Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(1025,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.e (of order \(2\), degree \(1\), not 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: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.540942598144.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 16x^{6} + 71x^{4} + 56x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.6 | ||
Root | \(0.854013i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1025 |
Dual form | 2304.3.e.o.1025.4 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.07498i | 0.214997i | 0.994205 | + | 0.107498i | \(0.0342840\pi\) | ||||
−0.994205 | + | 0.107498i | \(0.965716\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.21110 | 1.03016 | 0.515079 | − | 0.857143i | \(-0.327763\pi\) | ||||
0.515079 | + | 0.857143i | \(0.327763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 16.3517i | − 1.48652i | −0.669004 | − | 0.743258i | \(-0.733279\pi\) | ||||
0.669004 | − | 0.743258i | \(-0.266721\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.6045 | 1.66189 | 0.830943 | − | 0.556357i | \(-0.187801\pi\) | ||||
0.830943 | + | 0.556357i | \(0.187801\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 18.9819i | − 1.11658i | −0.829646 | − | 0.558290i | \(-0.811458\pi\) | ||||
0.829646 | − | 0.558290i | \(-0.188542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.0438 | 0.897040 | 0.448520 | − | 0.893773i | \(-0.351951\pi\) | ||||
0.448520 | + | 0.893773i | \(0.351951\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.11567i | − 0.0485074i | −0.999706 | − | 0.0242537i | \(-0.992279\pi\) | ||||
0.999706 | − | 0.0242537i | \(-0.00772094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.8444 | 0.953776 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.4784i | 1.01650i | 0.861210 | + | 0.508249i | \(0.169707\pi\) | ||||
−0.861210 | + | 0.508249i | \(0.830293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.63331 | −0.181720 | −0.0908598 | − | 0.995864i | \(-0.528962\pi\) | ||||
−0.0908598 | + | 0.995864i | \(0.528962\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.75182i | 0.221480i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −17.0438 | −0.460642 | −0.230321 | − | 0.973115i | \(-0.573978\pi\) | ||||
−0.230321 | + | 0.973115i | \(0.573978\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 27.4671i | − 0.669930i | −0.942231 | − | 0.334965i | \(-0.891275\pi\) | ||||
0.942231 | − | 0.334965i | \(-0.108725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −52.3306 | −1.21699 | −0.608495 | − | 0.793558i | \(-0.708226\pi\) | ||||
−0.608495 | + | 0.793558i | \(0.708226\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 64.5352i | − 1.37309i | −0.727087 | − | 0.686545i | \(-0.759126\pi\) | ||||
0.727087 | − | 0.686545i | \(-0.240874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.0612245 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 35.9283i | − 0.677893i | −0.940806 | − | 0.338946i | \(-0.889929\pi\) | ||||
0.940806 | − | 0.338946i | \(-0.110071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.5778 | 0.319596 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 56.8069i | 0.962828i | 0.876493 | + | 0.481414i | \(0.159877\pi\) | ||||
−0.876493 | + | 0.481414i | \(0.840123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −69.3743 | −1.13728 | −0.568642 | − | 0.822585i | \(-0.692531\pi\) | ||||
−0.568642 | + | 0.822585i | \(0.692531\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.2245i | 0.357300i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −69.3743 | −1.03544 | −0.517719 | − | 0.855551i | \(-0.673219\pi\) | ||||
−0.517719 | + | 0.855551i | \(0.673219\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 98.4764i | − 1.38699i | −0.720461 | − | 0.693496i | \(-0.756070\pi\) | ||||
0.720461 | − | 0.693496i | \(-0.243930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −37.6888 | −0.516285 | −0.258143 | − | 0.966107i | \(-0.583110\pi\) | ||||
−0.258143 | + | 0.966107i | \(0.583110\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 117.914i | − 1.53135i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 127.322 | 1.61167 | 0.805836 | − | 0.592138i | \(-0.201716\pi\) | ||||
0.805836 | + | 0.592138i | \(0.201716\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.75182i | − 0.0933954i | −0.998909 | − | 0.0466977i | \(-0.985130\pi\) | ||||
0.998909 | − | 0.0466977i | \(-0.0148697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.4052 | 0.240061 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 76.1475i | 0.855590i | 0.903876 | + | 0.427795i | \(0.140709\pi\) | ||||
−0.903876 | + | 0.427795i | \(0.859291\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 155.792 | 1.71200 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.3218i | 0.192861i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.84441 | 0.0499424 | 0.0249712 | − | 0.999688i | \(-0.492051\pi\) | ||||
0.0249712 | + | 0.999688i | \(0.492051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 105.635i | 1.04589i | 0.852366 | + | 0.522946i | \(0.175167\pi\) | ||||
−0.852366 | + | 0.522946i | \(0.824833\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 104.789 | 1.01737 | 0.508684 | − | 0.860953i | \(-0.330132\pi\) | ||||
0.508684 | + | 0.860953i | \(0.330132\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 65.4067i | − 0.611278i | −0.952147 | − | 0.305639i | \(-0.901130\pi\) | ||||
0.952147 | − | 0.305639i | \(-0.0988701\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.36144 | −0.0308389 | −0.0154195 | − | 0.999881i | \(-0.504908\pi\) | ||||
−0.0154195 | + | 0.999881i | \(0.504908\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 84.1927i | 0.745068i | 0.928019 | + | 0.372534i | \(0.121511\pi\) | ||||
−0.928019 | + | 0.372534i | \(0.878489\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.19933 | 0.0104289 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 136.880i | − 1.15025i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −146.378 | −1.20973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 52.5069i | 0.420056i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 45.5223 | 0.358443 | 0.179222 | − | 0.983809i | \(-0.442642\pi\) | ||||
0.179222 | + | 0.983809i | \(0.442642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 129.117i | − 0.985629i | −0.870134 | − | 0.492814i | \(-0.835968\pi\) | ||||
0.870134 | − | 0.492814i | \(-0.164032\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 122.904 | 0.924092 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 10.9367i | − 0.0798296i | −0.999203 | − | 0.0399148i | \(-0.987291\pi\) | ||||
0.999203 | − | 0.0399148i | \(-0.0127087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.19933 | 0.00862825 | 0.00431412 | − | 0.999991i | \(-0.498627\pi\) | ||||
0.00431412 | + | 0.999991i | \(0.498627\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 353.270i | − 2.47042i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −31.6888 | −0.218544 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 29.9323i | 0.200888i | 0.994943 | + | 0.100444i | \(0.0320263\pi\) | ||||
−0.994943 | + | 0.100444i | \(0.967974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 61.5223 | 0.407432 | 0.203716 | − | 0.979030i | \(-0.434698\pi\) | ||||
0.203716 | + | 0.979030i | \(0.434698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.05571i | − 0.0390691i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 137.549 | 0.876110 | 0.438055 | − | 0.898948i | \(-0.355667\pi\) | ||||
0.438055 | + | 0.898948i | \(0.355667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 8.04521i | − 0.0499702i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 191.079 | 1.17227 | 0.586133 | − | 0.810215i | \(-0.300650\pi\) | ||||
0.586133 | + | 0.810215i | \(0.300650\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 233.125i | − 1.39596i | −0.716118 | − | 0.697980i | \(-0.754083\pi\) | ||||
0.716118 | − | 0.697980i | \(-0.245917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 297.755 | 1.76187 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 323.809i | 1.87173i | 0.352363 | + | 0.935864i | \(0.385378\pi\) | ||||
−0.352363 | + | 0.935864i | \(0.614622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 171.944 | 0.982540 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 185.924i | 1.03868i | 0.854567 | + | 0.519342i | \(0.173823\pi\) | ||||
−0.854567 | + | 0.519342i | \(0.826177\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −126.266 | −0.697600 | −0.348800 | − | 0.937197i | \(-0.613411\pi\) | ||||
−0.348800 | + | 0.937197i | \(0.613411\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 18.3218i | − 0.0990365i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −310.385 | −1.65982 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 233.125i | − 1.22055i | −0.792189 | − | 0.610275i | \(-0.791059\pi\) | ||||
0.792189 | − | 0.610275i | \(-0.208941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −117.378 | −0.608174 | −0.304087 | − | 0.952644i | \(-0.598351\pi\) | ||||
−0.304087 | + | 0.952644i | \(0.598351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 296.313i | − 1.50413i | −0.659091 | − | 0.752064i | \(-0.729059\pi\) | ||||
0.659091 | − | 0.752064i | \(-0.270941\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 233.011 | 1.17091 | 0.585455 | − | 0.810705i | \(-0.300916\pi\) | ||||
0.585455 | + | 0.810705i | \(0.300916\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 212.572i | 1.04715i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.5267 | 0.144033 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 278.694i | − 1.33346i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −35.2868 | −0.167236 | −0.0836181 | − | 0.996498i | \(-0.526648\pi\) | ||||
−0.0836181 | + | 0.996498i | \(0.526648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 56.2545i | − 0.261649i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −40.6224 | −0.187200 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 410.094i | − 1.85563i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 51.8335 | 0.232437 | 0.116219 | − | 0.993224i | \(-0.462923\pi\) | ||||
0.116219 | + | 0.993224i | \(0.462923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 334.786i | 1.47483i | 0.675442 | + | 0.737413i | \(0.263953\pi\) | ||||
−0.675442 | + | 0.737413i | \(0.736047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −219.407 | −0.958108 | −0.479054 | − | 0.877786i | \(-0.659020\pi\) | ||||
−0.479054 | + | 0.877786i | \(0.659020\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 203.867i | − 0.874965i | −0.899227 | − | 0.437482i | \(-0.855870\pi\) | ||||
0.899227 | − | 0.437482i | \(-0.144130\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 69.3743 | 0.295210 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 54.0232i | − 0.226038i | −0.993593 | − | 0.113019i | \(-0.963948\pi\) | ||||
0.993593 | − | 0.113019i | \(-0.0360522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 327.600 | 1.35933 | 0.679667 | − | 0.733520i | \(-0.262124\pi\) | ||||
0.679667 | + | 0.733520i | \(0.262124\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.22495i | 0.0131631i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 368.222 | 1.49078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 362.281i | − 1.44335i | −0.692231 | − | 0.721676i | \(-0.743372\pi\) | ||||
0.692231 | − | 0.721676i | \(-0.256628\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.2431 | −0.0721070 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.2132i | 0.0825416i | 0.999148 | + | 0.0412708i | \(0.0131406\pi\) | ||||
−0.999148 | + | 0.0412708i | \(0.986859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −122.904 | −0.474534 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 205.878i | − 0.782806i | −0.920219 | − | 0.391403i | \(-0.871990\pi\) | ||||
0.920219 | − | 0.391403i | \(-0.128010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 38.6224 | 0.145745 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 2.77109i | − 0.0103014i | −0.999987 | − | 0.00515072i | \(-0.998360\pi\) | ||||
0.999987 | − | 0.00515072i | \(-0.00163953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 125.744 | 0.464001 | 0.232001 | − | 0.972716i | \(-0.425473\pi\) | ||||
0.232001 | + | 0.972716i | \(0.425473\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 389.896i | − 1.41780i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −162.752 | −0.587552 | −0.293776 | − | 0.955874i | \(-0.594912\pi\) | ||||
−0.293776 | + | 0.955874i | \(0.594912\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 301.227i | 1.07198i | 0.844223 | + | 0.535992i | \(0.180062\pi\) | ||||
−0.844223 | + | 0.535992i | \(0.819938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.6888 | 0.111975 | 0.0559874 | − | 0.998431i | \(-0.482169\pi\) | ||||
0.0559874 | + | 0.998431i | \(0.482169\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 198.068i | − 0.690134i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −71.3112 | −0.246751 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 304.913i | 1.04066i | 0.853966 | + | 0.520329i | \(0.174191\pi\) | ||||
−0.853966 | + | 0.520329i | \(0.825809\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −61.0665 | −0.207005 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 24.1035i | − 0.0806137i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −377.361 | −1.25369 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 74.5763i | − 0.244512i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −105.860 | −0.344822 | −0.172411 | − | 0.985025i | \(-0.555156\pi\) | ||||
−0.172411 | + | 0.985025i | \(0.555156\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 555.157i | − 1.78507i | −0.450978 | − | 0.892535i | \(-0.648925\pi\) | ||||
0.450978 | − | 0.892535i | \(-0.351075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −158.000 | −0.504792 | −0.252396 | − | 0.967624i | \(-0.581219\pi\) | ||||
−0.252396 | + | 0.967624i | \(0.581219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 97.0351i | 0.306105i | 0.988218 | + | 0.153052i | \(0.0489103\pi\) | ||||
−0.988218 | + | 0.153052i | \(0.951090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 482.022 | 1.51104 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 323.522i | − 1.00162i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 515.147 | 1.58507 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 465.370i | − 1.41450i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 619.572 | 1.87182 | 0.935909 | − | 0.352242i | \(-0.114581\pi\) | ||||
0.935909 | + | 0.352242i | \(0.114581\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 74.5763i | − 0.222616i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −170.755 | −0.506692 | −0.253346 | − | 0.967376i | \(-0.581531\pi\) | ||||
−0.253346 | + | 0.967376i | \(0.581531\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 92.1141i | 0.270129i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −331.711 | −0.967087 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 300.386i | 0.865666i | 0.901474 | + | 0.432833i | \(0.142486\pi\) | ||||
−0.901474 | + | 0.432833i | \(0.857514\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 53.5299 | 0.153381 | 0.0766904 | − | 0.997055i | \(-0.475565\pi\) | ||||
0.0766904 | + | 0.997055i | \(0.475565\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 600.475i | 1.70106i | 0.525925 | + | 0.850531i | \(0.323719\pi\) | ||||
−0.525925 | + | 0.850531i | \(0.676281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 105.860 | 0.298199 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 148.508i | 0.413671i | 0.978376 | + | 0.206836i | \(0.0663165\pi\) | ||||
−0.978376 | + | 0.206836i | \(0.933683\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −70.5106 | −0.195320 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 40.5149i | − 0.111000i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −316.389 | −0.862094 | −0.431047 | − | 0.902329i | \(-0.641856\pi\) | ||||
−0.431047 | + | 0.902329i | \(0.641856\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 259.083i | − 0.698336i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 626.768 | 1.68034 | 0.840171 | − | 0.542321i | \(-0.182455\pi\) | ||||
0.840171 | + | 0.542321i | \(0.182455\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 636.867i | 1.68930i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −331.027 | −0.873423 | −0.436711 | − | 0.899602i | \(-0.643857\pi\) | ||||
−0.436711 | + | 0.899602i | \(0.643857\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 407.765i | − 1.06466i | −0.846537 | − | 0.532330i | \(-0.821317\pi\) | ||||
0.846537 | − | 0.532330i | \(-0.178683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 126.755 | 0.329234 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 53.5819i | − 0.137743i | −0.997626 | − | 0.0688714i | \(-0.978060\pi\) | ||||
0.997626 | − | 0.0688714i | \(-0.0219398\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.1775 | −0.0541624 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 136.869i | 0.346504i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 289.744 | 0.729833 | 0.364917 | − | 0.931040i | \(-0.381098\pi\) | ||||
0.364917 | + | 0.931040i | \(0.381098\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 203.458i | 0.507376i | 0.967286 | + | 0.253688i | \(0.0816436\pi\) | ||||
−0.967286 | + | 0.253688i | \(0.918356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −121.705 | −0.301997 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 278.694i | 0.684752i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −412.844 | −1.00940 | −0.504700 | − | 0.863295i | \(-0.668397\pi\) | ||||
−0.504700 | + | 0.863295i | \(0.668397\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 409.640i | 0.991865i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.33308 | 0.0200797 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 336.482i | 0.803059i | 0.915846 | + | 0.401529i | \(0.131521\pi\) | ||||
−0.915846 | + | 0.401529i | \(0.868479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −217.481 | −0.516582 | −0.258291 | − | 0.966067i | \(-0.583159\pi\) | ||||
−0.258291 | + | 0.966067i | \(0.583159\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 452.611i | − 1.06497i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −500.265 | −1.17158 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 750.994i | 1.74245i | 0.490888 | + | 0.871223i | \(0.336672\pi\) | ||||
−0.490888 | + | 0.871223i | \(0.663328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −176.133 | −0.406773 | −0.203387 | − | 0.979098i | \(-0.565195\pi\) | ||||
−0.203387 | + | 0.979098i | \(0.565195\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 19.0152i | − 0.0435130i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 417.788 | 0.951681 | 0.475841 | − | 0.879531i | \(-0.342144\pi\) | ||||
0.475841 | + | 0.879531i | \(0.342144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 61.0471i | 0.137804i | 0.997623 | + | 0.0689020i | \(0.0219496\pi\) | ||||
−0.997623 | + | 0.0689020i | \(0.978050\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −81.8573 | −0.183949 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 182.905i | − 0.407360i | −0.979038 | − | 0.203680i | \(-0.934710\pi\) | ||||
0.979038 | − | 0.203680i | \(-0.0652902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −449.134 | −0.995863 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 167.474i | 0.368075i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 443.600 | 0.970678 | 0.485339 | − | 0.874326i | \(-0.338696\pi\) | ||||
0.485339 | + | 0.874326i | \(0.338696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 728.241i | − 1.57970i | −0.613301 | − | 0.789850i | \(-0.710159\pi\) | ||||
0.613301 | − | 0.789850i | \(-0.289841\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 107.722 | 0.232662 | 0.116331 | − | 0.993211i | \(-0.462887\pi\) | ||||
0.116331 | + | 0.993211i | \(0.462887\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 820.248i | 1.75642i | 0.478276 | + | 0.878210i | \(0.341262\pi\) | ||||
−0.478276 | + | 0.878210i | \(0.658738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −500.265 | −1.06666 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 855.693i | 1.80908i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 406.398 | 0.855575 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 120.790i | 0.252171i | 0.992019 | + | 0.126085i | \(0.0402413\pi\) | ||||
−0.992019 | + | 0.126085i | \(0.959759\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −368.222 | −0.765534 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.20766i | 0.0107374i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −128.234 | −0.263314 | −0.131657 | − | 0.991295i | \(-0.542030\pi\) | ||||
−0.131657 | + | 0.991295i | \(0.542030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 382.144i | − 0.778298i | −0.921175 | − | 0.389149i | \(-0.872769\pi\) | ||||
0.921175 | − | 0.389149i | \(-0.127231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 559.555 | 1.13500 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 710.123i | − 1.42882i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 554.995 | 1.11221 | 0.556107 | − | 0.831111i | \(-0.312295\pi\) | ||||
0.556107 | + | 0.831111i | \(0.312295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 78.3943i | − 0.155854i | −0.996959 | − | 0.0779268i | \(-0.975170\pi\) | ||||
0.996959 | − | 0.0779268i | \(-0.0248300\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −113.556 | −0.224863 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 514.941i | 1.01167i | 0.862630 | + | 0.505836i | \(0.168816\pi\) | ||||
−0.862630 | + | 0.505836i | \(0.831184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −271.778 | −0.531855 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 112.646i | 0.218731i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1055.26 | −2.04112 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 489.695i | − 0.939914i | −0.882689 | − | 0.469957i | \(-0.844270\pi\) | ||||
0.882689 | − | 0.469957i | \(-0.155730\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −774.165 | −1.48024 | −0.740119 | − | 0.672476i | \(-0.765231\pi\) | ||||
−0.740119 | + | 0.672476i | \(0.765231\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 106.931i | 0.202905i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 527.755 | 0.997647 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 593.415i | − 1.11335i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 70.3112 | 0.131423 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 49.0551i | − 0.0910112i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −590.045 | −1.09066 | −0.545328 | − | 0.838223i | \(-0.683595\pi\) | ||||
−0.545328 | + | 0.838223i | \(0.683595\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 3.61350i | − 0.00663027i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 707.189 | 1.29285 | 0.646425 | − | 0.762977i | \(-0.276263\pi\) | ||||
0.646425 | + | 0.762977i | \(0.276263\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 502.423i | 0.911838i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 918.133 | 1.66028 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 75.0816i | − 0.134796i | −0.997726 | − | 0.0673982i | \(-0.978530\pi\) | ||||
0.997726 | − | 0.0673982i | \(-0.0214698\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1130.58 | −2.02250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 114.462i | 0.203307i | 0.994820 | + | 0.101653i | \(0.0324133\pi\) | ||||
−0.994820 | + | 0.101653i | \(0.967587\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −90.5058 | −0.160187 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 45.8199i | − 0.0805270i | −0.999189 | − | 0.0402635i | \(-0.987180\pi\) | ||||
0.999189 | − | 0.0402635i | \(-0.0128197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 830.093 | 1.45375 | 0.726877 | − | 0.686768i | \(-0.240971\pi\) | ||||
0.726877 | + | 0.686768i | \(0.240971\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 26.6025i | − 0.0462652i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −69.3776 | −0.120239 | −0.0601193 | − | 0.998191i | \(-0.519148\pi\) | ||||
−0.0601193 | + | 0.998191i | \(0.519148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 55.8991i | − 0.0962120i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −587.489 | −1.00770 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 428.655i | − 0.730248i | −0.930959 | − | 0.365124i | \(-0.881027\pi\) | ||||
0.930959 | − | 0.365124i | \(-0.118973\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −96.0127 | −0.163010 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 77.0276i | − 0.129895i | −0.997889 | − | 0.0649474i | \(-0.979312\pi\) | ||||
0.997889 | − | 0.0649474i | \(-0.0206880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 147.144 | 0.247301 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 963.566i | 1.60862i | 0.594207 | + | 0.804312i | \(0.297466\pi\) | ||||
−0.594207 | + | 0.804312i | \(0.702534\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −840.133 | −1.39789 | −0.698946 | − | 0.715175i | \(-0.746347\pi\) | ||||
−0.698946 | + | 0.715175i | \(0.746347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 157.354i | − 0.260089i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −156.611 | −0.258008 | −0.129004 | − | 0.991644i | \(-0.541178\pi\) | ||||
−0.129004 | + | 0.991644i | \(0.541178\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1394.25i | − 2.28192i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 426.094 | 0.695096 | 0.347548 | − | 0.937662i | \(-0.387014\pi\) | ||||
0.347548 | + | 0.937662i | \(0.387014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 963.520i | − 1.56162i | −0.624769 | − | 0.780810i | \(-0.714807\pi\) | ||||
0.624769 | − | 0.780810i | \(-0.285193\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −175.235 | −0.283093 | −0.141547 | − | 0.989932i | \(-0.545208\pi\) | ||||
−0.141547 | + | 0.989932i | \(0.545208\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 549.107i | 0.881392i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 539.666 | 0.863466 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 323.522i | 0.514344i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1140.72 | −1.80780 | −0.903900 | − | 0.427744i | \(-0.859308\pi\) | ||||
−0.903900 | + | 0.427744i | \(0.859308\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 48.9357i | 0.0770641i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 64.8136 | 0.101748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 351.730i | 0.548721i | 0.961627 | + | 0.274360i | \(0.0884661\pi\) | ||||
−0.961627 | + | 0.274360i | \(0.911534\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −86.4181 | −0.134398 | −0.0671991 | − | 0.997740i | \(-0.521406\pi\) | ||||
−0.0671991 | + | 0.997740i | \(0.521406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 430.723i | 0.665723i | 0.942976 | + | 0.332861i | \(0.108014\pi\) | ||||
−0.942976 | + | 0.332861i | \(0.891986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 928.888 | 1.43126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 886.670i | 1.35784i | 0.734212 | + | 0.678920i | \(0.237552\pi\) | ||||
−0.734212 | + | 0.678920i | \(0.762448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 138.799 | 0.211907 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 352.833i | − 0.535407i | −0.963501 | − | 0.267704i | \(-0.913735\pi\) | ||||
0.963501 | − | 0.267704i | \(-0.0862648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1206.26 | 1.82489 | 0.912447 | − | 0.409195i | \(-0.134190\pi\) | ||||
0.912447 | + | 0.409195i | \(0.134190\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 132.120i | 0.198677i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.8882 | 0.0493076 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1134.39i | 1.69059i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −956.133 | −1.42070 | −0.710351 | − | 0.703847i | \(-0.751464\pi\) | ||||
−0.710351 | + | 0.703847i | \(0.751464\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 420.557i | − 0.621207i | −0.950540 | − | 0.310604i | \(-0.899469\pi\) | ||||
0.950540 | − | 0.310604i | \(-0.100531\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.9335 | 0.0514485 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 539.725i | 0.790227i | 0.918632 | + | 0.395113i | \(0.129295\pi\) | ||||
−0.918632 | + | 0.395113i | \(0.870705\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.7567 | 0.0171631 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 776.214i | − 1.12658i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −432.090 | −0.625312 | −0.312656 | − | 0.949866i | \(-0.601219\pi\) | ||||
−0.312656 | + | 0.949866i | \(0.601219\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.28926i | 0.00185504i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −521.378 | −0.748031 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 880.339i | − 1.25583i | −0.778280 | − | 0.627917i | \(-0.783908\pi\) | ||||
0.778280 | − | 0.627917i | \(-0.216092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −290.489 | −0.413214 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 761.745i | 1.07743i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 799.367 | 1.12746 | 0.563729 | − | 0.825960i | \(-0.309366\pi\) | ||||
0.563729 | + | 0.825960i | \(0.309366\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.28491i | 0.00881474i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 379.760 | 0.531133 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 258.786i | 0.359924i | 0.983674 | + | 0.179962i | \(0.0575975\pi\) | ||||
−0.983674 | + | 0.179962i | \(0.942402\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 755.643 | 1.04805 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 702.896i | 0.969511i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −663.211 | −0.912257 | −0.456129 | − | 0.889914i | \(-0.650764\pi\) | ||||
−0.456129 | + | 0.889914i | \(0.650764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 993.332i | 1.35887i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 908.826 | 1.23987 | 0.619936 | − | 0.784653i | \(-0.287159\pi\) | ||||
0.619936 | + | 0.784653i | \(0.287159\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1134.39i | 1.53920i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1112.39 | −1.50526 | −0.752631 | − | 0.658443i | \(-0.771215\pi\) | ||||
−0.752631 | + | 0.658443i | \(0.771215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 541.298i | 0.728530i | 0.931295 | + | 0.364265i | \(0.118680\pi\) | ||||
−0.931295 | + | 0.364265i | \(0.881320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.1767 | −0.0431902 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 471.655i | − 0.629713i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 763.699 | 1.01691 | 0.508455 | − | 0.861089i | \(-0.330217\pi\) | ||||
0.508455 | + | 0.861089i | \(0.330217\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 66.1354i | 0.0875966i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −419.134 | −0.553678 | −0.276839 | − | 0.960916i | \(-0.589287\pi\) | ||||
−0.276839 | + | 0.960916i | \(0.589287\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1330.24i | 1.74802i | 0.485912 | + | 0.874008i | \(0.338488\pi\) | ||||
−0.485912 | + | 0.874008i | \(0.661512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.2397 | −0.0317690 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1227.29i | 1.60011i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 671.511 | 0.873226 | 0.436613 | − | 0.899649i | \(-0.356178\pi\) | ||||
0.436613 | + | 0.899649i | \(0.356178\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1421.13i | 1.83846i | 0.393724 | + | 0.919229i | \(0.371187\pi\) | ||||
−0.393724 | + | 0.919229i | \(0.628813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −134.323 | −0.173320 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 468.143i | − 0.600954i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1610.25 | −2.06179 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 147.863i | 0.188361i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −649.808 | −0.825677 | −0.412839 | − | 0.910804i | \(-0.635463\pi\) | ||||
−0.412839 | + | 0.910804i | \(0.635463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 607.122i | 0.767538i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1498.80 | −1.89004 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 422.946i | 0.530672i | 0.964156 | + | 0.265336i | \(0.0854830\pi\) | ||||
−0.964156 | + | 0.265336i | \(0.914517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1225.00 | −1.53317 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 616.276i | 0.767467i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.64847 | 0.0107434 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 1353.87i | − 1.67351i | −0.547574 | − | 0.836757i | \(-0.684448\pi\) | ||||
0.547574 | − | 0.836757i | \(-0.315552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 842.340 | 1.03864 | 0.519322 | − | 0.854579i | \(-0.326185\pi\) | ||||
0.519322 | + | 0.854579i | \(0.326185\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 205.407i | 0.252033i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −891.909 | −1.09169 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 616.897i | 0.751397i | 0.926742 | + | 0.375698i | \(0.122597\pi\) | ||||
−0.926742 | + | 0.375698i | \(0.877403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 980.500 | 1.19137 | 0.595686 | − | 0.803217i | \(-0.296880\pi\) | ||||
0.595686 | + | 0.803217i | \(0.296880\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 70.4951i | − 0.0852419i | −0.999091 | − | 0.0426210i | \(-0.986429\pi\) | ||||
0.999091 | − | 0.0426210i | \(-0.0135708\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 515.147 | 0.621408 | 0.310704 | − | 0.950507i | \(-0.399435\pi\) | ||||
0.310704 | + | 0.950507i | \(0.399435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 56.9456i | − 0.0683621i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 250.606 | 0.300127 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 47.1556i | − 0.0562045i | −0.999605 | − | 0.0281022i | \(-0.991054\pi\) | ||||
0.999605 | − | 0.0281022i | \(-0.00894640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9773 | −0.0332667 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 320.082i | 0.378795i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1055.54 | −1.24622 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.0152i | 0.0223445i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −763.118 | −0.894628 | −0.447314 | − | 0.894377i | \(-0.647619\pi\) | ||||
−0.447314 | + | 0.894377i | \(0.647619\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1641.05i | 1.91488i | 0.288631 | + | 0.957440i | \(0.406800\pi\) | ||||
−0.288631 | + | 0.957440i | \(0.593200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1366.84 | −1.59120 | −0.795602 | − | 0.605819i | \(-0.792845\pi\) | ||||
−0.795602 | + | 0.605819i | \(0.792845\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 836.082i | 0.968809i | 0.874844 | + | 0.484405i | \(0.160964\pi\) | ||||
−0.874844 | + | 0.484405i | \(0.839036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −348.089 | −0.402415 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2081.93i | − 2.39578i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1498.80 | −1.72078 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 378.633i | 0.432723i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 158.191 | 0.180377 | 0.0901887 | − | 0.995925i | \(-0.471253\pi\) | ||||
0.0901887 | + | 0.995925i | \(0.471253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 237.430i | 0.269500i | 0.990880 | + | 0.134750i | \(0.0430232\pi\) | ||||
−0.990880 | + | 0.134750i | \(0.956977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 592.933 | 0.671499 | 0.335749 | − | 0.941951i | \(-0.391011\pi\) | ||||
0.335749 | + | 0.941951i | \(0.391011\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1420.72i | 1.60171i | 0.598858 | + | 0.800855i | \(0.295621\pi\) | ||||
−0.598858 | + | 0.800855i | \(0.704379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 328.266 | 0.369253 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1099.92i | − 1.23172i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −199.866 | −0.223313 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 166.061i | − 0.184717i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −681.987 | −0.756922 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 135.734i | − 0.149982i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −816.648 | −0.900383 | −0.450192 | − | 0.892932i | \(-0.648644\pi\) | ||||
−0.450192 | + | 0.892932i | \(0.648644\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 469.895i | − 0.515801i | −0.966171 | − | 0.257901i | \(-0.916969\pi\) | ||||
0.966171 | − | 0.257901i | \(-0.0830307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −126.755 | −0.138834 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 931.079i | − 1.01535i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1648.21 | −1.79348 | −0.896741 | − | 0.442555i | \(-0.854072\pi\) | ||||
−0.896741 | + | 0.442555i | \(0.854072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2127.53i | − 2.30502i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −406.398 | −0.439349 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 421.311i | 0.453510i | 0.973952 | + | 0.226755i | \(0.0728116\pi\) | ||||
−0.973952 | + | 0.226755i | \(0.927188\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.1313 | 0.0549208 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 333.659i | − 0.356855i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1434.27 | 1.53070 | 0.765350 | − | 0.643614i | \(-0.222566\pi\) | ||||
0.765350 | + | 0.643614i | \(0.222566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 732.876i | 0.778827i | 0.921063 | + | 0.389413i | \(0.127322\pi\) | ||||
−0.921063 | + | 0.389413i | \(0.872678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.6443 | −0.0324966 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1385.53i | − 1.46308i | −0.681800 | − | 0.731538i | \(-0.738803\pi\) | ||||
0.681800 | − | 0.731538i | \(-0.261197\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −814.249 | −0.858007 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 957.328i | 1.00454i | 0.864711 | + | 0.502270i | \(0.167502\pi\) | ||||
−0.864711 | + | 0.502270i | \(0.832498\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 250.606 | 0.262414 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 78.8654i | − 0.0822371i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −929.266 | −0.966978 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 126.179i | − 0.130755i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1225.90 | 1.26773 | 0.633867 | − | 0.773442i | \(-0.281467\pi\) | ||||
0.633867 | + | 0.773442i | \(0.281467\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 752.906i | 0.775393i | 0.921787 | + | 0.387696i | \(0.126729\pi\) | ||||
−0.921787 | + | 0.387696i | \(0.873271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.64847 | 0.00888845 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 642.932i | − 0.658068i | −0.944318 | − | 0.329034i | \(-0.893277\pi\) | ||||
0.944318 | − | 0.329034i | \(-0.106723\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1245.14 | 1.27185 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 161.251i | 0.164040i | 0.996631 | + | 0.0820200i | \(0.0261371\pi\) | ||||
−0.996631 | + | 0.0820200i | \(0.973863\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 318.532 | 0.323382 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58.3836i | 0.0590330i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −811.500 | −0.818870 | −0.409435 | − | 0.912339i | \(-0.634274\pi\) | ||||
−0.409435 | + | 0.912339i | \(0.634274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 250.483i | 0.251742i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 390.554 | 0.391729 | 0.195864 | − | 0.980631i | \(-0.437249\pi\) | ||||
0.195864 | + | 0.980631i | \(0.437249\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2304.3.e.o.1025.6 | 8 | ||
3.2 | odd | 2 | inner | 2304.3.e.o.1025.4 | 8 | ||
4.3 | odd | 2 | 2304.3.e.n.1025.6 | 8 | |||
8.3 | odd | 2 | 2304.3.e.n.1025.3 | 8 | |||
8.5 | even | 2 | inner | 2304.3.e.o.1025.3 | 8 | ||
12.11 | even | 2 | 2304.3.e.n.1025.4 | 8 | |||
16.3 | odd | 4 | 72.3.h.a.53.2 | yes | 8 | ||
16.5 | even | 4 | 288.3.h.a.17.3 | 8 | |||
16.11 | odd | 4 | 72.3.h.a.53.8 | yes | 8 | ||
16.13 | even | 4 | 288.3.h.a.17.6 | 8 | |||
24.5 | odd | 2 | inner | 2304.3.e.o.1025.5 | 8 | ||
24.11 | even | 2 | 2304.3.e.n.1025.5 | 8 | |||
48.5 | odd | 4 | 288.3.h.a.17.5 | 8 | |||
48.11 | even | 4 | 72.3.h.a.53.1 | ✓ | 8 | ||
48.29 | odd | 4 | 288.3.h.a.17.4 | 8 | |||
48.35 | even | 4 | 72.3.h.a.53.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.h.a.53.1 | ✓ | 8 | 48.11 | even | 4 | ||
72.3.h.a.53.2 | yes | 8 | 16.3 | odd | 4 | ||
72.3.h.a.53.7 | yes | 8 | 48.35 | even | 4 | ||
72.3.h.a.53.8 | yes | 8 | 16.11 | odd | 4 | ||
288.3.h.a.17.3 | 8 | 16.5 | even | 4 | |||
288.3.h.a.17.4 | 8 | 48.29 | odd | 4 | |||
288.3.h.a.17.5 | 8 | 48.5 | odd | 4 | |||
288.3.h.a.17.6 | 8 | 16.13 | even | 4 | |||
2304.3.e.n.1025.3 | 8 | 8.3 | odd | 2 | |||
2304.3.e.n.1025.4 | 8 | 12.11 | even | 2 | |||
2304.3.e.n.1025.5 | 8 | 24.11 | even | 2 | |||
2304.3.e.n.1025.6 | 8 | 4.3 | odd | 2 | |||
2304.3.e.o.1025.3 | 8 | 8.5 | even | 2 | inner | ||
2304.3.e.o.1025.4 | 8 | 3.2 | odd | 2 | inner | ||
2304.3.e.o.1025.5 | 8 | 24.5 | odd | 2 | inner | ||
2304.3.e.o.1025.6 | 8 | 1.1 | even | 1 | trivial |