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 | 521.6 | ||
Character | \(\chi\) | \(=\) | 588.521 |
Dual form | 588.4.k.e.509.6 |
$q$-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 | ||||||||
\(3\) | −3.41120 | + | 3.91966i | −0.656485 | + | 0.754339i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.50213 | + | 11.2620i | 0.581568 | + | 1.00731i | 0.995294 | + | 0.0969038i | \(0.0308939\pi\) |
−0.413726 | + | 0.910402i | \(0.635773\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.72746 | − | 26.7415i | −0.138054 | − | 0.990425i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.49726 | − | 2.59650i | −0.123271 | − | 0.0711703i | 0.437097 | − | 0.899414i | \(-0.356007\pi\) |
−0.560367 | + | 0.828244i | \(0.689340\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72.6603i | 1.55018i | 0.631850 | + | 0.775090i | \(0.282296\pi\) | ||||
−0.631850 | + | 0.775090i | \(0.717704\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −66.3233 | − | 12.9308i | −1.14164 | − | 0.222582i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 44.7733 | − | 77.5496i | 0.638772 | − | 1.10639i | −0.346931 | − | 0.937891i | \(-0.612776\pi\) |
0.985703 | − | 0.168495i | \(-0.0538906\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −113.080 | + | 65.2865i | −1.36538 | + | 0.788302i | −0.990334 | − | 0.138704i | \(-0.955706\pi\) |
−0.375046 | + | 0.927006i | \(0.622373\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −108.141 | + | 62.4354i | −0.980392 | + | 0.566029i | −0.902388 | − | 0.430924i | \(-0.858188\pi\) |
−0.0780033 | + | 0.996953i | \(0.524854\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −22.0553 | + | 38.2010i | −0.176443 | + | 0.305608i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 117.533 | + | 76.6101i | 0.837746 | + | 0.546060i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 63.1418i | 0.404315i | 0.979353 | + | 0.202158i | \(0.0647953\pi\) | ||||
−0.979353 | + | 0.202158i | \(0.935205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 91.6564 | + | 52.9179i | 0.531032 | + | 0.306591i | 0.741436 | − | 0.671023i | \(-0.234145\pi\) |
−0.210405 | + | 0.977614i | \(0.567478\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 25.5184 | − | 8.77058i | 0.134612 | − | 0.0462655i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 46.9184 | + | 81.2651i | 0.208469 | + | 0.361078i | 0.951232 | − | 0.308475i | \(-0.0998187\pi\) |
−0.742764 | + | 0.669554i | \(0.766485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −284.804 | − | 247.859i | −1.16936 | − | 1.01767i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −320.640 | −1.22136 | −0.610678 | − | 0.791879i | \(-0.709103\pi\) | ||||
−0.610678 | + | 0.791879i | \(0.709103\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −351.830 | −1.24776 | −0.623878 | − | 0.781522i | \(-0.714444\pi\) | ||||
−0.623878 | + | 0.781522i | \(0.714444\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 276.926 | − | 215.855i | 0.917372 | − | 0.715062i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 102.656 | + | 177.805i | 0.318593 | + | 0.551820i | 0.980195 | − | 0.198036i | \(-0.0634563\pi\) |
−0.661602 | + | 0.749856i | \(0.730123\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 151.238 | + | 440.033i | 0.415245 | + | 1.20818i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −68.9957 | − | 39.8347i | −0.178817 | − | 0.103240i | 0.407920 | − | 0.913018i | \(-0.366254\pi\) |
−0.586737 | + | 0.809778i | \(0.699588\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 67.5310i | − | 0.165561i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 129.836 | − | 665.938i | 0.301705 | − | 1.54747i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 449.621 | − | 778.767i | 0.992130 | − | 1.71842i | 0.387629 | − | 0.921815i | \(-0.373294\pi\) |
0.604501 | − | 0.796604i | \(-0.293373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 489.428 | − | 282.571i | 1.02729 | − | 0.593107i | 0.111084 | − | 0.993811i | \(-0.464568\pi\) |
0.916208 | + | 0.400703i | \(0.131234\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −818.302 | + | 472.447i | −1.56151 | + | 0.901536i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 41.1414 | − | 71.2591i | 0.0750183 | − | 0.129936i | −0.826076 | − | 0.563559i | \(-0.809432\pi\) |
0.901094 | + | 0.433623i | \(0.142765\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 124.166 | − | 636.856i | 0.216635 | − | 1.11114i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 457.950i | − | 0.765474i | −0.923857 | − | 0.382737i | \(-0.874982\pi\) | ||
0.923857 | − | 0.382737i | \(-0.125018\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −769.098 | − | 444.039i | −1.23310 | − | 0.711929i | −0.265423 | − | 0.964132i | \(-0.585512\pi\) |
−0.967674 | + | 0.252203i | \(0.918845\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −74.4997 | − | 216.761i | −0.114700 | − | 0.333725i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −247.926 | − | 429.421i | −0.353087 | − | 0.611565i | 0.633701 | − | 0.773578i | \(-0.281535\pi\) |
−0.986789 | + | 0.162013i | \(0.948201\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −701.212 | + | 199.355i | −0.961882 | + | 0.273464i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1022.84 | −1.35267 | −0.676336 | − | 0.736594i | \(-0.736433\pi\) | ||||
−0.676336 | + | 0.736594i | \(0.736433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1164.49 | 1.48596 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −247.494 | − | 215.389i | −0.304991 | − | 0.265427i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 65.5170 | + | 113.479i | 0.0780313 | + | 0.135154i | 0.902400 | − | 0.430898i | \(-0.141803\pi\) |
−0.824369 | + | 0.566053i | \(0.808470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −520.078 | + | 178.749i | −0.579888 | + | 0.199305i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1470.51 | − | 849.002i | −1.58812 | − | 0.916903i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 897.230i | 0.939174i | 0.882886 | + | 0.469587i | \(0.155597\pi\) | ||||
−0.882886 | + | 0.469587i | \(0.844403\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −52.6707 | + | 129.942i | −0.0534708 | + | 0.131915i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 574.855 | − | 995.677i | 0.566338 | − | 0.980927i | −0.430585 | − | 0.902550i | \(-0.641693\pi\) |
0.996924 | − | 0.0783770i | \(-0.0249738\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1425.92 | + | 823.254i | −1.36408 | + | 0.787550i | −0.990164 | − | 0.139914i | \(-0.955318\pi\) |
−0.373913 | + | 0.927464i | \(0.621984\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1701.12 | + | 982.145i | −1.53695 | + | 0.887360i | −0.537938 | + | 0.842985i | \(0.680796\pi\) |
−0.999015 | + | 0.0443752i | \(0.985870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −786.758 | + | 1362.70i | −0.691355 | + | 1.19746i | 0.280039 | + | 0.959989i | \(0.409653\pi\) |
−0.971394 | + | 0.237474i | \(0.923681\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −478.580 | − | 93.3071i | −0.409232 | − | 0.0797866i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2002.30i | − | 1.66691i | −0.552590 | − | 0.833454i | \(-0.686360\pi\) | ||
0.552590 | − | 0.833454i | \(-0.313640\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1406.30 | − | 811.926i | −1.14033 | − | 0.658369i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1943.04 | − | 270.838i | 1.53534 | − | 0.214009i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −652.016 | − | 1129.33i | −0.489870 | − | 0.848479i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1093.77 | − | 1256.80i | 0.801802 | − | 0.921316i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1051.91 | 0.752682 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −166.537 | −0.116361 | −0.0581803 | − | 0.998306i | \(-0.518530\pi\) | ||||
−0.0581803 | + | 0.998306i | \(0.518530\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1200.16 | − | 1379.05i | 0.819134 | − | 0.941231i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −157.967 | − | 273.606i | −0.105356 | − | 0.182482i | 0.808528 | − | 0.588458i | \(-0.200265\pi\) |
−0.913884 | + | 0.405976i | \(0.866931\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −98.5721 | + | 1821.78i | −0.0628425 | + | 1.16144i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 345.158 | + | 199.277i | 0.215247 | + | 0.124273i | 0.603747 | − | 0.797176i | \(-0.293674\pi\) |
−0.388501 | + | 0.921448i | \(0.627007\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 228.245i | 0.139277i | 0.997572 | + | 0.0696384i | \(0.0221845\pi\) | ||||
−0.997572 | + | 0.0696384i | \(0.977815\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1047.11 | − | 204.152i | −0.625411 | − | 0.121934i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 188.662 | − | 326.773i | 0.110327 | − | 0.191092i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −711.104 | + | 410.556i | −0.407269 | + | 0.235137i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3066.97 | − | 1770.71i | 1.68628 | − | 0.973574i | 0.728954 | − | 0.684563i | \(-0.240007\pi\) |
0.957326 | − | 0.289011i | \(-0.0933263\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 105.383 | − | 182.529i | 0.0567945 | − | 0.0983710i | −0.836230 | − | 0.548378i | \(-0.815245\pi\) |
0.893025 | + | 0.450007i | \(0.148579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2240.68 | − | 908.241i | −1.18398 | − | 0.479914i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1376.31i | 0.713215i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2462.26 | + | 1421.59i | 1.25166 | + | 0.722644i | 0.971438 | − | 0.237292i | \(-0.0762599\pi\) |
0.280218 | + | 0.959936i | \(0.409593\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 391.497 | − | 134.556i | 0.195269 | − | 0.0671130i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 228.833 | + | 396.350i | 0.109961 | + | 0.190457i | 0.915754 | − | 0.401739i | \(-0.131594\pi\) |
−0.805794 | + | 0.592197i | \(0.798261\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 264.698 | + | 230.362i | 0.124889 | + | 0.108689i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2108.64 | 0.977076 | 0.488538 | − | 0.872543i | \(-0.337530\pi\) | ||||
0.488538 | + | 0.872543i | \(0.337530\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3082.52 | −1.40306 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2167.36 | + | 2780.56i | 0.969250 | + | 1.24348i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 439.144 | + | 760.620i | 0.192991 | + | 0.334271i | 0.946240 | − | 0.323465i | \(-0.104848\pi\) |
−0.753249 | + | 0.657736i | \(0.771514\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1518.75 | + | 4418.89i | 0.644952 | + | 1.87652i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2742.00 | − | 1583.09i | −1.14495 | − | 0.661039i | −0.197301 | − | 0.980343i | \(-0.563218\pi\) |
−0.947652 | + | 0.319304i | \(0.896551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4000.19i | 1.64272i | 0.570413 | + | 0.821358i | \(0.306783\pi\) | ||||
−0.570413 | + | 0.821358i | \(0.693217\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −561.952 | + | 2882.30i | −0.226998 | + | 1.16429i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −610.139 | + | 1056.79i | −0.242478 | + | 0.419983i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −402.715 | + | 232.507i | −0.157483 | + | 0.0909231i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −861.175 | + | 497.200i | −0.326243 | + | 0.188357i | −0.654172 | − | 0.756346i | \(-0.726983\pi\) |
0.327929 | + | 0.944702i | \(0.393649\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1030.58 | − | 1785.02i | 0.384367 | − | 0.665743i | −0.607314 | − | 0.794462i | \(-0.707753\pi\) |
0.991681 | + | 0.128719i | \(0.0410864\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 939.559 | − | 4819.07i | 0.345042 | − | 1.76975i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 399.812i | 0.144596i | 0.997383 | + | 0.0722980i | \(0.0230333\pi\) | ||||
−0.997383 | + | 0.0722980i | \(0.976967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2516.96 | − | 1453.17i | −0.896597 | − | 0.517650i | −0.0205024 | − | 0.999790i | \(-0.506527\pi\) |
−0.876095 | + | 0.482139i | \(0.839860\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 138.970 | + | 404.339i | 0.0487670 | + | 0.141890i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2084.84 | − | 3611.06i | −0.710301 | − | 1.23028i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2072.71 | + | 2659.13i | 0.695957 | + | 0.892861i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 678.064 | 0.224415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2947.20 | 0.961582 | 0.480791 | − | 0.876835i | \(-0.340350\pi\) | ||||
0.480791 | + | 0.876835i | \(0.340350\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1795.01 | + | 1562.16i | 0.577426 | + | 0.502522i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2287.64 | − | 3962.31i | −0.725655 | − | 1.25687i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4364.03 | − | 1499.90i | 1.34655 | − | 0.462802i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5634.78 | + | 3253.24i | 1.71510 | + | 0.990212i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3481.59i | 1.04549i | 0.852489 | + | 0.522745i | \(0.175092\pi\) | ||||
−0.852489 | + | 0.522745i | \(0.824908\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1103.76 | + | 447.400i | 0.327040 | + | 0.132563i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1937.00 | + | 3354.98i | −0.566357 | + | 0.980959i | 0.430565 | + | 0.902560i | \(0.358314\pi\) |
−0.996922 | + | 0.0783996i | \(0.975019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3472.34 | + | 2004.76i | −1.00200 | + | 0.578507i | −0.908841 | − | 0.417144i | \(-0.863031\pi\) |
−0.0931632 | + | 0.995651i | \(0.529698\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4398.07 | − | 2539.23i | 1.23660 | − | 0.713949i | 0.268200 | − | 0.963363i | \(-0.413571\pi\) |
0.968397 | + | 0.249414i | \(0.0802380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1334.96 | + | 2312.22i | −0.370567 | + | 0.641841i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2528.91 | + | 493.053i | 0.693124 | + | 0.135136i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1081.25i | 0.292636i | 0.989238 | + | 0.146318i | \(0.0467423\pi\) | ||||
−0.989238 | + | 0.146318i | \(0.953258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2854.95 | − | 1648.31i | −0.763086 | − | 0.440568i | 0.0673168 | − | 0.997732i | \(-0.478556\pi\) |
−0.830403 | + | 0.557164i | \(0.811890\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1610.57 | − | 3428.55i | 0.425177 | − | 0.905110i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4743.74 | − | 8216.40i | −1.22201 | − | 2.11659i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3489.12 | − | 4009.20i | 0.888009 | − | 1.02037i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −690.705 | −0.173693 | −0.0868464 | − | 0.996222i | \(-0.527679\pi\) | ||||
−0.0868464 | + | 0.996222i | \(0.527679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 648.453 | 0.161138 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3972.30 | + | 4564.39i | −0.975509 | + | 1.12092i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3948.33 | + | 6838.71i | 0.958327 | + | 1.65987i | 0.726563 | + | 0.687100i | \(0.241117\pi\) |
0.231764 | + | 0.972772i | \(0.425550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1688.50 | − | 235.359i | 0.400444 | − | 0.0558173i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2595.62 | + | 1498.58i | 0.608567 | + | 0.351356i | 0.772404 | − | 0.635131i | \(-0.219054\pi\) |
−0.163838 | + | 0.986487i | \(0.552387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1036.04i | − | 0.240164i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −668.289 | − | 130.294i | −0.153178 | − | 0.0298647i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4041.71 | + | 7000.45i | −0.916087 | + | 1.58671i | −0.110785 | + | 0.993844i | \(0.535337\pi\) |
−0.805302 | + | 0.592865i | \(0.797997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2865.50 | + | 1654.40i | −0.642313 | + | 0.370840i | −0.785505 | − | 0.618855i | \(-0.787597\pi\) |
0.143192 | + | 0.989695i | \(0.454263\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 198.377 | − | 114.533i | 0.0435004 | − | 0.0251150i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2497.77 | + | 4326.26i | −0.541792 | + | 0.938411i | 0.457009 | + | 0.889462i | \(0.348921\pi\) |
−0.998801 | + | 0.0489494i | \(0.984413\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1073.46 | − | 2648.28i | 0.230344 | − | 0.568273i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4123.67i | 0.875436i | 0.899112 | + | 0.437718i | \(0.144213\pi\) | ||||
−0.899112 | + | 0.437718i | \(0.855787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1586.09 | − | 915.727i | −0.333155 | − | 0.192347i | 0.324086 | − | 0.946028i | \(-0.394943\pi\) |
−0.657241 | + | 0.753680i | \(0.728277\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8344.02 | − | 2867.80i | 1.73423 | − | 0.596049i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1552.80 | − | 2689.52i | −0.316059 | − | 0.547430i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3516.84 | − | 3060.63i | −0.708456 | − | 0.616554i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2676.36 | −0.533634 | −0.266817 | − | 0.963747i | \(-0.585972\pi\) | ||||
−0.266817 | + | 0.963747i | \(0.585972\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11694.0 | 2.30796 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −329.657 | − | 649.708i | −0.0644062 | − | 0.126936i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4536.58 | − | 7857.58i | −0.877448 | − | 1.51978i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1941.77 | + | 5649.69i | 0.368158 | + | 1.07118i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6364.65 | + | 3674.63i | 1.19488 | + | 0.689865i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 384.925i | − | 0.0715597i | −0.999360 | − | 0.0357798i | \(-0.988608\pi\) | ||
0.999360 | − | 0.0357798i | \(-0.0113915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1637.21 | − | 8397.40i | 0.301417 | − | 1.54599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1220.95 | + | 2114.75i | −0.222617 | + | 0.385584i | −0.955602 | − | 0.294661i | \(-0.904793\pi\) |
0.732985 | + | 0.680245i | \(0.238127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3573.75 | + | 2063.30i | −0.645368 | + | 0.372603i | −0.786679 | − | 0.617362i | \(-0.788201\pi\) |
0.141312 | + | 0.989965i | \(0.454868\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5833.28 | − | 3367.85i | 1.03353 | − | 0.596710i | 0.115538 | − | 0.993303i | \(-0.463141\pi\) |
0.917995 | + | 0.396593i | \(0.129808\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 163.947 | − | 283.965i | 0.0287752 | − | 0.0498401i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1953.20 | − | 10018.1i | 0.339617 | − | 1.74192i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11692.4i | 2.01418i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2775.70 | − | 1602.55i | −0.473747 | − | 0.273518i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2657.55 | − | 7732.28i | −0.449428 | − | 1.30763i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2059.35 | + | 3566.90i | 0.341970 | + | 0.592310i | 0.984799 | − | 0.173700i | \(-0.0555724\pi\) |
−0.642828 | + | 0.766010i | \(0.722239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1998.26 | − | 1557.58i | 0.328841 | − | 0.256321i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1070.03 | 0.174513 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4453.87 | −0.719934 | −0.359967 | − | 0.932965i | \(-0.617212\pi\) | ||||
−0.359967 | + | 0.932965i | \(0.617212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7848.33 | + | 6830.24i | 1.25741 | + | 1.09430i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −274.802 | − | 475.971i | −0.0436404 | − | 0.0755873i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7979.63 | − | 2742.56i | 1.24524 | − | 0.427985i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4468.22 | + | 2579.73i | 0.691258 | + | 0.399098i | 0.804083 | − | 0.594517i | \(-0.202657\pi\) |
−0.112825 | + | 0.993615i | \(0.535990\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2662.35i | 0.408345i | 0.978935 | + | 0.204173i | \(0.0654504\pi\) | ||||
−0.978935 | + | 0.204173i | \(0.934550\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5566.51 | + | 8539.95i | −0.846491 | + | 1.29866i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 294.789 | − | 510.590i | 0.0444477 | − | 0.0769857i | −0.842946 | − | 0.537999i | \(-0.819181\pi\) |
0.887393 | + | 0.461013i | \(0.152514\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5157.44 | − | 2977.65i | 0.771066 | − | 0.445175i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7391.47 | + | 4267.47i | −1.08665 | + | 0.627377i | −0.932682 | − | 0.360699i | \(-0.882538\pi\) |
−0.153967 | + | 0.988076i | \(0.549205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5095.15 | − | 8825.06i | 0.742841 | − | 1.28664i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6650.73 | + | 1296.67i | 0.961633 | + | 0.187486i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 11548.8i | − | 1.65614i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6753.50 | + | 3899.13i | 0.960571 | + | 0.554586i | 0.896349 | − | 0.443350i | \(-0.146210\pi\) |
0.0642224 | + | 0.997936i | \(0.479543\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1195.17 | + | 8574.39i | 0.168613 | + | 1.20966i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −602.802 | − | 1044.08i | −0.0836780 | − | 0.144934i | 0.821149 | − | 0.570714i | \(-0.193333\pi\) |
−0.904827 | + | 0.425779i | \(0.860000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3588.26 | + | 4123.11i | −0.494125 | + | 0.567777i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4587.90 | −0.626762 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8527.67 | −1.15577 | −0.577885 | − | 0.816118i | \(-0.696122\pi\) | ||||
−0.577885 | + | 0.816118i | \(0.696122\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 568.091 | − | 652.769i | 0.0763890 | − | 0.0877753i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4723.71 | + | 8181.71i | 0.630210 | + | 1.09156i | 0.987509 | + | 0.157566i | \(0.0503645\pi\) |
−0.357299 | + | 0.933990i | \(0.616302\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1311.43 | + | 9408.44i | 0.172258 | + | 1.23581i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8117.13 | − | 4686.42i | −1.05798 | − | 0.610826i | −0.133108 | − | 0.991102i | \(-0.542496\pi\) |
−0.924873 | + | 0.380276i | \(0.875829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11181.8i | 1.44625i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1611.30 | + | 314.150i | 0.206818 | + | 0.0403225i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3224.10 | − | 5584.30i | 0.410688 | − | 0.711333i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1236.96 | + | 714.160i | −0.156376 | + | 0.0902837i | −0.576146 | − | 0.817347i | \(-0.695444\pi\) |
0.419770 | + | 0.907630i | \(0.362111\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2535.87 | − | 1464.08i | 0.315799 | − | 0.182326i | −0.333720 | − | 0.942672i | \(-0.608304\pi\) |
0.649518 | + | 0.760346i | \(0.274971\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3845.03 | + | 6659.79i | −0.475272 | + | 0.823195i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6804.52 | − | 6600.83i | −0.834862 | − | 0.809871i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 487.294i | − | 0.0593471i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7106.97 | − | 4103.21i | −0.859210 | − | 0.496065i | 0.00453767 | − | 0.999990i | \(-0.498556\pi\) |
−0.863748 | + | 0.503925i | \(0.831889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1958.50 | + | 673.128i | −0.235050 | + | 0.0807857i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6650.66 | − | 11519.3i | −0.786670 | − | 1.36255i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −894.642 | − | 778.588i | −0.105062 | − | 0.0914332i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 191.679 | 0.0223487 | 0.0111744 | − | 0.999938i | \(-0.496443\pi\) | ||||
0.0111744 | + | 0.999938i | \(0.496443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5722.17 | −0.662427 | −0.331213 | − | 0.943556i | \(-0.607458\pi\) | ||||
−0.331213 | + | 0.943556i | \(0.607458\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4372.12 | − | 3407.93i | 0.502553 | − | 0.391723i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1974.98 | + | 3420.77i | 0.225413 | + | 0.390427i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 637.273 | + | 1854.18i | 0.0717199 | + | 0.208673i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11254.2 | − | 6497.61i | −1.25776 | − | 0.726169i | −0.285122 | − | 0.958491i | \(-0.592034\pi\) |
−0.972639 | + | 0.232323i | \(0.925368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7022.02i | 0.779346i | 0.920953 | + | 0.389673i | \(0.127412\pi\) | ||||
−0.920953 | + | 0.389673i | \(0.872588\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 816.476 | − | 4187.77i | 0.0899932 | − | 0.461582i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8152.37 | − | 14120.3i | 0.892405 | − | 1.54569i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10337.2 | + | 5968.16i | −1.12384 | + | 0.648849i | −0.942378 | − | 0.334549i | \(-0.891416\pi\) |
−0.181461 | + | 0.983398i | \(0.558083\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6650.98 | + | 3839.94i | −0.713313 | + | 0.411831i | −0.812286 | − | 0.583259i | \(-0.801777\pi\) |
0.0989738 | + | 0.995090i | \(0.468444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −851.999 | + | 1475.71i | −0.0907610 | + | 0.157203i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3521.43 | + | 18061.7i | −0.372613 | + | 1.91116i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1268.09i | − | 0.133285i | −0.997777 | − | 0.0666425i | \(-0.978771\pi\) | ||
0.997777 | − | 0.0666425i | \(-0.0212287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1442.00 | + | 832.541i | 0.150557 | + | 0.0869242i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 355.969 | + | 1035.71i | 0.0369203 | + | 0.107421i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1900.21 | − | 3291.25i | −0.194503 | − | 0.336889i | 0.752234 | − | 0.658896i | \(-0.228976\pi\) |
−0.946738 | + | 0.322006i | \(0.895643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11203.4 | − | 5684.52i | 1.13928 | − | 0.578063i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11736.5 | 1.18573 | 0.592866 | − | 0.805301i | \(-0.297996\pi\) | ||||
0.592866 | + | 0.805301i | \(0.297996\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5696.66 | −0.571806 | −0.285903 | − | 0.958259i | \(-0.592294\pi\) | ||||
−0.285903 | + | 0.958259i | \(0.592294\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5394.68 | − | 4694.88i | −0.538005 | − | 0.468215i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8339.06 | − | 14443.7i | −0.826307 | − | 1.43121i | −0.900916 | − | 0.433993i | \(-0.857104\pi\) |
0.0746089 | − | 0.997213i | \(-0.476229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13971.4 | + | 4801.92i | −1.36681 | + | 0.469768i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1582.27 | + | 913.524i | 0.153812 | + | 0.0888032i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5759.66i | − | 0.556361i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −808.060 | + | 1993.53i | −0.0775650 | + | 0.191357i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −528.256 | + | 914.966i | −0.0503896 | + | 0.0872774i | −0.890120 | − | 0.455726i | \(-0.849380\pi\) |
0.839730 | + | 0.543004i | \(0.182713\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5904.75 | + | 3409.11i | −0.559737 | + | 0.323164i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10104.6 | + | 5833.90i | −0.946035 | + | 0.546194i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4919.83 | + | 8521.40i | −0.457780 | + | 0.792898i | −0.998843 | − | 0.0480836i | \(-0.984689\pi\) |
0.541063 | + | 0.840982i | \(0.318022\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2334.15 | − | 455.082i | −0.215857 | − | 0.0420849i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5838.19i | − | 0.536606i | −0.963335 | − | 0.268303i | \(-0.913537\pi\) | ||
0.963335 | − | 0.268303i | \(-0.0864629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4896.62 | + | 2827.07i | 0.447328 | + | 0.258265i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1805.88 | + | 251.719i | −0.163976 | + | 0.0228564i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9197.15 | + | 15929.9i | 0.825092 | + | 1.42910i | 0.901849 | + | 0.432052i | \(0.142210\pi\) |
−0.0767565 | + | 0.997050i | \(0.524456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7193.00 | + | 8265.16i | −0.641436 | + | 0.737047i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5908.41 | 0.523743 | 0.261872 | − | 0.965103i | \(-0.415660\pi\) | ||||
0.261872 | + | 0.965103i | \(0.415660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14951.1 | 1.31746 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10515.1 | − | 12082.4i | 0.921089 | − | 1.05838i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8348.77 | + | 14460.5i | 0.727019 | + | 1.25923i | 0.958138 | + | 0.286308i | \(0.0924282\pi\) |
−0.231118 | + | 0.972926i | \(0.574238\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18292.1 | − | 989.741i | −1.57430 | − | 0.0851816i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18543.0 | − | 10705.8i | −1.58661 | − | 0.916028i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1066.18i | − | 0.0906974i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4479.38 | − | 873.330i | −0.378850 | − | 0.0738631i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3648.66 | − | 6319.67i | 0.306815 | − | 0.531420i | −0.670849 | − | 0.741594i | \(-0.734070\pi\) |
0.977664 | + | 0.210175i | \(0.0674033\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5470.78 | − | 3158.56i | 0.457401 | − | 0.264080i | −0.253550 | − | 0.967322i | \(-0.581598\pi\) |
0.710951 | + | 0.703242i | \(0.248265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8207.52 | − | 4738.61i | 0.678416 | − | 0.391684i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1712.85 | − | 2966.75i | 0.140779 | − | 0.243836i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22501.3 | − | 9120.71i | −1.83893 | − | 0.745395i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 23297.8i | − | 1.89332i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22121.9 | − | 12772.1i | −1.78768 | − | 1.03212i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15558.7 | − | 5347.46i | 1.25029 | − | 0.429720i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6292.24 | + | 10898.5i | 0.500045 | + | 0.866104i | 1.00000 | 5.25096e-5i | \(1.67143e-5\pi\) | |
−0.499955 | + | 0.866052i | \(0.666650\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15679.4 | − | 13645.4i | −1.23916 | − | 1.07842i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20462.4 | −1.60828 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15886.3 | 1.24177 | 0.620887 | − | 0.783900i | \(-0.286773\pi\) | ||||
0.620887 | + | 0.783900i | \(0.286773\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9380.70 | − | 12034.7i | −0.729250 | − | 0.935575i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4122.31 | − | 7140.04i | −0.318723 | − | 0.552044i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2060.96 | − | 5996.47i | −0.157627 | − | 0.458623i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10421.1 | − | 6016.60i | −0.792737 | − | 0.457687i | 0.0481881 | − | 0.998838i | \(-0.484655\pi\) |
−0.840925 | + | 0.541151i | \(0.817989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 25564.1i | − | 1.93425i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 462.389 | − | 2371.63i | 0.0347987 | − | 0.178486i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1019.73 | − | 1766.23i | 0.0763351 | − | 0.132216i | −0.825331 | − | 0.564649i | \(-0.809011\pi\) |
0.901666 | + | 0.432433i | \(0.142345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22549.9 | − | 13019.2i | 1.67908 | − | 0.969420i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11615.0 | + | 6705.91i | −0.855756 | + | 0.494071i | −0.862589 | − | 0.505906i | \(-0.831158\pi\) |
0.00683300 | + | 0.999977i | \(0.497825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2317.42 | − | 4013.88i | 0.169844 | − | 0.294178i | −0.768521 | − | 0.639825i | \(-0.779007\pi\) |
0.938365 | + | 0.345646i | \(0.112340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 988.786 | − | 5071.56i | 0.0720892 | − | 0.369751i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5508.13i | − | 0.399487i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18977.8 | + | 10956.9i | 1.36925 | + | 0.790538i | 0.990832 | − | 0.135097i | \(-0.0431346\pi\) |
0.378419 | + | 0.925634i | \(0.376468\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3481.15 | + | 10128.6i | 0.249865 | + | 0.726993i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 206.861 | + | 358.294i | 0.0146952 | + | 0.0254529i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15684.1 | + | 20121.6i | 1.10848 | + | 1.42209i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3112.06 | −0.218822 | −0.109411 | − | 0.993997i | \(-0.534896\pi\) | ||||
−0.109411 | + | 0.993997i | \(0.534896\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13819.3 | −0.966746 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1567.13 | − | 1363.84i | −0.109074 | − | 0.0949252i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −610.968 | − | 1058.23i | −0.0423094 | − | 0.0732820i | 0.844095 | − | 0.536193i | \(-0.180138\pi\) |
−0.886405 | + | 0.462911i | \(0.846805\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14281.8 | − | 4908.59i | 0.979087 | − | 0.336508i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7696.43 | + | 4443.53i | 0.524987 | + | 0.303102i | 0.738973 | − | 0.673735i | \(-0.235311\pi\) |
−0.213985 | + | 0.976837i | \(0.568645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6820.42i | 0.462913i | 0.972845 | + | 0.231457i | \(0.0743491\pi\) | ||||
−0.972845 | + | 0.231457i | \(0.925651\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2058.92 | − | 834.567i | −0.139048 | − | 0.0563619i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8478.99 | − | 14686.0i | 0.569785 | − | 0.986897i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11643.9 | − | 6722.61i | 0.778602 | − | 0.449526i | −0.0573326 | − | 0.998355i | \(-0.518260\pi\) |
0.835935 | + | 0.548829i | \(0.184926\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12919.4 | + | 7459.00i | −0.855420 | + | 0.493877i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5472.47 | − | 9478.60i | 0.360573 | − | 0.624530i | −0.627482 | − | 0.778631i | \(-0.715915\pi\) |
0.988055 | + | 0.154100i | \(0.0492479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21265.9 | + | 4146.15i | 1.39435 | + | 0.271852i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14042.9i | − | 0.916283i | −0.888879 | − | 0.458141i | \(-0.848515\pi\) | ||
0.888879 | − | 0.458141i | \(-0.151485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4108.96 | − | 2372.31i | −0.266806 | − | 0.154041i | 0.360629 | − | 0.932709i | \(-0.382562\pi\) |
−0.627435 | + | 0.778669i | \(0.715895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17493.3 | − | 946.519i | −1.13041 | − | 0.0611634i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9596.54 | + | 16621.7i | 0.614179 | + | 1.06379i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2313.01 | + | 2657.78i | −0.147325 | + | 0.169285i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8402.77 | 0.532656 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10939.3 | 0.690151 | 0.345075 | − | 0.938575i | \(-0.387853\pi\) | ||||
0.345075 | + | 0.938575i | \(0.387853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10053.5 | + | 11552.0i | −0.631264 | + | 0.725358i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1082.85 | − | 1875.54i | −0.0676716 | − | 0.117211i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12246.2 | + | 1706.99i | −0.758144 | + | 0.105677i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3499.79 | + | 2020.61i | 0.215653 | + | 0.124507i | 0.603936 | − | 0.797033i | \(-0.293598\pi\) |
−0.388283 | + | 0.921540i | \(0.626932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25370.2i | − | 1.55599i | −0.628268 | − | 0.777997i | \(-0.716236\pi\) | ||
0.628268 | − | 0.777997i | \(-0.283764\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23334.5 | + | 4549.45i | 1.42449 | + | 0.277728i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1094.96 | + | 1896.53i | −0.0665339 | + | 0.115240i | −0.897373 | − | 0.441272i | \(-0.854527\pi\) |
0.830839 | + | 0.556512i | \(0.187861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4044.13 | + | 2334.88i | −0.244601 | + | 0.141220i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8980.82 | − | 5185.08i | 0.538203 | − | 0.310732i | −0.206147 | − | 0.978521i | \(-0.566093\pi\) |
0.744350 | + | 0.667789i | \(0.232759\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2054.24 | − | 3558.05i | 0.122543 | − | 0.212251i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9007.47 | + | 22221.9i | −0.534878 | + | 1.31957i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26192.1i | 1.54825i | 0.633032 | + | 0.774126i | \(0.281810\pi\) | ||||
−0.633032 | + | 0.774126i | \(0.718190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7399.81 | + | 4272.28i | 0.435430 | + | 0.251396i | 0.701657 | − | 0.712515i | \(-0.252444\pi\) |
−0.266227 | + | 0.963910i | \(0.585777\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31973.0 | + | 10989.0i | −1.87289 | + | 0.643705i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3942.28 | − | 6828.23i | −0.228854 | − | 0.396387i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13646.6 | − | 11876.4i | −0.788654 | − | 0.686349i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2934.78 | −0.168846 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32802.3 | −1.87881 | −0.939404 | − | 0.342813i | \(-0.888620\pi\) | ||||
−0.939404 | + | 0.342813i | \(0.888620\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5518.80 | + | 2800.20i | −0.314694 | + | 0.159674i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −968.152 | − | 1676.89i | −0.0549617 | − | 0.0951965i | 0.837236 | − | 0.546842i | \(-0.184170\pi\) |
−0.892197 | + | 0.451646i | \(0.850837\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6542.89 | − | 19036.9i | −0.368171 | − | 1.07121i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1697.40 | + | 979.995i | 0.0950940 | + | 0.0549026i | 0.546793 | − | 0.837268i | \(-0.315849\pi\) |
−0.451699 | + | 0.892170i | \(0.649182\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5182.89i | 0.289092i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3986.88 | − | 20449.0i | 0.221410 | − | 1.13563i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2894.40 | − | 5013.25i | 0.160041 | − | 0.277198i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17263.4 | − | 9967.05i | 0.950408 | − | 0.548718i | 0.0572002 | − | 0.998363i | \(-0.481783\pi\) |
0.893208 | + | 0.449645i | \(0.148449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2570.50 | + | 1484.08i | −0.140294 | + | 0.0809989i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14356.1 | + | 24865.5i | −0.780168 | + | 1.35129i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5049.78 | + | 25900.7i | −0.273248 | + | 1.40151i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26738.5i | 1.44065i | 0.693635 | + | 0.720327i | \(0.256008\pi\) | ||||
−0.693635 | + | 0.720327i | \(0.743992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10611.0 | − | 6126.28i | −0.569278 | − | 0.328673i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4509.30 | − | 13120.0i | −0.240894 | − | 0.700893i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6441.45 | − | 11156.9i | −0.341204 | − | 0.590983i | 0.643452 | − | 0.765486i | \(-0.277501\pi\) |
−0.984657 | + | 0.174503i | \(0.944168\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10559.2 | + | 8230.56i | −0.556964 | + | 0.434135i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13215.8 | −0.694159 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4906.82 | 0.256650 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4238.12 | − | 3688.34i | −0.220747 | − | 0.192111i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13721.5 | + | 23766.3i | 0.711717 | + | 1.23273i | 0.964212 | + | 0.265131i | \(0.0854153\pi\) |
−0.252496 | + | 0.967598i | \(0.581251\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16199.6 | − | 5567.74i | 0.833292 | − | 0.286399i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2412.08 | − | 1392.61i | −0.123562 | − | 0.0713385i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10869.4i | 0.554501i | 0.960798 | + | 0.277250i | \(0.0894231\pi\) | ||||
−0.960798 | + | 0.277250i | \(0.910577\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7944.80 | + | 18008.4i | 0.403638 | + | 0.914919i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15752.6 | + | 27284.3i | −0.797032 | + | 1.38050i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28893.2 | + | 16681.5i | −1.45593 | + | 0.840580i | −0.998807 | − | 0.0488247i | \(-0.984452\pi\) |
−0.457120 | + | 0.889405i | \(0.651119\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −370.048 | + | 213.647i | −0.0184951 | + | 0.0106781i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18226.4 | − | 31569.0i | 0.907265 | − | 1.57143i | 0.0894168 | − | 0.995994i | \(-0.471500\pi\) |
0.817848 | − | 0.575434i | \(-0.195167\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 48387.3 | + | 9433.91i | 2.39886 | + | 0.467697i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 139.301i | 0.00687814i | 0.999994 | + | 0.00343907i | \(0.00109469\pi\) | ||||
−0.999994 | + | 0.00343907i | \(0.998905\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39883.6 | + | 23026.8i | 1.96137 | + | 1.13240i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3812.61 | + | 27352.4i | 0.186742 | + | 1.33972i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8485.28 | + | 14696.9i | 0.412293 | + | 0.714113i | 0.995140 | − | 0.0984692i | \(-0.0313946\pi\) |
−0.582847 | + | 0.812582i | \(0.698061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2356.13 | − | 2707.33i | 0.114027 | − | 0.131023i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2740.86 | 0.132120 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29233.1 | −1.40356 | −0.701781 | − | 0.712393i | \(-0.747611\pi\) | ||||
−0.701781 | + | 0.712393i | \(0.747611\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2212.00 | + | 2541.71i | −0.105785 | + | 0.121553i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5497.11 | − | 9521.27i | −0.261853 | − | 0.453542i | 0.704882 | − | 0.709325i | \(-0.251000\pi\) |
−0.966734 | + | 0.255783i | \(0.917667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4340.58 | − | 31140.1i | −0.205142 | − | 1.47173i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56585.4 | + | 32669.6i | 2.66386 | + | 1.53798i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1694.37i | 0.0794547i | 0.999211 | + | 0.0397273i | \(0.0126489\pi\) | ||||
−0.999211 | + | 0.0397273i | \(0.987351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40274.0 | − | 7852.08i | −1.88123 | − | 0.366778i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16225.5 | + | 28103.4i | −0.754969 | + | 1.30764i | 0.190421 | + | 0.981702i | \(0.439015\pi\) |
−0.945390 | + | 0.325942i | \(0.894319\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4043.03 | + | 2334.24i | −0.187393 | + | 0.108192i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36257.8 | − | 20933.5i | 1.66761 | − | 0.962798i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1189.06 | + | 2059.52i | −0.0544790 | + | 0.0943603i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4837.30 | + | 7421.22i | −0.220780 | + | 0.338713i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36973.4i | 1.68107i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18152.9 | + | 10480.6i | 0.822212 | + | 0.474704i | 0.851179 | − | 0.524876i | \(-0.175888\pi\) |
−0.0289667 | + | 0.999580i | \(0.509222\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14728.1 | + | 5061.99i | −0.664557 | + | 0.228405i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20531.7 | + | 35562.0i | 0.919424 | + | 1.59249i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4060.93 | + | 3534.14i | 0.181165 | + | 0.157664i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30873.3 | 1.37213 | 0.686066 | − | 0.727540i | \(-0.259336\pi\) | ||||
0.686066 | + | 0.727540i | \(0.259336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18384.9 | 0.814033 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2790.38 | − | 2175.01i | 0.123087 | − | 0.0959427i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2305.89 | + | 3993.92i | 0.101336 | + | 0.175520i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13652.3 | − | 39722.0i | −0.595519 | − | 1.73269i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23921.2 | + | 13810.9i | 1.03958 | + | 0.600204i | 0.919716 | − | 0.392585i | \(-0.128419\pi\) |
0.119869 | + | 0.992790i | \(0.461753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20022.9i | − | 0.866954i | −0.901165 | − | 0.433477i | \(-0.857287\pi\) | ||
0.901165 | − | 0.433477i | \(-0.142713\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3290.11 | − | 16875.3i | 0.141930 | − | 0.727972i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2975.80 | + | 5154.24i | −0.127899 | + | 0.221528i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39784.7 | − | 22969.7i | 1.70366 | − | 0.983609i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6115.05 | − | 3530.52i | 0.259947 | − | 0.150081i | −0.364363 | − | 0.931257i | \(-0.618713\pi\) |
0.624310 | + | 0.781176i | \(0.285380\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18834.7 | − | 32622.6i | 0.797734 | − | 1.38172i | −0.123354 | − | 0.992363i | \(-0.539365\pi\) |
0.921089 | − | 0.389353i | \(-0.127301\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −227.773 | + | 1168.27i | −0.00961217 | + | 0.0493016i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5566.45i | − | 0.234056i | −0.993129 | − | 0.117028i | \(-0.962663\pi\) | ||
0.993129 | − | 0.117028i | \(-0.0373368\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9558.42 | + | 5518.56i | 0.400455 | + | 0.231203i | 0.686680 | − | 0.726959i | \(-0.259067\pi\) |
−0.286225 | + | 0.958162i | \(0.592400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8437.09 | − | 24548.1i | −0.352202 | − | 1.02475i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13710.7 | + | 23747.6i | 0.568236 | + | 0.984214i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6718.57 | + | 13241.4i | 0.277453 | + | 0.546821i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28936.3 | −1.19069 | −0.595347 | − | 0.803469i | \(-0.702986\pi\) | ||||
−0.595347 | + | 0.803469i | \(0.702986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20402.1 | 0.836529 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16163.4 | − | 14066.7i | −0.660375 | − | 0.574711i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20043.0 | − | 34715.4i | −0.815975 | − | 1.41331i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8999.79 | − | 3093.19i | 0.363807 | − | 0.125039i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10147.6 | − | 5858.74i | −0.408762 | − | 0.235999i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25646.9i | − | 1.02946i | −0.857351 | − | 0.514732i | \(-0.827891\pi\) | ||
0.857351 | − | 0.514732i | \(-0.172109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17222.3 | + | 42488.3i | −0.688877 | + | 1.69950i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2745.33 | + | 4755.06i | −0.109427 | + | 0.189533i | −0.915538 | − | 0.402231i | \(-0.868235\pi\) |
0.806111 | + | 0.591764i | \(0.201568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7955.53 | − | 4593.13i | 0.315994 | − | 0.182439i | −0.333611 | − | 0.942711i | \(-0.608267\pi\) |
0.649606 | + | 0.760271i | \(0.274934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38541.3 | − | 22251.9i | 1.52023 | − | 0.877708i | 0.520520 | − | 0.853850i | \(-0.325738\pi\) |
0.999715 | − | 0.0238583i | \(-0.00759505\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5710.74 | + | 9891.30i | −0.224475 | + | 0.388803i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15838.9 | + | 3088.06i | 0.620436 | + | 0.120964i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2574.96i | 0.100517i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5177.71 | + | 2989.35i | 0.201424 | + | 0.116292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23993.2 | − | 3344.39i | 0.930181 | − | 0.129657i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9236.70 | + | 15998.4i | 0.355645 | + | 0.615996i | 0.987228 | − | 0.159312i | \(-0.0509277\pi\) |
−0.631583 | + | 0.775308i | \(0.717594\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9129.60 | − | 10490.4i | 0.350323 | − | 0.402541i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9245.06 | −0.353546 | −0.176773 | − | 0.984252i | \(-0.556566\pi\) | ||||
−0.176773 | + | 0.984252i | \(0.556566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14216.8 | 0.541827 | 0.270913 | − | 0.962604i | \(-0.412674\pi\) | ||||
0.270913 | + | 0.962604i | \(0.412674\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −39890.5 | + | 45836.4i | −1.51514 | + | 1.74099i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15492.2 | + | 26833.3i | 0.586445 | + | 1.01575i | 0.994694 | + | 0.102882i | \(0.0328065\pi\) |
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3671.16 | + | 924.140i | 0.138034 | + | 0.0347473i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23216.5 | − | 13404.1i | −0.870001 | − | 0.502296i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 41173.9i | − | 1.53776i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 46274.2 | + | 9021.93i | 1.72246 | + | 0.335823i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3341.33 | + | 5787.35i | −0.123959 | + | 0.214704i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6178.33 | + | 3567.06i | −0.228446 | + | 0.131894i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −45050.2 | + | 26009.7i | −1.65472 | + | 0.955351i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22640.9 | + | 39215.3i | −0.828865 | + | 1.43564i | 0.0700650 | + | 0.997542i | \(0.477679\pi\) |
−0.898930 | + | 0.438093i | \(0.855654\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28768.6 | − | 11661.1i | −1.04972 | − | 0.425495i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1202.70i | − | 0.0437402i | −0.999761 | − | 0.0218701i | \(-0.993038\pi\) | ||
0.999761 | − | 0.0218701i | \(-0.00696202\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4600.00 | + | 2655.81i | 0.166744 | + | 0.0962700i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −36114.4 | + | 12412.4i | −1.30481 | + | 0.448459i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5398.13 | + | 9349.83i | 0.193763 | + | 0.335607i | 0.946494 | − | 0.322721i | \(-0.104598\pi\) |
−0.752732 | + | 0.658328i | \(0.771264\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1508.77 | + | 1313.05i | 0.0539802 | + | 0.0469779i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33274.8 | 1.18662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4139.21 | −0.147131 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27330.1 | + | 35062.5i | 0.968325 | + | 1.24229i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4138.39 | − | 7167.89i | −0.146153 | − | 0.253144i | 0.783650 | − | 0.621203i | \(-0.213356\pi\) |
−0.929802 | + | 0.368059i | \(0.880022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4124.20 | − | 11999.6i | −0.144716 | − | 0.421059i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5237.00 | − | 3023.59i | −0.183175 | − | 0.105756i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13731.8i | − | 0.478760i | −0.970926 | − | 0.239380i | \(-0.923056\pi\) | ||
0.970926 | − | 0.239380i | \(-0.0769441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4103.31 | − | 21046.2i | 0.142605 | − | 0.731434i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24731.9 | + | 42837.0i | −0.856789 | + | 1.48400i | 0.0181872 | + | 0.999835i | \(0.494211\pi\) |
−0.874976 | + | 0.484167i | \(0.839123\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34674.4 | − | 20019.3i | 1.19741 | − | 0.691323i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16333.6 | − | 9430.23i | 0.560477 | − | 0.323592i | −0.192860 | − | 0.981226i | \(-0.561776\pi\) |
0.753337 | + | 0.657635i | \(0.228443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32264.0 | − | 55882.9i | 1.10362 | − | 1.91152i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6697.67 | + | 34352.9i | −0.228377 | + | 1.17136i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26144.6i | 0.888674i | 0.895860 | + | 0.444337i | \(0.146561\pi\) | ||||
−0.895860 | + | 0.444337i | \(0.853439\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11198.9 | − | 6465.72i | −0.379465 | − | 0.219084i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 553.790 | + | 1611.28i | 0.0187058 | + | 0.0544256i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9294.90 | − | 16099.2i | −0.312004 | − | 0.540406i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 32604.9 | + | 41829.7i | 1.09105 | + | 1.39973i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26803.9 | 0.894142 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12791.3 | −0.425377 | −0.212688 | − | 0.977120i | \(-0.568222\pi\) | ||||
−0.212688 | + | 0.977120i | \(0.568222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −45830.1 | − | 39885.0i | −1.51938 | − | 1.32228i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7487.53 | − | 12968.8i | −0.247463 | − | 0.428618i | 0.715359 | − | 0.698758i | \(-0.246263\pi\) |
−0.962821 | + | 0.270140i | \(0.912930\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15749.9 | − | 5413.17i | 0.517334 | − | 0.177805i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26012.8 | + | 15018.5i | 0.851815 | + | 0.491796i | 0.861263 | − | 0.508160i | \(-0.169674\pi\) |
−0.00944779 | + | 0.999955i | \(0.503007\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 680.458i | − | 0.0222140i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39373.3 | + | 15959.6i | 1.28144 | + | 0.519421i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8226.35 | − | 14248.5i | 0.266918 | − | 0.462315i | −0.701147 | − | 0.713017i | \(-0.747328\pi\) |
0.968064 | + | 0.250702i | \(0.0806615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4502.69 | + | 2599.63i | −0.145652 | + | 0.0840924i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38047.3 | − | 21966.6i | 1.22329 | − | 0.706267i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12196.1 | + | 21124.3i | −0.390941 | + | 0.677130i | −0.992574 | − | 0.121643i | \(-0.961184\pi\) |
0.601633 | + | 0.798773i | \(0.294517\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21005.9 | − | 4095.45i | −0.671301 | − | 0.130881i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 37794.8i | − | 1.20420i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15826.1 | − | 9137.19i | −0.502725 | − | 0.290249i | 0.227113 | − | 0.973868i | \(-0.427071\pi\) |
−0.729838 | + | 0.683620i | \(0.760405\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −711.282 | + | 13145.7i | −0.0225265 | + | 0.416329i |
(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.521.6 | 48 | ||
3.2 | odd | 2 | inner | 588.4.k.e.521.13 | 48 | ||
7.2 | even | 3 | inner | 588.4.k.e.509.12 | 48 | ||
7.3 | odd | 6 | 588.4.f.d.293.3 | ✓ | 24 | ||
7.4 | even | 3 | 588.4.f.d.293.22 | yes | 24 | ||
7.5 | odd | 6 | inner | 588.4.k.e.509.13 | 48 | ||
7.6 | odd | 2 | inner | 588.4.k.e.521.19 | 48 | ||
21.2 | odd | 6 | inner | 588.4.k.e.509.19 | 48 | ||
21.5 | even | 6 | inner | 588.4.k.e.509.6 | 48 | ||
21.11 | odd | 6 | 588.4.f.d.293.4 | yes | 24 | ||
21.17 | even | 6 | 588.4.f.d.293.21 | yes | 24 | ||
21.20 | even | 2 | inner | 588.4.k.e.521.12 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.f.d.293.3 | ✓ | 24 | 7.3 | odd | 6 | ||
588.4.f.d.293.4 | yes | 24 | 21.11 | odd | 6 | ||
588.4.f.d.293.21 | yes | 24 | 21.17 | even | 6 | ||
588.4.f.d.293.22 | yes | 24 | 7.4 | even | 3 | ||
588.4.k.e.509.6 | 48 | 21.5 | even | 6 | inner | ||
588.4.k.e.509.12 | 48 | 7.2 | even | 3 | inner | ||
588.4.k.e.509.13 | 48 | 7.5 | odd | 6 | inner | ||
588.4.k.e.509.19 | 48 | 21.2 | odd | 6 | inner | ||
588.4.k.e.521.6 | 48 | 1.1 | even | 1 | trivial | ||
588.4.k.e.521.12 | 48 | 21.20 | even | 2 | inner | ||
588.4.k.e.521.13 | 48 | 3.2 | odd | 2 | inner | ||
588.4.k.e.521.19 | 48 | 7.6 | odd | 2 | inner |