −2.08613 | −0.283886 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | 7.52420 | 0.996605 | ||||||||
\(58\) | 11.8990 | 1.56242 | ||||||||
\(59\) | 4.79001 | 0.623606 | 0.311803 | − | 0.950147i | \(-0.399067\pi\) | ||||
0.311803 | + | 0.950147i | \(0.399067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.87614 | −1.00844 | −0.504218 | − | 0.863576i | \(-0.668219\pi\) | ||||
−0.504218 | + | 0.863576i | \(0.668219\pi\) | |||||||
\(62\) | 11.7039 | 1.48639 | ||||||||
\(63\) | 4.08613 | 0.514804 | ||||||||
\(64\) | −10.5242 | −1.31552 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.17226 | 0.882844 | ||||||||
\(67\) | −6.20257 | −0.757765 | −0.378882 | − | 0.925445i | \(-0.623692\pi\) | ||||
−0.378882 | + | 0.925445i | \(0.623692\pi\) | |||||||
\(68\) | 16.8687 | 2.04563 | ||||||||
\(69\) | −2.82032 | −0.339527 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.475800 | −0.0564671 | −0.0282336 | − | 0.999601i | \(-0.508988\pi\) | ||||
−0.0282336 | + | 0.999601i | \(0.508988\pi\) | |||||||
\(72\) | −0.734191 | −0.0865252 | ||||||||
\(73\) | 9.35194 | 1.09456 | 0.547281 | − | 0.836949i | \(-0.315663\pi\) | ||||
0.547281 | + | 0.836949i | \(0.315663\pi\) | |||||||
\(74\) | −10.0558 | −1.16897 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17.6965 | 2.02992 | ||||||||
\(77\) | −14.0484 | −1.60096 | ||||||||
\(78\) | −2.08613 | −0.236208 | ||||||||
\(79\) | 11.6965 | 1.31595 | 0.657977 | − | 0.753038i | \(-0.271412\pi\) | ||||
0.657977 | + | 0.753038i | \(0.271412\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.5242 | −1.27263 | ||||||||
\(83\) | 16.4307 | 1.80350 | 0.901749 | − | 0.432260i | \(-0.142284\pi\) | ||||
0.901749 | + | 0.432260i | \(0.142284\pi\) | |||||||
\(84\) | 9.61033 | 1.04857 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.28870 | 0.462463 | ||||||||
\(87\) | −5.70388 | −0.611520 | ||||||||
\(88\) | 2.52420 | 0.269081 | ||||||||
\(89\) | −10.1723 | −1.07826 | −0.539129 | − | 0.842223i | \(-0.681246\pi\) | ||||
−0.539129 | + | 0.842223i | \(0.681246\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.08613 | 0.428343 | ||||||||
\(92\) | −6.63322 | −0.691561 | ||||||||
\(93\) | −5.61033 | −0.581764 | ||||||||
\(94\) | 15.6332 | 1.61244 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.08613 | 0.825287 | ||||||||
\(97\) | 14.8761 | 1.51044 | 0.755222 | − | 0.655470i | \(-0.227529\pi\) | ||||
0.755222 | + | 0.655470i | \(0.227529\pi\) | |||||||
\(98\) | −20.2281 | −2.04334 | ||||||||
\(99\) | −3.43807 | −0.345539 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.94418 | −0.491965 | −0.245982 | − | 0.969274i | \(-0.579111\pi\) | ||||
−0.245982 | + | 0.969274i | \(0.579111\pi\) | |||||||
\(102\) | −14.9623 | −1.48149 | ||||||||
\(103\) | −8.28870 | −0.816710 | −0.408355 | − | 0.912823i | \(-0.633897\pi\) | ||||
−0.408355 | + | 0.912823i | \(0.633897\pi\) | |||||||
\(104\) | −0.734191 | −0.0719934 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.26581 | 0.511461 | ||||||||
\(107\) | 12.5168 | 1.21004 | 0.605021 | − | 0.796209i | \(-0.293165\pi\) | ||||
0.605021 | + | 0.796209i | \(0.293165\pi\) | |||||||
\(108\) | 2.35194 | 0.226315 | ||||||||
\(109\) | 11.6965 | 1.12032 | 0.560159 | − | 0.828385i | \(-0.310740\pi\) | ||||
0.560159 | + | 0.828385i | \(0.310740\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.82032 | 0.457525 | ||||||||
\(112\) | −12.9623 | −1.22482 | ||||||||
\(113\) | 1.23550 | 0.116226 | 0.0581129 | − | 0.998310i | \(-0.481492\pi\) | ||||
0.0581129 | + | 0.998310i | \(0.481492\pi\) | |||||||
\(114\) | −15.6965 | −1.47011 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.4152 | −1.24557 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −9.99258 | −0.919892 | ||||||||
\(119\) | 29.3068 | 2.68655 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.820321 | 0.0745747 | ||||||||
\(122\) | 16.4307 | 1.48756 | ||||||||
\(123\) | 5.52420 | 0.498100 | ||||||||
\(124\) | −13.1952 | −1.18496 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.52420 | −0.759396 | ||||||||
\(127\) | −9.52420 | −0.845136 | −0.422568 | − | 0.906331i | \(-0.638871\pi\) | ||||
−0.422568 | + | 0.906331i | \(0.638871\pi\) | |||||||
\(128\) | 5.78259 | 0.511114 | ||||||||
\(129\) | −2.05582 | −0.181005 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5726 | 0.923732 | 0.461866 | − | 0.886950i | \(-0.347180\pi\) | ||||
0.461866 | + | 0.886950i | \(0.347180\pi\) | |||||||
\(132\) | −8.08613 | −0.703807 | ||||||||
\(133\) | 30.7449 | 2.66592 | ||||||||
\(134\) | 12.9394 | 1.11779 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.26581 | −0.451539 | ||||||||
\(137\) | 4.53162 | 0.387162 | 0.193581 | − | 0.981084i | \(-0.437990\pi\) | ||||
0.193581 | + | 0.981084i | \(0.437990\pi\) | |||||||
\(138\) | 5.88356 | 0.500842 | ||||||||
\(139\) | −14.4562 | −1.22616 | −0.613078 | − | 0.790023i | \(-0.710069\pi\) | ||||
−0.613078 | + | 0.790023i | \(0.710069\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.49389 | −0.631099 | ||||||||
\(142\) | 0.992582 | 0.0832956 | ||||||||
\(143\) | −3.43807 | −0.287506 | ||||||||
\(144\) | −3.17226 | −0.264355 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.5094 | −1.61461 | ||||||||
\(147\) | 9.69646 | 0.799751 | ||||||||
\(148\) | 11.3371 | 0.931904 | ||||||||
\(149\) | 12.2839 | 1.00634 | 0.503168 | − | 0.864189i | \(-0.332168\pi\) | ||||
0.503168 | + | 0.864189i | \(0.332168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.6029 | 1.83940 | 0.919699 | − | 0.392623i | \(-0.128432\pi\) | ||||
0.919699 | + | 0.392623i | \(0.128432\pi\) | |||||||
\(152\) | −5.52420 | −0.448072 | ||||||||
\(153\) | 7.17226 | 0.579843 | ||||||||
\(154\) | 29.3068 | 2.36161 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.35194 | 0.188306 | ||||||||
\(157\) | 3.64806 | 0.291147 | 0.145573 | − | 0.989347i | \(-0.453497\pi\) | ||||
0.145573 | + | 0.989347i | \(0.453497\pi\) | |||||||
\(158\) | −24.4003 | −1.94119 | ||||||||
\(159\) | −2.52420 | −0.200182 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.5242 | −0.908234 | ||||||||
\(162\) | −2.08613 | −0.163902 | ||||||||
\(163\) | −0.820321 | −0.0642525 | −0.0321263 | − | 0.999484i | \(-0.510228\pi\) | ||||
−0.0321263 | + | 0.999484i | \(0.510228\pi\) | |||||||
\(164\) | 12.9926 | 1.01455 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −34.2765 | −2.66037 | ||||||||
\(167\) | 9.46357 | 0.732313 | 0.366157 | − | 0.930553i | \(-0.380673\pi\) | ||||
0.366157 | + | 0.930553i | \(0.380673\pi\) | |||||||
\(168\) | −3.00000 | −0.231455 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.52420 | 0.575390 | ||||||||
\(172\) | −4.83516 | −0.368677 | ||||||||
\(173\) | −6.69646 | −0.509122 | −0.254561 | − | 0.967057i | \(-0.581931\pi\) | ||||
−0.254561 | + | 0.967057i | \(0.581931\pi\) | |||||||
\(174\) | 11.8990 | 0.902063 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.9065 | 0.822105 | ||||||||
\(177\) | 4.79001 | 0.360039 | ||||||||
\(178\) | 21.2207 | 1.59056 | ||||||||
\(179\) | −15.1042 | −1.12894 | −0.564471 | − | 0.825453i | \(-0.690920\pi\) | ||||
−0.564471 | + | 0.825453i | \(0.690920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.70869 | −0.127006 | −0.0635028 | − | 0.997982i | \(-0.520227\pi\) | ||||
−0.0635028 | + | 0.997982i | \(0.520227\pi\) | |||||||
\(182\) | −8.52420 | −0.631856 | ||||||||
\(183\) | −7.87614 | −0.582221 | ||||||||
\(184\) | 2.07065 | 0.152651 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.7039 | 0.858170 | ||||||||
\(187\) | −24.6587 | −1.80322 | ||||||||
\(188\) | −17.6252 | −1.28545 | ||||||||
\(189\) | 4.08613 | 0.297222 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.6406 | −1.71058 | −0.855288 | − | 0.518152i | \(-0.826620\pi\) | ||||
−0.855288 | + | 0.518152i | \(0.826620\pi\) | |||||||
\(192\) | −10.5242 | −0.759519 | ||||||||
\(193\) | −21.4487 | −1.54391 | −0.771957 | − | 0.635675i | \(-0.780722\pi\) | ||||
−0.771957 | + | 0.635675i | \(0.780722\pi\) | |||||||
\(194\) | −31.0336 | −2.22808 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.8055 | 1.62896 | ||||||||
\(197\) | 4.57260 | 0.325784 | 0.162892 | − | 0.986644i | \(-0.447918\pi\) | ||||
0.162892 | + | 0.986644i | \(0.447918\pi\) | |||||||
\(198\) | 7.17226 | 0.509710 | ||||||||
\(199\) | 5.65548 | 0.400906 | 0.200453 | − | 0.979703i | \(-0.435759\pi\) | ||||
0.200453 | + | 0.979703i | \(0.435759\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.20257 | −0.437496 | ||||||||
\(202\) | 10.3142 | 0.725705 | ||||||||
\(203\) | −23.3068 | −1.63582 | ||||||||
\(204\) | 16.8687 | 1.18105 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.2913 | 1.20474 | ||||||||
\(207\) | −2.82032 | −0.196026 | ||||||||
\(208\) | −3.17226 | −0.219957 | ||||||||
\(209\) | −25.8687 | −1.78938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.63583 | −0.387987 | −0.193993 | − | 0.981003i | \(-0.562144\pi\) | ||||
−0.193993 | + | 0.981003i | \(0.562144\pi\) | |||||||
\(212\) | −5.93676 | −0.407739 | ||||||||
\(213\) | −0.475800 | −0.0326013 | ||||||||
\(214\) | −26.1116 | −1.78495 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.734191 | −0.0499554 | ||||||||
\(217\) | −22.9245 | −1.55622 | ||||||||
\(218\) | −24.4003 | −1.65260 | ||||||||
\(219\) | 9.35194 | 0.631945 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.17226 | 0.482458 | ||||||||
\(222\) | −10.0558 | −0.674902 | ||||||||
\(223\) | −6.22808 | −0.417063 | −0.208531 | − | 0.978016i | \(-0.566868\pi\) | ||||
−0.208531 | + | 0.978016i | \(0.566868\pi\) | |||||||
\(224\) | 33.0410 | 2.20764 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.57741 | −0.171447 | ||||||||
\(227\) | −14.8458 | −0.985352 | −0.492676 | − | 0.870213i | \(-0.663981\pi\) | ||||
−0.492676 | + | 0.870213i | \(0.663981\pi\) | |||||||
\(228\) | 17.6965 | 1.17198 | ||||||||
\(229\) | −25.5046 | −1.68539 | −0.842694 | − | 0.538392i | \(-0.819032\pi\) | ||||
−0.842694 | + | 0.538392i | \(0.819032\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.0484 | −0.924317 | ||||||||
\(232\) | 4.18774 | 0.274938 | ||||||||
\(233\) | 4.17226 | 0.273334 | 0.136667 | − | 0.990617i | \(-0.456361\pi\) | ||||
0.136667 | + | 0.990617i | \(0.456361\pi\) | |||||||
\(234\) | −2.08613 | −0.136375 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.2658 | 0.733342 | ||||||||
\(237\) | 11.6965 | 0.759767 | ||||||||
\(238\) | −61.1378 | −3.96297 | ||||||||
\(239\) | 23.3068 | 1.50759 | 0.753795 | − | 0.657109i | \(-0.228221\pi\) | ||||
0.753795 | + | 0.657109i | \(0.228221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.3371 | −1.63211 | −0.816053 | − | 0.577977i | \(-0.803842\pi\) | ||||
−0.816053 | + | 0.577977i | \(0.803842\pi\) | |||||||
\(242\) | −1.71130 | −0.110006 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −18.5242 | −1.18589 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.5242 | −0.734756 | ||||||||
\(247\) | 7.52420 | 0.478753 | ||||||||
\(248\) | 4.11905 | 0.261560 | ||||||||
\(249\) | 16.4307 | 1.04125 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.24030 | −0.330765 | −0.165383 | − | 0.986229i | \(-0.552886\pi\) | ||||
−0.165383 | + | 0.986229i | \(0.552886\pi\) | |||||||
\(252\) | 9.61033 | 0.605394 | ||||||||
\(253\) | 9.69646 | 0.609611 | ||||||||
\(254\) | 19.8687 | 1.24667 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.98516 | 0.561573 | ||||||||
\(257\) | 23.4610 | 1.46345 | 0.731727 | − | 0.681597i | \(-0.238714\pi\) | ||||
0.731727 | + | 0.681597i | \(0.238714\pi\) | |||||||
\(258\) | 4.28870 | 0.267003 | ||||||||
\(259\) | 19.6965 | 1.22388 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.70388 | −0.353061 | ||||||||
\(262\) | −22.0558 | −1.36261 | ||||||||
\(263\) | 18.0410 | 1.11245 | 0.556227 | − | 0.831030i | \(-0.312248\pi\) | ||||
0.556227 | + | 0.831030i | \(0.312248\pi\) | |||||||
\(264\) | 2.52420 | 0.155354 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −64.1378 | −3.93254 | ||||||||
\(267\) | −10.1723 | −0.622532 | ||||||||
\(268\) | −14.5881 | −0.891108 | ||||||||
\(269\) | −27.8761 | −1.69964 | −0.849819 | − | 0.527074i | \(-0.823289\pi\) | ||||
−0.849819 | + | 0.527074i | \(0.823289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0713 | −1.21924 | −0.609622 | − | 0.792692i | \(-0.708679\pi\) | ||||
−0.609622 | + | 0.792692i | \(0.708679\pi\) | |||||||
\(272\) | −22.7523 | −1.37956 | ||||||||
\(273\) | 4.08613 | 0.247304 | ||||||||
\(274\) | −9.45355 | −0.571110 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.63322 | −0.399273 | ||||||||
\(277\) | −8.40515 | −0.505016 | −0.252508 | − | 0.967595i | \(-0.581255\pi\) | ||||
−0.252508 | + | 0.967595i | \(0.581255\pi\) | |||||||
\(278\) | 30.1574 | 1.80872 | ||||||||
\(279\) | −5.61033 | −0.335882 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4562 | −0.623762 | −0.311881 | − | 0.950121i | \(-0.600959\pi\) | ||||
−0.311881 | + | 0.950121i | \(0.600959\pi\) | |||||||
\(282\) | 15.6332 | 0.930945 | ||||||||
\(283\) | −18.3445 | −1.09047 | −0.545234 | − | 0.838284i | \(-0.683559\pi\) | ||||
−0.545234 | + | 0.838284i | \(0.683559\pi\) | |||||||
\(284\) | −1.11905 | −0.0664036 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.17226 | 0.424105 | ||||||||
\(287\) | 22.5726 | 1.33242 | ||||||||
\(288\) | 8.08613 | 0.476480 | ||||||||
\(289\) | 34.4413 | 2.02596 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.8761 | 0.872055 | ||||||||
\(292\) | 21.9952 | 1.28717 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | −20.2281 | −1.17973 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.53904 | −0.205702 | ||||||||
\(297\) | −3.43807 | −0.199497 | ||||||||
\(298\) | −25.6258 | −1.48446 | ||||||||
\(299\) | −2.82032 | −0.163103 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.40034 | −0.484187 | ||||||||
\(302\) | −47.1526 | −2.71333 | ||||||||
\(303\) | −4.94418 | −0.284036 | ||||||||
\(304\) | −23.8687 | −1.36897 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −14.9623 | −0.855336 | ||||||||
\(307\) | −13.9293 | −0.794990 | −0.397495 | − | 0.917604i | \(-0.630120\pi\) | ||||
−0.397495 | + | 0.917604i | \(0.630120\pi\) | |||||||
\(308\) | −33.0410 | −1.88268 | ||||||||
\(309\) | −8.28870 | −0.471528 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | −0.734191 | −0.0415654 | ||||||||
\(313\) | −30.0894 | −1.70075 | −0.850376 | − | 0.526175i | \(-0.823626\pi\) | ||||
−0.850376 | + | 0.526175i | \(0.823626\pi\) | |||||||
\(314\) | −7.61033 | −0.429476 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 27.5094 | 1.54752 | ||||||||
\(317\) | −4.05582 | −0.227797 | −0.113899 | − | 0.993492i | \(-0.536334\pi\) | ||||
−0.113899 | + | 0.993492i | \(0.536334\pi\) | |||||||
\(318\) | 5.26581 | 0.295292 | ||||||||
\(319\) | 19.6103 | 1.09797 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.5168 | 0.698619 | ||||||||
\(322\) | 24.0410 | 1.33975 | ||||||||
\(323\) | 53.9655 | 3.00272 | ||||||||
\(324\) | 2.35194 | 0.130663 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.71130 | 0.0947800 | ||||||||
\(327\) | 11.6965 | 0.646816 | ||||||||
\(328\) | −4.05582 | −0.223945 | ||||||||
\(329\) | −30.6210 | −1.68819 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.4126 | −1.06701 | −0.533506 | − | 0.845797i | \(-0.679126\pi\) | ||||
−0.533506 | + | 0.845797i | \(0.679126\pi\) | |||||||
\(332\) | 38.6439 | 2.12086 | ||||||||
\(333\) | 4.82032 | 0.264152 | ||||||||
\(334\) | −19.7422 | −1.08025 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.9623 | −0.707150 | ||||||||
\(337\) | 20.1797 | 1.09926 | 0.549629 | − | 0.835409i | \(-0.314769\pi\) | ||||
0.549629 | + | 0.835409i | \(0.314769\pi\) | |||||||
\(338\) | −2.08613 | −0.113471 | ||||||||
\(339\) | 1.23550 | 0.0671030 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.2887 | 1.04454 | ||||||||
\(342\) | −15.6965 | −0.848767 | ||||||||
\(343\) | 11.0181 | 0.594921 | ||||||||
\(344\) | 1.50936 | 0.0813794 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.9697 | 0.751015 | ||||||||
\(347\) | 18.8007 | 1.00927 | 0.504637 | − | 0.863332i | \(-0.331626\pi\) | ||||
0.504637 | + | 0.863332i | \(0.331626\pi\) | |||||||
\(348\) | −13.4152 | −0.719129 | ||||||||
\(349\) | −4.47580 | −0.239584 | −0.119792 | − | 0.992799i | \(-0.538223\pi\) | ||||
−0.119792 | + | 0.992799i | \(0.538223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −27.8007 | −1.48178 | ||||||||
\(353\) | 26.8203 | 1.42750 | 0.713751 | − | 0.700400i | \(-0.246995\pi\) | ||||
0.713751 | + | 0.700400i | \(0.246995\pi\) | |||||||
\(354\) | −9.99258 | −0.531100 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −23.9245 | −1.26800 | ||||||||
\(357\) | 29.3068 | 1.55108 | ||||||||
\(358\) | 31.5094 | 1.66532 | ||||||||
\(359\) | −5.89903 | −0.311339 | −0.155670 | − | 0.987809i | \(-0.549753\pi\) | ||||
−0.155670 | + | 0.987809i | \(0.549753\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.6136 | 1.97966 | ||||||||
\(362\) | 3.56454 | 0.187348 | ||||||||
\(363\) | 0.820321 | 0.0430557 | ||||||||
\(364\) | 9.61033 | 0.503718 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16.4307 | 0.858844 | ||||||||
\(367\) | 18.0968 | 0.944645 | 0.472323 | − | 0.881426i | \(-0.343416\pi\) | ||||
0.472323 | + | 0.881426i | \(0.343416\pi\) | |||||||
\(368\) | 8.94679 | 0.466384 | ||||||||
\(369\) | 5.52420 | 0.287578 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.3142 | −0.535487 | ||||||||
\(372\) | −13.1952 | −0.684137 | ||||||||
\(373\) | −12.8836 | −0.667085 | −0.333543 | − | 0.942735i | \(-0.608244\pi\) | ||||
−0.333543 | + | 0.942735i | \(0.608244\pi\) | |||||||
\(374\) | 51.4413 | 2.65997 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.50194 | 0.283741 | ||||||||
\(377\) | −5.70388 | −0.293765 | ||||||||
\(378\) | −8.52420 | −0.438438 | ||||||||
\(379\) | −19.0032 | −0.976131 | −0.488066 | − | 0.872807i | \(-0.662297\pi\) | ||||
−0.488066 | + | 0.872807i | \(0.662297\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.52420 | −0.487940 | ||||||||
\(382\) | 49.3175 | 2.52330 | ||||||||
\(383\) | 9.62100 | 0.491610 | 0.245805 | − | 0.969319i | \(-0.420948\pi\) | ||||
0.245805 | + | 0.969319i | \(0.420948\pi\) | |||||||
\(384\) | 5.78259 | 0.295092 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 44.7449 | 2.27745 | ||||||||
\(387\) | −2.05582 | −0.104503 | ||||||||
\(388\) | 34.9878 | 1.77624 | ||||||||
\(389\) | −2.41998 | −0.122698 | −0.0613490 | − | 0.998116i | \(-0.519540\pi\) | ||||
−0.0613490 | + | 0.998116i | \(0.519540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.2281 | −1.02298 | ||||||||
\(392\) | −7.11905 | −0.359567 | ||||||||
\(393\) | 10.5726 | 0.533317 | ||||||||
\(394\) | −9.53904 | −0.480570 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.08613 | −0.406343 | ||||||||
\(397\) | −26.6136 | −1.33570 | −0.667849 | − | 0.744297i | \(-0.732785\pi\) | ||||
−0.667849 | + | 0.744297i | \(0.732785\pi\) | |||||||
\(398\) | −11.7981 | −0.591384 | ||||||||
\(399\) | 30.7449 | 1.53917 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4758 | 0.623012 | 0.311506 | − | 0.950244i | \(-0.399167\pi\) | ||||
0.311506 | + | 0.950244i | \(0.399167\pi\) | |||||||
\(402\) | 12.9394 | 0.645357 | ||||||||
\(403\) | −5.61033 | −0.279470 | ||||||||
\(404\) | −11.6284 | −0.578535 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 48.6210 | 2.41302 | ||||||||
\(407\) | −16.5726 | −0.821473 | ||||||||
\(408\) | −5.26581 | −0.260696 | ||||||||
\(409\) | 16.2281 | 0.802427 | 0.401213 | − | 0.915985i | \(-0.368589\pi\) | ||||
0.401213 | + | 0.915985i | \(0.368589\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.53162 | 0.223528 | ||||||||
\(412\) | −19.4945 | −0.960426 | ||||||||
\(413\) | 19.5726 | 0.963105 | ||||||||
\(414\) | 5.88356 | 0.289161 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8.08613 | 0.396455 | ||||||||
\(417\) | −14.4562 | −0.707921 | ||||||||
\(418\) | 53.9655 | 2.63954 | ||||||||
\(419\) | −38.3855 | −1.87525 | −0.937627 | − | 0.347642i | \(-0.886982\pi\) | ||||
−0.937627 | + | 0.347642i | \(0.886982\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.95160 | 0.436274 | 0.218137 | − | 0.975918i | \(-0.430002\pi\) | ||||
0.218137 | + | 0.975918i | \(0.430002\pi\) | |||||||
\(422\) | 11.7571 | 0.572326 | ||||||||
\(423\) | −7.49389 | −0.364365 | ||||||||
\(424\) | 1.85324 | 0.0900015 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.992582 | 0.0480907 | ||||||||
\(427\) | −32.1829 | −1.55744 | ||||||||
\(428\) | 29.4387 | 1.42297 | ||||||||
\(429\) | −3.43807 | −0.165992 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.99519 | −0.0961050 | −0.0480525 | − | 0.998845i | \(-0.515301\pi\) | ||||
−0.0480525 | + | 0.998845i | \(0.515301\pi\) | |||||||
\(432\) | −3.17226 | −0.152625 | ||||||||
\(433\) | 36.9729 | 1.77681 | 0.888403 | − | 0.459064i | \(-0.151815\pi\) | ||||
0.888403 | + | 0.459064i | \(0.151815\pi\) | |||||||
\(434\) | 47.8236 | 2.29560 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.5094 | 1.31746 | ||||||||
\(437\) | −21.2207 | −1.01512 | ||||||||
\(438\) | −19.5094 | −0.932193 | ||||||||
\(439\) | −5.06804 | −0.241885 | −0.120942 | − | 0.992660i | \(-0.538592\pi\) | ||||
−0.120942 | + | 0.992660i | \(0.538592\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.69646 | 0.461736 | ||||||||
\(442\) | −14.9623 | −0.711683 | ||||||||
\(443\) | 5.59966 | 0.266048 | 0.133024 | − | 0.991113i | \(-0.457531\pi\) | ||||
0.133024 | + | 0.991113i | \(0.457531\pi\) | |||||||
\(444\) | 11.3371 | 0.538035 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.9926 | 0.615217 | ||||||||
\(447\) | 12.2839 | 0.581008 | ||||||||
\(448\) | −43.0032 | −2.03171 | ||||||||
\(449\) | 13.9852 | 0.660001 | 0.330000 | − | 0.943981i | \(-0.392951\pi\) | ||||
0.330000 | + | 0.943981i | \(0.392951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.9926 | −0.894326 | ||||||||
\(452\) | 2.90581 | 0.136678 | ||||||||
\(453\) | 22.6029 | 1.06198 | ||||||||
\(454\) | 30.9703 | 1.45351 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.52420 | −0.258694 | ||||||||
\(457\) | −31.6210 | −1.47917 | −0.739584 | − | 0.673064i | \(-0.764978\pi\) | ||||
−0.739584 | + | 0.673064i | \(0.764978\pi\) | |||||||
\(458\) | 53.2058 | 2.48614 | ||||||||
\(459\) | 7.17226 | 0.334772 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.0484 | 1.35292 | 0.676459 | − | 0.736480i | \(-0.263513\pi\) | ||||
0.676459 | + | 0.736480i | \(0.263513\pi\) | |||||||
\(462\) | 29.3068 | 1.36348 | ||||||||
\(463\) | −30.8458 | −1.43353 | −0.716764 | − | 0.697316i | \(-0.754377\pi\) | ||||
−0.716764 | + | 0.697316i | \(0.754377\pi\) | |||||||
\(464\) | 18.0942 | 0.840002 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.70388 | −0.403199 | ||||||||
\(467\) | −17.3323 | −0.802043 | −0.401021 | − | 0.916069i | \(-0.631345\pi\) | ||||
−0.401021 | + | 0.916069i | \(0.631345\pi\) | |||||||
\(468\) | 2.35194 | 0.108718 | ||||||||
\(469\) | −25.3445 | −1.17030 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.64806 | 0.168094 | ||||||||
\(472\) | −3.51678 | −0.161873 | ||||||||
\(473\) | 7.06804 | 0.324989 | ||||||||
\(474\) | −24.4003 | −1.12074 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 68.9278 | 3.15930 | ||||||||
\(477\) | −2.52420 | −0.115575 | ||||||||
\(478\) | −48.6210 | −2.22387 | ||||||||
\(479\) | −9.20518 | −0.420596 | −0.210298 | − | 0.977637i | \(-0.567443\pi\) | ||||
−0.210298 | + | 0.977637i | \(0.567443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.82032 | 0.219788 | ||||||||
\(482\) | 52.8565 | 2.40755 | ||||||||
\(483\) | −11.5242 | −0.524369 | ||||||||
\(484\) | 1.92935 | 0.0876975 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.08613 | −0.0946288 | ||||||||
\(487\) | 27.8432 | 1.26170 | 0.630848 | − | 0.775906i | \(-0.282707\pi\) | ||||
0.630848 | + | 0.775906i | \(0.282707\pi\) | |||||||
\(488\) | 5.78259 | 0.261766 | ||||||||
\(489\) | −0.820321 | −0.0370962 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.6406 | −1.06689 | −0.533444 | − | 0.845836i | \(-0.679102\pi\) | ||||
−0.533444 | + | 0.845836i | \(0.679102\pi\) | |||||||
\(492\) | 12.9926 | 0.585751 | ||||||||
\(493\) | −40.9097 | −1.84248 | ||||||||
\(494\) | −15.6965 | −0.706217 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.7974 | 0.799128 | ||||||||
\(497\) | −1.94418 | −0.0872085 | ||||||||
\(498\) | −34.2765 | −1.53597 | ||||||||
\(499\) | −16.1829 | −0.724447 | −0.362224 | − | 0.932091i | \(-0.617982\pi\) | ||||
−0.362224 | + | 0.932091i | \(0.617982\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.46357 | 0.422801 | ||||||||
\(502\) | 10.9320 | 0.487917 | ||||||||
\(503\) | −12.4758 | −0.556268 | −0.278134 | − | 0.960542i | \(-0.589716\pi\) | ||||
−0.278134 | + | 0.960542i | \(0.589716\pi\) | |||||||
\(504\) | −3.00000 | −0.133631 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −20.2281 | −0.899248 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −22.4003 | −0.993854 | ||||||||
\(509\) | −10.0558 | −0.445716 | −0.222858 | − | 0.974851i | \(-0.571539\pi\) | ||||
−0.222858 | + | 0.974851i | \(0.571539\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.2132 | 1.69045 | ||||||||
\(512\) | −30.3094 | −1.33950 | ||||||||
\(513\) | 7.52420 | 0.332202 | ||||||||
\(514\) | −48.9426 | −2.15877 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.83516 | −0.212856 | ||||||||
\(517\) | 25.7645 | 1.13312 | ||||||||
\(518\) | −41.0894 | −1.80536 | ||||||||
\(519\) | −6.69646 | −0.293942 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.7523 | 1.39109 | 0.695546 | − | 0.718481i | \(-0.255162\pi\) | ||||
0.695546 | + | 0.718481i | \(0.255162\pi\) | |||||||
\(522\) | 11.8990 | 0.520807 | ||||||||
\(523\) | −18.9878 | −0.830277 | −0.415139 | − | 0.909758i | \(-0.636267\pi\) | ||||
−0.415139 | + | 0.909758i | \(0.636267\pi\) | |||||||
\(524\) | 24.8661 | 1.08628 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −37.6358 | −1.64100 | ||||||||
\(527\) | −40.2387 | −1.75283 | ||||||||
\(528\) | 10.9065 | 0.474642 | ||||||||
\(529\) | −15.0458 | −0.654165 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.79001 | 0.207869 | ||||||||
\(532\) | 72.3100 | 3.13504 | ||||||||
\(533\) | 5.52420 | 0.239280 | ||||||||
\(534\) | 21.2207 | 0.918308 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.55387 | 0.196697 | ||||||||
\(537\) | −15.1042 | −0.651795 | ||||||||
\(538\) | 58.1533 | 2.50716 | ||||||||
\(539\) | −33.3371 | −1.43593 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.00742 | 0.0433123 | 0.0216562 | − | 0.999765i | \(-0.493106\pi\) | ||||
0.0216562 | + | 0.999765i | \(0.493106\pi\) | |||||||
\(542\) | 41.8713 | 1.79853 | ||||||||
\(543\) | −1.70869 | −0.0733267 | ||||||||
\(544\) | 57.9958 | 2.48655 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.52420 | −0.364802 | ||||||||
\(547\) | −0.662898 | −0.0283435 | −0.0141717 | − | 0.999900i | \(-0.504511\pi\) | ||||
−0.0141717 | + | 0.999900i | \(0.504511\pi\) | |||||||
\(548\) | 10.6581 | 0.455291 | ||||||||
\(549\) | −7.87614 | −0.336145 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.9171 | −1.82833 | ||||||||
\(552\) | 2.07065 | 0.0881329 | ||||||||
\(553\) | 47.7933 | 2.03238 | ||||||||
\(554\) | 17.5342 | 0.744958 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −34.0000 | −1.44192 | ||||||||
\(557\) | −16.8809 | −0.715269 | −0.357634 | − | 0.933862i | \(-0.616417\pi\) | ||||
−0.357634 | + | 0.933862i | \(0.616417\pi\) | |||||||
\(558\) | 11.7039 | 0.495465 | ||||||||
\(559\) | −2.05582 | −0.0869518 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.6587 | −1.04109 | ||||||||
\(562\) | 21.8129 | 0.920122 | ||||||||
\(563\) | 18.7087 | 0.788477 | 0.394239 | − | 0.919008i | \(-0.371008\pi\) | ||||
0.394239 | + | 0.919008i | \(0.371008\pi\) | |||||||
\(564\) | −17.6252 | −0.742153 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 38.2691 | 1.60857 | ||||||||
\(567\) | 4.08613 | 0.171601 | ||||||||
\(568\) | 0.349328 | 0.0146575 | ||||||||
\(569\) | −16.5848 | −0.695272 | −0.347636 | − | 0.937630i | \(-0.613016\pi\) | ||||
−0.347636 | + | 0.937630i | \(0.613016\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.460964 | −0.0192907 | −0.00964536 | − | 0.999953i | \(-0.503070\pi\) | ||||
−0.00964536 | + | 0.999953i | \(0.503070\pi\) | |||||||
\(572\) | −8.08613 | −0.338098 | ||||||||
\(573\) | −23.6406 | −0.987602 | ||||||||
\(574\) | −47.0894 | −1.96547 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10.5242 | −0.438508 | ||||||||
\(577\) | 23.9394 | 0.996609 | 0.498305 | − | 0.867002i | \(-0.333956\pi\) | ||||
0.498305 | + | 0.867002i | \(0.333956\pi\) | |||||||
\(578\) | −71.8491 | −2.98853 | ||||||||
\(579\) | −21.4487 | −0.891379 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 67.1378 | 2.78534 | ||||||||
\(582\) | −31.0336 | −1.28638 | ||||||||
\(583\) | 8.67837 | 0.359422 | ||||||||
\(584\) | −6.86611 | −0.284122 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.5168 | −0.517063 | ||||||||
\(587\) | −32.7194 | −1.35047 | −0.675236 | − | 0.737602i | \(-0.735958\pi\) | ||||
−0.675236 | + | 0.737602i | \(0.735958\pi\) | |||||||
\(588\) | 22.8055 | 0.940482 | ||||||||
\(589\) | −42.2132 | −1.73937 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.57260 | 0.188092 | ||||||||
\(592\) | −15.2913 | −0.628469 | ||||||||
\(593\) | 0.825129 | 0.0338840 | 0.0169420 | − | 0.999856i | \(-0.494607\pi\) | ||||
0.0169420 | + | 0.999856i | \(0.494607\pi\) | |||||||
\(594\) | 7.17226 | 0.294281 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 28.8910 | 1.18342 | ||||||||
\(597\) | 5.65548 | 0.231463 | ||||||||
\(598\) | 5.88356 | 0.240597 | ||||||||
\(599\) | −11.2913 | −0.461351 | −0.230675 | − | 0.973031i | \(-0.574094\pi\) | ||||
−0.230675 | + | 0.973031i | \(0.574094\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.64806 | 0.393553 | 0.196776 | − | 0.980448i | \(-0.436953\pi\) | ||||
0.196776 | + | 0.980448i | \(0.436953\pi\) | |||||||
\(602\) | 17.5242 | 0.714233 | ||||||||
\(603\) | −6.20257 | −0.252588 | ||||||||
\(604\) | 53.1607 | 2.16308 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.3142 | 0.418986 | ||||||||
\(607\) | −24.6284 | −0.999637 | −0.499818 | − | 0.866130i | \(-0.666600\pi\) | ||||
−0.499818 | + | 0.866130i | \(0.666600\pi\) | |||||||
\(608\) | 60.8417 | 2.46746 | ||||||||
\(609\) | −23.3068 | −0.944439 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.49389 | −0.303170 | ||||||||
\(612\) | 16.8687 | 0.681878 | ||||||||
\(613\) | 10.3445 | 0.417811 | 0.208906 | − | 0.977936i | \(-0.433010\pi\) | ||||
0.208906 | + | 0.977936i | \(0.433010\pi\) | |||||||
\(614\) | 29.0584 | 1.17270 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.3142 | 0.415571 | ||||||||
\(617\) | 32.8613 | 1.32295 | 0.661473 | − | 0.749969i | \(-0.269932\pi\) | ||||
0.661473 | + | 0.749969i | \(0.269932\pi\) | |||||||
\(618\) | 17.2913 | 0.695559 | ||||||||
\(619\) | 36.8565 | 1.48139 | 0.740694 | − | 0.671843i | \(-0.234497\pi\) | ||||
0.740694 | + | 0.671843i | \(0.234497\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.82032 | −0.113176 | ||||||||
\(622\) | 37.5503 | 1.50563 | ||||||||
\(623\) | −41.5652 | −1.66527 | ||||||||
\(624\) | −3.17226 | −0.126992 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 62.7704 | 2.50881 | ||||||||
\(627\) | −25.8687 | −1.03310 | ||||||||
\(628\) | 8.58002 | 0.342380 | ||||||||
\(629\) | 34.5726 | 1.37850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6965 | −1.02296 | −0.511480 | − | 0.859295i | \(-0.670903\pi\) | ||||
−0.511480 | + | 0.859295i | \(0.670903\pi\) | |||||||
\(632\) | −8.58744 | −0.341590 | ||||||||
\(633\) | −5.63583 | −0.224004 | ||||||||
\(634\) | 8.46096 | 0.336028 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.93676 | −0.235408 | ||||||||
\(637\) | 9.69646 | 0.384188 | ||||||||
\(638\) | −40.9097 | −1.61963 | ||||||||
\(639\) | −0.475800 | −0.0188224 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.4535 | 0.728871 | 0.364436 | − | 0.931229i | \(-0.381262\pi\) | ||||
0.364436 | + | 0.931229i | \(0.381262\pi\) | |||||||
\(642\) | −26.1116 | −1.03054 | ||||||||
\(643\) | −16.7087 | −0.658926 | −0.329463 | − | 0.944168i | \(-0.606868\pi\) | ||||
−0.329463 | + | 0.944168i | \(0.606868\pi\) | |||||||
\(644\) | −27.1042 | −1.06806 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −112.579 | −4.42937 | ||||||||
\(647\) | 28.6136 | 1.12492 | 0.562458 | − | 0.826826i | \(-0.309856\pi\) | ||||
0.562458 | + | 0.826826i | \(0.309856\pi\) | |||||||
\(648\) | −0.734191 | −0.0288417 | ||||||||
\(649\) | −16.4684 | −0.646441 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.9245 | −0.898483 | ||||||||
\(652\) | −1.92935 | −0.0755590 | ||||||||
\(653\) | −39.7252 | −1.55457 | −0.777284 | − | 0.629150i | \(-0.783403\pi\) | ||||
−0.777284 | + | 0.629150i | \(0.783403\pi\) | |||||||
\(654\) | −24.4003 | −0.954129 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.5242 | −0.684205 | ||||||||
\(657\) | 9.35194 | 0.364854 | ||||||||
\(658\) | 63.8794 | 2.49028 | ||||||||
\(659\) | 5.21585 | 0.203181 | 0.101590 | − | 0.994826i | \(-0.467607\pi\) | ||||
0.101590 | + | 0.994826i | \(0.467607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.3493 | 0.791497 | 0.395749 | − | 0.918359i | \(-0.370485\pi\) | ||||
0.395749 | + | 0.918359i | \(0.370485\pi\) | |||||||
\(662\) | 40.4971 | 1.57397 | ||||||||
\(663\) | 7.17226 | 0.278548 | ||||||||
\(664\) | −12.0632 | −0.468144 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.0558 | −0.389655 | ||||||||
\(667\) | 16.0868 | 0.622882 | ||||||||
\(668\) | 22.2578 | 0.861178 | ||||||||
\(669\) | −6.22808 | −0.240791 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.0787 | 1.04536 | ||||||||
\(672\) | 33.0410 | 1.27458 | ||||||||
\(673\) | 18.2765 | 0.704506 | 0.352253 | − | 0.935905i | \(-0.385416\pi\) | ||||
0.352253 | + | 0.935905i | \(0.385416\pi\) | |||||||
\(674\) | −42.0974 | −1.62153 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.35194 | 0.0904592 | ||||||||
\(677\) | −43.2664 | −1.66286 | −0.831432 | − | 0.555626i | \(-0.812479\pi\) | ||||
−0.831432 | + | 0.555626i | \(0.812479\pi\) | |||||||
\(678\) | −2.57741 | −0.0989847 | ||||||||
\(679\) | 60.7858 | 2.33275 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8458 | −0.568893 | ||||||||
\(682\) | −40.2387 | −1.54082 | ||||||||
\(683\) | −25.8432 | −0.988863 | −0.494432 | − | 0.869217i | \(-0.664624\pi\) | ||||
−0.494432 | + | 0.869217i | \(0.664624\pi\) | |||||||
\(684\) | 17.6965 | 0.676641 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −22.9852 | −0.877578 | ||||||||
\(687\) | −25.5046 | −0.973059 | ||||||||
\(688\) | 6.52159 | 0.248633 | ||||||||
\(689\) | −2.52420 | −0.0961643 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.94743 | −0.340376 | −0.170188 | − | 0.985412i | \(-0.554438\pi\) | ||||
−0.170188 | + | 0.985412i | \(0.554438\pi\) | |||||||
\(692\) | −15.7497 | −0.598712 | ||||||||
\(693\) | −14.0484 | −0.533655 | ||||||||
\(694\) | −39.2207 | −1.48880 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.18774 | 0.158736 | ||||||||
\(697\) | 39.6210 | 1.50075 | ||||||||
\(698\) | 9.33710 | 0.353415 | ||||||||
\(699\) | 4.17226 | 0.157809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.4897 | −1.00050 | −0.500251 | − | 0.865880i | \(-0.666759\pi\) | ||||
−0.500251 | + | 0.865880i | \(0.666759\pi\) | |||||||
\(702\) | −2.08613 | −0.0787359 | ||||||||
\(703\) | 36.2691 | 1.36791 | ||||||||
\(704\) | 36.1829 | 1.36370 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −55.9507 | −2.10573 | ||||||||
\(707\) | −20.2026 | −0.759796 | ||||||||
\(708\) | 11.2658 | 0.423395 | ||||||||
\(709\) | 19.3977 | 0.728497 | 0.364248 | − | 0.931302i | \(-0.381326\pi\) | ||||
0.364248 | + | 0.931302i | \(0.381326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.6965 | 0.438652 | ||||||||
\(712\) | 7.46838 | 0.279889 | ||||||||
\(713\) | 15.8229 | 0.592573 | ||||||||
\(714\) | −61.1378 | −2.28802 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −35.5242 | −1.32760 | ||||||||
\(717\) | 23.3068 | 0.870408 | ||||||||
\(718\) | 12.3062 | 0.459261 | ||||||||
\(719\) | −32.0261 | −1.19437 | −0.597187 | − | 0.802102i | \(-0.703715\pi\) | ||||
−0.597187 | + | 0.802102i | \(0.703715\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.8687 | −1.26134 | ||||||||
\(722\) | −78.4668 | −2.92023 | ||||||||
\(723\) | −25.3371 | −0.942297 | ||||||||
\(724\) | −4.01873 | −0.149355 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.71130 | −0.0635122 | ||||||||
\(727\) | 5.46357 | 0.202633 | 0.101316 | − | 0.994854i | \(-0.467695\pi\) | ||||
0.101316 | + | 0.994854i | \(0.467695\pi\) | |||||||
\(728\) | −3.00000 | −0.111187 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.7449 | −0.545358 | ||||||||
\(732\) | −18.5242 | −0.684674 | ||||||||
\(733\) | −45.6406 | −1.68578 | −0.842888 | − | 0.538089i | \(-0.819146\pi\) | ||||
−0.842888 | + | 0.538089i | \(0.819146\pi\) | |||||||
\(734\) | −37.7523 | −1.39346 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.8055 | −0.840621 | ||||||||
\(737\) | 21.3249 | 0.785512 | ||||||||
\(738\) | −11.5242 | −0.424212 | ||||||||
\(739\) | 34.9278 | 1.28484 | 0.642420 | − | 0.766353i | \(-0.277931\pi\) | ||||
0.642420 | + | 0.766353i | \(0.277931\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.52420 | 0.276408 | ||||||||
\(742\) | 21.5168 | 0.789906 | ||||||||
\(743\) | −52.3962 | −1.92223 | −0.961115 | − | 0.276150i | \(-0.910941\pi\) | ||||
−0.961115 | + | 0.276150i | \(0.910941\pi\) | |||||||
\(744\) | 4.11905 | 0.151012 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.8768 | 0.984029 | ||||||||
\(747\) | 16.4307 | 0.601166 | ||||||||
\(748\) | −57.9958 | −2.12054 | ||||||||
\(749\) | 51.1452 | 1.86880 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.9655 | 1.16644 | 0.583219 | − | 0.812315i | \(-0.301793\pi\) | ||||
0.583219 | + | 0.812315i | \(0.301793\pi\) | |||||||
\(752\) | 23.7726 | 0.866896 | ||||||||
\(753\) | −5.24030 | −0.190967 | ||||||||
\(754\) | 11.8990 | 0.433337 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.61033 | 0.349524 | ||||||||
\(757\) | 34.4897 | 1.25355 | 0.626775 | − | 0.779200i | \(-0.284374\pi\) | ||||
0.626775 | + | 0.779200i | \(0.284374\pi\) | |||||||
\(758\) | 39.6433 | 1.43991 | ||||||||
\(759\) | 9.69646 | 0.351959 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.7933 | −0.717505 | −0.358753 | − | 0.933433i | \(-0.616798\pi\) | ||||
−0.358753 | + | 0.933433i | \(0.616798\pi\) | |||||||
\(762\) | 19.8687 | 0.719768 | ||||||||
\(763\) | 47.7933 | 1.73023 | ||||||||
\(764\) | −55.6014 | −2.01159 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.0707 | −0.725182 | ||||||||
\(767\) | 4.79001 | 0.172957 | ||||||||
\(768\) | 8.98516 | 0.324224 | ||||||||
\(769\) | 4.65287 | 0.167787 | 0.0838934 | − | 0.996475i | \(-0.473264\pi\) | ||||
0.0838934 | + | 0.996475i | \(0.473264\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.4610 | 0.844926 | ||||||||
\(772\) | −50.4461 | −1.81560 | ||||||||
\(773\) | 20.6284 | 0.741953 | 0.370976 | − | 0.928642i | \(-0.379023\pi\) | ||||
0.370976 | + | 0.928642i | \(0.379023\pi\) | |||||||
\(774\) | 4.28870 | 0.154154 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.9219 | −0.392074 | ||||||||
\(777\) | 19.6965 | 0.706607 | ||||||||
\(778\) | 5.04840 | 0.180994 | ||||||||
\(779\) | 41.5652 | 1.48923 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.63583 | 0.0585348 | ||||||||
\(782\) | 42.1984 | 1.50901 | ||||||||
\(783\) | −5.70388 | −0.203840 | ||||||||
\(784\) | −30.7597 | −1.09856 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −22.0558 | −0.786705 | ||||||||
\(787\) | −26.1877 | −0.933492 | −0.466746 | − | 0.884391i | \(-0.654574\pi\) | ||||
−0.466746 | + | 0.884391i | \(0.654574\pi\) | |||||||
\(788\) | 10.7545 | 0.383112 | ||||||||
\(789\) | 18.0410 | 0.642276 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.04840 | 0.179500 | ||||||||
\(792\) | 2.52420 | 0.0896935 | ||||||||
\(793\) | −7.87614 | −0.279690 | ||||||||
\(794\) | 55.5194 | 1.97031 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.3013 | 0.471454 | ||||||||
\(797\) | 17.2180 | 0.609895 | 0.304947 | − | 0.952369i | \(-0.401361\pi\) | ||||
0.304947 | + | 0.952369i | \(0.401361\pi\) | |||||||
\(798\) | −64.1378 | −2.27045 | ||||||||
\(799\) | −53.7481 | −1.90147 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.1723 | −0.359419 | ||||||||
\(802\) | −26.0261 | −0.919015 | ||||||||
\(803\) | −32.1526 | −1.13464 | ||||||||
\(804\) | −14.5881 | −0.514482 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.7039 | 0.412252 | ||||||||
\(807\) | −27.8761 | −0.981287 | ||||||||
\(808\) | 3.62997 | 0.127702 | ||||||||
\(809\) | 13.4684 | 0.473523 | 0.236762 | − | 0.971568i | \(-0.423914\pi\) | ||||
0.236762 | + | 0.971568i | \(0.423914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.83841 | −0.275244 | −0.137622 | − | 0.990485i | \(-0.543946\pi\) | ||||
−0.137622 | + | 0.990485i | \(0.543946\pi\) | |||||||
\(812\) | −54.8162 | −1.92367 | ||||||||
\(813\) | −20.0713 | −0.703931 | ||||||||
\(814\) | 34.5726 | 1.21177 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −22.7523 | −0.796489 | ||||||||
\(817\) | −15.4684 | −0.541170 | ||||||||
\(818\) | −33.8539 | −1.18367 | ||||||||
\(819\) | 4.08613 | 0.142781 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.8203 | 1.14544 | 0.572719 | − | 0.819752i | \(-0.305889\pi\) | ||||
0.572719 | + | 0.819752i | \(0.305889\pi\) | |||||||
\(822\) | −9.45355 | −0.329730 | ||||||||
\(823\) | 24.1478 | 0.841740 | 0.420870 | − | 0.907121i | \(-0.361725\pi\) | ||||
0.420870 | + | 0.907121i | \(0.361725\pi\) | |||||||
\(824\) | 6.08549 | 0.211998 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −40.8310 | −1.42069 | ||||||||
\(827\) | −10.1058 | −0.351412 | −0.175706 | − | 0.984443i | \(-0.556221\pi\) | ||||
−0.175706 | + | 0.984443i | \(0.556221\pi\) | |||||||
\(828\) | −6.63322 | −0.230520 | ||||||||
\(829\) | −3.54645 | −0.123173 | −0.0615867 | − | 0.998102i | \(-0.519616\pi\) | ||||
−0.0615867 | + | 0.998102i | \(0.519616\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.40515 | −0.291571 | ||||||||
\(832\) | −10.5242 | −0.364861 | ||||||||
\(833\) | 69.5455 | 2.40961 | ||||||||
\(834\) | 30.1574 | 1.04427 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −60.8417 | −2.10425 | ||||||||
\(837\) | −5.61033 | −0.193921 | ||||||||
\(838\) | 80.0772 | 2.76622 | ||||||||
\(839\) | −27.1797 | −0.938347 | −0.469173 | − | 0.883106i | \(-0.655448\pi\) | ||||
−0.469173 | + | 0.883106i | \(0.655448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.53423 | 0.121870 | ||||||||
\(842\) | −18.6742 | −0.643556 | ||||||||
\(843\) | −10.4562 | −0.360129 | ||||||||
\(844\) | −13.2551 | −0.456261 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.6332 | 0.537481 | ||||||||
\(847\) | 3.35194 | 0.115174 | ||||||||
\(848\) | 8.00742 | 0.274976 | ||||||||
\(849\) | −18.3445 | −0.629582 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.5949 | −0.466026 | ||||||||
\(852\) | −1.11905 | −0.0383381 | ||||||||
\(853\) | 14.4413 | 0.494461 | 0.247231 | − | 0.968957i | \(-0.420479\pi\) | ||||
0.247231 | + | 0.968957i | \(0.420479\pi\) | |||||||
\(854\) | 67.1378 | 2.29741 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.18971 | −0.314098 | ||||||||
\(857\) | −20.7858 | −0.710031 | −0.355015 | − | 0.934860i | \(-0.615524\pi\) | ||||
−0.355015 | + | 0.934860i | \(0.615524\pi\) | |||||||
\(858\) | 7.17226 | 0.244857 | ||||||||
\(859\) | 20.9926 | 0.716258 | 0.358129 | − | 0.933672i | \(-0.383415\pi\) | ||||
0.358129 | + | 0.933672i | \(0.383415\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.5726 | 0.769272 | ||||||||
\(862\) | 4.16223 | 0.141766 | ||||||||
\(863\) | −25.3020 | −0.861289 | −0.430645 | − | 0.902522i | \(-0.641714\pi\) | ||||
−0.430645 | + | 0.902522i | \(0.641714\pi\) | |||||||
\(864\) | 8.08613 | 0.275096 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −77.1304 | −2.62100 | ||||||||
\(867\) | 34.4413 | 1.16969 | ||||||||
\(868\) | −53.9171 | −1.83007 | ||||||||
\(869\) | −40.2132 | −1.36414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.20257 | −0.210166 | ||||||||
\(872\) | −8.58744 | −0.290807 | ||||||||
\(873\) | 14.8761 | 0.503481 | ||||||||
\(874\) | 44.2691 | 1.49742 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.9952 | 0.743149 | ||||||||
\(877\) | 27.9342 | 0.943269 | 0.471635 | − | 0.881794i | \(-0.343664\pi\) | ||||
0.471635 | + | 0.881794i | \(0.343664\pi\) | |||||||
\(878\) | 10.5726 | 0.356808 | ||||||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.9900 | −1.31361 | −0.656803 | − | 0.754062i | \(-0.728092\pi\) | ||||
−0.656803 | + | 0.754062i | \(0.728092\pi\) | |||||||
\(882\) | −20.2281 | −0.681115 | ||||||||
\(883\) | −12.1871 | −0.410128 | −0.205064 | − | 0.978749i | \(-0.565740\pi\) | ||||
−0.205064 | + | 0.978749i | \(0.565740\pi\) | |||||||
\(884\) | 16.8687 | 0.567356 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.6816 | −0.392452 | ||||||||
\(887\) | 32.1526 | 1.07958 | 0.539790 | − | 0.841800i | \(-0.318504\pi\) | ||||
0.539790 | + | 0.841800i | \(0.318504\pi\) | |||||||
\(888\) | −3.53904 | −0.118762 | ||||||||
\(889\) | −38.9171 | −1.30524 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.43807 | −0.115180 | ||||||||
\(892\) | −14.6481 | −0.490453 | ||||||||
\(893\) | −56.3855 | −1.88687 | ||||||||
\(894\) | −25.6258 | −0.857055 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 23.6284 | 0.789370 | ||||||||
\(897\) | −2.82032 | −0.0941678 | ||||||||
\(898\) | −29.1749 | −0.973578 | ||||||||
\(899\) | 32.0006 | 1.06728 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1042 | −0.603139 | ||||||||
\(902\) | 39.6210 | 1.31923 | ||||||||
\(903\) | −8.40034 | −0.279546 | ||||||||
\(904\) | −0.907090 | −0.0301694 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −47.1526 | −1.56654 | ||||||||
\(907\) | −42.9368 | −1.42569 | −0.712846 | − | 0.701321i | \(-0.752594\pi\) | ||||
−0.712846 | + | 0.701321i | \(0.752594\pi\) | |||||||
\(908\) | −34.9165 | −1.15874 | ||||||||
\(909\) | −4.94418 | −0.163988 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.22808 | 0.272608 | 0.136304 | − | 0.990667i | \(-0.456478\pi\) | ||||
0.136304 | + | 0.990667i | \(0.456478\pi\) | |||||||
\(912\) | −23.8687 | −0.790372 | ||||||||
\(913\) | −56.4897 | −1.86954 | ||||||||
\(914\) | 65.9655 | 2.18195 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −59.9852 | −1.98197 | ||||||||
\(917\) | 43.2010 | 1.42662 | ||||||||
\(918\) | −14.9623 | −0.493828 | ||||||||
\(919\) | −27.5652 | −0.909291 | −0.454646 | − | 0.890672i | \(-0.650234\pi\) | ||||
−0.454646 | + | 0.890672i | \(0.650234\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.9293 | −0.458988 | ||||||||
\(922\) | −60.5987 | −1.99571 | ||||||||
\(923\) | −0.475800 | −0.0156612 | ||||||||
\(924\) | −33.0410 | −1.08697 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 64.3484 | 2.11462 | ||||||||
\(927\) | −8.28870 | −0.272237 | ||||||||
\(928\) | −46.1223 | −1.51404 | ||||||||
\(929\) | −24.2084 | −0.794253 | −0.397126 | − | 0.917764i | \(-0.629993\pi\) | ||||
−0.397126 | + | 0.917764i | \(0.629993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 72.9581 | 2.39111 | ||||||||
\(932\) | 9.81290 | 0.321432 | ||||||||
\(933\) | −18.0000 | −0.589294 | ||||||||
\(934\) | 36.1574 | 1.18311 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.734191 | −0.0239978 | ||||||||
\(937\) | 2.58002 | 0.0842855 | 0.0421427 | − | 0.999112i | \(-0.486582\pi\) | ||||
0.0421427 | + | 0.999112i | \(0.486582\pi\) | |||||||
\(938\) | 52.8720 | 1.72633 | ||||||||
\(939\) | −30.0894 | −0.981930 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.6088 | 0.997817 | 0.498909 | − | 0.866655i | \(-0.333734\pi\) | ||||
0.498909 | + | 0.866655i | \(0.333734\pi\) | |||||||
\(942\) | −7.61033 | −0.247958 | ||||||||
\(943\) | −15.5800 | −0.507355 | ||||||||
\(944\) | −15.1952 | −0.494560 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.7449 | −0.479397 | ||||||||
\(947\) | −51.3626 | −1.66906 | −0.834530 | − | 0.550962i | \(-0.814261\pi\) | ||||
−0.834530 | + | 0.550962i | \(0.814261\pi\) | |||||||
\(948\) | 27.5094 | 0.893463 | ||||||||
\(949\) | 9.35194 | 0.303577 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.05582 | −0.131519 | ||||||||
\(952\) | −21.5168 | −0.697363 | ||||||||
\(953\) | 9.06543 | 0.293658 | 0.146829 | − | 0.989162i | \(-0.453093\pi\) | ||||
0.146829 | + | 0.989162i | \(0.453093\pi\) | |||||||
\(954\) | 5.26581 | 0.170487 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 54.8162 | 1.77288 | ||||||||
\(957\) | 19.6103 | 0.633912 | ||||||||
\(958\) | 19.2032 | 0.620428 | ||||||||
\(959\) | 18.5168 | 0.597938 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.475800 | 0.0153484 | ||||||||
\(962\) | −10.0558 | −0.324213 | ||||||||
\(963\) | 12.5168 | 0.403348 | ||||||||
\(964\) | −59.5913 | −1.91931 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 24.0410 | 0.773506 | ||||||||
\(967\) | −47.8942 | −1.54017 | −0.770087 | − | 0.637939i | \(-0.779787\pi\) | ||||
−0.770087 | + | 0.637939i | \(0.779787\pi\) | |||||||
\(968\) | −0.602272 | −0.0193578 | ||||||||
\(969\) | 53.9655 | 1.73362 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.59485 | −0.243730 | −0.121865 | − | 0.992547i | \(-0.538888\pi\) | ||||
−0.121865 | + | 0.992547i | \(0.538888\pi\) | |||||||
\(972\) | 2.35194 | 0.0754385 | ||||||||
\(973\) | −59.0697 | −1.89369 | ||||||||
\(974\) | −58.0846 | −1.86115 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.9852 | 0.799756 | ||||||||
\(977\) | −23.0484 | −0.737384 | −0.368692 | − | 0.929552i | \(-0.620194\pi\) | ||||
−0.368692 | + | 0.929552i | \(0.620194\pi\) | |||||||
\(978\) | 1.71130 | 0.0547212 | ||||||||
\(979\) | 34.9729 | 1.11774 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.6965 | 0.373439 | ||||||||
\(982\) | 49.3175 | 1.57378 | ||||||||
\(983\) | −26.2026 | −0.835732 | −0.417866 | − | 0.908509i | \(-0.637222\pi\) | ||||
−0.417866 | + | 0.908509i | \(0.637222\pi\) | |||||||
\(984\) | −4.05582 | −0.129295 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 85.3430 | 2.71787 | ||||||||
\(987\) | −30.6210 | −0.974677 | ||||||||
\(988\) | 17.6965 | 0.562999 | ||||||||
\(989\) | 5.79807 | 0.184368 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.9023 | 1.48990 | 0.744950 | − | 0.667120i | \(-0.232473\pi\) | ||||
0.744950 | + | 0.667120i | \(0.232473\pi\) | |||||||
\(992\) | −45.3659 | −1.44037 | ||||||||
\(993\) | −19.4126 | −0.616039 | ||||||||
\(994\) | 4.05582 | 0.128643 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 38.6439 | 1.22448 | ||||||||
\(997\) | 36.5503 | 1.15756 | 0.578780 | − | 0.815483i | \(-0.303529\pi\) | ||||
0.578780 | + | 0.815483i | \(0.303529\pi\) | |||||||
\(998\) | 33.7597 | 1.06864 | ||||||||
\(999\) | 4.82032 | 0.152508 |
(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 | 975.2.a.p.1.1 | yes | 3 | |
3.2 | odd | 2 | 2925.2.a.bg.1.3 | 3 | |||
5.2 | odd | 4 | 975.2.c.j.274.2 | 6 | |||
5.3 | odd | 4 | 975.2.c.j.274.5 | 6 | |||
5.4 | even | 2 | 975.2.a.n.1.3 | ✓ | 3 | ||
15.2 | even | 4 | 2925.2.c.x.2224.5 | 6 | |||
15.8 | even | 4 | 2925.2.c.x.2224.2 | 6 | |||
15.14 | odd | 2 | 2925.2.a.bi.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
975.2.a.n.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
975.2.a.p.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
975.2.c.j.274.2 | 6 | 5.2 | odd | 4 | |||
975.2.c.j.274.5 | 6 | 5.3 | odd | 4 | |||
2925.2.a.bg.1.3 | 3 | 3.2 | odd | 2 | |||
2925.2.a.bi.1.1 | 3 | 15.14 | odd | 2 | |||
2925.2.c.x.2224.2 | 6 | 15.8 | even | 4 | |||
2925.2.c.x.2224.5 | 6 | 15.2 | even | 4 |