Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,4,Mod(191,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, 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("192.191");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.3283667211\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{2} + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.2 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.191 |
Dual form | 192.4.c.c.191.1 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.89898 | + | 1.73205i | −0.942809 | + | 0.333333i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.9706i | 1.51789i | 0.651153 | + | 0.758947i | \(0.274286\pi\) | ||||
−0.651153 | + | 0.758947i | \(0.725714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.3205i | 0.935220i | 0.883935 | + | 0.467610i | \(0.154885\pi\) | ||||
−0.883935 | + | 0.467610i | \(0.845115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 21.0000 | − | 16.9706i | 0.777778 | − | 0.628539i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −29.3939 | −0.805690 | −0.402845 | − | 0.915268i | \(-0.631979\pi\) | ||||
−0.402845 | + | 0.915268i | \(0.631979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 26.0000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −29.3939 | − | 83.1384i | −0.505964 | − | 1.43108i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 67.8823i | 0.968463i | 0.874940 | + | 0.484231i | \(0.160901\pi\) | ||||
−0.874940 | + | 0.484231i | \(0.839099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 107.387i | − | 1.29665i | −0.761365 | − | 0.648324i | \(-0.775470\pi\) | ||
0.761365 | − | 0.648324i | \(-0.224530\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −30.0000 | − | 84.8528i | −0.311740 | − | 0.881733i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −176.363 | −1.59888 | −0.799441 | − | 0.600745i | \(-0.794871\pi\) | ||||
−0.799441 | + | 0.600745i | \(0.794871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −163.000 | −1.30400 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −73.4847 | + | 119.512i | −0.523783 | + | 0.851852i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 16.9706i | − | 0.108667i | −0.998523 | − | 0.0543337i | \(-0.982697\pi\) | ||
0.998523 | − | 0.0543337i | \(-0.0173035\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.1769i | 0.180630i | 0.995913 | + | 0.0903151i | \(0.0287874\pi\) | ||||
−0.995913 | + | 0.0903151i | \(0.971213\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 144.000 | − | 50.9117i | 0.759612 | − | 0.268563i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −293.939 | −1.41956 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −206.000 | −0.915302 | −0.457651 | − | 0.889132i | \(-0.651309\pi\) | ||||
−0.457651 | + | 0.889132i | \(0.651309\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −127.373 | + | 45.0333i | −0.522976 | + | 0.184900i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 305.470i | − | 1.16357i | −0.813342 | − | 0.581786i | \(-0.802354\pi\) | ||
0.813342 | − | 0.581786i | \(-0.197646\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 93.5307i | − | 0.331705i | −0.986151 | − | 0.165852i | \(-0.946962\pi\) | ||
0.986151 | − | 0.165852i | \(-0.0530375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 288.000 | + | 356.382i | 0.954056 | + | 1.18058i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 117.576 | 0.364897 | 0.182448 | − | 0.983215i | \(-0.441598\pi\) | ||||
0.182448 | + | 0.983215i | \(0.441598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 43.0000 | 0.125364 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −117.576 | − | 332.554i | −0.322821 | − | 0.913075i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 50.9117i | − | 0.131948i | −0.997821 | − | 0.0659741i | \(-0.978985\pi\) | ||
0.997821 | − | 0.0659741i | \(-0.0210155\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 498.831i | − | 1.22295i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 186.000 | + | 526.087i | 0.432216 | + | 1.22249i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 558.484 | 1.23235 | 0.616173 | − | 0.787611i | \(-0.288682\pi\) | ||||
0.616173 | + | 0.787611i | \(0.288682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −278.000 | −0.583512 | −0.291756 | − | 0.956493i | \(-0.594240\pi\) | ||||
−0.291756 | + | 0.956493i | \(0.594240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 293.939 | + | 363.731i | 0.587822 | + | 0.727393i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 441.235i | 0.841976i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 890.274i | 1.62335i | 0.584111 | + | 0.811674i | \(0.301443\pi\) | ||||
−0.584111 | + | 0.811674i | \(0.698557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 864.000 | − | 305.470i | 1.50744 | − | 0.532961i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −58.7878 | −0.0982651 | −0.0491326 | − | 0.998792i | \(-0.515646\pi\) | ||||
−0.0491326 | + | 0.998792i | \(0.515646\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −422.000 | −0.676594 | −0.338297 | − | 0.941039i | \(-0.609851\pi\) | ||||
−0.338297 | + | 0.941039i | \(0.609851\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 798.534 | − | 282.324i | 1.22942 | − | 0.434667i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 509.117i | − | 0.753497i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 668.572i | 0.952154i | 0.879404 | + | 0.476077i | \(0.157942\pi\) | ||||
−0.879404 | + | 0.476077i | \(0.842058\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 153.000 | − | 712.764i | 0.209877 | − | 0.977728i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 29.3939 | 0.0388723 | 0.0194361 | − | 0.999811i | \(-0.493813\pi\) | ||||
0.0194361 | + | 0.999811i | \(0.493813\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1152.00 | −1.47002 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 29.3939 | + | 83.1384i | 0.0362225 | + | 0.102453i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 373.352i | − | 0.444666i | −0.974971 | − | 0.222333i | \(-0.928633\pi\) | ||
0.974971 | − | 0.222333i | \(-0.0713672\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 450.333i | 0.518766i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −54.0000 | − | 152.735i | −0.0602101 | − | 0.170300i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1822.42 | 1.96817 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1070.00 | −1.12002 | −0.560011 | − | 0.828486i | \(-0.689203\pi\) | ||||
−0.560011 | + | 0.828486i | \(0.689203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −617.271 | + | 498.831i | −0.626648 | + | 0.506408i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1781.91i | 1.75551i | 0.479109 | + | 0.877755i | \(0.340960\pi\) | ||||
−0.479109 | + | 0.877755i | \(0.659040\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.3205i | 0.0165693i | 0.999966 | + | 0.00828466i | \(0.00263712\pi\) | ||||
−0.999966 | + | 0.00828466i | \(0.997363\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1440.00 | − | 509.117i | 1.33838 | − | 0.473188i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1381.51 | 1.24819 | 0.624093 | − | 0.781350i | \(-0.285469\pi\) | ||||
0.624093 | + | 0.781350i | \(0.285469\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −358.000 | −0.314589 | −0.157294 | − | 0.987552i | \(-0.550277\pi\) | ||||
−0.157294 | + | 0.987552i | \(0.550277\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1009.19 | − | 356.802i | 0.862955 | − | 0.305101i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 67.8823i | 0.0565117i | 0.999601 | + | 0.0282559i | \(0.00899532\pi\) | ||||
−0.999601 | + | 0.0282559i | \(0.991005\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2992.98i | − | 2.42693i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 546.000 | − | 441.235i | 0.431433 | − | 0.348651i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1175.76 | −0.905725 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −467.000 | −0.350864 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 529.090 | + | 1496.49i | 0.387857 | + | 1.09703i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 644.881i | − | 0.461440i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 31.1769i | 0.0217835i | 0.999941 | + | 0.0108917i | \(0.00346702\pi\) | ||||
−0.999941 | + | 0.0108917i | \(0.996533\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 162.000 | + | 458.205i | 0.110568 | + | 0.312734i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1734.24 | −1.15665 | −0.578325 | − | 0.815806i | \(-0.696293\pi\) | ||||
−0.578325 | + | 0.815806i | \(0.696293\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1860.00 | 1.21265 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2028.18 | − | 1247.08i | −1.29302 | − | 0.795046i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2274.06i | 1.41814i | 0.705136 | + | 0.709072i | \(0.250886\pi\) | ||||
−0.705136 | + | 0.709072i | \(0.749114\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1541.53i | 0.940651i | 0.882493 | + | 0.470325i | \(0.155863\pi\) | ||||
−0.882493 | + | 0.470325i | \(0.844137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −576.000 | + | 203.647i | −0.344028 | + | 0.121632i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −764.241 | −0.446916 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 288.000 | 0.164946 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −210.656 | + | 74.4782i | −0.118195 | + | 0.0417881i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2358.91i | − | 1.29698i | −0.761225 | − | 0.648488i | \(-0.775402\pi\) | ||
0.761225 | − | 0.648488i | \(-0.224598\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2040.36i | 1.09961i | 0.835292 | + | 0.549807i | \(0.185299\pi\) | ||||
−0.835292 | + | 0.549807i | \(0.814701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1152.00 | + | 1425.53i | 0.608717 | + | 0.753249i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −529.090 | −0.274178 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 106.000 | 0.0538836 | 0.0269418 | − | 0.999637i | \(-0.491423\pi\) | ||||
0.0269418 | + | 0.999637i | \(0.491423\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 88.1816 | + | 249.415i | 0.0439828 | + | 0.124402i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3054.70i | − | 1.49531i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 79.6743i | − | 0.0382857i | −0.999817 | − | 0.0191429i | \(-0.993906\pi\) | ||
0.999817 | − | 0.0191429i | \(-0.00609374\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 864.000 | + | 2443.76i | 0.407650 | + | 1.15301i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3115.75 | −1.44374 | −0.721868 | − | 0.692030i | \(-0.756716\pi\) | ||||
−0.721868 | + | 0.692030i | \(0.756716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1521.00 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1822.42 | − | 2255.13i | −0.814994 | − | 1.00850i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2223.14i | 0.977009i | 0.872561 | + | 0.488504i | \(0.162457\pi\) | ||||
−0.872561 | + | 0.488504i | \(0.837543\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2823.24i | − | 1.21953i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2736.00 | + | 967.322i | −1.16187 | + | 0.410782i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2792.42 | −1.16601 | −0.583003 | − | 0.812470i | \(-0.698122\pi\) | ||||
−0.583003 | + | 0.812470i | \(0.698122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4510.00 | −1.85208 | −0.926038 | − | 0.377431i | \(-0.876808\pi\) | ||||
−0.926038 | + | 0.377431i | \(0.876808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1361.92 | − | 481.510i | 0.550141 | − | 0.194504i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3495.94i | − | 1.38933i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1995.32i | − | 0.780280i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2070.00 | − | 1272.79i | −0.796668 | − | 0.489852i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1881.21 | 0.712667 | 0.356334 | − | 0.934359i | \(-0.384027\pi\) | ||||
0.356334 | + | 0.934359i | \(0.384027\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4994.00 | 1.86257 | 0.931285 | − | 0.364292i | \(-0.118689\pi\) | ||||
0.931285 | + | 0.364292i | \(0.118689\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −764.241 | − | 2161.60i | −0.280659 | − | 0.793822i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2155.26i | − | 0.779472i | −0.920927 | − | 0.389736i | \(-0.872566\pi\) | ||
0.920927 | − | 0.389736i | \(-0.127434\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3973.32i | − | 1.41538i | −0.706521 | − | 0.707692i | \(-0.749736\pi\) | ||
0.706521 | − | 0.707692i | \(-0.250264\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1542.00 | − | 4361.43i | −0.541116 | − | 1.53051i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 293.939 | 0.101628 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5184.00 | 1.76618 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3703.63 | + | 2992.98i | −1.24357 | + | 1.00496i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3156.52i | 1.04470i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4908.63i | 1.60154i | 0.598974 | + | 0.800768i | \(0.295575\pi\) | ||||
−0.598974 | + | 0.800768i | \(0.704425\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 288.000 | − | 101.823i | 0.0926452 | − | 0.0327550i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1587.27 | 0.503492 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −540.000 | −0.168929 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2067.37 | − | 730.925i | 0.637899 | − | 0.225531i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1764.94i | 0.537206i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4021.82i | 1.20772i | 0.797091 | + | 0.603859i | \(0.206371\pi\) | ||||
−0.797091 | + | 0.603859i | \(0.793629\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3423.00 | + | 2766.20i | −1.01422 | + | 0.819615i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2968.78 | 0.868039 | 0.434020 | − | 0.900903i | \(-0.357095\pi\) | ||||
0.434020 | + | 0.900903i | \(0.357095\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −430.000 | −0.124084 | −0.0620419 | − | 0.998074i | \(-0.519761\pi\) | ||||
−0.0620419 | + | 0.998074i | \(0.519761\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 881.816 | + | 2494.15i | 0.251166 | + | 0.710404i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6346.99i | 1.78457i | 0.451471 | + | 0.892286i | \(0.350899\pi\) | ||||
−0.451471 | + | 0.892286i | \(0.649101\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1995.32i | 0.553874i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1158.00 | − | 3275.32i | −0.317385 | − | 0.897700i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4115.14 | −1.11375 | −0.556875 | − | 0.830596i | \(-0.688000\pi\) | ||||
−0.556875 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4690.00 | 1.25357 | 0.626783 | − | 0.779194i | \(-0.284371\pi\) | ||||
0.626783 | + | 0.779194i | \(0.284371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 484.999 | + | 3756.82i | 0.128036 | + | 0.991770i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 729.734i | 0.190290i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2792.07i | − | 0.719251i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −144.000 | + | 50.9117i | −0.0366491 | + | 0.0129574i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1263.94 | 0.317845 | 0.158922 | − | 0.987291i | \(-0.449198\pi\) | ||||
0.158922 | + | 0.987291i | \(0.449198\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5184.00 | 1.28820 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5643.62 | − | 1995.32i | 1.38595 | − | 0.490008i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 271.529i | − | 0.0659047i | −0.999457 | − | 0.0329524i | \(-0.989509\pi\) | ||
0.999457 | − | 0.0329524i | \(-0.0104910\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3568.02i | − | 0.856009i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −288.000 | − | 356.382i | −0.0683017 | − | 0.0845191i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5114.53 | 1.19915 | 0.599574 | − | 0.800320i | \(-0.295337\pi\) | ||||
0.599574 | + | 0.800320i | \(0.295337\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 864.000 | 0.200283 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 646.665 | + | 1829.05i | 0.148222 | + | 0.419235i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3173.50i | 0.719299i | 0.933087 | + | 0.359649i | \(0.117104\pi\) | ||||
−0.933087 | + | 0.359649i | \(0.882896\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 668.572i | 0.149863i | 0.997189 | + | 0.0749314i | \(0.0238738\pi\) | ||||
−0.997189 | + | 0.0749314i | \(0.976126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −780.000 | − | 2206.17i | −0.172922 | − | 0.489098i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4791.20 | 1.05062 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2018.00 | 0.437725 | 0.218863 | − | 0.975756i | \(-0.429765\pi\) | ||||
0.218863 | + | 0.975756i | \(0.429765\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 529.090 | + | 654.715i | 0.113533 | + | 0.140490i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4717.82i | − | 1.00157i | −0.865572 | − | 0.500785i | \(-0.833045\pi\) | ||
0.865572 | − | 0.500785i | \(-0.166955\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5081.84i | − | 1.06743i | −0.845663 | − | 0.533717i | \(-0.820795\pi\) | ||
0.845663 | − | 0.533717i | \(-0.179205\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8928.00 | + | 3156.52i | −1.85561 | + | 0.656057i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5290.90 | 1.08819 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 305.000 | 0.0620802 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5241.91 | − | 1853.29i | 1.05597 | − | 0.373340i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 424.264i | 0.0845931i | 0.999105 | + | 0.0422965i | \(0.0134674\pi\) | ||||
−0.999105 | + | 0.0422965i | \(0.986533\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9477.78i | 1.87057i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2160.00 | − | 3512.91i | 0.422006 | − | 0.686328i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4585.44 | −0.886900 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1620.00 | 0.310217 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3086.36 | − | 8729.54i | −0.585170 | − | 1.65511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4717.82i | − | 0.885709i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3522.99i | 0.654944i | 0.944861 | + | 0.327472i | \(0.106197\pi\) | ||||
−0.944861 | + | 0.327472i | \(0.893803\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −30.0000 | − | 84.8528i | −0.00552311 | − | 0.0156217i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9464.83 | 1.72573 | 0.862864 | − | 0.505437i | \(-0.168669\pi\) | ||||
0.862864 | + | 0.505437i | \(0.168669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3718.00 | −0.671418 | −0.335709 | − | 0.941966i | \(-0.608976\pi\) | ||||
−0.335709 | + | 0.941966i | \(0.608976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6172.71 | + | 4988.31i | −1.10410 | + | 0.892251i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7212.49i | − | 1.27790i | −0.769249 | − | 0.638949i | \(-0.779369\pi\) | ||
0.769249 | − | 0.638949i | \(-0.220631\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 498.831i | 0.0875522i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6768.00 | + | 2392.85i | −1.17680 | + | 0.416062i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7289.68 | 1.25575 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4238.00 | −0.723329 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1753.83 | − | 620.074i | 0.296597 | − | 0.104863i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2036.47i | 0.341259i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1541.53i | 0.255982i | 0.991775 | + | 0.127991i | \(0.0408528\pi\) | ||||
−0.991775 | + | 0.127991i | \(0.959147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4326.00 | + | 3495.94i | −0.711902 | + | 0.575304i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15108.5 | −2.46407 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2530.00 | 0.408955 | 0.204478 | − | 0.978871i | \(-0.434450\pi\) | ||||
0.204478 | + | 0.978871i | \(0.434450\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −117.576 | − | 332.554i | −0.0188372 | − | 0.0532798i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 916.410i | − | 0.145532i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6685.72i | 1.05246i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5184.00 | + | 14662.6i | 0.808977 | + | 2.28813i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5555.44 | −0.859458 | −0.429729 | − | 0.902958i | \(-0.641391\pi\) | ||||
−0.429729 | + | 0.902958i | \(0.641391\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7786.00 | 1.19420 | 0.597099 | − | 0.802168i | \(-0.296320\pi\) | ||||
0.597099 | + | 0.802168i | \(0.296320\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1910.60 | + | 3107.30i | −0.290542 | + | 0.472522i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 407.294i | − | 0.0614109i | −0.999528 | − | 0.0307054i | \(-0.990225\pi\) | ||
0.999528 | − | 0.0307054i | \(-0.00977538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 997.661i | − | 0.149156i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5760.00 | − | 2036.47i | 0.853926 | − | 0.301908i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8759.38 | −1.28775 | −0.643875 | − | 0.765131i | \(-0.722674\pi\) | ||||
−0.643875 | + | 0.765131i | \(0.722674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4673.00 | −0.681295 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2287.82 | − | 808.868i | 0.330798 | − | 0.116955i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 7161.58i | − | 1.02700i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12578.2i | − | 1.78903i | −0.447037 | − | 0.894515i | \(-0.647521\pi\) | ||
0.447037 | − | 0.894515i | \(-0.352479\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5184.00 | − | 6414.87i | −0.731350 | − | 0.905000i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 881.816 | 0.123401 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4258.00 | 0.591075 | 0.295537 | − | 0.955331i | \(-0.404501\pi\) | ||||
0.295537 | + | 0.955331i | \(0.404501\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1116.97 | + | 3159.26i | 0.153813 | + | 0.435049i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 441.235i | − | 0.0602778i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2726.25i | − | 0.369493i | −0.982786 | − | 0.184747i | \(-0.940854\pi\) | ||
0.982786 | − | 0.184747i | \(-0.0591465\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −54.0000 | − | 152.735i | −0.00726116 | − | 0.0205377i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4232.72 | 0.564704 | 0.282352 | − | 0.959311i | \(-0.408885\pi\) | ||||
0.282352 | + | 0.959311i | \(0.408885\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8640.00 | 1.14373 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1587.27 | − | 1964.15i | −0.208489 | − | 0.257993i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5447.55i | 0.710030i | 0.934861 | + | 0.355015i | \(0.115524\pi\) | ||||
−0.934861 | + | 0.355015i | \(0.884476\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 11971.9i | − | 1.54846i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8496.00 | − | 3003.79i | 1.09050 | − | 0.385550i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11346.0 | −1.44527 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13574.0 | −1.71602 | −0.858009 | − | 0.513634i | \(-0.828299\pi\) | ||||
−0.858009 | + | 0.513634i | \(0.828299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9112.10 | + | 3221.61i | −1.14330 | + | 0.404217i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11743.6i | 1.46247i | 0.682128 | + | 0.731233i | \(0.261055\pi\) | ||||
−0.682128 | + | 0.731233i | \(0.738945\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 810.600i | 0.100196i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12096.0 | + | 2596.50i | 1.48409 | + | 0.318570i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6055.14 | 0.737450 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2890.00 | 0.349392 | 0.174696 | − | 0.984622i | \(-0.444106\pi\) | ||||
0.174696 | + | 0.984622i | \(0.444106\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3938.78 | − | 11140.6i | −0.472715 | − | 1.33704i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9673.22i | 1.15251i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 498.831i | 0.0590039i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2670.00 | − | 7551.90i | −0.313550 | − | 0.886854i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8318.47 | −0.969890 | −0.484945 | − | 0.874545i | \(-0.661160\pi\) | ||||
−0.484945 | + | 0.874545i | \(0.661160\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10414.0 | −1.20558 | −0.602788 | − | 0.797902i | \(-0.705943\pi\) | ||||
−0.602788 | + | 0.797902i | \(0.705943\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2469.09 | − | 1995.32i | 0.283809 | − | 0.229352i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 11064.8i | − | 1.26288i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4815.10i | − | 0.545712i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3744.00 | − | 1323.70i | 0.421357 | − | 0.148972i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13050.9 | −1.45856 | −0.729279 | − | 0.684216i | \(-0.760145\pi\) | ||||
−0.729279 | + | 0.684216i | \(0.760145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9214.00 | −1.02262 | −0.511312 | − | 0.859395i | \(-0.670841\pi\) | ||||
−0.511312 | + | 0.859395i | \(0.670841\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1410.91 | + | 498.831i | −0.155512 | + | 0.0549818i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18939.1i | 2.07319i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7326.57i | − | 0.796534i | −0.917270 | − | 0.398267i | \(-0.869612\pi\) | ||
0.917270 | − | 0.398267i | \(-0.130388\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 903.000 | − | 729.734i | 0.0975057 | − | 0.0787965i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2204.54 | 0.236435 | 0.118218 | − | 0.992988i | \(-0.462282\pi\) | ||||
0.118218 | + | 0.992988i | \(0.462282\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6336.00 | 0.674956 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4085.75 | + | 11556.2i | 0.432325 | + | 1.22280i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2851.05i | 0.299665i | 0.988711 | + | 0.149832i | \(0.0478734\pi\) | ||||
−0.988711 | + | 0.149832i | \(0.952127\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8978.95i | 0.937477i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3534.00 | − | 9995.66i | −0.366538 | − | 1.03673i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7642.41 | −0.787432 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.0000 | −0.00388964 | −0.00194482 | − | 0.999998i | \(-0.500619\pi\) | ||||
−0.00194482 | + | 0.999998i | \(0.500619\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8112.71 | − | 4988.31i | −0.824987 | − | 0.507264i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 15833.5i | − | 1.59966i | −0.600230 | − | 0.799828i | \(-0.704924\pi\) | ||
0.600230 | − | 0.799828i | \(-0.295076\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11365.7i | 1.14084i | 0.821353 | + | 0.570421i | \(0.193220\pi\) | ||||
−0.821353 | + | 0.570421i | \(0.806780\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2592.00 | − | 916.410i | 0.258497 | − | 0.0913925i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 499.696 | 0.0495143 | 0.0247571 | − | 0.999693i | \(-0.492119\pi\) | ||||
0.0247571 | + | 0.999693i | \(0.492119\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15420.0 | −1.51819 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −519.292 | + | 183.597i | −0.0508019 | + | 0.0179612i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2749.23i | 0.267251i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17504.1i | 1.69083i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −864.000 | − | 1069.15i | −0.0829347 | − | 0.102626i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8700.59 | 0.829937 | 0.414969 | − | 0.909836i | \(-0.363793\pi\) | ||||
0.414969 | + | 0.909836i | \(0.363793\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5356.00 | −0.507718 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5290.90 | + | 14964.9i | 0.498435 | + | 1.40979i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 18158.5i | − | 1.70007i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4007.97i | 0.372933i | 0.982461 | + | 0.186466i | \(0.0597035\pi\) | ||||
−0.982461 | + | 0.186466i | \(0.940296\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 138.000 | + | 390.323i | 0.0127619 | + | 0.0360961i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16901.5 | 1.55347 | 0.776734 | − | 0.629828i | \(-0.216875\pi\) | ||||
0.776734 | + | 0.629828i | \(0.216875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1152.00 | 0.105240 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8465.44 | − | 10475.4i | −0.768673 | − | 0.951184i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1018.23i | − | 0.0918994i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 12439.6i | − | 1.11598i | −0.829849 | − | 0.557988i | \(-0.811573\pi\) | ||
0.829849 | − | 0.557988i | \(-0.188427\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15264.0 | − | 5396.64i | 1.36117 | − | 0.481246i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12756.9 | 1.13082 | 0.565411 | − | 0.824809i | \(-0.308717\pi\) | ||||
0.565411 | + | 0.824809i | \(0.308717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30240.0 | −2.66468 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7451.35 | − | 2634.45i | 0.652714 | − | 0.230769i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5549.37i | 0.483245i | 0.970370 | + | 0.241622i | \(0.0776796\pi\) | ||||
−0.970370 | + | 0.241622i | \(0.922320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7309.25i | − | 0.632764i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12834.0 | + | 7891.31i | 1.10455 | + | 0.679162i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −293.939 | −0.0251505 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3456.00 | −0.293994 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3850.60 | − | 10891.1i | −0.325670 | − | 0.921133i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11506.0i | 0.967541i | 0.875195 | + | 0.483770i | \(0.160733\pi\) | ||||
−0.875195 | + | 0.483770i | \(0.839267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 17441.8i | − | 1.45827i | −0.684371 | − | 0.729134i | \(-0.739923\pi\) | ||
0.684371 | − | 0.729134i | \(-0.260077\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4890.00 | + | 13831.0i | 0.406509 | + | 1.14978i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2116.36 | −0.174934 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18937.0 | 1.55642 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11728.2 | − | 9477.78i | 0.958491 | − | 0.774578i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 7942.22i | − | 0.645433i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23445.0i | 1.89461i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13680.0 | − | 4836.61i | 1.09932 | − | 0.388669i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1263.94 | −0.101005 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6794.00 | 0.539920 | 0.269960 | − | 0.962871i | \(-0.412989\pi\) | ||||
0.269960 | + | 0.962871i | \(0.412989\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22094.4 | − | 7811.55i | 1.74615 | − | 0.617358i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6075.46i | − | 0.477512i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3910.97i | 0.305706i | 0.988249 | + | 0.152853i | \(0.0488461\pi\) | ||||
−0.988249 | + | 0.152853i | \(0.951154\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5838.00 | + | 4717.82i | −0.453843 | + | 0.366760i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1822.42 | −0.140903 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11580.0 | −0.890473 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6055.14 | + | 17126.5i | 0.463110 | + | 1.30987i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22587.8i | 1.71827i | 0.511749 | + | 0.859135i | \(0.328998\pi\) | ||||
−0.511749 | + | 0.859135i | \(0.671002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2431.80i | − | 0.183997i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3456.00 | + | 9775.04i | 0.260093 | + | 0.735655i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8729.98 | 0.653508 | 0.326754 | − | 0.945109i | \(-0.394045\pi\) | ||||
0.326754 | + | 0.945109i | \(0.394045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1152.00 | −0.0857788 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12345.4 | + | 2650.04i | 0.914390 | + | 0.196281i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 16122.0i | − | 1.18782i | −0.804531 | − | 0.593911i | \(-0.797583\pi\) | ||
0.804531 | − | 0.593911i | \(-0.202417\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9495.10i | 0.695898i | 0.937513 | + | 0.347949i | \(0.113122\pi\) | ||||
−0.937513 | + | 0.347949i | \(0.886878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9216.00 | + | 3258.35i | −0.671909 | + | 0.237556i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28747.2 | 2.08494 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8974.00 | −0.647474 | −0.323737 | − | 0.946147i | \(-0.604939\pi\) | ||||
−0.323737 | + | 0.946147i | \(0.604939\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24465.5 | + | 8649.86i | −1.75605 | + | 0.620857i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 509.117i | 0.0363541i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1496.49i | 0.106309i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7488.00 | + | 9265.93i | 0.529215 | + | 0.654870i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4908.78 | 0.345157 | 0.172578 | − | 0.984996i | \(-0.444790\pi\) | ||||
0.172578 | + | 0.984996i | \(0.444790\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3348.00 | 0.234214 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3733.02 | + | 10558.6i | 0.259824 | + | 0.734893i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14730.4i | − | 1.02008i | −0.860151 | − | 0.510040i | \(-0.829631\pi\) | ||
0.860151 | − | 0.510040i | \(-0.170369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 19953.2i | − | 1.37479i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6882.00 | + | 19465.2i | 0.471795 | + | 1.33444i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10052.7 | −0.685714 | −0.342857 | − | 0.939388i | \(-0.611395\pi\) | ||||
−0.342857 | + | 0.939388i | \(0.611395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23690.0 | 1.60788 | 0.803939 | − | 0.594711i | \(-0.202734\pi\) | ||||
0.803939 | + | 0.594711i | \(0.202734\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15108.5 | + | 18695.8i | 1.02034 | + | 1.26260i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 7925.25i | − | 0.532574i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22589.4i | 1.51050i | 0.655435 | + | 0.755252i | \(0.272485\pi\) | ||||
−0.655435 | + | 0.755252i | \(0.727515\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1440.00 | + | 509.117i | −0.0958157 | + | 0.0338760i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3056.96 | 0.202408 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9422.00 | −0.620801 | −0.310400 | − | 0.950606i | \(-0.600463\pi\) | ||||
−0.310400 | + | 0.950606i | \(0.600463\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25396.3 | + | 8978.95i | −1.66517 | + | 0.588726i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 984.293i | − | 0.0642239i | −0.999484 | − | 0.0321119i | \(-0.989777\pi\) | ||
0.999484 | − | 0.0321119i | \(-0.0102233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12238.7i | 0.794691i | 0.917669 | + | 0.397345i | \(0.130069\pi\) | ||||
−0.917669 | + | 0.397345i | \(0.869931\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12960.0 | − | 21077.4i | 0.837467 | − | 1.36201i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6466.65 | 0.415860 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9431.00 | −0.603584 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5467.26 | − | 15463.7i | −0.348232 | − | 0.984948i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 13983.7i | − | 0.886436i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 13922.2i | − | 0.878344i | −0.898403 | − | 0.439172i | \(-0.855272\pi\) | ||
0.898403 | − | 0.439172i | \(-0.144728\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8502.00 | − | 24047.3i | −0.533845 | − | 1.50994i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −529.090 | −0.0330650 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1118.00 | 0.0695397 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1234.54 | + | 997.661i | −0.0764284 | + | 0.0617635i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16427.5i | 1.01224i | 0.862462 | + | 0.506121i | \(0.168921\pi\) | ||||
−0.862462 | + | 0.506121i | \(0.831079\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1465.31i | − | 0.0898700i | −0.998990 | − | 0.0449350i | \(-0.985692\pi\) | ||
0.998990 | − | 0.0449350i | \(-0.0143081\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7776.00 | + | 2749.23i | −0.474697 | + | 0.167831i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12286.6 | −0.746581 | −0.373290 | − | 0.927715i | \(-0.621770\pi\) | ||||
−0.373290 | + | 0.927715i | \(0.621770\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16416.0 | −0.992888 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2645.45 | − | 935.307i | 0.159268 | − | 0.0563097i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 8502.25i | − | 0.509523i | −0.967004 | − | 0.254762i | \(-0.918003\pi\) | ||
0.967004 | − | 0.254762i | \(-0.0819970\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 29431.0i | − | 1.75567i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8862.00 | + | 7161.58i | −0.526240 | + | 0.425266i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17136.6 | −1.01297 | −0.506486 | − | 0.862248i | \(-0.669056\pi\) | ||||
−0.506486 | + | 0.862248i | \(0.669056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10018.0 | 0.589493 | 0.294747 | − | 0.955575i | \(-0.404765\pi\) | ||||
0.294747 | + | 0.955575i | \(0.404765\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3056.96 | − | 8646.40i | −0.179069 | − | 0.506483i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 31565.2i | 1.84067i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2992.98i | 0.173746i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6966.00 | − | 19702.8i | −0.402573 | − | 1.13865i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8171.50 | 0.470130 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1682.00 | 0.0963393 | 0.0481696 | − | 0.998839i | \(-0.484661\pi\) | ||||
0.0481696 | + | 0.998839i | \(0.484661\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11978.0 | − | 19480.4i | 0.683013 | − | 1.11081i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9113.19i | 0.517354i | 0.965964 | + | 0.258677i | \(0.0832865\pi\) | ||||
−0.965964 | + | 0.258677i | \(0.916714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 18532.9i | − | 1.04747i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14544.0 | + | 5142.08i | −0.818395 | + | 0.289346i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23250.6 | 1.30257 | 0.651287 | − | 0.758832i | \(-0.274229\pi\) | ||||
0.651287 | + | 0.758832i | \(0.274229\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38592.0 | −2.15259 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2106.56 | − | 744.782i | 0.116987 | − | 0.0413613i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1323.70i | − | 0.0731917i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25222.1i | 1.38856i | 0.719705 | + | 0.694280i | \(0.244277\pi\) | ||||
−0.719705 | + | 0.694280i | \(0.755723\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8640.00 | − | 10691.5i | −0.473602 | − | 0.586053i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26160.6 | −1.42781 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20736.0 | 1.12688 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10993.3 | − | 31093.8i | −0.594857 | − | 1.68251i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16410.5i | 0.884190i | 0.896968 | + | 0.442095i | \(0.145765\pi\) | ||||
−0.896968 | + | 0.442095i | \(0.854235\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22121.8i | 1.18682i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3456.00 | − | 9775.04i | −0.184625 | − | 0.522198i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30863.6 | −1.64179 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27602.0 | 1.46208 | 0.731040 | − | 0.682334i | \(-0.239035\pi\) | ||||
0.731040 | + | 0.682334i | \(0.239035\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11346.0 | + | 14040.0i | 0.598466 | + | 0.740564i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5498.46i | − | 0.288806i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 12969.6i | − | 0.678371i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20160.0 | − | 7127.64i | 1.05005 | − | 0.371250i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31627.8 | −1.64050 | −0.820249 | − | 0.572006i | \(-0.806165\pi\) | ||||
−0.820249 | + | 0.572006i | \(0.806165\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −300.000 | −0.0154960 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22976.2 | + | 8123.32i | −1.18187 | + | 0.417855i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2766.20i | 0.141702i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 27279.8i | − | 1.39168i | −0.718197 | − | 0.695840i | \(-0.755032\pi\) | ||
0.718197 | − | 0.695840i | \(-0.244968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8883.00 | − | 17564.5i | −0.451303 | − | 0.892371i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6349.08 | 0.321244 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15914.0 | 0.801906 | 0.400953 | − | 0.916099i | \(-0.368679\pi\) | ||||
0.400953 | + | 0.916099i | \(0.368679\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1263.94 | − | 3574.95i | −0.0634299 | − | 0.179407i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 26168.6i | − | 1.30791i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2275.91i | 0.113289i | 0.998394 | + | 0.0566447i | \(0.0180402\pi\) | ||||
−0.998394 | + | 0.0566447i | \(0.981960\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4836.00 | + | 13678.3i | 0.239750 | + | 0.678116i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8641.80 | 0.426698 | 0.213349 | − | 0.976976i | \(-0.431563\pi\) | ||||
0.213349 | + | 0.976976i | \(0.431563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40032.0 | 1.96867 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 617.271 | − | 498.831i | 0.0302340 | − | 0.0244327i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23928.5i | 1.16733i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16631.2i | 0.808095i | 0.914738 | + | 0.404048i | \(0.132397\pi\) | ||||
−0.914738 | + | 0.404048i | \(0.867603\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6192.00 | + | 2189.20i | −0.299667 | + | 0.105948i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34626.0 | −1.66910 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11422.0 | −0.548401 | −0.274201 | − | 0.961673i | \(-0.588413\pi\) | ||||
−0.274201 | + | 0.961673i | \(0.588413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25396.3 | + | 8978.95i | −1.21453 | + | 0.429401i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12660.0i | 0.603057i | 0.953457 | + | 0.301528i | \(0.0974968\pi\) | ||||
−0.953457 | + | 0.301528i | \(0.902503\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 6200.74i | − | 0.294210i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −24192.0 | + | 19550.1i | −1.14335 | + | 0.923967i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14520.6 | 0.683582 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18818.0 | 0.882437 | 0.441219 | − | 0.897400i | \(-0.354546\pi\) | ||||
0.441219 | + | 0.897400i | \(0.354546\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 470.302 | + | 1330.22i | 0.0219682 | + | 0.0621356i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1917.67i | 0.0892289i | 0.999004 | + | 0.0446144i | \(0.0142059\pi\) | ||||
−0.999004 | + | 0.0446144i | \(0.985794\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5081.84i | − | 0.235542i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6180.00 | + | 17479.7i | 0.285336 | + | 0.807053i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32803.6 | −1.50874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1728.00 | 0.0791712 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2028.18 | + | 1247.08i | 0.0925685 | + | 0.0569181i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1798.88i | 0.0817895i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19845.8i | 0.898892i | 0.893308 | + | 0.449446i | \(0.148379\pi\) | ||||
−0.893308 | + | 0.449446i | \(0.851621\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25056.0 | + | 8858.63i | −1.13057 | + | 0.399716i | ||||
\(790\) | 0 | 0 |