Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, 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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.13366265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 12x^{6} + 10x^{5} + 41x^{4} - 20x^{3} - 48x^{2} + 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1875) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.59716\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59716 | 1.83647 | 0.918235 | − | 0.396035i | \(-0.129614\pi\) | ||||
0.918235 | + | 0.396035i | \(0.129614\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.74525 | 2.37263 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.28414 | −1.24129 | −0.620643 | − | 0.784093i | \(-0.713129\pi\) | ||||
−0.620643 | + | 0.784093i | \(0.713129\pi\) | |||||||
\(8\) | 7.12986 | 2.52079 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.30834 | −1.29901 | −0.649507 | − | 0.760356i | \(-0.725025\pi\) | ||||
−0.649507 | + | 0.760356i | \(0.725025\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46120 | 0.959964 | 0.479982 | − | 0.877278i | \(-0.340643\pi\) | ||||
0.479982 | + | 0.877278i | \(0.340643\pi\) | |||||||
\(14\) | −8.52943 | −2.27959 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.02691 | 2.25673 | ||||||||
\(17\) | −5.44757 | −1.32123 | −0.660615 | − | 0.750725i | \(-0.729705\pi\) | ||||
−0.660615 | + | 0.750725i | \(0.729705\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.63427 | −1.75142 | −0.875711 | − | 0.482835i | \(-0.839607\pi\) | ||||
−0.875711 | + | 0.482835i | \(0.839607\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.1895 | −2.38560 | ||||||||
\(23\) | −5.04986 | −1.05297 | −0.526484 | − | 0.850185i | \(-0.676490\pi\) | ||||
−0.526484 | + | 0.850185i | \(0.676490\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.98929 | 1.76295 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −15.5841 | −2.94511 | ||||||||
\(29\) | 3.12329 | 0.579981 | 0.289990 | − | 0.957030i | \(-0.406348\pi\) | ||||
0.289990 | + | 0.957030i | \(0.406348\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.06658 | −0.371169 | −0.185584 | − | 0.982628i | \(-0.559418\pi\) | ||||
−0.185584 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(32\) | 9.18462 | 1.62363 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.1482 | −2.42640 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.89142 | 0.310947 | 0.155474 | − | 0.987840i | \(-0.450310\pi\) | ||||
0.155474 | + | 0.987840i | \(0.450310\pi\) | |||||||
\(38\) | −19.8274 | −3.21644 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.89896 | −0.608915 | −0.304457 | − | 0.952526i | \(-0.598475\pi\) | ||||
−0.304457 | + | 0.952526i | \(0.598475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.20815 | 0.489238 | 0.244619 | − | 0.969619i | \(-0.421337\pi\) | ||||
0.244619 | + | 0.969619i | \(0.421337\pi\) | |||||||
\(44\) | −20.4442 | −3.08207 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.1153 | −1.93375 | ||||||||
\(47\) | 6.28577 | 0.916874 | 0.458437 | − | 0.888727i | \(-0.348409\pi\) | ||||
0.458437 | + | 0.888727i | \(0.348409\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.78555 | 0.540793 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.4243 | 2.27763 | ||||||||
\(53\) | −2.51480 | −0.345434 | −0.172717 | − | 0.984971i | \(-0.555255\pi\) | ||||
−0.172717 | + | 0.984971i | \(0.555255\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −23.4154 | −3.12902 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.11170 | 1.06512 | ||||||||
\(59\) | −7.72948 | −1.00629 | −0.503146 | − | 0.864201i | \(-0.667824\pi\) | ||||
−0.503146 | + | 0.864201i | \(0.667824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.95661 | −0.378555 | −0.189278 | − | 0.981924i | \(-0.560615\pi\) | ||||
−0.189278 | + | 0.981924i | \(0.560615\pi\) | |||||||
\(62\) | −5.36725 | −0.681641 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.80013 | 0.725016 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9952 | −1.58762 | −0.793811 | − | 0.608165i | \(-0.791906\pi\) | ||||
−0.793811 | + | 0.608165i | \(0.791906\pi\) | |||||||
\(68\) | −25.8501 | −3.13479 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.72665 | 0.560950 | 0.280475 | − | 0.959861i | \(-0.409508\pi\) | ||||
0.280475 | + | 0.959861i | \(0.409508\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.64933 | 0.193040 | 0.0965198 | − | 0.995331i | \(-0.469229\pi\) | ||||
0.0965198 | + | 0.995331i | \(0.469229\pi\) | |||||||
\(74\) | 4.91232 | 0.571046 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −36.2265 | −4.15547 | ||||||||
\(77\) | 14.1492 | 1.61245 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7349 | 1.54530 | 0.772648 | − | 0.634835i | \(-0.218932\pi\) | ||||
0.772648 | + | 0.634835i | \(0.218932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.1262 | −1.11825 | ||||||||
\(83\) | −5.01687 | −0.550673 | −0.275336 | − | 0.961348i | \(-0.588789\pi\) | ||||
−0.275336 | + | 0.961348i | \(0.588789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.33208 | 0.898472 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −30.7179 | −3.27454 | ||||||||
\(89\) | 9.00209 | 0.954220 | 0.477110 | − | 0.878844i | \(-0.341684\pi\) | ||||
0.477110 | + | 0.878844i | \(0.341684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3670 | −1.19159 | ||||||||
\(92\) | −23.9628 | −2.49830 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 16.3252 | 1.68381 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.57278 | −0.261226 | −0.130613 | − | 0.991433i | \(-0.541695\pi\) | ||||
−0.130613 | + | 0.991433i | \(0.541695\pi\) | |||||||
\(98\) | 9.83169 | 0.993150 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.87863 | −0.783953 | −0.391976 | − | 0.919975i | \(-0.628209\pi\) | ||||
−0.391976 | + | 0.919975i | \(0.628209\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4046 | −1.22226 | −0.611131 | − | 0.791530i | \(-0.709285\pi\) | ||||
−0.611131 | + | 0.791530i | \(0.709285\pi\) | |||||||
\(104\) | 24.6779 | 2.41986 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.53134 | −0.634380 | ||||||||
\(107\) | 8.52094 | 0.823750 | 0.411875 | − | 0.911240i | \(-0.364874\pi\) | ||||
0.411875 | + | 0.911240i | \(0.364874\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.5139 | 1.67752 | 0.838762 | − | 0.544499i | \(-0.183280\pi\) | ||||
0.838762 | + | 0.544499i | \(0.183280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −29.6456 | −2.80125 | ||||||||
\(113\) | 4.17711 | 0.392949 | 0.196475 | − | 0.980509i | \(-0.437051\pi\) | ||||
0.196475 | + | 0.980509i | \(0.437051\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 14.8208 | 1.37608 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20.0747 | −1.84803 | ||||||||
\(119\) | 17.8906 | 1.64003 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.56181 | 0.687438 | ||||||||
\(122\) | −7.67880 | −0.695206 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.80645 | −0.880645 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2112 | −0.906097 | −0.453049 | − | 0.891486i | \(-0.649664\pi\) | ||||
−0.453049 | + | 0.891486i | \(0.649664\pi\) | |||||||
\(128\) | −3.30537 | −0.292156 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.91686 | 0.429588 | 0.214794 | − | 0.976659i | \(-0.431092\pi\) | ||||
0.214794 | + | 0.976659i | \(0.431092\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.0720 | 2.17402 | ||||||||
\(134\) | −33.7508 | −2.91562 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −38.8404 | −3.33054 | ||||||||
\(137\) | −12.3817 | −1.05784 | −0.528919 | − | 0.848672i | \(-0.677403\pi\) | ||||
−0.528919 | + | 0.848672i | \(0.677403\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.2420 | 1.12317 | 0.561584 | − | 0.827420i | \(-0.310192\pi\) | ||||
0.561584 | + | 0.827420i | \(0.310192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.2759 | 1.03017 | ||||||||
\(143\) | −14.9120 | −1.24701 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.28358 | 0.354512 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.97526 | 0.737762 | ||||||||
\(149\) | −5.20686 | −0.426563 | −0.213281 | − | 0.976991i | \(-0.568415\pi\) | ||||
−0.213281 | + | 0.976991i | \(0.568415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.78162 | 0.633259 | 0.316630 | − | 0.948549i | \(-0.397449\pi\) | ||||
0.316630 | + | 0.948549i | \(0.397449\pi\) | |||||||
\(152\) | −54.4313 | −4.41496 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 36.7477 | 2.96122 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4474 | 1.31264 | 0.656322 | − | 0.754481i | \(-0.272111\pi\) | ||||
0.656322 | + | 0.754481i | \(0.272111\pi\) | |||||||
\(158\) | 35.6717 | 2.83789 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.5844 | 1.30704 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.81342 | −0.611994 | −0.305997 | − | 0.952032i | \(-0.598990\pi\) | ||||
−0.305997 | + | 0.952032i | \(0.598990\pi\) | |||||||
\(164\) | −18.5015 | −1.44473 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.0296 | −1.01129 | ||||||||
\(167\) | −2.77030 | −0.214372 | −0.107186 | − | 0.994239i | \(-0.534184\pi\) | ||||
−0.107186 | + | 0.994239i | \(0.534184\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.02011 | −0.0784700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.2235 | 1.16078 | ||||||||
\(173\) | −16.9573 | −1.28924 | −0.644620 | − | 0.764503i | \(-0.722985\pi\) | ||||
−0.644620 | + | 0.764503i | \(0.722985\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −38.8910 | −2.93152 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 23.3799 | 1.75240 | ||||||||
\(179\) | −1.56173 | −0.116729 | −0.0583645 | − | 0.998295i | \(-0.518589\pi\) | ||||
−0.0583645 | + | 0.998295i | \(0.518589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.55277 | 0.115416 | 0.0577081 | − | 0.998333i | \(-0.481621\pi\) | ||||
0.0577081 | + | 0.998333i | \(0.481621\pi\) | |||||||
\(182\) | −29.5221 | −2.18832 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −36.0048 | −2.65431 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.4700 | 1.71630 | ||||||||
\(188\) | 29.8276 | 2.17540 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.5640 | −1.92211 | −0.961054 | − | 0.276362i | \(-0.910871\pi\) | ||||
−0.961054 | + | 0.276362i | \(0.910871\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7642 | 0.990772 | 0.495386 | − | 0.868673i | \(-0.335027\pi\) | ||||
0.495386 | + | 0.868673i | \(0.335027\pi\) | |||||||
\(194\) | −6.68192 | −0.479734 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.9634 | 1.28310 | ||||||||
\(197\) | 6.25851 | 0.445901 | 0.222950 | − | 0.974830i | \(-0.428431\pi\) | ||||
0.222950 | + | 0.974830i | \(0.428431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.35009 | 0.237482 | 0.118741 | − | 0.992925i | \(-0.462114\pi\) | ||||
0.118741 | + | 0.992925i | \(0.462114\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −20.4621 | −1.43971 | ||||||||
\(203\) | −10.2573 | −0.719923 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −32.2168 | −2.24465 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 31.2439 | 2.16638 | ||||||||
\(209\) | 32.8911 | 2.27512 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.0984 | 1.65900 | 0.829502 | − | 0.558504i | \(-0.188624\pi\) | ||||
0.829502 | + | 0.558504i | \(0.188624\pi\) | |||||||
\(212\) | −11.9333 | −0.819586 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 22.1303 | 1.51279 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.78693 | 0.460727 | ||||||||
\(218\) | 45.4863 | 3.08072 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.8551 | −1.26833 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.2697 | 1.22343 | 0.611714 | − | 0.791079i | \(-0.290480\pi\) | ||||
0.611714 | + | 0.791079i | \(0.290480\pi\) | |||||||
\(224\) | −30.1635 | −2.01539 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.8486 | 0.721640 | ||||||||
\(227\) | −17.9602 | −1.19206 | −0.596031 | − | 0.802962i | \(-0.703256\pi\) | ||||
−0.596031 | + | 0.802962i | \(0.703256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00658 | 0.396926 | 0.198463 | − | 0.980108i | \(-0.436405\pi\) | ||||
0.198463 | + | 0.980108i | \(0.436405\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.2687 | 1.46201 | ||||||||
\(233\) | −20.8526 | −1.36610 | −0.683049 | − | 0.730373i | \(-0.739346\pi\) | ||||
−0.683049 | + | 0.730373i | \(0.739346\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −36.6783 | −2.38755 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 46.4647 | 3.01186 | ||||||||
\(239\) | 27.8722 | 1.80290 | 0.901452 | − | 0.432880i | \(-0.142503\pi\) | ||||
0.901452 | + | 0.432880i | \(0.142503\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.7159 | −1.20560 | −0.602798 | − | 0.797894i | \(-0.705947\pi\) | ||||
−0.602798 | + | 0.797894i | \(0.705947\pi\) | |||||||
\(242\) | 19.6393 | 1.26246 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.0299 | −0.898170 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.4237 | −1.68130 | ||||||||
\(248\) | −14.7344 | −0.935638 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.0995 | −0.700594 | −0.350297 | − | 0.936639i | \(-0.613919\pi\) | ||||
−0.350297 | + | 0.936639i | \(0.613919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.7565 | 1.36782 | ||||||||
\(254\) | −26.5201 | −1.66402 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −20.1848 | −1.26155 | ||||||||
\(257\) | −17.8844 | −1.11560 | −0.557800 | − | 0.829975i | \(-0.688354\pi\) | ||||
−0.557800 | + | 0.829975i | \(0.688354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.21168 | −0.385975 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.7699 | 0.788927 | ||||||||
\(263\) | −18.1341 | −1.11819 | −0.559097 | − | 0.829102i | \(-0.688852\pi\) | ||||
−0.559097 | + | 0.829102i | \(0.688852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 65.1160 | 3.99252 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −61.6657 | −3.76683 | ||||||||
\(269\) | 22.2963 | 1.35943 | 0.679714 | − | 0.733477i | \(-0.262104\pi\) | ||||
0.679714 | + | 0.733477i | \(0.262104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.8621 | 1.02430 | 0.512149 | − | 0.858896i | \(-0.328849\pi\) | ||||
0.512149 | + | 0.858896i | \(0.328849\pi\) | |||||||
\(272\) | −49.1747 | −2.98166 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −32.1572 | −1.94269 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.6929 | 1.12315 | 0.561575 | − | 0.827426i | \(-0.310196\pi\) | ||||
0.561575 | + | 0.827426i | \(0.310196\pi\) | |||||||
\(278\) | 34.3915 | 2.06266 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.9852 | −1.55015 | −0.775075 | − | 0.631870i | \(-0.782288\pi\) | ||||
−0.775075 | + | 0.631870i | \(0.782288\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9219 | −1.00591 | −0.502953 | − | 0.864314i | \(-0.667753\pi\) | ||||
−0.502953 | + | 0.864314i | \(0.667753\pi\) | |||||||
\(284\) | 22.4291 | 1.33092 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −38.7289 | −2.29009 | ||||||||
\(287\) | 12.8047 | 0.755838 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6760 | 0.745650 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.82649 | 0.458011 | ||||||||
\(293\) | 1.05979 | 0.0619134 | 0.0309567 | − | 0.999521i | \(-0.490145\pi\) | ||||
0.0309567 | + | 0.999521i | \(0.490145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.4856 | 0.783832 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.5231 | −0.783370 | ||||||||
\(299\) | −17.4786 | −1.01081 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5360 | −0.607285 | ||||||||
\(302\) | 20.2101 | 1.16296 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −68.9139 | −3.95248 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.7239 | −1.69643 | −0.848215 | − | 0.529652i | \(-0.822323\pi\) | ||||
−0.848215 | + | 0.529652i | \(0.822323\pi\) | |||||||
\(308\) | 67.1414 | 3.82574 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.08513 | −0.288351 | −0.144176 | − | 0.989552i | \(-0.546053\pi\) | ||||
−0.144176 | + | 0.989552i | \(0.546053\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.9388 | −1.46615 | −0.733074 | − | 0.680149i | \(-0.761915\pi\) | ||||
−0.733074 | + | 0.680149i | \(0.761915\pi\) | |||||||
\(314\) | 42.7165 | 2.41063 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 65.1755 | 3.66641 | ||||||||
\(317\) | 19.7727 | 1.11054 | 0.555271 | − | 0.831669i | \(-0.312614\pi\) | ||||
0.555271 | + | 0.831669i | \(0.312614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.4562 | −0.753403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 43.0724 | 2.40033 | ||||||||
\(323\) | 41.5883 | 2.31403 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.2927 | −1.12391 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −27.7990 | −1.53494 | ||||||||
\(329\) | −20.6433 | −1.13810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.9589 | −1.31690 | −0.658449 | − | 0.752625i | \(-0.728787\pi\) | ||||
−0.658449 | + | 0.752625i | \(0.728787\pi\) | |||||||
\(332\) | −23.8063 | −1.30654 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.19492 | −0.393689 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.6779 | 1.50771 | 0.753857 | − | 0.657039i | \(-0.228191\pi\) | ||||
0.753857 | + | 0.657039i | \(0.228191\pi\) | |||||||
\(338\) | −2.64939 | −0.144108 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.90354 | 0.482154 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.5567 | 0.570008 | ||||||||
\(344\) | 22.8737 | 1.23327 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −44.0409 | −2.36765 | ||||||||
\(347\) | −13.4880 | −0.724075 | −0.362037 | − | 0.932164i | \(-0.617919\pi\) | ||||
−0.362037 | + | 0.932164i | \(0.617919\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.1678 | 1.02603 | 0.513015 | − | 0.858379i | \(-0.328528\pi\) | ||||
0.513015 | + | 0.858379i | \(0.328528\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −39.5705 | −2.10911 | ||||||||
\(353\) | 7.61950 | 0.405545 | 0.202773 | − | 0.979226i | \(-0.435005\pi\) | ||||
0.202773 | + | 0.979226i | \(0.435005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 42.7172 | 2.26401 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.05606 | −0.214369 | ||||||||
\(359\) | −31.2943 | −1.65165 | −0.825826 | − | 0.563925i | \(-0.809291\pi\) | ||||
−0.825826 | + | 0.563925i | \(0.809291\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.2821 | 2.06748 | ||||||||
\(362\) | 4.03279 | 0.211959 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −53.9395 | −2.82720 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.35079 | 0.331508 | 0.165754 | − | 0.986167i | \(-0.446994\pi\) | ||||
0.165754 | + | 0.986167i | \(0.446994\pi\) | |||||||
\(368\) | −45.5846 | −2.37626 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.25894 | 0.428783 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1710 | −0.578410 | −0.289205 | − | 0.957267i | \(-0.593391\pi\) | ||||
−0.289205 | + | 0.957267i | \(0.593391\pi\) | |||||||
\(374\) | 60.9554 | 3.15193 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 44.8167 | 2.31124 | ||||||||
\(377\) | 10.8103 | 0.556761 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.7113 | −1.06387 | −0.531933 | − | 0.846787i | \(-0.678534\pi\) | ||||
−0.531933 | + | 0.846787i | \(0.678534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −68.9911 | −3.52989 | ||||||||
\(383\) | −12.5869 | −0.643158 | −0.321579 | − | 0.946883i | \(-0.604214\pi\) | ||||
−0.321579 | + | 0.946883i | \(0.604214\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 35.7480 | 1.81952 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.2085 | −0.619792 | ||||||||
\(389\) | −10.8301 | −0.549110 | −0.274555 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274555 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.5095 | 1.39121 | ||||||||
\(392\) | 26.9905 | 1.36322 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.2544 | 0.818884 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.90704 | 0.246277 | 0.123139 | − | 0.992389i | \(-0.460704\pi\) | ||||
0.123139 | + | 0.992389i | \(0.460704\pi\) | |||||||
\(398\) | 8.70072 | 0.436128 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.5223 | 1.37440 | 0.687198 | − | 0.726470i | \(-0.258840\pi\) | ||||
0.687198 | + | 0.726470i | \(0.258840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.15285 | −0.356309 | ||||||||
\(404\) | −37.3861 | −1.86003 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −26.6399 | −1.32212 | ||||||||
\(407\) | −8.14888 | −0.403925 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.7665 | 0.977390 | 0.488695 | − | 0.872455i | \(-0.337473\pi\) | ||||
0.488695 | + | 0.872455i | \(0.337473\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −58.8630 | −2.89997 | ||||||||
\(413\) | 25.3847 | 1.24910 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 31.7898 | 1.55862 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 85.4234 | 4.17820 | ||||||||
\(419\) | 6.67948 | 0.326314 | 0.163157 | − | 0.986600i | \(-0.447832\pi\) | ||||
0.163157 | + | 0.986600i | \(0.447832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.65996 | 0.275849 | 0.137925 | − | 0.990443i | \(-0.455957\pi\) | ||||
0.137925 | + | 0.990443i | \(0.455957\pi\) | |||||||
\(422\) | 62.5875 | 3.04671 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.9302 | −0.870766 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.70991 | 0.469896 | ||||||||
\(428\) | 40.4340 | 1.95445 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.41717 | −0.309104 | −0.154552 | − | 0.987985i | \(-0.549393\pi\) | ||||
−0.154552 | + | 0.987985i | \(0.549393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.10506 | 0.0531059 | 0.0265530 | − | 0.999647i | \(-0.491547\pi\) | ||||
0.0265530 | + | 0.999647i | \(0.491547\pi\) | |||||||
\(434\) | 17.6268 | 0.846112 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 83.1077 | 3.98014 | ||||||||
\(437\) | 38.5520 | 1.84419 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.11313 | −0.244036 | −0.122018 | − | 0.992528i | \(-0.538937\pi\) | ||||
−0.122018 | + | 0.992528i | \(0.538937\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.9698 | −2.32926 | ||||||||
\(443\) | −17.9079 | −0.850829 | −0.425414 | − | 0.904999i | \(-0.639872\pi\) | ||||
−0.425414 | + | 0.904999i | \(0.639872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 47.4493 | 2.24679 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.0484 | −0.899953 | ||||||||
\(449\) | −27.3710 | −1.29172 | −0.645859 | − | 0.763457i | \(-0.723501\pi\) | ||||
−0.645859 | + | 0.763457i | \(0.723501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.7980 | 0.790989 | ||||||||
\(452\) | 19.8214 | 0.932322 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −46.6456 | −2.18919 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.92806 | −0.417637 | −0.208819 | − | 0.977954i | \(-0.566962\pi\) | ||||
−0.208819 | + | 0.977954i | \(0.566962\pi\) | |||||||
\(458\) | 15.6001 | 0.728943 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.81204 | −0.0843952 | −0.0421976 | − | 0.999109i | \(-0.513436\pi\) | ||||
−0.0421976 | + | 0.999109i | \(0.513436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.72192 | −0.126498 | −0.0632492 | − | 0.997998i | \(-0.520146\pi\) | ||||
−0.0632492 | + | 0.997998i | \(0.520146\pi\) | |||||||
\(464\) | 28.1937 | 1.30886 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −54.1575 | −2.50880 | ||||||||
\(467\) | −40.2261 | −1.86144 | −0.930721 | − | 0.365729i | \(-0.880820\pi\) | ||||
−0.930721 | + | 0.365729i | \(0.880820\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.6781 | 1.97069 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −55.1101 | −2.53665 | ||||||||
\(473\) | −13.8218 | −0.635527 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 84.8953 | 3.89117 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 72.3886 | 3.31098 | ||||||||
\(479\) | 27.9457 | 1.27687 | 0.638435 | − | 0.769676i | \(-0.279582\pi\) | ||||
0.638435 | + | 0.769676i | \(0.279582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.54657 | 0.298498 | ||||||||
\(482\) | −48.6082 | −2.21404 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 35.8827 | 1.63103 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.8089 | 1.16951 | 0.584756 | − | 0.811209i | \(-0.301190\pi\) | ||||
0.584756 | + | 0.811209i | \(0.301190\pi\) | |||||||
\(488\) | −21.0802 | −0.954257 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.7044 | −1.06976 | −0.534882 | − | 0.844927i | \(-0.679644\pi\) | ||||
−0.534882 | + | 0.844927i | \(0.679644\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.0144 | −0.766288 | ||||||||
\(494\) | −68.6267 | −3.08766 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.6548 | −0.837627 | ||||||||
\(497\) | −15.5230 | −0.696300 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.95752 | 0.400994 | 0.200497 | − | 0.979694i | \(-0.435744\pi\) | ||||
0.200497 | + | 0.979694i | \(0.435744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −28.8272 | −1.28662 | ||||||||
\(503\) | 10.1655 | 0.453256 | 0.226628 | − | 0.973981i | \(-0.427230\pi\) | ||||
0.226628 | + | 0.973981i | \(0.427230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 56.5052 | 2.51196 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −48.4547 | −2.14983 | ||||||||
\(509\) | 6.54473 | 0.290090 | 0.145045 | − | 0.989425i | \(-0.453667\pi\) | ||||
0.145045 | + | 0.989425i | \(0.453667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.41663 | −0.239618 | ||||||||
\(512\) | −45.8125 | −2.02465 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −46.4488 | −2.04877 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.0813 | −1.19103 | ||||||||
\(518\) | −16.1327 | −0.708832 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.6022 | 1.12165 | 0.560827 | − | 0.827933i | \(-0.310483\pi\) | ||||
0.560827 | + | 0.827933i | \(0.310483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.02210 | −0.219601 | −0.109801 | − | 0.993954i | \(-0.535021\pi\) | ||||
−0.109801 | + | 0.993954i | \(0.535021\pi\) | |||||||
\(524\) | 23.3318 | 1.01925 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −47.0971 | −2.05353 | ||||||||
\(527\) | 11.2579 | 0.490400 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.50105 | 0.108741 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 118.973 | 5.15813 | ||||||||
\(533\) | −13.4951 | −0.584536 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −92.6543 | −4.00206 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 57.9071 | 2.49655 | ||||||||
\(539\) | −16.3094 | −0.702498 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.99099 | −0.343560 | −0.171780 | − | 0.985135i | \(-0.554952\pi\) | ||||
−0.171780 | + | 0.985135i | \(0.554952\pi\) | |||||||
\(542\) | 43.7936 | 1.88109 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −50.0339 | −2.14518 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.9399 | 0.938084 | 0.469042 | − | 0.883176i | \(-0.344599\pi\) | ||||
0.469042 | + | 0.883176i | \(0.344599\pi\) | |||||||
\(548\) | −58.7542 | −2.50986 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.8441 | −1.01579 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.1072 | −1.91815 | ||||||||
\(554\) | 48.5486 | 2.06263 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 62.8364 | 2.66486 | ||||||||
\(557\) | 32.6366 | 1.38286 | 0.691429 | − | 0.722444i | \(-0.256981\pi\) | ||||
0.691429 | + | 0.722444i | \(0.256981\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.1040 | 0.469651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −67.4879 | −2.84680 | ||||||||
\(563\) | −5.25771 | −0.221586 | −0.110793 | − | 0.993843i | \(-0.535339\pi\) | ||||
−0.110793 | + | 0.993843i | \(0.535339\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −43.9490 | −1.84732 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 33.7004 | 1.41404 | ||||||||
\(569\) | −15.1931 | −0.636926 | −0.318463 | − | 0.947935i | \(-0.603167\pi\) | ||||
−0.318463 | + | 0.947935i | \(0.603167\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.29434 | −0.347107 | −0.173554 | − | 0.984824i | \(-0.555525\pi\) | ||||
−0.173554 | + | 0.984824i | \(0.555525\pi\) | |||||||
\(572\) | −70.7613 | −2.95868 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 33.2559 | 1.38807 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.69155 | −0.112051 | −0.0560253 | − | 0.998429i | \(-0.517843\pi\) | ||||
−0.0560253 | + | 0.998429i | \(0.517843\pi\) | |||||||
\(578\) | 32.9218 | 1.36936 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.4761 | 0.683543 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.8346 | 0.448724 | ||||||||
\(584\) | 11.7595 | 0.486612 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.75244 | 0.113702 | ||||||||
\(587\) | 27.2841 | 1.12613 | 0.563067 | − | 0.826411i | \(-0.309621\pi\) | ||||
0.563067 | + | 0.826411i | \(0.309621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.7768 | 0.650074 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.0737 | 0.701723 | ||||||||
\(593\) | −3.04738 | −0.125141 | −0.0625704 | − | 0.998041i | \(-0.519930\pi\) | ||||
−0.0625704 | + | 0.998041i | \(0.519930\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −24.7079 | −1.01207 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −45.3946 | −1.85632 | ||||||||
\(599\) | 21.1104 | 0.862549 | 0.431274 | − | 0.902221i | \(-0.358064\pi\) | ||||
0.431274 | + | 0.902221i | \(0.358064\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.78443 | 0.0727884 | 0.0363942 | − | 0.999338i | \(-0.488413\pi\) | ||||
0.0363942 | + | 0.999338i | \(0.488413\pi\) | |||||||
\(602\) | −27.3637 | −1.11526 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 36.9258 | 1.50249 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.9927 | −1.78561 | −0.892805 | − | 0.450444i | \(-0.851266\pi\) | ||||
−0.892805 | + | 0.450444i | \(0.851266\pi\) | |||||||
\(608\) | −70.1179 | −2.84366 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.7563 | 0.880166 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.9419 | 1.53246 | 0.766230 | − | 0.642567i | \(-0.222130\pi\) | ||||
0.766230 | + | 0.642567i | \(0.222130\pi\) | |||||||
\(614\) | −77.1977 | −3.11544 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 100.882 | 4.06464 | ||||||||
\(617\) | −7.92668 | −0.319116 | −0.159558 | − | 0.987189i | \(-0.551007\pi\) | ||||
−0.159558 | + | 0.987189i | \(0.551007\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.83411 | −0.314880 | −0.157440 | − | 0.987529i | \(-0.550324\pi\) | ||||
−0.157440 | + | 0.987529i | \(0.550324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.2069 | −0.529548 | ||||||||
\(623\) | −29.5641 | −1.18446 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −67.3673 | −2.69254 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 78.0469 | 3.11441 | ||||||||
\(629\) | −10.3036 | −0.410833 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0248 | 0.757366 | 0.378683 | − | 0.925526i | \(-0.376377\pi\) | ||||
0.378683 | + | 0.925526i | \(0.376377\pi\) | |||||||
\(632\) | 97.9279 | 3.89536 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 51.3528 | 2.03948 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.1025 | 0.519141 | ||||||||
\(638\) | −34.9480 | −1.38360 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.5783 | 1.28677 | 0.643383 | − | 0.765545i | \(-0.277530\pi\) | ||||
0.643383 | + | 0.765545i | \(0.277530\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.0025 | −1.57755 | −0.788773 | − | 0.614684i | \(-0.789283\pi\) | ||||
−0.788773 | + | 0.614684i | \(0.789283\pi\) | |||||||
\(644\) | 78.6972 | 3.10111 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 108.011 | 4.24965 | ||||||||
\(647\) | −20.0199 | −0.787063 | −0.393532 | − | 0.919311i | \(-0.628747\pi\) | ||||
−0.393532 | + | 0.919311i | \(0.628747\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.3012 | 1.30719 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −37.0766 | −1.45203 | ||||||||
\(653\) | −10.3332 | −0.404369 | −0.202185 | − | 0.979347i | \(-0.564804\pi\) | ||||
−0.202185 | + | 0.979347i | \(0.564804\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −35.1955 | −1.37415 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −53.6141 | −2.09009 | ||||||||
\(659\) | 47.2403 | 1.84022 | 0.920111 | − | 0.391657i | \(-0.128098\pi\) | ||||
0.920111 | + | 0.391657i | \(0.128098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 51.3528 | 1.99739 | 0.998696 | − | 0.0510604i | \(-0.0162601\pi\) | ||||
0.998696 | + | 0.0510604i | \(0.0162601\pi\) | |||||||
\(662\) | −62.2250 | −2.41844 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −35.7696 | −1.38813 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.7722 | −0.610701 | ||||||||
\(668\) | −13.1458 | −0.508625 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.7381 | 0.491749 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.5790 | −1.56420 | −0.782102 | − | 0.623150i | \(-0.785853\pi\) | ||||
−0.782102 | + | 0.623150i | \(0.785853\pi\) | |||||||
\(674\) | 71.8841 | 2.76887 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.84068 | −0.186180 | ||||||||
\(677\) | 9.21482 | 0.354154 | 0.177077 | − | 0.984197i | \(-0.443336\pi\) | ||||
0.177077 | + | 0.984197i | \(0.443336\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.44935 | 0.324256 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.1239 | 0.885461 | ||||||||
\(683\) | 13.3281 | 0.509987 | 0.254994 | − | 0.966943i | \(-0.417927\pi\) | ||||
0.254994 | + | 0.966943i | \(0.417927\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.4174 | 1.04680 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.9597 | 1.10408 | ||||||||
\(689\) | −8.70421 | −0.331604 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.5862 | −1.23964 | −0.619819 | − | 0.784745i | \(-0.712794\pi\) | ||||
−0.619819 | + | 0.784745i | \(0.712794\pi\) | |||||||
\(692\) | −80.4667 | −3.05889 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −35.0306 | −1.32974 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.2398 | 0.804516 | ||||||||
\(698\) | 49.7820 | 1.88428 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.5547 | 1.26734 | 0.633672 | − | 0.773602i | \(-0.281547\pi\) | ||||
0.633672 | + | 0.773602i | \(0.281547\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.4396 | −0.544600 | ||||||||
\(704\) | −24.9889 | −0.941806 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.7891 | 0.744772 | ||||||||
\(707\) | 25.8745 | 0.973110 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.4731 | 0.468436 | 0.234218 | − | 0.972184i | \(-0.424747\pi\) | ||||
0.234218 | + | 0.972184i | \(0.424747\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 64.1837 | 2.40539 | ||||||||
\(713\) | 10.4359 | 0.390829 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.41079 | −0.276954 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −81.2765 | −3.03321 | ||||||||
\(719\) | 7.53586 | 0.281040 | 0.140520 | − | 0.990078i | \(-0.455123\pi\) | ||||
0.140520 | + | 0.990078i | \(0.455123\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.7384 | 1.51718 | ||||||||
\(722\) | 102.022 | 3.79687 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.36827 | 0.273839 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.8265 | 1.58835 | 0.794173 | − | 0.607691i | \(-0.207904\pi\) | ||||
0.794173 | + | 0.607691i | \(0.207904\pi\) | |||||||
\(728\) | −81.0455 | −3.00375 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.4766 | −0.646396 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.4170 | −1.78832 | −0.894161 | − | 0.447745i | \(-0.852227\pi\) | ||||
−0.894161 | + | 0.447745i | \(0.852227\pi\) | |||||||
\(734\) | 16.4940 | 0.608806 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −46.3810 | −1.70963 | ||||||||
\(737\) | 55.9880 | 2.06234 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.1926 | 1.14744 | 0.573720 | − | 0.819052i | \(-0.305500\pi\) | ||||
0.573720 | + | 0.819052i | \(0.305500\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21.4498 | 0.787447 | ||||||||
\(743\) | 45.9840 | 1.68699 | 0.843495 | − | 0.537137i | \(-0.180494\pi\) | ||||
0.843495 | + | 0.537137i | \(0.180494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −29.0128 | −1.06223 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 111.371 | 4.07213 | ||||||||
\(749\) | −27.9839 | −1.02251 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.51488 | 0.0917695 | 0.0458847 | − | 0.998947i | \(-0.485389\pi\) | ||||
0.0458847 | + | 0.998947i | \(0.485389\pi\) | |||||||
\(752\) | 56.7411 | 2.06913 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 28.0762 | 1.02247 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.6597 | 1.44146 | 0.720728 | − | 0.693218i | \(-0.243808\pi\) | ||||
0.720728 | + | 0.693218i | \(0.243808\pi\) | |||||||
\(758\) | −53.7905 | −1.95376 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.2752 | −0.626225 | −0.313113 | − | 0.949716i | \(-0.601372\pi\) | ||||
−0.313113 | + | 0.949716i | \(0.601372\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −57.5179 | −2.08229 | ||||||||
\(764\) | −126.053 | −4.56044 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.6901 | −1.18114 | ||||||||
\(767\) | −26.7533 | −0.966004 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.50943 | −0.162614 | −0.0813071 | − | 0.996689i | \(-0.525909\pi\) | ||||
−0.0813071 | + | 0.996689i | \(0.525909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 65.3148 | 2.35073 | ||||||||
\(773\) | −33.6503 | −1.21032 | −0.605159 | − | 0.796105i | \(-0.706890\pi\) | ||||
−0.605159 | + | 0.796105i | \(0.706890\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.3436 | −0.658495 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.1276 | −1.00842 | ||||||||
\(779\) | 29.7657 | 1.06647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.3640 | −0.728682 | ||||||||
\(782\) | 71.4465 | 2.55492 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 34.1718 | 1.22042 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.8366 | −1.31308 | −0.656542 | − | 0.754289i | \(-0.727982\pi\) | ||||
−0.656542 | + | 0.754289i | \(0.727982\pi\) | |||||||
\(788\) | 29.6982 | 1.05796 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.7182 | −0.487763 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2334 | −0.363399 | ||||||||
\(794\) | 12.7444 | 0.452281 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.8970 | 0.563455 | ||||||||
\(797\) | −40.4962 | −1.43445 | −0.717224 | − | 0.696843i | \(-0.754588\pi\) | ||||
−0.717224 | + | 0.696843i | \(0.754588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.2422 | −1.21140 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 71.4798 | 2.52404 | ||||||||
\(803\) | −7.10589 | −0.250761 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.5771 | −0.654350 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −56.1735 | −1.97618 | ||||||||
\(809\) | 11.9110 | 0.418767 | 0.209384 | − | 0.977834i | \(-0.432854\pi\) | ||||
0.209384 | + | 0.977834i | \(0.432854\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.2433 | −1.48336 | −0.741681 | − | 0.670752i | \(-0.765971\pi\) | ||||
−0.741681 | + | 0.670752i | \(0.765971\pi\) | |||||||
\(812\) | −48.6736 | −1.70811 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21.1640 | −0.741796 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.4919 | −0.856863 | ||||||||
\(818\) | 51.3368 | 1.79495 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.5710 | −1.55554 | −0.777769 | − | 0.628551i | \(-0.783648\pi\) | ||||
−0.777769 | + | 0.628551i | \(0.783648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.3125 | −0.429186 | −0.214593 | − | 0.976704i | \(-0.568843\pi\) | ||||
−0.214593 | + | 0.976704i | \(0.568843\pi\) | |||||||
\(824\) | −88.4431 | −3.08106 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 65.9281 | 2.29393 | ||||||||
\(827\) | −24.7421 | −0.860367 | −0.430183 | − | 0.902742i | \(-0.641551\pi\) | ||||
−0.430183 | + | 0.902742i | \(0.641551\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.7221 | −1.86584 | −0.932922 | − | 0.360077i | \(-0.882750\pi\) | ||||
−0.932922 | + | 0.360077i | \(0.882750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.0754 | 0.695989 | ||||||||
\(833\) | −20.6221 | −0.714512 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 156.076 | 5.39801 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.3477 | 0.599266 | ||||||||
\(839\) | 45.7865 | 1.58073 | 0.790363 | − | 0.612639i | \(-0.209892\pi\) | ||||
0.790363 | + | 0.612639i | \(0.209892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.2450 | −0.663622 | ||||||||
\(842\) | 14.6998 | 0.506589 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 114.353 | 3.93620 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.8340 | −0.853307 | ||||||||
\(848\) | −22.7009 | −0.779550 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.55139 | −0.327418 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.3074 | 0.695311 | 0.347655 | − | 0.937622i | \(-0.386978\pi\) | ||||
0.347655 | + | 0.937622i | \(0.386978\pi\) | |||||||
\(854\) | 25.2182 | 0.862950 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 60.7531 | 2.07650 | ||||||||
\(857\) | −47.4031 | −1.61926 | −0.809630 | − | 0.586941i | \(-0.800332\pi\) | ||||
−0.809630 | + | 0.586941i | \(0.800332\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.37538 | −0.183406 | −0.0917028 | − | 0.995786i | \(-0.529231\pi\) | ||||
−0.0917028 | + | 0.995786i | \(0.529231\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.6664 | −0.567661 | ||||||||
\(863\) | −15.0679 | −0.512916 | −0.256458 | − | 0.966555i | \(-0.582556\pi\) | ||||
−0.256458 | + | 0.966555i | \(0.582556\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.87003 | 0.0975275 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.2057 | 1.09313 | ||||||||
\(869\) | −59.1746 | −2.00736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.9791 | −1.52406 | ||||||||
\(872\) | 124.871 | 4.22868 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 100.126 | 3.38680 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.43572 | −0.217319 | −0.108659 | − | 0.994079i | \(-0.534656\pi\) | ||||
−0.108659 | + | 0.994079i | \(0.534656\pi\) | |||||||
\(878\) | −13.2796 | −0.448165 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.2411 | −1.55790 | −0.778950 | − | 0.627085i | \(-0.784248\pi\) | ||||
−0.778950 | + | 0.627085i | \(0.784248\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8545 | 0.432590 | 0.216295 | − | 0.976328i | \(-0.430603\pi\) | ||||
0.216295 | + | 0.976328i | \(0.430603\pi\) | |||||||
\(884\) | −89.4723 | −3.00928 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −46.5097 | −1.56252 | ||||||||
\(887\) | −33.5617 | −1.12689 | −0.563446 | − | 0.826153i | \(-0.690525\pi\) | ||||
−0.563446 | + | 0.826153i | \(0.690525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.5350 | 1.12473 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 86.6942 | 2.90274 | ||||||||
\(893\) | −47.9873 | −1.60583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10.8553 | 0.362649 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −71.0870 | −2.37220 | ||||||||
\(899\) | −6.45454 | −0.215271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.6995 | 0.456398 | ||||||||
\(902\) | 43.6272 | 1.45263 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.7822 | 0.990542 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.73678 | −0.190487 | −0.0952433 | − | 0.995454i | \(-0.530363\pi\) | ||||
−0.0952433 | + | 0.995454i | \(0.530363\pi\) | |||||||
\(908\) | −85.2257 | −2.82831 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.08321 | −0.135283 | −0.0676413 | − | 0.997710i | \(-0.521547\pi\) | ||||
−0.0676413 | + | 0.997710i | \(0.521547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.6144 | 0.715332 | ||||||||
\(914\) | −23.1876 | −0.766978 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.5027 | 0.941757 | ||||||||
\(917\) | −16.1476 | −0.533242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.1894 | 1.12780 | 0.563902 | − | 0.825842i | \(-0.309300\pi\) | ||||
0.563902 | + | 0.825842i | \(0.309300\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.70617 | −0.154989 | ||||||||
\(923\) | 16.3599 | 0.538492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.06927 | −0.232311 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 28.6863 | 0.941672 | ||||||||
\(929\) | 23.9398 | 0.785438 | 0.392719 | − | 0.919659i | \(-0.371535\pi\) | ||||
0.392719 | + | 0.919659i | \(0.371535\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.8999 | −0.947157 | ||||||||
\(932\) | −98.9507 | −3.24124 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −104.474 | −3.41849 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.4640 | −0.701199 | −0.350600 | − | 0.936525i | \(-0.614022\pi\) | ||||
−0.350600 | + | 0.936525i | \(0.614022\pi\) | |||||||
\(938\) | 110.842 | 3.61912 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.78646 | 0.0582371 | 0.0291185 | − | 0.999576i | \(-0.490730\pi\) | ||||
0.0291185 | + | 0.999576i | \(0.490730\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.6892 | 0.641167 | ||||||||
\(944\) | −69.7733 | −2.27093 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35.8975 | −1.16713 | ||||||||
\(947\) | −45.4097 | −1.47562 | −0.737809 | − | 0.675009i | \(-0.764140\pi\) | ||||
−0.737809 | + | 0.675009i | \(0.764140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.70866 | 0.185311 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 127.557 | 4.13416 | ||||||||
\(953\) | 1.00850 | 0.0326686 | 0.0163343 | − | 0.999867i | \(-0.494800\pi\) | ||||
0.0163343 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 132.261 | 4.27761 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 72.5794 | 2.34493 | ||||||||
\(959\) | 40.6631 | 1.31308 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7292 | −0.862234 | ||||||||
\(962\) | 17.0025 | 0.548183 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −88.8115 | −2.86043 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.4625 | −0.690188 | −0.345094 | − | 0.938568i | \(-0.612153\pi\) | ||||
−0.345094 | + | 0.938568i | \(0.612153\pi\) | |||||||
\(968\) | 53.9147 | 1.73288 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.3619 | −1.51992 | −0.759958 | − | 0.649972i | \(-0.774781\pi\) | ||||
−0.759958 | + | 0.649972i | \(0.774781\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −43.4884 | −1.39417 | ||||||||
\(974\) | 67.0298 | 2.14777 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.6891 | −0.854296 | ||||||||
\(977\) | 6.29459 | 0.201382 | 0.100691 | − | 0.994918i | \(-0.467895\pi\) | ||||
0.100691 | + | 0.994918i | \(0.467895\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38.7841 | −1.23955 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −61.5641 | −1.96459 | ||||||||
\(983\) | −7.80790 | −0.249033 | −0.124517 | − | 0.992218i | \(-0.539738\pi\) | ||||
−0.124517 | + | 0.992218i | \(0.539738\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −44.1891 | −1.40727 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −125.387 | −3.98910 | ||||||||
\(989\) | −16.2007 | −0.515152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.0569 | −0.668896 | −0.334448 | − | 0.942414i | \(-0.608550\pi\) | ||||
−0.334448 | + | 0.942414i | \(0.608550\pi\) | |||||||
\(992\) | −18.9808 | −0.602640 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −40.3156 | −1.27873 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.3042 | −0.928072 | −0.464036 | − | 0.885816i | \(-0.653599\pi\) | ||||
−0.464036 | + | 0.885816i | \(0.653599\pi\) | |||||||
\(998\) | 23.2641 | 0.736413 | ||||||||
\(999\) | 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 | 5625.2.a.bc.1.8 | 8 | ||
3.2 | odd | 2 | 1875.2.a.n.1.1 | ✓ | 8 | ||
5.4 | even | 2 | 5625.2.a.u.1.1 | 8 | |||
15.2 | even | 4 | 1875.2.b.g.1249.2 | 16 | |||
15.8 | even | 4 | 1875.2.b.g.1249.15 | 16 | |||
15.14 | odd | 2 | 1875.2.a.o.1.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.n.1.1 | ✓ | 8 | 3.2 | odd | 2 | ||
1875.2.a.o.1.8 | yes | 8 | 15.14 | odd | 2 | ||
1875.2.b.g.1249.2 | 16 | 15.2 | even | 4 | |||
1875.2.b.g.1249.15 | 16 | 15.8 | even | 4 | |||
5625.2.a.u.1.1 | 8 | 5.4 | even | 2 | |||
5625.2.a.bc.1.8 | 8 | 1.1 | even | 1 | trivial |