Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.a (trivial) |
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: | yes |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −2.64575 | −1.52753 | −0.763763 | − | 0.645497i | \(-0.776650\pi\) | ||||
−0.763763 | + | 0.645497i | \(0.776650\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.64575 | 0.736002 | 0.368001 | − | 0.929825i | \(-0.380042\pi\) | ||||
0.368001 | + | 0.929825i | \(0.380042\pi\) | |||||||
\(6\) | 2.64575 | 1.08012 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.00000 | 1.33333 | ||||||||
\(10\) | −1.64575 | −0.520432 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.64575 | −0.763763 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.35425 | −1.12426 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | −4.00000 | −0.942809 | ||||||||
\(19\) | 5.64575 | 1.29522 | 0.647612 | − | 0.761970i | \(-0.275768\pi\) | ||||
0.647612 | + | 0.761970i | \(0.275768\pi\) | |||||||
\(20\) | 1.64575 | 0.368001 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 1.64575 | 0.343163 | 0.171581 | − | 0.985170i | \(-0.445112\pi\) | ||||
0.171581 | + | 0.985170i | \(0.445112\pi\) | |||||||
\(24\) | 2.64575 | 0.540062 | ||||||||
\(25\) | −2.29150 | −0.458301 | ||||||||
\(26\) | 5.00000 | 0.980581 | ||||||||
\(27\) | −2.64575 | −0.509175 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.29150 | 1.16830 | 0.584151 | − | 0.811645i | \(-0.301427\pi\) | ||||
0.584151 | + | 0.811645i | \(0.301427\pi\) | |||||||
\(30\) | 4.35425 | 0.794973 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.64575 | −0.460566 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.00000 | 0.666667 | ||||||||
\(37\) | 3.64575 | 0.599358 | 0.299679 | − | 0.954040i | \(-0.403120\pi\) | ||||
0.299679 | + | 0.954040i | \(0.403120\pi\) | |||||||
\(38\) | −5.64575 | −0.915862 | ||||||||
\(39\) | 13.2288 | 2.11830 | ||||||||
\(40\) | −1.64575 | −0.260216 | ||||||||
\(41\) | −10.9373 | −1.70811 | −0.854056 | − | 0.520181i | \(-0.825864\pi\) | ||||
−0.854056 | + | 0.520181i | \(0.825864\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 6.58301 | 0.981336 | ||||||||
\(46\) | −1.64575 | −0.242653 | ||||||||
\(47\) | −2.70850 | −0.395075 | −0.197537 | − | 0.980295i | \(-0.563294\pi\) | ||||
−0.197537 | + | 0.980295i | \(0.563294\pi\) | |||||||
\(48\) | −2.64575 | −0.381881 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.29150 | 0.324067 | ||||||||
\(51\) | 15.8745 | 2.22288 | ||||||||
\(52\) | −5.00000 | −0.693375 | ||||||||
\(53\) | 1.64575 | 0.226061 | 0.113031 | − | 0.993592i | \(-0.463944\pi\) | ||||
0.113031 | + | 0.993592i | \(0.463944\pi\) | |||||||
\(54\) | 2.64575 | 0.360041 | ||||||||
\(55\) | 1.64575 | 0.221913 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.9373 | −1.97849 | ||||||||
\(58\) | −6.29150 | −0.826115 | ||||||||
\(59\) | −4.64575 | −0.604825 | −0.302413 | − | 0.953177i | \(-0.597792\pi\) | ||||
−0.302413 | + | 0.953177i | \(0.597792\pi\) | |||||||
\(60\) | −4.35425 | −0.562131 | ||||||||
\(61\) | −14.2915 | −1.82984 | −0.914920 | − | 0.403636i | \(-0.867746\pi\) | ||||
−0.914920 | + | 0.403636i | \(0.867746\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.22876 | −1.02065 | ||||||||
\(66\) | 2.64575 | 0.325669 | ||||||||
\(67\) | −11.9373 | −1.45837 | −0.729184 | − | 0.684318i | \(-0.760100\pi\) | ||||
−0.729184 | + | 0.684318i | \(0.760100\pi\) | |||||||
\(68\) | −6.00000 | −0.727607 | ||||||||
\(69\) | −4.35425 | −0.524190 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.35425 | 0.516754 | 0.258377 | − | 0.966044i | \(-0.416812\pi\) | ||||
0.258377 | + | 0.966044i | \(0.416812\pi\) | |||||||
\(72\) | −4.00000 | −0.471405 | ||||||||
\(73\) | −0.354249 | −0.0414617 | −0.0207308 | − | 0.999785i | \(-0.506599\pi\) | ||||
−0.0207308 | + | 0.999785i | \(0.506599\pi\) | |||||||
\(74\) | −3.64575 | −0.423810 | ||||||||
\(75\) | 6.06275 | 0.700066 | ||||||||
\(76\) | 5.64575 | 0.647612 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.2288 | −1.49786 | ||||||||
\(79\) | −2.64575 | −0.297670 | −0.148835 | − | 0.988862i | \(-0.547552\pi\) | ||||
−0.148835 | + | 0.988862i | \(0.547552\pi\) | |||||||
\(80\) | 1.64575 | 0.184001 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 10.9373 | 1.20782 | ||||||||
\(83\) | −2.70850 | −0.297296 | −0.148648 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148648 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.87451 | −1.07104 | ||||||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | −16.6458 | −1.78461 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −6.58301 | −0.697797 | −0.348899 | − | 0.937160i | \(-0.613444\pi\) | ||||
−0.348899 | + | 0.937160i | \(0.613444\pi\) | |||||||
\(90\) | −6.58301 | −0.693910 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.64575 | 0.171581 | ||||||||
\(93\) | −10.5830 | −1.09741 | ||||||||
\(94\) | 2.70850 | 0.279360 | ||||||||
\(95\) | 9.29150 | 0.953288 | ||||||||
\(96\) | 2.64575 | 0.270031 | ||||||||
\(97\) | 16.2915 | 1.65415 | 0.827076 | − | 0.562090i | \(-0.190003\pi\) | ||||
0.827076 | + | 0.562090i | \(0.190003\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | −2.29150 | −0.229150 | ||||||||
\(101\) | −3.00000 | −0.298511 | −0.149256 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149256 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(102\) | −15.8745 | −1.57181 | ||||||||
\(103\) | 2.93725 | 0.289416 | 0.144708 | − | 0.989474i | \(-0.453776\pi\) | ||||
0.144708 | + | 0.989474i | \(0.453776\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.64575 | −0.159849 | ||||||||
\(107\) | −10.9373 | −1.05734 | −0.528672 | − | 0.848826i | \(-0.677310\pi\) | ||||
−0.528672 | + | 0.848826i | \(0.677310\pi\) | |||||||
\(108\) | −2.64575 | −0.254588 | ||||||||
\(109\) | −10.5830 | −1.01367 | −0.506834 | − | 0.862044i | \(-0.669184\pi\) | ||||
−0.506834 | + | 0.862044i | \(0.669184\pi\) | |||||||
\(110\) | −1.64575 | −0.156916 | ||||||||
\(111\) | −9.64575 | −0.915534 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.2915 | −1.72072 | −0.860360 | − | 0.509687i | \(-0.829761\pi\) | ||||
−0.860360 | + | 0.509687i | \(0.829761\pi\) | |||||||
\(114\) | 14.9373 | 1.39900 | ||||||||
\(115\) | 2.70850 | 0.252569 | ||||||||
\(116\) | 6.29150 | 0.584151 | ||||||||
\(117\) | −20.0000 | −1.84900 | ||||||||
\(118\) | 4.64575 | 0.427676 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.35425 | 0.397487 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 14.2915 | 1.29389 | ||||||||
\(123\) | 28.9373 | 2.60918 | ||||||||
\(124\) | 4.00000 | 0.359211 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9373 | 1.41420 | 0.707101 | − | 0.707112i | \(-0.250002\pi\) | ||||
0.707101 | + | 0.707112i | \(0.250002\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.5830 | 0.931782 | ||||||||
\(130\) | 8.22876 | 0.721710 | ||||||||
\(131\) | −10.3542 | −0.904655 | −0.452327 | − | 0.891852i | \(-0.649406\pi\) | ||||
−0.452327 | + | 0.891852i | \(0.649406\pi\) | |||||||
\(132\) | −2.64575 | −0.230283 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.9373 | 1.03122 | ||||||||
\(135\) | −4.35425 | −0.374754 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | −12.8745 | −1.09994 | −0.549972 | − | 0.835183i | \(-0.685362\pi\) | ||||
−0.549972 | + | 0.835183i | \(0.685362\pi\) | |||||||
\(138\) | 4.35425 | 0.370658 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.16601 | 0.603487 | ||||||||
\(142\) | −4.35425 | −0.365400 | ||||||||
\(143\) | −5.00000 | −0.418121 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 10.3542 | 0.859874 | ||||||||
\(146\) | 0.354249 | 0.0293178 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.64575 | 0.299679 | ||||||||
\(149\) | −15.2915 | −1.25273 | −0.626364 | − | 0.779530i | \(-0.715458\pi\) | ||||
−0.626364 | + | 0.779530i | \(0.715458\pi\) | |||||||
\(150\) | −6.06275 | −0.495021 | ||||||||
\(151\) | −8.64575 | −0.703581 | −0.351791 | − | 0.936079i | \(-0.614427\pi\) | ||||
−0.351791 | + | 0.936079i | \(0.614427\pi\) | |||||||
\(152\) | −5.64575 | −0.457931 | ||||||||
\(153\) | −24.0000 | −1.94029 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.58301 | 0.528760 | ||||||||
\(156\) | 13.2288 | 1.05915 | ||||||||
\(157\) | −21.1660 | −1.68923 | −0.844616 | − | 0.535373i | \(-0.820171\pi\) | ||||
−0.844616 | + | 0.535373i | \(0.820171\pi\) | |||||||
\(158\) | 2.64575 | 0.210485 | ||||||||
\(159\) | −4.35425 | −0.345314 | ||||||||
\(160\) | −1.64575 | −0.130108 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 5.00000 | 0.392837 | ||||||||
\(163\) | 0.645751 | 0.0505791 | 0.0252896 | − | 0.999680i | \(-0.491949\pi\) | ||||
0.0252896 | + | 0.999680i | \(0.491949\pi\) | |||||||
\(164\) | −10.9373 | −0.854056 | ||||||||
\(165\) | −4.35425 | −0.338978 | ||||||||
\(166\) | 2.70850 | 0.210220 | ||||||||
\(167\) | 11.2288 | 0.868907 | 0.434454 | − | 0.900694i | \(-0.356941\pi\) | ||||
0.434454 | + | 0.900694i | \(0.356941\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 9.87451 | 0.757340 | ||||||||
\(171\) | 22.5830 | 1.72697 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | 0.291503 | 0.0221625 | 0.0110813 | − | 0.999939i | \(-0.496473\pi\) | ||||
0.0110813 | + | 0.999939i | \(0.496473\pi\) | |||||||
\(174\) | 16.6458 | 1.26191 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 12.2915 | 0.923886 | ||||||||
\(178\) | 6.58301 | 0.493417 | ||||||||
\(179\) | −19.9373 | −1.49018 | −0.745090 | − | 0.666964i | \(-0.767594\pi\) | ||||
−0.745090 | + | 0.666964i | \(0.767594\pi\) | |||||||
\(180\) | 6.58301 | 0.490668 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 37.8118 | 2.79513 | ||||||||
\(184\) | −1.64575 | −0.121326 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 10.5830 | 0.775984 | ||||||||
\(187\) | −6.00000 | −0.438763 | ||||||||
\(188\) | −2.70850 | −0.197537 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.29150 | −0.674076 | ||||||||
\(191\) | −2.70850 | −0.195980 | −0.0979900 | − | 0.995187i | \(-0.531241\pi\) | ||||
−0.0979900 | + | 0.995187i | \(0.531241\pi\) | |||||||
\(192\) | −2.64575 | −0.190941 | ||||||||
\(193\) | 25.5203 | 1.83699 | 0.918494 | − | 0.395434i | \(-0.129406\pi\) | ||||
0.918494 | + | 0.395434i | \(0.129406\pi\) | |||||||
\(194\) | −16.2915 | −1.16966 | ||||||||
\(195\) | 21.7712 | 1.55907 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.8745 | −0.917271 | −0.458635 | − | 0.888625i | \(-0.651662\pi\) | ||||
−0.458635 | + | 0.888625i | \(0.651662\pi\) | |||||||
\(198\) | −4.00000 | −0.284268 | ||||||||
\(199\) | −4.22876 | −0.299769 | −0.149884 | − | 0.988704i | \(-0.547890\pi\) | ||||
−0.149884 | + | 0.988704i | \(0.547890\pi\) | |||||||
\(200\) | 2.29150 | 0.162034 | ||||||||
\(201\) | 31.5830 | 2.22769 | ||||||||
\(202\) | 3.00000 | 0.211079 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 15.8745 | 1.11144 | ||||||||
\(205\) | −18.0000 | −1.25717 | ||||||||
\(206\) | −2.93725 | −0.204648 | ||||||||
\(207\) | 6.58301 | 0.457550 | ||||||||
\(208\) | −5.00000 | −0.346688 | ||||||||
\(209\) | 5.64575 | 0.390525 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.937254 | 0.0645232 | 0.0322616 | − | 0.999479i | \(-0.489729\pi\) | ||||
0.0322616 | + | 0.999479i | \(0.489729\pi\) | |||||||
\(212\) | 1.64575 | 0.113031 | ||||||||
\(213\) | −11.5203 | −0.789355 | ||||||||
\(214\) | 10.9373 | 0.747655 | ||||||||
\(215\) | −6.58301 | −0.448957 | ||||||||
\(216\) | 2.64575 | 0.180021 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.5830 | 0.716772 | ||||||||
\(219\) | 0.937254 | 0.0633338 | ||||||||
\(220\) | 1.64575 | 0.110957 | ||||||||
\(221\) | 30.0000 | 2.01802 | ||||||||
\(222\) | 9.64575 | 0.647380 | ||||||||
\(223\) | 17.6458 | 1.18165 | 0.590823 | − | 0.806801i | \(-0.298803\pi\) | ||||
0.590823 | + | 0.806801i | \(0.298803\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.16601 | −0.611067 | ||||||||
\(226\) | 18.2915 | 1.21673 | ||||||||
\(227\) | 2.70850 | 0.179769 | 0.0898846 | − | 0.995952i | \(-0.471350\pi\) | ||||
0.0898846 | + | 0.995952i | \(0.471350\pi\) | |||||||
\(228\) | −14.9373 | −0.989244 | ||||||||
\(229\) | 16.0000 | 1.05731 | 0.528655 | − | 0.848837i | \(-0.322697\pi\) | ||||
0.528655 | + | 0.848837i | \(0.322697\pi\) | |||||||
\(230\) | −2.70850 | −0.178593 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.29150 | −0.413057 | ||||||||
\(233\) | 1.06275 | 0.0696228 | 0.0348114 | − | 0.999394i | \(-0.488917\pi\) | ||||
0.0348114 | + | 0.999394i | \(0.488917\pi\) | |||||||
\(234\) | 20.0000 | 1.30744 | ||||||||
\(235\) | −4.45751 | −0.290776 | ||||||||
\(236\) | −4.64575 | −0.302413 | ||||||||
\(237\) | 7.00000 | 0.454699 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.2288 | −1.11444 | −0.557218 | − | 0.830366i | \(-0.688131\pi\) | ||||
−0.557218 | + | 0.830366i | \(0.688131\pi\) | |||||||
\(240\) | −4.35425 | −0.281066 | ||||||||
\(241\) | 24.8118 | 1.59827 | 0.799133 | − | 0.601154i | \(-0.205292\pi\) | ||||
0.799133 | + | 0.601154i | \(0.205292\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 21.1660 | 1.35780 | ||||||||
\(244\) | −14.2915 | −0.914920 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −28.9373 | −1.84497 | ||||||||
\(247\) | −28.2288 | −1.79615 | ||||||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | 7.16601 | 0.454127 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | 3.29150 | 0.207758 | 0.103879 | − | 0.994590i | \(-0.466875\pi\) | ||||
0.103879 | + | 0.994590i | \(0.466875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.64575 | 0.103467 | ||||||||
\(254\) | −15.9373 | −0.999992 | ||||||||
\(255\) | 26.1255 | 1.63604 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.5830 | 1.34631 | 0.673155 | − | 0.739501i | \(-0.264938\pi\) | ||||
0.673155 | + | 0.739501i | \(0.264938\pi\) | |||||||
\(258\) | −10.5830 | −0.658869 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.22876 | −0.510326 | ||||||||
\(261\) | 25.1660 | 1.55774 | ||||||||
\(262\) | 10.3542 | 0.639688 | ||||||||
\(263\) | 19.9373 | 1.22938 | 0.614692 | − | 0.788767i | \(-0.289280\pi\) | ||||
0.614692 | + | 0.788767i | \(0.289280\pi\) | |||||||
\(264\) | 2.64575 | 0.162835 | ||||||||
\(265\) | 2.70850 | 0.166382 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.4170 | 1.06590 | ||||||||
\(268\) | −11.9373 | −0.729184 | ||||||||
\(269\) | −5.41699 | −0.330280 | −0.165140 | − | 0.986270i | \(-0.552808\pi\) | ||||
−0.165140 | + | 0.986270i | \(0.552808\pi\) | |||||||
\(270\) | 4.35425 | 0.264991 | ||||||||
\(271\) | 2.06275 | 0.125303 | 0.0626514 | − | 0.998035i | \(-0.480044\pi\) | ||||
0.0626514 | + | 0.998035i | \(0.480044\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.8745 | 0.777777 | ||||||||
\(275\) | −2.29150 | −0.138183 | ||||||||
\(276\) | −4.35425 | −0.262095 | ||||||||
\(277\) | −22.2915 | −1.33937 | −0.669683 | − | 0.742647i | \(-0.733570\pi\) | ||||
−0.669683 | + | 0.742647i | \(0.733570\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | 16.0000 | 0.957895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.9373 | −1.36832 | −0.684161 | − | 0.729331i | \(-0.739831\pi\) | ||||
−0.684161 | + | 0.729331i | \(0.739831\pi\) | |||||||
\(282\) | −7.16601 | −0.426730 | ||||||||
\(283\) | 2.35425 | 0.139946 | 0.0699728 | − | 0.997549i | \(-0.477709\pi\) | ||||
0.0699728 | + | 0.997549i | \(0.477709\pi\) | |||||||
\(284\) | 4.35425 | 0.258377 | ||||||||
\(285\) | −24.5830 | −1.45617 | ||||||||
\(286\) | 5.00000 | 0.295656 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.00000 | −0.235702 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | −10.3542 | −0.608022 | ||||||||
\(291\) | −43.1033 | −2.52676 | ||||||||
\(292\) | −0.354249 | −0.0207308 | ||||||||
\(293\) | −12.0000 | −0.701047 | −0.350524 | − | 0.936554i | \(-0.613996\pi\) | ||||
−0.350524 | + | 0.936554i | \(0.613996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.64575 | −0.445153 | ||||||||
\(296\) | −3.64575 | −0.211905 | ||||||||
\(297\) | −2.64575 | −0.153522 | ||||||||
\(298\) | 15.2915 | 0.885813 | ||||||||
\(299\) | −8.22876 | −0.475881 | ||||||||
\(300\) | 6.06275 | 0.350033 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.64575 | 0.497507 | ||||||||
\(303\) | 7.93725 | 0.455983 | ||||||||
\(304\) | 5.64575 | 0.323806 | ||||||||
\(305\) | −23.5203 | −1.34677 | ||||||||
\(306\) | 24.0000 | 1.37199 | ||||||||
\(307\) | −22.2288 | −1.26866 | −0.634331 | − | 0.773062i | \(-0.718724\pi\) | ||||
−0.634331 | + | 0.773062i | \(0.718724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.77124 | −0.442091 | ||||||||
\(310\) | −6.58301 | −0.373890 | ||||||||
\(311\) | −1.06275 | −0.0602628 | −0.0301314 | − | 0.999546i | \(-0.509593\pi\) | ||||
−0.0301314 | + | 0.999546i | \(0.509593\pi\) | |||||||
\(312\) | −13.2288 | −0.748931 | ||||||||
\(313\) | −23.5830 | −1.33299 | −0.666495 | − | 0.745509i | \(-0.732206\pi\) | ||||
−0.666495 | + | 0.745509i | \(0.732206\pi\) | |||||||
\(314\) | 21.1660 | 1.19447 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.64575 | −0.148835 | ||||||||
\(317\) | 12.0000 | 0.673987 | 0.336994 | − | 0.941507i | \(-0.390590\pi\) | ||||
0.336994 | + | 0.941507i | \(0.390590\pi\) | |||||||
\(318\) | 4.35425 | 0.244174 | ||||||||
\(319\) | 6.29150 | 0.352257 | ||||||||
\(320\) | 1.64575 | 0.0920003 | ||||||||
\(321\) | 28.9373 | 1.61512 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.8745 | −1.88483 | ||||||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | 11.4575 | 0.635548 | ||||||||
\(326\) | −0.645751 | −0.0357649 | ||||||||
\(327\) | 28.0000 | 1.54840 | ||||||||
\(328\) | 10.9373 | 0.603909 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.35425 | 0.239694 | ||||||||
\(331\) | −20.6458 | −1.13479 | −0.567397 | − | 0.823445i | \(-0.692049\pi\) | ||||
−0.567397 | + | 0.823445i | \(0.692049\pi\) | |||||||
\(332\) | −2.70850 | −0.148648 | ||||||||
\(333\) | 14.5830 | 0.799144 | ||||||||
\(334\) | −11.2288 | −0.614410 | ||||||||
\(335\) | −19.6458 | −1.07336 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.06275 | 0.493679 | 0.246840 | − | 0.969056i | \(-0.420608\pi\) | ||||
0.246840 | + | 0.969056i | \(0.420608\pi\) | |||||||
\(338\) | −12.0000 | −0.652714 | ||||||||
\(339\) | 48.3948 | 2.62844 | ||||||||
\(340\) | −9.87451 | −0.535520 | ||||||||
\(341\) | 4.00000 | 0.216612 | ||||||||
\(342\) | −22.5830 | −1.22115 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | −7.16601 | −0.385805 | ||||||||
\(346\) | −0.291503 | −0.0156713 | ||||||||
\(347\) | −20.8118 | −1.11723 | −0.558617 | − | 0.829426i | \(-0.688668\pi\) | ||||
−0.558617 | + | 0.829426i | \(0.688668\pi\) | |||||||
\(348\) | −16.6458 | −0.892306 | ||||||||
\(349\) | 1.87451 | 0.100340 | 0.0501701 | − | 0.998741i | \(-0.484024\pi\) | ||||
0.0501701 | + | 0.998741i | \(0.484024\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.2288 | 0.706099 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −7.16601 | −0.381408 | −0.190704 | − | 0.981648i | \(-0.561077\pi\) | ||||
−0.190704 | + | 0.981648i | \(0.561077\pi\) | |||||||
\(354\) | −12.2915 | −0.653286 | ||||||||
\(355\) | 7.16601 | 0.380332 | ||||||||
\(356\) | −6.58301 | −0.348899 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.9373 | 1.05372 | ||||||||
\(359\) | −25.9373 | −1.36892 | −0.684458 | − | 0.729052i | \(-0.739961\pi\) | ||||
−0.684458 | + | 0.729052i | \(0.739961\pi\) | |||||||
\(360\) | −6.58301 | −0.346955 | ||||||||
\(361\) | 12.8745 | 0.677606 | ||||||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | −2.64575 | −0.138866 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.583005 | −0.0305159 | ||||||||
\(366\) | −37.8118 | −1.97645 | ||||||||
\(367\) | 36.2288 | 1.89113 | 0.945563 | − | 0.325440i | \(-0.105512\pi\) | ||||
0.945563 | + | 0.325440i | \(0.105512\pi\) | |||||||
\(368\) | 1.64575 | 0.0857907 | ||||||||
\(369\) | −43.7490 | −2.27748 | ||||||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.5830 | −0.548703 | ||||||||
\(373\) | 20.8745 | 1.08084 | 0.540421 | − | 0.841395i | \(-0.318265\pi\) | ||||
0.540421 | + | 0.841395i | \(0.318265\pi\) | |||||||
\(374\) | 6.00000 | 0.310253 | ||||||||
\(375\) | 31.7490 | 1.63951 | ||||||||
\(376\) | 2.70850 | 0.139680 | ||||||||
\(377\) | −31.4575 | −1.62014 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.06275 | 0.311422 | 0.155711 | − | 0.987803i | \(-0.450233\pi\) | ||||
0.155711 | + | 0.987803i | \(0.450233\pi\) | |||||||
\(380\) | 9.29150 | 0.476644 | ||||||||
\(381\) | −42.1660 | −2.16023 | ||||||||
\(382\) | 2.70850 | 0.138579 | ||||||||
\(383\) | −24.1033 | −1.23162 | −0.615810 | − | 0.787895i | \(-0.711171\pi\) | ||||
−0.615810 | + | 0.787895i | \(0.711171\pi\) | |||||||
\(384\) | 2.64575 | 0.135015 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.5203 | −1.29895 | ||||||||
\(387\) | −16.0000 | −0.813326 | ||||||||
\(388\) | 16.2915 | 0.827076 | ||||||||
\(389\) | 26.8118 | 1.35941 | 0.679705 | − | 0.733485i | \(-0.262108\pi\) | ||||
0.679705 | + | 0.733485i | \(0.262108\pi\) | |||||||
\(390\) | −21.7712 | −1.10243 | ||||||||
\(391\) | −9.87451 | −0.499375 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.3948 | 1.38188 | ||||||||
\(394\) | 12.8745 | 0.648608 | ||||||||
\(395\) | −4.35425 | −0.219086 | ||||||||
\(396\) | 4.00000 | 0.201008 | ||||||||
\(397\) | 11.1660 | 0.560406 | 0.280203 | − | 0.959941i | \(-0.409598\pi\) | ||||
0.280203 | + | 0.959941i | \(0.409598\pi\) | |||||||
\(398\) | 4.22876 | 0.211968 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.29150 | −0.114575 | ||||||||
\(401\) | 21.5830 | 1.07780 | 0.538902 | − | 0.842369i | \(-0.318839\pi\) | ||||
0.538902 | + | 0.842369i | \(0.318839\pi\) | |||||||
\(402\) | −31.5830 | −1.57522 | ||||||||
\(403\) | −20.0000 | −0.996271 | ||||||||
\(404\) | −3.00000 | −0.149256 | ||||||||
\(405\) | −8.22876 | −0.408890 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.64575 | 0.180713 | ||||||||
\(408\) | −15.8745 | −0.785905 | ||||||||
\(409\) | −3.06275 | −0.151443 | −0.0757215 | − | 0.997129i | \(-0.524126\pi\) | ||||
−0.0757215 | + | 0.997129i | \(0.524126\pi\) | |||||||
\(410\) | 18.0000 | 0.888957 | ||||||||
\(411\) | 34.0627 | 1.68019 | ||||||||
\(412\) | 2.93725 | 0.144708 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.58301 | −0.323537 | ||||||||
\(415\) | −4.45751 | −0.218811 | ||||||||
\(416\) | 5.00000 | 0.245145 | ||||||||
\(417\) | −10.5830 | −0.518252 | ||||||||
\(418\) | −5.64575 | −0.276143 | ||||||||
\(419\) | 9.87451 | 0.482401 | 0.241201 | − | 0.970475i | \(-0.422459\pi\) | ||||
0.241201 | + | 0.970475i | \(0.422459\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.16601 | 0.446724 | 0.223362 | − | 0.974736i | \(-0.428297\pi\) | ||||
0.223362 | + | 0.974736i | \(0.428297\pi\) | |||||||
\(422\) | −0.937254 | −0.0456248 | ||||||||
\(423\) | −10.8340 | −0.526767 | ||||||||
\(424\) | −1.64575 | −0.0799247 | ||||||||
\(425\) | 13.7490 | 0.666925 | ||||||||
\(426\) | 11.5203 | 0.558158 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.9373 | −0.528672 | ||||||||
\(429\) | 13.2288 | 0.638690 | ||||||||
\(430\) | 6.58301 | 0.317461 | ||||||||
\(431\) | 29.2288 | 1.40790 | 0.703950 | − | 0.710250i | \(-0.251418\pi\) | ||||
0.703950 | + | 0.710250i | \(0.251418\pi\) | |||||||
\(432\) | −2.64575 | −0.127294 | ||||||||
\(433\) | 16.0000 | 0.768911 | 0.384455 | − | 0.923144i | \(-0.374389\pi\) | ||||
0.384455 | + | 0.923144i | \(0.374389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −27.3948 | −1.31348 | ||||||||
\(436\) | −10.5830 | −0.506834 | ||||||||
\(437\) | 9.29150 | 0.444473 | ||||||||
\(438\) | −0.937254 | −0.0447837 | ||||||||
\(439\) | −3.93725 | −0.187915 | −0.0939574 | − | 0.995576i | \(-0.529952\pi\) | ||||
−0.0939574 | + | 0.995576i | \(0.529952\pi\) | |||||||
\(440\) | −1.64575 | −0.0784581 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30.0000 | −1.42695 | ||||||||
\(443\) | 34.4575 | 1.63713 | 0.818563 | − | 0.574417i | \(-0.194771\pi\) | ||||
0.818563 | + | 0.574417i | \(0.194771\pi\) | |||||||
\(444\) | −9.64575 | −0.457767 | ||||||||
\(445\) | −10.8340 | −0.513580 | ||||||||
\(446\) | −17.6458 | −0.835551 | ||||||||
\(447\) | 40.4575 | 1.91357 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.8745 | −1.03232 | −0.516161 | − | 0.856492i | \(-0.672639\pi\) | ||||
−0.516161 | + | 0.856492i | \(0.672639\pi\) | |||||||
\(450\) | 9.16601 | 0.432090 | ||||||||
\(451\) | −10.9373 | −0.515015 | ||||||||
\(452\) | −18.2915 | −0.860360 | ||||||||
\(453\) | 22.8745 | 1.07474 | ||||||||
\(454\) | −2.70850 | −0.127116 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.9373 | 0.699501 | ||||||||
\(457\) | 3.16601 | 0.148100 | 0.0740499 | − | 0.997255i | \(-0.476408\pi\) | ||||
0.0740499 | + | 0.997255i | \(0.476408\pi\) | |||||||
\(458\) | −16.0000 | −0.747631 | ||||||||
\(459\) | 15.8745 | 0.740959 | ||||||||
\(460\) | 2.70850 | 0.126284 | ||||||||
\(461\) | −10.1660 | −0.473478 | −0.236739 | − | 0.971573i | \(-0.576079\pi\) | ||||
−0.236739 | + | 0.971573i | \(0.576079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.4575 | 1.41548 | 0.707740 | − | 0.706473i | \(-0.249715\pi\) | ||||
0.707740 | + | 0.706473i | \(0.249715\pi\) | |||||||
\(464\) | 6.29150 | 0.292076 | ||||||||
\(465\) | −17.4170 | −0.807694 | ||||||||
\(466\) | −1.06275 | −0.0492308 | ||||||||
\(467\) | −21.2915 | −0.985253 | −0.492627 | − | 0.870241i | \(-0.663963\pi\) | ||||
−0.492627 | + | 0.870241i | \(0.663963\pi\) | |||||||
\(468\) | −20.0000 | −0.924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.45751 | 0.205610 | ||||||||
\(471\) | 56.0000 | 2.58034 | ||||||||
\(472\) | 4.64575 | 0.213838 | ||||||||
\(473\) | −4.00000 | −0.183920 | ||||||||
\(474\) | −7.00000 | −0.321521 | ||||||||
\(475\) | −12.9373 | −0.593602 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.58301 | 0.301415 | ||||||||
\(478\) | 17.2288 | 0.788025 | ||||||||
\(479\) | 10.0627 | 0.459779 | 0.229889 | − | 0.973217i | \(-0.426164\pi\) | ||||
0.229889 | + | 0.973217i | \(0.426164\pi\) | |||||||
\(480\) | 4.35425 | 0.198743 | ||||||||
\(481\) | −18.2288 | −0.831160 | ||||||||
\(482\) | −24.8118 | −1.13014 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 26.8118 | 1.21746 | ||||||||
\(486\) | −21.1660 | −0.960110 | ||||||||
\(487\) | −9.41699 | −0.426725 | −0.213362 | − | 0.976973i | \(-0.568441\pi\) | ||||
−0.213362 | + | 0.976973i | \(0.568441\pi\) | |||||||
\(488\) | 14.2915 | 0.646946 | ||||||||
\(489\) | −1.70850 | −0.0772609 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.2915 | 0.960872 | 0.480436 | − | 0.877030i | \(-0.340478\pi\) | ||||
0.480436 | + | 0.877030i | \(0.340478\pi\) | |||||||
\(492\) | 28.9373 | 1.30459 | ||||||||
\(493\) | −37.7490 | −1.70013 | ||||||||
\(494\) | 28.2288 | 1.27007 | ||||||||
\(495\) | 6.58301 | 0.295884 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.16601 | −0.321117 | ||||||||
\(499\) | −13.8745 | −0.621108 | −0.310554 | − | 0.950556i | \(-0.600515\pi\) | ||||
−0.310554 | + | 0.950556i | \(0.600515\pi\) | |||||||
\(500\) | −12.0000 | −0.536656 | ||||||||
\(501\) | −29.7085 | −1.32728 | ||||||||
\(502\) | −3.29150 | −0.146907 | ||||||||
\(503\) | 4.06275 | 0.181149 | 0.0905744 | − | 0.995890i | \(-0.471130\pi\) | ||||
0.0905744 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.93725 | −0.219705 | ||||||||
\(506\) | −1.64575 | −0.0731626 | ||||||||
\(507\) | −31.7490 | −1.41002 | ||||||||
\(508\) | 15.9373 | 0.707101 | ||||||||
\(509\) | 0.583005 | 0.0258413 | 0.0129206 | − | 0.999917i | \(-0.495887\pi\) | ||||
0.0129206 | + | 0.999917i | \(0.495887\pi\) | |||||||
\(510\) | −26.1255 | −1.15686 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −14.9373 | −0.659496 | ||||||||
\(514\) | −21.5830 | −0.951986 | ||||||||
\(515\) | 4.83399 | 0.213011 | ||||||||
\(516\) | 10.5830 | 0.465891 | ||||||||
\(517\) | −2.70850 | −0.119120 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.771243 | −0.0338538 | ||||||||
\(520\) | 8.22876 | 0.360855 | ||||||||
\(521\) | 33.8745 | 1.48407 | 0.742035 | − | 0.670362i | \(-0.233861\pi\) | ||||
0.742035 | + | 0.670362i | \(0.233861\pi\) | |||||||
\(522\) | −25.1660 | −1.10149 | ||||||||
\(523\) | 21.5203 | 0.941015 | 0.470508 | − | 0.882396i | \(-0.344071\pi\) | ||||
0.470508 | + | 0.882396i | \(0.344071\pi\) | |||||||
\(524\) | −10.3542 | −0.452327 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.9373 | −0.869306 | ||||||||
\(527\) | −24.0000 | −1.04546 | ||||||||
\(528\) | −2.64575 | −0.115142 | ||||||||
\(529\) | −20.2915 | −0.882239 | ||||||||
\(530\) | −2.70850 | −0.117650 | ||||||||
\(531\) | −18.5830 | −0.806434 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 54.6863 | 2.36873 | ||||||||
\(534\) | −17.4170 | −0.753707 | ||||||||
\(535\) | −18.0000 | −0.778208 | ||||||||
\(536\) | 11.9373 | 0.515611 | ||||||||
\(537\) | 52.7490 | 2.27629 | ||||||||
\(538\) | 5.41699 | 0.233543 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.35425 | −0.187377 | ||||||||
\(541\) | 2.29150 | 0.0985194 | 0.0492597 | − | 0.998786i | \(-0.484314\pi\) | ||||
0.0492597 | + | 0.998786i | \(0.484314\pi\) | |||||||
\(542\) | −2.06275 | −0.0886025 | ||||||||
\(543\) | −26.4575 | −1.13540 | ||||||||
\(544\) | 6.00000 | 0.257248 | ||||||||
\(545\) | −17.4170 | −0.746062 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.52026 | −0.407057 | −0.203528 | − | 0.979069i | \(-0.565241\pi\) | ||||
−0.203528 | + | 0.979069i | \(0.565241\pi\) | |||||||
\(548\) | −12.8745 | −0.549972 | ||||||||
\(549\) | −57.1660 | −2.43979 | ||||||||
\(550\) | 2.29150 | 0.0977100 | ||||||||
\(551\) | 35.5203 | 1.51321 | ||||||||
\(552\) | 4.35425 | 0.185329 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.2915 | 0.947075 | ||||||||
\(555\) | −15.8745 | −0.673835 | ||||||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | −31.7490 | −1.34525 | −0.672624 | − | 0.739984i | \(-0.734833\pi\) | ||||
−0.672624 | + | 0.739984i | \(0.734833\pi\) | |||||||
\(558\) | −16.0000 | −0.677334 | ||||||||
\(559\) | 20.0000 | 0.845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8745 | 0.670222 | ||||||||
\(562\) | 22.9373 | 0.967550 | ||||||||
\(563\) | −28.9373 | −1.21956 | −0.609780 | − | 0.792571i | \(-0.708742\pi\) | ||||
−0.609780 | + | 0.792571i | \(0.708742\pi\) | |||||||
\(564\) | 7.16601 | 0.301743 | ||||||||
\(565\) | −30.1033 | −1.26645 | ||||||||
\(566\) | −2.35425 | −0.0989565 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.35425 | −0.182700 | ||||||||
\(569\) | 1.16601 | 0.0488817 | 0.0244409 | − | 0.999701i | \(-0.492219\pi\) | ||||
0.0244409 | + | 0.999701i | \(0.492219\pi\) | |||||||
\(570\) | 24.5830 | 1.02967 | ||||||||
\(571\) | −29.0627 | −1.21624 | −0.608119 | − | 0.793846i | \(-0.708076\pi\) | ||||
−0.608119 | + | 0.793846i | \(0.708076\pi\) | |||||||
\(572\) | −5.00000 | −0.209061 | ||||||||
\(573\) | 7.16601 | 0.299364 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.77124 | −0.157272 | ||||||||
\(576\) | 4.00000 | 0.166667 | ||||||||
\(577\) | −27.4575 | −1.14307 | −0.571536 | − | 0.820577i | \(-0.693652\pi\) | ||||
−0.571536 | + | 0.820577i | \(0.693652\pi\) | |||||||
\(578\) | −19.0000 | −0.790296 | ||||||||
\(579\) | −67.5203 | −2.80605 | ||||||||
\(580\) | 10.3542 | 0.429937 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 43.1033 | 1.78669 | ||||||||
\(583\) | 1.64575 | 0.0681601 | ||||||||
\(584\) | 0.354249 | 0.0146589 | ||||||||
\(585\) | −32.9150 | −1.36087 | ||||||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | −7.93725 | −0.327606 | −0.163803 | − | 0.986493i | \(-0.552376\pi\) | ||||
−0.163803 | + | 0.986493i | \(0.552376\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.5830 | 0.930517 | ||||||||
\(590\) | 7.64575 | 0.314771 | ||||||||
\(591\) | 34.0627 | 1.40115 | ||||||||
\(592\) | 3.64575 | 0.149839 | ||||||||
\(593\) | −7.06275 | −0.290032 | −0.145016 | − | 0.989429i | \(-0.546323\pi\) | ||||
−0.145016 | + | 0.989429i | \(0.546323\pi\) | |||||||
\(594\) | 2.64575 | 0.108556 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.2915 | −0.626364 | ||||||||
\(597\) | 11.1882 | 0.457904 | ||||||||
\(598\) | 8.22876 | 0.336499 | ||||||||
\(599\) | 43.7490 | 1.78754 | 0.893768 | − | 0.448529i | \(-0.148052\pi\) | ||||
0.893768 | + | 0.448529i | \(0.148052\pi\) | |||||||
\(600\) | −6.06275 | −0.247511 | ||||||||
\(601\) | 3.41699 | 0.139382 | 0.0696911 | − | 0.997569i | \(-0.477799\pi\) | ||||
0.0696911 | + | 0.997569i | \(0.477799\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −47.7490 | −1.94449 | ||||||||
\(604\) | −8.64575 | −0.351791 | ||||||||
\(605\) | 1.64575 | 0.0669093 | ||||||||
\(606\) | −7.93725 | −0.322429 | ||||||||
\(607\) | −10.7085 | −0.434645 | −0.217322 | − | 0.976100i | \(-0.569732\pi\) | ||||
−0.217322 | + | 0.976100i | \(0.569732\pi\) | |||||||
\(608\) | −5.64575 | −0.228965 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23.5203 | 0.952307 | ||||||||
\(611\) | 13.5425 | 0.547870 | ||||||||
\(612\) | −24.0000 | −0.970143 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 22.2288 | 0.897080 | ||||||||
\(615\) | 47.6235 | 1.92037 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.70850 | −0.229815 | −0.114908 | − | 0.993376i | \(-0.536657\pi\) | ||||
−0.114908 | + | 0.993376i | \(0.536657\pi\) | |||||||
\(618\) | 7.77124 | 0.312605 | ||||||||
\(619\) | −13.4170 | −0.539275 | −0.269637 | − | 0.962962i | \(-0.586904\pi\) | ||||
−0.269637 | + | 0.962962i | \(0.586904\pi\) | |||||||
\(620\) | 6.58301 | 0.264380 | ||||||||
\(621\) | −4.35425 | −0.174730 | ||||||||
\(622\) | 1.06275 | 0.0426122 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 13.2288 | 0.529574 | ||||||||
\(625\) | −8.29150 | −0.331660 | ||||||||
\(626\) | 23.5830 | 0.942566 | ||||||||
\(627\) | −14.9373 | −0.596536 | ||||||||
\(628\) | −21.1660 | −0.844616 | ||||||||
\(629\) | −21.8745 | −0.872194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8118 | −0.510028 | −0.255014 | − | 0.966937i | \(-0.582080\pi\) | ||||
−0.255014 | + | 0.966937i | \(0.582080\pi\) | |||||||
\(632\) | 2.64575 | 0.105242 | ||||||||
\(633\) | −2.47974 | −0.0985608 | ||||||||
\(634\) | −12.0000 | −0.476581 | ||||||||
\(635\) | 26.2288 | 1.04086 | ||||||||
\(636\) | −4.35425 | −0.172657 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.29150 | −0.249083 | ||||||||
\(639\) | 17.4170 | 0.689006 | ||||||||
\(640\) | −1.64575 | −0.0650540 | ||||||||
\(641\) | 12.8745 | 0.508512 | 0.254256 | − | 0.967137i | \(-0.418169\pi\) | ||||
0.254256 | + | 0.967137i | \(0.418169\pi\) | |||||||
\(642\) | −28.9373 | −1.14206 | ||||||||
\(643\) | 30.5203 | 1.20360 | 0.601801 | − | 0.798646i | \(-0.294450\pi\) | ||||
0.601801 | + | 0.798646i | \(0.294450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.4170 | 0.685793 | ||||||||
\(646\) | 33.8745 | 1.33277 | ||||||||
\(647\) | 8.81176 | 0.346426 | 0.173213 | − | 0.984884i | \(-0.444585\pi\) | ||||
0.173213 | + | 0.984884i | \(0.444585\pi\) | |||||||
\(648\) | 5.00000 | 0.196419 | ||||||||
\(649\) | −4.64575 | −0.182362 | ||||||||
\(650\) | −11.4575 | −0.449401 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.645751 | 0.0252896 | ||||||||
\(653\) | 7.64575 | 0.299201 | 0.149601 | − | 0.988746i | \(-0.452201\pi\) | ||||
0.149601 | + | 0.988746i | \(0.452201\pi\) | |||||||
\(654\) | −28.0000 | −1.09489 | ||||||||
\(655\) | −17.0405 | −0.665828 | ||||||||
\(656\) | −10.9373 | −0.427028 | ||||||||
\(657\) | −1.41699 | −0.0552822 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.58301 | −0.256437 | −0.128219 | − | 0.991746i | \(-0.540926\pi\) | ||||
−0.128219 | + | 0.991746i | \(0.540926\pi\) | |||||||
\(660\) | −4.35425 | −0.169489 | ||||||||
\(661\) | −7.41699 | −0.288488 | −0.144244 | − | 0.989542i | \(-0.546075\pi\) | ||||
−0.144244 | + | 0.989542i | \(0.546075\pi\) | |||||||
\(662\) | 20.6458 | 0.802420 | ||||||||
\(663\) | −79.3725 | −3.08257 | ||||||||
\(664\) | 2.70850 | 0.105110 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.5830 | −0.565080 | ||||||||
\(667\) | 10.3542 | 0.400918 | ||||||||
\(668\) | 11.2288 | 0.434454 | ||||||||
\(669\) | −46.6863 | −1.80500 | ||||||||
\(670\) | 19.6458 | 0.758982 | ||||||||
\(671\) | −14.2915 | −0.551717 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.937254 | 0.0361285 | 0.0180642 | − | 0.999837i | \(-0.494250\pi\) | ||||
0.0180642 | + | 0.999837i | \(0.494250\pi\) | |||||||
\(674\) | −9.06275 | −0.349084 | ||||||||
\(675\) | 6.06275 | 0.233355 | ||||||||
\(676\) | 12.0000 | 0.461538 | ||||||||
\(677\) | 33.8745 | 1.30190 | 0.650952 | − | 0.759119i | \(-0.274370\pi\) | ||||
0.650952 | + | 0.759119i | \(0.274370\pi\) | |||||||
\(678\) | −48.3948 | −1.85859 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.87451 | 0.378670 | ||||||||
\(681\) | −7.16601 | −0.274602 | ||||||||
\(682\) | −4.00000 | −0.153168 | ||||||||
\(683\) | 1.93725 | 0.0741270 | 0.0370635 | − | 0.999313i | \(-0.488200\pi\) | ||||
0.0370635 | + | 0.999313i | \(0.488200\pi\) | |||||||
\(684\) | 22.5830 | 0.863483 | ||||||||
\(685\) | −21.1882 | −0.809561 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −42.3320 | −1.61507 | ||||||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | −8.22876 | −0.313491 | ||||||||
\(690\) | 7.16601 | 0.272805 | ||||||||
\(691\) | 45.2288 | 1.72058 | 0.860291 | − | 0.509802i | \(-0.170282\pi\) | ||||
0.860291 | + | 0.509802i | \(0.170282\pi\) | |||||||
\(692\) | 0.291503 | 0.0110813 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.8118 | 0.790004 | ||||||||
\(695\) | 6.58301 | 0.249708 | ||||||||
\(696\) | 16.6458 | 0.630956 | ||||||||
\(697\) | 65.6235 | 2.48567 | ||||||||
\(698\) | −1.87451 | −0.0709512 | ||||||||
\(699\) | −2.81176 | −0.106351 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.8745 | 0.939497 | 0.469749 | − | 0.882800i | \(-0.344345\pi\) | ||||
0.469749 | + | 0.882800i | \(0.344345\pi\) | |||||||
\(702\) | −13.2288 | −0.499287 | ||||||||
\(703\) | 20.5830 | 0.776303 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 11.7935 | 0.444168 | ||||||||
\(706\) | 7.16601 | 0.269696 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.2915 | 0.461943 | ||||||||
\(709\) | 40.8118 | 1.53272 | 0.766359 | − | 0.642413i | \(-0.222066\pi\) | ||||
0.766359 | + | 0.642413i | \(0.222066\pi\) | |||||||
\(710\) | −7.16601 | −0.268936 | ||||||||
\(711\) | −10.5830 | −0.396894 | ||||||||
\(712\) | 6.58301 | 0.246709 | ||||||||
\(713\) | 6.58301 | 0.246535 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.22876 | −0.307738 | ||||||||
\(716\) | −19.9373 | −0.745090 | ||||||||
\(717\) | 45.5830 | 1.70233 | ||||||||
\(718\) | 25.9373 | 0.967970 | ||||||||
\(719\) | −27.8745 | −1.03954 | −0.519772 | − | 0.854305i | \(-0.673983\pi\) | ||||
−0.519772 | + | 0.854305i | \(0.673983\pi\) | |||||||
\(720\) | 6.58301 | 0.245334 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.8745 | −0.479140 | ||||||||
\(723\) | −65.6458 | −2.44139 | ||||||||
\(724\) | 10.0000 | 0.371647 | ||||||||
\(725\) | −14.4170 | −0.535434 | ||||||||
\(726\) | 2.64575 | 0.0981930 | ||||||||
\(727\) | 6.70850 | 0.248804 | 0.124402 | − | 0.992232i | \(-0.460299\pi\) | ||||
0.124402 | + | 0.992232i | \(0.460299\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.0000 | −1.51852 | ||||||||
\(730\) | 0.583005 | 0.0215780 | ||||||||
\(731\) | 24.0000 | 0.887672 | ||||||||
\(732\) | 37.8118 | 1.39756 | ||||||||
\(733\) | 11.4575 | 0.423193 | 0.211596 | − | 0.977357i | \(-0.432134\pi\) | ||||
0.211596 | + | 0.977357i | \(0.432134\pi\) | |||||||
\(734\) | −36.2288 | −1.33723 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.64575 | −0.0606632 | ||||||||
\(737\) | −11.9373 | −0.439714 | ||||||||
\(738\) | 43.7490 | 1.61042 | ||||||||
\(739\) | 23.8745 | 0.878238 | 0.439119 | − | 0.898429i | \(-0.355291\pi\) | ||||
0.439119 | + | 0.898429i | \(0.355291\pi\) | |||||||
\(740\) | 6.00000 | 0.220564 | ||||||||
\(741\) | 74.6863 | 2.74367 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.2915 | −1.66158 | −0.830792 | − | 0.556583i | \(-0.812112\pi\) | ||||
−0.830792 | + | 0.556583i | \(0.812112\pi\) | |||||||
\(744\) | 10.5830 | 0.387992 | ||||||||
\(745\) | −25.1660 | −0.922011 | ||||||||
\(746\) | −20.8745 | −0.764270 | ||||||||
\(747\) | −10.8340 | −0.396395 | ||||||||
\(748\) | −6.00000 | −0.219382 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −31.7490 | −1.15931 | ||||||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | −2.70850 | −0.0987687 | ||||||||
\(753\) | −8.70850 | −0.317355 | ||||||||
\(754\) | 31.4575 | 1.14562 | ||||||||
\(755\) | −14.2288 | −0.517837 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.1660 | −0.841983 | −0.420991 | − | 0.907065i | \(-0.638318\pi\) | ||||
−0.420991 | + | 0.907065i | \(0.638318\pi\) | |||||||
\(758\) | −6.06275 | −0.220209 | ||||||||
\(759\) | −4.35425 | −0.158049 | ||||||||
\(760\) | −9.29150 | −0.337038 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 42.1660 | 1.52751 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.70850 | −0.0979900 | ||||||||
\(765\) | −39.4980 | −1.42805 | ||||||||
\(766\) | 24.1033 | 0.870886 | ||||||||
\(767\) | 23.2288 | 0.838742 | ||||||||
\(768\) | −2.64575 | −0.0954703 | ||||||||
\(769\) | −27.1660 | −0.979631 | −0.489816 | − | 0.871826i | \(-0.662936\pi\) | ||||
−0.489816 | + | 0.871826i | \(0.662936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −57.1033 | −2.05652 | ||||||||
\(772\) | 25.5203 | 0.918494 | ||||||||
\(773\) | 18.5830 | 0.668384 | 0.334192 | − | 0.942505i | \(-0.391537\pi\) | ||||
0.334192 | + | 0.942505i | \(0.391537\pi\) | |||||||
\(774\) | 16.0000 | 0.575108 | ||||||||
\(775\) | −9.16601 | −0.329253 | ||||||||
\(776\) | −16.2915 | −0.584831 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.8118 | −0.961248 | ||||||||
\(779\) | −61.7490 | −2.21239 | ||||||||
\(780\) | 21.7712 | 0.779536 | ||||||||
\(781\) | 4.35425 | 0.155807 | ||||||||
\(782\) | 9.87451 | 0.353112 | ||||||||
\(783\) | −16.6458 | −0.594871 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.8340 | −1.24328 | ||||||||
\(786\) | −27.3948 | −0.977139 | ||||||||
\(787\) | −46.8118 | −1.66866 | −0.834330 | − | 0.551266i | \(-0.814145\pi\) | ||||
−0.834330 | + | 0.551266i | \(0.814145\pi\) | |||||||
\(788\) | −12.8745 | −0.458635 | ||||||||
\(789\) | −52.7490 | −1.87791 | ||||||||
\(790\) | 4.35425 | 0.154917 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.00000 | −0.142134 | ||||||||
\(793\) | 71.4575 | 2.53753 | ||||||||
\(794\) | −11.1660 | −0.396267 | ||||||||
\(795\) | −7.16601 | −0.254152 | ||||||||
\(796\) | −4.22876 | −0.149884 | ||||||||
\(797\) | −7.16601 | −0.253833 | −0.126917 | − | 0.991913i | \(-0.540508\pi\) | ||||
−0.126917 | + | 0.991913i | \(0.540508\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.2510 | 0.574918 | ||||||||
\(800\) | 2.29150 | 0.0810169 | ||||||||
\(801\) | −26.3320 | −0.930396 | ||||||||
\(802\) | −21.5830 | −0.762122 | ||||||||
\(803\) | −0.354249 | −0.0125012 | ||||||||
\(804\) | 31.5830 | 1.11385 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.0000 | 0.704470 | ||||||||
\(807\) | 14.3320 | 0.504511 | ||||||||
\(808\) | 3.00000 | 0.105540 | ||||||||
\(809\) | 29.4170 | 1.03425 | 0.517123 | − | 0.855911i | \(-0.327003\pi\) | ||||
0.517123 | + | 0.855911i | \(0.327003\pi\) | |||||||
\(810\) | 8.22876 | 0.289129 | ||||||||
\(811\) | 35.7490 | 1.25532 | 0.627659 | − | 0.778489i | \(-0.284013\pi\) | ||||
0.627659 | + | 0.778489i | \(0.284013\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.45751 | −0.191403 | ||||||||
\(814\) | −3.64575 | −0.127784 | ||||||||
\(815\) | 1.06275 | 0.0372264 | ||||||||
\(816\) | 15.8745 | 0.555719 | ||||||||
\(817\) | −22.5830 | −0.790079 | ||||||||
\(818\) | 3.06275 | 0.107086 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.0000 | −0.628587 | ||||||||
\(821\) | −18.2915 | −0.638378 | −0.319189 | − | 0.947691i | \(-0.603410\pi\) | ||||
−0.319189 | + | 0.947691i | \(0.603410\pi\) | |||||||
\(822\) | −34.0627 | −1.18807 | ||||||||
\(823\) | −12.1255 | −0.422668 | −0.211334 | − | 0.977414i | \(-0.567781\pi\) | ||||
−0.211334 | + | 0.977414i | \(0.567781\pi\) | |||||||
\(824\) | −2.93725 | −0.102324 | ||||||||
\(825\) | 6.06275 | 0.211078 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.3948 | 1.16125 | 0.580625 | − | 0.814171i | \(-0.302808\pi\) | ||||
0.580625 | + | 0.814171i | \(0.302808\pi\) | |||||||
\(828\) | 6.58301 | 0.228775 | ||||||||
\(829\) | 25.3948 | 0.881997 | 0.440998 | − | 0.897508i | \(-0.354624\pi\) | ||||
0.440998 | + | 0.897508i | \(0.354624\pi\) | |||||||
\(830\) | 4.45751 | 0.154723 | ||||||||
\(831\) | 58.9778 | 2.04592 | ||||||||
\(832\) | −5.00000 | −0.173344 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.5830 | 0.366460 | ||||||||
\(835\) | 18.4797 | 0.639518 | ||||||||
\(836\) | 5.64575 | 0.195262 | ||||||||
\(837\) | −10.5830 | −0.365802 | ||||||||
\(838\) | −9.87451 | −0.341109 | ||||||||
\(839\) | 3.87451 | 0.133763 | 0.0668814 | − | 0.997761i | \(-0.478695\pi\) | ||||
0.0668814 | + | 0.997761i | \(0.478695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.5830 | 0.364931 | ||||||||
\(842\) | −9.16601 | −0.315882 | ||||||||
\(843\) | 60.6863 | 2.09015 | ||||||||
\(844\) | 0.937254 | 0.0322616 | ||||||||
\(845\) | 19.7490 | 0.679387 | ||||||||
\(846\) | 10.8340 | 0.372480 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.64575 | 0.0565153 | ||||||||
\(849\) | −6.22876 | −0.213770 | ||||||||
\(850\) | −13.7490 | −0.471587 | ||||||||
\(851\) | 6.00000 | 0.205677 | ||||||||
\(852\) | −11.5203 | −0.394678 | ||||||||
\(853\) | −39.1660 | −1.34102 | −0.670509 | − | 0.741901i | \(-0.733924\pi\) | ||||
−0.670509 | + | 0.741901i | \(0.733924\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 37.1660 | 1.27105 | ||||||||
\(856\) | 10.9373 | 0.373828 | ||||||||
\(857\) | −36.0000 | −1.22974 | −0.614868 | − | 0.788630i | \(-0.710791\pi\) | ||||
−0.614868 | + | 0.788630i | \(0.710791\pi\) | |||||||
\(858\) | −13.2288 | −0.451622 | ||||||||
\(859\) | 9.81176 | 0.334773 | 0.167386 | − | 0.985891i | \(-0.446467\pi\) | ||||
0.167386 | + | 0.985891i | \(0.446467\pi\) | |||||||
\(860\) | −6.58301 | −0.224479 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.2288 | −0.995535 | ||||||||
\(863\) | −12.4797 | −0.424815 | −0.212408 | − | 0.977181i | \(-0.568130\pi\) | ||||
−0.212408 | + | 0.977181i | \(0.568130\pi\) | |||||||
\(864\) | 2.64575 | 0.0900103 | ||||||||
\(865\) | 0.479741 | 0.0163117 | ||||||||
\(866\) | −16.0000 | −0.543702 | ||||||||
\(867\) | −50.2693 | −1.70723 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.64575 | −0.0897510 | ||||||||
\(870\) | 27.3948 | 0.928770 | ||||||||
\(871\) | 59.6863 | 2.02239 | ||||||||
\(872\) | 10.5830 | 0.358386 | ||||||||
\(873\) | 65.1660 | 2.20554 | ||||||||
\(874\) | −9.29150 | −0.314290 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.937254 | 0.0316669 | ||||||||
\(877\) | −22.8745 | −0.772417 | −0.386209 | − | 0.922411i | \(-0.626216\pi\) | ||||
−0.386209 | + | 0.922411i | \(0.626216\pi\) | |||||||
\(878\) | 3.93725 | 0.132876 | ||||||||
\(879\) | 31.7490 | 1.07087 | ||||||||
\(880\) | 1.64575 | 0.0554783 | ||||||||
\(881\) | 24.8745 | 0.838043 | 0.419022 | − | 0.907976i | \(-0.362373\pi\) | ||||
0.419022 | + | 0.907976i | \(0.362373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.9373 | 0.738247 | 0.369124 | − | 0.929380i | \(-0.379658\pi\) | ||||
0.369124 | + | 0.929380i | \(0.379658\pi\) | |||||||
\(884\) | 30.0000 | 1.00901 | ||||||||
\(885\) | 20.2288 | 0.679982 | ||||||||
\(886\) | −34.4575 | −1.15762 | ||||||||
\(887\) | −45.1033 | −1.51442 | −0.757210 | − | 0.653172i | \(-0.773438\pi\) | ||||
−0.757210 | + | 0.653172i | \(0.773438\pi\) | |||||||
\(888\) | 9.64575 | 0.323690 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.8340 | 0.363156 | ||||||||
\(891\) | −5.00000 | −0.167506 | ||||||||
\(892\) | 17.6458 | 0.590823 | ||||||||
\(893\) | −15.2915 | −0.511711 | ||||||||
\(894\) | −40.4575 | −1.35310 | ||||||||
\(895\) | −32.8118 | −1.09678 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.7712 | 0.726921 | ||||||||
\(898\) | 21.8745 | 0.729962 | ||||||||
\(899\) | 25.1660 | 0.839333 | ||||||||
\(900\) | −9.16601 | −0.305534 | ||||||||
\(901\) | −9.87451 | −0.328968 | ||||||||
\(902\) | 10.9373 | 0.364171 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.2915 | 0.608366 | ||||||||
\(905\) | 16.4575 | 0.547066 | ||||||||
\(906\) | −22.8745 | −0.759955 | ||||||||
\(907\) | 42.4575 | 1.40978 | 0.704889 | − | 0.709317i | \(-0.250997\pi\) | ||||
0.704889 | + | 0.709317i | \(0.250997\pi\) | |||||||
\(908\) | 2.70850 | 0.0898846 | ||||||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.29150 | 0.307841 | 0.153921 | − | 0.988083i | \(-0.450810\pi\) | ||||
0.153921 | + | 0.988083i | \(0.450810\pi\) | |||||||
\(912\) | −14.9373 | −0.494622 | ||||||||
\(913\) | −2.70850 | −0.0896382 | ||||||||
\(914\) | −3.16601 | −0.104722 | ||||||||
\(915\) | 62.2288 | 2.05722 | ||||||||
\(916\) | 16.0000 | 0.528655 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −15.8745 | −0.523937 | ||||||||
\(919\) | −24.7085 | −0.815058 | −0.407529 | − | 0.913192i | \(-0.633609\pi\) | ||||
−0.407529 | + | 0.913192i | \(0.633609\pi\) | |||||||
\(920\) | −2.70850 | −0.0892965 | ||||||||
\(921\) | 58.8118 | 1.93791 | ||||||||
\(922\) | 10.1660 | 0.334800 | ||||||||
\(923\) | −21.7712 | −0.716609 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.35425 | −0.274686 | ||||||||
\(926\) | −30.4575 | −1.00090 | ||||||||
\(927\) | 11.7490 | 0.385888 | ||||||||
\(928\) | −6.29150 | −0.206529 | ||||||||
\(929\) | −14.4170 | −0.473006 | −0.236503 | − | 0.971631i | \(-0.576001\pi\) | ||||
−0.236503 | + | 0.971631i | \(0.576001\pi\) | |||||||
\(930\) | 17.4170 | 0.571126 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.06275 | 0.0348114 | ||||||||
\(933\) | 2.81176 | 0.0920529 | ||||||||
\(934\) | 21.2915 | 0.696679 | ||||||||
\(935\) | −9.87451 | −0.322931 | ||||||||
\(936\) | 20.0000 | 0.653720 | ||||||||
\(937\) | −32.6863 | −1.06781 | −0.533907 | − | 0.845543i | \(-0.679277\pi\) | ||||
−0.533907 | + | 0.845543i | \(0.679277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.3948 | 2.03618 | ||||||||
\(940\) | −4.45751 | −0.145388 | ||||||||
\(941\) | −50.6235 | −1.65028 | −0.825140 | − | 0.564929i | \(-0.808904\pi\) | ||||
−0.825140 | + | 0.564929i | \(0.808904\pi\) | |||||||
\(942\) | −56.0000 | −1.82458 | ||||||||
\(943\) | −18.0000 | −0.586161 | ||||||||
\(944\) | −4.64575 | −0.151206 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | −2.12549 | −0.0690692 | −0.0345346 | − | 0.999404i | \(-0.510995\pi\) | ||||
−0.0345346 | + | 0.999404i | \(0.510995\pi\) | |||||||
\(948\) | 7.00000 | 0.227349 | ||||||||
\(949\) | 1.77124 | 0.0574970 | ||||||||
\(950\) | 12.9373 | 0.419740 | ||||||||
\(951\) | −31.7490 | −1.02953 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.5203 | 0.373178 | 0.186589 | − | 0.982438i | \(-0.440257\pi\) | ||||
0.186589 | + | 0.982438i | \(0.440257\pi\) | |||||||
\(954\) | −6.58301 | −0.213133 | ||||||||
\(955\) | −4.45751 | −0.144242 | ||||||||
\(956\) | −17.2288 | −0.557218 | ||||||||
\(957\) | −16.6458 | −0.538081 | ||||||||
\(958\) | −10.0627 | −0.325113 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.35425 | −0.140533 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 18.2288 | 0.587719 | ||||||||
\(963\) | −43.7490 | −1.40979 | ||||||||
\(964\) | 24.8118 | 0.799133 | ||||||||
\(965\) | 42.0000 | 1.35203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.3320 | 1.87583 | 0.937916 | − | 0.346863i | \(-0.112753\pi\) | ||||
0.937916 | + | 0.346863i | \(0.112753\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 89.6235 | 2.87912 | ||||||||
\(970\) | −26.8118 | −0.860874 | ||||||||
\(971\) | 10.0627 | 0.322929 | 0.161464 | − | 0.986879i | \(-0.448378\pi\) | ||||
0.161464 | + | 0.986879i | \(0.448378\pi\) | |||||||
\(972\) | 21.1660 | 0.678900 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.41699 | 0.301740 | ||||||||
\(975\) | −30.3137 | −0.970816 | ||||||||
\(976\) | −14.2915 | −0.457460 | ||||||||
\(977\) | −16.4575 | −0.526522 | −0.263261 | − | 0.964725i | \(-0.584798\pi\) | ||||
−0.263261 | + | 0.964725i | \(0.584798\pi\) | |||||||
\(978\) | 1.70850 | 0.0546317 | ||||||||
\(979\) | −6.58301 | −0.210394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.3320 | −1.35156 | ||||||||
\(982\) | −21.2915 | −0.679439 | ||||||||
\(983\) | 26.7085 | 0.851869 | 0.425934 | − | 0.904754i | \(-0.359945\pi\) | ||||
0.425934 | + | 0.904754i | \(0.359945\pi\) | |||||||
\(984\) | −28.9373 | −0.922486 | ||||||||
\(985\) | −21.1882 | −0.675113 | ||||||||
\(986\) | 37.7490 | 1.20217 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −28.2288 | −0.898076 | ||||||||
\(989\) | −6.58301 | −0.209327 | ||||||||
\(990\) | −6.58301 | −0.209222 | ||||||||
\(991\) | −22.6863 | −0.720653 | −0.360327 | − | 0.932826i | \(-0.617335\pi\) | ||||
−0.360327 | + | 0.932826i | \(0.617335\pi\) | |||||||
\(992\) | −4.00000 | −0.127000 | ||||||||
\(993\) | 54.6235 | 1.73343 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.95948 | −0.220630 | ||||||||
\(996\) | 7.16601 | 0.227064 | ||||||||
\(997\) | 21.4170 | 0.678283 | 0.339142 | − | 0.940735i | \(-0.389863\pi\) | ||||
0.339142 | + | 0.940735i | \(0.389863\pi\) | |||||||
\(998\) | 13.8745 | 0.439190 | ||||||||
\(999\) | −9.64575 | −0.305178 |
(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 | 1078.2.a.n.1.1 | 2 | ||
3.2 | odd | 2 | 9702.2.a.dr.1.1 | 2 | |||
4.3 | odd | 2 | 8624.2.a.bk.1.2 | 2 | |||
7.2 | even | 3 | 1078.2.e.v.67.2 | 4 | |||
7.3 | odd | 6 | 154.2.e.f.23.1 | ✓ | 4 | ||
7.4 | even | 3 | 1078.2.e.v.177.2 | 4 | |||
7.5 | odd | 6 | 154.2.e.f.67.1 | yes | 4 | ||
7.6 | odd | 2 | 1078.2.a.s.1.2 | 2 | |||
21.5 | even | 6 | 1386.2.k.s.991.1 | 4 | |||
21.17 | even | 6 | 1386.2.k.s.793.1 | 4 | |||
21.20 | even | 2 | 9702.2.a.cz.1.2 | 2 | |||
28.3 | even | 6 | 1232.2.q.g.177.2 | 4 | |||
28.19 | even | 6 | 1232.2.q.g.529.2 | 4 | |||
28.27 | even | 2 | 8624.2.a.ca.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.f.23.1 | ✓ | 4 | 7.3 | odd | 6 | ||
154.2.e.f.67.1 | yes | 4 | 7.5 | odd | 6 | ||
1078.2.a.n.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1078.2.a.s.1.2 | 2 | 7.6 | odd | 2 | |||
1078.2.e.v.67.2 | 4 | 7.2 | even | 3 | |||
1078.2.e.v.177.2 | 4 | 7.4 | even | 3 | |||
1232.2.q.g.177.2 | 4 | 28.3 | even | 6 | |||
1232.2.q.g.529.2 | 4 | 28.19 | even | 6 | |||
1386.2.k.s.793.1 | 4 | 21.17 | even | 6 | |||
1386.2.k.s.991.1 | 4 | 21.5 | even | 6 | |||
8624.2.a.bk.1.2 | 2 | 4.3 | odd | 2 | |||
8624.2.a.ca.1.1 | 2 | 28.27 | even | 2 | |||
9702.2.a.cz.1.2 | 2 | 21.20 | even | 2 | |||
9702.2.a.dr.1.1 | 2 | 3.2 | odd | 2 |