Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7350,2,Mod(1,7350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7350, 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("7350.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7350.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: | \(58.6900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2700.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 15x - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.41883\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7350.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.10725 | 1.84141 | 0.920703 | − | 0.390265i | \(-0.127617\pi\) | ||||
0.920703 | + | 0.390265i | \(0.127617\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.68842 | −0.468283 | −0.234141 | − | 0.972203i | \(-0.575228\pi\) | ||||
−0.234141 | + | 0.972203i | \(0.575228\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.83767 | 1.65838 | 0.829189 | − | 0.558969i | \(-0.188803\pi\) | ||||
0.829189 | + | 0.558969i | \(0.188803\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.68842 | −0.387349 | −0.193675 | − | 0.981066i | \(-0.562041\pi\) | ||||
−0.193675 | + | 0.981066i | \(0.562041\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.10725 | 1.30207 | ||||||||
\(23\) | 2.31158 | 0.481998 | 0.240999 | − | 0.970525i | \(-0.422525\pi\) | ||||
0.240999 | + | 0.970525i | \(0.422525\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.68842 | −0.331126 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.41883 | 1.56334 | 0.781669 | − | 0.623694i | \(-0.214369\pi\) | ||||
0.781669 | + | 0.623694i | \(0.214369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.688417 | 0.123643 | 0.0618217 | − | 0.998087i | \(-0.480309\pi\) | ||||
0.0618217 | + | 0.998087i | \(0.480309\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.10725 | −1.06314 | ||||||||
\(34\) | 6.83767 | 1.17265 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.31158 | 0.380022 | 0.190011 | − | 0.981782i | \(-0.439148\pi\) | ||||
0.190011 | + | 0.981782i | \(0.439148\pi\) | |||||||
\(38\) | −1.68842 | −0.273897 | ||||||||
\(39\) | 1.68842 | 0.270363 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.14925 | −0.804178 | −0.402089 | − | 0.915601i | \(-0.631716\pi\) | ||||
−0.402089 | + | 0.915601i | \(0.631716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 6.10725 | 0.920703 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.31158 | 0.340824 | ||||||||
\(47\) | 3.06525 | 0.447113 | 0.223556 | − | 0.974691i | \(-0.428233\pi\) | ||||
0.223556 | + | 0.974691i | \(0.428233\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.83767 | −0.957465 | ||||||||
\(52\) | −1.68842 | −0.234141 | ||||||||
\(53\) | −10.4608 | −1.43691 | −0.718453 | − | 0.695576i | \(-0.755149\pi\) | ||||
−0.718453 | + | 0.695576i | \(0.755149\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.68842 | 0.223636 | ||||||||
\(58\) | 8.41883 | 1.10545 | ||||||||
\(59\) | 7.04200 | 0.916790 | 0.458395 | − | 0.888749i | \(-0.348424\pi\) | ||||
0.458395 | + | 0.888749i | \(0.348424\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.46083 | −1.21134 | −0.605668 | − | 0.795718i | \(-0.707094\pi\) | ||||
−0.605668 | + | 0.795718i | \(0.707094\pi\) | |||||||
\(62\) | 0.688417 | 0.0874290 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.10725 | −0.751750 | ||||||||
\(67\) | −12.2145 | −1.49224 | −0.746119 | − | 0.665812i | \(-0.768085\pi\) | ||||
−0.746119 | + | 0.665812i | \(0.768085\pi\) | |||||||
\(68\) | 6.83767 | 0.829189 | ||||||||
\(69\) | −2.31158 | −0.278282 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 2.31158 | 0.268716 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.68842 | −0.193675 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.68842 | 0.191176 | ||||||||
\(79\) | 7.31158 | 0.822617 | 0.411309 | − | 0.911496i | \(-0.365072\pi\) | ||||
0.411309 | + | 0.911496i | \(0.365072\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.14925 | −0.568639 | ||||||||
\(83\) | −13.5261 | −1.48468 | −0.742340 | − | 0.670023i | \(-0.766284\pi\) | ||||
−0.742340 | + | 0.670023i | \(0.766284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | −8.41883 | −0.902594 | ||||||||
\(88\) | 6.10725 | 0.651035 | ||||||||
\(89\) | 12.2145 | 1.29473 | 0.647367 | − | 0.762178i | \(-0.275870\pi\) | ||||
0.647367 | + | 0.762178i | \(0.275870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.31158 | 0.240999 | ||||||||
\(93\) | −0.688417 | −0.0713855 | ||||||||
\(94\) | 3.06525 | 0.316156 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.95800 | 0.503409 | 0.251704 | − | 0.967804i | \(-0.419009\pi\) | ||||
0.251704 | + | 0.967804i | \(0.419009\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.10725 | 0.613802 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00000 | 0.796030 | 0.398015 | − | 0.917379i | \(-0.369699\pi\) | ||||
0.398015 | + | 0.917379i | \(0.369699\pi\) | |||||||
\(102\) | −6.83767 | −0.677030 | ||||||||
\(103\) | −0.837665 | −0.0825376 | −0.0412688 | − | 0.999148i | \(-0.513140\pi\) | ||||
−0.0412688 | + | 0.999148i | \(0.513140\pi\) | |||||||
\(104\) | −1.68842 | −0.165563 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4608 | −1.01605 | ||||||||
\(107\) | 15.5261 | 1.50096 | 0.750482 | − | 0.660891i | \(-0.229822\pi\) | ||||
0.750482 | + | 0.660891i | \(0.229822\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −11.6753 | −1.11829 | −0.559147 | − | 0.829069i | \(-0.688871\pi\) | ||||
−0.559147 | + | 0.829069i | \(0.688871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.31158 | −0.219406 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.37683 | −0.317666 | −0.158833 | − | 0.987305i | \(-0.550773\pi\) | ||||
−0.158833 | + | 0.987305i | \(0.550773\pi\) | |||||||
\(114\) | 1.68842 | 0.158135 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.41883 | 0.781669 | ||||||||
\(117\) | −1.68842 | −0.156094 | ||||||||
\(118\) | 7.04200 | 0.648269 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.2985 | 2.39077 | ||||||||
\(122\) | −9.46083 | −0.856543 | ||||||||
\(123\) | 5.14925 | 0.464292 | ||||||||
\(124\) | 0.688417 | 0.0618217 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.94491 | −0.438790 | −0.219395 | − | 0.975636i | \(-0.570408\pi\) | ||||
−0.219395 | + | 0.975636i | \(0.570408\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.00000 | 0.176090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.73042 | 0.588039 | 0.294020 | − | 0.955799i | \(-0.405007\pi\) | ||||
0.294020 | + | 0.955799i | \(0.405007\pi\) | |||||||
\(132\) | −6.10725 | −0.531568 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.2145 | −1.05517 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.83767 | 0.586325 | ||||||||
\(137\) | 19.0522 | 1.62774 | 0.813868 | − | 0.581050i | \(-0.197358\pi\) | ||||
0.813868 | + | 0.581050i | \(0.197358\pi\) | |||||||
\(138\) | −2.31158 | −0.196775 | ||||||||
\(139\) | −13.3768 | −1.13461 | −0.567304 | − | 0.823508i | \(-0.692014\pi\) | ||||
−0.567304 | + | 0.823508i | \(0.692014\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.06525 | −0.258141 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | −10.3116 | −0.862298 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.31158 | 0.190011 | ||||||||
\(149\) | 12.6232 | 1.03413 | 0.517065 | − | 0.855946i | \(-0.327025\pi\) | ||||
0.517065 | + | 0.855946i | \(0.327025\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.93475 | 0.157448 | 0.0787238 | − | 0.996896i | \(-0.474915\pi\) | ||||
0.0787238 | + | 0.996896i | \(0.474915\pi\) | |||||||
\(152\) | −1.68842 | −0.136949 | ||||||||
\(153\) | 6.83767 | 0.552792 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.68842 | 0.135182 | ||||||||
\(157\) | −17.1492 | −1.36866 | −0.684330 | − | 0.729173i | \(-0.739905\pi\) | ||||
−0.684330 | + | 0.729173i | \(0.739905\pi\) | |||||||
\(158\) | 7.31158 | 0.581678 | ||||||||
\(159\) | 10.4608 | 0.829598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 0.539168 | 0.0422309 | 0.0211155 | − | 0.999777i | \(-0.493278\pi\) | ||||
0.0211155 | + | 0.999777i | \(0.493278\pi\) | |||||||
\(164\) | −5.14925 | −0.402089 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.5261 | −1.04983 | ||||||||
\(167\) | 3.14925 | 0.243696 | 0.121848 | − | 0.992549i | \(-0.461118\pi\) | ||||
0.121848 | + | 0.992549i | \(0.461118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1492 | −0.780711 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.68842 | −0.129116 | ||||||||
\(172\) | −2.00000 | −0.152499 | ||||||||
\(173\) | 10.5261 | 0.800283 | 0.400142 | − | 0.916453i | \(-0.368961\pi\) | ||||
0.400142 | + | 0.916453i | \(0.368961\pi\) | |||||||
\(174\) | −8.41883 | −0.638230 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.10725 | 0.460351 | ||||||||
\(177\) | −7.04200 | −0.529309 | ||||||||
\(178\) | 12.2145 | 0.915515 | ||||||||
\(179\) | 4.93475 | 0.368840 | 0.184420 | − | 0.982847i | \(-0.440959\pi\) | ||||
0.184420 | + | 0.982847i | \(0.440959\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.13050 | −0.455677 | −0.227838 | − | 0.973699i | \(-0.573166\pi\) | ||||
−0.227838 | + | 0.973699i | \(0.573166\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.46083 | 0.699365 | ||||||||
\(184\) | 2.31158 | 0.170412 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.688417 | −0.0504772 | ||||||||
\(187\) | 41.7593 | 3.05374 | ||||||||
\(188\) | 3.06525 | 0.223556 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9217 | −1.07969 | −0.539847 | − | 0.841763i | \(-0.681518\pi\) | ||||
−0.539847 | + | 0.841763i | \(0.681518\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −5.58117 | −0.401741 | −0.200871 | − | 0.979618i | \(-0.564377\pi\) | ||||
−0.200871 | + | 0.979618i | \(0.564377\pi\) | |||||||
\(194\) | 4.95800 | 0.355964 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.5261 | 1.03494 | 0.517470 | − | 0.855701i | \(-0.326874\pi\) | ||||
0.517470 | + | 0.855701i | \(0.326874\pi\) | |||||||
\(198\) | 6.10725 | 0.434023 | ||||||||
\(199\) | 8.62317 | 0.611280 | 0.305640 | − | 0.952147i | \(-0.401130\pi\) | ||||
0.305640 | + | 0.952147i | \(0.401130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.2145 | 0.861544 | ||||||||
\(202\) | 8.00000 | 0.562878 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.83767 | −0.478732 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.837665 | −0.0583629 | ||||||||
\(207\) | 2.31158 | 0.160666 | ||||||||
\(208\) | −1.68842 | −0.117071 | ||||||||
\(209\) | −10.3116 | −0.713267 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.68842 | −0.529292 | −0.264646 | − | 0.964346i | \(-0.585255\pi\) | ||||
−0.264646 | + | 0.964346i | \(0.585255\pi\) | |||||||
\(212\) | −10.4608 | −0.718453 | ||||||||
\(213\) | −6.00000 | −0.411113 | ||||||||
\(214\) | 15.5261 | 1.06134 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.6753 | −0.790753 | ||||||||
\(219\) | 4.00000 | 0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.5448 | −0.776589 | ||||||||
\(222\) | −2.31158 | −0.155143 | ||||||||
\(223\) | 11.1725 | 0.748166 | 0.374083 | − | 0.927395i | \(-0.377958\pi\) | ||||
0.374083 | + | 0.927395i | \(0.377958\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.37683 | −0.224624 | ||||||||
\(227\) | −3.85075 | −0.255583 | −0.127792 | − | 0.991801i | \(-0.540789\pi\) | ||||
−0.127792 | + | 0.991801i | \(0.540789\pi\) | |||||||
\(228\) | 1.68842 | 0.111818 | ||||||||
\(229\) | −5.67533 | −0.375036 | −0.187518 | − | 0.982261i | \(-0.560044\pi\) | ||||
−0.187518 | + | 0.982261i | \(0.560044\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.41883 | 0.552723 | ||||||||
\(233\) | −11.4608 | −0.750824 | −0.375412 | − | 0.926858i | \(-0.622499\pi\) | ||||
−0.375412 | + | 0.926858i | \(0.622499\pi\) | |||||||
\(234\) | −1.68842 | −0.110375 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.04200 | 0.458395 | ||||||||
\(237\) | −7.31158 | −0.474938 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4608 | 1.00008 | 0.500039 | − | 0.866003i | \(-0.333319\pi\) | ||||
0.500039 | + | 0.866003i | \(0.333319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.37683 | −0.281937 | −0.140968 | − | 0.990014i | \(-0.545022\pi\) | ||||
−0.140968 | + | 0.990014i | \(0.545022\pi\) | |||||||
\(242\) | 26.2985 | 1.69053 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.46083 | −0.605668 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.14925 | 0.328304 | ||||||||
\(247\) | 2.85075 | 0.181389 | ||||||||
\(248\) | 0.688417 | 0.0437145 | ||||||||
\(249\) | 13.5261 | 0.857181 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.5362 | 1.67495 | 0.837477 | − | 0.546473i | \(-0.184030\pi\) | ||||
0.837477 | + | 0.546473i | \(0.184030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.1174 | 0.887554 | ||||||||
\(254\) | −4.94491 | −0.310272 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.4290 | −1.39908 | −0.699541 | − | 0.714592i | \(-0.746612\pi\) | ||||
−0.699541 | + | 0.714592i | \(0.746612\pi\) | |||||||
\(258\) | 2.00000 | 0.124515 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.41883 | 0.521113 | ||||||||
\(262\) | 6.73042 | 0.415806 | ||||||||
\(263\) | −19.5913 | −1.20805 | −0.604027 | − | 0.796964i | \(-0.706438\pi\) | ||||
−0.604027 | + | 0.796964i | \(0.706438\pi\) | |||||||
\(264\) | −6.10725 | −0.375875 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.2145 | −0.747515 | ||||||||
\(268\) | −12.2145 | −0.746119 | ||||||||
\(269\) | 6.95800 | 0.424237 | 0.212118 | − | 0.977244i | \(-0.431964\pi\) | ||||
0.212118 | + | 0.977244i | \(0.431964\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.3637 | 1.72297 | 0.861487 | − | 0.507779i | \(-0.169533\pi\) | ||||
0.861487 | + | 0.507779i | \(0.169533\pi\) | |||||||
\(272\) | 6.83767 | 0.414594 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.0522 | 1.15098 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.31158 | −0.139141 | ||||||||
\(277\) | 5.05216 | 0.303555 | 0.151778 | − | 0.988415i | \(-0.451500\pi\) | ||||
0.151778 | + | 0.988415i | \(0.451500\pi\) | |||||||
\(278\) | −13.3768 | −0.802289 | ||||||||
\(279\) | 0.688417 | 0.0412144 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.68842 | 0.458652 | 0.229326 | − | 0.973350i | \(-0.426348\pi\) | ||||
0.229326 | + | 0.973350i | \(0.426348\pi\) | |||||||
\(282\) | −3.06525 | −0.182533 | ||||||||
\(283\) | −18.4290 | −1.09549 | −0.547745 | − | 0.836645i | \(-0.684514\pi\) | ||||
−0.547745 | + | 0.836645i | \(0.684514\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.3116 | −0.609737 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 29.7537 | 1.75022 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.95800 | −0.290643 | ||||||||
\(292\) | −4.00000 | −0.234082 | ||||||||
\(293\) | 1.83767 | 0.107358 | 0.0536788 | − | 0.998558i | \(-0.482905\pi\) | ||||
0.0536788 | + | 0.998558i | \(0.482905\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.31158 | 0.134358 | ||||||||
\(297\) | −6.10725 | −0.354379 | ||||||||
\(298\) | 12.6232 | 0.731240 | ||||||||
\(299\) | −3.90292 | −0.225711 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.93475 | 0.111332 | ||||||||
\(303\) | −8.00000 | −0.459588 | ||||||||
\(304\) | −1.68842 | −0.0968373 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.83767 | 0.390883 | ||||||||
\(307\) | 16.0840 | 0.917962 | 0.458981 | − | 0.888446i | \(-0.348215\pi\) | ||||
0.458981 | + | 0.888446i | \(0.348215\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.837665 | 0.0476531 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.3768 | 0.871940 | 0.435970 | − | 0.899961i | \(-0.356405\pi\) | ||||
0.435970 | + | 0.899961i | \(0.356405\pi\) | |||||||
\(312\) | 1.68842 | 0.0955878 | ||||||||
\(313\) | 22.4188 | 1.26719 | 0.633594 | − | 0.773666i | \(-0.281579\pi\) | ||||
0.633594 | + | 0.773666i | \(0.281579\pi\) | |||||||
\(314\) | −17.1492 | −0.967788 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.31158 | 0.411309 | ||||||||
\(317\) | −10.0653 | −0.565321 | −0.282660 | − | 0.959220i | \(-0.591217\pi\) | ||||
−0.282660 | + | 0.959220i | \(0.591217\pi\) | |||||||
\(318\) | 10.4608 | 0.586614 | ||||||||
\(319\) | 51.4159 | 2.87874 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.5261 | −0.866581 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.5448 | −0.642371 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.539168 | 0.0298618 | ||||||||
\(327\) | 11.6753 | 0.645647 | ||||||||
\(328\) | −5.14925 | −0.284320 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.2797 | 1.27957 | 0.639785 | − | 0.768554i | \(-0.279023\pi\) | ||||
0.639785 | + | 0.768554i | \(0.279023\pi\) | |||||||
\(332\) | −13.5261 | −0.742340 | ||||||||
\(333\) | 2.31158 | 0.126674 | ||||||||
\(334\) | 3.14925 | 0.172319 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.17250 | −0.281764 | −0.140882 | − | 0.990026i | \(-0.544994\pi\) | ||||
−0.140882 | + | 0.990026i | \(0.544994\pi\) | |||||||
\(338\) | −10.1492 | −0.552046 | ||||||||
\(339\) | 3.37683 | 0.183404 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.20433 | 0.227677 | ||||||||
\(342\) | −1.68842 | −0.0912991 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5261 | 0.565886 | ||||||||
\(347\) | −9.67533 | −0.519399 | −0.259699 | − | 0.965689i | \(-0.583624\pi\) | ||||
−0.259699 | + | 0.965689i | \(0.583624\pi\) | |||||||
\(348\) | −8.41883 | −0.451297 | ||||||||
\(349\) | −28.2985 | −1.51478 | −0.757392 | − | 0.652961i | \(-0.773527\pi\) | ||||
−0.757392 | + | 0.652961i | \(0.773527\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.68842 | 0.0901210 | ||||||||
\(352\) | 6.10725 | 0.325517 | ||||||||
\(353\) | −17.6753 | −0.940763 | −0.470381 | − | 0.882463i | \(-0.655884\pi\) | ||||
−0.470381 | + | 0.882463i | \(0.655884\pi\) | |||||||
\(354\) | −7.04200 | −0.374278 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.2145 | 0.647367 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.93475 | 0.260810 | ||||||||
\(359\) | −4.83767 | −0.255322 | −0.127661 | − | 0.991818i | \(-0.540747\pi\) | ||||
−0.127661 | + | 0.991818i | \(0.540747\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1492 | −0.849960 | ||||||||
\(362\) | −6.13050 | −0.322212 | ||||||||
\(363\) | −26.2985 | −1.38031 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.46083 | 0.494526 | ||||||||
\(367\) | 10.6464 | 0.555738 | 0.277869 | − | 0.960619i | \(-0.410372\pi\) | ||||
0.277869 | + | 0.960619i | \(0.410372\pi\) | |||||||
\(368\) | 2.31158 | 0.120500 | ||||||||
\(369\) | −5.14925 | −0.268059 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.688417 | −0.0356928 | ||||||||
\(373\) | 34.7275 | 1.79812 | 0.899061 | − | 0.437824i | \(-0.144251\pi\) | ||||
0.899061 | + | 0.437824i | \(0.144251\pi\) | |||||||
\(374\) | 41.7593 | 2.15932 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.06525 | 0.158078 | ||||||||
\(377\) | −14.2145 | −0.732084 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.4477 | −0.998964 | −0.499482 | − | 0.866324i | \(-0.666476\pi\) | ||||
−0.499482 | + | 0.866324i | \(0.666476\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.94491 | 0.253336 | ||||||||
\(382\) | −14.9217 | −0.763459 | ||||||||
\(383\) | 0.850752 | 0.0434714 | 0.0217357 | − | 0.999764i | \(-0.493081\pi\) | ||||
0.0217357 | + | 0.999764i | \(0.493081\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.58117 | −0.284074 | ||||||||
\(387\) | −2.00000 | −0.101666 | ||||||||
\(388\) | 4.95800 | 0.251704 | ||||||||
\(389\) | 26.2985 | 1.33339 | 0.666693 | − | 0.745332i | \(-0.267709\pi\) | ||||
0.666693 | + | 0.745332i | \(0.267709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8058 | 0.799335 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.73042 | −0.339505 | ||||||||
\(394\) | 14.5261 | 0.731813 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.10725 | 0.306901 | ||||||||
\(397\) | 1.70150 | 0.0853960 | 0.0426980 | − | 0.999088i | \(-0.486405\pi\) | ||||
0.0426980 | + | 0.999088i | \(0.486405\pi\) | |||||||
\(398\) | 8.62317 | 0.432240 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.01875 | 0.150749 | 0.0753745 | − | 0.997155i | \(-0.475985\pi\) | ||||
0.0753745 | + | 0.997155i | \(0.475985\pi\) | |||||||
\(402\) | 12.2145 | 0.609204 | ||||||||
\(403\) | −1.16233 | −0.0579000 | ||||||||
\(404\) | 8.00000 | 0.398015 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.1174 | 0.699774 | ||||||||
\(408\) | −6.83767 | −0.338515 | ||||||||
\(409\) | 4.14925 | 0.205167 | 0.102584 | − | 0.994724i | \(-0.467289\pi\) | ||||
0.102584 | + | 0.994724i | \(0.467289\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.0522 | −0.939774 | ||||||||
\(412\) | −0.837665 | −0.0412688 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.31158 | 0.113608 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.68842 | −0.0827814 | ||||||||
\(417\) | 13.3768 | 0.655066 | ||||||||
\(418\) | −10.3116 | −0.504356 | ||||||||
\(419\) | −13.8189 | −0.675098 | −0.337549 | − | 0.941308i | \(-0.609598\pi\) | ||||
−0.337549 | + | 0.941308i | \(0.609598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.2667 | 1.23142 | 0.615711 | − | 0.787972i | \(-0.288869\pi\) | ||||
0.615711 | + | 0.787972i | \(0.288869\pi\) | |||||||
\(422\) | −7.68842 | −0.374266 | ||||||||
\(423\) | 3.06525 | 0.149038 | ||||||||
\(424\) | −10.4608 | −0.508023 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.5261 | 0.750482 | ||||||||
\(429\) | 10.3116 | 0.497848 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.5448 | 0.941441 | 0.470721 | − | 0.882282i | \(-0.343994\pi\) | ||||
0.470721 | + | 0.882282i | \(0.343994\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 14.7537 | 0.709016 | 0.354508 | − | 0.935053i | \(-0.384648\pi\) | ||||
0.354508 | + | 0.935053i | \(0.384648\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.6753 | −0.559147 | ||||||||
\(437\) | −3.90292 | −0.186702 | ||||||||
\(438\) | 4.00000 | 0.191127 | ||||||||
\(439\) | 15.9347 | 0.760524 | 0.380262 | − | 0.924879i | \(-0.375834\pi\) | ||||
0.380262 | + | 0.924879i | \(0.375834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.5448 | −0.549132 | ||||||||
\(443\) | 21.8246 | 1.03692 | 0.518459 | − | 0.855103i | \(-0.326506\pi\) | ||||
0.518459 | + | 0.855103i | \(0.326506\pi\) | |||||||
\(444\) | −2.31158 | −0.109703 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.1725 | 0.529033 | ||||||||
\(447\) | −12.6232 | −0.597055 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.3637 | −0.536288 | −0.268144 | − | 0.963379i | \(-0.586410\pi\) | ||||
−0.268144 | + | 0.963379i | \(0.586410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.4477 | −1.48082 | ||||||||
\(452\) | −3.37683 | −0.158833 | ||||||||
\(453\) | −1.93475 | −0.0909025 | ||||||||
\(454\) | −3.85075 | −0.180725 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.68842 | 0.0790674 | ||||||||
\(457\) | 6.41883 | 0.300260 | 0.150130 | − | 0.988666i | \(-0.452031\pi\) | ||||
0.150130 | + | 0.988666i | \(0.452031\pi\) | |||||||
\(458\) | −5.67533 | −0.265191 | ||||||||
\(459\) | −6.83767 | −0.319155 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.50733 | −0.0702036 | −0.0351018 | − | 0.999384i | \(-0.511176\pi\) | ||||
−0.0351018 | + | 0.999384i | \(0.511176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.1174 | −1.12083 | −0.560416 | − | 0.828211i | \(-0.689359\pi\) | ||||
−0.560416 | + | 0.828211i | \(0.689359\pi\) | |||||||
\(464\) | 8.41883 | 0.390834 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.4608 | −0.530913 | ||||||||
\(467\) | −23.5448 | −1.08952 | −0.544762 | − | 0.838590i | \(-0.683380\pi\) | ||||
−0.544762 | + | 0.838590i | \(0.683380\pi\) | |||||||
\(468\) | −1.68842 | −0.0780471 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.1492 | 0.790196 | ||||||||
\(472\) | 7.04200 | 0.324134 | ||||||||
\(473\) | −12.2145 | −0.561623 | ||||||||
\(474\) | −7.31158 | −0.335832 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.4608 | −0.478969 | ||||||||
\(478\) | 15.4608 | 0.707162 | ||||||||
\(479\) | −29.9738 | −1.36954 | −0.684770 | − | 0.728760i | \(-0.740097\pi\) | ||||
−0.684770 | + | 0.728760i | \(0.740097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.90292 | −0.177958 | ||||||||
\(482\) | −4.37683 | −0.199359 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 26.2985 | 1.19539 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −30.5028 | −1.38222 | −0.691108 | − | 0.722752i | \(-0.742877\pi\) | ||||
−0.691108 | + | 0.722752i | \(0.742877\pi\) | |||||||
\(488\) | −9.46083 | −0.428272 | ||||||||
\(489\) | −0.539168 | −0.0243820 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.87966 | −0.175087 | −0.0875434 | − | 0.996161i | \(-0.527902\pi\) | ||||
−0.0875434 | + | 0.996161i | \(0.527902\pi\) | |||||||
\(492\) | 5.14925 | 0.232146 | ||||||||
\(493\) | 57.5652 | 2.59260 | ||||||||
\(494\) | 2.85075 | 0.128261 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.688417 | 0.0309108 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.5261 | 0.606118 | ||||||||
\(499\) | 9.37683 | 0.419765 | 0.209882 | − | 0.977727i | \(-0.432692\pi\) | ||||
0.209882 | + | 0.977727i | \(0.432692\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.14925 | −0.140698 | ||||||||
\(502\) | 26.5362 | 1.18437 | ||||||||
\(503\) | −14.2145 | −0.633793 | −0.316897 | − | 0.948460i | \(-0.602641\pi\) | ||||
−0.316897 | + | 0.948460i | \(0.602641\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.1174 | 0.627596 | ||||||||
\(507\) | 10.1492 | 0.450744 | ||||||||
\(508\) | −4.94491 | −0.219395 | ||||||||
\(509\) | −31.9637 | −1.41676 | −0.708382 | − | 0.705829i | \(-0.750575\pi\) | ||||
−0.708382 | + | 0.705829i | \(0.750575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.68842 | 0.0745454 | ||||||||
\(514\) | −22.4290 | −0.989301 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.00000 | 0.0880451 | ||||||||
\(517\) | 18.7203 | 0.823316 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.5261 | −0.462044 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.2014 | 1.58601 | 0.793006 | − | 0.609213i | \(-0.208515\pi\) | ||||
0.793006 | + | 0.609213i | \(0.208515\pi\) | |||||||
\(522\) | 8.41883 | 0.368482 | ||||||||
\(523\) | 36.9682 | 1.61651 | 0.808253 | − | 0.588836i | \(-0.200414\pi\) | ||||
0.808253 | + | 0.588836i | \(0.200414\pi\) | |||||||
\(524\) | 6.73042 | 0.294020 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.5913 | −0.854223 | ||||||||
\(527\) | 4.70716 | 0.205047 | ||||||||
\(528\) | −6.10725 | −0.265784 | ||||||||
\(529\) | −17.6566 | −0.767678 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.04200 | 0.305597 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.69408 | 0.376582 | ||||||||
\(534\) | −12.2145 | −0.528573 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.2145 | −0.527586 | ||||||||
\(537\) | −4.93475 | −0.212950 | ||||||||
\(538\) | 6.95800 | 0.299981 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2667 | −0.742352 | −0.371176 | − | 0.928563i | \(-0.621045\pi\) | ||||
−0.371176 | + | 0.928563i | \(0.621045\pi\) | |||||||
\(542\) | 28.3637 | 1.21833 | ||||||||
\(543\) | 6.13050 | 0.263085 | ||||||||
\(544\) | 6.83767 | 0.293162 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.4347 | 1.68610 | 0.843052 | − | 0.537832i | \(-0.180756\pi\) | ||||
0.843052 | + | 0.537832i | \(0.180756\pi\) | |||||||
\(548\) | 19.0522 | 0.813868 | ||||||||
\(549\) | −9.46083 | −0.403778 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.2145 | −0.605558 | ||||||||
\(552\) | −2.31158 | −0.0983875 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.05216 | 0.214646 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.3768 | −0.567304 | ||||||||
\(557\) | −32.8898 | −1.39359 | −0.696793 | − | 0.717272i | \(-0.745391\pi\) | ||||
−0.696793 | + | 0.717272i | \(0.745391\pi\) | |||||||
\(558\) | 0.688417 | 0.0291430 | ||||||||
\(559\) | 3.37683 | 0.142825 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −41.7593 | −1.76308 | ||||||||
\(562\) | 7.68842 | 0.324316 | ||||||||
\(563\) | 35.2014 | 1.48356 | 0.741781 | − | 0.670642i | \(-0.233981\pi\) | ||||
0.741781 | + | 0.670642i | \(0.233981\pi\) | |||||||
\(564\) | −3.06525 | −0.129070 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.4290 | −0.774629 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 17.4942 | 0.733397 | 0.366699 | − | 0.930340i | \(-0.380488\pi\) | ||||
0.366699 | + | 0.930340i | \(0.380488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.83767 | 0.369845 | 0.184922 | − | 0.982753i | \(-0.440797\pi\) | ||||
0.184922 | + | 0.982753i | \(0.440797\pi\) | |||||||
\(572\) | −10.3116 | −0.431149 | ||||||||
\(573\) | 14.9217 | 0.623361 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 40.3087 | 1.67807 | 0.839036 | − | 0.544076i | \(-0.183120\pi\) | ||||
0.839036 | + | 0.544076i | \(0.183120\pi\) | |||||||
\(578\) | 29.7537 | 1.23759 | ||||||||
\(579\) | 5.58117 | 0.231945 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.95800 | −0.205516 | ||||||||
\(583\) | −63.8869 | −2.64593 | ||||||||
\(584\) | −4.00000 | −0.165521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.83767 | 0.0759133 | ||||||||
\(587\) | −36.1492 | −1.49204 | −0.746020 | − | 0.665924i | \(-0.768037\pi\) | ||||
−0.746020 | + | 0.665924i | \(0.768037\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.16233 | −0.0478932 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.5261 | −0.597523 | ||||||||
\(592\) | 2.31158 | 0.0950055 | ||||||||
\(593\) | 4.08400 | 0.167710 | 0.0838548 | − | 0.996478i | \(-0.473277\pi\) | ||||
0.0838548 | + | 0.996478i | \(0.473277\pi\) | |||||||
\(594\) | −6.10725 | −0.250583 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.6232 | 0.517065 | ||||||||
\(597\) | −8.62317 | −0.352923 | ||||||||
\(598\) | −3.90292 | −0.159602 | ||||||||
\(599\) | −19.7593 | −0.807344 | −0.403672 | − | 0.914904i | \(-0.632266\pi\) | ||||
−0.403672 | + | 0.914904i | \(0.632266\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.72025 | −0.151752 | −0.0758761 | − | 0.997117i | \(-0.524175\pi\) | ||||
−0.0758761 | + | 0.997117i | \(0.524175\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.2145 | −0.497413 | ||||||||
\(604\) | 1.93475 | 0.0787238 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.00000 | −0.324978 | ||||||||
\(607\) | −11.2434 | −0.456356 | −0.228178 | − | 0.973619i | \(-0.573277\pi\) | ||||
−0.228178 | + | 0.973619i | \(0.573277\pi\) | |||||||
\(608\) | −1.68842 | −0.0684743 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.17542 | −0.209375 | ||||||||
\(612\) | 6.83767 | 0.276396 | ||||||||
\(613\) | −26.9347 | −1.08788 | −0.543942 | − | 0.839123i | \(-0.683069\pi\) | ||||
−0.543942 | + | 0.839123i | \(0.683069\pi\) | |||||||
\(614\) | 16.0840 | 0.649097 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.4608 | −1.34708 | −0.673541 | − | 0.739150i | \(-0.735228\pi\) | ||||
−0.673541 | + | 0.739150i | \(0.735228\pi\) | |||||||
\(618\) | 0.837665 | 0.0336958 | ||||||||
\(619\) | 34.8711 | 1.40159 | 0.700794 | − | 0.713364i | \(-0.252829\pi\) | ||||
0.700794 | + | 0.713364i | \(0.252829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.31158 | −0.0927606 | ||||||||
\(622\) | 15.3768 | 0.616555 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.68842 | 0.0675908 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22.4188 | 0.896037 | ||||||||
\(627\) | 10.3116 | 0.411805 | ||||||||
\(628\) | −17.1492 | −0.684330 | ||||||||
\(629\) | 15.8058 | 0.630220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4942 | −0.417769 | −0.208885 | − | 0.977940i | \(-0.566983\pi\) | ||||
−0.208885 | + | 0.977940i | \(0.566983\pi\) | |||||||
\(632\) | 7.31158 | 0.290839 | ||||||||
\(633\) | 7.68842 | 0.305587 | ||||||||
\(634\) | −10.0653 | −0.399742 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.4608 | 0.414799 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 51.4159 | 2.03558 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.77241 | 0.306992 | 0.153496 | − | 0.988149i | \(-0.450947\pi\) | ||||
0.153496 | + | 0.988149i | \(0.450947\pi\) | |||||||
\(642\) | −15.5261 | −0.612766 | ||||||||
\(643\) | −21.7218 | −0.856626 | −0.428313 | − | 0.903631i | \(-0.640892\pi\) | ||||
−0.428313 | + | 0.903631i | \(0.640892\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.5448 | −0.454225 | ||||||||
\(647\) | 9.55792 | 0.375760 | 0.187880 | − | 0.982192i | \(-0.439838\pi\) | ||||
0.187880 | + | 0.982192i | \(0.439838\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 43.0072 | 1.68818 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.539168 | 0.0211155 | ||||||||
\(653\) | −50.2667 | −1.96709 | −0.983543 | − | 0.180673i | \(-0.942173\pi\) | ||||
−0.983543 | + | 0.180673i | \(0.942173\pi\) | |||||||
\(654\) | 11.6753 | 0.456542 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.14925 | −0.201044 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.1623 | 0.434823 | 0.217411 | − | 0.976080i | \(-0.430239\pi\) | ||||
0.217411 | + | 0.976080i | \(0.430239\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.3450 | −0.557956 | −0.278978 | − | 0.960298i | \(-0.589996\pi\) | ||||
−0.278978 | + | 0.960298i | \(0.589996\pi\) | |||||||
\(662\) | 23.2797 | 0.904793 | ||||||||
\(663\) | 11.5448 | 0.448364 | ||||||||
\(664\) | −13.5261 | −0.524914 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.31158 | 0.0895720 | ||||||||
\(667\) | 19.4608 | 0.753526 | ||||||||
\(668\) | 3.14925 | 0.121848 | ||||||||
\(669\) | −11.1725 | −0.431954 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −57.7797 | −2.23056 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.8013 | −1.18730 | −0.593652 | − | 0.804722i | \(-0.702314\pi\) | ||||
−0.593652 | + | 0.804722i | \(0.702314\pi\) | |||||||
\(674\) | −5.17250 | −0.199237 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.1492 | −0.390356 | ||||||||
\(677\) | −14.1623 | −0.544303 | −0.272151 | − | 0.962254i | \(-0.587735\pi\) | ||||
−0.272151 | + | 0.962254i | \(0.587735\pi\) | |||||||
\(678\) | 3.37683 | 0.129687 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.85075 | 0.147561 | ||||||||
\(682\) | 4.20433 | 0.160992 | ||||||||
\(683\) | 30.7087 | 1.17504 | 0.587519 | − | 0.809211i | \(-0.300105\pi\) | ||||
0.587519 | + | 0.809211i | \(0.300105\pi\) | |||||||
\(684\) | −1.68842 | −0.0645582 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.67533 | 0.216527 | ||||||||
\(688\) | −2.00000 | −0.0762493 | ||||||||
\(689\) | 17.6622 | 0.672878 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.3507 | 1.49697 | 0.748485 | − | 0.663152i | \(-0.230782\pi\) | ||||
0.748485 | + | 0.663152i | \(0.230782\pi\) | |||||||
\(692\) | 10.5261 | 0.400142 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.67533 | −0.367271 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.41883 | −0.319115 | ||||||||
\(697\) | −35.2088 | −1.33363 | ||||||||
\(698\) | −28.2985 | −1.07111 | ||||||||
\(699\) | 11.4608 | 0.433488 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.79567 | −0.143360 | −0.0716802 | − | 0.997428i | \(-0.522836\pi\) | ||||
−0.0716802 | + | 0.997428i | \(0.522836\pi\) | |||||||
\(702\) | 1.68842 | 0.0637252 | ||||||||
\(703\) | −3.90292 | −0.147201 | ||||||||
\(704\) | 6.10725 | 0.230176 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.6753 | −0.665220 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.04200 | −0.264655 | ||||||||
\(709\) | −20.5595 | −0.772128 | −0.386064 | − | 0.922472i | \(-0.626166\pi\) | ||||
−0.386064 | + | 0.922472i | \(0.626166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.31158 | 0.274206 | ||||||||
\(712\) | 12.2145 | 0.457758 | ||||||||
\(713\) | 1.59133 | 0.0595959 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.93475 | 0.184420 | ||||||||
\(717\) | −15.4608 | −0.577395 | ||||||||
\(718\) | −4.83767 | −0.180540 | ||||||||
\(719\) | 24.8115 | 0.925313 | 0.462656 | − | 0.886538i | \(-0.346896\pi\) | ||||
0.462656 | + | 0.886538i | \(0.346896\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −16.1492 | −0.601013 | ||||||||
\(723\) | 4.37683 | 0.162776 | ||||||||
\(724\) | −6.13050 | −0.227838 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −26.2985 | −0.976029 | ||||||||
\(727\) | 39.2899 | 1.45718 | 0.728591 | − | 0.684949i | \(-0.240175\pi\) | ||||
0.728591 | + | 0.684949i | \(0.240175\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.6753 | −0.505800 | ||||||||
\(732\) | 9.46083 | 0.349682 | ||||||||
\(733\) | 9.01875 | 0.333115 | 0.166558 | − | 0.986032i | \(-0.446735\pi\) | ||||
0.166558 | + | 0.986032i | \(0.446735\pi\) | |||||||
\(734\) | 10.6464 | 0.392966 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.31158 | 0.0852061 | ||||||||
\(737\) | −74.5970 | −2.74782 | ||||||||
\(738\) | −5.14925 | −0.189546 | ||||||||
\(739\) | −14.0709 | −0.517607 | −0.258803 | − | 0.965930i | \(-0.583328\pi\) | ||||
−0.258803 | + | 0.965930i | \(0.583328\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.85075 | −0.104725 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.1492 | −1.43625 | −0.718123 | − | 0.695916i | \(-0.754999\pi\) | ||||
−0.718123 | + | 0.695916i | \(0.754999\pi\) | |||||||
\(744\) | −0.688417 | −0.0252386 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 34.7275 | 1.27146 | ||||||||
\(747\) | −13.5261 | −0.494893 | ||||||||
\(748\) | 41.7593 | 1.52687 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.2854 | −1.43355 | −0.716773 | − | 0.697307i | \(-0.754381\pi\) | ||||
−0.716773 | + | 0.697307i | \(0.754381\pi\) | |||||||
\(752\) | 3.06525 | 0.111778 | ||||||||
\(753\) | −26.5362 | −0.967035 | ||||||||
\(754\) | −14.2145 | −0.517662 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.9217 | −1.05118 | −0.525588 | − | 0.850739i | \(-0.676155\pi\) | ||||
−0.525588 | + | 0.850739i | \(0.676155\pi\) | |||||||
\(758\) | −19.4477 | −0.706374 | ||||||||
\(759\) | −14.1174 | −0.512430 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.5579 | −0.563974 | −0.281987 | − | 0.959418i | \(-0.590994\pi\) | ||||
−0.281987 | + | 0.959418i | \(0.590994\pi\) | |||||||
\(762\) | 4.94491 | 0.179135 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.9217 | −0.539847 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.850752 | 0.0307389 | ||||||||
\(767\) | −11.8898 | −0.429317 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 4.05216 | 0.146125 | 0.0730624 | − | 0.997327i | \(-0.476723\pi\) | ||||
0.0730624 | + | 0.997327i | \(0.476723\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.4290 | 0.807761 | ||||||||
\(772\) | −5.58117 | −0.200871 | ||||||||
\(773\) | 21.4477 | 0.771422 | 0.385711 | − | 0.922620i | \(-0.373956\pi\) | ||||
0.385711 | + | 0.922620i | \(0.373956\pi\) | |||||||
\(774\) | −2.00000 | −0.0718885 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.95800 | 0.177982 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.2985 | 0.942847 | ||||||||
\(779\) | 8.69408 | 0.311498 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.6435 | 1.31121 | ||||||||
\(782\) | 15.8058 | 0.565215 | ||||||||
\(783\) | −8.41883 | −0.300865 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.73042 | −0.240066 | ||||||||
\(787\) | 4.32467 | 0.154158 | 0.0770789 | − | 0.997025i | \(-0.475441\pi\) | ||||
0.0770789 | + | 0.997025i | \(0.475441\pi\) | |||||||
\(788\) | 14.5261 | 0.517470 | ||||||||
\(789\) | 19.5913 | 0.697470 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.10725 | 0.217012 | ||||||||
\(793\) | 15.9738 | 0.567247 | ||||||||
\(794\) | 1.70150 | 0.0603841 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.62317 | 0.305640 | ||||||||
\(797\) | −41.1549 | −1.45778 | −0.728891 | − | 0.684630i | \(-0.759964\pi\) | ||||
−0.728891 | + | 0.684630i | \(0.759964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9592 | 0.741482 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.2145 | 0.431578 | ||||||||
\(802\) | 3.01875 | 0.106596 | ||||||||
\(803\) | −24.4290 | −0.862081 | ||||||||
\(804\) | 12.2145 | 0.430772 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.16233 | −0.0409415 | ||||||||
\(807\) | −6.95800 | −0.244933 | ||||||||
\(808\) | 8.00000 | 0.281439 | ||||||||
\(809\) | −17.7724 | −0.624845 | −0.312422 | − | 0.949943i | \(-0.601140\pi\) | ||||
−0.312422 | + | 0.949943i | \(0.601140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.1231 | −1.65472 | −0.827358 | − | 0.561676i | \(-0.810157\pi\) | ||||
−0.827358 | + | 0.561676i | \(0.810157\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.3637 | −0.994760 | ||||||||
\(814\) | 14.1174 | 0.494815 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.83767 | −0.239366 | ||||||||
\(817\) | 3.37683 | 0.118140 | ||||||||
\(818\) | 4.14925 | 0.145075 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.71167 | 0.199339 | 0.0996693 | − | 0.995021i | \(-0.468222\pi\) | ||||
0.0996693 | + | 0.995021i | \(0.468222\pi\) | |||||||
\(822\) | −19.0522 | −0.664521 | ||||||||
\(823\) | −30.3450 | −1.05776 | −0.528880 | − | 0.848697i | \(-0.677388\pi\) | ||||
−0.528880 | + | 0.848697i | \(0.677388\pi\) | |||||||
\(824\) | −0.837665 | −0.0291815 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.2014 | −0.945886 | −0.472943 | − | 0.881093i | \(-0.656808\pi\) | ||||
−0.472943 | + | 0.881093i | \(0.656808\pi\) | |||||||
\(828\) | 2.31158 | 0.0803331 | ||||||||
\(829\) | −10.8377 | −0.376408 | −0.188204 | − | 0.982130i | \(-0.560267\pi\) | ||||
−0.188204 | + | 0.982130i | \(0.560267\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.05216 | −0.175258 | ||||||||
\(832\) | −1.68842 | −0.0585353 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.3768 | 0.463202 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.3116 | −0.356634 | ||||||||
\(837\) | −0.688417 | −0.0237952 | ||||||||
\(838\) | −13.8189 | −0.477367 | ||||||||
\(839\) | 1.59133 | 0.0549389 | 0.0274695 | − | 0.999623i | \(-0.491255\pi\) | ||||
0.0274695 | + | 0.999623i | \(0.491255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.8767 | 1.44403 | ||||||||
\(842\) | 25.2667 | 0.870747 | ||||||||
\(843\) | −7.68842 | −0.264803 | ||||||||
\(844\) | −7.68842 | −0.264646 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.06525 | 0.105385 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.4608 | −0.359226 | ||||||||
\(849\) | 18.4290 | 0.632482 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.34342 | 0.183170 | ||||||||
\(852\) | −6.00000 | −0.205557 | ||||||||
\(853\) | 29.9869 | 1.02673 | 0.513366 | − | 0.858170i | \(-0.328398\pi\) | ||||
0.513366 | + | 0.858170i | \(0.328398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.5261 | 0.530671 | ||||||||
\(857\) | −37.0057 | −1.26409 | −0.632045 | − | 0.774932i | \(-0.717784\pi\) | ||||
−0.632045 | + | 0.774932i | \(0.717784\pi\) | |||||||
\(858\) | 10.3116 | 0.352032 | ||||||||
\(859\) | −27.7593 | −0.947136 | −0.473568 | − | 0.880757i | \(-0.657034\pi\) | ||||
−0.473568 | + | 0.880757i | \(0.657034\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.5448 | 0.665700 | ||||||||
\(863\) | −3.60442 | −0.122696 | −0.0613479 | − | 0.998116i | \(-0.519540\pi\) | ||||
−0.0613479 | + | 0.998116i | \(0.519540\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.7537 | 0.501350 | ||||||||
\(867\) | −29.7537 | −1.01049 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.6537 | 1.51477 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.6232 | 0.698789 | ||||||||
\(872\) | −11.6753 | −0.395377 | ||||||||
\(873\) | 4.95800 | 0.167803 | ||||||||
\(874\) | −3.90292 | −0.132018 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | −12.0971 | −0.408490 | −0.204245 | − | 0.978920i | \(-0.565474\pi\) | ||||
−0.204245 | + | 0.978920i | \(0.565474\pi\) | |||||||
\(878\) | 15.9347 | 0.537772 | ||||||||
\(879\) | −1.83767 | −0.0619829 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7406 | 1.50735 | 0.753674 | − | 0.657248i | \(-0.228280\pi\) | ||||
0.753674 | + | 0.657248i | \(0.228280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.5970 | 1.23159 | 0.615793 | − | 0.787908i | \(-0.288836\pi\) | ||||
0.615793 | + | 0.787908i | \(0.288836\pi\) | |||||||
\(884\) | −11.5448 | −0.388295 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.8246 | 0.733211 | ||||||||
\(887\) | 56.0578 | 1.88224 | 0.941119 | − | 0.338076i | \(-0.109776\pi\) | ||||
0.941119 | + | 0.338076i | \(0.109776\pi\) | |||||||
\(888\) | −2.31158 | −0.0775717 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.10725 | 0.204601 | ||||||||
\(892\) | 11.1725 | 0.374083 | ||||||||
\(893\) | −5.17542 | −0.173189 | ||||||||
\(894\) | −12.6232 | −0.422182 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.90292 | 0.130315 | ||||||||
\(898\) | −11.3637 | −0.379213 | ||||||||
\(899\) | 5.79567 | 0.193296 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −71.5277 | −2.38293 | ||||||||
\(902\) | −31.4477 | −1.04710 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.37683 | −0.112312 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.93475 | −0.0642777 | ||||||||
\(907\) | 18.6435 | 0.619047 | 0.309524 | − | 0.950892i | \(-0.399830\pi\) | ||||
0.309524 | + | 0.950892i | \(0.399830\pi\) | |||||||
\(908\) | −3.85075 | −0.127792 | ||||||||
\(909\) | 8.00000 | 0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 1.68842 | 0.0559091 | ||||||||
\(913\) | −82.6072 | −2.73390 | ||||||||
\(914\) | 6.41883 | 0.212316 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.67533 | −0.187518 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.83767 | −0.225677 | ||||||||
\(919\) | −38.9217 | −1.28391 | −0.641954 | − | 0.766743i | \(-0.721876\pi\) | ||||
−0.641954 | + | 0.766743i | \(0.721876\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0840 | −0.529986 | ||||||||
\(922\) | −1.50733 | −0.0496414 | ||||||||
\(923\) | −10.1305 | −0.333450 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −24.1174 | −0.792547 | ||||||||
\(927\) | −0.837665 | −0.0275125 | ||||||||
\(928\) | 8.41883 | 0.276362 | ||||||||
\(929\) | −13.7349 | −0.450628 | −0.225314 | − | 0.974286i | \(-0.572341\pi\) | ||||
−0.225314 | + | 0.974286i | \(0.572341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.4608 | −0.375412 | ||||||||
\(933\) | −15.3768 | −0.503415 | ||||||||
\(934\) | −23.5448 | −0.770410 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.68842 | −0.0551876 | ||||||||
\(937\) | 20.7435 | 0.677661 | 0.338830 | − | 0.940847i | \(-0.389969\pi\) | ||||
0.338830 | + | 0.940847i | \(0.389969\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.4188 | −0.731611 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.0885 | −0.426673 | −0.213336 | − | 0.976979i | \(-0.568433\pi\) | ||||
−0.213336 | + | 0.976979i | \(0.568433\pi\) | |||||||
\(942\) | 17.1492 | 0.558753 | ||||||||
\(943\) | −11.9029 | −0.387612 | ||||||||
\(944\) | 7.04200 | 0.229198 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.2145 | −0.397128 | ||||||||
\(947\) | 20.2610 | 0.658394 | 0.329197 | − | 0.944261i | \(-0.393222\pi\) | ||||
0.329197 | + | 0.944261i | \(0.393222\pi\) | |||||||
\(948\) | −7.31158 | −0.237469 | ||||||||
\(949\) | 6.75367 | 0.219233 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.0653 | 0.326388 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.65500 | 0.0536107 | 0.0268053 | − | 0.999641i | \(-0.491467\pi\) | ||||
0.0268053 | + | 0.999641i | \(0.491467\pi\) | |||||||
\(954\) | −10.4608 | −0.338682 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.4608 | 0.500039 | ||||||||
\(957\) | −51.4159 | −1.66204 | ||||||||
\(958\) | −29.9738 | −0.968410 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5261 | −0.984712 | ||||||||
\(962\) | −3.90292 | −0.125835 | ||||||||
\(963\) | 15.5261 | 0.500321 | ||||||||
\(964\) | −4.37683 | −0.140968 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.3405 | −0.493317 | −0.246659 | − | 0.969102i | \(-0.579333\pi\) | ||||
−0.246659 | + | 0.969102i | \(0.579333\pi\) | |||||||
\(968\) | 26.2985 | 0.845266 | ||||||||
\(969\) | 11.5448 | 0.370873 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.1129 | −1.51193 | −0.755963 | − | 0.654615i | \(-0.772831\pi\) | ||||
−0.755963 | + | 0.654615i | \(0.772831\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −30.5028 | −0.977374 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.46083 | −0.302834 | ||||||||
\(977\) | 29.8898 | 0.956260 | 0.478130 | − | 0.878289i | \(-0.341315\pi\) | ||||
0.478130 | + | 0.878289i | \(0.341315\pi\) | |||||||
\(978\) | −0.539168 | −0.0172407 | ||||||||
\(979\) | 74.5970 | 2.38413 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.6753 | −0.372765 | ||||||||
\(982\) | −3.87966 | −0.123805 | ||||||||
\(983\) | −5.14925 | −0.164236 | −0.0821178 | − | 0.996623i | \(-0.526168\pi\) | ||||
−0.0821178 | + | 0.996623i | \(0.526168\pi\) | |||||||
\(984\) | 5.14925 | 0.164152 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 57.5652 | 1.83325 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.85075 | 0.0906945 | ||||||||
\(989\) | −4.62317 | −0.147008 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.81892 | 0.216610 | 0.108305 | − | 0.994118i | \(-0.465458\pi\) | ||||
0.108305 | + | 0.994118i | \(0.465458\pi\) | |||||||
\(992\) | 0.688417 | 0.0218573 | ||||||||
\(993\) | −23.2797 | −0.738761 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.5261 | 0.428590 | ||||||||
\(997\) | −51.5652 | −1.63309 | −0.816543 | − | 0.577285i | \(-0.804112\pi\) | ||||
−0.816543 | + | 0.577285i | \(0.804112\pi\) | |||||||
\(998\) | 9.37683 | 0.296818 | ||||||||
\(999\) | −2.31158 | −0.0731353 |
(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 | 7350.2.a.dp.1.3 | 3 | ||
5.2 | odd | 4 | 1470.2.g.h.589.4 | 6 | |||
5.3 | odd | 4 | 1470.2.g.h.589.1 | 6 | |||
5.4 | even | 2 | 7350.2.a.do.1.3 | 3 | |||
7.3 | odd | 6 | 1050.2.i.u.751.1 | 6 | |||
7.5 | odd | 6 | 1050.2.i.u.151.1 | 6 | |||
7.6 | odd | 2 | 7350.2.a.dq.1.3 | 3 | |||
35.2 | odd | 12 | 1470.2.n.j.949.5 | 12 | |||
35.3 | even | 12 | 210.2.n.b.79.5 | yes | 12 | ||
35.12 | even | 12 | 210.2.n.b.109.5 | yes | 12 | ||
35.13 | even | 4 | 1470.2.g.i.589.3 | 6 | |||
35.17 | even | 12 | 210.2.n.b.79.1 | ✓ | 12 | ||
35.18 | odd | 12 | 1470.2.n.j.79.5 | 12 | |||
35.19 | odd | 6 | 1050.2.i.v.151.3 | 6 | |||
35.23 | odd | 12 | 1470.2.n.j.949.3 | 12 | |||
35.24 | odd | 6 | 1050.2.i.v.751.3 | 6 | |||
35.27 | even | 4 | 1470.2.g.i.589.6 | 6 | |||
35.32 | odd | 12 | 1470.2.n.j.79.3 | 12 | |||
35.33 | even | 12 | 210.2.n.b.109.1 | yes | 12 | ||
35.34 | odd | 2 | 7350.2.a.dn.1.3 | 3 | |||
105.17 | odd | 12 | 630.2.u.f.289.6 | 12 | |||
105.38 | odd | 12 | 630.2.u.f.289.2 | 12 | |||
105.47 | odd | 12 | 630.2.u.f.109.2 | 12 | |||
105.68 | odd | 12 | 630.2.u.f.109.6 | 12 | |||
140.3 | odd | 12 | 1680.2.di.c.289.2 | 12 | |||
140.47 | odd | 12 | 1680.2.di.c.529.2 | 12 | |||
140.87 | odd | 12 | 1680.2.di.c.289.4 | 12 | |||
140.103 | odd | 12 | 1680.2.di.c.529.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.n.b.79.1 | ✓ | 12 | 35.17 | even | 12 | ||
210.2.n.b.79.5 | yes | 12 | 35.3 | even | 12 | ||
210.2.n.b.109.1 | yes | 12 | 35.33 | even | 12 | ||
210.2.n.b.109.5 | yes | 12 | 35.12 | even | 12 | ||
630.2.u.f.109.2 | 12 | 105.47 | odd | 12 | |||
630.2.u.f.109.6 | 12 | 105.68 | odd | 12 | |||
630.2.u.f.289.2 | 12 | 105.38 | odd | 12 | |||
630.2.u.f.289.6 | 12 | 105.17 | odd | 12 | |||
1050.2.i.u.151.1 | 6 | 7.5 | odd | 6 | |||
1050.2.i.u.751.1 | 6 | 7.3 | odd | 6 | |||
1050.2.i.v.151.3 | 6 | 35.19 | odd | 6 | |||
1050.2.i.v.751.3 | 6 | 35.24 | odd | 6 | |||
1470.2.g.h.589.1 | 6 | 5.3 | odd | 4 | |||
1470.2.g.h.589.4 | 6 | 5.2 | odd | 4 | |||
1470.2.g.i.589.3 | 6 | 35.13 | even | 4 | |||
1470.2.g.i.589.6 | 6 | 35.27 | even | 4 | |||
1470.2.n.j.79.3 | 12 | 35.32 | odd | 12 | |||
1470.2.n.j.79.5 | 12 | 35.18 | odd | 12 | |||
1470.2.n.j.949.3 | 12 | 35.23 | odd | 12 | |||
1470.2.n.j.949.5 | 12 | 35.2 | odd | 12 | |||
1680.2.di.c.289.2 | 12 | 140.3 | odd | 12 | |||
1680.2.di.c.289.4 | 12 | 140.87 | odd | 12 | |||
1680.2.di.c.529.2 | 12 | 140.47 | odd | 12 | |||
1680.2.di.c.529.4 | 12 | 140.103 | odd | 12 | |||
7350.2.a.dn.1.3 | 3 | 35.34 | odd | 2 | |||
7350.2.a.do.1.3 | 3 | 5.4 | even | 2 | |||
7350.2.a.dp.1.3 | 3 | 1.1 | even | 1 | trivial | ||
7350.2.a.dq.1.3 | 3 | 7.6 | odd | 2 |