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 | 509.14 | ||
Character | \(\chi\) | \(=\) | 588.509 |
Dual form | 588.4.k.e.521.14 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 1.84944 | + | 4.85588i | 0.355925 | + | 0.934515i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.01459 | − | 1.75732i | 0.0907475 | − | 0.157179i | −0.817078 | − | 0.576527i | \(-0.804408\pi\) |
0.907826 | + | 0.419347i | \(0.137741\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −20.1591 | + | 17.9613i | −0.746635 | + | 0.665234i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25.2834 | − | 14.5974i | 0.693022 | − | 0.400116i | −0.111721 | − | 0.993740i | \(-0.535636\pi\) |
0.804743 | + | 0.593623i | \(0.202303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 25.7266i | − | 0.548867i | −0.961606 | − | 0.274433i | \(-0.911510\pi\) | ||
0.961606 | − | 0.274433i | \(-0.0884903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.4097 | + | 1.67666i | 0.179186 | + | 0.0288608i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.39964 | − | 2.42425i | −0.0199684 | − | 0.0345862i | 0.855869 | − | 0.517193i | \(-0.173023\pi\) |
−0.875837 | + | 0.482607i | \(0.839690\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 92.8920 | + | 53.6312i | 1.12163 | + | 0.647571i | 0.941815 | − | 0.336130i | \(-0.109118\pi\) |
0.179810 | + | 0.983701i | \(0.442452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 70.3580 | + | 40.6212i | 0.637855 | + | 0.368266i | 0.783788 | − | 0.621029i | \(-0.213285\pi\) |
−0.145933 | + | 0.989295i | \(0.546618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 60.4412 | + | 104.687i | 0.483530 | + | 0.837498i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −124.501 | − | 64.6720i | −0.887417 | − | 0.460968i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 170.862i | 1.09408i | 0.837107 | + | 0.547039i | \(0.184245\pi\) | ||||
−0.837107 | + | 0.547039i | \(0.815755\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.4394 | − | 12.9554i | 0.130007 | − | 0.0750598i | −0.433586 | − | 0.901112i | \(-0.642752\pi\) |
0.563593 | + | 0.826052i | \(0.309419\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 117.643 | + | 95.7762i | 0.620578 | + | 0.505227i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −90.6133 | + | 156.947i | −0.402615 | + | 0.697349i | −0.994041 | − | 0.109010i | \(-0.965232\pi\) |
0.591426 | + | 0.806359i | \(0.298565\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 124.925 | − | 47.5798i | 0.512924 | − | 0.195355i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −257.354 | −0.980289 | −0.490145 | − | 0.871641i | \(-0.663056\pi\) | ||||
−0.490145 | + | 0.871641i | \(0.663056\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 239.983 | 0.851095 | 0.425548 | − | 0.904936i | \(-0.360082\pi\) | ||||
0.425548 | + | 0.904936i | \(0.360082\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.1105 | + | 53.6493i | 0.0368058 | + | 0.177724i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −186.576 | + | 323.160i | −0.579041 | + | 1.00293i | 0.416548 | + | 0.909114i | \(0.363240\pi\) |
−0.995590 | + | 0.0938154i | \(0.970094\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.18329 | − | 11.2800i | 0.0252141 | − | 0.0309708i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 489.335 | − | 282.517i | 1.26821 | − | 0.732203i | 0.293563 | − | 0.955940i | \(-0.405159\pi\) |
0.974650 | + | 0.223737i | \(0.0718256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 59.2413i | − | 0.145238i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −88.6285 | + | 550.260i | −0.205950 | + | 1.27866i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 189.642 | + | 328.470i | 0.418463 | + | 0.724800i | 0.995785 | − | 0.0917170i | \(-0.0292355\pi\) |
−0.577322 | + | 0.816517i | \(0.695902\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −194.113 | − | 112.071i | −0.407436 | − | 0.235233i | 0.282251 | − | 0.959340i | \(-0.408919\pi\) |
−0.689687 | + | 0.724107i | \(0.742252\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −45.2098 | − | 26.1019i | −0.0862705 | − | 0.0498083i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −167.761 | − | 290.571i | −0.305900 | − | 0.529835i | 0.671561 | − | 0.740949i | \(-0.265624\pi\) |
−0.977461 | + | 0.211114i | \(0.932291\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −67.1288 | + | 416.777i | −0.117121 | + | 0.727160i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1029.35i | 1.72057i | 0.509809 | + | 0.860287i | \(0.329716\pi\) | ||||
−0.509809 | + | 0.860287i | \(0.670284\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 505.848 | − | 292.052i | 0.811028 | − | 0.468247i | −0.0362846 | − | 0.999341i | \(-0.511552\pi\) |
0.847313 | + | 0.531094i | \(0.178219\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −396.566 | + | 487.108i | −0.610554 | + | 0.749952i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 497.128 | − | 861.051i | 0.707991 | − | 1.22628i | −0.257610 | − | 0.966249i | \(-0.582935\pi\) |
0.965601 | − | 0.260027i | \(-0.0837316\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 83.7817 | − | 724.170i | 0.114927 | − | 0.993374i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1281.20 | −1.69434 | −0.847171 | − | 0.531320i | \(-0.821696\pi\) | ||||
−0.847171 | + | 0.531320i | \(0.821696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.68022 | −0.00724832 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −829.684 | + | 315.999i | −1.02243 | + | 0.389409i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −738.927 | + | 1279.86i | −0.880068 | + | 1.52432i | −0.0288039 | + | 0.999585i | \(0.509170\pi\) |
−0.851264 | + | 0.524737i | \(0.824164\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 104.410 | + | 85.0026i | 0.116417 | + | 0.0947781i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 188.494 | − | 108.827i | 0.203569 | − | 0.117531i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1228.85i | 1.28630i | 0.765742 | + | 0.643148i | \(0.222372\pi\) | ||||
−0.765742 | + | 0.643148i | \(0.777628\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −247.504 | + | 748.394i | −0.251263 | + | 0.759762i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 219.708 | + | 380.545i | 0.216453 | + | 0.374907i | 0.953721 | − | 0.300693i | \(-0.0972179\pi\) |
−0.737268 | + | 0.675600i | \(0.763885\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −963.292 | − | 556.157i | −0.921514 | − | 0.532037i | −0.0373965 | − | 0.999301i | \(-0.511906\pi\) |
−0.884118 | + | 0.467264i | \(0.845240\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 51.9337 | + | 29.9839i | 0.0469217 | + | 0.0270903i | 0.523277 | − | 0.852162i | \(-0.324709\pi\) |
−0.476356 | + | 0.879253i | \(0.658043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 119.650 | + | 207.239i | 0.105141 | + | 0.182109i | 0.913796 | − | 0.406174i | \(-0.133137\pi\) |
−0.808655 | + | 0.588283i | \(0.799804\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −929.699 | − | 149.744i | −0.794983 | − | 0.128045i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1701.80i | 1.41674i | 0.705841 | + | 0.708370i | \(0.250569\pi\) | ||||
−0.705841 | + | 0.708370i | \(0.749431\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 142.769 | − | 82.4276i | 0.115767 | − | 0.0668384i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 462.083 | + | 518.626i | 0.365125 | + | 0.409803i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −239.333 | + | 414.536i | −0.179814 | + | 0.311447i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −475.960 | − | 1249.68i | −0.348910 | − | 0.916095i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 498.939 | 0.357011 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1848.04 | 1.29124 | 0.645618 | − | 0.763661i | \(-0.276600\pi\) | ||||
0.645618 | + | 0.763661i | \(0.276600\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 443.835 | + | 1165.33i | 0.302926 | + | 0.795361i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −149.935 | + | 259.695i | −0.0999991 | + | 0.173203i | −0.911684 | − | 0.410892i | \(-0.865217\pi\) |
0.811685 | + | 0.584095i | \(0.198551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −239.967 | + | 153.173i | −0.152985 | + | 0.0976519i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2035.18 | − | 1175.01i | 1.26917 | − | 0.732758i | 0.294342 | − | 0.955700i | \(-0.404899\pi\) |
0.974832 | + | 0.222942i | \(0.0715660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1518.73i | − | 0.926740i | −0.886165 | − | 0.463370i | \(-0.846640\pi\) | ||
0.886165 | − | 0.463370i | \(-0.153360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1914.29 | − | 308.327i | −1.14335 | − | 0.184155i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −375.541 | − | 650.456i | −0.219610 | − | 0.380377i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 300.258 | + | 173.354i | 0.171966 | + | 0.0992847i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 128.269 | + | 74.0563i | 0.0705250 | + | 0.0407176i | 0.534848 | − | 0.844948i | \(-0.320369\pi\) |
−0.464323 | + | 0.885666i | \(0.653702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1246.02 | + | 2158.17i | 0.671522 | + | 1.16311i | 0.977472 | + | 0.211063i | \(0.0676926\pi\) |
−0.305950 | + | 0.952048i | \(0.598974\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 71.7582 | + | 23.7313i | 0.0379170 | + | 0.0125396i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 52.5774i | − | 0.0272459i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2561.86 | − | 1479.09i | 1.30228 | − | 0.751874i | 0.321489 | − | 0.946913i | \(-0.395817\pi\) |
0.980795 | + | 0.195039i | \(0.0624834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2276.87 | + | 1853.65i | 1.13564 | + | 0.924554i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 76.2823 | − | 132.125i | 0.0366558 | − | 0.0634897i | −0.847115 | − | 0.531409i | \(-0.821663\pi\) |
0.883771 | + | 0.467919i | \(0.154996\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 287.669 | − | 109.563i | 0.135727 | − | 0.0516939i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1312.37 | −0.608110 | −0.304055 | − | 0.952655i | \(-0.598341\pi\) | ||||
−0.304055 | + | 0.952655i | \(0.598341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1535.14 | 0.698745 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2835.91 | + | 587.304i | −1.26823 | + | 0.262645i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1296.27 | − | 2245.20i | 0.569673 | − | 0.986703i | −0.426925 | − | 0.904287i | \(-0.640403\pi\) |
0.996598 | − | 0.0824156i | \(-0.0262635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1244.28 | + | 1528.37i | −0.528394 | + | 0.649034i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2924.92 | + | 1688.71i | −1.22134 | + | 0.705138i | −0.965203 | − | 0.261503i | \(-0.915782\pi\) |
−0.256133 | + | 0.966642i | \(0.582448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1525.85i | − | 0.626606i | −0.949653 | − | 0.313303i | \(-0.898564\pi\) | ||
0.949653 | − | 0.313303i | \(-0.101436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 185.204 | − | 1149.86i | 0.0748122 | − | 0.464480i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 183.870 | + | 318.473i | 0.0730725 | + | 0.126565i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −70.7753 | − | 40.8621i | −0.0276770 | − | 0.0159793i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1311.45 | + | 757.169i | 0.496825 | + | 0.286842i | 0.727401 | − | 0.686212i | \(-0.240728\pi\) |
−0.230577 | + | 0.973054i | \(0.574061\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1487.21 | + | 2575.93i | 0.554674 | + | 0.960723i | 0.997929 | + | 0.0643273i | \(0.0204902\pi\) |
−0.443255 | + | 0.896395i | \(0.646176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 43.1348 | − | 267.807i | 0.0158407 | − | 0.0983490i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2886.30i | − | 1.04386i | −0.852989 | − | 0.521930i | \(-0.825212\pi\) | ||
0.852989 | − | 0.521930i | \(-0.174788\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2555.15 | − | 1475.22i | 0.910200 | − | 0.525504i | 0.0297042 | − | 0.999559i | \(-0.490543\pi\) |
0.880495 | + | 0.474055i | \(0.157210\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1100.71 | − | 1352.02i | 0.386261 | − | 0.474450i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −261.108 | + | 452.252i | −0.0889588 | + | 0.154081i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2147.97 | + | 444.834i | −0.721228 | + | 0.149363i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3131.50 | 1.03641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 760.988 | 0.248287 | 0.124144 | − | 0.992264i | \(-0.460382\pi\) | ||||
0.124144 | + | 0.992264i | \(0.460382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4998.38 | + | 1903.71i | −1.60790 | + | 0.612396i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 243.484 | − | 421.727i | 0.0772347 | − | 0.133775i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2353.70 | + | 1916.21i | 0.726249 | + | 0.591257i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −62.3675 | + | 36.0079i | −0.0189832 | + | 0.0109600i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 575.704i | 0.172879i | 0.996257 | + | 0.0864395i | \(0.0275489\pi\) | ||||
−0.996257 | + | 0.0864395i | \(0.972451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3098.76 | − | 1024.80i | −0.918153 | − | 0.303645i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1415.12 | − | 2451.05i | −0.413765 | − | 0.716662i | 0.581533 | − | 0.813523i | \(-0.302453\pi\) |
−0.995298 | + | 0.0968611i | \(0.969120\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3271.23 | − | 1888.65i | −0.943969 | − | 0.545001i | −0.0527668 | − | 0.998607i | \(-0.516804\pi\) |
−0.891202 | + | 0.453606i | \(0.850137\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4879.34 | − | 2817.09i | −1.37192 | − | 0.792076i | −0.380746 | − | 0.924680i | \(-0.624333\pi\) |
−0.991169 | + | 0.132604i | \(0.957666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 378.596 | + | 655.747i | 0.105093 | + | 0.182027i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5100.57 | + | 821.531i | 1.39796 | + | 0.225165i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6082.58i | − | 1.64623i | −0.567873 | − | 0.823116i | \(-0.692233\pi\) | ||
0.567873 | − | 0.823116i | \(-0.307767\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2662.28 | − | 1537.07i | 0.711587 | − | 0.410835i | −0.100061 | − | 0.994981i | \(-0.531904\pi\) |
0.811648 | + | 0.584146i | \(0.198571\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3671.43 | − | 932.475i | 0.969228 | − | 0.246166i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1379.75 | − | 2389.79i | 0.355430 | − | 0.615623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2369.51 | − | 6221.37i | −0.603059 | − | 1.58339i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2619.44 | 0.658715 | 0.329357 | − | 0.944205i | \(-0.393168\pi\) | ||||
0.329357 | + | 0.944205i | \(0.393168\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2371.86 | 0.589396 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.5052 | − | 27.5825i | −0.00257986 | − | 0.00677366i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2128.61 | − | 3686.86i | 0.516650 | − | 0.894864i | −0.483163 | − | 0.875530i | \(-0.660512\pi\) |
0.999813 | − | 0.0193338i | \(-0.00615452\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3068.90 | − | 3444.43i | −0.727818 | − | 0.816876i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6041.88 | + | 3488.28i | −1.41657 | + | 0.817858i | −0.995996 | − | 0.0894000i | \(-0.971505\pi\) |
−0.420575 | + | 0.907258i | \(0.638172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1146.55i | − | 0.265782i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7581.44 | − | 1221.12i | −1.73774 | − | 0.279892i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2334.12 | + | 4042.81i | 0.529047 | + | 0.916337i | 0.999426 | + | 0.0338722i | \(0.0107839\pi\) |
−0.470379 | + | 0.882465i | \(0.655883\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7572.04 | − | 4371.72i | −1.69730 | − | 0.979938i | −0.948303 | − | 0.317366i | \(-0.897202\pi\) |
−0.748998 | − | 0.662572i | \(-0.769465\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3056.32 | + | 1764.57i | 0.670193 | + | 0.386936i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 300.073 | + | 519.742i | 0.0650890 | + | 0.112737i | 0.896733 | − | 0.442571i | \(-0.145934\pi\) |
−0.831644 | + | 0.555308i | \(0.812600\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −219.662 | + | 664.209i | −0.0471357 | + | 0.142528i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4503.57i | − | 0.956087i | −0.878336 | − | 0.478044i | \(-0.841346\pi\) | ||
0.878336 | − | 0.478044i | \(-0.158654\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 385.112 | − | 222.345i | 0.0808924 | − | 0.0467032i | −0.459008 | − | 0.888432i | \(-0.651795\pi\) |
0.539901 | + | 0.841729i | \(0.318462\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 877.060 | + | 714.036i | 0.182290 | + | 0.148406i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2452.58 | − | 4248.00i | 0.499203 | − | 0.864644i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5967.14 | + | 2272.68i | −1.20206 | + | 0.457825i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6302.01 | 1.25654 | 0.628272 | − | 0.777994i | \(-0.283763\pi\) | ||||
0.628272 | + | 0.777994i | \(0.283763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 769.635 | 0.151898 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4091.86 | + | 182.264i | −0.799440 | + | 0.0356095i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1045.05 | − | 1810.07i | 0.202129 | − | 0.350097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1441.54 | + | 1770.67i | −0.273315 | + | 0.335717i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −393.889 | + | 227.412i | −0.0739476 | + | 0.0426937i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7530.38i | 1.39994i | 0.714172 | + | 0.699970i | \(0.246803\pi\) | ||||
−0.714172 | + | 0.699970i | \(0.753197\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 919.080 | − | 5706.21i | 0.169206 | − | 1.05053i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4683.11 | − | 8111.38i | −0.853873 | − | 1.47895i | −0.877686 | − | 0.479236i | \(-0.840914\pi\) |
0.0238130 | − | 0.999716i | \(-0.492419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3393.99 | − | 1959.52i | −0.612906 | − | 0.353861i | 0.161196 | − | 0.986922i | \(-0.448465\pi\) |
−0.774102 | + | 0.633061i | \(0.781798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −483.723 | − | 279.278i | −0.0857054 | − | 0.0494820i | 0.456535 | − | 0.889706i | \(-0.349090\pi\) |
−0.542240 | + | 0.840224i | \(0.682424\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2494.14 | + | 4319.97i | 0.437758 | + | 0.758219i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −49.5501 | + | 307.637i | −0.00861563 | + | 0.0534911i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 300.257i | − | 0.0517237i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2693.25 | − | 1554.95i | 0.459675 | − | 0.265393i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −785.044 | + | 964.281i | −0.132762 | + | 0.163073i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −549.892 | + | 952.441i | −0.0913136 | + | 0.158160i | −0.908064 | − | 0.418831i | \(-0.862440\pi\) |
0.816751 | + | 0.576991i | \(0.195773\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −992.287 | − | 4791.45i | −0.163294 | − | 0.788498i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −680.835 | −0.111039 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3838.95 | 0.620537 | 0.310268 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310268 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8263.72 | + | 3147.37i | −1.32396 | + | 0.504253i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 378.229 | − | 655.112i | 0.0600652 | − | 0.104036i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 664.301 | + | 540.823i | 0.103666 | + | 0.0843969i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4113.91 | + | 2375.17i | −0.636445 | + | 0.367452i | −0.783244 | − | 0.621715i | \(-0.786436\pi\) |
0.146799 | + | 0.989166i | \(0.453103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9257.25i | − | 1.41985i | −0.704275 | − | 0.709927i | \(-0.748728\pi\) | ||
0.704275 | − | 0.709927i | \(-0.251272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1663.79 | + | 3202.99i | −0.253010 | + | 0.487074i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2270.09 | + | 3931.92i | 0.342280 | + | 0.592847i | 0.984856 | − | 0.173376i | \(-0.0554675\pi\) |
−0.642576 | + | 0.766222i | \(0.722134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1808.89 | + | 1044.36i | 0.270439 | + | 0.156138i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3512.47 | + | 2027.93i | 0.516382 | + | 0.298133i | 0.735453 | − | 0.677575i | \(-0.236969\pi\) |
−0.219071 | + | 0.975709i | \(0.570303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2323.12 | + | 4023.76i | 0.338696 | + | 0.586639i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2455.57 | − | 395.510i | −0.355052 | − | 0.0571870i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1185.25i | − | 0.169969i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11844.5 | − | 6838.44i | 1.68468 | − | 0.972653i | 0.726210 | − | 0.687473i | \(-0.241280\pi\) |
0.958474 | − | 0.285180i | \(-0.0920533\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5188.03 | − | 4622.41i | 0.731918 | − | 0.652122i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −84.0879 | + | 145.645i | −0.0116727 | + | 0.0202177i | −0.871803 | − | 0.489857i | \(-0.837049\pi\) |
0.860130 | + | 0.510075i | \(0.170382\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 922.757 | + | 2422.79i | 0.127069 | + | 0.333632i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4395.69 | 0.600503 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −398.381 | −0.0539933 | −0.0269966 | − | 0.999636i | \(-0.508594\pi\) | ||||
−0.0269966 | + | 0.999636i | \(0.508594\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3417.84 | + | 8973.85i | 0.459583 | + | 1.20668i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1531.44 | + | 2652.54i | −0.204316 | + | 0.353886i | −0.949915 | − | 0.312510i | \(-0.898830\pi\) |
0.745599 | + | 0.666395i | \(0.232164\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4837.85 | + | 4310.42i | −0.635457 | + | 0.566178i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10631.5 | − | 6138.08i | 1.38570 | − | 0.800033i | 0.392871 | − | 0.919594i | \(-0.371482\pi\) |
0.992827 | + | 0.119561i | \(0.0381487\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 227.420i | − | 0.0294147i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1538.34 | − | 247.776i | −0.197453 | − | 0.0318031i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1008.76 | − | 1747.22i | −0.128497 | − | 0.222563i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6831.34 | + | 3944.07i | 0.863614 | + | 0.498608i | 0.865221 | − | 0.501391i | \(-0.167178\pi\) |
−0.00160665 | + | 0.999999i | \(0.500511\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4883.77 | − | 2819.65i | −0.608189 | − | 0.351138i | 0.164067 | − | 0.986449i | \(-0.447539\pi\) |
−0.772257 | + | 0.635311i | \(0.780872\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −333.297 | − | 577.288i | −0.0411978 | − | 0.0713567i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1187.59 | − | 881.965i | −0.145708 | − | 0.108210i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5290.87i | 0.644371i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2342.59 | + | 1352.49i | −0.283212 | + | 0.163512i | −0.634876 | − | 0.772614i | \(-0.718949\pi\) |
0.351665 | + | 0.936126i | \(0.385616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9469.64 | + | 7709.46i | 1.13650 | + | 0.925255i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1299.89 | + | 2251.48i | −0.153757 | + | 0.266315i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7374.76 | − | 2808.80i | 0.866052 | − | 0.329850i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13118.4 | −1.52953 | −0.764766 | − | 0.644309i | \(-0.777145\pi\) | ||||
−0.764766 | + | 0.644309i | \(0.777145\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5668.08 | 0.656165 | 0.328082 | − | 0.944649i | \(-0.393598\pi\) | ||||
0.328082 | + | 0.944649i | \(0.393598\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2043.16 | − | 9865.77i | −0.234850 | − | 1.13402i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 169.192 | − | 293.049i | 0.0193106 | − | 0.0334469i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2463.99 | − | 3026.56i | 0.277303 | − | 0.340615i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 806.205 | − | 465.463i | 0.0901010 | − | 0.0520199i | −0.454273 | − | 0.890863i | \(-0.650101\pi\) |
0.544374 | + | 0.838843i | \(0.316767\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10673.2i | − | 1.18458i | −0.805725 | − | 0.592290i | \(-0.798224\pi\) | ||
0.805725 | − | 0.592290i | \(-0.201776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −286.477 | + | 1778.63i | −0.0315760 | + | 0.196043i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4357.13 | + | 7546.78i | 0.476956 | + | 0.826113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2870.95 | − | 1657.54i | −0.312125 | − | 0.180206i | 0.335752 | − | 0.941950i | \(-0.391010\pi\) |
−0.647877 | + | 0.761745i | \(0.724343\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3223.65 | + | 1861.18i | 0.345734 | + | 0.199610i | 0.662805 | − | 0.748792i | \(-0.269366\pi\) |
−0.317071 | + | 0.948402i | \(0.602699\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1499.41 | + | 2597.06i | 0.159728 | + | 0.276657i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −122.382 | + | 759.823i | −0.0129496 | + | 0.0803991i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8582.14i | 0.902041i | 0.892514 | + | 0.451021i | \(0.148940\pi\) | ||||
−0.892514 | + | 0.451021i | \(0.851060\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6506.78 | + | 3756.69i | −0.679362 | + | 0.392230i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8175.39 | + | 10042.0i | −0.847932 | + | 1.04153i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6516.79 | + | 11287.4i | −0.667052 | + | 1.15537i | 0.311673 | + | 0.950189i | \(0.399111\pi\) |
−0.978725 | + | 0.205178i | \(0.934223\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.4760 | + | 392.339i | 0.00177714 | + | 0.0398972i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9125.03 | −0.921898 | −0.460949 | − | 0.887427i | \(-0.652491\pi\) | ||||
−0.460949 | + | 0.887427i | \(0.652491\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6710.20 | 0.673541 | 0.336770 | − | 0.941587i | \(-0.390665\pi\) | ||||
0.336770 | + | 0.941587i | \(0.390665\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 255.310 | − | 97.2388i | 0.0254617 | − | 0.00969751i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2451.93 | + | 4246.87i | −0.242959 | + | 0.420818i | −0.961556 | − | 0.274610i | \(-0.911451\pi\) |
0.718597 | + | 0.695427i | \(0.244785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11920.3 | + | 9704.59i | 1.16615 | + | 0.949393i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6067.59 | − | 3503.13i | 0.589827 | − | 0.340537i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12966.1i | 1.25248i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4790.18 | + | 14484.4i | −0.459805 | + | 1.39035i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 704.962 | + | 1221.03i | 0.0672454 | + | 0.116472i | 0.897688 | − | 0.440632i | \(-0.145246\pi\) |
−0.830442 | + | 0.557104i | \(0.811912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4037.71 | + | 2331.17i | 0.382752 | + | 0.220982i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2159.48 | + | 1246.77i | 0.202179 | + | 0.116728i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1007.21 | + | 1744.54i | 0.0937186 | + | 0.162325i | 0.909073 | − | 0.416637i | \(-0.136791\pi\) |
−0.815355 | + | 0.578962i | \(0.803458\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 782.662 | + | 126.061i | 0.0723788 | + | 0.0116578i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13955.7i | 1.28271i | 0.767243 | + | 0.641357i | \(0.221628\pi\) | ||||
−0.767243 | + | 0.641357i | \(0.778372\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 414.211 | − | 239.145i | 0.0378400 | − | 0.0218469i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1064.05 | + | 1194.25i | 0.0966174 | + | 0.108440i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6464.30 | − | 11196.5i | 0.579923 | − | 1.00446i | −0.415564 | − | 0.909564i | \(-0.636416\pi\) |
0.995487 | − | 0.0948930i | \(-0.0302509\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2427.15 | − | 6372.72i | −0.216441 | − | 0.568287i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13733.1 | −1.21735 | −0.608676 | − | 0.793419i | \(-0.708299\pi\) | ||||
−0.608676 | + | 0.793419i | \(0.708299\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 891.651 | 0.0785702 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2839.16 | + | 7454.47i | 0.248701 | + | 0.652988i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6588.20 | + | 11411.1i | −0.573707 | + | 0.993690i | 0.422474 | + | 0.906375i | \(0.361162\pi\) |
−0.996181 | + | 0.0873148i | \(0.972171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8096.73 | − | 12684.7i | −0.696841 | − | 1.09170i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1954.69 | + | 1128.54i | −0.167250 | + | 0.0965620i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10894.1i | 0.926735i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13299.8 | + | 2142.15i | 1.12485 | + | 0.181176i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2649.64 | − | 4589.31i | −0.222808 | − | 0.385914i | 0.732852 | − | 0.680388i | \(-0.238189\pi\) |
−0.955659 | + | 0.294474i | \(0.904855\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3395.81 | − | 1960.57i | −0.283917 | − | 0.163920i | 0.351278 | − | 0.936271i | \(-0.385747\pi\) |
−0.635195 | + | 0.772352i | \(0.719080\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −62.8140 | − | 36.2657i | −0.00519207 | − | 0.00299764i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2783.33 | − | 4820.87i | −0.228761 | − | 0.396225i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9722.79 | − | 3215.45i | −0.794601 | − | 0.262785i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6620.83i | 0.538048i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 105.383 | − | 60.8427i | 0.00851605 | − | 0.00491675i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13609.6 | − | 11079.9i | −1.09367 | − | 0.890379i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2550.35 | − | 4417.33i | 0.202676 | − | 0.351046i | −0.746714 | − | 0.665146i | \(-0.768369\pi\) |
0.949390 | + | 0.314100i | \(0.101703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7409.35 | − | 2821.97i | 0.585572 | − | 0.223025i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 485.580 | 0.0381651 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23173.5 | −1.81138 | −0.905691 | − | 0.423939i | \(-0.860647\pi\) | ||||
−0.905691 | + | 0.423939i | \(0.860647\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5926.09 | − | 1227.27i | 0.460691 | − | 0.0954070i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9163.53 | + | 15871.7i | −0.708492 | + | 1.22714i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1206.41 | + | 1481.85i | −0.0922688 | + | 0.113335i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18408.7 | − | 10628.3i | 1.40036 | − | 0.808501i | 0.405934 | − | 0.913902i | \(-0.366946\pi\) |
0.994430 | + | 0.105402i | \(0.0336129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6173.95i | − | 0.467138i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 67.5269 | − | 419.248i | 0.00508198 | − | 0.0315520i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4931.19 | + | 8541.07i | 0.369138 | + | 0.639366i | 0.989431 | − | 0.145004i | \(-0.0463196\pi\) |
−0.620293 | + | 0.784370i | \(0.712986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2990.60 | + | 1726.62i | 0.222682 | + | 0.128566i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15573.7 | − | 8991.49i | −1.14742 | − | 0.662466i | −0.199166 | − | 0.979966i | \(-0.563823\pi\) |
−0.948258 | + | 0.317500i | \(0.897157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13285.5 | − | 23011.2i | −0.973699 | − | 1.68650i | −0.684163 | − | 0.729330i | \(-0.739832\pi\) |
−0.289537 | − | 0.957167i | \(-0.593501\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1251.26 | + | 7768.60i | −0.0912255 | + | 0.566384i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9820.79i | 0.712270i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3400.09 | − | 1963.04i | 0.245317 | − | 0.141634i | −0.372301 | − | 0.928112i | \(-0.621431\pi\) |
0.617618 | + | 0.786478i | \(0.288098\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9757.89 | + | 11985.8i | −0.700387 | + | 0.860296i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8248.03 | − | 14286.0i | 0.585932 | − | 1.01486i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1380.21 | − | 285.836i | 0.0975467 | − | 0.0202015i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9284.76 | 0.652850 | 0.326425 | − | 0.945223i | \(-0.394156\pi\) | ||||
0.326425 | + | 0.945223i | \(0.394156\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2779.25 | 0.194426 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14015.5 | − | 5338.04i | 0.975502 | − | 0.371536i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2701.61 | − | 4679.32i | 0.187085 | − | 0.324041i | −0.757192 | − | 0.653193i | \(-0.773429\pi\) |
0.944277 | + | 0.329151i | \(0.106763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11889.1 | + | 9679.17i | 0.815054 | + | 0.663555i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1165.84 | + | 673.101i | −0.0795244 | + | 0.0459134i | −0.539235 | − | 0.842155i | \(-0.681287\pi\) |
0.459711 | + | 0.888069i | \(0.347953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15011.2i | 1.01884i | 0.860519 | + | 0.509418i | \(0.170139\pi\) | ||||
−0.860519 | + | 0.509418i | \(0.829861\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8600.97 | + | 2844.45i | 0.580860 | + | 0.192098i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 485.648 | + | 841.167i | 0.0326354 | + | 0.0565261i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9270.02 | − | 5352.05i | −0.619866 | − | 0.357880i | 0.156951 | − | 0.987606i | \(-0.449834\pi\) |
−0.776817 | + | 0.629727i | \(0.783167\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8313.79 | + | 4799.97i | 0.550474 | + | 0.317817i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1496.91 | − | 2592.72i | −0.0986290 | − | 0.170830i | 0.812488 | − | 0.582977i | \(-0.198112\pi\) |
−0.911117 | + | 0.412147i | \(0.864779\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2678.98 | − | 431.495i | −0.175654 | − | 0.0282920i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15265.5i | 0.996056i | 0.867161 | + | 0.498028i | \(0.165942\pi\) | ||||
−0.867161 | + | 0.498028i | \(0.834058\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19456.4 | + | 11233.2i | −1.26336 | + | 0.729402i | −0.973723 | − | 0.227735i | \(-0.926868\pi\) |
−0.289637 | + | 0.957136i | \(0.593535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6132.60 | − | 9607.58i | −0.396285 | − | 0.620836i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7048.94 | + | 12209.1i | −0.451132 | + | 0.781383i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5791.53 | + | 15206.2i | 0.368886 | + | 0.968544i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 507.304 | 0.0321582 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6614.90 | 0.417330 | 0.208665 | − | 0.977987i | \(-0.433088\pi\) | ||||
0.208665 | + | 0.977987i | \(0.433088\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1407.40 | + | 3695.27i | 0.0883716 | + | 0.232028i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1875.00 | − | 3247.59i | 0.117176 | − | 0.202955i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18488.4 | − | 20750.7i | −1.14459 | − | 1.28464i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10414.2 | + | 6012.64i | −0.641710 | + | 0.370492i | −0.785273 | − | 0.619150i | \(-0.787477\pi\) |
0.143563 | + | 0.989641i | \(0.454144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12374.3i | − | 0.758936i | −0.925205 | − | 0.379468i | \(-0.876107\pi\) | ||
0.925205 | − | 0.379468i | \(-0.123893\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2498.16 | + | 402.371i | 0.152504 | + | 0.0245633i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −860.863 | − | 1491.06i | −0.0523091 | − | 0.0906021i | 0.838685 | − | 0.544617i | \(-0.183325\pi\) |
−0.890994 | + | 0.454014i | \(0.849991\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9589.62 | + | 5536.57i | 0.580008 | + | 0.334868i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19110.1 | + | 11033.2i | 1.14523 | + | 0.661201i | 0.947721 | − | 0.319099i | \(-0.103380\pi\) |
0.197513 | + | 0.980300i | \(0.436714\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 304.244 | + | 526.967i | 0.0181493 | + | 0.0314356i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4951.83 | + | 14973.2i | −0.294048 | + | 0.889134i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2582.20i | − | 0.152638i | −0.997083 | − | 0.0763190i | \(-0.975683\pi\) | ||
0.997083 | − | 0.0763190i | \(-0.0243167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8695.88 | + | 5020.57i | −0.511695 | + | 0.295427i | −0.733530 | − | 0.679657i | \(-0.762129\pi\) |
0.221835 | + | 0.975084i | \(0.428795\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −290.195 | − | 236.255i | −0.0169989 | − | 0.0138392i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6940.62 | + | 12021.5i | −0.402911 | + | 0.697863i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2795.55 | + | 1064.73i | −0.161558 | + | 0.0615319i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6543.78 | −0.376483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15931.2 | −0.912488 | −0.456244 | − | 0.889855i | \(-0.650806\pi\) | ||||
−0.456244 | + | 0.889855i | \(0.650806\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −754.672 | − | 16942.5i | −0.0430331 | − | 0.966102i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3485.21 | + | 6036.57i | −0.197855 | + | 0.342694i | −0.947833 | − | 0.318768i | \(-0.896731\pi\) |
0.749978 | + | 0.661463i | \(0.230064\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9284.85 | − | 11404.7i | 0.522461 | − | 0.641747i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5897.72 | − | 3405.05i | 0.330410 | − | 0.190762i | −0.325613 | − | 0.945503i | \(-0.605571\pi\) |
0.656023 | + | 0.754741i | \(0.272237\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4768.60i | − | 0.265984i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3121.09 | − | 19377.6i | 0.173329 | − | 1.07613i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7268.21 | − | 12588.9i | −0.401882 | − | 0.696080i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10542.5 | + | 6086.72i | 0.580399 | + | 0.335094i | 0.761292 | − | 0.648409i | \(-0.224565\pi\) |
−0.180893 | + | 0.983503i | \(0.557899\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2668.89 | − | 1540.88i | −0.145664 | − | 0.0840993i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 360.202 | + | 623.888i | 0.0195748 | + | 0.0339045i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4655.39 | − | 28903.5i | 0.251907 | − | 1.56399i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31903.7i | − | 1.71895i | −0.511176 | − | 0.859476i | \(-0.670790\pi\) | ||
0.511176 | − | 0.859476i | \(-0.329210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16834.5 | + | 9719.41i | −0.903166 | + | 0.521443i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2484.04 | + | 3051.18i | −0.132701 | + | 0.162999i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11558.0 | + | 20019.0i | −0.612228 | + | 1.06041i | 0.378636 | + | 0.925546i | \(0.376393\pi\) |
−0.990864 | + | 0.134865i | \(0.956940\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5443.94 | + | 26287.1i | 0.287150 | + | 1.38656i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2105.05 | 0.110568 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1524.08 | −0.0797164 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29536.3 | − | 11249.4i | 1.53843 | − | 0.585935i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11738.3 | − | 20331.3i | 0.608852 | − | 1.05456i | −0.382578 | − | 0.923923i | \(-0.624964\pi\) |
0.991430 | − | 0.130639i | \(-0.0417028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12387.5 | + | 10085.0i | 0.637203 | + | 0.518762i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17887.1 | + | 10327.1i | −0.916288 | + | 0.529019i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16192.1i | 0.826040i | 0.910722 | + | 0.413020i | \(0.135526\pi\) | ||||
−0.910722 | + | 0.413020i | \(0.864474\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11318.1 | + | 16103.5i | 0.575018 | + | 0.818141i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −335.890 | − | 581.778i | −0.0169950 | − | 0.0294362i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31235.2 | + | 18033.7i | 1.57394 | + | 0.908716i | 0.995679 | + | 0.0928663i | \(0.0296029\pi\) |
0.578264 | + | 0.815850i | \(0.303730\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8483.16 | − | 4897.76i | −0.423991 | − | 0.244791i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10083.4 | − | 17464.9i | −0.501925 | − | 0.869360i | −0.999998 | − | 0.00222472i | \(-0.999292\pi\) |
0.498072 | − | 0.867136i | \(-0.334041\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14156.3 | + | 2280.11i | 0.701815 | + | 0.113039i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24217.4i | − | 1.19576i | −0.801585 | − | 0.597881i | \(-0.796009\pi\) | ||
0.801585 | − | 0.597881i | \(-0.203991\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 260.281 | − | 150.273i | 0.0127999 | − | 0.00739005i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25828.0 | − | 23012.1i | 1.26505 | − | 1.12713i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3037.56 | − | 5261.20i | 0.147592 | − | 0.255638i | −0.782745 | − | 0.622343i | \(-0.786181\pi\) |
0.930337 | + | 0.366705i | \(0.119514\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4844.50 | + | 12719.7i | 0.234453 | + | 0.615579i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5056.80 | 0.243756 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34408.2 | −1.65203 | −0.826015 | − | 0.563648i | \(-0.809397\pi\) | ||||
−0.826015 | + | 0.563648i | \(0.809397\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4386.61 | + | 11517.4i | 0.209781 | + | 0.550799i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7900.11 | − | 13683.4i | 0.376319 | − | 0.651804i | −0.614204 | − | 0.789147i | \(-0.710523\pi\) |
0.990524 | + | 0.137343i | \(0.0438563\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 114.508 | − | 102.024i | 0.00541184 | − | 0.00482183i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8450.42 | − | 4878.85i | 0.397819 | − | 0.229681i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 35637.1i | − | 1.67114i | −0.549383 | − | 0.835571i | \(-0.685137\pi\) | ||
0.549383 | − | 0.835571i | \(-0.314863\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21839.7 | + | 3517.65i | 1.02015 | + | 0.164312i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8586.42 | + | 14872.1i | 0.399524 | + | 0.691996i | 0.993667 | − | 0.112364i | \(-0.0358422\pi\) |
−0.594143 | + | 0.804359i | \(0.702509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2712.52 | + | 1566.08i | 0.125725 | + | 0.0725873i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23906.1 | − | 13802.2i | −1.09952 | − | 0.634807i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15025.8 | + | 26025.4i | 0.688430 | + | 1.19240i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11050.0 | − | 21272.5i | 0.504334 | − | 0.970903i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6002.67i | − | 0.272923i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9242.80 | + | 5336.33i | −0.418641 | + | 0.241702i | −0.694496 | − | 0.719497i | \(-0.744372\pi\) |
0.275855 | + | 0.961199i | \(0.411039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28112.8 | − | 22887.3i | −1.26849 | − | 1.03271i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2883.20 | + | 4993.86i | −0.129112 | + | 0.223628i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5567.53 | − | 2120.49i | 0.248377 | − | 0.0945986i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30569.6 | 1.35863 | 0.679317 | − | 0.733845i | \(-0.262276\pi\) | ||||
0.679317 | + | 0.733845i | \(0.262276\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1044.56 | 0.0462500 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8091.83 | − | 39072.9i | −0.356942 | − | 1.72356i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8526.38 | − | 14768.1i | 0.374707 | − | 0.649011i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15314.6 | + | 18811.1i | −0.668029 | + | 0.820550i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18066.6 | + | 10430.7i | −0.785150 | + | 0.453307i | −0.838252 | − | 0.545282i | \(-0.816422\pi\) |
0.0531022 | + | 0.998589i | \(0.483089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1052.96i | − | 0.0455911i | −0.999740 | − | 0.0227956i | \(-0.992743\pi\) | ||
0.999740 | − | 0.0227956i | \(-0.00725668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7224.51 | − | 44854.2i | 0.311654 | − | 1.93494i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −154.790 | − | 268.105i | −0.00665284 | − | 0.0115231i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22292.5 | + | 12870.6i | 0.954610 | + | 0.551144i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29358.8 | + | 16950.3i | 1.24803 | + | 0.720548i | 0.970715 | − | 0.240233i | \(-0.0772237\pi\) |
0.277310 | + | 0.960780i | \(0.410557\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11801.0 | − | 20439.9i | −0.499826 | − | 0.865725i | 0.500174 | − | 0.865925i | \(-0.333269\pi\) |
−1.00000 | 0.000200564i | \(0.999936\pi\) | ||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2916.04 | + | 18104.6i | −0.123059 | + | 0.764025i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 26002.1i | − | 1.09333i | −0.837353 | − | 0.546663i | \(-0.815898\pi\) | ||
0.837353 | − | 0.546663i | \(-0.184102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18600.2 | + | 10738.8i | −0.779266 | + | 0.449910i | −0.836170 | − | 0.548470i | \(-0.815210\pi\) |
0.0569040 | + | 0.998380i | \(0.481877\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1968.84 | + | 2418.35i | −0.0821880 | + | 0.100953i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1331.52 | + | 2306.25i | −0.0551844 | + | 0.0955822i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3631.57 | + | 161.761i | −0.149971 | + | 0.00668016i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26619.1 | 1.09534 | 0.547671 | − | 0.836694i | \(-0.315515\pi\) | ||||
0.547671 | + | 0.836694i | \(0.315515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4804.75 | −0.197005 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21868.8 | − | 8329.09i | 0.893477 | − | 0.340295i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1557.54 | − | 2697.73i | 0.0634094 | − | 0.109828i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1791.92 | + | 1458.85i | 0.0724365 | + | 0.0589723i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12750.8 | + | 7361.65i | −0.513620 | + | 0.296538i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10440.3i | 0.419075i | 0.977801 | + | 0.209537i | \(0.0671958\pi\) | ||||
−0.977801 | + | 0.209537i | \(0.932804\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1845.20 | + | 5579.47i | −0.0738065 | + | 0.223174i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13344.9 | − | 23114.1i | −0.531918 | − | 0.921310i | −0.999306 | − | 0.0372570i | \(-0.988138\pi\) |
0.467387 | − | 0.884053i | \(-0.345195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15540.5 | − | 8972.31i | −0.617270 | − | 0.356381i | 0.158535 | − | 0.987353i | \(-0.449323\pi\) |
−0.775805 | + | 0.630972i | \(0.782656\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8043.37 | − | 4643.84i | −0.317265 | − | 0.183173i | 0.332908 | − | 0.942959i | \(-0.391970\pi\) |
−0.650173 | + | 0.759786i | \(0.725304\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2630.36 | − | 4555.91i | −0.103393 | − | 0.179082i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25163.7 | + | 4053.03i | 0.985701 | + | 0.158764i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 29027.1i | − | 1.13311i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7475.40 | + | 4315.93i | −0.290809 | + | 0.167898i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22071.8 | − | 24772.5i | −0.855688 | − | 0.960393i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1716.56 | − | 2973.16i | 0.0660935 | − | 0.114477i | −0.831085 | − | 0.556145i | \(-0.812280\pi\) |
0.897179 | + | 0.441668i | \(0.145613\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11655.2 | + | 30601.8i | 0.447235 | + | 1.17426i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30222.9 | −1.15577 | −0.577885 | − | 0.816118i | \(-0.696122\pi\) | ||||
−0.577885 | + | 0.816118i | \(0.696122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8445.55 | −0.321875 | −0.160937 | − | 0.986965i | \(-0.551452\pi\) | ||||
−0.160937 | + | 0.986965i | \(0.551452\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1423.39 | + | 3737.26i | 0.0540643 | + | 0.141951i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3758.68 | − | 6510.22i | 0.142282 | − | 0.246439i | −0.786074 | − | 0.618133i | \(-0.787889\pi\) |
0.928356 | + | 0.371693i | \(0.121223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8452.70 | − | 19532.5i | −0.317818 | − | 0.734414i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34662.9 | + | 20012.6i | −1.29894 | + | 0.749941i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6853.36i | 0.255958i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10722.2 | + | 1726.99i | 0.399114 | + | 0.0642839i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2213.58 | + | 3834.03i | 0.0821212 | + | 0.142238i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1369.78 | − | 790.845i | −0.0506483 | − | 0.0292418i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2681.41 | − | 1548.11i | −0.0984894 | − | 0.0568629i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4833.51 | − | 8371.88i | −0.176950 | − | 0.306487i | 0.763884 | − | 0.645353i | \(-0.223290\pi\) |
−0.940834 | + | 0.338866i | \(0.889957\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11264.2 | − | 3725.21i | −0.411012 | − | 0.135927i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 13633.2i | − | 0.495815i | −0.968784 | − | 0.247908i | \(-0.920257\pi\) | ||
0.968784 | − | 0.247908i | \(-0.0797429\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32393.2 | + | 18702.2i | −1.17422 | + | 0.677934i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1832.76 | − | 1492.09i | −0.0662176 | − | 0.0539093i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15801.4 | − | 27368.9i | 0.567183 | − | 0.982389i | −0.429660 | − | 0.902991i | \(-0.641367\pi\) |
0.996843 | − | 0.0793984i | \(-0.0252999\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36566.6 | + | 13927.0i | −1.30826 | + | 0.498274i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26481.5 | 0.944367 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21907.1 | −0.778705 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29408.5 | − | 6090.36i | 1.04196 | − | 0.215786i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15455.3 | − | 26769.3i | 0.545825 | − | 0.945396i | −0.452730 | − | 0.891648i | \(-0.649550\pi\) |
0.998555 | − | 0.0537486i | \(-0.0171169\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30726.8 | − | 37742.1i | 1.07819 | − | 1.32435i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −143.615 | + | 82.9164i | −0.00502324 | + | 0.00290017i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12018.0i | 0.419010i | 0.977808 | + | 0.209505i | \(0.0671852\pi\) | ||||
−0.977808 | + | 0.209505i | \(0.932815\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3238.21 | − | 20104.8i | 0.112540 | − | 0.698718i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11957.3 | − | 20710.7i | −0.414237 | − | 0.717479i | 0.581111 | − | 0.813824i | \(-0.302618\pi\) |
−0.995348 | + | 0.0963449i | \(0.969285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18106.9 | − | 10454.0i | −0.625283 | − | 0.361007i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15175.1 | − | 8761.35i | −0.520723 | − | 0.300640i | 0.216507 | − | 0.976281i | \(-0.430533\pi\) |
−0.737230 | + | 0.675641i | \(0.763867\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7513.49 | − | 13013.7i | −0.257005 | − | 0.445147i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 461.522 | − | 2865.41i | 0.0157370 | − | 0.0977048i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30378.0i | 1.03257i | 0.856417 | + | 0.516285i | \(0.172686\pi\) | ||||
−0.856417 | + | 0.516285i | \(0.827314\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2661.17 | − | 1536.43i | 0.0901712 | − | 0.0520604i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16364.5 | + | 20100.8i | −0.552758 | + | 0.678960i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14559.8 | + | 25218.3i | −0.488732 | + | 0.846509i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1585.49 | + | 328.348i | −0.0530547 | + | 0.0109874i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6035.64 | 0.201341 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39792.1 | −1.32330 | −0.661648 | − | 0.749814i | \(-0.730143\pi\) | ||||
−0.661648 | + | 0.749814i | \(0.730143\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1458.01 | − | 555.308i | 0.0483366 | − | 0.0184098i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7925.17 | + | 13726.8i | −0.261927 | + | 0.453670i | −0.966754 | − | 0.255709i | \(-0.917691\pi\) |
0.704827 | + | 0.709379i | \(0.251024\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12531.6 | + | 10202.3i | 0.411624 | + | 0.335113i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14545.6 | − | 8397.90i | 0.476310 | − | 0.274998i | −0.242568 | − | 0.970135i | \(-0.577990\pi\) |
0.718877 | + | 0.695137i | \(0.244656\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43145.6i | 1.40852i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6134.33 | − | 2028.70i | −0.199647 | − | 0.0660259i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7308.50 | + | 12658.7i | 0.237136 | + | 0.410732i | 0.959891 | − | 0.280372i | \(-0.0904578\pi\) |
−0.722755 | + | 0.691104i | \(0.757125\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5072.14 | − | 2928.40i | −0.164073 | − | 0.0947276i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16884.7 | + | 9748.41i | 0.542875 | + | 0.313429i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24857.9 | − | 43055.2i | −0.796809 | − | 1.38011i | −0.921684 | − | 0.387941i | \(-0.873186\pi\) |
0.124875 | − | 0.992172i | \(-0.460147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5641.93 | − | 908.727i | −0.180303 | − | 0.0290409i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5986.94i | − | 0.190753i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23841.9 | − | 13765.2i | 0.757354 | − | 0.437259i | −0.0709909 | − | 0.997477i | \(-0.522616\pi\) |
0.828345 | + | 0.560218i | \(0.189283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21431.5 | − | 13679.9i | 0.678742 | − | 0.433247i |
(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.509.14 | 48 | ||
3.2 | odd | 2 | inner | 588.4.k.e.509.7 | 48 | ||
7.2 | even | 3 | 588.4.f.d.293.1 | ✓ | 24 | ||
7.3 | odd | 6 | inner | 588.4.k.e.521.7 | 48 | ||
7.4 | even | 3 | inner | 588.4.k.e.521.18 | 48 | ||
7.5 | odd | 6 | 588.4.f.d.293.24 | yes | 24 | ||
7.6 | odd | 2 | inner | 588.4.k.e.509.11 | 48 | ||
21.2 | odd | 6 | 588.4.f.d.293.23 | yes | 24 | ||
21.5 | even | 6 | 588.4.f.d.293.2 | yes | 24 | ||
21.11 | odd | 6 | inner | 588.4.k.e.521.11 | 48 | ||
21.17 | even | 6 | inner | 588.4.k.e.521.14 | 48 | ||
21.20 | even | 2 | inner | 588.4.k.e.509.18 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.f.d.293.1 | ✓ | 24 | 7.2 | even | 3 | ||
588.4.f.d.293.2 | yes | 24 | 21.5 | even | 6 | ||
588.4.f.d.293.23 | yes | 24 | 21.2 | odd | 6 | ||
588.4.f.d.293.24 | yes | 24 | 7.5 | odd | 6 | ||
588.4.k.e.509.7 | 48 | 3.2 | odd | 2 | inner | ||
588.4.k.e.509.11 | 48 | 7.6 | odd | 2 | inner | ||
588.4.k.e.509.14 | 48 | 1.1 | even | 1 | trivial | ||
588.4.k.e.509.18 | 48 | 21.20 | even | 2 | inner | ||
588.4.k.e.521.7 | 48 | 7.3 | odd | 6 | inner | ||
588.4.k.e.521.11 | 48 | 21.11 | odd | 6 | inner | ||
588.4.k.e.521.14 | 48 | 21.17 | even | 6 | inner | ||
588.4.k.e.521.18 | 48 | 7.4 | even | 3 | inner |