Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7744,2,Mod(1,7744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7744, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7744.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7744 = 2^{6} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7744.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: | \(61.8361513253\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.19898000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 10x^{4} + 7x^{3} + 24x^{2} - 15x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 352) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.05906\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7744.1 |
$q$-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 | ||||||||
\(3\) | 3.05906 | 1.76615 | 0.883075 | − | 0.469232i | \(-0.155469\pi\) | ||||
0.883075 | + | 0.469232i | \(0.155469\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00593 | −1.34429 | −0.672147 | − | 0.740418i | \(-0.734628\pi\) | ||||
−0.672147 | + | 0.740418i | \(0.734628\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.56490 | −0.591478 | −0.295739 | − | 0.955269i | \(-0.595566\pi\) | ||||
−0.295739 | + | 0.955269i | \(0.595566\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.35786 | 2.11929 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.65733 | 1.01436 | 0.507181 | − | 0.861840i | \(-0.330688\pi\) | ||||
0.507181 | + | 0.861840i | \(0.330688\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.19533 | −2.37422 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47580 | 1.08554 | 0.542771 | − | 0.839881i | \(-0.317375\pi\) | ||||
0.542771 | + | 0.839881i | \(0.317375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.74643 | −0.630075 | −0.315037 | − | 0.949079i | \(-0.602017\pi\) | ||||
−0.315037 | + | 0.949079i | \(0.602017\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.78714 | −1.04464 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.77580 | −0.995823 | −0.497911 | − | 0.867228i | \(-0.665899\pi\) | ||||
−0.497911 | + | 0.867228i | \(0.665899\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.03563 | 0.807126 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.2719 | 1.97683 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.96996 | 0.922898 | 0.461449 | − | 0.887167i | \(-0.347330\pi\) | ||||
0.461449 | + | 0.887167i | \(0.347330\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.487696 | −0.0875927 | −0.0437964 | − | 0.999040i | \(-0.513945\pi\) | ||||
−0.0437964 | + | 0.999040i | \(0.513945\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.70400 | 0.795121 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6449 | 1.75001 | 0.875006 | − | 0.484112i | \(-0.160857\pi\) | ||||
0.875006 | + | 0.484112i | \(0.160857\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.1880 | 1.79151 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.5417 | 1.95868 | 0.979338 | − | 0.202228i | \(-0.0648182\pi\) | ||||
0.979338 | + | 0.202228i | \(0.0648182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.45745 | −1.13725 | −0.568625 | − | 0.822597i | \(-0.692524\pi\) | ||||
−0.568625 | + | 0.822597i | \(0.692524\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −19.1113 | −2.84894 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.0370 | −1.46405 | −0.732026 | − | 0.681276i | \(-0.761425\pi\) | ||||
−0.732026 | + | 0.681276i | \(0.761425\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.55107 | −0.650153 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.6918 | 1.91723 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.26661 | 0.723424 | 0.361712 | − | 0.932290i | \(-0.382192\pi\) | ||||
0.361712 | + | 0.932290i | \(0.382192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.40151 | −1.11281 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.93411 | −1.16312 | −0.581561 | − | 0.813503i | \(-0.697558\pi\) | ||||
−0.581561 | + | 0.813503i | \(0.697558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.16446 | 0.277131 | 0.138566 | − | 0.990353i | \(-0.455751\pi\) | ||||
0.138566 | + | 0.990353i | \(0.455751\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.94944 | −1.25351 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.9937 | −1.36360 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.709392 | 0.0866661 | 0.0433330 | − | 0.999061i | \(-0.486202\pi\) | ||||
0.0433330 | + | 0.999061i | \(0.486202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.6095 | −1.75877 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.808454 | −0.0959459 | −0.0479729 | − | 0.998849i | \(-0.515276\pi\) | ||||
−0.0479729 | + | 0.998849i | \(0.515276\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.528076 | 0.0618066 | 0.0309033 | − | 0.999522i | \(-0.490162\pi\) | ||||
0.0309033 | + | 0.999522i | \(0.490162\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.3452 | 1.42551 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.81422 | 0.654151 | 0.327076 | − | 0.944998i | \(-0.393937\pi\) | ||||
0.327076 | + | 0.944998i | \(0.393937\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 12.3488 | 1.37209 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.09133 | 0.778375 | 0.389187 | − | 0.921159i | \(-0.372756\pi\) | ||||
0.389187 | + | 0.921159i | \(0.372756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.4540 | −1.45929 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.2034 | 1.62998 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.76282 | 0.822857 | 0.411429 | − | 0.911442i | \(-0.365030\pi\) | ||||
0.411429 | + | 0.911442i | \(0.365030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.72337 | −0.599973 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.49189 | −0.154702 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.25559 | 0.847006 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.62990 | 0.368560 | 0.184280 | − | 0.982874i | \(-0.441005\pi\) | ||||
0.184280 | + | 0.982874i | \(0.441005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.23031 | −0.122421 | −0.0612104 | − | 0.998125i | \(-0.519496\pi\) | ||||
−0.0612104 | + | 0.998125i | \(0.519496\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.56508 | 0.252745 | 0.126373 | − | 0.991983i | \(-0.459667\pi\) | ||||
0.126373 | + | 0.991983i | \(0.459667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.3898 | 1.40430 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.6612 | 1.32068 | 0.660338 | − | 0.750968i | \(-0.270413\pi\) | ||||
0.660338 | + | 0.750968i | \(0.270413\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.935861 | 0.0896393 | 0.0448196 | − | 0.998995i | \(-0.485729\pi\) | ||||
0.0448196 | + | 0.998995i | \(0.485729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 32.5634 | 3.09078 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.21175 | −0.302136 | −0.151068 | − | 0.988523i | \(-0.548271\pi\) | ||||
−0.151068 | + | 0.988523i | \(0.548271\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.3557 | 1.33868 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.2528 | 2.14972 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.00421 | −0.642074 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 38.3657 | 3.45932 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.89883 | 0.259279 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.1602 | 0.901576 | 0.450788 | − | 0.892631i | \(-0.351143\pi\) | ||||
0.450788 | + | 0.892631i | \(0.351143\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.8128 | −2.00855 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.01348 | 0.263289 | 0.131644 | − | 0.991297i | \(-0.457974\pi\) | ||||
0.131644 | + | 0.991297i | \(0.457974\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.29791 | 0.372676 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −30.8766 | −2.65744 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.03790 | 0.0886735 | 0.0443367 | − | 0.999017i | \(-0.485883\pi\) | ||||
0.0443367 | + | 0.999017i | \(0.485883\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.93490 | 0.248935 | 0.124467 | − | 0.992224i | \(-0.460278\pi\) | ||||
0.124467 | + | 0.992224i | \(0.460278\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.7039 | −2.58574 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.9394 | −1.24065 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.9220 | −1.14827 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.3003 | 1.00768 | 0.503842 | − | 0.863796i | \(-0.331920\pi\) | ||||
0.503842 | + | 0.863796i | \(0.331920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1834 | 1.64250 | 0.821251 | − | 0.570567i | \(-0.193276\pi\) | ||||
0.821251 | + | 0.570567i | \(0.193276\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 28.4565 | 2.30057 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.46598 | 0.117750 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.2045 | 1.05383 | 0.526917 | − | 0.849917i | \(-0.323348\pi\) | ||||
0.526917 | + | 0.849917i | \(0.323348\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.1109 | 1.27768 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.47367 | 0.589008 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.51087 | −0.274993 | −0.137496 | − | 0.990502i | \(-0.543906\pi\) | ||||
−0.137496 | + | 0.990502i | \(0.543906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.0092 | 0.774537 | 0.387269 | − | 0.921967i | \(-0.373419\pi\) | ||||
0.387269 | + | 0.921967i | \(0.373419\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.376067 | 0.0289283 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.4614 | −1.33531 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.50969 | −0.190808 | −0.0954040 | − | 0.995439i | \(-0.530414\pi\) | ||||
−0.0954040 | + | 0.995439i | \(0.530414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.31538 | −0.477398 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.3300 | −2.05425 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.7954 | 1.25535 | 0.627675 | − | 0.778476i | \(-0.284007\pi\) | ||||
0.627675 | + | 0.778476i | \(0.284007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.93834 | 0.441393 | 0.220697 | − | 0.975342i | \(-0.429167\pi\) | ||||
0.220697 | + | 0.975342i | \(0.429167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.62123 | 0.489455 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31.9979 | −2.35253 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.0745 | −1.16925 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.94136 | −0.502259 | −0.251130 | − | 0.967953i | \(-0.580802\pi\) | ||||
−0.251130 | + | 0.967953i | \(0.580802\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.65943 | −0.263412 | −0.131706 | − | 0.991289i | \(-0.542045\pi\) | ||||
−0.131706 | + | 0.991289i | \(0.542045\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −33.6304 | −2.40832 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.5687 | 1.25172 | 0.625859 | − | 0.779936i | \(-0.284749\pi\) | ||||
0.625859 | + | 0.779936i | \(0.284749\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.12699 | −0.505219 | −0.252609 | − | 0.967568i | \(-0.581289\pi\) | ||||
−0.252609 | + | 0.967568i | \(0.581289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.17007 | 0.153065 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.77751 | −0.545874 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −37.6994 | −2.63304 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −30.3638 | −2.11043 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.5140 | 1.41224 | 0.706121 | − | 0.708091i | \(-0.250443\pi\) | ||||
0.706121 | + | 0.708091i | \(0.250443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.47311 | −0.169455 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.4166 | 1.52880 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.763197 | 0.0518092 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.61542 | 0.109160 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3695 | 1.10113 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.24503 | −0.418198 | −0.209099 | − | 0.977894i | \(-0.567053\pi\) | ||||
−0.209099 | + | 0.977894i | \(0.567053\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 25.6580 | 1.71053 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.7568 | −1.04581 | −0.522907 | − | 0.852390i | \(-0.675152\pi\) | ||||
−0.522907 | + | 0.852390i | \(0.675152\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7277 | 1.10540 | 0.552699 | − | 0.833381i | \(-0.313598\pi\) | ||||
0.552699 | + | 0.833381i | \(0.313598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.7221 | 0.767940 | 0.383970 | − | 0.923345i | \(-0.374557\pi\) | ||||
0.383970 | + | 0.923345i | \(0.374557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.1707 | 1.96812 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.7861 | 1.15533 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.3503 | −1.63978 | −0.819889 | − | 0.572523i | \(-0.805965\pi\) | ||||
−0.819889 | + | 0.572523i | \(0.805965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.25667 | −0.0809490 | −0.0404745 | − | 0.999181i | \(-0.512887\pi\) | ||||
−0.0404745 | + | 0.999181i | \(0.512887\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.96000 | 0.446484 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.6802 | 0.873997 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0446 | −0.639123 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.6928 | 1.37473 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.0548 | 1.45521 | 0.727604 | − | 0.685998i | \(-0.240634\pi\) | ||||
0.727604 | + | 0.685998i | \(0.240634\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −41.1565 | −2.57732 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.39585 | −0.336584 | −0.168292 | − | 0.985737i | \(-0.553825\pi\) | ||||
−0.168292 | + | 0.985737i | \(0.553825\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.6583 | −1.03509 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.5983 | 1.95589 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.3375 | −1.00742 | −0.503708 | − | 0.863874i | \(-0.668031\pi\) | ||||
−0.503708 | + | 0.863874i | \(0.668031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.8311 | −0.972495 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.7469 | 1.45329 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.6384 | 1.68514 | 0.842572 | − | 0.538583i | \(-0.181040\pi\) | ||||
0.842572 | + | 0.538583i | \(0.181040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.8843 | −1.81534 | −0.907670 | − | 0.419684i | \(-0.862141\pi\) | ||||
−0.907670 | + | 0.419684i | \(0.862141\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.5082 | −1.05964 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.9789 | −1.44075 | −0.720375 | − | 0.693584i | \(-0.756030\pi\) | ||||
−0.720375 | + | 0.693584i | \(0.756030\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.10070 | −0.185634 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.4834 | −0.685044 | −0.342522 | − | 0.939510i | \(-0.611281\pi\) | ||||
−0.342522 | + | 0.939510i | \(0.611281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.4096 | 0.975447 | 0.487724 | − | 0.872998i | \(-0.337827\pi\) | ||||
0.487724 | + | 0.872998i | \(0.337827\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.2544 | 1.49594 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.6265 | −1.15852 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.03281 | 0.178400 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1041 | 0.650933 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.8060 | 0.981818 | 0.490909 | − | 0.871211i | \(-0.336665\pi\) | ||||
0.490909 | + | 0.871211i | \(0.336665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.8553 | 1.56358 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.4667 | −1.01012 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.6702 | 0.672659 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.76361 | −0.216213 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.50623 | −0.372546 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3071 | −0.702403 | −0.351201 | − | 0.936300i | \(-0.614227\pi\) | ||||
−0.351201 | + | 0.936300i | \(0.614227\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.84675 | 0.446386 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5968 | 0.941119 | 0.470559 | − | 0.882368i | \(-0.344052\pi\) | ||||
0.470559 | + | 0.882368i | \(0.344052\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.8326 | −1.29057 | −0.645287 | − | 0.763941i | \(-0.723262\pi\) | ||||
−0.645287 | + | 0.763941i | \(0.723262\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 29.9074 | 1.68509 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.76722 | 0.267754 | 0.133877 | − | 0.990998i | \(-0.457257\pi\) | ||||
0.133877 | + | 0.990998i | \(0.457257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 41.7904 | 2.33251 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.2925 | −0.683973 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.7596 | 0.818717 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.86286 | 0.158316 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.7070 | 0.865956 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.4925 | −1.78595 | −0.892976 | − | 0.450105i | \(-0.851387\pi\) | ||||
−0.892976 | + | 0.450105i | \(0.851387\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 67.6788 | 3.70878 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.13239 | −0.116505 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.49799 | 0.517388 | 0.258694 | − | 0.965959i | \(-0.416708\pi\) | ||||
0.258694 | + | 0.965959i | \(0.416708\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.82493 | −0.533617 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0763 | 0.976030 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 43.9150 | 2.36431 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.8397 | 1.92398 | 0.961989 | − | 0.273088i | \(-0.0880450\pi\) | ||||
0.961989 | + | 0.273088i | \(0.0880450\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.9988 | 1.39168 | 0.695842 | − | 0.718195i | \(-0.255031\pi\) | ||||
0.695842 | + | 0.718195i | \(0.255031\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.5677 | 2.00522 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.3264 | −0.868969 | −0.434484 | − | 0.900679i | \(-0.643069\pi\) | ||||
−0.434484 | + | 0.900679i | \(0.643069\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.43016 | 0.128979 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.4263 | −1.13400 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.72256 | −0.407581 | −0.203791 | − | 0.979015i | \(-0.565326\pi\) | ||||
−0.203791 | + | 0.979015i | \(0.565326\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4571 | −0.603006 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.58736 | −0.0830863 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.23615 | 0.325525 | 0.162762 | − | 0.986665i | \(-0.447960\pi\) | ||||
0.162762 | + | 0.986665i | \(0.447960\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 79.7380 | 4.15100 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.24174 | −0.427890 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.84081 | 0.250648 | 0.125324 | − | 0.992116i | \(-0.460003\pi\) | ||||
0.125324 | + | 0.992116i | \(0.460003\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.86770 | 0.457926 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.1768 | 0.936152 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6788 | 0.702634 | 0.351317 | − | 0.936257i | \(-0.385734\pi\) | ||||
0.351317 | + | 0.936257i | \(0.385734\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 31.0808 | 1.59232 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.5039 | −0.587823 | −0.293911 | − | 0.955833i | \(-0.594957\pi\) | ||||
−0.293911 | + | 0.955833i | \(0.594957\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −47.4134 | −2.41016 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.29913 | −0.471485 | −0.235742 | − | 0.971816i | \(-0.575752\pi\) | ||||
−0.235742 | + | 0.971816i | \(0.575752\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.3755 | −1.08101 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.21841 | 0.465007 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.4772 | −0.879371 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.3379 | −1.92413 | −0.962063 | − | 0.272828i | \(-0.912041\pi\) | ||||
−0.962063 | + | 0.272828i | \(0.912041\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.1476 | 0.658201 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3130 | 0.864571 | 0.432285 | − | 0.901737i | \(-0.357707\pi\) | ||||
0.432285 | + | 0.901737i | \(0.357707\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.78366 | −0.0888506 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −37.1196 | −1.84449 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.69257 | −0.133139 | −0.0665696 | − | 0.997782i | \(-0.521205\pi\) | ||||
−0.0665696 | + | 0.997782i | \(0.521205\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.17499 | 0.156611 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.9810 | 0.687961 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.3161 | −1.04636 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.97803 | 0.439656 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.3425 | 0.651824 | 0.325912 | − | 0.945400i | \(-0.394329\pi\) | ||||
0.325912 | + | 0.945400i | \(0.394329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.1838 | −1.03243 | −0.516217 | − | 0.856458i | \(-0.672660\pi\) | ||||
−0.516217 | + | 0.856458i | \(0.672660\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −63.8141 | −3.10275 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.0627 | 0.876169 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.38718 | −0.163917 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.4050 | −0.838367 | −0.419184 | − | 0.907901i | \(-0.637684\pi\) | ||||
−0.419184 | + | 0.907901i | \(0.637684\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.12280 | 0.198129 | 0.0990645 | − | 0.995081i | \(-0.468415\pi\) | ||||
0.0990645 | + | 0.995081i | \(0.468415\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −45.7004 | −2.19117 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.1164 | 0.627443 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.8478 | 1.47229 | 0.736143 | − | 0.676826i | \(-0.236645\pi\) | ||||
0.736143 | + | 0.676826i | \(0.236645\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −28.9351 | −1.37786 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.35946 | 0.444681 | 0.222341 | − | 0.974969i | \(-0.428630\pi\) | ||||
0.222341 | + | 0.974969i | \(0.428630\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.3345 | −1.10616 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 37.6275 | 1.77972 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.68708 | −0.174004 | −0.0870021 | − | 0.996208i | \(-0.527729\pi\) | ||||
−0.0870021 | + | 0.996208i | \(0.527729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 61.7423 | 2.90091 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.2041 | 0.806540 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.1488 | −1.50386 | −0.751930 | − | 0.659243i | \(-0.770877\pi\) | ||||
−0.751930 | + | 0.659243i | \(0.770877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 45.9750 | 2.14593 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.41140 | −0.158885 | −0.0794423 | − | 0.996839i | \(-0.525314\pi\) | ||||
−0.0794423 | + | 0.996839i | \(0.525314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.72640 | −0.173181 | −0.0865903 | − | 0.996244i | \(-0.527597\pi\) | ||||
−0.0865903 | + | 0.996244i | \(0.527597\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.48452 | 0.207965 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.92963 | −0.0892928 | −0.0446464 | − | 0.999003i | \(-0.514216\pi\) | ||||
−0.0446464 | + | 0.999003i | \(0.514216\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.11013 | −0.0512611 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.3934 | 1.86123 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.0836 | −0.508550 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.4844 | 1.53314 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.2867 | −1.29245 | −0.646226 | − | 0.763146i | \(-0.723654\pi\) | ||||
−0.646226 | + | 0.763146i | \(0.723654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.9320 | 1.77514 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.8624 | 1.04028 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.9112 | −0.495453 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.6571 | 0.528236 | 0.264118 | − | 0.964490i | \(-0.414919\pi\) | ||||
0.264118 | + | 0.964490i | \(0.414919\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.7400 | −0.485678 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.5772 | −0.838377 | −0.419189 | − | 0.907899i | \(-0.637685\pi\) | ||||
−0.419189 | + | 0.907899i | \(0.637685\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.2446 | 1.00184 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.26515 | 0.0567499 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.70872 | 0.166025 | 0.0830125 | − | 0.996549i | \(-0.473546\pi\) | ||||
0.0830125 | + | 0.996549i | \(0.473546\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.6188 | 1.36795 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.0826 | 1.38590 | 0.692952 | − | 0.720984i | \(-0.256310\pi\) | ||||
0.692952 | + | 0.720984i | \(0.256310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.69824 | 0.164570 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.15041 | 0.0510917 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.9603 | −1.72689 | −0.863443 | − | 0.504446i | \(-0.831697\pi\) | ||||
−0.863443 | + | 0.504446i | \(0.831697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.826389 | −0.0365573 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.2111 | −1.24555 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.71047 | −0.339764 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.67729 | −0.336996 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.6240 | −0.509258 | −0.254629 | − | 0.967039i | \(-0.581953\pi\) | ||||
−0.254629 | + | 0.967039i | \(0.581953\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.7528 | 0.776275 | 0.388137 | − | 0.921602i | \(-0.373119\pi\) | ||||
0.388137 | + | 0.921602i | \(0.373119\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.3191 | −0.843156 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.18283 | −0.0950855 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.191763 | −0.00833752 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −56.8018 | −2.46499 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45.8690 | 1.98681 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.0646 | −1.77538 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 51.3783 | 2.21714 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.2627 | −1.04313 | −0.521567 | − | 0.853210i | \(-0.674652\pi\) | ||||
−0.521567 | + | 0.853210i | \(0.674652\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.1657 | 0.779567 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.81314 | −0.120501 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.29110 | 0.354502 | 0.177251 | − | 0.984166i | \(-0.443280\pi\) | ||||
0.177251 | + | 0.984166i | \(0.443280\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.7614 | 0.587320 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.6497 | −0.581495 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.09870 | −0.386916 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −97.8835 | −4.15492 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.9655 | −1.77814 | −0.889068 | − | 0.457775i | \(-0.848646\pi\) | ||||
−0.889068 | + | 0.457775i | \(0.848646\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.2744 | −1.15358 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.8969 | −1.42859 | −0.714293 | − | 0.699847i | \(-0.753251\pi\) | ||||
−0.714293 | + | 0.699847i | \(0.753251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.65430 | 0.406159 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.3247 | −0.811560 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.3055 | 0.725485 | 0.362742 | − | 0.931889i | \(-0.381841\pi\) | ||||
0.362742 | + | 0.931889i | \(0.381841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8559 | −0.663551 | −0.331775 | − | 0.943358i | \(-0.607648\pi\) | ||||
−0.331775 | + | 0.943358i | \(0.607648\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.2340 | −0.887065 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.2734 | −0.803754 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.8545 | −1.20123 | −0.600615 | − | 0.799538i | \(-0.705078\pi\) | ||||
−0.600615 | + | 0.799538i | \(0.705078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.1944 | −0.465224 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0973 | −0.460392 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −69.8963 | −2.88986 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.3318 | 1.12811 | 0.564053 | − | 0.825739i | \(-0.309241\pi\) | ||||
0.564053 | + | 0.825739i | \(0.309241\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.33942 | 0.0551900 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 53.7437 | 2.21072 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.4666 | 1.37431 | 0.687154 | − | 0.726512i | \(-0.258860\pi\) | ||||
0.687154 | + | 0.726512i | \(0.258860\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.0542 | 0.863137 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.8019 | −0.892292 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.9832 | 0.693915 | 0.346957 | − | 0.937881i | \(-0.387215\pi\) | ||||
0.346957 | + | 0.937881i | \(0.387215\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.0293746 | −0.00119821 | −0.000599107 | − | 1.00000i | \(-0.500191\pi\) | ||||
−0.000599107 | 1.00000i | \(0.500191\pi\) | ||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.51021 | 0.183670 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.0033 | −1.05544 | −0.527721 | − | 0.849418i | \(-0.676953\pi\) | ||||
−0.527721 | + | 0.849418i | \(0.676953\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.7919 | −0.964096 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.7088 | −1.48508 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.3947 | −1.22763 | −0.613815 | − | 0.789450i | \(-0.710366\pi\) | ||||
−0.613815 | + | 0.789450i | \(0.710366\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −115.325 | −4.65034 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.3795 | 0.900966 | 0.450483 | − | 0.892785i | \(-0.351252\pi\) | ||||
0.450483 | + | 0.892785i | \(0.351252\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.0882 | 0.927994 | 0.463997 | − | 0.885837i | \(-0.346415\pi\) | ||||
0.463997 | + | 0.885837i | \(0.346415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.0565 | −1.96857 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.1481 | −0.486702 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.8918 | −1.15567 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.6445 | 1.89971 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.0478 | −1.19618 | −0.598092 | − | 0.801427i | \(-0.704074\pi\) | ||||
−0.598092 | + | 0.801427i | \(0.704074\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 62.7536 | 2.49423 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.5410 | −1.21198 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.6448 | −0.659490 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.14004 | −0.203337 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.9682 | 1.42066 | 0.710328 | − | 0.703870i | \(-0.248546\pi\) | ||||
0.710328 | + | 0.703870i | \(0.248546\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.2238 | 0.718675 | 0.359337 | − | 0.933208i | \(-0.383003\pi\) | ||||
0.359337 | + | 0.933208i | \(0.383003\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 68.5737 | 2.70009 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.1258 | −0.437401 | −0.218701 | − | 0.975792i | \(-0.570182\pi\) | ||||
−0.218701 | + | 0.975792i | \(0.570182\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.33467 | 0.0915028 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.5405 | 0.647282 | 0.323641 | − | 0.946180i | \(-0.395093\pi\) | ||||
0.323641 | + | 0.946180i | \(0.395093\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.05831 | −0.353937 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.35743 | 0.130986 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.0957 | 1.01655 | 0.508273 | − | 0.861196i | \(-0.330284\pi\) | ||||
0.508273 | + | 0.861196i | \(0.330284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.3262 | −0.596121 | −0.298061 | − | 0.954547i | \(-0.596340\pi\) | ||||
−0.298061 | + | 0.954547i | \(0.596340\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 50.0753 | 1.94476 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.9192 | −0.500986 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.7355 | −0.919043 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.1039 | −0.738600 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.9654 | −1.23218 | −0.616088 | − | 0.787678i | \(-0.711283\pi\) | ||||
−0.616088 | + | 0.787678i | \(0.711283\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 41.4536 | 1.59555 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.4878 | 0.479945 | 0.239973 | − | 0.970780i | \(-0.422862\pi\) | ||||
0.239973 | + | 0.970780i | \(0.422862\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.68045 | −0.217996 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −48.2009 | −1.84706 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.0471 | −0.996665 | −0.498332 | − | 0.866986i | \(-0.666054\pi\) | ||||
−0.498332 | + | 0.866986i | \(0.666054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.11985 | −0.119203 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 51.1711 | 1.95230 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.2617 | 0.733814 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.4545 | −1.76721 | −0.883605 | − | 0.468232i | \(-0.844891\pi\) | ||||
−0.883605 | + | 0.468232i | \(0.844891\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.82210 | −0.334641 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.1340 | 2.12623 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.8586 | 1.35630 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.2518 | −0.953747 | −0.476873 | − | 0.878972i | \(-0.658230\pi\) | ||||
−0.476873 | + | 0.878972i | \(0.658230\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.2355 | −1.10264 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 92.2939 | 3.47599 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.92532 | 0.0724093 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.80505 | 0.218013 | 0.109007 | − | 0.994041i | \(-0.465233\pi\) | ||||
0.109007 | + | 0.994041i | \(0.465233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.9660 | 1.38633 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.32913 | 0.0872268 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −77.5483 | −2.89609 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.7231 | 1.18307 | 0.591537 | − | 0.806278i | \(-0.298522\pi\) | ||||
0.591537 | + | 0.806278i | \(0.298522\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.01411 | −0.149493 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.84422 | −0.142968 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.0569 | 0.744895 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.2435 | −1.90052 | −0.950258 | − | 0.311464i | \(-0.899181\pi\) | ||||
−0.950258 | + | 0.311464i | \(0.899181\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.7553 | −0.583529 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.3781 | −1.23453 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.8519 | 1.61971 | 0.809853 | − | 0.586633i | \(-0.199547\pi\) | ||||
0.809853 | + | 0.586633i | \(0.199547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 41.8486 | 1.54361 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.0297 | −1.14145 | −0.570723 | − | 0.821142i | \(-0.693337\pi\) | ||||
−0.570723 | + | 0.821142i | \(0.693337\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −30.7271 | −1.12879 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.7687 | 0.871991 | 0.435995 | − | 0.899949i | \(-0.356396\pi\) | ||||
0.435995 | + | 0.899949i | \(0.356396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.9740 | −1.35462 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 45.0857 | 1.64960 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.3785 | −0.781152 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.6882 | 1.55771 | 0.778857 | − | 0.627202i | \(-0.215800\pi\) | ||||
0.778857 | + | 0.627202i | \(0.215800\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 70.5261 | 2.57011 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −60.6700 | −2.20801 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.1511 | −0.877785 | −0.438893 | − | 0.898540i | \(-0.644629\pi\) | ||||
−0.438893 | + | 0.898540i | \(0.644629\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.6328 | −0.494190 | −0.247095 | − | 0.968991i | \(-0.579476\pi\) | ||||
−0.247095 | + | 0.968991i | \(0.579476\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.46453 | −0.0530197 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −85.5384 | −3.09265 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32.6750 | −1.17983 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.6960 | −0.638135 | −0.319068 | − | 0.947732i | \(-0.603370\pi\) | ||||
−0.319068 | + | 0.947732i | \(0.603370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.5063 | −0.594458 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.6029 | 0.992809 | 0.496404 | − | 0.868091i | \(-0.334653\pi\) | ||||
0.496404 | + | 0.868091i | \(0.334653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.96816 | −0.0706983 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −50.9587 | −1.82813 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −34.4448 | −1.23411 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 51.0509 | 1.82441 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.6918 | −1.41666 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.1012 | 0.716529 | 0.358265 | − | 0.933620i | \(-0.383369\pi\) | ||||
0.358265 | + | 0.933620i | \(0.383369\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −49.9775 | −1.77925 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.02608 | 0.178707 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.91616 | 0.281111 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −48.4282 | −1.71757 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.4666 | −0.477011 | −0.238506 | − | 0.971141i | \(-0.576658\pi\) | ||||
−0.238506 | + | 0.971141i | \(0.576658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.9238 | −1.58929 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 49.3549 | 1.74387 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.4653 | −0.791799 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 84.5477 | 2.97622 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.69714 | −0.305775 | −0.152888 | − | 0.988244i | \(-0.548857\pi\) | ||||
−0.152888 | + | 0.988244i | \(0.548857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.5832 | −0.441855 | −0.220928 | − | 0.975290i | \(-0.570908\pi\) | ||||
−0.220928 | + | 0.975290i | \(0.570908\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −91.4178 | −3.20616 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5534 | 0.369671 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.4814 | 0.716553 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −36.3884 | −1.27151 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.6064 | −1.20777 | −0.603886 | − | 0.797071i | \(-0.706382\pi\) | ||||
−0.603886 | + | 0.797071i | \(0.706382\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.2135 | −1.61090 | −0.805451 | − | 0.592662i | \(-0.798077\pi\) | ||||
−0.805451 | + | 0.592662i | \(0.798077\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.5933 | 0.437913 | 0.218957 | − | 0.975735i | \(-0.429735\pi\) | ||||
0.218957 | + | 0.975735i | \(0.429735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.3556 | 1.12376 | 0.561879 | − | 0.827220i | \(-0.310079\pi\) | ||||
0.561879 | + | 0.827220i | \(0.310079\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −73.3528 | −2.54458 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.3697 | −0.705768 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.0871 | −1.04121 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.00956 | −0.173156 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.0636 | 0.796245 | 0.398123 | − | 0.917332i | \(-0.369662\pi\) | ||||
0.398123 | + | 0.917332i | \(0.369662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.29951 | −0.148259 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.1285 | −1.20989 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.13043 | −0.0388881 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 50.1979 | 1.72279 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.8379 | −1.74270 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.6465 | −1.56290 | −0.781452 | − | 0.623965i | \(-0.785521\pi\) | ||||
−0.781452 | + | 0.623965i | \(0.785521\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 52.4879 | 1.79505 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.6018 | −0.874541 | −0.437271 | − | 0.899330i | \(-0.644055\pi\) | ||||
−0.437271 | + | 0.899330i | \(0.644055\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.93870 | −0.134387 | −0.0671934 | − | 0.997740i | \(-0.521404\pi\) | ||||
−0.0671934 | + | 0.997740i | \(0.521404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −60.0386 | −2.04611 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.1546 | 0.890313 | 0.445156 | − | 0.895453i | \(-0.353148\pi\) | ||||
0.445156 | + | 0.895453i | \(0.353148\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.54395 | 0.256502 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.27754 | 0.315082 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.59448 | 0.0879107 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.0784 | 0.781085 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.53639 | −0.153358 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.9876 | −0.607397 | −0.303699 | − | 0.952768i | \(-0.598222\pi\) | ||||
−0.303699 | + | 0.952768i | \(0.598222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 51.4106 | 1.73404 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.1327 | −0.442453 | −0.221227 | − | 0.975222i | \(-0.571006\pi\) | ||||
−0.221227 | + | 0.975222i | \(0.571006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.6832 | 0.830655 | 0.415328 | − | 0.909672i | \(-0.363667\pi\) | ||||
0.415328 | + | 0.909672i | \(0.363667\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 82.1521 | 2.76151 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.5929 | 0.792173 | 0.396086 | − | 0.918213i | \(-0.370368\pi\) | ||||
0.396086 | + | 0.918213i | \(0.370368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.8998 | −0.533263 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.5661 | 0.922463 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −50.4859 | −1.68756 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −53.4316 | −1.78403 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.42383 | −0.0808391 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.5723 | 0.785307 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 35.6999 | 1.18802 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.8502 | −0.593362 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.7002 | 1.58386 | 0.791930 | − | 0.610612i | \(-0.209076\pi\) | ||||
0.791930 | + | 0.610612i | \(0.209076\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.82216 | −0.259445 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.986775 | 0.0326933 | 0.0163467 | − | 0.999866i | \(-0.494796\pi\) | ||||
0.0163467 | + | 0.999866i | \(0.494796\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.9030 | −0.657972 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.71581 | −0.155730 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.9561 | 0.658291 | 0.329146 | − | 0.944279i | \(-0.393239\pi\) | ||||
0.329146 | + | 0.944279i | \(0.393239\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −37.6481 | −1.24055 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.95678 | −0.0973238 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.9589 | 1.41248 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.3084 | 0.535639 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.0216 | 0.886550 | 0.443275 | − | 0.896386i | \(-0.353817\pi\) | ||||
0.443275 | + | 0.896386i | \(0.353817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.4992 | 0.409645 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50.7707 | 1.66216 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.5367 | −1.29161 | −0.645803 | − | 0.763504i | \(-0.723477\pi\) | ||||
−0.645803 | + | 0.763504i | \(0.723477\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −69.8462 | −2.27935 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.0796 | 0.784972 | 0.392486 | − | 0.919758i | \(-0.371615\pi\) | ||||
0.392486 | + | 0.919758i | \(0.371615\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −59.8964 | −1.95049 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 48.3190 | 1.57182 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.6471 | −1.12588 | −0.562940 | − | 0.826498i | \(-0.690330\pi\) | ||||
−0.562940 | + | 0.826498i | \(0.690330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.93135 | 0.0626943 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.5832 | 0.472893 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.916697 | −0.0296947 | −0.0148474 | − | 0.999890i | \(-0.504726\pi\) | ||||
−0.0148474 | + | 0.999890i | \(0.504726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.8653 | 0.675184 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.62421 | −0.0524484 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7622 | −0.992328 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 86.8559 | 2.79889 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0000 | 0.354103 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.8240 | 1.31281 | 0.656406 | − | 0.754408i | \(-0.272076\pi\) | ||||
0.656406 | + | 0.754408i | \(0.272076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −37.6035 | −1.20800 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.4231 | −1.58606 | −0.793031 | − | 0.609181i | \(-0.791498\pi\) | ||||
−0.793031 | + | 0.609181i | \(0.791498\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.59283 | −0.147239 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 45.1506 | 1.44598 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.5440 | −0.753239 | −0.376619 | − | 0.926368i | \(-0.622914\pi\) | ||||
−0.376619 | + | 0.926368i | \(0.622914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.95007 | 0.189971 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.82382 | −0.185751 | −0.0928755 | − | 0.995678i | \(-0.529606\pi\) | ||||
−0.0928755 | + | 0.995678i | \(0.529606\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.8103 | −1.68268 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 48.0487 | 1.52941 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.6153 | 1.13250 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3008 | 0.454280 | 0.227140 | − | 0.973862i | \(-0.427062\pi\) | ||||
0.227140 | + | 0.973862i | \(0.427062\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −99.3967 | −3.15426 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.4232 | 0.679163 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.2737 | −0.895437 | −0.447719 | − | 0.894174i | \(-0.647763\pi\) | ||||
−0.447719 | + | 0.894174i | \(0.647763\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 109.343 | 3.45947 |
(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 | 7744.2.a.dw.1.5 | 6 | ||
4.3 | odd | 2 | 7744.2.a.dt.1.2 | 6 | |||
8.3 | odd | 2 | 3872.2.a.bp.1.5 | 6 | |||
8.5 | even | 2 | 3872.2.a.bo.1.2 | 6 | |||
11.2 | odd | 10 | 704.2.m.n.257.3 | 12 | |||
11.6 | odd | 10 | 704.2.m.n.641.3 | 12 | |||
11.10 | odd | 2 | 7744.2.a.dv.1.5 | 6 | |||
44.35 | even | 10 | 704.2.m.m.257.1 | 12 | |||
44.39 | even | 10 | 704.2.m.m.641.1 | 12 | |||
44.43 | even | 2 | 7744.2.a.du.1.2 | 6 | |||
88.13 | odd | 10 | 352.2.m.f.257.1 | yes | 12 | ||
88.21 | odd | 2 | 3872.2.a.bn.1.2 | 6 | |||
88.35 | even | 10 | 352.2.m.e.257.3 | ✓ | 12 | ||
88.43 | even | 2 | 3872.2.a.bq.1.5 | 6 | |||
88.61 | odd | 10 | 352.2.m.f.289.1 | yes | 12 | ||
88.83 | even | 10 | 352.2.m.e.289.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.2.m.e.257.3 | ✓ | 12 | 88.35 | even | 10 | ||
352.2.m.e.289.3 | yes | 12 | 88.83 | even | 10 | ||
352.2.m.f.257.1 | yes | 12 | 88.13 | odd | 10 | ||
352.2.m.f.289.1 | yes | 12 | 88.61 | odd | 10 | ||
704.2.m.m.257.1 | 12 | 44.35 | even | 10 | |||
704.2.m.m.641.1 | 12 | 44.39 | even | 10 | |||
704.2.m.n.257.3 | 12 | 11.2 | odd | 10 | |||
704.2.m.n.641.3 | 12 | 11.6 | odd | 10 | |||
3872.2.a.bn.1.2 | 6 | 88.21 | odd | 2 | |||
3872.2.a.bo.1.2 | 6 | 8.5 | even | 2 | |||
3872.2.a.bp.1.5 | 6 | 8.3 | odd | 2 | |||
3872.2.a.bq.1.5 | 6 | 88.43 | even | 2 | |||
7744.2.a.dt.1.2 | 6 | 4.3 | odd | 2 | |||
7744.2.a.du.1.2 | 6 | 44.43 | even | 2 | |||
7744.2.a.dv.1.5 | 6 | 11.10 | odd | 2 | |||
7744.2.a.dw.1.5 | 6 | 1.1 | even | 1 | trivial |