Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(449,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.q (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.7 | ||
Character | \(\chi\) | \(=\) | 1728.1601 |
Dual form | 1728.3.q.l.449.7 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.15965 | − | 0.669525i | 0.231930 | − | 0.133905i | −0.379532 | − | 0.925179i | \(-0.623915\pi\) |
0.611462 | + | 0.791274i | \(0.290582\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.328661 | + | 0.569258i | −0.0469516 | + | 0.0813226i | −0.888546 | − | 0.458787i | \(-0.848284\pi\) |
0.841595 | + | 0.540110i | \(0.181617\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.33786 | − | 4.23651i | −0.667078 | − | 0.385138i | 0.127891 | − | 0.991788i | \(-0.459179\pi\) |
−0.794968 | + | 0.606651i | \(0.792513\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.615997 | + | 1.06694i | 0.0473844 | + | 0.0820722i | 0.888745 | − | 0.458402i | \(-0.151578\pi\) |
−0.841360 | + | 0.540474i | \(0.818245\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.78107i | 0.340063i | 0.985439 | + | 0.170032i | \(0.0543870\pi\) | ||||
−0.985439 | + | 0.170032i | \(0.945613\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.7103 | 1.19528 | 0.597639 | − | 0.801765i | \(-0.296106\pi\) | ||||
0.597639 | + | 0.801765i | \(0.296106\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.4792 | − | 10.0916i | 0.759963 | − | 0.438765i | −0.0693192 | − | 0.997595i | \(-0.522083\pi\) |
0.829283 | + | 0.558829i | \(0.188749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.6035 | + | 20.0978i | −0.464139 | + | 0.803912i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −35.5451 | − | 20.5220i | −1.22569 | − | 0.707655i | −0.259568 | − | 0.965725i | \(-0.583580\pi\) |
−0.966126 | + | 0.258070i | \(0.916913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.57415 | − | 13.1188i | −0.244328 | − | 0.423188i | 0.717615 | − | 0.696440i | \(-0.245234\pi\) |
−0.961942 | + | 0.273253i | \(0.911901\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.880187i | 0.0251482i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 51.2271 | 1.38452 | 0.692258 | − | 0.721651i | \(-0.256616\pi\) | ||||
0.692258 | + | 0.721651i | \(0.256616\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17.7563 | + | 10.2516i | −0.433079 | + | 0.250038i | −0.700658 | − | 0.713498i | \(-0.747110\pi\) |
0.267578 | + | 0.963536i | \(0.413777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.14476 | − | 5.44689i | 0.0731340 | − | 0.126672i | −0.827139 | − | 0.561997i | \(-0.810033\pi\) |
0.900273 | + | 0.435325i | \(0.143367\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 31.9185 | + | 18.4281i | 0.679117 | + | 0.392088i | 0.799522 | − | 0.600637i | \(-0.205086\pi\) |
−0.120406 | + | 0.992725i | \(0.538419\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 24.2840 | + | 42.0611i | 0.495591 | + | 0.858389i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 85.9624i | − | 1.62193i | −0.585094 | − | 0.810966i | \(-0.698942\pi\) | ||
0.585094 | − | 0.810966i | \(-0.301058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.3458 | −0.206287 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 51.2682 | − | 29.5997i | 0.868953 | − | 0.501690i | 0.00195303 | − | 0.999998i | \(-0.499378\pi\) |
0.867000 | + | 0.498308i | \(0.166045\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38.1516 | − | 66.0806i | 0.625437 | − | 1.08329i | −0.363020 | − | 0.931781i | \(-0.618254\pi\) |
0.988456 | − | 0.151506i | \(-0.0484124\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.42868 | + | 0.824851i | 0.0219797 | + | 0.0126900i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −48.2337 | − | 83.5433i | −0.719907 | − | 1.24691i | −0.961036 | − | 0.276422i | \(-0.910851\pi\) |
0.241130 | − | 0.970493i | \(-0.422482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 31.2026i | − | 0.439473i | −0.975559 | − | 0.219737i | \(-0.929480\pi\) | ||
0.975559 | − | 0.219737i | \(-0.0705198\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −24.9673 | −0.342018 | −0.171009 | − | 0.985269i | \(-0.554703\pi\) | ||||
−0.171009 | + | 0.985269i | \(0.554703\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.82334 | − | 2.78475i | 0.0626407 | − | 0.0361656i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 67.4448 | − | 116.818i | 0.853732 | − | 1.47871i | −0.0240847 | − | 0.999710i | \(-0.507667\pi\) |
0.877817 | − | 0.478997i | \(-0.159000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 98.6013 | + | 56.9275i | 1.18797 | + | 0.685873i | 0.957844 | − | 0.287288i | \(-0.0927538\pi\) |
0.230123 | + | 0.973162i | \(0.426087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.87057 | + | 6.70403i | 0.0455361 | + | 0.0788709i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 135.098i | 1.51795i | 0.651118 | + | 0.758977i | \(0.274300\pi\) | ||||
−0.651118 | + | 0.758977i | \(0.725700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.809818 | −0.00889909 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26.3360 | − | 15.2051i | 0.277221 | − | 0.160054i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −68.8218 | + | 119.203i | −0.709503 | + | 1.22890i | 0.255538 | + | 0.966799i | \(0.417747\pi\) |
−0.965042 | + | 0.262097i | \(0.915586\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −102.305 | − | 59.0659i | −1.01292 | − | 0.584811i | −0.100876 | − | 0.994899i | \(-0.532165\pi\) |
−0.912046 | + | 0.410088i | \(0.865498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.9512 | + | 31.0923i | 0.174283 | + | 0.301867i | 0.939913 | − | 0.341414i | \(-0.110906\pi\) |
−0.765630 | + | 0.643281i | \(0.777573\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 51.3746i | − | 0.480136i | −0.970756 | − | 0.240068i | \(-0.922830\pi\) | ||
0.970756 | − | 0.240068i | \(-0.0771698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 65.4476 | 0.600436 | 0.300218 | − | 0.953871i | \(-0.402940\pi\) | ||||
0.300218 | + | 0.953871i | \(0.402940\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 49.6877 | − | 28.6872i | 0.439714 | − | 0.253869i | −0.263762 | − | 0.964588i | \(-0.584963\pi\) |
0.703476 | + | 0.710719i | \(0.251630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.5131 | − | 23.4055i | 0.117506 | − | 0.203526i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.29092 | − | 1.90001i | −0.0276548 | − | 0.0159665i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.6039 | − | 42.6152i | −0.203338 | − | 0.352192i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 64.5515i | 0.516412i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.5134 | −0.0985308 | −0.0492654 | − | 0.998786i | \(-0.515688\pi\) | ||||
−0.0492654 | + | 0.998786i | \(0.515688\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 100.368 | − | 57.9476i | 0.766169 | − | 0.442348i | −0.0653374 | − | 0.997863i | \(-0.520812\pi\) |
0.831506 | + | 0.555515i | \(0.187479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.46399 | + | 12.9280i | −0.0561202 | + | 0.0972031i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 55.9545 | + | 32.3053i | 0.408427 | + | 0.235805i | 0.690114 | − | 0.723701i | \(-0.257561\pi\) |
−0.281687 | + | 0.959506i | \(0.590894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −86.2101 | − | 149.320i | −0.620216 | − | 1.07425i | −0.989445 | − | 0.144908i | \(-0.953711\pi\) |
0.369229 | − | 0.929339i | \(-0.379622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 10.4387i | − | 0.0729980i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −54.9599 | −0.379034 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 145.339 | − | 83.9114i | 0.975428 | − | 0.563163i | 0.0745411 | − | 0.997218i | \(-0.476251\pi\) |
0.900887 | + | 0.434055i | \(0.142917\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 118.439 | − | 205.142i | 0.784363 | − | 1.35856i | −0.145015 | − | 0.989429i | \(-0.546323\pi\) |
0.929379 | − | 0.369128i | \(-0.120343\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.5667 | − | 10.1422i | −0.113334 | − | 0.0654333i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −80.3922 | − | 139.243i | −0.512052 | − | 0.886900i | −0.999902 | − | 0.0139730i | \(-0.995552\pi\) |
0.487850 | − | 0.872927i | \(-0.337781\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.2669i | 0.0824029i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 279.703 | 1.71597 | 0.857986 | − | 0.513673i | \(-0.171716\pi\) | ||||
0.857986 | + | 0.513673i | \(0.171716\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 199.901 | − | 115.413i | 1.19701 | − | 0.691096i | 0.237125 | − | 0.971479i | \(-0.423795\pi\) |
0.959888 | + | 0.280383i | \(0.0904615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 83.7411 | − | 145.044i | 0.495509 | − | 0.858248i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 91.9688 | + | 53.0982i | 0.531612 | + | 0.306926i | 0.741673 | − | 0.670762i | \(-0.234033\pi\) |
−0.210061 | + | 0.977688i | \(0.567366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.62722 | − | 13.2107i | −0.0435841 | − | 0.0754899i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.14055i | − | 0.0231315i | −0.999933 | − | 0.0115658i | \(-0.996318\pi\) | ||
0.999933 | − | 0.0115658i | \(-0.00368158\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −186.430 | −1.03000 | −0.515001 | − | 0.857190i | \(-0.672208\pi\) | ||||
−0.515001 | + | 0.857190i | \(0.672208\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 59.4055 | − | 34.2978i | 0.321111 | − | 0.185393i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.4916 | − | 42.4207i | 0.130971 | − | 0.226849i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 209.368 | + | 120.879i | 1.09617 | + | 0.632872i | 0.935211 | − | 0.354090i | \(-0.115209\pi\) |
0.160955 | + | 0.986962i | \(0.448543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −44.3377 | − | 76.7952i | −0.229729 | − | 0.397903i | 0.727999 | − | 0.685579i | \(-0.240451\pi\) |
−0.957728 | + | 0.287676i | \(0.907117\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 224.293i | 1.13854i | 0.822149 | + | 0.569272i | \(0.192775\pi\) | ||||
−0.822149 | + | 0.569272i | \(0.807225\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −371.640 | −1.86754 | −0.933770 | − | 0.357874i | \(-0.883502\pi\) | ||||
−0.933770 | + | 0.357874i | \(0.883502\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.3646 | − | 13.4896i | 0.115097 | − | 0.0664510i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.7274 | + | 23.7765i | −0.0669628 | + | 0.115983i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −166.645 | − | 96.2124i | −0.797343 | − | 0.460346i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −69.1170 | − | 119.714i | −0.327569 | − | 0.567365i | 0.654460 | − | 0.756096i | \(-0.272896\pi\) |
−0.982029 | + | 0.188731i | \(0.939563\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.42198i | − | 0.0391720i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.95732 | 0.0458863 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.16805 | + | 3.56113i | −0.0279097 | + | 0.0161137i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 112.891 | − | 195.533i | 0.506238 | − | 0.876829i | −0.493736 | − | 0.869612i | \(-0.664369\pi\) |
0.999974 | − | 0.00721770i | \(-0.00229749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 110.292 | + | 63.6769i | 0.485866 | + | 0.280515i | 0.722858 | − | 0.690997i | \(-0.242828\pi\) |
−0.236992 | + | 0.971512i | \(0.576161\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 77.1871 | + | 133.692i | 0.337061 | + | 0.583807i | 0.983879 | − | 0.178838i | \(-0.0572337\pi\) |
−0.646817 | + | 0.762645i | \(0.723900\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3013i | 0.0871300i | 0.999051 | + | 0.0435650i | \(0.0138716\pi\) | ||||
−0.999051 | + | 0.0435650i | \(0.986128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 49.3524 | 0.210010 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 223.391 | − | 128.975i | 0.934691 | − | 0.539644i | 0.0463986 | − | 0.998923i | \(-0.485226\pi\) |
0.888292 | + | 0.459279i | \(0.151892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 38.0826 | − | 65.9610i | 0.158019 | − | 0.273697i | −0.776135 | − | 0.630567i | \(-0.782823\pi\) |
0.934154 | + | 0.356869i | \(0.116156\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 56.3218 | + | 32.5174i | 0.229885 | + | 0.132724i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.9895 | + | 24.2305i | 0.0566375 | + | 0.0980991i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 108.320i | − | 0.431555i | −0.976443 | − | 0.215778i | \(-0.930771\pi\) | ||
0.976443 | − | 0.215778i | \(-0.0692286\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −171.013 | −0.675940 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 289.661 | − | 167.236i | 1.12709 | − | 0.650723i | 0.183885 | − | 0.982948i | \(-0.441133\pi\) |
0.943200 | + | 0.332225i | \(0.107799\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.8363 | + | 29.1614i | −0.0650052 | + | 0.112592i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.4612 | − | 10.6586i | −0.0701946 | − | 0.0405269i | 0.464492 | − | 0.885577i | \(-0.346237\pi\) |
−0.534687 | + | 0.845050i | \(0.679570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −57.5539 | − | 99.6863i | −0.217185 | − | 0.376175i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 411.961i | 1.53145i | 0.643167 | + | 0.765726i | \(0.277620\pi\) | ||||
−0.643167 | + | 0.765726i | \(0.722380\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 169.050 | 0.623803 | 0.311901 | − | 0.950115i | \(-0.399034\pi\) | ||||
0.311901 | + | 0.950115i | \(0.399034\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 170.289 | − | 98.3165i | 0.619234 | − | 0.357515i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −183.385 | + | 317.632i | −0.662040 | + | 1.14669i | 0.318039 | + | 0.948078i | \(0.396976\pi\) |
−0.980079 | + | 0.198609i | \(0.936357\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −212.102 | − | 122.457i | −0.754812 | − | 0.435791i | 0.0726179 | − | 0.997360i | \(-0.476865\pi\) |
−0.827430 | + | 0.561569i | \(0.810198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −134.798 | − | 233.478i | −0.476320 | − | 0.825010i | 0.523312 | − | 0.852141i | \(-0.324696\pi\) |
−0.999632 | + | 0.0271311i | \(0.991363\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 13.4772i | − | 0.0469588i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 255.579 | 0.884357 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 109.202 | − | 63.0479i | 0.372704 | − | 0.215181i | −0.301935 | − | 0.953328i | \(-0.597633\pi\) |
0.674639 | + | 0.738148i | \(0.264299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39.6355 | − | 68.6507i | 0.134358 | − | 0.232714i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.5342 | + | 12.4328i | 0.0720208 | + | 0.0415812i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.06712 | + | 3.58036i | 0.00686752 | + | 0.0118949i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 102.174i | − | 0.334996i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 254.097 | 0.827679 | 0.413840 | − | 0.910350i | \(-0.364187\pi\) | ||||
0.413840 | + | 0.910350i | \(0.364187\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −450.132 | + | 259.884i | −1.44737 | + | 0.835640i | −0.998324 | − | 0.0578683i | \(-0.981570\pi\) |
−0.449047 | + | 0.893508i | \(0.648236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 188.807 | − | 327.023i | 0.603217 | − | 1.04480i | −0.389113 | − | 0.921190i | \(-0.627219\pi\) |
0.992331 | − | 0.123613i | \(-0.0394481\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.7374 | + | 12.5501i | 0.0685722 | + | 0.0395902i | 0.533894 | − | 0.845551i | \(-0.320728\pi\) |
−0.465322 | + | 0.885142i | \(0.654061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 173.883 | + | 301.175i | 0.545089 | + | 0.944121i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 131.290i | 0.406470i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.5908 | −0.0879718 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.9807 | + | 12.1132i | −0.0637712 | + | 0.0368183i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −267.865 | + | 463.956i | −0.809261 | + | 1.40168i | 0.104116 | + | 0.994565i | \(0.466799\pi\) |
−0.913377 | + | 0.407116i | \(0.866535\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −111.869 | − | 64.5873i | −0.333936 | − | 0.192798i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 108.211 | + | 187.427i | 0.321101 | + | 0.556164i | 0.980716 | − | 0.195440i | \(-0.0626136\pi\) |
−0.659614 | + | 0.751604i | \(0.729280\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 128.352i | 0.376399i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −64.1336 | −0.186978 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −205.090 | + | 118.409i | −0.591036 | + | 0.341235i | −0.765507 | − | 0.643427i | \(-0.777512\pi\) |
0.174471 | + | 0.984662i | \(0.444179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −69.5513 | + | 120.466i | −0.199287 | + | 0.345176i | −0.948298 | − | 0.317383i | \(-0.897196\pi\) |
0.749010 | + | 0.662558i | \(0.230529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −533.791 | − | 308.184i | −1.51216 | − | 0.873044i | −0.999899 | − | 0.0142112i | \(-0.995476\pi\) |
−0.512257 | − | 0.858832i | \(-0.671190\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.8909 | − | 36.1841i | −0.0588476 | − | 0.101927i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 337.595i | − | 0.940375i | −0.882567 | − | 0.470187i | \(-0.844186\pi\) | ||
0.882567 | − | 0.470187i | \(-0.155814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 154.757 | 0.428690 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.9534 | + | 16.7162i | −0.0793243 | + | 0.0457979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 60.3827 | − | 104.586i | 0.164530 | − | 0.284975i | −0.771958 | − | 0.635674i | \(-0.780722\pi\) |
0.936488 | + | 0.350698i | \(0.114056\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 48.9347 | + | 28.2525i | 0.131900 | + | 0.0761523i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 154.120 | + | 266.943i | 0.413190 | + | 0.715666i | 0.995237 | − | 0.0974896i | \(-0.0310813\pi\) |
−0.582047 | + | 0.813155i | \(0.697748\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 50.5659i | − | 0.134127i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −231.359 | −0.610446 | −0.305223 | − | 0.952281i | \(-0.598731\pi\) | ||||
−0.305223 | + | 0.952281i | \(0.598731\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −167.447 | + | 96.6758i | −0.437200 | + | 0.252417i | −0.702409 | − | 0.711773i | \(-0.747892\pi\) |
0.265209 | + | 0.964191i | \(0.414559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.72892 | − | 6.45869i | 0.00968552 | − | 0.0167758i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −590.703 | − | 341.042i | −1.51852 | − | 0.876715i | −0.999763 | − | 0.0217913i | \(-0.993063\pi\) |
−0.518753 | − | 0.854924i | \(-0.673604\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 58.3403 | + | 101.048i | 0.149208 | + | 0.258436i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 180.624i | − | 0.457276i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 233.681 | 0.588618 | 0.294309 | − | 0.955710i | \(-0.404911\pi\) | ||||
0.294309 | + | 0.955710i | \(0.404911\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 235.711 | − | 136.088i | 0.587809 | − | 0.339372i | −0.176422 | − | 0.984315i | \(-0.556452\pi\) |
0.764231 | + | 0.644943i | \(0.223119\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.33132 | − | 16.1623i | 0.0231546 | − | 0.0401050i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −375.897 | − | 217.024i | −0.923579 | − | 0.533229i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 92.1194 | + | 159.555i | 0.225231 | + | 0.390111i | 0.956389 | − | 0.292097i | \(-0.0943531\pi\) |
−0.731158 | + | 0.682208i | \(0.761020\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 38.9131i | 0.0942207i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 152.457 | 0.367367 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −72.1233 | + | 41.6404i | −0.172132 | + | 0.0993805i | −0.583591 | − | 0.812048i | \(-0.698353\pi\) |
0.411459 | + | 0.911428i | \(0.365019\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 213.853 | − | 370.405i | 0.507965 | − | 0.879821i | −0.491992 | − | 0.870599i | \(-0.663731\pi\) |
0.999957 | − | 0.00922184i | \(-0.00293544\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −116.187 | − | 67.0805i | −0.273381 | − | 0.157837i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.0779 | + | 43.4362i | 0.0587305 | + | 0.101724i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 698.818i | 1.62139i | 0.585470 | + | 0.810694i | \(0.300910\pi\) | ||||
−0.585470 | + | 0.810694i | \(0.699090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −70.4515 | −0.162705 | −0.0813527 | − | 0.996685i | \(-0.525924\pi\) | ||||
−0.0813527 | + | 0.996685i | \(0.525924\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 396.957 | − | 229.183i | 0.908368 | − | 0.524446i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −365.285 | + | 632.692i | −0.832084 | + | 1.44121i | 0.0642994 | + | 0.997931i | \(0.479519\pi\) |
−0.896383 | + | 0.443280i | \(0.853815\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −511.433 | − | 295.276i | −1.15448 | − | 0.666538i | −0.204503 | − | 0.978866i | \(-0.565558\pi\) |
−0.949974 | + | 0.312328i | \(0.898891\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 90.4514 | + | 156.666i | 0.203261 | + | 0.352059i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 386.044i | 0.859785i | 0.902880 | + | 0.429893i | \(0.141449\pi\) | ||||
−0.902880 | + | 0.429893i | \(0.858551\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 173.724 | 0.385197 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.939105 | + | 0.542193i | −0.00206397 | + | 0.00119163i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −209.179 | + | 362.309i | −0.457722 | + | 0.792798i | −0.998840 | − | 0.0481488i | \(-0.984668\pi\) |
0.541118 | + | 0.840947i | \(0.318001\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −462.178 | − | 266.838i | −1.00255 | − | 0.578825i | −0.0935513 | − | 0.995614i | \(-0.529822\pi\) |
−0.909003 | + | 0.416789i | \(0.863155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.1080 | − | 36.5602i | −0.0455897 | − | 0.0789637i | 0.842330 | − | 0.538962i | \(-0.181183\pi\) |
−0.887920 | + | 0.459998i | \(0.847850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 734.531i | 1.57287i | 0.617673 | + | 0.786435i | \(0.288076\pi\) | ||||
−0.617673 | + | 0.786435i | \(0.711924\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 63.4102 | 0.135203 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −46.1516 | + | 26.6457i | −0.0975722 | + | 0.0563333i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −263.518 | + | 456.427i | −0.554775 | + | 0.960899i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 577.408 | + | 333.367i | 1.20544 | + | 0.695964i | 0.961761 | − | 0.273891i | \(-0.0883107\pi\) |
0.243684 | + | 0.969855i | \(0.421644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.5557 | + | 54.6561i | 0.0656044 | + | 0.113630i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 184.312i | 0.380024i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −788.556 | −1.61921 | −0.809606 | − | 0.586974i | \(-0.800319\pi\) | ||||
−0.809606 | + | 0.586974i | \(0.800319\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −300.390 | + | 173.430i | −0.611792 | + | 0.353218i | −0.773667 | − | 0.633593i | \(-0.781579\pi\) |
0.161874 | + | 0.986811i | \(0.448246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 118.639 | − | 205.489i | 0.240647 | − | 0.416813i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.7623 | + | 10.2551i | 0.0357391 | + | 0.0206340i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 260.871 | + | 451.841i | 0.522787 | + | 0.905493i | 0.999648 | + | 0.0265150i | \(0.00844096\pi\) |
−0.476862 | + | 0.878978i | \(0.658226\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 244.735i | − | 0.486550i | −0.969957 | − | 0.243275i | \(-0.921778\pi\) | ||
0.969957 | − | 0.243275i | \(-0.0782217\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −158.184 | −0.313236 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 278.949 | − | 161.051i | 0.548034 | − | 0.316407i | −0.200295 | − | 0.979736i | \(-0.564190\pi\) |
0.748329 | + | 0.663328i | \(0.230857\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.20579 | − | 14.2128i | 0.0160583 | − | 0.0278138i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 41.6341 | + | 24.0375i | 0.0808430 | + | 0.0466747i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −156.142 | − | 270.446i | −0.302016 | − | 0.523107i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 486.479i | 0.933740i | 0.884326 | + | 0.466870i | \(0.154618\pi\) | ||||
−0.884326 | + | 0.466870i | \(0.845382\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −337.116 | −0.644582 | −0.322291 | − | 0.946641i | \(-0.604453\pi\) | ||||
−0.322291 | + | 0.946641i | \(0.604453\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 75.8409 | − | 43.7867i | 0.143911 | − | 0.0830868i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −60.8194 | + | 105.342i | −0.114970 | + | 0.199135i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.8756 | − | 12.6299i | −0.0410424 | − | 0.0236958i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.3965 | − | 59.5766i | −0.0642926 | − | 0.111358i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 411.517i | − | 0.763483i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.2083 | −0.0650800 | −0.0325400 | − | 0.999470i | \(-0.510360\pi\) | ||||
−0.0325400 | + | 0.999470i | \(0.510360\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 75.8963 | − | 43.8188i | 0.139259 | − | 0.0804014i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 321.377 | − | 556.641i | 0.587526 | − | 1.01762i | −0.407030 | − | 0.913415i | \(-0.633435\pi\) |
0.994555 | − | 0.104210i | \(-0.0332313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −807.240 | − | 466.060i | −1.46504 | − | 0.845844i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.3330 | + | 76.7870i | 0.0801681 | + | 0.138855i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 602.553i | − | 1.08178i | −0.841092 | − | 0.540892i | \(-0.818087\pi\) | ||
0.841092 | − | 0.540892i | \(-0.181913\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.74866 | 0.0138616 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −601.451 | + | 347.248i | −1.06830 | + | 0.616782i | −0.927716 | − | 0.373288i | \(-0.878230\pi\) |
−0.140581 | + | 0.990069i | \(0.544897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.4136 | − | 66.5343i | 0.0679886 | − | 0.117760i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 283.950 | + | 163.939i | 0.499033 | + | 0.288117i | 0.728314 | − | 0.685243i | \(-0.240304\pi\) |
−0.229281 | + | 0.973360i | \(0.573637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 440.493 | + | 762.956i | 0.771441 | + | 1.33617i | 0.936773 | + | 0.349937i | \(0.113797\pi\) |
−0.165332 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 468.390i | 0.814592i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −394.926 | −0.684447 | −0.342224 | − | 0.939619i | \(-0.611180\pi\) | ||||
−0.342224 | + | 0.939619i | \(0.611180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −64.8128 | + | 37.4197i | −0.111554 | + | 0.0644057i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −364.181 | + | 630.779i | −0.624667 | + | 1.08195i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −821.405 | − | 474.238i | −1.39933 | − | 0.807902i | −0.405005 | − | 0.914314i | \(-0.632730\pi\) |
−0.994322 | + | 0.106413i | \(0.966064\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −172.011 | − | 297.932i | −0.292039 | − | 0.505827i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1138.81i | 1.92043i | 0.279269 | + | 0.960213i | \(0.409908\pi\) | ||||
−0.279269 | + | 0.960213i | \(0.590092\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.08843 | −0.00855198 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −286.895 | + | 165.639i | −0.478956 | + | 0.276525i | −0.719981 | − | 0.693993i | \(-0.755850\pi\) |
0.241025 | + | 0.970519i | \(0.422516\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −416.186 | + | 720.856i | −0.692490 | + | 1.19943i | 0.278530 | + | 0.960428i | \(0.410153\pi\) |
−0.971020 | + | 0.239000i | \(0.923180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −57.0639 | − | 32.9459i | −0.0943205 | − | 0.0544560i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 395.479 | + | 684.990i | 0.651531 | + | 1.12848i | 0.982751 | + | 0.184931i | \(0.0592063\pi\) |
−0.331220 | + | 0.943553i | \(0.607460\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 45.4067i | 0.0743154i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 795.300 | 1.29739 | 0.648695 | − | 0.761049i | \(-0.275315\pi\) | ||||
0.648695 | + | 0.761049i | \(0.275315\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 512.491 | − | 295.887i | 0.830618 | − | 0.479558i | −0.0234462 | − | 0.999725i | \(-0.507464\pi\) |
0.854064 | + | 0.520168i | \(0.174131\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −198.357 | + | 343.565i | −0.320448 | + | 0.555033i | −0.980581 | − | 0.196117i | \(-0.937167\pi\) |
0.660132 | + | 0.751149i | \(0.270500\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −76.9055 | − | 44.4014i | −0.123444 | − | 0.0712704i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −246.868 | − | 427.588i | −0.394989 | − | 0.684141i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 296.147i | 0.470823i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 451.164 | 0.714999 | 0.357499 | − | 0.933913i | \(-0.383629\pi\) | ||||
0.357499 | + | 0.933913i | \(0.383629\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.5112 | + | 8.37804i | −0.0228523 | + | 0.0131938i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.9177 | + | 51.8190i | −0.0469666 | + | 0.0813485i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 488.625 | + | 282.108i | 0.762285 | + | 0.440105i | 0.830116 | − | 0.557591i | \(-0.188274\pi\) |
−0.0678306 | + | 0.997697i | \(0.521608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 209.098 | + | 362.169i | 0.325192 | + | 0.563248i | 0.981551 | − | 0.191200i | \(-0.0612379\pi\) |
−0.656360 | + | 0.754448i | \(0.727905\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 38.3697i | − | 0.0593040i | −0.999560 | − | 0.0296520i | \(-0.990560\pi\) | ||
0.999560 | − | 0.0296520i | \(-0.00943991\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −501.599 | −0.772879 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 89.3873 | − | 51.6078i | 0.136887 | − | 0.0790318i | −0.429993 | − | 0.902832i | \(-0.641484\pi\) |
0.566880 | + | 0.823801i | \(0.308150\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 77.5946 | − | 134.398i | 0.118465 | − | 0.205188i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 680.807 | + | 393.064i | 1.03309 | + | 0.596455i | 0.917869 | − | 0.396885i | \(-0.129909\pi\) |
0.115222 | + | 0.993340i | \(0.463242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −431.654 | − | 747.646i | −0.653031 | − | 1.13108i | −0.982384 | − | 0.186876i | \(-0.940164\pi\) |
0.329353 | − | 0.944207i | \(-0.393170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.9893i | 0.0300591i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −828.398 | −1.24198 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −559.902 | + | 323.260i | −0.834430 | + | 0.481758i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.0001 | − | 55.4259i | 0.0475485 | − | 0.0823564i | −0.841272 | − | 0.540613i | \(-0.818192\pi\) |
0.888820 | + | 0.458256i | \(0.151526\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −365.558 | − | 211.055i | −0.539967 | − | 0.311750i | 0.205098 | − | 0.978741i | \(-0.434249\pi\) |
−0.745066 | + | 0.666991i | \(0.767582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.2381 | − | 78.3547i | −0.0666246 | − | 0.115397i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 59.7457i | 0.0874754i | 0.999043 | + | 0.0437377i | \(0.0139266\pi\) | ||||
−0.999043 | + | 0.0437377i | \(0.986073\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 86.5169 | 0.126302 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 91.7165 | − | 52.9526i | 0.133115 | − | 0.0768542i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.7385 | − | 23.7959i | 0.0198821 | − | 0.0344368i | −0.855913 | − | 0.517120i | \(-0.827004\pi\) |
0.875795 | + | 0.482683i | \(0.160338\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −199.947 | − | 115.440i | −0.287694 | − | 0.166100i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −59.2651 | − | 102.650i | −0.0850289 | − | 0.147274i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 440.657i | − | 0.628611i | −0.949322 | − | 0.314306i | \(-0.898228\pi\) | ||
0.949322 | − | 0.314306i | \(-0.101772\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1163.38 | 1.65488 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 67.2474 | − | 38.8253i | 0.0951166 | − | 0.0549156i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 562.466 | − | 974.219i | 0.793323 | − | 1.37408i | −0.130576 | − | 0.991438i | \(-0.541683\pi\) |
0.923899 | − | 0.382637i | \(-0.124984\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −264.780 | − | 152.871i | −0.371360 | − | 0.214405i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.98898 | − | 12.1053i | −0.00977480 | − | 0.0169304i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 734.502i | − | 1.02156i | −0.859711 | − | 0.510780i | \(-0.829357\pi\) | ||
0.859711 | − | 0.510780i | \(-0.170643\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.5994 | −0.0327315 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 824.894 | − | 476.253i | 1.13778 | − | 0.656900i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −605.328 | + | 1048.46i | −0.832639 | + | 1.44217i | 0.0632997 | + | 0.997995i | \(0.479838\pi\) |
−0.895938 | + | 0.444178i | \(0.853496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.4889 | + | 18.1801i | 0.0430764 | + | 0.0248702i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 212.490 | + | 368.044i | 0.289891 | + | 0.502106i | 0.973783 | − | 0.227477i | \(-0.0730476\pi\) |
−0.683893 | + | 0.729583i | \(0.739714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 817.371i | 1.10905i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.6676 | 0.0266138 | 0.0133069 | − | 0.999911i | \(-0.495764\pi\) | ||||
0.0133069 | + | 0.999911i | \(0.495764\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −673.114 | + | 388.622i | −0.905940 | + | 0.523045i | −0.879123 | − | 0.476595i | \(-0.841871\pi\) |
−0.0268177 | + | 0.999640i | \(0.508537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 112.361 | − | 194.616i | 0.150821 | − | 0.261229i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.2454 | + | 16.8848i | 0.0390459 | + | 0.0225432i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −372.532 | − | 645.245i | −0.496048 | − | 0.859181i | 0.503941 | − | 0.863738i | \(-0.331883\pi\) |
−0.999990 | + | 0.00455689i | \(0.998549\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 317.191i | − | 0.420120i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1278.50 | −1.68890 | −0.844449 | − | 0.535635i | \(-0.820072\pi\) | ||||
−0.844449 | + | 0.535635i | \(0.820072\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 95.3728 | − | 55.0635i | 0.125326 | − | 0.0723568i | −0.436027 | − | 0.899934i | \(-0.643615\pi\) |
0.561352 | + | 0.827577i | \(0.310281\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.5101 | + | 37.2565i | −0.0281915 | + | 0.0488290i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 63.1622 | + | 36.4667i | 0.0823497 | + | 0.0475446i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −76.7696 | − | 132.969i | −0.0998304 | − | 0.172911i | 0.811784 | − | 0.583958i | \(-0.198497\pi\) |
−0.911614 | + | 0.411047i | \(0.865163\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1448.17i | 1.87344i | 0.350073 | + | 0.936722i | \(0.386157\pi\) | ||||
−0.350073 | + | 0.936722i | \(0.613843\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 351.546 | 0.453608 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −403.249 | + | 232.816i | −0.517650 | + | 0.298865i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −132.190 | + | 228.960i | −0.169258 | + | 0.293163i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −186.454 | − | 107.649i | −0.237521 | − | 0.137133i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 91.2986 | + | 158.134i | 0.116008 | + | 0.200932i | 0.918182 | − | 0.396158i | \(-0.129657\pi\) |
−0.802174 | + | 0.597090i | \(0.796323\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.7135i | 0.0476782i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 94.0052 | 0.118544 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 622.667 | − | 359.497i | 0.781263 | − | 0.451063i | −0.0556145 | − | 0.998452i | \(-0.517712\pi\) |
0.836878 | + | 0.547390i | \(0.184378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −106.534 | + | 184.523i | −0.133335 | + | 0.230943i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 183.207 | + | 105.774i | 0.228153 | + | 0.131724i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.88249 | + | 15.3849i | 0.0110342 | + | 0.0191117i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 967.469i | − | 1.19588i | −0.801540 | − | 0.597942i | \(-0.795985\pi\) | ||
0.801540 | − | 0.597942i | \(-0.204015\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1014.11 | −1.25044 | −0.625221 | − | 0.780448i | \(-0.714991\pi\) | ||||
−0.625221 | + | 0.780448i | \(0.714991\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 324.358 | − | 187.268i | 0.397985 | − | 0.229777i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 71.4185 | − | 123.700i | 0.0874155 | − | 0.151408i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −71.8562 | − | 41.4862i | −0.0875228 | − | 0.0505313i | 0.455600 | − | 0.890185i | \(-0.349425\pi\) |
−0.543123 | + | 0.839653i | \(0.682758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −491.669 | − | 851.595i | −0.597410 | − | 1.03474i | −0.993202 | − | 0.116404i | \(-0.962863\pi\) |
0.395792 | − | 0.918340i | \(-0.370470\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 352.196i | 0.425871i | 0.977066 | + | 0.212936i | \(0.0683025\pi\) | ||||
−0.977066 | + | 0.212936i | \(0.931697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 63.3448 | 0.0764111 | 0.0382055 | − | 0.999270i | \(-0.487836\pi\) | ||||
0.0382055 | + | 0.999270i | \(0.487836\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −243.158 | + | 140.387i | −0.291907 | + | 0.168532i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 154.544 | − | 267.678i | 0.185082 | − | 0.320572i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −394.812 | − | 227.945i | −0.470575 | − | 0.271686i | 0.245906 | − | 0.969294i | \(-0.420915\pi\) |
−0.716480 | + | 0.697607i | \(0.754248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 421.804 | + | 730.586i | 0.501550 | + | 0.868710i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 224.267i | − | 0.265405i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.3454 | 0.0381882 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 895.406 | − | 516.963i | 1.05218 | − | 0.607477i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −413.061 | + | 715.443i | −0.484245 | + | 0.838737i | −0.999836 | − | 0.0180976i | \(-0.994239\pi\) |
0.515591 | + | 0.856835i | \(0.327572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 304.917 | + | 176.044i | 0.355796 | + | 0.205419i | 0.667235 | − | 0.744847i | \(-0.267478\pi\) |
−0.311439 | + | 0.950266i | \(0.600811\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −346.426 | − | 600.028i | −0.403290 | − | 0.698519i | 0.590831 | − | 0.806796i | \(-0.298800\pi\) |
−0.994121 | + | 0.108276i | \(0.965467\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1288.63i | 1.49319i | 0.665277 | + | 0.746596i | \(0.268313\pi\) | ||||
−0.665277 | + | 0.746596i | \(0.731687\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 142.202 | 0.164396 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −989.801 | + | 571.462i | −1.13901 | + | 0.657608i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 59.4237 | − | 102.925i | 0.0682247 | − | 0.118169i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −36.7464 | − | 21.2156i | −0.0419959 | − | 0.0242464i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 285.241 | + | 494.051i | 0.325246 | + | 0.563342i | 0.981562 | − | 0.191144i | \(-0.0612196\pi\) |
−0.656316 | + | 0.754486i | \(0.727886\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 42.1382i | − | 0.0478300i | −0.999714 | − | 0.0239150i | \(-0.992387\pi\) | ||
0.999714 | − | 0.0239150i | \(-0.00761310\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 99.1902 | 0.112333 | 0.0561666 | − | 0.998421i | \(-0.482112\pi\) | ||||
0.0561666 | + | 0.998421i | \(0.482112\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1167.87 | − | 674.272i | 1.31666 | − | 0.760172i | 0.333467 | − | 0.942762i | \(-0.391782\pi\) |
0.983189 | + | 0.182590i | \(0.0584482\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.11267 | − | 7.12336i | 0.00462618 | − | 0.00801278i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 724.878 | + | 418.508i | 0.811733 | + | 0.468654i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.77220 | − | 4.80159i | −0.00309743 | − | 0.00536490i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 621.747i | 0.691598i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 496.955 | 0.551559 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −216.194 | + | 124.820i | −0.238888 | + | 0.137922i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 462.420 | − | 800.935i | 0.509835 | − | 0.883059i | −0.490100 | − | 0.871666i | \(-0.663040\pi\) |
0.999935 | − | 0.0113935i | \(-0.00362674\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1134.47 | + | 654.987i | 1.24530 | + | 0.718976i | 0.970169 | − | 0.242430i | \(-0.0779443\pi\) |
0.275134 | + | 0.961406i | \(0.411278\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −482.348 | − | 835.451i | −0.528311 | − | 0.915062i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 76.1805i | 0.0830757i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −591.406 | −0.643532 | −0.321766 | − | 0.946819i | \(-0.604277\pi\) | ||||
−0.321766 | + | 0.946819i | \(0.604277\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.2912 | − | 19.2207i | 0.0360685 | − | 0.0208242i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −594.412 | + | 1029.55i | −0.642607 | + | 1.11303i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1063.25 | − | 613.870i | −1.14452 | − | 0.660786i | −0.196971 | − | 0.980409i | \(-0.563110\pi\) |
−0.947545 | + | 0.319623i | \(0.896444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 551.496 | + | 955.219i | 0.592369 | + | 1.02601i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 65.5909i | − | 0.0701507i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 528.681 | 0.564228 | 0.282114 | − | 0.959381i | \(-0.408964\pi\) | ||||
0.282114 | + | 0.959381i | \(0.408964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1554.27 | + | 897.360i | −1.65172 | + | 0.953624i | −0.675361 | + | 0.737487i | \(0.736012\pi\) |
−0.976363 | + | 0.216137i | \(0.930654\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −206.910 | + | 358.378i | −0.219416 | + | 0.380040i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −162.093 | − | 93.5844i | −0.171165 | − | 0.0988220i | 0.411970 | − | 0.911197i | \(-0.364841\pi\) |
−0.583135 | + | 0.812375i | \(0.698174\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.3798 | − | 26.6386i | −0.0162063 | − | 0.0280702i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1473.92i | − | 1.54661i | −0.634035 | − | 0.773304i | \(-0.718602\pi\) | ||
0.634035 | − | 0.773304i | \(-0.281398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 323.725 | 0.338979 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.7801 | + | 21.2350i | −0.0383526 | + | 0.0221429i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 365.764 | − | 633.523i | 0.380608 | − | 0.659233i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −102.833 | − | 59.3704i | −0.106562 | − | 0.0615237i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −526.580 | − | 912.063i | −0.544550 | − | 0.943189i | −0.998635 | − | 0.0522302i | \(-0.983367\pi\) |
0.454085 | − | 0.890958i | \(-0.349966\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 691.453i | − | 0.712104i | −0.934466 | − | 0.356052i | \(-0.884123\pi\) | ||
0.934466 | − | 0.356052i | \(-0.115877\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 113.336 | 0.116481 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 730.566 | − | 421.793i | 0.747765 | − | 0.431722i | −0.0771208 | − | 0.997022i | \(-0.524573\pi\) |
0.824886 | + | 0.565299i | \(0.191239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 572.344 | − | 991.329i | 0.584621 | − | 1.01259i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 365.413 | + | 210.971i | 0.371732 | + | 0.214620i | 0.674215 | − | 0.738535i | \(-0.264482\pi\) |
−0.302483 | + | 0.953155i | \(0.597815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 150.170 | + | 260.102i | 0.152457 | + | 0.264063i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 126.943i | − | 0.128355i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1063.60 | 1.07326 | 0.536630 | − | 0.843818i | \(-0.319697\pi\) | ||||
0.536630 | + | 0.843818i | \(0.319697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −430.973 | + | 248.822i | −0.433139 | + | 0.250073i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −276.703 | + | 479.264i | −0.277536 | + | 0.480706i | −0.970772 | − | 0.240005i | \(-0.922851\pi\) |
0.693236 | + | 0.720711i | \(0.256184\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.q.l.1601.7 | 24 | ||
3.2 | odd | 2 | 576.3.q.k.65.12 | 24 | |||
4.3 | odd | 2 | inner | 1728.3.q.l.1601.8 | 24 | ||
8.3 | odd | 2 | 864.3.q.b.737.6 | 24 | |||
8.5 | even | 2 | 864.3.q.b.737.5 | 24 | |||
9.4 | even | 3 | 576.3.q.k.257.12 | 24 | |||
9.5 | odd | 6 | inner | 1728.3.q.l.449.7 | 24 | ||
12.11 | even | 2 | 576.3.q.k.65.1 | 24 | |||
24.5 | odd | 2 | 288.3.q.a.65.1 | ✓ | 24 | ||
24.11 | even | 2 | 288.3.q.a.65.12 | yes | 24 | ||
36.23 | even | 6 | inner | 1728.3.q.l.449.8 | 24 | ||
36.31 | odd | 6 | 576.3.q.k.257.1 | 24 | |||
72.5 | odd | 6 | 864.3.q.b.449.5 | 24 | |||
72.11 | even | 6 | 2592.3.e.j.161.14 | 24 | |||
72.13 | even | 6 | 288.3.q.a.257.1 | yes | 24 | ||
72.29 | odd | 6 | 2592.3.e.j.161.12 | 24 | |||
72.43 | odd | 6 | 2592.3.e.j.161.13 | 24 | |||
72.59 | even | 6 | 864.3.q.b.449.6 | 24 | |||
72.61 | even | 6 | 2592.3.e.j.161.11 | 24 | |||
72.67 | odd | 6 | 288.3.q.a.257.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.3.q.a.65.1 | ✓ | 24 | 24.5 | odd | 2 | ||
288.3.q.a.65.12 | yes | 24 | 24.11 | even | 2 | ||
288.3.q.a.257.1 | yes | 24 | 72.13 | even | 6 | ||
288.3.q.a.257.12 | yes | 24 | 72.67 | odd | 6 | ||
576.3.q.k.65.1 | 24 | 12.11 | even | 2 | |||
576.3.q.k.65.12 | 24 | 3.2 | odd | 2 | |||
576.3.q.k.257.1 | 24 | 36.31 | odd | 6 | |||
576.3.q.k.257.12 | 24 | 9.4 | even | 3 | |||
864.3.q.b.449.5 | 24 | 72.5 | odd | 6 | |||
864.3.q.b.449.6 | 24 | 72.59 | even | 6 | |||
864.3.q.b.737.5 | 24 | 8.5 | even | 2 | |||
864.3.q.b.737.6 | 24 | 8.3 | odd | 2 | |||
1728.3.q.l.449.7 | 24 | 9.5 | odd | 6 | inner | ||
1728.3.q.l.449.8 | 24 | 36.23 | even | 6 | inner | ||
1728.3.q.l.1601.7 | 24 | 1.1 | even | 1 | trivial | ||
1728.3.q.l.1601.8 | 24 | 4.3 | odd | 2 | inner | ||
2592.3.e.j.161.11 | 24 | 72.61 | even | 6 | |||
2592.3.e.j.161.12 | 24 | 72.29 | odd | 6 | |||
2592.3.e.j.161.13 | 24 | 72.43 | odd | 6 | |||
2592.3.e.j.161.14 | 24 | 72.11 | even | 6 |