Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1155.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.58874\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.58874 | 1.83051 | 0.915257 | − | 0.402871i | \(-0.131988\pi\) | ||||
0.915257 | + | 0.402871i | \(0.131988\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.70156 | 2.35078 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.58874 | 1.05685 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 6.99364 | 2.47262 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.58874 | −0.818631 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 4.70156 | 1.35722 | ||||||||
\(13\) | 6.40490 | 1.77640 | 0.888200 | − | 0.459458i | \(-0.151956\pi\) | ||||
0.888200 | + | 0.459458i | \(0.151956\pi\) | |||||||
\(14\) | −2.58874 | −0.691869 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 8.70156 | 2.17539 | ||||||||
\(17\) | −3.70156 | −0.897761 | −0.448880 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448880 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(18\) | 2.58874 | 0.610171 | ||||||||
\(19\) | 7.24672 | 1.66251 | 0.831255 | − | 0.555891i | \(-0.187623\pi\) | ||||
0.831255 | + | 0.555891i | \(0.187623\pi\) | |||||||
\(20\) | −4.70156 | −1.05130 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −2.58874 | −0.551921 | ||||||||
\(23\) | −7.33388 | −1.52922 | −0.764610 | − | 0.644493i | \(-0.777068\pi\) | ||||
−0.764610 | + | 0.644493i | \(0.777068\pi\) | |||||||
\(24\) | 6.99364 | 1.42757 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 16.5806 | 3.25172 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.70156 | −0.888512 | ||||||||
\(29\) | −8.10646 | −1.50533 | −0.752666 | − | 0.658403i | \(-0.771232\pi\) | ||||
−0.752666 | + | 0.658403i | \(0.771232\pi\) | |||||||
\(30\) | −2.58874 | −0.472637 | ||||||||
\(31\) | 6.77258 | 1.21639 | 0.608195 | − | 0.793787i | \(-0.291894\pi\) | ||||
0.608195 | + | 0.793787i | \(0.291894\pi\) | |||||||
\(32\) | 8.53879 | 1.50946 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −9.58237 | −1.64336 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 4.70156 | 0.783594 | ||||||||
\(37\) | −3.95005 | −0.649385 | −0.324692 | − | 0.945820i | \(-0.605261\pi\) | ||||
−0.324692 | + | 0.945820i | \(0.605261\pi\) | |||||||
\(38\) | 18.7598 | 3.04325 | ||||||||
\(39\) | 6.40490 | 1.02560 | ||||||||
\(40\) | −6.99364 | −1.10579 | ||||||||
\(41\) | −2.31773 | −0.361969 | −0.180984 | − | 0.983486i | \(-0.557928\pi\) | ||||
−0.180984 | + | 0.983486i | \(0.557928\pi\) | |||||||
\(42\) | −2.58874 | −0.399451 | ||||||||
\(43\) | −7.65161 | −1.16686 | −0.583430 | − | 0.812163i | \(-0.698290\pi\) | ||||
−0.583430 | + | 0.812163i | \(0.698290\pi\) | |||||||
\(44\) | −4.70156 | −0.708787 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −18.9855 | −2.79926 | ||||||||
\(47\) | 1.45307 | 0.211952 | 0.105976 | − | 0.994369i | \(-0.466203\pi\) | ||||
0.105976 | + | 0.994369i | \(0.466203\pi\) | |||||||
\(48\) | 8.70156 | 1.25596 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.58874 | 0.366103 | ||||||||
\(51\) | −3.70156 | −0.518322 | ||||||||
\(52\) | 30.1130 | 4.17593 | ||||||||
\(53\) | 9.10823 | 1.25111 | 0.625556 | − | 0.780179i | \(-0.284872\pi\) | ||||
0.625556 | + | 0.780179i | \(0.284872\pi\) | |||||||
\(54\) | 2.58874 | 0.352283 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −6.99364 | −0.934564 | ||||||||
\(57\) | 7.24672 | 0.959851 | ||||||||
\(58\) | −20.9855 | −2.75553 | ||||||||
\(59\) | −2.92898 | −0.381321 | −0.190661 | − | 0.981656i | \(-0.561063\pi\) | ||||
−0.190661 | + | 0.981656i | \(0.561063\pi\) | |||||||
\(60\) | −4.70156 | −0.606969 | ||||||||
\(61\) | −8.42419 | −1.07861 | −0.539304 | − | 0.842111i | \(-0.681312\pi\) | ||||
−0.539304 | + | 0.842111i | \(0.681312\pi\) | |||||||
\(62\) | 17.5324 | 2.22662 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 4.70156 | 0.587695 | ||||||||
\(65\) | −6.40490 | −0.794430 | ||||||||
\(66\) | −2.58874 | −0.318652 | ||||||||
\(67\) | −8.72263 | −1.06564 | −0.532819 | − | 0.846229i | \(-0.678868\pi\) | ||||
−0.532819 | + | 0.846229i | \(0.678868\pi\) | |||||||
\(68\) | −17.4031 | −2.11044 | ||||||||
\(69\) | −7.33388 | −0.882896 | ||||||||
\(70\) | 2.58874 | 0.309413 | ||||||||
\(71\) | −4.40490 | −0.522765 | −0.261383 | − | 0.965235i | \(-0.584178\pi\) | ||||
−0.261383 | + | 0.965235i | \(0.584178\pi\) | |||||||
\(72\) | 6.99364 | 0.824208 | ||||||||
\(73\) | 3.40667 | 0.398721 | 0.199360 | − | 0.979926i | \(-0.436114\pi\) | ||||
0.199360 | + | 0.979926i | \(0.436114\pi\) | |||||||
\(74\) | −10.2256 | −1.18871 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 34.0709 | 3.90820 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 16.5806 | 1.87738 | ||||||||
\(79\) | 4.40490 | 0.495590 | 0.247795 | − | 0.968813i | \(-0.420294\pi\) | ||||
0.247795 | + | 0.968813i | \(0.420294\pi\) | |||||||
\(80\) | −8.70156 | −0.972864 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | −8.96620 | −0.984169 | −0.492084 | − | 0.870548i | \(-0.663765\pi\) | ||||
−0.492084 | + | 0.870548i | \(0.663765\pi\) | |||||||
\(84\) | −4.70156 | −0.512982 | ||||||||
\(85\) | 3.70156 | 0.401491 | ||||||||
\(86\) | −19.8080 | −2.13595 | ||||||||
\(87\) | −8.10646 | −0.869104 | ||||||||
\(88\) | −6.99364 | −0.745524 | ||||||||
\(89\) | 0.206355 | 0.0218736 | 0.0109368 | − | 0.999940i | \(-0.496519\pi\) | ||||
0.0109368 | + | 0.999940i | \(0.496519\pi\) | |||||||
\(90\) | −2.58874 | −0.272877 | ||||||||
\(91\) | −6.40490 | −0.671416 | ||||||||
\(92\) | −34.4807 | −3.59486 | ||||||||
\(93\) | 6.77258 | 0.702284 | ||||||||
\(94\) | 3.76162 | 0.387982 | ||||||||
\(95\) | −7.24672 | −0.743497 | ||||||||
\(96\) | 8.53879 | 0.871487 | ||||||||
\(97\) | −13.9644 | −1.41787 | −0.708936 | − | 0.705272i | \(-0.750825\pi\) | ||||
−0.708936 | + | 0.705272i | \(0.750825\pi\) | |||||||
\(98\) | 2.58874 | 0.261502 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 4.70156 | 0.470156 | ||||||||
\(101\) | 3.77080 | 0.375209 | 0.187605 | − | 0.982245i | \(-0.439928\pi\) | ||||
0.187605 | + | 0.982245i | \(0.439928\pi\) | |||||||
\(102\) | −9.58237 | −0.948796 | ||||||||
\(103\) | −8.56131 | −0.843570 | −0.421785 | − | 0.906696i | \(-0.638596\pi\) | ||||
−0.421785 | + | 0.906696i | \(0.638596\pi\) | |||||||
\(104\) | 44.7935 | 4.39237 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 23.5788 | 2.29018 | ||||||||
\(107\) | 14.1630 | 1.36919 | 0.684593 | − | 0.728925i | \(-0.259980\pi\) | ||||
0.684593 | + | 0.728925i | \(0.259980\pi\) | |||||||
\(108\) | 4.70156 | 0.452408 | ||||||||
\(109\) | 7.14026 | 0.683913 | 0.341956 | − | 0.939716i | \(-0.388911\pi\) | ||||
0.341956 | + | 0.939716i | \(0.388911\pi\) | |||||||
\(110\) | 2.58874 | 0.246826 | ||||||||
\(111\) | −3.95005 | −0.374922 | ||||||||
\(112\) | −8.70156 | −0.822220 | ||||||||
\(113\) | −1.10823 | −0.104254 | −0.0521269 | − | 0.998640i | \(-0.516600\pi\) | ||||
−0.0521269 | + | 0.998640i | \(0.516600\pi\) | |||||||
\(114\) | 18.7598 | 1.75702 | ||||||||
\(115\) | 7.33388 | 0.683888 | ||||||||
\(116\) | −38.1130 | −3.53871 | ||||||||
\(117\) | 6.40490 | 0.592133 | ||||||||
\(118\) | −7.58237 | −0.698014 | ||||||||
\(119\) | 3.70156 | 0.339322 | ||||||||
\(120\) | −6.99364 | −0.638429 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −21.8080 | −1.97441 | ||||||||
\(123\) | −2.31773 | −0.208983 | ||||||||
\(124\) | 31.8417 | 2.85947 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.58874 | −0.230623 | ||||||||
\(127\) | 11.6516 | 1.03391 | 0.516957 | − | 0.856011i | \(-0.327065\pi\) | ||||
0.516957 | + | 0.856011i | \(0.327065\pi\) | |||||||
\(128\) | −4.90647 | −0.433675 | ||||||||
\(129\) | −7.65161 | −0.673687 | ||||||||
\(130\) | −16.5806 | −1.45421 | ||||||||
\(131\) | −13.8116 | −1.20672 | −0.603361 | − | 0.797468i | \(-0.706172\pi\) | ||||
−0.603361 | + | 0.797468i | \(0.706172\pi\) | |||||||
\(132\) | −4.70156 | −0.409218 | ||||||||
\(133\) | −7.24672 | −0.628370 | ||||||||
\(134\) | −22.5806 | −1.95067 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −25.8874 | −2.21982 | ||||||||
\(137\) | 9.40312 | 0.803363 | 0.401682 | − | 0.915779i | \(-0.368426\pi\) | ||||
0.401682 | + | 0.915779i | \(0.368426\pi\) | |||||||
\(138\) | −18.9855 | −1.61615 | ||||||||
\(139\) | 16.3128 | 1.38363 | 0.691817 | − | 0.722072i | \(-0.256810\pi\) | ||||
0.691817 | + | 0.722072i | \(0.256810\pi\) | |||||||
\(140\) | 4.70156 | 0.397355 | ||||||||
\(141\) | 1.45307 | 0.122371 | ||||||||
\(142\) | −11.4031 | −0.956929 | ||||||||
\(143\) | −6.40490 | −0.535604 | ||||||||
\(144\) | 8.70156 | 0.725130 | ||||||||
\(145\) | 8.10646 | 0.673205 | ||||||||
\(146\) | 8.81898 | 0.729864 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −18.5714 | −1.52656 | ||||||||
\(149\) | 9.90010 | 0.811048 | 0.405524 | − | 0.914084i | \(-0.367089\pi\) | ||||
0.405524 | + | 0.914084i | \(0.367089\pi\) | |||||||
\(150\) | 2.58874 | 0.211370 | ||||||||
\(151\) | −17.7581 | −1.44513 | −0.722566 | − | 0.691302i | \(-0.757037\pi\) | ||||
−0.722566 | + | 0.691302i | \(0.757037\pi\) | |||||||
\(152\) | 50.6809 | 4.11076 | ||||||||
\(153\) | −3.70156 | −0.299254 | ||||||||
\(154\) | 2.58874 | 0.208606 | ||||||||
\(155\) | −6.77258 | −0.543987 | ||||||||
\(156\) | 30.1130 | 2.41097 | ||||||||
\(157\) | 17.0547 | 1.36112 | 0.680558 | − | 0.732694i | \(-0.261737\pi\) | ||||
0.680558 | + | 0.732694i | \(0.261737\pi\) | |||||||
\(158\) | 11.4031 | 0.907184 | ||||||||
\(159\) | 9.10823 | 0.722330 | ||||||||
\(160\) | −8.53879 | −0.675051 | ||||||||
\(161\) | 7.33388 | 0.577991 | ||||||||
\(162\) | 2.58874 | 0.203390 | ||||||||
\(163\) | −19.9338 | −1.56133 | −0.780667 | − | 0.624947i | \(-0.785120\pi\) | ||||
−0.780667 | + | 0.624947i | \(0.785120\pi\) | |||||||
\(164\) | −10.8970 | −0.850910 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | −23.2111 | −1.80153 | ||||||||
\(167\) | −2.95183 | −0.228419 | −0.114210 | − | 0.993457i | \(-0.536434\pi\) | ||||
−0.114210 | + | 0.993457i | \(0.536434\pi\) | |||||||
\(168\) | −6.99364 | −0.539571 | ||||||||
\(169\) | 28.0227 | 2.15559 | ||||||||
\(170\) | 9.58237 | 0.734934 | ||||||||
\(171\) | 7.24672 | 0.554170 | ||||||||
\(172\) | −35.9745 | −2.74303 | ||||||||
\(173\) | 20.2094 | 1.53649 | 0.768245 | − | 0.640156i | \(-0.221130\pi\) | ||||
0.768245 | + | 0.640156i | \(0.221130\pi\) | |||||||
\(174\) | −20.9855 | −1.59091 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −8.70156 | −0.655905 | ||||||||
\(177\) | −2.92898 | −0.220156 | ||||||||
\(178\) | 0.534199 | 0.0400399 | ||||||||
\(179\) | 5.95005 | 0.444728 | 0.222364 | − | 0.974964i | \(-0.428623\pi\) | ||||
0.222364 | + | 0.974964i | \(0.428623\pi\) | |||||||
\(180\) | −4.70156 | −0.350434 | ||||||||
\(181\) | −20.0709 | −1.49186 | −0.745929 | − | 0.666026i | \(-0.767994\pi\) | ||||
−0.745929 | + | 0.666026i | \(0.767994\pi\) | |||||||
\(182\) | −16.5806 | −1.22904 | ||||||||
\(183\) | −8.42419 | −0.622734 | ||||||||
\(184\) | −51.2905 | −3.78119 | ||||||||
\(185\) | 3.95005 | 0.290414 | ||||||||
\(186\) | 17.5324 | 1.28554 | ||||||||
\(187\) | 3.70156 | 0.270685 | ||||||||
\(188\) | 6.83171 | 0.498253 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −18.7598 | −1.36098 | ||||||||
\(191\) | 19.7159 | 1.42660 | 0.713298 | − | 0.700861i | \(-0.247201\pi\) | ||||
0.713298 | + | 0.700861i | \(0.247201\pi\) | |||||||
\(192\) | 4.70156 | 0.339306 | ||||||||
\(193\) | −5.49029 | −0.395200 | −0.197600 | − | 0.980283i | \(-0.563315\pi\) | ||||
−0.197600 | + | 0.980283i | \(0.563315\pi\) | |||||||
\(194\) | −36.1502 | −2.59544 | ||||||||
\(195\) | −6.40490 | −0.458664 | ||||||||
\(196\) | 4.70156 | 0.335826 | ||||||||
\(197\) | 20.4421 | 1.45644 | 0.728220 | − | 0.685343i | \(-0.240348\pi\) | ||||
0.728220 | + | 0.685343i | \(0.240348\pi\) | |||||||
\(198\) | −2.58874 | −0.183974 | ||||||||
\(199\) | 22.9391 | 1.62611 | 0.813055 | − | 0.582187i | \(-0.197803\pi\) | ||||
0.813055 | + | 0.582187i | \(0.197803\pi\) | |||||||
\(200\) | 6.99364 | 0.494525 | ||||||||
\(201\) | −8.72263 | −0.615247 | ||||||||
\(202\) | 9.76162 | 0.686825 | ||||||||
\(203\) | 8.10646 | 0.568962 | ||||||||
\(204\) | −17.4031 | −1.21846 | ||||||||
\(205\) | 2.31773 | 0.161877 | ||||||||
\(206\) | −22.1630 | −1.54417 | ||||||||
\(207\) | −7.33388 | −0.509740 | ||||||||
\(208\) | 55.7326 | 3.86436 | ||||||||
\(209\) | −7.24672 | −0.501266 | ||||||||
\(210\) | 2.58874 | 0.178640 | ||||||||
\(211\) | −6.59333 | −0.453903 | −0.226952 | − | 0.973906i | \(-0.572876\pi\) | ||||
−0.226952 | + | 0.973906i | \(0.572876\pi\) | |||||||
\(212\) | 42.8229 | 2.94109 | ||||||||
\(213\) | −4.40490 | −0.301819 | ||||||||
\(214\) | 36.6642 | 2.50631 | ||||||||
\(215\) | 7.65161 | 0.521836 | ||||||||
\(216\) | 6.99364 | 0.475857 | ||||||||
\(217\) | −6.77258 | −0.459753 | ||||||||
\(218\) | 18.4843 | 1.25191 | ||||||||
\(219\) | 3.40667 | 0.230202 | ||||||||
\(220\) | 4.70156 | 0.316979 | ||||||||
\(221\) | −23.7081 | −1.59478 | ||||||||
\(222\) | −10.2256 | −0.686301 | ||||||||
\(223\) | 11.0162 | 0.737696 | 0.368848 | − | 0.929490i | \(-0.379752\pi\) | ||||
0.368848 | + | 0.929490i | \(0.379752\pi\) | |||||||
\(224\) | −8.53879 | −0.570522 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −2.86893 | −0.190838 | ||||||||
\(227\) | −21.0048 | −1.39414 | −0.697068 | − | 0.717005i | \(-0.745513\pi\) | ||||
−0.697068 | + | 0.717005i | \(0.745513\pi\) | |||||||
\(228\) | 34.0709 | 2.25640 | ||||||||
\(229\) | −19.5661 | −1.29296 | −0.646482 | − | 0.762929i | \(-0.723760\pi\) | ||||
−0.646482 | + | 0.762929i | \(0.723760\pi\) | |||||||
\(230\) | 18.9855 | 1.25187 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | −56.6936 | −3.72212 | ||||||||
\(233\) | 16.3886 | 1.07365 | 0.536827 | − | 0.843692i | \(-0.319623\pi\) | ||||
0.536827 | + | 0.843692i | \(0.319623\pi\) | |||||||
\(234\) | 16.5806 | 1.08391 | ||||||||
\(235\) | −1.45307 | −0.0947880 | ||||||||
\(236\) | −13.7708 | −0.896403 | ||||||||
\(237\) | 4.40490 | 0.286129 | ||||||||
\(238\) | 9.58237 | 0.621133 | ||||||||
\(239\) | 18.0066 | 1.16475 | 0.582374 | − | 0.812921i | \(-0.302124\pi\) | ||||
0.582374 | + | 0.812921i | \(0.302124\pi\) | |||||||
\(240\) | −8.70156 | −0.561683 | ||||||||
\(241\) | 27.0740 | 1.74399 | 0.871996 | − | 0.489513i | \(-0.162826\pi\) | ||||
0.871996 | + | 0.489513i | \(0.162826\pi\) | |||||||
\(242\) | 2.58874 | 0.166410 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −39.6069 | −2.53557 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 46.4145 | 2.95328 | ||||||||
\(248\) | 47.3649 | 3.00768 | ||||||||
\(249\) | −8.96620 | −0.568210 | ||||||||
\(250\) | −2.58874 | −0.163726 | ||||||||
\(251\) | 8.58415 | 0.541827 | 0.270913 | − | 0.962604i | \(-0.412674\pi\) | ||||
0.270913 | + | 0.962604i | \(0.412674\pi\) | |||||||
\(252\) | −4.70156 | −0.296171 | ||||||||
\(253\) | 7.33388 | 0.461077 | ||||||||
\(254\) | 30.1630 | 1.89259 | ||||||||
\(255\) | 3.70156 | 0.231801 | ||||||||
\(256\) | −22.1047 | −1.38154 | ||||||||
\(257\) | 0.0885359 | 0.00552272 | 0.00276136 | − | 0.999996i | \(-0.499121\pi\) | ||||
0.00276136 | + | 0.999996i | \(0.499121\pi\) | |||||||
\(258\) | −19.8080 | −1.23319 | ||||||||
\(259\) | 3.95005 | 0.245444 | ||||||||
\(260\) | −30.1130 | −1.86753 | ||||||||
\(261\) | −8.10646 | −0.501777 | ||||||||
\(262\) | −35.7545 | −2.20892 | ||||||||
\(263\) | −17.5452 | −1.08188 | −0.540940 | − | 0.841061i | \(-0.681932\pi\) | ||||
−0.540940 | + | 0.841061i | \(0.681932\pi\) | |||||||
\(264\) | −6.99364 | −0.430428 | ||||||||
\(265\) | −9.10823 | −0.559514 | ||||||||
\(266\) | −18.7598 | −1.15024 | ||||||||
\(267\) | 0.206355 | 0.0126287 | ||||||||
\(268\) | −41.0100 | −2.50508 | ||||||||
\(269\) | 12.2520 | 0.747020 | 0.373510 | − | 0.927626i | \(-0.378154\pi\) | ||||
0.373510 | + | 0.927626i | \(0.378154\pi\) | |||||||
\(270\) | −2.58874 | −0.157546 | ||||||||
\(271\) | −1.91448 | −0.116296 | −0.0581482 | − | 0.998308i | \(-0.518520\pi\) | ||||
−0.0581482 | + | 0.998308i | \(0.518520\pi\) | |||||||
\(272\) | −32.2094 | −1.95298 | ||||||||
\(273\) | −6.40490 | −0.387642 | ||||||||
\(274\) | 24.3422 | 1.47057 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −34.4807 | −2.07549 | ||||||||
\(277\) | 5.62877 | 0.338200 | 0.169100 | − | 0.985599i | \(-0.445914\pi\) | ||||
0.169100 | + | 0.985599i | \(0.445914\pi\) | |||||||
\(278\) | 42.2296 | 2.53276 | ||||||||
\(279\) | 6.77258 | 0.405464 | ||||||||
\(280\) | 6.99364 | 0.417950 | ||||||||
\(281\) | −29.3032 | −1.74808 | −0.874042 | − | 0.485850i | \(-0.838510\pi\) | ||||
−0.874042 | + | 0.485850i | \(0.838510\pi\) | |||||||
\(282\) | 3.76162 | 0.224001 | ||||||||
\(283\) | 6.89833 | 0.410063 | 0.205032 | − | 0.978755i | \(-0.434270\pi\) | ||||
0.205032 | + | 0.978755i | \(0.434270\pi\) | |||||||
\(284\) | −20.7099 | −1.22891 | ||||||||
\(285\) | −7.24672 | −0.429258 | ||||||||
\(286\) | −16.5806 | −0.980431 | ||||||||
\(287\) | 2.31773 | 0.136811 | ||||||||
\(288\) | 8.53879 | 0.503153 | ||||||||
\(289\) | −3.29844 | −0.194026 | ||||||||
\(290\) | 20.9855 | 1.23231 | ||||||||
\(291\) | −13.9644 | −0.818609 | ||||||||
\(292\) | 16.0167 | 0.937305 | ||||||||
\(293\) | −28.7243 | −1.67809 | −0.839045 | − | 0.544062i | \(-0.816886\pi\) | ||||
−0.839045 | + | 0.544062i | \(0.816886\pi\) | |||||||
\(294\) | 2.58874 | 0.150978 | ||||||||
\(295\) | 2.92898 | 0.170532 | ||||||||
\(296\) | −27.6252 | −1.60568 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 25.6288 | 1.48463 | ||||||||
\(299\) | −46.9728 | −2.71651 | ||||||||
\(300\) | 4.70156 | 0.271445 | ||||||||
\(301\) | 7.65161 | 0.441032 | ||||||||
\(302\) | −45.9710 | −2.64533 | ||||||||
\(303\) | 3.77080 | 0.216627 | ||||||||
\(304\) | 63.0578 | 3.61661 | ||||||||
\(305\) | 8.42419 | 0.482368 | ||||||||
\(306\) | −9.58237 | −0.547788 | ||||||||
\(307\) | 15.7616 | 0.899563 | 0.449782 | − | 0.893139i | \(-0.351502\pi\) | ||||
0.449782 | + | 0.893139i | \(0.351502\pi\) | |||||||
\(308\) | 4.70156 | 0.267896 | ||||||||
\(309\) | −8.56131 | −0.487036 | ||||||||
\(310\) | −17.5324 | −0.995775 | ||||||||
\(311\) | 18.7549 | 1.06349 | 0.531747 | − | 0.846903i | \(-0.321536\pi\) | ||||
0.531747 | + | 0.846903i | \(0.321536\pi\) | |||||||
\(312\) | 44.7935 | 2.53593 | ||||||||
\(313\) | 8.45786 | 0.478067 | 0.239033 | − | 0.971011i | \(-0.423169\pi\) | ||||
0.239033 | + | 0.971011i | \(0.423169\pi\) | |||||||
\(314\) | 44.1502 | 2.49154 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 20.7099 | 1.16502 | ||||||||
\(317\) | −12.8519 | −0.721836 | −0.360918 | − | 0.932597i | \(-0.617537\pi\) | ||||
−0.360918 | + | 0.932597i | \(0.617537\pi\) | |||||||
\(318\) | 23.5788 | 1.32223 | ||||||||
\(319\) | 8.10646 | 0.453875 | ||||||||
\(320\) | −4.70156 | −0.262825 | ||||||||
\(321\) | 14.1630 | 0.790500 | ||||||||
\(322\) | 18.9855 | 1.05802 | ||||||||
\(323\) | −26.8242 | −1.49254 | ||||||||
\(324\) | 4.70156 | 0.261198 | ||||||||
\(325\) | 6.40490 | 0.355280 | ||||||||
\(326\) | −51.6033 | −2.85804 | ||||||||
\(327\) | 7.14026 | 0.394857 | ||||||||
\(328\) | −16.2094 | −0.895013 | ||||||||
\(329\) | −1.45307 | −0.0801104 | ||||||||
\(330\) | 2.58874 | 0.142505 | ||||||||
\(331\) | −6.64984 | −0.365508 | −0.182754 | − | 0.983159i | \(-0.558501\pi\) | ||||
−0.182754 | + | 0.983159i | \(0.558501\pi\) | |||||||
\(332\) | −42.1552 | −2.31356 | ||||||||
\(333\) | −3.95005 | −0.216462 | ||||||||
\(334\) | −7.64150 | −0.418124 | ||||||||
\(335\) | 8.72263 | 0.476568 | ||||||||
\(336\) | −8.70156 | −0.474709 | ||||||||
\(337\) | −18.0228 | −0.981767 | −0.490883 | − | 0.871225i | \(-0.663326\pi\) | ||||
−0.490883 | + | 0.871225i | \(0.663326\pi\) | |||||||
\(338\) | 72.5435 | 3.94584 | ||||||||
\(339\) | −1.10823 | −0.0601910 | ||||||||
\(340\) | 17.4031 | 0.943817 | ||||||||
\(341\) | −6.77258 | −0.366756 | ||||||||
\(342\) | 18.7598 | 1.01442 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −53.5126 | −2.88521 | ||||||||
\(345\) | 7.33388 | 0.394843 | ||||||||
\(346\) | 52.3168 | 2.81257 | ||||||||
\(347\) | −2.00355 | −0.107556 | −0.0537780 | − | 0.998553i | \(-0.517126\pi\) | ||||
−0.0537780 | + | 0.998553i | \(0.517126\pi\) | |||||||
\(348\) | −38.1130 | −2.04307 | ||||||||
\(349\) | 1.15955 | 0.0620693 | 0.0310347 | − | 0.999518i | \(-0.490120\pi\) | ||||
0.0310347 | + | 0.999518i | \(0.490120\pi\) | |||||||
\(350\) | −2.58874 | −0.138374 | ||||||||
\(351\) | 6.40490 | 0.341868 | ||||||||
\(352\) | −8.53879 | −0.455119 | ||||||||
\(353\) | 29.6160 | 1.57630 | 0.788151 | − | 0.615481i | \(-0.211038\pi\) | ||||
0.788151 | + | 0.615481i | \(0.211038\pi\) | |||||||
\(354\) | −7.58237 | −0.402999 | ||||||||
\(355\) | 4.40490 | 0.233788 | ||||||||
\(356\) | 0.970191 | 0.0514200 | ||||||||
\(357\) | 3.70156 | 0.195907 | ||||||||
\(358\) | 15.4031 | 0.814080 | ||||||||
\(359\) | −22.4650 | −1.18566 | −0.592828 | − | 0.805329i | \(-0.701988\pi\) | ||||
−0.592828 | + | 0.805329i | \(0.701988\pi\) | |||||||
\(360\) | −6.99364 | −0.368597 | ||||||||
\(361\) | 33.5149 | 1.76394 | ||||||||
\(362\) | −51.9583 | −2.73087 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −30.1130 | −1.57835 | ||||||||
\(365\) | −3.40667 | −0.178313 | ||||||||
\(366\) | −21.8080 | −1.13992 | ||||||||
\(367\) | 5.12233 | 0.267384 | 0.133692 | − | 0.991023i | \(-0.457317\pi\) | ||||
0.133692 | + | 0.991023i | \(0.457317\pi\) | |||||||
\(368\) | −63.8162 | −3.32665 | ||||||||
\(369\) | −2.31773 | −0.120656 | ||||||||
\(370\) | 10.2256 | 0.531606 | ||||||||
\(371\) | −9.10823 | −0.472876 | ||||||||
\(372\) | 31.8417 | 1.65091 | ||||||||
\(373\) | −26.2358 | −1.35844 | −0.679218 | − | 0.733936i | \(-0.737681\pi\) | ||||
−0.679218 | + | 0.733936i | \(0.737681\pi\) | |||||||
\(374\) | 9.58237 | 0.495493 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 10.1623 | 0.524078 | ||||||||
\(377\) | −51.9210 | −2.67407 | ||||||||
\(378\) | −2.58874 | −0.133150 | ||||||||
\(379\) | −9.60167 | −0.493205 | −0.246602 | − | 0.969117i | \(-0.579314\pi\) | ||||
−0.246602 | + | 0.969117i | \(0.579314\pi\) | |||||||
\(380\) | −34.0709 | −1.74780 | ||||||||
\(381\) | 11.6516 | 0.596930 | ||||||||
\(382\) | 51.0394 | 2.61140 | ||||||||
\(383\) | 10.1244 | 0.517332 | 0.258666 | − | 0.965967i | \(-0.416717\pi\) | ||||
0.258666 | + | 0.965967i | \(0.416717\pi\) | |||||||
\(384\) | −4.90647 | −0.250382 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | −14.2129 | −0.723419 | ||||||||
\(387\) | −7.65161 | −0.388953 | ||||||||
\(388\) | −65.6546 | −3.33311 | ||||||||
\(389\) | 16.9342 | 0.858597 | 0.429298 | − | 0.903163i | \(-0.358761\pi\) | ||||
0.429298 | + | 0.903163i | \(0.358761\pi\) | |||||||
\(390\) | −16.5806 | −0.839591 | ||||||||
\(391\) | 27.1468 | 1.37287 | ||||||||
\(392\) | 6.99364 | 0.353232 | ||||||||
\(393\) | −13.8116 | −0.696701 | ||||||||
\(394\) | 52.9193 | 2.66603 | ||||||||
\(395\) | −4.40490 | −0.221634 | ||||||||
\(396\) | −4.70156 | −0.236262 | ||||||||
\(397\) | 13.7616 | 0.690676 | 0.345338 | − | 0.938478i | \(-0.387764\pi\) | ||||
0.345338 | + | 0.938478i | \(0.387764\pi\) | |||||||
\(398\) | 59.3833 | 2.97662 | ||||||||
\(399\) | −7.24672 | −0.362790 | ||||||||
\(400\) | 8.70156 | 0.435078 | ||||||||
\(401\) | 35.6118 | 1.77837 | 0.889184 | − | 0.457550i | \(-0.151273\pi\) | ||||
0.889184 | + | 0.457550i | \(0.151273\pi\) | |||||||
\(402\) | −22.5806 | −1.12622 | ||||||||
\(403\) | 43.3777 | 2.16080 | ||||||||
\(404\) | 17.7287 | 0.882034 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 20.9855 | 1.04149 | ||||||||
\(407\) | 3.95005 | 0.195797 | ||||||||
\(408\) | −25.8874 | −1.28162 | ||||||||
\(409\) | 9.17748 | 0.453797 | 0.226898 | − | 0.973918i | \(-0.427141\pi\) | ||||
0.226898 | + | 0.973918i | \(0.427141\pi\) | |||||||
\(410\) | 6.00000 | 0.296319 | ||||||||
\(411\) | 9.40312 | 0.463822 | ||||||||
\(412\) | −40.2515 | −1.98305 | ||||||||
\(413\) | 2.92898 | 0.144126 | ||||||||
\(414\) | −18.9855 | −0.933086 | ||||||||
\(415\) | 8.96620 | 0.440134 | ||||||||
\(416\) | 54.6901 | 2.68140 | ||||||||
\(417\) | 16.3128 | 0.798842 | ||||||||
\(418\) | −18.7598 | −0.917574 | ||||||||
\(419\) | 37.8554 | 1.84935 | 0.924677 | − | 0.380751i | \(-0.124335\pi\) | ||||
0.924677 | + | 0.380751i | \(0.124335\pi\) | |||||||
\(420\) | 4.70156 | 0.229413 | ||||||||
\(421\) | 3.10469 | 0.151313 | 0.0756566 | − | 0.997134i | \(-0.475895\pi\) | ||||
0.0756566 | + | 0.997134i | \(0.475895\pi\) | |||||||
\(422\) | −17.0684 | −0.830877 | ||||||||
\(423\) | 1.45307 | 0.0706508 | ||||||||
\(424\) | 63.6997 | 3.09353 | ||||||||
\(425\) | −3.70156 | −0.179552 | ||||||||
\(426\) | −11.4031 | −0.552483 | ||||||||
\(427\) | 8.42419 | 0.407675 | ||||||||
\(428\) | 66.5881 | 3.21866 | ||||||||
\(429\) | −6.40490 | −0.309231 | ||||||||
\(430\) | 19.8080 | 0.955228 | ||||||||
\(431\) | −10.4548 | −0.503592 | −0.251796 | − | 0.967780i | \(-0.581021\pi\) | ||||
−0.251796 | + | 0.967780i | \(0.581021\pi\) | |||||||
\(432\) | 8.70156 | 0.418654 | ||||||||
\(433\) | −7.82212 | −0.375907 | −0.187954 | − | 0.982178i | \(-0.560185\pi\) | ||||
−0.187954 | + | 0.982178i | \(0.560185\pi\) | |||||||
\(434\) | −17.5324 | −0.841583 | ||||||||
\(435\) | 8.10646 | 0.388675 | ||||||||
\(436\) | 33.5704 | 1.60773 | ||||||||
\(437\) | −53.1466 | −2.54235 | ||||||||
\(438\) | 8.81898 | 0.421387 | ||||||||
\(439\) | −29.8146 | −1.42297 | −0.711486 | − | 0.702700i | \(-0.751978\pi\) | ||||
−0.711486 | + | 0.702700i | \(0.751978\pi\) | |||||||
\(440\) | 6.99364 | 0.333408 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −61.3741 | −2.91927 | ||||||||
\(443\) | −11.2774 | −0.535804 | −0.267902 | − | 0.963446i | \(-0.586330\pi\) | ||||
−0.267902 | + | 0.963446i | \(0.586330\pi\) | |||||||
\(444\) | −18.5714 | −0.881360 | ||||||||
\(445\) | −0.206355 | −0.00978216 | ||||||||
\(446\) | 28.5179 | 1.35036 | ||||||||
\(447\) | 9.90010 | 0.468259 | ||||||||
\(448\) | −4.70156 | −0.222128 | ||||||||
\(449\) | 11.2787 | 0.532277 | 0.266138 | − | 0.963935i | \(-0.414252\pi\) | ||||
0.266138 | + | 0.963935i | \(0.414252\pi\) | |||||||
\(450\) | 2.58874 | 0.122034 | ||||||||
\(451\) | 2.31773 | 0.109138 | ||||||||
\(452\) | −5.21043 | −0.245078 | ||||||||
\(453\) | −17.7581 | −0.834347 | ||||||||
\(454\) | −54.3759 | −2.55199 | ||||||||
\(455\) | 6.40490 | 0.300266 | ||||||||
\(456\) | 50.6809 | 2.37335 | ||||||||
\(457\) | −0.403250 | −0.0188632 | −0.00943162 | − | 0.999956i | \(-0.503002\pi\) | ||||
−0.00943162 | + | 0.999956i | \(0.503002\pi\) | |||||||
\(458\) | −50.6515 | −2.36679 | ||||||||
\(459\) | −3.70156 | −0.172774 | ||||||||
\(460\) | 34.4807 | 1.60767 | ||||||||
\(461\) | 34.9355 | 1.62711 | 0.813555 | − | 0.581487i | \(-0.197529\pi\) | ||||
0.813555 | + | 0.581487i | \(0.197529\pi\) | |||||||
\(462\) | 2.58874 | 0.120439 | ||||||||
\(463\) | 4.36413 | 0.202818 | 0.101409 | − | 0.994845i | \(-0.467665\pi\) | ||||
0.101409 | + | 0.994845i | \(0.467665\pi\) | |||||||
\(464\) | −70.5389 | −3.27468 | ||||||||
\(465\) | −6.77258 | −0.314071 | ||||||||
\(466\) | 42.4258 | 1.96534 | ||||||||
\(467\) | −30.2551 | −1.40004 | −0.700018 | − | 0.714125i | \(-0.746825\pi\) | ||||
−0.700018 | + | 0.714125i | \(0.746825\pi\) | |||||||
\(468\) | 30.1130 | 1.39198 | ||||||||
\(469\) | 8.72263 | 0.402774 | ||||||||
\(470\) | −3.76162 | −0.173511 | ||||||||
\(471\) | 17.0547 | 0.785841 | ||||||||
\(472\) | −20.4843 | −0.942864 | ||||||||
\(473\) | 7.65161 | 0.351822 | ||||||||
\(474\) | 11.4031 | 0.523763 | ||||||||
\(475\) | 7.24672 | 0.332502 | ||||||||
\(476\) | 17.4031 | 0.797671 | ||||||||
\(477\) | 9.10823 | 0.417037 | ||||||||
\(478\) | 46.6143 | 2.13209 | ||||||||
\(479\) | 11.8151 | 0.539846 | 0.269923 | − | 0.962882i | \(-0.413002\pi\) | ||||
0.269923 | + | 0.962882i | \(0.413002\pi\) | |||||||
\(480\) | −8.53879 | −0.389741 | ||||||||
\(481\) | −25.2997 | −1.15357 | ||||||||
\(482\) | 70.0876 | 3.19240 | ||||||||
\(483\) | 7.33388 | 0.333703 | ||||||||
\(484\) | 4.70156 | 0.213707 | ||||||||
\(485\) | 13.9644 | 0.634092 | ||||||||
\(486\) | 2.58874 | 0.117428 | ||||||||
\(487\) | 36.3387 | 1.64666 | 0.823331 | − | 0.567561i | \(-0.192113\pi\) | ||||
0.823331 | + | 0.567561i | \(0.192113\pi\) | |||||||
\(488\) | −58.9157 | −2.66699 | ||||||||
\(489\) | −19.9338 | −0.901437 | ||||||||
\(490\) | −2.58874 | −0.116947 | ||||||||
\(491\) | −41.4554 | −1.87085 | −0.935427 | − | 0.353519i | \(-0.884985\pi\) | ||||
−0.935427 | + | 0.353519i | \(0.884985\pi\) | |||||||
\(492\) | −10.8970 | −0.491273 | ||||||||
\(493\) | 30.0066 | 1.35143 | ||||||||
\(494\) | 120.155 | 5.40602 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 58.9320 | 2.64613 | ||||||||
\(497\) | 4.40490 | 0.197587 | ||||||||
\(498\) | −23.2111 | −1.04012 | ||||||||
\(499\) | 2.41146 | 0.107952 | 0.0539759 | − | 0.998542i | \(-0.482811\pi\) | ||||
0.0539759 | + | 0.998542i | \(0.482811\pi\) | |||||||
\(500\) | −4.70156 | −0.210260 | ||||||||
\(501\) | −2.95183 | −0.131878 | ||||||||
\(502\) | 22.2221 | 0.991821 | ||||||||
\(503\) | −24.3335 | −1.08498 | −0.542488 | − | 0.840063i | \(-0.682518\pi\) | ||||
−0.542488 | + | 0.840063i | \(0.682518\pi\) | |||||||
\(504\) | −6.99364 | −0.311521 | ||||||||
\(505\) | −3.77080 | −0.167799 | ||||||||
\(506\) | 18.9855 | 0.844008 | ||||||||
\(507\) | 28.0227 | 1.24453 | ||||||||
\(508\) | 54.7808 | 2.43050 | ||||||||
\(509\) | 21.3388 | 0.945826 | 0.472913 | − | 0.881109i | \(-0.343203\pi\) | ||||
0.472913 | + | 0.881109i | \(0.343203\pi\) | |||||||
\(510\) | 9.58237 | 0.424315 | ||||||||
\(511\) | −3.40667 | −0.150702 | ||||||||
\(512\) | −47.4103 | −2.09526 | ||||||||
\(513\) | 7.24672 | 0.319950 | ||||||||
\(514\) | 0.229196 | 0.0101094 | ||||||||
\(515\) | 8.56131 | 0.377256 | ||||||||
\(516\) | −35.9745 | −1.58369 | ||||||||
\(517\) | −1.45307 | −0.0639060 | ||||||||
\(518\) | 10.2256 | 0.449289 | ||||||||
\(519\) | 20.2094 | 0.887093 | ||||||||
\(520\) | −44.7935 | −1.96433 | ||||||||
\(521\) | 2.03557 | 0.0891800 | 0.0445900 | − | 0.999005i | \(-0.485802\pi\) | ||||
0.0445900 | + | 0.999005i | \(0.485802\pi\) | |||||||
\(522\) | −20.9855 | −0.918510 | ||||||||
\(523\) | −11.1647 | −0.488200 | −0.244100 | − | 0.969750i | \(-0.578493\pi\) | ||||
−0.244100 | + | 0.969750i | \(0.578493\pi\) | |||||||
\(524\) | −64.9359 | −2.83674 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −45.4198 | −1.98040 | ||||||||
\(527\) | −25.0691 | −1.09203 | ||||||||
\(528\) | −8.70156 | −0.378687 | ||||||||
\(529\) | 30.7858 | 1.33851 | ||||||||
\(530\) | −23.5788 | −1.02420 | ||||||||
\(531\) | −2.92898 | −0.127107 | ||||||||
\(532\) | −34.0709 | −1.47716 | ||||||||
\(533\) | −14.8448 | −0.643001 | ||||||||
\(534\) | 0.534199 | 0.0231170 | ||||||||
\(535\) | −14.1630 | −0.612319 | ||||||||
\(536\) | −61.0029 | −2.63492 | ||||||||
\(537\) | 5.95005 | 0.256764 | ||||||||
\(538\) | 31.7173 | 1.36743 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | −4.70156 | −0.202323 | ||||||||
\(541\) | −37.8212 | −1.62606 | −0.813029 | − | 0.582223i | \(-0.802183\pi\) | ||||
−0.813029 | + | 0.582223i | \(0.802183\pi\) | |||||||
\(542\) | −4.95609 | −0.212882 | ||||||||
\(543\) | −20.0709 | −0.861324 | ||||||||
\(544\) | −31.6069 | −1.35513 | ||||||||
\(545\) | −7.14026 | −0.305855 | ||||||||
\(546\) | −16.5806 | −0.709584 | ||||||||
\(547\) | −32.2871 | −1.38050 | −0.690248 | − | 0.723573i | \(-0.742499\pi\) | ||||
−0.690248 | + | 0.723573i | \(0.742499\pi\) | |||||||
\(548\) | 44.2094 | 1.88853 | ||||||||
\(549\) | −8.42419 | −0.359536 | ||||||||
\(550\) | −2.58874 | −0.110384 | ||||||||
\(551\) | −58.7452 | −2.50263 | ||||||||
\(552\) | −51.2905 | −2.18307 | ||||||||
\(553\) | −4.40490 | −0.187315 | ||||||||
\(554\) | 14.5714 | 0.619080 | ||||||||
\(555\) | 3.95005 | 0.167670 | ||||||||
\(556\) | 76.6957 | 3.25262 | ||||||||
\(557\) | 17.9416 | 0.760209 | 0.380105 | − | 0.924943i | \(-0.375888\pi\) | ||||
0.380105 | + | 0.924943i | \(0.375888\pi\) | |||||||
\(558\) | 17.5324 | 0.742207 | ||||||||
\(559\) | −49.0078 | −2.07281 | ||||||||
\(560\) | 8.70156 | 0.367708 | ||||||||
\(561\) | 3.70156 | 0.156280 | ||||||||
\(562\) | −75.8584 | −3.19989 | ||||||||
\(563\) | −1.40667 | −0.0592841 | −0.0296421 | − | 0.999561i | \(-0.509437\pi\) | ||||
−0.0296421 | + | 0.999561i | \(0.509437\pi\) | |||||||
\(564\) | 6.83171 | 0.287667 | ||||||||
\(565\) | 1.10823 | 0.0466237 | ||||||||
\(566\) | 17.8580 | 0.750626 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −30.8062 | −1.29260 | ||||||||
\(569\) | 9.36755 | 0.392708 | 0.196354 | − | 0.980533i | \(-0.437090\pi\) | ||||
0.196354 | + | 0.980533i | \(0.437090\pi\) | |||||||
\(570\) | −18.7598 | −0.785764 | ||||||||
\(571\) | −24.8562 | −1.04020 | −0.520100 | − | 0.854106i | \(-0.674105\pi\) | ||||
−0.520100 | + | 0.854106i | \(0.674105\pi\) | |||||||
\(572\) | −30.1130 | −1.25909 | ||||||||
\(573\) | 19.7159 | 0.823645 | ||||||||
\(574\) | 6.00000 | 0.250435 | ||||||||
\(575\) | −7.33388 | −0.305844 | ||||||||
\(576\) | 4.70156 | 0.195898 | ||||||||
\(577\) | 6.17433 | 0.257041 | 0.128520 | − | 0.991707i | \(-0.458977\pi\) | ||||
0.128520 | + | 0.991707i | \(0.458977\pi\) | |||||||
\(578\) | −8.53879 | −0.355167 | ||||||||
\(579\) | −5.49029 | −0.228169 | ||||||||
\(580\) | 38.1130 | 1.58256 | ||||||||
\(581\) | 8.96620 | 0.371981 | ||||||||
\(582\) | −36.1502 | −1.49848 | ||||||||
\(583\) | −9.10823 | −0.377224 | ||||||||
\(584\) | 23.8250 | 0.985886 | ||||||||
\(585\) | −6.40490 | −0.264810 | ||||||||
\(586\) | −74.3596 | −3.07177 | ||||||||
\(587\) | 2.04995 | 0.0846104 | 0.0423052 | − | 0.999105i | \(-0.486530\pi\) | ||||
0.0423052 | + | 0.999105i | \(0.486530\pi\) | |||||||
\(588\) | 4.70156 | 0.193889 | ||||||||
\(589\) | 49.0790 | 2.02226 | ||||||||
\(590\) | 7.58237 | 0.312161 | ||||||||
\(591\) | 20.4421 | 0.840876 | ||||||||
\(592\) | −34.3716 | −1.41267 | ||||||||
\(593\) | −7.85797 | −0.322688 | −0.161344 | − | 0.986898i | \(-0.551583\pi\) | ||||
−0.161344 | + | 0.986898i | \(0.551583\pi\) | |||||||
\(594\) | −2.58874 | −0.106217 | ||||||||
\(595\) | −3.70156 | −0.151749 | ||||||||
\(596\) | 46.5460 | 1.90660 | ||||||||
\(597\) | 22.9391 | 0.938835 | ||||||||
\(598\) | −121.600 | −4.97260 | ||||||||
\(599\) | −11.2190 | −0.458394 | −0.229197 | − | 0.973380i | \(-0.573610\pi\) | ||||
−0.229197 | + | 0.973380i | \(0.573610\pi\) | |||||||
\(600\) | 6.99364 | 0.285514 | ||||||||
\(601\) | 19.5047 | 0.795612 | 0.397806 | − | 0.917470i | \(-0.369772\pi\) | ||||
0.397806 | + | 0.917470i | \(0.369772\pi\) | |||||||
\(602\) | 19.8080 | 0.807315 | ||||||||
\(603\) | −8.72263 | −0.355213 | ||||||||
\(604\) | −83.4907 | −3.39719 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 9.76162 | 0.396539 | ||||||||
\(607\) | −16.9483 | −0.687909 | −0.343955 | − | 0.938986i | \(-0.611767\pi\) | ||||
−0.343955 | + | 0.938986i | \(0.611767\pi\) | |||||||
\(608\) | 61.8782 | 2.50949 | ||||||||
\(609\) | 8.10646 | 0.328490 | ||||||||
\(610\) | 21.8080 | 0.882981 | ||||||||
\(611\) | 9.30678 | 0.376512 | ||||||||
\(612\) | −17.4031 | −0.703480 | ||||||||
\(613\) | −12.3964 | −0.500687 | −0.250344 | − | 0.968157i | \(-0.580544\pi\) | ||||
−0.250344 | + | 0.968157i | \(0.580544\pi\) | |||||||
\(614\) | 40.8027 | 1.64666 | ||||||||
\(615\) | 2.31773 | 0.0934600 | ||||||||
\(616\) | 6.99364 | 0.281782 | ||||||||
\(617\) | −21.0192 | −0.846200 | −0.423100 | − | 0.906083i | \(-0.639058\pi\) | ||||
−0.423100 | + | 0.906083i | \(0.639058\pi\) | |||||||
\(618\) | −22.1630 | −0.891525 | ||||||||
\(619\) | 11.5289 | 0.463385 | 0.231692 | − | 0.972789i | \(-0.425574\pi\) | ||||
0.231692 | + | 0.972789i | \(0.425574\pi\) | |||||||
\(620\) | −31.8417 | −1.27879 | ||||||||
\(621\) | −7.33388 | −0.294299 | ||||||||
\(622\) | 48.5516 | 1.94674 | ||||||||
\(623\) | −0.206355 | −0.00826744 | ||||||||
\(624\) | 55.7326 | 2.23109 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 21.8952 | 0.875108 | ||||||||
\(627\) | −7.24672 | −0.289406 | ||||||||
\(628\) | 80.1839 | 3.19969 | ||||||||
\(629\) | 14.6214 | 0.582992 | ||||||||
\(630\) | 2.58874 | 0.103138 | ||||||||
\(631\) | 33.9988 | 1.35347 | 0.676734 | − | 0.736227i | \(-0.263395\pi\) | ||||
0.676734 | + | 0.736227i | \(0.263395\pi\) | |||||||
\(632\) | 30.8062 | 1.22541 | ||||||||
\(633\) | −6.59333 | −0.262061 | ||||||||
\(634\) | −33.2703 | −1.32133 | ||||||||
\(635\) | −11.6516 | −0.462380 | ||||||||
\(636\) | 42.8229 | 1.69804 | ||||||||
\(637\) | 6.40490 | 0.253771 | ||||||||
\(638\) | 20.9855 | 0.830824 | ||||||||
\(639\) | −4.40490 | −0.174255 | ||||||||
\(640\) | 4.90647 | 0.193945 | ||||||||
\(641\) | −20.5293 | −0.810858 | −0.405429 | − | 0.914127i | \(-0.632878\pi\) | ||||
−0.405429 | + | 0.914127i | \(0.632878\pi\) | |||||||
\(642\) | 36.6642 | 1.44702 | ||||||||
\(643\) | −16.9584 | −0.668774 | −0.334387 | − | 0.942436i | \(-0.608529\pi\) | ||||
−0.334387 | + | 0.942436i | \(0.608529\pi\) | |||||||
\(644\) | 34.4807 | 1.35873 | ||||||||
\(645\) | 7.65161 | 0.301282 | ||||||||
\(646\) | −69.4407 | −2.73211 | ||||||||
\(647\) | −2.25506 | −0.0886554 | −0.0443277 | − | 0.999017i | \(-0.514115\pi\) | ||||
−0.0443277 | + | 0.999017i | \(0.514115\pi\) | |||||||
\(648\) | 6.99364 | 0.274736 | ||||||||
\(649\) | 2.92898 | 0.114973 | ||||||||
\(650\) | 16.5806 | 0.650345 | ||||||||
\(651\) | −6.77258 | −0.265438 | ||||||||
\(652\) | −93.7199 | −3.67035 | ||||||||
\(653\) | 1.98917 | 0.0778422 | 0.0389211 | − | 0.999242i | \(-0.487608\pi\) | ||||
0.0389211 | + | 0.999242i | \(0.487608\pi\) | |||||||
\(654\) | 18.4843 | 0.722791 | ||||||||
\(655\) | 13.8116 | 0.539663 | ||||||||
\(656\) | −20.1679 | −0.787424 | ||||||||
\(657\) | 3.40667 | 0.132907 | ||||||||
\(658\) | −3.76162 | −0.146643 | ||||||||
\(659\) | 3.41324 | 0.132961 | 0.0664804 | − | 0.997788i | \(-0.478823\pi\) | ||||
0.0664804 | + | 0.997788i | \(0.478823\pi\) | |||||||
\(660\) | 4.70156 | 0.183008 | ||||||||
\(661\) | 15.4988 | 0.602832 | 0.301416 | − | 0.953493i | \(-0.402541\pi\) | ||||
0.301416 | + | 0.953493i | \(0.402541\pi\) | |||||||
\(662\) | −17.2147 | −0.669068 | ||||||||
\(663\) | −23.7081 | −0.920747 | ||||||||
\(664\) | −62.7064 | −2.43348 | ||||||||
\(665\) | 7.24672 | 0.281016 | ||||||||
\(666\) | −10.2256 | −0.396236 | ||||||||
\(667\) | 59.4518 | 2.30198 | ||||||||
\(668\) | −13.8782 | −0.536963 | ||||||||
\(669\) | 11.0162 | 0.425909 | ||||||||
\(670\) | 22.5806 | 0.872365 | ||||||||
\(671\) | 8.42419 | 0.325212 | ||||||||
\(672\) | −8.53879 | −0.329391 | ||||||||
\(673\) | −40.6449 | −1.56675 | −0.783373 | − | 0.621551i | \(-0.786503\pi\) | ||||
−0.783373 | + | 0.621551i | \(0.786503\pi\) | |||||||
\(674\) | −46.6564 | −1.79714 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 131.751 | 5.06733 | ||||||||
\(677\) | 41.1756 | 1.58251 | 0.791253 | − | 0.611489i | \(-0.209429\pi\) | ||||
0.791253 | + | 0.611489i | \(0.209429\pi\) | |||||||
\(678\) | −2.86893 | −0.110180 | ||||||||
\(679\) | 13.9644 | 0.535906 | ||||||||
\(680\) | 25.8874 | 0.992736 | ||||||||
\(681\) | −21.0048 | −0.804905 | ||||||||
\(682\) | −17.5324 | −0.671351 | ||||||||
\(683\) | 4.86111 | 0.186005 | 0.0930027 | − | 0.995666i | \(-0.470353\pi\) | ||||
0.0930027 | + | 0.995666i | \(0.470353\pi\) | |||||||
\(684\) | 34.0709 | 1.30273 | ||||||||
\(685\) | −9.40312 | −0.359275 | ||||||||
\(686\) | −2.58874 | −0.0988385 | ||||||||
\(687\) | −19.5661 | −0.746493 | ||||||||
\(688\) | −66.5810 | −2.53838 | ||||||||
\(689\) | 58.3373 | 2.22247 | ||||||||
\(690\) | 18.9855 | 0.722766 | ||||||||
\(691\) | 41.8838 | 1.59334 | 0.796668 | − | 0.604417i | \(-0.206594\pi\) | ||||
0.796668 | + | 0.604417i | \(0.206594\pi\) | |||||||
\(692\) | 95.0156 | 3.61195 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | −5.18666 | −0.196883 | ||||||||
\(695\) | −16.3128 | −0.618780 | ||||||||
\(696\) | −56.6936 | −2.14897 | ||||||||
\(697\) | 8.57923 | 0.324961 | ||||||||
\(698\) | 3.00177 | 0.113619 | ||||||||
\(699\) | 16.3886 | 0.619875 | ||||||||
\(700\) | −4.70156 | −0.177702 | ||||||||
\(701\) | 4.10646 | 0.155099 | 0.0775494 | − | 0.996989i | \(-0.475290\pi\) | ||||
0.0775494 | + | 0.996989i | \(0.475290\pi\) | |||||||
\(702\) | 16.5806 | 0.625794 | ||||||||
\(703\) | −28.6249 | −1.07961 | ||||||||
\(704\) | −4.70156 | −0.177197 | ||||||||
\(705\) | −1.45307 | −0.0547258 | ||||||||
\(706\) | 76.6682 | 2.88544 | ||||||||
\(707\) | −3.77080 | −0.141816 | ||||||||
\(708\) | −13.7708 | −0.517539 | ||||||||
\(709\) | 9.52094 | 0.357567 | 0.178783 | − | 0.983888i | \(-0.442784\pi\) | ||||
0.178783 | + | 0.983888i | \(0.442784\pi\) | |||||||
\(710\) | 11.4031 | 0.427952 | ||||||||
\(711\) | 4.40490 | 0.165197 | ||||||||
\(712\) | 1.44317 | 0.0540851 | ||||||||
\(713\) | −49.6693 | −1.86013 | ||||||||
\(714\) | 9.58237 | 0.358611 | ||||||||
\(715\) | 6.40490 | 0.239530 | ||||||||
\(716\) | 27.9745 | 1.04546 | ||||||||
\(717\) | 18.0066 | 0.672467 | ||||||||
\(718\) | −58.1559 | −2.17036 | ||||||||
\(719\) | 17.4969 | 0.652523 | 0.326261 | − | 0.945280i | \(-0.394211\pi\) | ||||
0.326261 | + | 0.945280i | \(0.394211\pi\) | |||||||
\(720\) | −8.70156 | −0.324288 | ||||||||
\(721\) | 8.56131 | 0.318840 | ||||||||
\(722\) | 86.7613 | 3.22892 | ||||||||
\(723\) | 27.0740 | 1.00689 | ||||||||
\(724\) | −94.3645 | −3.50703 | ||||||||
\(725\) | −8.10646 | −0.301066 | ||||||||
\(726\) | 2.58874 | 0.0960771 | ||||||||
\(727\) | −46.8908 | −1.73908 | −0.869542 | − | 0.493860i | \(-0.835586\pi\) | ||||
−0.869542 | + | 0.493860i | \(0.835586\pi\) | |||||||
\(728\) | −44.7935 | −1.66016 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.81898 | −0.326405 | ||||||||
\(731\) | 28.3229 | 1.04756 | ||||||||
\(732\) | −39.6069 | −1.46391 | ||||||||
\(733\) | −15.8038 | −0.583725 | −0.291863 | − | 0.956460i | \(-0.594275\pi\) | ||||
−0.291863 | + | 0.956460i | \(0.594275\pi\) | |||||||
\(734\) | 13.2604 | 0.489449 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | −62.6225 | −2.30830 | ||||||||
\(737\) | 8.72263 | 0.321302 | ||||||||
\(738\) | −6.00000 | −0.220863 | ||||||||
\(739\) | −5.69073 | −0.209337 | −0.104668 | − | 0.994507i | \(-0.533378\pi\) | ||||
−0.104668 | + | 0.994507i | \(0.533378\pi\) | |||||||
\(740\) | 18.5714 | 0.682699 | ||||||||
\(741\) | 46.4145 | 1.70508 | ||||||||
\(742\) | −23.5788 | −0.865606 | ||||||||
\(743\) | 22.2909 | 0.817774 | 0.408887 | − | 0.912585i | \(-0.365917\pi\) | ||||
0.408887 | + | 0.912585i | \(0.365917\pi\) | |||||||
\(744\) | 47.3649 | 1.73648 | ||||||||
\(745\) | −9.90010 | −0.362712 | ||||||||
\(746\) | −67.9175 | −2.48664 | ||||||||
\(747\) | −8.96620 | −0.328056 | ||||||||
\(748\) | 17.4031 | 0.636321 | ||||||||
\(749\) | −14.1630 | −0.517504 | ||||||||
\(750\) | −2.58874 | −0.0945273 | ||||||||
\(751\) | 38.6786 | 1.41140 | 0.705701 | − | 0.708510i | \(-0.250632\pi\) | ||||
0.705701 | + | 0.708510i | \(0.250632\pi\) | |||||||
\(752\) | 12.6440 | 0.461079 | ||||||||
\(753\) | 8.58415 | 0.312824 | ||||||||
\(754\) | −134.410 | −4.89492 | ||||||||
\(755\) | 17.7581 | 0.646283 | ||||||||
\(756\) | −4.70156 | −0.170994 | ||||||||
\(757\) | 43.7967 | 1.59182 | 0.795908 | − | 0.605417i | \(-0.206994\pi\) | ||||
0.795908 | + | 0.605417i | \(0.206994\pi\) | |||||||
\(758\) | −24.8562 | −0.902818 | ||||||||
\(759\) | 7.33388 | 0.266203 | ||||||||
\(760\) | −50.6809 | −1.83839 | ||||||||
\(761\) | 40.1966 | 1.45713 | 0.728564 | − | 0.684978i | \(-0.240188\pi\) | ||||
0.728564 | + | 0.684978i | \(0.240188\pi\) | |||||||
\(762\) | 30.1630 | 1.09269 | ||||||||
\(763\) | −7.14026 | −0.258495 | ||||||||
\(764\) | 92.6957 | 3.35361 | ||||||||
\(765\) | 3.70156 | 0.133830 | ||||||||
\(766\) | 26.2094 | 0.946983 | ||||||||
\(767\) | −18.7598 | −0.677379 | ||||||||
\(768\) | −22.1047 | −0.797634 | ||||||||
\(769\) | 1.32679 | 0.0478452 | 0.0239226 | − | 0.999714i | \(-0.492384\pi\) | ||||
0.0239226 | + | 0.999714i | \(0.492384\pi\) | |||||||
\(770\) | −2.58874 | −0.0932916 | ||||||||
\(771\) | 0.0885359 | 0.00318854 | ||||||||
\(772\) | −25.8129 | −0.929028 | ||||||||
\(773\) | −9.62314 | −0.346120 | −0.173060 | − | 0.984911i | \(-0.555365\pi\) | ||||
−0.173060 | + | 0.984911i | \(0.555365\pi\) | |||||||
\(774\) | −19.8080 | −0.711985 | ||||||||
\(775\) | 6.77258 | 0.243278 | ||||||||
\(776\) | −97.6621 | −3.50587 | ||||||||
\(777\) | 3.95005 | 0.141707 | ||||||||
\(778\) | 43.8381 | 1.57167 | ||||||||
\(779\) | −16.7959 | −0.601777 | ||||||||
\(780\) | −30.1130 | −1.07822 | ||||||||
\(781\) | 4.40490 | 0.157620 | ||||||||
\(782\) | 70.2760 | 2.51306 | ||||||||
\(783\) | −8.10646 | −0.289701 | ||||||||
\(784\) | 8.70156 | 0.310770 | ||||||||
\(785\) | −17.0547 | −0.608710 | ||||||||
\(786\) | −35.7545 | −1.27532 | ||||||||
\(787\) | 44.1489 | 1.57374 | 0.786869 | − | 0.617120i | \(-0.211701\pi\) | ||||
0.786869 | + | 0.617120i | \(0.211701\pi\) | |||||||
\(788\) | 96.1099 | 3.42377 | ||||||||
\(789\) | −17.5452 | −0.624624 | ||||||||
\(790\) | −11.4031 | −0.405705 | ||||||||
\(791\) | 1.10823 | 0.0394042 | ||||||||
\(792\) | −6.99364 | −0.248508 | ||||||||
\(793\) | −53.9561 | −1.91604 | ||||||||
\(794\) | 35.6252 | 1.26429 | ||||||||
\(795\) | −9.10823 | −0.323036 | ||||||||
\(796\) | 107.850 | 3.82263 | ||||||||
\(797\) | −18.5257 | −0.656215 | −0.328108 | − | 0.944640i | \(-0.606411\pi\) | ||||
−0.328108 | + | 0.944640i | \(0.606411\pi\) | |||||||
\(798\) | −18.7598 | −0.664091 | ||||||||
\(799\) | −5.37864 | −0.190282 | ||||||||
\(800\) | 8.53879 | 0.301892 | ||||||||
\(801\) | 0.206355 | 0.00729119 | ||||||||
\(802\) | 92.1895 | 3.25533 | ||||||||
\(803\) | −3.40667 | −0.120219 | ||||||||
\(804\) | −41.0100 | −1.44631 | ||||||||
\(805\) | −7.33388 | −0.258485 | ||||||||
\(806\) | 112.293 | 3.95537 | ||||||||
\(807\) | 12.2520 | 0.431292 | ||||||||
\(808\) | 26.3716 | 0.927751 | ||||||||
\(809\) | 38.1516 | 1.34134 | 0.670670 | − | 0.741756i | \(-0.266007\pi\) | ||||
0.670670 | + | 0.741756i | \(0.266007\pi\) | |||||||
\(810\) | −2.58874 | −0.0909590 | ||||||||
\(811\) | −37.3355 | −1.31103 | −0.655514 | − | 0.755183i | \(-0.727548\pi\) | ||||
−0.655514 | + | 0.755183i | \(0.727548\pi\) | |||||||
\(812\) | 38.1130 | 1.33750 | ||||||||
\(813\) | −1.91448 | −0.0671438 | ||||||||
\(814\) | 10.2256 | 0.358409 | ||||||||
\(815\) | 19.9338 | 0.698250 | ||||||||
\(816\) | −32.2094 | −1.12755 | ||||||||
\(817\) | −55.4491 | −1.93992 | ||||||||
\(818\) | 23.7581 | 0.830682 | ||||||||
\(819\) | −6.40490 | −0.223805 | ||||||||
\(820\) | 10.8970 | 0.380538 | ||||||||
\(821\) | −19.9039 | −0.694652 | −0.347326 | − | 0.937744i | \(-0.612910\pi\) | ||||
−0.347326 | + | 0.937744i | \(0.612910\pi\) | |||||||
\(822\) | 24.3422 | 0.849032 | ||||||||
\(823\) | −50.8399 | −1.77217 | −0.886084 | − | 0.463525i | \(-0.846585\pi\) | ||||
−0.886084 | + | 0.463525i | \(0.846585\pi\) | |||||||
\(824\) | −59.8746 | −2.08583 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 7.58237 | 0.263824 | ||||||||
\(827\) | −43.7003 | −1.51961 | −0.759804 | − | 0.650152i | \(-0.774705\pi\) | ||||
−0.759804 | + | 0.650152i | \(0.774705\pi\) | |||||||
\(828\) | −34.4807 | −1.19829 | ||||||||
\(829\) | 51.5197 | 1.78935 | 0.894677 | − | 0.446715i | \(-0.147406\pi\) | ||||
0.894677 | + | 0.446715i | \(0.147406\pi\) | |||||||
\(830\) | 23.2111 | 0.805671 | ||||||||
\(831\) | 5.62877 | 0.195260 | ||||||||
\(832\) | 30.1130 | 1.04398 | ||||||||
\(833\) | −3.70156 | −0.128252 | ||||||||
\(834\) | 42.2296 | 1.46229 | ||||||||
\(835\) | 2.95183 | 0.102152 | ||||||||
\(836\) | −34.0709 | −1.17837 | ||||||||
\(837\) | 6.77258 | 0.234095 | ||||||||
\(838\) | 97.9976 | 3.38527 | ||||||||
\(839\) | −18.7834 | −0.648475 | −0.324238 | − | 0.945976i | \(-0.605108\pi\) | ||||
−0.324238 | + | 0.945976i | \(0.605108\pi\) | |||||||
\(840\) | 6.99364 | 0.241303 | ||||||||
\(841\) | 36.7147 | 1.26602 | ||||||||
\(842\) | 8.03722 | 0.276981 | ||||||||
\(843\) | −29.3032 | −1.00926 | ||||||||
\(844\) | −30.9989 | −1.06703 | ||||||||
\(845\) | −28.0227 | −0.964011 | ||||||||
\(846\) | 3.76162 | 0.129327 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 79.2559 | 2.72166 | ||||||||
\(849\) | 6.89833 | 0.236750 | ||||||||
\(850\) | −9.58237 | −0.328673 | ||||||||
\(851\) | 28.9692 | 0.993052 | ||||||||
\(852\) | −20.7099 | −0.709509 | ||||||||
\(853\) | −10.4506 | −0.357821 | −0.178911 | − | 0.983865i | \(-0.557257\pi\) | ||||
−0.178911 | + | 0.983865i | \(0.557257\pi\) | |||||||
\(854\) | 21.8080 | 0.746255 | ||||||||
\(855\) | −7.24672 | −0.247832 | ||||||||
\(856\) | 99.0507 | 3.38548 | ||||||||
\(857\) | 33.2646 | 1.13630 | 0.568149 | − | 0.822926i | \(-0.307660\pi\) | ||||
0.568149 | + | 0.822926i | \(0.307660\pi\) | |||||||
\(858\) | −16.5806 | −0.566052 | ||||||||
\(859\) | 27.5569 | 0.940230 | 0.470115 | − | 0.882605i | \(-0.344212\pi\) | ||||
0.470115 | + | 0.882605i | \(0.344212\pi\) | |||||||
\(860\) | 35.9745 | 1.22672 | ||||||||
\(861\) | 2.31773 | 0.0789881 | ||||||||
\(862\) | −27.0649 | −0.921832 | ||||||||
\(863\) | −10.2042 | −0.347354 | −0.173677 | − | 0.984803i | \(-0.555565\pi\) | ||||
−0.173677 | + | 0.984803i | \(0.555565\pi\) | |||||||
\(864\) | 8.53879 | 0.290496 | ||||||||
\(865\) | −20.2094 | −0.687139 | ||||||||
\(866\) | −20.2494 | −0.688103 | ||||||||
\(867\) | −3.29844 | −0.112021 | ||||||||
\(868\) | −31.8417 | −1.08078 | ||||||||
\(869\) | −4.40490 | −0.149426 | ||||||||
\(870\) | 20.9855 | 0.711475 | ||||||||
\(871\) | −55.8676 | −1.89300 | ||||||||
\(872\) | 49.9364 | 1.69106 | ||||||||
\(873\) | −13.9644 | −0.472624 | ||||||||
\(874\) | −137.583 | −4.65380 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 16.0167 | 0.541153 | ||||||||
\(877\) | 57.5319 | 1.94271 | 0.971357 | − | 0.237625i | \(-0.0763688\pi\) | ||||
0.971357 | + | 0.237625i | \(0.0763688\pi\) | |||||||
\(878\) | −77.1821 | −2.60477 | ||||||||
\(879\) | −28.7243 | −0.968846 | ||||||||
\(880\) | 8.70156 | 0.293330 | ||||||||
\(881\) | −1.05474 | −0.0355351 | −0.0177675 | − | 0.999842i | \(-0.505656\pi\) | ||||
−0.0177675 | + | 0.999842i | \(0.505656\pi\) | |||||||
\(882\) | 2.58874 | 0.0871673 | ||||||||
\(883\) | 14.4063 | 0.484810 | 0.242405 | − | 0.970175i | \(-0.422064\pi\) | ||||
0.242405 | + | 0.970175i | \(0.422064\pi\) | |||||||
\(884\) | −111.465 | −3.74898 | ||||||||
\(885\) | 2.92898 | 0.0984567 | ||||||||
\(886\) | −29.1942 | −0.980797 | ||||||||
\(887\) | −16.3792 | −0.549958 | −0.274979 | − | 0.961450i | \(-0.588671\pi\) | ||||
−0.274979 | + | 0.961450i | \(0.588671\pi\) | |||||||
\(888\) | −27.6252 | −0.927042 | ||||||||
\(889\) | −11.6516 | −0.390783 | ||||||||
\(890\) | −0.534199 | −0.0179064 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 51.7931 | 1.73416 | ||||||||
\(893\) | 10.5300 | 0.352373 | ||||||||
\(894\) | 25.6288 | 0.857154 | ||||||||
\(895\) | −5.95005 | −0.198888 | ||||||||
\(896\) | 4.90647 | 0.163914 | ||||||||
\(897\) | −46.9728 | −1.56838 | ||||||||
\(898\) | 29.1977 | 0.974340 | ||||||||
\(899\) | −54.9016 | −1.83107 | ||||||||
\(900\) | 4.70156 | 0.156719 | ||||||||
\(901\) | −33.7147 | −1.12320 | ||||||||
\(902\) | 6.00000 | 0.199778 | ||||||||
\(903\) | 7.65161 | 0.254630 | ||||||||
\(904\) | −7.75058 | −0.257780 | ||||||||
\(905\) | 20.0709 | 0.667179 | ||||||||
\(906\) | −45.9710 | −1.52728 | ||||||||
\(907\) | −26.0372 | −0.864552 | −0.432276 | − | 0.901741i | \(-0.642289\pi\) | ||||
−0.432276 | + | 0.901741i | \(0.642289\pi\) | |||||||
\(908\) | −98.7553 | −3.27731 | ||||||||
\(909\) | 3.77080 | 0.125070 | ||||||||
\(910\) | 16.5806 | 0.549642 | ||||||||
\(911\) | 25.5381 | 0.846114 | 0.423057 | − | 0.906103i | \(-0.360957\pi\) | ||||
0.423057 | + | 0.906103i | \(0.360957\pi\) | |||||||
\(912\) | 63.0578 | 2.08805 | ||||||||
\(913\) | 8.96620 | 0.296738 | ||||||||
\(914\) | −1.04391 | −0.0345294 | ||||||||
\(915\) | 8.42419 | 0.278495 | ||||||||
\(916\) | −91.9912 | −3.03948 | ||||||||
\(917\) | 13.8116 | 0.456098 | ||||||||
\(918\) | −9.58237 | −0.316265 | ||||||||
\(919\) | −28.3971 | −0.936733 | −0.468367 | − | 0.883534i | \(-0.655157\pi\) | ||||
−0.468367 | + | 0.883534i | \(0.655157\pi\) | |||||||
\(920\) | 51.2905 | 1.69100 | ||||||||
\(921\) | 15.7616 | 0.519363 | ||||||||
\(922\) | 90.4390 | 2.97845 | ||||||||
\(923\) | −28.2129 | −0.928640 | ||||||||
\(924\) | 4.70156 | 0.154670 | ||||||||
\(925\) | −3.95005 | −0.129877 | ||||||||
\(926\) | 11.2976 | 0.371262 | ||||||||
\(927\) | −8.56131 | −0.281190 | ||||||||
\(928\) | −69.2194 | −2.27224 | ||||||||
\(929\) | −10.7485 | −0.352646 | −0.176323 | − | 0.984332i | \(-0.556420\pi\) | ||||
−0.176323 | + | 0.984332i | \(0.556420\pi\) | |||||||
\(930\) | −17.5324 | −0.574911 | ||||||||
\(931\) | 7.24672 | 0.237502 | ||||||||
\(932\) | 77.0521 | 2.52393 | ||||||||
\(933\) | 18.7549 | 0.614009 | ||||||||
\(934\) | −78.3224 | −2.56279 | ||||||||
\(935\) | −3.70156 | −0.121054 | ||||||||
\(936\) | 44.7935 | 1.46412 | ||||||||
\(937\) | −34.9763 | −1.14263 | −0.571313 | − | 0.820732i | \(-0.693566\pi\) | ||||
−0.571313 | + | 0.820732i | \(0.693566\pi\) | |||||||
\(938\) | 22.5806 | 0.737283 | ||||||||
\(939\) | 8.45786 | 0.276012 | ||||||||
\(940\) | −6.83171 | −0.222826 | ||||||||
\(941\) | 25.8979 | 0.844248 | 0.422124 | − | 0.906538i | \(-0.361285\pi\) | ||||
0.422124 | + | 0.906538i | \(0.361285\pi\) | |||||||
\(942\) | 44.1502 | 1.43849 | ||||||||
\(943\) | 16.9980 | 0.553530 | ||||||||
\(944\) | −25.4867 | −0.829523 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 19.8080 | 0.644014 | ||||||||
\(947\) | −15.9623 | −0.518704 | −0.259352 | − | 0.965783i | \(-0.583509\pi\) | ||||
−0.259352 | + | 0.965783i | \(0.583509\pi\) | |||||||
\(948\) | 20.7099 | 0.672626 | ||||||||
\(949\) | 21.8194 | 0.708287 | ||||||||
\(950\) | 18.7598 | 0.608650 | ||||||||
\(951\) | −12.8519 | −0.416752 | ||||||||
\(952\) | 25.8874 | 0.839015 | ||||||||
\(953\) | −30.8611 | −0.999690 | −0.499845 | − | 0.866115i | \(-0.666610\pi\) | ||||
−0.499845 | + | 0.866115i | \(0.666610\pi\) | |||||||
\(954\) | 23.5788 | 0.763393 | ||||||||
\(955\) | −19.7159 | −0.637993 | ||||||||
\(956\) | 84.6590 | 2.73807 | ||||||||
\(957\) | 8.10646 | 0.262045 | ||||||||
\(958\) | 30.5862 | 0.988196 | ||||||||
\(959\) | −9.40312 | −0.303643 | ||||||||
\(960\) | −4.70156 | −0.151742 | ||||||||
\(961\) | 14.8678 | 0.479607 | ||||||||
\(962\) | −65.4942 | −2.11162 | ||||||||
\(963\) | 14.1630 | 0.456395 | ||||||||
\(964\) | 127.290 | 4.09974 | ||||||||
\(965\) | 5.49029 | 0.176739 | ||||||||
\(966\) | 18.9855 | 0.610848 | ||||||||
\(967\) | −38.9934 | −1.25394 | −0.626972 | − | 0.779042i | \(-0.715706\pi\) | ||||
−0.626972 | + | 0.779042i | \(0.715706\pi\) | |||||||
\(968\) | 6.99364 | 0.224784 | ||||||||
\(969\) | −26.8242 | −0.861717 | ||||||||
\(970\) | 36.1502 | 1.16071 | ||||||||
\(971\) | −1.98071 | −0.0635639 | −0.0317819 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317819 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(972\) | 4.70156 | 0.150803 | ||||||||
\(973\) | −16.3128 | −0.522965 | ||||||||
\(974\) | 94.0713 | 3.01424 | ||||||||
\(975\) | 6.40490 | 0.205121 | ||||||||
\(976\) | −73.3036 | −2.34639 | ||||||||
\(977\) | 9.66926 | 0.309347 | 0.154674 | − | 0.987966i | \(-0.450567\pi\) | ||||
0.154674 | + | 0.987966i | \(0.450567\pi\) | |||||||
\(978\) | −51.6033 | −1.65009 | ||||||||
\(979\) | −0.206355 | −0.00659513 | ||||||||
\(980\) | −4.70156 | −0.150186 | ||||||||
\(981\) | 7.14026 | 0.227971 | ||||||||
\(982\) | −107.317 | −3.42463 | ||||||||
\(983\) | −31.1289 | −0.992858 | −0.496429 | − | 0.868077i | \(-0.665356\pi\) | ||||
−0.496429 | + | 0.868077i | \(0.665356\pi\) | |||||||
\(984\) | −16.2094 | −0.516736 | ||||||||
\(985\) | −20.4421 | −0.651340 | ||||||||
\(986\) | 77.6791 | 2.47381 | ||||||||
\(987\) | −1.45307 | −0.0462518 | ||||||||
\(988\) | 218.221 | 6.94252 | ||||||||
\(989\) | 56.1160 | 1.78439 | ||||||||
\(990\) | 2.58874 | 0.0822755 | ||||||||
\(991\) | 30.4473 | 0.967191 | 0.483595 | − | 0.875292i | \(-0.339331\pi\) | ||||
0.483595 | + | 0.875292i | \(0.339331\pi\) | |||||||
\(992\) | 57.8296 | 1.83609 | ||||||||
\(993\) | −6.64984 | −0.211026 | ||||||||
\(994\) | 11.4031 | 0.361685 | ||||||||
\(995\) | −22.9391 | −0.727218 | ||||||||
\(996\) | −42.1552 | −1.33574 | ||||||||
\(997\) | −27.1612 | −0.860204 | −0.430102 | − | 0.902780i | \(-0.641522\pi\) | ||||
−0.430102 | + | 0.902780i | \(0.641522\pi\) | |||||||
\(998\) | 6.24264 | 0.197607 | ||||||||
\(999\) | −3.95005 | −0.124974 |
(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 | 1155.2.a.u.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 3465.2.a.bl.1.1 | 4 | |||
5.4 | even | 2 | 5775.2.a.bz.1.1 | 4 | |||
7.6 | odd | 2 | 8085.2.a.bn.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.u.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3465.2.a.bl.1.1 | 4 | 3.2 | odd | 2 | |||
5775.2.a.bz.1.1 | 4 | 5.4 | even | 2 | |||
8085.2.a.bn.1.4 | 4 | 7.6 | odd | 2 |