Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(643,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.643");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.g (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 3x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 643.4 | ||
Root | \(-1.32288 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.643 |
Dual form | 966.2.g.c.643.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 2.64575i | 1.00000i | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.29150i | − | 1.59545i | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||
0.603023 | − | 0.797724i | \(-0.293963\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | − | 2.64575i | − | 0.707107i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.29150 | 1.28338 | 0.641689 | − | 0.766965i | \(-0.278234\pi\) | ||||
0.641689 | + | 0.766965i | \(0.278234\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 5.29150 | 1.21395 | 0.606977 | − | 0.794719i | \(-0.292382\pi\) | ||||
0.606977 | + | 0.794719i | \(0.292382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64575 | −0.577350 | ||||||||
\(22\) | 5.29150i | 1.12815i | ||||||||
\(23\) | 4.00000 | − | 2.64575i | 0.834058 | − | 0.551677i | ||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 2.00000i | 0.392232i | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.64575i | 0.500000i | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0000i | 1.79605i | 0.439941 | + | 0.898027i | \(0.354999\pi\) | ||||
−0.439941 | + | 0.898027i | \(0.645001\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.29150 | 0.921132 | ||||||||
\(34\) | −5.29150 | −0.907485 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −5.29150 | −0.858395 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.0000i | 1.87409i | 0.349215 | + | 0.937043i | \(0.386448\pi\) | ||||
−0.349215 | + | 0.937043i | \(0.613552\pi\) | |||||||
\(42\) | 2.64575 | 0.408248 | ||||||||
\(43\) | − | 5.29150i | − | 0.806947i | −0.914991 | − | 0.403473i | \(-0.867803\pi\) | ||
0.914991 | − | 0.403473i | \(-0.132197\pi\) | |||||||
\(44\) | − | 5.29150i | − | 0.797724i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | + | 2.64575i | −0.589768 | + | 0.390095i | ||||
\(47\) | − | 6.00000i | − | 0.875190i | −0.899172 | − | 0.437595i | \(-0.855830\pi\) | ||
0.899172 | − | 0.437595i | \(-0.144170\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 5.29150i | 0.740959i | ||||||||
\(52\) | − | 2.00000i | − | 0.277350i | ||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 2.64575i | − | 0.353553i | ||||||
\(57\) | 5.29150i | 0.700877i | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5830 | 1.35501 | 0.677507 | − | 0.735516i | \(-0.263060\pi\) | ||||
0.677507 | + | 0.735516i | \(0.263060\pi\) | |||||||
\(62\) | − | 10.0000i | − | 1.27000i | ||||||
\(63\) | − | 2.64575i | − | 0.333333i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.29150 | −0.651339 | ||||||||
\(67\) | 5.29150i | 0.646460i | 0.946320 | + | 0.323230i | \(0.104769\pi\) | ||||
−0.946320 | + | 0.323230i | \(0.895231\pi\) | |||||||
\(68\) | 5.29150 | 0.641689 | ||||||||
\(69\) | 2.64575 | + | 4.00000i | 0.318511 | + | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 5.00000i | − | 0.577350i | ||||||
\(76\) | 5.29150 | 0.606977 | ||||||||
\(77\) | 14.0000 | 1.59545 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | 5.29150i | 0.595341i | 0.954669 | + | 0.297670i | \(0.0962096\pi\) | ||||
−0.954669 | + | 0.297670i | \(0.903790\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 12.0000i | − | 1.32518i | ||||||
\(83\) | 15.8745 | 1.74245 | 0.871227 | − | 0.490881i | \(-0.163325\pi\) | ||||
0.871227 | + | 0.490881i | \(0.163325\pi\) | |||||||
\(84\) | −2.64575 | −0.288675 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.29150i | 0.570597i | ||||||||
\(87\) | 6.00000i | 0.643268i | ||||||||
\(88\) | 5.29150i | 0.564076i | ||||||||
\(89\) | 5.29150 | 0.560898 | 0.280449 | − | 0.959869i | \(-0.409517\pi\) | ||||
0.280449 | + | 0.959869i | \(0.409517\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.29150 | 0.554700 | ||||||||
\(92\) | 4.00000 | − | 2.64575i | 0.417029 | − | 0.275839i | ||||
\(93\) | −10.0000 | −1.03695 | ||||||||
\(94\) | 6.00000i | 0.618853i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 5.29150 | 0.537271 | 0.268635 | − | 0.963242i | \(-0.413427\pi\) | ||||
0.268635 | + | 0.963242i | \(0.413427\pi\) | |||||||
\(98\) | 7.00000 | 0.707107 | ||||||||
\(99\) | 5.29150i | 0.531816i | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | 14.0000i | 1.39305i | 0.717532 | + | 0.696526i | \(0.245272\pi\) | ||||
−0.717532 | + | 0.696526i | \(0.754728\pi\) | |||||||
\(102\) | − | 5.29150i | − | 0.523937i | ||||||
\(103\) | −10.5830 | −1.04277 | −0.521387 | − | 0.853320i | \(-0.674585\pi\) | ||||
−0.521387 | + | 0.853320i | \(0.674585\pi\) | |||||||
\(104\) | 2.00000i | 0.196116i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.8745i | − | 1.53465i | −0.641260 | − | 0.767323i | \(-0.721588\pi\) | ||
0.641260 | − | 0.767323i | \(-0.278412\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 10.5830i | 1.01367i | 0.862044 | + | 0.506834i | \(0.169184\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.64575i | 0.250000i | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | − | 5.29150i | − | 0.495595i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.0000i | 1.28338i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.0000 | −1.54545 | ||||||||
\(122\) | −10.5830 | −0.958140 | ||||||||
\(123\) | −12.0000 | −1.08200 | ||||||||
\(124\) | 10.0000i | 0.898027i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.64575i | 0.235702i | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.29150 | 0.465891 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.00000i | − | 0.698963i | −0.936943 | − | 0.349482i | \(-0.886358\pi\) | ||
0.936943 | − | 0.349482i | \(-0.113642\pi\) | |||||||
\(132\) | 5.29150 | 0.460566 | ||||||||
\(133\) | 14.0000i | 1.21395i | ||||||||
\(134\) | − | 5.29150i | − | 0.457116i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.29150 | −0.453743 | ||||||||
\(137\) | − | 21.1660i | − | 1.80833i | −0.427179 | − | 0.904167i | \(-0.640493\pi\) | ||
0.427179 | − | 0.904167i | \(-0.359507\pi\) | |||||||
\(138\) | −2.64575 | − | 4.00000i | −0.225221 | − | 0.340503i | ||||
\(139\) | − | 12.0000i | − | 1.01783i | −0.860818 | − | 0.508913i | \(-0.830047\pi\) | ||
0.860818 | − | 0.508913i | \(-0.169953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | −10.5830 | −0.884995 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 4.00000i | − | 0.331042i | ||||||
\(147\) | − | 7.00000i | − | 0.577350i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5830i | 0.866994i | 0.901155 | + | 0.433497i | \(0.142720\pi\) | ||||
−0.901155 | + | 0.433497i | \(0.857280\pi\) | |||||||
\(150\) | 5.00000i | 0.408248i | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | −5.29150 | −0.429198 | ||||||||
\(153\) | −5.29150 | −0.427793 | ||||||||
\(154\) | −14.0000 | −1.12815 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | 10.5830 | 0.844616 | 0.422308 | − | 0.906452i | \(-0.361220\pi\) | ||||
0.422308 | + | 0.906452i | \(0.361220\pi\) | |||||||
\(158\) | − | 5.29150i | − | 0.420969i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.00000 | + | 10.5830i | 0.551677 | + | 0.834058i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 24.0000 | 1.87983 | 0.939913 | − | 0.341415i | \(-0.110906\pi\) | ||||
0.939913 | + | 0.341415i | \(0.110906\pi\) | |||||||
\(164\) | 12.0000i | 0.937043i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.8745 | −1.23210 | ||||||||
\(167\) | − | 14.0000i | − | 1.08335i | −0.840587 | − | 0.541676i | \(-0.817790\pi\) | ||
0.840587 | − | 0.541676i | \(-0.182210\pi\) | |||||||
\(168\) | 2.64575 | 0.204124 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.29150 | −0.404651 | ||||||||
\(172\) | − | 5.29150i | − | 0.403473i | ||||||
\(173\) | − | 14.0000i | − | 1.06440i | −0.846619 | − | 0.532200i | \(-0.821365\pi\) | ||
0.846619 | − | 0.532200i | \(-0.178635\pi\) | |||||||
\(174\) | − | 6.00000i | − | 0.454859i | ||||||
\(175\) | − | 13.2288i | − | 1.00000i | ||||||
\(176\) | − | 5.29150i | − | 0.398862i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.29150 | −0.396615 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | −5.29150 | −0.392232 | ||||||||
\(183\) | 10.5830i | 0.782318i | ||||||||
\(184\) | −4.00000 | + | 2.64575i | −0.294884 | + | 0.195047i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.0000 | 0.733236 | ||||||||
\(187\) | − | 28.0000i | − | 2.04756i | ||||||
\(188\) | − | 6.00000i | − | 0.437595i | ||||||
\(189\) | 2.64575 | 0.192450 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 15.8745i | − | 1.14864i | −0.818631 | − | 0.574320i | \(-0.805267\pi\) | ||
0.818631 | − | 0.574320i | \(-0.194733\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | −5.29150 | −0.379908 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | − | 5.29150i | − | 0.376051i | ||||||
\(199\) | −21.1660 | −1.50042 | −0.750209 | − | 0.661200i | \(-0.770047\pi\) | ||||
−0.750209 | + | 0.661200i | \(0.770047\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | −5.29150 | −0.373234 | ||||||||
\(202\) | − | 14.0000i | − | 0.985037i | ||||||
\(203\) | 15.8745i | 1.11417i | ||||||||
\(204\) | 5.29150i | 0.370479i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.5830 | 0.737353 | ||||||||
\(207\) | −4.00000 | + | 2.64575i | −0.278019 | + | 0.183892i | ||||
\(208\) | − | 2.00000i | − | 0.138675i | ||||||
\(209\) | − | 28.0000i | − | 1.93680i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.00000i | − | 0.548151i | ||||||
\(214\) | 15.8745i | 1.08516i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −26.4575 | −1.79605 | ||||||||
\(218\) | − | 10.5830i | − | 0.716772i | ||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 10.5830i | − | 0.711890i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000i | 0.937509i | 0.883328 | + | 0.468755i | \(0.155297\pi\) | ||||
−0.883328 | + | 0.468755i | \(0.844703\pi\) | |||||||
\(224\) | − | 2.64575i | − | 0.176777i | ||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.4575 | −1.75605 | −0.878023 | − | 0.478618i | \(-0.841138\pi\) | ||||
−0.878023 | + | 0.478618i | \(0.841138\pi\) | |||||||
\(228\) | 5.29150i | 0.350438i | ||||||||
\(229\) | 21.1660 | 1.39869 | 0.699345 | − | 0.714785i | \(-0.253475\pi\) | ||||
0.699345 | + | 0.714785i | \(0.253475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.0000i | 0.921132i | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | − | 2.00000i | − | 0.130744i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.29150 | −0.343720 | ||||||||
\(238\) | − | 14.0000i | − | 0.907485i | ||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.8745 | −1.02257 | −0.511283 | − | 0.859412i | \(-0.670830\pi\) | ||||
−0.511283 | + | 0.859412i | \(0.670830\pi\) | |||||||
\(242\) | 17.0000 | 1.09280 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 10.5830 | 0.677507 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | − | 10.5830i | − | 0.673380i | ||||||
\(248\) | − | 10.0000i | − | 0.635001i | ||||||
\(249\) | 15.8745i | 1.00601i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.8745 | −1.00199 | −0.500995 | − | 0.865450i | \(-0.667033\pi\) | ||||
−0.500995 | + | 0.865450i | \(0.667033\pi\) | |||||||
\(252\) | − | 2.64575i | − | 0.166667i | ||||||
\(253\) | −14.0000 | − | 21.1660i | −0.880172 | − | 1.33070i | ||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.00000i | 0.499026i | 0.968371 | + | 0.249513i | \(0.0802706\pi\) | ||||
−0.968371 | + | 0.249513i | \(0.919729\pi\) | |||||||
\(258\) | −5.29150 | −0.329435 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 8.00000i | 0.494242i | ||||||||
\(263\) | 5.29150i | 0.326288i | 0.986602 | + | 0.163144i | \(0.0521635\pi\) | ||||
−0.986602 | + | 0.163144i | \(0.947836\pi\) | |||||||
\(264\) | −5.29150 | −0.325669 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 14.0000i | − | 0.858395i | ||||||
\(267\) | 5.29150i | 0.323835i | ||||||||
\(268\) | 5.29150i | 0.323230i | ||||||||
\(269\) | 18.0000i | 1.09748i | 0.835993 | + | 0.548740i | \(0.184892\pi\) | ||||
−0.835993 | + | 0.548740i | \(0.815108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.0000i | − | 0.850439i | −0.905090 | − | 0.425220i | \(-0.860197\pi\) | ||
0.905090 | − | 0.425220i | \(-0.139803\pi\) | |||||||
\(272\) | 5.29150 | 0.320844 | ||||||||
\(273\) | 5.29150i | 0.320256i | ||||||||
\(274\) | 21.1660i | 1.27869i | ||||||||
\(275\) | 26.4575i | 1.59545i | ||||||||
\(276\) | 2.64575 | + | 4.00000i | 0.159256 | + | 0.240772i | ||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 12.0000i | 0.719712i | ||||||||
\(279\) | − | 10.0000i | − | 0.598684i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | −6.00000 | −0.357295 | ||||||||
\(283\) | −26.4575 | −1.57274 | −0.786368 | − | 0.617758i | \(-0.788041\pi\) | ||||
−0.786368 | + | 0.617758i | \(0.788041\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.5830 | 0.625786 | ||||||||
\(287\) | −31.7490 | −1.87409 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 11.0000 | 0.647059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.29150i | 0.310193i | ||||||||
\(292\) | 4.00000i | 0.234082i | ||||||||
\(293\) | −10.5830 | −0.618266 | −0.309133 | − | 0.951019i | \(-0.600039\pi\) | ||||
−0.309133 | + | 0.951019i | \(0.600039\pi\) | |||||||
\(294\) | 7.00000i | 0.408248i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.29150 | −0.307044 | ||||||||
\(298\) | − | 10.5830i | − | 0.613057i | ||||||
\(299\) | −5.29150 | − | 8.00000i | −0.306015 | − | 0.462652i | ||||
\(300\) | − | 5.00000i | − | 0.288675i | ||||||
\(301\) | 14.0000 | 0.806947 | ||||||||
\(302\) | −16.0000 | −0.920697 | ||||||||
\(303\) | −14.0000 | −0.804279 | ||||||||
\(304\) | 5.29150 | 0.303488 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.29150 | 0.302495 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 14.0000 | 0.797724 | ||||||||
\(309\) | − | 10.5830i | − | 0.602046i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0000i | 0.567048i | 0.958965 | + | 0.283524i | \(0.0915036\pi\) | ||||
−0.958965 | + | 0.283524i | \(0.908496\pi\) | |||||||
\(312\) | −2.00000 | −0.113228 | ||||||||
\(313\) | 5.29150 | 0.299093 | 0.149547 | − | 0.988755i | \(-0.452219\pi\) | ||||
0.149547 | + | 0.988755i | \(0.452219\pi\) | |||||||
\(314\) | −10.5830 | −0.597234 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.29150i | 0.297670i | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 31.7490i | − | 1.77760i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.8745 | 0.886029 | ||||||||
\(322\) | −7.00000 | − | 10.5830i | −0.390095 | − | 0.589768i | ||||
\(323\) | 28.0000 | 1.55796 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 10.0000i | 0.554700i | ||||||||
\(326\) | −24.0000 | −1.32924 | ||||||||
\(327\) | −10.5830 | −0.585242 | ||||||||
\(328\) | − | 12.0000i | − | 0.662589i | ||||||
\(329\) | 15.8745 | 0.875190 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 15.8745 | 0.871227 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.0000i | 0.766046i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.64575 | −0.144338 | ||||||||
\(337\) | 21.1660i | 1.15299i | 0.817102 | + | 0.576493i | \(0.195579\pi\) | ||||
−0.817102 | + | 0.576493i | \(0.804421\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 52.9150 | 2.86551 | ||||||||
\(342\) | 5.29150 | 0.286132 | ||||||||
\(343\) | − | 18.5203i | − | 1.00000i | ||||||
\(344\) | 5.29150i | 0.285299i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0000i | 0.752645i | ||||||||
\(347\) | −32.0000 | −1.71785 | −0.858925 | − | 0.512101i | \(-0.828867\pi\) | ||||
−0.858925 | + | 0.512101i | \(0.828867\pi\) | |||||||
\(348\) | 6.00000i | 0.321634i | ||||||||
\(349\) | − | 30.0000i | − | 1.60586i | −0.596071 | − | 0.802932i | \(-0.703272\pi\) | ||
0.596071 | − | 0.802932i | \(-0.296728\pi\) | |||||||
\(350\) | 13.2288i | 0.707107i | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 5.29150i | 0.282038i | ||||||||
\(353\) | − | 4.00000i | − | 0.212899i | −0.994318 | − | 0.106449i | \(-0.966052\pi\) | ||
0.994318 | − | 0.106449i | \(-0.0339482\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.29150 | 0.280449 | ||||||||
\(357\) | −14.0000 | −0.740959 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | − | 5.29150i | − | 0.279275i | −0.990203 | − | 0.139637i | \(-0.955406\pi\) | ||
0.990203 | − | 0.139637i | \(-0.0445937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | 0.473684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 17.0000i | − | 0.892269i | ||||||
\(364\) | 5.29150 | 0.277350 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 10.5830i | − | 0.553183i | ||||||
\(367\) | −21.1660 | −1.10486 | −0.552428 | − | 0.833560i | \(-0.686299\pi\) | ||||
−0.552428 | + | 0.833560i | \(0.686299\pi\) | |||||||
\(368\) | 4.00000 | − | 2.64575i | 0.208514 | − | 0.137919i | ||||
\(369\) | − | 12.0000i | − | 0.624695i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.0000 | −0.518476 | ||||||||
\(373\) | 21.1660i | 1.09593i | 0.836500 | + | 0.547967i | \(0.184598\pi\) | ||||
−0.836500 | + | 0.547967i | \(0.815402\pi\) | |||||||
\(374\) | 28.0000i | 1.44785i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000i | 0.309426i | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | −2.64575 | −0.136083 | ||||||||
\(379\) | − | 15.8745i | − | 0.815419i | −0.913112 | − | 0.407709i | \(-0.866328\pi\) | ||
0.913112 | − | 0.407709i | \(-0.133672\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000i | 0.409852i | ||||||||
\(382\) | 15.8745i | 0.812210i | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 5.29150i | 0.268982i | ||||||||
\(388\) | 5.29150 | 0.268635 | ||||||||
\(389\) | 21.1660i | 1.07316i | 0.843850 | + | 0.536580i | \(0.180284\pi\) | ||||
−0.843850 | + | 0.536580i | \(0.819716\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.1660 | − | 14.0000i | 1.07041 | − | 0.708010i | ||||
\(392\) | 7.00000 | 0.353553 | ||||||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | 22.0000 | 1.10834 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.29150i | 0.265908i | ||||||||
\(397\) | 22.0000i | 1.10415i | 0.833795 | + | 0.552074i | \(0.186163\pi\) | ||||
−0.833795 | + | 0.552074i | \(0.813837\pi\) | |||||||
\(398\) | 21.1660 | 1.06096 | ||||||||
\(399\) | −14.0000 | −0.700877 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 5.29150 | 0.263916 | ||||||||
\(403\) | 20.0000 | 0.996271 | ||||||||
\(404\) | 14.0000i | 0.696526i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 15.8745i | − | 0.787839i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 5.29150i | − | 0.261968i | ||||||
\(409\) | 4.00000i | 0.197787i | 0.995098 | + | 0.0988936i | \(0.0315304\pi\) | ||||
−0.995098 | + | 0.0988936i | \(0.968470\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.1660 | 1.04404 | ||||||||
\(412\) | −10.5830 | −0.521387 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.00000 | − | 2.64575i | 0.196589 | − | 0.130032i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000i | 0.0980581i | ||||||||
\(417\) | 12.0000 | 0.587643 | ||||||||
\(418\) | 28.0000i | 1.36952i | ||||||||
\(419\) | 5.29150 | 0.258507 | 0.129253 | − | 0.991612i | \(-0.458742\pi\) | ||||
0.129253 | + | 0.991612i | \(0.458742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 31.7490i | − | 1.54735i | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||
0.633581 | − | 0.773676i | \(-0.281584\pi\) | |||||||
\(422\) | 16.0000 | 0.778868 | ||||||||
\(423\) | 6.00000i | 0.291730i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.4575 | −1.28338 | ||||||||
\(426\) | 8.00000i | 0.387601i | ||||||||
\(427\) | 28.0000i | 1.35501i | ||||||||
\(428\) | − | 15.8745i | − | 0.767323i | ||||||
\(429\) | − | 10.5830i | − | 0.510952i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.8745i | 0.764648i | 0.924028 | + | 0.382324i | \(0.124876\pi\) | ||||
−0.924028 | + | 0.382324i | \(0.875124\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 37.0405 | 1.78005 | 0.890027 | − | 0.455908i | \(-0.150685\pi\) | ||||
0.890027 | + | 0.455908i | \(0.150685\pi\) | |||||||
\(434\) | 26.4575 | 1.27000 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.5830i | 0.506834i | ||||||||
\(437\) | 21.1660 | − | 14.0000i | 1.01251 | − | 0.669711i | ||||
\(438\) | 4.00000 | 0.191127 | ||||||||
\(439\) | − | 6.00000i | − | 0.286364i | −0.989696 | − | 0.143182i | \(-0.954267\pi\) | ||
0.989696 | − | 0.143182i | \(-0.0457335\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.00000 | 0.333333 | ||||||||
\(442\) | 10.5830i | 0.503382i | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 14.0000i | − | 0.662919i | ||||||
\(447\) | −10.5830 | −0.500559 | ||||||||
\(448\) | 2.64575i | 0.125000i | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | −5.00000 | −0.235702 | ||||||||
\(451\) | 63.4980 | 2.99001 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.0000i | 0.751746i | ||||||||
\(454\) | 26.4575 | 1.24171 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 5.29150i | − | 0.247797i | ||||||
\(457\) | − | 21.1660i | − | 0.990104i | −0.868863 | − | 0.495052i | \(-0.835149\pi\) | ||
0.868863 | − | 0.495052i | \(-0.164851\pi\) | |||||||
\(458\) | −21.1660 | −0.989023 | ||||||||
\(459\) | − | 5.29150i | − | 0.246986i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0000i | 1.39724i | 0.715493 | + | 0.698620i | \(0.246202\pi\) | ||||
−0.715493 | + | 0.698620i | \(0.753798\pi\) | |||||||
\(462\) | − | 14.0000i | − | 0.651339i | ||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.0000 | −0.463241 | ||||||||
\(467\) | −15.8745 | −0.734585 | −0.367292 | − | 0.930106i | \(-0.619715\pi\) | ||||
−0.367292 | + | 0.930106i | \(0.619715\pi\) | |||||||
\(468\) | 2.00000i | 0.0924500i | ||||||||
\(469\) | −14.0000 | −0.646460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.5830i | 0.487639i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.0000 | −1.28744 | ||||||||
\(474\) | 5.29150 | 0.243047 | ||||||||
\(475\) | −26.4575 | −1.21395 | ||||||||
\(476\) | 14.0000i | 0.641689i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | 21.1660 | 0.967100 | 0.483550 | − | 0.875317i | \(-0.339347\pi\) | ||||
0.483550 | + | 0.875317i | \(0.339347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 15.8745 | 0.723064 | ||||||||
\(483\) | −10.5830 | + | 7.00000i | −0.481543 | + | 0.318511i | ||||
\(484\) | −17.0000 | −0.772727 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 40.0000 | 1.81257 | 0.906287 | − | 0.422664i | \(-0.138905\pi\) | ||||
0.906287 | + | 0.422664i | \(0.138905\pi\) | |||||||
\(488\) | −10.5830 | −0.479070 | ||||||||
\(489\) | 24.0000i | 1.08532i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.00000 | −0.361035 | −0.180517 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(492\) | −12.0000 | −0.541002 | ||||||||
\(493\) | 31.7490 | 1.42990 | ||||||||
\(494\) | 10.5830i | 0.476152i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.0000i | 0.449013i | ||||||||
\(497\) | − | 21.1660i | − | 0.949425i | ||||||
\(498\) | − | 15.8745i | − | 0.711354i | ||||||
\(499\) | −24.0000 | −1.07439 | −0.537194 | − | 0.843459i | \(-0.680516\pi\) | ||||
−0.537194 | + | 0.843459i | \(0.680516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.0000 | 0.625474 | ||||||||
\(502\) | 15.8745 | 0.708514 | ||||||||
\(503\) | 31.7490 | 1.41562 | 0.707809 | − | 0.706404i | \(-0.249684\pi\) | ||||
0.707809 | + | 0.706404i | \(0.249684\pi\) | |||||||
\(504\) | 2.64575i | 0.117851i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.0000 | + | 21.1660i | 0.622376 | + | 0.940944i | ||||
\(507\) | 9.00000i | 0.399704i | ||||||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | − | 6.00000i | − | 0.265945i | −0.991120 | − | 0.132973i | \(-0.957548\pi\) | ||
0.991120 | − | 0.132973i | \(-0.0424523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5830 | −0.468165 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 5.29150i | − | 0.233626i | ||||||
\(514\) | − | 8.00000i | − | 0.352865i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.29150 | 0.232945 | ||||||||
\(517\) | −31.7490 | −1.39632 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0000 | 0.614532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.0405 | −1.62277 | −0.811387 | − | 0.584509i | \(-0.801287\pi\) | ||||
−0.811387 | + | 0.584509i | \(0.801287\pi\) | |||||||
\(522\) | 6.00000 | 0.262613 | ||||||||
\(523\) | −37.0405 | −1.61967 | −0.809834 | − | 0.586659i | \(-0.800443\pi\) | ||||
−0.809834 | + | 0.586659i | \(0.800443\pi\) | |||||||
\(524\) | − | 8.00000i | − | 0.349482i | ||||||
\(525\) | 13.2288 | 0.577350 | ||||||||
\(526\) | − | 5.29150i | − | 0.230720i | ||||||
\(527\) | 52.9150i | 2.30501i | ||||||||
\(528\) | 5.29150 | 0.230283 | ||||||||
\(529\) | 9.00000 | − | 21.1660i | 0.391304 | − | 0.920261i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.0000i | 0.606977i | ||||||||
\(533\) | 24.0000 | 1.03956 | ||||||||
\(534\) | − | 5.29150i | − | 0.228986i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 5.29150i | − | 0.228558i | ||||||
\(537\) | − | 12.0000i | − | 0.517838i | ||||||
\(538\) | − | 18.0000i | − | 0.776035i | ||||||
\(539\) | 37.0405i | 1.59545i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.0000 | 0.773880 | 0.386940 | − | 0.922105i | \(-0.373532\pi\) | ||||
0.386940 | + | 0.922105i | \(0.373532\pi\) | |||||||
\(542\) | 14.0000i | 0.601351i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.29150 | −0.226871 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 5.29150i | − | 0.226455i | ||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | − | 21.1660i | − | 0.904167i | ||||||
\(549\) | −10.5830 | −0.451672 | ||||||||
\(550\) | − | 26.4575i | − | 1.12815i | ||||||
\(551\) | 31.7490 | 1.35255 | ||||||||
\(552\) | −2.64575 | − | 4.00000i | −0.112611 | − | 0.170251i | ||||
\(553\) | −14.0000 | −0.595341 | ||||||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 12.0000i | − | 0.508913i | ||||||
\(557\) | − | 31.7490i | − | 1.34525i | −0.739984 | − | 0.672624i | \(-0.765167\pi\) | ||
0.739984 | − | 0.672624i | \(-0.234833\pi\) | |||||||
\(558\) | 10.0000i | 0.423334i | ||||||||
\(559\) | −10.5830 | −0.447613 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.0000 | 1.18216 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.29150 | −0.223010 | −0.111505 | − | 0.993764i | \(-0.535567\pi\) | ||||
−0.111505 | + | 0.993764i | \(0.535567\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26.4575 | 1.11209 | ||||||||
\(567\) | 2.64575i | 0.111111i | ||||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.8745i | 0.664327i | 0.943222 | + | 0.332164i | \(0.107779\pi\) | ||||
−0.943222 | + | 0.332164i | \(0.892221\pi\) | |||||||
\(572\) | −10.5830 | −0.442498 | ||||||||
\(573\) | 15.8745 | 0.663167 | ||||||||
\(574\) | 31.7490 | 1.32518 | ||||||||
\(575\) | −20.0000 | + | 13.2288i | −0.834058 | + | 0.551677i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − | 4.00000i | − | 0.166522i | −0.996528 | − | 0.0832611i | \(-0.973466\pi\) | ||
0.996528 | − | 0.0832611i | \(-0.0265335\pi\) | |||||||
\(578\) | −11.0000 | −0.457540 | ||||||||
\(579\) | − | 2.00000i | − | 0.0831172i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.0000i | 1.74245i | ||||||||
\(582\) | − | 5.29150i | − | 0.219340i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 4.00000i | − | 0.165521i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.5830 | 0.437180 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | − | 7.00000i | − | 0.288675i | ||||||
\(589\) | 52.9150i | 2.18033i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 22.0000i | − | 0.904959i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 5.29150 | 0.217113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.5830i | 0.433497i | ||||||||
\(597\) | − | 21.1660i | − | 0.866267i | ||||||
\(598\) | 5.29150 | + | 8.00000i | 0.216386 | + | 0.327144i | ||||
\(599\) | −32.0000 | −1.30748 | −0.653742 | − | 0.756717i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756717i | \(0.726802\pi\) | |||||||
\(600\) | 5.00000i | 0.204124i | ||||||||
\(601\) | 44.0000i | 1.79480i | 0.441221 | + | 0.897399i | \(0.354546\pi\) | ||||
−0.441221 | + | 0.897399i | \(0.645454\pi\) | |||||||
\(602\) | −14.0000 | −0.570597 | ||||||||
\(603\) | − | 5.29150i | − | 0.215487i | ||||||
\(604\) | 16.0000 | 0.651031 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.0000 | 0.568711 | ||||||||
\(607\) | − | 42.0000i | − | 1.70473i | −0.522949 | − | 0.852364i | \(-0.675168\pi\) | ||
0.522949 | − | 0.852364i | \(-0.324832\pi\) | |||||||
\(608\) | −5.29150 | −0.214599 | ||||||||
\(609\) | −15.8745 | −0.643268 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | −0.485468 | ||||||||
\(612\) | −5.29150 | −0.213896 | ||||||||
\(613\) | − | 10.5830i | − | 0.427444i | −0.976895 | − | 0.213722i | \(-0.931441\pi\) | ||
0.976895 | − | 0.213722i | \(-0.0685586\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.0000 | −0.564076 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 10.5830i | 0.425711i | ||||||||
\(619\) | 5.29150 | 0.212683 | 0.106342 | − | 0.994330i | \(-0.466086\pi\) | ||||
0.106342 | + | 0.994330i | \(0.466086\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.64575 | − | 4.00000i | −0.106170 | − | 0.160514i | ||||
\(622\) | − | 10.0000i | − | 0.400963i | ||||||
\(623\) | 14.0000i | 0.560898i | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −5.29150 | −0.211491 | ||||||||
\(627\) | 28.0000 | 1.11821 | ||||||||
\(628\) | 10.5830 | 0.422308 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 37.0405i | − | 1.47456i | −0.675587 | − | 0.737280i | \(-0.736110\pi\) | ||
0.675587 | − | 0.737280i | \(-0.263890\pi\) | |||||||
\(632\) | − | 5.29150i | − | 0.210485i | ||||||
\(633\) | − | 16.0000i | − | 0.635943i | ||||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.0000i | 0.554700i | ||||||||
\(638\) | 31.7490i | 1.25696i | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | −15.8745 | −0.626517 | ||||||||
\(643\) | 15.8745 | 0.626029 | 0.313015 | − | 0.949748i | \(-0.398661\pi\) | ||||
0.313015 | + | 0.949748i | \(0.398661\pi\) | |||||||
\(644\) | 7.00000 | + | 10.5830i | 0.275839 | + | 0.417029i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −28.0000 | −1.10165 | ||||||||
\(647\) | − | 18.0000i | − | 0.707653i | −0.935311 | − | 0.353827i | \(-0.884880\pi\) | ||
0.935311 | − | 0.353827i | \(-0.115120\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 10.0000i | − | 0.392232i | ||||||
\(651\) | − | 26.4575i | − | 1.03695i | ||||||
\(652\) | 24.0000 | 0.939913 | ||||||||
\(653\) | −38.0000 | −1.48705 | −0.743527 | − | 0.668705i | \(-0.766849\pi\) | ||||
−0.743527 | + | 0.668705i | \(0.766849\pi\) | |||||||
\(654\) | 10.5830 | 0.413828 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.0000i | 0.468521i | ||||||||
\(657\) | − | 4.00000i | − | 0.156055i | ||||||
\(658\) | −15.8745 | −0.618853 | ||||||||
\(659\) | − | 15.8745i | − | 0.618383i | −0.951000 | − | 0.309192i | \(-0.899942\pi\) | ||
0.951000 | − | 0.309192i | \(-0.100058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5830 | 0.411631 | 0.205816 | − | 0.978591i | \(-0.434015\pi\) | ||||
0.205816 | + | 0.978591i | \(0.434015\pi\) | |||||||
\(662\) | −4.00000 | −0.155464 | ||||||||
\(663\) | 10.5830 | 0.411010 | ||||||||
\(664\) | −15.8745 | −0.616050 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.0000 | − | 15.8745i | 0.929284 | − | 0.614663i | ||||
\(668\) | − | 14.0000i | − | 0.541676i | ||||||
\(669\) | −14.0000 | −0.541271 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 56.0000i | − | 2.16186i | ||||||
\(672\) | 2.64575 | 0.102062 | ||||||||
\(673\) | −22.0000 | −0.848038 | −0.424019 | − | 0.905653i | \(-0.639381\pi\) | ||||
−0.424019 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(674\) | − | 21.1660i | − | 0.815284i | ||||||
\(675\) | 5.00000i | 0.192450i | ||||||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | −31.7490 | −1.22021 | −0.610107 | − | 0.792319i | \(-0.708874\pi\) | ||||
−0.610107 | + | 0.792319i | \(0.708874\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.0000i | 0.537271i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 26.4575i | − | 1.01385i | ||||||
\(682\) | −52.9150 | −2.02622 | ||||||||
\(683\) | −16.0000 | −0.612223 | −0.306111 | − | 0.951996i | \(-0.599028\pi\) | ||||
−0.306111 | + | 0.951996i | \(0.599028\pi\) | |||||||
\(684\) | −5.29150 | −0.202326 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.5203i | 0.707107i | ||||||||
\(687\) | 21.1660i | 0.807534i | ||||||||
\(688\) | − | 5.29150i | − | 0.201737i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000i | 1.06517i | 0.846376 | + | 0.532585i | \(0.178779\pi\) | ||||
−0.846376 | + | 0.532585i | \(0.821221\pi\) | |||||||
\(692\) | − | 14.0000i | − | 0.532200i | ||||||
\(693\) | −14.0000 | −0.531816 | ||||||||
\(694\) | 32.0000 | 1.21470 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 6.00000i | − | 0.227429i | ||||||
\(697\) | 63.4980i | 2.40516i | ||||||||
\(698\) | 30.0000i | 1.13552i | ||||||||
\(699\) | 10.0000i | 0.378235i | ||||||||
\(700\) | − | 13.2288i | − | 0.500000i | ||||||
\(701\) | 31.7490i | 1.19914i | 0.800321 | + | 0.599572i | \(0.204662\pi\) | ||||
−0.800321 | + | 0.599572i | \(0.795338\pi\) | |||||||
\(702\) | 2.00000 | 0.0754851 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 5.29150i | − | 0.199431i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.00000i | 0.150542i | ||||||||
\(707\) | −37.0405 | −1.39305 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1660i | 0.794906i | 0.917622 | + | 0.397453i | \(0.130106\pi\) | ||||
−0.917622 | + | 0.397453i | \(0.869894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 5.29150i | − | 0.198447i | ||||||
\(712\) | −5.29150 | −0.198307 | ||||||||
\(713\) | 26.4575 | + | 40.0000i | 0.990842 | + | 1.49801i | ||||
\(714\) | 14.0000 | 0.523937 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 8.00000i | 0.298765i | ||||||||
\(718\) | 5.29150i | 0.197477i | ||||||||
\(719\) | − | 42.0000i | − | 1.56634i | −0.621810 | − | 0.783168i | \(-0.713603\pi\) | ||
0.621810 | − | 0.783168i | \(-0.286397\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 28.0000i | − | 1.04277i | ||||||
\(722\) | −9.00000 | −0.334945 | ||||||||
\(723\) | − | 15.8745i | − | 0.590379i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.0000 | −1.11417 | ||||||||
\(726\) | 17.0000i | 0.630929i | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | −5.29150 | −0.196116 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 28.0000i | − | 1.03562i | ||||||
\(732\) | 10.5830i | 0.391159i | ||||||||
\(733\) | 10.5830 | 0.390892 | 0.195446 | − | 0.980714i | \(-0.437385\pi\) | ||||
0.195446 | + | 0.980714i | \(0.437385\pi\) | |||||||
\(734\) | 21.1660 | 0.781252 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | + | 2.64575i | −0.147442 | + | 0.0975237i | ||||
\(737\) | 28.0000 | 1.03139 | ||||||||
\(738\) | 12.0000i | 0.441726i | ||||||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.5830 | 0.388776 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.8745i | 0.582379i | 0.956665 | + | 0.291190i | \(0.0940511\pi\) | ||||
−0.956665 | + | 0.291190i | \(0.905949\pi\) | |||||||
\(744\) | 10.0000 | 0.366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 21.1660i | − | 0.774943i | ||||||
\(747\) | −15.8745 | −0.580818 | ||||||||
\(748\) | − | 28.0000i | − | 1.02378i | ||||||
\(749\) | 42.0000 | 1.53465 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8745i | 0.579269i | 0.957137 | + | 0.289635i | \(0.0935338\pi\) | ||||
−0.957137 | + | 0.289635i | \(0.906466\pi\) | |||||||
\(752\) | − | 6.00000i | − | 0.218797i | ||||||
\(753\) | − | 15.8745i | − | 0.578499i | ||||||
\(754\) | 12.0000i | 0.437014i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.64575 | 0.0962250 | ||||||||
\(757\) | 10.5830i | 0.384646i | 0.981332 | + | 0.192323i | \(0.0616021\pi\) | ||||
−0.981332 | + | 0.192323i | \(0.938398\pi\) | |||||||
\(758\) | 15.8745i | 0.576588i | ||||||||
\(759\) | 21.1660 | − | 14.0000i | 0.768278 | − | 0.508168i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.00000i | 0.290000i | 0.989432 | + | 0.145000i | \(0.0463182\pi\) | ||||
−0.989432 | + | 0.145000i | \(0.953682\pi\) | |||||||
\(762\) | − | 8.00000i | − | 0.289809i | ||||||
\(763\) | −28.0000 | −1.01367 | ||||||||
\(764\) | − | 15.8745i | − | 0.574320i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −5.29150 | −0.190816 | −0.0954082 | − | 0.995438i | \(-0.530416\pi\) | ||||
−0.0954082 | + | 0.995438i | \(0.530416\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.00000 | −0.288113 | ||||||||
\(772\) | −2.00000 | −0.0719816 | ||||||||
\(773\) | 52.9150 | 1.90322 | 0.951611 | − | 0.307306i | \(-0.0994277\pi\) | ||||
0.951611 | + | 0.307306i | \(0.0994277\pi\) | |||||||
\(774\) | − | 5.29150i | − | 0.190199i | ||||||
\(775\) | − | 50.0000i | − | 1.79605i | ||||||
\(776\) | −5.29150 | −0.189954 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 21.1660i | − | 0.758838i | ||||||
\(779\) | 63.4980i | 2.27505i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42.3320i | 1.51476i | ||||||||
\(782\) | −21.1660 | + | 14.0000i | −0.756895 | + | 0.500639i | ||||
\(783\) | − | 6.00000i | − | 0.214423i | ||||||
\(784\) | −7.00000 | −0.250000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.00000 | −0.285351 | ||||||||
\(787\) | −37.0405 | −1.32035 | −0.660176 | − | 0.751111i | \(-0.729518\pi\) | ||||
−0.660176 | + | 0.751111i | \(0.729518\pi\) | |||||||
\(788\) | −22.0000 | −0.783718 | ||||||||
\(789\) | −5.29150 | −0.188382 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 5.29150i | − | 0.188025i | ||||||
\(793\) | − | 21.1660i | − | 0.751627i | ||||||
\(794\) | − | 22.0000i | − | 0.780751i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.1660 | −0.750209 | ||||||||
\(797\) | −21.1660 | −0.749739 | −0.374869 | − | 0.927078i | \(-0.622312\pi\) | ||||
−0.374869 | + | 0.927078i | \(0.622312\pi\) | |||||||
\(798\) | 14.0000 | 0.495595 | ||||||||
\(799\) | − | 31.7490i | − | 1.12320i | ||||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | −5.29150 | −0.186966 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.1660 | 0.746932 | ||||||||
\(804\) | −5.29150 | −0.186617 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | −18.0000 | −0.633630 | ||||||||
\(808\) | − | 14.0000i | − | 0.492518i | ||||||
\(809\) | −10.0000 | −0.351581 | −0.175791 | − | 0.984428i | \(-0.556248\pi\) | ||||
−0.175791 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.0000i | − | 0.561836i | −0.959732 | − | 0.280918i | \(-0.909361\pi\) | ||
0.959732 | − | 0.280918i | \(-0.0906389\pi\) | |||||||
\(812\) | 15.8745i | 0.557086i | ||||||||
\(813\) | 14.0000 | 0.491001 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.29150i | 0.185240i | ||||||||
\(817\) | − | 28.0000i | − | 0.979596i | ||||||
\(818\) | − | 4.00000i | − | 0.139857i | ||||||
\(819\) | −5.29150 | −0.184900 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | 0.209401 | 0.104701 | − | 0.994504i | \(-0.466612\pi\) | ||||
0.104701 | + | 0.994504i | \(0.466612\pi\) | |||||||
\(822\) | −21.1660 | −0.738249 | ||||||||
\(823\) | 40.0000 | 1.39431 | 0.697156 | − | 0.716919i | \(-0.254448\pi\) | ||||
0.697156 | + | 0.716919i | \(0.254448\pi\) | |||||||
\(824\) | 10.5830 | 0.368676 | ||||||||
\(825\) | −26.4575 | −0.921132 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.8745i | − | 0.552011i | −0.961156 | − | 0.276005i | \(-0.910989\pi\) | ||
0.961156 | − | 0.276005i | \(-0.0890108\pi\) | |||||||
\(828\) | −4.00000 | + | 2.64575i | −0.139010 | + | 0.0919462i | ||||
\(829\) | 14.0000i | 0.486240i | 0.969996 | + | 0.243120i | \(0.0781709\pi\) | ||||
−0.969996 | + | 0.243120i | \(0.921829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000i | 0.0693792i | ||||||||
\(832\) | − | 2.00000i | − | 0.0693375i | ||||||
\(833\) | −37.0405 | −1.28338 | ||||||||
\(834\) | −12.0000 | −0.415526 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 28.0000i | − | 0.968400i | ||||||
\(837\) | 10.0000 | 0.345651 | ||||||||
\(838\) | −5.29150 | −0.182792 | ||||||||
\(839\) | −42.3320 | −1.46146 | −0.730732 | − | 0.682665i | \(-0.760821\pi\) | ||||
−0.730732 | + | 0.682665i | \(0.760821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 31.7490i | 1.09414i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.0000 | −0.550743 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 6.00000i | − | 0.206284i | ||||||
\(847\) | − | 44.9778i | − | 1.54545i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 26.4575i | − | 0.908019i | ||||||
\(850\) | 26.4575 | 0.907485 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | − | 8.00000i | − | 0.274075i | ||||||
\(853\) | 14.0000i | 0.479351i | 0.970853 | + | 0.239675i | \(0.0770410\pi\) | ||||
−0.970853 | + | 0.239675i | \(0.922959\pi\) | |||||||
\(854\) | − | 28.0000i | − | 0.958140i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.8745i | 0.542580i | ||||||||
\(857\) | − | 24.0000i | − | 0.819824i | −0.912125 | − | 0.409912i | \(-0.865559\pi\) | ||
0.912125 | − | 0.409912i | \(-0.134441\pi\) | |||||||
\(858\) | 10.5830i | 0.361298i | ||||||||
\(859\) | 48.0000i | 1.63774i | 0.573980 | + | 0.818869i | \(0.305399\pi\) | ||||
−0.573980 | + | 0.818869i | \(0.694601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 31.7490i | − | 1.08200i | ||||||
\(862\) | − | 15.8745i | − | 0.540688i | ||||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −37.0405 | −1.25869 | ||||||||
\(867\) | 11.0000i | 0.373580i | ||||||||
\(868\) | −26.4575 | −0.898027 | ||||||||
\(869\) | 28.0000 | 0.949835 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5830 | 0.358591 | ||||||||
\(872\) | − | 10.5830i | − | 0.358386i | ||||||
\(873\) | −5.29150 | −0.179090 | ||||||||
\(874\) | −21.1660 | + | 14.0000i | −0.715951 | + | 0.473557i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | −6.00000 | −0.202606 | −0.101303 | − | 0.994856i | \(-0.532301\pi\) | ||||
−0.101303 | + | 0.994856i | \(0.532301\pi\) | |||||||
\(878\) | 6.00000i | 0.202490i | ||||||||
\(879\) | − | 10.5830i | − | 0.356956i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.6235 | −1.60448 | −0.802239 | − | 0.597003i | \(-0.796358\pi\) | ||||
−0.802239 | + | 0.597003i | \(0.796358\pi\) | |||||||
\(882\) | −7.00000 | −0.235702 | ||||||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | − | 10.5830i | − | 0.355945i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0000 | −0.806296 | ||||||||
\(887\) | 34.0000i | 1.14161i | 0.821086 | + | 0.570804i | \(0.193368\pi\) | ||||
−0.821086 | + | 0.570804i | \(0.806632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.1660i | 0.709885i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 5.29150i | − | 0.177272i | ||||||
\(892\) | 14.0000i | 0.468755i | ||||||||
\(893\) | − | 31.7490i | − | 1.06244i | ||||||
\(894\) | 10.5830 | 0.353949 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 2.64575i | − | 0.0883883i | ||||||
\(897\) | 8.00000 | − | 5.29150i | 0.267112 | − | 0.176678i | ||||
\(898\) | 30.0000 | 1.00111 | ||||||||
\(899\) | 60.0000i | 2.00111i | ||||||||
\(900\) | 5.00000 | 0.166667 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −63.4980 | −2.11425 | ||||||||
\(903\) | 14.0000i | 0.465891i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 16.0000i | − | 0.531564i | ||||||
\(907\) | 37.0405i | 1.22991i | 0.788562 | + | 0.614955i | \(0.210826\pi\) | ||||
−0.788562 | + | 0.614955i | \(0.789174\pi\) | |||||||
\(908\) | −26.4575 | −0.878023 | ||||||||
\(909\) | − | 14.0000i | − | 0.464351i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 26.4575i | − | 0.876577i | −0.898834 | − | 0.438288i | \(-0.855585\pi\) | ||
0.898834 | − | 0.438288i | \(-0.144415\pi\) | |||||||
\(912\) | 5.29150i | 0.175219i | ||||||||
\(913\) | − | 84.0000i | − | 2.77999i | ||||||
\(914\) | 21.1660i | 0.700109i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.1660 | 0.699345 | ||||||||
\(917\) | 21.1660 | 0.698963 | ||||||||
\(918\) | 5.29150i | 0.174646i | ||||||||
\(919\) | − | 15.8745i | − | 0.523652i | −0.965115 | − | 0.261826i | \(-0.915675\pi\) | ||
0.965115 | − | 0.261826i | \(-0.0843246\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 30.0000i | − | 0.987997i | ||||||
\(923\) | 16.0000i | 0.526646i | ||||||||
\(924\) | 14.0000i | 0.460566i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.0000 | 0.525793 | ||||||||
\(927\) | 10.5830 | 0.347591 | ||||||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | 20.0000i | 0.656179i | 0.944647 | + | 0.328089i | \(0.106405\pi\) | ||||
−0.944647 | + | 0.328089i | \(0.893595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.0405 | −1.21395 | ||||||||
\(932\) | 10.0000 | 0.327561 | ||||||||
\(933\) | −10.0000 | −0.327385 | ||||||||
\(934\) | 15.8745 | 0.519430 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 2.00000i | − | 0.0653720i | ||||||
\(937\) | −47.6235 | −1.55579 | −0.777896 | − | 0.628393i | \(-0.783713\pi\) | ||||
−0.777896 | + | 0.628393i | \(0.783713\pi\) | |||||||
\(938\) | 14.0000 | 0.457116 | ||||||||
\(939\) | 5.29150i | 0.172682i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.3320 | 1.37998 | 0.689992 | − | 0.723817i | \(-0.257614\pi\) | ||||
0.689992 | + | 0.723817i | \(0.257614\pi\) | |||||||
\(942\) | − | 10.5830i | − | 0.344813i | ||||||
\(943\) | 31.7490 | + | 48.0000i | 1.03389 | + | 1.56310i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.0000 | 0.910359 | ||||||||
\(947\) | −24.0000 | −0.779895 | −0.389948 | − | 0.920837i | \(-0.627507\pi\) | ||||
−0.389948 | + | 0.920837i | \(0.627507\pi\) | |||||||
\(948\) | −5.29150 | −0.171860 | ||||||||
\(949\) | 8.00000 | 0.259691 | ||||||||
\(950\) | 26.4575 | 0.858395 | ||||||||
\(951\) | 6.00000i | 0.194563i | ||||||||
\(952\) | − | 14.0000i | − | 0.453743i | ||||||
\(953\) | 42.3320i | 1.37127i | 0.727946 | + | 0.685634i | \(0.240475\pi\) | ||||
−0.727946 | + | 0.685634i | \(0.759525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.00000 | 0.258738 | ||||||||
\(957\) | 31.7490 | 1.02630 | ||||||||
\(958\) | −21.1660 | −0.683843 | ||||||||
\(959\) | 56.0000 | 1.80833 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −69.0000 | −2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.8745i | 0.511549i | ||||||||
\(964\) | −15.8745 | −0.511283 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 10.5830 | − | 7.00000i | 0.340503 | − | 0.225221i | ||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 17.0000 | 0.546401 | ||||||||
\(969\) | 28.0000i | 0.899490i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.4575 | 0.849062 | 0.424531 | − | 0.905413i | \(-0.360439\pi\) | ||||
0.424531 | + | 0.905413i | \(0.360439\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 31.7490 | 1.01783 | ||||||||
\(974\) | −40.0000 | −1.28168 | ||||||||
\(975\) | −10.0000 | −0.320256 | ||||||||
\(976\) | 10.5830 | 0.338754 | ||||||||
\(977\) | − | 42.3320i | − | 1.35432i | −0.735835 | − | 0.677161i | \(-0.763210\pi\) | ||
0.735835 | − | 0.677161i | \(-0.236790\pi\) | |||||||
\(978\) | − | 24.0000i | − | 0.767435i | ||||||
\(979\) | − | 28.0000i | − | 0.894884i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 10.5830i | − | 0.337889i | ||||||
\(982\) | 8.00000 | 0.255290 | ||||||||
\(983\) | −31.7490 | −1.01264 | −0.506318 | − | 0.862347i | \(-0.668994\pi\) | ||||
−0.506318 | + | 0.862347i | \(0.668994\pi\) | |||||||
\(984\) | 12.0000 | 0.382546 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −31.7490 | −1.01109 | ||||||||
\(987\) | 15.8745i | 0.505291i | ||||||||
\(988\) | − | 10.5830i | − | 0.336690i | ||||||
\(989\) | −14.0000 | − | 21.1660i | −0.445174 | − | 0.673040i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | − | 10.0000i | − | 0.317500i | ||||||
\(993\) | 4.00000i | 0.126936i | ||||||||
\(994\) | 21.1660i | 0.671345i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15.8745i | 0.503003i | ||||||||
\(997\) | − | 42.0000i | − | 1.33015i | −0.746775 | − | 0.665077i | \(-0.768399\pi\) | ||
0.746775 | − | 0.665077i | \(-0.231601\pi\) | |||||||
\(998\) | 24.0000 | 0.759707 | ||||||||
\(999\) | 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 | 966.2.g.c.643.4 | yes | 4 | |
3.2 | odd | 2 | 2898.2.g.c.2575.3 | 4 | |||
7.6 | odd | 2 | inner | 966.2.g.c.643.2 | yes | 4 | |
21.20 | even | 2 | 2898.2.g.c.2575.4 | 4 | |||
23.22 | odd | 2 | inner | 966.2.g.c.643.3 | yes | 4 | |
69.68 | even | 2 | 2898.2.g.c.2575.1 | 4 | |||
161.160 | even | 2 | inner | 966.2.g.c.643.1 | ✓ | 4 | |
483.482 | odd | 2 | 2898.2.g.c.2575.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.g.c.643.1 | ✓ | 4 | 161.160 | even | 2 | inner | |
966.2.g.c.643.2 | yes | 4 | 7.6 | odd | 2 | inner | |
966.2.g.c.643.3 | yes | 4 | 23.22 | odd | 2 | inner | |
966.2.g.c.643.4 | yes | 4 | 1.1 | even | 1 | trivial | |
2898.2.g.c.2575.1 | 4 | 69.68 | even | 2 | |||
2898.2.g.c.2575.2 | 4 | 483.482 | odd | 2 | |||
2898.2.g.c.2575.3 | 4 | 3.2 | odd | 2 | |||
2898.2.g.c.2575.4 | 4 | 21.20 | even | 2 |