Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.244558277.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 13x^{4} + 11x^{3} + 29x^{2} + 5x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.50454\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.50454 | −1.44600 | −0.722999 | − | 0.690849i | \(-0.757237\pi\) | ||||
−0.722999 | + | 0.690849i | \(0.757237\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.40126 | −1.52109 | −0.760545 | − | 0.649285i | \(-0.775068\pi\) | ||||
−0.760545 | + | 0.649285i | \(0.775068\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.27272 | 1.09091 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.51859 | 2.19949 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.74921 | 1.15185 | 0.575927 | − | 0.817501i | \(-0.304641\pi\) | ||||
0.575927 | + | 0.817501i | \(0.304641\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.83057 | 1.56704 | 0.783520 | − | 0.621366i | \(-0.213422\pi\) | ||||
0.783520 | + | 0.621366i | \(0.213422\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50454 | −0.546536 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.61279 | 0.961834 | 0.480917 | − | 0.876766i | \(-0.340304\pi\) | ||||
0.480917 | + | 0.876766i | \(0.340304\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.56857 | 1.31371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.683051 | −0.131453 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.06403 | 0.940367 | 0.470183 | − | 0.882569i | \(-0.344188\pi\) | ||||
0.470183 | + | 0.882569i | \(0.344188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.54877 | 0.637377 | 0.318689 | − | 0.947859i | \(-0.396758\pi\) | ||||
0.318689 | + | 0.947859i | \(0.396758\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.50454 | 0.435985 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.40126 | −0.574918 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.49334 | −1.06750 | −0.533749 | − | 0.845643i | \(-0.679217\pi\) | ||||
−0.533749 | + | 0.845643i | \(0.679217\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.50454 | 0.401048 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.94505 | −0.303766 | −0.151883 | − | 0.988398i | \(-0.548534\pi\) | ||||
−0.151883 | + | 0.988398i | \(0.548534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.11733 | −0.475389 | −0.237695 | − | 0.971340i | \(-0.576392\pi\) | ||||
−0.237695 | + | 0.971340i | \(0.576392\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.1314 | −1.65937 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.72893 | 0.543921 | 0.271960 | − | 0.962308i | \(-0.412328\pi\) | ||||
0.271960 | + | 0.962308i | \(0.412328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.8946 | −1.66558 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.20492 | 0.302869 | 0.151435 | − | 0.988467i | \(-0.451611\pi\) | ||||
0.151435 | + | 0.988467i | \(0.451611\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.40126 | 0.458626 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.1074 | −2.26594 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.10214 | −0.924620 | −0.462310 | − | 0.886718i | \(-0.652979\pi\) | ||||
−0.462310 | + | 0.886718i | \(0.652979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.05283 | 0.390875 | 0.195437 | − | 0.980716i | \(-0.437387\pi\) | ||||
0.195437 | + | 0.980716i | \(0.437387\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.27272 | 0.412325 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.40126 | 0.421874 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.11450 | −1.11351 | −0.556757 | − | 0.830676i | \(-0.687954\pi\) | ||||
−0.556757 | + | 0.830676i | \(0.687954\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.5529 | −1.39081 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.73636 | −0.562102 | −0.281051 | − | 0.959693i | \(-0.590683\pi\) | ||||
−0.281051 | + | 0.959693i | \(0.590683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.08595 | 0.244142 | 0.122071 | − | 0.992521i | \(-0.461046\pi\) | ||||
0.122071 | + | 0.992521i | \(0.461046\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.4513 | −1.89963 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.96819 | −1.00900 | −0.504500 | − | 0.863412i | \(-0.668323\pi\) | ||||
−0.504500 | + | 0.863412i | \(0.668323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.10745 | −0.900827 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.9901 | 1.53561 | 0.767807 | − | 0.640681i | \(-0.221348\pi\) | ||||
0.767807 | + | 0.640681i | \(0.221348\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.1533 | −1.75207 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.6831 | −1.35977 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.62399 | 0.914142 | 0.457071 | − | 0.889430i | \(-0.348899\pi\) | ||||
0.457071 | + | 0.889430i | \(0.348899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.88803 | −0.921645 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −23.2326 | −2.38361 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.09042 | 0.313785 | 0.156892 | − | 0.987616i | \(-0.449852\pi\) | ||||
0.156892 | + | 0.987616i | \(0.449852\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.27272 | −0.328921 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.86205 | 0.583296 | 0.291648 | − | 0.956526i | \(-0.405796\pi\) | ||||
0.291648 | + | 0.956526i | \(0.405796\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.51859 | 0.831330 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.01980 | −0.388609 | −0.194305 | − | 0.980941i | \(-0.562245\pi\) | ||||
−0.194305 | + | 0.980941i | \(0.562245\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.89460 | 0.564600 | 0.282300 | − | 0.959326i | \(-0.408903\pi\) | ||||
0.282300 | + | 0.959326i | \(0.408903\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.2628 | 1.54360 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.216621 | −0.0203780 | −0.0101890 | − | 0.999948i | \(-0.503243\pi\) | ||||
−0.0101890 | + | 0.999948i | \(0.503243\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.6893 | −1.46304 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.27272 | −0.302564 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.74921 | 0.435360 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.87146 | 0.439245 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.33511 | −0.477187 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.75255 | −0.865398 | −0.432699 | − | 0.901538i | \(-0.642439\pi\) | ||||
−0.432699 | + | 0.901538i | \(0.642439\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.80749 | 0.687411 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.4120 | −0.909701 | −0.454850 | − | 0.890568i | \(-0.650307\pi\) | ||||
−0.454850 | + | 0.890568i | \(0.650307\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.83057 | 0.592286 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.32323 | 0.199952 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.54877 | 0.815806 | 0.407903 | − | 0.913025i | \(-0.366260\pi\) | ||||
0.407903 | + | 0.913025i | \(0.366260\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.79344 | 0.321755 | 0.160878 | − | 0.986974i | \(-0.448568\pi\) | ||||
0.160878 | + | 0.986974i | \(0.448568\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.33926 | −0.786508 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.2241 | −1.43038 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.50454 | −0.206571 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.9128 | −0.975932 | −0.487966 | − | 0.872863i | \(-0.662261\pi\) | ||||
−0.487966 | + | 0.872863i | \(0.662261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.72691 | 0.221913 | 0.110957 | − | 0.993825i | \(-0.464609\pi\) | ||||
0.110957 | + | 0.993825i | \(0.464609\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.5429 | 1.25657 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0703 | −0.969508 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.6826 | −1.33142 | −0.665709 | − | 0.746211i | \(-0.731871\pi\) | ||||
−0.665709 | + | 0.746211i | \(0.731871\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.52231 | −0.437948 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.61279 | 0.363539 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.436737 | −0.0342079 | −0.0171039 | − | 0.999854i | \(-0.505445\pi\) | ||||
−0.0171039 | + | 0.999854i | \(0.505445\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.51859 | −0.663172 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.7177 | 1.21627 | 0.608137 | − | 0.793832i | \(-0.291917\pi\) | ||||
0.608137 | + | 0.793832i | \(0.291917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.3546 | 1.70950 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.8487 | 1.12893 | 0.564464 | − | 0.825458i | \(-0.309083\pi\) | ||||
0.564464 | + | 0.825458i | \(0.309083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.56857 | 0.496537 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.7876 | 1.33700 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.9789 | −1.64278 | −0.821391 | − | 0.570365i | \(-0.806802\pi\) | ||||
−0.821391 | + | 0.570365i | \(0.806802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.68399 | −0.125170 | −0.0625849 | − | 0.998040i | \(-0.519934\pi\) | ||||
−0.0625849 | + | 0.998040i | \(0.519934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.64593 | −0.565204 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.0855 | 1.62376 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.74921 | −0.347297 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.683051 | −0.0496846 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2190 | 1.60771 | 0.803855 | − | 0.594825i | \(-0.202779\pi\) | ||||
0.803855 | + | 0.594825i | \(0.202779\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.53425 | −0.470346 | −0.235173 | − | 0.971954i | \(-0.575566\pi\) | ||||
−0.235173 | + | 0.971954i | \(0.575566\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.51859 | −0.610029 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.53473 | 0.251839 | 0.125919 | − | 0.992040i | \(-0.459812\pi\) | ||||
0.125919 | + | 0.992040i | \(0.459812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.268731 | 0.0190498 | 0.00952491 | − | 0.999955i | \(-0.496968\pi\) | ||||
0.00952491 | + | 0.999955i | \(0.496968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.8276 | 1.61014 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.06403 | 0.355425 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.61563 | 0.462056 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.0964 | 1.04927 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.83057 | −0.472481 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.7257 | −1.70218 | −0.851092 | − | 0.525016i | \(-0.824059\pi\) | ||||
−0.851092 | + | 0.525016i | \(0.824059\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.8624 | 0.812798 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.6029 | 0.723109 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.54877 | 0.240906 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.22435 | −0.353029 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.74921 | −0.319467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.2239 | 0.751608 | 0.375804 | − | 0.926699i | \(-0.377367\pi\) | ||||
0.375804 | + | 0.926699i | \(0.377367\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.4971 | 1.43314 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.36710 | 0.289854 | 0.144927 | − | 0.989442i | \(-0.453705\pi\) | ||||
0.144927 | + | 0.989442i | \(0.453705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.3914 | 1.67791 | 0.838956 | − | 0.544199i | \(-0.183166\pi\) | ||||
0.838956 | + | 0.544199i | \(0.183166\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.50454 | 0.164787 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.39913 | 0.288196 | 0.144098 | − | 0.989563i | \(-0.453972\pi\) | ||||
0.144098 | + | 0.989563i | \(0.453972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.6831 | −0.827352 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.4612 | 1.45901 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.3408 | −0.862945 | −0.431472 | − | 0.902126i | \(-0.642006\pi\) | ||||
−0.431472 | + | 0.902126i | \(0.642006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.3475 | 0.795372 | 0.397686 | − | 0.917522i | \(-0.369813\pi\) | ||||
0.397686 | + | 0.917522i | \(0.369813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3546 | 1.43405 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.40126 | −0.217299 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.83057 | −0.434619 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −35.0388 | −2.22049 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6268 | −0.923238 | −0.461619 | − | 0.887078i | \(-0.652731\pi\) | ||||
−0.461619 | + | 0.887078i | \(0.652731\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.61279 | −0.290004 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 40.4566 | 2.53349 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.6285 | −0.912501 | −0.456251 | − | 0.889851i | \(-0.650808\pi\) | ||||
−0.456251 | + | 0.889851i | \(0.650808\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.49334 | −0.403477 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.5732 | 1.02585 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.40458 | 0.148272 | 0.0741362 | − | 0.997248i | \(-0.476380\pi\) | ||||
0.0741362 | + | 0.997248i | \(0.476380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.49951 | −0.460691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.5991 | −1.32185 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.60040 | −0.402433 | −0.201217 | − | 0.979547i | \(-0.564490\pi\) | ||||
−0.201217 | + | 0.979547i | \(0.564490\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.1119 | −0.796494 | −0.398247 | − | 0.917278i | \(-0.630381\pi\) | ||||
−0.398247 | + | 0.917278i | \(0.630381\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.50454 | 0.151582 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.56857 | −0.396100 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.1888 | −0.912607 | −0.456303 | − | 0.889824i | \(-0.650827\pi\) | ||||
−0.456303 | + | 0.889824i | \(0.650827\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.6141 | 0.695320 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.0642 | 1.49520 | 0.747601 | − | 0.664148i | \(-0.231205\pi\) | ||||
0.747601 | + | 0.664148i | \(0.231205\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.5239 | −1.81446 | −0.907229 | − | 0.420638i | \(-0.861806\pi\) | ||||
−0.907229 | + | 0.420638i | \(0.861806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 58.1869 | 3.44669 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.94505 | −0.114813 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.55503 | 0.326767 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.74009 | −0.453732 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.9785 | 1.28399 | 0.641997 | − | 0.766707i | \(-0.278106\pi\) | ||||
0.641997 | + | 0.766707i | \(0.278106\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.1562 | 1.40643 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.683051 | 0.0396346 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.61279 | −0.266765 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.11733 | −0.179680 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.6818 | −0.843445 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.3835 | −0.594555 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.13713 | 0.350265 | 0.175132 | − | 0.984545i | \(-0.443965\pi\) | ||||
0.175132 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.0363 | −1.13983 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.4644 | −0.876904 | −0.438452 | − | 0.898755i | \(-0.644473\pi\) | ||||
−0.438452 | + | 0.898755i | \(0.644473\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.61948 | −0.430679 | −0.215339 | − | 0.976539i | \(-0.569086\pi\) | ||||
−0.215339 | + | 0.976539i | \(0.569086\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.1314 | −0.627183 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.9807 | 1.68388 | 0.841942 | − | 0.539568i | \(-0.181412\pi\) | ||||
0.841942 | + | 0.539568i | \(0.181412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.06403 | −0.283531 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.0678 | 0.561928 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.4398 | 1.80500 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.56857 | −0.364359 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.7633 | −0.816411 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.72893 | 0.205583 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.8728 | 1.03735 | 0.518673 | − | 0.854973i | \(-0.326426\pi\) | ||||
0.518673 | + | 0.854973i | \(0.326426\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.2509 | −1.16454 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 31.0008 | 1.69375 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.5367 | 1.11871 | 0.559354 | − | 0.828929i | \(-0.311049\pi\) | ||||
0.559354 | + | 0.828929i | \(0.311049\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.542537 | 0.0294666 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.54877 | −0.192176 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 39.2945 | 2.11555 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.6848 | 0.734636 | 0.367318 | − | 0.930095i | \(-0.380276\pi\) | ||||
0.367318 | + | 0.930095i | \(0.380276\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.4422 | −1.09425 | −0.547123 | − | 0.837052i | \(-0.684277\pi\) | ||||
−0.547123 | + | 0.837052i | \(0.684277\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.683051 | 0.0364586 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.2096 | −1.12887 | −0.564437 | − | 0.825476i | \(-0.690907\pi\) | ||||
−0.564437 | + | 0.825476i | \(0.690907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.1096 | 0.855008 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.8946 | −0.629529 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.2260 | 1.70082 | 0.850411 | − | 0.526118i | \(-0.176353\pi\) | ||||
0.850411 | + | 0.526118i | \(0.176353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.6567 | 1.45562 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.50454 | −0.131454 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.09486 | −0.371362 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.03712 | 0.0541371 | 0.0270686 | − | 0.999634i | \(-0.491383\pi\) | ||||
0.0270686 | + | 0.999634i | \(0.491383\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.36562 | −0.331381 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.20492 | 0.114474 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.5811 | 1.53165 | 0.765826 | − | 0.643048i | \(-0.222331\pi\) | ||||
0.765826 | + | 0.643048i | \(0.222331\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.3620 | 0.690011 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.06403 | −0.260811 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.9666 | −1.74475 | −0.872373 | − | 0.488841i | \(-0.837420\pi\) | ||||
−0.872373 | + | 0.488841i | \(0.837420\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.4256 | 1.25136 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.0491 | −0.820071 | −0.410036 | − | 0.912070i | \(-0.634484\pi\) | ||||
−0.410036 | + | 0.912070i | \(0.634484\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.40126 | 0.173344 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.2022 | −0.518606 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.8381 | 1.41145 | 0.705723 | − | 0.708488i | \(-0.250622\pi\) | ||||
0.705723 | + | 0.708488i | \(0.250622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.9071 | 1.10789 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.0773 | 1.31542 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.5031 | 1.53478 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.4662 | 1.22792 | 0.613961 | − | 0.789337i | \(-0.289575\pi\) | ||||
0.613961 | + | 0.789337i | \(0.289575\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.1074 | −0.856444 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.96408 | 0.247894 | 0.123947 | − | 0.992289i | \(-0.460445\pi\) | ||||
0.123947 | + | 0.992289i | \(0.460445\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.54877 | −0.176777 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.5755 | 1.37024 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.49334 | 0.321863 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.91251 | 0.0945674 | 0.0472837 | − | 0.998882i | \(-0.484944\pi\) | ||||
0.0472837 | + | 0.998882i | \(0.484944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.9153 | −1.17965 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.10214 | −0.349473 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −47.5840 | −2.33581 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.50082 | −0.465257 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3762 | −0.848882 | −0.424441 | − | 0.905456i | \(-0.639529\pi\) | ||||
−0.424441 | + | 0.905456i | \(0.639529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.4971 | −1.19391 | −0.596957 | − | 0.802273i | \(-0.703624\pi\) | ||||
−0.596957 | + | 0.802273i | \(0.703624\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.2038 | 0.593368 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31.1955 | 1.51321 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.05283 | 0.147737 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.50454 | −0.120920 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.8775 | −1.34281 | −0.671407 | − | 0.741089i | \(-0.734310\pi\) | ||||
−0.671407 | + | 0.741089i | \(0.734310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.2563 | −1.55014 | −0.775069 | − | 0.631877i | \(-0.782285\pi\) | ||||
−0.775069 | + | 0.631877i | \(0.782285\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 43.1384 | 2.06833 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.5080 | 1.50723 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.4958 | 0.787301 | 0.393651 | − | 0.919260i | \(-0.371212\pi\) | ||||
0.393651 | + | 0.919260i | \(0.371212\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.27272 | 0.155844 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.3952 | −0.588912 | −0.294456 | − | 0.955665i | \(-0.595138\pi\) | ||||
−0.294456 | + | 0.955665i | \(0.595138\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.3324 | −1.39049 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.8360 | 1.41119 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.4891 | 1.25010 | 0.625049 | − | 0.780585i | \(-0.285079\pi\) | ||||
0.625049 | + | 0.780585i | \(0.285079\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.94505 | 0.0915890 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.82966 | −0.320886 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.40126 | 0.159454 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.8706 | −0.976284 | −0.488142 | − | 0.872764i | \(-0.662325\pi\) | ||||
−0.488142 | + | 0.872764i | \(0.662325\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.24395 | −0.151415 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.7483 | −0.547171 | −0.273585 | − | 0.961848i | \(-0.588210\pi\) | ||||
−0.273585 | + | 0.961848i | \(0.588210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.97159 | 0.323997 | 0.161999 | − | 0.986791i | \(-0.448206\pi\) | ||||
0.161999 | + | 0.986791i | \(0.448206\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.2305 | 1.40191 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.51362 | −0.162591 | −0.0812955 | − | 0.996690i | \(-0.525906\pi\) | ||||
−0.0812955 | + | 0.996690i | \(0.525906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.11450 | −0.420868 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 41.7823 | 1.92523 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.11733 | 0.143335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 44.8671 | 2.05864 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.21610 | 0.330402 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.8321 | −0.494932 | −0.247466 | − | 0.968897i | \(-0.579598\pi\) | ||||
−0.247466 | + | 0.968897i | \(0.579598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.49334 | 0.296071 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.5529 | −0.525677 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.5113 | −0.477295 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.96237 | 0.134238 | 0.0671188 | − | 0.997745i | \(-0.478619\pi\) | ||||
0.0671188 | + | 0.997745i | \(0.478619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.09383 | 0.0494645 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.3620 | 1.59586 | 0.797932 | − | 0.602748i | \(-0.205927\pi\) | ||||
0.797932 | + | 0.602748i | \(0.205927\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.0502 | 1.08316 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.1314 | 0.500319 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.73636 | −0.212455 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.49035 | 0.335314 | 0.167657 | − | 0.985845i | \(-0.446380\pi\) | ||||
0.167657 | + | 0.985845i | \(0.446380\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.3657 | −1.75873 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.0239 | 0.803645 | 0.401822 | − | 0.915718i | \(-0.368377\pi\) | ||||
0.401822 | + | 0.915718i | \(0.368377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.9384 | −0.887246 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.50454 | −0.111231 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.6268 | 1.09156 | 0.545782 | − | 0.837927i | \(-0.316233\pi\) | ||||
0.545782 | + | 0.837927i | \(0.316233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.08595 | 0.0922771 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.66563 | −0.205992 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27.2101 | −1.19902 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.72893 | −0.163998 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.1893 | −1.63243 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.1145 | 0.705989 | 0.352995 | − | 0.935625i | \(-0.385163\pi\) | ||||
0.352995 | + | 0.935625i | \(0.385163\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.9776 | 0.786106 | 0.393053 | − | 0.919516i | \(-0.371419\pi\) | ||||
0.393053 | + | 0.919516i | \(0.371419\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.4513 | −0.717991 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.8538 | 0.734165 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.72213 | −0.0748754 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.2434 | −1.00868 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.94505 | 0.0842496 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6724 | 0.591109 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 55.0471 | 2.37546 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.1662 | 1.85586 | 0.927931 | − | 0.372753i | \(-0.121586\pi\) | ||||
0.927931 | + | 0.372753i | \(0.121586\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.21762 | 0.180995 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.0491 | −0.858808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.23891 | −0.352270 | −0.176135 | − | 0.984366i | \(-0.556360\pi\) | ||||
−0.176135 | + | 0.984366i | \(0.556360\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.99107 | 0.426408 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.5902 | 1.47359 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.96819 | −0.381366 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −55.3141 | −2.34795 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.7434 | −1.13315 | −0.566577 | − | 0.824009i | \(-0.691733\pi\) | ||||
−0.566577 | + | 0.824009i | \(0.691733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.11733 | 0.131849 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.8946 | 0.502190 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.9277 | −1.64061 | −0.820303 | − | 0.571929i | \(-0.806195\pi\) | ||||
−0.820303 | + | 0.571929i | \(0.806195\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.736785 | 0.0309968 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.10745 | −0.340481 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.66753 | 0.363362 | 0.181681 | − | 0.983358i | \(-0.441846\pi\) | ||||
0.181681 | + | 0.983358i | \(0.441846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5391 | 0.608443 | 0.304221 | − | 0.952601i | \(-0.401604\pi\) | ||||
0.304221 | + | 0.952601i | \(0.401604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −55.6484 | −2.32474 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.2995 | 1.26357 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.1304 | 1.08782 | 0.543912 | − | 0.839143i | \(-0.316943\pi\) | ||||
0.543912 | + | 0.839143i | \(0.316943\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.3653 | 0.680118 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.9901 | 0.580408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.20492 | −0.0913185 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.1314 | 0.460226 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 47.8062 | 1.97317 | 0.986587 | − | 0.163238i | \(-0.0521939\pi\) | ||||
0.986587 | + | 0.163238i | \(0.0521939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.2401 | 0.998796 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.85287 | −0.364158 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.7336 | 0.605035 | 0.302518 | − | 0.953144i | \(-0.402173\pi\) | ||||
0.302518 | + | 0.953144i | \(0.402173\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.1533 | −0.662221 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.673047 | −0.0275460 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.3876 | −0.792155 | −0.396077 | − | 0.918217i | \(-0.629629\pi\) | ||||
−0.396077 | + | 0.918217i | \(0.629629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.0650 | 0.940841 | 0.470421 | − | 0.882442i | \(-0.344102\pi\) | ||||
0.470421 | + | 0.882442i | \(0.344102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.8292 | −1.21474 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.40126 | −0.138281 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.6912 | 0.961596 | 0.480798 | − | 0.876831i | \(-0.340347\pi\) | ||||
0.480798 | + | 0.876831i | \(0.340347\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.6831 | −0.513944 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.72893 | −0.150856 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9990 | 0.484637 | 0.242318 | − | 0.970197i | \(-0.422092\pi\) | ||||
0.242318 | + | 0.970197i | \(0.422092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.5691 | −0.668131 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6930 | 0.511001 | 0.255501 | − | 0.966809i | \(-0.417760\pi\) | ||||
0.255501 | + | 0.966809i | \(0.417760\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.1566 | −1.21210 | −0.606048 | − | 0.795428i | \(-0.707246\pi\) | ||||
−0.606048 | + | 0.795428i | \(0.707246\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.15077 | −0.126436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.62399 | 0.345513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.6967 | −0.587870 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.1074 | 0.683206 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.8383 | −1.22960 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5643 | 0.619606 | 0.309803 | − | 0.950801i | \(-0.399737\pi\) | ||||
0.309803 | + | 0.950801i | \(0.399737\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 61.9264 | 2.46135 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33.1709 | 1.31635 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.5008 | −0.613202 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.1761 | 1.03389 | 0.516946 | − | 0.856018i | \(-0.327069\pi\) | ||||
0.516946 | + | 0.856018i | \(0.327069\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.8826 | −0.665786 | −0.332893 | − | 0.942965i | \(-0.608025\pi\) | ||||
−0.332893 | + | 0.942965i | \(0.608025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −26.5553 | −1.04561 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.3352 | 0.799458 | 0.399729 | − | 0.916633i | \(-0.369104\pi\) | ||||
0.399729 | + | 0.916633i | \(0.369104\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.10214 | 0.278783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.88803 | −0.348349 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.4731 | 1.50557 | 0.752784 | − | 0.658268i | \(-0.228710\pi\) | ||||
0.752784 | + | 0.658268i | \(0.228710\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.4139 | 1.38374 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.82675 | 0.266337 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.6248 | 1.46566 | 0.732828 | − | 0.680414i | \(-0.238200\pi\) | ||||
0.732828 | + | 0.680414i | \(0.238200\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.03341 | 0.195777 | 0.0978884 | − | 0.995197i | \(-0.468791\pi\) | ||||
0.0978884 | + | 0.995197i | \(0.468791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.8946 | 0.461948 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.2326 | −0.900920 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.3593 | 0.904476 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.1107 | −1.08682 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.05283 | −0.117853 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.3284 | −0.552320 | −0.276160 | − | 0.961112i | \(-0.589062\pi\) | ||||
−0.276160 | + | 0.961112i | \(0.589062\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.48667 | −0.172692 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.5366 | 0.597119 | 0.298560 | − | 0.954391i | \(-0.403494\pi\) | ||||
0.298560 | + | 0.954391i | \(0.403494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.09042 | 0.118600 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.9376 | −0.419129 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.8595 | 0.912959 | 0.456479 | − | 0.889734i | \(-0.349110\pi\) | ||||
0.456479 | + | 0.889734i | \(0.349110\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.4778 | −1.24091 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −63.5939 | −2.42626 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.20492 | −0.0840008 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.5720 | −0.934761 | −0.467381 | − | 0.884056i | \(-0.654802\pi\) | ||||
−0.467381 | + | 0.884056i | \(0.654802\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.27272 | −0.124321 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.9025 | −0.489419 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.23747 | −0.349894 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.0178 | −0.416731 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.3814 | 0.580946 | 0.290473 | − | 0.956883i | \(-0.406187\pi\) | ||||
0.290473 | + | 0.956883i | \(0.406187\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.3532 | −1.67281 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31.7653 | 1.19635 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.86205 | 0.220465 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.55709 | −0.0584777 | −0.0292388 | − | 0.999572i | \(-0.509308\pi\) | ||||
−0.0292388 | + | 0.999572i | \(0.509308\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.3504 | −1.10073 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.3697 | 0.613051 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.40126 | −0.127200 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.4126 | 1.24782 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.0280 | −0.858799 | −0.429399 | − | 0.903115i | \(-0.641275\pi\) | ||||
−0.429399 | + | 0.903115i | \(0.641275\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.9248 | −1.15011 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.2634 | 1.23537 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.73851 | −0.249918 | −0.124959 | − | 0.992162i | \(-0.539880\pi\) | ||||
−0.124959 | + | 0.992162i | \(0.539880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31.6656 | −1.17280 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.8049 | −0.547579 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.3830 | 1.86094 | 0.930470 | − | 0.366368i | \(-0.119399\pi\) | ||||
0.930470 | + | 0.366368i | \(0.119399\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.51859 | 0.314213 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.11450 | 0.335737 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.4220 | −0.935162 | −0.467581 | − | 0.883950i | \(-0.654874\pi\) | ||||
−0.467581 | + | 0.883950i | \(0.654874\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.1074 | 0.628458 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.3196 | −0.525336 | −0.262668 | − | 0.964886i | \(-0.584602\pi\) | ||||
−0.262668 | + | 0.964886i | \(0.584602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.5184 | 1.48448 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 45.7858 | 1.67521 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.01980 | −0.146880 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.7786 | −1.45154 | −0.725770 | − | 0.687937i | \(-0.758517\pi\) | ||||
−0.725770 | + | 0.687937i | \(0.758517\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.6335 | 1.33500 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.27494 | −0.337550 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.33088 | −0.157409 | −0.0787043 | − | 0.996898i | \(-0.525078\pi\) | ||||
−0.0787043 | + | 0.996898i | \(0.525078\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.5529 | 0.419345 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.27636 | 0.0825179 | 0.0412590 | − | 0.999148i | \(-0.486863\pi\) | ||||
0.0412590 | + | 0.999148i | \(0.486863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.89460 | 0.213399 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −52.8653 | −1.91135 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.10214 | 0.256443 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.6391 | 1.24912 | 0.624559 | − | 0.780977i | \(-0.285279\pi\) | ||||
0.624559 | + | 0.780977i | \(0.285279\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.6377 | 1.31947 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −47.7438 | −1.71723 | −0.858613 | − | 0.512624i | \(-0.828674\pi\) | ||||
−0.858613 | + | 0.512624i | \(0.828674\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.3103 | 0.837331 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.2628 | 0.583426 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.2858 | −0.476014 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.73636 | 0.169480 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.45899 | −0.123614 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.7419 | 2.02521 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.8931 | −1.63591 | −0.817956 | − | 0.575280i | \(-0.804893\pi\) | ||||
−0.817956 | + | 0.575280i | \(0.804893\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.02236 | −0.214402 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.216621 | −0.00770217 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.05283 | −0.108409 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.7828 | 0.666158 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.3065 | −0.435918 | −0.217959 | − | 0.975958i | \(-0.569940\pi\) | ||||
−0.217959 | + | 0.975958i | \(0.569940\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.7095 | 0.626517 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.2240 | 0.997245 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.08595 | −0.0736116 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.6893 | −0.552976 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.5310 | 0.581917 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.8801 | −1.22632 | −0.613160 | − | 0.789959i | \(-0.710102\pi\) | ||||
−0.613160 | + | 0.789959i | \(0.710102\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.9109 | 1.57703 | 0.788517 | − | 0.615013i | \(-0.210849\pi\) | ||||
0.788517 | + | 0.615013i | \(0.210849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.8394 | 1.15173 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.48546 | 0.0520332 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.2932 | −0.744954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.27272 | −0.114358 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4159 | −0.747420 | −0.373710 | − | 0.927546i | \(-0.621914\pi\) | ||||
−0.373710 | + | 0.927546i | \(0.621914\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.2815 | −1.09040 | −0.545202 | − | 0.838305i | \(-0.683547\pi\) | ||||
−0.545202 | + | 0.838305i | \(0.683547\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.4513 | 0.572759 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.0389 | 1.46183 | 0.730917 | − | 0.682466i | \(-0.239093\pi\) | ||||
0.730917 | + | 0.682466i | \(0.239093\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.9982 | 0.625104 | 0.312552 | − | 0.949901i | \(-0.398816\pi\) | ||||
0.312552 | + | 0.949901i | \(0.398816\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 38.0410 | 1.31963 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.74921 | 0.164551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −53.4601 | −1.85006 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.42399 | −0.0837852 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.6970 | −1.40502 | −0.702509 | − | 0.711675i | \(-0.747937\pi\) | ||||
−0.702509 | + | 0.711675i | \(0.747937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.35561 | −0.115711 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −62.7742 | −2.16206 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.40126 | −0.117007 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 76.4484 | 2.62370 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.9524 | −1.02676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.1941 | −0.588715 | −0.294357 | − | 0.955695i | \(-0.595106\pi\) | ||||
−0.294357 | + | 0.955695i | \(0.595106\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −76.0337 | −2.60030 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.5654 | 0.770820 | 0.385410 | − | 0.922745i | \(-0.374060\pi\) | ||||
0.385410 | + | 0.922745i | \(0.374060\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.9268 | −1.56700 | −0.783500 | − | 0.621391i | \(-0.786568\pi\) | ||||
−0.783500 | + | 0.621391i | \(0.786568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.87146 | 0.166019 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.8399 | 1.93485 | 0.967426 | − | 0.253154i | \(-0.0814679\pi\) | ||||
0.967426 | + | 0.253154i | \(0.0814679\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.5044 | −1.71720 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.9128 | −0.472504 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.96819 | 0.304225 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.11450 | 0.308833 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.1141 | 0.342311 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.33511 | −0.180360 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.50993 | −0.253592 | −0.126796 | − | 0.991929i | \(-0.540469\pi\) | ||||
−0.126796 | + | 0.991929i | \(0.540469\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −55.0459 | −1.85665 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.1431 | −0.948165 | −0.474083 | − | 0.880480i | \(-0.657220\pi\) | ||||
−0.474083 | + | 0.880480i | \(0.657220\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.6109 | −1.70319 | −0.851596 | − | 0.524199i | \(-0.824365\pi\) | ||||
−0.851596 | + | 0.524199i | \(0.824365\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −60.5003 | −2.03369 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.3430 | 0.481592 | 0.240796 | − | 0.970576i | \(-0.422592\pi\) | ||||
0.240796 | + | 0.970576i | \(0.422592\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.75255 | −0.327090 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.10745 | 0.271610 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.4707 | 0.852346 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 74.7560 | 2.49882 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.5529 | 0.385741 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9710 | 0.599368 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.4716 | 0.348861 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.80749 | 0.259817 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.72768 | 0.190395 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5218 | −0.448982 | −0.224491 | − | 0.974476i | \(-0.572072\pi\) | ||||
−0.224491 | + | 0.974476i | \(0.572072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.1849 | 0.636323 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.2557 | −1.76444 | −0.882221 | − | 0.470836i | \(-0.843952\pi\) | ||||
−0.882221 | + | 0.470836i | \(0.843952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.9901 | −0.463005 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.0058 | 0.859725 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.4120 | −0.343834 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.04948 | −0.265528 | −0.132764 | − | 0.991148i | \(-0.542385\pi\) | ||||
−0.132764 | + | 0.991148i | \(0.542385\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3707 | −0.506482 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.73636 | 0.155899 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.6520 | −1.40239 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.1818 | 0.859923 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.3219 | −1.06045 | −0.530224 | − | 0.847857i | \(-0.677892\pi\) | ||||
−0.530224 | + | 0.847857i | \(0.677892\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.83057 | 0.223863 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38.7311 | 1.26800 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.1533 | 0.528270 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.72242 | −0.219612 | −0.109806 | − | 0.993953i | \(-0.535023\pi\) | ||||
−0.109806 | + | 0.993953i | \(0.535023\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.0833 | 0.622760 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.0779 | 1.37170 | 0.685850 | − | 0.727743i | \(-0.259431\pi\) | ||||
0.685850 | + | 0.727743i | \(0.259431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.97213 | −0.292173 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.32323 | 0.0755748 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.2864 | −0.431750 | −0.215875 | − | 0.976421i | \(-0.569260\pi\) | ||||
−0.215875 | + | 0.976421i | \(0.569260\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.08595 | −0.0677129 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −75.0879 | −2.43489 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.28886 | −0.203716 | −0.101858 | − | 0.994799i | \(-0.532479\pi\) | ||||
−0.101858 | + | 0.994799i | \(0.532479\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −75.5726 | −2.44547 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.6831 | 0.409985 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.54877 | 0.308346 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.4063 | −0.593751 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.1557 | −0.423937 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.2247 | 0.715438 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.8963 | −1.76535 | −0.882674 | − | 0.469987i | \(-0.844259\pi\) | ||||
−0.882674 | + | 0.469987i | \(0.844259\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −81.2469 | −2.61003 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.6192 | 0.501244 | 0.250622 | − | 0.968085i | \(-0.419365\pi\) | ||||
0.250622 | + | 0.968085i | \(0.419365\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.79344 | 0.121612 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.4513 | 0.526862 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.7243 | 1.81477 | 0.907385 | − | 0.420300i | \(-0.138075\pi\) | ||||
0.907385 | + | 0.420300i | \(0.138075\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.62399 | −0.275624 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.2914 | 0.615927 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.1589 | −1.08950 | −0.544750 | − | 0.838598i | \(-0.683376\pi\) | ||||
−0.544750 | + | 0.838598i | \(0.683376\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0225 | −0.383070 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.33926 | −0.297272 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.3796 | −0.457245 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0774 | −0.637779 | −0.318889 | − | 0.947792i | \(-0.603310\pi\) | ||||
−0.318889 | + | 0.947792i | \(0.603310\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −47.2678 | −1.50000 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.914023 | −0.0289765 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.6440 | −0.368769 | −0.184384 | − | 0.982854i | \(-0.559029\pi\) | ||||
−0.184384 | + | 0.982854i | \(0.559029\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.43528 | 0.140326 |
(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 | 8008.2.a.k.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.k.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |