Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(1727,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1727");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.c (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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + \cdots + 9496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{12} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1727.8 | ||
Root | \(-0.453986 + 2.07664i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1727 |
Dual form | 1728.4.c.j.1727.5 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 1.49508i | 0.133724i | 0.997762 | + | 0.0668622i | \(0.0212988\pi\) | ||||
−0.997762 | + | 0.0668622i | \(0.978701\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.1852i | 1.41387i | 0.707279 | + | 0.706935i | \(0.249923\pi\) | ||||
−0.707279 | + | 0.706935i | \(0.750077\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 56.3941 | 1.54577 | 0.772885 | − | 0.634546i | \(-0.218813\pi\) | ||||
0.772885 | + | 0.634546i | \(0.218813\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 41.3170 | 0.881482 | 0.440741 | − | 0.897634i | \(-0.354716\pi\) | ||||
0.440741 | + | 0.897634i | \(0.354716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 51.0410i | − 0.728192i | −0.931361 | − | 0.364096i | \(-0.881378\pi\) | ||||
0.931361 | − | 0.364096i | \(-0.118622\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 79.0640i | − 0.954659i | −0.878724 | − | 0.477330i | \(-0.841605\pi\) | ||||
0.878724 | − | 0.477330i | \(-0.158395\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −27.3688 | −0.248121 | −0.124061 | − | 0.992275i | \(-0.539592\pi\) | ||||
−0.124061 | + | 0.992275i | \(0.539592\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 122.765 | 0.982118 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 134.567i | − 0.861674i | −0.902430 | − | 0.430837i | \(-0.858218\pi\) | ||||
0.902430 | − | 0.430837i | \(-0.141782\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 187.192i | 1.08454i | 0.840204 | + | 0.542270i | \(0.182435\pi\) | ||||
−0.840204 | + | 0.542270i | \(0.817565\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −39.1491 | −0.189069 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 196.585 | 0.873469 | 0.436734 | − | 0.899590i | \(-0.356135\pi\) | ||||
0.436734 | + | 0.899590i | \(0.356135\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 298.015i | − 1.13517i | −0.823313 | − | 0.567587i | \(-0.807877\pi\) | ||||
0.823313 | − | 0.567587i | \(-0.192123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 465.576i | − 1.65115i | −0.564289 | − | 0.825577i | \(-0.690850\pi\) | ||||
0.564289 | − | 0.825577i | \(-0.309150\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 373.845 | 1.16023 | 0.580116 | − | 0.814534i | \(-0.303007\pi\) | ||||
0.580116 | + | 0.814534i | \(0.303007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.667 | −0.999028 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 620.093i | − 1.60710i | −0.595237 | − | 0.803550i | \(-0.702942\pi\) | ||||
0.595237 | − | 0.803550i | \(-0.297058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 84.3140i | 0.206707i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −321.152 | −0.708652 | −0.354326 | − | 0.935122i | \(-0.615290\pi\) | ||||
−0.354326 | + | 0.935122i | \(0.615290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −674.699 | −1.41617 | −0.708085 | − | 0.706127i | \(-0.750441\pi\) | ||||
−0.708085 | + | 0.706127i | \(0.750441\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 61.7724i | 0.117876i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 576.075i | 1.05043i | 0.850970 | + | 0.525215i | \(0.176015\pi\) | ||||
−0.850970 | + | 0.525215i | \(0.823985\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −223.813 | −0.374110 | −0.187055 | − | 0.982349i | \(-0.559894\pi\) | ||||
−0.187055 | + | 0.982349i | \(0.559894\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70.1371 | 0.112451 | 0.0562255 | − | 0.998418i | \(-0.482093\pi\) | ||||
0.0562255 | + | 0.998418i | \(0.482093\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1476.69i | 2.18552i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 1052.32i | − 1.49868i | −0.662187 | − | 0.749338i | \(-0.730372\pi\) | ||||
0.662187 | − | 0.749338i | \(-0.269628\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1219.05 | 1.61214 | 0.806070 | − | 0.591820i | \(-0.201591\pi\) | ||||
0.806070 | + | 0.591820i | \(0.201591\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 76.3107 | 0.0973771 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1340.64i | 1.59672i | 0.602183 | + | 0.798358i | \(0.294298\pi\) | ||||
−0.602183 | + | 0.798358i | \(0.705702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1081.89i | 1.24630i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 118.207 | 0.127661 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −576.059 | −0.602989 | −0.301494 | − | 0.953468i | \(-0.597485\pi\) | ||||
−0.301494 | + | 0.953468i | \(0.597485\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 116.079i | − 0.114359i | −0.998364 | − | 0.0571797i | \(-0.981789\pi\) | ||||
0.998364 | − | 0.0571797i | \(-0.0182108\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 165.074i | − 0.157915i | −0.996878 | − | 0.0789573i | \(-0.974841\pi\) | ||||
0.996878 | − | 0.0789573i | \(-0.0251591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 936.718 | 0.846318 | 0.423159 | − | 0.906056i | \(-0.360921\pi\) | ||||
0.423159 | + | 0.906056i | \(0.360921\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −346.957 | −0.304885 | −0.152443 | − | 0.988312i | \(-0.548714\pi\) | ||||
−0.152443 | + | 0.988312i | \(0.548714\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1462.22i | − 1.21729i | −0.793443 | − | 0.608645i | \(-0.791713\pi\) | ||||
0.793443 | − | 0.608645i | \(-0.208287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 40.9187i | − 0.0331799i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1336.52 | 1.02957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1849.30 | 1.38941 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 370.429i | 0.265058i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 265.004i | 0.185160i | 0.995705 | + | 0.0925800i | \(0.0295114\pi\) | ||||
−0.995705 | + | 0.0925800i | \(0.970489\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1151.86 | 0.768231 | 0.384115 | − | 0.923285i | \(-0.374507\pi\) | ||||
0.384115 | + | 0.923285i | \(0.374507\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2070.31 | 1.34976 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2348.67i | 1.46467i | 0.680943 | + | 0.732337i | \(0.261570\pi\) | ||||
−0.680943 | + | 0.732337i | \(0.738430\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 215.240i | 0.131341i | 0.997841 | + | 0.0656706i | \(0.0209187\pi\) | ||||
−0.997841 | + | 0.0656706i | \(0.979081\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2330.04 | 1.36257 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 201.190 | 0.115227 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 219.954i | − 0.120935i | −0.998170 | − | 0.0604674i | \(-0.980741\pi\) | ||||
0.998170 | − | 0.0604674i | \(-0.0192591\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 1148.02i | − 0.618703i | −0.950948 | − | 0.309351i | \(-0.899888\pi\) | ||||
0.950948 | − | 0.309351i | \(-0.100112\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −279.869 | −0.145030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 276.320 | 0.140463 | 0.0702316 | − | 0.997531i | \(-0.477626\pi\) | ||||
0.0702316 | + | 0.997531i | \(0.477626\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 716.659i | − 0.350811i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1419.15i | − 0.681941i | −0.940074 | − | 0.340971i | \(-0.889244\pi\) | ||||
0.940074 | − | 0.340971i | \(-0.110756\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3508.69 | 1.62581 | 0.812906 | − | 0.582394i | \(-0.197884\pi\) | ||||
0.812906 | + | 0.582394i | \(0.197884\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −489.908 | −0.222990 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 330.965i | 0.145450i | 0.997352 | + | 0.0727248i | \(0.0231695\pi\) | ||||
−0.997352 | + | 0.0727248i | \(0.976831\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3214.62i | 1.38859i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1136.75 | 0.474662 | 0.237331 | − | 0.971429i | \(-0.423727\pi\) | ||||
0.237331 | + | 0.971429i | \(0.423727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2056.92 | −0.844692 | −0.422346 | − | 0.906435i | \(-0.638793\pi\) | ||||
−0.422346 | + | 0.906435i | \(0.638793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 293.911i | 0.116804i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2878.42i | − 1.12562i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1983.23 | −0.751316 | −0.375658 | − | 0.926758i | \(-0.622583\pi\) | ||||
−0.375658 | + | 0.926758i | \(0.622583\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −189.908 | −0.0708283 | −0.0354141 | − | 0.999373i | \(-0.511275\pi\) | ||||
−0.0354141 | + | 0.999373i | \(0.511275\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2160.42i | − 0.781337i | −0.920531 | − | 0.390669i | \(-0.872244\pi\) | ||||
0.920531 | − | 0.390669i | \(-0.127756\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2656.23i | 0.946205i | 0.881007 | + | 0.473103i | \(0.156866\pi\) | ||||
−0.881007 | + | 0.473103i | \(0.843134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3523.68 | 1.21829 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 445.558 | 0.151801 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 4458.75i | − 1.47568i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1001.20i | − 0.326662i | −0.986571 | − | 0.163331i | \(-0.947776\pi\) | ||||
0.986571 | − | 0.163331i | \(-0.0522239\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 696.075 | 0.220800 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4901.68 | −1.53340 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2108.86i | − 0.641888i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3193.62i | 0.959015i | 0.877538 | + | 0.479507i | \(0.159185\pi\) | ||||
−0.877538 | + | 0.479507i | \(0.840815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1714.72 | 0.501366 | 0.250683 | − | 0.968069i | \(-0.419345\pi\) | ||||
0.250683 | + | 0.968069i | \(0.419345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 407.497 | 0.117590 | 0.0587951 | − | 0.998270i | \(-0.481274\pi\) | ||||
0.0587951 | + | 0.998270i | \(0.481274\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3210.54i | − 0.902702i | −0.892346 | − | 0.451351i | \(-0.850942\pi\) | ||||
0.892346 | − | 0.451351i | \(-0.149058\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 558.930i | 0.155151i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1561.19 | 0.422532 | 0.211266 | − | 0.977429i | \(-0.432241\pi\) | ||||
0.211266 | + | 0.977429i | \(0.432241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1460.89 | 0.390475 | 0.195238 | − | 0.980756i | \(-0.437452\pi\) | ||||
0.195238 | + | 0.980756i | \(0.437452\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 512.316i | − 0.133594i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3266.69i | − 0.841515i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6868.44 | 1.72722 | 0.863609 | − | 0.504162i | \(-0.168198\pi\) | ||||
0.863609 | + | 0.504162i | \(0.168198\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1543.44 | −0.383539 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4450.84i | 1.08029i | 0.841570 | + | 0.540147i | \(0.181632\pi\) | ||||
−0.841570 | + | 0.540147i | \(0.818368\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5147.62i | 1.23497i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6525.31 | 1.52991 | 0.764957 | − | 0.644081i | \(-0.222760\pi\) | ||||
0.764957 | + | 0.644081i | \(0.222760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 927.091 | 0.214909 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3222.22i | 0.730343i | 0.930940 | + | 0.365171i | \(0.118990\pi\) | ||||
−0.930940 | + | 0.365171i | \(0.881010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 7368.93i | − 1.65177i | −0.563837 | − | 0.825886i | \(-0.690675\pi\) | ||||
0.563837 | − | 0.825886i | \(-0.309325\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6923.21 | 1.51813 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9078.61 | −1.96924 | −0.984622 | − | 0.174699i | \(-0.944105\pi\) | ||||
−0.984622 | + | 0.174699i | \(0.944105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 2613.34i | − 0.554801i | −0.960754 | − | 0.277400i | \(-0.910527\pi\) | ||||
0.960754 | − | 0.277400i | \(-0.0894729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 927.970i | 0.194919i | 0.995239 | + | 0.0974596i | \(0.0310717\pi\) | ||||
−0.995239 | + | 0.0974596i | \(0.968928\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7803.60 | 1.60499 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2307.81 | 0.469736 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5351.73i | − 1.06707i | −0.845778 | − | 0.533535i | \(-0.820863\pi\) | ||||
0.845778 | − | 0.533535i | \(-0.179137\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 480.150i | − 0.0947641i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1130.80 | −0.218714 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12191.2 | 2.33452 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 1008.73i | − 0.189377i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1892.38i | − 0.351804i | −0.984408 | − | 0.175902i | \(-0.943716\pi\) | ||||
0.984408 | − | 0.175902i | \(-0.0562842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5645.22 | 1.02930 | 0.514648 | − | 0.857402i | \(-0.327923\pi\) | ||||
0.514648 | + | 0.857402i | \(0.327923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −818.001 | −0.147719 | −0.0738597 | − | 0.997269i | \(-0.523532\pi\) | ||||
−0.0738597 | + | 0.997269i | \(0.523532\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1946.72i | 0.344917i | 0.985017 | + | 0.172458i | \(0.0551710\pi\) | ||||
−0.985017 | + | 0.172458i | \(0.944829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 7588.81i | − 1.33195i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4035.51 | −0.695176 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5072.27 | 0.865719 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9789.22i | 1.64042i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3404.83i | 0.565396i | 0.959209 | + | 0.282698i | \(0.0912295\pi\) | ||||
−0.959209 | + | 0.282698i | \(0.908771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −861.281 | −0.140468 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7072.15 | 1.14316 | 0.571579 | − | 0.820547i | \(-0.306331\pi\) | ||||
0.571579 | + | 0.820547i | \(0.306331\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10556.6i | 1.67645i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.73194i | 0.00137458i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5783.02 | −0.894665 | −0.447332 | − | 0.894368i | \(-0.647626\pi\) | ||||
−0.447332 | + | 0.894368i | \(0.647626\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1748.60 | −0.268196 | −0.134098 | − | 0.990968i | \(-0.542814\pi\) | ||||
−0.134098 | + | 0.990968i | \(0.542814\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9552.31i | 1.44028i | 0.693830 | + | 0.720139i | \(0.255922\pi\) | ||||
−0.693830 | + | 0.720139i | \(0.744078\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 334.620i | − 0.0500276i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 921.392 | 0.135457 | 0.0677287 | − | 0.997704i | \(-0.478425\pi\) | ||||
0.0677287 | + | 0.997704i | \(0.478425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 607.881 | 0.0886254 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 104.861i | 0.0150375i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8490.66i | 1.20765i | 0.797115 | + | 0.603827i | \(0.206358\pi\) | ||||
−0.797115 | + | 0.603827i | \(0.793642\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16237.3 | 2.27223 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2824.92 | −0.392142 | −0.196071 | − | 0.980590i | \(-0.562818\pi\) | ||||
−0.196071 | + | 0.980590i | \(0.562818\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 5559.92i | − 0.759550i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5322.35i | 0.721348i | 0.932692 | + | 0.360674i | \(0.117453\pi\) | ||||
−0.932692 | + | 0.360674i | \(0.882547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8320.49 | −1.11007 | −0.555035 | − | 0.831827i | \(-0.687295\pi\) | ||||
−0.555035 | + | 0.831827i | \(0.687295\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2207.78 | −0.292257 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8358.52i | 1.08944i | 0.838617 | + | 0.544722i | \(0.183365\pi\) | ||||
−0.838617 | + | 0.544722i | \(0.816635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1396.93i | 0.180680i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1573.31 | 0.200410 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7283.17 | −0.920735 | −0.460367 | − | 0.887728i | \(-0.652282\pi\) | ||||
−0.460367 | + | 0.887728i | \(0.652282\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 1549.41i | − 0.192952i | −0.995335 | − | 0.0964759i | \(-0.969243\pi\) | ||||
0.995335 | − | 0.0964759i | \(-0.0307571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7734.22i | 0.956003i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11086.2 | 1.35018 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3291.67 | 0.397952 | 0.198976 | − | 0.980004i | \(-0.436238\pi\) | ||||
0.198976 | + | 0.980004i | \(0.436238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8409.45i | − 1.00194i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1822.58i | 0.215583i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5299.78 | 0.617927 | 0.308964 | − | 0.951074i | \(-0.400018\pi\) | ||||
0.308964 | + | 0.951074i | \(0.400018\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10681.4 | 1.23653 | 0.618265 | − | 0.785970i | \(-0.287836\pi\) | ||||
0.618265 | + | 0.785970i | \(0.287836\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 6266.04i | − 0.715170i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 17667.2i | − 2.00228i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9866.13 | −1.10263 | −0.551316 | − | 0.834296i | \(-0.685874\pi\) | ||||
−0.551316 | + | 0.834296i | \(0.685874\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12560.2 | −1.39400 | −0.697002 | − | 0.717069i | \(-0.745483\pi\) | ||||
−0.697002 | + | 0.717069i | \(0.745483\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2163.89i | 0.236871i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 929.228i | 0.101024i | 0.998723 | + | 0.0505121i | \(0.0160854\pi\) | ||||
−0.998723 | + | 0.0505121i | \(0.983915\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4373.85 | −0.469092 | −0.234546 | − | 0.972105i | \(-0.575360\pi\) | ||||
−0.234546 | + | 0.972105i | \(0.575360\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2004.37 | −0.213520 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14149.5i | 1.48721i | 0.668618 | + | 0.743606i | \(0.266886\pi\) | ||||
−0.668618 | + | 0.743606i | \(0.733114\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 16806.3i | − 1.75472i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1617.52 | −0.166661 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12582.4 | −1.28792 | −0.643960 | − | 0.765059i | \(-0.722710\pi\) | ||||
−0.643960 | + | 0.765059i | \(0.722710\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 10602.2i | − 1.07114i | −0.844492 | − | 0.535568i | \(-0.820098\pi\) | ||||
0.844492 | − | 0.535568i | \(-0.179902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5080.88i | 0.509997i | 0.966941 | + | 0.254999i | \(0.0820750\pi\) | ||||
−0.966941 | + | 0.254999i | \(0.917925\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6903.92 | 0.684102 | 0.342051 | − | 0.939681i | \(-0.388879\pi\) | ||||
0.342051 | + | 0.939681i | \(0.388879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15084.7 | −1.48517 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 26255.8i | − 2.55231i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 9706.27i | − 0.937588i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5114.56 | 0.487871 | 0.243936 | − | 0.969791i | \(-0.421561\pi\) | ||||
0.243936 | + | 0.969791i | \(0.421561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8122.29 | 0.769947 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 861.257i | − 0.0806344i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15594.2i | 1.45101i | 0.688218 | + | 0.725504i | \(0.258393\pi\) | ||||
−0.688218 | + | 0.725504i | \(0.741607\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10521.0 | −0.967023 | −0.483511 | − | 0.875338i | \(-0.660639\pi\) | ||||
−0.483511 | + | 0.875338i | \(0.660639\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6868.46 | −0.627464 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 5860.61i | − 0.528942i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8984.43i | 0.806009i | 0.915198 | + | 0.403004i | \(0.132034\pi\) | ||||
−0.915198 | + | 0.403004i | \(0.867966\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4299.12 | 0.381090 | 0.190545 | − | 0.981678i | \(-0.438974\pi\) | ||||
0.190545 | + | 0.981678i | \(0.438974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 173.548 | 0.0152926 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 2984.83i | − 0.259922i | −0.991519 | − | 0.129961i | \(-0.958515\pi\) | ||||
0.991519 | − | 0.129961i | \(-0.0414853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1836.56i | 0.158991i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 246.799 | 0.0211170 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21082.7 | 1.79345 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12255.7i | 1.03058i | 0.857016 | + | 0.515290i | \(0.172316\pi\) | ||||
−0.857016 | + | 0.515290i | \(0.827684\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15148.5i | 1.26654i | 0.773932 | + | 0.633269i | \(0.218287\pi\) | ||||
−0.773932 | + | 0.633269i | \(0.781713\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9554.49 | 0.789754 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11417.9 | −0.938436 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 12313.1i | − 1.00064i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1400.47i | 0.113173i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19324.4 | −1.54427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5723.84 | −0.454875 | −0.227437 | − | 0.973793i | \(-0.573035\pi\) | ||||
−0.227437 | + | 0.973793i | \(0.573035\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 518.730i | − 0.0407706i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 8367.43i | − 0.654051i | −0.945016 | − | 0.327025i | \(-0.893954\pi\) | ||||
0.945016 | − | 0.327025i | \(-0.106046\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10639.4 | −0.822605 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27555.3 | 2.11893 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 15824.2i | − 1.20375i | −0.798589 | − | 0.601877i | \(-0.794420\pi\) | ||||
0.798589 | − | 0.601877i | \(-0.205580\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 19236.2i | − 1.45546i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2781.72 | −0.208233 | −0.104117 | − | 0.994565i | \(-0.533202\pi\) | ||||
−0.104117 | + | 0.994565i | \(0.533202\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2186.14 | 0.162781 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4687.63i | 0.345370i | 0.984977 | + | 0.172685i | \(0.0552443\pi\) | ||||
−0.984977 | + | 0.172685i | \(0.944756\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15169.4i | 1.11177i | 0.831259 | + | 0.555885i | \(0.187621\pi\) | ||||
−0.831259 | + | 0.555885i | \(0.812379\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3359.92 | −0.243684 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14452.3 | −1.04273 | −0.521367 | − | 0.853332i | \(-0.674578\pi\) | ||||
−0.521367 | + | 0.853332i | \(0.674578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31921.0i | 2.27936i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 34969.6i | − 2.48421i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7405.55 | −0.520715 | −0.260358 | − | 0.965512i | \(-0.583840\pi\) | ||||
−0.260358 | + | 0.965512i | \(0.583840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14800.2 | 1.03537 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 19888.1i | − 1.37725i | −0.725120 | − | 0.688623i | \(-0.758216\pi\) | ||||
0.725120 | − | 0.688623i | \(-0.241784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1998.21i | 0.137679i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2335.49 | 0.159308 | 0.0796539 | − | 0.996823i | \(-0.474618\pi\) | ||||
0.0796539 | + | 0.996823i | \(0.474618\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24547.9 | 1.66611 | 0.833054 | − | 0.553192i | \(-0.186590\pi\) | ||||
0.833054 | + | 0.553192i | \(0.186590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2764.86i | 0.185798i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18328.9i | 1.22561i | 0.790233 | + | 0.612806i | \(0.209959\pi\) | ||||
−0.790233 | + | 0.612806i | \(0.790041\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15446.1 | 1.02272 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6450.01 | −0.424981 | −0.212491 | − | 0.977163i | \(-0.568157\pi\) | ||||
−0.212491 | + | 0.977163i | \(0.568157\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6724.96i | 0.438795i | 0.975636 | + | 0.219398i | \(0.0704092\pi\) | ||||
−0.975636 | + | 0.219398i | \(0.929591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3136.55i | 0.203665i | 0.994802 | + | 0.101832i | \(0.0324705\pi\) | ||||
−0.994802 | + | 0.101832i | \(0.967529\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35105.0 | −2.25755 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14791.8 | 0.946673 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 10033.9i | − 0.636053i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6061.57i | 0.382420i | 0.981549 | + | 0.191210i | \(0.0612412\pi\) | ||||
−0.981549 | + | 0.191210i | \(0.938759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −396.204 | −0.0247604 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14157.9 | −0.880625 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18603.3i | 1.14631i | 0.819446 | + | 0.573157i | \(0.194281\pi\) | ||||
−0.819446 | + | 0.573157i | \(0.805719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21602.4i | 1.32491i | 0.749103 | + | 0.662453i | \(0.230485\pi\) | ||||
−0.749103 | + | 0.662453i | \(0.769515\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −672.754 | −0.0408790 | −0.0204395 | − | 0.999791i | \(-0.506507\pi\) | ||||
−0.0204395 | + | 0.999791i | \(0.506507\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18111.1 | −1.09541 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3322.88i | 0.199134i | 0.995031 | + | 0.0995668i | \(0.0317457\pi\) | ||||
−0.995031 | + | 0.0995668i | \(0.968254\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1722.12i | 0.102731i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25093.7 | −1.48332 | −0.741662 | − | 0.670773i | \(-0.765962\pi\) | ||||
−0.741662 | + | 0.670773i | \(0.765962\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28966.3 | 1.70447 | 0.852237 | − | 0.523157i | \(-0.175246\pi\) | ||||
0.852237 | + | 0.523157i | \(0.175246\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3095.29i | 0.180496i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3682.95i | 0.213800i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38049.1 | −2.18907 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4710.36 | −0.269793 | −0.134897 | − | 0.990860i | \(-0.543070\pi\) | ||||
−0.134897 | + | 0.990860i | \(0.543070\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 4784.53i | − 0.271617i | −0.990735 | − | 0.135808i | \(-0.956637\pi\) | ||||
0.990735 | − | 0.135808i | \(-0.0433631\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 15084.2i | − 0.852548i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18019.8 | −1.00953 | −0.504764 | − | 0.863258i | \(-0.668420\pi\) | ||||
−0.504764 | + | 0.863258i | \(0.668420\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3511.46 | −0.195863 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 25620.4i | − 1.41663i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 16956.5i | − 0.933511i | −0.884386 | − | 0.466756i | \(-0.845423\pi\) | ||||
0.884386 | − | 0.466756i | \(-0.154577\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −321.802 | −0.0175635 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15211.0 | −0.826625 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30620.5i | 1.64982i | 0.565266 | + | 0.824909i | \(0.308774\pi\) | ||||
−0.565266 | + | 0.824909i | \(0.691226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 15542.8i | − 0.833865i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3039.56 | 0.161689 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24192.8 | −1.28149 | −0.640747 | − | 0.767752i | \(-0.721375\pi\) | ||||
−0.640747 | + | 0.767752i | \(0.721375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 5123.23i | − 0.269098i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3483.60i | 0.182209i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37146.6 | −1.92675 | −0.963377 | − | 0.268151i | \(-0.913588\pi\) | ||||
−0.963377 | + | 0.268151i | \(0.913588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4322.49 | 0.223271 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 16520.1i | − 0.846265i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14614.3i | 0.745551i | 0.927922 | + | 0.372775i | \(0.121594\pi\) | ||||
−0.927922 | + | 0.372775i | \(0.878406\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23763.5 | −1.20236 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8044.73 | 0.405374 | 0.202687 | − | 0.979244i | \(-0.435033\pi\) | ||||
0.202687 | + | 0.979244i | \(0.435033\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32487.3i | 1.62372i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7025.01i | 0.349688i | 0.984596 | + | 0.174844i | \(0.0559420\pi\) | ||||
−0.984596 | + | 0.174844i | \(0.944058\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27063.4 | 1.33629 | 0.668143 | − | 0.744033i | \(-0.267089\pi\) | ||||
0.668143 | + | 0.744033i | \(0.267089\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 328.849 | 0.0161719 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24528.2i | 1.19658i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 11434.2i | − 0.555579i | −0.960642 | − | 0.277789i | \(-0.910398\pi\) | ||||
0.960642 | − | 0.277789i | \(-0.0896017\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1716.38 | 0.0827357 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22087.2 | −1.06046 | −0.530232 | − | 0.847853i | \(-0.677895\pi\) | ||||
−0.530232 | + | 0.847853i | \(0.677895\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35524.0i | 1.69218i | 0.533043 | + | 0.846088i | \(0.321048\pi\) | ||||
−0.533043 | + | 0.846088i | \(0.678952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9085.16i | − 0.431068i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13269.0 | −0.624664 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21213.0 | 0.994745 | 0.497372 | − | 0.867537i | \(-0.334298\pi\) | ||||
0.497372 | + | 0.867537i | \(0.334298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 14370.7i | − 0.668663i | −0.942456 | − | 0.334332i | \(-0.891489\pi\) | ||||
0.942456 | − | 0.334332i | \(-0.108511\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22980.6i | 1.06515i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23562.3 | −1.08371 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12621.8 | −0.578287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 413.122i | 0.0187834i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 41642.9i | − 1.88616i | −0.332564 | − | 0.943081i | \(-0.607914\pi\) | ||||
0.332564 | − | 0.943081i | \(-0.392086\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38288.5 | 1.72109 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27876.5 | −1.24833 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23527.1i | 1.04564i | 0.852445 | + | 0.522818i | \(0.175119\pi\) | ||||
−0.852445 | + | 0.522818i | \(0.824881\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 19081.4i | − 0.844872i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3955.32 | 0.173823 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1071.47 | 0.0469120 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 7508.22i | − 0.326298i | −0.986601 | − | 0.163149i | \(-0.947835\pi\) | ||||
0.986601 | − | 0.163149i | \(-0.0521651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 15834.0i | − 0.685581i | −0.939412 | − | 0.342791i | \(-0.888628\pi\) | ||||
0.939412 | − | 0.342791i | \(-0.111372\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2121.75 | 0.0911923 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36810.3 | −1.57629 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13279.1i | 0.564486i | 0.959343 | + | 0.282243i | \(0.0910784\pi\) | ||||
−0.959343 | + | 0.282243i | \(0.908922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27997.4i | 1.18582i | 0.805270 | + | 0.592909i | \(0.202021\pi\) | ||||
−0.805270 | + | 0.592909i | \(0.797979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35177.8 | −1.47914 | −0.739571 | − | 0.673078i | \(-0.764972\pi\) | ||||
−0.739571 | + | 0.673078i | \(0.764972\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13390.3 | 0.560996 | 0.280498 | − | 0.959855i | \(-0.409500\pi\) | ||||
0.280498 | + | 0.959855i | \(0.409500\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17490.1i | 0.727484i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5245.79i | 0.217411i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8466.38 | −0.348381 | −0.174191 | − | 0.984712i | \(-0.555731\pi\) | ||||
−0.174191 | + | 0.984712i | \(0.555731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6280.62 | 0.257518 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 732.454i | − 0.0298192i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48424.4i | 1.96444i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5380.29 | −0.216726 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16448.2 | 0.660229 | 0.330114 | − | 0.943941i | \(-0.392913\pi\) | ||||
0.330114 | + | 0.943941i | \(0.392913\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 13593.7i | − 0.541832i | −0.962603 | − | 0.270916i | \(-0.912673\pi\) | ||||
0.962603 | − | 0.270916i | \(-0.0873266\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 15107.9i | − 0.600086i | −0.953926 | − | 0.300043i | \(-0.902999\pi\) | ||||
0.953926 | − | 0.300043i | \(-0.0970011\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43717.5 | −1.72440 | −0.862202 | − | 0.506565i | \(-0.830915\pi\) | ||||
−0.862202 | + | 0.506565i | \(0.830915\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −494.820 | −0.0194502 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 59344.8i | − 2.31661i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23801.7i | 0.925935i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9699.78 | −0.374757 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23868.3 | 0.919012 | 0.459506 | − | 0.888175i | \(-0.348026\pi\) | ||||
0.459506 | + | 0.888175i | \(0.348026\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 48039.2i | − 1.83710i | −0.395310 | − | 0.918548i | \(-0.629363\pi\) | ||||
0.395310 | − | 0.918548i | \(-0.370637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10091.3i | 0.384595i | 0.981337 | + | 0.192298i | \(0.0615939\pi\) | ||||
−0.981337 | + | 0.192298i | \(0.938406\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37951.2 | −1.43661 | −0.718307 | − | 0.695726i | \(-0.755083\pi\) | ||||
−0.718307 | + | 0.695726i | \(0.755083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6939.20 | −0.261792 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 29557.7i | − 1.10763i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1699.53i | 0.0634739i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25190.0 | 0.934520 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31650.2 | −1.17028 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 3075.26i | − 0.112956i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 23697.4i | − 0.867540i | −0.901024 | − | 0.433770i | \(-0.857183\pi\) | ||||
0.901024 | − | 0.433770i | \(-0.142817\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11833.0 | 0.430347 | 0.215174 | − | 0.976576i | \(-0.430968\pi\) | ||||
0.215174 | + | 0.976576i | \(0.430968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 68747.0 | 2.49200 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30161.6i | 1.08618i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 51576.2i | − 1.85130i | −0.378386 | − | 0.925648i | \(-0.623521\pi\) | ||||
0.378386 | − | 0.925648i | \(-0.376479\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9247.29 | −0.329771 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24133.7 | 0.857849 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 46577.3i | − 1.64494i | −0.568807 | − | 0.822471i | \(-0.692595\pi\) | ||||
0.568807 | − | 0.822471i | \(-0.307405\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27092.6i | 0.953731i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4303.47 | 0.150523 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11409.2 | 0.397783 | 0.198891 | − | 0.980022i | \(-0.436266\pi\) | ||||
0.198891 | + | 0.980022i | \(0.436266\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 32444.9i | − 1.12399i | −0.827141 | − | 0.561994i | \(-0.810034\pi\) | ||||
0.827141 | − | 0.561994i | \(-0.189966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8156.32i | 0.281661i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22327.6 | 0.766154 | 0.383077 | − | 0.923716i | \(-0.374864\pi\) | ||||
0.383077 | + | 0.923716i | \(0.374864\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2897.85 | 0.0991236 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 15314.3i | − 0.520546i | −0.965535 | − | 0.260273i | \(-0.916187\pi\) | ||||
0.965535 | − | 0.260273i | \(-0.0838126\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2965.09i | − 0.100469i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −61500.4 | −2.07086 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5250.01 | −0.176228 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 283.928i | − 0.00947147i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 16913.6i | − 0.562465i | −0.959640 | − | 0.281232i | \(-0.909257\pi\) | ||||
0.959640 | − | 0.281232i | \(-0.0907431\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56451.5 | −1.86572 | −0.932861 | − | 0.360237i | \(-0.882696\pi\) | ||||
−0.932861 | + | 0.360237i | \(0.882696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5636.12 | −0.185699 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7397.50i | 0.242238i | 0.992638 | + | 0.121119i | \(0.0386483\pi\) | ||||
−0.992638 | + | 0.121119i | \(0.961352\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75604.3i | 2.46816i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18261.7 | 0.592532 | 0.296266 | − | 0.955105i | \(-0.404258\pi\) | ||||
0.296266 | + | 0.955105i | \(0.404258\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3230.01 | 0.104484 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12742.3i | 0.409687i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 7020.98i | − 0.225054i | −0.993649 | − | 0.112527i | \(-0.964105\pi\) | ||||
0.993649 | − | 0.112527i | \(-0.0358945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3971.28 | −0.126531 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6983.34 | −0.221830 | −0.110915 | − | 0.993830i | \(-0.535378\pi\) | ||||
−0.110915 | + | 0.993830i | \(0.535378\pi\) | |||||||
\(998\) | 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 | 1728.4.c.j.1727.8 | 12 | ||
3.2 | odd | 2 | inner | 1728.4.c.j.1727.6 | 12 | ||
4.3 | odd | 2 | inner | 1728.4.c.j.1727.7 | 12 | ||
8.3 | odd | 2 | 108.4.b.b.107.6 | yes | 12 | ||
8.5 | even | 2 | 108.4.b.b.107.8 | yes | 12 | ||
12.11 | even | 2 | inner | 1728.4.c.j.1727.5 | 12 | ||
24.5 | odd | 2 | 108.4.b.b.107.5 | ✓ | 12 | ||
24.11 | even | 2 | 108.4.b.b.107.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.b.b.107.5 | ✓ | 12 | 24.5 | odd | 2 | ||
108.4.b.b.107.6 | yes | 12 | 8.3 | odd | 2 | ||
108.4.b.b.107.7 | yes | 12 | 24.11 | even | 2 | ||
108.4.b.b.107.8 | yes | 12 | 8.5 | even | 2 | ||
1728.4.c.j.1727.5 | 12 | 12.11 | even | 2 | inner | ||
1728.4.c.j.1727.6 | 12 | 3.2 | odd | 2 | inner | ||
1728.4.c.j.1727.7 | 12 | 4.3 | odd | 2 | inner | ||
1728.4.c.j.1727.8 | 12 | 1.1 | even | 1 | trivial |