Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(1,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, 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("1386.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.1 |
$q$-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 | ||||||||
\(5\) | −3.16228 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.16228 | −1.00000 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.16228 | 1.73711 | 0.868554 | − | 0.495595i | \(-0.165050\pi\) | ||||
0.868554 | + | 0.495595i | \(0.165050\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.16228 | 1.18431 | 0.592154 | − | 0.805825i | \(-0.298278\pi\) | ||||
0.592154 | + | 0.805825i | \(0.298278\pi\) | |||||||
\(20\) | −3.16228 | −0.707107 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −6.32456 | −1.31876 | −0.659380 | − | 0.751809i | \(-0.729181\pi\) | ||||
−0.659380 | + | 0.751809i | \(0.729181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.16228 | 1.64559 | 0.822797 | − | 0.568336i | \(-0.192412\pi\) | ||||
0.822797 | + | 0.568336i | \(0.192412\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.16228 | 1.22832 | ||||||||
\(35\) | 3.16228 | 0.534522 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.32456 | 1.36855 | 0.684274 | − | 0.729225i | \(-0.260119\pi\) | ||||
0.684274 | + | 0.729225i | \(0.260119\pi\) | |||||||
\(38\) | 5.16228 | 0.837432 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.16228 | −0.500000 | ||||||||
\(41\) | −7.16228 | −1.11856 | −0.559280 | − | 0.828979i | \(-0.688922\pi\) | ||||
−0.559280 | + | 0.828979i | \(0.688922\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.32456 | −0.964486 | −0.482243 | − | 0.876038i | \(-0.660178\pi\) | ||||
−0.482243 | + | 0.876038i | \(0.660178\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.32456 | −0.932505 | ||||||||
\(47\) | 11.4868 | 1.67553 | 0.837763 | − | 0.546033i | \(-0.183863\pi\) | ||||
0.837763 | + | 0.546033i | \(0.183863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 4.32456 | 0.594023 | 0.297012 | − | 0.954874i | \(-0.404010\pi\) | ||||
0.297012 | + | 0.954874i | \(0.404010\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.16228 | 0.426401 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | 0.525226 | ||||||||
\(59\) | −1.67544 | −0.218124 | −0.109062 | − | 0.994035i | \(-0.534785\pi\) | ||||
−0.109062 | + | 0.994035i | \(0.534785\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 9.16228 | 1.16361 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.32456 | −0.784465 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.32456 | 0.528329 | 0.264164 | − | 0.964478i | \(-0.414904\pi\) | ||||
0.264164 | + | 0.964478i | \(0.414904\pi\) | |||||||
\(68\) | 7.16228 | 0.868554 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.16228 | 0.377964 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.48683 | −0.642185 | −0.321093 | − | 0.947048i | \(-0.604050\pi\) | ||||
−0.321093 | + | 0.947048i | \(0.604050\pi\) | |||||||
\(74\) | 8.32456 | 0.967710 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.16228 | 0.592154 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.32456 | −0.486550 | −0.243275 | − | 0.969957i | \(-0.578222\pi\) | ||||
−0.243275 | + | 0.969957i | \(0.578222\pi\) | |||||||
\(80\) | −3.16228 | −0.353553 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.16228 | −0.790941 | ||||||||
\(83\) | −5.16228 | −0.566634 | −0.283317 | − | 0.959026i | \(-0.591435\pi\) | ||||
−0.283317 | + | 0.959026i | \(0.591435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.6491 | −2.45664 | ||||||||
\(86\) | −6.32456 | −0.681994 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 16.3246 | 1.73040 | 0.865200 | − | 0.501427i | \(-0.167192\pi\) | ||||
0.865200 | + | 0.501427i | \(0.167192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | −6.32456 | −0.659380 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.4868 | 1.18478 | ||||||||
\(95\) | −16.3246 | −1.67486 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6491 | −1.08125 | −0.540627 | − | 0.841263i | \(-0.681813\pi\) | ||||
−0.540627 | + | 0.841263i | \(0.681813\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000 | 0.500000 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8114 | 1.36088 | 0.680438 | − | 0.732805i | \(-0.261789\pi\) | ||||
0.680438 | + | 0.732805i | \(0.261789\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.32456 | 0.420038 | ||||||||
\(107\) | −14.3246 | −1.38481 | −0.692404 | − | 0.721510i | \(-0.743448\pi\) | ||||
−0.692404 | + | 0.721510i | \(0.743448\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.00000 | −0.766261 | −0.383131 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383131 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(110\) | 3.16228 | 0.301511 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.0000 | 1.86501 | ||||||||
\(116\) | 4.00000 | 0.371391 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.67544 | −0.154237 | ||||||||
\(119\) | −7.16228 | −0.656565 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 10.0000 | 0.905357 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.16228 | 0.822797 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9737 | 1.86111 | 0.930556 | − | 0.366150i | \(-0.119324\pi\) | ||||
0.930556 | + | 0.366150i | \(0.119324\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.32456 | −0.554700 | ||||||||
\(131\) | 5.16228 | 0.451030 | 0.225515 | − | 0.974240i | \(-0.427593\pi\) | ||||
0.225515 | + | 0.974240i | \(0.427593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.16228 | −0.447626 | ||||||||
\(134\) | 4.32456 | 0.373585 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.16228 | 0.614160 | ||||||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.48683 | −0.635025 | −0.317512 | − | 0.948254i | \(-0.602848\pi\) | ||||
−0.317512 | + | 0.948254i | \(0.602848\pi\) | |||||||
\(140\) | 3.16228 | 0.267261 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | −2.00000 | −0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.6491 | −1.05045 | ||||||||
\(146\) | −5.48683 | −0.454094 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.32456 | 0.684274 | ||||||||
\(149\) | 2.00000 | 0.163846 | 0.0819232 | − | 0.996639i | \(-0.473894\pi\) | ||||
0.0819232 | + | 0.996639i | \(0.473894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.6491 | 1.68040 | 0.840200 | − | 0.542276i | \(-0.182437\pi\) | ||||
0.840200 | + | 0.542276i | \(0.182437\pi\) | |||||||
\(152\) | 5.16228 | 0.418716 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −28.9737 | −2.32722 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.48683 | −0.437897 | −0.218948 | − | 0.975736i | \(-0.570263\pi\) | ||||
−0.218948 | + | 0.975736i | \(0.570263\pi\) | |||||||
\(158\) | −4.32456 | −0.344043 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.16228 | −0.250000 | ||||||||
\(161\) | 6.32456 | 0.498445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.6491 | −1.30406 | −0.652029 | − | 0.758194i | \(-0.726082\pi\) | ||||
−0.652029 | + | 0.758194i | \(0.726082\pi\) | |||||||
\(164\) | −7.16228 | −0.559280 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.16228 | −0.400670 | ||||||||
\(167\) | −6.32456 | −0.489409 | −0.244704 | − | 0.969598i | \(-0.578691\pi\) | ||||
−0.244704 | + | 0.969598i | \(0.578691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −22.6491 | −1.73711 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.32456 | −0.482243 | ||||||||
\(173\) | −12.3246 | −0.937019 | −0.468509 | − | 0.883459i | \(-0.655209\pi\) | ||||
−0.468509 | + | 0.883459i | \(0.655209\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.00000 | −0.377964 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.3246 | 1.22358 | ||||||||
\(179\) | −3.67544 | −0.274716 | −0.137358 | − | 0.990521i | \(-0.543861\pi\) | ||||
−0.137358 | + | 0.990521i | \(0.543861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4868 | 1.29979 | 0.649893 | − | 0.760026i | \(-0.274814\pi\) | ||||
0.649893 | + | 0.760026i | \(0.274814\pi\) | |||||||
\(182\) | −2.00000 | −0.148250 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.32456 | −0.466252 | ||||||||
\(185\) | −26.3246 | −1.93542 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.16228 | −0.523758 | ||||||||
\(188\) | 11.4868 | 0.837763 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.3246 | −1.18431 | ||||||||
\(191\) | −5.67544 | −0.410661 | −0.205330 | − | 0.978693i | \(-0.565827\pi\) | ||||
−0.205330 | + | 0.978693i | \(0.565827\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.6491 | 0.766540 | 0.383270 | − | 0.923636i | \(-0.374798\pi\) | ||||
0.383270 | + | 0.923636i | \(0.374798\pi\) | |||||||
\(194\) | −10.6491 | −0.764562 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 24.0000 | 1.70993 | 0.854965 | − | 0.518686i | \(-0.173579\pi\) | ||||
0.854965 | + | 0.518686i | \(0.173579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.4868 | 1.38138 | 0.690692 | − | 0.723149i | \(-0.257306\pi\) | ||||
0.690692 | + | 0.723149i | \(0.257306\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.00000 | −0.422159 | ||||||||
\(203\) | −4.00000 | −0.280745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.6491 | 1.58188 | ||||||||
\(206\) | 13.8114 | 0.962285 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −5.16228 | −0.357082 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.3246 | −1.26151 | −0.630757 | − | 0.775980i | \(-0.717256\pi\) | ||||
−0.630757 | + | 0.775980i | \(0.717256\pi\) | |||||||
\(212\) | 4.32456 | 0.297012 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.3246 | −0.979206 | ||||||||
\(215\) | 20.0000 | 1.36399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.16228 | −0.621976 | ||||||||
\(218\) | −8.00000 | −0.541828 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.16228 | 0.213201 | ||||||||
\(221\) | 14.3246 | 0.963574 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.4868 | −0.769215 | −0.384608 | − | 0.923080i | \(-0.625663\pi\) | ||||
−0.384608 | + | 0.923080i | \(0.625663\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | 0.133038 | ||||||||
\(227\) | 7.48683 | 0.496919 | 0.248459 | − | 0.968642i | \(-0.420076\pi\) | ||||
0.248459 | + | 0.968642i | \(0.420076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.4868 | −1.68422 | −0.842109 | − | 0.539308i | \(-0.818686\pi\) | ||||
−0.842109 | + | 0.539308i | \(0.818686\pi\) | |||||||
\(230\) | 20.0000 | 1.31876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.00000 | 0.262613 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.3246 | −2.36955 | ||||||||
\(236\) | −1.67544 | −0.109062 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.16228 | −0.464262 | ||||||||
\(239\) | 12.6491 | 0.818203 | 0.409101 | − | 0.912489i | \(-0.365842\pi\) | ||||
0.409101 | + | 0.912489i | \(0.365842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.837722 | 0.0539624 | 0.0269812 | − | 0.999636i | \(-0.491411\pi\) | ||||
0.0269812 | + | 0.999636i | \(0.491411\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | −3.16228 | −0.202031 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3246 | 0.656936 | ||||||||
\(248\) | 9.16228 | 0.581805 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.6754 | −0.863186 | −0.431593 | − | 0.902068i | \(-0.642048\pi\) | ||||
−0.431593 | + | 0.902068i | \(0.642048\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.32456 | 0.397621 | ||||||||
\(254\) | 20.9737 | 1.31600 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.67544 | 0.478781 | 0.239391 | − | 0.970923i | \(-0.423052\pi\) | ||||
0.239391 | + | 0.970923i | \(0.423052\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.32456 | −0.517263 | ||||||||
\(260\) | −6.32456 | −0.392232 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.16228 | 0.318927 | ||||||||
\(263\) | 24.9737 | 1.53994 | 0.769971 | − | 0.638079i | \(-0.220271\pi\) | ||||
0.769971 | + | 0.638079i | \(0.220271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.6754 | −0.840076 | ||||||||
\(266\) | −5.16228 | −0.316520 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.32456 | 0.264164 | ||||||||
\(269\) | 11.1623 | 0.680576 | 0.340288 | − | 0.940321i | \(-0.389475\pi\) | ||||
0.340288 | + | 0.940321i | \(0.389475\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.32456 | −0.384189 | −0.192095 | − | 0.981376i | \(-0.561528\pi\) | ||||
−0.192095 | + | 0.981376i | \(0.561528\pi\) | |||||||
\(272\) | 7.16228 | 0.434277 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | −5.00000 | −0.301511 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.0000 | −1.44202 | −0.721010 | − | 0.692925i | \(-0.756322\pi\) | ||||
−0.721010 | + | 0.692925i | \(0.756322\pi\) | |||||||
\(278\) | −7.48683 | −0.449030 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.16228 | 0.188982 | ||||||||
\(281\) | 22.6491 | 1.35113 | 0.675566 | − | 0.737299i | \(-0.263899\pi\) | ||||
0.675566 | + | 0.737299i | \(0.263899\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.4868 | −0.920597 | −0.460298 | − | 0.887764i | \(-0.652258\pi\) | ||||
−0.460298 | + | 0.887764i | \(0.652258\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | −0.118262 | ||||||||
\(287\) | 7.16228 | 0.422776 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.2982 | 2.01754 | ||||||||
\(290\) | −12.6491 | −0.742781 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.48683 | −0.321093 | ||||||||
\(293\) | 24.9737 | 1.45898 | 0.729489 | − | 0.683993i | \(-0.239758\pi\) | ||||
0.729489 | + | 0.683993i | \(0.239758\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.29822 | 0.308474 | ||||||||
\(296\) | 8.32456 | 0.483855 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.00000 | 0.115857 | ||||||||
\(299\) | −12.6491 | −0.731517 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.32456 | 0.364541 | ||||||||
\(302\) | 20.6491 | 1.18822 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.16228 | 0.296077 | ||||||||
\(305\) | −31.6228 | −1.81071 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.1623 | −1.20779 | −0.603897 | − | 0.797062i | \(-0.706386\pi\) | ||||
−0.603897 | + | 0.797062i | \(0.706386\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −28.9737 | −1.64559 | ||||||||
\(311\) | −29.8114 | −1.69045 | −0.845224 | − | 0.534412i | \(-0.820533\pi\) | ||||
−0.845224 | + | 0.534412i | \(0.820533\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.3246 | 1.14881 | 0.574406 | − | 0.818571i | \(-0.305233\pi\) | ||||
0.574406 | + | 0.818571i | \(0.305233\pi\) | |||||||
\(314\) | −5.48683 | −0.309640 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.32456 | −0.243275 | ||||||||
\(317\) | 12.9737 | 0.728674 | 0.364337 | − | 0.931267i | \(-0.381296\pi\) | ||||
0.364337 | + | 0.931267i | \(0.381296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | −3.16228 | −0.176777 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.32456 | 0.352454 | ||||||||
\(323\) | 36.9737 | 2.05727 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.0000 | 0.554700 | ||||||||
\(326\) | −16.6491 | −0.922109 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.16228 | −0.395471 | ||||||||
\(329\) | −11.4868 | −0.633290 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.97367 | −0.493237 | −0.246619 | − | 0.969113i | \(-0.579320\pi\) | ||||
−0.246619 | + | 0.969113i | \(0.579320\pi\) | |||||||
\(332\) | −5.16228 | −0.283317 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.32456 | −0.346064 | ||||||||
\(335\) | −13.6754 | −0.747169 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.6754 | −1.07179 | −0.535895 | − | 0.844285i | \(-0.680026\pi\) | ||||
−0.535895 | + | 0.844285i | \(0.680026\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −22.6491 | −1.22832 | ||||||||
\(341\) | −9.16228 | −0.496165 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.32456 | −0.340997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.3246 | −0.662572 | ||||||||
\(347\) | −14.3246 | −0.768982 | −0.384491 | − | 0.923129i | \(-0.625623\pi\) | ||||
−0.384491 | + | 0.923129i | \(0.625623\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.97367 | 0.480349 | 0.240175 | − | 0.970730i | \(-0.422795\pi\) | ||||
0.240175 | + | 0.970730i | \(0.422795\pi\) | |||||||
\(350\) | −5.00000 | −0.267261 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 7.67544 | 0.408523 | 0.204261 | − | 0.978916i | \(-0.434521\pi\) | ||||
0.204261 | + | 0.978916i | \(0.434521\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.2982 | 1.34269 | ||||||||
\(356\) | 16.3246 | 0.865200 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.67544 | −0.194253 | ||||||||
\(359\) | 3.67544 | 0.193983 | 0.0969913 | − | 0.995285i | \(-0.469078\pi\) | ||||
0.0969913 | + | 0.995285i | \(0.469078\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.64911 | 0.402585 | ||||||||
\(362\) | 17.4868 | 0.919088 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 17.3509 | 0.908187 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.16228 | −0.0606704 | −0.0303352 | − | 0.999540i | \(-0.509657\pi\) | ||||
−0.0303352 | + | 0.999540i | \(0.509657\pi\) | |||||||
\(368\) | −6.32456 | −0.329690 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −26.3246 | −1.36855 | ||||||||
\(371\) | −4.32456 | −0.224520 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | −7.16228 | −0.370353 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.4868 | 0.592388 | ||||||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.2982 | −0.683084 | −0.341542 | − | 0.939867i | \(-0.610949\pi\) | ||||
−0.341542 | + | 0.939867i | \(0.610949\pi\) | |||||||
\(380\) | −16.3246 | −0.837432 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.67544 | −0.290381 | ||||||||
\(383\) | −9.16228 | −0.468171 | −0.234085 | − | 0.972216i | \(-0.575209\pi\) | ||||
−0.234085 | + | 0.972216i | \(0.575209\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.16228 | −0.161165 | ||||||||
\(386\) | 10.6491 | 0.542025 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.6491 | −0.540627 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.2982 | −2.29083 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.0000 | 1.20910 | ||||||||
\(395\) | 13.6754 | 0.688086 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.4868 | 1.07839 | 0.539197 | − | 0.842180i | \(-0.318728\pi\) | ||||
0.539197 | + | 0.842180i | \(0.318728\pi\) | |||||||
\(398\) | 19.4868 | 0.976787 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | 23.2982 | 1.16346 | 0.581729 | − | 0.813383i | \(-0.302376\pi\) | ||||
0.581729 | + | 0.813383i | \(0.302376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.3246 | 0.912811 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.00000 | −0.198517 | ||||||||
\(407\) | −8.32456 | −0.412633 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.1623 | 1.34309 | 0.671544 | − | 0.740965i | \(-0.265631\pi\) | ||||
0.671544 | + | 0.740965i | \(0.265631\pi\) | |||||||
\(410\) | 22.6491 | 1.11856 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.8114 | 0.680438 | ||||||||
\(413\) | 1.67544 | 0.0824432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.3246 | 0.801341 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.16228 | −0.252495 | ||||||||
\(419\) | −16.6491 | −0.813362 | −0.406681 | − | 0.913570i | \(-0.633314\pi\) | ||||
−0.406681 | + | 0.913570i | \(0.633314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.9473 | −1.94691 | −0.973457 | − | 0.228870i | \(-0.926497\pi\) | ||||
−0.973457 | + | 0.228870i | \(0.926497\pi\) | |||||||
\(422\) | −18.3246 | −0.892025 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.32456 | 0.210019 | ||||||||
\(425\) | 35.8114 | 1.73711 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0000 | −0.483934 | ||||||||
\(428\) | −14.3246 | −0.692404 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.0000 | 0.964486 | ||||||||
\(431\) | −8.97367 | −0.432246 | −0.216123 | − | 0.976366i | \(-0.569341\pi\) | ||||
−0.216123 | + | 0.976366i | \(0.569341\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.0000 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | −9.16228 | −0.439803 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | −0.383131 | ||||||||
\(437\) | −32.6491 | −1.56182 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.32456 | −0.301855 | −0.150927 | − | 0.988545i | \(-0.548226\pi\) | ||||
−0.150927 | + | 0.988545i | \(0.548226\pi\) | |||||||
\(440\) | 3.16228 | 0.150756 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.3246 | 0.681350 | ||||||||
\(443\) | 4.32456 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −51.6228 | −2.44715 | ||||||||
\(446\) | −11.4868 | −0.543917 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.16228 | 0.337258 | ||||||||
\(452\) | 2.00000 | 0.0940721 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.48683 | 0.351374 | ||||||||
\(455\) | 6.32456 | 0.296500 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3509 | 0.811640 | 0.405820 | − | 0.913953i | \(-0.366986\pi\) | ||||
0.405820 | + | 0.913953i | \(0.366986\pi\) | |||||||
\(458\) | −25.4868 | −1.19092 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20.0000 | 0.932505 | ||||||||
\(461\) | −23.2982 | −1.08511 | −0.542553 | − | 0.840021i | \(-0.682542\pi\) | ||||
−0.542553 | + | 0.840021i | \(0.682542\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.6491 | −1.33144 | −0.665719 | − | 0.746203i | \(-0.731875\pi\) | ||||
−0.665719 | + | 0.746203i | \(0.731875\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | −17.2982 | −0.800466 | −0.400233 | − | 0.916413i | \(-0.631071\pi\) | ||||
−0.400233 | + | 0.916413i | \(0.631071\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.32456 | −0.199689 | ||||||||
\(470\) | −36.3246 | −1.67553 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.67544 | −0.0771186 | ||||||||
\(473\) | 6.32456 | 0.290803 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.8114 | 1.18431 | ||||||||
\(476\) | −7.16228 | −0.328282 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.6491 | 0.578557 | ||||||||
\(479\) | −21.2982 | −0.973141 | −0.486570 | − | 0.873641i | \(-0.661752\pi\) | ||||
−0.486570 | + | 0.873641i | \(0.661752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.6491 | 0.759134 | ||||||||
\(482\) | 0.837722 | 0.0381572 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 33.6754 | 1.52912 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.3246 | −0.649108 | −0.324554 | − | 0.945867i | \(-0.605214\pi\) | ||||
−0.324554 | + | 0.945867i | \(0.605214\pi\) | |||||||
\(488\) | 10.0000 | 0.452679 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.16228 | −0.142857 | ||||||||
\(491\) | 8.64911 | 0.390329 | 0.195164 | − | 0.980771i | \(-0.437476\pi\) | ||||
0.195164 | + | 0.980771i | \(0.437476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.6491 | 1.29029 | ||||||||
\(494\) | 10.3246 | 0.464524 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.16228 | 0.411398 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.9737 | −0.759846 | −0.379923 | − | 0.925018i | \(-0.624049\pi\) | ||||
−0.379923 | + | 0.925018i | \(0.624049\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.6754 | −0.610365 | ||||||||
\(503\) | −5.02633 | −0.224113 | −0.112057 | − | 0.993702i | \(-0.535744\pi\) | ||||
−0.112057 | + | 0.993702i | \(0.535744\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.9737 | 0.844317 | ||||||||
\(506\) | 6.32456 | 0.281161 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.9737 | 0.930556 | ||||||||
\(509\) | 39.8114 | 1.76461 | 0.882304 | − | 0.470679i | \(-0.155991\pi\) | ||||
0.882304 | + | 0.470679i | \(0.155991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.48683 | 0.242723 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.67544 | 0.338549 | ||||||||
\(515\) | −43.6754 | −1.92457 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.4868 | −0.505190 | ||||||||
\(518\) | −8.32456 | −0.365760 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.32456 | −0.277350 | ||||||||
\(521\) | 20.3246 | 0.890435 | 0.445217 | − | 0.895422i | \(-0.353126\pi\) | ||||
0.445217 | + | 0.895422i | \(0.353126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.13594 | −0.180852 | −0.0904261 | − | 0.995903i | \(-0.528823\pi\) | ||||
−0.0904261 | + | 0.995903i | \(0.528823\pi\) | |||||||
\(524\) | 5.16228 | 0.225515 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.9737 | 1.08890 | ||||||||
\(527\) | 65.6228 | 2.85857 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0000 | 0.739130 | ||||||||
\(530\) | −13.6754 | −0.594023 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.16228 | −0.223813 | ||||||||
\(533\) | −14.3246 | −0.620465 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 45.2982 | 1.95841 | ||||||||
\(536\) | 4.32456 | 0.186792 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.1623 | 0.481240 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.2982 | 1.34562 | 0.672808 | − | 0.739817i | \(-0.265088\pi\) | ||||
0.672808 | + | 0.739817i | \(0.265088\pi\) | |||||||
\(542\) | −6.32456 | −0.271663 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.16228 | 0.307080 | ||||||||
\(545\) | 25.2982 | 1.08366 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.2982 | −1.76578 | −0.882892 | − | 0.469576i | \(-0.844407\pi\) | ||||
−0.882892 | + | 0.469576i | \(0.844407\pi\) | |||||||
\(548\) | −18.0000 | −0.768922 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.00000 | −0.213201 | ||||||||
\(551\) | 20.6491 | 0.879682 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.32456 | 0.183899 | ||||||||
\(554\) | −24.0000 | −1.01966 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.48683 | −0.317512 | ||||||||
\(557\) | −33.2982 | −1.41089 | −0.705445 | − | 0.708764i | \(-0.749253\pi\) | ||||
−0.705445 | + | 0.708764i | \(0.749253\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.6491 | −0.535000 | ||||||||
\(560\) | 3.16228 | 0.133631 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.6491 | 0.955395 | ||||||||
\(563\) | 20.1359 | 0.848629 | 0.424314 | − | 0.905515i | \(-0.360515\pi\) | ||||
0.424314 | + | 0.905515i | \(0.360515\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.32456 | −0.266076 | ||||||||
\(566\) | −15.4868 | −0.650960 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | 26.6491 | 1.11719 | 0.558594 | − | 0.829441i | \(-0.311341\pi\) | ||||
0.558594 | + | 0.829441i | \(0.311341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.6491 | 0.529349 | 0.264674 | − | 0.964338i | \(-0.414736\pi\) | ||||
0.264674 | + | 0.964338i | \(0.414736\pi\) | |||||||
\(572\) | −2.00000 | −0.0836242 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.16228 | 0.298948 | ||||||||
\(575\) | −31.6228 | −1.31876 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.6754 | 0.652577 | 0.326289 | − | 0.945270i | \(-0.394202\pi\) | ||||
0.326289 | + | 0.945270i | \(0.394202\pi\) | |||||||
\(578\) | 34.2982 | 1.42662 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.6491 | −0.525226 | ||||||||
\(581\) | 5.16228 | 0.214167 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.32456 | −0.179105 | ||||||||
\(584\) | −5.48683 | −0.227047 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.9737 | 1.03165 | ||||||||
\(587\) | 6.97367 | 0.287834 | 0.143917 | − | 0.989590i | \(-0.454030\pi\) | ||||
0.143917 | + | 0.989590i | \(0.454030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 47.2982 | 1.94889 | ||||||||
\(590\) | 5.29822 | 0.218124 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.32456 | 0.342137 | ||||||||
\(593\) | −16.4605 | −0.675952 | −0.337976 | − | 0.941155i | \(-0.609742\pi\) | ||||
−0.337976 | + | 0.941155i | \(0.609742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.6491 | 0.928523 | ||||||||
\(596\) | 2.00000 | 0.0819232 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.6491 | −0.517261 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.1623 | 0.781646 | 0.390823 | − | 0.920466i | \(-0.372191\pi\) | ||||
0.390823 | + | 0.920466i | \(0.372191\pi\) | |||||||
\(602\) | 6.32456 | 0.257770 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.6491 | 0.840200 | ||||||||
\(605\) | −3.16228 | −0.128565 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.64911 | 0.188702 | 0.0943508 | − | 0.995539i | \(-0.469922\pi\) | ||||
0.0943508 | + | 0.995539i | \(0.469922\pi\) | |||||||
\(608\) | 5.16228 | 0.209358 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −31.6228 | −1.28037 | ||||||||
\(611\) | 22.9737 | 0.929415 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.2982 | −1.26412 | −0.632062 | − | 0.774918i | \(-0.717791\pi\) | ||||
−0.632062 | + | 0.774918i | \(0.717791\pi\) | |||||||
\(614\) | −21.1623 | −0.854040 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | 20.6491 | 0.831302 | 0.415651 | − | 0.909524i | \(-0.363554\pi\) | ||||
0.415651 | + | 0.909524i | \(0.363554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.3509 | 0.938551 | 0.469276 | − | 0.883052i | \(-0.344515\pi\) | ||||
0.469276 | + | 0.883052i | \(0.344515\pi\) | |||||||
\(620\) | −28.9737 | −1.16361 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −29.8114 | −1.19533 | ||||||||
\(623\) | −16.3246 | −0.654029 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 20.3246 | 0.812333 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.48683 | −0.218948 | ||||||||
\(629\) | 59.6228 | 2.37732 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.6228 | −1.09965 | −0.549823 | − | 0.835281i | \(-0.685305\pi\) | ||||
−0.549823 | + | 0.835281i | \(0.685305\pi\) | |||||||
\(632\) | −4.32456 | −0.172022 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.9737 | 0.515250 | ||||||||
\(635\) | −66.3246 | −2.63201 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.16228 | −0.125000 | ||||||||
\(641\) | 37.9473 | 1.49883 | 0.749415 | − | 0.662101i | \(-0.230335\pi\) | ||||
0.749415 | + | 0.662101i | \(0.230335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.9737 | 1.37923 | 0.689613 | − | 0.724178i | \(-0.257780\pi\) | ||||
0.689613 | + | 0.724178i | \(0.257780\pi\) | |||||||
\(644\) | 6.32456 | 0.249222 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.9737 | 1.45471 | ||||||||
\(647\) | 3.48683 | 0.137082 | 0.0685408 | − | 0.997648i | \(-0.478166\pi\) | ||||
0.0685408 | + | 0.997648i | \(0.478166\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.67544 | 0.0657670 | ||||||||
\(650\) | 10.0000 | 0.392232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.6491 | −0.652029 | ||||||||
\(653\) | −43.2982 | −1.69439 | −0.847195 | − | 0.531282i | \(-0.821711\pi\) | ||||
−0.847195 | + | 0.531282i | \(0.821711\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.3246 | −0.637853 | ||||||||
\(656\) | −7.16228 | −0.279640 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.4868 | −0.447803 | ||||||||
\(659\) | 22.9737 | 0.894927 | 0.447463 | − | 0.894302i | \(-0.352327\pi\) | ||||
0.447463 | + | 0.894302i | \(0.352327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.1359 | −0.860988 | −0.430494 | − | 0.902593i | \(-0.641661\pi\) | ||||
−0.430494 | + | 0.902593i | \(0.641661\pi\) | |||||||
\(662\) | −8.97367 | −0.348771 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.16228 | −0.200335 | ||||||||
\(665\) | 16.3246 | 0.633039 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.2982 | −0.979551 | ||||||||
\(668\) | −6.32456 | −0.244704 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.6754 | −0.528329 | ||||||||
\(671\) | −10.0000 | −0.386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.6228 | 0.525119 | 0.262560 | − | 0.964916i | \(-0.415433\pi\) | ||||
0.262560 | + | 0.964916i | \(0.415433\pi\) | |||||||
\(674\) | −19.6754 | −0.757870 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −8.32456 | −0.319939 | −0.159969 | − | 0.987122i | \(-0.551140\pi\) | ||||
−0.159969 | + | 0.987122i | \(0.551140\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.6491 | 0.408675 | ||||||||
\(680\) | −22.6491 | −0.868554 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.16228 | −0.350842 | ||||||||
\(683\) | −24.9737 | −0.955591 | −0.477795 | − | 0.878471i | \(-0.658564\pi\) | ||||
−0.477795 | + | 0.878471i | \(0.658564\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 56.9210 | 2.17484 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.32456 | −0.241121 | ||||||||
\(689\) | 8.64911 | 0.329505 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.97367 | −0.265291 | −0.132645 | − | 0.991164i | \(-0.542347\pi\) | ||||
−0.132645 | + | 0.991164i | \(0.542347\pi\) | |||||||
\(692\) | −12.3246 | −0.468509 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.3246 | −0.543753 | ||||||||
\(695\) | 23.6754 | 0.898061 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.2982 | −1.94306 | ||||||||
\(698\) | 8.97367 | 0.339658 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.00000 | −0.188982 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.9737 | 1.62078 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.67544 | 0.288869 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.3246 | 1.51442 | 0.757210 | − | 0.653171i | \(-0.226562\pi\) | ||||
0.757210 | + | 0.653171i | \(0.226562\pi\) | |||||||
\(710\) | 25.2982 | 0.949425 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.3246 | 0.611789 | ||||||||
\(713\) | −57.9473 | −2.17014 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.32456 | 0.236525 | ||||||||
\(716\) | −3.67544 | −0.137358 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.67544 | 0.137166 | ||||||||
\(719\) | 22.8377 | 0.851703 | 0.425852 | − | 0.904793i | \(-0.359975\pi\) | ||||
0.425852 | + | 0.904793i | \(0.359975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.8114 | −0.514363 | ||||||||
\(722\) | 7.64911 | 0.284670 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.4868 | 0.649893 | ||||||||
\(725\) | 20.0000 | 0.742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.1359 | −1.48856 | −0.744280 | − | 0.667868i | \(-0.767207\pi\) | ||||
−0.744280 | + | 0.667868i | \(0.767207\pi\) | |||||||
\(728\) | −2.00000 | −0.0741249 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 17.3509 | 0.642185 | ||||||||
\(731\) | −45.2982 | −1.67542 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.35089 | 0.197640 | 0.0988198 | − | 0.995105i | \(-0.468493\pi\) | ||||
0.0988198 | + | 0.995105i | \(0.468493\pi\) | |||||||
\(734\) | −1.16228 | −0.0429005 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.32456 | −0.233126 | ||||||||
\(737\) | −4.32456 | −0.159297 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.35089 | 0.123264 | 0.0616322 | − | 0.998099i | \(-0.480369\pi\) | ||||
0.0616322 | + | 0.998099i | \(0.480369\pi\) | |||||||
\(740\) | −26.3246 | −0.967710 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.32456 | −0.158759 | ||||||||
\(743\) | 3.35089 | 0.122932 | 0.0614661 | − | 0.998109i | \(-0.480422\pi\) | ||||
0.0614661 | + | 0.998109i | \(0.480422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.32456 | −0.231714 | ||||||||
\(746\) | −10.0000 | −0.366126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.16228 | −0.261879 | ||||||||
\(749\) | 14.3246 | 0.523408 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.67544 | 0.207100 | 0.103550 | − | 0.994624i | \(-0.466980\pi\) | ||||
0.103550 | + | 0.994624i | \(0.466980\pi\) | |||||||
\(752\) | 11.4868 | 0.418882 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | −65.2982 | −2.37645 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.6228 | 1.07666 | 0.538329 | − | 0.842735i | \(-0.319056\pi\) | ||||
0.538329 | + | 0.842735i | \(0.319056\pi\) | |||||||
\(758\) | −13.2982 | −0.483013 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.3246 | −0.592154 | ||||||||
\(761\) | −9.48683 | −0.343897 | −0.171949 | − | 0.985106i | \(-0.555006\pi\) | ||||
−0.171949 | + | 0.985106i | \(0.555006\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | 0.289619 | ||||||||
\(764\) | −5.67544 | −0.205330 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.16228 | −0.331047 | ||||||||
\(767\) | −3.35089 | −0.120994 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.4868 | 0.919079 | 0.459539 | − | 0.888157i | \(-0.348015\pi\) | ||||
0.459539 | + | 0.888157i | \(0.348015\pi\) | |||||||
\(770\) | −3.16228 | −0.113961 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.6491 | 0.383270 | ||||||||
\(773\) | −5.86406 | −0.210915 | −0.105458 | − | 0.994424i | \(-0.533631\pi\) | ||||
−0.105458 | + | 0.994424i | \(0.533631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.8114 | 1.64559 | ||||||||
\(776\) | −10.6491 | −0.382281 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000 | 0.215110 | ||||||||
\(779\) | −36.9737 | −1.32472 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | −45.2982 | −1.61986 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 17.3509 | 0.619280 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.46050 | 0.230292 | 0.115146 | − | 0.993349i | \(-0.463266\pi\) | ||||
0.115146 | + | 0.993349i | \(0.463266\pi\) | |||||||
\(788\) | 24.0000 | 0.854965 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.6754 | 0.486550 | ||||||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0000 | 0.710221 | ||||||||
\(794\) | 21.4868 | 0.762539 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.4868 | 0.690692 | ||||||||
\(797\) | 8.83772 | 0.313048 | 0.156524 | − | 0.987674i | \(-0.449971\pi\) | ||||
0.156524 | + | 0.987674i | \(0.449971\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 82.2719 | 2.91057 | ||||||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.2982 | 0.822689 | ||||||||
\(803\) | 5.48683 | 0.193626 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.0000 | −0.704907 | ||||||||
\(806\) | 18.3246 | 0.645455 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.00000 | −0.211079 | ||||||||
\(809\) | 43.6754 | 1.53555 | 0.767773 | − | 0.640721i | \(-0.221365\pi\) | ||||
0.767773 | + | 0.640721i | \(0.221365\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.48683 | −0.262898 | −0.131449 | − | 0.991323i | \(-0.541963\pi\) | ||||
−0.131449 | + | 0.991323i | \(0.541963\pi\) | |||||||
\(812\) | −4.00000 | −0.140372 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.32456 | −0.291776 | ||||||||
\(815\) | 52.6491 | 1.84422 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.6491 | −1.14225 | ||||||||
\(818\) | 27.1623 | 0.949707 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22.6491 | 0.790941 | ||||||||
\(821\) | −52.5964 | −1.83563 | −0.917814 | − | 0.397010i | \(-0.870048\pi\) | ||||
−0.917814 | + | 0.397010i | \(0.870048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.02633 | −0.314638 | −0.157319 | − | 0.987548i | \(-0.550285\pi\) | ||||
−0.157319 | + | 0.987548i | \(0.550285\pi\) | |||||||
\(824\) | 13.8114 | 0.481143 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.67544 | 0.0582962 | ||||||||
\(827\) | 33.9473 | 1.18046 | 0.590232 | − | 0.807234i | \(-0.299036\pi\) | ||||
0.590232 | + | 0.807234i | \(0.299036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.4605 | −0.432771 | −0.216386 | − | 0.976308i | \(-0.569427\pi\) | ||||
−0.216386 | + | 0.976308i | \(0.569427\pi\) | |||||||
\(830\) | 16.3246 | 0.566634 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | 7.16228 | 0.248158 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.0000 | 0.692129 | ||||||||
\(836\) | −5.16228 | −0.178541 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.6491 | −0.575134 | ||||||||
\(839\) | −34.4605 | −1.18971 | −0.594854 | − | 0.803834i | \(-0.702790\pi\) | ||||
−0.594854 | + | 0.803834i | \(0.702790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | −39.9473 | −1.37668 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.3246 | −0.630757 | ||||||||
\(845\) | 28.4605 | 0.979071 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 4.32456 | 0.148506 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 35.8114 | 1.22832 | ||||||||
\(851\) | −52.6491 | −1.80479 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.64911 | −0.227661 | −0.113831 | − | 0.993500i | \(-0.536312\pi\) | ||||
−0.113831 | + | 0.993500i | \(0.536312\pi\) | |||||||
\(854\) | −10.0000 | −0.342193 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.3246 | −0.489603 | ||||||||
\(857\) | 24.1886 | 0.826267 | 0.413134 | − | 0.910670i | \(-0.364434\pi\) | ||||
0.413134 | + | 0.910670i | \(0.364434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.3246 | −1.03466 | −0.517330 | − | 0.855786i | \(-0.673074\pi\) | ||||
−0.517330 | + | 0.855786i | \(0.673074\pi\) | |||||||
\(860\) | 20.0000 | 0.681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.97367 | −0.305644 | ||||||||
\(863\) | 17.6754 | 0.601679 | 0.300840 | − | 0.953675i | \(-0.402733\pi\) | ||||
0.300840 | + | 0.953675i | \(0.402733\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.9737 | 1.32514 | ||||||||
\(866\) | −34.0000 | −1.15537 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.16228 | −0.310988 | ||||||||
\(869\) | 4.32456 | 0.146700 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.64911 | 0.293064 | ||||||||
\(872\) | −8.00000 | −0.270914 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32.6491 | −1.10437 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.3509 | −0.788504 | −0.394252 | − | 0.919002i | \(-0.628996\pi\) | ||||
−0.394252 | + | 0.919002i | \(0.628996\pi\) | |||||||
\(878\) | −6.32456 | −0.213443 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.16228 | 0.106600 | ||||||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.2982 | −0.447521 | −0.223760 | − | 0.974644i | \(-0.571833\pi\) | ||||
−0.223760 | + | 0.974644i | \(0.571833\pi\) | |||||||
\(884\) | 14.3246 | 0.481787 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.32456 | 0.145286 | ||||||||
\(887\) | 16.0000 | 0.537227 | 0.268614 | − | 0.963248i | \(-0.413434\pi\) | ||||
0.268614 | + | 0.963248i | \(0.413434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.9737 | −0.703434 | ||||||||
\(890\) | −51.6228 | −1.73040 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.4868 | −0.384608 | ||||||||
\(893\) | 59.2982 | 1.98434 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.6228 | 0.388507 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.00000 | −0.200223 | ||||||||
\(899\) | 36.6491 | 1.22232 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.9737 | 1.03188 | ||||||||
\(902\) | 7.16228 | 0.238478 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.00000 | 0.0665190 | ||||||||
\(905\) | −55.2982 | −1.83818 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.6228 | 1.78052 | 0.890258 | − | 0.455457i | \(-0.150524\pi\) | ||||
0.890258 | + | 0.455457i | \(0.150524\pi\) | |||||||
\(908\) | 7.48683 | 0.248459 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.32456 | 0.209657 | ||||||||
\(911\) | −22.3246 | −0.739646 | −0.369823 | − | 0.929102i | \(-0.620582\pi\) | ||||
−0.369823 | + | 0.929102i | \(0.620582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.16228 | 0.170846 | ||||||||
\(914\) | 17.3509 | 0.573916 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25.4868 | −0.842109 | ||||||||
\(917\) | −5.16228 | −0.170473 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.2982 | −0.570616 | −0.285308 | − | 0.958436i | \(-0.592096\pi\) | ||||
−0.285308 | + | 0.958436i | \(0.592096\pi\) | |||||||
\(920\) | 20.0000 | 0.659380 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.2982 | −0.767286 | ||||||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.6228 | 1.36855 | ||||||||
\(926\) | −28.6491 | −0.941468 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.00000 | 0.131306 | ||||||||
\(929\) | 33.6228 | 1.10313 | 0.551564 | − | 0.834133i | \(-0.314031\pi\) | ||||
0.551564 | + | 0.834133i | \(0.314031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.16228 | 0.169187 | ||||||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.2982 | −0.566015 | ||||||||
\(935\) | 22.6491 | 0.740705 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.1359 | −1.37652 | −0.688261 | − | 0.725464i | \(-0.741625\pi\) | ||||
−0.688261 | + | 0.725464i | \(0.741625\pi\) | |||||||
\(938\) | −4.32456 | −0.141202 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −36.3246 | −1.18478 | ||||||||
\(941\) | −27.6754 | −0.902194 | −0.451097 | − | 0.892475i | \(-0.648967\pi\) | ||||
−0.451097 | + | 0.892475i | \(0.648967\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.2982 | 1.47511 | ||||||||
\(944\) | −1.67544 | −0.0545311 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.32456 | 0.205629 | ||||||||
\(947\) | 2.70178 | 0.0877960 | 0.0438980 | − | 0.999036i | \(-0.486022\pi\) | ||||
0.0438980 | + | 0.999036i | \(0.486022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.9737 | −0.356220 | ||||||||
\(950\) | 25.8114 | 0.837432 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.16228 | −0.232131 | ||||||||
\(953\) | −4.97367 | −0.161113 | −0.0805564 | − | 0.996750i | \(-0.525670\pi\) | ||||
−0.0805564 | + | 0.996750i | \(0.525670\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.9473 | 0.580762 | ||||||||
\(956\) | 12.6491 | 0.409101 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.2982 | −0.688114 | ||||||||
\(959\) | 18.0000 | 0.581250 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.9473 | 1.70798 | ||||||||
\(962\) | 16.6491 | 0.536789 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.837722 | 0.0269812 | ||||||||
\(965\) | −33.6754 | −1.08405 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57.2982 | −1.84259 | −0.921293 | − | 0.388868i | \(-0.872866\pi\) | ||||
−0.921293 | + | 0.388868i | \(0.872866\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 33.6754 | 1.08125 | ||||||||
\(971\) | −7.35089 | −0.235901 | −0.117951 | − | 0.993019i | \(-0.537632\pi\) | ||||
−0.117951 | + | 0.993019i | \(0.537632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.48683 | 0.240017 | ||||||||
\(974\) | −14.3246 | −0.458988 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | −24.6491 | −0.788595 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.3246 | −0.521735 | ||||||||
\(980\) | −3.16228 | −0.101015 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.64911 | 0.276004 | ||||||||
\(983\) | 48.1359 | 1.53530 | 0.767649 | − | 0.640870i | \(-0.221426\pi\) | ||||
0.767649 | + | 0.640870i | \(0.221426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −75.8947 | −2.41821 | ||||||||
\(986\) | 28.6491 | 0.912374 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.3246 | 0.328468 | ||||||||
\(989\) | 40.0000 | 1.27193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.2982 | −1.94720 | −0.973601 | − | 0.228256i | \(-0.926698\pi\) | ||||
−0.973601 | + | 0.228256i | \(0.926698\pi\) | |||||||
\(992\) | 9.16228 | 0.290903 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | −61.6228 | −1.95357 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.9737 | 1.55101 | 0.775506 | − | 0.631340i | \(-0.217495\pi\) | ||||
0.775506 | + | 0.631340i | \(0.217495\pi\) | |||||||
\(998\) | −16.9737 | −0.537292 | ||||||||
\(999\) | 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 | 1386.2.a.o.1.1 | yes | 2 | |
3.2 | odd | 2 | 1386.2.a.n.1.2 | ✓ | 2 | ||
7.6 | odd | 2 | 9702.2.a.dc.1.2 | 2 | |||
21.20 | even | 2 | 9702.2.a.cn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.a.n.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
1386.2.a.o.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
9702.2.a.cn.1.1 | 2 | 21.20 | even | 2 | |||
9702.2.a.dc.1.2 | 2 | 7.6 | odd | 2 |