Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, 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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 14x^{5} + 12x^{4} + 50x^{3} - 36x^{2} - 38x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 446) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.01250\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.52490 | −0.681954 | −0.340977 | − | 0.940072i | \(-0.610758\pi\) | ||||
−0.340977 | + | 0.940072i | \(0.610758\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.908231 | 0.343279 | 0.171639 | − | 0.985160i | \(-0.445094\pi\) | ||||
0.171639 | + | 0.985160i | \(0.445094\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.52490 | 0.482214 | ||||||||
\(11\) | −5.03528 | −1.51819 | −0.759097 | − | 0.650977i | \(-0.774359\pi\) | ||||
−0.759097 | + | 0.650977i | \(0.774359\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.51425 | −1.52938 | −0.764689 | − | 0.644400i | \(-0.777107\pi\) | ||||
−0.764689 | + | 0.644400i | \(0.777107\pi\) | |||||||
\(14\) | −0.908231 | −0.242735 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.38428 | −1.30588 | −0.652939 | − | 0.757410i | \(-0.726464\pi\) | ||||
−0.652939 | + | 0.757410i | \(0.726464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.02500 | 0.923399 | 0.461699 | − | 0.887036i | \(-0.347240\pi\) | ||||
0.461699 | + | 0.887036i | \(0.347240\pi\) | |||||||
\(20\) | −1.52490 | −0.340977 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.03528 | 1.07353 | ||||||||
\(23\) | −0.290419 | −0.0605566 | −0.0302783 | − | 0.999542i | \(-0.509639\pi\) | ||||
−0.0302783 | + | 0.999542i | \(0.509639\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.67470 | −0.534939 | ||||||||
\(26\) | 5.51425 | 1.08143 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.908231 | 0.171639 | ||||||||
\(29\) | −8.72171 | −1.61958 | −0.809791 | − | 0.586719i | \(-0.800419\pi\) | ||||
−0.809791 | + | 0.586719i | \(0.800419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2440 | 1.83987 | 0.919936 | − | 0.392069i | \(-0.128241\pi\) | ||||
0.919936 | + | 0.392069i | \(0.128241\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.38428 | 0.923396 | ||||||||
\(35\) | −1.38496 | −0.234100 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.80493 | −1.11872 | −0.559362 | − | 0.828924i | \(-0.688954\pi\) | ||||
−0.559362 | + | 0.828924i | \(0.688954\pi\) | |||||||
\(38\) | −4.02500 | −0.652942 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.52490 | 0.241107 | ||||||||
\(41\) | 6.15244 | 0.960850 | 0.480425 | − | 0.877036i | \(-0.340482\pi\) | ||||
0.480425 | + | 0.877036i | \(0.340482\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.03714 | −1.07315 | −0.536577 | − | 0.843852i | \(-0.680283\pi\) | ||||
−0.536577 | + | 0.843852i | \(0.680283\pi\) | |||||||
\(44\) | −5.03528 | −0.759097 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.290419 | 0.0428200 | ||||||||
\(47\) | 10.5033 | 1.53206 | 0.766031 | − | 0.642803i | \(-0.222229\pi\) | ||||
0.766031 | + | 0.642803i | \(0.222229\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.17512 | −0.882160 | ||||||||
\(50\) | 2.67470 | 0.378259 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.51425 | −0.764689 | ||||||||
\(53\) | −4.35234 | −0.597840 | −0.298920 | − | 0.954278i | \(-0.596626\pi\) | ||||
−0.298920 | + | 0.954278i | \(0.596626\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.67827 | 1.03534 | ||||||||
\(56\) | −0.908231 | −0.121367 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.72171 | 1.14522 | ||||||||
\(59\) | 10.0783 | 1.31209 | 0.656045 | − | 0.754722i | \(-0.272228\pi\) | ||||
0.656045 | + | 0.754722i | \(0.272228\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.04184 | −0.133394 | −0.0666968 | − | 0.997773i | \(-0.521246\pi\) | ||||
−0.0666968 | + | 0.997773i | \(0.521246\pi\) | |||||||
\(62\) | −10.2440 | −1.30099 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.40865 | 1.04296 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.3492 | 1.87520 | 0.937599 | − | 0.347718i | \(-0.113043\pi\) | ||||
0.937599 | + | 0.347718i | \(0.113043\pi\) | |||||||
\(68\) | −5.38428 | −0.652939 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.38496 | 0.165534 | ||||||||
\(71\) | 2.68271 | 0.318380 | 0.159190 | − | 0.987248i | \(-0.449112\pi\) | ||||
0.159190 | + | 0.987248i | \(0.449112\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2734 | −1.20242 | −0.601208 | − | 0.799093i | \(-0.705314\pi\) | ||||
−0.601208 | + | 0.799093i | \(0.705314\pi\) | |||||||
\(74\) | 6.80493 | 0.791057 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.02500 | 0.461699 | ||||||||
\(77\) | −4.57320 | −0.521164 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5693 | 1.18914 | 0.594568 | − | 0.804045i | \(-0.297323\pi\) | ||||
0.594568 | + | 0.804045i | \(0.297323\pi\) | |||||||
\(80\) | −1.52490 | −0.170488 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.15244 | −0.679423 | ||||||||
\(83\) | 11.5427 | 1.26697 | 0.633485 | − | 0.773755i | \(-0.281624\pi\) | ||||
0.633485 | + | 0.773755i | \(0.281624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.21046 | 0.890549 | ||||||||
\(86\) | 7.03714 | 0.758834 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.03528 | 0.536763 | ||||||||
\(89\) | 13.7906 | 1.46180 | 0.730899 | − | 0.682486i | \(-0.239101\pi\) | ||||
0.730899 | + | 0.682486i | \(0.239101\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00821 | −0.525003 | ||||||||
\(92\) | −0.290419 | −0.0302783 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.5033 | −1.08333 | ||||||||
\(95\) | −6.13771 | −0.629715 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.46450 | 0.250232 | 0.125116 | − | 0.992142i | \(-0.460070\pi\) | ||||
0.125116 | + | 0.992142i | \(0.460070\pi\) | |||||||
\(98\) | 6.17512 | 0.623781 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.67470 | −0.267470 | ||||||||
\(101\) | 14.6472 | 1.45745 | 0.728726 | − | 0.684805i | \(-0.240113\pi\) | ||||
0.728726 | + | 0.684805i | \(0.240113\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.320702 | 0.0315997 | 0.0157998 | − | 0.999875i | \(-0.494971\pi\) | ||||
0.0157998 | + | 0.999875i | \(0.494971\pi\) | |||||||
\(104\) | 5.51425 | 0.540717 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.35234 | 0.422737 | ||||||||
\(107\) | −13.9377 | −1.34741 | −0.673705 | − | 0.739000i | \(-0.735298\pi\) | ||||
−0.673705 | + | 0.739000i | \(0.735298\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.707255 | −0.0677427 | −0.0338714 | − | 0.999426i | \(-0.510784\pi\) | ||||
−0.0338714 | + | 0.999426i | \(0.510784\pi\) | |||||||
\(110\) | −7.67827 | −0.732095 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.908231 | 0.0858197 | ||||||||
\(113\) | −10.8700 | −1.02256 | −0.511280 | − | 0.859414i | \(-0.670829\pi\) | ||||
−0.511280 | + | 0.859414i | \(0.670829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.442859 | 0.0412968 | ||||||||
\(116\) | −8.72171 | −0.809791 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.0783 | −0.927787 | ||||||||
\(119\) | −4.89017 | −0.448281 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.3541 | 1.30491 | ||||||||
\(122\) | 1.04184 | 0.0943236 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.2440 | 0.919936 | ||||||||
\(125\) | 11.7031 | 1.04676 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.08270 | −0.805959 | −0.402979 | − | 0.915209i | \(-0.632025\pi\) | ||||
−0.402979 | + | 0.915209i | \(0.632025\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.40865 | −0.737488 | ||||||||
\(131\) | −13.8183 | −1.20731 | −0.603657 | − | 0.797244i | \(-0.706290\pi\) | ||||
−0.603657 | + | 0.797244i | \(0.706290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.65563 | 0.316983 | ||||||||
\(134\) | −15.3492 | −1.32597 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.38428 | 0.461698 | ||||||||
\(137\) | 13.2046 | 1.12815 | 0.564073 | − | 0.825725i | \(-0.309234\pi\) | ||||
0.564073 | + | 0.825725i | \(0.309234\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.84073 | −0.665042 | −0.332521 | − | 0.943096i | \(-0.607899\pi\) | ||||
−0.332521 | + | 0.943096i | \(0.607899\pi\) | |||||||
\(140\) | −1.38496 | −0.117050 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.68271 | −0.225128 | ||||||||
\(143\) | 27.7658 | 2.32189 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.2997 | 1.10448 | ||||||||
\(146\) | 10.2734 | 0.850236 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.80493 | −0.559362 | ||||||||
\(149\) | −18.2537 | −1.49540 | −0.747701 | − | 0.664036i | \(-0.768842\pi\) | ||||
−0.747701 | + | 0.664036i | \(0.768842\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.78861 | −0.633828 | −0.316914 | − | 0.948454i | \(-0.602647\pi\) | ||||
−0.316914 | + | 0.948454i | \(0.602647\pi\) | |||||||
\(152\) | −4.02500 | −0.326471 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.57320 | 0.368519 | ||||||||
\(155\) | −15.6210 | −1.25471 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.14015 | 0.729464 | 0.364732 | − | 0.931113i | \(-0.381161\pi\) | ||||
0.364732 | + | 0.931113i | \(0.381161\pi\) | |||||||
\(158\) | −10.5693 | −0.840846 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.52490 | 0.120554 | ||||||||
\(161\) | −0.263768 | −0.0207878 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.5330 | −1.60827 | −0.804134 | − | 0.594449i | \(-0.797370\pi\) | ||||
−0.804134 | + | 0.594449i | \(0.797370\pi\) | |||||||
\(164\) | 6.15244 | 0.480425 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.5427 | −0.895884 | ||||||||
\(167\) | 2.99767 | 0.231967 | 0.115983 | − | 0.993251i | \(-0.462998\pi\) | ||||
0.115983 | + | 0.993251i | \(0.462998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.4070 | 1.33900 | ||||||||
\(170\) | −8.21046 | −0.629713 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.03714 | −0.536577 | ||||||||
\(173\) | −8.96255 | −0.681410 | −0.340705 | − | 0.940170i | \(-0.610666\pi\) | ||||
−0.340705 | + | 0.940170i | \(0.610666\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.42924 | −0.183633 | ||||||||
\(176\) | −5.03528 | −0.379549 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.7906 | −1.03365 | ||||||||
\(179\) | −0.418318 | −0.0312665 | −0.0156333 | − | 0.999878i | \(-0.504976\pi\) | ||||
−0.0156333 | + | 0.999878i | \(0.504976\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.84683 | 0.285932 | 0.142966 | − | 0.989728i | \(-0.454336\pi\) | ||||
0.142966 | + | 0.989728i | \(0.454336\pi\) | |||||||
\(182\) | 5.00821 | 0.371233 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.290419 | 0.0214100 | ||||||||
\(185\) | 10.3768 | 0.762918 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.1113 | 1.98258 | ||||||||
\(188\) | 10.5033 | 0.766031 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.13771 | 0.445276 | ||||||||
\(191\) | 12.5869 | 0.910757 | 0.455379 | − | 0.890298i | \(-0.349504\pi\) | ||||
0.455379 | + | 0.890298i | \(0.349504\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.54364 | 0.183096 | 0.0915478 | − | 0.995801i | \(-0.470819\pi\) | ||||
0.0915478 | + | 0.995801i | \(0.470819\pi\) | |||||||
\(194\) | −2.46450 | −0.176941 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.17512 | −0.441080 | ||||||||
\(197\) | −14.2791 | −1.01734 | −0.508672 | − | 0.860960i | \(-0.669863\pi\) | ||||
−0.508672 | + | 0.860960i | \(0.669863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.63234 | 0.328378 | 0.164189 | − | 0.986429i | \(-0.447499\pi\) | ||||
0.164189 | + | 0.986429i | \(0.447499\pi\) | |||||||
\(200\) | 2.67470 | 0.189130 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.6472 | −1.03057 | ||||||||
\(203\) | −7.92133 | −0.555968 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.38182 | −0.655255 | ||||||||
\(206\) | −0.320702 | −0.0223443 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.51425 | −0.382344 | ||||||||
\(209\) | −20.2670 | −1.40190 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4454 | 1.26983 | 0.634916 | − | 0.772581i | \(-0.281035\pi\) | ||||
0.634916 | + | 0.772581i | \(0.281035\pi\) | |||||||
\(212\) | −4.35234 | −0.298920 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.9377 | 0.952763 | ||||||||
\(215\) | 10.7309 | 0.731841 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.30389 | 0.631589 | ||||||||
\(218\) | 0.707255 | 0.0479013 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.67827 | 0.517669 | ||||||||
\(221\) | 29.6902 | 1.99718 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | −0.908231 | −0.0606837 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.8700 | 0.723059 | ||||||||
\(227\) | 24.1870 | 1.60535 | 0.802673 | − | 0.596420i | \(-0.203411\pi\) | ||||
0.802673 | + | 0.596420i | \(0.203411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.01632 | −0.265406 | −0.132703 | − | 0.991156i | \(-0.542366\pi\) | ||||
−0.132703 | + | 0.991156i | \(0.542366\pi\) | |||||||
\(230\) | −0.442859 | −0.0292013 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.72171 | 0.572609 | ||||||||
\(233\) | 26.4607 | 1.73350 | 0.866751 | − | 0.498742i | \(-0.166204\pi\) | ||||
0.866751 | + | 0.498742i | \(0.166204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.0164 | −1.04480 | ||||||||
\(236\) | 10.0783 | 0.656045 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.89017 | 0.316982 | ||||||||
\(239\) | 4.41114 | 0.285333 | 0.142667 | − | 0.989771i | \(-0.454432\pi\) | ||||
0.142667 | + | 0.989771i | \(0.454432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.9584 | −0.899140 | −0.449570 | − | 0.893245i | \(-0.648423\pi\) | ||||
−0.449570 | + | 0.893245i | \(0.648423\pi\) | |||||||
\(242\) | −14.3541 | −0.922713 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.04184 | −0.0666968 | ||||||||
\(245\) | 9.41640 | 0.601592 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.1949 | −1.41223 | ||||||||
\(248\) | −10.2440 | −0.650493 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.7031 | −0.740169 | ||||||||
\(251\) | 7.55760 | 0.477032 | 0.238516 | − | 0.971139i | \(-0.423339\pi\) | ||||
0.238516 | + | 0.971139i | \(0.423339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.46234 | 0.0919367 | ||||||||
\(254\) | 9.08270 | 0.569899 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.1502 | −0.882664 | −0.441332 | − | 0.897344i | \(-0.645494\pi\) | ||||
−0.441332 | + | 0.897344i | \(0.645494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.18045 | −0.384034 | ||||||||
\(260\) | 8.40865 | 0.521482 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.8183 | 0.853700 | ||||||||
\(263\) | −6.88918 | −0.424805 | −0.212403 | − | 0.977182i | \(-0.568129\pi\) | ||||
−0.212403 | + | 0.977182i | \(0.568129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.63687 | 0.407700 | ||||||||
\(266\) | −3.65563 | −0.224141 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.3492 | 0.937599 | ||||||||
\(269\) | −12.5832 | −0.767208 | −0.383604 | − | 0.923498i | \(-0.625317\pi\) | ||||
−0.383604 | + | 0.923498i | \(0.625317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.8747 | 1.38954 | 0.694769 | − | 0.719232i | \(-0.255506\pi\) | ||||
0.694769 | + | 0.719232i | \(0.255506\pi\) | |||||||
\(272\) | −5.38428 | −0.326470 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.2046 | −0.797719 | ||||||||
\(275\) | 13.4678 | 0.812141 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.30561 | 0.559120 | 0.279560 | − | 0.960128i | \(-0.409811\pi\) | ||||
0.279560 | + | 0.960128i | \(0.409811\pi\) | |||||||
\(278\) | 7.84073 | 0.470256 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.38496 | 0.0827670 | ||||||||
\(281\) | −0.0277078 | −0.00165291 | −0.000826453 | − | 1.00000i | \(-0.500263\pi\) | ||||
−0.000826453 | 1.00000i | \(0.500263\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3178 | 1.20777 | 0.603884 | − | 0.797072i | \(-0.293619\pi\) | ||||
0.603884 | + | 0.797072i | \(0.293619\pi\) | |||||||
\(284\) | 2.68271 | 0.159190 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −27.7658 | −1.64183 | ||||||||
\(287\) | 5.58784 | 0.329840 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.9904 | 0.705319 | ||||||||
\(290\) | −13.2997 | −0.780985 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.2734 | −0.601208 | ||||||||
\(293\) | −0.635336 | −0.0371167 | −0.0185584 | − | 0.999828i | \(-0.505908\pi\) | ||||
−0.0185584 | + | 0.999828i | \(0.505908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.3684 | −0.894784 | ||||||||
\(296\) | 6.80493 | 0.395528 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.2537 | 1.05741 | ||||||||
\(299\) | 1.60145 | 0.0926140 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.39134 | −0.368391 | ||||||||
\(302\) | 7.78861 | 0.448184 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.02500 | 0.230850 | ||||||||
\(305\) | 1.58869 | 0.0909683 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.1386 | −0.749860 | −0.374930 | − | 0.927053i | \(-0.622333\pi\) | ||||
−0.374930 | + | 0.927053i | \(0.622333\pi\) | |||||||
\(308\) | −4.57320 | −0.260582 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.6210 | 0.887212 | ||||||||
\(311\) | 13.8305 | 0.784253 | 0.392127 | − | 0.919911i | \(-0.371739\pi\) | ||||
0.392127 | + | 0.919911i | \(0.371739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.5707 | 1.38882 | 0.694409 | − | 0.719581i | \(-0.255666\pi\) | ||||
0.694409 | + | 0.719581i | \(0.255666\pi\) | |||||||
\(314\) | −9.14015 | −0.515809 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.5693 | 0.594568 | ||||||||
\(317\) | 21.9969 | 1.23547 | 0.617734 | − | 0.786387i | \(-0.288051\pi\) | ||||
0.617734 | + | 0.786387i | \(0.288051\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43.9163 | 2.45884 | ||||||||
\(320\) | −1.52490 | −0.0852442 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.263768 | 0.0146992 | ||||||||
\(323\) | −21.6717 | −1.20585 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.7489 | 0.818124 | ||||||||
\(326\) | 20.5330 | 1.13722 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.15244 | −0.339712 | ||||||||
\(329\) | 9.53941 | 0.525925 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2357 | 1.05729 | 0.528645 | − | 0.848843i | \(-0.322700\pi\) | ||||
0.528645 | + | 0.848843i | \(0.322700\pi\) | |||||||
\(332\) | 11.5427 | 0.633485 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.99767 | −0.164025 | ||||||||
\(335\) | −23.4059 | −1.27880 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.5164 | −1.00865 | −0.504326 | − | 0.863513i | \(-0.668259\pi\) | ||||
−0.504326 | + | 0.863513i | \(0.668259\pi\) | |||||||
\(338\) | −17.4070 | −0.946813 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.21046 | 0.445274 | ||||||||
\(341\) | −51.5813 | −2.79328 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.9660 | −0.646106 | ||||||||
\(344\) | 7.03714 | 0.379417 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.96255 | 0.481829 | ||||||||
\(347\) | −12.3571 | −0.663363 | −0.331681 | − | 0.943391i | \(-0.607616\pi\) | ||||
−0.331681 | + | 0.943391i | \(0.607616\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.72893 | −0.0925476 | −0.0462738 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462738 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(350\) | 2.42924 | 0.129848 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.03528 | 0.268381 | ||||||||
\(353\) | 31.0336 | 1.65175 | 0.825876 | − | 0.563852i | \(-0.190681\pi\) | ||||
0.825876 | + | 0.563852i | \(0.190681\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.09086 | −0.217120 | ||||||||
\(356\) | 13.7906 | 0.730899 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.418318 | 0.0221088 | ||||||||
\(359\) | −8.32739 | −0.439503 | −0.219751 | − | 0.975556i | \(-0.570525\pi\) | ||||
−0.219751 | + | 0.975556i | \(0.570525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.79935 | −0.147334 | ||||||||
\(362\) | −3.84683 | −0.202185 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.00821 | −0.262502 | ||||||||
\(365\) | 15.6659 | 0.819992 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.8316 | −0.722004 | −0.361002 | − | 0.932565i | \(-0.617565\pi\) | ||||
−0.361002 | + | 0.932565i | \(0.617565\pi\) | |||||||
\(368\) | −0.290419 | −0.0151392 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.3768 | −0.539464 | ||||||||
\(371\) | −3.95293 | −0.205226 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7740 | 0.661411 | 0.330705 | − | 0.943734i | \(-0.392713\pi\) | ||||
0.330705 | + | 0.943734i | \(0.392713\pi\) | |||||||
\(374\) | −27.1113 | −1.40189 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.5033 | −0.541666 | ||||||||
\(377\) | 48.0937 | 2.47695 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.95926 | 0.100640 | 0.0503202 | − | 0.998733i | \(-0.483976\pi\) | ||||
0.0503202 | + | 0.998733i | \(0.483976\pi\) | |||||||
\(380\) | −6.13771 | −0.314858 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.5869 | −0.644003 | ||||||||
\(383\) | 19.1951 | 0.980824 | 0.490412 | − | 0.871491i | \(-0.336846\pi\) | ||||
0.490412 | + | 0.871491i | \(0.336846\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.97365 | 0.355410 | ||||||||
\(386\) | −2.54364 | −0.129468 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.46450 | 0.125116 | ||||||||
\(389\) | −8.18936 | −0.415217 | −0.207609 | − | 0.978212i | \(-0.566568\pi\) | ||||
−0.207609 | + | 0.978212i | \(0.566568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.56370 | 0.0790796 | ||||||||
\(392\) | 6.17512 | 0.311890 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.2791 | 0.719371 | ||||||||
\(395\) | −16.1170 | −0.810936 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7832 | 0.591381 | 0.295690 | − | 0.955284i | \(-0.404450\pi\) | ||||
0.295690 | + | 0.955284i | \(0.404450\pi\) | |||||||
\(398\) | −4.63234 | −0.232198 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.67470 | −0.133735 | ||||||||
\(401\) | 12.9957 | 0.648976 | 0.324488 | − | 0.945890i | \(-0.394808\pi\) | ||||
0.324488 | + | 0.945890i | \(0.394808\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −56.4878 | −2.81386 | ||||||||
\(404\) | 14.6472 | 0.728726 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.92133 | 0.393129 | ||||||||
\(407\) | 34.2647 | 1.69844 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.1795 | −1.49228 | −0.746140 | − | 0.665789i | \(-0.768095\pi\) | ||||
−0.746140 | + | 0.665789i | \(0.768095\pi\) | |||||||
\(410\) | 9.38182 | 0.463335 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.320702 | 0.0157998 | ||||||||
\(413\) | 9.15347 | 0.450413 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.6013 | −0.864016 | ||||||||
\(416\) | 5.51425 | 0.270358 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.2670 | 0.991292 | ||||||||
\(419\) | −6.69506 | −0.327075 | −0.163538 | − | 0.986537i | \(-0.552291\pi\) | ||||
−0.163538 | + | 0.986537i | \(0.552291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.6958 | 0.570017 | 0.285009 | − | 0.958525i | \(-0.408004\pi\) | ||||
0.285009 | + | 0.958525i | \(0.408004\pi\) | |||||||
\(422\) | −18.4454 | −0.897906 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.35234 | 0.211368 | ||||||||
\(425\) | 14.4013 | 0.698565 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.946229 | −0.0457913 | ||||||||
\(428\) | −13.9377 | −0.673705 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.7309 | −0.517490 | ||||||||
\(431\) | −33.6223 | −1.61953 | −0.809764 | − | 0.586755i | \(-0.800405\pi\) | ||||
−0.809764 | + | 0.586755i | \(0.800405\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.58333 | −0.124147 | −0.0620735 | − | 0.998072i | \(-0.519771\pi\) | ||||
−0.0620735 | + | 0.998072i | \(0.519771\pi\) | |||||||
\(434\) | −9.30389 | −0.446601 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.707255 | −0.0338714 | ||||||||
\(437\) | −1.16894 | −0.0559179 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.5324 | 1.50496 | 0.752479 | − | 0.658616i | \(-0.228858\pi\) | ||||
0.752479 | + | 0.658616i | \(0.228858\pi\) | |||||||
\(440\) | −7.67827 | −0.366047 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −29.6902 | −1.41222 | ||||||||
\(443\) | −9.94030 | −0.472278 | −0.236139 | − | 0.971719i | \(-0.575882\pi\) | ||||
−0.236139 | + | 0.971719i | \(0.575882\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.0292 | −0.996878 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.908231 | 0.0429099 | ||||||||
\(449\) | −8.86967 | −0.418586 | −0.209293 | − | 0.977853i | \(-0.567116\pi\) | ||||
−0.209293 | + | 0.977853i | \(0.567116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.9793 | −1.45876 | ||||||||
\(452\) | −10.8700 | −0.511280 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.1870 | −1.13515 | ||||||||
\(455\) | 7.63700 | 0.358028 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3932 | −0.673287 | −0.336643 | − | 0.941632i | \(-0.609292\pi\) | ||||
−0.336643 | + | 0.941632i | \(0.609292\pi\) | |||||||
\(458\) | 4.01632 | 0.187670 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.442859 | 0.0206484 | ||||||||
\(461\) | −8.86502 | −0.412885 | −0.206443 | − | 0.978459i | \(-0.566189\pi\) | ||||
−0.206443 | + | 0.978459i | \(0.566189\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4206 | 1.27434 | 0.637172 | − | 0.770722i | \(-0.280104\pi\) | ||||
0.637172 | + | 0.770722i | \(0.280104\pi\) | |||||||
\(464\) | −8.72171 | −0.404895 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.4607 | −1.22577 | ||||||||
\(467\) | 3.28901 | 0.152197 | 0.0760987 | − | 0.997100i | \(-0.475754\pi\) | ||||
0.0760987 | + | 0.997100i | \(0.475754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.9406 | 0.643716 | ||||||||
\(470\) | 16.0164 | 0.738782 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.0783 | −0.463894 | ||||||||
\(473\) | 35.4340 | 1.62926 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.7657 | −0.493962 | ||||||||
\(476\) | −4.89017 | −0.224140 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.41114 | −0.201761 | ||||||||
\(479\) | 22.5687 | 1.03119 | 0.515595 | − | 0.856832i | \(-0.327571\pi\) | ||||
0.515595 | + | 0.856832i | \(0.327571\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.5241 | 1.71095 | ||||||||
\(482\) | 13.9584 | 0.635788 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.3541 | 0.652457 | ||||||||
\(485\) | −3.75811 | −0.170647 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.2461 | −1.59715 | −0.798576 | − | 0.601894i | \(-0.794413\pi\) | ||||
−0.798576 | + | 0.601894i | \(0.794413\pi\) | |||||||
\(488\) | 1.04184 | 0.0471618 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.41640 | −0.425390 | ||||||||
\(491\) | 42.7367 | 1.92868 | 0.964340 | − | 0.264667i | \(-0.0852620\pi\) | ||||
0.964340 | + | 0.264667i | \(0.0852620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.9601 | 2.11498 | ||||||||
\(494\) | 22.1949 | 0.998594 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.2440 | 0.459968 | ||||||||
\(497\) | 2.43652 | 0.109293 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.9919 | 0.492067 | 0.246034 | − | 0.969261i | \(-0.420873\pi\) | ||||
0.246034 | + | 0.969261i | \(0.420873\pi\) | |||||||
\(500\) | 11.7031 | 0.523379 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.55760 | −0.337312 | ||||||||
\(503\) | 14.2266 | 0.634333 | 0.317166 | − | 0.948370i | \(-0.397269\pi\) | ||||
0.317166 | + | 0.948370i | \(0.397269\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.3355 | −0.993915 | ||||||||
\(506\) | −1.46234 | −0.0650091 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.08270 | −0.402979 | ||||||||
\(509\) | −15.3802 | −0.681716 | −0.340858 | − | 0.940115i | \(-0.610718\pi\) | ||||
−0.340858 | + | 0.940115i | \(0.610718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.33066 | −0.412764 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.1502 | 0.624137 | ||||||||
\(515\) | −0.489036 | −0.0215495 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −52.8870 | −2.32597 | ||||||||
\(518\) | 6.18045 | 0.271553 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.40865 | −0.368744 | ||||||||
\(521\) | 9.90684 | 0.434027 | 0.217013 | − | 0.976169i | \(-0.430368\pi\) | ||||
0.217013 | + | 0.976169i | \(0.430368\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.2497 | −1.14782 | −0.573910 | − | 0.818919i | \(-0.694574\pi\) | ||||
−0.573910 | + | 0.818919i | \(0.694574\pi\) | |||||||
\(524\) | −13.8183 | −0.603657 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.88918 | 0.300383 | ||||||||
\(527\) | −55.1564 | −2.40265 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9157 | −0.996333 | ||||||||
\(530\) | −6.63687 | −0.288287 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.65563 | 0.158492 | ||||||||
\(533\) | −33.9261 | −1.46950 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.2536 | 0.918872 | ||||||||
\(536\) | −15.3492 | −0.662983 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.5832 | 0.542498 | ||||||||
\(539\) | 31.0934 | 1.33929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.3950 | −1.22080 | −0.610398 | − | 0.792094i | \(-0.708991\pi\) | ||||
−0.610398 | + | 0.792094i | \(0.708991\pi\) | |||||||
\(542\) | −22.8747 | −0.982552 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.38428 | 0.230849 | ||||||||
\(545\) | 1.07849 | 0.0461974 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.1196 | 0.903009 | 0.451504 | − | 0.892269i | \(-0.350887\pi\) | ||||
0.451504 | + | 0.892269i | \(0.350887\pi\) | |||||||
\(548\) | 13.2046 | 0.564073 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −13.4678 | −0.574271 | ||||||||
\(551\) | −35.1049 | −1.49552 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.59934 | 0.408206 | ||||||||
\(554\) | −9.30561 | −0.395357 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.84073 | −0.332521 | ||||||||
\(557\) | 30.5016 | 1.29239 | 0.646197 | − | 0.763170i | \(-0.276358\pi\) | ||||
0.646197 | + | 0.763170i | \(0.276358\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.8045 | 1.64126 | ||||||||
\(560\) | −1.38496 | −0.0585251 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.0277078 | 0.00116878 | ||||||||
\(563\) | −15.5201 | −0.654094 | −0.327047 | − | 0.945008i | \(-0.606053\pi\) | ||||
−0.327047 | + | 0.945008i | \(0.606053\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.5756 | 0.697339 | ||||||||
\(566\) | −20.3178 | −0.854021 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.68271 | −0.112564 | ||||||||
\(569\) | 16.3185 | 0.684106 | 0.342053 | − | 0.939681i | \(-0.388878\pi\) | ||||
0.342053 | + | 0.939681i | \(0.388878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.45287 | 0.228195 | 0.114098 | − | 0.993470i | \(-0.463602\pi\) | ||||
0.114098 | + | 0.993470i | \(0.463602\pi\) | |||||||
\(572\) | 27.7658 | 1.16095 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.58784 | −0.233232 | ||||||||
\(575\) | 0.776783 | 0.0323941 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.9033 | 1.41141 | 0.705707 | − | 0.708503i | \(-0.250629\pi\) | ||||
0.705707 | + | 0.708503i | \(0.250629\pi\) | |||||||
\(578\) | −11.9904 | −0.498736 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.2997 | 0.552240 | ||||||||
\(581\) | 10.4834 | 0.434925 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.9153 | 0.907638 | ||||||||
\(584\) | 10.2734 | 0.425118 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.635336 | 0.0262455 | ||||||||
\(587\) | −9.34004 | −0.385505 | −0.192752 | − | 0.981247i | \(-0.561741\pi\) | ||||
−0.192752 | + | 0.981247i | \(0.561741\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.2320 | 1.69894 | ||||||||
\(590\) | 15.3684 | 0.632708 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.80493 | −0.279681 | ||||||||
\(593\) | −28.4943 | −1.17012 | −0.585061 | − | 0.810989i | \(-0.698929\pi\) | ||||
−0.585061 | + | 0.810989i | \(0.698929\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.45699 | 0.305707 | ||||||||
\(596\) | −18.2537 | −0.747701 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.60145 | −0.0654880 | ||||||||
\(599\) | 3.57992 | 0.146271 | 0.0731357 | − | 0.997322i | \(-0.476699\pi\) | ||||
0.0731357 | + | 0.997322i | \(0.476699\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.3665 | −0.667603 | −0.333802 | − | 0.942643i | \(-0.608332\pi\) | ||||
−0.333802 | + | 0.942643i | \(0.608332\pi\) | |||||||
\(602\) | 6.39134 | 0.260492 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.78861 | −0.316914 | ||||||||
\(605\) | −21.8884 | −0.889891 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.6254 | 0.512448 | 0.256224 | − | 0.966617i | \(-0.417521\pi\) | ||||
0.256224 | + | 0.966617i | \(0.417521\pi\) | |||||||
\(608\) | −4.02500 | −0.163235 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.58869 | −0.0643243 | ||||||||
\(611\) | −57.9178 | −2.34310 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.72129 | 0.190691 | 0.0953456 | − | 0.995444i | \(-0.469604\pi\) | ||||
0.0953456 | + | 0.995444i | \(0.469604\pi\) | |||||||
\(614\) | 13.1386 | 0.530231 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.57320 | 0.184259 | ||||||||
\(617\) | 29.6369 | 1.19314 | 0.596569 | − | 0.802562i | \(-0.296530\pi\) | ||||
0.596569 | + | 0.802562i | \(0.296530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0913 | 1.00850 | 0.504252 | − | 0.863556i | \(-0.331768\pi\) | ||||
0.504252 | + | 0.863556i | \(0.331768\pi\) | |||||||
\(620\) | −15.6210 | −0.627354 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.8305 | −0.554551 | ||||||||
\(623\) | 12.5250 | 0.501804 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.47253 | −0.178901 | ||||||||
\(626\) | −24.5707 | −0.982042 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.14015 | 0.364732 | ||||||||
\(629\) | 36.6396 | 1.46092 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.69600 | 0.147135 | 0.0735676 | − | 0.997290i | \(-0.476562\pi\) | ||||
0.0735676 | + | 0.997290i | \(0.476562\pi\) | |||||||
\(632\) | −10.5693 | −0.420423 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.9969 | −0.873608 | ||||||||
\(635\) | 13.8502 | 0.549627 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.0511 | 1.34916 | ||||||||
\(638\) | −43.9163 | −1.73866 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.52490 | 0.0602768 | ||||||||
\(641\) | −21.2458 | −0.839160 | −0.419580 | − | 0.907718i | \(-0.637823\pi\) | ||||
−0.419580 | + | 0.907718i | \(0.637823\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.22312 | 0.205980 | 0.102990 | − | 0.994682i | \(-0.467159\pi\) | ||||
0.102990 | + | 0.994682i | \(0.467159\pi\) | |||||||
\(644\) | −0.263768 | −0.0103939 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.6717 | 0.852663 | ||||||||
\(647\) | −2.07581 | −0.0816084 | −0.0408042 | − | 0.999167i | \(-0.512992\pi\) | ||||
−0.0408042 | + | 0.999167i | \(0.512992\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −50.7473 | −1.99201 | ||||||||
\(650\) | −14.7489 | −0.578501 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.5330 | −0.804134 | ||||||||
\(653\) | −9.83876 | −0.385020 | −0.192510 | − | 0.981295i | \(-0.561663\pi\) | ||||
−0.192510 | + | 0.981295i | \(0.561663\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.0715 | 0.823332 | ||||||||
\(656\) | 6.15244 | 0.240212 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.53941 | −0.371885 | ||||||||
\(659\) | 16.2116 | 0.631515 | 0.315758 | − | 0.948840i | \(-0.397741\pi\) | ||||
0.315758 | + | 0.948840i | \(0.397741\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.9954 | 1.63343 | 0.816715 | − | 0.577041i | \(-0.195793\pi\) | ||||
0.816715 | + | 0.577041i | \(0.195793\pi\) | |||||||
\(662\) | −19.2357 | −0.747617 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.5427 | −0.447942 | ||||||||
\(665\) | −5.57445 | −0.216168 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.53296 | 0.0980764 | ||||||||
\(668\) | 2.99767 | 0.115983 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.4059 | 0.904247 | ||||||||
\(671\) | 5.24595 | 0.202518 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.5836 | 1.33310 | 0.666550 | − | 0.745460i | \(-0.267770\pi\) | ||||
0.666550 | + | 0.745460i | \(0.267770\pi\) | |||||||
\(674\) | 18.5164 | 0.713225 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.4070 | 0.669498 | ||||||||
\(677\) | −23.8982 | −0.918481 | −0.459241 | − | 0.888312i | \(-0.651878\pi\) | ||||
−0.459241 | + | 0.888312i | \(0.651878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.23834 | 0.0858996 | ||||||||
\(680\) | −8.21046 | −0.314857 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 51.5813 | 1.97515 | ||||||||
\(683\) | −5.70608 | −0.218337 | −0.109169 | − | 0.994023i | \(-0.534819\pi\) | ||||
−0.109169 | + | 0.994023i | \(0.534819\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.1356 | −0.769343 | ||||||||
\(686\) | 11.9660 | 0.456866 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.03714 | −0.268288 | ||||||||
\(689\) | 23.9999 | 0.914324 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.9937 | 1.36926 | 0.684632 | − | 0.728889i | \(-0.259963\pi\) | ||||
0.684632 | + | 0.728889i | \(0.259963\pi\) | |||||||
\(692\) | −8.96255 | −0.340705 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.3571 | 0.469068 | ||||||||
\(695\) | 11.9563 | 0.453528 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.1264 | −1.25475 | ||||||||
\(698\) | 1.72893 | 0.0654410 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.42924 | −0.0918167 | ||||||||
\(701\) | 0.382733 | 0.0144556 | 0.00722780 | − | 0.999974i | \(-0.497699\pi\) | ||||
0.00722780 | + | 0.999974i | \(0.497699\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.3899 | −1.03303 | ||||||||
\(704\) | −5.03528 | −0.189774 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.0336 | −1.16797 | ||||||||
\(707\) | 13.3030 | 0.500313 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.6028 | −0.961533 | −0.480766 | − | 0.876849i | \(-0.659641\pi\) | ||||
−0.480766 | + | 0.876849i | \(0.659641\pi\) | |||||||
\(710\) | 4.09086 | 0.153527 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.7906 | −0.516823 | ||||||||
\(713\) | −2.97505 | −0.111416 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.3399 | −1.58342 | ||||||||
\(716\) | −0.418318 | −0.0156333 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.32739 | 0.310776 | ||||||||
\(719\) | 14.7259 | 0.549183 | 0.274592 | − | 0.961561i | \(-0.411457\pi\) | ||||
0.274592 | + | 0.961561i | \(0.411457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.291271 | 0.0108475 | ||||||||
\(722\) | 2.79935 | 0.104181 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.84683 | 0.142966 | ||||||||
\(725\) | 23.3279 | 0.866377 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.91099 | −0.256314 | −0.128157 | − | 0.991754i | \(-0.540906\pi\) | ||||
−0.128157 | + | 0.991754i | \(0.540906\pi\) | |||||||
\(728\) | 5.00821 | 0.185617 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.6659 | −0.579822 | ||||||||
\(731\) | 37.8899 | 1.40141 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.5110 | −0.609847 | −0.304923 | − | 0.952377i | \(-0.598631\pi\) | ||||
−0.304923 | + | 0.952377i | \(0.598631\pi\) | |||||||
\(734\) | 13.8316 | 0.510534 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.290419 | 0.0107050 | ||||||||
\(737\) | −77.2873 | −2.84691 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.8814 | 0.694565 | 0.347283 | − | 0.937761i | \(-0.387104\pi\) | ||||
0.347283 | + | 0.937761i | \(0.387104\pi\) | |||||||
\(740\) | 10.3768 | 0.381459 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.95293 | 0.145117 | ||||||||
\(743\) | −31.2072 | −1.14488 | −0.572440 | − | 0.819947i | \(-0.694003\pi\) | ||||
−0.572440 | + | 0.819947i | \(0.694003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.8350 | 1.01979 | ||||||||
\(746\) | −12.7740 | −0.467688 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27.1113 | 0.991289 | ||||||||
\(749\) | −12.6587 | −0.462538 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.5905 | −1.40819 | −0.704093 | − | 0.710108i | \(-0.748646\pi\) | ||||
−0.704093 | + | 0.710108i | \(0.748646\pi\) | |||||||
\(752\) | 10.5033 | 0.383016 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −48.0937 | −1.75147 | ||||||||
\(755\) | 11.8768 | 0.432242 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.2037 | −0.807009 | −0.403504 | − | 0.914978i | \(-0.632208\pi\) | ||||
−0.403504 | + | 0.914978i | \(0.632208\pi\) | |||||||
\(758\) | −1.95926 | −0.0711635 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.13771 | 0.222638 | ||||||||
\(761\) | 27.3025 | 0.989713 | 0.494857 | − | 0.868975i | \(-0.335221\pi\) | ||||
0.494857 | + | 0.868975i | \(0.335221\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.642351 | −0.0232547 | ||||||||
\(764\) | 12.5869 | 0.455379 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.1951 | −0.693548 | ||||||||
\(767\) | −55.5745 | −2.00668 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.7062 | −0.890927 | −0.445464 | − | 0.895300i | \(-0.646961\pi\) | ||||
−0.445464 | + | 0.895300i | \(0.646961\pi\) | |||||||
\(770\) | −6.97365 | −0.251313 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.54364 | 0.0915478 | ||||||||
\(773\) | 36.8687 | 1.32607 | 0.663037 | − | 0.748587i | \(-0.269267\pi\) | ||||
0.663037 | + | 0.748587i | \(0.269267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.3995 | −0.984219 | ||||||||
\(776\) | −2.46450 | −0.0884705 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.18936 | 0.293603 | ||||||||
\(779\) | 24.7636 | 0.887248 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.5082 | −0.483362 | ||||||||
\(782\) | −1.56370 | −0.0559177 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.17512 | −0.220540 | ||||||||
\(785\) | −13.9378 | −0.497461 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.7605 | −0.704387 | −0.352193 | − | 0.935927i | \(-0.614564\pi\) | ||||
−0.352193 | + | 0.935927i | \(0.614564\pi\) | |||||||
\(788\) | −14.2791 | −0.508672 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.1170 | 0.573418 | ||||||||
\(791\) | −9.87244 | −0.351023 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.74496 | 0.204009 | ||||||||
\(794\) | −11.7832 | −0.418169 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.63234 | 0.164189 | ||||||||
\(797\) | −31.6917 | −1.12258 | −0.561289 | − | 0.827620i | \(-0.689694\pi\) | ||||
−0.561289 | + | 0.827620i | \(0.689694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −56.5526 | −2.00069 | ||||||||
\(800\) | 2.67470 | 0.0945648 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.9957 | −0.458895 | ||||||||
\(803\) | 51.7297 | 1.82550 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.402218 | 0.0141763 | ||||||||
\(806\) | 56.4878 | 1.98970 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.6472 | −0.515287 | ||||||||
\(809\) | −26.4988 | −0.931647 | −0.465823 | − | 0.884878i | \(-0.654242\pi\) | ||||
−0.465823 | + | 0.884878i | \(0.654242\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.9381 | 1.29707 | 0.648536 | − | 0.761184i | \(-0.275382\pi\) | ||||
0.648536 | + | 0.761184i | \(0.275382\pi\) | |||||||
\(812\) | −7.92133 | −0.277984 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −34.2647 | −1.20098 | ||||||||
\(815\) | 31.3106 | 1.09676 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.3245 | −0.990949 | ||||||||
\(818\) | 30.1795 | 1.05520 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.38182 | −0.327628 | ||||||||
\(821\) | −29.6401 | −1.03445 | −0.517223 | − | 0.855851i | \(-0.673034\pi\) | ||||
−0.517223 | + | 0.855851i | \(0.673034\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.64120 | 0.231498 | 0.115749 | − | 0.993279i | \(-0.463073\pi\) | ||||
0.115749 | + | 0.993279i | \(0.463073\pi\) | |||||||
\(824\) | −0.320702 | −0.0111722 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.15347 | −0.318490 | ||||||||
\(827\) | −20.4247 | −0.710235 | −0.355118 | − | 0.934822i | \(-0.615559\pi\) | ||||
−0.355118 | + | 0.934822i | \(0.615559\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5687 | −1.09643 | −0.548214 | − | 0.836338i | \(-0.684692\pi\) | ||||
−0.548214 | + | 0.836338i | \(0.684692\pi\) | |||||||
\(830\) | 17.6013 | 0.610951 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.51425 | −0.191172 | ||||||||
\(833\) | 33.2485 | 1.15199 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.57114 | −0.158191 | ||||||||
\(836\) | −20.2670 | −0.700950 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.69506 | 0.231277 | ||||||||
\(839\) | −8.97841 | −0.309969 | −0.154984 | − | 0.987917i | \(-0.549533\pi\) | ||||
−0.154984 | + | 0.987917i | \(0.549533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.0683 | 1.62305 | ||||||||
\(842\) | −11.6958 | −0.403063 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.4454 | 0.634916 | ||||||||
\(845\) | −26.5438 | −0.913134 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.0368 | 0.447949 | ||||||||
\(848\) | −4.35234 | −0.149460 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −14.4013 | −0.493960 | ||||||||
\(851\) | 1.97628 | 0.0677461 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.1879 | 0.451544 | 0.225772 | − | 0.974180i | \(-0.427510\pi\) | ||||
0.225772 | + | 0.974180i | \(0.427510\pi\) | |||||||
\(854\) | 0.946229 | 0.0323793 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.9377 | 0.476382 | ||||||||
\(857\) | −29.7611 | −1.01662 | −0.508310 | − | 0.861174i | \(-0.669730\pi\) | ||||
−0.508310 | + | 0.861174i | \(0.669730\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.6554 | 1.25067 | 0.625333 | − | 0.780358i | \(-0.284963\pi\) | ||||
0.625333 | + | 0.780358i | \(0.284963\pi\) | |||||||
\(860\) | 10.7309 | 0.365920 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.6223 | 1.14518 | ||||||||
\(863\) | −4.53228 | −0.154280 | −0.0771402 | − | 0.997020i | \(-0.524579\pi\) | ||||
−0.0771402 | + | 0.997020i | \(0.524579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.6669 | 0.464690 | ||||||||
\(866\) | 2.58333 | 0.0877852 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.30389 | 0.315795 | ||||||||
\(869\) | −53.2193 | −1.80534 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −84.6391 | −2.86789 | ||||||||
\(872\) | 0.707255 | 0.0239507 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.16894 | 0.0395400 | ||||||||
\(875\) | 10.6291 | 0.359330 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.4562 | 1.12974 | 0.564868 | − | 0.825182i | \(-0.308927\pi\) | ||||
0.564868 | + | 0.825182i | \(0.308927\pi\) | |||||||
\(878\) | −31.5324 | −1.06417 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.67827 | 0.258835 | ||||||||
\(881\) | −52.4396 | −1.76673 | −0.883367 | − | 0.468682i | \(-0.844729\pi\) | ||||
−0.883367 | + | 0.468682i | \(0.844729\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.7867 | 0.733181 | 0.366591 | − | 0.930382i | \(-0.380525\pi\) | ||||
0.366591 | + | 0.930382i | \(0.380525\pi\) | |||||||
\(884\) | 29.6902 | 0.998591 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.94030 | 0.333951 | ||||||||
\(887\) | 4.88790 | 0.164120 | 0.0820598 | − | 0.996627i | \(-0.473850\pi\) | ||||
0.0820598 | + | 0.996627i | \(0.473850\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.24918 | −0.276669 | ||||||||
\(890\) | 21.0292 | 0.704899 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 42.2758 | 1.41470 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.637891 | 0.0213223 | ||||||||
\(896\) | −0.908231 | −0.0303419 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.86967 | 0.295985 | ||||||||
\(899\) | −89.3450 | −2.97982 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.4342 | 0.780707 | ||||||||
\(902\) | 30.9793 | 1.03150 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.8700 | 0.361530 | ||||||||
\(905\) | −5.86601 | −0.194993 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53.5480 | −1.77803 | −0.889016 | − | 0.457877i | \(-0.848610\pi\) | ||||
−0.889016 | + | 0.457877i | \(0.848610\pi\) | |||||||
\(908\) | 24.1870 | 0.802673 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.63700 | −0.253164 | ||||||||
\(911\) | −1.21606 | −0.0402900 | −0.0201450 | − | 0.999797i | \(-0.506413\pi\) | ||||
−0.0201450 | + | 0.999797i | \(0.506413\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.1205 | −1.92351 | ||||||||
\(914\) | 14.3932 | 0.476086 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.01632 | −0.132703 | ||||||||
\(917\) | −12.5502 | −0.414446 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.768926 | −0.0253645 | −0.0126823 | − | 0.999920i | \(-0.504037\pi\) | ||||
−0.0126823 | + | 0.999920i | \(0.504037\pi\) | |||||||
\(920\) | −0.442859 | −0.0146006 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.86502 | 0.291954 | ||||||||
\(923\) | −14.7932 | −0.486923 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.2011 | 0.598449 | ||||||||
\(926\) | −27.4206 | −0.901097 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.72171 | 0.286304 | ||||||||
\(929\) | 9.48407 | 0.311162 | 0.155581 | − | 0.987823i | \(-0.450275\pi\) | ||||
0.155581 | + | 0.987823i | \(0.450275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.8549 | −0.814585 | ||||||||
\(932\) | 26.4607 | 0.866751 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.28901 | −0.107620 | ||||||||
\(935\) | −41.3419 | −1.35203 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.32884 | 0.272091 | 0.136046 | − | 0.990703i | \(-0.456561\pi\) | ||||
0.136046 | + | 0.990703i | \(0.456561\pi\) | |||||||
\(938\) | −13.9406 | −0.455176 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.0164 | −0.522398 | ||||||||
\(941\) | 15.5635 | 0.507356 | 0.253678 | − | 0.967289i | \(-0.418360\pi\) | ||||
0.253678 | + | 0.967289i | \(0.418360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.78679 | −0.0581858 | ||||||||
\(944\) | 10.0783 | 0.328022 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35.4340 | −1.15206 | ||||||||
\(947\) | 28.0142 | 0.910340 | 0.455170 | − | 0.890405i | \(-0.349578\pi\) | ||||
0.455170 | + | 0.890405i | \(0.349578\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56.6503 | 1.83895 | ||||||||
\(950\) | 10.7657 | 0.349284 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.89017 | 0.158491 | ||||||||
\(953\) | 21.0679 | 0.682458 | 0.341229 | − | 0.939980i | \(-0.389157\pi\) | ||||
0.341229 | + | 0.939980i | \(0.389157\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.1937 | −0.621095 | ||||||||
\(956\) | 4.41114 | 0.142667 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.5687 | −0.729162 | ||||||||
\(959\) | 11.9928 | 0.387269 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9389 | 2.38513 | ||||||||
\(962\) | −37.5241 | −1.20982 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.9584 | −0.449570 | ||||||||
\(965\) | −3.87879 | −0.124863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.1650 | 1.29162 | 0.645810 | − | 0.763498i | \(-0.276520\pi\) | ||||
0.645810 | + | 0.763498i | \(0.276520\pi\) | |||||||
\(968\) | −14.3541 | −0.461357 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.75811 | 0.120666 | ||||||||
\(971\) | −22.7819 | −0.731107 | −0.365553 | − | 0.930790i | \(-0.619120\pi\) | ||||
−0.365553 | + | 0.930790i | \(0.619120\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.12119 | −0.228295 | ||||||||
\(974\) | 35.2461 | 1.12936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.04184 | −0.0333484 | ||||||||
\(977\) | −20.8218 | −0.666148 | −0.333074 | − | 0.942901i | \(-0.608086\pi\) | ||||
−0.333074 | + | 0.942901i | \(0.608086\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −69.4394 | −2.21929 | ||||||||
\(980\) | 9.41640 | 0.300796 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −42.7367 | −1.36378 | ||||||||
\(983\) | −27.2774 | −0.870014 | −0.435007 | − | 0.900427i | \(-0.643254\pi\) | ||||
−0.435007 | + | 0.900427i | \(0.643254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.7741 | 0.693782 | ||||||||
\(986\) | −46.9601 | −1.49551 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.1949 | −0.706113 | ||||||||
\(989\) | 2.04372 | 0.0649866 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.1352 | −0.449020 | −0.224510 | − | 0.974472i | \(-0.572078\pi\) | ||||
−0.224510 | + | 0.974472i | \(0.572078\pi\) | |||||||
\(992\) | −10.2440 | −0.325246 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.43652 | −0.0772818 | ||||||||
\(995\) | −7.06383 | −0.223938 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.9727 | −1.39263 | −0.696314 | − | 0.717737i | \(-0.745178\pi\) | ||||
−0.696314 | + | 0.717737i | \(0.745178\pi\) | |||||||
\(998\) | −10.9919 | −0.347944 | ||||||||
\(999\) | 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 | 4014.2.a.w.1.3 | 7 | ||
3.2 | odd | 2 | 446.2.a.e.1.2 | ✓ | 7 | ||
12.11 | even | 2 | 3568.2.a.l.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
446.2.a.e.1.2 | ✓ | 7 | 3.2 | odd | 2 | ||
3568.2.a.l.1.6 | 7 | 12.11 | even | 2 | |||
4014.2.a.w.1.3 | 7 | 1.1 | even | 1 | trivial |