Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 605) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.86620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.34889 | 1.66092 | 0.830460 | − | 0.557079i | \(-0.188078\pi\) | ||||
0.830460 | + | 0.557079i | \(0.188078\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.51730 | 1.75865 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.38350 | 1.27884 | 0.639422 | − | 0.768856i | \(-0.279174\pi\) | ||||
0.639422 | + | 0.768856i | \(0.279174\pi\) | |||||||
\(8\) | 3.56399 | 1.26006 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.34889 | 0.742786 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.48270 | −0.411226 | −0.205613 | − | 0.978633i | \(-0.565919\pi\) | ||||
−0.205613 | + | 0.978633i | \(0.565919\pi\) | |||||||
\(14\) | 7.94749 | 2.12406 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.33682 | 0.334205 | ||||||||
\(17\) | −3.73240 | −0.905239 | −0.452620 | − | 0.891704i | \(-0.649510\pi\) | ||||
−0.452620 | + | 0.891704i | \(0.649510\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.21509 | 0.737593 | 0.368796 | − | 0.929510i | \(-0.379770\pi\) | ||||
0.368796 | + | 0.929510i | \(0.379770\pi\) | |||||||
\(20\) | 3.51730 | 0.786493 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.51730 | 0.524894 | 0.262447 | − | 0.964946i | \(-0.415470\pi\) | ||||
0.262447 | + | 0.964946i | \(0.415470\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.48270 | −0.683013 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 11.9008 | 2.24904 | ||||||||
\(29\) | 4.69779 | 0.872357 | 0.436179 | − | 0.899860i | \(-0.356332\pi\) | ||||
0.436179 | + | 0.899860i | \(0.356332\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.21509 | 1.65508 | 0.827540 | − | 0.561407i | \(-0.189740\pi\) | ||||
0.827540 | + | 0.561407i | \(0.189740\pi\) | |||||||
\(32\) | −3.98793 | −0.704972 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.76700 | −1.50353 | ||||||||
\(35\) | 3.38350 | 0.571916 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.69779 | −0.443514 | −0.221757 | − | 0.975102i | \(-0.571179\pi\) | ||||
−0.221757 | + | 0.975102i | \(0.571179\pi\) | |||||||
\(38\) | 7.55191 | 1.22508 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.56399 | 0.563516 | ||||||||
\(41\) | 4.55191 | 0.710889 | 0.355445 | − | 0.934697i | \(-0.384329\pi\) | ||||
0.355445 | + | 0.934697i | \(0.384329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.38350 | −0.820976 | −0.410488 | − | 0.911866i | \(-0.634642\pi\) | ||||
−0.410488 | + | 0.911866i | \(0.634642\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.91288 | 0.871807 | ||||||||
\(47\) | 10.5294 | 1.53587 | 0.767934 | − | 0.640529i | \(-0.221285\pi\) | ||||
0.767934 | + | 0.640529i | \(0.221285\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.44809 | 0.635441 | ||||||||
\(50\) | 2.34889 | 0.332184 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.21509 | −0.723203 | ||||||||
\(53\) | 2.51730 | 0.345778 | 0.172889 | − | 0.984941i | \(-0.444690\pi\) | ||||
0.172889 | + | 0.984941i | \(0.444690\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.0588 | 1.61142 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.0346 | 1.44892 | ||||||||
\(59\) | −11.9129 | −1.55092 | −0.775462 | − | 0.631394i | \(-0.782483\pi\) | ||||
−0.775462 | + | 0.631394i | \(0.782483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.6799 | 1.75153 | 0.875765 | − | 0.482738i | \(-0.160358\pi\) | ||||
0.875765 | + | 0.482738i | \(0.160358\pi\) | |||||||
\(62\) | 21.6453 | 2.74895 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.0409 | −1.50511 | ||||||||
\(65\) | −1.48270 | −0.183906 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.83159 | 0.956781 | 0.478391 | − | 0.878147i | \(-0.341220\pi\) | ||||
0.478391 | + | 0.878147i | \(0.341220\pi\) | |||||||
\(68\) | −13.1280 | −1.59200 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.94749 | 0.949907 | ||||||||
\(71\) | −2.51730 | −0.298749 | −0.149375 | − | 0.988781i | \(-0.547726\pi\) | ||||
−0.149375 | + | 0.988781i | \(0.547726\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.96539 | 0.347073 | 0.173536 | − | 0.984827i | \(-0.444481\pi\) | ||||
0.173536 | + | 0.984827i | \(0.444481\pi\) | |||||||
\(74\) | −6.33682 | −0.736640 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.3085 | 1.29717 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.76700 | −0.761348 | −0.380674 | − | 0.924709i | \(-0.624308\pi\) | ||||
−0.380674 | + | 0.924709i | \(0.624308\pi\) | |||||||
\(80\) | 1.33682 | 0.149461 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.6920 | 1.18073 | ||||||||
\(83\) | 7.55191 | 0.828930 | 0.414465 | − | 0.910065i | \(-0.363969\pi\) | ||||
0.414465 | + | 0.910065i | \(0.363969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.73240 | −0.404835 | ||||||||
\(86\) | −12.6453 | −1.36358 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8016 | −1.14497 | −0.572484 | − | 0.819916i | \(-0.694020\pi\) | ||||
−0.572484 | + | 0.819916i | \(0.694020\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.01671 | −0.525894 | ||||||||
\(92\) | 8.85412 | 0.923106 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 24.7324 | 2.55095 | ||||||||
\(95\) | 3.21509 | 0.329862 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0167 | 1.11858 | 0.559288 | − | 0.828973i | \(-0.311074\pi\) | ||||
0.559288 | + | 0.828973i | \(0.311074\pi\) | |||||||
\(98\) | 10.4481 | 1.05542 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.51730 | 0.351730 | ||||||||
\(101\) | −12.7324 | −1.26692 | −0.633460 | − | 0.773775i | \(-0.718366\pi\) | ||||
−0.633460 | + | 0.773775i | \(0.718366\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.3431 | −1.80740 | −0.903698 | − | 0.428170i | \(-0.859158\pi\) | ||||
−0.903698 | + | 0.428170i | \(0.859158\pi\) | |||||||
\(104\) | −5.28431 | −0.518169 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.91288 | 0.574310 | ||||||||
\(107\) | 7.13380 | 0.689651 | 0.344825 | − | 0.938667i | \(-0.387938\pi\) | ||||
0.344825 | + | 0.938667i | \(0.387938\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.14588 | −0.397103 | −0.198551 | − | 0.980090i | \(-0.563624\pi\) | ||||
−0.198551 | + | 0.980090i | \(0.563624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.52313 | 0.427396 | ||||||||
\(113\) | −1.46479 | −0.137796 | −0.0688981 | − | 0.997624i | \(-0.521948\pi\) | ||||
−0.0688981 | + | 0.997624i | \(0.521948\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.51730 | 0.234740 | ||||||||
\(116\) | 16.5236 | 1.53417 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −27.9821 | −2.57596 | ||||||||
\(119\) | −12.6286 | −1.15766 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 32.1326 | 2.90915 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 32.4123 | 2.91071 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2964 | −1.00239 | −0.501196 | − | 0.865334i | \(-0.667106\pi\) | ||||
−0.501196 | + | 0.865334i | \(0.667106\pi\) | |||||||
\(128\) | −20.3068 | −1.79489 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.48270 | −0.305453 | ||||||||
\(131\) | −14.6799 | −1.28259 | −0.641294 | − | 0.767295i | \(-0.721602\pi\) | ||||
−0.641294 | + | 0.767295i | \(0.721602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.8783 | 0.943266 | ||||||||
\(134\) | 18.3956 | 1.58914 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.3022 | −1.14066 | ||||||||
\(137\) | 15.6453 | 1.33667 | 0.668333 | − | 0.743862i | \(-0.267008\pi\) | ||||
0.668333 | + | 0.743862i | \(0.267008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.64528 | −0.648464 | −0.324232 | − | 0.945978i | \(-0.605106\pi\) | ||||
−0.324232 | + | 0.945978i | \(0.605106\pi\) | |||||||
\(140\) | 11.9008 | 1.00580 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.91288 | −0.496198 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.69779 | 0.390130 | ||||||||
\(146\) | 6.96539 | 0.576460 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.48894 | −0.779986 | ||||||||
\(149\) | 6.48270 | 0.531083 | 0.265542 | − | 0.964099i | \(-0.414449\pi\) | ||||
0.265542 | + | 0.964099i | \(0.414449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.8783 | −0.885261 | −0.442631 | − | 0.896704i | \(-0.645955\pi\) | ||||
−0.442631 | + | 0.896704i | \(0.645955\pi\) | |||||||
\(152\) | 11.4585 | 0.929411 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.21509 | 0.740174 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4302 | 0.832419 | 0.416210 | − | 0.909269i | \(-0.363358\pi\) | ||||
0.416210 | + | 0.909269i | \(0.363358\pi\) | |||||||
\(158\) | −15.8950 | −1.26454 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.98793 | −0.315273 | ||||||||
\(161\) | 8.51730 | 0.671258 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.2439 | −0.802362 | −0.401181 | − | 0.915999i | \(-0.631400\pi\) | ||||
−0.401181 | + | 0.915999i | \(0.631400\pi\) | |||||||
\(164\) | 16.0105 | 1.25021 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.7386 | 1.37679 | ||||||||
\(167\) | −1.04668 | −0.0809947 | −0.0404974 | − | 0.999180i | \(-0.512894\pi\) | ||||
−0.0404974 | + | 0.999180i | \(0.512894\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8016 | −0.830893 | ||||||||
\(170\) | −8.76700 | −0.672399 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −18.9354 | −1.44381 | ||||||||
\(173\) | 11.9129 | 0.905720 | 0.452860 | − | 0.891582i | \(-0.350404\pi\) | ||||
0.452860 | + | 0.891582i | \(0.350404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.38350 | 0.255769 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −25.3718 | −1.90170 | ||||||||
\(179\) | 3.39558 | 0.253797 | 0.126899 | − | 0.991916i | \(-0.459498\pi\) | ||||
0.126899 | + | 0.991916i | \(0.459498\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.69779 | −0.423513 | −0.211757 | − | 0.977322i | \(-0.567918\pi\) | ||||
−0.211757 | + | 0.977322i | \(0.567918\pi\) | |||||||
\(182\) | −11.7837 | −0.873467 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.97164 | 0.661398 | ||||||||
\(185\) | −2.69779 | −0.198345 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 37.0350 | 2.70106 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.55191 | 0.547873 | ||||||||
\(191\) | 9.01671 | 0.652426 | 0.326213 | − | 0.945296i | \(-0.394227\pi\) | ||||
0.326213 | + | 0.945296i | \(0.394227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.2318 | −1.88821 | −0.944103 | − | 0.329650i | \(-0.893069\pi\) | ||||
−0.944103 | + | 0.329650i | \(0.893069\pi\) | |||||||
\(194\) | 25.8771 | 1.85787 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.6453 | 1.11752 | ||||||||
\(197\) | −16.6978 | −1.18967 | −0.594834 | − | 0.803849i | \(-0.702782\pi\) | ||||
−0.594834 | + | 0.803849i | \(0.702782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7912 | −1.19029 | −0.595147 | − | 0.803617i | \(-0.702906\pi\) | ||||
−0.595147 | + | 0.803617i | \(0.702906\pi\) | |||||||
\(200\) | 3.56399 | 0.252012 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −29.9071 | −2.10425 | ||||||||
\(203\) | 15.8950 | 1.11561 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.55191 | 0.317919 | ||||||||
\(206\) | −43.0859 | −3.00194 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.98210 | −0.137434 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.64528 | −0.526323 | −0.263161 | − | 0.964752i | \(-0.584765\pi\) | ||||
−0.263161 | + | 0.964752i | \(0.584765\pi\) | |||||||
\(212\) | 8.85412 | 0.608104 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.7565 | 1.14545 | ||||||||
\(215\) | −5.38350 | −0.367152 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 31.1793 | 2.11659 | ||||||||
\(218\) | −9.73822 | −0.659556 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.53401 | 0.372258 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.78954 | −0.253766 | −0.126883 | − | 0.991918i | \(-0.540497\pi\) | ||||
−0.126883 | + | 0.991918i | \(0.540497\pi\) | |||||||
\(224\) | −13.4932 | −0.901549 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.44064 | −0.228868 | ||||||||
\(227\) | −19.5461 | −1.29732 | −0.648660 | − | 0.761079i | \(-0.724670\pi\) | ||||
−0.648660 | + | 0.761079i | \(0.724670\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.16258 | 0.341153 | 0.170576 | − | 0.985344i | \(-0.445437\pi\) | ||||
0.170576 | + | 0.985344i | \(0.445437\pi\) | |||||||
\(230\) | 5.91288 | 0.389884 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.7429 | 1.09922 | ||||||||
\(233\) | 6.24970 | 0.409431 | 0.204716 | − | 0.978821i | \(-0.434373\pi\) | ||||
0.204716 | + | 0.978821i | \(0.434373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.5294 | 0.686861 | ||||||||
\(236\) | −41.9012 | −2.72754 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −29.6632 | −1.92278 | ||||||||
\(239\) | 4.61067 | 0.298239 | 0.149120 | − | 0.988819i | \(-0.452356\pi\) | ||||
0.149120 | + | 0.988819i | \(0.452356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.87827 | −0.507484 | −0.253742 | − | 0.967272i | \(-0.581661\pi\) | ||||
−0.253742 | + | 0.967272i | \(0.581661\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 48.1163 | 3.08033 | ||||||||
\(245\) | 4.44809 | 0.284178 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.76700 | −0.303317 | ||||||||
\(248\) | 32.8425 | 2.08550 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.34889 | 0.148557 | ||||||||
\(251\) | −10.6557 | −0.672584 | −0.336292 | − | 0.941758i | \(-0.609173\pi\) | ||||
−0.336292 | + | 0.941758i | \(0.609173\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −26.5340 | −1.66489 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −23.6169 | −1.47606 | ||||||||
\(257\) | −2.80906 | −0.175224 | −0.0876121 | − | 0.996155i | \(-0.527924\pi\) | ||||
−0.0876121 | + | 0.996155i | \(0.527924\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.12797 | −0.567185 | ||||||||
\(260\) | −5.21509 | −0.323426 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −34.4815 | −2.13027 | ||||||||
\(263\) | 27.6453 | 1.70468 | 0.852340 | − | 0.522987i | \(-0.175183\pi\) | ||||
0.852340 | + | 0.522987i | \(0.175183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.51730 | 0.154637 | ||||||||
\(266\) | 25.5519 | 1.56669 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 27.5461 | 1.68264 | ||||||||
\(269\) | 14.5761 | 0.888718 | 0.444359 | − | 0.895849i | \(-0.353431\pi\) | ||||
0.444359 | + | 0.895849i | \(0.353431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.16258 | 0.131367 | 0.0656837 | − | 0.997840i | \(-0.479077\pi\) | ||||
0.0656837 | + | 0.997840i | \(0.479077\pi\) | |||||||
\(272\) | −4.98954 | −0.302535 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 36.7491 | 2.22009 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.3022 | 0.919421 | 0.459710 | − | 0.888069i | \(-0.347953\pi\) | ||||
0.459710 | + | 0.888069i | \(0.347953\pi\) | |||||||
\(278\) | −17.9579 | −1.07705 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.0588 | 0.720649 | ||||||||
\(281\) | 2.13843 | 0.127568 | 0.0637841 | − | 0.997964i | \(-0.479683\pi\) | ||||
0.0637841 | + | 0.997964i | \(0.479683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.33099 | −0.257451 | −0.128725 | − | 0.991680i | \(-0.541089\pi\) | ||||
−0.128725 | + | 0.991680i | \(0.541089\pi\) | |||||||
\(284\) | −8.85412 | −0.525396 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.4014 | 0.909116 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.06922 | −0.180542 | ||||||||
\(290\) | 11.0346 | 0.647974 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.4302 | 0.610380 | ||||||||
\(293\) | −13.5068 | −0.789078 | −0.394539 | − | 0.918879i | \(-0.629096\pi\) | ||||
−0.394539 | + | 0.918879i | \(0.629096\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9129 | −0.693595 | ||||||||
\(296\) | −9.61488 | −0.558854 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2272 | 0.882086 | ||||||||
\(299\) | −3.73240 | −0.215850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.2151 | −1.04990 | ||||||||
\(302\) | −25.5519 | −1.47035 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.29800 | 0.246507 | ||||||||
\(305\) | 13.6799 | 0.783308 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.37887 | 0.135769 | 0.0678847 | − | 0.997693i | \(-0.478375\pi\) | ||||
0.0678847 | + | 0.997693i | \(0.478375\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21.6453 | 1.22937 | ||||||||
\(311\) | 22.1447 | 1.25571 | 0.627855 | − | 0.778331i | \(-0.283933\pi\) | ||||
0.627855 | + | 0.778331i | \(0.283933\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.2843 | −1.54220 | −0.771100 | − | 0.636714i | \(-0.780293\pi\) | ||||
−0.771100 | + | 0.636714i | \(0.780293\pi\) | |||||||
\(314\) | 24.4994 | 1.38258 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.8016 | −1.33895 | ||||||||
\(317\) | 15.3956 | 0.864702 | 0.432351 | − | 0.901705i | \(-0.357684\pi\) | ||||
0.432351 | + | 0.901705i | \(0.357684\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −12.0409 | −0.673104 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 20.0062 | 1.11490 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.48270 | −0.0822452 | ||||||||
\(326\) | −24.0618 | −1.33266 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.2230 | 0.895763 | ||||||||
\(329\) | 35.6262 | 1.96413 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9129 | 1.42430 | 0.712150 | − | 0.702027i | \(-0.247721\pi\) | ||||
0.712150 | + | 0.702027i | \(0.247721\pi\) | |||||||
\(332\) | 26.5624 | 1.45780 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.45855 | −0.134526 | ||||||||
\(335\) | 7.83159 | 0.427885 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.9821 | −0.761653 | −0.380827 | − | 0.924646i | \(-0.624361\pi\) | ||||
−0.380827 | + | 0.924646i | \(0.624361\pi\) | |||||||
\(338\) | −25.3718 | −1.38005 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.1280 | −0.711964 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.63440 | −0.466214 | ||||||||
\(344\) | −19.1867 | −1.03448 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 27.9821 | 1.50433 | ||||||||
\(347\) | −31.0467 | −1.66667 | −0.833337 | − | 0.552766i | \(-0.813572\pi\) | ||||
−0.833337 | + | 0.552766i | \(0.813572\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.66318 | −0.196086 | −0.0980428 | − | 0.995182i | \(-0.531258\pi\) | ||||
−0.0980428 | + | 0.995182i | \(0.531258\pi\) | |||||||
\(350\) | 7.94749 | 0.424811 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.5749 | −1.30799 | −0.653994 | − | 0.756500i | \(-0.726908\pi\) | ||||
−0.653994 | + | 0.756500i | \(0.726908\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.51730 | −0.133605 | ||||||||
\(356\) | −37.9926 | −2.01360 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.97585 | 0.421537 | ||||||||
\(359\) | −6.58652 | −0.347623 | −0.173812 | − | 0.984779i | \(-0.555608\pi\) | ||||
−0.173812 | + | 0.984779i | \(0.555608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.66318 | −0.455957 | ||||||||
\(362\) | −13.3835 | −0.703421 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.6453 | −0.924864 | ||||||||
\(365\) | 2.96539 | 0.155216 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.16841 | 0.426388 | 0.213194 | − | 0.977010i | \(-0.431613\pi\) | ||||
0.213194 | + | 0.977010i | \(0.431613\pi\) | |||||||
\(368\) | 3.36518 | 0.175422 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.33682 | −0.329436 | ||||||||
\(371\) | 8.51730 | 0.442196 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.0409 | 1.40012 | 0.700061 | − | 0.714083i | \(-0.253156\pi\) | ||||
0.700061 | + | 0.714083i | \(0.253156\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 37.5266 | 1.93528 | ||||||||
\(377\) | −6.96539 | −0.358736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.6620 | 1.67773 | 0.838867 | − | 0.544337i | \(-0.183219\pi\) | ||||
0.838867 | + | 0.544337i | \(0.183219\pi\) | |||||||
\(380\) | 11.3085 | 0.580112 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.1793 | 1.08363 | ||||||||
\(383\) | 2.64648 | 0.135229 | 0.0676143 | − | 0.997712i | \(-0.478461\pi\) | ||||
0.0676143 | + | 0.997712i | \(0.478461\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −61.6157 | −3.13616 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 38.7491 | 1.96719 | ||||||||
\(389\) | 29.0513 | 1.47296 | 0.736480 | − | 0.676459i | \(-0.236487\pi\) | ||||
0.736480 | + | 0.676459i | \(0.236487\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.39558 | −0.475155 | ||||||||
\(392\) | 15.8529 | 0.800694 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −39.2213 | −1.97594 | ||||||||
\(395\) | −6.76700 | −0.340485 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.35977 | −0.469753 | −0.234877 | − | 0.972025i | \(-0.575469\pi\) | ||||
−0.234877 | + | 0.972025i | \(0.575469\pi\) | |||||||
\(398\) | −39.4406 | −1.97698 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.33682 | 0.0668410 | ||||||||
\(401\) | −4.93078 | −0.246232 | −0.123116 | − | 0.992392i | \(-0.539289\pi\) | ||||
−0.123116 | + | 0.992392i | \(0.539289\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.6632 | −0.680611 | ||||||||
\(404\) | −44.7837 | −2.22807 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 37.3356 | 1.85294 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.3085 | 1.89423 | 0.947116 | − | 0.320892i | \(-0.103983\pi\) | ||||
0.947116 | + | 0.320892i | \(0.103983\pi\) | |||||||
\(410\) | 10.6920 | 0.528038 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −64.5181 | −3.17858 | ||||||||
\(413\) | −40.3073 | −1.98339 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.55191 | 0.370709 | ||||||||
\(416\) | 5.91288 | 0.289903 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.3777 | −1.82602 | −0.913009 | − | 0.407938i | \(-0.866248\pi\) | ||||
−0.913009 | + | 0.407938i | \(0.866248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.4123 | 1.43347 | 0.716733 | − | 0.697347i | \(-0.245636\pi\) | ||||
0.716733 | + | 0.697347i | \(0.245636\pi\) | |||||||
\(422\) | −17.9579 | −0.874179 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.97164 | 0.435701 | ||||||||
\(425\) | −3.73240 | −0.181048 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 46.2859 | 2.23993 | ||||||||
\(428\) | 25.0917 | 1.21286 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.6453 | −0.609809 | ||||||||
\(431\) | 1.76820 | 0.0851713 | 0.0425857 | − | 0.999093i | \(-0.486440\pi\) | ||||
0.0425857 | + | 0.999093i | \(0.486440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0513 | 0.483035 | 0.241518 | − | 0.970396i | \(-0.422355\pi\) | ||||
0.241518 | + | 0.970396i | \(0.422355\pi\) | |||||||
\(434\) | 73.2368 | 3.51548 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.5823 | −0.698366 | ||||||||
\(437\) | 8.09337 | 0.387158 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.1972 | −1.87078 | −0.935390 | − | 0.353618i | \(-0.884951\pi\) | ||||
−0.935390 | + | 0.353618i | \(0.884951\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.9988 | 0.618290 | ||||||||
\(443\) | 14.0121 | 0.665734 | 0.332867 | − | 0.942974i | \(-0.391984\pi\) | ||||
0.332867 | + | 0.942974i | \(0.391984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.8016 | −0.512046 | ||||||||
\(446\) | −8.90122 | −0.421485 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −40.7403 | −1.92480 | ||||||||
\(449\) | −2.57606 | −0.121572 | −0.0607859 | − | 0.998151i | \(-0.519361\pi\) | ||||
−0.0607859 | + | 0.998151i | \(0.519361\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.15212 | −0.242335 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −45.9117 | −2.15474 | ||||||||
\(455\) | −5.01671 | −0.235187 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.1217 | −0.707365 | −0.353682 | − | 0.935366i | \(-0.615071\pi\) | ||||
−0.353682 | + | 0.935366i | \(0.615071\pi\) | |||||||
\(458\) | 12.1264 | 0.566627 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.85412 | 0.412826 | ||||||||
\(461\) | 9.83622 | 0.458118 | 0.229059 | − | 0.973412i | \(-0.426435\pi\) | ||||
0.229059 | + | 0.973412i | \(0.426435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.2093 | 0.985678 | 0.492839 | − | 0.870120i | \(-0.335959\pi\) | ||||
0.492839 | + | 0.870120i | \(0.335959\pi\) | |||||||
\(464\) | 6.28010 | 0.291546 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.6799 | 0.680033 | ||||||||
\(467\) | 9.56399 | 0.442569 | 0.221284 | − | 0.975209i | \(-0.428975\pi\) | ||||
0.221284 | + | 0.975209i | \(0.428975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.4982 | 1.22357 | ||||||||
\(470\) | 24.7324 | 1.14082 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −42.4573 | −1.95426 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.21509 | 0.147519 | ||||||||
\(476\) | −44.4185 | −2.03592 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.8300 | 0.495352 | ||||||||
\(479\) | −17.1972 | −0.785760 | −0.392880 | − | 0.919590i | \(-0.628521\pi\) | ||||
−0.392880 | + | 0.919590i | \(0.628521\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | −18.5052 | −0.842890 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.0167 | 0.500243 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5519 | 0.704724 | 0.352362 | − | 0.935864i | \(-0.385379\pi\) | ||||
0.352362 | + | 0.935864i | \(0.385379\pi\) | |||||||
\(488\) | 48.7549 | 2.20703 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.4481 | 0.471996 | ||||||||
\(491\) | −9.05876 | −0.408816 | −0.204408 | − | 0.978886i | \(-0.565527\pi\) | ||||
−0.204408 | + | 0.978886i | \(0.565527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.5340 | −0.789692 | ||||||||
\(494\) | −11.1972 | −0.503785 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.3189 | 0.553136 | ||||||||
\(497\) | −8.51730 | −0.382053 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.5686 | 1.09984 | 0.549921 | − | 0.835217i | \(-0.314658\pi\) | ||||
0.549921 | + | 0.835217i | \(0.314658\pi\) | |||||||
\(500\) | 3.51730 | 0.157299 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.0292 | −1.11711 | ||||||||
\(503\) | −11.3322 | −0.505277 | −0.252639 | − | 0.967561i | \(-0.581298\pi\) | ||||
−0.252639 | + | 0.967561i | \(0.581298\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.7324 | −0.566584 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −39.7328 | −1.76286 | ||||||||
\(509\) | 26.4889 | 1.17410 | 0.587051 | − | 0.809550i | \(-0.300289\pi\) | ||||
0.587051 | + | 0.809550i | \(0.300289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0334 | 0.443852 | ||||||||
\(512\) | −14.8600 | −0.656723 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.59818 | −0.291033 | ||||||||
\(515\) | −18.3431 | −0.808292 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −21.4406 | −0.942048 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.28431 | −0.231732 | ||||||||
\(521\) | −26.6966 | −1.16960 | −0.584799 | − | 0.811178i | \(-0.698827\pi\) | ||||
−0.584799 | + | 0.811178i | \(0.698827\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.85412 | 0.212256 | 0.106128 | − | 0.994352i | \(-0.466155\pi\) | ||||
0.106128 | + | 0.994352i | \(0.466155\pi\) | |||||||
\(524\) | −51.6336 | −2.25563 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 64.9358 | 2.83134 | ||||||||
\(527\) | −34.3944 | −1.49824 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6632 | −0.724486 | ||||||||
\(530\) | 5.91288 | 0.256839 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 38.2622 | 1.65888 | ||||||||
\(533\) | −6.74910 | −0.292336 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.13380 | 0.308421 | ||||||||
\(536\) | 27.9117 | 1.20560 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.2376 | 1.47609 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.8246 | −0.852325 | −0.426162 | − | 0.904647i | \(-0.640135\pi\) | ||||
−0.426162 | + | 0.904647i | \(0.640135\pi\) | |||||||
\(542\) | 5.07968 | 0.218191 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14.8845 | 0.638168 | ||||||||
\(545\) | −4.14588 | −0.177590 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6557 | −0.626634 | −0.313317 | − | 0.949649i | \(-0.601440\pi\) | ||||
−0.313317 | + | 0.949649i | \(0.601440\pi\) | |||||||
\(548\) | 55.0292 | 2.35073 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.1038 | 0.643445 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.8962 | −0.973644 | ||||||||
\(554\) | 35.9433 | 1.52708 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.8908 | −1.14042 | ||||||||
\(557\) | 5.83742 | 0.247339 | 0.123670 | − | 0.992323i | \(-0.460534\pi\) | ||||
0.123670 | + | 0.992323i | \(0.460534\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.98210 | 0.337607 | ||||||||
\(560\) | 4.52313 | 0.191137 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.02295 | 0.211880 | ||||||||
\(563\) | −39.3026 | −1.65641 | −0.828204 | − | 0.560426i | \(-0.810637\pi\) | ||||
−0.828204 | + | 0.560426i | \(0.810637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.46479 | −0.0616243 | ||||||||
\(566\) | −10.1730 | −0.427605 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.97164 | −0.376442 | ||||||||
\(569\) | −8.11007 | −0.339992 | −0.169996 | − | 0.985445i | \(-0.554375\pi\) | ||||
−0.169996 | + | 0.985445i | \(0.554375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.6274 | −1.49096 | −0.745480 | − | 0.666528i | \(-0.767780\pi\) | ||||
−0.745480 | + | 0.666528i | \(0.767780\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 36.1763 | 1.50997 | ||||||||
\(575\) | 2.51730 | 0.104979 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.8529 | −1.32605 | −0.663027 | − | 0.748595i | \(-0.730729\pi\) | ||||
−0.663027 | + | 0.748595i | \(0.730729\pi\) | |||||||
\(578\) | −7.20926 | −0.299866 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.5236 | 0.686103 | ||||||||
\(581\) | 25.5519 | 1.06007 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 10.5686 | 0.437332 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.7262 | −1.31060 | ||||||||
\(587\) | 44.3823 | 1.83185 | 0.915927 | − | 0.401345i | \(-0.131457\pi\) | ||||
0.915927 | + | 0.401345i | \(0.131457\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.6274 | 1.22077 | ||||||||
\(590\) | −27.9821 | −1.15200 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.60646 | −0.148224 | ||||||||
\(593\) | −41.9463 | −1.72253 | −0.861264 | − | 0.508158i | \(-0.830327\pi\) | ||||
−0.861264 | + | 0.508158i | \(0.830327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.6286 | −0.517721 | ||||||||
\(596\) | 22.8016 | 0.933990 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.76700 | −0.358509 | ||||||||
\(599\) | −16.6107 | −0.678694 | −0.339347 | − | 0.940661i | \(-0.610206\pi\) | ||||
−0.339347 | + | 0.940661i | \(0.610206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.1972 | 0.538325 | 0.269162 | − | 0.963095i | \(-0.413253\pi\) | ||||
0.269162 | + | 0.963095i | \(0.413253\pi\) | |||||||
\(602\) | −42.7853 | −1.74380 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −38.2622 | −1.55687 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.04085 | 0.366957 | 0.183478 | − | 0.983024i | \(-0.441264\pi\) | ||||
0.183478 | + | 0.983024i | \(0.441264\pi\) | |||||||
\(608\) | −12.8215 | −0.519982 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.1326 | 1.30101 | ||||||||
\(611\) | −15.6119 | −0.631589 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.66318 | 0.309513 | 0.154756 | − | 0.987953i | \(-0.450541\pi\) | ||||
0.154756 | + | 0.987953i | \(0.450541\pi\) | |||||||
\(614\) | 5.58772 | 0.225502 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.67989 | 0.107888 | 0.0539441 | − | 0.998544i | \(-0.482821\pi\) | ||||
0.0539441 | + | 0.998544i | \(0.482821\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.17424 | 0.328550 | 0.164275 | − | 0.986415i | \(-0.447471\pi\) | ||||
0.164275 | + | 0.986415i | \(0.447471\pi\) | |||||||
\(620\) | 32.4123 | 1.30171 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 52.0155 | 2.08563 | ||||||||
\(623\) | −36.5473 | −1.46424 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −64.0880 | −2.56147 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.6861 | 1.46394 | ||||||||
\(629\) | 10.0692 | 0.401486 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.56982 | 0.221731 | 0.110865 | − | 0.993835i | \(-0.464638\pi\) | ||||
0.110865 | + | 0.993835i | \(0.464638\pi\) | |||||||
\(632\) | −24.1175 | −0.959343 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 36.1626 | 1.43620 | ||||||||
\(635\) | −11.2964 | −0.448283 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.59516 | −0.261310 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −20.3068 | −0.802698 | ||||||||
\(641\) | 13.2906 | 0.524945 | 0.262473 | − | 0.964939i | \(-0.415462\pi\) | ||||
0.262473 | + | 0.964939i | \(0.415462\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.8137 | 0.702503 | 0.351252 | − | 0.936281i | \(-0.385756\pi\) | ||||
0.351252 | + | 0.936281i | \(0.385756\pi\) | |||||||
\(644\) | 29.9579 | 1.18051 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −28.1867 | −1.10899 | ||||||||
\(647\) | 25.8829 | 1.01756 | 0.508781 | − | 0.860896i | \(-0.330096\pi\) | ||||
0.508781 | + | 0.860896i | \(0.330096\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.48270 | −0.136603 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −36.0308 | −1.41108 | ||||||||
\(653\) | −13.3356 | −0.521863 | −0.260932 | − | 0.965357i | \(-0.584030\pi\) | ||||
−0.260932 | + | 0.965357i | \(0.584030\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.6799 | −0.573591 | ||||||||
\(656\) | 6.08509 | 0.237583 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 83.6821 | 3.26227 | ||||||||
\(659\) | −24.4877 | −0.953907 | −0.476954 | − | 0.878929i | \(-0.658259\pi\) | ||||
−0.476954 | + | 0.878929i | \(0.658259\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2738 | −0.905248 | −0.452624 | − | 0.891702i | \(-0.649512\pi\) | ||||
−0.452624 | + | 0.891702i | \(0.649512\pi\) | |||||||
\(662\) | 60.8666 | 2.36565 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.9149 | 1.04450 | ||||||||
\(665\) | 10.8783 | 0.421841 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.8258 | 0.457895 | ||||||||
\(668\) | −3.68150 | −0.142442 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.3956 | 0.710683 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.3443 | −0.437289 | −0.218645 | − | 0.975805i | \(-0.570164\pi\) | ||||
−0.218645 | + | 0.975805i | \(0.570164\pi\) | |||||||
\(674\) | −32.8425 | −1.26504 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −37.9926 | −1.46125 | ||||||||
\(677\) | −21.3956 | −0.822299 | −0.411149 | − | 0.911568i | \(-0.634873\pi\) | ||||
−0.411149 | + | 0.911568i | \(0.634873\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.2750 | 1.43049 | ||||||||
\(680\) | −13.3022 | −0.510117 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.11590 | 0.195754 | 0.0978772 | − | 0.995198i | \(-0.468795\pi\) | ||||
0.0978772 | + | 0.995198i | \(0.468795\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.6453 | 0.597775 | ||||||||
\(686\) | −20.2813 | −0.774343 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.19677 | −0.274374 | ||||||||
\(689\) | −3.73240 | −0.142193 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.9117 | −0.871602 | −0.435801 | − | 0.900043i | \(-0.643535\pi\) | ||||
−0.435801 | + | 0.900043i | \(0.643535\pi\) | |||||||
\(692\) | 41.9012 | 1.59285 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −72.9254 | −2.76821 | ||||||||
\(695\) | −7.64528 | −0.290002 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.9895 | −0.643525 | ||||||||
\(698\) | −8.60442 | −0.325682 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.9008 | 0.449808 | ||||||||
\(701\) | −37.9191 | −1.43219 | −0.716093 | − | 0.698005i | \(-0.754071\pi\) | ||||
−0.716093 | + | 0.698005i | \(0.754071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.67364 | −0.327133 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −57.7238 | −2.17246 | ||||||||
\(707\) | −43.0801 | −1.62019 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.27686 | −0.198177 | −0.0990884 | − | 0.995079i | \(-0.531593\pi\) | ||||
−0.0990884 | + | 0.995079i | \(0.531593\pi\) | |||||||
\(710\) | −5.91288 | −0.221906 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −38.4968 | −1.44273 | ||||||||
\(713\) | 23.1972 | 0.868742 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.9433 | 0.446341 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.4710 | −0.577374 | ||||||||
\(719\) | −30.9117 | −1.15281 | −0.576406 | − | 0.817164i | \(-0.695545\pi\) | ||||
−0.576406 | + | 0.817164i | \(0.695545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −62.0638 | −2.31138 | ||||||||
\(722\) | −20.3489 | −0.757307 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.0409 | −0.744812 | ||||||||
\(725\) | 4.69779 | 0.174471 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.24387 | 0.305748 | 0.152874 | − | 0.988246i | \(-0.451147\pi\) | ||||
0.152874 | + | 0.988246i | \(0.451147\pi\) | |||||||
\(728\) | −17.8795 | −0.662657 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.96539 | 0.257801 | ||||||||
\(731\) | 20.0934 | 0.743180 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.3839 | −1.60242 | −0.801211 | − | 0.598382i | \(-0.795810\pi\) | ||||
−0.801211 | + | 0.598382i | \(0.795810\pi\) | |||||||
\(734\) | 19.1867 | 0.708195 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.0388 | −0.370036 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.301014 | −0.0110730 | −0.00553649 | − | 0.999985i | \(-0.501762\pi\) | ||||
−0.00553649 | + | 0.999985i | \(0.501762\pi\) | |||||||
\(740\) | −9.48894 | −0.348820 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.0062 | 0.734452 | ||||||||
\(743\) | 31.5040 | 1.15577 | 0.577885 | − | 0.816118i | \(-0.303878\pi\) | ||||
0.577885 | + | 0.816118i | \(0.303878\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.48270 | 0.237508 | ||||||||
\(746\) | 63.5161 | 2.32549 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.1372 | 0.881955 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.2906 | 1.21479 | 0.607395 | − | 0.794400i | \(-0.292215\pi\) | ||||
0.607395 | + | 0.794400i | \(0.292215\pi\) | |||||||
\(752\) | 14.0759 | 0.513295 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.3610 | −0.595831 | ||||||||
\(755\) | −10.8783 | −0.395901 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5068 | 0.563606 | 0.281803 | − | 0.959472i | \(-0.409068\pi\) | ||||
0.281803 | + | 0.959472i | \(0.409068\pi\) | |||||||
\(758\) | 76.7195 | 2.78658 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.4585 | 0.415645 | ||||||||
\(761\) | −52.3944 | −1.89929 | −0.949647 | − | 0.313321i | \(-0.898559\pi\) | ||||
−0.949647 | + | 0.313321i | \(0.898559\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.0276 | −0.507833 | ||||||||
\(764\) | 31.7145 | 1.14739 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.21629 | 0.224604 | ||||||||
\(767\) | 17.6632 | 0.637780 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.2652 | −1.59624 | −0.798122 | − | 0.602496i | \(-0.794173\pi\) | ||||
−0.798122 | + | 0.602496i | \(0.794173\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −92.2652 | −3.32070 | ||||||||
\(773\) | 35.3177 | 1.27029 | 0.635145 | − | 0.772393i | \(-0.280940\pi\) | ||||
0.635145 | + | 0.772393i | \(0.280940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.21509 | 0.331016 | ||||||||
\(776\) | 39.2634 | 1.40947 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 68.2385 | 2.44647 | ||||||||
\(779\) | 14.6348 | 0.524347 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −22.0692 | −0.789194 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.94629 | 0.212368 | ||||||||
\(785\) | 10.4302 | 0.372269 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.6920 | 1.30793 | 0.653964 | − | 0.756526i | \(-0.273105\pi\) | ||||
0.653964 | + | 0.756526i | \(0.273105\pi\) | |||||||
\(788\) | −58.7312 | −2.09221 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.8950 | −0.565518 | ||||||||
\(791\) | −4.95613 | −0.176220 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.2831 | −0.720274 | ||||||||
\(794\) | −21.9851 | −0.780222 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −59.0596 | −2.09331 | ||||||||
\(797\) | 2.85412 | 0.101098 | 0.0505491 | − | 0.998722i | \(-0.483903\pi\) | ||||
0.0505491 | + | 0.998722i | \(0.483903\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.2998 | −1.39033 | ||||||||
\(800\) | −3.98793 | −0.140994 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.5819 | −0.408971 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.51730 | 0.300196 | ||||||||
\(806\) | −32.0934 | −1.13044 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −45.3781 | −1.59640 | ||||||||
\(809\) | −26.0934 | −0.917394 | −0.458697 | − | 0.888593i | \(-0.651684\pi\) | ||||
−0.458697 | + | 0.888593i | \(0.651684\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.6453 | −0.689839 | −0.344919 | − | 0.938632i | \(-0.612094\pi\) | ||||
−0.344919 | + | 0.938632i | \(0.612094\pi\) | |||||||
\(812\) | 55.9075 | 1.96197 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.2439 | −0.358827 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.3085 | −0.605546 | ||||||||
\(818\) | 89.9825 | 3.14616 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.0105 | 0.559109 | ||||||||
\(821\) | 51.9117 | 1.81173 | 0.905865 | − | 0.423566i | \(-0.139222\pi\) | ||||
0.905865 | + | 0.423566i | \(0.139222\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.9250 | 0.555109 | 0.277555 | − | 0.960710i | \(-0.410476\pi\) | ||||
0.277555 | + | 0.960710i | \(0.410476\pi\) | |||||||
\(824\) | −65.3744 | −2.27743 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −94.6775 | −3.29425 | ||||||||
\(827\) | −9.77164 | −0.339793 | −0.169897 | − | 0.985462i | \(-0.554343\pi\) | ||||
−0.169897 | + | 0.985462i | \(0.554343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.01790 | 0.0353532 | 0.0176766 | − | 0.999844i | \(-0.494373\pi\) | ||||
0.0176766 | + | 0.999844i | \(0.494373\pi\) | |||||||
\(830\) | 17.7386 | 0.615717 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17.8529 | 0.618939 | ||||||||
\(833\) | −16.6020 | −0.575226 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.04668 | −0.0362219 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −87.7962 | −3.03287 | ||||||||
\(839\) | −13.7900 | −0.476082 | −0.238041 | − | 0.971255i | \(-0.576505\pi\) | ||||
−0.238041 | + | 0.971255i | \(0.576505\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.93078 | −0.238993 | ||||||||
\(842\) | 69.0863 | 2.38087 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −26.8908 | −0.925618 | ||||||||
\(845\) | −10.8016 | −0.371587 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.36518 | 0.115561 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.76700 | −0.300706 | ||||||||
\(851\) | −6.79115 | −0.232798 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.3264 | −0.935637 | −0.467818 | − | 0.883825i | \(-0.654960\pi\) | ||||
−0.467818 | + | 0.883825i | \(0.654960\pi\) | |||||||
\(854\) | 108.721 | 3.72035 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.4248 | 0.869001 | ||||||||
\(857\) | 22.2318 | 0.759424 | 0.379712 | − | 0.925105i | \(-0.376023\pi\) | ||||
0.379712 | + | 0.925105i | \(0.376023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5173 | 0.972998 | 0.486499 | − | 0.873681i | \(-0.338274\pi\) | ||||
0.486499 | + | 0.873681i | \(0.338274\pi\) | |||||||
\(860\) | −18.9354 | −0.645692 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.15332 | 0.141463 | ||||||||
\(863\) | −52.2594 | −1.77893 | −0.889465 | − | 0.457003i | \(-0.848923\pi\) | ||||
−0.889465 | + | 0.457003i | \(0.848923\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.9129 | 0.405050 | ||||||||
\(866\) | 23.6095 | 0.802283 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 109.667 | 3.72234 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.6119 | −0.393453 | ||||||||
\(872\) | −14.7758 | −0.500373 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.0105 | 0.643038 | ||||||||
\(875\) | 3.38350 | 0.114383 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.0074 | 0.709371 | 0.354685 | − | 0.934986i | \(-0.384588\pi\) | ||||
0.354685 | + | 0.934986i | \(0.384588\pi\) | |||||||
\(878\) | −92.0701 | −3.10721 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.0743 | −1.55228 | −0.776141 | − | 0.630560i | \(-0.782825\pi\) | ||||
−0.776141 | + | 0.630560i | \(0.782825\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.622326 | 0.0209429 | 0.0104715 | − | 0.999945i | \(-0.496667\pi\) | ||||
0.0104715 | + | 0.999945i | \(0.496667\pi\) | |||||||
\(884\) | 19.4648 | 0.654672 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.9129 | 1.10573 | ||||||||
\(887\) | 11.4077 | 0.383031 | 0.191516 | − | 0.981490i | \(-0.438660\pi\) | ||||
0.191516 | + | 0.981490i | \(0.438660\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.2213 | −1.28190 | ||||||||
\(890\) | −25.3718 | −0.850466 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.3290 | −0.446287 | ||||||||
\(893\) | 33.8529 | 1.13284 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.39558 | 0.113502 | ||||||||
\(896\) | −68.7082 | −2.29538 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.05090 | −0.201921 | ||||||||
\(899\) | 43.2906 | 1.44382 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.39558 | −0.313012 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.22050 | −0.173631 | ||||||||
\(905\) | −5.69779 | −0.189401 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.9175 | 1.29223 | 0.646117 | − | 0.763238i | \(-0.276392\pi\) | ||||
0.646117 | + | 0.763238i | \(0.276392\pi\) | |||||||
\(908\) | −68.7495 | −2.28153 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.7837 | −0.390626 | ||||||||
\(911\) | −38.0934 | −1.26209 | −0.631045 | − | 0.775746i | \(-0.717374\pi\) | ||||
−0.631045 | + | 0.775746i | \(0.717374\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −35.5193 | −1.17488 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.1584 | 0.599969 | ||||||||
\(917\) | −49.6694 | −1.64023 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.2727 | 0.635746 | 0.317873 | − | 0.948133i | \(-0.397031\pi\) | ||||
0.317873 | + | 0.948133i | \(0.397031\pi\) | |||||||
\(920\) | 8.97164 | 0.295786 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.1042 | 0.760898 | ||||||||
\(923\) | 3.73240 | 0.122853 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.69779 | −0.0887027 | ||||||||
\(926\) | 49.8183 | 1.63713 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18.7344 | −0.614988 | ||||||||
\(929\) | −31.1730 | −1.02275 | −0.511377 | − | 0.859356i | \(-0.670864\pi\) | ||||
−0.511377 | + | 0.859356i | \(0.670864\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.3010 | 0.468697 | ||||||||
\(932\) | 21.9821 | 0.720048 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.4648 | 0.735070 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.8708 | 0.845163 | 0.422582 | − | 0.906325i | \(-0.361124\pi\) | ||||
0.422582 | + | 0.906325i | \(0.361124\pi\) | |||||||
\(938\) | 62.2415 | 2.03226 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 37.0350 | 1.20795 | ||||||||
\(941\) | −29.4636 | −0.960486 | −0.480243 | − | 0.877136i | \(-0.659451\pi\) | ||||
−0.480243 | + | 0.877136i | \(0.659451\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.4585 | 0.373142 | ||||||||
\(944\) | −15.9254 | −0.518327 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.3881 | 0.467551 | 0.233776 | − | 0.972291i | \(-0.424892\pi\) | ||||
0.233776 | + | 0.972291i | \(0.424892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.39677 | −0.142725 | ||||||||
\(950\) | 7.55191 | 0.245016 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −45.0081 | −1.45872 | ||||||||
\(953\) | 31.9191 | 1.03396 | 0.516981 | − | 0.855997i | \(-0.327056\pi\) | ||||
0.516981 | + | 0.855997i | \(0.327056\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.01671 | 0.291774 | ||||||||
\(956\) | 16.2171 | 0.524499 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −40.3944 | −1.30508 | ||||||||
\(959\) | 52.9358 | 1.70939 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.9179 | 1.73929 | ||||||||
\(962\) | 9.39558 | 0.302926 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −27.7103 | −0.892488 | ||||||||
\(965\) | −26.2318 | −0.844431 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.8425 | 1.50635 | 0.753176 | − | 0.657819i | \(-0.228521\pi\) | ||||
0.753176 | + | 0.657819i | \(0.228521\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25.8771 | 0.830863 | ||||||||
\(971\) | 6.66198 | 0.213793 | 0.106897 | − | 0.994270i | \(-0.465909\pi\) | ||||
0.106897 | + | 0.994270i | \(0.465909\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.8678 | −0.829284 | ||||||||
\(974\) | 36.5298 | 1.17049 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.2875 | 0.585370 | ||||||||
\(977\) | 24.1960 | 0.774098 | 0.387049 | − | 0.922059i | \(-0.373494\pi\) | ||||
0.387049 | + | 0.922059i | \(0.373494\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 15.6453 | 0.499770 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.2781 | −0.679010 | ||||||||
\(983\) | 27.7716 | 0.885778 | 0.442889 | − | 0.896577i | \(-0.353954\pi\) | ||||
0.442889 | + | 0.896577i | \(0.353954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.6978 | −0.532036 | ||||||||
\(986\) | −41.1855 | −1.31161 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.7670 | −0.533429 | ||||||||
\(989\) | −13.5519 | −0.430926 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.4227 | 1.44290 | 0.721450 | − | 0.692466i | \(-0.243476\pi\) | ||||
0.721450 | + | 0.692466i | \(0.243476\pi\) | |||||||
\(992\) | −36.7491 | −1.16679 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.0062 | −0.634560 | ||||||||
\(995\) | −16.7912 | −0.532315 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.7491 | 1.60724 | 0.803620 | − | 0.595143i | \(-0.202904\pi\) | ||||
0.803620 | + | 0.595143i | \(0.202904\pi\) | |||||||
\(998\) | 57.7091 | 1.82675 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5445.2.a.bd.1.3 | 3 | ||
3.2 | odd | 2 | 605.2.a.g.1.1 | ✓ | 3 | ||
11.10 | odd | 2 | 5445.2.a.bb.1.1 | 3 | |||
12.11 | even | 2 | 9680.2.a.bz.1.1 | 3 | |||
15.14 | odd | 2 | 3025.2.a.u.1.3 | 3 | |||
33.2 | even | 10 | 605.2.g.o.81.1 | 12 | |||
33.5 | odd | 10 | 605.2.g.p.366.3 | 12 | |||
33.8 | even | 10 | 605.2.g.o.251.3 | 12 | |||
33.14 | odd | 10 | 605.2.g.p.251.1 | 12 | |||
33.17 | even | 10 | 605.2.g.o.366.1 | 12 | |||
33.20 | odd | 10 | 605.2.g.p.81.3 | 12 | |||
33.26 | odd | 10 | 605.2.g.p.511.1 | 12 | |||
33.29 | even | 10 | 605.2.g.o.511.3 | 12 | |||
33.32 | even | 2 | 605.2.a.h.1.3 | yes | 3 | ||
132.131 | odd | 2 | 9680.2.a.cb.1.1 | 3 | |||
165.164 | even | 2 | 3025.2.a.p.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.g.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
605.2.a.h.1.3 | yes | 3 | 33.32 | even | 2 | ||
605.2.g.o.81.1 | 12 | 33.2 | even | 10 | |||
605.2.g.o.251.3 | 12 | 33.8 | even | 10 | |||
605.2.g.o.366.1 | 12 | 33.17 | even | 10 | |||
605.2.g.o.511.3 | 12 | 33.29 | even | 10 | |||
605.2.g.p.81.3 | 12 | 33.20 | odd | 10 | |||
605.2.g.p.251.1 | 12 | 33.14 | odd | 10 | |||
605.2.g.p.366.3 | 12 | 33.5 | odd | 10 | |||
605.2.g.p.511.1 | 12 | 33.26 | odd | 10 | |||
3025.2.a.p.1.1 | 3 | 165.164 | even | 2 | |||
3025.2.a.u.1.3 | 3 | 15.14 | odd | 2 | |||
5445.2.a.bb.1.1 | 3 | 11.10 | odd | 2 | |||
5445.2.a.bd.1.3 | 3 | 1.1 | even | 1 | trivial | ||
9680.2.a.bz.1.1 | 3 | 12.11 | even | 2 | |||
9680.2.a.cb.1.1 | 3 | 132.131 | odd | 2 |