Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5760,2,Mod(1,5760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5760, 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("5760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5760 = 2^{7} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5760.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: | \(45.9938315643\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 640) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5760.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.47214 | 1.02598 | 0.512989 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512989 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.76393 | −0.993348 | −0.496674 | − | 0.867937i | \(-0.665446\pi\) | ||||
−0.496674 | + | 0.867937i | \(0.665446\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.47214 | −1.16243 | −0.581215 | − | 0.813750i | \(-0.697422\pi\) | ||||
−0.581215 | + | 0.813750i | \(0.697422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.23607 | 0.546995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.94427 | 1.14163 | 0.570816 | − | 0.821078i | \(-0.306627\pi\) | ||||
0.570816 | + | 0.821078i | \(0.306627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4721 | −1.94782 | −0.973910 | − | 0.226934i | \(-0.927130\pi\) | ||||
−0.973910 | + | 0.226934i | \(0.927130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.70820 | 1.17549 | 0.587745 | − | 0.809046i | \(-0.300016\pi\) | ||||
0.587745 | + | 0.809046i | \(0.300016\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.23607 | −1.05549 | −0.527744 | − | 0.849403i | \(-0.676962\pi\) | ||||
−0.527744 | + | 0.849403i | \(0.676962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.47214 | −1.10298 | −0.551489 | − | 0.834182i | \(-0.685940\pi\) | ||||
−0.551489 | + | 0.834182i | \(0.685940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.70820 | −0.941707 | −0.470853 | − | 0.882211i | \(-0.656054\pi\) | ||||
−0.470853 | + | 0.882211i | \(0.656054\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.47214 | −0.293389 | −0.146694 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146694 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.47214 | 0.523424 | 0.261712 | − | 0.965146i | \(-0.415713\pi\) | ||||
0.261712 | + | 0.965146i | \(0.415713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.47214 | −0.737568 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9443 | −1.45634 | −0.728172 | − | 0.685394i | \(-0.759630\pi\) | ||||
−0.728172 | + | 0.685394i | \(0.759630\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.70820 | −0.407028 | −0.203514 | − | 0.979072i | \(-0.565236\pi\) | ||||
−0.203514 | + | 0.979072i | \(0.565236\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.47214 | −0.485071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.9443 | 1.58409 | 0.792045 | − | 0.610463i | \(-0.209017\pi\) | ||||
0.792045 | + | 0.610463i | \(0.209017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.4721 | −1.51709 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.47214 | 0.458831 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.4721 | −1.67249 | −0.836246 | − | 0.548354i | \(-0.815254\pi\) | ||||
−0.836246 | + | 0.548354i | \(0.815254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.23607 | −0.318859 | −0.159430 | − | 0.987209i | \(-0.550966\pi\) | ||||
−0.159430 | + | 0.987209i | \(0.550966\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.2361 | −1.66627 | −0.833137 | − | 0.553067i | \(-0.813457\pi\) | ||||
−0.833137 | + | 0.553067i | \(0.813457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9443 | 1.43140 | 0.715701 | − | 0.698407i | \(-0.246107\pi\) | ||||
0.715701 | + | 0.698407i | \(0.246107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.94427 | 0.276974 | 0.138487 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138487 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.76393 | −0.444239 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.4721 | −1.32666 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.1803 | 1.79072 | 0.895358 | − | 0.445348i | \(-0.146920\pi\) | ||||
0.895358 | + | 0.445348i | \(0.146920\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9443 | 1.30569 | 0.652844 | − | 0.757493i | \(-0.273576\pi\) | ||||
0.652844 | + | 0.757493i | \(0.273576\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4721 | 1.25489 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.4721 | −1.73642 | −0.868212 | − | 0.496194i | \(-0.834731\pi\) | ||||
−0.868212 | + | 0.496194i | \(0.834731\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.94427 | 0.747958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.94427 | −0.568897 | −0.284448 | − | 0.958691i | \(-0.591810\pi\) | ||||
−0.284448 | + | 0.958691i | \(0.591810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.4164 | −1.90560 | −0.952800 | − | 0.303598i | \(-0.901812\pi\) | ||||
−0.952800 | + | 0.303598i | \(0.901812\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.47214 | −0.519854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.05573 | 0.403491 | 0.201746 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201746 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.4164 | −1.21498 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7082 | 0.917057 | 0.458529 | − | 0.888680i | \(-0.348377\pi\) | ||||
0.458529 | + | 0.888680i | \(0.348377\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.6525 | 1.13384 | 0.566921 | − | 0.823772i | \(-0.308134\pi\) | ||||
0.566921 | + | 0.823772i | \(0.308134\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9443 | 0.832078 | 0.416039 | − | 0.909347i | \(-0.363418\pi\) | ||||
0.416039 | + | 0.909347i | \(0.363418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.23607 | 0.244624 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.4721 | −1.53016 | −0.765080 | − | 0.643936i | \(-0.777300\pi\) | ||||
−0.765080 | + | 0.643936i | \(0.777300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9443 | 0.813481 | 0.406741 | − | 0.913544i | \(-0.366665\pi\) | ||||
0.406741 | + | 0.913544i | \(0.366665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.94427 | 0.510553 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.94427 | 0.654070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.4164 | 0.826062 | 0.413031 | − | 0.910717i | \(-0.364470\pi\) | ||||
0.413031 | + | 0.910717i | \(0.364470\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5279 | −0.829794 | −0.414897 | − | 0.909868i | \(-0.636182\pi\) | ||||
−0.414897 | + | 0.909868i | \(0.636182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.472136 | −0.0336383 | −0.0168191 | − | 0.999859i | \(-0.505354\pi\) | ||||
−0.0168191 | + | 0.999859i | \(0.505354\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.944272 | 0.0669377 | 0.0334688 | − | 0.999440i | \(-0.489345\pi\) | ||||
0.0334688 | + | 0.999440i | \(0.489345\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.47214 | 0.454255 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.4721 | −0.871092 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.94427 | −0.618688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.05573 | 0.0726793 | 0.0363397 | − | 0.999339i | \(-0.488430\pi\) | ||||
0.0363397 | + | 0.999339i | \(0.488430\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.70820 | 0.525695 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.9443 | −1.42179 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0000 | 1.34535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.76393 | 0.586876 | 0.293438 | − | 0.955978i | \(-0.405201\pi\) | ||||
0.293438 | + | 0.955978i | \(0.405201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.1803 | −0.675693 | −0.337846 | − | 0.941201i | \(-0.609698\pi\) | ||||
−0.337846 | + | 0.941201i | \(0.609698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.94427 | 0.194563 | 0.0972815 | − | 0.995257i | \(-0.468985\pi\) | ||||
0.0972815 | + | 0.995257i | \(0.468985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.5279 | −1.01726 | −0.508632 | − | 0.860984i | \(-0.669849\pi\) | ||||
−0.508632 | + | 0.860984i | \(0.669849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.23607 | −0.472029 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.9443 | −0.837295 | −0.418648 | − | 0.908149i | \(-0.637496\pi\) | ||||
−0.418648 | + | 0.908149i | \(0.637496\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.3607 | 1.69804 | 0.849020 | − | 0.528360i | \(-0.177193\pi\) | ||||
0.849020 | + | 0.528360i | \(0.177193\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.47214 | 0.221827 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.0000 | −1.27257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.00000 | −0.126239 | −0.0631194 | − | 0.998006i | \(-0.520105\pi\) | ||||
−0.0631194 | + | 0.998006i | \(0.520105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.52786 | 0.599012 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.94427 | 0.183659 | 0.0918293 | − | 0.995775i | \(-0.470729\pi\) | ||||
0.0918293 | + | 0.995775i | \(0.470729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.4721 | 1.39635 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.7082 | −1.09193 | −0.545967 | − | 0.837806i | \(-0.683838\pi\) | ||||
−0.545967 | + | 0.837806i | \(0.683838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.472136 | −0.0290031 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.8885 | 1.45651 | 0.728255 | − | 0.685306i | \(-0.240332\pi\) | ||||
0.728255 | + | 0.685306i | \(0.240332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.3607 | 1.47981 | 0.739903 | − | 0.672714i | \(-0.234871\pi\) | ||||
0.739903 | + | 0.672714i | \(0.234871\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.9443 | −0.657578 | −0.328789 | − | 0.944403i | \(-0.606640\pi\) | ||||
−0.328789 | + | 0.944403i | \(0.606640\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.52786 | −0.210455 | −0.105227 | − | 0.994448i | \(-0.533557\pi\) | ||||
−0.105227 | + | 0.994448i | \(0.533557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.29180 | −0.492896 | −0.246448 | − | 0.969156i | \(-0.579263\pi\) | ||||
−0.246448 | + | 0.969156i | \(0.579263\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.3607 | −2.38242 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.8885 | 1.39558 | 0.697792 | − | 0.716301i | \(-0.254166\pi\) | ||||
0.697792 | + | 0.716301i | \(0.254166\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.47214 | −0.493267 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.3050 | 1.23210 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.9443 | 1.43776 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.291796 | 0.0166537 | 0.00832684 | − | 0.999965i | \(-0.497349\pi\) | ||||
0.00832684 | + | 0.999965i | \(0.497349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.4164 | −0.874184 | −0.437092 | − | 0.899417i | \(-0.643992\pi\) | ||||
−0.437092 | + | 0.899417i | \(0.643992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.8328 | −1.62973 | −0.814864 | − | 0.579653i | \(-0.803188\pi\) | ||||
−0.814864 | + | 0.579653i | \(0.803188\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.4721 | 1.14983 | 0.574915 | − | 0.818213i | \(-0.305035\pi\) | ||||
0.574915 | + | 0.818213i | \(0.305035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0000 | −1.11283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.47214 | −0.248069 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.4164 | −1.29099 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.8885 | −0.873313 | −0.436657 | − | 0.899628i | \(-0.643838\pi\) | ||||
−0.436657 | + | 0.899628i | \(0.643838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.70820 | −0.421144 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.05573 | 0.275403 | 0.137702 | − | 0.990474i | \(-0.456029\pi\) | ||||
0.137702 | + | 0.990474i | \(0.456029\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.9443 | 0.700972 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.2361 | −0.925281 | −0.462640 | − | 0.886546i | \(-0.653098\pi\) | ||||
−0.462640 | + | 0.886546i | \(0.653098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.9443 | −0.799949 | −0.399974 | − | 0.916526i | \(-0.630981\pi\) | ||||
−0.399974 | + | 0.916526i | \(0.630981\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.05573 | −0.269089 | −0.134545 | − | 0.990908i | \(-0.542957\pi\) | ||||
−0.134545 | + | 0.990908i | \(0.542957\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.47214 | −0.131207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0557 | −0.794611 | −0.397305 | − | 0.917686i | \(-0.630055\pi\) | ||||
−0.397305 | + | 0.917686i | \(0.630055\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.47214 | 0.234082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2918 | 0.954824 | 0.477412 | − | 0.878680i | \(-0.341575\pi\) | ||||
0.477412 | + | 0.878680i | \(0.341575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.52786 | −0.0793227 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.05573 | 0.261776 | 0.130888 | − | 0.991397i | \(-0.458217\pi\) | ||||
0.130888 | + | 0.991397i | \(0.458217\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.94427 | −0.460653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.5279 | −0.797613 | −0.398806 | − | 0.917035i | \(-0.630575\pi\) | ||||
−0.398806 | + | 0.917035i | \(0.630575\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.2918 | 0.525886 | 0.262943 | − | 0.964811i | \(-0.415307\pi\) | ||||
0.262943 | + | 0.964811i | \(0.415307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.47214 | −0.329851 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.8885 | −0.602773 | −0.301387 | − | 0.953502i | \(-0.597449\pi\) | ||||
−0.301387 | + | 0.953502i | \(0.597449\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.3050 | 1.07744 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.9443 | −0.651297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.4721 | −0.625959 | −0.312979 | − | 0.949760i | \(-0.601327\pi\) | ||||
−0.312979 | + | 0.949760i | \(0.601327\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.9443 | 1.44182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.8885 | −0.688430 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.4164 | 0.861186 | 0.430593 | − | 0.902546i | \(-0.358304\pi\) | ||||
0.430593 | + | 0.902546i | \(0.358304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.4164 | −1.34907 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.70820 | −0.182029 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.47214 | −0.218478 | −0.109239 | − | 0.994016i | \(-0.534841\pi\) | ||||
−0.109239 | + | 0.994016i | \(0.534841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.8328 | −1.40523 | −0.702613 | − | 0.711572i | \(-0.747983\pi\) | ||||
−0.702613 | + | 0.711572i | \(0.747983\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.47214 | −0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.4164 | −0.939626 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.3607 | −1.17341 | −0.586706 | − | 0.809800i | \(-0.699576\pi\) | ||||
−0.586706 | + | 0.809800i | \(0.699576\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.472136 | −0.0226894 | −0.0113447 | − | 0.999936i | \(-0.503611\pi\) | ||||
−0.0113447 | + | 0.999936i | \(0.503611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.3050 | −1.01915 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.0557 | −0.718571 | −0.359285 | − | 0.933228i | \(-0.616980\pi\) | ||||
−0.359285 | + | 0.933228i | \(0.616980\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.65248 | −0.221046 | −0.110523 | − | 0.993874i | \(-0.535253\pi\) | ||||
−0.110523 | + | 0.993874i | \(0.535253\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.9443 | 0.708426 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.41641 | 0.0668444 | 0.0334222 | − | 0.999441i | \(-0.489359\pi\) | ||||
0.0334222 | + | 0.999441i | \(0.489359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.9443 | 1.17458 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.4721 | −0.678464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.88854 | 0.181898 | 0.0909492 | − | 0.995856i | \(-0.471010\pi\) | ||||
0.0909492 | + | 0.995856i | \(0.471010\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41.7771 | −1.94575 | −0.972876 | − | 0.231325i | \(-0.925694\pi\) | ||||
−0.972876 | + | 0.231325i | \(0.925694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.12461 | −0.0522651 | −0.0261326 | − | 0.999658i | \(-0.508319\pi\) | ||||
−0.0261326 | + | 0.999658i | \(0.508319\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.5967 | 1.92487 | 0.962434 | − | 0.271516i | \(-0.0875249\pi\) | ||||
0.962434 | + | 0.271516i | \(0.0875249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.9443 | −1.15182 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.4164 | −0.708847 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.47214 | 0.205196 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.9443 | 0.591439 | 0.295719 | − | 0.955275i | \(-0.404441\pi\) | ||||
0.295719 | + | 0.955275i | \(0.404441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.0557 | −1.41602 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.4721 | −0.747961 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.7639 | −0.578389 | −0.289194 | − | 0.957270i | \(-0.593387\pi\) | ||||
−0.289194 | + | 0.957270i | \(0.593387\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.0557 | −0.950232 | −0.475116 | − | 0.879923i | \(-0.657594\pi\) | ||||
−0.475116 | + | 0.879923i | \(0.657594\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.94427 | −0.402830 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5836 | −0.652851 | −0.326426 | − | 0.945223i | \(-0.605844\pi\) | ||||
−0.326426 | + | 0.945223i | \(0.605844\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.12461 | 0.228495 | 0.114248 | − | 0.993452i | \(-0.463554\pi\) | ||||
0.114248 | + | 0.993452i | \(0.463554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.8328 | 0.746101 | 0.373051 | − | 0.927811i | \(-0.378312\pi\) | ||||
0.373051 | + | 0.927811i | \(0.378312\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.4721 | 0.640210 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.23607 | −0.142598 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.4721 | 0.636484 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.8885 | 0.696090 | 0.348045 | − | 0.937478i | \(-0.386846\pi\) | ||||
0.348045 | + | 0.937478i | \(0.386846\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0689 | −0.877551 | −0.438776 | − | 0.898597i | \(-0.644588\pi\) | ||||
−0.438776 | + | 0.898597i | \(0.644588\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.9443 | 1.26083 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.304952 | −0.0132588 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 55.7771 | 2.41597 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.2361 | −0.745180 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.94427 | −0.299111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.8885 | 1.02705 | 0.513524 | − | 0.858075i | \(-0.328340\pi\) | ||||
0.513524 | + | 0.858075i | \(0.328340\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.9443 | 0.640142 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.6525 | −0.883036 | −0.441518 | − | 0.897252i | \(-0.645560\pi\) | ||||
−0.441518 | + | 0.897252i | \(0.645560\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.94427 | 0.381039 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.8885 | −1.78128 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.0557 | −0.553189 | −0.276594 | − | 0.960987i | \(-0.589206\pi\) | ||||
−0.276594 | + | 0.960987i | \(0.589206\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.4721 | −1.45802 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.29180 | 0.180878 | 0.0904388 | − | 0.995902i | \(-0.471173\pi\) | ||||
0.0904388 | + | 0.995902i | \(0.471173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.94427 | 0.123866 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.3607 | 1.44047 | 0.720237 | − | 0.693728i | \(-0.244033\pi\) | ||||
0.720237 | + | 0.693728i | \(0.244033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.8328 | 0.704431 | 0.352216 | − | 0.935919i | \(-0.385428\pi\) | ||||
0.352216 | + | 0.935919i | \(0.385428\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.76393 | −0.198670 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.8885 | 0.827971 | 0.413985 | − | 0.910283i | \(-0.364136\pi\) | ||||
0.413985 | + | 0.910283i | \(0.364136\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.944272 | 0.0391077 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.65248 | 0.357126 | 0.178563 | − | 0.983928i | \(-0.442855\pi\) | ||||
0.178563 | + | 0.983928i | \(0.442855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.9443 | −1.19263 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.0000 | 0.574911 | 0.287456 | − | 0.957794i | \(-0.407191\pi\) | ||||
0.287456 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.4721 | −0.593300 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.8885 | −0.894342 | −0.447171 | − | 0.894449i | \(-0.647568\pi\) | ||||
−0.447171 | + | 0.894449i | \(0.647568\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.3607 | −0.912111 | −0.456056 | − | 0.889951i | \(-0.650738\pi\) | ||||
−0.456056 | + | 0.889951i | \(0.650738\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.87539 | −0.279063 | −0.139532 | − | 0.990218i | \(-0.544560\pi\) | ||||
−0.139532 | + | 0.990218i | \(0.544560\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.3607 | 1.30917 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5279 | 0.788723 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4164 | −1.02323 | −0.511613 | − | 0.859216i | \(-0.670952\pi\) | ||||
−0.511613 | + | 0.859216i | \(0.670952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.4721 | −0.822845 | −0.411422 | − | 0.911445i | \(-0.634968\pi\) | ||||
−0.411422 | + | 0.911445i | \(0.634968\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 48.3607 | 1.93753 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.0557 | −1.23827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.4721 | 1.37231 | 0.686157 | − | 0.727453i | \(-0.259296\pi\) | ||||
0.686157 | + | 0.727453i | \(0.259296\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.1803 | 0.800832 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5279 | −0.615236 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.472136 | −0.0186482 | −0.00932412 | − | 0.999957i | \(-0.502968\pi\) | ||||
−0.00932412 | + | 0.999957i | \(0.502968\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.1803 | −0.874707 | −0.437354 | − | 0.899290i | \(-0.644084\pi\) | ||||
−0.437354 | + | 0.899290i | \(0.644084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.7639 | 0.501802 | 0.250901 | − | 0.968013i | \(-0.419273\pi\) | ||||
0.250901 | + | 0.968013i | \(0.419273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.9443 | 0.665121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 49.4164 | 1.93381 | 0.966907 | − | 0.255130i | \(-0.0821183\pi\) | ||||
0.966907 | + | 0.255130i | \(0.0821183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.9443 | 0.583921 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.4164 | 0.834265 | 0.417132 | − | 0.908846i | \(-0.363035\pi\) | ||||
0.417132 | + | 0.908846i | \(0.363035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.8885 | 1.39590 | 0.697951 | − | 0.716145i | \(-0.254095\pi\) | ||||
0.697951 | + | 0.716145i | \(0.254095\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.4721 | 0.561205 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.52786 | −0.368920 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.3050 | −0.898340 | −0.449170 | − | 0.893446i | \(-0.648280\pi\) | ||||
−0.449170 | + | 0.893446i | \(0.648280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.3607 | 1.16686 | 0.583428 | − | 0.812165i | \(-0.301711\pi\) | ||||
0.583428 | + | 0.812165i | \(0.301711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −53.3050 | −2.04566 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.2918 | 0.929500 | 0.464750 | − | 0.885442i | \(-0.346144\pi\) | ||||
0.464750 | + | 0.885442i | \(0.346144\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.11146 | 0.0804401 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0000 | 1.14125 | 0.570627 | − | 0.821209i | \(-0.306700\pi\) | ||||
0.570627 | + | 0.821209i | \(0.306700\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.4721 | −0.776552 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 55.7771 | 2.11271 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.05573 | 0.342030 | 0.171015 | − | 0.985268i | \(-0.445295\pi\) | ||||
0.171015 | + | 0.985268i | \(0.445295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.0557 | 1.17129 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 32.3607 | 1.21705 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0000 | −0.676004 | −0.338002 | − | 0.941145i | \(-0.609751\pi\) | ||||
−0.338002 | + | 0.941145i | \(0.609751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.8328 | 1.15470 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.94427 | 0.334497 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.8328 | 0.851520 | 0.425760 | − | 0.904836i | \(-0.360007\pi\) | ||||
0.425760 | + | 0.904836i | \(0.360007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.4721 | −0.390003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.70820 | −0.0633538 | −0.0316769 | − | 0.999498i | \(-0.510085\pi\) | ||||
−0.0316769 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.4721 | −1.27500 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.8885 | 1.91655 | 0.958274 | − | 0.285853i | \(-0.0922768\pi\) | ||||
0.958274 | + | 0.285853i | \(0.0922768\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.4164 | 0.567871 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.1935 | −1.80961 | −0.904806 | − | 0.425824i | \(-0.859984\pi\) | ||||
−0.904806 | + | 0.425824i | \(0.859984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.6525 | −1.12453 | −0.562265 | − | 0.826957i | \(-0.690070\pi\) | ||||
−0.562265 | + | 0.826957i | \(0.690070\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.94427 | −0.254418 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −55.7771 | −2.03805 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.3607 | −0.597010 | −0.298505 | − | 0.954408i | \(-0.596488\pi\) | ||||
−0.298505 | + | 0.954408i | \(0.596488\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.4164 | −0.852210 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.8885 | 0.722861 | 0.361431 | − | 0.932399i | \(-0.382288\pi\) | ||||
0.361431 | + | 0.932399i | \(0.382288\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.88854 | −0.140960 | −0.0704798 | − | 0.997513i | \(-0.522453\pi\) | ||||
−0.0704798 | + | 0.997513i | \(0.522453\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.3607 | 1.75077 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.8885 | 1.36808 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.9443 | −0.538904 | −0.269452 | − | 0.963014i | \(-0.586843\pi\) | ||||
−0.269452 | + | 0.963014i | \(0.586843\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.3607 | −0.660388 | −0.330194 | − | 0.943913i | \(-0.607114\pi\) | ||||
−0.330194 | + | 0.943913i | \(0.607114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.47214 | −0.232486 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −55.7771 | −1.99842 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.94427 | 0.176920 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.05573 | 0.180447 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.0689 | 1.57089 | 0.785443 | − | 0.618934i | \(-0.212435\pi\) | ||||
0.785443 | + | 0.618934i | \(0.212435\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.52786 | 0.338772 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.8328 | 0.952861 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.4164 | 0.900295 | 0.450148 | − | 0.892954i | \(-0.351371\pi\) | ||||
0.450148 | + | 0.892954i | \(0.351371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.3607 | 1.14484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.94427 | −0.315637 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.4164 | −0.543357 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.1115 | 0.425816 | 0.212908 | − | 0.977072i | \(-0.431707\pi\) | ||||
0.212908 | + | 0.977072i | \(0.431707\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.7082 | 0.410120 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.4721 | 1.20603 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0557 | −0.734850 | −0.367425 | − | 0.930053i | \(-0.619761\pi\) | ||||
−0.367425 | + | 0.930053i | \(0.619761\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.70820 | 0.0595442 | 0.0297721 | − | 0.999557i | \(-0.490522\pi\) | ||||
0.0297721 | + | 0.999557i | \(0.490522\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.18034 | −0.214911 | −0.107456 | − | 0.994210i | \(-0.534270\pi\) | ||||
−0.107456 | + | 0.994210i | \(0.534270\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.5279 | −0.538009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.6525 | 0.507070 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.00000 | 0.240807 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.6525 | −0.778348 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.0820 | −1.13404 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.52786 | −0.257749 | −0.128875 | − | 0.991661i | \(-0.541136\pi\) | ||||
−0.128875 | + | 0.991661i | \(0.541136\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.8328 | −0.848273 | −0.424136 | − | 0.905598i | \(-0.639422\pi\) | ||||
−0.424136 | + | 0.905598i | \(0.639422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.4164 | −1.68607 | −0.843033 | − | 0.537862i | \(-0.819232\pi\) | ||||
−0.843033 | + | 0.537862i | \(0.819232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.2918 | 0.622660 | 0.311330 | − | 0.950302i | \(-0.399226\pi\) | ||||
0.311330 | + | 0.950302i | \(0.399226\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.9443 | 0.372116 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.8885 | 0.878209 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.4721 | 1.16804 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.23607 | 0.109399 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.8885 | 1.75215 | 0.876076 | − | 0.482173i | \(-0.160152\pi\) | ||||
0.876076 | + | 0.482173i | \(0.160152\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.4721 | 0.824487 | 0.412244 | − | 0.911074i | \(-0.364745\pi\) | ||||
0.412244 | + | 0.911074i | \(0.364745\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.7082 | 0.932455 | 0.466228 | − | 0.884665i | \(-0.345613\pi\) | ||||
0.466228 | + | 0.884665i | \(0.345613\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.5967 | 0.389381 | 0.194690 | − | 0.980865i | \(-0.437630\pi\) | ||||
0.194690 | + | 0.980865i | \(0.437630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 65.3050 | 2.19026 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.3607 | −1.08291 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.4721 | −0.684308 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.9443 | −0.431716 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.11146 | 0.0703428 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.9443 | 0.363800 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.23607 | 0.306679 | 0.153339 | − | 0.988174i | \(-0.450997\pi\) | ||||
0.153339 | + | 0.988174i | \(0.450997\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.3050 | −1.76607 | −0.883036 | − | 0.469305i | \(-0.844504\pi\) | ||||
−0.883036 | + | 0.469305i | \(0.844504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.41641 | 0.245447 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48.3607 | 1.59701 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.88854 | 0.194245 | 0.0971226 | − | 0.995272i | \(-0.469036\pi\) | ||||
0.0971226 | + | 0.995272i | \(0.469036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.0557 | 0.363904 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.94427 | 0.228326 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.4721 | −0.802905 | −0.401452 | − | 0.915880i | \(-0.631494\pi\) | ||||
−0.401452 | + | 0.915880i | \(0.631494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5279 | 0.508905 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.94427 | 0.292509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.52786 | −0.115250 | −0.0576251 | − | 0.998338i | \(-0.518353\pi\) | ||||
−0.0576251 | + | 0.998338i | \(0.518353\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.8328 | −1.46151 | −0.730754 | − | 0.682641i | \(-0.760831\pi\) | ||||
−0.730754 | + | 0.682641i | \(0.760831\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59.4164 | 1.93486 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.8197 | 0.709044 | 0.354522 | − | 0.935048i | \(-0.384644\pi\) | ||||
0.354522 | + | 0.935048i | \(0.384644\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0000 | −0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.7771 | −1.48287 | −0.741433 | − | 0.671027i | \(-0.765853\pi\) | ||||
−0.741433 | + | 0.671027i | \(0.765853\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.4164 | 0.369426 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.47214 | −0.208996 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.5279 | −0.371095 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.34752 | 0.0433335 | 0.0216667 | − | 0.999765i | \(-0.493103\pi\) | ||||
0.0216667 | + | 0.999765i | \(0.493103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.8885 | 0.766620 | 0.383310 | − | 0.923620i | \(-0.374784\pi\) | ||||
0.383310 | + | 0.923620i | \(0.374784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −66.2492 | −2.12385 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.3050 | 1.25748 | 0.628738 | − | 0.777617i | \(-0.283572\pi\) | ||||
0.628738 | + | 0.777617i | \(0.283572\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.8885 | −0.955242 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.0132 | 1.24433 | 0.622163 | − | 0.782888i | \(-0.286254\pi\) | ||||
0.622163 | + | 0.782888i | \(0.286254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.472136 | −0.0150435 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.7214 | −1.16767 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.5279 | 0.556791 | 0.278395 | − | 0.960467i | \(-0.410197\pi\) | ||||
0.278395 | + | 0.960467i | \(0.410197\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.944272 | 0.0299354 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.5836 | −1.09527 | −0.547637 | − | 0.836716i | \(-0.684472\pi\) | ||||
−0.547637 | + | 0.836716i | \(0.684472\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5760.2.a.ci.1.2 | 2 | ||
3.2 | odd | 2 | 640.2.a.k.1.1 | yes | 2 | ||
4.3 | odd | 2 | 5760.2.a.ch.1.1 | 2 | |||
8.3 | odd | 2 | 5760.2.a.bw.1.1 | 2 | |||
8.5 | even | 2 | 5760.2.a.cd.1.2 | 2 | |||
12.11 | even | 2 | 640.2.a.i.1.2 | ✓ | 2 | ||
15.2 | even | 4 | 3200.2.c.w.2049.3 | 4 | |||
15.8 | even | 4 | 3200.2.c.w.2049.2 | 4 | |||
15.14 | odd | 2 | 3200.2.a.be.1.2 | 2 | |||
24.5 | odd | 2 | 640.2.a.j.1.2 | yes | 2 | ||
24.11 | even | 2 | 640.2.a.l.1.1 | yes | 2 | ||
48.5 | odd | 4 | 1280.2.d.k.641.3 | 4 | |||
48.11 | even | 4 | 1280.2.d.m.641.2 | 4 | |||
48.29 | odd | 4 | 1280.2.d.k.641.2 | 4 | |||
48.35 | even | 4 | 1280.2.d.m.641.3 | 4 | |||
60.23 | odd | 4 | 3200.2.c.u.2049.3 | 4 | |||
60.47 | odd | 4 | 3200.2.c.u.2049.2 | 4 | |||
60.59 | even | 2 | 3200.2.a.bl.1.1 | 2 | |||
120.29 | odd | 2 | 3200.2.a.bk.1.1 | 2 | |||
120.53 | even | 4 | 3200.2.c.v.2049.3 | 4 | |||
120.59 | even | 2 | 3200.2.a.bf.1.2 | 2 | |||
120.77 | even | 4 | 3200.2.c.v.2049.2 | 4 | |||
120.83 | odd | 4 | 3200.2.c.x.2049.2 | 4 | |||
120.107 | odd | 4 | 3200.2.c.x.2049.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.a.i.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
640.2.a.j.1.2 | yes | 2 | 24.5 | odd | 2 | ||
640.2.a.k.1.1 | yes | 2 | 3.2 | odd | 2 | ||
640.2.a.l.1.1 | yes | 2 | 24.11 | even | 2 | ||
1280.2.d.k.641.2 | 4 | 48.29 | odd | 4 | |||
1280.2.d.k.641.3 | 4 | 48.5 | odd | 4 | |||
1280.2.d.m.641.2 | 4 | 48.11 | even | 4 | |||
1280.2.d.m.641.3 | 4 | 48.35 | even | 4 | |||
3200.2.a.be.1.2 | 2 | 15.14 | odd | 2 | |||
3200.2.a.bf.1.2 | 2 | 120.59 | even | 2 | |||
3200.2.a.bk.1.1 | 2 | 120.29 | odd | 2 | |||
3200.2.a.bl.1.1 | 2 | 60.59 | even | 2 | |||
3200.2.c.u.2049.2 | 4 | 60.47 | odd | 4 | |||
3200.2.c.u.2049.3 | 4 | 60.23 | odd | 4 | |||
3200.2.c.v.2049.2 | 4 | 120.77 | even | 4 | |||
3200.2.c.v.2049.3 | 4 | 120.53 | even | 4 | |||
3200.2.c.w.2049.2 | 4 | 15.8 | even | 4 | |||
3200.2.c.w.2049.3 | 4 | 15.2 | even | 4 | |||
3200.2.c.x.2049.2 | 4 | 120.83 | odd | 4 | |||
3200.2.c.x.2049.3 | 4 | 120.107 | odd | 4 | |||
5760.2.a.bw.1.1 | 2 | 8.3 | odd | 2 | |||
5760.2.a.cd.1.2 | 2 | 8.5 | even | 2 | |||
5760.2.a.ch.1.1 | 2 | 4.3 | odd | 2 | |||
5760.2.a.ci.1.2 | 2 | 1.1 | even | 1 | trivial |