Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(1,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.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: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 5.65685 | 1.70561 | 0.852803 | − | 0.522233i | \(-0.174901\pi\) | ||||
0.852803 | + | 0.522233i | \(0.174901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.82843 | −0.755929 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.82843 | 1.17107 | 0.585533 | − | 0.810649i | \(-0.300885\pi\) | ||||
0.585533 | + | 0.810649i | \(0.300885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.65685 | −1.20605 | ||||||||
\(23\) | −8.48528 | −1.76930 | −0.884652 | − | 0.466252i | \(-0.845604\pi\) | ||||
−0.884652 | + | 0.466252i | \(0.845604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.82843 | 0.534522 | ||||||||
\(29\) | 3.17157 | 0.588946 | 0.294473 | − | 0.955660i | \(-0.404856\pi\) | ||||
0.294473 | + | 0.955660i | \(0.404856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.82843 | −0.828068 | ||||||||
\(35\) | −2.82843 | −0.478091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.343146 | −0.0564128 | −0.0282064 | − | 0.999602i | \(-0.508980\pi\) | ||||
−0.0282064 | + | 0.999602i | \(0.508980\pi\) | |||||||
\(38\) | 2.82843 | 0.458831 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.65685 | −0.571105 | −0.285552 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285552 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.65685 | −0.252668 | −0.126334 | − | 0.991988i | \(-0.540321\pi\) | ||||
−0.126334 | + | 0.991988i | \(0.540321\pi\) | |||||||
\(44\) | 5.65685 | 0.852803 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.48528 | 1.25109 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 9.31371 | 1.27934 | 0.639668 | − | 0.768651i | \(-0.279072\pi\) | ||||
0.639668 | + | 0.768651i | \(0.279072\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | −2.82843 | −0.377964 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.17157 | −0.416448 | ||||||||
\(59\) | 13.6569 | 1.77797 | 0.888985 | − | 0.457935i | \(-0.151411\pi\) | ||||
0.888985 | + | 0.457935i | \(0.151411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 4.82843 | 0.585533 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.82843 | 0.338062 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.48528 | 0.290880 | 0.145440 | − | 0.989367i | \(-0.453540\pi\) | ||||
0.145440 | + | 0.989367i | \(0.453540\pi\) | |||||||
\(74\) | 0.343146 | 0.0398899 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.82843 | −0.324443 | ||||||||
\(77\) | 16.0000 | 1.82337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6569 | 1.53652 | 0.768258 | − | 0.640140i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640140i | \(0.221124\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.65685 | 0.403832 | ||||||||
\(83\) | −17.6569 | −1.93809 | −0.969046 | − | 0.246881i | \(-0.920594\pi\) | ||||
−0.969046 | + | 0.246881i | \(0.920594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.82843 | −0.523716 | ||||||||
\(86\) | 1.65685 | 0.178663 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.65685 | −0.603023 | ||||||||
\(89\) | 4.34315 | 0.460373 | 0.230186 | − | 0.973147i | \(-0.426066\pi\) | ||||
0.230186 | + | 0.973147i | \(0.426066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | −8.48528 | −0.884652 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 2.82843 | 0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.82843 | −0.896391 | −0.448195 | − | 0.893936i | \(-0.647933\pi\) | ||||
−0.448195 | + | 0.893936i | \(0.647933\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.1421 | 1.20819 | 0.604094 | − | 0.796913i | \(-0.293535\pi\) | ||||
0.604094 | + | 0.796913i | \(0.293535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.65685 | 0.951518 | 0.475759 | − | 0.879576i | \(-0.342173\pi\) | ||||
0.475759 | + | 0.879576i | \(0.342173\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.31371 | −0.904627 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.17157 | 0.303782 | 0.151891 | − | 0.988397i | \(-0.451464\pi\) | ||||
0.151891 | + | 0.988397i | \(0.451464\pi\) | |||||||
\(110\) | 5.65685 | 0.539360 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.82843 | 0.267261 | ||||||||
\(113\) | 10.4853 | 0.986372 | 0.493186 | − | 0.869924i | \(-0.335832\pi\) | ||||
0.493186 | + | 0.869924i | \(0.335832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.48528 | 0.791257 | ||||||||
\(116\) | 3.17157 | 0.294473 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.6569 | −1.25722 | ||||||||
\(119\) | 13.6569 | 1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | −6.00000 | −0.543214 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.00000 | 0.359211 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.65685 | −0.147022 | −0.0735110 | − | 0.997294i | \(-0.523420\pi\) | ||||
−0.0735110 | + | 0.997294i | \(0.523420\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.00000 | −0.0877058 | ||||||||
\(131\) | −22.1421 | −1.93457 | −0.967284 | − | 0.253697i | \(-0.918353\pi\) | ||||
−0.967284 | + | 0.253697i | \(0.918353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 5.65685 | 0.488678 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.82843 | −0.414034 | ||||||||
\(137\) | −5.31371 | −0.453981 | −0.226990 | − | 0.973897i | \(-0.572889\pi\) | ||||
−0.226990 | + | 0.973897i | \(0.572889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6569 | 1.49763 | 0.748817 | − | 0.662776i | \(-0.230622\pi\) | ||||
0.748817 | + | 0.662776i | \(0.230622\pi\) | |||||||
\(140\) | −2.82843 | −0.239046 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.65685 | 0.474713 | ||||||||
\(143\) | −5.65685 | −0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.17157 | −0.263385 | ||||||||
\(146\) | −2.48528 | −0.205683 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.343146 | −0.0282064 | ||||||||
\(149\) | 7.65685 | 0.627274 | 0.313637 | − | 0.949543i | \(-0.398453\pi\) | ||||
0.313637 | + | 0.949543i | \(0.398453\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 2.82843 | 0.229416 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.0000 | −1.28932 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3137 | −1.38178 | −0.690892 | − | 0.722958i | \(-0.742782\pi\) | ||||
−0.690892 | + | 0.722958i | \(0.742782\pi\) | |||||||
\(158\) | −13.6569 | −1.08648 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −24.0000 | −1.89146 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3137 | −0.886158 | −0.443079 | − | 0.896483i | \(-0.646114\pi\) | ||||
−0.443079 | + | 0.896483i | \(0.646114\pi\) | |||||||
\(164\) | −3.65685 | −0.285552 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.6569 | 1.37044 | ||||||||
\(167\) | 24.9706 | 1.93228 | 0.966140 | − | 0.258018i | \(-0.0830694\pi\) | ||||
0.966140 | + | 0.258018i | \(0.0830694\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.82843 | 0.370323 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.65685 | −0.126334 | ||||||||
\(173\) | −13.3137 | −1.01222 | −0.506111 | − | 0.862468i | \(-0.668917\pi\) | ||||
−0.506111 | + | 0.862468i | \(0.668917\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.82843 | 0.213809 | ||||||||
\(176\) | 5.65685 | 0.426401 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.34315 | −0.325533 | ||||||||
\(179\) | −24.4853 | −1.83012 | −0.915058 | − | 0.403322i | \(-0.867855\pi\) | ||||
−0.915058 | + | 0.403322i | \(0.867855\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.65685 | 0.271812 | 0.135906 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135906 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(182\) | 2.82843 | 0.209657 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.48528 | 0.625543 | ||||||||
\(185\) | 0.343146 | 0.0252286 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.3137 | 1.99738 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.82843 | −0.205196 | ||||||||
\(191\) | 11.3137 | 0.818631 | 0.409316 | − | 0.912393i | \(-0.365768\pi\) | ||||
0.409316 | + | 0.912393i | \(0.365768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.4853 | −1.04267 | −0.521337 | − | 0.853351i | \(-0.674566\pi\) | ||||
−0.521337 | + | 0.853351i | \(0.674566\pi\) | |||||||
\(194\) | 8.82843 | 0.633844 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −9.31371 | −0.663574 | −0.331787 | − | 0.943354i | \(-0.607652\pi\) | ||||
−0.331787 | + | 0.943354i | \(0.607652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6569 | 1.53521 | 0.767607 | − | 0.640921i | \(-0.221447\pi\) | ||||
0.767607 | + | 0.640921i | \(0.221447\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.1421 | −0.854318 | ||||||||
\(203\) | 8.97056 | 0.629610 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.65685 | 0.255406 | ||||||||
\(206\) | −9.65685 | −0.672825 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3137 | 1.60498 | 0.802491 | − | 0.596664i | \(-0.203508\pi\) | ||||
0.802491 | + | 0.596664i | \(0.203508\pi\) | |||||||
\(212\) | 9.31371 | 0.639668 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | 1.65685 | 0.112997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3137 | 0.768025 | ||||||||
\(218\) | −3.17157 | −0.214806 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.65685 | −0.381385 | ||||||||
\(221\) | −4.82843 | −0.324795 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.17157 | 0.346314 | 0.173157 | − | 0.984894i | \(-0.444603\pi\) | ||||
0.173157 | + | 0.984894i | \(0.444603\pi\) | |||||||
\(224\) | −2.82843 | −0.188982 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.4853 | −0.697471 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.1421 | −1.59536 | −0.797679 | − | 0.603083i | \(-0.793939\pi\) | ||||
−0.797679 | + | 0.603083i | \(0.793939\pi\) | |||||||
\(230\) | −8.48528 | −0.559503 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.17157 | −0.208224 | ||||||||
\(233\) | −22.4853 | −1.47306 | −0.736530 | − | 0.676405i | \(-0.763537\pi\) | ||||
−0.736530 | + | 0.676405i | \(0.763537\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 13.6569 | 0.888985 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13.6569 | −0.885242 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.3137 | −1.11527 | −0.557637 | − | 0.830085i | \(-0.688292\pi\) | ||||
−0.557637 | + | 0.830085i | \(0.688292\pi\) | |||||||
\(242\) | −21.0000 | −1.34993 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.82843 | 0.179969 | ||||||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −5.17157 | −0.326427 | −0.163213 | − | 0.986591i | \(-0.552186\pi\) | ||||
−0.163213 | + | 0.986591i | \(0.552186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −48.0000 | −3.01773 | ||||||||
\(254\) | 1.65685 | 0.103960 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.828427 | −0.0516759 | −0.0258379 | − | 0.999666i | \(-0.508225\pi\) | ||||
−0.0258379 | + | 0.999666i | \(0.508225\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.970563 | −0.0603078 | ||||||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.1421 | 1.36795 | ||||||||
\(263\) | 0.485281 | 0.0299237 | 0.0149619 | − | 0.999888i | \(-0.495237\pi\) | ||||
0.0149619 | + | 0.999888i | \(0.495237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.31371 | −0.572137 | ||||||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.65685 | −0.345547 | ||||||||
\(269\) | −2.48528 | −0.151530 | −0.0757651 | − | 0.997126i | \(-0.524140\pi\) | ||||
−0.0757651 | + | 0.997126i | \(0.524140\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3137 | −0.930242 | −0.465121 | − | 0.885247i | \(-0.653989\pi\) | ||||
−0.465121 | + | 0.885247i | \(0.653989\pi\) | |||||||
\(272\) | 4.82843 | 0.292766 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.31371 | 0.321013 | ||||||||
\(275\) | 5.65685 | 0.341121 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0000 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | −17.6569 | −1.05899 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.82843 | 0.169031 | ||||||||
\(281\) | −19.6569 | −1.17263 | −0.586315 | − | 0.810083i | \(-0.699422\pi\) | ||||
−0.586315 | + | 0.810083i | \(0.699422\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.34315 | −0.377061 | −0.188530 | − | 0.982067i | \(-0.560372\pi\) | ||||
−0.188530 | + | 0.982067i | \(0.560372\pi\) | |||||||
\(284\) | −5.65685 | −0.335673 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.65685 | 0.334497 | ||||||||
\(287\) | −10.3431 | −0.610537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.31371 | 0.371395 | ||||||||
\(290\) | 3.17157 | 0.186241 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.48528 | 0.145440 | ||||||||
\(293\) | −28.6274 | −1.67243 | −0.836216 | − | 0.548401i | \(-0.815237\pi\) | ||||
−0.836216 | + | 0.548401i | \(0.815237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.6569 | −0.795133 | ||||||||
\(296\) | 0.343146 | 0.0199449 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.65685 | −0.443550 | ||||||||
\(299\) | 8.48528 | 0.490716 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.68629 | −0.270113 | ||||||||
\(302\) | −12.0000 | −0.690522 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.82843 | −0.162221 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3431 | −0.590315 | −0.295157 | − | 0.955449i | \(-0.595372\pi\) | ||||
−0.295157 | + | 0.955449i | \(0.595372\pi\) | |||||||
\(308\) | 16.0000 | 0.911685 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.00000 | 0.227185 | ||||||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.97056 | 0.167906 | 0.0839531 | − | 0.996470i | \(-0.473245\pi\) | ||||
0.0839531 | + | 0.996470i | \(0.473245\pi\) | |||||||
\(314\) | 17.3137 | 0.977069 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.6569 | 0.768258 | ||||||||
\(317\) | −2.68629 | −0.150877 | −0.0754386 | − | 0.997150i | \(-0.524036\pi\) | ||||
−0.0754386 | + | 0.997150i | \(0.524036\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.9411 | 1.00451 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.0000 | 1.33747 | ||||||||
\(323\) | −13.6569 | −0.759888 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 11.3137 | 0.626608 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.65685 | 0.201916 | ||||||||
\(329\) | 22.6274 | 1.24749 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.48528 | 0.466393 | 0.233197 | − | 0.972430i | \(-0.425081\pi\) | ||||
0.233197 | + | 0.972430i | \(0.425081\pi\) | |||||||
\(332\) | −17.6569 | −0.969046 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.9706 | −1.36633 | ||||||||
\(335\) | 5.65685 | 0.309067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.9706 | −1.25129 | −0.625643 | − | 0.780109i | \(-0.715163\pi\) | ||||
−0.625643 | + | 0.780109i | \(0.715163\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.82843 | −0.261858 | ||||||||
\(341\) | 22.6274 | 1.22534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 1.65685 | 0.0893316 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.3137 | 0.715749 | ||||||||
\(347\) | −1.65685 | −0.0889446 | −0.0444723 | − | 0.999011i | \(-0.514161\pi\) | ||||
−0.0444723 | + | 0.999011i | \(0.514161\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1421 | −0.864069 | −0.432034 | − | 0.901857i | \(-0.642204\pi\) | ||||
−0.432034 | + | 0.901857i | \(0.642204\pi\) | |||||||
\(350\) | −2.82843 | −0.151186 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.65685 | −0.301511 | ||||||||
\(353\) | 17.3137 | 0.921516 | 0.460758 | − | 0.887526i | \(-0.347578\pi\) | ||||
0.460758 | + | 0.887526i | \(0.347578\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.65685 | 0.300235 | ||||||||
\(356\) | 4.34315 | 0.230186 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.4853 | 1.29409 | ||||||||
\(359\) | −28.2843 | −1.49279 | −0.746393 | − | 0.665505i | \(-0.768216\pi\) | ||||
−0.746393 | + | 0.665505i | \(0.768216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −3.65685 | −0.192200 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.82843 | −0.148250 | ||||||||
\(365\) | −2.48528 | −0.130086 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.3431 | 0.748706 | 0.374353 | − | 0.927286i | \(-0.377865\pi\) | ||||
0.374353 | + | 0.927286i | \(0.377865\pi\) | |||||||
\(368\) | −8.48528 | −0.442326 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.343146 | −0.0178393 | ||||||||
\(371\) | 26.3431 | 1.36767 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.3137 | −1.31069 | −0.655347 | − | 0.755328i | \(-0.727478\pi\) | ||||
−0.655347 | + | 0.755328i | \(0.727478\pi\) | |||||||
\(374\) | −27.3137 | −1.41236 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | −3.17157 | −0.163344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.4853 | −1.25772 | −0.628862 | − | 0.777517i | \(-0.716479\pi\) | ||||
−0.628862 | + | 0.777517i | \(0.716479\pi\) | |||||||
\(380\) | 2.82843 | 0.145095 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.3137 | −0.578860 | ||||||||
\(383\) | 18.3431 | 0.937291 | 0.468645 | − | 0.883386i | \(-0.344742\pi\) | ||||
0.468645 | + | 0.883386i | \(0.344742\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0000 | −0.815436 | ||||||||
\(386\) | 14.4853 | 0.737281 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.82843 | −0.448195 | ||||||||
\(389\) | −10.4853 | −0.531625 | −0.265812 | − | 0.964025i | \(-0.585640\pi\) | ||||
−0.265812 | + | 0.964025i | \(0.585640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.9706 | −2.07197 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.31371 | 0.469218 | ||||||||
\(395\) | −13.6569 | −0.687151 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.2843 | −1.31917 | −0.659585 | − | 0.751630i | \(-0.729268\pi\) | ||||
−0.659585 | + | 0.751630i | \(0.729268\pi\) | |||||||
\(398\) | −21.6569 | −1.08556 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −6.97056 | −0.348093 | −0.174047 | − | 0.984737i | \(-0.555684\pi\) | ||||
−0.174047 | + | 0.984737i | \(0.555684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 12.1421 | 0.604094 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.97056 | −0.445202 | ||||||||
\(407\) | −1.94113 | −0.0962180 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.65685 | 0.378607 | 0.189304 | − | 0.981919i | \(-0.439377\pi\) | ||||
0.189304 | + | 0.981919i | \(0.439377\pi\) | |||||||
\(410\) | −3.65685 | −0.180599 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.65685 | 0.475759 | ||||||||
\(413\) | 38.6274 | 1.90073 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.6569 | 0.866741 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.0000 | 0.782586 | ||||||||
\(419\) | 5.17157 | 0.252648 | 0.126324 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126324 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.14214 | 0.201875 | 0.100938 | − | 0.994893i | \(-0.467816\pi\) | ||||
0.100938 | + | 0.994893i | \(0.467816\pi\) | |||||||
\(422\) | −23.3137 | −1.13489 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.31371 | −0.452314 | ||||||||
\(425\) | 4.82843 | 0.234213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.9706 | 0.821263 | ||||||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.65685 | −0.0799006 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.9706 | 0.527212 | 0.263606 | − | 0.964630i | \(-0.415088\pi\) | ||||
0.263606 | + | 0.964630i | \(0.415088\pi\) | |||||||
\(434\) | −11.3137 | −0.543075 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.17157 | 0.151891 | ||||||||
\(437\) | 24.0000 | 1.14808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.6274 | −1.07995 | −0.539974 | − | 0.841682i | \(-0.681566\pi\) | ||||
−0.539974 | + | 0.841682i | \(0.681566\pi\) | |||||||
\(440\) | 5.65685 | 0.269680 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.82843 | 0.229665 | ||||||||
\(443\) | −41.6569 | −1.97918 | −0.989588 | − | 0.143926i | \(-0.954027\pi\) | ||||
−0.989588 | + | 0.143926i | \(0.954027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.34315 | −0.205885 | ||||||||
\(446\) | −5.17157 | −0.244881 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.82843 | 0.133631 | ||||||||
\(449\) | 30.2843 | 1.42920 | 0.714602 | − | 0.699532i | \(-0.246608\pi\) | ||||
0.714602 | + | 0.699532i | \(0.246608\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.6863 | −0.974079 | ||||||||
\(452\) | 10.4853 | 0.493186 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 2.82843 | 0.132599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1716 | 0.709696 | 0.354848 | − | 0.934924i | \(-0.384533\pi\) | ||||
0.354848 | + | 0.934924i | \(0.384533\pi\) | |||||||
\(458\) | 24.1421 | 1.12809 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.48528 | 0.395628 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7990 | 1.66372 | 0.831860 | − | 0.554985i | \(-0.187276\pi\) | ||||
0.831860 | + | 0.554985i | \(0.187276\pi\) | |||||||
\(464\) | 3.17157 | 0.147237 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.4853 | 1.04161 | ||||||||
\(467\) | 15.3137 | 0.708634 | 0.354317 | − | 0.935125i | \(-0.384713\pi\) | ||||
0.354317 | + | 0.935125i | \(0.384713\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 8.00000 | 0.369012 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.6569 | −0.628608 | ||||||||
\(473\) | −9.37258 | −0.430952 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.82843 | −0.129777 | ||||||||
\(476\) | 13.6569 | 0.625961 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.0000 | 0.731823 | ||||||||
\(479\) | −11.3137 | −0.516937 | −0.258468 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258468 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.343146 | 0.0156461 | ||||||||
\(482\) | 17.3137 | 0.788618 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.0000 | 0.954545 | ||||||||
\(485\) | 8.82843 | 0.400878 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.485281 | −0.0219902 | −0.0109951 | − | 0.999940i | \(-0.503500\pi\) | ||||
−0.0109951 | + | 0.999940i | \(0.503500\pi\) | |||||||
\(488\) | −6.00000 | −0.271607 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 9.85786 | 0.444879 | 0.222440 | − | 0.974946i | \(-0.428598\pi\) | ||||
0.222440 | + | 0.974946i | \(0.428598\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.3137 | 0.689695 | ||||||||
\(494\) | −2.82843 | −0.127257 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.4853 | −0.737983 | −0.368991 | − | 0.929433i | \(-0.620297\pi\) | ||||
−0.368991 | + | 0.929433i | \(0.620297\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.17157 | 0.230819 | ||||||||
\(503\) | 40.4853 | 1.80515 | 0.902575 | − | 0.430533i | \(-0.141674\pi\) | ||||
0.902575 | + | 0.430533i | \(0.141674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.1421 | −0.540318 | ||||||||
\(506\) | 48.0000 | 2.13386 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.65685 | −0.0735110 | ||||||||
\(509\) | 14.6863 | 0.650958 | 0.325479 | − | 0.945549i | \(-0.394474\pi\) | ||||
0.325479 | + | 0.945549i | \(0.394474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.02944 | 0.310964 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.828427 | 0.0365404 | ||||||||
\(515\) | −9.65685 | −0.425532 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.2548 | 1.99031 | ||||||||
\(518\) | 0.970563 | 0.0426441 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.00000 | −0.0438529 | ||||||||
\(521\) | 6.97056 | 0.305386 | 0.152693 | − | 0.988274i | \(-0.451205\pi\) | ||||
0.152693 | + | 0.988274i | \(0.451205\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.6274 | 1.51415 | 0.757076 | − | 0.653327i | \(-0.226627\pi\) | ||||
0.757076 | + | 0.653327i | \(0.226627\pi\) | |||||||
\(524\) | −22.1421 | −0.967284 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.485281 | −0.0211593 | ||||||||
\(527\) | 19.3137 | 0.841318 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.0000 | 2.13043 | ||||||||
\(530\) | 9.31371 | 0.404562 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.00000 | −0.346844 | ||||||||
\(533\) | 3.65685 | 0.158396 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | 5.65685 | 0.244339 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.48528 | 0.107148 | ||||||||
\(539\) | 5.65685 | 0.243658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.48528 | −0.106851 | −0.0534253 | − | 0.998572i | \(-0.517014\pi\) | ||||
−0.0534253 | + | 0.998572i | \(0.517014\pi\) | |||||||
\(542\) | 15.3137 | 0.657780 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.82843 | −0.207017 | ||||||||
\(545\) | −3.17157 | −0.135855 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3137 | 0.996822 | 0.498411 | − | 0.866941i | \(-0.333917\pi\) | ||||
0.498411 | + | 0.866941i | \(0.333917\pi\) | |||||||
\(548\) | −5.31371 | −0.226990 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.65685 | −0.241209 | ||||||||
\(551\) | −8.97056 | −0.382159 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.6274 | 1.64260 | ||||||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.6569 | 0.748817 | ||||||||
\(557\) | −33.3137 | −1.41155 | −0.705774 | − | 0.708437i | \(-0.749400\pi\) | ||||
−0.705774 | + | 0.708437i | \(0.749400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.65685 | 0.0700775 | ||||||||
\(560\) | −2.82843 | −0.119523 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.6569 | 0.829174 | ||||||||
\(563\) | 41.6569 | 1.75563 | 0.877814 | − | 0.479002i | \(-0.159002\pi\) | ||||
0.877814 | + | 0.479002i | \(0.159002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.4853 | −0.441119 | ||||||||
\(566\) | 6.34315 | 0.266622 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.65685 | 0.237356 | ||||||||
\(569\) | −20.3431 | −0.852829 | −0.426415 | − | 0.904528i | \(-0.640224\pi\) | ||||
−0.426415 | + | 0.904528i | \(0.640224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9706 | −0.542801 | −0.271401 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271401 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(572\) | −5.65685 | −0.236525 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.3431 | 0.431715 | ||||||||
\(575\) | −8.48528 | −0.353861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.4558 | 1.14300 | 0.571501 | − | 0.820601i | \(-0.306361\pi\) | ||||
0.571501 | + | 0.820601i | \(0.306361\pi\) | |||||||
\(578\) | −6.31371 | −0.262616 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.17157 | −0.131692 | ||||||||
\(581\) | −49.9411 | −2.07191 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.6863 | 2.18204 | ||||||||
\(584\) | −2.48528 | −0.102842 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.6274 | 1.18259 | ||||||||
\(587\) | 42.6274 | 1.75942 | 0.879711 | − | 0.475509i | \(-0.157736\pi\) | ||||
0.879711 | + | 0.475509i | \(0.157736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.3137 | −0.466173 | ||||||||
\(590\) | 13.6569 | 0.562244 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.343146 | −0.0141032 | ||||||||
\(593\) | 11.6569 | 0.478690 | 0.239345 | − | 0.970935i | \(-0.423067\pi\) | ||||
0.239345 | + | 0.970935i | \(0.423067\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.6569 | −0.559876 | ||||||||
\(596\) | 7.65685 | 0.313637 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.48528 | −0.346989 | ||||||||
\(599\) | −40.0000 | −1.63436 | −0.817178 | − | 0.576386i | \(-0.804463\pi\) | ||||
−0.817178 | + | 0.576386i | \(0.804463\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.68629 | 0.272740 | 0.136370 | − | 0.990658i | \(-0.456456\pi\) | ||||
0.136370 | + | 0.990658i | \(0.456456\pi\) | |||||||
\(602\) | 4.68629 | 0.190999 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.0000 | 0.488273 | ||||||||
\(605\) | −21.0000 | −0.853771 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.97056 | −0.201749 | −0.100874 | − | 0.994899i | \(-0.532164\pi\) | ||||
−0.100874 | + | 0.994899i | \(0.532164\pi\) | |||||||
\(608\) | 2.82843 | 0.114708 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2843 | −1.38473 | −0.692364 | − | 0.721548i | \(-0.743431\pi\) | ||||
−0.692364 | + | 0.721548i | \(0.743431\pi\) | |||||||
\(614\) | 10.3431 | 0.417415 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.0000 | −0.644658 | ||||||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.1716 | −1.17250 | −0.586252 | − | 0.810129i | \(-0.699397\pi\) | ||||
−0.586252 | + | 0.810129i | \(0.699397\pi\) | |||||||
\(620\) | −4.00000 | −0.160644 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.0000 | −0.962312 | ||||||||
\(623\) | 12.2843 | 0.492159 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.97056 | −0.118728 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.3137 | −0.690892 | ||||||||
\(629\) | −1.65685 | −0.0660631 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.3431 | −0.889467 | −0.444733 | − | 0.895663i | \(-0.646702\pi\) | ||||
−0.444733 | + | 0.895663i | \(0.646702\pi\) | |||||||
\(632\) | −13.6569 | −0.543240 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.68629 | 0.106686 | ||||||||
\(635\) | 1.65685 | 0.0657503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | −17.9411 | −0.710296 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −40.6274 | −1.60469 | −0.802343 | − | 0.596863i | \(-0.796414\pi\) | ||||
−0.802343 | + | 0.596863i | \(0.796414\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.5980 | −1.56159 | −0.780796 | − | 0.624786i | \(-0.785186\pi\) | ||||
−0.780796 | + | 0.624786i | \(0.785186\pi\) | |||||||
\(644\) | −24.0000 | −0.945732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.6569 | 0.537322 | ||||||||
\(647\) | 8.48528 | 0.333591 | 0.166795 | − | 0.985992i | \(-0.446658\pi\) | ||||
0.166795 | + | 0.985992i | \(0.446658\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 77.2548 | 3.03252 | ||||||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.3137 | −0.443079 | ||||||||
\(653\) | −14.2843 | −0.558987 | −0.279493 | − | 0.960148i | \(-0.590166\pi\) | ||||
−0.279493 | + | 0.960148i | \(0.590166\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.1421 | 0.865165 | ||||||||
\(656\) | −3.65685 | −0.142776 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.6274 | −0.882109 | ||||||||
\(659\) | 24.4853 | 0.953811 | 0.476906 | − | 0.878955i | \(-0.341758\pi\) | ||||
0.476906 | + | 0.878955i | \(0.341758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.1421 | 0.783438 | 0.391719 | − | 0.920085i | \(-0.371880\pi\) | ||||
0.391719 | + | 0.920085i | \(0.371880\pi\) | |||||||
\(662\) | −8.48528 | −0.329790 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.6569 | 0.685219 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.9117 | −1.04202 | ||||||||
\(668\) | 24.9706 | 0.966140 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.65685 | −0.218543 | ||||||||
\(671\) | 33.9411 | 1.31028 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.6274 | −0.486751 | −0.243376 | − | 0.969932i | \(-0.578255\pi\) | ||||
−0.243376 | + | 0.969932i | \(0.578255\pi\) | |||||||
\(674\) | 22.9706 | 0.884793 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −23.6569 | −0.909207 | −0.454603 | − | 0.890694i | \(-0.650219\pi\) | ||||
−0.454603 | + | 0.890694i | \(0.650219\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.9706 | −0.958282 | ||||||||
\(680\) | 4.82843 | 0.185162 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22.6274 | −0.866449 | ||||||||
\(683\) | −22.3431 | −0.854937 | −0.427468 | − | 0.904030i | \(-0.640594\pi\) | ||||
−0.427468 | + | 0.904030i | \(0.640594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.31371 | 0.203026 | ||||||||
\(686\) | 16.9706 | 0.647939 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.65685 | −0.0631670 | ||||||||
\(689\) | −9.31371 | −0.354824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7990 | 0.448855 | 0.224427 | − | 0.974491i | \(-0.427949\pi\) | ||||
0.224427 | + | 0.974491i | \(0.427949\pi\) | |||||||
\(692\) | −13.3137 | −0.506111 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.65685 | 0.0628933 | ||||||||
\(695\) | −17.6569 | −0.669763 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.6569 | −0.668801 | ||||||||
\(698\) | 16.1421 | 0.610989 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.82843 | 0.106904 | ||||||||
\(701\) | 28.1421 | 1.06291 | 0.531457 | − | 0.847085i | \(-0.321645\pi\) | ||||
0.531457 | + | 0.847085i | \(0.321645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.970563 | 0.0366055 | ||||||||
\(704\) | 5.65685 | 0.213201 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.3137 | −0.651610 | ||||||||
\(707\) | 34.3431 | 1.29161 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.8284 | −0.481782 | −0.240891 | − | 0.970552i | \(-0.577440\pi\) | ||||
−0.240891 | + | 0.970552i | \(0.577440\pi\) | |||||||
\(710\) | −5.65685 | −0.212298 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.34315 | −0.162766 | ||||||||
\(713\) | −33.9411 | −1.27111 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.65685 | 0.211554 | ||||||||
\(716\) | −24.4853 | −0.915058 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.2843 | 1.05556 | ||||||||
\(719\) | 18.3431 | 0.684084 | 0.342042 | − | 0.939685i | \(-0.388882\pi\) | ||||
0.342042 | + | 0.939685i | \(0.388882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.3137 | 1.01722 | ||||||||
\(722\) | 11.0000 | 0.409378 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.65685 | 0.135906 | ||||||||
\(725\) | 3.17157 | 0.117789 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.9411 | 0.813751 | 0.406876 | − | 0.913484i | \(-0.366618\pi\) | ||||
0.406876 | + | 0.913484i | \(0.366618\pi\) | |||||||
\(728\) | 2.82843 | 0.104828 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.48528 | 0.0919844 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.6569 | −0.430556 | −0.215278 | − | 0.976553i | \(-0.569066\pi\) | ||||
−0.215278 | + | 0.976553i | \(0.569066\pi\) | |||||||
\(734\) | −14.3431 | −0.529415 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.48528 | 0.312772 | ||||||||
\(737\) | −32.0000 | −1.17874 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1421 | 0.520227 | 0.260113 | − | 0.965578i | \(-0.416240\pi\) | ||||
0.260113 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(740\) | 0.343146 | 0.0126143 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26.3431 | −0.967087 | ||||||||
\(743\) | −20.2843 | −0.744158 | −0.372079 | − | 0.928201i | \(-0.621355\pi\) | ||||
−0.372079 | + | 0.928201i | \(0.621355\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.65685 | −0.280525 | ||||||||
\(746\) | 25.3137 | 0.926801 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27.3137 | 0.998688 | ||||||||
\(749\) | 11.3137 | 0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3137 | −0.412843 | −0.206422 | − | 0.978463i | \(-0.566182\pi\) | ||||
−0.206422 | + | 0.978463i | \(0.566182\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.17157 | 0.115502 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.9411 | −1.74245 | −0.871225 | − | 0.490884i | \(-0.836674\pi\) | ||||
−0.871225 | + | 0.490884i | \(0.836674\pi\) | |||||||
\(758\) | 24.4853 | 0.889345 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.82843 | −0.102598 | ||||||||
\(761\) | −16.3431 | −0.592439 | −0.296219 | − | 0.955120i | \(-0.595726\pi\) | ||||
−0.296219 | + | 0.955120i | \(0.595726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.97056 | 0.324756 | ||||||||
\(764\) | 11.3137 | 0.409316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.3431 | −0.662765 | ||||||||
\(767\) | −13.6569 | −0.493120 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 16.0000 | 0.576600 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.4853 | −0.521337 | ||||||||
\(773\) | 30.6863 | 1.10371 | 0.551855 | − | 0.833940i | \(-0.313920\pi\) | ||||
0.551855 | + | 0.833940i | \(0.313920\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 8.82843 | 0.316922 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.4853 | 0.375916 | ||||||||
\(779\) | 10.3431 | 0.370582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 40.9706 | 1.46510 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 17.3137 | 0.617953 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.0000 | −0.855508 | −0.427754 | − | 0.903895i | \(-0.640695\pi\) | ||||
−0.427754 | + | 0.903895i | \(0.640695\pi\) | |||||||
\(788\) | −9.31371 | −0.331787 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.6569 | 0.485889 | ||||||||
\(791\) | 29.6569 | 1.05448 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.00000 | −0.213066 | ||||||||
\(794\) | 26.2843 | 0.932794 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.6569 | 0.767607 | ||||||||
\(797\) | 28.6274 | 1.01404 | 0.507018 | − | 0.861936i | \(-0.330748\pi\) | ||||
0.507018 | + | 0.861936i | \(0.330748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.6274 | 1.36654 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.97056 | 0.246139 | ||||||||
\(803\) | 14.0589 | 0.496127 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.0000 | 0.845889 | ||||||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.1421 | −0.427159 | ||||||||
\(809\) | 9.31371 | 0.327453 | 0.163726 | − | 0.986506i | \(-0.447649\pi\) | ||||
0.163726 | + | 0.986506i | \(0.447649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.1421 | −1.05843 | −0.529217 | − | 0.848487i | \(-0.677514\pi\) | ||||
−0.529217 | + | 0.848487i | \(0.677514\pi\) | |||||||
\(812\) | 8.97056 | 0.314805 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.94113 | 0.0680364 | ||||||||
\(815\) | 11.3137 | 0.396302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.68629 | 0.163953 | ||||||||
\(818\) | −7.65685 | −0.267716 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.65685 | 0.127703 | ||||||||
\(821\) | 22.2843 | 0.777726 | 0.388863 | − | 0.921296i | \(-0.372868\pi\) | ||||
0.388863 | + | 0.921296i | \(0.372868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.0294 | −0.663324 | −0.331662 | − | 0.943398i | \(-0.607609\pi\) | ||||
−0.331662 | + | 0.943398i | \(0.607609\pi\) | |||||||
\(824\) | −9.65685 | −0.336412 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38.6274 | −1.34402 | ||||||||
\(827\) | 1.65685 | 0.0576145 | 0.0288072 | − | 0.999585i | \(-0.490829\pi\) | ||||
0.0288072 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.6863 | −1.06578 | −0.532889 | − | 0.846185i | \(-0.678894\pi\) | ||||
−0.532889 | + | 0.846185i | \(0.678894\pi\) | |||||||
\(830\) | −17.6569 | −0.612878 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 4.82843 | 0.167295 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.9706 | −0.864142 | ||||||||
\(836\) | −16.0000 | −0.553372 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.17157 | −0.178649 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | −4.14214 | −0.142747 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.3137 | 0.802491 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 59.3970 | 2.04090 | ||||||||
\(848\) | 9.31371 | 0.319834 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.82843 | −0.165614 | ||||||||
\(851\) | 2.91169 | 0.0998114 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.2843 | −0.626042 | −0.313021 | − | 0.949746i | \(-0.601341\pi\) | ||||
−0.313021 | + | 0.949746i | \(0.601341\pi\) | |||||||
\(854\) | −16.9706 | −0.580721 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 15.1716 | 0.518251 | 0.259126 | − | 0.965844i | \(-0.416566\pi\) | ||||
0.259126 | + | 0.965844i | \(0.416566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.9411 | −1.02158 | −0.510789 | − | 0.859706i | \(-0.670647\pi\) | ||||
−0.510789 | + | 0.859706i | \(0.670647\pi\) | |||||||
\(860\) | 1.65685 | 0.0564983 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | −28.2843 | −0.962808 | −0.481404 | − | 0.876499i | \(-0.659873\pi\) | ||||
−0.481404 | + | 0.876499i | \(0.659873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.3137 | 0.452680 | ||||||||
\(866\) | −10.9706 | −0.372795 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.3137 | 0.384012 | ||||||||
\(869\) | 77.2548 | 2.62069 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.65685 | 0.191675 | ||||||||
\(872\) | −3.17157 | −0.107403 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | −2.82843 | −0.0956183 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.2548 | 1.32554 | 0.662771 | − | 0.748822i | \(-0.269380\pi\) | ||||
0.662771 | + | 0.748822i | \(0.269380\pi\) | |||||||
\(878\) | 22.6274 | 0.763638 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.65685 | −0.190693 | ||||||||
\(881\) | −46.2843 | −1.55936 | −0.779678 | − | 0.626180i | \(-0.784617\pi\) | ||||
−0.779678 | + | 0.626180i | \(0.784617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.68629 | 0.292317 | 0.146158 | − | 0.989261i | \(-0.453309\pi\) | ||||
0.146158 | + | 0.989261i | \(0.453309\pi\) | |||||||
\(884\) | −4.82843 | −0.162398 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 41.6569 | 1.39949 | ||||||||
\(887\) | 23.5147 | 0.789547 | 0.394773 | − | 0.918778i | \(-0.370823\pi\) | ||||
0.394773 | + | 0.918778i | \(0.370823\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.68629 | −0.157173 | ||||||||
\(890\) | 4.34315 | 0.145583 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.17157 | 0.173157 | ||||||||
\(893\) | −22.6274 | −0.757198 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.4853 | 0.818453 | ||||||||
\(896\) | −2.82843 | −0.0944911 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.2843 | −1.01060 | ||||||||
\(899\) | 12.6863 | 0.423112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.9706 | 1.49819 | ||||||||
\(902\) | 20.6863 | 0.688778 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.4853 | −0.348735 | ||||||||
\(905\) | −3.65685 | −0.121558 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.2843 | −1.60325 | −0.801626 | − | 0.597825i | \(-0.796032\pi\) | ||||
−0.801626 | + | 0.597825i | \(0.796032\pi\) | |||||||
\(908\) | −4.00000 | −0.132745 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.82843 | −0.0937614 | ||||||||
\(911\) | 8.97056 | 0.297208 | 0.148604 | − | 0.988897i | \(-0.452522\pi\) | ||||
0.148604 | + | 0.988897i | \(0.452522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −99.8823 | −3.30562 | ||||||||
\(914\) | −15.1716 | −0.501831 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.1421 | −0.797679 | ||||||||
\(917\) | −62.6274 | −2.06814 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.9411 | −0.855719 | −0.427859 | − | 0.903845i | \(-0.640732\pi\) | ||||
−0.427859 | + | 0.903845i | \(0.640732\pi\) | |||||||
\(920\) | −8.48528 | −0.279751 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.0000 | 0.461065 | ||||||||
\(923\) | 5.65685 | 0.186198 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.343146 | −0.0112826 | ||||||||
\(926\) | −35.7990 | −1.17643 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.17157 | −0.104112 | ||||||||
\(929\) | −45.5980 | −1.49602 | −0.748011 | − | 0.663687i | \(-0.768991\pi\) | ||||
−0.748011 | + | 0.663687i | \(0.768991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | −22.4853 | −0.736530 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.3137 | −0.501080 | ||||||||
\(935\) | −27.3137 | −0.893254 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.6274 | −0.935217 | −0.467608 | − | 0.883936i | \(-0.654884\pi\) | ||||
−0.467608 | + | 0.883936i | \(0.654884\pi\) | |||||||
\(938\) | 16.0000 | 0.522419 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.00000 | −0.260931 | ||||||||
\(941\) | −21.0294 | −0.685540 | −0.342770 | − | 0.939419i | \(-0.611365\pi\) | ||||
−0.342770 | + | 0.939419i | \(0.611365\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.0294 | 1.01046 | ||||||||
\(944\) | 13.6569 | 0.444493 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.37258 | 0.304729 | ||||||||
\(947\) | −41.6569 | −1.35367 | −0.676833 | − | 0.736137i | \(-0.736648\pi\) | ||||
−0.676833 | + | 0.736137i | \(0.736648\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.48528 | −0.0806756 | ||||||||
\(950\) | 2.82843 | 0.0917663 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.6569 | −0.442621 | ||||||||
\(953\) | 56.1421 | 1.81862 | 0.909311 | − | 0.416117i | \(-0.136609\pi\) | ||||
0.909311 | + | 0.416117i | \(0.136609\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.3137 | −0.366103 | ||||||||
\(956\) | −16.0000 | −0.517477 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.3137 | 0.365529 | ||||||||
\(959\) | −15.0294 | −0.485326 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −0.343146 | −0.0110635 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.3137 | −0.557637 | ||||||||
\(965\) | 14.4853 | 0.466298 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4853 | −0.787394 | −0.393697 | − | 0.919240i | \(-0.628804\pi\) | ||||
−0.393697 | + | 0.919240i | \(0.628804\pi\) | |||||||
\(968\) | −21.0000 | −0.674966 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.82843 | −0.283464 | ||||||||
\(971\) | −32.4853 | −1.04250 | −0.521251 | − | 0.853403i | \(-0.674535\pi\) | ||||
−0.521251 | + | 0.853403i | \(0.674535\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.9411 | 1.60104 | ||||||||
\(974\) | 0.485281 | 0.0155494 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 19.6569 | 0.628878 | 0.314439 | − | 0.949278i | \(-0.398184\pi\) | ||||
0.314439 | + | 0.949278i | \(0.398184\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.5685 | 0.785214 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.85786 | −0.314577 | ||||||||
\(983\) | 13.6569 | 0.435586 | 0.217793 | − | 0.975995i | \(-0.430114\pi\) | ||||
0.217793 | + | 0.975995i | \(0.430114\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.31371 | 0.296759 | ||||||||
\(986\) | −15.3137 | −0.487688 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.82843 | 0.0899843 | ||||||||
\(989\) | 14.0589 | 0.447046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.9117 | 1.87139 | 0.935696 | − | 0.352808i | \(-0.114773\pi\) | ||||
0.935696 | + | 0.352808i | \(0.114773\pi\) | |||||||
\(992\) | −4.00000 | −0.127000 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.0000 | 0.507489 | ||||||||
\(995\) | −21.6569 | −0.686568 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.6863 | 1.22521 | 0.612604 | − | 0.790390i | \(-0.290122\pi\) | ||||
0.612604 | + | 0.790390i | \(0.290122\pi\) | |||||||
\(998\) | 16.4853 | 0.521832 | ||||||||
\(999\) | 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 | 1170.2.a.o.1.2 | 2 | ||
3.2 | odd | 2 | 390.2.a.h.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 9360.2.a.ch.1.1 | 2 | |||
5.2 | odd | 4 | 5850.2.e.bk.5149.2 | 4 | |||
5.3 | odd | 4 | 5850.2.e.bk.5149.3 | 4 | |||
5.4 | even | 2 | 5850.2.a.cl.1.1 | 2 | |||
12.11 | even | 2 | 3120.2.a.bc.1.1 | 2 | |||
15.2 | even | 4 | 1950.2.e.o.1249.4 | 4 | |||
15.8 | even | 4 | 1950.2.e.o.1249.1 | 4 | |||
15.14 | odd | 2 | 1950.2.a.bd.1.1 | 2 | |||
39.5 | even | 4 | 5070.2.b.q.1351.2 | 4 | |||
39.8 | even | 4 | 5070.2.b.q.1351.3 | 4 | |||
39.38 | odd | 2 | 5070.2.a.bc.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.a.h.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
1170.2.a.o.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1950.2.a.bd.1.1 | 2 | 15.14 | odd | 2 | |||
1950.2.e.o.1249.1 | 4 | 15.8 | even | 4 | |||
1950.2.e.o.1249.4 | 4 | 15.2 | even | 4 | |||
3120.2.a.bc.1.1 | 2 | 12.11 | even | 2 | |||
5070.2.a.bc.1.1 | 2 | 39.38 | odd | 2 | |||
5070.2.b.q.1351.2 | 4 | 39.5 | even | 4 | |||
5070.2.b.q.1351.3 | 4 | 39.8 | even | 4 | |||
5850.2.a.cl.1.1 | 2 | 5.4 | even | 2 | |||
5850.2.e.bk.5149.2 | 4 | 5.2 | odd | 4 | |||
5850.2.e.bk.5149.3 | 4 | 5.3 | odd | 4 | |||
9360.2.a.ch.1.1 | 2 | 4.3 | odd | 2 |