Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (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: | \(79.2985670477\) |
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: | \( x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.12 | ||
Root | \(0.965027 - 2.65871i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.g.895.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 19.4608i | 1.74062i | 0.492501 | + | 0.870312i | \(0.336083\pi\) | ||||
−0.492501 | + | 0.870312i | \(0.663917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.95109 | + | 18.4172i | −0.105349 | + | 0.994435i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24.6621i | 0.675991i | 0.941148 | + | 0.337996i | \(0.109749\pi\) | ||||
−0.941148 | + | 0.337996i | \(0.890251\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.25549i | 0.112124i | 0.998427 | + | 0.0560619i | \(0.0178544\pi\) | ||||
−0.998427 | + | 0.0560619i | \(0.982146\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 58.3823i | − | 1.00495i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 80.8832i | − | 1.15394i | −0.816764 | − | 0.576972i | \(-0.804234\pi\) | ||
0.816764 | − | 0.576972i | \(-0.195766\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −86.5920 | −1.04556 | −0.522778 | − | 0.852469i | \(-0.675104\pi\) | ||||
−0.522778 | + | 0.852469i | \(0.675104\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.85328 | − | 55.2516i | 0.0608234 | − | 0.574137i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 108.350i | 0.982285i | 0.871079 | + | 0.491143i | \(0.163421\pi\) | ||||
−0.871079 | + | 0.491143i | \(0.836579\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −253.721 | −2.02977 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −278.744 | −1.78488 | −0.892440 | − | 0.451167i | \(-0.851008\pi\) | ||||
−0.892440 | + | 0.451167i | \(0.851008\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 116.511 | 0.675032 | 0.337516 | − | 0.941320i | \(-0.390413\pi\) | ||||
0.337516 | + | 0.941320i | \(0.390413\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 73.9863i | − | 0.390284i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −358.413 | − | 37.9698i | −1.73094 | − | 0.183373i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −53.5203 | −0.237802 | −0.118901 | − | 0.992906i | \(-0.537937\pi\) | ||||
−0.118901 | + | 0.992906i | \(0.537937\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 15.7665i | − | 0.0647347i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 303.555i | 1.15628i | 0.815938 | + | 0.578139i | \(0.196221\pi\) | ||||
−0.815938 | + | 0.578139i | \(0.803779\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 176.565i | 0.626183i | 0.949723 | + | 0.313092i | \(0.101365\pi\) | ||||
−0.949723 | + | 0.313092i | \(0.898635\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 175.147i | 0.580208i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 102.276 | 0.317414 | 0.158707 | − | 0.987326i | \(-0.449268\pi\) | ||||
0.158707 | + | 0.987326i | \(0.449268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −335.386 | − | 71.8674i | −0.977803 | − | 0.209526i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 242.650i | 0.666230i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −185.933 | −0.481885 | −0.240942 | − | 0.970539i | \(-0.577457\pi\) | ||||
−0.240942 | + | 0.970539i | \(0.577457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −479.943 | −1.17665 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 259.776 | 0.603652 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 732.951 | 1.61732 | 0.808662 | − | 0.588274i | \(-0.200192\pi\) | ||||
0.808662 | + | 0.588274i | \(0.200192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 443.155i | − | 0.930167i | −0.885267 | − | 0.465083i | \(-0.846024\pi\) | ||
0.885267 | − | 0.465083i | \(-0.153976\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −17.5599 | + | 165.755i | −0.0351164 | + | 0.331478i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −102.276 | −0.195165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 166.969i | − | 0.304455i | −0.988345 | − | 0.152227i | \(-0.951355\pi\) | ||
0.988345 | − | 0.152227i | \(-0.0486446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 325.050i | − | 0.567123i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 378.024i | 0.631877i | 0.948780 | + | 0.315938i | \(0.102319\pi\) | ||||
−0.948780 | + | 0.315938i | \(0.897681\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 664.824i | − | 1.06592i | −0.846142 | − | 0.532958i | \(-0.821081\pi\) | ||
0.846142 | − | 0.532958i | \(-0.178919\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 761.164 | 1.17189 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −454.207 | − | 48.1181i | −0.672229 | − | 0.0712151i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 737.826i | 1.05078i | 0.850860 | + | 0.525392i | \(0.176081\pi\) | ||||
−0.850860 | + | 0.525392i | \(0.823919\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 913.229 | 1.20771 | 0.603855 | − | 0.797094i | \(-0.293631\pi\) | ||||
0.603855 | + | 0.797094i | \(0.293631\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1574.05 | 2.00858 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 836.233 | 1.03050 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1497.53i | − | 1.78358i | −0.452453 | − | 0.891788i | \(-0.649451\pi\) | ||
0.452453 | − | 0.891788i | \(-0.350549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −96.7913 | − | 10.2540i | −0.111500 | − | 0.0118122i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −349.533 | −0.389730 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1685.15i | − | 1.81992i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1445.52i | 1.51309i | 0.653940 | + | 0.756547i | \(0.273115\pi\) | ||||
−0.653940 | + | 0.756547i | \(0.726885\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 221.959i | 0.225330i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 240.349i | − | 0.236788i | −0.992967 | − | 0.118394i | \(-0.962225\pi\) | ||
0.992967 | − | 0.118394i | \(-0.0377746\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1698.72 | −1.62505 | −0.812524 | − | 0.582927i | \(-0.801907\pi\) | ||||
−0.812524 | + | 0.582927i | \(0.801907\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1075.24 | + | 113.909i | 0.999357 | + | 0.105871i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 287.075i | 0.259370i | 0.991555 | + | 0.129685i | \(0.0413966\pi\) | ||||
−0.991555 | + | 0.129685i | \(0.958603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9647 | 0.0131500 | 0.00657502 | − | 0.999978i | \(-0.497907\pi\) | ||||
0.00657502 | + | 0.999978i | \(0.497907\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 160.561 | 0.137295 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −737.215 | −0.613729 | −0.306864 | − | 0.951753i | \(-0.599280\pi\) | ||||
−0.306864 | + | 0.951753i | \(0.599280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2108.58 | −1.70979 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 47.2994i | 0.0373746i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1489.64 | + | 157.811i | 1.14752 | + | 0.121567i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 722.781 | 0.543036 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 910.666i | − | 0.667577i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2505.01i | − | 1.79244i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1572.28i | 1.09856i | 0.835637 | + | 0.549282i | \(0.185099\pi\) | ||||
−0.835637 | + | 0.549282i | \(0.814901\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 529.694i | − | 0.361527i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −941.864 | −0.628176 | −0.314088 | − | 0.949394i | \(-0.601699\pi\) | ||||
−0.314088 | + | 0.949394i | \(0.601699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 168.949 | − | 1594.78i | 0.110149 | − | 1.03974i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 525.441i | − | 0.334983i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2087.46 | 1.30178 | 0.650889 | − | 0.759173i | \(-0.274396\pi\) | ||||
0.650889 | + | 0.759173i | \(0.274396\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1894.46 | −1.15602 | −0.578008 | − | 0.816031i | \(-0.696170\pi\) | ||||
−0.578008 | + | 0.816031i | \(0.696170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −306.827 | −0.183259 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −129.611 | −0.0757947 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5424.57i | − | 3.10680i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1006.16 | + | 215.602i | 0.564535 | + | 0.120970i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2506.20 | 1.37796 | 0.688981 | − | 0.724780i | \(-0.258058\pi\) | ||||
0.688981 | + | 0.724780i | \(0.258058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 465.035i | 0.250623i | 0.992117 | + | 0.125311i | \(0.0399930\pi\) | ||||
−0.992117 | + | 0.125311i | \(0.960007\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 727.949i | − | 0.384648i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2267.39i | 1.17498i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 441.217i | 0.224286i | 0.993692 | + | 0.112143i | \(0.0357715\pi\) | ||||
−0.993692 | + | 0.112143i | \(0.964228\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 557.800 | 0.278216 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1995.51 | − | 211.401i | −0.976819 | − | 0.103483i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 374.876i | 0.180139i | 0.995936 | + | 0.0900693i | \(0.0287089\pi\) | ||||
−0.995936 | + | 0.0900693i | \(0.971291\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1439.83 | 0.679337 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 986.292 | 0.457015 | 0.228508 | − | 0.973542i | \(-0.426615\pi\) | ||||
0.228508 | + | 0.973542i | \(0.426615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2169.38 | 0.987428 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −779.328 | −0.348519 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1618.78i | 0.711407i | 0.934599 | + | 0.355704i | \(0.115759\pi\) | ||||
−0.934599 | + | 0.355704i | \(0.884241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 495.034 | − | 4672.83i | 0.213835 | − | 2.01847i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2198.85 | −0.933762 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3693.28i | − | 1.54217i | −0.636730 | − | 0.771087i | \(-0.719714\pi\) | ||
0.636730 | − | 0.771087i | \(-0.280286\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2447.09i | − | 1.00492i | −0.864600 | − | 0.502461i | \(-0.832428\pi\) | ||
0.864600 | − | 0.502461i | \(-0.167572\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1329.46i | 0.537032i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1041.55i | − | 0.413924i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1994.75 | 0.780056 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 52.6796 | − | 497.264i | 0.0202745 | − | 0.191379i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.19972i | 0.00348518i | 0.999998 | + | 0.00174259i | \(0.000554683\pi\) | ||||
−0.999998 | + | 0.00174259i | \(0.999445\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1468.72 | −0.547776 | −0.273888 | − | 0.961762i | \(-0.588310\pi\) | ||||
−0.273888 | + | 0.961762i | \(0.588310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 306.827 | 0.112679 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3914.64 | −1.41577 | −0.707884 | − | 0.706328i | \(-0.750350\pi\) | ||||
−0.707884 | + | 0.706328i | \(0.750350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2960.22 | −1.05449 | −0.527247 | − | 0.849712i | \(-0.676776\pi\) | ||||
−0.527247 | + | 0.849712i | \(0.676776\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 500.906i | 0.175777i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 543.856 | − | 5133.69i | 0.188036 | − | 1.77495i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5907.42 | −2.01264 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 975.151i | 0.327428i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2135.54i | − | 0.706787i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1329.13i | 0.433654i | 0.976210 | + | 0.216827i | \(0.0695708\pi\) | ||||
−0.976210 | + | 0.216827i | \(0.930429\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1134.07i | − | 0.364814i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3436.08 | −1.08995 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −227.324 | + | 2145.81i | −0.0711141 | + | 0.671276i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1994.47i | 0.615406i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 425.080 | 0.129385 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 850.725 | 0.255465 | 0.127733 | − | 0.991809i | \(-0.459230\pi\) | ||||
0.127733 | + | 0.991809i | \(0.459230\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2283.49 | −0.676590 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2626.60 | 0.767988 | 0.383994 | − | 0.923336i | \(-0.374548\pi\) | ||||
0.383994 | + | 0.923336i | \(0.374548\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1681.55i | − | 0.485239i | −0.970122 | − | 0.242620i | \(-0.921993\pi\) | ||
0.970122 | − | 0.242620i | \(-0.0780067\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1362.62 | + | 144.354i | 0.388112 | + | 0.0411161i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1824.86 | −0.513093 | −0.256547 | − | 0.966532i | \(-0.582585\pi\) | ||||
−0.256547 | + | 0.966532i | \(0.582585\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1990.36i | 0.552498i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2213.48i | − | 0.606671i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 776.076i | − | 0.210043i | −0.994470 | − | 0.105021i | \(-0.966509\pi\) | ||
0.994470 | − | 0.105021i | \(-0.0334911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 40.5909i | − | 0.0108493i | −0.999985 | − | 0.00542466i | \(-0.998273\pi\) | ||
0.999985 | − | 0.00542466i | \(-0.00172673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1398.59 | − | 6526.88i | 0.364706 | − | 1.70199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 455.083i | − | 0.117232i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2739.69 | −0.697272 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4231.68 | −1.06415 | −0.532074 | − | 0.846698i | \(-0.678587\pi\) | ||||
−0.532074 | + | 0.846698i | \(0.678587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2672.14 | −0.664016 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4722.14 | −1.15966 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1872.50i | − | 0.454489i | −0.973838 | − | 0.227244i | \(-0.927028\pi\) | ||
0.973838 | − | 0.227244i | \(-0.0729716\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 104.423 | − | 985.694i | 0.0250523 | − | 0.236479i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2508.70 | −0.594960 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5126.25i | − | 1.20190i | −0.799288 | − | 0.600948i | \(-0.794790\pi\) | ||
0.799288 | − | 0.600948i | \(-0.205210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3618.40i | − | 0.838780i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4492.60i | 1.02975i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2399.98i | − | 0.543975i | −0.962301 | − | 0.271988i | \(-0.912319\pi\) | ||
0.962301 | − | 0.271988i | \(-0.0876810\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5666.29 | 1.27012 | 0.635060 | − | 0.772462i | \(-0.280975\pi\) | ||||
0.635060 | + | 0.772462i | \(0.280975\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 290.374 | + | 30.7619i | 0.0643745 | + | 0.00681975i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 6257.30i | − | 1.37211i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1089.92 | 0.236414 | 0.118207 | − | 0.992989i | \(-0.462285\pi\) | ||||
0.118207 | + | 0.992989i | \(0.462285\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1048.60 | 0.225011 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3251.98 | −0.690381 | −0.345191 | − | 0.938533i | \(-0.612186\pi\) | ||||
−0.345191 | + | 0.938533i | \(0.612186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8087.11 | 1.69869 | 0.849344 | − | 0.527840i | \(-0.176998\pi\) | ||||
0.849344 | + | 0.527840i | \(0.176998\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5055.44i | 1.05073i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5590.64 | − | 592.265i | −1.14984 | − | 0.121813i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1629.09 | −0.331587 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4336.55i | − | 0.873585i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1615.35i | − | 0.322080i | −0.986948 | − | 0.161040i | \(-0.948515\pi\) | ||
0.986948 | − | 0.161040i | \(-0.0514849\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14263.8i | 2.81515i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 665.877i | − | 0.130095i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −569.433 | −0.110138 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3251.83 | − | 344.495i | −0.622699 | − | 0.0659679i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 721.046i | 0.136710i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8624.13 | 1.61907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2726.45 | 0.506863 | 0.253431 | − | 0.967353i | \(-0.418441\pi\) | ||||
0.253431 | + | 0.967353i | \(0.418441\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5096.17 | 0.938222 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6495.92 | 1.18441 | 0.592203 | − | 0.805789i | \(-0.298258\pi\) | ||||
0.592203 | + | 0.805789i | \(0.298258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2315.02i | − | 0.418059i | −0.977909 | − | 0.209030i | \(-0.932970\pi\) | ||
0.977909 | − | 0.209030i | \(-0.0670305\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3225.71 | − | 341.728i | −0.576979 | − | 0.0611244i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3545.18 | 0.628130 | 0.314065 | − | 0.949402i | \(-0.398309\pi\) | ||||
0.314065 | + | 0.949402i | \(0.398309\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6874.42i | − | 1.20656i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 861.225i | − | 0.149747i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7003.83i | 1.20651i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1333.43i | − | 0.227585i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −44.8940 | −0.00759218 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −199.550 | + | 1883.63i | −0.0334393 | + | 0.315648i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5480.40i | 0.910060i | 0.890476 | + | 0.455030i | \(0.150371\pi\) | ||||
−0.890476 | + | 0.455030i | \(0.849629\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −481.683 | −0.0792674 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3249.34 | 0.529941 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −142.057 | −0.0229624 | −0.0114812 | − | 0.999934i | \(-0.503655\pi\) | ||||
−0.0114812 | + | 0.999934i | \(0.503655\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2211.64 | 0.354336 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2873.41i | 0.456316i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1977.97 | − | 6036.66i | 0.311371 | − | 0.950288i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6325.73 | 0.987147 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1106.02i | 0.171108i | 0.996334 | + | 0.0855540i | \(0.0272660\pi\) | ||||
−0.996334 | + | 0.0855540i | \(0.972734\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5314.57i | 0.815136i | 0.913175 | + | 0.407568i | \(0.133623\pi\) | ||||
−0.913175 | + | 0.407568i | \(0.866377\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 141.898i | − | 0.0215782i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10581.0i | − | 1.59538i | −0.603068 | − | 0.797690i | \(-0.706055\pi\) | ||
0.603068 | − | 0.797690i | \(-0.293945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7356.64 | −1.09986 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4468.92 | − | 473.432i | −0.662523 | − | 0.0701868i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2661.07i | − | 0.391214i | −0.980682 | − | 0.195607i | \(-0.937332\pi\) | ||
0.980682 | − | 0.195607i | \(-0.0626677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 639.174 | 0.0931876 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2168.34 | −0.313522 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12938.0 | 1.85536 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5895.68 | 0.838562 | 0.419281 | − | 0.907857i | \(-0.362282\pi\) | ||||
0.419281 | + | 0.907857i | \(0.362282\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2732.00i | 0.385426i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 362.774 | − | 3424.37i | 0.0507662 | − | 0.479203i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6208.52 | 0.861837 | 0.430918 | − | 0.902391i | \(-0.358190\pi\) | ||||
0.430918 | + | 0.902391i | \(0.358190\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7515.04i | 1.03487i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1464.94i | − | 0.200127i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3532.73i | − | 0.478797i | −0.970921 | − | 0.239399i | \(-0.923050\pi\) | ||
0.970921 | − | 0.239399i | \(-0.0769503\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 4716.85i | − | 0.634256i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9380.75 | −1.25153 | −0.625763 | − | 0.780014i | \(-0.715212\pi\) | ||||
−0.625763 | + | 0.780014i | \(0.715212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 936.414 | − | 8839.21i | 0.123959 | − | 1.17010i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1589.08i | 0.208728i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5267.14 | −0.686516 | −0.343258 | − | 0.939241i | \(-0.611531\pi\) | ||||
−0.343258 | + | 0.939241i | \(0.611531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8763.70 | 1.13350 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2825.59 | 0.362678 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14358.7 | −1.82902 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8515.34i | − | 1.07651i | −0.842783 | − | 0.538253i | \(-0.819085\pi\) | ||
0.842783 | − | 0.538253i | \(-0.180915\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −506.848 | + | 4784.35i | −0.0635943 | + | 0.600293i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2804.56 | −0.349259 | −0.174629 | − | 0.984634i | \(-0.555873\pi\) | ||||
−0.174629 | + | 0.984634i | \(0.555873\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 612.322i | 0.0756872i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1576.32i | 0.193403i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1319.92i | − | 0.160752i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13823.4i | 1.67121i | 0.549334 | + | 0.835603i | \(0.314882\pi\) | ||||
−0.549334 | + | 0.835603i | \(0.685118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6262.38 | −0.751582 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1430.06 | + | 13498.9i | −0.170384 | + | 1.60832i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17772.1i | 2.10217i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5683.39 | 0.667426 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5047.91 | 0.588560 | 0.294280 | − | 0.955719i | \(-0.404920\pi\) | ||||
0.294280 | + | 0.955719i | \(0.404920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6467.30 | −0.748686 | −0.374343 | − | 0.927290i | \(-0.622132\pi\) | ||||
−0.374343 | + | 0.927290i | \(0.622132\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 920.482 | 0.105805 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20521.8i | 2.34224i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8161.67 | + | 864.637i | 0.924990 | + | 0.0979923i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 388.834 | 0.0437601 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12799.9i | − | 1.43051i | −0.698861 | − | 0.715257i | \(-0.746309\pi\) | ||
0.698861 | − | 0.715257i | \(-0.253691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7154.28i | 0.794025i | 0.917813 | + | 0.397013i | \(0.129953\pi\) | ||||
−0.917813 | + | 0.397013i | \(0.870047\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16273.7i | 1.79371i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9382.25i | − | 1.02703i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10688.8 | −1.16207 | −0.581034 | − | 0.813879i | \(-0.697352\pi\) | ||||
−0.581034 | + | 0.813879i | \(0.697352\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3018.48 | − | 646.807i | −0.325934 | − | 0.0698420i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4652.95i | − | 0.499025i | −0.968372 | − | 0.249513i | \(-0.919730\pi\) | ||
0.968372 | − | 0.249513i | \(-0.0802704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29143.2 | 3.10453 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7518.61 | −0.795567 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16721.0 | 1.75749 | 0.878743 | − | 0.477296i | \(-0.158383\pi\) | ||||
0.878743 | + | 0.477296i | \(0.158383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7486.31 | −0.781633 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1395.10i | − | 0.144697i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 199.550 | − | 1883.63i | 0.0205605 | − | 0.194079i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7571.11 | −0.774971 | −0.387485 | − | 0.921876i | \(-0.626656\pi\) | ||||
−0.387485 | + | 0.921876i | \(0.626656\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2183.85i | 0.222077i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8410.07i | 0.849666i | 0.905272 | + | 0.424833i | \(0.139667\pi\) | ||||
−0.905272 | + | 0.424833i | \(0.860333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10100.0i | 1.01379i | 0.862007 | + | 0.506897i | \(0.169208\pi\) | ||||
−0.862007 | + | 0.506897i | \(0.830792\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 6802.18i | − | 0.678373i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2012.75 | −0.199441 | −0.0997207 | − | 0.995015i | \(-0.531795\pi\) | ||||
−0.0997207 | + | 0.995015i | \(0.531795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3075.10 | + | 325.772i | 0.302761 | + | 0.0320741i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1323.65i | − | 0.129492i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4354.46 | −0.423294 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21970.2 | 2.12224 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1673.40 | −0.160628 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13299.9 | −1.26866 | −0.634330 | − | 0.773062i | \(-0.718724\pi\) | ||||
−0.634330 | + | 0.773062i | \(0.718724\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 281.275i | − | 0.0266633i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5986.52 | + | 634.204i | 0.563967 | + | 0.0597459i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28130.9 | −2.63372 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2587.62i | − | 0.240773i | −0.992727 | − | 0.120386i | \(-0.961587\pi\) | ||
0.992727 | − | 0.120386i | \(-0.0384134\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1124.63i | − | 0.104003i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 588.505i | 0.0540913i | 0.999634 | + | 0.0270457i | \(0.00860996\pi\) | ||||
−0.999634 | + | 0.0270457i | \(0.991390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22545.7i | 2.05965i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4319.49 | −0.392215 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6962.15 | − | 737.561i | −0.628360 | − | 0.0665677i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16006.0i | 1.43592i | 0.696083 | + | 0.717961i | \(0.254925\pi\) | ||||
−0.696083 | + | 0.717961i | \(0.745075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2958.88 | −0.263858 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10633.0 | −0.942551 | −0.471276 | − | 0.881986i | \(-0.656206\pi\) | ||||
−0.471276 | + | 0.881986i | \(0.656206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4677.36 | 0.412158 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6508.14 | −0.570092 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2697.13i | − | 0.234869i | −0.993081 | − | 0.117434i | \(-0.962533\pi\) | ||
0.993081 | − | 0.117434i | \(-0.0374670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12244.2 | + | 1297.14i | 1.05998 | + | 0.112293i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2337.98 | 0.201217 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 33058.4i | − | 2.82860i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2522.33i | 0.214569i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4856.33i | − | 0.410731i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11342.2i | 0.953766i | 0.878967 | + | 0.476883i | \(0.158233\pi\) | ||||
−0.878967 | + | 0.476883i | \(0.841767\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4722.12 | 0.394807 | 0.197403 | − | 0.980322i | \(-0.436749\pi\) | ||||
0.197403 | + | 0.980322i | \(0.436749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1485.10 | + | 14018.5i | −0.123457 | + | 1.16537i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 9423.78i | − | 0.778950i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 427.252 | 0.0351156 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6596.56 | 0.539108 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1595.33 | −0.129646 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5586.70 | −0.451465 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11079.9i | 0.890374i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1772.40 | − | 8271.33i | 0.141638 | − | 0.660986i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6125.28 | 0.486777 | 0.243389 | − | 0.969929i | \(-0.421741\pi\) | ||||
0.243389 | + | 0.969929i | \(0.421741\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7341.27i | 0.580192i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 291.224i | 0.0228893i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25304.7i | − | 1.97797i | −0.148015 | − | 0.988985i | \(-0.547288\pi\) | ||
0.148015 | − | 0.988985i | \(-0.452712\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 3988.39i | − | 0.310056i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24137.0 | 1.86619 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13588.7 | − | 1439.57i | −1.04494 | − | 0.110699i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3124.64i | 0.238979i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9686.90 | −0.736889 | −0.368444 | − | 0.929650i | \(-0.620109\pi\) | ||||
−0.368444 | + | 0.929650i | \(0.620109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −927.934 | −0.0702100 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5984.24 | −0.450365 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6110.70 | 0.457434 | 0.228717 | − | 0.973493i | \(-0.426547\pi\) | ||||
0.228717 | + | 0.973493i | \(0.426547\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14346.8i | − | 1.06827i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −158.039 | + | 1491.79i | −0.0117055 | + | 0.110493i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16843.7 | −1.24099 | −0.620497 | − | 0.784209i | \(-0.713069\pi\) | ||||
−0.620497 | + | 0.784209i | \(0.713069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15796.9i | 1.15775i | 0.815415 | + | 0.578877i | \(0.196509\pi\) | ||||
−0.815415 | + | 0.578877i | \(0.803491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 27.5992i | − | 0.00201217i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 27490.7i | − | 1.99381i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6756.48i | 0.487480i | 0.969841 | + | 0.243740i | \(0.0783743\pi\) | ||||
−0.969841 | + | 0.243740i | \(0.921626\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4406.16 | 0.316259 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1781.80 | + | 16819.1i | −0.127231 | + | 1.20099i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4585.50i | − | 0.325750i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −920.482 | −0.0650551 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20504.0 | 1.44172 | 0.720861 | − | 0.693080i | \(-0.243747\pi\) | ||||
0.720861 | + | 0.693080i | \(0.243747\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10088.9 | −0.705784 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11743.9 | 0.817394 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1432.90i | 0.0992281i | 0.998768 | + | 0.0496140i | \(0.0157991\pi\) | ||||
−0.998768 | + | 0.0496140i | \(0.984201\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3071.12 | + | 28989.6i | −0.211603 | + | 1.99740i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8880.65 | 0.608812 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21643.1i | 1.47632i | 0.674628 | + | 0.738158i | \(0.264304\pi\) | ||||
−0.674628 | + | 0.738158i | \(0.735696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9462.88i | 0.642261i | 0.947035 | + | 0.321131i | \(0.104063\pi\) | ||||
−0.947035 | + | 0.321131i | \(0.895937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1502.72i | − | 0.101485i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14065.9i | 0.945221i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −523.640 | −0.0350146 | −0.0175073 | − | 0.999847i | \(-0.505573\pi\) | ||||
−0.0175073 | + | 0.999847i | \(0.505573\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1631.57 | + | 15401.1i | −0.108562 | + | 1.02477i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 537.509i | 0.0355897i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25130.7 | −1.65582 | −0.827912 | − | 0.560858i | \(-0.810471\pi\) | ||||
−0.827912 | + | 0.560858i | \(0.810471\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17722.3 | 1.16200 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22315.2 | −1.45604 | −0.728021 | − | 0.685555i | \(-0.759560\pi\) | ||||
−0.728021 | + | 0.685555i | \(0.759560\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20000.9 | −1.29871 | −0.649357 | − | 0.760484i | \(-0.724962\pi\) | ||||
−0.649357 | + | 0.760484i | \(0.724962\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 2925.45i | − | 0.189041i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27580.4 | + | 2921.83i | 1.77365 | + | 0.187898i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17034.3 | 1.09019 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6406.62i | 0.408063i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4328.89i | 0.274411i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6793.62i | 0.428605i | 0.976767 | + | 0.214302i | \(0.0687478\pi\) | ||||
−0.976767 | + | 0.214302i | \(0.931252\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 3987.39i | − | 0.250370i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30597.8 | −1.91218 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 377.698 | − | 1762.62i | 0.0234928 | − | 0.109635i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3402.22i | 0.210626i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1369.18 | −0.0843675 | −0.0421837 | − | 0.999110i | \(-0.513431\pi\) | ||||
−0.0421837 | + | 0.999110i | \(0.513431\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24036.2 | −1.47417 | −0.737087 | − | 0.675797i | \(-0.763799\pi\) | ||||
−0.737087 | + | 0.675797i | \(0.763799\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10308.3 | 0.629282 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13781.3 | −0.837403 | −0.418702 | − | 0.908124i | \(-0.637515\pi\) | ||||
−0.418702 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18076.1i | 1.09330i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 681.972 | − | 6437.42i | 0.0410578 | − | 0.387561i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10312.2 | 0.617991 | 0.308995 | − | 0.951064i | \(-0.400007\pi\) | ||||
0.308995 | + | 0.951064i | \(0.400007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 18329.4i | − | 1.09342i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5983.42i | − | 0.355305i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 18371.4i | − | 1.08596i | −0.839745 | − | 0.542980i | \(-0.817296\pi\) | ||
0.839745 | − | 0.542980i | \(-0.182704\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19068.1i | 1.12203i | 0.827806 | + | 0.561015i | \(0.189589\pi\) | ||||
−0.827806 | + | 0.561015i | \(0.810411\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1275.24 | −0.0747002 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 31035.7 | + | 3287.88i | 1.80979 | + | 0.191727i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 30202.0i | − | 1.75326i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2552.17 | −0.147493 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10929.1 | 0.628784 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5215.69 | −0.298737 | −0.149368 | − | 0.988782i | \(-0.547724\pi\) | ||||
−0.149368 | + | 0.988782i | \(0.547724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6850.47 | 0.390629 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5346.63i | − | 0.303527i | −0.988417 | − | 0.151764i | \(-0.951505\pi\) | ||
0.988417 | − | 0.151764i | \(-0.0484952\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26622.4 | − | 2820.34i | −1.50467 | − | 0.159403i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7879.79 | −0.443398 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7087.40i | 0.397060i | 0.980095 | + | 0.198530i | \(0.0636167\pi\) | ||||
−0.980095 | + | 0.198530i | \(0.936383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40623.5i | 2.26591i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5044.64i | 0.280153i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 977.170i | − | 0.0540308i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29981.3 | −1.65057 | −0.825284 | − | 0.564718i | \(-0.808985\pi\) | ||||
−0.825284 | + | 0.564718i | \(0.808985\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4087.86 | − | 433.063i | −0.224076 | − | 0.0237384i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 36867.7i | − | 2.01219i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24552.5 | 1.33428 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5474.59 | 0.296235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4928.54 | 0.265547 | 0.132773 | − | 0.991146i | \(-0.457612\pi\) | ||||
0.132773 | + | 0.991146i | \(0.457612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4634.43 | 0.248636 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 5971.09i | − | 0.318985i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4426.55 | + | 468.943i | 0.235470 | + | 0.0249454i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22659.0 | −1.20025 | −0.600125 | − | 0.799906i | \(-0.704883\pi\) | ||||
−0.600125 | + | 0.799906i | \(0.704883\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6640.44i | 0.350261i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12624.0i | 0.663074i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2522.33i | − | 0.131930i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2328.23i | 0.121268i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23078.3 | −1.19705 | −0.598523 | − | 0.801106i | \(-0.704246\pi\) | ||||
−0.598523 | + | 0.801106i | \(0.704246\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3314.37 | − | 31285.7i | 0.171198 | − | 1.61601i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 121.773i | 0.00626386i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 70723.3 | 3.62289 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24974.6 | −1.27408 | −0.637039 | − | 0.770831i | \(-0.719841\pi\) | ||||
−0.637039 | + | 0.770831i | \(0.719841\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14281.1 | 0.722580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 642.353i | 0.0323682i | 0.999869 | + | 0.0161841i | \(0.00515178\pi\) | ||||
−0.999869 | + | 0.0161841i | \(0.994848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4195.78 | + | 19580.6i | −0.210563 | + | 0.982643i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4117.80 | 0.205809 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32931.9i | 1.63927i | 0.572888 | + | 0.819633i | \(0.305823\pi\) | ||||
−0.572888 | + | 0.819633i | \(0.694177\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1365.25i | 0.0676838i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24636.6i | − | 1.21646i | −0.793762 | − | 0.608229i | \(-0.791880\pi\) | ||
0.793762 | − | 0.608229i | \(-0.208120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48772.6i | 2.39851i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8219.07 | 0.402570 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5287.12 | − | 560.110i | −0.257927 | − | 0.0273244i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32225.0i | 1.56579i | 0.622156 | + | 0.782893i | \(0.286257\pi\) | ||||
−0.622156 | + | 0.782893i | \(0.713743\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12695.0 | 0.614386 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9049.93 | −0.436240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16949.5 | 0.813792 | 0.406896 | − | 0.913474i | \(-0.366611\pi\) | ||||
0.406896 | + | 0.913474i | \(0.366611\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8016.42 | 0.383370 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3896.80i | 0.185623i | 0.995684 | + | 0.0928114i | \(0.0295854\pi\) | ||||
−0.995684 | + | 0.0928114i | \(0.970415\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.1975 | + | 275.607i | −0.00138535 | + | 0.0130769i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14166.4 | 0.669527 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3852.01i | 0.181340i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 18651.6i | − | 0.874634i | −0.899307 | − | 0.437317i | \(-0.855929\pi\) | ||
0.899307 | − | 0.437317i | \(-0.144071\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5617.51i | 0.262399i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 30262.1i | − | 1.40809i | −0.710156 | − | 0.704045i | \(-0.751376\pi\) | ||
0.710156 | − | 0.704045i | \(-0.248624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29561.3 | −1.37016 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −313.270 | + | 2957.08i | −0.0144639 | + | 0.136531i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 26285.5i | − | 1.20895i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9322.87 | −0.427143 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7526.09 | 0.343500 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8586.42 | −0.390398 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25673.9 | 1.16286 | 0.581432 | − | 0.813595i | \(-0.302493\pi\) | ||||
0.581432 | + | 0.813595i | \(0.302493\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15378.8i | 0.693914i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1438.38 | − | 13577.4i | 0.0646558 | − | 0.610314i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2328.99 | 0.104294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10855.2i | 0.484270i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9725.85i | 0.432255i | 0.976365 | + | 0.216127i | \(0.0693427\pi\) | ||||
−0.976365 | + | 0.216127i | \(0.930657\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8272.39i | − | 0.366278i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13477.8i | − | 0.594525i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16396.0 | 0.720549 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4114.03 | − | 38834.1i | 0.180125 | − | 1.70027i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7199.94i | 0.314064i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22322.4 | 0.970106 | 0.485053 | − | 0.874485i | \(-0.338800\pi\) | ||||
0.485053 | + | 0.874485i | \(0.338800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8693.62 | 0.376417 | 0.188209 | − | 0.982129i | \(-0.439732\pi\) | ||||
0.188209 | + | 0.982129i | \(0.439732\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16998.9 | −0.733305 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7295.38 | −0.313553 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 15289.1i | − | 0.654710i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −871.122 | − | 92.2856i | −0.0371666 | − | 0.00393739i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15530.6 | 0.660196 | 0.330098 | − | 0.943947i | \(-0.392918\pi\) | ||||
0.330098 | + | 0.943947i | \(0.392918\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37619.9i | 1.59337i | 0.604392 | + | 0.796687i | \(0.293416\pi\) | ||||
−0.604392 | + | 0.796687i | \(0.706584\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18771.9i | 0.792186i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22298.2i | − | 0.937587i | −0.883308 | − | 0.468794i | \(-0.844689\pi\) | ||
0.883308 | − | 0.468794i | \(-0.155311\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26664.3i | 1.11712i | 0.829465 | + | 0.558559i | \(0.188646\pi\) | ||||
−0.829465 | + | 0.558559i | \(0.811354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3269.75 | −0.136494 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5812.86 | + | 27127.1i | −0.241781 | + | 1.12833i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19194.0i | 0.795491i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3145.80 | −0.129910 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33449.9 | 1.37642 | 0.688212 | − | 0.725510i | \(-0.258396\pi\) | ||||
0.688212 | + | 0.725510i | \(0.258396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53309.3 | 2.18579 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9755.95 | 0.398592 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42217.8i | 1.71874i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1410.21 | + | 13311.6i | −0.0572084 | + | 0.540014i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24261.3 | −0.980738 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 5798.93i | − | 0.233590i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 47864.2i | − | 1.92127i | −0.277822 | − | 0.960633i | \(-0.589613\pi\) | ||
0.277822 | − | 0.960633i | \(-0.410387\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 15166.3i | − | 0.606640i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2792.59i | − | 0.111310i | −0.998450 | − | 0.0556552i | \(-0.982275\pi\) | ||
0.998450 | − | 0.0556552i | \(-0.0177248\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24841.7 | −0.986715 | −0.493357 | − | 0.869827i | \(-0.664231\pi\) | ||||
−0.493357 | + | 0.869827i | \(0.664231\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16771.9 | + | 1776.80i | 0.663862 | + | 0.0703287i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12119.8i | − | 0.478058i | −0.971012 | − | 0.239029i | \(-0.923171\pi\) | ||
0.971012 | − | 0.239029i | \(-0.0768291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31502.7 | −1.23829 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4887.26 | 0.191442 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18196.3 | −0.710321 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 877.502 | 0.0341366 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13009.7i | 0.504364i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 46135.3 | + | 4887.52i | 1.78247 | + | 0.188832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14849.8 | −0.571770 | −0.285885 | − | 0.958264i | \(-0.592288\pi\) | ||||
−0.285885 | + | 0.958264i | \(0.592288\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4846.04i | 0.185953i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20213.3i | − | 0.772990i | −0.922291 | − | 0.386495i | \(-0.873686\pi\) | ||
0.922291 | − | 0.386495i | \(-0.126314\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 9218.17i | − | 0.351321i | −0.984451 | − | 0.175660i | \(-0.943794\pi\) | ||
0.984451 | − | 0.175660i | \(-0.0562061\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 42791.3i | − | 1.62533i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42349.9 | −1.60312 | −0.801561 | − | 0.597913i | \(-0.795997\pi\) | ||||
−0.801561 | + | 0.597913i | \(0.795997\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28957.0 | − | 3067.67i | −1.09245 | − | 0.115733i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1997.63i | 0.0751101i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8856.26 | −0.331874 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71874.1 | 2.68434 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1708.30 | 0.0635880 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32476.8 | −1.20485 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15038.9i | 0.556068i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9755.49 | + | 1033.48i | 0.359515 | + | 0.0380866i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 47622.2 | 1.74919 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40185.9i | 1.47117i | 0.677432 | + | 0.735586i | \(0.263093\pi\) | ||||
−0.677432 | + | 0.735586i | \(0.736907\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2163.14i | − | 0.0789293i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 11410.6i | − | 0.414984i | −0.978237 | − | 0.207492i | \(-0.933470\pi\) | ||
0.978237 | − | 0.207492i | \(-0.0665301\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22522.2i | 0.816401i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −25872.4 | −0.934770 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1837.67 | − | 17346.5i | 0.0661779 | − | 0.624680i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27571.5i | − | 0.989662i | −0.868989 | − | 0.494831i | \(-0.835230\pi\) | ||
0.868989 | − | 0.494831i | \(-0.164770\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8179.36 | −0.292637 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1986.70 | −0.0708484 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13579.2 | 0.482684 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15288.5 | −0.541683 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 25071.2i | − | 0.885424i | −0.896664 | − | 0.442712i | \(-0.854016\pi\) | ||
0.896664 | − | 0.442712i | \(-0.145984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29041.8 | + | 6223.14i | 1.02235 | + | 0.219071i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19487.8 | −0.683817 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38819.3i | 1.35778i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19811.3i | 0.690721i | 0.938470 | + | 0.345360i | \(0.112243\pi\) | ||||
−0.938470 | + | 0.345360i | \(0.887757\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6945.05i | 0.241367i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3182.72i | − | 0.110259i | −0.998479 | − | 0.0551295i | \(-0.982443\pi\) | ||
0.998479 | − | 0.0551295i | \(-0.0175572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32890.3 | −1.13579 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9677.14 | + | 1025.18i | 0.333119 | + | 0.0352902i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25087.2i | 0.860848i | 0.902627 | + | 0.430424i | \(0.141636\pi\) | ||||
−0.902627 | + | 0.430424i | \(0.858364\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3493.97 | 0.119514 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10635.5 | −0.362651 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 247.587 | 0.00841568 | 0.00420784 | − | 0.999991i | \(-0.498661\pi\) | ||||
0.00420784 | + | 0.999991i | \(0.498661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −179.034 | −0.00606638 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20623.2i | 0.696609i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4072.83 | + | 38445.1i | −0.137141 | + | 1.29453i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16216.2 | −0.544331 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2583.67i | 0.0864566i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 28582.4i | − | 0.953471i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31623.0i | − | 1.05163i | −0.850598 | − | 0.525816i | \(-0.823760\pi\) | ||
0.850598 | − | 0.525816i | \(-0.176240\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 21011.5i | − | 0.696581i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33729.9 | −1.11477 | −0.557386 | − | 0.830253i | \(-0.688196\pi\) | ||||
−0.557386 | + | 0.830253i | \(0.688196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3696.28 | − | 34890.7i | 0.121785 | − | 1.14958i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4000.28i | 0.131397i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45295.7 | −1.48325 | −0.741626 | − | 0.670813i | \(-0.765945\pi\) | ||||
−0.741626 | + | 0.670813i | \(0.765945\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36932.3 | 1.20568 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 134.682 | 0.00438335 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43789.8 | 1.42083 | 0.710416 | − | 0.703782i | \(-0.248507\pi\) | ||||
0.710416 | + | 0.703782i | \(0.248507\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 76181.8i | − | 2.46432i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 598.649 | − | 5650.90i | 0.0193062 | − | 0.182239i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19130.8 | −0.615090 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 398.825i | 0.0127842i | 0.999980 | + | 0.00639208i | \(0.00203468\pi\) | ||||
−0.999980 | + | 0.00639208i | \(0.997965\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 16441.2i | − | 0.525423i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 57608.1i | − | 1.83548i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40219.6i | 1.27760i | 0.769373 | + | 0.638800i | \(0.220569\pi\) | ||||
−0.769373 | + | 0.638800i | \(0.779431\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1445.05 | 0.0457651 |
(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 | 1344.4.b.g.895.12 | 12 | ||
4.3 | odd | 2 | 1344.4.b.h.895.12 | 12 | |||
7.6 | odd | 2 | 1344.4.b.h.895.1 | 12 | |||
8.3 | odd | 2 | 84.4.b.a.55.8 | yes | 12 | ||
8.5 | even | 2 | 84.4.b.b.55.7 | yes | 12 | ||
24.5 | odd | 2 | 252.4.b.e.55.6 | 12 | |||
24.11 | even | 2 | 252.4.b.f.55.5 | 12 | |||
28.27 | even | 2 | inner | 1344.4.b.g.895.1 | 12 | ||
56.13 | odd | 2 | 84.4.b.a.55.7 | ✓ | 12 | ||
56.27 | even | 2 | 84.4.b.b.55.8 | yes | 12 | ||
168.83 | odd | 2 | 252.4.b.e.55.5 | 12 | |||
168.125 | even | 2 | 252.4.b.f.55.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.b.a.55.7 | ✓ | 12 | 56.13 | odd | 2 | ||
84.4.b.a.55.8 | yes | 12 | 8.3 | odd | 2 | ||
84.4.b.b.55.7 | yes | 12 | 8.5 | even | 2 | ||
84.4.b.b.55.8 | yes | 12 | 56.27 | even | 2 | ||
252.4.b.e.55.5 | 12 | 168.83 | odd | 2 | |||
252.4.b.e.55.6 | 12 | 24.5 | odd | 2 | |||
252.4.b.f.55.5 | 12 | 24.11 | even | 2 | |||
252.4.b.f.55.6 | 12 | 168.125 | even | 2 | |||
1344.4.b.g.895.1 | 12 | 28.27 | even | 2 | inner | ||
1344.4.b.g.895.12 | 12 | 1.1 | even | 1 | trivial | ||
1344.4.b.h.895.1 | 12 | 7.6 | odd | 2 | |||
1344.4.b.h.895.12 | 12 | 4.3 | odd | 2 |