Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
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: | \( x^{12} - x^{11} - 16 x^{10} + 13 x^{9} + 93 x^{8} - 59 x^{7} - 238 x^{6} + 108 x^{5} + 257 x^{4} - 71 x^{3} - 93 x^{2} + 13 x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.26879\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.26879 | 1.60428 | 0.802139 | − | 0.597138i | \(-0.203696\pi\) | ||||
0.802139 | + | 0.597138i | \(0.203696\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.14741 | 1.57370 | ||||||||
\(5\) | 2.83484 | 1.26778 | 0.633889 | − | 0.773424i | \(-0.281458\pi\) | ||||
0.633889 | + | 0.773424i | \(0.281458\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.72992 | −1.78774 | −0.893872 | − | 0.448323i | \(-0.852022\pi\) | ||||
−0.893872 | + | 0.448323i | \(0.852022\pi\) | |||||||
\(8\) | 2.60323 | 0.920382 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.43165 | 2.03387 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.329272 | −0.0913237 | −0.0456619 | − | 0.998957i | \(-0.514540\pi\) | ||||
−0.0456619 | + | 0.998957i | \(0.514540\pi\) | |||||||
\(14\) | −10.7312 | −2.86804 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.388631 | −0.0971577 | ||||||||
\(17\) | −6.43807 | −1.56146 | −0.780731 | − | 0.624868i | \(-0.785153\pi\) | ||||
−0.780731 | + | 0.624868i | \(0.785153\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.41366 | −1.47139 | −0.735697 | − | 0.677310i | \(-0.763145\pi\) | ||||
−0.735697 | + | 0.677310i | \(0.763145\pi\) | |||||||
\(20\) | 8.92240 | 1.99511 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.26879 | 0.483708 | ||||||||
\(23\) | −0.000241797 0 | −5.04181e−5 0 | −2.52091e−5 | − | 1.00000i | \(-0.500008\pi\) | ||||
−2.52091e−5 | 1.00000i | \(0.500008\pi\) | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.03631 | 0.607261 | ||||||||
\(26\) | −0.747050 | −0.146509 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −14.8870 | −2.81338 | ||||||||
\(29\) | −8.79711 | −1.63358 | −0.816791 | − | 0.576933i | \(-0.804249\pi\) | ||||
−0.816791 | + | 0.576933i | \(0.804249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.66189 | 1.01691 | 0.508453 | − | 0.861090i | \(-0.330218\pi\) | ||||
0.508453 | + | 0.861090i | \(0.330218\pi\) | |||||||
\(32\) | −6.08819 | −1.07625 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.6066 | −2.50502 | ||||||||
\(35\) | −13.4086 | −2.26646 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.385555 | −0.0633849 | −0.0316924 | − | 0.999498i | \(-0.510090\pi\) | ||||
−0.0316924 | + | 0.999498i | \(0.510090\pi\) | |||||||
\(38\) | −14.5513 | −2.36052 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.37974 | 1.16684 | ||||||||
\(41\) | −4.58536 | −0.716113 | −0.358056 | − | 0.933700i | \(-0.616560\pi\) | ||||
−0.358056 | + | 0.933700i | \(0.616560\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.75220 | −0.419707 | −0.209854 | − | 0.977733i | \(-0.567299\pi\) | ||||
−0.209854 | + | 0.977733i | \(0.567299\pi\) | |||||||
\(44\) | 3.14741 | 0.474490 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.000548586 0 | −8.08846e−5 0 | ||||||||
\(47\) | 4.95298 | 0.722466 | 0.361233 | − | 0.932475i | \(-0.382356\pi\) | ||||
0.361233 | + | 0.932475i | \(0.382356\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.3722 | 2.19603 | ||||||||
\(50\) | 6.88874 | 0.974216 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.03636 | −0.143717 | ||||||||
\(53\) | 2.98816 | 0.410455 | 0.205228 | − | 0.978714i | \(-0.434207\pi\) | ||||
0.205228 | + | 0.978714i | \(0.434207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.83484 | 0.382249 | ||||||||
\(56\) | −12.3131 | −1.64541 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.9588 | −2.62072 | ||||||||
\(59\) | −11.8673 | −1.54499 | −0.772494 | − | 0.635022i | \(-0.780991\pi\) | ||||
−0.772494 | + | 0.635022i | \(0.780991\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 12.8456 | 1.63140 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0356 | −1.62944 | ||||||||
\(65\) | −0.933434 | −0.115778 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.49341 | −0.915465 | −0.457733 | − | 0.889090i | \(-0.651338\pi\) | ||||
−0.457733 | + | 0.889090i | \(0.651338\pi\) | |||||||
\(68\) | −20.2632 | −2.45728 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −30.4212 | −3.63603 | ||||||||
\(71\) | 3.18076 | 0.377487 | 0.188743 | − | 0.982026i | \(-0.439559\pi\) | ||||
0.188743 | + | 0.982026i | \(0.439559\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.3598 | 1.44661 | 0.723303 | − | 0.690530i | \(-0.242623\pi\) | ||||
0.723303 | + | 0.690530i | \(0.242623\pi\) | |||||||
\(74\) | −0.874744 | −0.101687 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.1864 | −2.31554 | ||||||||
\(77\) | −4.72992 | −0.539025 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.72569 | 0.644190 | 0.322095 | − | 0.946707i | \(-0.395613\pi\) | ||||
0.322095 | + | 0.946707i | \(0.395613\pi\) | |||||||
\(80\) | −1.10171 | −0.123174 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.4032 | −1.14884 | ||||||||
\(83\) | 10.3351 | 1.13443 | 0.567214 | − | 0.823570i | \(-0.308021\pi\) | ||||
0.567214 | + | 0.823570i | \(0.308021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.2509 | −1.97959 | ||||||||
\(86\) | −6.24417 | −0.673326 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.60323 | 0.277506 | ||||||||
\(89\) | 3.95881 | 0.419634 | 0.209817 | − | 0.977741i | \(-0.432713\pi\) | ||||
0.209817 | + | 0.977741i | \(0.432713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.55743 | 0.163263 | ||||||||
\(92\) | −0.000761033 0 | −7.93432e−5 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.2373 | 1.15904 | ||||||||
\(95\) | −18.1817 | −1.86540 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.5563 | −1.17337 | −0.586684 | − | 0.809816i | \(-0.699567\pi\) | ||||
−0.586684 | + | 0.809816i | \(0.699567\pi\) | |||||||
\(98\) | 34.8763 | 3.52304 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.55650 | 0.955650 | ||||||||
\(101\) | −16.8491 | −1.67655 | −0.838276 | − | 0.545247i | \(-0.816436\pi\) | ||||
−0.838276 | + | 0.545247i | \(0.816436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.38045 | 0.234553 | 0.117276 | − | 0.993099i | \(-0.462584\pi\) | ||||
0.117276 | + | 0.993099i | \(0.462584\pi\) | |||||||
\(104\) | −0.857173 | −0.0840527 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.77951 | 0.658484 | ||||||||
\(107\) | 12.2216 | 1.18150 | 0.590751 | − | 0.806854i | \(-0.298831\pi\) | ||||
0.590751 | + | 0.806854i | \(0.298831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.27529 | 0.601064 | 0.300532 | − | 0.953772i | \(-0.402836\pi\) | ||||
0.300532 | + | 0.953772i | \(0.402836\pi\) | |||||||
\(110\) | 6.43165 | 0.613234 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.83820 | 0.173693 | ||||||||
\(113\) | −12.6571 | −1.19068 | −0.595342 | − | 0.803472i | \(-0.702984\pi\) | ||||
−0.595342 | + | 0.803472i | \(0.702984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.000685455 0 | −6.39190e−5 0 | ||||||||
\(116\) | −27.6881 | −2.57078 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −26.9244 | −2.47859 | ||||||||
\(119\) | 30.4516 | 2.79149 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.26879 | −0.205407 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17.8203 | 1.60031 | ||||||||
\(125\) | −5.56675 | −0.497905 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2420 | 1.61871 | 0.809356 | − | 0.587318i | \(-0.199816\pi\) | ||||
0.809356 | + | 0.587318i | \(0.199816\pi\) | |||||||
\(128\) | −17.3986 | −1.53783 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.11777 | −0.185740 | ||||||||
\(131\) | 9.31461 | 0.813821 | 0.406911 | − | 0.913468i | \(-0.366606\pi\) | ||||
0.406911 | + | 0.913468i | \(0.366606\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.3361 | 2.63048 | ||||||||
\(134\) | −17.0010 | −1.46866 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.7598 | −1.43714 | ||||||||
\(137\) | 11.2029 | 0.957129 | 0.478565 | − | 0.878052i | \(-0.341157\pi\) | ||||
0.478565 | + | 0.878052i | \(0.341157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8177 | 1.51127 | 0.755637 | − | 0.654990i | \(-0.227327\pi\) | ||||
0.755637 | + | 0.654990i | \(0.227327\pi\) | |||||||
\(140\) | −42.2023 | −3.56674 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.21648 | 0.605594 | ||||||||
\(143\) | −0.329272 | −0.0275351 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.9384 | −2.07102 | ||||||||
\(146\) | 28.0418 | 2.32076 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.21350 | −0.0997491 | ||||||||
\(149\) | 8.25059 | 0.675915 | 0.337958 | − | 0.941161i | \(-0.390264\pi\) | ||||
0.337958 | + | 0.941161i | \(0.390264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.72341 | −0.791280 | −0.395640 | − | 0.918406i | \(-0.629477\pi\) | ||||
−0.395640 | + | 0.918406i | \(0.629477\pi\) | |||||||
\(152\) | −16.6962 | −1.35424 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.7312 | −0.864745 | ||||||||
\(155\) | 16.0505 | 1.28921 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.6011 | −0.846059 | −0.423030 | − | 0.906116i | \(-0.639033\pi\) | ||||
−0.423030 | + | 0.906116i | \(0.639033\pi\) | |||||||
\(158\) | 12.9904 | 1.03346 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −17.2590 | −1.36445 | ||||||||
\(161\) | 0.00114368 | 9.01346e−5 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.7755 | −0.843999 | −0.422000 | − | 0.906596i | \(-0.638672\pi\) | ||||
−0.422000 | + | 0.906596i | \(0.638672\pi\) | |||||||
\(164\) | −14.4320 | −1.12695 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.4483 | 1.81994 | ||||||||
\(167\) | −0.523617 | −0.0405187 | −0.0202594 | − | 0.999795i | \(-0.506449\pi\) | ||||
−0.0202594 | + | 0.999795i | \(0.506449\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8916 | −0.991660 | ||||||||
\(170\) | −41.4074 | −3.17581 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.66231 | −0.660495 | ||||||||
\(173\) | −6.06345 | −0.460995 | −0.230498 | − | 0.973073i | \(-0.574035\pi\) | ||||
−0.230498 | + | 0.973073i | \(0.574035\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.3615 | −1.08563 | ||||||||
\(176\) | −0.388631 | −0.0292942 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.98172 | 0.673208 | ||||||||
\(179\) | 22.6875 | 1.69574 | 0.847871 | − | 0.530202i | \(-0.177884\pi\) | ||||
0.847871 | + | 0.530202i | \(0.177884\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.9241 | −1.70394 | −0.851969 | − | 0.523593i | \(-0.824591\pi\) | ||||
−0.851969 | + | 0.523593i | \(0.824591\pi\) | |||||||
\(182\) | 3.53349 | 0.261920 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.000629453 0 | −4.64039e−5 0 | ||||||||
\(185\) | −1.09299 | −0.0803579 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.43807 | −0.470798 | ||||||||
\(188\) | 15.5891 | 1.13695 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −41.2504 | −2.99262 | ||||||||
\(191\) | −22.9356 | −1.65956 | −0.829780 | − | 0.558091i | \(-0.811534\pi\) | ||||
−0.829780 | + | 0.558091i | \(0.811534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.8045 | −1.35358 | −0.676789 | − | 0.736177i | \(-0.736629\pi\) | ||||
−0.676789 | + | 0.736177i | \(0.736629\pi\) | |||||||
\(194\) | −26.2189 | −1.88241 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 48.3826 | 3.45590 | ||||||||
\(197\) | −8.55113 | −0.609243 | −0.304621 | − | 0.952474i | \(-0.598530\pi\) | ||||
−0.304621 | + | 0.952474i | \(0.598530\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5926 | 0.750890 | 0.375445 | − | 0.926845i | \(-0.377490\pi\) | ||||
0.375445 | + | 0.926845i | \(0.377490\pi\) | |||||||
\(200\) | 7.90421 | 0.558912 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −38.2271 | −2.68965 | ||||||||
\(203\) | 41.6097 | 2.92043 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.9988 | −0.907872 | ||||||||
\(206\) | 5.40074 | 0.376287 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.127965 | 0.00887281 | ||||||||
\(209\) | −6.41366 | −0.443642 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.4180 | −1.26794 | −0.633972 | − | 0.773356i | \(-0.718577\pi\) | ||||
−0.633972 | + | 0.773356i | \(0.718577\pi\) | |||||||
\(212\) | 9.40496 | 0.645936 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 27.7281 | 1.89546 | ||||||||
\(215\) | −7.80205 | −0.532095 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.7803 | −1.81797 | ||||||||
\(218\) | 14.2373 | 0.964273 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.92240 | 0.601548 | ||||||||
\(221\) | 2.11988 | 0.142598 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.52442 | −0.236013 | −0.118006 | − | 0.993013i | \(-0.537650\pi\) | ||||
−0.118006 | + | 0.993013i | \(0.537650\pi\) | |||||||
\(224\) | 28.7967 | 1.92406 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −28.7164 | −1.91019 | ||||||||
\(227\) | 3.96905 | 0.263435 | 0.131718 | − | 0.991287i | \(-0.457951\pi\) | ||||
0.131718 | + | 0.991287i | \(0.457951\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0640 | 1.45803 | 0.729013 | − | 0.684499i | \(-0.239979\pi\) | ||||
0.729013 | + | 0.684499i | \(0.239979\pi\) | |||||||
\(230\) | −0.00155515 | −0.000102544 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −22.9009 | −1.50352 | ||||||||
\(233\) | 25.1375 | 1.64681 | 0.823405 | − | 0.567454i | \(-0.192072\pi\) | ||||
0.823405 | + | 0.567454i | \(0.192072\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.0409 | 0.915927 | ||||||||
\(236\) | −37.3512 | −2.43136 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 69.0883 | 4.47833 | ||||||||
\(239\) | −14.8916 | −0.963259 | −0.481629 | − | 0.876375i | \(-0.659955\pi\) | ||||
−0.481629 | + | 0.876375i | \(0.659955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7364 | −1.27134 | −0.635668 | − | 0.771963i | \(-0.719275\pi\) | ||||
−0.635668 | + | 0.771963i | \(0.719275\pi\) | |||||||
\(242\) | 2.26879 | 0.145843 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.14741 | −0.201492 | ||||||||
\(245\) | 43.5777 | 2.78407 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.11184 | 0.134373 | ||||||||
\(248\) | 14.7392 | 0.935941 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.6298 | −0.798778 | ||||||||
\(251\) | 22.4411 | 1.41647 | 0.708235 | − | 0.705977i | \(-0.249492\pi\) | ||||
0.708235 | + | 0.705977i | \(0.249492\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.000241797 0 | −1.52016e−5 0 | ||||||||
\(254\) | 41.3872 | 2.59686 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.4026 | −0.837663 | ||||||||
\(257\) | −7.08903 | −0.442201 | −0.221101 | − | 0.975251i | \(-0.570965\pi\) | ||||
−0.221101 | + | 0.975251i | \(0.570965\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.82365 | 0.113316 | ||||||||
\(260\) | −2.93790 | −0.182201 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.1329 | 1.30559 | ||||||||
\(263\) | −6.00950 | −0.370562 | −0.185281 | − | 0.982686i | \(-0.559319\pi\) | ||||
−0.185281 | + | 0.982686i | \(0.559319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.47095 | 0.520366 | ||||||||
\(266\) | 68.8263 | 4.22001 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.5848 | −1.44067 | ||||||||
\(269\) | 20.6863 | 1.26126 | 0.630632 | − | 0.776082i | \(-0.282796\pi\) | ||||
0.630632 | + | 0.776082i | \(0.282796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2338 | −0.621661 | −0.310831 | − | 0.950465i | \(-0.600607\pi\) | ||||
−0.310831 | + | 0.950465i | \(0.600607\pi\) | |||||||
\(272\) | 2.50203 | 0.151708 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.4171 | 1.53550 | ||||||||
\(275\) | 3.03631 | 0.183096 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.41552 | 0.505640 | 0.252820 | − | 0.967513i | \(-0.418642\pi\) | ||||
0.252820 | + | 0.967513i | \(0.418642\pi\) | |||||||
\(278\) | 40.4245 | 2.42450 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −34.9056 | −2.08601 | ||||||||
\(281\) | −24.4089 | −1.45611 | −0.728057 | − | 0.685516i | \(-0.759577\pi\) | ||||
−0.728057 | + | 0.685516i | \(0.759577\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.5811 | −1.22342 | −0.611709 | − | 0.791083i | \(-0.709518\pi\) | ||||
−0.611709 | + | 0.791083i | \(0.709518\pi\) | |||||||
\(284\) | 10.0112 | 0.594053 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.747050 | −0.0441740 | ||||||||
\(287\) | 21.6884 | 1.28023 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.4488 | 1.43816 | ||||||||
\(290\) | −56.5800 | −3.32249 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 38.9014 | 2.27653 | ||||||||
\(293\) | 2.38810 | 0.139515 | 0.0697573 | − | 0.997564i | \(-0.477778\pi\) | ||||
0.0697573 | + | 0.997564i | \(0.477778\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.6418 | −1.95870 | ||||||||
\(296\) | −1.00369 | −0.0583383 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.7189 | 1.08436 | ||||||||
\(299\) | 7.96170e−5 0 | 4.60437e−6 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.0177 | 0.750329 | ||||||||
\(302\) | −22.0604 | −1.26943 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.49255 | 0.142957 | ||||||||
\(305\) | −2.83484 | −0.162322 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0250 | 1.37118 | 0.685588 | − | 0.727990i | \(-0.259545\pi\) | ||||
0.685588 | + | 0.727990i | \(0.259545\pi\) | |||||||
\(308\) | −14.8870 | −0.848266 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 36.4153 | 2.06825 | ||||||||
\(311\) | −16.3407 | −0.926595 | −0.463297 | − | 0.886203i | \(-0.653334\pi\) | ||||
−0.463297 | + | 0.886203i | \(0.653334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.9694 | −1.46787 | −0.733937 | − | 0.679217i | \(-0.762319\pi\) | ||||
−0.733937 | + | 0.679217i | \(0.762319\pi\) | |||||||
\(314\) | −24.0517 | −1.35731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.0211 | 1.01377 | ||||||||
\(317\) | 0.168883 | 0.00948539 | 0.00474270 | − | 0.999989i | \(-0.498490\pi\) | ||||
0.00474270 | + | 0.999989i | \(0.498490\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.79711 | −0.492544 | ||||||||
\(320\) | −36.9537 | −2.06577 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.00259477 | 0.000144601 0 | ||||||||
\(323\) | 41.2916 | 2.29753 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.999772 | −0.0554574 | ||||||||
\(326\) | −24.4473 | −1.35401 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.9368 | −0.659097 | ||||||||
\(329\) | −23.4272 | −1.29158 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0242 | 0.825804 | 0.412902 | − | 0.910776i | \(-0.364515\pi\) | ||||
0.412902 | + | 0.910776i | \(0.364515\pi\) | |||||||
\(332\) | 32.5289 | 1.78526 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.18798 | −0.0650033 | ||||||||
\(335\) | −21.2426 | −1.16061 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6051 | 0.632172 | 0.316086 | − | 0.948731i | \(-0.397631\pi\) | ||||
0.316086 | + | 0.948731i | \(0.397631\pi\) | |||||||
\(338\) | −29.2483 | −1.59090 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −57.4430 | −3.11529 | ||||||||
\(341\) | 5.66189 | 0.306609 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −39.5998 | −2.13819 | ||||||||
\(344\) | −7.16463 | −0.386291 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.7567 | −0.739564 | ||||||||
\(347\) | −35.9376 | −1.92923 | −0.964615 | − | 0.263661i | \(-0.915070\pi\) | ||||
−0.964615 | + | 0.263661i | \(0.915070\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.25292 | −0.174125 | −0.0870624 | − | 0.996203i | \(-0.527748\pi\) | ||||
−0.0870624 | + | 0.996203i | \(0.527748\pi\) | |||||||
\(350\) | −32.5832 | −1.74165 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.08819 | −0.324501 | ||||||||
\(353\) | 23.5713 | 1.25457 | 0.627286 | − | 0.778789i | \(-0.284166\pi\) | ||||
0.627286 | + | 0.778789i | \(0.284166\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.01694 | 0.478570 | ||||||||
\(356\) | 12.4600 | 0.660379 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 51.4732 | 2.72044 | ||||||||
\(359\) | 6.43776 | 0.339772 | 0.169886 | − | 0.985464i | \(-0.445660\pi\) | ||||
0.169886 | + | 0.985464i | \(0.445660\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.1350 | 1.16500 | ||||||||
\(362\) | −52.0101 | −2.73359 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.90188 | 0.256928 | ||||||||
\(365\) | 35.0381 | 1.83398 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.8180 | −0.564693 | −0.282346 | − | 0.959313i | \(-0.591113\pi\) | ||||
−0.282346 | + | 0.959313i | \(0.591113\pi\) | |||||||
\(368\) | 9.39697e−5 0 | 4.89851e−6 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.47976 | −0.128916 | ||||||||
\(371\) | −14.1338 | −0.733789 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.6020 | −1.22207 | −0.611033 | − | 0.791605i | \(-0.709246\pi\) | ||||
−0.611033 | + | 0.791605i | \(0.709246\pi\) | |||||||
\(374\) | −14.6066 | −0.755291 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.8938 | 0.664945 | ||||||||
\(377\) | 2.89665 | 0.149185 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0391 | 1.33754 | 0.668769 | − | 0.743470i | \(-0.266821\pi\) | ||||
0.668769 | + | 0.743470i | \(0.266821\pi\) | |||||||
\(380\) | −57.2252 | −2.93559 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −52.0360 | −2.66239 | ||||||||
\(383\) | 17.5297 | 0.895726 | 0.447863 | − | 0.894102i | \(-0.352185\pi\) | ||||
0.447863 | + | 0.894102i | \(0.352185\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.4086 | −0.683364 | ||||||||
\(386\) | −42.6635 | −2.17151 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −36.3725 | −1.84653 | ||||||||
\(389\) | −21.2431 | −1.07707 | −0.538535 | − | 0.842603i | \(-0.681022\pi\) | ||||
−0.538535 | + | 0.842603i | \(0.681022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.00155670 | 7.87259e−5 0 | ||||||||
\(392\) | 40.0174 | 2.02118 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −19.4007 | −0.977394 | ||||||||
\(395\) | 16.2314 | 0.816690 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0596 | −0.806006 | −0.403003 | − | 0.915199i | \(-0.632034\pi\) | ||||
−0.403003 | + | 0.915199i | \(0.632034\pi\) | |||||||
\(398\) | 24.0324 | 1.20464 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.18000 | −0.0590001 | ||||||||
\(401\) | −12.2725 | −0.612861 | −0.306431 | − | 0.951893i | \(-0.599135\pi\) | ||||
−0.306431 | + | 0.951893i | \(0.599135\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.86430 | −0.0928676 | ||||||||
\(404\) | −53.0311 | −2.63840 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 94.4037 | 4.68517 | ||||||||
\(407\) | −0.385555 | −0.0191113 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.71520 | −0.430939 | −0.215470 | − | 0.976511i | \(-0.569128\pi\) | ||||
−0.215470 | + | 0.976511i | \(0.569128\pi\) | |||||||
\(410\) | −29.4914 | −1.45648 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.49225 | 0.369117 | ||||||||
\(413\) | 56.1313 | 2.76204 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.2984 | 1.43820 | ||||||||
\(416\) | 2.00467 | 0.0982871 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.5513 | −0.711725 | ||||||||
\(419\) | 27.6500 | 1.35079 | 0.675396 | − | 0.737455i | \(-0.263973\pi\) | ||||
0.675396 | + | 0.737455i | \(0.263973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.5245 | −1.04904 | −0.524520 | − | 0.851398i | \(-0.675755\pi\) | ||||
−0.524520 | + | 0.851398i | \(0.675755\pi\) | |||||||
\(422\) | −41.7865 | −2.03413 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.77887 | 0.377776 | ||||||||
\(425\) | −19.5480 | −0.948215 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.72992 | 0.228897 | ||||||||
\(428\) | 38.4662 | 1.85934 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.7012 | −0.853629 | ||||||||
\(431\) | −35.6418 | −1.71681 | −0.858403 | − | 0.512977i | \(-0.828543\pi\) | ||||
−0.858403 | + | 0.512977i | \(0.828543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.8670 | −1.24309 | −0.621543 | − | 0.783380i | \(-0.713494\pi\) | ||||
−0.621543 | + | 0.783380i | \(0.713494\pi\) | |||||||
\(434\) | −60.7589 | −2.91652 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.7509 | 0.945897 | ||||||||
\(437\) | 0.00155080 | 7.41849e−5 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.60137 | −0.315066 | −0.157533 | − | 0.987514i | \(-0.550354\pi\) | ||||
−0.157533 | + | 0.987514i | \(0.550354\pi\) | |||||||
\(440\) | 7.37974 | 0.351815 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.80956 | 0.228767 | ||||||||
\(443\) | −20.7297 | −0.984900 | −0.492450 | − | 0.870341i | \(-0.663898\pi\) | ||||
−0.492450 | + | 0.870341i | \(0.663898\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.2226 | 0.532002 | ||||||||
\(446\) | −7.99617 | −0.378630 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 61.6572 | 2.91303 | ||||||||
\(449\) | −11.8139 | −0.557534 | −0.278767 | − | 0.960359i | \(-0.589926\pi\) | ||||
−0.278767 | + | 0.960359i | \(0.589926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.58536 | −0.215916 | ||||||||
\(452\) | −39.8372 | −1.87379 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.00495 | 0.422623 | ||||||||
\(455\) | 4.41507 | 0.206982 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.7970 | 1.34707 | 0.673535 | − | 0.739156i | \(-0.264775\pi\) | ||||
0.673535 | + | 0.739156i | \(0.264775\pi\) | |||||||
\(458\) | 50.0585 | 2.33908 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.00215741 | −0.000100590 0 | ||||||||
\(461\) | 0.622970 | 0.0290146 | 0.0145073 | − | 0.999895i | \(-0.495382\pi\) | ||||
0.0145073 | + | 0.999895i | \(0.495382\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.1613 | 0.936974 | 0.468487 | − | 0.883470i | \(-0.344799\pi\) | ||||
0.468487 | + | 0.883470i | \(0.344799\pi\) | |||||||
\(464\) | 3.41883 | 0.158715 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 57.0316 | 2.64194 | ||||||||
\(467\) | 10.3857 | 0.480594 | 0.240297 | − | 0.970699i | \(-0.422755\pi\) | ||||
0.240297 | + | 0.970699i | \(0.422755\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.4433 | 1.63662 | ||||||||
\(470\) | 31.8559 | 1.46940 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −30.8933 | −1.42198 | ||||||||
\(473\) | −2.75220 | −0.126546 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.4738 | −0.893521 | ||||||||
\(476\) | 95.8436 | 4.39299 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −33.7860 | −1.54533 | ||||||||
\(479\) | −24.6590 | −1.12670 | −0.563348 | − | 0.826220i | \(-0.690487\pi\) | ||||
−0.563348 | + | 0.826220i | \(0.690487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.126953 | 0.00578854 | ||||||||
\(482\) | −44.7778 | −2.03958 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.14741 | 0.143064 | ||||||||
\(485\) | −32.7603 | −1.48757 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.7342 | 1.21144 | 0.605720 | − | 0.795678i | \(-0.292885\pi\) | ||||
0.605720 | + | 0.795678i | \(0.292885\pi\) | |||||||
\(488\) | −2.60323 | −0.117843 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 98.8686 | 4.46643 | ||||||||
\(491\) | −26.1263 | −1.17906 | −0.589532 | − | 0.807745i | \(-0.700688\pi\) | ||||
−0.589532 | + | 0.807745i | \(0.700688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 56.6364 | 2.55078 | ||||||||
\(494\) | 4.79132 | 0.215572 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.20039 | −0.0988002 | ||||||||
\(497\) | −15.0448 | −0.674850 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.3139 | 1.17797 | 0.588987 | − | 0.808143i | \(-0.299527\pi\) | ||||
0.588987 | + | 0.808143i | \(0.299527\pi\) | |||||||
\(500\) | −17.5208 | −0.783556 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 50.9142 | 2.27241 | ||||||||
\(503\) | −1.89384 | −0.0844421 | −0.0422211 | − | 0.999108i | \(-0.513443\pi\) | ||||
−0.0422211 | + | 0.999108i | \(0.513443\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −47.7646 | −2.12549 | ||||||||
\(506\) | −0.000548586 0 | −2.43876e−5 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 57.4149 | 2.54738 | ||||||||
\(509\) | −4.01793 | −0.178092 | −0.0890458 | − | 0.996028i | \(-0.528382\pi\) | ||||
−0.0890458 | + | 0.996028i | \(0.528382\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −58.4610 | −2.58616 | ||||||||
\(512\) | 4.38945 | 0.193988 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.0835 | −0.709414 | ||||||||
\(515\) | 6.74819 | 0.297361 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.95298 | 0.217832 | ||||||||
\(518\) | 4.13747 | 0.181790 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.42995 | −0.106560 | ||||||||
\(521\) | 31.3527 | 1.37359 | 0.686794 | − | 0.726852i | \(-0.259018\pi\) | ||||
0.686794 | + | 0.726852i | \(0.259018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.6005 | 1.51297 | 0.756487 | − | 0.654009i | \(-0.226914\pi\) | ||||
0.756487 | + | 0.654009i | \(0.226914\pi\) | |||||||
\(524\) | 29.3169 | 1.28071 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.6343 | −0.594484 | ||||||||
\(527\) | −36.4516 | −1.58786 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 19.2188 | 0.834812 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 95.4802 | 4.13959 | ||||||||
\(533\) | 1.50983 | 0.0653981 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.6461 | 1.49788 | ||||||||
\(536\) | −19.5071 | −0.842578 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 46.9328 | 2.02342 | ||||||||
\(539\) | 15.3722 | 0.662127 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.6021 | 0.670786 | 0.335393 | − | 0.942078i | \(-0.391131\pi\) | ||||
0.335393 | + | 0.942078i | \(0.391131\pi\) | |||||||
\(542\) | −23.2184 | −0.997317 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 39.1962 | 1.68052 | ||||||||
\(545\) | 17.7894 | 0.762015 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.9091 | −1.27882 | −0.639411 | − | 0.768865i | \(-0.720822\pi\) | ||||
−0.639411 | + | 0.768865i | \(0.720822\pi\) | |||||||
\(548\) | 35.2601 | 1.50624 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.88874 | 0.293737 | ||||||||
\(551\) | 56.4217 | 2.40365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.0821 | −1.15165 | ||||||||
\(554\) | 19.0931 | 0.811186 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 56.0795 | 2.37830 | ||||||||
\(557\) | −28.1835 | −1.19417 | −0.597087 | − | 0.802177i | \(-0.703675\pi\) | ||||
−0.597087 | + | 0.802177i | \(0.703675\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.906225 | 0.0383292 | ||||||||
\(560\) | 5.21099 | 0.220204 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −55.3787 | −2.33601 | ||||||||
\(563\) | −9.46021 | −0.398700 | −0.199350 | − | 0.979928i | \(-0.563883\pi\) | ||||
−0.199350 | + | 0.979928i | \(0.563883\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.8810 | −1.50952 | ||||||||
\(566\) | −46.6942 | −1.96270 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.28026 | 0.347432 | ||||||||
\(569\) | 11.2370 | 0.471082 | 0.235541 | − | 0.971864i | \(-0.424314\pi\) | ||||
0.235541 | + | 0.971864i | \(0.424314\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.43482 | 0.227440 | 0.113720 | − | 0.993513i | \(-0.463723\pi\) | ||||
0.113720 | + | 0.993513i | \(0.463723\pi\) | |||||||
\(572\) | −1.03636 | −0.0433322 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 49.2065 | 2.05384 | ||||||||
\(575\) | −0.000734169 0 | −3.06170e−5 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.5185 | 0.687676 | 0.343838 | − | 0.939029i | \(-0.388273\pi\) | ||||
0.343838 | + | 0.939029i | \(0.388273\pi\) | |||||||
\(578\) | 55.4691 | 2.30721 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −78.4913 | −3.25918 | ||||||||
\(581\) | −48.8844 | −2.02807 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.98816 | 0.123757 | ||||||||
\(584\) | 32.1755 | 1.33143 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.41811 | 0.223820 | ||||||||
\(587\) | 26.9141 | 1.11086 | 0.555432 | − | 0.831562i | \(-0.312553\pi\) | ||||
0.555432 | + | 0.831562i | \(0.312553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.3134 | −1.49627 | ||||||||
\(590\) | −76.3262 | −3.14230 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.149839 | 0.00615833 | ||||||||
\(593\) | 19.3983 | 0.796593 | 0.398296 | − | 0.917257i | \(-0.369602\pi\) | ||||
0.398296 | + | 0.917257i | \(0.369602\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 86.3253 | 3.53899 | ||||||||
\(596\) | 25.9680 | 1.06369 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.000180634 0 | 7.38668e−6 0 | ||||||||
\(599\) | 21.6311 | 0.883825 | 0.441912 | − | 0.897058i | \(-0.354300\pi\) | ||||
0.441912 | + | 0.897058i | \(0.354300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.4181 | 1.64869 | 0.824345 | − | 0.566088i | \(-0.191544\pi\) | ||||
0.824345 | + | 0.566088i | \(0.191544\pi\) | |||||||
\(602\) | 29.5345 | 1.20374 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −30.6036 | −1.24524 | ||||||||
\(605\) | 2.83484 | 0.115253 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.54357 | −0.184418 | −0.0922089 | − | 0.995740i | \(-0.529393\pi\) | ||||
−0.0922089 | + | 0.995740i | \(0.529393\pi\) | |||||||
\(608\) | 39.0476 | 1.58359 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.43165 | −0.260410 | ||||||||
\(611\) | −1.63088 | −0.0659783 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.1325 | −1.25743 | −0.628715 | − | 0.777636i | \(-0.716419\pi\) | ||||
−0.628715 | + | 0.777636i | \(0.716419\pi\) | |||||||
\(614\) | 54.5076 | 2.19975 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.3131 | −0.496109 | ||||||||
\(617\) | 8.28328 | 0.333472 | 0.166736 | − | 0.986002i | \(-0.446677\pi\) | ||||
0.166736 | + | 0.986002i | \(0.446677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.5704 | −1.14834 | −0.574170 | − | 0.818736i | \(-0.694675\pi\) | ||||
−0.574170 | + | 0.818736i | \(0.694675\pi\) | |||||||
\(620\) | 50.5176 | 2.02884 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −37.0736 | −1.48651 | ||||||||
\(623\) | −18.7249 | −0.750197 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9624 | −1.23849 | ||||||||
\(626\) | −58.9190 | −2.35488 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33.3660 | −1.33145 | ||||||||
\(629\) | 2.48223 | 0.0989730 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.8212 | −0.669641 | −0.334820 | − | 0.942282i | \(-0.608676\pi\) | ||||
−0.334820 | + | 0.942282i | \(0.608676\pi\) | |||||||
\(632\) | 14.9053 | 0.592901 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.383159 | 0.0152172 | ||||||||
\(635\) | 51.7130 | 2.05217 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.06164 | −0.200549 | ||||||||
\(638\) | −19.9588 | −0.790177 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −49.3221 | −1.94963 | ||||||||
\(641\) | 13.3915 | 0.528931 | 0.264466 | − | 0.964395i | \(-0.414804\pi\) | ||||
0.264466 | + | 0.964395i | \(0.414804\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.2370 | −0.995249 | −0.497625 | − | 0.867393i | \(-0.665794\pi\) | ||||
−0.497625 | + | 0.867393i | \(0.665794\pi\) | |||||||
\(644\) | 0.00359963 | 0.000141845 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 93.6820 | 3.68587 | ||||||||
\(647\) | −17.6479 | −0.693812 | −0.346906 | − | 0.937900i | \(-0.612768\pi\) | ||||
−0.346906 | + | 0.937900i | \(0.612768\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.8673 | −0.465832 | ||||||||
\(650\) | −2.26827 | −0.0889690 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33.9148 | −1.32821 | ||||||||
\(653\) | −45.1007 | −1.76493 | −0.882464 | − | 0.470380i | \(-0.844117\pi\) | ||||
−0.882464 | + | 0.470380i | \(0.844117\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.4054 | 1.03174 | ||||||||
\(656\) | 1.78201 | 0.0695759 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −53.1515 | −2.07206 | ||||||||
\(659\) | 10.7525 | 0.418857 | 0.209428 | − | 0.977824i | \(-0.432840\pi\) | ||||
0.209428 | + | 0.977824i | \(0.432840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4223 | −0.755438 | −0.377719 | − | 0.925920i | \(-0.623292\pi\) | ||||
−0.377719 | + | 0.925920i | \(0.623292\pi\) | |||||||
\(662\) | 34.0867 | 1.32482 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.9048 | 1.04411 | ||||||||
\(665\) | 85.9980 | 3.33486 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.00212711 | 8.23621e−5 0 | ||||||||
\(668\) | −1.64804 | −0.0637645 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −48.1950 | −1.86194 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.38436 | 0.169005 | 0.0845024 | − | 0.996423i | \(-0.473070\pi\) | ||||
0.0845024 | + | 0.996423i | \(0.473070\pi\) | |||||||
\(674\) | 26.3296 | 1.01418 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −40.5751 | −1.56058 | ||||||||
\(677\) | −7.27907 | −0.279757 | −0.139879 | − | 0.990169i | \(-0.544671\pi\) | ||||
−0.139879 | + | 0.990169i | \(0.544671\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 54.6606 | 2.09768 | ||||||||
\(680\) | −47.5113 | −1.82198 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.8456 | 0.491885 | ||||||||
\(683\) | −3.20425 | −0.122607 | −0.0613035 | − | 0.998119i | \(-0.519526\pi\) | ||||
−0.0613035 | + | 0.998119i | \(0.519526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.7584 | 1.21343 | ||||||||
\(686\) | −89.8437 | −3.43025 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.06959 | 0.0407778 | ||||||||
\(689\) | −0.983918 | −0.0374843 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.5148 | −1.57930 | −0.789649 | − | 0.613559i | \(-0.789737\pi\) | ||||
−0.789649 | + | 0.613559i | \(0.789737\pi\) | |||||||
\(692\) | −19.0842 | −0.725471 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −81.5348 | −3.09502 | ||||||||
\(695\) | 50.5102 | 1.91596 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.5209 | 1.11818 | ||||||||
\(698\) | −7.38020 | −0.279345 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −45.2015 | −1.70846 | ||||||||
\(701\) | 6.73449 | 0.254358 | 0.127179 | − | 0.991880i | \(-0.459408\pi\) | ||||
0.127179 | + | 0.991880i | \(0.459408\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.47282 | 0.0932641 | ||||||||
\(704\) | −13.0356 | −0.491296 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.4782 | 2.01268 | ||||||||
\(707\) | 79.6951 | 2.99724 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8524 | 0.745574 | 0.372787 | − | 0.927917i | \(-0.378402\pi\) | ||||
0.372787 | + | 0.927917i | \(0.378402\pi\) | |||||||
\(710\) | 20.4576 | 0.767758 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.3057 | 0.386223 | ||||||||
\(713\) | −0.00136903 | −5.12704e−5 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.933434 | −0.0349084 | ||||||||
\(716\) | 71.4068 | 2.66860 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.6059 | 0.545088 | ||||||||
\(719\) | 40.2186 | 1.49990 | 0.749950 | − | 0.661494i | \(-0.230077\pi\) | ||||
0.749950 | + | 0.661494i | \(0.230077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.2593 | −0.419320 | ||||||||
\(722\) | 50.2198 | 1.86899 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −72.1516 | −2.68149 | ||||||||
\(725\) | −26.7107 | −0.992012 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.55895 | −0.317434 | −0.158717 | − | 0.987324i | \(-0.550736\pi\) | ||||
−0.158717 | + | 0.987324i | \(0.550736\pi\) | |||||||
\(728\) | 4.05436 | 0.150265 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 79.4940 | 2.94221 | ||||||||
\(731\) | 17.7189 | 0.655356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.8567 | 0.770360 | 0.385180 | − | 0.922842i | \(-0.374139\pi\) | ||||
0.385180 | + | 0.922842i | \(0.374139\pi\) | |||||||
\(734\) | −24.5437 | −0.905924 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.00147210 | 5.42625e−5 0 | ||||||||
\(737\) | −7.49341 | −0.276023 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.12261 | 0.0780816 | 0.0390408 | − | 0.999238i | \(-0.487570\pi\) | ||||
0.0390408 | + | 0.999238i | \(0.487570\pi\) | |||||||
\(740\) | −3.44008 | −0.126460 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −32.0666 | −1.17720 | ||||||||
\(743\) | −24.8996 | −0.913476 | −0.456738 | − | 0.889601i | \(-0.650982\pi\) | ||||
−0.456738 | + | 0.889601i | \(0.650982\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.3891 | 0.856910 | ||||||||
\(746\) | −53.5480 | −1.96053 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.2632 | −0.740898 | ||||||||
\(749\) | −57.8070 | −2.11222 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.6679 | −0.644709 | −0.322355 | − | 0.946619i | \(-0.604474\pi\) | ||||
−0.322355 | + | 0.946619i | \(0.604474\pi\) | |||||||
\(752\) | −1.92488 | −0.0701932 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.57188 | 0.239334 | ||||||||
\(755\) | −27.5643 | −1.00317 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.7774 | 1.66381 | 0.831903 | − | 0.554921i | \(-0.187252\pi\) | ||||
0.831903 | + | 0.554921i | \(0.187252\pi\) | |||||||
\(758\) | 59.0772 | 2.14578 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −47.3312 | −1.71688 | ||||||||
\(761\) | −37.3960 | −1.35561 | −0.677803 | − | 0.735244i | \(-0.737068\pi\) | ||||
−0.677803 | + | 0.735244i | \(0.737068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.6816 | −1.07455 | ||||||||
\(764\) | −72.1876 | −2.61166 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 39.7712 | 1.43699 | ||||||||
\(767\) | 3.90757 | 0.141094 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.617028 | −0.0222506 | −0.0111253 | − | 0.999938i | \(-0.503541\pi\) | ||||
−0.0111253 | + | 0.999938i | \(0.503541\pi\) | |||||||
\(770\) | −30.4212 | −1.09631 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −59.1855 | −2.13013 | ||||||||
\(773\) | 3.60037 | 0.129496 | 0.0647482 | − | 0.997902i | \(-0.479376\pi\) | ||||
0.0647482 | + | 0.997902i | \(0.479376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.1912 | 0.617527 | ||||||||
\(776\) | −30.0838 | −1.07995 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −48.1963 | −1.72792 | ||||||||
\(779\) | 29.4089 | 1.05368 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.18076 | 0.113817 | ||||||||
\(782\) | 0.00353184 | 0.000126298 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.97411 | −0.213361 | ||||||||
\(785\) | −30.0524 | −1.07262 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.622093 | −0.0221752 | −0.0110876 | − | 0.999939i | \(-0.503529\pi\) | ||||
−0.0110876 | + | 0.999939i | \(0.503529\pi\) | |||||||
\(788\) | −26.9139 | −0.958768 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 36.8256 | 1.31020 | ||||||||
\(791\) | 59.8674 | 2.12864 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.329272 | 0.0116928 | ||||||||
\(794\) | −36.4358 | −1.29306 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33.3393 | 1.18168 | ||||||||
\(797\) | 37.7027 | 1.33550 | 0.667749 | − | 0.744387i | \(-0.267258\pi\) | ||||
0.667749 | + | 0.744387i | \(0.267258\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.8876 | −1.12810 | ||||||||
\(800\) | −18.4856 | −0.653565 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27.8438 | −0.983199 | ||||||||
\(803\) | 12.3598 | 0.436168 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.00324215 | 0.000114271 0 | ||||||||
\(806\) | −4.22971 | −0.148985 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −43.8622 | −1.54307 | ||||||||
\(809\) | −4.49791 | −0.158138 | −0.0790690 | − | 0.996869i | \(-0.525195\pi\) | ||||
−0.0790690 | + | 0.996869i | \(0.525195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6392 | −0.478939 | −0.239469 | − | 0.970904i | \(-0.576973\pi\) | ||||
−0.239469 | + | 0.970904i | \(0.576973\pi\) | |||||||
\(812\) | 130.963 | 4.59589 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.874744 | −0.0306597 | ||||||||
\(815\) | −30.5467 | −1.07000 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.6517 | 0.617555 | ||||||||
\(818\) | −19.7730 | −0.691346 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −40.9124 | −1.42872 | ||||||||
\(821\) | 30.9469 | 1.08006 | 0.540028 | − | 0.841647i | \(-0.318414\pi\) | ||||
0.540028 | + | 0.841647i | \(0.318414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.6941 | −0.686492 | −0.343246 | − | 0.939246i | \(-0.611526\pi\) | ||||
−0.343246 | + | 0.939246i | \(0.611526\pi\) | |||||||
\(824\) | 6.19686 | 0.215878 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 127.350 | 4.43108 | ||||||||
\(827\) | −15.5540 | −0.540866 | −0.270433 | − | 0.962739i | \(-0.587167\pi\) | ||||
−0.270433 | + | 0.962739i | \(0.587167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.4496 | −1.09229 | −0.546145 | − | 0.837691i | \(-0.683905\pi\) | ||||
−0.546145 | + | 0.837691i | \(0.683905\pi\) | |||||||
\(830\) | 66.4720 | 2.30728 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.29225 | 0.148807 | ||||||||
\(833\) | −98.9672 | −3.42901 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.48437 | −0.0513687 | ||||||||
\(836\) | −20.1864 | −0.698162 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 62.7322 | 2.16705 | ||||||||
\(839\) | −35.4721 | −1.22463 | −0.612316 | − | 0.790613i | \(-0.709762\pi\) | ||||
−0.612316 | + | 0.790613i | \(0.709762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.3892 | 1.66859 | ||||||||
\(842\) | −48.8345 | −1.68295 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −57.9688 | −1.99537 | ||||||||
\(845\) | −36.5455 | −1.25720 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.72992 | −0.162522 | ||||||||
\(848\) | −1.16129 | −0.0398789 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −44.3502 | −1.52120 | ||||||||
\(851\) | 9.32259e−5 0 | 3.19574e−6 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.8898 | −1.70819 | −0.854097 | − | 0.520113i | \(-0.825890\pi\) | ||||
−0.854097 | + | 0.520113i | \(0.825890\pi\) | |||||||
\(854\) | 10.7312 | 0.367214 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.8156 | 1.08743 | ||||||||
\(857\) | −25.0717 | −0.856434 | −0.428217 | − | 0.903676i | \(-0.640858\pi\) | ||||
−0.428217 | + | 0.903676i | \(0.640858\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.1566 | 0.380657 | 0.190328 | − | 0.981720i | \(-0.439045\pi\) | ||||
0.190328 | + | 0.981720i | \(0.439045\pi\) | |||||||
\(860\) | −24.5563 | −0.837361 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −80.8638 | −2.75423 | ||||||||
\(863\) | 32.0664 | 1.09155 | 0.545777 | − | 0.837930i | \(-0.316235\pi\) | ||||
0.545777 | + | 0.837930i | \(0.316235\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.1889 | −0.584440 | ||||||||
\(866\) | −58.6867 | −1.99425 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −84.2886 | −2.86094 | ||||||||
\(869\) | 5.72569 | 0.194231 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.46737 | 0.0836037 | ||||||||
\(872\) | 16.3360 | 0.553208 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.00351844 | 0.000119013 0 | ||||||||
\(875\) | 26.3303 | 0.890127 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0650 | −0.677547 | −0.338774 | − | 0.940868i | \(-0.610012\pi\) | ||||
−0.338774 | + | 0.940868i | \(0.610012\pi\) | |||||||
\(878\) | −14.9771 | −0.505454 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.10171 | −0.0371385 | ||||||||
\(881\) | −7.46246 | −0.251417 | −0.125708 | − | 0.992067i | \(-0.540120\pi\) | ||||
−0.125708 | + | 0.992067i | \(0.540120\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.8751 | 0.837114 | 0.418557 | − | 0.908190i | \(-0.362536\pi\) | ||||
0.418557 | + | 0.908190i | \(0.362536\pi\) | |||||||
\(884\) | 6.67213 | 0.224408 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −47.0314 | −1.58005 | ||||||||
\(887\) | 15.9928 | 0.536986 | 0.268493 | − | 0.963282i | \(-0.413474\pi\) | ||||
0.268493 | + | 0.963282i | \(0.413474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −86.2831 | −2.89384 | ||||||||
\(890\) | 25.4617 | 0.853479 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.0928 | −0.371414 | ||||||||
\(893\) | −31.7667 | −1.06303 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.3154 | 2.14983 | ||||||||
\(896\) | 82.2940 | 2.74925 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.8033 | −0.894439 | ||||||||
\(899\) | −49.8083 | −1.66120 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.2380 | −0.640910 | ||||||||
\(902\) | −10.4032 | −0.346389 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.9495 | −1.09588 | ||||||||
\(905\) | −64.9862 | −2.16021 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.8839 | −1.09189 | −0.545946 | − | 0.837820i | \(-0.683830\pi\) | ||||
−0.545946 | + | 0.837820i | \(0.683830\pi\) | |||||||
\(908\) | 12.4922 | 0.414569 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.0169 | 0.332056 | ||||||||
\(911\) | 32.1720 | 1.06590 | 0.532952 | − | 0.846145i | \(-0.321082\pi\) | ||||
0.532952 | + | 0.846145i | \(0.321082\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.3351 | 0.342043 | ||||||||
\(914\) | 65.3345 | 2.16107 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 69.4443 | 2.29450 | ||||||||
\(917\) | −44.0574 | −1.45490 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.19518 | 0.303321 | 0.151660 | − | 0.988433i | \(-0.451538\pi\) | ||||
0.151660 | + | 0.988433i | \(0.451538\pi\) | |||||||
\(920\) | −0.00178440 | −5.88298e−5 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.41339 | 0.0465474 | ||||||||
\(923\) | −1.04734 | −0.0344735 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.17066 | −0.0384912 | ||||||||
\(926\) | 45.7417 | 1.50317 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 53.5585 | 1.75814 | ||||||||
\(929\) | 28.3672 | 0.930699 | 0.465349 | − | 0.885127i | \(-0.345929\pi\) | ||||
0.465349 | + | 0.885127i | \(0.345929\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −98.5920 | −3.23122 | ||||||||
\(932\) | 79.1179 | 2.59159 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.5630 | 0.771006 | ||||||||
\(935\) | −18.2509 | −0.596868 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.49399 | 0.212149 | 0.106075 | − | 0.994358i | \(-0.466172\pi\) | ||||
0.106075 | + | 0.994358i | \(0.466172\pi\) | |||||||
\(938\) | 80.4133 | 2.62559 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 44.1925 | 1.44140 | ||||||||
\(941\) | 46.4185 | 1.51320 | 0.756600 | − | 0.653878i | \(-0.226859\pi\) | ||||
0.756600 | + | 0.653878i | \(0.226859\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.00110873 | 3.61051e−5 0 | ||||||||
\(944\) | 4.61199 | 0.150108 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.24417 | −0.203016 | ||||||||
\(947\) | 37.2359 | 1.21000 | 0.605001 | − | 0.796224i | \(-0.293173\pi\) | ||||
0.605001 | + | 0.796224i | \(0.293173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.06975 | −0.132110 | ||||||||
\(950\) | −44.1821 | −1.43346 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 79.2726 | 2.56924 | ||||||||
\(953\) | −0.668787 | −0.0216641 | −0.0108321 | − | 0.999941i | \(-0.503448\pi\) | ||||
−0.0108321 | + | 0.999941i | \(0.503448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −65.0186 | −2.10395 | ||||||||
\(956\) | −46.8700 | −1.51588 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −55.9460 | −1.80753 | ||||||||
\(959\) | −52.9889 | −1.71110 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.05700 | 0.0340967 | ||||||||
\(962\) | 0.288029 | 0.00928642 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −62.1187 | −2.00071 | ||||||||
\(965\) | −53.3077 | −1.71604 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.461767 | 0.0148494 | 0.00742471 | − | 0.999972i | \(-0.497637\pi\) | ||||
0.00742471 | + | 0.999972i | \(0.497637\pi\) | |||||||
\(968\) | 2.60323 | 0.0836711 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −74.3263 | −2.38647 | ||||||||
\(971\) | −18.7299 | −0.601071 | −0.300536 | − | 0.953771i | \(-0.597165\pi\) | ||||
−0.300536 | + | 0.953771i | \(0.597165\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −84.2762 | −2.70177 | ||||||||
\(974\) | 60.6542 | 1.94349 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.388631 | 0.0124398 | ||||||||
\(977\) | −59.5054 | −1.90375 | −0.951874 | − | 0.306490i | \(-0.900845\pi\) | ||||
−0.951874 | + | 0.306490i | \(0.900845\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.95881 | 0.126524 | ||||||||
\(980\) | 137.157 | 4.38131 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −59.2751 | −1.89154 | ||||||||
\(983\) | −13.0408 | −0.415936 | −0.207968 | − | 0.978136i | \(-0.566685\pi\) | ||||
−0.207968 | + | 0.978136i | \(0.566685\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.2411 | −0.772384 | ||||||||
\(986\) | 128.496 | 4.09215 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.64683 | 0.211464 | ||||||||
\(989\) | 0.000665474 0 | 2.11608e−5 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.1630 | 1.02169 | 0.510846 | − | 0.859672i | \(-0.329332\pi\) | ||||
0.510846 | + | 0.859672i | \(0.329332\pi\) | |||||||
\(992\) | −34.4706 | −1.09444 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −34.1334 | −1.08265 | ||||||||
\(995\) | 30.0283 | 0.951962 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.44042 | 0.203970 | 0.101985 | − | 0.994786i | \(-0.467481\pi\) | ||||
0.101985 | + | 0.994786i | \(0.467481\pi\) | |||||||
\(998\) | 59.7008 | 1.88980 | ||||||||
\(999\) | 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 | 6039.2.a.e.1.12 | 12 | ||
3.2 | odd | 2 | 2013.2.a.d.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.d.1.1 | ✓ | 12 | 3.2 | odd | 2 | ||
6039.2.a.e.1.12 | 12 | 1.1 | even | 1 | trivial |