Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.9248.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 2 \) |
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 | 1.4 | ||
Root | \(0.662153\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.35829 | 1.36156 | 0.680781 | − | 0.732487i | \(-0.261641\pi\) | ||||
0.680781 | + | 0.732487i | \(0.261641\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.662153 | −0.296124 | −0.148062 | − | 0.988978i | \(-0.547304\pi\) | ||||
−0.148062 | + | 0.988978i | \(0.547304\pi\) | |||||||
\(6\) | −2.35829 | −0.962770 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.56155 | 0.853851 | ||||||||
\(10\) | 0.662153 | 0.209391 | ||||||||
\(11\) | −0.438447 | −0.132197 | −0.0660984 | − | 0.997813i | \(-0.521055\pi\) | ||||
−0.0660984 | + | 0.997813i | \(0.521055\pi\) | |||||||
\(12\) | 2.35829 | 0.680781 | ||||||||
\(13\) | −4.05444 | −1.12450 | −0.562249 | − | 0.826968i | \(-0.690064\pi\) | ||||
−0.562249 | + | 0.826968i | \(0.690064\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.34475 | −1.05376 | −0.526879 | − | 0.849940i | \(-0.676638\pi\) | ||||
−0.526879 | + | 0.849940i | \(0.676638\pi\) | |||||||
\(18\) | −2.56155 | −0.603764 | ||||||||
\(19\) | 7.36520 | 1.68969 | 0.844847 | − | 0.535008i | \(-0.179692\pi\) | ||||
0.844847 | + | 0.535008i | \(0.179692\pi\) | |||||||
\(20\) | −0.662153 | −0.148062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.438447 | 0.0934773 | ||||||||
\(23\) | −8.24621 | −1.71945 | −0.859727 | − | 0.510754i | \(-0.829366\pi\) | ||||
−0.859727 | + | 0.510754i | \(0.829366\pi\) | |||||||
\(24\) | −2.35829 | −0.481385 | ||||||||
\(25\) | −4.56155 | −0.912311 | ||||||||
\(26\) | 4.05444 | 0.795140 | ||||||||
\(27\) | −1.03399 | −0.198991 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 1.56155 | 0.285099 | ||||||||
\(31\) | −4.05444 | −0.728198 | −0.364099 | − | 0.931360i | \(-0.618623\pi\) | ||||
−0.364099 | + | 0.931360i | \(0.618623\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.03399 | −0.179994 | ||||||||
\(34\) | 4.34475 | 0.745119 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.56155 | 0.426925 | ||||||||
\(37\) | 7.12311 | 1.17103 | 0.585516 | − | 0.810661i | \(-0.300892\pi\) | ||||
0.585516 | + | 0.810661i | \(0.300892\pi\) | |||||||
\(38\) | −7.36520 | −1.19479 | ||||||||
\(39\) | −9.56155 | −1.53107 | ||||||||
\(40\) | 0.662153 | 0.104696 | ||||||||
\(41\) | −4.34475 | −0.678537 | −0.339268 | − | 0.940690i | \(-0.610179\pi\) | ||||
−0.339268 | + | 0.940690i | \(0.610179\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.68466 | −0.714404 | −0.357202 | − | 0.934027i | \(-0.616269\pi\) | ||||
−0.357202 | + | 0.934027i | \(0.616269\pi\) | |||||||
\(44\) | −0.438447 | −0.0660984 | ||||||||
\(45\) | −1.69614 | −0.252846 | ||||||||
\(46\) | 8.24621 | 1.21584 | ||||||||
\(47\) | −0.662153 | −0.0965850 | −0.0482925 | − | 0.998833i | \(-0.515378\pi\) | ||||
−0.0482925 | + | 0.998833i | \(0.515378\pi\) | |||||||
\(48\) | 2.35829 | 0.340390 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.56155 | 0.645101 | ||||||||
\(51\) | −10.2462 | −1.43476 | ||||||||
\(52\) | −4.05444 | −0.562249 | ||||||||
\(53\) | −11.5616 | −1.58810 | −0.794051 | − | 0.607852i | \(-0.792032\pi\) | ||||
−0.794051 | + | 0.607852i | \(0.792032\pi\) | |||||||
\(54\) | 1.03399 | 0.140708 | ||||||||
\(55\) | 0.290319 | 0.0391466 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.3693 | 2.30062 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 4.34475 | 0.565639 | 0.282819 | − | 0.959173i | \(-0.408730\pi\) | ||||
0.282819 | + | 0.959173i | \(0.408730\pi\) | |||||||
\(60\) | −1.56155 | −0.201596 | ||||||||
\(61\) | 1.32431 | 0.169560 | 0.0847801 | − | 0.996400i | \(-0.472981\pi\) | ||||
0.0847801 | + | 0.996400i | \(0.472981\pi\) | |||||||
\(62\) | 4.05444 | 0.514914 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.68466 | 0.332991 | ||||||||
\(66\) | 1.03399 | 0.127275 | ||||||||
\(67\) | −4.87689 | −0.595807 | −0.297904 | − | 0.954596i | \(-0.596287\pi\) | ||||
−0.297904 | + | 0.954596i | \(0.596287\pi\) | |||||||
\(68\) | −4.34475 | −0.526879 | ||||||||
\(69\) | −19.4470 | −2.34114 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3693 | 1.34929 | 0.674645 | − | 0.738142i | \(-0.264297\pi\) | ||||
0.674645 | + | 0.738142i | \(0.264297\pi\) | |||||||
\(72\) | −2.56155 | −0.301882 | ||||||||
\(73\) | −8.48071 | −0.992591 | −0.496296 | − | 0.868154i | \(-0.665307\pi\) | ||||
−0.496296 | + | 0.868154i | \(0.665307\pi\) | |||||||
\(74\) | −7.12311 | −0.828044 | ||||||||
\(75\) | −10.7575 | −1.24217 | ||||||||
\(76\) | 7.36520 | 0.844847 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.56155 | 1.08263 | ||||||||
\(79\) | 7.80776 | 0.878442 | 0.439221 | − | 0.898379i | \(-0.355254\pi\) | ||||
0.439221 | + | 0.898379i | \(0.355254\pi\) | |||||||
\(80\) | −0.662153 | −0.0740310 | ||||||||
\(81\) | −10.1231 | −1.12479 | ||||||||
\(82\) | 4.34475 | 0.479798 | ||||||||
\(83\) | −5.08842 | −0.558527 | −0.279263 | − | 0.960215i | \(-0.590090\pi\) | ||||
−0.279263 | + | 0.960215i | \(0.590090\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.87689 | 0.312043 | ||||||||
\(86\) | 4.68466 | 0.505160 | ||||||||
\(87\) | 2.35829 | 0.252836 | ||||||||
\(88\) | 0.438447 | 0.0467386 | ||||||||
\(89\) | −9.06134 | −0.960501 | −0.480250 | − | 0.877132i | \(-0.659454\pi\) | ||||
−0.480250 | + | 0.877132i | \(0.659454\pi\) | |||||||
\(90\) | 1.69614 | 0.178789 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.24621 | −0.859727 | ||||||||
\(93\) | −9.56155 | −0.991487 | ||||||||
\(94\) | 0.662153 | 0.0682959 | ||||||||
\(95\) | −4.87689 | −0.500359 | ||||||||
\(96\) | −2.35829 | −0.240692 | ||||||||
\(97\) | −6.99337 | −0.710069 | −0.355034 | − | 0.934853i | \(-0.615531\pi\) | ||||
−0.355034 | + | 0.934853i | \(0.615531\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.12311 | −0.112876 | ||||||||
\(100\) | −4.56155 | −0.456155 | ||||||||
\(101\) | 11.3381 | 1.12819 | 0.564093 | − | 0.825711i | \(-0.309226\pi\) | ||||
0.564093 | + | 0.825711i | \(0.309226\pi\) | |||||||
\(102\) | 10.2462 | 1.01453 | ||||||||
\(103\) | 12.8255 | 1.26373 | 0.631865 | − | 0.775078i | \(-0.282290\pi\) | ||||
0.631865 | + | 0.775078i | \(0.282290\pi\) | |||||||
\(104\) | 4.05444 | 0.397570 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.5616 | 1.12296 | ||||||||
\(107\) | −0.876894 | −0.0847726 | −0.0423863 | − | 0.999101i | \(-0.513496\pi\) | ||||
−0.0423863 | + | 0.999101i | \(0.513496\pi\) | |||||||
\(108\) | −1.03399 | −0.0994955 | ||||||||
\(109\) | 10.6847 | 1.02340 | 0.511702 | − | 0.859163i | \(-0.329015\pi\) | ||||
0.511702 | + | 0.859163i | \(0.329015\pi\) | |||||||
\(110\) | −0.290319 | −0.0276809 | ||||||||
\(111\) | 16.7984 | 1.59443 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.3693 | −1.82211 | −0.911056 | − | 0.412283i | \(-0.864732\pi\) | ||||
−0.911056 | + | 0.412283i | \(0.864732\pi\) | |||||||
\(114\) | −17.3693 | −1.62679 | ||||||||
\(115\) | 5.46026 | 0.509172 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −10.3857 | −0.960154 | ||||||||
\(118\) | −4.34475 | −0.399967 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.56155 | 0.142550 | ||||||||
\(121\) | −10.8078 | −0.982524 | ||||||||
\(122\) | −1.32431 | −0.119897 | ||||||||
\(123\) | −10.2462 | −0.923870 | ||||||||
\(124\) | −4.05444 | −0.364099 | ||||||||
\(125\) | 6.33122 | 0.566281 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.24621 | −0.199319 | −0.0996595 | − | 0.995022i | \(-0.531775\pi\) | ||||
−0.0996595 | + | 0.995022i | \(0.531775\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.0478 | −0.972705 | ||||||||
\(130\) | −2.68466 | −0.235460 | ||||||||
\(131\) | −2.06798 | −0.180680 | −0.0903399 | − | 0.995911i | \(-0.528795\pi\) | ||||
−0.0903399 | + | 0.995911i | \(0.528795\pi\) | |||||||
\(132\) | −1.03399 | −0.0899971 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.87689 | 0.421300 | ||||||||
\(135\) | 0.684658 | 0.0589260 | ||||||||
\(136\) | 4.34475 | 0.372560 | ||||||||
\(137\) | −8.24621 | −0.704521 | −0.352261 | − | 0.935902i | \(-0.614587\pi\) | ||||
−0.352261 | + | 0.935902i | \(0.614587\pi\) | |||||||
\(138\) | 19.4470 | 1.65544 | ||||||||
\(139\) | −8.31768 | −0.705496 | −0.352748 | − | 0.935718i | \(-0.614753\pi\) | ||||
−0.352748 | + | 0.935718i | \(0.614753\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.56155 | −0.131506 | ||||||||
\(142\) | −11.3693 | −0.954092 | ||||||||
\(143\) | 1.77766 | 0.148655 | ||||||||
\(144\) | 2.56155 | 0.213463 | ||||||||
\(145\) | −0.662153 | −0.0549889 | ||||||||
\(146\) | 8.48071 | 0.701868 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.12311 | 0.585516 | ||||||||
\(149\) | 2.68466 | 0.219936 | 0.109968 | − | 0.993935i | \(-0.464925\pi\) | ||||
0.109968 | + | 0.993935i | \(0.464925\pi\) | |||||||
\(150\) | 10.7575 | 0.878345 | ||||||||
\(151\) | 4.24621 | 0.345552 | 0.172776 | − | 0.984961i | \(-0.444726\pi\) | ||||
0.172776 | + | 0.984961i | \(0.444726\pi\) | |||||||
\(152\) | −7.36520 | −0.597397 | ||||||||
\(153\) | −11.1293 | −0.899752 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.68466 | 0.215637 | ||||||||
\(156\) | −9.56155 | −0.765537 | ||||||||
\(157\) | −17.3790 | −1.38700 | −0.693498 | − | 0.720458i | \(-0.743932\pi\) | ||||
−0.693498 | + | 0.720458i | \(0.743932\pi\) | |||||||
\(158\) | −7.80776 | −0.621152 | ||||||||
\(159\) | −27.2655 | −2.16230 | ||||||||
\(160\) | 0.662153 | 0.0523478 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 10.1231 | 0.795346 | ||||||||
\(163\) | −4.43845 | −0.347646 | −0.173823 | − | 0.984777i | \(-0.555612\pi\) | ||||
−0.173823 | + | 0.984777i | \(0.555612\pi\) | |||||||
\(164\) | −4.34475 | −0.339268 | ||||||||
\(165\) | 0.684658 | 0.0533006 | ||||||||
\(166\) | 5.08842 | 0.394938 | ||||||||
\(167\) | 9.43318 | 0.729961 | 0.364981 | − | 0.931015i | \(-0.381076\pi\) | ||||
0.364981 | + | 0.931015i | \(0.381076\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.43845 | 0.264496 | ||||||||
\(170\) | −2.87689 | −0.220648 | ||||||||
\(171\) | 18.8664 | 1.44275 | ||||||||
\(172\) | −4.68466 | −0.357202 | ||||||||
\(173\) | 11.1293 | 0.846146 | 0.423073 | − | 0.906095i | \(-0.360951\pi\) | ||||
0.423073 | + | 0.906095i | \(0.360951\pi\) | |||||||
\(174\) | −2.35829 | −0.178782 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.438447 | −0.0330492 | ||||||||
\(177\) | 10.2462 | 0.770152 | ||||||||
\(178\) | 9.06134 | 0.679176 | ||||||||
\(179\) | −1.75379 | −0.131084 | −0.0655422 | − | 0.997850i | \(-0.520878\pi\) | ||||
−0.0655422 | + | 0.997850i | \(0.520878\pi\) | |||||||
\(180\) | −1.69614 | −0.126423 | ||||||||
\(181\) | 22.1771 | 1.64841 | 0.824206 | − | 0.566290i | \(-0.191622\pi\) | ||||
0.824206 | + | 0.566290i | \(0.191622\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.12311 | 0.230867 | ||||||||
\(184\) | 8.24621 | 0.607919 | ||||||||
\(185\) | −4.71659 | −0.346771 | ||||||||
\(186\) | 9.56155 | 0.701087 | ||||||||
\(187\) | 1.90495 | 0.139303 | ||||||||
\(188\) | −0.662153 | −0.0482925 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.87689 | 0.353807 | ||||||||
\(191\) | −10.2462 | −0.741390 | −0.370695 | − | 0.928755i | \(-0.620880\pi\) | ||||
−0.370695 | + | 0.928755i | \(0.620880\pi\) | |||||||
\(192\) | 2.35829 | 0.170195 | ||||||||
\(193\) | −3.36932 | −0.242529 | −0.121264 | − | 0.992620i | \(-0.538695\pi\) | ||||
−0.121264 | + | 0.992620i | \(0.538695\pi\) | |||||||
\(194\) | 6.99337 | 0.502095 | ||||||||
\(195\) | 6.33122 | 0.453388 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.75379 | −0.267446 | −0.133723 | − | 0.991019i | \(-0.542693\pi\) | ||||
−0.133723 | + | 0.991019i | \(0.542693\pi\) | |||||||
\(198\) | 1.12311 | 0.0798156 | ||||||||
\(199\) | 20.7713 | 1.47244 | 0.736219 | − | 0.676743i | \(-0.236609\pi\) | ||||
0.736219 | + | 0.676743i | \(0.236609\pi\) | |||||||
\(200\) | 4.56155 | 0.322550 | ||||||||
\(201\) | −11.5012 | −0.811229 | ||||||||
\(202\) | −11.3381 | −0.797748 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.2462 | −0.717378 | ||||||||
\(205\) | 2.87689 | 0.200931 | ||||||||
\(206\) | −12.8255 | −0.893592 | ||||||||
\(207\) | −21.1231 | −1.46816 | ||||||||
\(208\) | −4.05444 | −0.281125 | ||||||||
\(209\) | −3.22925 | −0.223372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.68466 | 0.322505 | 0.161253 | − | 0.986913i | \(-0.448447\pi\) | ||||
0.161253 | + | 0.986913i | \(0.448447\pi\) | |||||||
\(212\) | −11.5616 | −0.794051 | ||||||||
\(213\) | 26.8122 | 1.83714 | ||||||||
\(214\) | 0.876894 | 0.0599433 | ||||||||
\(215\) | 3.10196 | 0.211552 | ||||||||
\(216\) | 1.03399 | 0.0703539 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.6847 | −0.723656 | ||||||||
\(219\) | −20.0000 | −1.35147 | ||||||||
\(220\) | 0.290319 | 0.0195733 | ||||||||
\(221\) | 17.6155 | 1.18495 | ||||||||
\(222\) | −16.7984 | −1.12743 | ||||||||
\(223\) | 3.39228 | 0.227164 | 0.113582 | − | 0.993529i | \(-0.463768\pi\) | ||||
0.113582 | + | 0.993529i | \(0.463768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.6847 | −0.778977 | ||||||||
\(226\) | 19.3693 | 1.28843 | ||||||||
\(227\) | 12.4536 | 0.826576 | 0.413288 | − | 0.910600i | \(-0.364380\pi\) | ||||
0.413288 | + | 0.910600i | \(0.364380\pi\) | |||||||
\(228\) | 17.3693 | 1.15031 | ||||||||
\(229\) | 23.5829 | 1.55840 | 0.779202 | − | 0.626772i | \(-0.215624\pi\) | ||||
0.779202 | + | 0.626772i | \(0.215624\pi\) | |||||||
\(230\) | −5.46026 | −0.360039 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −12.9309 | −0.847129 | −0.423565 | − | 0.905866i | \(-0.639221\pi\) | ||||
−0.423565 | + | 0.905866i | \(0.639221\pi\) | |||||||
\(234\) | 10.3857 | 0.678931 | ||||||||
\(235\) | 0.438447 | 0.0286011 | ||||||||
\(236\) | 4.34475 | 0.282819 | ||||||||
\(237\) | 18.4130 | 1.19605 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −1.56155 | −0.100798 | ||||||||
\(241\) | −24.6169 | −1.58572 | −0.792858 | − | 0.609406i | \(-0.791408\pi\) | ||||
−0.792858 | + | 0.609406i | \(0.791408\pi\) | |||||||
\(242\) | 10.8078 | 0.694749 | ||||||||
\(243\) | −20.7713 | −1.33248 | ||||||||
\(244\) | 1.32431 | 0.0847801 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.2462 | 0.653275 | ||||||||
\(247\) | −29.8617 | −1.90006 | ||||||||
\(248\) | 4.05444 | 0.257457 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | −6.33122 | −0.400421 | ||||||||
\(251\) | 22.5490 | 1.42328 | 0.711639 | − | 0.702546i | \(-0.247953\pi\) | ||||
0.711639 | + | 0.702546i | \(0.247953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.61553 | 0.227306 | ||||||||
\(254\) | 2.24621 | 0.140940 | ||||||||
\(255\) | 6.78456 | 0.424866 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.8594 | 0.864529 | 0.432264 | − | 0.901747i | \(-0.357715\pi\) | ||||
0.432264 | + | 0.901747i | \(0.357715\pi\) | |||||||
\(258\) | 11.0478 | 0.687806 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.68466 | 0.166495 | ||||||||
\(261\) | 2.56155 | 0.158556 | ||||||||
\(262\) | 2.06798 | 0.127760 | ||||||||
\(263\) | −15.8078 | −0.974748 | −0.487374 | − | 0.873193i | \(-0.662045\pi\) | ||||
−0.487374 | + | 0.873193i | \(0.662045\pi\) | |||||||
\(264\) | 1.03399 | 0.0636375 | ||||||||
\(265\) | 7.65552 | 0.470275 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.3693 | −1.30778 | ||||||||
\(268\) | −4.87689 | −0.297904 | ||||||||
\(269\) | 24.9073 | 1.51862 | 0.759311 | − | 0.650728i | \(-0.225536\pi\) | ||||
0.759311 | + | 0.650728i | \(0.225536\pi\) | |||||||
\(270\) | −0.684658 | −0.0416670 | ||||||||
\(271\) | −12.0003 | −0.728965 | −0.364482 | − | 0.931210i | \(-0.618754\pi\) | ||||
−0.364482 | + | 0.931210i | \(0.618754\pi\) | |||||||
\(272\) | −4.34475 | −0.263439 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.24621 | 0.498172 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | −19.4470 | −1.17057 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 8.31768 | 0.498861 | ||||||||
\(279\) | −10.3857 | −0.621773 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.1771 | −1.74056 | −0.870279 | − | 0.492558i | \(-0.836062\pi\) | ||||
−0.870279 | + | 0.492558i | \(0.836062\pi\) | |||||||
\(282\) | 1.56155 | 0.0929891 | ||||||||
\(283\) | 10.5487 | 0.627054 | 0.313527 | − | 0.949579i | \(-0.398489\pi\) | ||||
0.313527 | + | 0.949579i | \(0.398489\pi\) | |||||||
\(284\) | 11.3693 | 0.674645 | ||||||||
\(285\) | −11.5012 | −0.681270 | ||||||||
\(286\) | −1.77766 | −0.105115 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.56155 | −0.150941 | ||||||||
\(289\) | 1.87689 | 0.110406 | ||||||||
\(290\) | 0.662153 | 0.0388830 | ||||||||
\(291\) | −16.4924 | −0.966803 | ||||||||
\(292\) | −8.48071 | −0.496296 | ||||||||
\(293\) | −11.5012 | −0.671905 | −0.335952 | − | 0.941879i | \(-0.609058\pi\) | ||||
−0.335952 | + | 0.941879i | \(0.609058\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.87689 | −0.167499 | ||||||||
\(296\) | −7.12311 | −0.414022 | ||||||||
\(297\) | 0.453349 | 0.0263060 | ||||||||
\(298\) | −2.68466 | −0.155518 | ||||||||
\(299\) | 33.4337 | 1.93352 | ||||||||
\(300\) | −10.7575 | −0.621084 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.24621 | −0.244342 | ||||||||
\(303\) | 26.7386 | 1.53609 | ||||||||
\(304\) | 7.36520 | 0.422423 | ||||||||
\(305\) | −0.876894 | −0.0502108 | ||||||||
\(306\) | 11.1293 | 0.636221 | ||||||||
\(307\) | 11.2108 | 0.639836 | 0.319918 | − | 0.947445i | \(-0.396345\pi\) | ||||
0.319918 | + | 0.947445i | \(0.396345\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.2462 | 1.72065 | ||||||||
\(310\) | −2.68466 | −0.152478 | ||||||||
\(311\) | −9.80501 | −0.555991 | −0.277996 | − | 0.960582i | \(-0.589670\pi\) | ||||
−0.277996 | + | 0.960582i | \(0.589670\pi\) | |||||||
\(312\) | 9.56155 | 0.541316 | ||||||||
\(313\) | 27.2655 | 1.54114 | 0.770570 | − | 0.637356i | \(-0.219972\pi\) | ||||
0.770570 | + | 0.637356i | \(0.219972\pi\) | |||||||
\(314\) | 17.3790 | 0.980755 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.80776 | 0.439221 | ||||||||
\(317\) | 14.4924 | 0.813976 | 0.406988 | − | 0.913434i | \(-0.366579\pi\) | ||||
0.406988 | + | 0.913434i | \(0.366579\pi\) | |||||||
\(318\) | 27.2655 | 1.52898 | ||||||||
\(319\) | −0.438447 | −0.0245483 | ||||||||
\(320\) | −0.662153 | −0.0370155 | ||||||||
\(321\) | −2.06798 | −0.115423 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.0000 | −1.78053 | ||||||||
\(324\) | −10.1231 | −0.562395 | ||||||||
\(325\) | 18.4945 | 1.02589 | ||||||||
\(326\) | 4.43845 | 0.245823 | ||||||||
\(327\) | 25.1976 | 1.39343 | ||||||||
\(328\) | 4.34475 | 0.239899 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.684658 | −0.0376892 | ||||||||
\(331\) | 36.3002 | 1.99524 | 0.997619 | − | 0.0689611i | \(-0.0219684\pi\) | ||||
0.997619 | + | 0.0689611i | \(0.0219684\pi\) | |||||||
\(332\) | −5.08842 | −0.279263 | ||||||||
\(333\) | 18.2462 | 0.999886 | ||||||||
\(334\) | −9.43318 | −0.516161 | ||||||||
\(335\) | 3.22925 | 0.176433 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2462 | −1.32078 | −0.660388 | − | 0.750925i | \(-0.729608\pi\) | ||||
−0.660388 | + | 0.750925i | \(0.729608\pi\) | |||||||
\(338\) | −3.43845 | −0.187027 | ||||||||
\(339\) | −45.6786 | −2.48092 | ||||||||
\(340\) | 2.87689 | 0.156022 | ||||||||
\(341\) | 1.77766 | 0.0962655 | ||||||||
\(342\) | −18.8664 | −1.02018 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.68466 | 0.252580 | ||||||||
\(345\) | 12.8769 | 0.693269 | ||||||||
\(346\) | −11.1293 | −0.598316 | ||||||||
\(347\) | −31.1231 | −1.67078 | −0.835388 | − | 0.549661i | \(-0.814757\pi\) | ||||
−0.835388 | + | 0.549661i | \(0.814757\pi\) | |||||||
\(348\) | 2.35829 | 0.126418 | ||||||||
\(349\) | −22.9208 | −1.22692 | −0.613461 | − | 0.789725i | \(-0.710223\pi\) | ||||
−0.613461 | + | 0.789725i | \(0.710223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.19224 | 0.223765 | ||||||||
\(352\) | 0.438447 | 0.0233693 | ||||||||
\(353\) | −9.43318 | −0.502077 | −0.251039 | − | 0.967977i | \(-0.580772\pi\) | ||||
−0.251039 | + | 0.967977i | \(0.580772\pi\) | |||||||
\(354\) | −10.2462 | −0.544580 | ||||||||
\(355\) | −7.52823 | −0.399557 | ||||||||
\(356\) | −9.06134 | −0.480250 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.75379 | 0.0926906 | ||||||||
\(359\) | −28.6847 | −1.51392 | −0.756959 | − | 0.653462i | \(-0.773316\pi\) | ||||
−0.756959 | + | 0.653462i | \(0.773316\pi\) | |||||||
\(360\) | 1.69614 | 0.0893945 | ||||||||
\(361\) | 35.2462 | 1.85506 | ||||||||
\(362\) | −22.1771 | −1.16560 | ||||||||
\(363\) | −25.4879 | −1.33777 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.61553 | 0.293930 | ||||||||
\(366\) | −3.12311 | −0.163247 | ||||||||
\(367\) | −0.371834 | −0.0194096 | −0.00970479 | − | 0.999953i | \(-0.503089\pi\) | ||||
−0.00970479 | + | 0.999953i | \(0.503089\pi\) | |||||||
\(368\) | −8.24621 | −0.429863 | ||||||||
\(369\) | −11.1293 | −0.579369 | ||||||||
\(370\) | 4.71659 | 0.245204 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.56155 | −0.495743 | ||||||||
\(373\) | −21.8078 | −1.12916 | −0.564582 | − | 0.825377i | \(-0.690962\pi\) | ||||
−0.564582 | + | 0.825377i | \(0.690962\pi\) | |||||||
\(374\) | −1.90495 | −0.0985024 | ||||||||
\(375\) | 14.9309 | 0.771027 | ||||||||
\(376\) | 0.662153 | 0.0341480 | ||||||||
\(377\) | −4.05444 | −0.208814 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.4924 | 1.66902 | 0.834512 | − | 0.550990i | \(-0.185750\pi\) | ||||
0.834512 | + | 0.550990i | \(0.185750\pi\) | |||||||
\(380\) | −4.87689 | −0.250179 | ||||||||
\(381\) | −5.29723 | −0.271385 | ||||||||
\(382\) | 10.2462 | 0.524242 | ||||||||
\(383\) | −7.36520 | −0.376344 | −0.188172 | − | 0.982136i | \(-0.560256\pi\) | ||||
−0.188172 | + | 0.982136i | \(0.560256\pi\) | |||||||
\(384\) | −2.35829 | −0.120346 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.36932 | 0.171494 | ||||||||
\(387\) | −12.0000 | −0.609994 | ||||||||
\(388\) | −6.99337 | −0.355034 | ||||||||
\(389\) | −32.9848 | −1.67240 | −0.836199 | − | 0.548426i | \(-0.815227\pi\) | ||||
−0.836199 | + | 0.548426i | \(0.815227\pi\) | |||||||
\(390\) | −6.33122 | −0.320594 | ||||||||
\(391\) | 35.8278 | 1.81189 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.87689 | −0.246007 | ||||||||
\(394\) | 3.75379 | 0.189113 | ||||||||
\(395\) | −5.16994 | −0.260128 | ||||||||
\(396\) | −1.12311 | −0.0564382 | ||||||||
\(397\) | 10.2584 | 0.514852 | 0.257426 | − | 0.966298i | \(-0.417126\pi\) | ||||
0.257426 | + | 0.966298i | \(0.417126\pi\) | |||||||
\(398\) | −20.7713 | −1.04117 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.56155 | −0.228078 | ||||||||
\(401\) | 14.1922 | 0.708726 | 0.354363 | − | 0.935108i | \(-0.384698\pi\) | ||||
0.354363 | + | 0.935108i | \(0.384698\pi\) | |||||||
\(402\) | 11.5012 | 0.573625 | ||||||||
\(403\) | 16.4384 | 0.818857 | ||||||||
\(404\) | 11.3381 | 0.564093 | ||||||||
\(405\) | 6.70305 | 0.333077 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.12311 | −0.154807 | ||||||||
\(408\) | 10.2462 | 0.507263 | ||||||||
\(409\) | −29.9957 | −1.48319 | −0.741595 | − | 0.670848i | \(-0.765931\pi\) | ||||
−0.741595 | + | 0.670848i | \(0.765931\pi\) | |||||||
\(410\) | −2.87689 | −0.142080 | ||||||||
\(411\) | −19.4470 | −0.959249 | ||||||||
\(412\) | 12.8255 | 0.631865 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 21.1231 | 1.03814 | ||||||||
\(415\) | 3.36932 | 0.165393 | ||||||||
\(416\) | 4.05444 | 0.198785 | ||||||||
\(417\) | −19.6155 | −0.960577 | ||||||||
\(418\) | 3.22925 | 0.157948 | ||||||||
\(419\) | −5.83209 | −0.284916 | −0.142458 | − | 0.989801i | \(-0.545501\pi\) | ||||
−0.142458 | + | 0.989801i | \(0.545501\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.1231 | −1.51685 | −0.758424 | − | 0.651762i | \(-0.774030\pi\) | ||||
−0.758424 | + | 0.651762i | \(0.774030\pi\) | |||||||
\(422\) | −4.68466 | −0.228046 | ||||||||
\(423\) | −1.69614 | −0.0824692 | ||||||||
\(424\) | 11.5616 | 0.561479 | ||||||||
\(425\) | 19.8188 | 0.961354 | ||||||||
\(426\) | −26.8122 | −1.29906 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.876894 | −0.0423863 | ||||||||
\(429\) | 4.19224 | 0.202403 | ||||||||
\(430\) | −3.10196 | −0.149590 | ||||||||
\(431\) | 8.00000 | 0.385346 | 0.192673 | − | 0.981263i | \(-0.438284\pi\) | ||||
0.192673 | + | 0.981263i | \(0.438284\pi\) | |||||||
\(432\) | −1.03399 | −0.0497478 | ||||||||
\(433\) | 16.5896 | 0.797244 | 0.398622 | − | 0.917115i | \(-0.369489\pi\) | ||||
0.398622 | + | 0.917115i | \(0.369489\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.56155 | −0.0748707 | ||||||||
\(436\) | 10.6847 | 0.511702 | ||||||||
\(437\) | −60.7350 | −2.90535 | ||||||||
\(438\) | 20.0000 | 0.955637 | ||||||||
\(439\) | −35.6647 | −1.70218 | −0.851092 | − | 0.525016i | \(-0.824059\pi\) | ||||
−0.851092 | + | 0.525016i | \(0.824059\pi\) | |||||||
\(440\) | −0.290319 | −0.0138404 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.6155 | −0.837885 | ||||||||
\(443\) | 33.1231 | 1.57373 | 0.786863 | − | 0.617128i | \(-0.211704\pi\) | ||||
0.786863 | + | 0.617128i | \(0.211704\pi\) | |||||||
\(444\) | 16.7984 | 0.797216 | ||||||||
\(445\) | 6.00000 | 0.284427 | ||||||||
\(446\) | −3.39228 | −0.160629 | ||||||||
\(447\) | 6.33122 | 0.299456 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.3693 | −0.914095 | −0.457047 | − | 0.889442i | \(-0.651093\pi\) | ||||
−0.457047 | + | 0.889442i | \(0.651093\pi\) | |||||||
\(450\) | 11.6847 | 0.550820 | ||||||||
\(451\) | 1.90495 | 0.0897004 | ||||||||
\(452\) | −19.3693 | −0.911056 | ||||||||
\(453\) | 10.0138 | 0.470490 | ||||||||
\(454\) | −12.4536 | −0.584478 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17.3693 | −0.813393 | ||||||||
\(457\) | 29.3693 | 1.37384 | 0.686919 | − | 0.726734i | \(-0.258963\pi\) | ||||
0.686919 | + | 0.726734i | \(0.258963\pi\) | |||||||
\(458\) | −23.5829 | −1.10196 | ||||||||
\(459\) | 4.49242 | 0.209688 | ||||||||
\(460\) | 5.46026 | 0.254586 | ||||||||
\(461\) | −23.4199 | −1.09077 | −0.545387 | − | 0.838184i | \(-0.683617\pi\) | ||||
−0.545387 | + | 0.838184i | \(0.683617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.3693 | −1.08606 | −0.543032 | − | 0.839712i | \(-0.682724\pi\) | ||||
−0.543032 | + | 0.839712i | \(0.682724\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 6.33122 | 0.293603 | ||||||||
\(466\) | 12.9309 | 0.599011 | ||||||||
\(467\) | −6.33122 | −0.292974 | −0.146487 | − | 0.989213i | \(-0.546797\pi\) | ||||
−0.146487 | + | 0.989213i | \(0.546797\pi\) | |||||||
\(468\) | −10.3857 | −0.480077 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.438447 | −0.0202241 | ||||||||
\(471\) | −40.9848 | −1.88848 | ||||||||
\(472\) | −4.34475 | −0.199984 | ||||||||
\(473\) | 2.05398 | 0.0944419 | ||||||||
\(474\) | −18.4130 | −0.845737 | ||||||||
\(475\) | −33.5968 | −1.54153 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.6155 | −1.35600 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.2998 | −1.84135 | −0.920673 | − | 0.390336i | \(-0.872359\pi\) | ||||
−0.920673 | + | 0.390336i | \(0.872359\pi\) | |||||||
\(480\) | 1.56155 | 0.0712748 | ||||||||
\(481\) | −28.8802 | −1.31682 | ||||||||
\(482\) | 24.6169 | 1.12127 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8078 | −0.491262 | ||||||||
\(485\) | 4.63068 | 0.210268 | ||||||||
\(486\) | 20.7713 | 0.942205 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | −1.32431 | −0.0599486 | ||||||||
\(489\) | −10.4672 | −0.473342 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.1771 | −1.13623 | −0.568113 | − | 0.822951i | \(-0.692326\pi\) | ||||
−0.568113 | + | 0.822951i | \(0.692326\pi\) | |||||||
\(492\) | −10.2462 | −0.461935 | ||||||||
\(493\) | −4.34475 | −0.195678 | ||||||||
\(494\) | 29.8617 | 1.34354 | ||||||||
\(495\) | 0.743668 | 0.0334254 | ||||||||
\(496\) | −4.05444 | −0.182050 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.0000 | 0.537733 | ||||||||
\(499\) | 3.12311 | 0.139809 | 0.0699047 | − | 0.997554i | \(-0.477730\pi\) | ||||
0.0699047 | + | 0.997554i | \(0.477730\pi\) | |||||||
\(500\) | 6.33122 | 0.283141 | ||||||||
\(501\) | 22.2462 | 0.993887 | ||||||||
\(502\) | −22.5490 | −1.00641 | ||||||||
\(503\) | 33.6783 | 1.50164 | 0.750820 | − | 0.660507i | \(-0.229659\pi\) | ||||
0.750820 | + | 0.660507i | \(0.229659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.50758 | −0.334083 | ||||||||
\(506\) | −3.61553 | −0.160730 | ||||||||
\(507\) | 8.10887 | 0.360128 | ||||||||
\(508\) | −2.24621 | −0.0996595 | ||||||||
\(509\) | 34.4219 | 1.52573 | 0.762863 | − | 0.646560i | \(-0.223793\pi\) | ||||
0.762863 | + | 0.646560i | \(0.223793\pi\) | |||||||
\(510\) | −6.78456 | −0.300426 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.61553 | −0.336234 | ||||||||
\(514\) | −13.8594 | −0.611314 | ||||||||
\(515\) | −8.49242 | −0.374221 | ||||||||
\(516\) | −11.0478 | −0.486352 | ||||||||
\(517\) | 0.290319 | 0.0127682 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.2462 | 1.15208 | ||||||||
\(520\) | −2.68466 | −0.117730 | ||||||||
\(521\) | −24.4539 | −1.07134 | −0.535672 | − | 0.844426i | \(-0.679942\pi\) | ||||
−0.535672 | + | 0.844426i | \(0.679942\pi\) | |||||||
\(522\) | −2.56155 | −0.112116 | ||||||||
\(523\) | 43.8194 | 1.91609 | 0.958044 | − | 0.286621i | \(-0.0925322\pi\) | ||||
0.958044 | + | 0.286621i | \(0.0925322\pi\) | |||||||
\(524\) | −2.06798 | −0.0903399 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.8078 | 0.689251 | ||||||||
\(527\) | 17.6155 | 0.767344 | ||||||||
\(528\) | −1.03399 | −0.0449985 | ||||||||
\(529\) | 45.0000 | 1.95652 | ||||||||
\(530\) | −7.65552 | −0.332535 | ||||||||
\(531\) | 11.1293 | 0.482971 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.6155 | 0.763013 | ||||||||
\(534\) | 21.3693 | 0.924741 | ||||||||
\(535\) | 0.580639 | 0.0251032 | ||||||||
\(536\) | 4.87689 | 0.210650 | ||||||||
\(537\) | −4.13595 | −0.178479 | ||||||||
\(538\) | −24.9073 | −1.07383 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.684658 | 0.0294630 | ||||||||
\(541\) | 9.12311 | 0.392233 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(542\) | 12.0003 | 0.515456 | ||||||||
\(543\) | 52.3002 | 2.24442 | ||||||||
\(544\) | 4.34475 | 0.186280 | ||||||||
\(545\) | −7.07488 | −0.303055 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.61553 | 0.325616 | 0.162808 | − | 0.986658i | \(-0.447945\pi\) | ||||
0.162808 | + | 0.986658i | \(0.447945\pi\) | |||||||
\(548\) | −8.24621 | −0.352261 | ||||||||
\(549\) | 3.39228 | 0.144779 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | 7.36520 | 0.313768 | ||||||||
\(552\) | 19.4470 | 0.827719 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | −11.1231 | −0.472150 | ||||||||
\(556\) | −8.31768 | −0.352748 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 10.3857 | 0.439660 | ||||||||
\(559\) | 18.9936 | 0.803346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.49242 | 0.189670 | ||||||||
\(562\) | 29.1771 | 1.23076 | ||||||||
\(563\) | 18.4130 | 0.776016 | 0.388008 | − | 0.921656i | \(-0.373163\pi\) | ||||
0.388008 | + | 0.921656i | \(0.373163\pi\) | |||||||
\(564\) | −1.56155 | −0.0657532 | ||||||||
\(565\) | 12.8255 | 0.539571 | ||||||||
\(566\) | −10.5487 | −0.443394 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.3693 | −0.477046 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 11.5012 | 0.481730 | ||||||||
\(571\) | 16.8769 | 0.706276 | 0.353138 | − | 0.935571i | \(-0.385115\pi\) | ||||
0.353138 | + | 0.935571i | \(0.385115\pi\) | |||||||
\(572\) | 1.77766 | 0.0743275 | ||||||||
\(573\) | −24.1636 | −1.00945 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37.6155 | 1.56868 | ||||||||
\(576\) | 2.56155 | 0.106731 | ||||||||
\(577\) | 4.18173 | 0.174087 | 0.0870437 | − | 0.996204i | \(-0.472258\pi\) | ||||
0.0870437 | + | 0.996204i | \(0.472258\pi\) | |||||||
\(578\) | −1.87689 | −0.0780685 | ||||||||
\(579\) | −7.94584 | −0.330218 | ||||||||
\(580\) | −0.662153 | −0.0274944 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 16.4924 | 0.683633 | ||||||||
\(583\) | 5.06913 | 0.209942 | ||||||||
\(584\) | 8.48071 | 0.350934 | ||||||||
\(585\) | 6.87689 | 0.284325 | ||||||||
\(586\) | 11.5012 | 0.475108 | ||||||||
\(587\) | 35.8735 | 1.48066 | 0.740330 | − | 0.672244i | \(-0.234669\pi\) | ||||
0.740330 | + | 0.672244i | \(0.234669\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.8617 | −1.23043 | ||||||||
\(590\) | 2.87689 | 0.118440 | ||||||||
\(591\) | −8.85254 | −0.364145 | ||||||||
\(592\) | 7.12311 | 0.292758 | ||||||||
\(593\) | −11.6284 | −0.477523 | −0.238761 | − | 0.971078i | \(-0.576741\pi\) | ||||
−0.238761 | + | 0.971078i | \(0.576741\pi\) | |||||||
\(594\) | −0.453349 | −0.0186011 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.68466 | 0.109968 | ||||||||
\(597\) | 48.9848 | 2.00482 | ||||||||
\(598\) | −33.4337 | −1.36721 | ||||||||
\(599\) | −24.6847 | −1.00859 | −0.504294 | − | 0.863532i | \(-0.668247\pi\) | ||||
−0.504294 | + | 0.863532i | \(0.668247\pi\) | |||||||
\(600\) | 10.7575 | 0.439172 | ||||||||
\(601\) | 5.83209 | 0.237896 | 0.118948 | − | 0.992900i | \(-0.462048\pi\) | ||||
0.118948 | + | 0.992900i | \(0.462048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.4924 | −0.508731 | ||||||||
\(604\) | 4.24621 | 0.172776 | ||||||||
\(605\) | 7.15640 | 0.290949 | ||||||||
\(606\) | −26.7386 | −1.08618 | ||||||||
\(607\) | 32.9346 | 1.33677 | 0.668387 | − | 0.743813i | \(-0.266985\pi\) | ||||
0.668387 | + | 0.743813i | \(0.266985\pi\) | |||||||
\(608\) | −7.36520 | −0.298698 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.876894 | 0.0355044 | ||||||||
\(611\) | 2.68466 | 0.108610 | ||||||||
\(612\) | −11.1293 | −0.449876 | ||||||||
\(613\) | 20.0540 | 0.809972 | 0.404986 | − | 0.914323i | \(-0.367276\pi\) | ||||
0.404986 | + | 0.914323i | \(0.367276\pi\) | |||||||
\(614\) | −11.2108 | −0.452432 | ||||||||
\(615\) | 6.78456 | 0.273580 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.36932 | 0.296678 | 0.148339 | − | 0.988937i | \(-0.452607\pi\) | ||||
0.148339 | + | 0.988937i | \(0.452607\pi\) | |||||||
\(618\) | −30.2462 | −1.21668 | ||||||||
\(619\) | 31.4015 | 1.26213 | 0.631066 | − | 0.775729i | \(-0.282618\pi\) | ||||
0.631066 | + | 0.775729i | \(0.282618\pi\) | |||||||
\(620\) | 2.68466 | 0.107818 | ||||||||
\(621\) | 8.52648 | 0.342156 | ||||||||
\(622\) | 9.80501 | 0.393145 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9.56155 | −0.382768 | ||||||||
\(625\) | 18.6155 | 0.744621 | ||||||||
\(626\) | −27.2655 | −1.08975 | ||||||||
\(627\) | −7.61553 | −0.304135 | ||||||||
\(628\) | −17.3790 | −0.693498 | ||||||||
\(629\) | −30.9481 | −1.23398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2462 | 0.885608 | 0.442804 | − | 0.896619i | \(-0.353984\pi\) | ||||
0.442804 | + | 0.896619i | \(0.353984\pi\) | |||||||
\(632\) | −7.80776 | −0.310576 | ||||||||
\(633\) | 11.0478 | 0.439111 | ||||||||
\(634\) | −14.4924 | −0.575568 | ||||||||
\(635\) | 1.48734 | 0.0590231 | ||||||||
\(636\) | −27.2655 | −1.08115 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.438447 | 0.0173583 | ||||||||
\(639\) | 29.1231 | 1.15209 | ||||||||
\(640\) | 0.662153 | 0.0261739 | ||||||||
\(641\) | 7.36932 | 0.291071 | 0.145535 | − | 0.989353i | \(-0.453510\pi\) | ||||
0.145535 | + | 0.989353i | \(0.453510\pi\) | |||||||
\(642\) | 2.06798 | 0.0816165 | ||||||||
\(643\) | −13.0343 | −0.514021 | −0.257011 | − | 0.966409i | \(-0.582738\pi\) | ||||
−0.257011 | + | 0.966409i | \(0.582738\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.31534 | 0.288041 | ||||||||
\(646\) | 32.0000 | 1.25902 | ||||||||
\(647\) | 0.743668 | 0.0292366 | 0.0146183 | − | 0.999893i | \(-0.495347\pi\) | ||||
0.0146183 | + | 0.999893i | \(0.495347\pi\) | |||||||
\(648\) | 10.1231 | 0.397673 | ||||||||
\(649\) | −1.90495 | −0.0747757 | ||||||||
\(650\) | −18.4945 | −0.725415 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.43845 | −0.173823 | ||||||||
\(653\) | 47.8617 | 1.87297 | 0.936487 | − | 0.350701i | \(-0.114057\pi\) | ||||
0.936487 | + | 0.350701i | \(0.114057\pi\) | |||||||
\(654\) | −25.1976 | −0.985303 | ||||||||
\(655\) | 1.36932 | 0.0535036 | ||||||||
\(656\) | −4.34475 | −0.169634 | ||||||||
\(657\) | −21.7238 | −0.847525 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.3002 | −1.33615 | −0.668073 | − | 0.744096i | \(-0.732881\pi\) | ||||
−0.668073 | + | 0.744096i | \(0.732881\pi\) | |||||||
\(660\) | 0.684658 | 0.0266503 | ||||||||
\(661\) | −25.8597 | −1.00583 | −0.502913 | − | 0.864337i | \(-0.667739\pi\) | ||||
−0.502913 | + | 0.864337i | \(0.667739\pi\) | |||||||
\(662\) | −36.3002 | −1.41085 | ||||||||
\(663\) | 41.5426 | 1.61338 | ||||||||
\(664\) | 5.08842 | 0.197469 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.2462 | −0.707026 | ||||||||
\(667\) | −8.24621 | −0.319295 | ||||||||
\(668\) | 9.43318 | 0.364981 | ||||||||
\(669\) | 8.00000 | 0.309298 | ||||||||
\(670\) | −3.22925 | −0.124757 | ||||||||
\(671\) | −0.580639 | −0.0224153 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.6695 | 1.60624 | 0.803121 | − | 0.595816i | \(-0.203171\pi\) | ||||
0.803121 | + | 0.595816i | \(0.203171\pi\) | |||||||
\(674\) | 24.2462 | 0.933929 | ||||||||
\(675\) | 4.71659 | 0.181542 | ||||||||
\(676\) | 3.43845 | 0.132248 | ||||||||
\(677\) | 1.16128 | 0.0446315 | 0.0223158 | − | 0.999751i | \(-0.492896\pi\) | ||||
0.0223158 | + | 0.999751i | \(0.492896\pi\) | |||||||
\(678\) | 45.6786 | 1.75427 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.87689 | −0.110324 | ||||||||
\(681\) | 29.3693 | 1.12543 | ||||||||
\(682\) | −1.77766 | −0.0680700 | ||||||||
\(683\) | −22.2462 | −0.851228 | −0.425614 | − | 0.904905i | \(-0.639942\pi\) | ||||
−0.425614 | + | 0.904905i | \(0.639942\pi\) | |||||||
\(684\) | 18.8664 | 0.721373 | ||||||||
\(685\) | 5.46026 | 0.208626 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 55.6155 | 2.12186 | ||||||||
\(688\) | −4.68466 | −0.178601 | ||||||||
\(689\) | 46.8756 | 1.78582 | ||||||||
\(690\) | −12.8769 | −0.490215 | ||||||||
\(691\) | −29.9957 | −1.14109 | −0.570545 | − | 0.821267i | \(-0.693268\pi\) | ||||
−0.570545 | + | 0.821267i | \(0.693268\pi\) | |||||||
\(692\) | 11.1293 | 0.423073 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.1231 | 1.18142 | ||||||||
\(695\) | 5.50758 | 0.208914 | ||||||||
\(696\) | −2.35829 | −0.0893909 | ||||||||
\(697\) | 18.8769 | 0.715013 | ||||||||
\(698\) | 22.9208 | 0.867565 | ||||||||
\(699\) | −30.4948 | −1.15342 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0540 | −0.455272 | −0.227636 | − | 0.973746i | \(-0.573100\pi\) | ||||
−0.227636 | + | 0.973746i | \(0.573100\pi\) | |||||||
\(702\) | −4.19224 | −0.158226 | ||||||||
\(703\) | 52.4631 | 1.97868 | ||||||||
\(704\) | −0.438447 | −0.0165246 | ||||||||
\(705\) | 1.03399 | 0.0389422 | ||||||||
\(706\) | 9.43318 | 0.355022 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.2462 | 0.385076 | ||||||||
\(709\) | 3.06913 | 0.115264 | 0.0576318 | − | 0.998338i | \(-0.481645\pi\) | ||||
0.0576318 | + | 0.998338i | \(0.481645\pi\) | |||||||
\(710\) | 7.52823 | 0.282530 | ||||||||
\(711\) | 20.0000 | 0.750059 | ||||||||
\(712\) | 9.06134 | 0.339588 | ||||||||
\(713\) | 33.4337 | 1.25210 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.17708 | −0.0440203 | ||||||||
\(716\) | −1.75379 | −0.0655422 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.6847 | 1.07050 | ||||||||
\(719\) | −29.6238 | −1.10478 | −0.552391 | − | 0.833585i | \(-0.686285\pi\) | ||||
−0.552391 | + | 0.833585i | \(0.686285\pi\) | |||||||
\(720\) | −1.69614 | −0.0632114 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −35.2462 | −1.31173 | ||||||||
\(723\) | −58.0540 | −2.15905 | ||||||||
\(724\) | 22.1771 | 0.824206 | ||||||||
\(725\) | −4.56155 | −0.169412 | ||||||||
\(726\) | 25.4879 | 0.945944 | ||||||||
\(727\) | −34.7123 | −1.28741 | −0.643703 | − | 0.765275i | \(-0.722603\pi\) | ||||
−0.643703 | + | 0.765275i | \(0.722603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.6155 | −0.689464 | ||||||||
\(730\) | −5.61553 | −0.207840 | ||||||||
\(731\) | 20.3537 | 0.752809 | ||||||||
\(732\) | 3.12311 | 0.115433 | ||||||||
\(733\) | 24.3266 | 0.898524 | 0.449262 | − | 0.893400i | \(-0.351687\pi\) | ||||
0.449262 | + | 0.893400i | \(0.351687\pi\) | |||||||
\(734\) | 0.371834 | 0.0137246 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.24621 | 0.303959 | ||||||||
\(737\) | 2.13826 | 0.0787638 | ||||||||
\(738\) | 11.1293 | 0.409676 | ||||||||
\(739\) | −22.0540 | −0.811269 | −0.405634 | − | 0.914035i | \(-0.632949\pi\) | ||||
−0.405634 | + | 0.914035i | \(0.632949\pi\) | |||||||
\(740\) | −4.71659 | −0.173385 | ||||||||
\(741\) | −70.4228 | −2.58705 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.9848 | 1.65033 | 0.825167 | − | 0.564889i | \(-0.191081\pi\) | ||||
0.825167 | + | 0.564889i | \(0.191081\pi\) | |||||||
\(744\) | 9.56155 | 0.350544 | ||||||||
\(745\) | −1.77766 | −0.0651283 | ||||||||
\(746\) | 21.8078 | 0.798439 | ||||||||
\(747\) | −13.0343 | −0.476899 | ||||||||
\(748\) | 1.90495 | 0.0696517 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −14.9309 | −0.545198 | ||||||||
\(751\) | 30.7386 | 1.12167 | 0.560834 | − | 0.827928i | \(-0.310480\pi\) | ||||
0.560834 | + | 0.827928i | \(0.310480\pi\) | |||||||
\(752\) | −0.662153 | −0.0241463 | ||||||||
\(753\) | 53.1771 | 1.93788 | ||||||||
\(754\) | 4.05444 | 0.147654 | ||||||||
\(755\) | −2.81164 | −0.102326 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.492423 | −0.0178974 | −0.00894870 | − | 0.999960i | \(-0.502848\pi\) | ||||
−0.00894870 | + | 0.999960i | \(0.502848\pi\) | |||||||
\(758\) | −32.4924 | −1.18018 | ||||||||
\(759\) | 8.52648 | 0.309492 | ||||||||
\(760\) | 4.87689 | 0.176904 | ||||||||
\(761\) | −27.1383 | −0.983761 | −0.491881 | − | 0.870663i | \(-0.663690\pi\) | ||||
−0.491881 | + | 0.870663i | \(0.663690\pi\) | |||||||
\(762\) | 5.29723 | 0.191898 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.2462 | −0.370695 | ||||||||
\(765\) | 7.36932 | 0.266438 | ||||||||
\(766\) | 7.36520 | 0.266116 | ||||||||
\(767\) | −17.6155 | −0.636060 | ||||||||
\(768\) | 2.35829 | 0.0850976 | ||||||||
\(769\) | −24.6984 | −0.890649 | −0.445324 | − | 0.895369i | \(-0.646912\pi\) | ||||
−0.445324 | + | 0.895369i | \(0.646912\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.6847 | 1.17711 | ||||||||
\(772\) | −3.36932 | −0.121264 | ||||||||
\(773\) | 43.0299 | 1.54768 | 0.773840 | − | 0.633382i | \(-0.218334\pi\) | ||||
0.773840 | + | 0.633382i | \(0.218334\pi\) | |||||||
\(774\) | 12.0000 | 0.431331 | ||||||||
\(775\) | 18.4945 | 0.664343 | ||||||||
\(776\) | 6.99337 | 0.251047 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.9848 | 1.18256 | ||||||||
\(779\) | −32.0000 | −1.14652 | ||||||||
\(780\) | 6.33122 | 0.226694 | ||||||||
\(781\) | −4.98485 | −0.178372 | ||||||||
\(782\) | −35.8278 | −1.28120 | ||||||||
\(783\) | −1.03399 | −0.0369517 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.5076 | 0.410723 | ||||||||
\(786\) | 4.87689 | 0.173953 | ||||||||
\(787\) | 29.9957 | 1.06923 | 0.534615 | − | 0.845096i | \(-0.320457\pi\) | ||||
0.534615 | + | 0.845096i | \(0.320457\pi\) | |||||||
\(788\) | −3.75379 | −0.133723 | ||||||||
\(789\) | −37.2794 | −1.32718 | ||||||||
\(790\) | 5.16994 | 0.183938 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.12311 | 0.0399078 | ||||||||
\(793\) | −5.36932 | −0.190670 | ||||||||
\(794\) | −10.2584 | −0.364056 | ||||||||
\(795\) | 18.0540 | 0.640309 | ||||||||
\(796\) | 20.7713 | 0.736219 | ||||||||
\(797\) | 47.1659 | 1.67070 | 0.835351 | − | 0.549717i | \(-0.185265\pi\) | ||||
0.835351 | + | 0.549717i | \(0.185265\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.87689 | 0.101777 | ||||||||
\(800\) | 4.56155 | 0.161275 | ||||||||
\(801\) | −23.2111 | −0.820124 | ||||||||
\(802\) | −14.1922 | −0.501145 | ||||||||
\(803\) | 3.71834 | 0.131217 | ||||||||
\(804\) | −11.5012 | −0.405614 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.4384 | −0.579020 | ||||||||
\(807\) | 58.7386 | 2.06770 | ||||||||
\(808\) | −11.3381 | −0.398874 | ||||||||
\(809\) | 42.9848 | 1.51127 | 0.755633 | − | 0.654995i | \(-0.227329\pi\) | ||||
0.755633 | + | 0.654995i | \(0.227329\pi\) | |||||||
\(810\) | −6.70305 | −0.235521 | ||||||||
\(811\) | 54.7399 | 1.92218 | 0.961089 | − | 0.276239i | \(-0.0890882\pi\) | ||||
0.961089 | + | 0.276239i | \(0.0890882\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.3002 | −0.992531 | ||||||||
\(814\) | 3.12311 | 0.109465 | ||||||||
\(815\) | 2.93893 | 0.102946 | ||||||||
\(816\) | −10.2462 | −0.358689 | ||||||||
\(817\) | −34.5035 | −1.20712 | ||||||||
\(818\) | 29.9957 | 1.04877 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.87689 | 0.100466 | ||||||||
\(821\) | −16.9309 | −0.590891 | −0.295446 | − | 0.955360i | \(-0.595468\pi\) | ||||
−0.295446 | + | 0.955360i | \(0.595468\pi\) | |||||||
\(822\) | 19.4470 | 0.678292 | ||||||||
\(823\) | 26.2462 | 0.914885 | 0.457443 | − | 0.889239i | \(-0.348765\pi\) | ||||
0.457443 | + | 0.889239i | \(0.348765\pi\) | |||||||
\(824\) | −12.8255 | −0.446796 | ||||||||
\(825\) | 4.71659 | 0.164211 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.3153 | −0.880301 | −0.440150 | − | 0.897924i | \(-0.645075\pi\) | ||||
−0.440150 | + | 0.897924i | \(0.645075\pi\) | |||||||
\(828\) | −21.1231 | −0.734079 | ||||||||
\(829\) | 22.2586 | 0.773074 | 0.386537 | − | 0.922274i | \(-0.373671\pi\) | ||||
0.386537 | + | 0.922274i | \(0.373671\pi\) | |||||||
\(830\) | −3.36932 | −0.116951 | ||||||||
\(831\) | −23.5829 | −0.818083 | ||||||||
\(832\) | −4.05444 | −0.140562 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.6155 | 0.679230 | ||||||||
\(835\) | −6.24621 | −0.216159 | ||||||||
\(836\) | −3.22925 | −0.111686 | ||||||||
\(837\) | 4.19224 | 0.144905 | ||||||||
\(838\) | 5.83209 | 0.201466 | ||||||||
\(839\) | 21.4335 | 0.739965 | 0.369983 | − | 0.929039i | \(-0.379364\pi\) | ||||
0.369983 | + | 0.929039i | \(0.379364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 31.1231 | 1.07257 | ||||||||
\(843\) | −68.8081 | −2.36988 | ||||||||
\(844\) | 4.68466 | 0.161253 | ||||||||
\(845\) | −2.27678 | −0.0783236 | ||||||||
\(846\) | 1.69614 | 0.0583145 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.5616 | −0.397025 | ||||||||
\(849\) | 24.8769 | 0.853773 | ||||||||
\(850\) | −19.8188 | −0.679780 | ||||||||
\(851\) | −58.7386 | −2.01353 | ||||||||
\(852\) | 26.8122 | 0.918571 | ||||||||
\(853\) | 36.0823 | 1.23544 | 0.617718 | − | 0.786400i | \(-0.288057\pi\) | ||||
0.617718 | + | 0.786400i | \(0.288057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.4924 | −0.427232 | ||||||||
\(856\) | 0.876894 | 0.0299716 | ||||||||
\(857\) | −32.5628 | −1.11232 | −0.556162 | − | 0.831074i | \(-0.687726\pi\) | ||||
−0.556162 | + | 0.831074i | \(0.687726\pi\) | |||||||
\(858\) | −4.19224 | −0.143121 | ||||||||
\(859\) | −33.8871 | −1.15621 | −0.578106 | − | 0.815962i | \(-0.696208\pi\) | ||||
−0.578106 | + | 0.815962i | \(0.696208\pi\) | |||||||
\(860\) | 3.10196 | 0.105776 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.00000 | −0.272481 | ||||||||
\(863\) | −14.0000 | −0.476566 | −0.238283 | − | 0.971196i | \(-0.576585\pi\) | ||||
−0.238283 | + | 0.971196i | \(0.576585\pi\) | |||||||
\(864\) | 1.03399 | 0.0351770 | ||||||||
\(865\) | −7.36932 | −0.250564 | ||||||||
\(866\) | −16.5896 | −0.563737 | ||||||||
\(867\) | 4.42627 | 0.150324 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.42329 | −0.116127 | ||||||||
\(870\) | 1.56155 | 0.0529416 | ||||||||
\(871\) | 19.7731 | 0.669984 | ||||||||
\(872\) | −10.6847 | −0.361828 | ||||||||
\(873\) | −17.9139 | −0.606293 | ||||||||
\(874\) | 60.7350 | 2.05439 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20.0000 | −0.675737 | ||||||||
\(877\) | −30.6847 | −1.03615 | −0.518074 | − | 0.855336i | \(-0.673351\pi\) | ||||
−0.518074 | + | 0.855336i | \(0.673351\pi\) | |||||||
\(878\) | 35.6647 | 1.20363 | ||||||||
\(879\) | −27.1231 | −0.914840 | ||||||||
\(880\) | 0.290319 | 0.00978666 | ||||||||
\(881\) | 32.4813 | 1.09432 | 0.547161 | − | 0.837028i | \(-0.315709\pi\) | ||||
0.547161 | + | 0.837028i | \(0.315709\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.1231 | −1.18199 | −0.590993 | − | 0.806676i | \(-0.701264\pi\) | ||||
−0.590993 | + | 0.806676i | \(0.701264\pi\) | |||||||
\(884\) | 17.6155 | 0.592474 | ||||||||
\(885\) | −6.78456 | −0.228061 | ||||||||
\(886\) | −33.1231 | −1.11279 | ||||||||
\(887\) | −6.28544 | −0.211044 | −0.105522 | − | 0.994417i | \(-0.533651\pi\) | ||||
−0.105522 | + | 0.994417i | \(0.533651\pi\) | |||||||
\(888\) | −16.7984 | −0.563717 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.00000 | −0.201120 | ||||||||
\(891\) | 4.43845 | 0.148694 | ||||||||
\(892\) | 3.39228 | 0.113582 | ||||||||
\(893\) | −4.87689 | −0.163199 | ||||||||
\(894\) | −6.33122 | −0.211748 | ||||||||
\(895\) | 1.16128 | 0.0388172 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 78.8466 | 2.63261 | ||||||||
\(898\) | 19.3693 | 0.646362 | ||||||||
\(899\) | −4.05444 | −0.135223 | ||||||||
\(900\) | −11.6847 | −0.389489 | ||||||||
\(901\) | 50.2321 | 1.67347 | ||||||||
\(902\) | −1.90495 | −0.0634277 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.3693 | 0.644214 | ||||||||
\(905\) | −14.6847 | −0.488135 | ||||||||
\(906\) | −10.0138 | −0.332687 | ||||||||
\(907\) | 19.3693 | 0.643148 | 0.321574 | − | 0.946885i | \(-0.395788\pi\) | ||||
0.321574 | + | 0.946885i | \(0.395788\pi\) | |||||||
\(908\) | 12.4536 | 0.413288 | ||||||||
\(909\) | 29.0432 | 0.963302 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.300187 | 0.00994562 | 0.00497281 | − | 0.999988i | \(-0.498417\pi\) | ||||
0.00497281 | + | 0.999988i | \(0.498417\pi\) | |||||||
\(912\) | 17.3693 | 0.575156 | ||||||||
\(913\) | 2.23100 | 0.0738355 | ||||||||
\(914\) | −29.3693 | −0.971451 | ||||||||
\(915\) | −2.06798 | −0.0683651 | ||||||||
\(916\) | 23.5829 | 0.779202 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.49242 | −0.148272 | ||||||||
\(919\) | 18.0000 | 0.593765 | 0.296883 | − | 0.954914i | \(-0.404053\pi\) | ||||
0.296883 | + | 0.954914i | \(0.404053\pi\) | |||||||
\(920\) | −5.46026 | −0.180019 | ||||||||
\(921\) | 26.4384 | 0.871176 | ||||||||
\(922\) | 23.4199 | 0.771294 | ||||||||
\(923\) | −46.0962 | −1.51727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.4924 | −1.06834 | ||||||||
\(926\) | 23.3693 | 0.767963 | ||||||||
\(927\) | 32.8531 | 1.07904 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | −24.1636 | −0.792781 | −0.396391 | − | 0.918082i | \(-0.629737\pi\) | ||||
−0.396391 | + | 0.918082i | \(0.629737\pi\) | |||||||
\(930\) | −6.33122 | −0.207609 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.9309 | −0.423565 | ||||||||
\(933\) | −23.1231 | −0.757016 | ||||||||
\(934\) | 6.33122 | 0.207164 | ||||||||
\(935\) | −1.26137 | −0.0412511 | ||||||||
\(936\) | 10.3857 | 0.339466 | ||||||||
\(937\) | −15.0565 | −0.491873 | −0.245937 | − | 0.969286i | \(-0.579096\pi\) | ||||
−0.245937 | + | 0.969286i | \(0.579096\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 64.3002 | 2.09836 | ||||||||
\(940\) | 0.438447 | 0.0143006 | ||||||||
\(941\) | 10.0953 | 0.329098 | 0.164549 | − | 0.986369i | \(-0.447383\pi\) | ||||
0.164549 | + | 0.986369i | \(0.447383\pi\) | |||||||
\(942\) | 40.9848 | 1.33536 | ||||||||
\(943\) | 35.8278 | 1.16671 | ||||||||
\(944\) | 4.34475 | 0.141410 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.05398 | −0.0667805 | ||||||||
\(947\) | −52.6847 | −1.71202 | −0.856011 | − | 0.516958i | \(-0.827064\pi\) | ||||
−0.856011 | + | 0.516958i | \(0.827064\pi\) | |||||||
\(948\) | 18.4130 | 0.598027 | ||||||||
\(949\) | 34.3845 | 1.11617 | ||||||||
\(950\) | 33.5968 | 1.09002 | ||||||||
\(951\) | 34.1774 | 1.10828 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.0540 | −1.23269 | −0.616345 | − | 0.787477i | \(-0.711387\pi\) | ||||
−0.616345 | + | 0.787477i | \(0.711387\pi\) | |||||||
\(954\) | 29.6155 | 0.958838 | ||||||||
\(955\) | 6.78456 | 0.219543 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.03399 | −0.0334241 | ||||||||
\(958\) | 40.2998 | 1.30203 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.56155 | −0.0503989 | ||||||||
\(961\) | −14.5616 | −0.469728 | ||||||||
\(962\) | 28.8802 | 0.931134 | ||||||||
\(963\) | −2.24621 | −0.0723831 | ||||||||
\(964\) | −24.6169 | −0.792858 | ||||||||
\(965\) | 2.23100 | 0.0718186 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.9309 | −0.737407 | −0.368704 | − | 0.929547i | \(-0.620198\pi\) | ||||
−0.368704 | + | 0.929547i | \(0.620198\pi\) | |||||||
\(968\) | 10.8078 | 0.347375 | ||||||||
\(969\) | −75.4654 | −2.42430 | ||||||||
\(970\) | −4.63068 | −0.148682 | ||||||||
\(971\) | −11.5012 | −0.369090 | −0.184545 | − | 0.982824i | \(-0.559081\pi\) | ||||
−0.184545 | + | 0.982824i | \(0.559081\pi\) | |||||||
\(972\) | −20.7713 | −0.666240 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.00000 | 0.256337 | ||||||||
\(975\) | 43.6155 | 1.39681 | ||||||||
\(976\) | 1.32431 | 0.0423900 | ||||||||
\(977\) | 17.6695 | 0.565297 | 0.282649 | − | 0.959223i | \(-0.408787\pi\) | ||||
0.282649 | + | 0.959223i | \(0.408787\pi\) | |||||||
\(978\) | 10.4672 | 0.334703 | ||||||||
\(979\) | 3.97292 | 0.126975 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.3693 | 0.873835 | ||||||||
\(982\) | 25.1771 | 0.803433 | ||||||||
\(983\) | 39.1385 | 1.24833 | 0.624163 | − | 0.781294i | \(-0.285440\pi\) | ||||
0.624163 | + | 0.781294i | \(0.285440\pi\) | |||||||
\(984\) | 10.2462 | 0.326637 | ||||||||
\(985\) | 2.48558 | 0.0791973 | ||||||||
\(986\) | 4.34475 | 0.138365 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29.8617 | −0.950028 | ||||||||
\(989\) | 38.6307 | 1.22838 | ||||||||
\(990\) | −0.743668 | −0.0236353 | ||||||||
\(991\) | −39.6155 | −1.25843 | −0.629214 | − | 0.777232i | \(-0.716623\pi\) | ||||
−0.629214 | + | 0.777232i | \(0.716623\pi\) | |||||||
\(992\) | 4.05444 | 0.128728 | ||||||||
\(993\) | 85.6065 | 2.71664 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.7538 | −0.436024 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | −25.4879 | −0.807210 | −0.403605 | − | 0.914933i | \(-0.632243\pi\) | ||||
−0.403605 | + | 0.914933i | \(0.632243\pi\) | |||||||
\(998\) | −3.12311 | −0.0988602 | ||||||||
\(999\) | −7.36520 | −0.233025 |
(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 | 2842.2.a.p.1.4 | yes | 4 | |
7.6 | odd | 2 | inner | 2842.2.a.p.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2842.2.a.p.1.1 | ✓ | 4 | 7.6 | odd | 2 | inner | |
2842.2.a.p.1.4 | yes | 4 | 1.1 | even | 1 | trivial |