Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(3149,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.3149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.d (of order \(2\), degree \(1\), 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.7442857984.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3149.8 | ||
Root | \(2.73923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.3149 |
Dual form | 3150.2.d.d.3149.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.93693 | + | 1.80230i | 0.732091 | + | 0.681207i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.87386i | − | 1.16801i | −0.811749 | − | 0.584007i | \(-0.801484\pi\) | ||
0.811749 | − | 0.584007i | \(-0.198516\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.60461 | 0.445038 | 0.222519 | − | 0.974928i | \(-0.428572\pi\) | ||||
0.222519 | + | 0.974928i | \(0.428572\pi\) | |||||||
\(14\) | 1.93693 | + | 1.80230i | 0.517667 | + | 0.481686i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 8.11650i | 1.96854i | 0.176667 | + | 0.984271i | \(0.443468\pi\) | ||||
−0.176667 | + | 0.984271i | \(0.556532\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.63803i | − | 0.605207i | −0.953117 | − | 0.302603i | \(-0.902144\pi\) | ||
0.953117 | − | 0.302603i | \(-0.0978557\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 3.87386i | − | 0.825910i | ||||||
\(23\) | 5.47847 | 1.14234 | 0.571170 | − | 0.820832i | \(-0.306490\pi\) | ||||
0.571170 | + | 0.820832i | \(0.306490\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.60461 | 0.314689 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.93693 | + | 1.80230i | 0.366046 | + | 0.340603i | ||||
\(29\) | 5.47847i | 1.01733i | 0.860966 | + | 0.508663i | \(0.169860\pi\) | ||||
−0.860966 | + | 0.508663i | \(0.830140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.73074i | − | 0.670061i | −0.942207 | − | 0.335031i | \(-0.891253\pi\) | ||
0.942207 | − | 0.335031i | \(-0.108747\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.11650i | 1.39197i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.51190i | − | 0.741751i | −0.928683 | − | 0.370876i | \(-0.879058\pi\) | ||
0.928683 | − | 0.370876i | \(-0.120942\pi\) | |||||||
\(38\) | − | 2.63803i | − | 0.427946i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.60461 | 0.250597 | 0.125299 | − | 0.992119i | \(-0.460011\pi\) | ||||
0.125299 | + | 0.992119i | \(0.460011\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.1165i | − | 1.54275i | −0.636379 | − | 0.771376i | \(-0.719569\pi\) | ||
0.636379 | − | 0.771376i | \(-0.280431\pi\) | |||||||
\(44\) | − | 3.87386i | − | 0.584007i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.47847 | 0.807756 | ||||||||
\(47\) | 11.1097i | 1.62052i | 0.586074 | + | 0.810258i | \(0.300673\pi\) | ||||
−0.586074 | + | 0.810258i | \(0.699327\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.503406 | + | 6.98188i | 0.0719152 | + | 0.997411i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.60461 | 0.222519 | ||||||||
\(53\) | −2.26926 | −0.311706 | −0.155853 | − | 0.987780i | \(-0.549813\pi\) | ||||
−0.155853 | + | 0.987780i | \(0.549813\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.93693 | + | 1.80230i | 0.258833 | + | 0.240843i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.47847i | 0.719358i | ||||||||
\(59\) | 4.61142 | 0.600356 | 0.300178 | − | 0.953883i | \(-0.402954\pi\) | ||||
0.300178 | + | 0.953883i | \(0.402954\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8472i | 1.51688i | 0.651740 | + | 0.758442i | \(0.274039\pi\) | ||||
−0.651740 | + | 0.758442i | \(0.725961\pi\) | |||||||
\(62\) | − | 3.73074i | − | 0.473805i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.90729i | − | 0.843860i | −0.906628 | − | 0.421930i | \(-0.861353\pi\) | ||
0.906628 | − | 0.421930i | \(-0.138647\pi\) | |||||||
\(68\) | 8.11650i | 0.984271i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.63803i | − | 0.313077i | −0.987672 | − | 0.156539i | \(-0.949966\pi\) | ||
0.987672 | − | 0.156539i | \(-0.0500335\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7477 | 1.60905 | 0.804525 | − | 0.593919i | \(-0.202420\pi\) | ||||
0.804525 | + | 0.593919i | \(0.202420\pi\) | |||||||
\(74\) | − | 4.51190i | − | 0.524497i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 2.63803i | − | 0.302603i | ||||||
\(77\) | 6.98188 | − | 7.50341i | 0.795659 | − | 0.855092i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.01698 | 0.901981 | 0.450990 | − | 0.892529i | \(-0.351071\pi\) | ||||
0.450990 | + | 0.892529i | \(0.351071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.60461 | 0.177199 | ||||||||
\(83\) | − | 3.20921i | − | 0.352257i | −0.984367 | − | 0.176128i | \(-0.943643\pi\) | ||
0.984367 | − | 0.176128i | \(-0.0563574\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 10.1165i | − | 1.09089i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 3.87386i | − | 0.412955i | ||||||
\(89\) | −17.8376 | −1.89078 | −0.945392 | − | 0.325937i | \(-0.894320\pi\) | ||||
−0.945392 | + | 0.325937i | \(0.894320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.10801 | + | 2.89199i | 0.325808 | + | 0.303163i | ||||
\(92\) | 5.47847 | 0.571170 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.1097i | 1.14588i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.68768 | 0.882100 | 0.441050 | − | 0.897482i | \(-0.354606\pi\) | ||||
0.441050 | + | 0.897482i | \(0.354606\pi\) | |||||||
\(98\) | 0.503406 | + | 6.98188i | 0.0508517 | + | 0.705276i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.21603 | −0.618518 | −0.309259 | − | 0.950978i | \(-0.600081\pi\) | ||||
−0.309259 | + | 0.950978i | \(0.600081\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8807 | −1.26917 | −0.634585 | − | 0.772853i | \(-0.718829\pi\) | ||||
−0.634585 | + | 0.772853i | \(0.718829\pi\) | |||||||
\(104\) | 1.60461 | 0.157345 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.26926 | −0.220410 | ||||||||
\(107\) | 19.9638 | 1.92997 | 0.964984 | − | 0.262308i | \(-0.0844835\pi\) | ||||
0.964984 | + | 0.262308i | \(0.0844835\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0238 | 1.43902 | 0.719509 | − | 0.694483i | \(-0.244367\pi\) | ||||
0.719509 | + | 0.694483i | \(0.244367\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.93693 | + | 1.80230i | 0.183023 | + | 0.170302i | ||||
\(113\) | −10.2330 | −0.962640 | −0.481320 | − | 0.876545i | \(-0.659843\pi\) | ||||
−0.481320 | + | 0.876545i | \(0.659843\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.47847i | 0.508663i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.61142 | 0.424515 | ||||||||
\(119\) | −14.6284 | + | 15.7211i | −1.34098 | + | 1.44115i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00681 | −0.364256 | ||||||||
\(122\) | 11.8472i | 1.07260i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 3.73074i | − | 0.335031i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.81382i | 0.249686i | 0.992177 | + | 0.124843i | \(0.0398427\pi\) | ||||
−0.992177 | + | 0.124843i | \(0.960157\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.62840 | 0.753867 | 0.376933 | − | 0.926240i | \(-0.376979\pi\) | ||||
0.376933 | + | 0.926240i | \(0.376979\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.75454 | − | 5.10969i | 0.412271 | − | 0.443066i | ||||
\(134\) | − | 6.90729i | − | 0.596699i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.11650i | 0.695984i | ||||||||
\(137\) | 0.723932 | 0.0618496 | 0.0309248 | − | 0.999522i | \(-0.490155\pi\) | ||||
0.0309248 | + | 0.999522i | \(0.490155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.84043i | 0.240923i | 0.992718 | + | 0.120461i | \(0.0384374\pi\) | ||||
−0.992718 | + | 0.120461i | \(0.961563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 2.63803i | − | 0.221379i | ||||||
\(143\) | − | 6.21603i | − | 0.519810i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.7477 | 1.13777 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 4.51190i | − | 0.370876i | ||||||
\(149\) | 3.00681i | 0.246328i | 0.992386 | + | 0.123164i | \(0.0393041\pi\) | ||||
−0.992386 | + | 0.123164i | \(0.960696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2262 | −1.23909 | −0.619545 | − | 0.784961i | \(-0.712683\pi\) | ||||
−0.619545 | + | 0.784961i | \(0.712683\pi\) | |||||||
\(152\) | − | 2.63803i | − | 0.213973i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.98188 | − | 7.50341i | 0.562616 | − | 0.604642i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.64767 | −0.211307 | −0.105653 | − | 0.994403i | \(-0.533693\pi\) | ||||
−0.105653 | + | 0.994403i | \(0.533693\pi\) | |||||||
\(158\) | 8.01698 | 0.637797 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.6114 | + | 9.87386i | 0.836297 | + | 0.778169i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.32572i | − | 0.730446i | −0.930920 | − | 0.365223i | \(-0.880993\pi\) | ||
0.930920 | − | 0.365223i | \(-0.119007\pi\) | |||||||
\(164\) | 1.60461 | 0.125299 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 3.20921i | − | 0.249083i | ||||||
\(167\) | 17.3257i | 1.34070i | 0.742043 | + | 0.670352i | \(0.233857\pi\) | ||||
−0.742043 | + | 0.670352i | \(0.766143\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4252 | −0.801941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 10.1165i | − | 0.771376i | ||||||
\(173\) | − | 2.99319i | − | 0.227568i | −0.993506 | − | 0.113784i | \(-0.963703\pi\) | ||
0.993506 | − | 0.113784i | \(-0.0362972\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.87386i | − | 0.292003i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.8376 | −1.33699 | ||||||||
\(179\) | 7.38858i | 0.552248i | 0.961122 | + | 0.276124i | \(0.0890501\pi\) | ||||
−0.961122 | + | 0.276124i | \(0.910950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.1097i | − | 0.825777i | −0.910782 | − | 0.412888i | \(-0.864520\pi\) | ||
0.910782 | − | 0.412888i | \(-0.135480\pi\) | |||||||
\(182\) | 3.10801 | + | 2.89199i | 0.230381 | + | 0.214368i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.47847 | 0.403878 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.4422 | 2.29928 | ||||||||
\(188\) | 11.1097i | 0.810258i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 9.36197i | − | 0.677408i | −0.940893 | − | 0.338704i | \(-0.890011\pi\) | ||
0.940893 | − | 0.338704i | \(-0.109989\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4422i | 1.25552i | 0.778408 | + | 0.627759i | \(0.216028\pi\) | ||||
−0.778408 | + | 0.627759i | \(0.783972\pi\) | |||||||
\(194\) | 8.68768 | 0.623739 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.503406 | + | 6.98188i | 0.0359576 | + | 0.498705i | ||||
\(197\) | −5.27607 | −0.375904 | −0.187952 | − | 0.982178i | \(-0.560185\pi\) | ||||
−0.187952 | + | 0.982178i | \(0.560185\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2160i | 0.865971i | 0.901401 | + | 0.432986i | \(0.142540\pi\) | ||||
−0.901401 | + | 0.432986i | \(0.857460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.21603 | −0.437358 | ||||||||
\(203\) | −9.87386 | + | 10.6114i | −0.693009 | + | 0.744776i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.8807 | −0.897439 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.60461 | 0.111259 | ||||||||
\(209\) | −10.2194 | −0.706889 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | −2.26926 | −0.155853 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.9638 | 1.36469 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.72393 | − | 7.22619i | 0.456450 | − | 0.490546i | ||||
\(218\) | 15.0238 | 1.01754 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.0238i | 0.876075i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.65784 | 0.244947 | 0.122473 | − | 0.992472i | \(-0.460917\pi\) | ||||
0.122473 | + | 0.992472i | \(0.460917\pi\) | |||||||
\(224\) | 1.93693 | + | 1.80230i | 0.129417 | + | 0.120421i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.2330 | −0.680689 | ||||||||
\(227\) | 4.23301i | 0.280955i | 0.990084 | + | 0.140477i | \(0.0448637\pi\) | ||||
−0.990084 | + | 0.140477i | \(0.955136\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.59497i | 0.501890i | 0.968001 | + | 0.250945i | \(0.0807413\pi\) | ||||
−0.968001 | + | 0.250945i | \(0.919259\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.47847i | 0.359679i | ||||||||
\(233\) | 9.94677 | 0.651634 | 0.325817 | − | 0.945433i | \(-0.394361\pi\) | ||||
0.325817 | + | 0.945433i | \(0.394361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.61142 | 0.300178 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.6284 | + | 15.7211i | −0.948218 | + | 1.01905i | ||||
\(239\) | − | 9.36197i | − | 0.605575i | −0.953058 | − | 0.302788i | \(-0.902083\pi\) | ||
0.953058 | − | 0.302788i | \(-0.0979173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.0408i | − | 1.48419i | −0.670296 | − | 0.742093i | \(-0.733833\pi\) | ||
0.670296 | − | 0.742093i | \(-0.266167\pi\) | |||||||
\(242\) | −4.00681 | −0.257568 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.8472i | 0.758442i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.23301i | − | 0.269340i | ||||||
\(248\) | − | 3.73074i | − | 0.236902i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.8376 | −1.50462 | −0.752308 | − | 0.658811i | \(-0.771060\pi\) | ||||
−0.752308 | + | 0.658811i | \(0.771060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 21.2228i | − | 1.33427i | ||||||
\(254\) | 2.81382i | 0.176555i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 29.7441i | − | 1.85539i | −0.373341 | − | 0.927694i | \(-0.621788\pi\) | ||
0.373341 | − | 0.927694i | \(-0.378212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.13181 | − | 8.73923i | 0.505286 | − | 0.543030i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.62840 | 0.533064 | ||||||||
\(263\) | −22.7545 | −1.40310 | −0.701552 | − | 0.712618i | \(-0.747509\pi\) | ||||
−0.701552 | + | 0.712618i | \(0.747509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.75454 | − | 5.10969i | 0.291519 | − | 0.313295i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 6.90729i | − | 0.421930i | ||||||
\(269\) | −0.202401 | −0.0123406 | −0.00617030 | − | 0.999981i | \(-0.501964\pi\) | ||||
−0.00617030 | + | 0.999981i | \(0.501964\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.4785i | − | 0.697267i | −0.937259 | − | 0.348634i | \(-0.886646\pi\) | ||
0.937259 | − | 0.348634i | \(-0.113354\pi\) | |||||||
\(272\) | 8.11650i | 0.492135i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.723932 | 0.0437343 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 23.7211i | − | 1.42526i | −0.701538 | − | 0.712632i | \(-0.747503\pi\) | ||
0.701538 | − | 0.712632i | \(-0.252497\pi\) | |||||||
\(278\) | 2.84043i | 0.170358i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.57194i | 0.332394i | 0.986093 | + | 0.166197i | \(0.0531488\pi\) | ||||
−0.986093 | + | 0.166197i | \(0.946851\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.1798 | 1.91289 | 0.956445 | − | 0.291914i | \(-0.0942921\pi\) | ||||
0.956445 | + | 0.291914i | \(0.0942921\pi\) | |||||||
\(284\) | − | 2.63803i | − | 0.156539i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 6.21603i | − | 0.367561i | ||||||
\(287\) | 3.10801 | + | 2.89199i | 0.183460 | + | 0.170709i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −48.8776 | −2.87515 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.7477 | 0.804525 | ||||||||
\(293\) | − | 15.8146i | − | 0.923898i | −0.886907 | − | 0.461949i | \(-0.847150\pi\) | ||
0.886907 | − | 0.461949i | \(-0.152850\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 4.51190i | − | 0.262249i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00681i | 0.174180i | ||||||||
\(299\) | 8.79079 | 0.508384 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.2330 | − | 19.5950i | 1.05093 | − | 1.12944i | ||||
\(302\) | −15.2262 | −0.876169 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 2.63803i | − | 0.151302i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.72393 | −0.383755 | −0.191878 | − | 0.981419i | \(-0.561458\pi\) | ||||
−0.191878 | + | 0.981419i | \(0.561458\pi\) | |||||||
\(308\) | 6.98188 | − | 7.50341i | 0.397829 | − | 0.427546i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.02379 | −0.0580540 | −0.0290270 | − | 0.999579i | \(-0.509241\pi\) | ||||
−0.0290270 | + | 0.999579i | \(0.509241\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.2568 | 1.31455 | 0.657276 | − | 0.753650i | \(-0.271709\pi\) | ||||
0.657276 | + | 0.753650i | \(0.271709\pi\) | |||||||
\(314\) | −2.64767 | −0.149417 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.01698 | 0.450990 | ||||||||
\(317\) | 4.46830 | 0.250965 | 0.125482 | − | 0.992096i | \(-0.459952\pi\) | ||||
0.125482 | + | 0.992096i | \(0.459952\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.2228 | 1.18825 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.6114 | + | 9.87386i | 0.591351 | + | 0.550249i | ||||
\(323\) | 21.4116 | 1.19137 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 9.32572i | − | 0.516504i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.60461 | 0.0885996 | ||||||||
\(329\) | −20.0230 | + | 21.5187i | −1.10391 | + | 1.18636i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.2160 | −0.781383 | −0.390692 | − | 0.920522i | \(-0.627764\pi\) | ||||
−0.390692 | + | 0.920522i | \(0.627764\pi\) | |||||||
\(332\) | − | 3.20921i | − | 0.176128i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.3257i | 0.948021i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 23.4286i | − | 1.27624i | −0.769938 | − | 0.638118i | \(-0.779713\pi\) | ||
0.769938 | − | 0.638118i | \(-0.220287\pi\) | |||||||
\(338\) | −10.4252 | −0.567058 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.4524 | −0.782641 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.6084 | + | 14.4307i | −0.626794 | + | 0.779185i | ||||
\(344\) | − | 10.1165i | − | 0.545445i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 2.99319i | − | 0.160915i | ||||||
\(347\) | −20.1798 | −1.08331 | −0.541654 | − | 0.840602i | \(-0.682202\pi\) | ||||
−0.541654 | + | 0.840602i | \(0.682202\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 27.0372i | − | 1.44727i | −0.690184 | − | 0.723634i | \(-0.742470\pi\) | ||
0.690184 | − | 0.723634i | \(-0.257530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 3.87386i | − | 0.206478i | ||||||
\(353\) | − | 12.3495i | − | 0.657298i | −0.944452 | − | 0.328649i | \(-0.893407\pi\) | ||
0.944452 | − | 0.328649i | \(-0.106593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −17.8376 | −0.945392 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.38858i | 0.390499i | ||||||||
\(359\) | 25.5757i | 1.34983i | 0.737894 | + | 0.674917i | \(0.235821\pi\) | ||||
−0.737894 | + | 0.674917i | \(0.764179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0408 | 0.633725 | ||||||||
\(362\) | − | 11.1097i | − | 0.583912i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.10801 | + | 2.89199i | 0.162904 | + | 0.151581i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.8444 | −1.08807 | −0.544035 | − | 0.839062i | \(-0.683104\pi\) | ||||
−0.544035 | + | 0.839062i | \(0.683104\pi\) | |||||||
\(368\) | 5.47847 | 0.285585 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.39539 | − | 4.08989i | −0.228197 | − | 0.212336i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.48810i | 0.387719i | 0.981029 | + | 0.193860i | \(0.0621006\pi\) | ||||
−0.981029 | + | 0.193860i | \(0.937899\pi\) | |||||||
\(374\) | 31.4422 | 1.62584 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.1097i | 0.572939i | ||||||||
\(377\) | 8.79079i | 0.452749i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.6651 | −1.67789 | −0.838946 | − | 0.544215i | \(-0.816827\pi\) | ||||
−0.838946 | + | 0.544215i | \(0.816827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 9.36197i | − | 0.479000i | ||||||
\(383\) | 0.890309i | 0.0454927i | 0.999741 | + | 0.0227463i | \(0.00724101\pi\) | ||||
−0.999741 | + | 0.0227463i | \(0.992759\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.4422i | 0.887786i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.68768 | 0.441050 | ||||||||
\(389\) | 13.5317i | 0.686084i | 0.939320 | + | 0.343042i | \(0.111457\pi\) | ||||
−0.939320 | + | 0.343042i | \(0.888543\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.4660i | 2.24874i | ||||||||
\(392\) | 0.503406 | + | 6.98188i | 0.0254258 | + | 0.352638i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.27607 | −0.265804 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2991 | −1.26973 | −0.634863 | − | 0.772625i | \(-0.718943\pi\) | ||||
−0.634863 | + | 0.772625i | \(0.718943\pi\) | |||||||
\(398\) | 12.2160i | 0.612334i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.7619i | 1.63605i | 0.575182 | + | 0.818025i | \(0.304931\pi\) | ||||
−0.575182 | + | 0.818025i | \(0.695069\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.98638i | − | 0.298203i | ||||||
\(404\) | −6.21603 | −0.309259 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.87386 | + | 10.6114i | −0.490032 | + | 0.526636i | ||||
\(407\) | −17.4785 | −0.866376 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.8807 | −0.634585 | ||||||||
\(413\) | 8.93200 | + | 8.31117i | 0.439515 | + | 0.408966i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.60461 | 0.0786723 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.2194 | −0.499846 | ||||||||
\(419\) | 4.17937 | 0.204176 | 0.102088 | − | 0.994775i | \(-0.467448\pi\) | ||||
0.102088 | + | 0.994775i | \(0.467448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.6514 | −1.59133 | −0.795667 | − | 0.605735i | \(-0.792879\pi\) | ||||
−0.795667 | + | 0.605735i | \(0.792879\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.26926 | −0.110205 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.3523 | + | 22.9473i | −1.03331 | + | 1.11050i | ||||
\(428\) | 19.9638 | 0.964984 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.3087i | 0.641059i | 0.947239 | + | 0.320530i | \(0.103861\pi\) | ||||
−0.947239 | + | 0.320530i | \(0.896139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.95358 | −0.334168 | −0.167084 | − | 0.985943i | \(-0.553435\pi\) | ||||
−0.167084 | + | 0.985943i | \(0.553435\pi\) | |||||||
\(434\) | 6.72393 | − | 7.22619i | 0.322759 | − | 0.346868i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.0238 | 0.719509 | ||||||||
\(437\) | − | 14.4524i | − | 0.691352i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 26.9739i | − | 1.28739i | −0.765280 | − | 0.643697i | \(-0.777400\pi\) | ||
0.765280 | − | 0.643697i | \(-0.222600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.0238i | 0.619479i | ||||||||
\(443\) | 2.80441 | 0.133242 | 0.0666208 | − | 0.997778i | \(-0.478778\pi\) | ||||
0.0666208 | + | 0.997778i | \(0.478778\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.65784 | 0.173204 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.93693 | + | 1.80230i | 0.0915114 | + | 0.0851508i | ||||
\(449\) | − | 30.1226i | − | 1.42157i | −0.703409 | − | 0.710786i | \(-0.748340\pi\) | ||
0.703409 | − | 0.710786i | \(-0.251660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.21603i | − | 0.292701i | ||||||
\(452\) | −10.2330 | −0.481320 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.23301i | 0.198665i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0340i | 1.03071i | 0.856978 | + | 0.515353i | \(0.172339\pi\) | ||||
−0.856978 | + | 0.515353i | \(0.827661\pi\) | |||||||
\(458\) | 7.59497i | 0.354890i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.4116 | −0.717790 | −0.358895 | − | 0.933378i | \(-0.616846\pi\) | ||||
−0.358895 | + | 0.933378i | \(0.616846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.0605i | − | 1.16466i | −0.812953 | − | 0.582329i | \(-0.802142\pi\) | ||
0.812953 | − | 0.582329i | \(-0.197858\pi\) | |||||||
\(464\) | 5.47847i | 0.254332i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.94677 | 0.460775 | ||||||||
\(467\) | 9.62764i | 0.445514i | 0.974874 | + | 0.222757i | \(0.0715056\pi\) | ||||
−0.974874 | + | 0.222757i | \(0.928494\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4490 | − | 13.3789i | 0.574843 | − | 0.617782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.61142 | 0.212258 | ||||||||
\(473\) | −39.1899 | −1.80196 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.6284 | + | 15.7211i | −0.670492 | + | 0.720576i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 9.36197i | − | 0.428206i | ||||||
\(479\) | −37.0238 | −1.69166 | −0.845830 | − | 0.533452i | \(-0.820894\pi\) | ||||
−0.845830 | + | 0.533452i | \(0.820894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7.23982i | − | 0.330107i | ||||||
\(482\) | − | 23.0408i | − | 1.04948i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.00681 | −0.182128 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.6386i | 0.527394i | 0.964606 | + | 0.263697i | \(0.0849419\pi\) | ||||
−0.964606 | + | 0.263697i | \(0.915058\pi\) | |||||||
\(488\) | 11.8472i | 0.536300i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.1069i | − | 1.44896i | −0.689294 | − | 0.724481i | \(-0.742079\pi\) | ||
0.689294 | − | 0.724481i | \(-0.257921\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.4660 | −2.00265 | ||||||||
\(494\) | − | 4.23301i | − | 0.190452i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.73074i | − | 0.167515i | ||||||
\(497\) | 4.75454 | − | 5.10969i | 0.213270 | − | 0.229201i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.6122 | −0.609365 | −0.304682 | − | 0.952454i | \(-0.598550\pi\) | ||||
−0.304682 | + | 0.952454i | \(0.598550\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.8376 | −1.06392 | ||||||||
\(503\) | − | 3.07573i | − | 0.137140i | −0.997646 | − | 0.0685700i | \(-0.978156\pi\) | ||
0.997646 | − | 0.0685700i | \(-0.0218436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 21.2228i | − | 0.943470i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.81382i | 0.124843i | ||||||||
\(509\) | −14.7908 | −0.655590 | −0.327795 | − | 0.944749i | \(-0.606306\pi\) | ||||
−0.327795 | + | 0.944749i | \(0.606306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.6284 | + | 24.7776i | 1.17797 | + | 1.09610i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 29.7441i | − | 1.31196i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.0374 | 1.89278 | ||||||||
\(518\) | 8.13181 | − | 8.73923i | 0.357291 | − | 0.383980i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0332 | −1.18435 | −0.592173 | − | 0.805811i | \(-0.701730\pi\) | ||||
−0.592173 | + | 0.805811i | \(0.701730\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.51472 | 0.153688 | 0.0768440 | − | 0.997043i | \(-0.475516\pi\) | ||||
0.0768440 | + | 0.997043i | \(0.475516\pi\) | |||||||
\(524\) | 8.62840 | 0.376933 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.7545 | −0.992145 | ||||||||
\(527\) | 30.2806 | 1.31904 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.01362 | 0.304940 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.75454 | − | 5.10969i | 0.206135 | − | 0.221533i | ||||
\(533\) | 2.57476 | 0.111525 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 6.90729i | − | 0.298350i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.202401 | −0.00872612 | ||||||||
\(539\) | 27.0468 | − | 1.95013i | 1.16499 | − | 0.0839979i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.6616 | −1.70519 | −0.852593 | − | 0.522576i | \(-0.824971\pi\) | ||||
−0.852593 | + | 0.522576i | \(0.824971\pi\) | |||||||
\(542\) | − | 11.4785i | − | 0.493042i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.11650i | 0.347992i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.3495i | 1.46868i | 0.678782 | + | 0.734339i | \(0.262508\pi\) | ||||
−0.678782 | + | 0.734339i | \(0.737492\pi\) | |||||||
\(548\) | 0.723932 | 0.0309248 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.4524 | 0.615692 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.5283 | + | 14.4490i | 0.660332 | + | 0.614435i | ||||
\(554\) | − | 23.7211i | − | 1.00781i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.84043i | 0.120461i | ||||||||
\(557\) | −38.4660 | −1.62986 | −0.814929 | − | 0.579561i | \(-0.803224\pi\) | ||||
−0.814929 | + | 0.579561i | \(0.803224\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16.2330i | − | 0.686583i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.57194i | 0.235038i | ||||||||
\(563\) | − | 10.2194i | − | 0.430696i | −0.976537 | − | 0.215348i | \(-0.930911\pi\) | ||
0.976537 | − | 0.215348i | \(-0.0690885\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 32.1798 | 1.35262 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.63803i | − | 0.110689i | ||||||
\(569\) | − | 2.48129i | − | 0.104021i | −0.998647 | − | 0.0520106i | \(-0.983437\pi\) | ||
0.998647 | − | 0.0520106i | \(-0.0165629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.6345 | 0.863525 | 0.431762 | − | 0.901987i | \(-0.357892\pi\) | ||||
0.431762 | + | 0.901987i | \(0.357892\pi\) | |||||||
\(572\) | − | 6.21603i | − | 0.259905i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.10801 | + | 2.89199i | 0.129726 | + | 0.120709i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.50455 | 0.104266 | 0.0521329 | − | 0.998640i | \(-0.483398\pi\) | ||||
0.0521329 | + | 0.998640i | \(0.483398\pi\) | |||||||
\(578\) | −48.8776 | −2.03304 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.78397 | − | 6.21603i | 0.239960 | − | 0.257884i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.79079i | 0.364077i | ||||||||
\(584\) | 13.7477 | 0.568885 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 15.8146i | − | 0.653294i | ||||||
\(587\) | − | 31.4422i | − | 1.29776i | −0.760891 | − | 0.648880i | \(-0.775238\pi\) | ||
0.760891 | − | 0.648880i | \(-0.224762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.84183 | −0.405526 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 4.51190i | − | 0.185438i | ||||||
\(593\) | 27.1267i | 1.11396i | 0.830526 | + | 0.556979i | \(0.188040\pi\) | ||||
−0.830526 | + | 0.556979i | \(0.811960\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.00681i | 0.123164i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.79079 | 0.359482 | ||||||||
\(599\) | − | 33.7747i | − | 1.38000i | −0.723810 | − | 0.689999i | \(-0.757611\pi\) | ||
0.723810 | − | 0.689999i | \(-0.242389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.4886i | − | 0.998912i | −0.866339 | − | 0.499456i | \(-0.833533\pi\) | ||
0.866339 | − | 0.499456i | \(-0.166467\pi\) | |||||||
\(602\) | 18.2330 | − | 19.5950i | 0.743122 | − | 0.798631i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.2262 | −0.619545 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.3331 | −1.10941 | −0.554707 | − | 0.832045i | \(-0.687170\pi\) | ||||
−0.554707 | + | 0.832045i | \(0.687170\pi\) | |||||||
\(608\) | − | 2.63803i | − | 0.106986i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.8267i | 0.721190i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.3163i | 0.457061i | 0.973537 | + | 0.228531i | \(0.0733921\pi\) | ||||
−0.973537 | + | 0.228531i | \(0.926608\pi\) | |||||||
\(614\) | −6.72393 | −0.271356 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.98188 | − | 7.50341i | 0.281308 | − | 0.302321i | ||||
\(617\) | −10.6843 | −0.430135 | −0.215067 | − | 0.976599i | \(-0.568997\pi\) | ||||
−0.215067 | + | 0.976599i | \(0.568997\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.56437i | − | 0.384424i | −0.981353 | − | 0.192212i | \(-0.938434\pi\) | ||
0.981353 | − | 0.192212i | \(-0.0615662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.02379 | −0.0410504 | ||||||||
\(623\) | −34.5502 | − | 32.1488i | −1.38423 | − | 1.28801i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.2568 | 0.929529 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.64767 | −0.105653 | ||||||||
\(629\) | 36.6208 | 1.46017 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1956 | 0.684546 | 0.342273 | − | 0.939601i | \(-0.388803\pi\) | ||||
0.342273 | + | 0.939601i | \(0.388803\pi\) | |||||||
\(632\) | 8.01698 | 0.318898 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.46830 | 0.177459 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.807769 | + | 11.2032i | 0.0320050 | + | 0.443885i | ||||
\(638\) | 21.2228 | 0.840220 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5289i | 0.652851i | 0.945223 | + | 0.326426i | \(0.105844\pi\) | ||||
−0.945223 | + | 0.326426i | \(0.894156\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.4286 | −1.47604 | −0.738020 | − | 0.674779i | \(-0.764239\pi\) | ||||
−0.738020 | + | 0.674779i | \(0.764239\pi\) | |||||||
\(644\) | 10.6114 | + | 9.87386i | 0.418148 | + | 0.389085i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.4116 | 0.842429 | ||||||||
\(647\) | 5.52812i | 0.217333i | 0.994078 | + | 0.108666i | \(0.0346580\pi\) | ||||
−0.994078 | + | 0.108666i | \(0.965342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 17.8640i | − | 0.701223i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 9.32572i | − | 0.365223i | ||||||
\(653\) | 18.5159 | 0.724583 | 0.362291 | − | 0.932065i | \(-0.381995\pi\) | ||||
0.362291 | + | 0.932065i | \(0.381995\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.60461 | 0.0626494 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −20.0230 | + | 21.5187i | −0.780579 | + | 0.838887i | ||||
\(659\) | − | 43.3693i | − | 1.68943i | −0.535217 | − | 0.844714i | \(-0.679770\pi\) | ||
0.535217 | − | 0.844714i | \(-0.320230\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.1142i | 1.40468i | 0.711842 | + | 0.702340i | \(0.247861\pi\) | ||||
−0.711842 | + | 0.702340i | \(0.752139\pi\) | |||||||
\(662\) | −14.2160 | −0.552522 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.20921i | − | 0.124542i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.0136i | 1.16213i | ||||||||
\(668\) | 17.3257i | 0.670352i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.8946 | 1.77174 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 33.8743i | − | 1.30576i | −0.757463 | − | 0.652879i | \(-0.773561\pi\) | ||
0.757463 | − | 0.652879i | \(-0.226439\pi\) | |||||||
\(674\) | − | 23.4286i | − | 0.902436i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.4252 | −0.400971 | ||||||||
\(677\) | 4.38446i | 0.168509i | 0.996444 | + | 0.0842543i | \(0.0268508\pi\) | ||||
−0.996444 | + | 0.0842543i | \(0.973149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8274 | + | 15.6578i | 0.645778 | + | 0.600893i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.4524 | −0.553411 | ||||||||
\(683\) | 1.95013 | 0.0746195 | 0.0373098 | − | 0.999304i | \(-0.488121\pi\) | ||||
0.0373098 | + | 0.999304i | \(0.488121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.6084 | + | 14.4307i | −0.443211 | + | 0.550967i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 10.1165i | − | 0.385688i | ||||||
\(689\) | −3.64126 | −0.138721 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1471i | 0.462098i | 0.972942 | + | 0.231049i | \(0.0742157\pi\) | ||||
−0.972942 | + | 0.231049i | \(0.925784\pi\) | |||||||
\(692\) | − | 2.99319i | − | 0.113784i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.1798 | −0.766014 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.0238i | 0.493311i | ||||||||
\(698\) | − | 27.0372i | − | 1.02337i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 11.0600i | − | 0.417732i | −0.977944 | − | 0.208866i | \(-0.933023\pi\) | ||
0.977944 | − | 0.208866i | \(-0.0669773\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.9025 | −0.448913 | ||||||||
\(704\) | − | 3.87386i | − | 0.146002i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 12.3495i | − | 0.464780i | ||||||
\(707\) | −12.0400 | − | 11.2032i | −0.452811 | − | 0.421338i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.2330 | −0.534532 | −0.267266 | − | 0.963623i | \(-0.586120\pi\) | ||||
−0.267266 | + | 0.963623i | \(0.586120\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.8376 | −0.668493 | ||||||||
\(713\) | − | 20.4388i | − | 0.765438i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.38858i | 0.276124i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25.5757i | 0.954477i | ||||||||
\(719\) | 20.4660 | 0.763254 | 0.381627 | − | 0.924317i | \(-0.375364\pi\) | ||||
0.381627 | + | 0.924317i | \(0.375364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.9490 | − | 23.2149i | −0.929149 | − | 0.864567i | ||||
\(722\) | 12.0408 | 0.448111 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 11.1097i | − | 0.412888i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.5717 | −0.948402 | −0.474201 | − | 0.880417i | \(-0.657263\pi\) | ||||
−0.474201 | + | 0.880417i | \(0.657263\pi\) | |||||||
\(728\) | 3.10801 | + | 2.89199i | 0.115191 | + | 0.107184i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 82.1106 | 3.03697 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.6624 | −0.837053 | −0.418527 | − | 0.908204i | \(-0.637453\pi\) | ||||
−0.418527 | + | 0.908204i | \(0.637453\pi\) | |||||||
\(734\) | −20.8444 | −0.769382 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.47847 | 0.201939 | ||||||||
\(737\) | −26.7579 | −0.985640 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.8675 | 1.65048 | 0.825238 | − | 0.564785i | \(-0.191041\pi\) | ||||
0.825238 | + | 0.564785i | \(0.191041\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.39539 | − | 4.08989i | −0.161360 | − | 0.150145i | ||||
\(743\) | −5.37536 | −0.197203 | −0.0986015 | − | 0.995127i | \(-0.531437\pi\) | ||||
−0.0986015 | + | 0.995127i | \(0.531437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.48810i | 0.274159i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 31.4422 | 1.14964 | ||||||||
\(749\) | 38.6684 | + | 35.9807i | 1.41291 | + | 1.31471i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6276 | 0.497280 | 0.248640 | − | 0.968596i | \(-0.420016\pi\) | ||||
0.248640 | + | 0.968596i | \(0.420016\pi\) | |||||||
\(752\) | 11.1097i | 0.405129i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.79079i | 0.320142i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.54586i | 0.165222i | 0.996582 | + | 0.0826110i | \(0.0263259\pi\) | ||||
−0.996582 | + | 0.0826110i | \(0.973674\pi\) | |||||||
\(758\) | −32.6651 | −1.18645 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.6522 | −0.567392 | −0.283696 | − | 0.958914i | \(-0.591561\pi\) | ||||
−0.283696 | + | 0.958914i | \(0.591561\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.1001 | + | 27.0774i | 1.05349 | + | 0.980269i | ||||
\(764\) | − | 9.36197i | − | 0.338704i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.890309i | 0.0321682i | ||||||||
\(767\) | 7.39951 | 0.267181 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.1922i | − | 0.619968i | −0.950742 | − | 0.309984i | \(-0.899676\pi\) | ||
0.950742 | − | 0.309984i | \(-0.100324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.4422i | 0.627759i | ||||||||
\(773\) | 42.6990i | 1.53578i | 0.640584 | + | 0.767889i | \(0.278693\pi\) | ||||
−0.640584 | + | 0.767889i | \(0.721307\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.68768 | 0.311870 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.5317i | 0.485135i | ||||||||
\(779\) | − | 4.23301i | − | 0.151663i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.2194 | −0.365678 | ||||||||
\(782\) | 44.4660i | 1.59010i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.503406 | + | 6.98188i | 0.0179788 | + | 0.249353i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.3992 | −1.08361 | −0.541806 | − | 0.840503i | \(-0.682259\pi\) | ||||
−0.541806 | + | 0.840503i | \(0.682259\pi\) | |||||||
\(788\) | −5.27607 | −0.187952 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.8206 | − | 18.4430i | −0.704741 | − | 0.655757i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.0102i | 0.675071i | ||||||||
\(794\) | −25.2991 | −0.897831 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.2160i | 0.432986i | ||||||||
\(797\) | − | 2.99319i | − | 0.106024i | −0.998594 | − | 0.0530121i | \(-0.983118\pi\) | ||
0.998594 | − | 0.0530121i | \(-0.0168822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −90.1718 | −3.19005 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 32.7619i | 1.15686i | ||||||||
\(803\) | − | 53.2568i | − | 1.87939i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 5.98638i | − | 0.210861i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.21603 | −0.218679 | ||||||||
\(809\) | 25.0334i | 0.880128i | 0.897966 | + | 0.440064i | \(0.145044\pi\) | ||||
−0.897966 | + | 0.440064i | \(0.854956\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.4782i | 0.683974i | 0.939705 | + | 0.341987i | \(0.111100\pi\) | ||||
−0.939705 | + | 0.341987i | \(0.888900\pi\) | |||||||
\(812\) | −9.87386 | + | 10.6114i | −0.346505 | + | 0.372388i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.4785 | −0.612620 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.6877 | −0.933684 | ||||||||
\(818\) | 12.0000i | 0.419570i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 45.3787i | − | 1.58373i | −0.610697 | − | 0.791864i | \(-0.709111\pi\) | ||
0.610697 | − | 0.791864i | \(-0.290889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.8512i | 0.901117i | 0.892747 | + | 0.450559i | \(0.148775\pi\) | ||||
−0.892747 | + | 0.450559i | \(0.851225\pi\) | |||||||
\(824\) | −12.8807 | −0.448720 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.93200 | + | 8.31117i | 0.310784 | + | 0.289183i | ||||
\(827\) | 19.3429 | 0.672619 | 0.336310 | − | 0.941751i | \(-0.390821\pi\) | ||||
0.336310 | + | 0.941751i | \(0.390821\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 43.4764i | − | 1.51000i | −0.655726 | − | 0.754999i | \(-0.727637\pi\) | ||
0.655726 | − | 0.754999i | \(-0.272363\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.60461 | 0.0556297 | ||||||||
\(833\) | −56.6684 | + | 4.08590i | −1.96344 | + | 0.141568i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.2194 | −0.353445 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.17937 | 0.144374 | ||||||||
\(839\) | 24.2670 | 0.837789 | 0.418894 | − | 0.908035i | \(-0.362418\pi\) | ||||
0.418894 | + | 0.908035i | \(0.362418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.01362 | −0.0349526 | ||||||||
\(842\) | −32.6514 | −1.12524 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.76092 | − | 7.22149i | −0.266668 | − | 0.248133i | ||||
\(848\) | −2.26926 | −0.0779266 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 24.7183i | − | 0.847332i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.2439 | −0.556182 | −0.278091 | − | 0.960555i | \(-0.589702\pi\) | ||||
−0.278091 | + | 0.960555i | \(0.589702\pi\) | |||||||
\(854\) | −21.3523 | + | 22.9473i | −0.730662 | + | 0.785241i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.9638 | 0.682347 | ||||||||
\(857\) | − | 40.5825i | − | 1.38627i | −0.720807 | − | 0.693136i | \(-0.756228\pi\) | ||
0.720807 | − | 0.693136i | \(-0.243772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.05310i | − | 0.172410i | −0.996277 | − | 0.0862048i | \(-0.972526\pi\) | ||
0.996277 | − | 0.0862048i | \(-0.0274739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.3087i | 0.453297i | ||||||||
\(863\) | 48.3289 | 1.64514 | 0.822568 | − | 0.568666i | \(-0.192540\pi\) | ||||
0.822568 | + | 0.568666i | \(0.192540\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.95358 | −0.236292 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.72393 | − | 7.22619i | 0.228225 | − | 0.245273i | ||||
\(869\) | − | 31.0567i | − | 1.05353i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 11.0835i | − | 0.375549i | ||||||
\(872\) | 15.0238 | 0.508770 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 14.4524i | − | 0.488859i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.3963i | 1.87060i | 0.353854 | + | 0.935301i | \(0.384871\pi\) | ||||
−0.353854 | + | 0.935301i | \(0.615129\pi\) | |||||||
\(878\) | − | 26.9739i | − | 0.910326i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.8716 | −1.68022 | −0.840108 | − | 0.542419i | \(-0.817509\pi\) | ||||
−0.840108 | + | 0.542419i | \(0.817509\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 43.3393i | − | 1.45848i | −0.684255 | − | 0.729242i | \(-0.739873\pi\) | ||
0.684255 | − | 0.729242i | \(-0.260127\pi\) | |||||||
\(884\) | 13.0238i | 0.438038i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.80441 | 0.0942160 | ||||||||
\(887\) | 33.1539i | 1.11320i | 0.830781 | + | 0.556600i | \(0.187894\pi\) | ||||
−0.830781 | + | 0.556600i | \(0.812106\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.07136 | + | 5.45018i | −0.170088 | + | 0.182793i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.65784 | 0.122473 | ||||||||
\(893\) | 29.3077 | 0.980746 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.93693 | + | 1.80230i | 0.0647083 | + | 0.0602107i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 30.1226i | − | 1.00520i | ||||||
\(899\) | 20.4388 | 0.681671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 18.4184i | − | 0.613607i | ||||||
\(902\) | − | 6.21603i | − | 0.206971i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.2330 | −0.340345 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 50.5553i | − | 1.67866i | −0.543622 | − | 0.839330i | \(-0.682948\pi\) | ||
0.543622 | − | 0.839330i | \(-0.317052\pi\) | |||||||
\(908\) | 4.23301i | 0.140477i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 21.6755i | − | 0.718140i | −0.933311 | − | 0.359070i | \(-0.883094\pi\) | ||
0.933311 | − | 0.359070i | \(-0.116906\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4321 | −0.411441 | ||||||||
\(914\) | 22.0340i | 0.728819i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.59497i | 0.250945i | ||||||||
\(917\) | 16.7126 | + | 15.5510i | 0.551899 | + | 0.513539i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.6616 | 0.846498 | 0.423249 | − | 0.906013i | \(-0.360890\pi\) | ||||
0.423249 | + | 0.906013i | \(0.360890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.4116 | −0.507554 | ||||||||
\(923\) | − | 4.23301i | − | 0.139331i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 25.0605i | − | 0.823538i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.47847i | 0.179840i | ||||||||
\(929\) | 31.6182 | 1.03736 | 0.518680 | − | 0.854968i | \(-0.326424\pi\) | ||||
0.518680 | + | 0.854968i | \(0.326424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.4184 | − | 1.32800i | 0.603640 | − | 0.0435235i | ||||
\(932\) | 9.94677 | 0.325817 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.62764i | 0.315026i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.7013 | −1.26432 | −0.632158 | − | 0.774839i | \(-0.717831\pi\) | ||||
−0.632158 | + | 0.774839i | \(0.717831\pi\) | |||||||
\(938\) | 12.4490 | − | 13.3789i | 0.406475 | − | 0.436838i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.9932 | −1.07555 | −0.537774 | − | 0.843089i | \(-0.680734\pi\) | ||||
−0.537774 | + | 0.843089i | \(0.680734\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.79079 | 0.286267 | ||||||||
\(944\) | 4.61142 | 0.150089 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.1899 | −1.27418 | ||||||||
\(947\) | 31.8452 | 1.03483 | 0.517415 | − | 0.855735i | \(-0.326894\pi\) | ||||
0.517415 | + | 0.855735i | \(0.326894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.0597 | 0.716088 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.6284 | + | 15.7211i | −0.474109 | + | 0.509524i | ||||
\(953\) | 45.9003 | 1.48686 | 0.743428 | − | 0.668817i | \(-0.233199\pi\) | ||||
0.743428 | + | 0.668817i | \(0.233199\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 9.36197i | − | 0.302788i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.0238 | −1.19618 | ||||||||
\(959\) | 1.40221 | + | 1.30474i | 0.0452796 | + | 0.0421324i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0816 | 0.551018 | ||||||||
\(962\) | − | 7.23982i | − | 0.233421i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 23.0408i | − | 0.742093i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.2662i | 1.32703i | 0.748162 | + | 0.663516i | \(0.230936\pi\) | ||||
−0.748162 | + | 0.663516i | \(0.769064\pi\) | |||||||
\(968\) | −4.00681 | −0.128784 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.0008 | −0.353031 | −0.176516 | − | 0.984298i | \(-0.556483\pi\) | ||||
−0.176516 | + | 0.984298i | \(0.556483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.11933 | + | 5.50173i | −0.164118 | + | 0.176377i | ||||
\(974\) | 11.6386i | 0.372924i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.8472i | 0.379221i | ||||||||
\(977\) | 2.48528 | 0.0795112 | 0.0397556 | − | 0.999209i | \(-0.487342\pi\) | ||||
0.0397556 | + | 0.999209i | \(0.487342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 69.1005i | 2.20846i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 32.1069i | − | 1.02457i | ||||||
\(983\) | 31.7408i | 1.01237i | 0.862424 | + | 0.506187i | \(0.168945\pi\) | ||||
−0.862424 | + | 0.506187i | \(0.831055\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −44.4660 | −1.41609 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 4.23301i | − | 0.134670i | ||||||
\(989\) | − | 55.4230i | − | 1.76235i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.3368 | 1.82136 | 0.910682 | − | 0.413108i | \(-0.135557\pi\) | ||||
0.910682 | + | 0.413108i | \(0.135557\pi\) | |||||||
\(992\) | − | 3.73074i | − | 0.118451i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.75454 | − | 5.10969i | 0.150805 | − | 0.162070i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.6760 | 1.66827 | 0.834133 | − | 0.551564i | \(-0.185969\pi\) | ||||
0.834133 | + | 0.551564i | \(0.185969\pi\) | |||||||
\(998\) | −13.6122 | −0.430886 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.d.d.3149.8 | 8 | ||
3.2 | odd | 2 | 3150.2.d.a.3149.8 | 8 | |||
5.2 | odd | 4 | 630.2.b.a.251.6 | yes | 8 | ||
5.3 | odd | 4 | 3150.2.b.e.251.3 | 8 | |||
5.4 | even | 2 | 3150.2.d.c.3149.1 | 8 | |||
7.6 | odd | 2 | 3150.2.d.f.3149.2 | 8 | |||
15.2 | even | 4 | 630.2.b.b.251.2 | yes | 8 | ||
15.8 | even | 4 | 3150.2.b.f.251.7 | 8 | |||
15.14 | odd | 2 | 3150.2.d.f.3149.1 | 8 | |||
20.7 | even | 4 | 5040.2.f.f.881.5 | 8 | |||
21.20 | even | 2 | 3150.2.d.c.3149.2 | 8 | |||
35.13 | even | 4 | 3150.2.b.f.251.3 | 8 | |||
35.27 | even | 4 | 630.2.b.b.251.6 | yes | 8 | ||
35.34 | odd | 2 | 3150.2.d.a.3149.7 | 8 | |||
60.47 | odd | 4 | 5040.2.f.i.881.5 | 8 | |||
105.62 | odd | 4 | 630.2.b.a.251.2 | ✓ | 8 | ||
105.83 | odd | 4 | 3150.2.b.e.251.7 | 8 | |||
105.104 | even | 2 | inner | 3150.2.d.d.3149.7 | 8 | ||
140.27 | odd | 4 | 5040.2.f.i.881.6 | 8 | |||
420.167 | even | 4 | 5040.2.f.f.881.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.b.a.251.2 | ✓ | 8 | 105.62 | odd | 4 | ||
630.2.b.a.251.6 | yes | 8 | 5.2 | odd | 4 | ||
630.2.b.b.251.2 | yes | 8 | 15.2 | even | 4 | ||
630.2.b.b.251.6 | yes | 8 | 35.27 | even | 4 | ||
3150.2.b.e.251.3 | 8 | 5.3 | odd | 4 | |||
3150.2.b.e.251.7 | 8 | 105.83 | odd | 4 | |||
3150.2.b.f.251.3 | 8 | 35.13 | even | 4 | |||
3150.2.b.f.251.7 | 8 | 15.8 | even | 4 | |||
3150.2.d.a.3149.7 | 8 | 35.34 | odd | 2 | |||
3150.2.d.a.3149.8 | 8 | 3.2 | odd | 2 | |||
3150.2.d.c.3149.1 | 8 | 5.4 | even | 2 | |||
3150.2.d.c.3149.2 | 8 | 21.20 | even | 2 | |||
3150.2.d.d.3149.7 | 8 | 105.104 | even | 2 | inner | ||
3150.2.d.d.3149.8 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.d.f.3149.1 | 8 | 15.14 | odd | 2 | |||
3150.2.d.f.3149.2 | 8 | 7.6 | odd | 2 | |||
5040.2.f.f.881.5 | 8 | 20.7 | even | 4 | |||
5040.2.f.f.881.6 | 8 | 420.167 | even | 4 | |||
5040.2.f.i.881.5 | 8 | 60.47 | odd | 4 | |||
5040.2.f.i.881.6 | 8 | 140.27 | odd | 4 |