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 | 521.16 | ||
Character | \(\chi\) | \(=\) | 588.521 |
Dual form | 588.4.k.e.509.16 |
$q$-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 | ||||||||
\(3\) | 2.69298 | + | 4.44386i | 0.518264 | + | 0.855221i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.87287 | + | 8.44005i | 0.435842 | + | 0.754901i | 0.997364 | − | 0.0725609i | \(-0.0231172\pi\) |
−0.561522 | + | 0.827462i | \(0.689784\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −12.4957 | + | 23.9344i | −0.462804 | + | 0.886460i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42.9817 | + | 24.8155i | 1.17813 | + | 0.680195i | 0.955582 | − | 0.294726i | \(-0.0952284\pi\) |
0.222551 | + | 0.974921i | \(0.428562\pi\) | |||||||
\(12\) | 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 | −0.986817 | − | 0.161843i | \(-0.948256\pi\) |
0.633568 | + | 0.773687i | \(0.281590\pi\) | |||||||
\(18\) | 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 | 0.368446 | − | 0.929649i | \(-0.379890\pi\) |
0.989323 | + | 0.145741i | \(0.0465567\pi\) | |||||||
\(24\) | 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 | \(0.141749\pi\) | ||||
−0.902474 | + | 0.430744i | \(0.858251\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 5.47234 | + | 257.832i | 0.0288670 | + | 1.36008i | ||||
\(34\) | 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 | ||||||||
\(39\) | 10.9985 | − | 6.66509i | 0.0451582 | − | 0.0273659i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 160.696 | 0.612111 | 0.306055 | − | 0.952014i | \(-0.400991\pi\) | ||||
0.306055 | + | 0.952014i | \(0.400991\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −442.678 | −1.56995 | −0.784973 | − | 0.619530i | \(-0.787323\pi\) | ||||
−0.784973 | + | 0.619530i | \(0.787323\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −262.898 | + | 11.1648i | −0.870900 | + | 0.0369854i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 155.814 | + | 269.879i | 0.483572 | + | 0.837571i | 0.999822 | − | 0.0188668i | \(-0.00600584\pi\) |
−0.516250 | + | 0.856438i | \(0.672673\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −257.257 | + | 5.46014i | −0.706337 | + | 0.0149916i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −248.907 | − | 143.706i | −0.645093 | − | 0.372445i | 0.141480 | − | 0.989941i | \(-0.454814\pi\) |
−0.786574 | + | 0.617496i | \(0.788147\pi\) | |||||||
\(54\) | 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 | \(-0.624577\pi\) |
0.991271 | − | 0.131842i | \(-0.0420892\pi\) | |||||||
\(60\) | 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 | \(0.307695\pi\) | ||||
−0.568058 | + | 0.822988i | \(0.692305\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | 155.957 | − | 3.31010i | 0.240111 | − | 0.00509623i | ||||
\(76\) | 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 | ||||||||
\(81\) | −416.714 | − | 598.156i | −0.571624 | − | 0.820516i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 351.902 | 0.465376 | 0.232688 | − | 0.972551i | \(-0.425248\pi\) | ||||
0.232688 | + | 0.972551i | \(0.425248\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −482.612 | −0.615842 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −597.869 | + | 362.309i | −0.736762 | + | 0.446478i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −544.376 | − | 942.887i | −0.648357 | − | 1.12299i | −0.983515 | − | 0.180825i | \(-0.942123\pi\) |
0.335159 | − | 0.942162i | \(-0.391210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.278207 | − | 13.1079i | −0.000310202 | − | 0.0146153i | ||||
\(94\) | 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 | \(0.388673\pi\) |
−0.984925 | + | 0.172980i | \(0.944660\pi\) | |||||||
\(102\) | 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 | −0.947652 | − | 0.319306i | \(-0.896550\pi\) |
−0.197299 | + | 0.980343i | \(0.563217\pi\) | |||||||
\(108\) | 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 | \(-0.962636\pi\) | ||
0.993119 | − | 0.117114i | \(-0.0373642\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1459.59 | + | 842.697i | 1.18355 | + | 0.683321i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 59.2374 | + | 30.9268i | 0.0468077 | + | 0.0244374i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 566.115 | + | 980.541i | 0.425331 | + | 0.736695i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 432.752 | + | 714.111i | 0.317235 | + | 0.523490i | ||||
\(124\) | 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 | ||||||||
\(129\) | −1192.12 | − | 1967.20i | −0.813647 | − | 1.34265i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1142.71 | + | 1979.23i | 0.762130 | + | 1.32005i | 0.941750 | + | 0.336313i | \(0.109180\pi\) |
−0.179620 | + | 0.983736i | \(0.557487\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −757.593 | − | 1138.21i | −0.482987 | − | 0.725643i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 892.802 | + | 515.459i | 0.556768 | + | 0.321450i | 0.751847 | − | 0.659337i | \(-0.229163\pi\) |
−0.195079 | + | 0.980787i | \(0.562496\pi\) | |||||||
\(138\) | 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 | 0.169830 | − | 0.985473i | \(-0.445678\pi\) |
0.938360 | + | 0.345660i | \(0.112345\pi\) | |||||||
\(150\) | 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 | ||||||||
\(159\) | −31.6903 | − | 1493.10i | −0.0158063 | − | 0.744722i | ||||
\(160\) | 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 | ||||||||
\(165\) | −2149.45 | + | 1302.57i | −1.01415 | + | 0.614574i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1657.35 | −0.767962 | −0.383981 | − | 0.923341i | \(-0.625447\pi\) | ||||
−0.383981 | + | 0.923341i | \(0.625447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2190.87 | 0.997212 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −127.075 | − | 2992.25i | −0.0568285 | − | 1.33815i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1663.55 | + | 2881.36i | 0.731084 | + | 1.26627i | 0.956420 | + | 0.291994i | \(0.0943186\pi\) |
−0.225336 | + | 0.974281i | \(0.572348\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2871.37 | − | 60.9433i | 1.21935 | − | 0.0258801i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 372.577 | + | 215.108i | 0.155574 | + | 0.0898206i | 0.575766 | − | 0.817615i | \(-0.304704\pi\) |
−0.420192 | + | 0.907435i | \(0.638037\pi\) | |||||||
\(180\) | 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 | −0.677855 | − | 0.735195i | \(-0.737090\pi\) |
0.297770 | + | 0.954638i | \(0.403757\pi\) | |||||||
\(192\) | 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 | \(-0.797863\pi\) | ||
0.805053 | − | 0.593203i | \(-0.202137\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | 4683.00 | − | 99.3940i | 1.64335 | − | 0.0348792i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 783.051 | + | 1356.28i | 0.266784 | + | 0.462083i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 198.117 | + | 4665.08i | 0.0665221 | + | 1.56640i | ||||
\(208\) | 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 | ||||||||
\(213\) | −4375.94 | + | 2651.82i | −1.40767 | + | 0.853051i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2157.11 | − | 3736.22i | −0.684249 | − | 1.18515i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.6664 | − | 1067.94i | −0.00699386 | − | 0.329519i | ||||
\(220\) | 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 | −0.668049 | − | 0.744118i | \(-0.732870\pi\) |
0.978449 | + | 0.206488i | \(0.0662035\pi\) | |||||||
\(228\) | 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 | −0.832430 | − | 0.554130i | \(-0.813051\pi\) |
0.0636761 | + | 0.997971i | \(0.479718\pi\) | |||||||
\(234\) | 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 | \(0.0890351\pi\) | ||||
−0.961135 | + | 0.276079i | \(0.910965\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 1535.92 | − | 3462.64i | 0.405470 | − | 0.914109i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 137.268 | + | 237.755i | 0.0353609 | + | 0.0612469i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 947.664 | + | 1563.80i | 0.241188 | + | 0.397999i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5848.44 | 1.47072 | 0.735359 | − | 0.677678i | \(-0.237014\pi\) | ||||
0.735359 | + | 0.677678i | \(0.237014\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8583.01 | 2.13284 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1299.66 | − | 2144.66i | −0.319169 | − | 0.526681i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3884.44 | − | 6728.05i | −0.942820 | − | 1.63301i | −0.760058 | − | 0.649855i | \(-0.774830\pi\) |
−0.182762 | − | 0.983157i | \(-0.558504\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3220.10 | − | 1681.15i | −0.763675 | − | 0.398700i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4077.64 | + | 2354.23i | 0.956038 | + | 0.551969i | 0.894951 | − | 0.446164i | \(-0.147210\pi\) |
0.0610865 | + | 0.998132i | \(0.480543\pi\) | |||||||
\(264\) | 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 | −0.533607 | − | 0.845732i | \(-0.679164\pi\) |
0.999229 | + | 0.0392514i | \(0.0124973\pi\) | |||||||
\(270\) | 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 | \(-0.956280\pi\) | ||
0.990582 | − | 0.136919i | \(-0.0437198\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | −119.196 | − | 5615.97i | −0.0247739 | − | 1.16723i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1230.37 | + | 2131.06i | 0.250431 | + | 0.433760i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6066.27 | + | 3676.16i | −1.22203 | + | 0.740551i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6187.72 | −1.23376 | −0.616878 | − | 0.787059i | \(-0.711603\pi\) | ||||
−0.616878 | + | 0.787059i | \(0.711603\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5386.66 | 1.06313 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6239.44 | − | 3090.82i | −1.21902 | − | 0.603863i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −214.008 | − | 370.673i | −0.0413926 | − | 0.0716941i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6773.49 | + | 143.764i | −1.28425 | + | 0.0272574i | ||||
\(304\) | 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 | \(0.350808\pi\) |
−0.998494 | + | 0.0548698i | \(0.982526\pi\) | |||||||
\(312\) | 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 | 0.113693 | − | 0.993516i | \(-0.463732\pi\) |
0.917257 | + | 0.398297i | \(0.130398\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | 11635.6 | − | 246.960i | 1.96774 | − | 0.0417643i | ||||
\(328\) | 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 | ||||||||
\(333\) | −3158.93 | + | 134.154i | −0.519845 | + | 0.0220768i | ||||
\(334\) | 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 | ||||||||
\(339\) | 1250.30 | − | 757.684i | 0.200316 | − | 0.121392i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −62.6139 | − | 108.450i | −0.00994349 | − | 0.0172226i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 185.833 | + | 8755.59i | 0.0289997 | + | 1.36633i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1092.59 | + | 630.806i | 0.169029 | + | 0.0975891i | 0.582128 | − | 0.813097i | \(-0.302220\pi\) |
−0.413099 | + | 0.910686i | \(0.635554\pi\) | |||||||
\(348\) | 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 | \(-0.646272\pi\) |
0.997948 | − | 0.0640280i | \(-0.0203947\pi\) | |||||||
\(354\) | 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 | −0.467885 | − | 0.883789i | \(-0.654984\pi\) |
0.531441 | + | 0.847095i | \(0.321651\pi\) | |||||||
\(360\) | 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 | ||||||||
\(369\) | −2008.01 | + | 3846.17i | −0.283287 | + | 0.542612i | ||||
\(370\) | 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 | ||||||||
\(375\) | 4068.53 | + | 6713.73i | 0.560261 | + | 0.924522i | ||||
\(376\) | 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 | ||||||||
\(381\) | −1551.41 | − | 2560.08i | −0.208612 | − | 0.344244i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2212.79 | + | 3832.66i | 0.295217 | + | 0.511331i | 0.975035 | − | 0.222049i | \(-0.0712746\pi\) |
−0.679818 | + | 0.733381i | \(0.737941\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5531.57 | − | 10595.2i | 0.726578 | − | 1.39170i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1558.98 | + | 900.077i | 0.203196 | + | 0.117315i | 0.598146 | − | 0.801388i | \(-0.295904\pi\) |
−0.394949 | + | 0.918703i | \(0.629238\pi\) | |||||||
\(390\) | 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 | −0.303244 | − | 0.952913i | \(-0.598070\pi\) |
0.673625 | + | 0.739074i | \(0.264736\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | 113.670 | + | 5355.61i | 0.0136421 | + | 0.642756i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1714.77 | + | 2970.07i | 0.202831 | + | 0.351313i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1042.07 | + | 631.496i | −0.122375 | + | 0.0741594i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10148.4 | −1.18325 | −0.591626 | − | 0.806213i | \(-0.701514\pi\) | ||||
−0.591626 | + | 0.806213i | \(0.701514\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6775.40 | −0.784354 | −0.392177 | − | 0.919890i | \(-0.628278\pi\) | ||||
−0.392177 | + | 0.919890i | \(0.628278\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8406.41 | + | 357.004i | −0.966273 | + | 0.0410357i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 743.317 | + | 1287.46i | 0.0848381 | + | 0.146944i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 638.131 | − | 13.5440i | 0.0718164 | − | 0.00152426i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14439.3 | + | 8336.51i | 1.61372 | + | 0.931684i | 0.988497 | + | 0.151241i | \(0.0483268\pi\) |
0.625227 | + | 0.780443i | \(0.285007\pi\) | |||||||
\(432\) | 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 | −0.711714 | − | 0.702469i | \(-0.752081\pi\) |
0.252499 | + | 0.967597i | \(0.418748\pi\) | |||||||
\(444\) | 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 | \(0.316858\pi\) | ||||
−0.544136 | + | 0.838997i | \(0.683142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6906.99 | + | 3987.75i | 0.721147 | + | 0.416355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5481.44 | + | 116.341i | −0.568522 | + | 0.0120666i | ||||
\(454\) | 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 | ||||||||
\(459\) | 3083.93 | − | 6225.53i | 0.313607 | − | 0.633078i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3468.42 | −0.350413 | −0.175207 | − | 0.984532i | \(-0.556059\pi\) | ||||
−0.175207 | + | 0.984532i | \(0.556059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9918.45 | −0.995572 | −0.497786 | − | 0.867300i | \(-0.665853\pi\) | ||||
−0.497786 | + | 0.867300i | \(0.665853\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 109.275 | − | 66.2210i | 0.0108979 | − | 0.00660414i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8430.55 | + | 14602.1i | 0.835373 | + | 1.44691i | 0.893726 | + | 0.448613i | \(0.148082\pi\) |
−0.0583529 | + | 0.998296i | \(0.518585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.88753 | + | 230.278i | 0.000478144 | + | 0.0225280i | ||||
\(472\) | 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 | −0.931426 | − | 0.363932i | \(-0.881434\pi\) |
0.780887 | + | 0.624672i | \(0.214768\pi\) | |||||||
\(480\) | 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 | \(-0.980901\pi\) | ||
0.998200 | − | 0.0599667i | \(-0.0190995\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5769.79 | − | 3331.19i | −0.527096 | − | 0.304319i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11576.8 | − | 6044.05i | −1.05119 | − | 0.548808i | ||||
\(496\) | 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 | ||||||||
\(501\) | −4463.21 | − | 7365.03i | −0.398007 | − | 0.656777i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −787.994 | −0.0698507 | −0.0349253 | − | 0.999390i | \(-0.511119\pi\) | ||||
−0.0349253 | + | 0.999390i | \(0.511119\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12707.0 | −1.11971 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5899.98 | + | 9735.93i | 0.516819 | + | 0.852836i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1538.89 | + | 2665.44i | 0.134008 | + | 0.232109i | 0.925218 | − | 0.379436i | \(-0.123882\pi\) |
−0.791210 | + | 0.611544i | \(0.790549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12954.9 | − | 8622.78i | 1.11496 | − | 0.742115i | ||||
\(514\) | 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 | −0.892559 | − | 0.450931i | \(-0.851092\pi\) |
0.836797 | + | 0.547513i | \(0.184425\pi\) | |||||||
\(522\) | 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 | ||||||||
\(537\) | 47.4358 | + | 2234.96i | 0.00381193 | + | 0.179601i | ||||
\(538\) | 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 | ||||||||
\(543\) | 9911.96 | − | 6006.66i | 0.783357 | − | 0.474715i | ||||
\(544\) | 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 | ||||||||
\(549\) | −667.945 | − | 15728.2i | −0.0519257 | − | 1.22270i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7461.77 | − | 12924.2i | −0.576918 | − | 0.999252i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5928.79 | + | 125.835i | −0.453447 | + | 0.00962417i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6062.22 | + | 3500.02i | 0.461157 | + | 0.266249i | 0.712531 | − | 0.701641i | \(-0.247549\pi\) |
−0.251374 | + | 0.967890i | \(0.580882\pi\) | |||||||
\(558\) | 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 | \(-0.555311\pi\) |
0.939430 | − | 0.342742i | \(-0.111356\pi\) | |||||||
\(564\) | 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 | −0.782239 | − | 0.622979i | \(-0.785922\pi\) |
0.148396 | + | 0.988928i | \(0.452589\pi\) | |||||||
\(570\) | 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 | ||||||||
\(579\) | 11718.2 | − | 248.713i | 0.841093 | − | 0.0178517i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7132.28 | − | 12353.5i | −0.506670 | − | 0.877579i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.6326 | + | 650.669i | 0.00195294 | + | 0.0459861i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25424.1 | 1.78768 | 0.893838 | − | 0.448390i | \(-0.148002\pi\) | ||||
0.893838 | + | 0.448390i | \(0.148002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 279.881 | 0.0195795 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14577.8 | − | 8834.16i | 1.01464 | − | 0.614871i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3832.38 | + | 6637.89i | 0.265392 | + | 0.459672i | 0.967666 | − | 0.252235i | \(-0.0811654\pi\) |
−0.702275 | + | 0.711906i | \(0.747832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 486.113 | + | 22903.4i | 0.0333254 | + | 1.57014i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23961.5 | − | 13834.2i | −1.63446 | − | 0.943655i | −0.982695 | − | 0.185233i | \(-0.940696\pi\) |
−0.651764 | − | 0.758422i | \(-0.725971\pi\) | |||||||
\(600\) | 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 | \(-0.886639\pi\) | ||
0.937252 | − | 0.348654i | \(-0.113361\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | −20197.4 | + | 13443.4i | −1.30514 | + | 0.868702i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5485.59 | + | 9501.31i | 0.351077 | + | 0.608084i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14825.6 | − | 24464.6i | −0.944300 | − | 1.55825i | ||||
\(628\) | 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 | ||||||||
\(633\) | 15135.8 | + | 24976.5i | 0.950385 | + | 1.56829i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2807.23 | − | 4862.27i | −0.175436 | − | 0.303864i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23568.6 | − | 12304.7i | −1.45909 | − | 0.761765i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14083.3 | + | 8131.00i | 0.867796 | + | 0.501022i | 0.866615 | − | 0.498977i | \(-0.166291\pi\) |
0.00118054 | + | 0.999999i | \(0.499624\pi\) | |||||||
\(642\) | 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 | \(0.355027\pi\) |
−0.997679 | + | 0.0680988i | \(0.978307\pi\) | |||||||
\(648\) | 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 | 0.0756247 | − | 0.997136i | \(-0.475905\pi\) |
0.901358 | + | 0.433075i | \(0.142572\pi\) | |||||||
\(654\) | 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 | \(-0.967273\pi\) | ||
0.994719 | − | 0.102634i | \(-0.0327270\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 13.5138 | + | 636.708i | 0.000791602 | + | 0.0372967i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11633.3 | + | 20149.5i | 0.675327 | + | 1.16970i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5042.11 | − | 3055.52i | 0.291389 | − | 0.176582i | ||||
\(670\) | 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 | ||||||||
\(675\) | −1869.57 | + | 3774.10i | −0.106607 | + | 0.215208i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1975.54 | + | 3421.74i | 0.112151 | + | 0.194251i | 0.916637 | − | 0.399720i | \(-0.130893\pi\) |
−0.804486 | + | 0.593971i | \(0.797559\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11030.0 | − | 234.106i | 0.620661 | − | 0.0131732i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22216.3 | + | 12826.6i | 1.24463 | + | 0.718589i | 0.970034 | − | 0.242970i | \(-0.0781218\pi\) |
0.274598 | + | 0.961559i | \(0.411455\pi\) | |||||||
\(684\) | 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 | \(0.239463\pi\) | ||||
−0.730122 | + | 0.683317i | \(0.760537\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11249.3 | − | 6494.77i | −0.603519 | − | 0.348442i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15777.4 | + | 334.867i | −0.842855 | + | 0.0178891i | ||||
\(706\) | 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 | ||||||||
\(711\) | 17353.1 | − | 736.952i | 0.915320 | − | 0.0388718i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −436.350 | −0.0229193 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1197.13 | 0.0626154 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9066.09 | + | 5494.05i | −0.472216 | + | 0.286163i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1802.02 | − | 3121.19i | −0.0934687 | − | 0.161893i | 0.815500 | − | 0.578757i | \(-0.196462\pi\) |
−0.908968 | + | 0.416865i | \(0.863129\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 504.007 | + | 23746.5i | 0.0259256 | + | 1.22150i | ||||
\(724\) | 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 | \(0.0971866\pi\) | ||||
−0.953751 | + | 0.300599i | \(0.902813\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19643.0 | + | 11340.9i | 0.965992 | + | 0.557716i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4397.27 | + | 8422.57i | −0.215378 | + | 0.412538i | ||||
\(748\) | 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 | ||||||||
\(753\) | 15749.7 | + | 25989.6i | 0.762220 | + | 1.25779i | ||||
\(754\) | 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 | ||||||||
\(759\) | 23113.9 | + | 38141.6i | 1.10538 | + | 1.82405i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5888.86 | − | 10199.8i | −0.280514 | − | 0.485864i | 0.690998 | − | 0.722857i | \(-0.257171\pi\) |
−0.971511 | + | 0.236993i | \(0.923838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6030.58 | − | 11551.0i | 0.285015 | − | 0.545920i | ||||
\(766\) | 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 | \(-0.642000\pi\) |
0.996999 | − | 0.0774157i | \(-0.0246668\pi\) | |||||||
\(774\) | 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 | ||||||||
\(789\) | 519.157 | + | 24460.3i | 0.0234252 | + | 1.10369i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 721.521 | + | 1249.71i | 0.0323102 | + | 0.0559629i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12447.4 | − | 7543.16i | 0.555303 | − | 0.336514i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5364.15 | 0.238404 | 0.119202 | − | 0.992870i | \(-0.461966\pi\) | ||||
0.119202 | + | 0.992870i | \(0.461966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15432.0 | −0.683284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29369.8 | − | 1247.28i | 1.29555 | − | 0.0550193i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5101.35 | − | 8835.80i | −0.224188 | − | 0.388305i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21344.0 | − | 453.015i | 0.931034 | − | 0.0197607i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10538.2 | + | 6084.21i | 0.457975 | + | 0.264412i | 0.711193 | − | 0.702997i | \(-0.248155\pi\) |
−0.253217 | + | 0.967409i | \(0.581489\pi\) | |||||||
\(810\) | 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 | −0.997606 | − | 0.0691595i | \(-0.977968\pi\) |
−0.438909 | + | 0.898532i | \(0.644635\pi\) | |||||||
\(822\) | 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 | \(-0.852527\pi\) | ||
0.894583 | − | 0.446902i | \(-0.147473\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | 38727.9 | − | 821.978i | 1.61667 | − | 0.0343130i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8076.05 | − | 13988.1i | −0.334711 | − | 0.579736i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 317.206 | + | 157.134i | 0.0130994 | + | 0.00648904i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39336.9 | −1.61867 | −0.809333 | − | 0.587350i | \(-0.800171\pi\) | ||||
−0.809333 | + | 0.587350i | \(0.800171\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6288.44 | 0.257839 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5732.07 | − | 3473.64i | 0.234191 | − | 0.141920i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10675.8 | + | 18491.1i | 0.434627 | + | 0.752796i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 950.566 | + | 44786.4i | 0.0384256 | + | 1.81044i | ||||
\(850\) | 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 | −0.838726 | − | 0.544553i | \(-0.816699\pi\) |
0.890960 | + | 0.454082i | \(0.150033\pi\) | |||||||
\(858\) | 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 | −0.168514 | − | 0.985699i | \(-0.553897\pi\) |
0.769384 | + | 0.638787i | \(0.220563\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | −32672.7 | − | 17057.8i | −1.26667 | − | 0.661305i | ||||
\(874\) | 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 | ||||||||
\(879\) | −16663.4 | − | 27497.3i | −0.639412 | − | 1.05513i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7990.91 | 0.305585 | 0.152793 | − | 0.988258i | \(-0.451173\pi\) | ||||
0.152793 | + | 0.988258i | \(0.451173\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2454.35 | 0.0935397 | 0.0467699 | − | 0.998906i | \(-0.485107\pi\) | ||||
0.0467699 | + | 0.998906i | \(0.485107\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14506.2 | + | 23937.6i | 0.550983 | + | 0.909212i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11813.7 | − | 20461.9i | −0.447197 | − | 0.774568i | 0.551005 | − | 0.834502i | \(-0.314244\pi\) |
−0.998202 | + | 0.0599335i | \(0.980911\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3067.54 | − | 36050.7i | −0.115338 | − | 1.35549i | ||||
\(892\) | 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 | \(-0.885215\pi\) | ||
0.935682 | − | 0.352844i | \(-0.114785\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15125.3 | + | 8732.61i | 0.548275 | + | 0.316547i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −626.529 | − | 29519.2i | −0.0226365 | − | 1.06653i | ||||
\(916\) | 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 | ||||||||
\(921\) | −16822.2 | + | 10194.3i | −0.601859 | + | 0.364727i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2437.16 | 0.0869124 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3515.51 | 0.124961 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1447.48 | − | 34083.9i | −0.0512852 | − | 1.20762i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8806.15 | − | 15252.7i | −0.311002 | − | 0.538671i | 0.667578 | − | 0.744540i | \(-0.267331\pi\) |
−0.978579 | + | 0.205869i | \(0.933998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31157.0 | + | 661.290i | −1.09328 | + | 0.0232044i | ||||
\(934\) | 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 | −0.826903 | − | 0.562345i | \(-0.809899\pi\) |
0.900456 | + | 0.434946i | \(0.143233\pi\) | |||||||
\(942\) | 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 | 0.0433905 | − | 0.999058i | \(-0.486184\pi\) |
0.886905 | + | 0.461952i | \(0.152851\pi\) | |||||||
\(948\) | 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 | \(-0.804744\pi\) | ||
0.817687 | − | 0.575663i | \(-0.195256\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9777.91 | − | 5645.28i | −0.331315 | − | 0.191285i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −34688.3 | + | 736.240i | −1.17170 | + | 0.0248686i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14892.3 | − | 25794.2i | −0.499893 | − | 0.865840i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1676.36 | − | 39473.4i | −0.0560954 | − | 1.32088i | ||||
\(964\) | 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 | ||||||||
\(969\) | 24410.1 | − | 14792.5i | 0.809252 | − | 0.490407i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6266.70 | − | 10854.2i | −0.207114 | − | 0.358732i | 0.743690 | − | 0.668525i | \(-0.233074\pi\) |
−0.950804 | + | 0.309792i | \(0.899740\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.19246 | − | 385.992i | −0.000269096 | − | 0.0126786i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33448.2 | + | 19311.4i | 1.09530 | + | 0.632369i | 0.934981 | − | 0.354697i | \(-0.115416\pi\) |
0.160314 | + | 0.987066i | \(0.448749\pi\) | |||||||
\(978\) | 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 | \(0.354315\pi\) |
−0.997828 | + | 0.0658685i | \(0.979018\pi\) | |||||||
\(984\) | 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 | ||||||||
\(999\) | −9103.10 | − | 13676.6i | −0.288298 | − | 0.433140i |
(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.521.16 | 48 | ||
3.2 | odd | 2 | inner | 588.4.k.e.521.24 | 48 | ||
7.2 | even | 3 | inner | 588.4.k.e.509.1 | 48 | ||
7.3 | odd | 6 | 588.4.f.d.293.8 | yes | 24 | ||
7.4 | even | 3 | 588.4.f.d.293.17 | yes | 24 | ||
7.5 | odd | 6 | inner | 588.4.k.e.509.24 | 48 | ||
7.6 | odd | 2 | inner | 588.4.k.e.521.9 | 48 | ||
21.2 | odd | 6 | inner | 588.4.k.e.509.9 | 48 | ||
21.5 | even | 6 | inner | 588.4.k.e.509.16 | 48 | ||
21.11 | odd | 6 | 588.4.f.d.293.7 | ✓ | 24 | ||
21.17 | even | 6 | 588.4.f.d.293.18 | yes | 24 | ||
21.20 | even | 2 | inner | 588.4.k.e.521.1 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.f.d.293.7 | ✓ | 24 | 21.11 | odd | 6 | ||
588.4.f.d.293.8 | yes | 24 | 7.3 | odd | 6 | ||
588.4.f.d.293.17 | yes | 24 | 7.4 | even | 3 | ||
588.4.f.d.293.18 | yes | 24 | 21.17 | even | 6 | ||
588.4.k.e.509.1 | 48 | 7.2 | even | 3 | inner | ||
588.4.k.e.509.9 | 48 | 21.2 | odd | 6 | inner | ||
588.4.k.e.509.16 | 48 | 21.5 | even | 6 | inner | ||
588.4.k.e.509.24 | 48 | 7.5 | odd | 6 | inner | ||
588.4.k.e.521.1 | 48 | 21.20 | even | 2 | inner | ||
588.4.k.e.521.9 | 48 | 7.6 | odd | 2 | inner | ||
588.4.k.e.521.16 | 48 | 1.1 | even | 1 | trivial | ||
588.4.k.e.521.24 | 48 | 3.2 | odd | 2 | inner |