Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2548,2,Mod(753,2548)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2548, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2548.753");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2548.y (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: | \(20.3458824350\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.11348687176217973595570176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{14} + 176x^{12} - 1016x^{10} + 4224x^{8} - 8512x^{6} + 12304x^{4} - 8448x^{2} + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 364) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 961.4 | ||
Root | \(1.12031 + 0.646813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2548.961 |
Dual form | 2548.2.y.e.753.4 |
$q$-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 \(\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(885\) | \(1275\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.646813 | − | 1.12031i | −0.373438 | − | 0.646813i | 0.616654 | − | 0.787234i | \(-0.288488\pi\) |
−0.990092 | + | 0.140421i | \(0.955154\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.42353 | + | 1.39923i | 1.08384 | + | 0.625754i | 0.931929 | − | 0.362641i | \(-0.118125\pi\) |
0.151909 | + | 0.988395i | \(0.451458\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.663266 | − | 1.14881i | 0.221089 | − | 0.382937i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.894522 | + | 0.516453i | −0.269709 | + | 0.155716i | −0.628755 | − | 0.777603i | \(-0.716435\pi\) |
0.359047 | + | 0.933320i | \(0.383102\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.79846 | − | 3.12499i | 0.498802 | − | 0.866716i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.62016i | − | 0.934721i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.47818 | − | 6.02438i | −0.843581 | − | 1.46113i | −0.886847 | − | 0.462062i | \(-0.847110\pi\) |
0.0432661 | − | 0.999064i | \(-0.486224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.19774 | + | 1.26887i | 0.504197 | + | 0.291098i | 0.730445 | − | 0.682971i | \(-0.239313\pi\) |
−0.226248 | + | 0.974070i | \(0.572646\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.91568 | − | 3.31806i | 0.399447 | − | 0.691863i | −0.594211 | − | 0.804309i | \(-0.702535\pi\) |
0.993658 | + | 0.112447i | \(0.0358688\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.41568 | + | 2.45203i | 0.283136 | + | 0.490406i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.59691 | −1.07713 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.10175 | −0.947370 | −0.473685 | − | 0.880694i | \(-0.657077\pi\) | ||||
−0.473685 | + | 0.880694i | \(0.657077\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.28119 | + | 1.89440i | −0.589320 | + | 0.340244i | −0.764828 | − | 0.644234i | \(-0.777176\pi\) |
0.175509 | + | 0.984478i | \(0.443843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.15718 | + | 0.668097i | 0.201439 | + | 0.116301i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.37577 | − | 3.10370i | −0.883772 | − | 0.510246i | −0.0118717 | − | 0.999930i | \(-0.503779\pi\) |
−0.871900 | + | 0.489684i | \(0.837112\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.66423 | + | 0.00644825i | −0.746875 | + | 0.00103255i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.990338i | 0.154665i | 0.997005 | + | 0.0773324i | \(0.0246403\pi\) | ||||
−0.997005 | + | 0.0773324i | \(0.975360\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.560979 | 0.0855485 | 0.0427743 | − | 0.999085i | \(-0.486380\pi\) | ||||
0.0427743 | + | 0.999085i | \(0.486380\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.21489 | − | 1.85612i | 0.479248 | − | 0.276694i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.22741 | + | 3.59540i | 0.908362 | + | 0.524443i | 0.879904 | − | 0.475152i | \(-0.157607\pi\) |
0.0284580 | + | 0.999595i | \(0.490940\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.49946 | + | 7.79329i | −0.630050 | + | 1.09128i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.589150 | − | 1.02044i | −0.0809260 | − | 0.140168i | 0.822722 | − | 0.568444i | \(-0.192454\pi\) |
−0.903648 | + | 0.428276i | \(0.859121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.89054 | −0.389760 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.28288i | − | 0.434828i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3260 | − | 5.96172i | 1.34433 | − | 0.776150i | 0.356892 | − | 0.934146i | \(-0.383837\pi\) |
0.987440 | + | 0.157996i | \(0.0505032\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.92345 | − | 11.9918i | 0.886456 | − | 1.53539i | 0.0424210 | − | 0.999100i | \(-0.486493\pi\) |
0.844035 | − | 0.536288i | \(-0.180174\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.73120 | − | 5.05707i | 1.08297 | − | 0.627252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.9348 | + | 6.89054i | −1.45806 | + | 0.841813i | −0.998916 | − | 0.0465465i | \(-0.985178\pi\) |
−0.459148 | + | 0.888360i | \(0.651845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.95635 | −0.596674 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.80432i | − | 0.451490i | −0.974186 | − | 0.225745i | \(-0.927518\pi\) | ||
0.974186 | − | 0.225745i | \(-0.0724816\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.76331 | − | 1.59540i | 0.323421 | − | 0.186727i | −0.329495 | − | 0.944157i | \(-0.606879\pi\) |
0.652917 | + | 0.757430i | \(0.273545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.83136 | − | 3.17201i | 0.211467 | − | 0.366272i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.66620 | + | 6.35004i | −0.412480 | + | 0.714436i | −0.995160 | − | 0.0982656i | \(-0.968671\pi\) |
0.582681 | + | 0.812701i | \(0.302004\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.63036 | + | 2.82387i | 0.181151 | + | 0.313763i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 16.6260i | − | 1.82494i | −0.409140 | − | 0.912472i | \(-0.634171\pi\) | ||
0.409140 | − | 0.912472i | \(-0.365829\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 19.4670i | − | 2.11150i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.29988 | + | 5.71555i | 0.353784 | + | 0.612772i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3026 | + | 5.94820i | 1.09207 | + | 0.630508i | 0.934127 | − | 0.356940i | \(-0.116180\pi\) |
0.157945 | + | 0.987448i | \(0.449513\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.24464 | + | 2.45064i | 0.440148 | + | 0.254120i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.55087 | + | 6.15029i | 0.364312 | + | 0.631007i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.60355i | − | 0.873558i | −0.899569 | − | 0.436779i | \(-0.856119\pi\) | ||
0.899569 | − | 0.436779i | \(-0.143881\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.37018i | 0.137708i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.18455 | + | 7.24785i | 0.416378 | + | 0.721188i | 0.995572 | − | 0.0940017i | \(-0.0299659\pi\) |
−0.579194 | + | 0.815190i | \(0.696633\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.260721 | − | 0.451582i | 0.0256896 | − | 0.0444957i | −0.852895 | − | 0.522083i | \(-0.825155\pi\) |
0.878584 | + | 0.477587i | \(0.158489\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.71761 | + | 8.17115i | −0.456069 | + | 0.789934i | −0.998749 | − | 0.0500050i | \(-0.984076\pi\) |
0.542680 | + | 0.839939i | \(0.317410\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.8524 | − | 6.84298i | 1.13525 | − | 0.655439i | 0.190003 | − | 0.981784i | \(-0.439150\pi\) |
0.945251 | + | 0.326345i | \(0.105817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.03007i | 0.762180i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.2655 | −1.15384 | −0.576921 | − | 0.816800i | \(-0.695746\pi\) | ||||
−0.576921 | + | 0.816800i | \(0.695746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.28544 | − | 5.36095i | 0.865872 | − | 0.499911i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.39716 | − | 4.13878i | −0.221618 | − | 0.382631i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.96655 | + | 8.60232i | −0.451505 | + | 0.782029i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.10949 | − | 0.640564i | 0.100039 | − | 0.0577577i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.06884i | − | 0.542814i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9331 | −0.970156 | −0.485078 | − | 0.874471i | \(-0.661209\pi\) | ||||
−0.485078 | + | 0.874471i | \(0.661209\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.362849 | − | 0.628472i | −0.0319470 | − | 0.0553339i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.29363 | + | 5.70473i | −0.287765 | + | 0.498424i | −0.973276 | − | 0.229638i | \(-0.926246\pi\) |
0.685511 | + | 0.728063i | \(0.259579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.5643 | − | 7.83136i | −1.16743 | − | 0.674016i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.1140 | − | 6.41665i | 0.949531 | − | 0.548212i | 0.0565956 | − | 0.998397i | \(-0.481975\pi\) |
0.892935 | + | 0.450185i | \(0.148642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.5998 | 1.57761 | 0.788805 | − | 0.614643i | \(-0.210700\pi\) | ||||
0.788805 | + | 0.614643i | \(0.210700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.30221i | − | 0.783387i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.00514865 | + | 3.72419i | 0.000430552 | + | 0.311432i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.3643 | − | 7.13851i | −1.02680 | − | 0.592821i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.64012 | − | 4.98838i | −0.707827 | − | 0.408664i | 0.102429 | − | 0.994740i | \(-0.467338\pi\) |
−0.810256 | + | 0.586076i | \(0.800672\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.1714 | + | 7.02715i | −0.990493 | + | 0.571861i | −0.905422 | − | 0.424513i | \(-0.860445\pi\) |
−0.0850714 | + | 0.996375i | \(0.527112\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.22782 | −0.746025 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.6028 | −0.851636 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.88429 | − | 6.72779i | −0.310000 | − | 0.536936i | 0.668362 | − | 0.743836i | \(-0.266996\pi\) |
−0.978362 | + | 0.206900i | \(0.933662\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.762140 | + | 1.32006i | −0.0604416 | + | 0.104688i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.40289 | + | 3.69671i | 0.501513 | + | 0.289549i | 0.729338 | − | 0.684153i | \(-0.239828\pi\) |
−0.227825 | + | 0.973702i | \(0.573161\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.86964 | + | 3.23831i | 0.145551 | + | 0.252102i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.7122i | 1.21585i | 0.793995 | + | 0.607925i | \(0.207998\pi\) | ||||
−0.793995 | + | 0.607925i | \(0.792002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.53110 | − | 11.2403i | −0.502393 | − | 0.864640i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.91538 | − | 1.68319i | 0.222944 | − | 0.128717i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.207792 | + | 0.359907i | −0.0157982 | + | 0.0273632i | −0.873816 | − | 0.486256i | \(-0.838362\pi\) |
0.858018 | + | 0.513619i | \(0.171696\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.3580 | − | 7.71224i | −1.00405 | − | 0.579688i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.95396 | − | 3.38436i | −0.146046 | − | 0.252959i | 0.783717 | − | 0.621118i | \(-0.213321\pi\) |
−0.929763 | + | 0.368160i | \(0.879988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.79151 | −0.356150 | −0.178075 | − | 0.984017i | \(-0.556987\pi\) | ||||
−0.178075 | + | 0.984017i | \(0.556987\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.9127 | −1.32414 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.68559 | − | 15.0439i | −0.638577 | − | 1.10605i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.22261 | + | 3.59262i | 0.455042 | + | 0.262719i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.31453 | − | 7.47298i | 0.312188 | − | 0.540726i | −0.666648 | − | 0.745373i | \(-0.732271\pi\) |
0.978836 | + | 0.204647i | \(0.0656047\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.1773 | − | 12.2267i | 1.52438 | − | 0.880100i | 0.524794 | − | 0.851229i | \(-0.324142\pi\) |
0.999583 | − | 0.0288702i | \(-0.00919095\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.3129 | − | 6.51070i | −0.810137 | − | 0.466241i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.14128i | − | 0.508795i | −0.967100 | − | 0.254398i | \(-0.918123\pi\) | ||
0.967100 | − | 0.254398i | \(-0.0818772\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.501418 | − | 0.868482i | −0.0355446 | − | 0.0615651i | 0.847706 | − | 0.530467i | \(-0.177983\pi\) |
−0.883250 | + | 0.468902i | \(0.844650\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.4391 | + | 8.91378i | 1.08899 | + | 0.628730i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.38571 | + | 2.40012i | −0.0967822 | + | 0.167632i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.54121 | − | 4.40151i | −0.176626 | − | 0.305926i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.62124 | −0.181315 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.2655 | 1.80819 | 0.904096 | − | 0.427329i | \(-0.140546\pi\) | ||||
0.904096 | + | 0.427329i | \(0.140546\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.26203 | + | 2.46069i | −0.292030 | + | 0.168603i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.35955 | + | 0.784938i | 0.0927207 | + | 0.0535323i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.57469 | − | 2.06385i | −0.241555 | − | 0.139462i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.0815 | + | 0.0346748i | −1.68716 | + | 0.00233248i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.7540i | − | 1.18890i | −0.804133 | − | 0.594449i | \(-0.797370\pi\) | ||
0.804133 | − | 0.594449i | \(-0.202630\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.75589 | 0.250393 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.4391 | + | 8.91378i | −1.02473 | + | 0.591629i | −0.915471 | − | 0.402385i | \(-0.868181\pi\) |
−0.109260 | + | 0.994013i | \(0.534848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.64963 | − | 2.10712i | −0.241175 | − | 0.139242i | 0.374542 | − | 0.927210i | \(-0.377800\pi\) |
−0.615716 | + | 0.787968i | \(0.711133\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.1440 | − | 24.4981i | 0.926604 | − | 1.60492i | 0.137642 | − | 0.990482i | \(-0.456048\pi\) |
0.788961 | − | 0.614443i | \(-0.210619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0616 | + | 17.4272i | 0.656344 | + | 1.13682i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.48538 | 0.616142 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.94385i | 0.578530i | 0.957249 | + | 0.289265i | \(0.0934108\pi\) | ||||
−0.957249 | + | 0.289265i | \(0.906589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7241 | − | 8.50097i | 0.948464 | − | 0.547596i | 0.0558604 | − | 0.998439i | \(-0.482210\pi\) |
0.892603 | + | 0.450843i | \(0.148876\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.28629 | + | 10.8882i | −0.403266 | + | 0.698477i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.91775 | − | 4.58592i | 0.503794 | − | 0.291795i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.6264 | + | 10.7539i | −1.18040 | + | 0.681503i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.70637 | 0.423303 | 0.211651 | − | 0.977345i | \(-0.432116\pi\) | ||||
0.211651 | + | 0.977345i | \(0.432116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.95743i | 0.248802i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −21.8092 | + | 12.5915i | −1.36574 | + | 0.788513i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.33278 | + | 12.7007i | −0.457406 | + | 0.792251i | −0.998823 | − | 0.0485035i | \(-0.984555\pi\) |
0.541417 | + | 0.840754i | \(0.317888\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.38381 | + | 5.86093i | −0.209453 | + | 0.362783i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.01314 | + | 5.21891i | 0.185798 | + | 0.321812i | 0.943845 | − | 0.330388i | \(-0.107180\pi\) |
−0.758047 | + | 0.652200i | \(0.773846\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.29742i | − | 0.202559i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 15.3895i | − | 0.941822i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.412748 | − | 0.714900i | −0.0251657 | − | 0.0435882i | 0.853168 | − | 0.521636i | \(-0.174678\pi\) |
−0.878334 | + | 0.478048i | \(0.841345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.51092 | − | 4.91378i | −0.517002 | − | 0.298491i | 0.218705 | − | 0.975791i | \(-0.429817\pi\) |
−0.735707 | + | 0.677300i | \(0.763150\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.53272 | − | 1.46226i | −0.152729 | − | 0.0881778i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.9258 | − | 24.1203i | −0.836722 | − | 1.44925i | −0.892620 | − | 0.450809i | \(-0.851135\pi\) |
0.0558978 | − | 0.998436i | \(-0.482198\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.02596i | 0.300896i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.04257i | 0.241159i | 0.992704 | + | 0.120580i | \(0.0384753\pi\) | ||||
−0.992704 | + | 0.120580i | \(0.961525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.8798 | − | 25.7726i | −0.884512 | − | 1.53202i | −0.846272 | − | 0.532751i | \(-0.821158\pi\) |
−0.0382402 | − | 0.999269i | \(-0.512175\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.59350 | − | 7.95618i | 0.272096 | − | 0.471283i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6954 | + | 27.1852i | −0.923259 | + | 1.59913i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.63867 | + | 5.56489i | −0.565029 | + | 0.326219i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.8091i | 1.74147i | 0.491755 | + | 0.870733i | \(0.336355\pi\) | ||||
−0.491755 | + | 0.870733i | \(0.663645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.3673 | 1.94272 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.00656 | − | 2.89054i | 0.290510 | − | 0.167726i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.92362 | − | 11.9539i | −0.400403 | − | 0.691310i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.41324 | − | 9.37601i | 0.310983 | − | 0.538638i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 33.5584 | − | 19.3750i | 1.92155 | − | 1.10941i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.5928i | − | 1.06115i | −0.847639 | − | 0.530574i | \(-0.821977\pi\) | ||
0.847639 | − | 0.530574i | \(-0.178023\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.674552 | −0.0383739 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.95597 | + | 13.7801i | 0.451142 | + | 0.781400i | 0.998457 | − | 0.0555262i | \(-0.0176836\pi\) |
−0.547316 | + | 0.836926i | \(0.684350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.897873 | + | 1.55516i | −0.0507508 | + | 0.0879029i | −0.890285 | − | 0.455404i | \(-0.849495\pi\) |
0.839534 | + | 0.543307i | \(0.182828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.8833 | + | 8.01553i | 0.779764 | + | 0.450197i | 0.836347 | − | 0.548201i | \(-0.184687\pi\) |
−0.0565827 | + | 0.998398i | \(0.518020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.56362 | − | 2.63481i | 0.255514 | − | 0.147521i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.2057 | 0.681253 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 17.6534i | − | 0.982260i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.2086 | − | 0.0141133i | 0.566272 | − | 0.000782865i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.3326 | − | 8.85226i | −0.847893 | − | 0.489531i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.90448 | − | 3.40895i | −0.324540 | − | 0.187373i | 0.328875 | − | 0.944374i | \(-0.393331\pi\) |
−0.653414 | + | 0.757001i | \(0.726664\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.13113 | + | 4.11716i | −0.390784 | + | 0.225619i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −38.5658 | −2.10707 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.418615 | 0.0228034 | 0.0114017 | − | 0.999935i | \(-0.496371\pi\) | ||||
0.0114017 | + | 0.999935i | \(0.496371\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.93349 | + | 13.7412i | 0.430888 | + | 0.746320i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.95673 | − | 3.38916i | 0.105963 | − | 0.183533i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.0119 | − | 6.93507i | −0.646698 | − | 0.373371i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.03291 | + | 8.71725i | 0.270180 | + | 0.467966i | 0.968908 | − | 0.247422i | \(-0.0795833\pi\) |
−0.698727 | + | 0.715388i | \(0.746250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.27233i | 0.442808i | 0.975182 | + | 0.221404i | \(0.0710639\pi\) | ||||
−0.975182 | + | 0.221404i | \(0.928936\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.0658 | + | 17.4903i | −0.537273 | + | 0.933563i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.1949 | + | 8.19541i | −0.755516 | + | 0.436197i | −0.827684 | − | 0.561195i | \(-0.810342\pi\) |
0.0721674 | + | 0.997393i | \(0.477008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.32312 | − | 9.21991i | 0.282522 | − | 0.489342i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.8437 | + | 16.0756i | 1.46954 | + | 0.848437i | 0.999416 | − | 0.0341658i | \(-0.0108774\pi\) |
0.470120 | + | 0.882603i | \(0.344211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.27995 | − | 10.8772i | −0.330524 | − | 0.572484i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.8497 | 0.674436 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.92931 | 0.467382 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.89787 | − | 6.75131i | −0.203467 | − | 0.352416i | 0.746176 | − | 0.665749i | \(-0.231888\pi\) |
−0.949643 | + | 0.313333i | \(0.898554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.13771 | + | 0.656857i | 0.0592268 | + | 0.0341946i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.8686 | + | 27.4851i | −0.821643 | + | 1.42313i | 0.0828156 | + | 0.996565i | \(0.473609\pi\) |
−0.904458 | + | 0.426562i | \(0.859725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.79900 | + | 3.92541i | −0.351099 | + | 0.202707i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.17527 | + | 15.9429i | −0.472550 | + | 0.821101i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.3236i | 1.55762i | 0.627261 | + | 0.778809i | \(0.284176\pi\) | ||||
−0.627261 | + | 0.778809i | \(0.715824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.07168 | + | 12.2485i | 0.362293 | + | 0.627510i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.1411 | + | 7.00966i | 0.620381 | + | 0.358177i | 0.777017 | − | 0.629479i | \(-0.216732\pi\) |
−0.156636 | + | 0.987656i | \(0.550065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.372078 | − | 0.644458i | 0.0189138 | − | 0.0327597i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.94435 | − | 17.2241i | −0.504198 | − | 0.873297i | −0.999988 | − | 0.00485467i | \(-0.998455\pi\) |
0.495790 | − | 0.868443i | \(-0.334879\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.6523 | −1.34786 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.52144 | 0.429850 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.7703 | + | 10.2597i | −0.894122 | + | 0.516222i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.7495 | + | 7.36095i | 0.639881 | + | 0.369436i | 0.784569 | − | 0.620042i | \(-0.212884\pi\) |
−0.144688 | + | 0.989477i | \(0.546218\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0098 | + | 9.82062i | 0.849429 | + | 0.490418i | 0.860458 | − | 0.509521i | \(-0.170177\pi\) |
−0.0110289 | + | 0.999939i | \(0.503511\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0188858 | + | 13.6607i | 0.000940766 | + | 0.680487i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.12499i | 0.453424i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.41166 | 0.317814 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.8826 | − | 12.0566i | 1.03258 | − | 0.596160i | 0.114856 | − | 0.993382i | \(-0.463359\pi\) |
0.917722 | + | 0.397223i | \(0.130026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.3773 | − | 8.30075i | −0.709181 | − | 0.409446i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.2636 | − | 40.2938i | 1.14197 | − | 1.97794i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0306 | − | 20.8375i | −0.589139 | − | 1.02042i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7818 | 0.966406 | 0.483203 | − | 0.875508i | \(-0.339473\pi\) | ||||
0.483203 | + | 0.875508i | \(0.339473\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.1237i | 0.932033i | 0.884776 | + | 0.466016i | \(0.154311\pi\) | ||||
−0.884776 | + | 0.466016i | \(0.845689\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.26086 | − | 4.76941i | 0.401657 | − | 0.231897i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.84797 | − | 17.0572i | 0.477697 | − | 0.827395i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.16893 | − | 2.41462i | 0.201278 | − | 0.116579i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.68673 | + | 4.43794i | −0.370257 | + | 0.213768i | −0.673571 | − | 0.739123i | \(-0.735240\pi\) |
0.303314 | + | 0.952891i | \(0.401907\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.9341 | 1.77494 | 0.887470 | − | 0.460866i | \(-0.152461\pi\) | ||||
0.887470 | + | 0.460866i | \(0.152461\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.4691i | 0.885527i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.42035 | − | 4.86149i | 0.402800 | − | 0.232557i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.3296 | + | 17.8913i | −0.493003 | + | 0.853906i | −0.999968 | − | 0.00806061i | \(-0.997434\pi\) |
0.506964 | + | 0.861967i | \(0.330768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.42746 | + | 2.47244i | −0.0678207 | + | 0.117469i | −0.897942 | − | 0.440114i | \(-0.854938\pi\) |
0.830121 | + | 0.557583i | \(0.188271\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.6458 | + | 28.8314i | 0.789086 | + | 1.36674i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.9062i | 0.610442i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0443i | 1.41788i | 0.705269 | + | 0.708940i | \(0.250826\pi\) | ||||
−0.705269 | + | 0.708940i | \(0.749174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.511463 | − | 0.885879i | −0.0240838 | − | 0.0417144i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.7452 | + | 9.09051i | 0.739775 | + | 0.427109i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.8109 | + | 14.3246i | 1.16060 | + | 0.670075i | 0.951449 | − | 0.307807i | \(-0.0995952\pi\) |
0.209156 | + | 0.977882i | \(0.432929\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.4670 | + | 33.7179i | 0.908644 | + | 1.57382i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.922363i | 0.0429587i | 0.999769 | + | 0.0214794i | \(0.00683762\pi\) | ||||
−0.999769 | + | 0.0214794i | \(0.993162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0929i | 1.21264i | 0.795220 | + | 0.606321i | \(0.207355\pi\) | ||||
−0.795220 | + | 0.606321i | \(0.792645\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.85802 | + | 11.8784i | 0.318033 | + | 0.550849i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.7777 | − | 25.5957i | 0.683829 | − | 1.18443i | −0.289974 | − | 0.957034i | \(-0.593647\pi\) |
0.973803 | − | 0.227392i | \(-0.0730199\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.02482 | + | 8.70324i | −0.231532 | + | 0.401024i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.501808 | + | 0.289719i | −0.0230732 | + | 0.0133213i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.18525i | 0.329682i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.56305 | −0.0715672 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7658 | − | 7.94771i | 0.628977 | − | 0.363140i | −0.151379 | − | 0.988476i | \(-0.548371\pi\) |
0.780356 | + | 0.625336i | \(0.215038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.3671 | + | 11.2174i | −0.883066 | + | 0.511467i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0383 | − | 20.8510i | 0.546632 | − | 0.946795i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.0737279 | − | 0.0425668i | 0.00334093 | − | 0.00192889i | −0.498329 | − | 0.866988i | \(-0.666053\pi\) |
0.501670 | + | 0.865059i | \(0.332719\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 9.56433i | − | 0.432514i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.56324 | 0.115678 | 0.0578388 | − | 0.998326i | \(-0.481579\pi\) | ||||
0.0578388 | + | 0.998326i | \(0.481579\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.7448 | + | 30.7348i | 0.799184 | + | 1.38423i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.91720 | + | 3.32068i | −0.0861716 | + | 0.149254i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.8498 | − | 14.3470i | −1.11243 | − | 0.642262i | −0.172973 | − | 0.984927i | \(-0.555337\pi\) |
−0.939458 | + | 0.342664i | \(0.888671\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.6026 | − | 10.1629i | 0.786428 | − | 0.454044i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.7056 | 1.45827 | 0.729136 | − | 0.684369i | \(-0.239922\pi\) | ||||
0.729136 | + | 0.684369i | \(0.239922\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.4206i | 1.04220i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.36827 | + | 14.5873i | −0.371648 | + | 0.647843i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.5979 | + | 13.0469i | 1.00164 | + | 0.578295i | 0.908732 | − | 0.417381i | \(-0.137052\pi\) |
0.0929037 | + | 0.995675i | \(0.470385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.3006 | − | 7.10175i | −0.543084 | − | 0.313550i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.26373 | − | 0.729617i | 0.0556868 | − | 0.0321508i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.42741 | −0.326657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.537611 | 0.0235985 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.877849 | − | 1.52048i | −0.0384592 | − | 0.0666134i | 0.846155 | − | 0.532937i | \(-0.178912\pi\) |
−0.884614 | + | 0.466323i | \(0.845578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.1890 | + | 28.0401i | −0.707893 | + | 1.22611i | 0.257744 | + | 0.966213i | \(0.417021\pi\) |
−0.965637 | + | 0.259894i | \(0.916312\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.8251 | + | 13.1781i | 0.994278 | + | 0.574047i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.16033 | + | 7.20591i | 0.180884 | + | 0.313300i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 15.8168i | − | 0.686392i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.09480 | + | 1.78108i | 0.134050 | + | 0.0771472i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.8666 | + | 13.2020i | −0.988609 | + | 0.570774i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.52769 | + | 4.37809i | −0.109078 | + | 0.188929i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.38318 | + | 4.26268i | 0.317428 | + | 0.183267i | 0.650245 | − | 0.759724i | \(-0.274666\pi\) |
−0.332818 | + | 0.942991i | \(0.607999\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.09921 | + | 5.36799i | 0.133000 | + | 0.230362i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.2996 | 1.64057 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.14355 | 0.0488945 | 0.0244473 | − | 0.999701i | \(-0.492217\pi\) | ||||
0.0244473 | + | 0.999701i | \(0.492217\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.18417 | − | 15.9074i | −0.391971 | − | 0.678913i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.2123 | − | 6.47344i | −0.477661 | − | 0.275778i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.2359 | + | 19.4612i | −0.476937 | + | 0.826080i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.0897 | − | 21.4137i | 1.57154 | − | 0.907329i | 0.575560 | − | 0.817760i | \(-0.304784\pi\) |
0.995981 | − | 0.0895693i | \(-0.0285491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00890 | − | 1.75305i | 0.0426718 | − | 0.0741463i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 9.29503i | − | 0.392436i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.78771 | + | 11.7567i | 0.286068 | + | 0.495484i | 0.972868 | − | 0.231363i | \(-0.0743183\pi\) |
−0.686800 | + | 0.726847i | \(0.740985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.7259 | − | 17.1622i | −1.25058 | − | 0.722021i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.43555 | − | 7.68259i | 0.185948 | − | 0.322071i | −0.757948 | − | 0.652315i | \(-0.773798\pi\) |
0.943895 | + | 0.330244i | \(0.107131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.14047 | − | 5.43945i | −0.131424 | − | 0.227634i | 0.792801 | − | 0.609480i | \(-0.208622\pi\) |
−0.924226 | + | 0.381846i | \(0.875288\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.1628 | −0.466331 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8480 | 0.452392 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.7376 | − | 12.5502i | 0.904950 | − | 0.522473i | 0.0261471 | − | 0.999658i | \(-0.491676\pi\) |
0.878803 | + | 0.477185i | \(0.158343\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.3955 | − | 15.8168i | −1.13852 | − | 0.657325i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.05401 | + | 0.608536i | 0.0436528 | + | 0.0252030i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0185042 | − | 13.3847i | −0.000765053 | − | 0.553388i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 28.2963i | − | 1.16791i | −0.811784 | − | 0.583957i | \(-0.801503\pi\) | ||
0.811784 | − | 0.583957i | \(-0.198497\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.61496 | −0.396178 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.00047 | + | 4.61907i | −0.329095 | + | 0.190003i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.1408 | − | 6.43213i | −0.457497 | − | 0.264136i | 0.253494 | − | 0.967337i | \(-0.418420\pi\) |
−0.710991 | + | 0.703201i | \(0.751753\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.648648 | + | 1.12349i | −0.0265474 | + | 0.0459814i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.7842 | − | 22.1429i | −0.522350 | − | 0.904736i | −0.999662 | − | 0.0260025i | \(-0.991722\pi\) |
0.477312 | − | 0.878734i | \(-0.341611\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.63763 | −0.270755 | −0.135377 | − | 0.990794i | \(-0.543225\pi\) | ||||
−0.135377 | + | 0.990794i | \(0.543225\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.2810i | 0.744461i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.0732 | + | 13.8987i | −0.978716 | + | 0.565062i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.1613 | − | 19.3319i | 0.453023 | − | 0.784660i | −0.545549 | − | 0.838079i | \(-0.683679\pi\) |
0.998572 | + | 0.0534195i | \(0.0170121\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.4353 | − | 12.9944i | 0.907636 | − | 0.525698i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.66910 | − | 2.11836i | 0.148194 | − | 0.0855596i | −0.424070 | − | 0.905630i | \(-0.639399\pi\) |
0.572263 | + | 0.820070i | \(0.306066\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.58518 | 0.144568 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.0193i | 0.564397i | 0.959356 | + | 0.282198i | \(0.0910636\pi\) | ||||
−0.959356 | + | 0.282198i | \(0.908936\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.6520 | + | 11.9234i | −0.830074 | + | 0.479244i | −0.853878 | − | 0.520473i | \(-0.825756\pi\) |
0.0238037 | + | 0.999717i | \(0.492422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.7219 | + | 18.5709i | −0.430255 | + | 0.745224i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5701 | − | 26.9682i | 0.622804 | − | 1.07873i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.69545 | + | 2.93661i | 0.0677099 | + | 0.117277i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.1809i | 1.72174i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.18624i | 0.286080i | 0.989717 | + | 0.143040i | \(0.0456877\pi\) | ||||
−0.989717 | + | 0.143040i | \(0.954312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.9889 | − | 29.4256i | −0.675247 | − | 1.16956i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.4968 | − | 15.2979i | −1.05149 | − | 0.607079i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.37044 | − | 2.52328i | −0.172892 | − | 0.0998193i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.02943 | + | 6.97918i | 0.159153 | + | 0.275661i | 0.934563 | − | 0.355796i | \(-0.115790\pi\) |
−0.775411 | + | 0.631457i | \(0.782457\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.4148i | 1.12057i | 0.828300 | + | 0.560286i | \(0.189309\pi\) | ||||
−0.828300 | + | 0.560286i | \(0.810691\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 2.03083i | − | 0.0799640i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.8396 | + | 32.6311i | 0.740659 | + | 1.28286i | 0.952195 | + | 0.305490i | \(0.0988201\pi\) |
−0.211536 | + | 0.977370i | \(0.567847\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.15789 | + | 10.6658i | −0.241718 | + | 0.418669i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.5243 | + | 32.0850i | −0.724911 | + | 1.25558i | 0.234100 | + | 0.972213i | \(0.424786\pi\) |
−0.959011 | + | 0.283370i | \(0.908547\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.9644 | + | 9.21707i | −0.623782 | + | 0.360141i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.23269i | − | 0.165133i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.4553 | 1.73173 | 0.865867 | − | 0.500274i | \(-0.166767\pi\) | ||||
0.865867 | + | 0.500274i | \(0.166767\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.9366 | + | 20.1706i | −1.35888 | + | 0.784547i | −0.989472 | − | 0.144722i | \(-0.953771\pi\) |
−0.369403 | + | 0.929269i | \(0.620438\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.2619 | + | 28.0767i | 0.631558 | + | 1.09041i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.77332 | + | 16.9279i | −0.378424 | + | 0.655450i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.8901 | + | 11.4835i | −0.768995 | + | 0.443980i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.3025i | 0.552143i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.8024 | −0.647684 | −0.323842 | − | 0.946111i | \(-0.604975\pi\) | ||||
−0.323842 | + | 0.946111i | \(0.604975\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.92345 | − | 13.7238i | −0.304974 | − | 0.528230i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.2825 | + | 40.3265i | −0.894819 | + | 1.54987i | −0.0607909 | + | 0.998151i | \(0.519362\pi\) |
−0.834028 | + | 0.551722i | \(0.813971\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.9725 | + | 11.5311i | 0.765346 | + | 0.441873i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.01860 | + | 2.89749i | −0.192031 | + | 0.110869i | −0.592933 | − | 0.805252i | \(-0.702030\pi\) |
0.400902 | + | 0.916121i | \(0.368697\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.9135 | 1.37218 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.45164i | 0.207993i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.24842 | + | 0.00587339i | −0.161852 | + | 0.000223758i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.4877 | − | 13.5606i | −0.893515 | − | 0.515871i | −0.0184246 | − | 0.999830i | \(-0.505865\pi\) |
−0.875091 | + | 0.483959i | \(0.839198\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 45.0771 | + | 26.0253i | 1.70987 | + | 0.987196i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.96617 | − | 3.44457i | 0.225985 | − | 0.130472i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −36.5941 | −1.38412 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.0283 | 0.416535 | 0.208267 | − | 0.978072i | \(-0.433218\pi\) | ||||
0.208267 | + | 0.978072i | \(0.433218\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.87638 | − | 13.6423i | −0.297063 | − | 0.514529i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.0159 | − | 22.5442i | 0.490208 | − | 0.849064i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.0844 | − | 24.8748i | −1.61807 | − | 0.934193i | −0.987419 | − | 0.158126i | \(-0.949455\pi\) |
−0.630651 | − | 0.776067i | \(-0.717212\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.86333 | + | 8.42353i | 0.182389 | + | 0.315907i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.5162i | 0.543638i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.19851 | + | 9.03291i | −0.194413 | + | 0.337811i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.0199 | − | 5.78500i | 0.374201 | − | 0.216045i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.2825 | − | 24.7380i | 0.532647 | − | 0.922572i | −0.466626 | − | 0.884455i | \(-0.654531\pi\) |
0.999273 | − | 0.0381175i | \(-0.0121361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.0475 | − | 10.9971i | −0.708384 | − | 0.408986i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.22244 | − | 12.5096i | −0.268235 | − | 0.464596i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.5250 | −1.35464 | −0.677318 | − | 0.735691i | \(-0.736858\pi\) | ||||
−0.677318 | + | 0.735691i | \(0.736858\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.0464 | 0.964681 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.95118 | − | 3.37955i | −0.0721671 | − | 0.124997i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2331 | + | 9.37219i | 0.599584 | + | 0.346170i | 0.768878 | − | 0.639396i | \(-0.220815\pi\) |
−0.169294 | + | 0.985566i | \(0.554149\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.11727 | − | 12.3275i | 0.262168 | − | 0.454089i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.68550 | + | 5.59192i | −0.356287 | + | 0.205702i | −0.667451 | − | 0.744654i | \(-0.732615\pi\) |
0.311164 | + | 0.950356i | \(0.399281\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.2590 | − | 5.90412i | −0.376873 | − | 0.216893i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.7986i | 1.20326i | 0.798774 | + | 0.601632i | \(0.205482\pi\) | ||||
−0.798774 | + | 0.601632i | \(0.794518\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.9598 | − | 24.1790i | −0.511446 | − | 0.885851i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.1001 | − | 11.0275i | −0.698838 | − | 0.403474i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.3726 | − | 24.8940i | 0.524463 | − | 0.908396i | −0.475132 | − | 0.879915i | \(-0.657600\pi\) |
0.999594 | − | 0.0284812i | \(-0.00906708\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.33777 | − | 7.51324i | −0.158077 | − | 0.273798i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.3304 | −1.43138 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.4952 | 0.454145 | 0.227072 | − | 0.973878i | \(-0.427085\pi\) | ||||
0.227072 | + | 0.973878i | \(0.427085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.43356 | − | 2.55972i | 0.160928 | − | 0.0929119i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.6888 | + | 14.8314i | 0.931218 | + | 0.537639i | 0.887196 | − | 0.461392i | \(-0.152650\pi\) |
0.0440211 | + | 0.999031i | \(0.485983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.3639 | − | 12.9118i | −0.808570 | − | 0.466828i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0594340 | − | 42.9906i | −0.00214604 | − | 1.55230i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.8488i | 1.47305i | 0.676412 | + | 0.736523i | \(0.263534\pi\) | ||||
−0.676412 | + | 0.736523i | \(0.736466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9718 | 0.683251 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.8048 | + | 9.70226i | −0.604427 | + | 0.348966i | −0.770781 | − | 0.637100i | \(-0.780134\pi\) |
0.166354 | + | 0.986066i | \(0.446800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.29025 | − | 5.36373i | −0.333715 | − | 0.192671i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.25661 | + | 2.17651i | −0.0450227 | + | 0.0779816i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.96475 | + | 3.40305i | 0.0703044 | + | 0.121771i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.5540 | 1.02044 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 21.7400i | − | 0.775935i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.73934 | − | 5.04566i | 0.311524 | − | 0.179858i | −0.336084 | − | 0.941832i | \(-0.609103\pi\) |
0.647608 | + | 0.761974i | \(0.275769\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.89787 | − | 6.75131i | 0.138768 | − | 0.240353i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.0226 | − | 43.2024i | −0.888578 | − | 1.53416i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.69414 | + | 2.13282i | −0.131018 | + | 0.0756432i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.2735 | 0.399329 | 0.199665 | − | 0.979864i | \(-0.436015\pi\) | ||||
0.199665 | + | 0.979864i | \(0.436015\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 50.0217i | − | 1.76964i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.6667 | − | 7.89048i | 0.482889 | − | 0.278796i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.64790 | + | 2.85424i | −0.0581530 | + | 0.100724i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.533941 | + | 0.924813i | −0.0187956 | + | 0.0325550i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.71180 | − | 15.0893i | −0.306290 | − | 0.530511i | 0.671257 | − | 0.741224i | \(-0.265755\pi\) |
−0.977548 | + | 0.210714i | \(0.932421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.9555i | − | 1.26257i | −0.775552 | − | 0.631284i | \(-0.782528\pi\) | ||
0.775552 | − | 0.631284i | \(-0.217472\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.7132i | 0.445871i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.3451 | + | 17.9182i | 0.362373 | + | 0.627648i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.23289 | + | 0.711808i | 0.0431333 | + | 0.0249030i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.0928 | + | 7.55913i | 0.456942 | + | 0.263816i | 0.710758 | − | 0.703437i | \(-0.248352\pi\) |
−0.253816 | + | 0.967253i | \(0.581686\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.6167 | − | 37.4413i | −0.753512 | − | 1.30512i | −0.946111 | − | 0.323843i | \(-0.895025\pi\) |
0.192599 | − | 0.981278i | \(-0.438308\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.78325i | 0.131716i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 50.4513i | − | 1.75436i | −0.480158 | − | 0.877182i | \(-0.659421\pi\) | ||
0.480158 | − | 0.877182i | \(-0.340579\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.898637 | + | 1.55649i | 0.0312110 | + | 0.0540590i | 0.881209 | − | 0.472727i | \(-0.156730\pi\) |
−0.849998 | + | 0.526786i | \(0.823397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0148 | + | 31.2026i | −0.624927 | + | 1.08241i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.9850 | + | 38.0792i | −0.760823 | + | 1.31778i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.3646 | − | 10.6028i | 0.634772 | − | 0.366486i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.72104i | − | 0.162988i | −0.996674 | − | 0.0814942i | \(-0.974031\pi\) | ||
0.996674 | − | 0.0814942i | \(-0.0259692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.97220 | −0.102490 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.52894 | − | 2.61479i | 0.155985 | − | 0.0900580i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.100590 | − | 36.3798i | −0.00346039 | − | 1.25150i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.2489 | + | 33.3401i | −0.660620 | + | 1.14423i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.5965 | + | 11.8914i | −0.706040 | + | 0.407633i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.8428i | 1.67234i | 0.548467 | + | 0.836172i | \(0.315212\pi\) | ||||
−0.548467 | + | 0.836172i | \(0.684788\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.42069 | 0.322181 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.49820 | + | 12.9873i | 0.256134 | + | 0.443636i | 0.965203 | − | 0.261502i | \(-0.0842180\pi\) |
−0.709069 | + | 0.705139i | \(0.750885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.5232 | + | 28.6190i | −0.563764 | + | 0.976468i | 0.433399 | + | 0.901202i | \(0.357314\pi\) |
−0.997163 | + | 0.0752662i | \(0.976019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.8004 | + | 23.5561i | 1.38886 | + | 0.801859i | 0.993187 | − | 0.116532i | \(-0.0371778\pi\) |
0.395674 | + | 0.918391i | \(0.370511\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.00718 | + | 0.581498i | −0.0342453 | + | 0.0197715i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.6080 | 1.37912 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.57367i | − | 0.256919i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0686936 | + | 49.6883i | 0.00232759 | + | 1.68363i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.88384 | − | 5.70644i | −0.334517 | − | 0.193134i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.84222 | − | 3.37301i | −0.197278 | − | 0.113898i | 0.398107 | − | 0.917339i | \(-0.369667\pi\) |
−0.595385 | + | 0.803441i | \(0.703000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.3955 | − | 19.2809i | 1.12640 | − | 0.650329i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.5679 | −0.760333 | −0.380166 | − | 0.924918i | \(-0.624133\pi\) | ||||
−0.380166 | + | 0.924918i | \(0.624133\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.2628 | −0.648245 | −0.324122 | − | 0.946015i | \(-0.605069\pi\) | ||||
−0.324122 | + | 0.946015i | \(0.605069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.5824 | − | 37.3818i | −0.725484 | − | 1.25657i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.426329 | + | 0.738424i | −0.0143147 | + | 0.0247938i | −0.873094 | − | 0.487552i | \(-0.837890\pi\) |
0.858779 | + | 0.512346i | \(0.171223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.91679 | − | 1.68401i | −0.0977160 | − | 0.0564164i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.12417 | + | 15.8035i | 0.305329 | + | 0.528845i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10.9361i | − | 0.365555i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.91378 | + | 15.4885i | −0.297623 | + | 0.517147i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.7398 | − | 9.66473i | 0.558304 | − | 0.322337i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.09833 | + | 7.09852i | −0.136535 | + | 0.236486i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.6124 | − | 6.70441i | −0.386009 | − | 0.222862i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.3797 | − | 40.4948i | −0.776310 | − | 1.34461i | −0.934055 | − | 0.357129i | \(-0.883756\pi\) |
0.157745 | − | 0.987480i | \(-0.449578\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.1019 | 0.368226 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.7415 | −1.11791 | −0.558954 | − | 0.829199i | \(-0.688797\pi\) | ||||
−0.558954 | + | 0.829199i | \(0.688797\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.58655 | + | 14.8723i | 0.284173 | + | 0.492203i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −43.4121 | − | 25.0640i | −1.43516 | − | 0.828589i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.7170 | − | 20.2945i | 0.386509 | − | 0.669453i | −0.605468 | − | 0.795869i | \(-0.707014\pi\) |
0.991977 | + | 0.126416i | \(0.0403475\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.8298 | + | 12.0261i | −0.686364 | + | 0.396272i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.8885 | − | 6.84191i | −0.391314 | − | 0.225204i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 17.5754i | − | 0.577876i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.345855 | − | 0.599038i | −0.0113594 | − | 0.0196750i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.51123 | − | 5.49131i | −0.312053 | − | 0.180164i | 0.335792 | − | 0.941936i | \(-0.390996\pi\) |
−0.647845 | + | 0.761772i | \(0.724330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.2920 | − | 17.8264i | 0.336947 | − | 0.583609i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.0538 | + | 17.4137i | 0.328795 | + | 0.569489i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.5028 | −1.55185 | −0.775924 | − | 0.630826i | \(-0.782716\pi\) | ||||
−0.775924 | + | 0.630826i | \(0.782716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.32302 | 0.0758090 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.00541 | + | 4.04458i | −0.228370 | + | 0.131849i | −0.609820 | − | 0.792540i | \(-0.708758\pi\) |
0.381450 | + | 0.924390i | \(0.375425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.28600 | + | 1.89717i | 0.107007 | + | 0.0617804i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.2176 | + | 9.36323i | 0.527001 | + | 0.304264i | 0.739794 | − | 0.672833i | \(-0.234923\pi\) |
−0.212793 | + | 0.977097i | \(0.568256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0159050 | − | 11.5046i | −0.000516297 | − | 0.373454i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 20.7382i | − | 0.672482i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.2451 | 1.53042 | 0.765209 | − | 0.643781i | \(-0.222635\pi\) | ||||
0.765209 | + | 0.643781i | \(0.222635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.9128 | − | 12.0740i | 0.676723 | − | 0.390706i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.90362 | − | 3.40846i | −0.190837 | − | 0.110180i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.32252 | + | 14.4150i | −0.268468 | + | 0.465001i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.25806 | + | 10.8393i | 0.201663 | + | 0.349291i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 68.4320 | 2.20290 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39.7889i | − | 1.27952i | −0.768573 | − | 0.639762i | \(-0.779033\pi\) | ||
0.768573 | − | 0.639762i | \(-0.220967\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.7773 | + | 11.4184i | −0.635339 | + | 0.366813i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.00663 | − | 8.67174i | 0.160670 | − | 0.278289i | −0.774439 | − | 0.632649i | \(-0.781968\pi\) |
0.935109 | + | 0.354359i | \(0.115301\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.61888 | − | 11.4277i | −0.211974 | − | 0.365980i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 51.0164 | − | 29.4543i | 1.63216 | − | 0.942328i | 0.648734 | − | 0.761015i | \(-0.275299\pi\) |
0.983425 | − | 0.181313i | \(-0.0580347\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.2879 | −0.392722 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 18.1549i | − | 0.579640i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.46527 | + | 2.57802i | −0.142420 | + | 0.0822262i | −0.569517 | − | 0.821980i | \(-0.692870\pi\) |
0.427097 | + | 0.904206i | \(0.359536\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.99229 | − | 17.3071i | 0.318381 | − | 0.551452i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.07466 | − | 1.86136i | 0.0341721 | − | 0.0591878i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3453 | + | 54.2916i | 0.995715 | + | 1.72463i | 0.577941 | + | 0.816078i | \(0.303856\pi\) |
0.417774 | + | 0.908551i | \(0.362810\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.81982i | 0.279889i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.80640i | − | 0.0889687i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.06884 | − | 12.2436i | −0.223872 | − | 0.387758i | 0.732108 | − | 0.681188i | \(-0.238537\pi\) |
−0.955981 | + | 0.293430i | \(0.905203\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.0877 | + | 17.3712i | 0.951934 | + | 0.549600i |
(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 | 2548.2.y.e.961.4 | 16 | ||
7.2 | even | 3 | 2548.2.g.g.2157.5 | 8 | |||
7.3 | odd | 6 | 2548.2.y.f.753.6 | 16 | |||
7.4 | even | 3 | inner | 2548.2.y.e.753.3 | 16 | ||
7.5 | odd | 6 | 364.2.g.a.337.4 | yes | 8 | ||
7.6 | odd | 2 | 2548.2.y.f.961.5 | 16 | |||
13.12 | even | 2 | inner | 2548.2.y.e.961.3 | 16 | ||
21.5 | even | 6 | 3276.2.e.f.2521.1 | 8 | |||
28.19 | even | 6 | 1456.2.k.d.337.6 | 8 | |||
91.5 | even | 12 | 4732.2.a.p.1.2 | 4 | |||
91.12 | odd | 6 | 364.2.g.a.337.3 | ✓ | 8 | ||
91.25 | even | 6 | inner | 2548.2.y.e.753.4 | 16 | ||
91.38 | odd | 6 | 2548.2.y.f.753.5 | 16 | |||
91.47 | even | 12 | 4732.2.a.o.1.2 | 4 | |||
91.51 | even | 6 | 2548.2.g.g.2157.6 | 8 | |||
91.90 | odd | 2 | 2548.2.y.f.961.6 | 16 | |||
273.194 | even | 6 | 3276.2.e.f.2521.8 | 8 | |||
364.103 | even | 6 | 1456.2.k.d.337.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
364.2.g.a.337.3 | ✓ | 8 | 91.12 | odd | 6 | ||
364.2.g.a.337.4 | yes | 8 | 7.5 | odd | 6 | ||
1456.2.k.d.337.5 | 8 | 364.103 | even | 6 | |||
1456.2.k.d.337.6 | 8 | 28.19 | even | 6 | |||
2548.2.g.g.2157.5 | 8 | 7.2 | even | 3 | |||
2548.2.g.g.2157.6 | 8 | 91.51 | even | 6 | |||
2548.2.y.e.753.3 | 16 | 7.4 | even | 3 | inner | ||
2548.2.y.e.753.4 | 16 | 91.25 | even | 6 | inner | ||
2548.2.y.e.961.3 | 16 | 13.12 | even | 2 | inner | ||
2548.2.y.e.961.4 | 16 | 1.1 | even | 1 | trivial | ||
2548.2.y.f.753.5 | 16 | 91.38 | odd | 6 | |||
2548.2.y.f.753.6 | 16 | 7.3 | odd | 6 | |||
2548.2.y.f.961.5 | 16 | 7.6 | odd | 2 | |||
2548.2.y.f.961.6 | 16 | 91.90 | odd | 2 | |||
3276.2.e.f.2521.1 | 8 | 21.5 | even | 6 | |||
3276.2.e.f.2521.8 | 8 | 273.194 | even | 6 | |||
4732.2.a.o.1.2 | 4 | 91.47 | even | 12 | |||
4732.2.a.p.1.2 | 4 | 91.5 | even | 12 |