Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, 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("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 23x^{8} + 23x^{7} + 170x^{6} - 165x^{5} - 411x^{4} + 360x^{3} + 111x^{2} - 48x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(3.12022\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-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 | ||||||||
\(3\) | 3.12022 | 1.80146 | 0.900729 | − | 0.434382i | \(-0.143033\pi\) | ||||
0.900729 | + | 0.434382i | \(0.143033\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.246641 | −0.110301 | −0.0551507 | − | 0.998478i | \(-0.517564\pi\) | ||||
−0.0551507 | + | 0.998478i | \(0.517564\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.73575 | 2.24525 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.769574 | −0.198703 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.45111 | −0.351945 | −0.175973 | − | 0.984395i | \(-0.556307\pi\) | ||||
−0.175973 | + | 0.984395i | \(0.556307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.30252 | 0.757650 | 0.378825 | − | 0.925468i | \(-0.376328\pi\) | ||||
0.378825 | + | 0.925468i | \(0.376328\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12022 | −0.680887 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.80480 | 1.83593 | 0.917963 | − | 0.396665i | \(-0.129833\pi\) | ||||
0.917963 | + | 0.396665i | \(0.129833\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.93917 | −0.987834 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.6563 | 2.24326 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.78276 | −1.63092 | −0.815458 | − | 0.578816i | \(-0.803515\pi\) | ||||
−0.815458 | + | 0.578816i | \(0.803515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.87495 | 1.59399 | 0.796994 | − | 0.603987i | \(-0.206422\pi\) | ||||
0.796994 | + | 0.603987i | \(0.206422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.12022 | 0.543160 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.246641 | 0.0416900 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.62416 | −0.267011 | −0.133506 | − | 0.991048i | \(-0.542623\pi\) | ||||
−0.133506 | + | 0.991048i | \(0.542623\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.12022 | 0.499634 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.42584 | −0.691199 | −0.345600 | − | 0.938382i | \(-0.612325\pi\) | ||||
−0.345600 | + | 0.938382i | \(0.612325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.05794 | 1.22882 | 0.614412 | − | 0.788985i | \(-0.289393\pi\) | ||||
0.614412 | + | 0.788985i | \(0.289393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.66131 | −0.247654 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.80480 | 1.28431 | 0.642156 | − | 0.766574i | \(-0.278040\pi\) | ||||
0.642156 | + | 0.766574i | \(0.278040\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.52777 | −0.634014 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.99343 | −0.823261 | −0.411631 | − | 0.911351i | \(-0.635041\pi\) | ||||
−0.411631 | + | 0.911351i | \(0.635041\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.246641 | −0.0332571 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.3046 | 1.36487 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.90780 | 0.248375 | 0.124187 | − | 0.992259i | \(-0.460368\pi\) | ||||
0.124187 | + | 0.992259i | \(0.460368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.06693 | 0.392680 | 0.196340 | − | 0.980536i | \(-0.437094\pi\) | ||||
0.196340 | + | 0.980536i | \(0.437094\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.73575 | −0.848624 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.246641 | −0.0305921 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.264888 | −0.0323612 | −0.0161806 | − | 0.999869i | \(-0.505151\pi\) | ||||
−0.0161806 | + | 0.999869i | \(0.505151\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 27.4729 | 3.30734 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.08119 | 0.246992 | 0.123496 | − | 0.992345i | \(-0.460589\pi\) | ||||
0.123496 | + | 0.992345i | \(0.460589\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.43101 | 0.869733 | 0.434867 | − | 0.900495i | \(-0.356795\pi\) | ||||
0.434867 | + | 0.900495i | \(0.356795\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −15.4113 | −1.77954 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.2638 | −1.26728 | −0.633638 | − | 0.773630i | \(-0.718439\pi\) | ||||
−0.633638 | + | 0.773630i | \(0.718439\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.1630 | 1.79589 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.9492 | 1.64088 | 0.820442 | − | 0.571729i | \(-0.193727\pi\) | ||||
0.820442 | + | 0.571729i | \(0.193727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.357903 | 0.0388200 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −27.4041 | −2.93803 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.9320 | −1.26479 | −0.632396 | − | 0.774645i | \(-0.717929\pi\) | ||||
−0.632396 | + | 0.774645i | \(0.717929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.6918 | 2.87150 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.814538 | −0.0835698 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.9656 | 1.92567 | 0.962834 | − | 0.270093i | \(-0.0870545\pi\) | ||||
0.962834 | + | 0.270093i | \(0.0870545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.73575 | 0.676968 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.5289 | −1.34617 | −0.673086 | − | 0.739564i | \(-0.735032\pi\) | ||||
−0.673086 | + | 0.739564i | \(0.735032\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.20200 | −0.315502 | −0.157751 | − | 0.987479i | \(-0.550424\pi\) | ||||
−0.157751 | + | 0.987479i | \(0.550424\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.769574 | 0.0751027 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 20.0200 | 1.93541 | 0.967704 | − | 0.252089i | \(-0.0811176\pi\) | ||||
0.967704 | + | 0.252089i | \(0.0811176\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.98578 | −0.669116 | −0.334558 | − | 0.942375i | \(-0.608587\pi\) | ||||
−0.334558 | + | 0.942375i | \(0.608587\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.06774 | −0.481009 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.9225 | −1.68601 | −0.843004 | − | 0.537908i | \(-0.819215\pi\) | ||||
−0.843004 | + | 0.537908i | \(0.819215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.17163 | −0.202505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.73575 | 0.622720 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.45111 | 0.133023 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.8096 | −1.24517 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.45141 | 0.219261 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3375 | −0.917307 | −0.458654 | − | 0.888615i | \(-0.651668\pi\) | ||||
−0.458654 | + | 0.888615i | \(0.651668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25.1425 | 2.21367 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1582 | −0.974894 | −0.487447 | − | 0.873153i | \(-0.662072\pi\) | ||||
−0.487447 | + | 0.873153i | \(0.662072\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.30252 | −0.286365 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.87493 | −0.247435 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.8367 | 1.35302 | 0.676512 | − | 0.736432i | \(-0.263491\pi\) | ||||
0.676512 | + | 0.736432i | \(0.263491\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2076 | −0.950619 | −0.475309 | − | 0.879819i | \(-0.657664\pi\) | ||||
−0.475309 | + | 0.879819i | \(0.657664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.4729 | 2.31363 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.16619 | 0.179892 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.12022 | 0.257351 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.9143 | 1.38567 | 0.692835 | − | 0.721096i | \(-0.256361\pi\) | ||||
0.692835 | + | 0.721096i | \(0.256361\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.4047 | −1.00948 | −0.504739 | − | 0.863272i | \(-0.668411\pi\) | ||||
−0.504739 | + | 0.863272i | \(0.668411\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.77429 | −0.790204 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.18893 | −0.175819 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.72448 | −0.536672 | −0.268336 | − | 0.963325i | \(-0.586474\pi\) | ||||
−0.268336 | + | 0.963325i | \(0.586474\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.7008 | −1.48307 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.80480 | −0.693915 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.3375 | 1.04467 | 0.522337 | − | 0.852739i | \(-0.325060\pi\) | ||||
0.522337 | + | 0.852739i | \(0.325060\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.769574 | −0.0599112 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.484770 | 0.0375127 | 0.0187563 | − | 0.999824i | \(-0.494029\pi\) | ||||
0.0187563 | + | 0.999824i | \(0.494029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.2449 | 1.70111 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.40825 | 0.487210 | 0.243605 | − | 0.969874i | \(-0.421670\pi\) | ||||
0.243605 | + | 0.969874i | \(0.421670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.93917 | 0.373366 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.95276 | 0.447437 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.9600 | 0.968676 | 0.484338 | − | 0.874881i | \(-0.339060\pi\) | ||||
0.484338 | + | 0.874881i | \(0.339060\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.52546 | 0.187716 | 0.0938578 | − | 0.995586i | \(-0.470080\pi\) | ||||
0.0938578 | + | 0.995586i | \(0.470080\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.56947 | 0.707396 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.400586 | 0.0294517 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.45111 | −0.106115 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.6563 | −0.847873 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.8302 | −1.36251 | −0.681253 | − | 0.732048i | \(-0.738565\pi\) | ||||
−0.681253 | + | 0.732048i | \(0.738565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.79522 | −0.129223 | −0.0646114 | − | 0.997910i | \(-0.520581\pi\) | ||||
−0.0646114 | + | 0.997910i | \(0.520581\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.769574 | −0.0551103 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.6981 | −0.904702 | −0.452351 | − | 0.891840i | \(-0.649415\pi\) | ||||
−0.452351 | + | 0.891840i | \(0.649415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.21430 | 0.440520 | 0.220260 | − | 0.975441i | \(-0.429309\pi\) | ||||
0.220260 | + | 0.975441i | \(0.429309\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.826507 | −0.0582973 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.78276 | 0.616429 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.09159 | 0.0762402 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 59.3069 | 4.12211 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.30252 | 0.228440 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4466 | 0.994548 | 0.497274 | − | 0.867593i | \(-0.334334\pi\) | ||||
0.497274 | + | 0.867593i | \(0.334334\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.49377 | 0.444946 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.98742 | −0.135541 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.87495 | −0.602471 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.1863 | 1.56679 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.45111 | −0.0976120 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.34190 | 0.558615 | 0.279307 | − | 0.960202i | \(-0.409895\pi\) | ||||
0.279307 | + | 0.960202i | \(0.409895\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −33.2690 | −2.21793 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.8094 | −1.38117 | −0.690585 | − | 0.723251i | \(-0.742647\pi\) | ||||
−0.690585 | + | 0.723251i | \(0.742647\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.94054 | −0.656889 | −0.328445 | − | 0.944523i | \(-0.606524\pi\) | ||||
−0.328445 | + | 0.944523i | \(0.606524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.12022 | −0.205295 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.34684 | −0.0882344 | −0.0441172 | − | 0.999026i | \(-0.514047\pi\) | ||||
−0.0441172 | + | 0.999026i | \(0.514047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.17163 | −0.141661 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −35.1455 | −2.28294 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0818 | 0.975558 | 0.487779 | − | 0.872967i | \(-0.337807\pi\) | ||||
0.487779 | + | 0.872967i | \(0.337807\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4514 | −0.930895 | −0.465448 | − | 0.885075i | \(-0.654107\pi\) | ||||
−0.465448 | + | 0.885075i | \(0.654107\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4631 | 0.991961 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.246641 | −0.0157573 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.30252 | 0.210134 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 46.6446 | 2.95598 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.30327 | −0.208500 | −0.104250 | − | 0.994551i | \(-0.533244\pi\) | ||||
−0.104250 | + | 0.994551i | \(0.533244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.80480 | 0.553553 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.11673 | 0.0699326 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30.8498 | 1.92436 | 0.962179 | − | 0.272417i | \(-0.0878230\pi\) | ||||
0.962179 | + | 0.272417i | \(0.0878230\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.62416 | 0.100921 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −59.1584 | −3.66181 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.90673 | 0.302562 | 0.151281 | − | 0.988491i | \(-0.451660\pi\) | ||||
0.151281 | + | 0.988491i | \(0.451660\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.47823 | 0.0908068 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −37.2305 | −2.27847 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.8566 | −0.783881 | −0.391940 | − | 0.919991i | \(-0.628196\pi\) | ||||
−0.391940 | + | 0.919991i | \(0.628196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.4601 | −1.12137 | −0.560686 | − | 0.828029i | \(-0.689462\pi\) | ||||
−0.560686 | + | 0.828029i | \(0.689462\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.12022 | −0.188844 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.93917 | −0.297843 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.53780 | −0.152482 | −0.0762409 | − | 0.997089i | \(-0.524292\pi\) | ||||
−0.0762409 | + | 0.997089i | \(0.524292\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 59.7794 | 3.57890 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.4565 | −1.10102 | −0.550511 | − | 0.834828i | \(-0.685567\pi\) | ||||
−0.550511 | + | 0.834828i | \(0.685567\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.9169 | 1.65949 | 0.829745 | − | 0.558143i | \(-0.188486\pi\) | ||||
0.829745 | + | 0.558143i | \(0.188486\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.54153 | −0.150548 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.42584 | 0.261249 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8943 | −0.876135 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 59.1769 | 3.46901 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.2614 | −1.41736 | −0.708682 | − | 0.705528i | \(-0.750710\pi\) | ||||
−0.708682 | + | 0.705528i | \(0.750710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.470543 | −0.0273961 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.6563 | 0.676369 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.80480 | 0.509194 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.05794 | −0.464452 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −42.2130 | −2.42507 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.756430 | −0.0433131 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.88269 | 0.278670 | 0.139335 | − | 0.990245i | \(-0.455504\pi\) | ||||
0.139335 | + | 0.990245i | \(0.455504\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.99093 | −0.568364 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.9849 | −1.58688 | −0.793439 | − | 0.608650i | \(-0.791712\pi\) | ||||
−0.793439 | + | 0.608650i | \(0.791712\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1400 | 1.08186 | 0.540928 | − | 0.841069i | \(-0.318073\pi\) | ||||
0.540928 | + | 0.841069i | \(0.318073\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.66131 | 0.0936044 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.21011 | 0.180298 | 0.0901488 | − | 0.995928i | \(-0.471266\pi\) | ||||
0.0901488 | + | 0.995928i | \(0.471266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.78276 | −0.491740 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 62.4668 | 3.48655 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.79231 | −0.266651 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.93917 | −0.273976 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.7971 | −1.20538 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.80480 | −0.485424 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.0455 | −1.65145 | −0.825726 | − | 0.564072i | \(-0.809234\pi\) | ||||
−0.825726 | + | 0.564072i | \(0.809234\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.9400 | −0.599506 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.0653322 | 0.00356948 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.09963 | −0.168848 | −0.0844239 | − | 0.996430i | \(-0.526905\pi\) | ||||
−0.0844239 | + | 0.996430i | \(0.526905\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −55.9221 | −3.03727 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.87495 | 0.480606 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.77594 | −0.364804 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.55586 | 0.244571 | 0.122286 | − | 0.992495i | \(-0.460978\pi\) | ||||
0.122286 | + | 0.992495i | \(0.460978\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.72763 | −0.413650 | −0.206825 | − | 0.978378i | \(-0.566313\pi\) | ||||
−0.206825 | + | 0.978378i | \(0.566313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.6563 | 0.622169 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.2886 | −0.654058 | −0.327029 | − | 0.945014i | \(-0.606047\pi\) | ||||
−0.327029 | + | 0.945014i | \(0.606047\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.513308 | −0.0272436 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.52777 | 0.239635 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.6415 | −1.40609 | −0.703043 | − | 0.711148i | \(-0.748176\pi\) | ||||
−0.703043 | + | 0.711148i | \(0.748176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.09335 | −0.425966 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.12022 | 0.163769 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.83279 | −0.0959327 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.6145 | −1.59807 | −0.799033 | − | 0.601287i | \(-0.794655\pi\) | ||||
−0.799033 | + | 0.601287i | \(0.794655\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −29.8113 | −1.55191 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.99343 | 0.311163 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.7859 | −1.17981 | −0.589904 | − | 0.807473i | \(-0.700834\pi\) | ||||
−0.589904 | + | 0.807473i | \(0.700834\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.64892 | 0.394989 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.78276 | −0.452335 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.8546 | 1.22533 | 0.612665 | − | 0.790343i | \(-0.290097\pi\) | ||||
0.612665 | + | 0.790343i | \(0.290097\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.2553 | −1.65249 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.8150 | −1.83006 | −0.915032 | − | 0.403382i | \(-0.867834\pi\) | ||||
−0.915032 | + | 0.403382i | \(0.867834\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.246641 | 0.0125700 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 54.2762 | 2.75902 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.1110 | 0.664753 | 0.332376 | − | 0.943147i | \(-0.392150\pi\) | ||||
0.332376 | + | 0.943147i | \(0.392150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7767 | −0.646146 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.8159 | −1.75623 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.77812 | 0.139782 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.1320 | −0.709262 | −0.354631 | − | 0.935006i | \(-0.615394\pi\) | ||||
−0.354631 | + | 0.935006i | \(0.615394\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.3046 | −0.515874 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1911 | 0.858482 | 0.429241 | − | 0.903190i | \(-0.358781\pi\) | ||||
0.429241 | + | 0.903190i | \(0.358781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.87495 | 0.442093 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.98647 | −0.198089 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.62416 | −0.0805069 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.6818 | 1.86324 | 0.931622 | − | 0.363429i | \(-0.118394\pi\) | ||||
0.931622 | + | 0.363429i | \(0.118394\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 49.4140 | 2.43741 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.90780 | −0.0938768 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.68708 | −0.180992 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.9702 | −1.71250 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.2049 | −1.42675 | −0.713376 | − | 0.700781i | \(-0.752835\pi\) | ||||
−0.713376 | + | 0.700781i | \(0.752835\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.76379 | −0.475858 | −0.237929 | − | 0.971283i | \(-0.576469\pi\) | ||||
−0.237929 | + | 0.971283i | \(0.576469\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 59.3069 | 2.88360 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.16726 | 0.347663 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.06693 | −0.148419 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.12022 | 0.150645 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.80548 | −0.424145 | −0.212073 | − | 0.977254i | \(-0.568021\pi\) | ||||
−0.212073 | + | 0.977254i | \(0.568021\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.63506 | −0.366918 | −0.183459 | − | 0.983027i | \(-0.558729\pi\) | ||||
−0.183459 | + | 0.983027i | \(0.558729\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.75898 | 0.324068 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 29.0780 | 1.39099 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.1844 | 1.24971 | 0.624857 | − | 0.780739i | \(-0.285157\pi\) | ||||
0.624857 | + | 0.780739i | \(0.285157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.73575 | 0.320750 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.72069 | −0.224287 | −0.112143 | − | 0.993692i | \(-0.535772\pi\) | ||||
−0.112143 | + | 0.993692i | \(0.535772\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.94293 | 0.139508 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 52.7761 | 2.49623 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.0257 | −1.36981 | −0.684903 | − | 0.728634i | \(-0.740155\pi\) | ||||
−0.684903 | + | 0.728634i | \(0.740155\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.42584 | −0.208404 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −38.7052 | −1.81853 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.246641 | 0.0115627 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.7749 | −1.39281 | −0.696406 | − | 0.717648i | \(-0.745219\pi\) | ||||
−0.696406 | + | 0.717648i | \(0.745219\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.9146 | −0.789505 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.0121450 | 0.000565650 0 | 0.000282825 | − | 1.00000i | \(-0.499910\pi\) | ||||
0.000282825 | 1.00000i | \(0.499910\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.37817 | 0.389366 | 0.194683 | − | 0.980866i | \(-0.437632\pi\) | ||||
0.194683 | + | 0.980866i | \(0.437632\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.82993 | −0.316730 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.6991 | −1.42058 | −0.710292 | − | 0.703907i | \(-0.751437\pi\) | ||||
−0.710292 | + | 0.703907i | \(0.751437\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.264888 | 0.0122314 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.9818 | −0.966792 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.05794 | 0.370504 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.3117 | −0.748433 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.3702 | −1.84843 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.3377 | 1.11202 | 0.556008 | − | 0.831177i | \(-0.312332\pi\) | ||||
0.556008 | + | 0.831177i | \(0.312332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.62416 | −0.0740555 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −27.4729 | −1.25006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.67771 | −0.212404 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.7875 | 0.760716 | 0.380358 | − | 0.924839i | \(-0.375801\pi\) | ||||
0.380358 | + | 0.924839i | \(0.375801\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 41.6159 | 1.88194 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.4680 | −1.42013 | −0.710066 | − | 0.704135i | \(-0.751335\pi\) | ||||
−0.710066 | + | 0.704135i | \(0.751335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.7447 | 0.573993 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.66131 | −0.0746704 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.08119 | −0.0933543 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.5021 | 1.09686 | 0.548432 | − | 0.836195i | \(-0.315225\pi\) | ||||
0.548432 | + | 0.836195i | \(0.315225\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.51259 | 0.0675774 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.2399 | −1.16998 | −0.584990 | − | 0.811041i | \(-0.698901\pi\) | ||||
−0.584990 | + | 0.811041i | \(0.698901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.33677 | 0.148484 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.12022 | 0.138574 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.58940 | −0.247746 | −0.123873 | − | 0.992298i | \(-0.539532\pi\) | ||||
−0.123873 | + | 0.992298i | \(0.539532\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.43101 | −0.328728 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 38.4953 | 1.69961 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.789745 | 0.0348003 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.80480 | 0.387234 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.9951 | 0.877689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0305 | 0.658497 | 0.329249 | − | 0.944243i | \(-0.393205\pi\) | ||||
0.329249 | + | 0.944243i | \(0.393205\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.35702 | −0.0593384 | −0.0296692 | − | 0.999560i | \(-0.509445\pi\) | ||||
−0.0296692 | + | 0.999560i | \(0.509445\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.4113 | 0.672603 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.8785 | −0.560997 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.5244 | 2.37063 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.8505 | 0.557663 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.42584 | −0.191704 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.93776 | −0.213478 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.4380 | 1.74503 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.2691 | −1.30137 | −0.650685 | − | 0.759348i | \(-0.725518\pi\) | ||||
−0.650685 | + | 0.759348i | \(0.725518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.87996 | 0.338162 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.72298 | 0.0738044 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6661 | −0.755349 | −0.377674 | − | 0.925938i | \(-0.623276\pi\) | ||||
−0.377674 | + | 0.925938i | \(0.623276\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.6580 | 0.881663 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.0052 | −1.23566 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.2638 | 0.478985 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.24991 | 0.0530559 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.11094 | −0.386043 | −0.193022 | − | 0.981195i | \(-0.561829\pi\) | ||||
−0.193022 | + | 0.981195i | \(0.561829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.05794 | 0.340815 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.52777 | −0.191163 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.2123 | 1.73689 | 0.868446 | − | 0.495783i | \(-0.165119\pi\) | ||||
0.868446 | + | 0.495783i | \(0.165119\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.42043 | 0.185969 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.1630 | −0.678783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.26404 | 0.136836 | 0.0684178 | − | 0.997657i | \(-0.478205\pi\) | ||||
0.0684178 | + | 0.997657i | \(0.478205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.17732 | 0.0492695 | 0.0246347 | − | 0.999697i | \(-0.492158\pi\) | ||||
0.0246347 | + | 0.999697i | \(0.492158\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −58.7543 | −2.45450 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −43.4884 | −1.81359 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.81878 | 0.0757166 | 0.0378583 | − | 0.999283i | \(-0.487946\pi\) | ||||
0.0378583 | + | 0.999283i | \(0.487946\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.60148 | −0.232789 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.9492 | −0.620196 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.99343 | −0.248223 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.66131 | −0.0686868 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.48078 | 0.184942 | 0.0924709 | − | 0.995715i | \(-0.470524\pi\) | ||||
0.0924709 | + | 0.995715i | \(0.470524\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.3097 | 1.20769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −39.6208 | −1.62978 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.36331 | 0.220245 | 0.110122 | − | 0.993918i | \(-0.464876\pi\) | ||||
0.110122 | + | 0.993918i | \(0.464876\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.357903 | −0.0146726 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.3900 | 0.793579 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.7972 | 0.972326 | 0.486163 | − | 0.873868i | \(-0.338396\pi\) | ||||
0.486163 | + | 0.873868i | \(0.338396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.4756 | 1.61024 | 0.805122 | − | 0.593110i | \(-0.202100\pi\) | ||||
0.805122 | + | 0.593110i | \(0.202100\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.78422 | −0.0726589 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.246641 | −0.0100274 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.1987 | −0.779250 | −0.389625 | − | 0.920974i | \(-0.627395\pi\) | ||||
−0.389625 | + | 0.920974i | \(0.627395\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.4041 | 1.11047 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.80480 | 0.356204 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.4147 | 1.91506 | 0.957531 | − | 0.288332i | \(-0.0931006\pi\) | ||||
0.957531 | + | 0.288332i | \(0.0931006\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.40601 | 0.137343 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.1718 | −0.570536 | −0.285268 | − | 0.958448i | \(-0.592083\pi\) | ||||
−0.285268 | + | 0.958448i | \(0.592083\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.2115 | 1.77701 | 0.888504 | − | 0.458869i | \(-0.151745\pi\) | ||||
0.888504 | + | 0.458869i | \(0.151745\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 102.632 | 4.11846 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.9320 | 0.478047 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0912 | 0.963649 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.3046 | 0.411525 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.35684 | 0.0939733 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.9981 | −0.915539 | −0.457769 | − | 0.889071i | \(-0.651351\pi\) | ||||
−0.457769 | + | 0.889071i | \(0.651351\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.0767 | 1.79164 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.54966 | 0.101180 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.0184 | 0.554559 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.7292 | −1.72720 | −0.863600 | − | 0.504178i | \(-0.831796\pi\) | ||||
−0.863600 | + | 0.504178i | \(0.831796\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.02229 | −0.237496 | −0.118748 | − | 0.992924i | \(-0.537888\pi\) | ||||
−0.118748 | + | 0.992924i | \(0.537888\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.20118 | −0.244171 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.7985 | −0.581789 | −0.290895 | − | 0.956755i | \(-0.593953\pi\) | ||||
−0.290895 | + | 0.956755i | \(0.593953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.90780 | 0.0748878 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.6918 | −1.08533 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.56561 | −0.100400 | −0.0502000 | − | 0.998739i | \(-0.515986\pi\) | ||||
−0.0502000 | + | 0.998739i | \(0.515986\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.75207 | 0.107532 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 50.0534 | 1.95277 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.4914 | 0.837184 | 0.418592 | − | 0.908174i | \(-0.362524\pi\) | ||||
0.418592 | + | 0.908174i | \(0.362524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.3383 | 1.76346 | 0.881728 | − | 0.471759i | \(-0.156381\pi\) | ||||
0.881728 | + | 0.471759i | \(0.156381\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.52777 | −0.175844 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.814538 | 0.0315864 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −77.3304 | −2.99424 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.0285 | 1.00632 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.06693 | 0.118397 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.1678 | −1.62545 | −0.812724 | − | 0.582649i | \(-0.802016\pi\) | ||||
−0.812724 | + | 0.582649i | \(0.802016\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −57.5726 | −2.21597 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.53077 | −0.135698 | −0.0678492 | − | 0.997696i | \(-0.521614\pi\) | ||||
−0.0678492 | + | 0.997696i | \(0.521614\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.9656 | −0.727834 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −64.9299 | −2.48812 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.2139 | 1.38569 | 0.692844 | − | 0.721088i | \(-0.256357\pi\) | ||||
0.692844 | + | 0.721088i | \(0.256357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.90599 | −0.149240 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31.0166 | −1.18336 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.99343 | −0.228332 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.2732 | 0.504937 | 0.252469 | − | 0.967605i | \(-0.418758\pi\) | ||||
0.252469 | + | 0.967605i | \(0.418758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.73575 | −0.255870 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.76426 | 0.104855 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.42236 | 0.243264 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.20243 | −0.158950 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.4283 | −0.658256 | −0.329128 | − | 0.944285i | \(-0.606755\pi\) | ||||
−0.329128 | + | 0.944285i | \(0.606755\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.36384 | −0.202301 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.77594 | −0.255197 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.5289 | 0.508805 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8523 | 1.15868 | 0.579341 | − | 0.815085i | \(-0.303310\pi\) | ||||
0.579341 | + | 0.815085i | \(0.303310\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −75.8700 | −2.84535 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 78.1421 | 2.92645 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.246641 | −0.00922386 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.0583 | 1.75743 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.0551 | 1.68027 | 0.840136 | − | 0.542375i | \(-0.182475\pi\) | ||||
0.840136 | + | 0.542375i | \(0.182475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.20200 | 0.119249 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −45.0914 | −1.67697 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 43.3795 | 1.61107 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.8003 | 0.586001 | 0.293000 | − | 0.956112i | \(-0.405346\pi\) | ||||
0.293000 | + | 0.956112i | \(0.405346\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.240761 | −0.00891709 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6929 | −0.432479 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.1625 | −0.744720 | −0.372360 | − | 0.928088i | \(-0.621451\pi\) | ||||
−0.372360 | + | 0.928088i | \(0.621451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.769574 | −0.0283862 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.264888 | −0.00975727 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.2538 | 0.708264 | 0.354132 | − | 0.935195i | \(-0.384776\pi\) | ||||
0.354132 | + | 0.935195i | \(0.384776\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.3046 | 0.378548 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.9952 | 0.440062 | 0.220031 | − | 0.975493i | \(-0.429384\pi\) | ||||
0.220031 | + | 0.975493i | \(0.429384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.17175 | −0.152841 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 100.694 | 3.68419 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.0200 | −0.731515 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.8063 | 1.63500 | 0.817502 | − | 0.575926i | \(-0.195358\pi\) | ||||
0.817502 | + | 0.575926i | \(0.195358\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.3069 | −0.375605 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.05950 | 0.111347 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.4954 | −1.18107 | −0.590533 | − | 0.807013i | \(-0.701082\pi\) | ||||
−0.590533 | + | 0.807013i | \(0.701082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.4729 | 0.997202 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.8480 | −0.936989 | −0.468494 | − | 0.883466i | \(-0.655203\pi\) | ||||
−0.468494 | + | 0.883466i | \(0.655203\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.98578 | 0.252902 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.41074 | 0.0871606 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.90780 | 0.0688868 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.44814 | −0.232526 | −0.116263 | − | 0.993218i | \(-0.537092\pi\) | ||||
−0.116263 | + | 0.993218i | \(0.537092\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 96.2581 | 3.46665 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.9792 | −1.76166 | −0.880830 | − | 0.473433i | \(-0.843014\pi\) | ||||
−0.880830 | + | 0.473433i | \(0.843014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −43.8349 | −1.57460 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.06774 | 0.181804 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.6164 | −0.523688 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.08119 | 0.0744710 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −102.375 | −3.65857 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.65853 | 0.0591956 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.0923 | −1.60737 | −0.803683 | − | 0.595058i | \(-0.797129\pi\) | ||||
−0.803683 | + | 0.595058i | \(0.797129\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.3100 | 0.545052 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.9225 | 0.637251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.06693 | 0.108910 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.61239 | 0.163585 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.3417 | −0.614276 | −0.307138 | − | 0.951665i | \(-0.599371\pi\) | ||||
−0.307138 | + | 0.951665i | \(0.599371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.7767 | −0.452007 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −80.3711 | −2.83977 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.43101 | 0.262235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.17163 | 0.0765397 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.1154 | −1.41213 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.8915 | −0.980612 | −0.490306 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490306 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.3954 | −1.62916 | −0.814581 | − | 0.580049i | \(-0.803033\pi\) | ||||
−0.814581 | + | 0.580049i | \(0.803033\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −57.5995 | −2.02010 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.28958 | −0.115229 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.6115 | 0.931019 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.73575 | −0.235366 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.7836 | 0.830053 | 0.415026 | − | 0.909809i | \(-0.363772\pi\) | ||||
0.415026 | + | 0.909809i | \(0.363772\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.35161 | −0.256261 | −0.128131 | − | 0.991757i | \(-0.540898\pi\) | ||||
−0.128131 | + | 0.991757i | \(0.540898\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.4113 | −0.536552 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.38289 | −0.0480879 | −0.0240440 | − | 0.999711i | \(-0.507654\pi\) | ||||
−0.0240440 | + | 0.999711i | \(0.507654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.20434 | 0.215486 | 0.107743 | − | 0.994179i | \(-0.465638\pi\) | ||||
0.107743 | + | 0.994179i | \(0.465638\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.91850 | −0.274690 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.45111 | −0.0502779 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.119564 | −0.00413770 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 103.449 | 3.57573 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.3007 | 0.700857 | 0.350429 | − | 0.936589i | \(-0.386036\pi\) | ||||
0.350429 | + | 0.936589i | \(0.386036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.1368 | 1.65989 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −57.5883 | −1.98345 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.246641 | −0.00848472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 87.1069 | 2.98950 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.3004 | −0.490213 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.89492 | −0.304556 | −0.152278 | − | 0.988338i | \(-0.548661\pi\) | ||||
−0.152278 | + | 0.988338i | \(0.548661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.48652 | −0.187635 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −52.5296 | −1.79438 | −0.897188 | − | 0.441648i | \(-0.854394\pi\) | ||||
−0.897188 | + | 0.441648i | \(0.854394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.46267 | 0.220503 | 0.110252 | − | 0.993904i | \(-0.464834\pi\) | ||||
0.110252 | + | 0.993904i | \(0.464834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.8096 | 0.470629 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.95039 | −0.134473 | −0.0672365 | − | 0.997737i | \(-0.521418\pi\) | ||||
−0.0672365 | + | 0.997737i | \(0.521418\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.58054 | −0.0537399 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −46.4734 | −1.57832 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.2638 | −0.382098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.264888 | −0.00897538 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 127.748 | 4.32360 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.45141 | −0.0828727 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.409047 | −0.0138125 | −0.00690626 | − | 0.999976i | \(-0.502198\pi\) | ||||
−0.00690626 | + | 0.999976i | \(0.502198\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −75.7007 | −2.55332 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.29247 | −0.0435444 | −0.0217722 | − | 0.999763i | \(-0.506931\pi\) | ||||
−0.0217722 | + | 0.999763i | \(0.506931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.7346 | −1.53909 | −0.769547 | − | 0.638591i | \(-0.779518\pi\) | ||||
−0.769547 | + | 0.638591i | \(0.779518\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.46820 | −0.0493528 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.6200 | −0.658774 | −0.329387 | − | 0.944195i | \(-0.606842\pi\) | ||||
−0.329387 | + | 0.944195i | \(0.606842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3375 | 0.346710 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.1630 | 0.541482 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.0780 | 0.973059 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.19647 | −0.106846 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.4729 | 0.917292 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −77.9465 | −2.59966 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.69711 | 0.289743 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.1425 | −0.836690 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.622881 | −0.0207053 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.8559 | 0.426873 | 0.213437 | − | 0.976957i | \(-0.431534\pi\) | ||||
0.213437 | + | 0.976957i | \(0.431534\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −91.1269 | −3.02249 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.6200 | 1.27954 | 0.639769 | − | 0.768567i | \(-0.279030\pi\) | ||||
0.639769 | + | 0.768567i | \(0.279030\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.9492 | 0.494745 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.36023 | −0.0780267 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.1582 | 0.368475 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.0157 | −0.396360 | −0.198180 | − | 0.980166i | \(-0.563503\pi\) | ||||
−0.198180 | + | 0.980166i | \(0.563503\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.2350 | 0.502011 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.08119 | 0.0685033 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.02202 | 0.263763 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.5679 | −0.708381 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.54856 | −0.247660 | −0.123830 | − | 0.992303i | \(-0.539518\pi\) | ||||
−0.123830 | + | 0.992303i | \(0.539518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.30252 | 0.108236 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −87.3189 | −2.85869 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.357903 | 0.0117047 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.8822 | −0.355504 | −0.177752 | − | 0.984075i | \(-0.556883\pi\) | ||||
−0.177752 | + | 0.984075i | \(0.556883\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 59.7209 | 1.94892 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.27321 | 0.139303 | 0.0696514 | − | 0.997571i | \(-0.477811\pi\) | ||||
0.0696514 | + | 0.997571i | \(0.477811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38.9686 | −1.26899 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.87493 | 0.0935215 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.27017 | 0.0412751 | 0.0206376 | − | 0.999787i | \(-0.493430\pi\) | ||||
0.0206376 | + | 0.999787i | \(0.493430\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.43101 | 0.241221 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.0162 | 0.324799 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.2446 | −0.429034 | −0.214517 | − | 0.976720i | \(-0.568818\pi\) | ||||
−0.214517 | + | 0.976720i | \(0.568818\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.64430 | 0.150286 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −27.4041 | −0.885848 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.8367 | −0.511395 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.7648 | 1.54080 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 134.850 | 4.34547 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.442776 | 0.0142535 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.8928 | 1.79739 | 0.898696 | − | 0.438572i | \(-0.144516\pi\) | ||||
0.898696 | + | 0.438572i | \(0.144516\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.9531 | −0.480361 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.5207 | −1.52501 | −0.762506 | − | 0.646982i | \(-0.776031\pi\) | ||||
−0.762506 | + | 0.646982i | \(0.776031\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.2076 | 0.359300 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.4113 | −0.493556 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.7370 | −0.695428 | −0.347714 | − | 0.937601i | \(-0.613042\pi\) | ||||
−0.347714 | + | 0.937601i | \(0.613042\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.9320 | −0.381349 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −47.0544 | −1.50233 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.7735 | −1.17289 | −0.586446 | − | 0.809988i | \(-0.699473\pi\) | ||||
−0.586446 | + | 0.809988i | \(0.699473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.13187 | 0.0997898 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.4729 | −0.874471 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 70.9485 | 2.25603 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.666569 | −0.0211743 | −0.0105871 | − | 0.999944i | \(-0.503370\pi\) | ||||
−0.0105871 | + | 0.999944i | \(0.503370\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −93.7485 | −2.97502 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.53270 | −0.0485900 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.1041 | −0.510021 | −0.255011 | − | 0.966938i | \(-0.582079\pi\) | ||||
−0.255011 | + | 0.966938i | \(0.582079\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.9318 | −0.598976 |
(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 | 4004.2.a.k.1.10 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.k.1.10 | ✓ | 10 | 1.1 | even | 1 | trivial |