Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(55,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, 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("252.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8684813214\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.6 | ||
Root | \(0.965027 + 2.65871i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.4.b.f.55.5 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965027 | + | 2.65871i | −0.341189 | + | 0.939995i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.13744 | − | 5.13145i | −0.767180 | − | 0.641431i | ||||
\(5\) | − | 19.4608i | − | 1.74062i | −0.492501 | − | 0.870312i | \(-0.663917\pi\) | ||
0.492501 | − | 0.870312i | \(-0.336083\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.95109 | + | 18.4172i | 0.105349 | + | 0.994435i | ||||
\(8\) | 19.5658 | − | 11.3657i | 0.864695 | − | 0.502297i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 51.7405 | + | 18.7802i | 1.63618 | + | 0.593881i | ||||
\(11\) | 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 | \(0.982146\pi\) | |||||||
\(14\) | −50.8488 | − | 12.5857i | −0.970708 | − | 0.240262i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.3364 | + | 62.9880i | 0.177132 | + | 0.984187i | ||||
\(17\) | − | 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 | \(0.675104\pi\) | |||||||
\(20\) | −99.8619 | + | 119.439i | −1.11649 | + | 1.33537i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −65.5693 | − | 23.7996i | −0.635428 | − | 0.230641i | ||||
\(23\) | − | 108.350i | − | 0.982285i | −0.871079 | − | 0.491143i | \(-0.836579\pi\) | ||
0.871079 | − | 0.491143i | \(-0.163421\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −253.721 | −2.02977 | ||||||||
\(26\) | −13.9728 | − | 5.07169i | −0.105396 | − | 0.0382554i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 82.5322 | − | 123.046i | 0.557040 | − | 0.830486i | ||||
\(29\) | −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 | \(-0.609587\pi\) | ||||
−0.337516 | + | 0.941320i | \(0.609587\pi\) | |||||||
\(32\) | −178.407 | − | 30.6449i | −0.985566 | − | 0.169291i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 215.045 | + | 78.0545i | 1.08470 | + | 0.393713i | ||||
\(35\) | 358.413 | − | 37.9698i | 1.73094 | − | 0.183373i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 53.5203 | 0.237802 | 0.118901 | − | 0.992906i | \(-0.462063\pi\) | ||||
0.118901 | + | 0.992906i | \(0.462063\pi\) | |||||||
\(38\) | 83.5637 | − | 230.223i | 0.356732 | − | 0.982817i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −221.185 | − | 380.766i | −0.874309 | − | 1.50511i | ||||
\(41\) | 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 | \(-0.898635\pi\) | ||
0.949723 | − | 0.313092i | \(-0.101365\pi\) | |||||||
\(44\) | 126.552 | − | 151.362i | 0.433602 | − | 0.518607i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 288.071 | + | 104.561i | 0.923343 | + | 0.335145i | ||||
\(47\) | 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 | ||||
\(50\) | 244.848 | − | 674.570i | 0.692534 | − | 1.90797i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 26.9683 | − | 32.2552i | 0.0719197 | − | 0.0860192i | ||||
\(53\) | −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 | ||||||||
\(56\) | 247.499 | + | 338.172i | 0.590596 | + | 0.806967i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 268.996 | − | 741.099i | 0.608981 | − | 1.67778i | ||||
\(59\) | −732.951 | −1.61732 | −0.808662 | − | 0.588274i | \(-0.799808\pi\) | ||||
−0.808662 | + | 0.588274i | \(0.799808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 443.155i | − | 0.930167i | −0.885267 | − | 0.465083i | \(-0.846024\pi\) | ||
0.885267 | − | 0.465083i | \(-0.153976\pi\) | |||||||
\(62\) | 112.436 | − | 309.769i | 0.230313 | − | 0.634527i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 253.643 | − | 444.758i | 0.495396 | − | 0.868667i | ||||
\(65\) | 102.276 | 0.195165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 166.969i | 0.304455i | 0.988345 | + | 0.152227i | \(0.0486446\pi\) | ||||
−0.988345 | + | 0.152227i | \(0.951355\pi\) | |||||||
\(68\) | −415.048 | + | 496.416i | −0.740176 | + | 0.885283i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −244.928 | + | 989.556i | −0.418206 | + | 1.68964i | ||||
\(71\) | − | 378.024i | − | 0.631877i | −0.948780 | − | 0.315938i | \(-0.897681\pi\) | ||
0.948780 | − | 0.315938i | \(-0.102319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 664.824i | 1.06592i | 0.846142 | + | 0.532958i | \(0.178919\pi\) | ||||
−0.846142 | + | 0.532958i | \(0.821081\pi\) | |||||||
\(74\) | −51.6486 | + | 142.295i | −0.0811354 | + | 0.223533i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 531.454 | + | 444.343i | 0.802130 | + | 0.670652i | ||||
\(77\) | −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 | \(0.823919\pi\) | |||||||
\(80\) | 1225.79 | − | 220.616i | 1.71310 | − | 0.308320i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −807.065 | − | 292.939i | −1.08689 | − | 0.394509i | ||||
\(83\) | −913.229 | −1.20771 | −0.603855 | − | 0.797094i | \(-0.706369\pi\) | ||||
−0.603855 | + | 0.797094i | \(0.706369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1574.05 | −2.00858 | ||||||||
\(86\) | 469.434 | + | 170.390i | 0.588609 | + | 0.213647i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 280.301 | + | 482.534i | 0.339548 | + | 0.584526i | ||||
\(89\) | − | 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 | ||||
\(92\) | −555.993 | + | 664.993i | −0.630069 | + | 0.753590i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −98.6989 | + | 271.921i | −0.108298 | + | 0.298367i | ||||
\(95\) | 1685.15i | 1.81992i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1445.52i | − | 1.51309i | −0.653940 | − | 0.756547i | \(-0.726885\pi\) | ||
0.653940 | − | 0.756547i | \(-0.273115\pi\) | |||||||
\(98\) | 132.583 | − | 961.048i | 0.136662 | − | 0.990618i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1557.20 | + | 1301.96i | 1.55720 | + | 1.30196i | ||||
\(101\) | 240.349i | 0.236788i | 0.992967 | + | 0.118394i | \(0.0377746\pi\) | ||||
−0.992967 | + | 0.118394i | \(0.962225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1698.72 | 1.62505 | 0.812524 | − | 0.582927i | \(-0.198093\pi\) | ||||
0.812524 | + | 0.582927i | \(0.198093\pi\) | |||||||
\(104\) | 59.7321 | + | 102.828i | 0.0563194 | + | 0.0969529i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 179.431 | − | 494.342i | 0.164414 | − | 0.452969i | ||||
\(107\) | 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 | \(-0.502093\pi\) | ||||
−0.00657502 | + | 0.999978i | \(0.502093\pi\) | |||||||
\(110\) | −463.158 | + | 1276.03i | −0.401458 | + | 1.10604i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1137.94 | + | 331.681i | −0.960050 | + | 0.279829i | ||||
\(113\) | 737.215 | 0.613729 | 0.306864 | − | 0.951753i | \(-0.400720\pi\) | ||||
0.306864 | + | 0.951753i | \(0.400720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2108.58 | −1.70979 | ||||||||
\(116\) | 1710.78 | + | 1430.36i | 1.36932 | + | 1.14488i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 707.318 | − | 1948.70i | 0.551813 | − | 1.52028i | ||||
\(119\) | 1489.64 | − | 157.811i | 1.14752 | − | 0.121567i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 722.781 | 0.543036 | ||||||||
\(122\) | 1178.22 | + | 427.657i | 0.874352 | + | 0.317362i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 715.080 | + | 597.871i | 0.517872 | + | 0.432987i | ||||
\(125\) | 2505.01i | 1.79244i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1572.28i | 1.09856i | 0.835637 | + | 0.549282i | \(0.185099\pi\) | ||||
−0.835637 | + | 0.549282i | \(0.814901\pi\) | |||||||
\(128\) | 937.708 | + | 1103.57i | 0.647519 | + | 0.762049i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −98.6989 | + | 271.921i | −0.0665882 | + | 0.183454i | ||||
\(131\) | 941.864 | 0.628176 | 0.314088 | − | 0.949394i | \(-0.398301\pi\) | ||||
0.314088 | + | 0.949394i | \(0.398301\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −168.949 | − | 1594.78i | −0.110149 | − | 1.03974i | ||||
\(134\) | −443.921 | − | 161.129i | −0.286186 | − | 0.103877i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −919.292 | − | 1582.55i | −0.579622 | − | 0.997810i | ||||
\(137\) | −2087.46 | −1.30178 | −0.650889 | − | 0.759173i | \(-0.725604\pi\) | ||||
−0.650889 | + | 0.759173i | \(0.725604\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1894.46 | −1.15602 | −0.578008 | − | 0.816031i | \(-0.696170\pi\) | ||||
−0.578008 | + | 0.816031i | \(0.696170\pi\) | |||||||
\(140\) | −2394.58 | − | 1606.14i | −1.44556 | − | 0.969597i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1005.06 | + | 364.804i | 0.593961 | + | 0.215589i | ||||
\(143\) | −129.611 | −0.0757947 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5424.57i | 3.10680i | ||||||||
\(146\) | −1767.57 | − | 641.574i | −1.00195 | − | 0.363678i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −328.478 | − | 274.637i | −0.182437 | − | 0.152534i | ||||
\(149\) | 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 | \(0.960007\pi\) | |||||||
\(152\) | −1694.24 | + | 984.176i | −0.904088 | + | 0.525179i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 310.390 | − | 1254.04i | 0.162415 | − | 0.656190i | ||||
\(155\) | 2267.39i | 1.17498i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 441.217i | 0.224286i | 0.993692 | + | 0.112143i | \(0.0357715\pi\) | ||||
−0.993692 | + | 0.112143i | \(0.964228\pi\) | |||||||
\(158\) | −1961.66 | − | 712.023i | −0.987732 | − | 0.358516i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −596.372 | + | 3471.93i | −0.294671 | + | 1.71550i | ||||
\(161\) | 1995.51 | − | 211.401i | 0.976819 | − | 0.103483i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 374.876i | − | 0.180139i | −0.995936 | − | 0.0900693i | \(-0.971291\pi\) | ||
0.995936 | − | 0.0900693i | \(-0.0287089\pi\) | |||||||
\(164\) | 1557.68 | − | 1863.05i | 0.741673 | − | 0.887074i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 881.292 | − | 2428.01i | 0.412057 | − | 1.13524i | ||||
\(167\) | 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 | ||||||||
\(170\) | 1519.00 | − | 4184.93i | 0.685306 | − | 1.88806i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −906.033 | + | 1083.66i | −0.401653 | + | 0.480395i | ||||
\(173\) | − | 1618.78i | − | 0.711407i | −0.934599 | − | 0.355704i | \(-0.884241\pi\) | ||
0.934599 | − | 0.355704i | \(-0.115759\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −495.034 | − | 4672.83i | −0.213835 | − | 2.01847i | ||||
\(176\) | −1553.42 | + | 279.580i | −0.665302 | + | 0.119740i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3981.50 | + | 1445.16i | 1.67655 | + | 0.608536i | ||||
\(179\) | − | 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 | \(-0.167572\pi\) | |||||||
\(182\) | 66.1440 | − | 267.235i | 0.0269391 | − | 0.108839i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1231.47 | − | 2119.96i | −0.493399 | − | 0.849378i | ||||
\(185\) | − | 1041.55i | − | 0.413924i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1994.75 | 0.780056 | ||||||||
\(188\) | −627.712 | − | 524.823i | −0.243514 | − | 0.203599i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4480.31 | − | 1626.21i | −1.71071 | − | 0.620936i | ||||
\(191\) | − | 9.19972i | − | 0.00348518i | −0.999998 | − | 0.00174259i | \(-0.999445\pi\) | ||
0.999998 | − | 0.00174259i | \(-0.000554683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1468.72 | −0.547776 | −0.273888 | − | 0.961762i | \(-0.588310\pi\) | ||||
−0.273888 | + | 0.961762i | \(0.588310\pi\) | |||||||
\(194\) | 3843.21 | + | 1394.96i | 1.42230 | + | 0.516250i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2427.20 | + | 1279.94i | 0.884548 | + | 0.466449i | ||||
\(197\) | −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 | \(-0.323224\pi\) | ||||
0.527247 | + | 0.849712i | \(0.323224\pi\) | |||||||
\(200\) | −4964.26 | + | 2883.71i | −1.75513 | + | 1.01955i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −639.016 | − | 231.943i | −0.222579 | − | 0.0807893i | ||||
\(203\) | −543.856 | − | 5133.69i | −0.188036 | − | 1.77495i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5907.42 | 2.01264 | ||||||||
\(206\) | −1639.31 | + | 4516.40i | −0.554448 | + | 1.52754i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −331.032 | + | 59.5785i | −0.110351 | + | 0.0198607i | ||||
\(209\) | − | 2135.54i | − | 0.706787i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1329.13i | − | 0.433654i | −0.976210 | − | 0.216827i | \(-0.930429\pi\) | ||
0.976210 | − | 0.216827i | \(-0.0695708\pi\) | |||||||
\(212\) | 1141.16 | + | 954.108i | 0.369693 | + | 0.309096i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −763.248 | − | 277.035i | −0.243806 | − | 0.0884941i | ||||
\(215\) | −3436.08 | −1.08995 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −227.324 | − | 2145.81i | −0.0711141 | − | 0.671276i | ||||
\(218\) | 14.4413 | − | 39.7866i | 0.00448665 | − | 0.0123610i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2945.62 | − | 2462.80i | −0.902700 | − | 0.754737i | ||||
\(221\) | 425.080 | 0.129385 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −850.725 | −0.255465 | −0.127733 | − | 0.991809i | \(-0.540770\pi\) | ||||
−0.127733 | + | 0.991809i | \(0.540770\pi\) | |||||||
\(224\) | 216.305 | − | 3345.54i | 0.0645199 | − | 0.997916i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −711.433 | + | 1960.04i | −0.209397 | + | 0.576902i | ||||
\(227\) | −2626.60 | −0.767988 | −0.383994 | − | 0.923336i | \(-0.625452\pi\) | ||||
−0.383994 | + | 0.923336i | \(0.625452\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1681.55i | − | 0.485239i | −0.970122 | − | 0.242620i | \(-0.921993\pi\) | ||
0.970122 | − | 0.242620i | \(-0.0780067\pi\) | |||||||
\(230\) | 2034.83 | − | 5606.08i | 0.583361 | − | 1.60719i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5453.86 | + | 3168.12i | −1.54338 | + | 0.896539i | ||||
\(233\) | 1824.86 | 0.513093 | 0.256547 | − | 0.966532i | \(-0.417415\pi\) | ||||
0.256547 | + | 0.966532i | \(0.417415\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1990.36i | − | 0.552498i | ||||||
\(236\) | 4498.45 | + | 3761.10i | 1.24078 | + | 1.03740i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1017.97 | + | 4112.81i | −0.277249 | + | 1.12014i | ||||
\(239\) | 776.076i | 0.210043i | 0.994470 | + | 0.105021i | \(0.0334911\pi\) | ||||
−0.994470 | + | 0.105021i | \(0.966509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 40.5909i | 0.0108493i | 0.999985 | + | 0.00542466i | \(0.00172673\pi\) | ||||
−0.999985 | + | 0.00542466i | \(0.998273\pi\) | |||||||
\(242\) | −697.504 | + | 1921.66i | −0.185278 | + | 0.510451i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2274.03 | + | 2719.84i | −0.596638 | + | 0.713606i | ||||
\(245\) | 1398.59 | + | 6526.88i | 0.364706 | + | 1.70199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 455.083i | − | 0.117232i | ||||||
\(248\) | −2279.64 | + | 1324.23i | −0.583697 | + | 0.339066i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6660.09 | − | 2417.41i | −1.68488 | − | 0.611561i | ||||
\(251\) | 4231.68 | 1.06415 | 0.532074 | − | 0.846698i | \(-0.321413\pi\) | ||||
0.532074 | + | 0.846698i | \(0.321413\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2672.14 | 0.664016 | ||||||||
\(254\) | −4180.24 | − | 1517.30i | −1.03264 | − | 0.374817i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3838.97 | + | 1428.12i | −0.937249 | + | 0.348662i | ||||
\(257\) | − | 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 | ||||
\(260\) | −627.712 | − | 524.823i | −0.149727 | − | 0.125185i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −908.925 | + | 2504.14i | −0.214327 | + | 0.590482i | ||||
\(263\) | 5126.25i | 1.20190i | 0.799288 | + | 0.600948i | \(0.205210\pi\) | ||||
−0.799288 | + | 0.600948i | \(0.794790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3618.40i | 0.838780i | ||||||||
\(266\) | 4403.10 | + | 1089.82i | 1.01493 | + | 0.251208i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 856.792 | − | 1024.76i | 0.195287 | − | 0.233572i | ||||
\(269\) | 2399.98i | 0.543975i | 0.962301 | + | 0.271988i | \(0.0876810\pi\) | ||||
−0.962301 | + | 0.271988i | \(0.912319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5666.29 | −1.27012 | −0.635060 | − | 0.772462i | \(-0.719025\pi\) | ||||
−0.635060 | + | 0.772462i | \(0.719025\pi\) | |||||||
\(272\) | 5094.67 | − | 916.927i | 1.13570 | − | 0.204400i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2014.45 | − | 5549.94i | 0.444152 | − | 1.22366i | ||||
\(275\) | − | 6257.30i | − | 1.37211i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1089.92 | −0.236414 | −0.118207 | − | 0.992989i | \(-0.537715\pi\) | ||||
−0.118207 | + | 0.992989i | \(0.537715\pi\) | |||||||
\(278\) | 1828.21 | − | 5036.82i | 0.394420 | − | 1.08665i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6581.09 | − | 4816.51i | 1.40463 | − | 1.02801i | ||||
\(281\) | 3251.98 | 0.690381 | 0.345191 | − | 0.938533i | \(-0.387814\pi\) | ||||
0.345191 | + | 0.938533i | \(0.387814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8087.11 | 1.69869 | 0.849344 | − | 0.527840i | \(-0.176998\pi\) | ||||
0.849344 | + | 0.527840i | \(0.176998\pi\) | |||||||
\(284\) | −1939.81 | + | 2320.10i | −0.405305 | + | 0.484763i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 125.078 | − | 344.598i | 0.0258603 | − | 0.0712466i | ||||
\(287\) | −5590.64 | + | 592.265i | −1.14984 | + | 0.121813i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1629.09 | −0.331587 | ||||||||
\(290\) | −14422.4 | − | 5234.86i | −2.92038 | − | 1.06001i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3411.51 | − | 4080.32i | 0.683711 | − | 0.817749i | ||||
\(293\) | 1615.35i | 0.322080i | 0.986948 | + | 0.161040i | \(0.0514849\pi\) | ||||
−0.986948 | + | 0.161040i | \(0.948515\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14263.8i | 2.81515i | ||||||||
\(296\) | 1047.17 | − | 608.294i | 0.205627 | − | 0.119447i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2418.56 | + | 6663.26i | −0.470145 | + | 1.29528i | ||||
\(299\) | 569.433 | 0.110138 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3251.83 | − | 344.495i | 0.622699 | − | 0.0659679i | ||||
\(302\) | −1236.39 | − | 448.772i | −0.235584 | − | 0.0855096i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −981.645 | − | 5454.25i | −0.185201 | − | 1.02902i | ||||
\(305\) | −8624.13 | −1.61907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2726.45 | 0.506863 | 0.253431 | − | 0.967353i | \(-0.418441\pi\) | ||||
0.253431 | + | 0.967353i | \(0.418441\pi\) | |||||||
\(308\) | 3034.58 | + | 2035.42i | 0.561401 | + | 0.376554i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6028.34 | − | 2188.10i | −1.10447 | − | 0.400889i | ||||
\(311\) | 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 | \(0.0670305\pi\) | ||||
−0.977909 | + | 0.209030i | \(0.932970\pi\) | |||||||
\(314\) | −1173.07 | − | 425.786i | −0.210828 | − | 0.0765239i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3786.12 | − | 4528.37i | 0.674006 | − | 0.806141i | ||||
\(317\) | 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 | ||||||
\(320\) | −8655.32 | − | 4936.08i | −1.51202 | − | 0.862298i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1363.66 | + | 5509.47i | −0.236006 | + | 0.953512i | ||||
\(323\) | 7003.83i | 1.20651i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1333.43i | − | 0.227585i | ||||||
\(326\) | 996.687 | + | 361.766i | 0.169329 | + | 0.0614613i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3450.11 | + | 5939.31i | 0.580794 | + | 0.999828i | ||||
\(329\) | 199.550 | + | 1883.63i | 0.0334393 | + | 0.315648i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 5480.40i | − | 0.910060i | −0.890476 | − | 0.455030i | \(-0.849629\pi\) | ||
0.890476 | − | 0.455030i | \(-0.150371\pi\) | |||||||
\(332\) | 5604.89 | + | 4686.19i | 0.926532 | + | 0.774663i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −951.799 | + | 2622.26i | −0.155928 | + | 0.429592i | ||||
\(335\) | 3249.34 | 0.529941 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −142.057 | −0.0229624 | −0.0114812 | − | 0.999934i | \(-0.503655\pi\) | ||||
−0.0114812 | + | 0.999934i | \(0.503655\pi\) | |||||||
\(338\) | −2093.51 | + | 5767.75i | −0.336899 | + | 0.928177i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9660.63 | + | 8077.15i | 1.54094 | + | 1.28837i | ||||
\(341\) | − | 2873.41i | − | 0.456316i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1977.97 | − | 6036.66i | −0.311371 | − | 0.950288i | ||||
\(344\) | −2006.78 | − | 3454.64i | −0.314530 | − | 0.541458i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4303.86 | + | 1562.17i | 0.668719 | + | 0.242724i | ||||
\(347\) | 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 | \(0.866377\pi\) | |||||||
\(350\) | 12901.4 | + | 3193.26i | 1.97031 | + | 0.487677i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 755.767 | − | 4399.88i | 0.114439 | − | 0.666234i | ||||
\(353\) | − | 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 | ||||||||
\(356\) | −7684.52 | + | 9191.03i | −1.14404 | + | 1.36832i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9819.36 | + | 3564.12i | 1.44963 | + | 0.526172i | ||||
\(359\) | 2661.07i | 0.391214i | 0.980682 | + | 0.195607i | \(0.0626677\pi\) | ||||
−0.980682 | + | 0.195607i | \(0.937332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 639.174 | 0.0931876 | ||||||||
\(362\) | 6506.10 | + | 2361.51i | 0.944621 | + | 0.342868i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 646.669 | + | 433.747i | 0.0931172 | + | 0.0624575i | ||||
\(365\) | 12938.0 | 1.85536 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5895.68 | −0.838562 | −0.419281 | − | 0.907857i | \(-0.637718\pi\) | ||||
−0.419281 | + | 0.907857i | \(0.637718\pi\) | |||||||
\(368\) | 6824.75 | − | 1228.30i | 0.966753 | − | 0.173994i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2769.16 | + | 1005.12i | 0.389087 | + | 0.141226i | ||||
\(371\) | −362.774 | − | 3424.37i | −0.0507662 | − | 0.479203i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6208.52 | −0.861837 | −0.430918 | − | 0.902391i | \(-0.641810\pi\) | ||||
−0.430918 | + | 0.902391i | \(0.641810\pi\) | |||||||
\(374\) | −1924.99 | + | 5303.45i | −0.266146 | + | 0.733248i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2001.11 | − | 1162.43i | 0.274466 | − | 0.159436i | ||||
\(377\) | − | 1464.94i | − | 0.200127i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3532.73i | 0.478797i | 0.970921 | + | 0.239399i | \(0.0769503\pi\) | ||||
−0.970921 | + | 0.239399i | \(0.923050\pi\) | |||||||
\(380\) | 8647.24 | − | 10342.5i | 1.16735 | − | 1.39621i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.4594 | + | 8.87799i | 0.00327605 | + | 0.00118910i | ||||
\(383\) | −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 | ||||
\(386\) | 1417.35 | − | 3904.89i | 0.186895 | − | 0.514907i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7417.60 | + | 8871.78i | −0.970545 | + | 1.16082i | ||||
\(389\) | −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 | ||||||||
\(392\) | −5745.29 | + | 5218.04i | −0.740258 | + | 0.672323i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3777.73 | − | 10407.9i | 0.483044 | − | 1.33082i | ||||
\(395\) | 14358.7 | 1.82902 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8515.34i | − | 1.07651i | −0.842783 | − | 0.538253i | \(-0.819085\pi\) | ||
0.842783 | − | 0.538253i | \(-0.180915\pi\) | |||||||
\(398\) | −2856.69 | + | 7870.35i | −0.359781 | + | 0.991218i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2876.29 | − | 15981.4i | −0.359537 | − | 1.99767i | ||||
\(401\) | 2804.56 | 0.349259 | 0.174629 | − | 0.984634i | \(-0.444127\pi\) | ||||
0.174629 | + | 0.984634i | \(0.444127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 612.322i | − | 0.0756872i | ||||||
\(404\) | 1233.34 | − | 1475.13i | 0.151883 | − | 0.181659i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14173.8 | + | 3508.19i | 1.73260 | + | 0.428839i | ||||
\(407\) | 1319.92i | 0.160752i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13823.4i | − | 1.67121i | −0.549334 | − | 0.835603i | \(-0.685118\pi\) | ||
0.549334 | − | 0.835603i | \(-0.314882\pi\) | |||||||
\(410\) | −5700.82 | + | 15706.1i | −0.686691 | + | 1.89187i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10425.8 | − | 8716.91i | −1.24671 | − | 1.04236i | ||||
\(413\) | −1430.06 | − | 13498.9i | −0.170384 | − | 1.60832i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17772.1i | 2.10217i | ||||||||
\(416\) | 161.054 | − | 937.613i | 0.0189815 | − | 0.110505i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5677.77 | + | 2060.85i | 0.664376 | + | 0.241148i | ||||
\(419\) | −5047.91 | −0.588560 | −0.294280 | − | 0.955719i | \(-0.595080\pi\) | ||||
−0.294280 | + | 0.955719i | \(0.595080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6467.30 | 0.748686 | 0.374343 | − | 0.927290i | \(-0.377868\pi\) | ||||
0.374343 | + | 0.927290i | \(0.377868\pi\) | |||||||
\(422\) | 3533.76 | + | 1282.65i | 0.407633 | + | 0.147958i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3637.94 | + | 2113.26i | −0.416684 | + | 0.242049i | ||||
\(425\) | 20521.8i | 2.34224i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8161.67 | − | 864.637i | 0.924990 | − | 0.0979923i | ||||
\(428\) | 1473.11 | − | 1761.91i | 0.166368 | − | 0.198984i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3315.92 | − | 9135.54i | 0.371878 | − | 1.02455i | ||||
\(431\) | 12799.9i | 1.43051i | 0.698861 | + | 0.715257i | \(0.253691\pi\) | ||||
−0.698861 | + | 0.715257i | \(0.746309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7154.28i | − | 0.794025i | −0.917813 | − | 0.397013i | \(-0.870047\pi\) | ||
0.917813 | − | 0.397013i | \(-0.129953\pi\) | |||||||
\(434\) | 5924.45 | + | 1466.38i | 0.655259 | + | 0.162185i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 91.8447 | + | 76.7904i | 0.0100885 | + | 0.00843485i | ||||
\(437\) | 9382.25i | 1.02703i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10688.8 | 1.16207 | 0.581034 | − | 0.813879i | \(-0.302648\pi\) | ||||
0.581034 | + | 0.813879i | \(0.302648\pi\) | |||||||
\(440\) | 9390.48 | − | 5454.88i | 1.01744 | − | 0.591025i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −410.214 | + | 1130.16i | −0.0441446 | + | 0.121621i | ||||
\(443\) | − | 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 | ||||||||
\(446\) | 820.973 | − | 2261.83i | 0.0871619 | − | 0.240136i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8686.07 | + | 3803.63i | 0.916023 | + | 0.401126i | ||||
\(449\) | −16721.0 | −1.75749 | −0.878743 | − | 0.477296i | \(-0.841617\pi\) | ||||
−0.878743 | + | 0.477296i | \(0.841617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7486.31 | −0.781633 | ||||||||
\(452\) | −4524.62 | − | 3782.98i | −0.470841 | − | 0.393665i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2534.74 | − | 6983.35i | 0.262029 | − | 0.721905i | ||||
\(455\) | 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 | \(0.626656\pi\) | |||||||
\(458\) | 4470.74 | + | 1622.74i | 0.456122 | + | 0.165558i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12941.3 | + | 10820.1i | 1.31172 | + | 1.09671i | ||||
\(461\) | − | 8410.07i | − | 0.849666i | −0.905272 | − | 0.424833i | \(-0.860333\pi\) | ||
0.905272 | − | 0.424833i | \(-0.139667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10100.0i | 1.01379i | 0.862007 | + | 0.506897i | \(0.169208\pi\) | ||||
−0.862007 | + | 0.506897i | \(0.830792\pi\) | |||||||
\(464\) | −3159.97 | − | 17557.5i | −0.316159 | − | 1.75666i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1761.04 | + | 4851.78i | −0.175062 | + | 0.482305i | ||||
\(467\) | 2012.75 | 0.199441 | 0.0997207 | − | 0.995015i | \(-0.468205\pi\) | ||||
0.0997207 | + | 0.995015i | \(0.468205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3075.10 | + | 325.772i | −0.302761 | + | 0.0320741i | ||||
\(470\) | 5291.79 | + | 1920.76i | 0.519345 | + | 0.188506i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14340.8 | + | 8330.48i | −1.39849 | + | 0.812376i | ||||
\(473\) | 4354.46 | 0.423294 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21970.2 | 2.12224 | ||||||||
\(476\) | −9952.39 | − | 6675.47i | −0.958334 | − | 0.642793i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2063.36 | − | 748.934i | −0.197439 | − | 0.0716641i | ||||
\(479\) | −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 | ||||||||
\(482\) | −107.919 | − | 39.1713i | −0.0101983 | − | 0.00370167i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4436.03 | − | 3708.92i | −0.416607 | − | 0.348320i | ||||
\(485\) | −28130.9 | −2.63372 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2587.62i | − | 0.240773i | −0.992727 | − | 0.120386i | \(-0.961587\pi\) | ||
0.992727 | − | 0.120386i | \(-0.0384134\pi\) | |||||||
\(488\) | −5036.75 | − | 8670.69i | −0.467219 | − | 0.804311i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −18702.7 | − | 2580.16i | −1.72429 | − | 0.237877i | ||||
\(491\) | 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 | ||||||||
\(494\) | 1209.93 | + | 439.168i | 0.110197 | + | 0.0399981i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1320.82 | − | 7338.80i | −0.119570 | − | 0.664358i | ||||
\(497\) | 6962.15 | − | 737.561i | 0.628360 | − | 0.0665677i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16006.0i | − | 1.43592i | −0.696083 | − | 0.717961i | \(-0.745075\pi\) | ||
0.696083 | − | 0.717961i | \(-0.254925\pi\) | |||||||
\(500\) | 12854.3 | − | 15374.4i | 1.14973 | − | 1.37513i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4083.69 | + | 11250.8i | −0.363075 | + | 1.00029i | ||||
\(503\) | −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 | ||||||||
\(506\) | −2578.69 | + | 7104.44i | −0.226555 | + | 0.624172i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8068.09 | − | 9649.80i | 0.704653 | − | 0.842796i | ||||
\(509\) | 2697.13i | 0.234869i | 0.993081 | + | 0.117434i | \(0.0374670\pi\) | ||||
−0.993081 | + | 0.117434i | \(0.962533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12244.2 | + | 1297.14i | −1.05998 | + | 0.112293i | ||||
\(512\) | −92.2362 | − | 11584.9i | −0.00796152 | − | 0.999968i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4978.44 | + | 1807.02i | 0.427217 | + | 0.155066i | ||||
\(515\) | − | 33058.4i | − | 2.82860i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2522.33i | 0.214569i | ||||||||
\(518\) | −2721.44 | − | 673.591i | −0.230837 | − | 0.0571349i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2001.11 | − | 1162.43i | 0.168759 | − | 0.0980309i | ||||
\(521\) | 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 | \(0.436749\pi\) | |||||||
\(524\) | −5780.64 | − | 4833.13i | −0.481924 | − | 0.402932i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13629.2 | − | 4946.98i | −1.12978 | − | 0.410073i | ||||
\(527\) | 9423.78i | 0.778950i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 427.252 | 0.0351156 | ||||||||
\(530\) | −9620.27 | − | 3491.86i | −0.788449 | − | 0.286182i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7146.63 | + | 10654.8i | −0.582417 | + | 0.868319i | ||||
\(533\) | −1595.33 | −0.129646 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5586.70 | 0.451465 | ||||||||
\(536\) | 1897.71 | + | 3266.88i | 0.152927 | + | 0.263261i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6380.84 | − | 2316.05i | −0.511334 | − | 0.185598i | ||||
\(539\) | −1772.40 | − | 8271.33i | −0.141638 | − | 0.660986i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6125.28 | −0.486777 | −0.243389 | − | 0.969929i | \(-0.578259\pi\) | ||||
−0.243389 | + | 0.969929i | \(0.578259\pi\) | |||||||
\(542\) | 5468.13 | − | 15065.0i | 0.433351 | − | 1.19391i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2478.65 | + | 14430.1i | −0.195352 | + | 1.13729i | ||||
\(545\) | 291.224i | 0.0228893i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25304.7i | 1.97797i | 0.148015 | + | 0.988985i | \(0.452712\pi\) | ||||
−0.148015 | + | 0.988985i | \(0.547288\pi\) | |||||||
\(548\) | 12811.7 | + | 10711.7i | 0.998699 | + | 0.835001i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 16636.3 | + | 6038.46i | 1.28977 | + | 0.468147i | ||||
\(551\) | 24137.0 | 1.86619 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13588.7 | + | 1439.57i | −1.04494 | + | 0.110699i | ||||
\(554\) | 1051.80 | − | 2897.77i | 0.0806620 | − | 0.222228i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11627.2 | + | 9721.34i | 0.886873 | + | 0.741505i | ||||
\(557\) | −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 | ||||||||
\(560\) | 6454.76 | + | 22145.2i | 0.487078 | + | 1.67108i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3138.25 | + | 8646.07i | −0.235550 | + | 0.648955i | ||||
\(563\) | −6110.70 | −0.457434 | −0.228717 | − | 0.973493i | \(-0.573453\pi\) | ||||
−0.228717 | + | 0.973493i | \(0.573453\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14346.8i | − | 1.06827i | ||||||
\(566\) | −7804.28 | + | 21501.2i | −0.579573 | + | 1.59676i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4296.50 | − | 7396.36i | −0.317389 | − | 0.546381i | ||||
\(569\) | 16843.7 | 1.24099 | 0.620497 | − | 0.784209i | \(-0.286931\pi\) | ||||
0.620497 | + | 0.784209i | \(0.286931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15796.9i | − | 1.15775i | −0.815415 | − | 0.578877i | \(-0.803491\pi\) | ||
0.815415 | − | 0.578877i | \(-0.196509\pi\) | |||||||
\(572\) | 795.482 | + | 665.094i | 0.0581482 | + | 0.0486171i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3820.46 | − | 15435.4i | 0.277810 | − | 1.12241i | ||||
\(575\) | 27490.7i | 1.99381i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6756.48i | − | 0.487480i | −0.969841 | − | 0.243740i | \(-0.921626\pi\) | ||
0.969841 | − | 0.243740i | \(-0.0783743\pi\) | |||||||
\(578\) | 1572.11 | − | 4331.26i | 0.113134 | − | 0.311690i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 27835.9 | − | 33293.0i | 1.99280 | − | 2.38348i | ||||
\(581\) | −1781.80 | − | 16819.1i | −0.127231 | − | 1.20099i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4585.50i | − | 0.325750i | ||||||
\(584\) | 7556.18 | + | 13007.8i | 0.535405 | + | 0.921692i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4294.73 | − | 1558.85i | −0.302754 | − | 0.109890i | ||||
\(587\) | −20504.0 | −1.44172 | −0.720861 | − | 0.693080i | \(-0.756253\pi\) | ||||
−0.720861 | + | 0.693080i | \(0.756253\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10088.9 | 0.705784 | ||||||||
\(590\) | −37923.2 | − | 13764.9i | −2.64623 | − | 0.960498i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 606.729 | + | 3371.14i | 0.0421223 | + | 0.234042i | ||||
\(593\) | 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 | ||||
\(596\) | −15381.7 | − | 12860.5i | −1.05715 | − | 0.883868i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −549.518 | + | 1513.95i | −0.0375777 | + | 0.103529i | ||||
\(599\) | − | 21643.1i | − | 1.47632i | −0.674628 | − | 0.738158i | \(-0.735696\pi\) | ||
0.674628 | − | 0.738158i | \(-0.264304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 9462.88i | − | 0.642261i | −0.947035 | − | 0.321131i | \(-0.895937\pi\) | ||
0.947035 | − | 0.321131i | \(-0.104063\pi\) | |||||||
\(602\) | −2222.19 | + | 8978.11i | −0.150448 | + | 0.607841i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2386.30 | − | 2854.13i | 0.160757 | − | 0.192273i | ||||
\(605\) | − | 14065.9i | − | 0.945221i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 523.640 | 0.0350146 | 0.0175073 | − | 0.999847i | \(-0.494427\pi\) | ||||
0.0175073 | + | 0.999847i | \(0.494427\pi\) | |||||||
\(608\) | 15448.6 | + | 2653.60i | 1.03046 | + | 0.177003i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8322.52 | − | 22929.0i | 0.552408 | − | 1.52192i | ||||
\(611\) | 537.509i | 0.0355897i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25130.7 | 1.65582 | 0.827912 | − | 0.560858i | \(-0.189529\pi\) | ||||
0.827912 | + | 0.560858i | \(0.189529\pi\) | |||||||
\(614\) | −2631.10 | + | 7248.84i | −0.172936 | + | 0.476448i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8340.03 | + | 6103.84i | −0.545503 | + | 0.399238i | ||||
\(617\) | 22315.2 | 1.45604 | 0.728021 | − | 0.685555i | \(-0.240440\pi\) | ||||
0.728021 | + | 0.685555i | \(0.240440\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20000.9 | −1.29871 | −0.649357 | − | 0.760484i | \(-0.724962\pi\) | ||||
−0.649357 | + | 0.760484i | \(0.724962\pi\) | |||||||
\(620\) | 11635.0 | − | 13916.0i | 0.753667 | − | 0.901420i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6268.75 | + | 17270.8i | −0.404106 | + | 1.11333i | ||||
\(623\) | 27580.4 | − | 2921.83i | 1.77365 | − | 0.187898i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17034.3 | 1.09019 | ||||||||
\(626\) | −6154.95 | − | 2234.06i | −0.392973 | − | 0.142637i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2264.08 | − | 2707.94i | 0.143864 | − | 0.172068i | ||||
\(629\) | − | 4328.89i | − | 0.274411i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6793.62i | 0.428605i | 0.976767 | + | 0.214302i | \(0.0687478\pi\) | ||||
−0.976767 | + | 0.214302i | \(0.931252\pi\) | |||||||
\(632\) | 8385.89 | + | 14436.2i | 0.527805 | + | 0.908608i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3421.20 | + | 9425.59i | −0.214311 | + | 0.590439i | ||||
\(635\) | 30597.8 | 1.91218 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −377.698 | − | 1762.62i | −0.0234928 | − | 0.109635i | ||||
\(638\) | 18277.1 | + | 6634.00i | 1.13416 | + | 0.411665i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21476.2 | − | 18248.5i | 1.32644 | − | 1.12709i | ||||
\(641\) | 1369.18 | 0.0843675 | 0.0421837 | − | 0.999110i | \(-0.486569\pi\) | ||||
0.0421837 | + | 0.999110i | \(0.486569\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24036.2 | −1.47417 | −0.737087 | − | 0.675797i | \(-0.763799\pi\) | ||||
−0.737087 | + | 0.675797i | \(0.763799\pi\) | |||||||
\(644\) | −13332.1 | − | 8942.37i | −0.815774 | − | 0.547172i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18621.1 | − | 6758.89i | −1.13412 | − | 0.411649i | ||||
\(647\) | −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 | ||||||
\(650\) | 3545.19 | + | 1286.79i | 0.213929 | + | 0.0776496i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1923.66 | + | 2300.78i | −0.115547 | + | 0.138199i | ||||
\(653\) | 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 | ||||||
\(656\) | −19120.3 | + | 3441.24i | −1.13799 | + | 0.204814i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5200.60 | − | 1287.21i | −0.308116 | − | 0.0762626i | ||||
\(659\) | − | 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 | \(0.810411\pi\) | |||||||
\(662\) | 14570.8 | + | 5288.73i | 0.855452 | + | 0.310502i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17868.1 | + | 10379.5i | −1.04430 | + | 0.606629i | ||||
\(665\) | −31035.7 | + | 3287.88i | −1.80979 | + | 0.191727i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30202.0i | 1.75326i | ||||||||
\(668\) | −6053.31 | − | 5061.11i | −0.350613 | − | 0.293144i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3135.70 | + | 8639.04i | −0.180810 | + | 0.498142i | ||||
\(671\) | 10929.1 | 0.628784 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5215.69 | −0.298737 | −0.149368 | − | 0.988782i | \(-0.547724\pi\) | ||||
−0.149368 | + | 0.988782i | \(0.547724\pi\) | |||||||
\(674\) | 137.089 | − | 377.688i | 0.00783453 | − | 0.0215846i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13314.4 | − | 11132.1i | −0.757536 | − | 0.633367i | ||||
\(677\) | 5346.63i | 0.303527i | 0.988417 | + | 0.151764i | \(0.0484952\pi\) | ||||
−0.988417 | + | 0.151764i | \(0.951505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26622.4 | − | 2820.34i | 1.50467 | − | 0.159403i | ||||
\(680\) | −30797.5 | + | 17890.1i | −1.73681 | + | 1.00890i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7639.55 | + | 2772.92i | 0.428935 | + | 0.155690i | ||||
\(683\) | 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 | ||||||||
\(686\) | 17958.5 | + | 566.707i | 0.999502 | + | 0.0315408i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11121.5 | − | 2001.62i | 0.616281 | − | 0.110917i | ||||
\(689\) | − | 977.170i | − | 0.0540308i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29981.3 | −1.65057 | −0.825284 | − | 0.564718i | \(-0.808985\pi\) | ||||
−0.825284 | + | 0.564718i | \(0.808985\pi\) | |||||||
\(692\) | −8306.68 | + | 9935.16i | −0.456319 | + | 0.545778i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2940.59 | − | 1067.34i | −0.160841 | − | 0.0583801i | ||||
\(695\) | 36867.7i | 2.01219i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24552.5 | 1.33428 | ||||||||
\(698\) | −14129.9 | − | 5128.71i | −0.766224 | − | 0.278115i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −20940.2 | + | 31219.5i | −1.13066 | + | 1.68569i | ||||
\(701\) | 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 | ||||||||
\(704\) | 10968.7 | + | 6255.37i | 0.587211 | + | 0.334883i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28131.7 | + | 10210.9i | 1.49965 | + | 0.544326i | ||||
\(707\) | −4426.55 | + | 468.943i | −0.235470 | + | 0.0249454i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22659.0 | 1.20025 | 0.600125 | − | 0.799906i | \(-0.295117\pi\) | ||||
0.600125 | + | 0.799906i | \(0.295117\pi\) | |||||||
\(710\) | 7099.36 | − | 19559.2i | 0.375260 | − | 1.03386i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17020.5 | − | 29300.5i | −0.895884 | − | 1.54225i | ||||
\(713\) | 12624.0i | 0.663074i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2522.33i | 0.131930i | ||||||||
\(716\) | −18951.9 | + | 22667.3i | −0.989198 | + | 1.18313i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7075.00 | − | 2568.01i | −0.367739 | − | 0.133478i | ||||
\(719\) | −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 | ||||
\(722\) | −616.820 | + | 1699.38i | −0.0317946 | + | 0.0875959i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12557.1 | + | 15018.9i | −0.644588 | + | 0.770956i | ||||
\(725\) | 70723.3 | 3.62289 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24974.6 | 1.27408 | 0.637039 | − | 0.770831i | \(-0.280159\pi\) | ||||
0.637039 | + | 0.770831i | \(0.280159\pi\) | |||||||
\(728\) | −1777.26 | + | 1300.73i | −0.0904802 | + | 0.0662199i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12485.5 | + | 34398.3i | −0.633027 | + | 1.74403i | ||||
\(731\) | −14281.1 | −0.722580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 642.353i | 0.0323682i | 0.999869 | + | 0.0161841i | \(0.00515178\pi\) | ||||
−0.999869 | + | 0.0161841i | \(0.994848\pi\) | |||||||
\(734\) | 5689.50 | − | 15674.9i | 0.286108 | − | 0.788244i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3320.37 | + | 19330.4i | −0.166292 | + | 0.968107i | ||||
\(737\) | −4117.80 | −0.205809 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 32931.9i | − | 1.63927i | −0.572888 | − | 0.819633i | \(-0.694177\pi\) | ||
0.572888 | − | 0.819633i | \(-0.305823\pi\) | |||||||
\(740\) | −5344.64 | + | 6392.43i | −0.265504 | + | 0.317555i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9454.48 | + | 2340.10i | 0.467770 | + | 0.115779i | ||||
\(743\) | 24636.6i | 1.21646i | 0.793762 | + | 0.608229i | \(0.208120\pi\) | ||||
−0.793762 | + | 0.608229i | \(0.791880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 48772.6i | − | 2.39851i | ||||||
\(746\) | 5991.40 | − | 16506.6i | 0.294049 | − | 0.810122i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12242.7 | − | 10236.0i | −0.598444 | − | 0.500352i | ||||
\(749\) | −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 | \(0.713743\pi\) | |||||||
\(752\) | 1159.44 | + | 6442.14i | 0.0562241 | + | 0.312395i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3894.84 | + | 1413.70i | 0.188119 | + | 0.0682812i | ||||
\(755\) | 9049.93 | 0.436240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16949.5 | −0.813792 | −0.406896 | − | 0.913474i | \(-0.633389\pi\) | ||||
−0.406896 | + | 0.913474i | \(0.633389\pi\) | |||||||
\(758\) | −9392.50 | − | 3409.18i | −0.450067 | − | 0.163360i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 19152.8 | + | 32971.3i | 0.914139 | + | 1.57368i | ||||
\(761\) | 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 | ||||
\(764\) | −47.2079 | + | 56.4628i | −0.00223550 | + | 0.00267376i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9052.69 | − | 24940.7i | 0.427006 | − | 1.17643i | ||||
\(767\) | − | 3852.01i | − | 0.181340i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18651.6i | 0.874634i | 0.899307 | + | 0.437317i | \(0.144071\pi\) | ||||
−0.899307 | + | 0.437317i | \(0.855929\pi\) | |||||||
\(770\) | −24404.5 | − | 6040.43i | −1.14218 | − | 0.282704i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9014.18 | + | 7536.66i | 0.420243 | + | 0.351361i | ||||
\(773\) | 30262.1i | 1.40809i | 0.710156 | + | 0.704045i | \(0.248624\pi\) | ||||
−0.710156 | + | 0.704045i | \(0.751376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29561.3 | 1.37016 | ||||||||
\(776\) | −16429.3 | − | 28282.7i | −0.760021 | − | 1.30836i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5082.94 | − | 14003.8i | 0.234232 | − | 0.645321i | ||||
\(779\) | − | 26285.5i | − | 1.20895i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9322.87 | 0.427143 | ||||||||
\(782\) | 8457.21 | − | 23300.1i | 0.386738 | − | 1.06549i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8328.87 | − | 20310.6i | −0.379413 | − | 0.925228i | ||||
\(785\) | 8586.42 | 0.390398 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25673.9 | 1.16286 | 0.581432 | − | 0.813595i | \(-0.302493\pi\) | ||||
0.581432 | + | 0.813595i | \(0.302493\pi\) | |||||||
\(788\) | 24025.9 | + | 20087.8i | 1.08615 | + | 0.908118i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13856.5 | + | 38175.5i | −0.624041 | + | 1.71927i | ||||
\(791\) | 1438.38 | + | 13577.4i | 0.0646558 | + | 0.610314i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2328.99 | 0.104294 | ||||||||
\(794\) | 22639.8 | + | 8217.54i | 1.01191 | + | 0.367292i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18168.2 | − | 15190.2i | −0.808987 | − | 0.676385i | ||||
\(797\) | − | 9725.85i | − | 0.432255i | −0.976365 | − | 0.216127i | \(-0.930657\pi\) | ||
0.976365 | − | 0.216127i | \(-0.0693427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8272.39i | − | 0.366278i | ||||||
\(800\) | 45265.5 | + | 7775.25i | 2.00047 | + | 0.343621i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2706.47 | + | 7456.49i | −0.119163 | + | 0.328301i | ||||
\(803\) | −16396.0 | −0.720549 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4114.03 | − | 38834.1i | −0.180125 | − | 1.70027i | ||||
\(806\) | 1627.99 | + | 590.908i | 0.0711456 | + | 0.0258236i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2731.72 | + | 4702.62i | 0.118938 | + | 0.204749i | ||||
\(809\) | −22322.4 | −0.970106 | −0.485053 | − | 0.874485i | \(-0.661200\pi\) | ||||
−0.485053 | + | 0.874485i | \(0.661200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8693.62 | 0.376417 | 0.188209 | − | 0.982129i | \(-0.439732\pi\) | ||||
0.188209 | + | 0.982129i | \(0.439732\pi\) | |||||||
\(812\) | −23005.4 | + | 34298.5i | −0.994249 | + | 1.48232i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3509.29 | − | 1273.76i | −0.151106 | − | 0.0548468i | ||||
\(815\) | −7295.38 | −0.313553 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15289.1i | 0.654710i | ||||||||
\(818\) | 36752.4 | + | 13340.0i | 1.57093 | + | 0.570197i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36256.4 | − | 30313.6i | −1.54406 | − | 1.29097i | ||||
\(821\) | 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 | \(0.706584\pi\) | |||||||
\(824\) | 33236.9 | − | 19307.1i | 1.40517 | − | 0.816256i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 37269.7 | + | 9224.71i | 1.56995 | + | 0.388582i | ||||
\(827\) | − | 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 | \(0.811354\pi\) | |||||||
\(830\) | −47250.9 | − | 17150.6i | −1.97603 | − | 0.717236i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2337.42 | + | 1333.02i | 0.0973983 | + | 0.0555457i | ||||
\(833\) | 5812.86 | + | 27127.1i | 0.241781 | + | 1.12833i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 19194.0i | − | 0.795491i | ||||||
\(836\) | −10958.4 | + | 13106.8i | −0.453355 | + | 0.542233i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4871.38 | − | 13420.9i | 0.200810 | − | 0.553244i | ||||
\(839\) | 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 | ||||||||
\(842\) | −6241.12 | + | 17194.6i | −0.255443 | + | 0.703761i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6820.36 | + | 8157.46i | −0.278159 | + | 0.332691i | ||||
\(845\) | − | 42217.8i | − | 1.71874i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1410.21 | + | 13311.6i | 0.0572084 | + | 0.540014i | ||||
\(848\) | −2107.82 | − | 11711.6i | −0.0853572 | − | 0.474265i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −54561.4 | − | 19804.1i | −2.20169 | − | 0.799146i | ||||
\(851\) | − | 5798.93i | − | 0.233590i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 47864.2i | − | 1.92127i | −0.277822 | − | 0.960633i | \(-0.589613\pi\) | ||
0.277822 | − | 0.960633i | \(-0.410387\pi\) | |||||||
\(854\) | −5577.42 | + | 22533.9i | −0.223484 | + | 0.902920i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3262.80 | + | 5616.86i | 0.130281 | + | 0.224276i | ||||
\(857\) | − | 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 | \(0.664231\pi\) | |||||||
\(860\) | 21088.8 | + | 17632.1i | 0.836188 | + | 0.699127i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34031.3 | − | 12352.3i | −1.34468 | − | 0.488076i | ||||
\(863\) | 12119.8i | 0.478058i | 0.971012 | + | 0.239029i | \(0.0768291\pi\) | ||||
−0.971012 | + | 0.239029i | \(0.923171\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31502.7 | −1.23829 | ||||||||
\(866\) | 19021.1 | + | 6904.08i | 0.746380 | + | 0.270912i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9615.92 | + | 14336.3i | −0.376020 | + | 0.560605i | ||||
\(869\) | −18196.3 | −0.710321 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −877.502 | −0.0341366 | ||||||||
\(872\) | −292.796 | + | 170.083i | −0.0113708 | + | 0.00660522i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24944.7 | − | 9054.13i | −0.965407 | − | 0.350413i | ||||
\(875\) | −46135.3 | + | 4887.52i | −1.78247 | + | 0.188832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14849.8 | 0.571770 | 0.285885 | − | 0.958264i | \(-0.407712\pi\) | ||||
0.285885 | + | 0.958264i | \(0.407712\pi\) | |||||||
\(878\) | −10315.0 | + | 28418.3i | −0.396484 | + | 1.09234i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5440.84 | + | 30230.6i | 0.208421 | + | 1.15804i | ||||
\(881\) | − | 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 | \(0.0562061\pi\) | ||||
−0.984451 | + | 0.175660i | \(0.943794\pi\) | |||||||
\(884\) | −2608.91 | − | 2181.28i | −0.0992613 | − | 0.0829913i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12370.8 | + | 4490.22i | 0.469081 | + | 0.170262i | ||||
\(887\) | −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 | ||||
\(890\) | 28123.9 | − | 77483.1i | 1.05923 | − | 2.91825i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5221.28 | + | 4365.45i | 0.195988 | + | 0.163863i | ||||
\(893\) | −8856.26 | −0.331874 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71874.1 | −2.68434 | ||||||||
\(896\) | −18495.0 | + | 19423.1i | −0.689593 | + | 0.724197i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16136.2 | − | 44456.1i | 0.599634 | − | 1.65203i | ||||
\(899\) | 32476.8 | 1.20485 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15038.9i | 0.556068i | ||||||||
\(902\) | 7224.50 | − | 19903.9i | 0.266684 | − | 0.734731i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14424.2 | − | 8378.94i | 0.530688 | − | 0.308274i | ||||
\(905\) | −47622.2 | −1.74919 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40185.9i | − | 1.47117i | −0.677432 | − | 0.735586i | \(-0.736907\pi\) | ||
0.677432 | − | 0.735586i | \(-0.263093\pi\) | |||||||
\(908\) | 16120.6 | + | 13478.3i | 0.589186 | + | 0.492612i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5200.60 | − | 1287.21i | −0.189449 | − | 0.0468909i | ||||
\(911\) | 11410.6i | 0.414984i | 0.978237 | + | 0.207492i | \(0.0665301\pi\) | ||||
−0.978237 | + | 0.207492i | \(0.933470\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 22522.2i | − | 0.816401i | ||||||
\(914\) | 7306.33 | − | 20129.4i | 0.264411 | − | 0.728469i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8628.77 | + | 10320.4i | −0.311247 | + | 0.372266i | ||||
\(917\) | 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 | \(-0.164770\pi\) | |||||||
\(920\) | −41256.0 | + | 23965.4i | −1.47845 | + | 0.858821i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22359.9 | + | 8115.95i | 0.798682 | + | 0.289896i | ||||
\(923\) | 1986.70 | 0.0708484 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13579.2 | −0.482684 | ||||||||
\(926\) | −26852.9 | − | 9746.77i | −0.952961 | − | 0.345895i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 49729.8 | + | 8542.08i | 1.75912 | + | 0.302163i | ||||
\(929\) | − | 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 | ||||
\(932\) | −11200.0 | − | 9364.19i | −0.393635 | − | 0.329114i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1942.36 | + | 5351.32i | −0.0680471 | + | 0.187474i | ||||
\(935\) | − | 38819.3i | − | 1.35778i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19811.3i | − | 0.690721i | −0.938470 | − | 0.345360i | \(-0.887757\pi\) | ||
0.938470 | − | 0.345360i | \(-0.112243\pi\) | |||||||
\(938\) | 2101.42 | − | 8490.16i | 0.0731491 | − | 0.295537i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10213.5 | + | 12215.7i | −0.354389 | + | 0.423866i | ||||
\(941\) | 3182.72i | 0.110259i | 0.998479 | + | 0.0551295i | \(0.0175572\pi\) | ||||
−0.998479 | + | 0.0551295i | \(0.982443\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32890.3 | 1.13579 | ||||||||
\(944\) | −8309.05 | − | 46167.1i | −0.286479 | − | 1.59175i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4202.17 | + | 11577.2i | −0.144423 | + | 0.397894i | ||||
\(947\) | 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 | ||||||||
\(950\) | −21201.9 | + | 58412.4i | −0.724084 | + | 1.99489i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 27352.4 | − | 20018.5i | 0.931195 | − | 0.681515i | ||||
\(953\) | −247.587 | −0.00841568 | −0.00420784 | − | 0.999991i | \(-0.501339\pi\) | ||||
−0.00420784 | + | 0.999991i | \(0.501339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −179.034 | −0.00606638 | ||||||||
\(956\) | 3982.39 | − | 4763.12i | 0.134728 | − | 0.161141i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12834.8 | − | 35360.6i | 0.432853 | − | 1.19253i | ||||
\(959\) | −4072.83 | − | 38445.1i | −0.137141 | − | 1.29453i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16216.2 | −0.544331 | ||||||||
\(962\) | −747.828 | − | 271.438i | −0.0250634 | − | 0.00909722i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 208.290 | − | 249.124i | 0.00695909 | − | 0.00832339i | ||||
\(965\) | 28582.4i | 0.953471i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31623.0i | − | 1.05163i | −0.850598 | − | 0.525816i | \(-0.823760\pi\) | ||
0.850598 | − | 0.525816i | \(-0.176240\pi\) | |||||||
\(968\) | 14141.8 | − | 8214.89i | 0.469561 | − | 0.272765i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 27147.1 | − | 74791.7i | 0.898597 | − | 2.47569i | ||||
\(971\) | 33729.9 | 1.11477 | 0.557386 | − | 0.830253i | \(-0.311804\pi\) | ||||
0.557386 | + | 0.830253i | \(0.311804\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3696.28 | − | 34890.7i | −0.121785 | − | 1.14958i | ||||
\(974\) | 6879.73 | + | 2497.13i | 0.226325 | + | 0.0821490i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27913.4 | − | 5023.80i | 0.915458 | − | 0.164762i | ||||
\(977\) | 45295.7 | 1.48325 | 0.741626 | − | 0.670813i | \(-0.234055\pi\) | ||||
0.741626 | + | 0.670813i | \(0.234055\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36932.3 | 1.20568 | ||||||||
\(980\) | 24908.5 | − | 47235.1i | 0.811912 | − | 1.53966i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1564.66 | − | 567.923i | −0.0508456 | − | 0.0184554i | ||||
\(983\) | 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 | ||||||||
\(986\) | −59942.4 | − | 21757.2i | −1.93606 | − | 0.702730i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2335.24 | + | 2793.05i | −0.0751961 | + | 0.0899379i | ||||
\(989\) | −19130.8 | −0.615090 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 398.825i | 0.0127842i | 0.999980 | + | 0.00639208i | \(0.00203468\pi\) | ||||
−0.999980 | + | 0.00639208i | \(0.997965\pi\) | |||||||
\(992\) | 20786.3 | + | 3570.47i | 0.665289 | + | 0.114277i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4757.71 | + | 19222.1i | −0.151816 | + | 0.613368i | ||||
\(995\) | − | 57608.1i | − | 1.83548i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40219.6i | 1.27760i | 0.769373 | + | 0.638800i | \(0.220569\pi\) | ||||
−0.769373 | + | 0.638800i | \(0.779431\pi\) | |||||||
\(998\) | 42555.2 | + | 15446.2i | 1.34976 | + | 0.489921i | ||||
\(999\) | 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 | 252.4.b.f.55.6 | 12 | ||
3.2 | odd | 2 | 84.4.b.a.55.7 | ✓ | 12 | ||
4.3 | odd | 2 | 252.4.b.e.55.5 | 12 | |||
7.6 | odd | 2 | 252.4.b.e.55.6 | 12 | |||
12.11 | even | 2 | 84.4.b.b.55.8 | yes | 12 | ||
21.20 | even | 2 | 84.4.b.b.55.7 | yes | 12 | ||
24.5 | odd | 2 | 1344.4.b.h.895.1 | 12 | |||
24.11 | even | 2 | 1344.4.b.g.895.1 | 12 | |||
28.27 | even | 2 | inner | 252.4.b.f.55.5 | 12 | ||
84.83 | odd | 2 | 84.4.b.a.55.8 | yes | 12 | ||
168.83 | odd | 2 | 1344.4.b.h.895.12 | 12 | |||
168.125 | even | 2 | 1344.4.b.g.895.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.b.a.55.7 | ✓ | 12 | 3.2 | odd | 2 | ||
84.4.b.a.55.8 | yes | 12 | 84.83 | odd | 2 | ||
84.4.b.b.55.7 | yes | 12 | 21.20 | even | 2 | ||
84.4.b.b.55.8 | yes | 12 | 12.11 | even | 2 | ||
252.4.b.e.55.5 | 12 | 4.3 | odd | 2 | |||
252.4.b.e.55.6 | 12 | 7.6 | odd | 2 | |||
252.4.b.f.55.5 | 12 | 28.27 | even | 2 | inner | ||
252.4.b.f.55.6 | 12 | 1.1 | even | 1 | trivial | ||
1344.4.b.g.895.1 | 12 | 24.11 | even | 2 | |||
1344.4.b.g.895.12 | 12 | 168.125 | even | 2 | |||
1344.4.b.h.895.1 | 12 | 24.5 | odd | 2 | |||
1344.4.b.h.895.12 | 12 | 168.83 | odd | 2 |