Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(509,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.509");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.k (of order \(6\), degree \(2\), 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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.24 | ||
Character | \(\chi\) | \(=\) | 588.521 |
Dual form | 588.4.k.e.509.24 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 5.19498 | + | 0.110261i | 0.999775 | + | 0.0212197i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.87287 | − | 8.44005i | −0.435842 | − | 0.754901i | 0.561522 | − | 0.827462i | \(-0.310216\pi\) |
−0.997364 | + | 0.0725609i | \(0.976883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 26.9757 | + | 1.14560i | 0.999099 | + | 0.0424298i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −42.9817 | − | 24.8155i | −1.17813 | − | 0.680195i | −0.222551 | − | 0.974921i | \(-0.571438\pi\) |
−0.955582 | + | 0.294726i | \(0.904772\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.47499i | − | 0.0528029i | −0.999651 | − | 0.0264015i | \(-0.991595\pi\) | ||
0.999651 | − | 0.0264015i | \(-0.00840482\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −24.3838 | − | 44.3832i | −0.419726 | − | 0.763980i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.7602 | − | 42.8858i | 0.353248 | − | 0.611844i | −0.633568 | − | 0.773687i | \(-0.718410\pi\) |
0.986817 | + | 0.161843i | \(0.0517438\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −96.0631 | + | 55.4620i | −1.15991 | + | 0.669677i | −0.951284 | − | 0.308317i | \(-0.900234\pi\) |
−0.208631 | + | 0.977994i | \(0.566901\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −149.767 | + | 86.4683i | −1.35777 | + | 0.783908i | −0.989323 | − | 0.145741i | \(-0.953443\pi\) |
−0.368446 | + | 0.929649i | \(0.620110\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15.0103 | − | 25.9987i | 0.120083 | − | 0.207989i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 140.012 | + | 8.92575i | 0.997974 | + | 0.0636208i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 134.538i | − | 0.861488i | −0.902474 | − | 0.430744i | \(-0.858251\pi\) | ||
0.902474 | − | 0.430744i | \(-0.141749\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.18514 | − | 1.26159i | −0.0126601 | − | 0.00730929i | 0.493657 | − | 0.869657i | \(-0.335660\pi\) |
−0.506317 | + | 0.862348i | \(0.668993\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −220.553 | − | 133.655i | −1.16343 | − | 0.705042i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 58.5515 | + | 101.414i | 0.260157 | + | 0.450605i | 0.966283 | − | 0.257481i | \(-0.0828924\pi\) |
−0.706127 | + | 0.708086i | \(0.749559\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.272894 | − | 12.8575i | 0.00112046 | − | 0.0527910i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −160.696 | −0.612111 | −0.306055 | − | 0.952014i | \(-0.599009\pi\) | ||||
−0.306055 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −442.678 | −1.56995 | −0.784973 | − | 0.619530i | \(-0.787323\pi\) | ||||
−0.784973 | + | 0.619530i | \(0.787323\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −121.780 | − | 233.259i | −0.403420 | − | 0.772714i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −155.814 | − | 269.879i | −0.483572 | − | 0.837571i | 0.516250 | − | 0.856438i | \(-0.327327\pi\) |
−0.999822 | + | 0.0188668i | \(0.993994\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 133.357 | − | 220.061i | 0.366152 | − | 0.604210i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 248.907 | + | 143.706i | 0.645093 | + | 0.372445i | 0.786574 | − | 0.617496i | \(-0.211853\pi\) |
−0.141480 | + | 0.989941i | \(0.545186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 483.690i | 1.18583i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −505.161 | + | 277.532i | −1.17386 | + | 0.644913i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −276.360 | + | 478.670i | −0.609814 | + | 1.05623i | 0.381457 | + | 0.924387i | \(0.375423\pi\) |
−0.991271 | + | 0.131842i | \(0.957911\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −504.937 | + | 291.525i | −1.05984 | + | 0.611901i | −0.925389 | − | 0.379018i | \(-0.876262\pi\) |
−0.134455 | + | 0.990920i | \(0.542928\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −20.8890 | + | 12.0603i | −0.0398610 | + | 0.0230138i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 450.723 | − | 780.675i | 0.821859 | − | 1.42350i | −0.0824369 | − | 0.996596i | \(-0.526270\pi\) |
0.904296 | − | 0.426906i | \(-0.140396\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −787.573 | + | 432.688i | −1.37410 | + | 0.754920i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 984.717i | − | 1.64598i | −0.568058 | − | 0.822988i | \(-0.692305\pi\) | ||
0.568058 | − | 0.822988i | \(-0.307695\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −178.030 | − | 102.786i | −0.285436 | − | 0.164797i | 0.350446 | − | 0.936583i | \(-0.386030\pi\) |
−0.635882 | + | 0.771786i | \(0.719363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 80.8451 | − | 133.408i | 0.124469 | − | 0.205394i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −321.643 | − | 557.103i | −0.458072 | − | 0.793405i | 0.540787 | − | 0.841160i | \(-0.318127\pi\) |
−0.998859 | + | 0.0477551i | \(0.984793\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 726.375 | + | 61.8069i | 0.996399 | + | 0.0847832i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −351.902 | −0.465376 | −0.232688 | − | 0.972551i | \(-0.574752\pi\) | ||||
−0.232688 | + | 0.972551i | \(0.574752\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −482.612 | −0.615842 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.8343 | − | 698.924i | 0.0182805 | − | 0.861294i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 544.376 | + | 942.887i | 0.648357 | + | 1.12299i | 0.983515 | + | 0.180825i | \(0.0578767\pi\) |
−0.335159 | + | 0.942162i | \(0.608790\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.2126 | − | 6.79487i | −0.0125021 | − | 0.00757629i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 936.205 | + | 540.518i | 1.01108 | + | 0.583747i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1365.09i | 1.42891i | 0.699683 | + | 0.714454i | \(0.253325\pi\) | ||||
−0.699683 | + | 0.714454i | \(0.746675\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1131.03 | − | 718.654i | −1.14821 | − | 0.729571i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 651.926 | − | 1129.17i | 0.642268 | − | 1.11244i | −0.342658 | − | 0.939460i | \(-0.611327\pi\) |
0.984925 | − | 0.172980i | \(-0.0553396\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1094.23 | + | 631.752i | −1.04677 | + | 0.604354i | −0.921744 | − | 0.387800i | \(-0.873235\pi\) |
−0.125027 | + | 0.992153i | \(0.539902\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1267.25 | − | 731.647i | 1.14495 | − | 0.661037i | 0.197299 | − | 0.980343i | \(-0.436783\pi\) |
0.947652 | + | 0.319306i | \(0.103450\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1119.89 | − | 1939.71i | 0.984093 | − | 1.70450i | 0.338193 | − | 0.941077i | \(-0.390184\pi\) |
0.645900 | − | 0.763422i | \(-0.276482\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 292.992 | + | 533.300i | 0.250536 | + | 0.456024i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 281.355i | 0.234227i | 0.993119 | + | 0.117114i | \(0.0373642\pi\) | ||||
−0.993119 | + | 0.117114i | \(0.962636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1459.59 | + | 842.697i | 1.18355 | + | 0.683321i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.83536 | − | 66.7645i | 0.00224042 | − | 0.0527554i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 566.115 | + | 980.541i | 0.425331 | + | 0.736695i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −834.814 | − | 17.7185i | −0.611973 | − | 0.0129888i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1510.79 | −1.08103 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −576.095 | −0.402521 | −0.201261 | − | 0.979538i | \(-0.564504\pi\) | ||||
−0.201261 | + | 0.979538i | \(0.564504\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2299.70 | − | 48.8099i | −1.56959 | − | 0.0333137i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1142.71 | − | 1979.23i | −0.762130 | − | 1.32005i | −0.941750 | − | 0.336313i | \(-0.890820\pi\) |
0.179620 | − | 0.983736i | \(-0.442513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −606.925 | − | 1225.20i | −0.386932 | − | 0.781101i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −892.802 | − | 515.459i | −0.556768 | − | 0.321450i | 0.195079 | − | 0.980787i | \(-0.437504\pi\) |
−0.751847 | + | 0.659337i | \(0.770837\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 234.497i | 0.143092i | 0.997437 | + | 0.0715460i | \(0.0227933\pi\) | ||||
−0.997437 | + | 0.0715460i | \(0.977207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −779.697 | − | 1419.19i | −0.465690 | − | 0.847644i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −61.4180 | + | 106.379i | −0.0359163 | + | 0.0622088i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1135.51 | + | 655.587i | −0.650338 | + | 0.375473i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2015.55 | + | 1163.68i | −1.10819 | + | 0.639814i | −0.938360 | − | 0.345660i | \(-0.887655\pi\) |
−0.169830 | + | 0.985473i | \(0.554322\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −527.571 | + | 913.779i | −0.284325 | + | 0.492466i | −0.972445 | − | 0.233131i | \(-0.925103\pi\) |
0.688120 | + | 0.725597i | \(0.258436\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 717.052 | − | 1128.51i | 0.378891 | − | 0.596305i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.5902i | 0.0127428i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 38.3884 | + | 22.1635i | 0.0195142 | + | 0.0112665i | 0.509725 | − | 0.860337i | \(-0.329747\pi\) |
−0.490211 | + | 0.871604i | \(0.663080\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1277.22 | + | 773.996i | 0.637045 | + | 0.386050i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 126.057 | + | 218.337i | 0.0605738 | + | 0.104917i | 0.894722 | − | 0.446623i | \(-0.147374\pi\) |
−0.834148 | + | 0.551540i | \(0.814040\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −53.3320 | + | 2512.76i | −0.0251630 | + | 1.18556i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1657.35 | 0.767962 | 0.383981 | − | 0.923341i | \(-0.374553\pi\) | ||||
0.383981 | + | 0.923341i | \(0.374553\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2190.87 | 0.997212 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2654.90 | + | 1386.08i | −1.18728 | + | 0.619859i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1663.55 | − | 2881.36i | −0.731084 | − | 1.26627i | −0.956420 | − | 0.291994i | \(-0.905681\pi\) |
0.225336 | − | 0.974281i | \(-0.427652\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1488.46 | + | 2456.21i | −0.632090 | + | 1.04305i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −372.577 | − | 215.108i | −0.155574 | − | 0.0898206i | 0.420192 | − | 0.907435i | \(-0.361963\pi\) |
−0.575766 | + | 0.817615i | \(0.695296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2230.49i | − | 0.915971i | −0.888960 | − | 0.457986i | \(-0.848571\pi\) | ||
0.888960 | − | 0.457986i | \(-0.151429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2655.28 | + | 1458.79i | −1.07259 | + | 0.589274i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 570.627 | − | 988.355i | 0.226775 | − | 0.392785i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2128.47 | + | 1228.87i | −0.832346 | + | 0.480555i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1003.30 | − | 579.256i | 0.380086 | − | 0.219442i | −0.297770 | − | 0.954638i | \(-0.596243\pi\) |
0.677855 | + | 0.735195i | \(0.262910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1127.84 | − | 1953.48i | 0.420641 | − | 0.728572i | −0.575361 | − | 0.817899i | \(-0.695138\pi\) |
0.996002 | + | 0.0893276i | \(0.0284718\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −109.848 | + | 60.3497i | −0.0403404 | + | 0.0221627i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3280.44i | 1.18641i | 0.805053 | + | 0.593203i | \(0.202137\pi\) | ||||
−0.805053 | + | 0.593203i | \(0.797863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3818.10 | + | 2204.38i | 1.36009 | + | 0.785248i | 0.989635 | − | 0.143603i | \(-0.0458687\pi\) |
0.370454 | + | 0.928851i | \(0.379202\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2427.58 | − | 4005.90i | 0.851880 | − | 1.40574i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 783.051 | + | 1356.28i | 0.266784 | + | 0.462083i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4139.14 | + | 2160.97i | −1.38981 | + | 0.725592i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5505.27 | 1.82204 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5620.46 | 1.83378 | 0.916892 | − | 0.399135i | \(-0.130689\pi\) | ||||
0.916892 | + | 0.399135i | \(0.130689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 108.576 | − | 5115.59i | 0.0349271 | − | 1.64561i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2157.11 | + | 3736.22i | 0.684249 | + | 1.18515i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −913.530 | − | 553.600i | −0.281875 | − | 0.170816i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −106.142 | − | 61.2811i | −0.0323072 | − | 0.0186525i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1134.63i | − | 0.340718i | −0.985382 | − | 0.170359i | \(-0.945507\pi\) | ||
0.985382 | − | 0.170359i | \(-0.0544928\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 434.699 | − | 684.136i | 0.128800 | − | 0.202707i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1061.60 | + | 1838.75i | −0.310400 | + | 0.537629i | −0.978449 | − | 0.206488i | \(-0.933796\pi\) |
0.668049 | + | 0.744118i | \(0.267130\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2299.77 | − | 1327.77i | 0.663638 | − | 0.383152i | −0.130023 | − | 0.991511i | \(-0.541505\pi\) |
0.793662 | + | 0.608359i | \(0.208172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2734.14 | − | 1578.56i | 0.768754 | − | 0.443840i | −0.0636761 | − | 0.997971i | \(-0.520282\pi\) |
0.832430 | + | 0.554130i | \(0.186949\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1518.53 | + | 2630.16i | −0.421522 | + | 0.730098i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1609.51 | − | 2929.60i | −0.441133 | − | 0.802946i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2040.14i | − | 0.552157i | −0.961135 | − | 0.276079i | \(-0.910965\pi\) | ||
0.961135 | − | 0.276079i | \(-0.0890351\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3958.64 | + | 2285.52i | 1.05809 | + | 0.610886i | 0.924902 | − | 0.380205i | \(-0.124147\pi\) |
0.133184 | + | 0.991091i | \(0.457480\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3766.69 | + | 401.177i | 0.994376 | + | 0.105907i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 137.268 | + | 237.755i | 0.0353609 | + | 0.0612469i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1828.12 | − | 38.8009i | −0.465272 | − | 0.00987513i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5848.44 | −1.47072 | −0.735359 | − | 0.677678i | \(-0.762986\pi\) | ||||
−0.735359 | + | 0.677678i | \(0.762986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8583.01 | 2.13284 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2507.16 | − | 53.2131i | −0.615704 | − | 0.0130680i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3884.44 | + | 6728.05i | 0.942820 | + | 1.63301i | 0.760058 | + | 0.649855i | \(0.225170\pi\) |
0.182762 | + | 0.983157i | \(0.441496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 154.128 | − | 3629.26i | 0.0365527 | − | 0.860712i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4077.64 | − | 2354.23i | −0.956038 | − | 0.551969i | −0.0610865 | − | 0.998132i | \(-0.519457\pi\) |
−0.894951 | + | 0.446164i | \(0.852790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2801.05i | − | 0.649309i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2724.06 | + | 4958.30i | 0.624381 | + | 1.13649i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2054.29 | + | 3558.14i | −0.465622 | + | 0.806481i | −0.999229 | − | 0.0392514i | \(-0.987503\pi\) |
0.533607 | + | 0.845732i | \(0.320836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 700.809 | − | 404.612i | 0.157089 | − | 0.0906953i | −0.419395 | − | 0.907804i | \(-0.637758\pi\) |
0.576484 | + | 0.817109i | \(0.304424\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1290.34 | + | 744.978i | −0.282947 | + | 0.163359i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3727.43 | − | 6456.10i | 0.808518 | − | 1.40039i | −0.105372 | − | 0.994433i | \(-0.533603\pi\) |
0.913890 | − | 0.405962i | \(-0.133063\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −57.5003 | − | 36.5355i | −0.0123385 | − | 0.00783988i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1289.89i | 0.273837i | 0.990582 | + | 0.136919i | \(0.0437198\pi\) | ||||
−0.990582 | + | 0.136919i | \(0.956280\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7466.08 | + | 4310.54i | 1.56824 | + | 0.905424i | 0.996374 | + | 0.0850780i | \(0.0271139\pi\) |
0.571867 | + | 0.820346i | \(0.306219\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4803.97 | + | 2911.21i | 0.998466 | + | 0.605071i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1230.37 | + | 2131.06i | 0.250431 | + | 0.433760i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −150.516 | + | 7091.62i | −0.0303209 | + | 1.42859i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6187.72 | 1.23376 | 0.616878 | − | 0.787059i | \(-0.288397\pi\) | ||||
0.616878 | + | 0.787059i | \(0.288397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5386.66 | 1.06313 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5796.45 | − | 3858.10i | −1.13247 | − | 0.753771i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 214.008 | + | 370.673i | 0.0413926 | + | 0.0716941i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3511.25 | − | 5794.13i | 0.665729 | − | 1.09856i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4920.98 | + | 2841.13i | 0.923850 | + | 0.533385i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3785.51i | 0.703747i | 0.936048 | + | 0.351873i | \(0.114455\pi\) | ||||
−0.936048 | + | 0.351873i | \(0.885545\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5754.15 | + | 3161.29i | −1.05936 | + | 0.582005i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2998.76 | − | 5194.00i | 0.546765 | − | 0.947025i | −0.451728 | − | 0.892156i | \(-0.649192\pi\) |
0.998494 | − | 0.0548698i | \(-0.0174744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4960.97 | − | 2864.22i | 0.895881 | − | 0.517237i | 0.0200193 | − | 0.999800i | \(-0.493627\pi\) |
0.875861 | + | 0.482563i | \(0.160294\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5818.71 | + | 3359.43i | −1.03095 | + | 0.595219i | −0.917257 | − | 0.398297i | \(-0.869602\pi\) |
−0.113693 | + | 0.993516i | \(0.536268\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3338.63 | + | 5782.68i | −0.585980 | + | 1.01495i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6664.01 | − | 3661.17i | 1.15872 | − | 0.636593i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5493.00i | 0.946249i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −64.3464 | − | 37.1504i | −0.0109825 | − | 0.00634072i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6031.69 | − | 9953.27i | 1.02004 | − | 1.68323i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −845.184 | − | 1463.90i | −0.140349 | − | 0.243092i | 0.787279 | − | 0.616597i | \(-0.211489\pi\) |
−0.927628 | + | 0.373505i | \(0.878156\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1463.29 | + | 2802.79i | 0.240803 | + | 0.461237i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8785.25 | −1.43280 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4257.51 | 0.688194 | 0.344097 | − | 0.938934i | \(-0.388185\pi\) | ||||
0.344097 | + | 0.938934i | \(0.388185\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.0224 | + | 1461.64i | −0.00497023 | + | 0.234174i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 62.6139 | + | 108.450i | 0.00994349 | + | 0.0172226i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7489.65 | + | 4538.73i | 1.16878 | + | 0.708281i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1092.59 | − | 630.806i | −0.169029 | − | 0.0975891i | 0.413099 | − | 0.910686i | \(-0.364446\pi\) |
−0.582128 | + | 0.813097i | \(0.697780\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10981.9i | − | 1.68438i | −0.539179 | − | 0.842191i | \(-0.681265\pi\) | ||
0.539179 | − | 0.842191i | \(-0.318735\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.0911 | − | 346.528i | 0.00335936 | − | 0.0526960i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3677.09 | + | 6368.90i | −0.554424 | + | 0.960290i | 0.443524 | + | 0.896262i | \(0.353728\pi\) |
−0.997948 | + | 0.0640280i | \(0.979605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8311.06 | + | 4798.39i | −1.24255 | + | 0.717387i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −432.312 | + | 249.595i | −0.0635559 | + | 0.0366940i | −0.531441 | − | 0.847095i | \(-0.678349\pi\) |
0.467885 | + | 0.883789i | \(0.345016\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2722.58 | − | 4715.64i | 0.396935 | − | 0.687511i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2832.84 | + | 5156.31i | 0.409603 | + | 0.745554i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2003.44i | 0.287302i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 282.908 | + | 163.337i | 0.0402390 | + | 0.0232320i | 0.519985 | − | 0.854176i | \(-0.325938\pi\) |
−0.479746 | + | 0.877408i | \(0.659271\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4334.89 | − | 184.094i | −0.611559 | − | 0.0259717i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 137.986 | + | 239.000i | 0.0191546 | + | 0.0331767i | 0.875444 | − | 0.483320i | \(-0.160569\pi\) |
−0.856289 | + | 0.516497i | \(0.827236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7848.53 | − | 166.581i | −1.08079 | − | 0.0229392i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −332.981 | −0.0454891 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 508.854 | 0.0689659 | 0.0344829 | − | 0.999405i | \(-0.489022\pi\) | ||||
0.0344829 | + | 0.999405i | \(0.489022\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2992.80 | − | 63.5206i | −0.402430 | − | 0.00854137i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2212.79 | − | 3832.66i | −0.295217 | − | 0.511331i | 0.679818 | − | 0.733381i | \(-0.262059\pi\) |
−0.975035 | + | 0.222049i | \(0.928725\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11941.5 | − | 507.133i | −1.56853 | − | 0.0666125i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1558.98 | − | 900.077i | −0.203196 | − | 0.117315i | 0.394949 | − | 0.918703i | \(-0.370762\pi\) |
−0.598146 | + | 0.801388i | \(0.704096\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8563.87i | 1.10766i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5718.13 | − | 10408.1i | −0.733948 | − | 1.33592i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3134.65 | + | 5429.38i | −0.399295 | + | 0.691599i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5601.29 | + | 3233.91i | −0.708113 | + | 0.408829i | −0.810362 | − | 0.585930i | \(-0.800729\pi\) |
0.102249 | + | 0.994759i | \(0.467396\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2974.16 | + | 1717.13i | −0.370381 | + | 0.213839i | −0.673625 | − | 0.739074i | \(-0.735264\pi\) |
0.303244 | + | 0.952913i | \(0.401930\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.12242 | + | 5.40819i | −0.000385952 | + | 0.000668489i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3017.88 | − | 6431.82i | −0.370270 | − | 0.789135i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5811.93i | − | 0.707829i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 817.228 | + | 471.827i | 0.0988003 | + | 0.0570424i | 0.548586 | − | 0.836094i | \(-0.315166\pi\) |
−0.449786 | + | 0.893136i | \(0.648500\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4581.26 | − | 2776.24i | −0.549822 | − | 0.333192i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1714.77 | + | 2970.07i | 0.202831 | + | 0.351313i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.8558 | + | 1218.21i | −0.00303637 | + | 0.143060i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10148.4 | 1.18325 | 0.591626 | − | 0.806213i | \(-0.298486\pi\) | ||||
0.591626 | + | 0.806213i | \(0.298486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6775.40 | −0.784354 | −0.392177 | − | 0.919890i | \(-0.628278\pi\) | ||||
−0.392177 | + | 0.919890i | \(0.628278\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3894.03 | − | 7458.66i | −0.447598 | − | 0.857335i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −743.317 | − | 1287.46i | −0.0848381 | − | 0.146944i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −330.795 | + | 545.865i | −0.0372283 | + | 0.0614327i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14439.3 | − | 8336.51i | −1.61372 | − | 0.931684i | −0.988497 | − | 0.151241i | \(-0.951673\pi\) |
−0.625227 | − | 0.780443i | \(-0.714993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2848.46i | 0.316140i | 0.987428 | + | 0.158070i | \(0.0505271\pi\) | ||||
−0.987428 | + | 0.158070i | \(0.949473\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5971.24 | + | 3280.56i | −0.658159 | + | 0.361588i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9591.41 | − | 16612.8i | 1.04993 | − | 1.81853i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8042.46 | + | 4643.32i | −0.874364 | + | 0.504814i | −0.868796 | − | 0.495170i | \(-0.835106\pi\) |
−0.00556785 | + | 0.999984i | \(0.501772\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4281.76 | − | 2472.08i | 0.459216 | − | 0.265128i | −0.252499 | − | 0.967597i | \(-0.581252\pi\) |
0.711714 | + | 0.702469i | \(0.247919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5305.34 | − | 9189.12i | 0.565163 | − | 0.978890i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10599.1 | + | 5823.05i | −1.12152 | + | 0.616154i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15964.7i | − | 1.67799i | −0.544136 | − | 0.838997i | \(-0.683142\pi\) | ||
0.544136 | − | 0.838997i | \(-0.316858\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6906.99 | + | 3987.75i | 0.721147 | + | 0.416355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2841.47 | + | 4688.90i | −0.294711 | + | 0.486321i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4133.41 | + | 7159.28i | 0.423092 | + | 0.732816i | 0.996240 | − | 0.0866354i | \(-0.0276115\pi\) |
−0.573148 | + | 0.819452i | \(0.694278\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3849.50 | − | 5783.53i | 0.391459 | − | 0.588130i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3468.42 | 0.350413 | 0.175207 | − | 0.984532i | \(-0.443941\pi\) | ||||
0.175207 | + | 0.984532i | \(0.443941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9918.45 | −0.995572 | −0.497786 | − | 0.867300i | \(-0.665853\pi\) | ||||
−0.497786 | + | 0.867300i | \(0.665853\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.71133 | + | 127.746i | −0.000270398 | + | 0.0127399i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8430.55 | − | 14602.1i | −0.835373 | − | 1.44691i | −0.893726 | − | 0.448613i | \(-0.851918\pi\) |
0.0583529 | − | 0.998296i | \(-0.481415\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 196.983 | + | 119.372i | 0.0192707 | + | 0.0116781i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19027.0 | + | 10985.3i | 1.84960 | + | 1.06787i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3330.02i | 0.321667i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6549.80 | + | 4161.72i | 0.628710 | + | 0.399481i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1578.16 | − | 2733.46i | 0.150539 | − | 0.260741i | −0.780887 | − | 0.624672i | \(-0.785232\pi\) |
0.931426 | + | 0.363932i | \(0.118566\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 250.999 | − | 144.914i | 0.0237932 | − | 0.0137370i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11521.4 | − | 6651.91i | 1.07868 | − | 0.622778i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1214.17 | + | 2103.01i | −0.112976 | + | 0.195681i | −0.916969 | − | 0.398958i | \(-0.869372\pi\) |
0.803993 | + | 0.594639i | \(0.202705\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 630.789 | + | 1148.15i | 0.0583339 | + | 0.106179i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1304.86i | 0.119933i | 0.998200 | + | 0.0599667i | \(0.0190995\pi\) | ||||
−0.998200 | + | 0.0599667i | \(0.980901\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5769.79 | − | 3331.19i | −0.527096 | − | 0.304319i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −554.117 | + | 13047.9i | −0.0503146 | + | 1.18476i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1272.72 | − | 2204.42i | −0.114178 | − | 0.197762i | 0.803273 | − | 0.595611i | \(-0.203090\pi\) |
−0.917451 | + | 0.397849i | \(0.869757\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8609.91 | + | 182.741i | 0.767789 | + | 0.0162959i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 787.994 | 0.0698507 | 0.0349253 | − | 0.999390i | \(-0.488881\pi\) | ||||
0.0349253 | + | 0.999390i | \(0.488881\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12707.0 | −1.11971 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11381.6 | + | 241.567i | 0.996987 | + | 0.0211605i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1538.89 | − | 2665.44i | −0.134008 | − | 0.232109i | 0.791210 | − | 0.611544i | \(-0.209451\pi\) |
−0.925218 | + | 0.379436i | \(0.876118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13945.0 | + | 6907.91i | −1.20017 | + | 0.594526i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10664.0 | + | 6156.89i | 0.912454 | + | 0.526806i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15466.4i | 1.31569i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8324.43 | − | 15152.0i | −0.704050 | − | 1.28150i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 663.114 | − | 1148.55i | 0.0557611 | − | 0.0965811i | −0.836797 | − | 0.547513i | \(-0.815575\pi\) |
0.892559 | + | 0.450931i | \(0.148908\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5799.32 | + | 3348.24i | −0.484869 | + | 0.279940i | −0.722444 | − | 0.691430i | \(-0.756981\pi\) |
0.237574 | + | 0.971369i | \(0.423648\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −108.209 | + | 62.4743i | −0.00894429 | + | 0.00516399i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8870.03 | − | 15363.3i | 0.729023 | − | 1.26271i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8003.37 | + | 12595.8i | −0.654080 | + | 1.02940i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 397.721i | 0.0323212i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12350.3 | − | 7130.44i | −0.998036 | − | 0.576216i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1911.81 | − | 1158.56i | −0.153633 | − | 0.0931016i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9558.74 | − | 16556.2i | −0.759634 | − | 1.31573i | −0.943037 | − | 0.332687i | \(-0.892045\pi\) |
0.183403 | − | 0.983038i | \(-0.441289\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 245.935 | − | 11587.3i | 0.0194366 | − | 0.915765i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21828.3 | −1.71564 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12400.5 | −0.969297 | −0.484649 | − | 0.874709i | \(-0.661053\pi\) | ||||
−0.484649 | + | 0.874709i | \(0.661053\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13955.0 | + | 7285.64i | −1.08485 | + | 0.566381i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7461.77 | + | 12924.2i | 0.576918 | + | 0.999252i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3073.37 | − | 5071.57i | 0.235058 | − | 0.387885i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6062.22 | − | 3500.02i | −0.461157 | − | 0.266249i | 0.251374 | − | 0.967890i | \(-0.419118\pi\) |
−0.712531 | + | 0.701641i | \(0.752451\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1095.62i | 0.0828978i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11192.8 | + | 6149.27i | −0.842356 | + | 0.462785i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10239.9 | + | 17736.1i | −0.766538 | + | 1.32768i | 0.172891 | + | 0.984941i | \(0.444689\pi\) |
−0.939430 | + | 0.342742i | \(0.888644\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2374.65 | − | 1371.01i | 0.176818 | − | 0.102086i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8603.00 | − | 4966.94i | 0.633843 | − | 0.365949i | −0.148396 | − | 0.988928i | \(-0.547411\pi\) |
0.782239 | + | 0.622979i | \(0.214078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2929.14 | + | 5073.42i | −0.214677 | + | 0.371832i | −0.953173 | − | 0.302427i | \(-0.902203\pi\) |
0.738496 | + | 0.674258i | \(0.235537\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5276.00 | − | 2898.60i | 0.384656 | − | 0.211328i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5191.68i | 0.376535i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15287.5 | − | 8826.26i | −1.10300 | − | 0.636815i | −0.165989 | − | 0.986128i | \(-0.553082\pi\) |
−0.937006 | + | 0.349313i | \(0.886415\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6074.50 | − | 10023.9i | 0.436006 | − | 0.719482i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7132.28 | − | 12353.5i | −0.506670 | − | 0.877579i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −577.312 | + | 301.404i | −0.0408016 | + | 0.0213017i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25424.1 | −1.78768 | −0.893838 | − | 0.448390i | \(-0.851998\pi\) | ||||
−0.893838 | + | 0.448390i | \(0.851998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 279.881 | 0.0195795 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −361.704 | + | 17041.8i | −0.0251751 | + | 1.18614i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3832.38 | − | 6637.89i | −0.265392 | − | 0.459672i | 0.702275 | − | 0.711906i | \(-0.252168\pi\) |
−0.967666 | + | 0.252235i | \(0.918835\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19591.9 | + | 11872.7i | 1.34312 | + | 0.813932i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23961.5 | + | 13834.2i | 1.63446 | + | 0.943655i | 0.982695 | + | 0.185233i | \(0.0593041\pi\) |
0.651764 | + | 0.758422i | \(0.274029\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11624.0i | 0.788937i | 0.918909 | + | 0.394469i | \(0.129071\pi\) | ||||
−0.918909 | + | 0.394469i | \(0.870929\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13052.9 | − | 20542.9i | 0.881518 | − | 1.38735i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5517.21 | − | 9556.09i | 0.370754 | − | 0.642166i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2675.97 | − | 1544.97i | 0.178936 | − | 0.103309i | −0.407857 | − | 0.913046i | \(-0.633724\pi\) |
0.586793 | + | 0.809737i | \(0.300390\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −667.946 | + | 385.639i | −0.0442262 | + | 0.0255340i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1623.78 | − | 2812.47i | 0.106989 | − | 0.185310i | −0.807560 | − | 0.589785i | \(-0.799213\pi\) |
0.914549 | + | 0.404475i | \(0.132546\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3918.39 | + | 7132.21i | 0.256918 | + | 0.467640i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10686.9i | 0.697307i | 0.937252 | + | 0.348654i | \(0.113361\pi\) | ||||
−0.937252 | + | 0.348654i | \(0.886639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4946.00 | + | 2855.58i | 0.321158 | + | 0.185420i | 0.651908 | − | 0.758298i | \(-0.273969\pi\) |
−0.330751 | + | 0.943718i | \(0.607302\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21741.0 | + | 10769.8i | −1.40489 | + | 0.695938i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5485.59 | + | 9501.31i | 0.351077 | + | 0.608084i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 28599.8 | + | 607.014i | 1.82163 | + | 0.0386632i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5798.97 | 0.367600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13708.4 | −0.864854 | −0.432427 | − | 0.901669i | \(-0.642343\pi\) | ||||
−0.432427 | + | 0.901669i | \(0.642343\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29198.2 | + | 619.716i | 1.83337 | + | 0.0389123i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2807.23 | + | 4862.27i | 0.175436 | + | 0.303864i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1128.10 | − | 26563.4i | 0.0698385 | − | 1.64449i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14083.3 | − | 8131.00i | −0.867796 | − | 0.501022i | −0.00118054 | − | 0.999999i | \(-0.500376\pi\) |
−0.866615 | + | 0.498977i | \(0.833709\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 13805.8i | − | 0.846729i | −0.905959 | − | 0.423365i | \(-0.860849\pi\) | ||
0.905959 | − | 0.423365i | \(-0.139151\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10794.2 | + | 19647.4i | 0.658947 | + | 1.19941i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9180.08 | − | 15900.4i | 0.557815 | − | 0.966163i | −0.439864 | − | 0.898064i | \(-0.644973\pi\) |
0.997679 | − | 0.0680988i | \(-0.0216933\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23756.8 | − | 13716.0i | 1.43688 | − | 0.829585i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16302.6 | + | 9412.30i | −0.976983 | + | 0.564061i | −0.901358 | − | 0.433075i | \(-0.857428\pi\) |
−0.0756247 | + | 0.997136i | \(0.524095\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11136.6 | + | 19289.1i | −0.664338 | + | 1.15067i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4684.73 | − | 2976.67i | −0.278187 | − | 0.176759i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3472.55i | 0.205268i | 0.994719 | + | 0.102634i | \(0.0327270\pi\) | ||||
−0.994719 | + | 0.102634i | \(0.967273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11328.2 | − | 6540.36i | −0.666592 | − | 0.384857i | 0.128192 | − | 0.991749i | \(-0.459083\pi\) |
−0.794784 | + | 0.606892i | \(0.792416\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −544.649 | − | 330.057i | −0.0319041 | − | 0.0193339i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11633.3 | + | 20149.5i | 0.675327 | + | 1.16970i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 125.105 | − | 5894.36i | 0.00722993 | − | 0.340641i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28937.3 | 1.66485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13701.5 | −0.784775 | −0.392388 | − | 0.919800i | \(-0.628351\pi\) | ||||
−0.392388 | + | 0.919800i | \(0.628351\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2333.68 | − | 3506.15i | 0.133072 | − | 0.199928i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1975.54 | − | 3421.74i | −0.112151 | − | 0.194251i | 0.804486 | − | 0.593971i | \(-0.202441\pi\) |
−0.916637 | + | 0.399720i | \(0.869107\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5717.74 | + | 9435.20i | −0.321739 | + | 0.530922i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22216.3 | − | 12826.6i | −1.24463 | − | 0.718589i | −0.274598 | − | 0.961559i | \(-0.588545\pi\) |
−0.970034 | + | 0.242970i | \(0.921878\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10047.1i | 0.560406i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12093.7 | − | 6644.19i | 0.671619 | − | 0.368983i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 355.671 | − | 616.041i | 0.0196662 | − | 0.0340628i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7142.53 | + | 4123.74i | −0.393219 | + | 0.227025i | −0.683554 | − | 0.729900i | \(-0.739567\pi\) |
0.290335 | + | 0.956925i | \(0.406233\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1979.17 | − | 1142.67i | 0.108020 | − | 0.0623655i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3978.86 | + | 6891.59i | −0.216227 | + | 0.374516i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14377.9 | − | 7899.11i | 0.777999 | − | 0.427428i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25364.7i | − | 1.36663i | −0.730122 | − | 0.683317i | \(-0.760537\pi\) | ||
0.730122 | − | 0.683317i | \(-0.239463\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11249.3 | − | 6494.77i | −0.603519 | − | 0.348442i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8178.72 | + | 13496.2i | −0.436920 | + | 0.720989i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14695.0 | − | 25452.5i | −0.778397 | − | 1.34822i | −0.932865 | − | 0.360225i | \(-0.882700\pi\) |
0.154469 | − | 0.987998i | \(-0.450633\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8038.33 | − | 15396.7i | −0.423996 | − | 0.812126i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 436.350 | 0.0229193 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1197.13 | 0.0626154 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 224.947 | − | 10598.5i | 0.0117166 | − | 0.552033i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1802.02 | + | 3121.19i | 0.0934687 | + | 0.161893i | 0.908968 | − | 0.416865i | \(-0.136871\pi\) |
−0.815500 | + | 0.578757i | \(0.803538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20313.1 | + | 12309.7i | 1.04488 | + | 0.633201i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3497.82 | − | 2019.47i | −0.179180 | − | 0.103450i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 35634.9i | − | 1.81792i | −0.416887 | − | 0.908958i | \(-0.636879\pi\) | ||
0.416887 | − | 0.908958i | \(-0.363121\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19523.7 | + | 2499.42i | 0.991905 | + | 0.126984i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10960.8 | + | 18984.6i | −0.554581 | + | 0.960562i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10831.6 | − | 6253.60i | 0.545802 | − | 0.315119i | −0.201625 | − | 0.979463i | \(-0.564622\pi\) |
0.747427 | + | 0.664344i | \(0.231289\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38745.6 | + | 22369.8i | −1.93652 | + | 1.11805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4972.17 | + | 8612.05i | −0.247502 | + | 0.428687i | −0.962832 | − | 0.270100i | \(-0.912943\pi\) |
0.715330 | + | 0.698787i | \(0.246276\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 686.889 | + | 1250.27i | 0.0340533 | + | 0.0619835i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 12175.9i | − | 0.601198i | −0.953751 | − | 0.300599i | \(-0.902813\pi\) | ||
0.953751 | − | 0.300599i | \(-0.0971866\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19643.0 | + | 11340.9i | 0.965992 | + | 0.557716i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9492.79 | − | 403.140i | −0.464957 | − | 0.0197458i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7950.95 | + | 13771.4i | 0.386331 | + | 0.669144i | 0.991953 | − | 0.126608i | \(-0.0404091\pi\) |
−0.605622 | + | 0.795752i | \(0.707076\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30382.5 | − | 644.853i | −1.47039 | − | 0.0312081i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10283.1 | 0.495684 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39209.6 | 1.88256 | 0.941279 | − | 0.337630i | \(-0.109625\pi\) | ||||
0.941279 | + | 0.337630i | \(0.109625\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 44588.6 | + | 946.368i | 2.13236 | + | 0.0452582i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5888.86 | + | 10199.8i | 0.280514 | + | 0.485864i | 0.971511 | − | 0.236993i | \(-0.0761619\pi\) |
−0.690998 | + | 0.722857i | \(0.742829\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13018.8 | − | 552.882i | −0.615288 | − | 0.0261301i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1184.70 | + | 683.988i | 0.0557720 | + | 0.0322000i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5932.67i | − | 0.278202i | −0.990278 | − | 0.139101i | \(-0.955579\pi\) | ||
0.990278 | − | 0.139101i | \(-0.0444213\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19437.8 | + | 35380.4i | 0.907956 | + | 1.65265i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12154.4 | + | 21052.1i | −0.565543 | + | 0.979550i | 0.431456 | + | 0.902134i | \(0.358000\pi\) |
−0.996999 | + | 0.0774157i | \(0.975333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −65.5993 | + | 37.8738i | −0.00304051 | + | 0.00175544i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15437.0 | − | 8912.54i | 0.709996 | − | 0.409916i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24436.2 | + | 42324.8i | −1.11959 | + | 1.93918i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1200.86 | − | 18837.0i | 0.0548085 | − | 0.859742i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 432.000i | − | 0.0196417i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32642.3 | − | 18846.0i | −1.47849 | − | 0.853606i | −0.478785 | − | 0.877932i | \(-0.658923\pi\) |
−0.999704 | + | 0.0243259i | \(0.992256\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20923.7 | − | 12679.8i | −0.944110 | − | 0.572131i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 721.521 | + | 1249.71i | 0.0323102 | + | 0.0559629i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 308.845 | − | 14551.4i | 0.0137781 | − | 0.649163i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5364.15 | −0.238404 | −0.119202 | − | 0.992870i | \(-0.538034\pi\) | ||||
−0.119202 | + | 0.992870i | \(0.538034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15432.0 | −0.683284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13604.7 | + | 26058.7i | 0.600125 | + | 1.14948i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5101.35 | + | 8835.80i | 0.224188 | + | 0.388305i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11064.3 | + | 18257.9i | −0.482630 | + | 0.796419i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10538.2 | − | 6084.21i | −0.457975 | − | 0.264412i | 0.253217 | − | 0.967409i | \(-0.418511\pi\) |
−0.711193 | + | 0.702997i | \(0.751845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24850.5i | − | 1.07598i | −0.842952 | − | 0.537989i | \(-0.819184\pi\) | ||
0.842952 | − | 0.537989i | \(-0.180816\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3685.30 | − | 2024.68i | 0.158978 | − | 0.0873415i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1228.52 | − | 2127.85i | 0.0528013 | − | 0.0914545i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42525.0 | − | 24551.8i | 1.82100 | − | 1.05136i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33792.8 | − | 19510.3i | 1.43651 | − | 0.829372i | 0.438909 | − | 0.898532i | \(-0.355365\pi\) |
0.997606 | + | 0.0691595i | \(0.0220317\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7694.67 | + | 13327.6i | −0.325905 | + | 0.564483i | −0.981695 | − | 0.190460i | \(-0.939002\pi\) |
0.655790 | + | 0.754943i | \(0.272335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6785.43 | + | 3727.87i | −0.286350 | + | 0.157319i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21256.9i | 0.893805i | 0.894583 | + | 0.446902i | \(0.147473\pi\) | ||||
−0.894583 | + | 0.446902i | \(0.852527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25539.6 | − | 14745.3i | −1.07000 | − | 0.617763i | −0.141817 | − | 0.989893i | \(-0.545294\pi\) |
−0.928181 | + | 0.372130i | \(0.878628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20075.8 | − | 33128.3i | 0.838052 | − | 1.38292i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8076.05 | − | 13988.1i | −0.334711 | − | 0.579736i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −294.685 | − | 196.142i | −0.0121694 | − | 0.00809993i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39336.9 | 1.61867 | 0.809333 | − | 0.587350i | \(-0.199829\pi\) | ||||
0.809333 | + | 0.587350i | \(0.199829\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6288.44 | 0.257839 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −142.224 | + | 6700.94i | −0.00581073 | + | 0.273775i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10675.8 | − | 18491.1i | −0.434627 | − | 0.752796i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 38310.9 | + | 23216.4i | 1.54868 | + | 0.938498i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17538.2 | − | 10125.7i | −0.706465 | − | 0.407878i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12458.2i | − | 0.500072i | −0.968237 | − | 0.250036i | \(-0.919558\pi\) | ||
0.968237 | − | 0.250036i | \(-0.0804424\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24635.6 | + | 15653.4i | 0.985401 | + | 0.626122i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1310.45 | + | 2269.77i | −0.0522337 | + | 0.0904714i | −0.890960 | − | 0.454082i | \(-0.849967\pi\) |
0.838726 | + | 0.544553i | \(0.183301\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17583.3 | − | 10151.7i | 0.698410 | − | 0.403227i | −0.108345 | − | 0.994113i | \(-0.534555\pi\) |
0.806755 | + | 0.590886i | \(0.201222\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15233.4 | + | 8795.00i | −0.600870 | + | 0.346912i | −0.769384 | − | 0.638787i | \(-0.779437\pi\) |
0.168514 | + | 0.985699i | \(0.446103\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16212.5 | + | 28080.9i | −0.637275 | + | 1.10379i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6156.77 | + | 11206.5i | 0.241171 | + | 0.438976i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31926.9i | 1.24631i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1932.16 | − | 1115.53i | −0.0751651 | − | 0.0433966i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1563.85 | + | 36824.3i | −0.0606282 | + | 1.42762i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9083.05 | − | 15732.3i | −0.349729 | − | 0.605749i | 0.636472 | − | 0.771300i | \(-0.280393\pi\) |
−0.986201 | + | 0.165551i | \(0.947060\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32145.1 | + | 682.262i | 1.23348 | + | 0.0261799i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7990.91 | −0.305585 | −0.152793 | − | 0.988258i | \(-0.548827\pi\) | ||||
−0.152793 | + | 0.988258i | \(0.548827\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2454.35 | 0.0935397 | 0.0467699 | − | 0.998906i | \(-0.485107\pi\) | ||||
0.0467699 | + | 0.998906i | \(0.485107\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27983.6 | + | 593.937i | 1.06289 | + | 0.0225593i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11813.7 | + | 20461.9i | 0.447197 | + | 0.774568i | 0.998202 | − | 0.0599335i | \(-0.0190889\pi\) |
−0.551005 | + | 0.834502i | \(0.685756\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29687.0 | − | 20681.9i | −1.11622 | − | 0.777632i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29936.0 | + | 17283.6i | 1.12180 | + | 0.647674i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4192.76i | 0.156591i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1070.90 | + | 1949.23i | 0.0398620 | + | 0.0725563i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −169.732 | + | 293.985i | −0.00629687 | + | 0.0109065i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12325.9 | − | 7116.38i | 0.455756 | − | 0.263131i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18825.4 | + | 10868.9i | −0.691468 | + | 0.399219i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4609.53 | − | 7983.94i | 0.168751 | − | 0.292285i | −0.769230 | − | 0.638972i | \(-0.779360\pi\) |
0.937981 | + | 0.346687i | \(0.112693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18879.7 | − | 29713.2i | 0.688890 | − | 1.08419i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19404.0i | 0.705688i | 0.935682 | + | 0.352844i | \(0.114785\pi\) | ||||
−0.935682 | + | 0.352844i | \(0.885215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15125.3 | + | 8732.61i | 0.548275 | + | 0.316547i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25251.1 | + | 15302.2i | 0.912324 | + | 0.552869i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13656.8 | + | 23654.2i | 0.490201 | + | 0.849053i | 0.999936 | − | 0.0112781i | \(-0.00359002\pi\) |
−0.509735 | + | 0.860331i | \(0.670257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −417.392 | + | 19665.6i | −0.0149333 | + | 0.703588i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2437.16 | −0.0869124 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3515.51 | 0.124961 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30241.3 | + | 15788.4i | −1.07147 | + | 0.559395i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8806.15 | + | 15252.7i | 0.311002 | + | 0.538671i | 0.978579 | − | 0.205869i | \(-0.0660022\pi\) |
−0.667578 | + | 0.744540i | \(0.732669\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16151.2 | − | 26652.1i | 0.566738 | − | 0.935210i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20743.5 | + | 11976.2i | 0.725544 | + | 0.418893i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18758.1i | 0.654004i | 0.945024 | + | 0.327002i | \(0.106038\pi\) | ||||
−0.945024 | + | 0.327002i | \(0.893962\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26088.0 | − | 14332.6i | 0.906655 | − | 0.498110i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2123.19 | + | 3677.48i | −0.0735538 | + | 0.127399i | −0.900456 | − | 0.434946i | \(-0.856767\pi\) |
0.826903 | + | 0.562345i | \(0.190101\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24067.1 | − | 13895.1i | 0.831104 | − | 0.479838i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27111.0 | + | 15652.6i | −0.930296 | + | 0.537106i | −0.886905 | − | 0.461952i | \(-0.847149\pi\) |
−0.0433905 | + | 0.999058i | \(0.513816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −254.393 | + | 440.622i | −0.00870175 | + | 0.0150719i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30598.5 | + | 16810.6i | −1.04335 | + | 0.573209i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33871.8i | 1.15133i | 0.817687 | + | 0.575663i | \(0.195256\pi\) | ||||
−0.817687 | + | 0.575663i | \(0.804744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9777.91 | − | 5645.28i | −0.331315 | − | 0.191285i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17981.7 | + | 29672.8i | −0.607385 | + | 1.00228i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14892.3 | − | 25794.2i | −0.499893 | − | 0.865840i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35023.1 | − | 18284.9i | 1.17197 | − | 0.611862i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21983.3 | −0.733333 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34214.9 | 1.13782 | 0.568912 | − | 0.822398i | \(-0.307364\pi\) | ||||
0.568912 | + | 0.822398i | \(0.307364\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −605.661 | + | 28536.0i | −0.0200791 | + | 0.946036i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6266.70 | + | 10854.2i | 0.207114 | + | 0.358732i | 0.950804 | − | 0.309792i | \(-0.100260\pi\) |
−0.743690 | + | 0.668525i | \(0.766926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −330.182 | − | 200.091i | −0.0108454 | − | 0.00657234i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33448.2 | − | 19311.4i | −1.09530 | − | 0.632369i | −0.160314 | − | 0.987066i | \(-0.551251\pi\) |
−0.934981 | + | 0.354697i | \(0.884584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 54035.8i | − | 1.76404i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32432.0 | − | 51042.0i | 1.05553 | − | 1.66121i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17134.5 | − | 29677.9i | 0.555958 | − | 0.962947i | −0.441870 | − | 0.897079i | \(-0.645685\pi\) |
0.997828 | − | 0.0658685i | \(-0.0209818\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27687.1 | − | 15985.2i | 0.895619 | − | 0.517086i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 66298.7 | − | 38277.6i | 2.13162 | − | 1.23069i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7547.62 | + | 13072.9i | −0.241935 | + | 0.419044i | −0.961266 | − | 0.275624i | \(-0.911116\pi\) |
0.719330 | + | 0.694668i | \(0.244449\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4229.31 | − | 7698.13i | −0.135159 | − | 0.246015i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 42966.6i | − | 1.36898i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1996.82 | − | 1152.87i | −0.0634303 | − | 0.0366215i | 0.467949 | − | 0.883755i | \(-0.344993\pi\) |
−0.531380 | + | 0.847134i | \(0.678326\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7292.70 | + | 14721.8i | 0.230962 | + | 0.466243i |
(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 | 588.4.k.e.521.24 | 48 | ||
3.2 | odd | 2 | inner | 588.4.k.e.521.16 | 48 | ||
7.2 | even | 3 | inner | 588.4.k.e.509.9 | 48 | ||
7.3 | odd | 6 | 588.4.f.d.293.18 | yes | 24 | ||
7.4 | even | 3 | 588.4.f.d.293.7 | ✓ | 24 | ||
7.5 | odd | 6 | inner | 588.4.k.e.509.16 | 48 | ||
7.6 | odd | 2 | inner | 588.4.k.e.521.1 | 48 | ||
21.2 | odd | 6 | inner | 588.4.k.e.509.1 | 48 | ||
21.5 | even | 6 | inner | 588.4.k.e.509.24 | 48 | ||
21.11 | odd | 6 | 588.4.f.d.293.17 | yes | 24 | ||
21.17 | even | 6 | 588.4.f.d.293.8 | yes | 24 | ||
21.20 | even | 2 | inner | 588.4.k.e.521.9 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.f.d.293.7 | ✓ | 24 | 7.4 | even | 3 | ||
588.4.f.d.293.8 | yes | 24 | 21.17 | even | 6 | ||
588.4.f.d.293.17 | yes | 24 | 21.11 | odd | 6 | ||
588.4.f.d.293.18 | yes | 24 | 7.3 | odd | 6 | ||
588.4.k.e.509.1 | 48 | 21.2 | odd | 6 | inner | ||
588.4.k.e.509.9 | 48 | 7.2 | even | 3 | inner | ||
588.4.k.e.509.16 | 48 | 7.5 | odd | 6 | inner | ||
588.4.k.e.509.24 | 48 | 21.5 | even | 6 | inner | ||
588.4.k.e.521.1 | 48 | 7.6 | odd | 2 | inner | ||
588.4.k.e.521.9 | 48 | 21.20 | even | 2 | inner | ||
588.4.k.e.521.16 | 48 | 3.2 | odd | 2 | inner | ||
588.4.k.e.521.24 | 48 | 1.1 | even | 1 | trivial |