Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} + 88x^{8} - 197x^{6} + 172x^{4} - 36x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.180824\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.180824 | −0.127862 | −0.0639308 | − | 0.997954i | \(-0.520364\pi\) | ||||
−0.0639308 | + | 0.997954i | \(0.520364\pi\) | |||||||
\(3\) | −1.82601 | −1.05425 | −0.527125 | − | 0.849788i | \(-0.676730\pi\) | ||||
−0.527125 | + | 0.849788i | \(0.676730\pi\) | |||||||
\(4\) | −1.96730 | −0.983651 | ||||||||
\(5\) | −2.68664 | −1.20150 | −0.600751 | − | 0.799436i | \(-0.705132\pi\) | ||||
−0.600751 | + | 0.799436i | \(0.705132\pi\) | |||||||
\(6\) | 0.330186 | 0.134798 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.717383 | 0.253633 | ||||||||
\(9\) | 0.334323 | 0.111441 | ||||||||
\(10\) | 0.485809 | 0.153626 | ||||||||
\(11\) | −2.69424 | −0.812345 | −0.406172 | − | 0.913796i | \(-0.633137\pi\) | ||||
−0.406172 | + | 0.913796i | \(0.633137\pi\) | |||||||
\(12\) | 3.59232 | 1.03701 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.90584 | 1.26668 | ||||||||
\(16\) | 3.80489 | 0.951221 | ||||||||
\(17\) | 4.76493 | 1.15567 | 0.577833 | − | 0.816155i | \(-0.303898\pi\) | ||||
0.577833 | + | 0.816155i | \(0.303898\pi\) | |||||||
\(18\) | −0.0604535 | −0.0142490 | ||||||||
\(19\) | −0.188424 | −0.0432275 | −0.0216138 | − | 0.999766i | \(-0.506880\pi\) | ||||
−0.0216138 | + | 0.999766i | \(0.506880\pi\) | |||||||
\(20\) | 5.28544 | 1.18186 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.487183 | 0.103868 | ||||||||
\(23\) | 4.39929 | 0.917315 | 0.458657 | − | 0.888613i | \(-0.348331\pi\) | ||||
0.458657 | + | 0.888613i | \(0.348331\pi\) | |||||||
\(24\) | −1.30995 | −0.267392 | ||||||||
\(25\) | 2.21804 | 0.443609 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.86756 | 0.936762 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.08560 | 1.31576 | 0.657882 | − | 0.753121i | \(-0.271453\pi\) | ||||
0.657882 | + | 0.753121i | \(0.271453\pi\) | |||||||
\(30\) | −0.887093 | −0.161960 | ||||||||
\(31\) | 3.69931 | 0.664415 | 0.332207 | − | 0.943206i | \(-0.392207\pi\) | ||||
0.332207 | + | 0.943206i | \(0.392207\pi\) | |||||||
\(32\) | −2.12278 | −0.375258 | ||||||||
\(33\) | 4.91972 | 0.856414 | ||||||||
\(34\) | −0.861613 | −0.147765 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.657715 | −0.109619 | ||||||||
\(37\) | −7.95413 | −1.30765 | −0.653826 | − | 0.756645i | \(-0.726837\pi\) | ||||
−0.653826 | + | 0.756645i | \(0.726837\pi\) | |||||||
\(38\) | 0.0340716 | 0.00552715 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.92735 | −0.304741 | ||||||||
\(41\) | −5.42958 | −0.847958 | −0.423979 | − | 0.905672i | \(-0.639367\pi\) | ||||
−0.423979 | + | 0.905672i | \(0.639367\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.01065 | −1.22161 | −0.610807 | − | 0.791780i | \(-0.709155\pi\) | ||||
−0.610807 | + | 0.791780i | \(0.709155\pi\) | |||||||
\(44\) | 5.30039 | 0.799064 | ||||||||
\(45\) | −0.898206 | −0.133897 | ||||||||
\(46\) | −0.795496 | −0.117289 | ||||||||
\(47\) | 1.84889 | 0.269688 | 0.134844 | − | 0.990867i | \(-0.456947\pi\) | ||||
0.134844 | + | 0.990867i | \(0.456947\pi\) | |||||||
\(48\) | −6.94777 | −1.00282 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.401075 | −0.0567206 | ||||||||
\(51\) | −8.70083 | −1.21836 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.07244 | −0.971474 | −0.485737 | − | 0.874105i | \(-0.661449\pi\) | ||||
−0.485737 | + | 0.874105i | \(0.661449\pi\) | |||||||
\(54\) | −0.880171 | −0.119776 | ||||||||
\(55\) | 7.23846 | 0.976034 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.344066 | 0.0455726 | ||||||||
\(58\) | −1.28125 | −0.168236 | ||||||||
\(59\) | −7.58888 | −0.987988 | −0.493994 | − | 0.869465i | \(-0.664464\pi\) | ||||
−0.493994 | + | 0.869465i | \(0.664464\pi\) | |||||||
\(60\) | −9.65128 | −1.24597 | ||||||||
\(61\) | −0.411564 | −0.0526954 | −0.0263477 | − | 0.999653i | \(-0.508388\pi\) | ||||
−0.0263477 | + | 0.999653i | \(0.508388\pi\) | |||||||
\(62\) | −0.668922 | −0.0849532 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.22592 | −0.903240 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.889602 | −0.109502 | ||||||||
\(67\) | −11.4010 | −1.39286 | −0.696429 | − | 0.717626i | \(-0.745229\pi\) | ||||
−0.696429 | + | 0.717626i | \(0.745229\pi\) | |||||||
\(68\) | −9.37407 | −1.13677 | ||||||||
\(69\) | −8.03315 | −0.967078 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.34488 | 0.396965 | 0.198482 | − | 0.980104i | \(-0.436399\pi\) | ||||
0.198482 | + | 0.980104i | \(0.436399\pi\) | |||||||
\(72\) | 0.239838 | 0.0282651 | ||||||||
\(73\) | 14.2158 | 1.66383 | 0.831917 | − | 0.554900i | \(-0.187244\pi\) | ||||
0.831917 | + | 0.554900i | \(0.187244\pi\) | |||||||
\(74\) | 1.43830 | 0.167199 | ||||||||
\(75\) | −4.05018 | −0.467674 | ||||||||
\(76\) | 0.370688 | 0.0425208 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.11059 | 1.02502 | 0.512511 | − | 0.858681i | \(-0.328715\pi\) | ||||
0.512511 | + | 0.858681i | \(0.328715\pi\) | |||||||
\(80\) | −10.2224 | −1.14290 | ||||||||
\(81\) | −9.89120 | −1.09902 | ||||||||
\(82\) | 0.981797 | 0.108421 | ||||||||
\(83\) | −16.5866 | −1.82061 | −0.910307 | − | 0.413934i | \(-0.864155\pi\) | ||||
−0.910307 | + | 0.413934i | \(0.864155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.8017 | −1.38854 | ||||||||
\(86\) | 1.44852 | 0.156198 | ||||||||
\(87\) | −12.9384 | −1.38714 | ||||||||
\(88\) | −1.93280 | −0.206037 | ||||||||
\(89\) | 5.89165 | 0.624513 | 0.312257 | − | 0.949998i | \(-0.398915\pi\) | ||||
0.312257 | + | 0.949998i | \(0.398915\pi\) | |||||||
\(90\) | 0.162417 | 0.0171203 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.65473 | −0.902318 | ||||||||
\(93\) | −6.75498 | −0.700459 | ||||||||
\(94\) | −0.334323 | −0.0344828 | ||||||||
\(95\) | 0.506229 | 0.0519380 | ||||||||
\(96\) | 3.87622 | 0.395615 | ||||||||
\(97\) | 0.451094 | 0.0458016 | 0.0229008 | − | 0.999738i | \(-0.492710\pi\) | ||||
0.0229008 | + | 0.999738i | \(0.492710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.900747 | −0.0905285 | ||||||||
\(100\) | −4.36356 | −0.436356 | ||||||||
\(101\) | −7.65680 | −0.761880 | −0.380940 | − | 0.924600i | \(-0.624400\pi\) | ||||
−0.380940 | + | 0.924600i | \(0.624400\pi\) | |||||||
\(102\) | 1.57332 | 0.155782 | ||||||||
\(103\) | 5.15740 | 0.508173 | 0.254087 | − | 0.967181i | \(-0.418225\pi\) | ||||
0.254087 | + | 0.967181i | \(0.418225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.27887 | 0.124214 | ||||||||
\(107\) | 8.03289 | 0.776569 | 0.388284 | − | 0.921540i | \(-0.373068\pi\) | ||||
0.388284 | + | 0.921540i | \(0.373068\pi\) | |||||||
\(108\) | −9.57597 | −0.921448 | ||||||||
\(109\) | −1.33356 | −0.127732 | −0.0638660 | − | 0.997958i | \(-0.520343\pi\) | ||||
−0.0638660 | + | 0.997958i | \(0.520343\pi\) | |||||||
\(110\) | −1.30889 | −0.124797 | ||||||||
\(111\) | 14.5243 | 1.37859 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.9383 | −1.87564 | −0.937821 | − | 0.347119i | \(-0.887160\pi\) | ||||
−0.937821 | + | 0.347119i | \(0.887160\pi\) | |||||||
\(114\) | −0.0622152 | −0.00582699 | ||||||||
\(115\) | −11.8193 | −1.10216 | ||||||||
\(116\) | −13.9395 | −1.29425 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.37225 | 0.126326 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.51937 | 0.321273 | ||||||||
\(121\) | −3.74106 | −0.340096 | ||||||||
\(122\) | 0.0744205 | 0.00673772 | ||||||||
\(123\) | 9.91448 | 0.893959 | ||||||||
\(124\) | −7.27765 | −0.653553 | ||||||||
\(125\) | 7.47412 | 0.668505 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.96722 | −0.706976 | −0.353488 | − | 0.935439i | \(-0.615005\pi\) | ||||
−0.353488 | + | 0.935439i | \(0.615005\pi\) | |||||||
\(128\) | 5.55218 | 0.490748 | ||||||||
\(129\) | 14.6276 | 1.28788 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0179 | 0.875271 | 0.437636 | − | 0.899152i | \(-0.355816\pi\) | ||||
0.437636 | + | 0.899152i | \(0.355816\pi\) | |||||||
\(132\) | −9.67858 | −0.842412 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.06158 | 0.178093 | ||||||||
\(135\) | −13.0774 | −1.12552 | ||||||||
\(136\) | 3.41828 | 0.293115 | ||||||||
\(137\) | 5.06696 | 0.432899 | 0.216450 | − | 0.976294i | \(-0.430552\pi\) | ||||
0.216450 | + | 0.976294i | \(0.430552\pi\) | |||||||
\(138\) | 1.45259 | 0.123652 | ||||||||
\(139\) | 7.72578 | 0.655292 | 0.327646 | − | 0.944800i | \(-0.393745\pi\) | ||||
0.327646 | + | 0.944800i | \(0.393745\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.37610 | −0.284319 | ||||||||
\(142\) | −0.604834 | −0.0507566 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.27206 | 0.106005 | ||||||||
\(145\) | −19.0365 | −1.58089 | ||||||||
\(146\) | −2.57055 | −0.212741 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.6482 | 1.28627 | ||||||||
\(149\) | −14.3185 | −1.17301 | −0.586507 | − | 0.809944i | \(-0.699498\pi\) | ||||
−0.586507 | + | 0.809944i | \(0.699498\pi\) | |||||||
\(150\) | 0.732368 | 0.0597976 | ||||||||
\(151\) | 6.47249 | 0.526724 | 0.263362 | − | 0.964697i | \(-0.415169\pi\) | ||||
0.263362 | + | 0.964697i | \(0.415169\pi\) | |||||||
\(152\) | −0.135172 | −0.0109639 | ||||||||
\(153\) | 1.59303 | 0.128789 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.93871 | −0.798296 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.9187 | 1.27045 | 0.635227 | − | 0.772326i | \(-0.280907\pi\) | ||||
0.635227 | + | 0.772326i | \(0.280907\pi\) | |||||||
\(158\) | −1.64741 | −0.131061 | ||||||||
\(159\) | 12.9144 | 1.02418 | ||||||||
\(160\) | 5.70315 | 0.450873 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.78856 | 0.140523 | ||||||||
\(163\) | −4.78162 | −0.374525 | −0.187263 | − | 0.982310i | \(-0.559962\pi\) | ||||
−0.187263 | + | 0.982310i | \(0.559962\pi\) | |||||||
\(164\) | 10.6816 | 0.834095 | ||||||||
\(165\) | −13.2175 | −1.02898 | ||||||||
\(166\) | 2.99925 | 0.232787 | ||||||||
\(167\) | −2.71042 | −0.209739 | −0.104869 | − | 0.994486i | \(-0.533442\pi\) | ||||
−0.104869 | + | 0.994486i | \(0.533442\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.31485 | 0.177541 | ||||||||
\(171\) | −0.0629946 | −0.00481732 | ||||||||
\(172\) | 15.7594 | 1.20164 | ||||||||
\(173\) | −0.899816 | −0.0684118 | −0.0342059 | − | 0.999415i | \(-0.510890\pi\) | ||||
−0.0342059 | + | 0.999415i | \(0.510890\pi\) | |||||||
\(174\) | 2.33957 | 0.177362 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.2513 | −0.772720 | ||||||||
\(177\) | 13.8574 | 1.04159 | ||||||||
\(178\) | −1.06535 | −0.0798513 | ||||||||
\(179\) | −11.0558 | −0.826351 | −0.413175 | − | 0.910651i | \(-0.635580\pi\) | ||||
−0.413175 | + | 0.910651i | \(0.635580\pi\) | |||||||
\(180\) | 1.76704 | 0.131708 | ||||||||
\(181\) | 3.52898 | 0.262307 | 0.131153 | − | 0.991362i | \(-0.458132\pi\) | ||||
0.131153 | + | 0.991362i | \(0.458132\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.751521 | 0.0555540 | ||||||||
\(184\) | 3.15597 | 0.232661 | ||||||||
\(185\) | 21.3699 | 1.57115 | ||||||||
\(186\) | 1.22146 | 0.0895619 | ||||||||
\(187\) | −12.8379 | −0.938799 | ||||||||
\(188\) | −3.63732 | −0.265279 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0915382 | −0.00664088 | ||||||||
\(191\) | −20.4004 | −1.47612 | −0.738059 | − | 0.674736i | \(-0.764258\pi\) | ||||
−0.738059 | + | 0.674736i | \(0.764258\pi\) | |||||||
\(192\) | 13.1946 | 0.952240 | ||||||||
\(193\) | 17.2646 | 1.24273 | 0.621365 | − | 0.783521i | \(-0.286578\pi\) | ||||
0.621365 | + | 0.783521i | \(0.286578\pi\) | |||||||
\(194\) | −0.0815684 | −0.00585627 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.95672 | 0.353152 | 0.176576 | − | 0.984287i | \(-0.443498\pi\) | ||||
0.176576 | + | 0.984287i | \(0.443498\pi\) | |||||||
\(198\) | 0.162877 | 0.0115751 | ||||||||
\(199\) | 7.18195 | 0.509115 | 0.254557 | − | 0.967058i | \(-0.418070\pi\) | ||||
0.254557 | + | 0.967058i | \(0.418070\pi\) | |||||||
\(200\) | 1.59119 | 0.112514 | ||||||||
\(201\) | 20.8184 | 1.46842 | ||||||||
\(202\) | 1.38453 | 0.0974153 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 17.1172 | 1.19844 | ||||||||
\(205\) | 14.5873 | 1.01882 | ||||||||
\(206\) | −0.932580 | −0.0649759 | ||||||||
\(207\) | 1.47078 | 0.102226 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.507661 | 0.0351157 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.5927 | −1.21113 | −0.605566 | − | 0.795795i | \(-0.707053\pi\) | ||||
−0.605566 | + | 0.795795i | \(0.707053\pi\) | |||||||
\(212\) | 13.9136 | 0.955592 | ||||||||
\(213\) | −6.10780 | −0.418499 | ||||||||
\(214\) | −1.45254 | −0.0992934 | ||||||||
\(215\) | 21.5218 | 1.46777 | ||||||||
\(216\) | 3.49190 | 0.237594 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.241140 | 0.0163320 | ||||||||
\(219\) | −25.9582 | −1.75410 | ||||||||
\(220\) | −14.2403 | −0.960078 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.62635 | −0.176269 | ||||||||
\(223\) | −14.1054 | −0.944569 | −0.472284 | − | 0.881446i | \(-0.656570\pi\) | ||||
−0.472284 | + | 0.881446i | \(0.656570\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.741543 | 0.0494362 | ||||||||
\(226\) | 3.60533 | 0.239823 | ||||||||
\(227\) | −2.86877 | −0.190407 | −0.0952035 | − | 0.995458i | \(-0.530350\pi\) | ||||
−0.0952035 | + | 0.995458i | \(0.530350\pi\) | |||||||
\(228\) | −0.676881 | −0.0448275 | ||||||||
\(229\) | −8.77411 | −0.579810 | −0.289905 | − | 0.957055i | \(-0.593624\pi\) | ||||
−0.289905 | + | 0.957055i | \(0.593624\pi\) | |||||||
\(230\) | 2.13721 | 0.140924 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.08309 | 0.333721 | ||||||||
\(233\) | 5.10743 | 0.334599 | 0.167299 | − | 0.985906i | \(-0.446495\pi\) | ||||
0.167299 | + | 0.985906i | \(0.446495\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.96730 | −0.324031 | ||||||||
\(236\) | 14.9296 | 0.971836 | ||||||||
\(237\) | −16.6361 | −1.08063 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.49797 | −0.161580 | −0.0807901 | − | 0.996731i | \(-0.525744\pi\) | ||||
−0.0807901 | + | 0.996731i | \(0.525744\pi\) | |||||||
\(240\) | 18.6662 | 1.20490 | ||||||||
\(241\) | 7.98512 | 0.514367 | 0.257183 | − | 0.966363i | \(-0.417206\pi\) | ||||
0.257183 | + | 0.966363i | \(0.417206\pi\) | |||||||
\(242\) | 0.676472 | 0.0434853 | ||||||||
\(243\) | 3.45877 | 0.221880 | ||||||||
\(244\) | 0.809671 | 0.0518339 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.79277 | −0.114303 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.65382 | 0.168518 | ||||||||
\(249\) | 30.2873 | 1.91938 | ||||||||
\(250\) | −1.35150 | −0.0854762 | ||||||||
\(251\) | 25.2570 | 1.59421 | 0.797105 | − | 0.603841i | \(-0.206364\pi\) | ||||
0.797105 | + | 0.603841i | \(0.206364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.8527 | −0.745176 | ||||||||
\(254\) | 1.44066 | 0.0903952 | ||||||||
\(255\) | 23.3760 | 1.46386 | ||||||||
\(256\) | 13.4479 | 0.840493 | ||||||||
\(257\) | −3.37363 | −0.210442 | −0.105221 | − | 0.994449i | \(-0.533555\pi\) | ||||
−0.105221 | + | 0.994449i | \(0.533555\pi\) | |||||||
\(258\) | −2.64501 | −0.164671 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.36888 | 0.146630 | ||||||||
\(262\) | −1.81148 | −0.111914 | ||||||||
\(263\) | −0.158935 | −0.00980037 | −0.00490019 | − | 0.999988i | \(-0.501560\pi\) | ||||
−0.00490019 | + | 0.999988i | \(0.501560\pi\) | |||||||
\(264\) | 3.52932 | 0.217215 | ||||||||
\(265\) | 19.0011 | 1.16723 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.7582 | −0.658392 | ||||||||
\(268\) | 22.4293 | 1.37009 | ||||||||
\(269\) | −23.3266 | −1.42225 | −0.711124 | − | 0.703066i | \(-0.751814\pi\) | ||||
−0.711124 | + | 0.703066i | \(0.751814\pi\) | |||||||
\(270\) | 2.36470 | 0.143911 | ||||||||
\(271\) | −11.8210 | −0.718074 | −0.359037 | − | 0.933323i | \(-0.616895\pi\) | ||||
−0.359037 | + | 0.933323i | \(0.616895\pi\) | |||||||
\(272\) | 18.1300 | 1.09929 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.916226 | −0.0553513 | ||||||||
\(275\) | −5.97595 | −0.360363 | ||||||||
\(276\) | 15.8036 | 0.951268 | ||||||||
\(277\) | −27.3653 | −1.64422 | −0.822111 | − | 0.569327i | \(-0.807204\pi\) | ||||
−0.822111 | + | 0.569327i | \(0.807204\pi\) | |||||||
\(278\) | −1.39701 | −0.0837868 | ||||||||
\(279\) | 1.23676 | 0.0740431 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.5383 | −1.70245 | −0.851225 | − | 0.524801i | \(-0.824140\pi\) | ||||
−0.851225 | + | 0.524801i | \(0.824140\pi\) | |||||||
\(282\) | 0.610478 | 0.0363534 | ||||||||
\(283\) | 17.9721 | 1.06833 | 0.534165 | − | 0.845380i | \(-0.320626\pi\) | ||||
0.534165 | + | 0.845380i | \(0.320626\pi\) | |||||||
\(284\) | −6.58040 | −0.390475 | ||||||||
\(285\) | −0.924381 | −0.0547556 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.709694 | −0.0418191 | ||||||||
\(289\) | 5.70459 | 0.335564 | ||||||||
\(290\) | 3.44225 | 0.202136 | ||||||||
\(291\) | −0.823703 | −0.0482863 | ||||||||
\(292\) | −27.9668 | −1.63663 | ||||||||
\(293\) | −14.8891 | −0.869828 | −0.434914 | − | 0.900472i | \(-0.643221\pi\) | ||||
−0.434914 | + | 0.900472i | \(0.643221\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.3886 | 1.18707 | ||||||||
\(296\) | −5.70616 | −0.331664 | ||||||||
\(297\) | −13.1144 | −0.760974 | ||||||||
\(298\) | 2.58912 | 0.149984 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.96793 | 0.460028 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.17038 | −0.0673478 | ||||||||
\(303\) | 13.9814 | 0.803211 | ||||||||
\(304\) | −0.716934 | −0.0411190 | ||||||||
\(305\) | 1.10572 | 0.0633136 | ||||||||
\(306\) | −0.288057 | −0.0164671 | ||||||||
\(307\) | 23.5161 | 1.34214 | 0.671068 | − | 0.741396i | \(-0.265836\pi\) | ||||
0.671068 | + | 0.741396i | \(0.265836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.41747 | −0.535741 | ||||||||
\(310\) | 1.79715 | 0.102072 | ||||||||
\(311\) | 1.63090 | 0.0924799 | 0.0462399 | − | 0.998930i | \(-0.485276\pi\) | ||||
0.0462399 | + | 0.998930i | \(0.485276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.696734 | −0.0393817 | −0.0196909 | − | 0.999806i | \(-0.506268\pi\) | ||||
−0.0196909 | + | 0.999806i | \(0.506268\pi\) | |||||||
\(314\) | −2.87849 | −0.162442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.9233 | −1.00826 | ||||||||
\(317\) | 21.4288 | 1.20356 | 0.601780 | − | 0.798662i | \(-0.294458\pi\) | ||||
0.601780 | + | 0.798662i | \(0.294458\pi\) | |||||||
\(318\) | −2.33522 | −0.130953 | ||||||||
\(319\) | −19.0903 | −1.06885 | ||||||||
\(320\) | 19.4135 | 1.08525 | ||||||||
\(321\) | −14.6682 | −0.818697 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.897830 | −0.0499566 | ||||||||
\(324\) | 19.4590 | 1.08105 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.864630 | 0.0478874 | ||||||||
\(327\) | 2.43510 | 0.134661 | ||||||||
\(328\) | −3.89509 | −0.215070 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.39004 | 0.131568 | ||||||||
\(331\) | 1.52046 | 0.0835722 | 0.0417861 | − | 0.999127i | \(-0.486695\pi\) | ||||
0.0417861 | + | 0.999127i | \(0.486695\pi\) | |||||||
\(332\) | 32.6308 | 1.79085 | ||||||||
\(333\) | −2.65925 | −0.145726 | ||||||||
\(334\) | 0.490108 | 0.0268175 | ||||||||
\(335\) | 30.6305 | 1.67352 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.2304 | 1.75570 | 0.877850 | − | 0.478936i | \(-0.158977\pi\) | ||||
0.877850 | + | 0.478936i | \(0.158977\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.4077 | 1.97739 | ||||||||
\(340\) | 25.1848 | 1.36584 | ||||||||
\(341\) | −9.96683 | −0.539734 | ||||||||
\(342\) | 0.0113909 | 0.000615951 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.74670 | −0.309841 | ||||||||
\(345\) | 21.5822 | 1.16195 | ||||||||
\(346\) | 0.162708 | 0.00874724 | ||||||||
\(347\) | 8.18431 | 0.439357 | 0.219678 | − | 0.975572i | \(-0.429499\pi\) | ||||
0.219678 | + | 0.975572i | \(0.429499\pi\) | |||||||
\(348\) | 25.4538 | 1.36446 | ||||||||
\(349\) | −21.8493 | −1.16956 | −0.584782 | − | 0.811190i | \(-0.698820\pi\) | ||||
−0.584782 | + | 0.811190i | \(0.698820\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.71928 | 0.304839 | ||||||||
\(353\) | −0.567179 | −0.0301879 | −0.0150940 | − | 0.999886i | \(-0.504805\pi\) | ||||
−0.0150940 | + | 0.999886i | \(0.504805\pi\) | |||||||
\(354\) | −2.50575 | −0.133179 | ||||||||
\(355\) | −8.98650 | −0.476954 | ||||||||
\(356\) | −11.5907 | −0.614303 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.99915 | 0.105659 | ||||||||
\(359\) | 32.4043 | 1.71024 | 0.855118 | − | 0.518434i | \(-0.173485\pi\) | ||||
0.855118 | + | 0.518434i | \(0.173485\pi\) | |||||||
\(360\) | −0.644358 | −0.0339606 | ||||||||
\(361\) | −18.9645 | −0.998131 | ||||||||
\(362\) | −0.638123 | −0.0335390 | ||||||||
\(363\) | 6.83122 | 0.358546 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −38.1928 | −1.99910 | ||||||||
\(366\) | −0.135893 | −0.00710323 | ||||||||
\(367\) | −7.86888 | −0.410752 | −0.205376 | − | 0.978683i | \(-0.565842\pi\) | ||||
−0.205376 | + | 0.978683i | \(0.565842\pi\) | |||||||
\(368\) | 16.7388 | 0.872569 | ||||||||
\(369\) | −1.81523 | −0.0944973 | ||||||||
\(370\) | −3.86419 | −0.200889 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 13.2891 | 0.689007 | ||||||||
\(373\) | −2.09163 | −0.108300 | −0.0541502 | − | 0.998533i | \(-0.517245\pi\) | ||||
−0.0541502 | + | 0.998533i | \(0.517245\pi\) | |||||||
\(374\) | 2.32139 | 0.120036 | ||||||||
\(375\) | −13.6478 | −0.704771 | ||||||||
\(376\) | 1.32636 | 0.0684018 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.3163 | −0.735381 | −0.367691 | − | 0.929948i | \(-0.619851\pi\) | ||||
−0.367691 | + | 0.929948i | \(0.619851\pi\) | |||||||
\(380\) | −0.995906 | −0.0510889 | ||||||||
\(381\) | 14.5482 | 0.745329 | ||||||||
\(382\) | 3.68887 | 0.188739 | ||||||||
\(383\) | −25.1873 | −1.28701 | −0.643507 | − | 0.765441i | \(-0.722521\pi\) | ||||
−0.643507 | + | 0.765441i | \(0.722521\pi\) | |||||||
\(384\) | −10.1383 | −0.517370 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.12184 | −0.158898 | ||||||||
\(387\) | −2.67815 | −0.136138 | ||||||||
\(388\) | −0.887438 | −0.0450528 | ||||||||
\(389\) | 28.1023 | 1.42484 | 0.712422 | − | 0.701752i | \(-0.247598\pi\) | ||||
0.712422 | + | 0.701752i | \(0.247598\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.9623 | 1.06011 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.2929 | −0.922754 | ||||||||
\(394\) | −0.896292 | −0.0451546 | ||||||||
\(395\) | −24.4769 | −1.23157 | ||||||||
\(396\) | 1.77204 | 0.0890485 | ||||||||
\(397\) | −21.7765 | −1.09293 | −0.546465 | − | 0.837482i | \(-0.684027\pi\) | ||||
−0.546465 | + | 0.837482i | \(0.684027\pi\) | |||||||
\(398\) | −1.29867 | −0.0650963 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.43941 | 0.421970 | ||||||||
\(401\) | 20.5290 | 1.02517 | 0.512584 | − | 0.858637i | \(-0.328688\pi\) | ||||
0.512584 | + | 0.858637i | \(0.328688\pi\) | |||||||
\(402\) | −3.76447 | −0.187754 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 15.0632 | 0.749424 | ||||||||
\(405\) | 26.5741 | 1.32048 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.4304 | 1.06226 | ||||||||
\(408\) | −6.24182 | −0.309016 | ||||||||
\(409\) | −6.26862 | −0.309963 | −0.154982 | − | 0.987917i | \(-0.549532\pi\) | ||||
−0.154982 | + | 0.987917i | \(0.549532\pi\) | |||||||
\(410\) | −2.63774 | −0.130269 | ||||||||
\(411\) | −9.25233 | −0.456384 | ||||||||
\(412\) | −10.1462 | −0.499865 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.265953 | −0.0130709 | ||||||||
\(415\) | 44.5622 | 2.18747 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.1074 | −0.690841 | ||||||||
\(418\) | −0.0917972 | −0.00448995 | ||||||||
\(419\) | 34.1635 | 1.66899 | 0.834497 | − | 0.551013i | \(-0.185758\pi\) | ||||
0.834497 | + | 0.551013i | \(0.185758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5233 | −0.561613 | −0.280806 | − | 0.959764i | \(-0.590602\pi\) | ||||
−0.280806 | + | 0.959764i | \(0.590602\pi\) | |||||||
\(422\) | 3.18118 | 0.154858 | ||||||||
\(423\) | 0.618126 | 0.0300543 | ||||||||
\(424\) | −5.07364 | −0.246398 | ||||||||
\(425\) | 10.5688 | 0.512664 | ||||||||
\(426\) | 1.10444 | 0.0535101 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −15.8031 | −0.763873 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.89164 | −0.187672 | ||||||||
\(431\) | −8.77001 | −0.422436 | −0.211218 | − | 0.977439i | \(-0.567743\pi\) | ||||
−0.211218 | + | 0.977439i | \(0.567743\pi\) | |||||||
\(432\) | 18.5205 | 0.891069 | ||||||||
\(433\) | 22.1069 | 1.06239 | 0.531196 | − | 0.847249i | \(-0.321743\pi\) | ||||
0.531196 | + | 0.847249i | \(0.321743\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 34.7609 | 1.66666 | ||||||||
\(436\) | 2.62352 | 0.125644 | ||||||||
\(437\) | −0.828933 | −0.0396533 | ||||||||
\(438\) | 4.69387 | 0.224282 | ||||||||
\(439\) | −10.3709 | −0.494978 | −0.247489 | − | 0.968891i | \(-0.579605\pi\) | ||||
−0.247489 | + | 0.968891i | \(0.579605\pi\) | |||||||
\(440\) | 5.19275 | 0.247555 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.8137 | 1.70156 | 0.850780 | − | 0.525522i | \(-0.176130\pi\) | ||||
0.850780 | + | 0.525522i | \(0.176130\pi\) | |||||||
\(444\) | −28.5738 | −1.35605 | ||||||||
\(445\) | −15.8287 | −0.750354 | ||||||||
\(446\) | 2.55059 | 0.120774 | ||||||||
\(447\) | 26.1457 | 1.23665 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.7502 | 1.07365 | 0.536825 | − | 0.843693i | \(-0.319623\pi\) | ||||
0.536825 | + | 0.843693i | \(0.319623\pi\) | |||||||
\(450\) | −0.134089 | −0.00632100 | ||||||||
\(451\) | 14.6286 | 0.688834 | ||||||||
\(452\) | 39.2248 | 1.84498 | ||||||||
\(453\) | −11.8188 | −0.555298 | ||||||||
\(454\) | 0.518742 | 0.0243458 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.246827 | 0.0115587 | ||||||||
\(457\) | −31.3172 | −1.46496 | −0.732478 | − | 0.680791i | \(-0.761636\pi\) | ||||
−0.732478 | + | 0.680791i | \(0.761636\pi\) | |||||||
\(458\) | 1.58657 | 0.0741354 | ||||||||
\(459\) | 23.1936 | 1.08258 | ||||||||
\(460\) | 23.2522 | 1.08414 | ||||||||
\(461\) | −8.40753 | −0.391578 | −0.195789 | − | 0.980646i | \(-0.562727\pi\) | ||||
−0.195789 | + | 0.980646i | \(0.562727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0392 | −0.466563 | −0.233281 | − | 0.972409i | \(-0.574946\pi\) | ||||
−0.233281 | + | 0.972409i | \(0.574946\pi\) | |||||||
\(464\) | 26.9599 | 1.25158 | ||||||||
\(465\) | 18.1482 | 0.841603 | ||||||||
\(466\) | −0.923545 | −0.0427824 | ||||||||
\(467\) | −26.3513 | −1.21939 | −0.609696 | − | 0.792635i | \(-0.708709\pi\) | ||||
−0.609696 | + | 0.792635i | \(0.708709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.898206 | 0.0414312 | ||||||||
\(471\) | −29.0678 | −1.33937 | ||||||||
\(472\) | −5.44413 | −0.250586 | ||||||||
\(473\) | 21.5826 | 0.992371 | ||||||||
\(474\) | 3.00819 | 0.138171 | ||||||||
\(475\) | −0.417934 | −0.0191761 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.36448 | −0.108262 | ||||||||
\(478\) | 0.451692 | 0.0206599 | ||||||||
\(479\) | 8.58414 | 0.392220 | 0.196110 | − | 0.980582i | \(-0.437169\pi\) | ||||
0.196110 | + | 0.980582i | \(0.437169\pi\) | |||||||
\(480\) | −10.4140 | −0.475333 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.44390 | −0.0657678 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.35979 | 0.334536 | ||||||||
\(485\) | −1.21193 | −0.0550308 | ||||||||
\(486\) | −0.625428 | −0.0283700 | ||||||||
\(487\) | −21.2562 | −0.963212 | −0.481606 | − | 0.876388i | \(-0.659946\pi\) | ||||
−0.481606 | + | 0.876388i | \(0.659946\pi\) | |||||||
\(488\) | −0.295249 | −0.0133653 | ||||||||
\(489\) | 8.73130 | 0.394843 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.4535 | −1.01331 | −0.506657 | − | 0.862148i | \(-0.669119\pi\) | ||||
−0.506657 | + | 0.862148i | \(0.669119\pi\) | |||||||
\(492\) | −19.5048 | −0.879344 | ||||||||
\(493\) | 33.7624 | 1.52058 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.41999 | 0.108770 | ||||||||
\(496\) | 14.0754 | 0.632006 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.47667 | −0.245415 | ||||||||
\(499\) | −38.8780 | −1.74042 | −0.870210 | − | 0.492681i | \(-0.836017\pi\) | ||||
−0.870210 | + | 0.492681i | \(0.836017\pi\) | |||||||
\(500\) | −14.7039 | −0.657576 | ||||||||
\(501\) | 4.94926 | 0.221117 | ||||||||
\(502\) | −4.56707 | −0.203838 | ||||||||
\(503\) | 5.45701 | 0.243316 | 0.121658 | − | 0.992572i | \(-0.461179\pi\) | ||||
0.121658 | + | 0.992572i | \(0.461179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.5711 | 0.915401 | ||||||||
\(506\) | 2.14326 | 0.0952794 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.6739 | 0.695418 | ||||||||
\(509\) | 10.8925 | 0.482800 | 0.241400 | − | 0.970426i | \(-0.422393\pi\) | ||||
0.241400 | + | 0.970426i | \(0.422393\pi\) | |||||||
\(510\) | −4.22694 | −0.187172 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −13.5360 | −0.598214 | ||||||||
\(513\) | −0.917168 | −0.0404939 | ||||||||
\(514\) | 0.610033 | 0.0269074 | ||||||||
\(515\) | −13.8561 | −0.610572 | ||||||||
\(516\) | −28.7768 | −1.26683 | ||||||||
\(517\) | −4.98136 | −0.219080 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.64308 | 0.0721230 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.8961 | 1.22215 | 0.611074 | − | 0.791573i | \(-0.290738\pi\) | ||||
0.611074 | + | 0.791573i | \(0.290738\pi\) | |||||||
\(522\) | −0.428350 | −0.0187484 | ||||||||
\(523\) | 16.7236 | 0.731272 | 0.365636 | − | 0.930758i | \(-0.380852\pi\) | ||||
0.365636 | + | 0.930758i | \(0.380852\pi\) | |||||||
\(524\) | −19.7083 | −0.860962 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0287393 | 0.00125309 | ||||||||
\(527\) | 17.6269 | 0.767842 | ||||||||
\(528\) | 18.7190 | 0.814639 | ||||||||
\(529\) | −3.64627 | −0.158534 | ||||||||
\(530\) | −3.43585 | −0.149244 | ||||||||
\(531\) | −2.53714 | −0.110102 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.94534 | 0.0841832 | ||||||||
\(535\) | −21.5815 | −0.933049 | ||||||||
\(536\) | −8.17890 | −0.353275 | ||||||||
\(537\) | 20.1881 | 0.871179 | ||||||||
\(538\) | 4.21800 | 0.181851 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 25.7272 | 1.10712 | ||||||||
\(541\) | −11.1605 | −0.479828 | −0.239914 | − | 0.970794i | \(-0.577119\pi\) | ||||
−0.239914 | + | 0.970794i | \(0.577119\pi\) | |||||||
\(542\) | 2.13751 | 0.0918141 | ||||||||
\(543\) | −6.44396 | −0.276537 | ||||||||
\(544\) | −10.1149 | −0.433673 | ||||||||
\(545\) | 3.58280 | 0.153470 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.6556 | 1.56728 | 0.783640 | − | 0.621215i | \(-0.213361\pi\) | ||||
0.783640 | + | 0.621215i | \(0.213361\pi\) | |||||||
\(548\) | −9.96824 | −0.425822 | ||||||||
\(549\) | −0.137595 | −0.00587242 | ||||||||
\(550\) | 1.08059 | 0.0460767 | ||||||||
\(551\) | −1.33510 | −0.0568772 | ||||||||
\(552\) | −5.76285 | −0.245283 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.94830 | 0.210233 | ||||||||
\(555\) | −39.0217 | −1.65638 | ||||||||
\(556\) | −15.1990 | −0.644579 | ||||||||
\(557\) | 33.0776 | 1.40154 | 0.700772 | − | 0.713386i | \(-0.252839\pi\) | ||||
0.700772 | + | 0.713386i | \(0.252839\pi\) | |||||||
\(558\) | −0.223636 | −0.00946727 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.4421 | 0.989728 | ||||||||
\(562\) | 5.16039 | 0.217678 | ||||||||
\(563\) | 17.7967 | 0.750043 | 0.375021 | − | 0.927016i | \(-0.377635\pi\) | ||||
0.375021 | + | 0.927016i | \(0.377635\pi\) | |||||||
\(564\) | 6.64180 | 0.279670 | ||||||||
\(565\) | 53.5672 | 2.25359 | ||||||||
\(566\) | −3.24978 | −0.136598 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.39956 | 0.100683 | ||||||||
\(569\) | −8.22094 | −0.344640 | −0.172320 | − | 0.985041i | \(-0.555126\pi\) | ||||
−0.172320 | + | 0.985041i | \(0.555126\pi\) | |||||||
\(570\) | 0.167150 | 0.00700114 | ||||||||
\(571\) | −25.7553 | −1.07782 | −0.538912 | − | 0.842362i | \(-0.681165\pi\) | ||||
−0.538912 | + | 0.842362i | \(0.681165\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.2513 | 1.55620 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.75781 | 0.406929 | ||||||||
\(576\) | −2.41579 | −0.100658 | ||||||||
\(577\) | 0.769393 | 0.0320302 | 0.0160151 | − | 0.999872i | \(-0.494902\pi\) | ||||
0.0160151 | + | 0.999872i | \(0.494902\pi\) | |||||||
\(578\) | −1.03152 | −0.0429058 | ||||||||
\(579\) | −31.5253 | −1.31015 | ||||||||
\(580\) | 37.4505 | 1.55505 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.148945 | 0.00617397 | ||||||||
\(583\) | 19.0549 | 0.789172 | ||||||||
\(584\) | 10.1982 | 0.422003 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.69229 | 0.111218 | ||||||||
\(587\) | 12.0929 | 0.499127 | 0.249563 | − | 0.968358i | \(-0.419713\pi\) | ||||
0.249563 | + | 0.968358i | \(0.419713\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.697040 | −0.0287210 | ||||||||
\(590\) | −3.68674 | −0.151781 | ||||||||
\(591\) | −9.05103 | −0.372310 | ||||||||
\(592\) | −30.2646 | −1.24387 | ||||||||
\(593\) | 15.9481 | 0.654911 | 0.327456 | − | 0.944867i | \(-0.393809\pi\) | ||||
0.327456 | + | 0.944867i | \(0.393809\pi\) | |||||||
\(594\) | 2.37139 | 0.0972994 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 28.1688 | 1.15384 | ||||||||
\(597\) | −13.1143 | −0.536734 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.11022 | −0.290516 | −0.145258 | − | 0.989394i | \(-0.546401\pi\) | ||||
−0.145258 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(600\) | −2.90553 | −0.118618 | ||||||||
\(601\) | 20.7905 | 0.848064 | 0.424032 | − | 0.905647i | \(-0.360614\pi\) | ||||
0.424032 | + | 0.905647i | \(0.360614\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.81163 | −0.155221 | ||||||||
\(604\) | −12.7333 | −0.518112 | ||||||||
\(605\) | 10.0509 | 0.408626 | ||||||||
\(606\) | −2.52817 | −0.102700 | ||||||||
\(607\) | −7.71405 | −0.313104 | −0.156552 | − | 0.987670i | \(-0.550038\pi\) | ||||
−0.156552 | + | 0.987670i | \(0.550038\pi\) | |||||||
\(608\) | 0.399983 | 0.0162215 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.199941 | −0.00809539 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.13397 | −0.126683 | ||||||||
\(613\) | −20.4378 | −0.825476 | −0.412738 | − | 0.910850i | \(-0.635428\pi\) | ||||
−0.412738 | + | 0.910850i | \(0.635428\pi\) | |||||||
\(614\) | −4.25227 | −0.171608 | ||||||||
\(615\) | −26.6367 | −1.07409 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.59812 | −0.185113 | −0.0925567 | − | 0.995707i | \(-0.529504\pi\) | ||||
−0.0925567 | + | 0.995707i | \(0.529504\pi\) | |||||||
\(618\) | 1.70290 | 0.0685008 | ||||||||
\(619\) | −10.0528 | −0.404057 | −0.202028 | − | 0.979380i | \(-0.564753\pi\) | ||||
−0.202028 | + | 0.979380i | \(0.564753\pi\) | |||||||
\(620\) | 19.5525 | 0.785245 | ||||||||
\(621\) | 21.4138 | 0.859306 | ||||||||
\(622\) | −0.294906 | −0.0118246 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1705 | −1.24682 | ||||||||
\(626\) | 0.125986 | 0.00503541 | ||||||||
\(627\) | −0.926996 | −0.0370207 | ||||||||
\(628\) | −31.3170 | −1.24968 | ||||||||
\(629\) | −37.9009 | −1.51121 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.27372 | 0.289562 | 0.144781 | − | 0.989464i | \(-0.453752\pi\) | ||||
0.144781 | + | 0.989464i | \(0.453752\pi\) | |||||||
\(632\) | 6.53578 | 0.259979 | ||||||||
\(633\) | 32.1245 | 1.27684 | ||||||||
\(634\) | −3.87483 | −0.153889 | ||||||||
\(635\) | 21.4051 | 0.849434 | ||||||||
\(636\) | −25.4065 | −1.00743 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.45199 | 0.136665 | ||||||||
\(639\) | 1.11827 | 0.0442381 | ||||||||
\(640\) | −14.9167 | −0.589635 | ||||||||
\(641\) | 3.85033 | 0.152079 | 0.0760394 | − | 0.997105i | \(-0.475773\pi\) | ||||
0.0760394 | + | 0.997105i | \(0.475773\pi\) | |||||||
\(642\) | 2.65235 | 0.104680 | ||||||||
\(643\) | 2.87709 | 0.113461 | 0.0567307 | − | 0.998390i | \(-0.481932\pi\) | ||||
0.0567307 | + | 0.998390i | \(0.481932\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −39.2990 | −1.54740 | ||||||||
\(646\) | 0.162349 | 0.00638754 | ||||||||
\(647\) | 37.1001 | 1.45856 | 0.729278 | − | 0.684218i | \(-0.239856\pi\) | ||||
0.729278 | + | 0.684218i | \(0.239856\pi\) | |||||||
\(648\) | −7.09577 | −0.278748 | ||||||||
\(649\) | 20.4463 | 0.802587 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.40689 | 0.368402 | ||||||||
\(653\) | 20.0950 | 0.786377 | 0.393189 | − | 0.919458i | \(-0.371372\pi\) | ||||
0.393189 | + | 0.919458i | \(0.371372\pi\) | |||||||
\(654\) | −0.440324 | −0.0172180 | ||||||||
\(655\) | −26.9146 | −1.05164 | ||||||||
\(656\) | −20.6589 | −0.806596 | ||||||||
\(657\) | 4.75267 | 0.185419 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.91058 | 0.386061 | 0.193031 | − | 0.981193i | \(-0.438168\pi\) | ||||
0.193031 | + | 0.981193i | \(0.438168\pi\) | |||||||
\(660\) | 26.0029 | 1.01216 | ||||||||
\(661\) | −47.2266 | −1.83690 | −0.918450 | − | 0.395537i | \(-0.870558\pi\) | ||||
−0.918450 | + | 0.395537i | \(0.870558\pi\) | |||||||
\(662\) | −0.274936 | −0.0106857 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.8989 | −0.461768 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.480855 | 0.0186328 | ||||||||
\(667\) | 31.1716 | 1.20697 | ||||||||
\(668\) | 5.33222 | 0.206310 | ||||||||
\(669\) | 25.7567 | 0.995811 | ||||||||
\(670\) | −5.53872 | −0.213979 | ||||||||
\(671\) | 1.10885 | 0.0428068 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.91689 | 0.266627 | 0.133313 | − | 0.991074i | \(-0.457438\pi\) | ||||
0.133313 | + | 0.991074i | \(0.457438\pi\) | |||||||
\(674\) | −5.82801 | −0.224487 | ||||||||
\(675\) | 10.7965 | 0.415556 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.3291 | −0.473844 | −0.236922 | − | 0.971529i | \(-0.576139\pi\) | ||||
−0.236922 | + | 0.971529i | \(0.576139\pi\) | |||||||
\(678\) | −6.58337 | −0.252833 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.18369 | −0.352179 | ||||||||
\(681\) | 5.23841 | 0.200736 | ||||||||
\(682\) | 1.80224 | 0.0690113 | ||||||||
\(683\) | 24.5364 | 0.938859 | 0.469430 | − | 0.882970i | \(-0.344460\pi\) | ||||
0.469430 | + | 0.882970i | \(0.344460\pi\) | |||||||
\(684\) | 0.123930 | 0.00473856 | ||||||||
\(685\) | −13.6131 | −0.520130 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.0216 | 0.611264 | ||||||||
\(688\) | −30.4796 | −1.16202 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.90258 | −0.148569 | ||||||||
\(691\) | −9.10716 | −0.346453 | −0.173226 | − | 0.984882i | \(-0.555419\pi\) | ||||
−0.173226 | + | 0.984882i | \(0.555419\pi\) | |||||||
\(692\) | 1.77021 | 0.0672933 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.47992 | −0.0561769 | ||||||||
\(695\) | −20.7564 | −0.787336 | ||||||||
\(696\) | −9.28179 | −0.351825 | ||||||||
\(697\) | −25.8716 | −0.979956 | ||||||||
\(698\) | 3.95087 | 0.149542 | ||||||||
\(699\) | −9.32623 | −0.352750 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.286950 | −0.0108380 | −0.00541898 | − | 0.999985i | \(-0.501725\pi\) | ||||
−0.00541898 | + | 0.999985i | \(0.501725\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.49875 | 0.0565265 | ||||||||
\(704\) | 19.4684 | 0.733742 | ||||||||
\(705\) | 9.07036 | 0.341609 | ||||||||
\(706\) | 0.102559 | 0.00385988 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −27.2617 | −1.02456 | ||||||||
\(709\) | 18.5848 | 0.697967 | 0.348984 | − | 0.937129i | \(-0.386527\pi\) | ||||
0.348984 | + | 0.937129i | \(0.386527\pi\) | |||||||
\(710\) | 1.62497 | 0.0609841 | ||||||||
\(711\) | 3.04588 | 0.114229 | ||||||||
\(712\) | 4.22656 | 0.158397 | ||||||||
\(713\) | 16.2743 | 0.609478 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.7501 | 0.812841 | ||||||||
\(717\) | 4.56132 | 0.170346 | ||||||||
\(718\) | −5.85947 | −0.218674 | ||||||||
\(719\) | 41.6949 | 1.55496 | 0.777479 | − | 0.628909i | \(-0.216498\pi\) | ||||
0.777479 | + | 0.628909i | \(0.216498\pi\) | |||||||
\(720\) | −3.41757 | −0.127365 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.42923 | 0.127623 | ||||||||
\(723\) | −14.5809 | −0.542271 | ||||||||
\(724\) | −6.94257 | −0.258019 | ||||||||
\(725\) | 15.7162 | 0.583684 | ||||||||
\(726\) | −1.23525 | −0.0458443 | ||||||||
\(727\) | −32.7039 | −1.21292 | −0.606461 | − | 0.795113i | \(-0.707411\pi\) | ||||
−0.606461 | + | 0.795113i | \(0.707411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.3578 | 0.865105 | ||||||||
\(730\) | 6.90616 | 0.255608 | ||||||||
\(731\) | −38.1702 | −1.41178 | ||||||||
\(732\) | −1.47847 | −0.0546458 | ||||||||
\(733\) | 9.93531 | 0.366969 | 0.183484 | − | 0.983023i | \(-0.441262\pi\) | ||||
0.183484 | + | 0.983023i | \(0.441262\pi\) | |||||||
\(734\) | 1.42288 | 0.0525195 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.33871 | −0.344230 | ||||||||
\(737\) | 30.7171 | 1.13148 | ||||||||
\(738\) | 0.328237 | 0.0120826 | ||||||||
\(739\) | 10.4022 | 0.382649 | 0.191325 | − | 0.981527i | \(-0.438722\pi\) | ||||
0.191325 | + | 0.981527i | \(0.438722\pi\) | |||||||
\(740\) | −42.0411 | −1.54546 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.70863 | 0.0626837 | 0.0313419 | − | 0.999509i | \(-0.490022\pi\) | ||||
0.0313419 | + | 0.999509i | \(0.490022\pi\) | |||||||
\(744\) | −4.84590 | −0.177659 | ||||||||
\(745\) | 38.4686 | 1.40938 | ||||||||
\(746\) | 0.378216 | 0.0138475 | ||||||||
\(747\) | −5.54528 | −0.202891 | ||||||||
\(748\) | 25.2560 | 0.923451 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.46785 | 0.0901132 | ||||||||
\(751\) | 29.9812 | 1.09403 | 0.547015 | − | 0.837123i | \(-0.315764\pi\) | ||||
0.547015 | + | 0.837123i | \(0.315764\pi\) | |||||||
\(752\) | 7.03481 | 0.256533 | ||||||||
\(753\) | −46.1197 | −1.68069 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.3893 | −0.632860 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.40458 | 0.305470 | 0.152735 | − | 0.988267i | \(-0.451192\pi\) | ||||
0.152735 | + | 0.988267i | \(0.451192\pi\) | |||||||
\(758\) | 2.58874 | 0.0940271 | ||||||||
\(759\) | 21.6433 | 0.785601 | ||||||||
\(760\) | 0.363160 | 0.0131732 | ||||||||
\(761\) | 51.0590 | 1.85089 | 0.925444 | − | 0.378885i | \(-0.123692\pi\) | ||||
0.925444 | + | 0.378885i | \(0.123692\pi\) | |||||||
\(762\) | −2.63067 | −0.0952990 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 40.1337 | 1.45199 | ||||||||
\(765\) | −4.27989 | −0.154740 | ||||||||
\(766\) | 4.55447 | 0.164560 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −24.5560 | −0.886088 | ||||||||
\(769\) | 0.704439 | 0.0254027 | 0.0127014 | − | 0.999919i | \(-0.495957\pi\) | ||||
0.0127014 | + | 0.999919i | \(0.495957\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.16030 | 0.221858 | ||||||||
\(772\) | −33.9646 | −1.22241 | ||||||||
\(773\) | 1.26521 | 0.0455066 | 0.0227533 | − | 0.999741i | \(-0.492757\pi\) | ||||
0.0227533 | + | 0.999741i | \(0.492757\pi\) | |||||||
\(774\) | 0.484272 | 0.0174068 | ||||||||
\(775\) | 8.20522 | 0.294740 | ||||||||
\(776\) | 0.323607 | 0.0116168 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.08156 | −0.182183 | ||||||||
\(779\) | 1.02307 | 0.0366551 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.01193 | −0.322472 | ||||||||
\(782\) | −3.79048 | −0.135547 | ||||||||
\(783\) | 34.4896 | 1.23256 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.7679 | −1.52645 | ||||||||
\(786\) | 3.30779 | 0.117985 | ||||||||
\(787\) | 43.7969 | 1.56119 | 0.780595 | − | 0.625037i | \(-0.214916\pi\) | ||||
0.780595 | + | 0.625037i | \(0.214916\pi\) | |||||||
\(788\) | −9.75137 | −0.347378 | ||||||||
\(789\) | 0.290218 | 0.0103320 | ||||||||
\(790\) | 4.42600 | 0.157470 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.646180 | −0.0229610 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 3.93770 | 0.139744 | ||||||||
\(795\) | −34.6963 | −1.23055 | ||||||||
\(796\) | −14.1291 | −0.500792 | ||||||||
\(797\) | 13.6837 | 0.484700 | 0.242350 | − | 0.970189i | \(-0.422082\pi\) | ||||
0.242350 | + | 0.970189i | \(0.422082\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.80983 | 0.311669 | ||||||||
\(800\) | −4.70842 | −0.166468 | ||||||||
\(801\) | 1.96971 | 0.0695964 | ||||||||
\(802\) | −3.71212 | −0.131080 | ||||||||
\(803\) | −38.3008 | −1.35161 | ||||||||
\(804\) | −40.9561 | −1.44441 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42.5947 | 1.49940 | ||||||||
\(808\) | −5.49285 | −0.193238 | ||||||||
\(809\) | 9.11375 | 0.320422 | 0.160211 | − | 0.987083i | \(-0.448782\pi\) | ||||
0.160211 | + | 0.987083i | \(0.448782\pi\) | |||||||
\(810\) | −4.80523 | −0.168839 | ||||||||
\(811\) | 2.31899 | 0.0814309 | 0.0407154 | − | 0.999171i | \(-0.487036\pi\) | ||||
0.0407154 | + | 0.999171i | \(0.487036\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.5853 | 0.757028 | ||||||||
\(814\) | −3.87512 | −0.135823 | ||||||||
\(815\) | 12.8465 | 0.449993 | ||||||||
\(816\) | −33.1057 | −1.15893 | ||||||||
\(817\) | 1.50940 | 0.0528073 | ||||||||
\(818\) | 1.13352 | 0.0396325 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −28.6977 | −1.00217 | ||||||||
\(821\) | 10.1447 | 0.354053 | 0.177026 | − | 0.984206i | \(-0.443352\pi\) | ||||
0.177026 | + | 0.984206i | \(0.443352\pi\) | |||||||
\(822\) | 1.67304 | 0.0583540 | ||||||||
\(823\) | −26.8178 | −0.934811 | −0.467405 | − | 0.884043i | \(-0.654811\pi\) | ||||
−0.467405 | + | 0.884043i | \(0.654811\pi\) | |||||||
\(824\) | 3.69983 | 0.128890 | ||||||||
\(825\) | 10.9122 | 0.379913 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.6015 | 1.16844 | 0.584219 | − | 0.811596i | \(-0.301401\pi\) | ||||
0.584219 | + | 0.811596i | \(0.301401\pi\) | |||||||
\(828\) | −2.89348 | −0.100555 | ||||||||
\(829\) | 11.8666 | 0.412142 | 0.206071 | − | 0.978537i | \(-0.433932\pi\) | ||||
0.206071 | + | 0.978537i | \(0.433932\pi\) | |||||||
\(830\) | −8.05791 | −0.279694 | ||||||||
\(831\) | 49.9694 | 1.73342 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.55095 | 0.0883322 | ||||||||
\(835\) | 7.28193 | 0.252001 | ||||||||
\(836\) | −0.998723 | −0.0345416 | ||||||||
\(837\) | 18.0066 | 0.622399 | ||||||||
\(838\) | −6.17756 | −0.213400 | ||||||||
\(839\) | 34.6177 | 1.19514 | 0.597568 | − | 0.801818i | \(-0.296134\pi\) | ||||
0.597568 | + | 0.801818i | \(0.296134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2058 | 0.731234 | ||||||||
\(842\) | 2.08369 | 0.0718088 | ||||||||
\(843\) | 52.1112 | 1.79481 | ||||||||
\(844\) | 34.6102 | 1.19133 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.111772 | −0.00384280 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −26.9098 | −0.924087 | ||||||||
\(849\) | −32.8173 | −1.12629 | ||||||||
\(850\) | −1.91110 | −0.0655500 | ||||||||
\(851\) | −34.9925 | −1.19953 | ||||||||
\(852\) | 12.0159 | 0.411658 | ||||||||
\(853\) | −29.1897 | −0.999436 | −0.499718 | − | 0.866188i | \(-0.666563\pi\) | ||||
−0.499718 | + | 0.866188i | \(0.666563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.169244 | 0.00578802 | ||||||||
\(856\) | 5.76265 | 0.196963 | ||||||||
\(857\) | −25.3198 | −0.864909 | −0.432455 | − | 0.901656i | \(-0.642352\pi\) | ||||
−0.432455 | + | 0.901656i | \(0.642352\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0849 | 0.890004 | 0.445002 | − | 0.895530i | \(-0.353203\pi\) | ||||
0.445002 | + | 0.895530i | \(0.353203\pi\) | |||||||
\(860\) | −42.3398 | −1.44378 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.58583 | 0.0540134 | ||||||||
\(863\) | 36.0337 | 1.22660 | 0.613302 | − | 0.789849i | \(-0.289841\pi\) | ||||
0.613302 | + | 0.789849i | \(0.289841\pi\) | |||||||
\(864\) | −10.3328 | −0.351527 | ||||||||
\(865\) | 2.41748 | 0.0821969 | ||||||||
\(866\) | −3.99746 | −0.135839 | ||||||||
\(867\) | −10.4166 | −0.353768 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.5461 | −0.832671 | ||||||||
\(870\) | −6.28559 | −0.213101 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.956674 | −0.0323971 | ||||||||
\(873\) | 0.150811 | 0.00510418 | ||||||||
\(874\) | 0.149891 | 0.00507013 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 51.0677 | 1.72542 | ||||||||
\(877\) | −9.12168 | −0.308017 | −0.154009 | − | 0.988070i | \(-0.549218\pi\) | ||||
−0.154009 | + | 0.988070i | \(0.549218\pi\) | |||||||
\(878\) | 1.87531 | 0.0632887 | ||||||||
\(879\) | 27.1876 | 0.917015 | ||||||||
\(880\) | 27.5415 | 0.928425 | ||||||||
\(881\) | 13.0331 | 0.439095 | 0.219548 | − | 0.975602i | \(-0.429542\pi\) | ||||
0.219548 | + | 0.975602i | \(0.429542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.13222 | 0.0717548 | 0.0358774 | − | 0.999356i | \(-0.488577\pi\) | ||||
0.0358774 | + | 0.999356i | \(0.488577\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −37.2299 | −1.25147 | ||||||||
\(886\) | −6.47597 | −0.217564 | ||||||||
\(887\) | −47.1715 | −1.58386 | −0.791932 | − | 0.610610i | \(-0.790924\pi\) | ||||
−0.791932 | + | 0.610610i | \(0.790924\pi\) | |||||||
\(888\) | 10.4195 | 0.349656 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.86221 | 0.0959416 | ||||||||
\(891\) | 26.6493 | 0.892785 | ||||||||
\(892\) | 27.7496 | 0.929126 | ||||||||
\(893\) | −0.348376 | −0.0116580 | ||||||||
\(894\) | −4.72777 | −0.158120 | ||||||||
\(895\) | 29.7030 | 0.992863 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.11378 | −0.137279 | ||||||||
\(899\) | 26.2118 | 0.874213 | ||||||||
\(900\) | −1.45884 | −0.0486280 | ||||||||
\(901\) | −33.6997 | −1.12270 | ||||||||
\(902\) | −2.64520 | −0.0880755 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.3034 | −0.475725 | ||||||||
\(905\) | −9.48110 | −0.315162 | ||||||||
\(906\) | 2.13713 | 0.0710013 | ||||||||
\(907\) | 16.0431 | 0.532702 | 0.266351 | − | 0.963876i | \(-0.414182\pi\) | ||||
0.266351 | + | 0.963876i | \(0.414182\pi\) | |||||||
\(908\) | 5.64374 | 0.187294 | ||||||||
\(909\) | −2.55984 | −0.0849047 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.4319 | −0.809466 | −0.404733 | − | 0.914435i | \(-0.632636\pi\) | ||||
−0.404733 | + | 0.914435i | \(0.632636\pi\) | |||||||
\(912\) | 1.30913 | 0.0433496 | ||||||||
\(913\) | 44.6883 | 1.47897 | ||||||||
\(914\) | 5.66289 | 0.187312 | ||||||||
\(915\) | −2.01907 | −0.0667483 | ||||||||
\(916\) | 17.2613 | 0.570331 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.19395 | −0.138421 | ||||||||
\(919\) | 15.9160 | 0.525020 | 0.262510 | − | 0.964929i | \(-0.415450\pi\) | ||||
0.262510 | + | 0.964929i | \(0.415450\pi\) | |||||||
\(920\) | −8.47897 | −0.279543 | ||||||||
\(921\) | −42.9407 | −1.41494 | ||||||||
\(922\) | 1.52028 | 0.0500678 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.6426 | −0.580086 | ||||||||
\(926\) | 1.81533 | 0.0596555 | ||||||||
\(927\) | 1.72424 | 0.0566314 | ||||||||
\(928\) | −15.0412 | −0.493751 | ||||||||
\(929\) | 47.3235 | 1.55263 | 0.776317 | − | 0.630342i | \(-0.217086\pi\) | ||||
0.776317 | + | 0.630342i | \(0.217086\pi\) | |||||||
\(930\) | −3.28163 | −0.107609 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.0479 | −0.329129 | ||||||||
\(933\) | −2.97805 | −0.0974968 | ||||||||
\(934\) | 4.76494 | 0.155914 | ||||||||
\(935\) | 34.4908 | 1.12797 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.7044 | −0.970401 | −0.485200 | − | 0.874403i | \(-0.661253\pi\) | ||||
−0.485200 | + | 0.874403i | \(0.661253\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.27224 | 0.0415181 | ||||||||
\(940\) | 9.77219 | 0.318734 | ||||||||
\(941\) | −40.4224 | −1.31773 | −0.658866 | − | 0.752260i | \(-0.728964\pi\) | ||||
−0.658866 | + | 0.752260i | \(0.728964\pi\) | |||||||
\(942\) | 5.25615 | 0.171255 | ||||||||
\(943\) | −23.8863 | −0.777844 | ||||||||
\(944\) | −28.8748 | −0.939795 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.90265 | −0.126886 | ||||||||
\(947\) | −45.9228 | −1.49229 | −0.746146 | − | 0.665783i | \(-0.768098\pi\) | ||||
−0.746146 | + | 0.665783i | \(0.768098\pi\) | |||||||
\(948\) | 32.7282 | 1.06296 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.0755724 | 0.00245189 | ||||||||
\(951\) | −39.1292 | −1.26885 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.3893 | 0.401329 | 0.200664 | − | 0.979660i | \(-0.435690\pi\) | ||||
0.200664 | + | 0.979660i | \(0.435690\pi\) | |||||||
\(954\) | 0.427554 | 0.0138426 | ||||||||
\(955\) | 54.8085 | 1.77356 | ||||||||
\(956\) | 4.91426 | 0.158939 | ||||||||
\(957\) | 34.8592 | 1.12684 | ||||||||
\(958\) | −1.55222 | −0.0501499 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −35.4492 | −1.14412 | ||||||||
\(961\) | −17.3151 | −0.558553 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.68558 | 0.0865416 | ||||||||
\(964\) | −15.7091 | −0.505958 | ||||||||
\(965\) | −46.3837 | −1.49314 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.44932 | −0.303870 | −0.151935 | − | 0.988391i | \(-0.548550\pi\) | ||||
−0.151935 | + | 0.988391i | \(0.548550\pi\) | |||||||
\(968\) | −2.68377 | −0.0862596 | ||||||||
\(969\) | 1.63945 | 0.0526667 | ||||||||
\(970\) | 0.219145 | 0.00703633 | ||||||||
\(971\) | −20.9763 | −0.673163 | −0.336581 | − | 0.941654i | \(-0.609271\pi\) | ||||
−0.336581 | + | 0.941654i | \(0.609271\pi\) | |||||||
\(972\) | −6.80445 | −0.218253 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.84363 | 0.123158 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.56595 | −0.0501249 | ||||||||
\(977\) | −13.1843 | −0.421802 | −0.210901 | − | 0.977507i | \(-0.567640\pi\) | ||||
−0.210901 | + | 0.977507i | \(0.567640\pi\) | |||||||
\(978\) | −1.57883 | −0.0504853 | ||||||||
\(979\) | −15.8735 | −0.507320 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.445840 | −0.0142346 | ||||||||
\(982\) | 4.06013 | 0.129564 | ||||||||
\(983\) | −23.3588 | −0.745032 | −0.372516 | − | 0.928026i | \(-0.621505\pi\) | ||||
−0.372516 | + | 0.928026i | \(0.621505\pi\) | |||||||
\(984\) | 7.11248 | 0.226738 | ||||||||
\(985\) | −13.3169 | −0.424313 | ||||||||
\(986\) | −6.10505 | −0.194424 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.2412 | −1.12060 | ||||||||
\(990\) | −0.437591 | −0.0139076 | ||||||||
\(991\) | 39.4929 | 1.25453 | 0.627267 | − | 0.778804i | \(-0.284173\pi\) | ||||
0.627267 | + | 0.778804i | \(0.284173\pi\) | |||||||
\(992\) | −7.85281 | −0.249327 | ||||||||
\(993\) | −2.77639 | −0.0881060 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.2953 | −0.611703 | ||||||||
\(996\) | −59.5843 | −1.88800 | ||||||||
\(997\) | −51.4791 | −1.63036 | −0.815180 | − | 0.579208i | \(-0.803362\pi\) | ||||
−0.815180 | + | 0.579208i | \(0.803362\pi\) | |||||||
\(998\) | 7.03007 | 0.222533 | ||||||||
\(999\) | −38.7172 | −1.22496 |
(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 | 8281.2.a.cp.1.6 | 12 | ||
7.2 | even | 3 | 1183.2.e.j.508.7 | 24 | |||
7.4 | even | 3 | 1183.2.e.j.170.7 | 24 | |||
7.6 | odd | 2 | 8281.2.a.co.1.6 | 12 | |||
13.6 | odd | 12 | 637.2.q.g.491.4 | 12 | |||
13.11 | odd | 12 | 637.2.q.g.589.4 | 12 | |||
13.12 | even | 2 | inner | 8281.2.a.cp.1.7 | 12 | ||
91.6 | even | 12 | 637.2.q.i.491.4 | 12 | |||
91.11 | odd | 12 | 91.2.u.b.30.3 | yes | 12 | ||
91.19 | even | 12 | 637.2.u.g.361.3 | 12 | |||
91.24 | even | 12 | 637.2.u.g.30.3 | 12 | |||
91.25 | even | 6 | 1183.2.e.j.170.6 | 24 | |||
91.32 | odd | 12 | 91.2.k.b.23.4 | yes | 12 | ||
91.37 | odd | 12 | 91.2.k.b.4.3 | ✓ | 12 | ||
91.45 | even | 12 | 637.2.k.i.569.4 | 12 | |||
91.51 | even | 6 | 1183.2.e.j.508.6 | 24 | |||
91.58 | odd | 12 | 91.2.u.b.88.3 | yes | 12 | ||
91.76 | even | 12 | 637.2.q.i.589.4 | 12 | |||
91.89 | even | 12 | 637.2.k.i.459.3 | 12 | |||
91.90 | odd | 2 | 8281.2.a.co.1.7 | 12 | |||
273.11 | even | 12 | 819.2.do.e.667.4 | 12 | |||
273.32 | even | 12 | 819.2.bm.f.478.3 | 12 | |||
273.128 | even | 12 | 819.2.bm.f.550.4 | 12 | |||
273.149 | even | 12 | 819.2.do.e.361.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.3 | ✓ | 12 | 91.37 | odd | 12 | ||
91.2.k.b.23.4 | yes | 12 | 91.32 | odd | 12 | ||
91.2.u.b.30.3 | yes | 12 | 91.11 | odd | 12 | ||
91.2.u.b.88.3 | yes | 12 | 91.58 | odd | 12 | ||
637.2.k.i.459.3 | 12 | 91.89 | even | 12 | |||
637.2.k.i.569.4 | 12 | 91.45 | even | 12 | |||
637.2.q.g.491.4 | 12 | 13.6 | odd | 12 | |||
637.2.q.g.589.4 | 12 | 13.11 | odd | 12 | |||
637.2.q.i.491.4 | 12 | 91.6 | even | 12 | |||
637.2.q.i.589.4 | 12 | 91.76 | even | 12 | |||
637.2.u.g.30.3 | 12 | 91.24 | even | 12 | |||
637.2.u.g.361.3 | 12 | 91.19 | even | 12 | |||
819.2.bm.f.478.3 | 12 | 273.32 | even | 12 | |||
819.2.bm.f.550.4 | 12 | 273.128 | even | 12 | |||
819.2.do.e.361.4 | 12 | 273.149 | even | 12 | |||
819.2.do.e.667.4 | 12 | 273.11 | even | 12 | |||
1183.2.e.j.170.6 | 24 | 91.25 | even | 6 | |||
1183.2.e.j.170.7 | 24 | 7.4 | even | 3 | |||
1183.2.e.j.508.6 | 24 | 91.51 | even | 6 | |||
1183.2.e.j.508.7 | 24 | 7.2 | even | 3 | |||
8281.2.a.co.1.6 | 12 | 7.6 | odd | 2 | |||
8281.2.a.co.1.7 | 12 | 91.90 | odd | 2 | |||
8281.2.a.cp.1.6 | 12 | 1.1 | even | 1 | trivial | ||
8281.2.a.cp.1.7 | 12 | 13.12 | even | 2 | inner |