Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3042,2,Mod(1,3042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3042, 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("3042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3042.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: | \(24.2904922949\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 338) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3042.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.60388 | 1.61170 | 0.805851 | − | 0.592118i | \(-0.201708\pi\) | ||||
0.805851 | + | 0.592118i | \(0.201708\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.10992 | 0.419509 | 0.209754 | − | 0.977754i | \(-0.432734\pi\) | ||||
0.209754 | + | 0.977754i | \(0.432734\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.60388 | 1.13965 | ||||||||
\(11\) | 2.35690 | 0.710631 | 0.355315 | − | 0.934746i | \(-0.384373\pi\) | ||||
0.355315 | + | 0.934746i | \(0.384373\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.10992 | 0.296638 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.96077 | −1.44570 | −0.722850 | − | 0.691005i | \(-0.757168\pi\) | ||||
−0.722850 | + | 0.691005i | \(0.757168\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.911854 | 0.209194 | 0.104597 | − | 0.994515i | \(-0.466645\pi\) | ||||
0.104597 | + | 0.994515i | \(0.466645\pi\) | |||||||
\(20\) | 3.60388 | 0.805851 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.35690 | 0.502492 | ||||||||
\(23\) | −3.38404 | −0.705622 | −0.352811 | − | 0.935695i | \(-0.614774\pi\) | ||||
−0.352811 | + | 0.935695i | \(0.614774\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.98792 | 1.59758 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.10992 | 0.209754 | ||||||||
\(29\) | 3.78017 | 0.701959 | 0.350980 | − | 0.936383i | \(-0.385849\pi\) | ||||
0.350980 | + | 0.936383i | \(0.385849\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.49396 | 1.52556 | 0.762780 | − | 0.646658i | \(-0.223834\pi\) | ||||
0.762780 | + | 0.646658i | \(0.223834\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.96077 | −1.02226 | ||||||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89008 | 0.803925 | 0.401962 | − | 0.915656i | \(-0.368328\pi\) | ||||
0.401962 | + | 0.915656i | \(0.368328\pi\) | |||||||
\(38\) | 0.911854 | 0.147922 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.60388 | 0.569823 | ||||||||
\(41\) | 7.18598 | 1.12226 | 0.561131 | − | 0.827727i | \(-0.310366\pi\) | ||||
0.561131 | + | 0.827727i | \(0.310366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.515729 | −0.0786480 | −0.0393240 | − | 0.999227i | \(-0.512520\pi\) | ||||
−0.0393240 | + | 0.999227i | \(0.512520\pi\) | |||||||
\(44\) | 2.35690 | 0.355315 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.38404 | −0.498950 | ||||||||
\(47\) | −6.98792 | −1.01929 | −0.509646 | − | 0.860384i | \(-0.670224\pi\) | ||||
−0.509646 | + | 0.860384i | \(0.670224\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.76809 | −0.824012 | ||||||||
\(50\) | 7.98792 | 1.12966 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.38404 | 0.464834 | 0.232417 | − | 0.972616i | \(-0.425337\pi\) | ||||
0.232417 | + | 0.972616i | \(0.425337\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.49396 | 1.14533 | ||||||||
\(56\) | 1.10992 | 0.148319 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.78017 | 0.496360 | ||||||||
\(59\) | −10.1468 | −1.32099 | −0.660497 | − | 0.750828i | \(-0.729655\pi\) | ||||
−0.660497 | + | 0.750828i | \(0.729655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.439665 | −0.0562933 | −0.0281467 | − | 0.999604i | \(-0.508961\pi\) | ||||
−0.0281467 | + | 0.999604i | \(0.508961\pi\) | |||||||
\(62\) | 8.49396 | 1.07873 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.14675 | 0.262268 | 0.131134 | − | 0.991365i | \(-0.458138\pi\) | ||||
0.131134 | + | 0.991365i | \(0.458138\pi\) | |||||||
\(68\) | −5.96077 | −0.722850 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.00000 | 0.478091 | ||||||||
\(71\) | −0.615957 | −0.0731007 | −0.0365503 | − | 0.999332i | \(-0.511637\pi\) | ||||
−0.0365503 | + | 0.999332i | \(0.511637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.32304 | 0.740056 | 0.370028 | − | 0.929021i | \(-0.379348\pi\) | ||||
0.370028 | + | 0.929021i | \(0.379348\pi\) | |||||||
\(74\) | 4.89008 | 0.568461 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.911854 | 0.104597 | ||||||||
\(77\) | 2.61596 | 0.298116 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4819 | −1.74185 | −0.870924 | − | 0.491418i | \(-0.836479\pi\) | ||||
−0.870924 | + | 0.491418i | \(0.836479\pi\) | |||||||
\(80\) | 3.60388 | 0.402926 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.18598 | 0.793559 | ||||||||
\(83\) | 0.911854 | 0.100089 | 0.0500445 | − | 0.998747i | \(-0.484064\pi\) | ||||
0.0500445 | + | 0.998747i | \(0.484064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.4819 | −2.33004 | ||||||||
\(86\) | −0.515729 | −0.0556125 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.35690 | 0.251246 | ||||||||
\(89\) | −3.75063 | −0.397566 | −0.198783 | − | 0.980044i | \(-0.563699\pi\) | ||||
−0.198783 | + | 0.980044i | \(0.563699\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.38404 | −0.352811 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.98792 | −0.720749 | ||||||||
\(95\) | 3.28621 | 0.337158 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.6746 | −1.48998 | −0.744988 | − | 0.667078i | \(-0.767545\pi\) | ||||
−0.744988 | + | 0.667078i | \(0.767545\pi\) | |||||||
\(98\) | −5.76809 | −0.582665 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.98792 | 0.798792 | ||||||||
\(101\) | −8.76809 | −0.872457 | −0.436229 | − | 0.899836i | \(-0.643686\pi\) | ||||
−0.436229 | + | 0.899836i | \(0.643686\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.8116 | 1.85356 | 0.926782 | − | 0.375599i | \(-0.122563\pi\) | ||||
0.926782 | + | 0.375599i | \(0.122563\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.38404 | 0.328687 | ||||||||
\(107\) | −18.0519 | −1.74514 | −0.872572 | − | 0.488486i | \(-0.837549\pi\) | ||||
−0.872572 | + | 0.488486i | \(0.837549\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.09783 | 0.584067 | 0.292033 | − | 0.956408i | \(-0.405668\pi\) | ||||
0.292033 | + | 0.956408i | \(0.405668\pi\) | |||||||
\(110\) | 8.49396 | 0.809867 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.10992 | 0.104877 | ||||||||
\(113\) | 12.2010 | 1.14778 | 0.573889 | − | 0.818933i | \(-0.305434\pi\) | ||||
0.573889 | + | 0.818933i | \(0.305434\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.1957 | −1.13725 | ||||||||
\(116\) | 3.78017 | 0.350980 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1468 | −0.934084 | ||||||||
\(119\) | −6.61596 | −0.606484 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.44504 | −0.495004 | ||||||||
\(122\) | −0.439665 | −0.0398054 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.49396 | 0.762780 | ||||||||
\(125\) | 10.7681 | 0.963127 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.4276 | 1.01403 | 0.507017 | − | 0.861936i | \(-0.330748\pi\) | ||||
0.507017 | + | 0.861936i | \(0.330748\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.29590 | −0.200593 | −0.100297 | − | 0.994958i | \(-0.531979\pi\) | ||||
−0.100297 | + | 0.994958i | \(0.531979\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.01208 | 0.0877586 | ||||||||
\(134\) | 2.14675 | 0.185451 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.96077 | −0.511132 | ||||||||
\(137\) | −9.08038 | −0.775789 | −0.387894 | − | 0.921704i | \(-0.626797\pi\) | ||||
−0.387894 | + | 0.921704i | \(0.626797\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9051 | 1.60351 | 0.801757 | − | 0.597650i | \(-0.203899\pi\) | ||||
0.801757 | + | 0.597650i | \(0.203899\pi\) | |||||||
\(140\) | 4.00000 | 0.338062 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.615957 | −0.0516900 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.6233 | 1.13135 | ||||||||
\(146\) | 6.32304 | 0.523299 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.89008 | 0.401962 | ||||||||
\(149\) | −18.6896 | −1.53111 | −0.765557 | − | 0.643368i | \(-0.777537\pi\) | ||||
−0.765557 | + | 0.643368i | \(0.777537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.317667 | −0.0258514 | −0.0129257 | − | 0.999916i | \(-0.504114\pi\) | ||||
−0.0129257 | + | 0.999916i | \(0.504114\pi\) | |||||||
\(152\) | 0.911854 | 0.0739611 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.61596 | 0.210800 | ||||||||
\(155\) | 30.6112 | 2.45875 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.8901 | 1.50759 | 0.753796 | − | 0.657108i | \(-0.228220\pi\) | ||||
0.753796 | + | 0.657108i | \(0.228220\pi\) | |||||||
\(158\) | −15.4819 | −1.23167 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.60388 | 0.284911 | ||||||||
\(161\) | −3.75600 | −0.296015 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.33273 | −0.339366 | −0.169683 | − | 0.985499i | \(-0.554274\pi\) | ||||
−0.169683 | + | 0.985499i | \(0.554274\pi\) | |||||||
\(164\) | 7.18598 | 0.561131 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.911854 | 0.0707736 | ||||||||
\(167\) | −14.0000 | −1.08335 | −0.541676 | − | 0.840587i | \(-0.682210\pi\) | ||||
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −21.4819 | −1.64758 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.515729 | −0.0393240 | ||||||||
\(173\) | 10.9879 | 0.835396 | 0.417698 | − | 0.908586i | \(-0.362837\pi\) | ||||
0.417698 | + | 0.908586i | \(0.362837\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.86592 | 0.670201 | ||||||||
\(176\) | 2.35690 | 0.177658 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.75063 | −0.281121 | ||||||||
\(179\) | −4.65519 | −0.347945 | −0.173972 | − | 0.984751i | \(-0.555660\pi\) | ||||
−0.173972 | + | 0.984751i | \(0.555660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.06638 | −0.0792631 | −0.0396315 | − | 0.999214i | \(-0.512618\pi\) | ||||
−0.0396315 | + | 0.999214i | \(0.512618\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.38404 | −0.249475 | ||||||||
\(185\) | 17.6233 | 1.29569 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.0489 | −1.02736 | ||||||||
\(188\) | −6.98792 | −0.509646 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.28621 | 0.238407 | ||||||||
\(191\) | −0.890084 | −0.0644042 | −0.0322021 | − | 0.999481i | \(-0.510252\pi\) | ||||
−0.0322021 | + | 0.999481i | \(0.510252\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.2174 | 1.16736 | 0.583678 | − | 0.811985i | \(-0.301613\pi\) | ||||
0.583678 | + | 0.811985i | \(0.301613\pi\) | |||||||
\(194\) | −14.6746 | −1.05357 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.76809 | −0.412006 | ||||||||
\(197\) | 11.4711 | 0.817284 | 0.408642 | − | 0.912695i | \(-0.366003\pi\) | ||||
0.408642 | + | 0.912695i | \(0.366003\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.79954 | −0.269343 | −0.134671 | − | 0.990890i | \(-0.542998\pi\) | ||||
−0.134671 | + | 0.990890i | \(0.542998\pi\) | |||||||
\(200\) | 7.98792 | 0.564831 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.76809 | −0.616920 | ||||||||
\(203\) | 4.19567 | 0.294478 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.8974 | 1.80875 | ||||||||
\(206\) | 18.8116 | 1.31067 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.14914 | 0.148659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0465 | −1.72427 | −0.862137 | − | 0.506675i | \(-0.830874\pi\) | ||||
−0.862137 | + | 0.506675i | \(0.830874\pi\) | |||||||
\(212\) | 3.38404 | 0.232417 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.0519 | −1.23400 | ||||||||
\(215\) | −1.85862 | −0.126757 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.42758 | 0.639986 | ||||||||
\(218\) | 6.09783 | 0.412997 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.49396 | 0.572663 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9879 | 0.869735 | 0.434868 | − | 0.900494i | \(-0.356795\pi\) | ||||
0.434868 | + | 0.900494i | \(0.356795\pi\) | |||||||
\(224\) | 1.10992 | 0.0741594 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.2010 | 0.811602 | ||||||||
\(227\) | 13.8049 | 0.916265 | 0.458132 | − | 0.888884i | \(-0.348519\pi\) | ||||
0.458132 | + | 0.888884i | \(0.348519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5603 | −0.763928 | −0.381964 | − | 0.924177i | \(-0.624752\pi\) | ||||
−0.381964 | + | 0.924177i | \(0.624752\pi\) | |||||||
\(230\) | −12.1957 | −0.804159 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.78017 | 0.248180 | ||||||||
\(233\) | −9.77479 | −0.640368 | −0.320184 | − | 0.947355i | \(-0.603745\pi\) | ||||
−0.320184 | + | 0.947355i | \(0.603745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.1836 | −1.64280 | ||||||||
\(236\) | −10.1468 | −0.660497 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.61596 | −0.428849 | ||||||||
\(239\) | 0.944378 | 0.0610867 | 0.0305434 | − | 0.999533i | \(-0.490276\pi\) | ||||
0.0305434 | + | 0.999533i | \(0.490276\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.219833 | −0.0141607 | −0.00708033 | − | 0.999975i | \(-0.502254\pi\) | ||||
−0.00708033 | + | 0.999975i | \(0.502254\pi\) | |||||||
\(242\) | −5.44504 | −0.350021 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.439665 | −0.0281467 | ||||||||
\(245\) | −20.7875 | −1.32806 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.49396 | 0.539367 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.7681 | 0.681034 | ||||||||
\(251\) | −16.2543 | −1.02596 | −0.512980 | − | 0.858400i | \(-0.671459\pi\) | ||||
−0.512980 | + | 0.858400i | \(0.671459\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.97584 | −0.501437 | ||||||||
\(254\) | 11.4276 | 0.717030 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.4373 | 1.39960 | 0.699799 | − | 0.714340i | \(-0.253273\pi\) | ||||
0.699799 | + | 0.714340i | \(0.253273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.42758 | 0.337254 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.29590 | −0.141841 | ||||||||
\(263\) | 10.4940 | 0.647085 | 0.323543 | − | 0.946214i | \(-0.395126\pi\) | ||||
0.323543 | + | 0.946214i | \(0.395126\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1957 | 0.749174 | ||||||||
\(266\) | 1.01208 | 0.0620547 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.14675 | 0.131134 | ||||||||
\(269\) | −26.4155 | −1.61058 | −0.805291 | − | 0.592880i | \(-0.797991\pi\) | ||||
−0.805291 | + | 0.592880i | \(0.797991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.0301 | −1.33824 | −0.669118 | − | 0.743157i | \(-0.733328\pi\) | ||||
−0.669118 | + | 0.743157i | \(0.733328\pi\) | |||||||
\(272\) | −5.96077 | −0.361425 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.08038 | −0.548566 | ||||||||
\(275\) | 18.8267 | 1.13529 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.17629 | 0.130761 | 0.0653804 | − | 0.997860i | \(-0.479174\pi\) | ||||
0.0653804 | + | 0.997860i | \(0.479174\pi\) | |||||||
\(278\) | 18.9051 | 1.13386 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.00000 | 0.239046 | ||||||||
\(281\) | −25.0030 | −1.49155 | −0.745776 | − | 0.666196i | \(-0.767921\pi\) | ||||
−0.745776 | + | 0.666196i | \(0.767921\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.3153 | −0.969842 | −0.484921 | − | 0.874558i | \(-0.661152\pi\) | ||||
−0.484921 | + | 0.874558i | \(0.661152\pi\) | |||||||
\(284\) | −0.615957 | −0.0365503 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.97584 | 0.470799 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.5308 | 1.09005 | ||||||||
\(290\) | 13.6233 | 0.799985 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.32304 | 0.370028 | ||||||||
\(293\) | 1.87800 | 0.109714 | 0.0548570 | − | 0.998494i | \(-0.482530\pi\) | ||||
0.0548570 | + | 0.998494i | \(0.482530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.5676 | −2.12905 | ||||||||
\(296\) | 4.89008 | 0.284230 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.6896 | −1.08266 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.572417 | −0.0329935 | ||||||||
\(302\) | −0.317667 | −0.0182797 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.911854 | 0.0522984 | ||||||||
\(305\) | −1.58450 | −0.0907281 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.9801 | −1.36862 | −0.684310 | − | 0.729192i | \(-0.739896\pi\) | ||||
−0.684310 | + | 0.729192i | \(0.739896\pi\) | |||||||
\(308\) | 2.61596 | 0.149058 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 30.6112 | 1.73860 | ||||||||
\(311\) | 5.38404 | 0.305301 | 0.152651 | − | 0.988280i | \(-0.451219\pi\) | ||||
0.152651 | + | 0.988280i | \(0.451219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.9487 | 1.07104 | 0.535522 | − | 0.844522i | \(-0.320115\pi\) | ||||
0.535522 | + | 0.844522i | \(0.320115\pi\) | |||||||
\(314\) | 18.8901 | 1.06603 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.4819 | −0.870924 | ||||||||
\(317\) | 11.5013 | 0.645975 | 0.322987 | − | 0.946403i | \(-0.395313\pi\) | ||||
0.322987 | + | 0.946403i | \(0.395313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.90946 | 0.498834 | ||||||||
\(320\) | 3.60388 | 0.201463 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.75600 | −0.209314 | ||||||||
\(323\) | −5.43535 | −0.302431 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.33273 | −0.239968 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.18598 | 0.396779 | ||||||||
\(329\) | −7.75600 | −0.427602 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.6112 | −1.90240 | −0.951201 | − | 0.308572i | \(-0.900149\pi\) | ||||
−0.951201 | + | 0.308572i | \(0.900149\pi\) | |||||||
\(332\) | 0.911854 | 0.0500445 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.0000 | −0.766046 | ||||||||
\(335\) | 7.73663 | 0.422697 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.95407 | 0.106445 | 0.0532224 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532224 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −21.4819 | −1.16502 | ||||||||
\(341\) | 20.0194 | 1.08411 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.1715 | −0.765189 | ||||||||
\(344\) | −0.515729 | −0.0278063 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.9879 | 0.590714 | ||||||||
\(347\) | 6.41550 | 0.344402 | 0.172201 | − | 0.985062i | \(-0.444912\pi\) | ||||
0.172201 | + | 0.985062i | \(0.444912\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.08575 | −0.0581190 | −0.0290595 | − | 0.999578i | \(-0.509251\pi\) | ||||
−0.0290595 | + | 0.999578i | \(0.509251\pi\) | |||||||
\(350\) | 8.86592 | 0.473903 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.35690 | 0.125623 | ||||||||
\(353\) | 4.28919 | 0.228291 | 0.114145 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114145 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.21983 | −0.117816 | ||||||||
\(356\) | −3.75063 | −0.198783 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.65519 | −0.246034 | ||||||||
\(359\) | −15.5060 | −0.818378 | −0.409189 | − | 0.912450i | \(-0.634188\pi\) | ||||
−0.409189 | + | 0.912450i | \(0.634188\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1685 | −0.956238 | ||||||||
\(362\) | −1.06638 | −0.0560475 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.7875 | 1.19275 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4276 | 0.909712 | 0.454856 | − | 0.890565i | \(-0.349691\pi\) | ||||
0.454856 | + | 0.890565i | \(0.349691\pi\) | |||||||
\(368\) | −3.38404 | −0.176405 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.6233 | 0.916189 | ||||||||
\(371\) | 3.75600 | 0.195002 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.19567 | 0.424356 | 0.212178 | − | 0.977231i | \(-0.431944\pi\) | ||||
0.212178 | + | 0.977231i | \(0.431944\pi\) | |||||||
\(374\) | −14.0489 | −0.726452 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.98792 | −0.360374 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0476 | 0.772943 | 0.386471 | − | 0.922301i | \(-0.373694\pi\) | ||||
0.386471 | + | 0.922301i | \(0.373694\pi\) | |||||||
\(380\) | 3.28621 | 0.168579 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.890084 | −0.0455406 | ||||||||
\(383\) | −11.1207 | −0.568240 | −0.284120 | − | 0.958789i | \(-0.591701\pi\) | ||||
−0.284120 | + | 0.958789i | \(0.591701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.42758 | 0.480474 | ||||||||
\(386\) | 16.2174 | 0.825446 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.6746 | −0.744988 | ||||||||
\(389\) | 8.04354 | 0.407824 | 0.203912 | − | 0.978989i | \(-0.434634\pi\) | ||||
0.203912 | + | 0.978989i | \(0.434634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.1715 | 1.02012 | ||||||||
\(392\) | −5.76809 | −0.291332 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.4711 | 0.577907 | ||||||||
\(395\) | −55.7948 | −2.80734 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.9081 | 1.09954 | 0.549769 | − | 0.835317i | \(-0.314716\pi\) | ||||
0.549769 | + | 0.835317i | \(0.314716\pi\) | |||||||
\(398\) | −3.79954 | −0.190454 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.98792 | 0.399396 | ||||||||
\(401\) | 17.4426 | 0.871044 | 0.435522 | − | 0.900178i | \(-0.356564\pi\) | ||||
0.435522 | + | 0.900178i | \(0.356564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.76809 | −0.436229 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.19567 | 0.208228 | ||||||||
\(407\) | 11.5254 | 0.571294 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.4330 | 0.862004 | 0.431002 | − | 0.902351i | \(-0.358160\pi\) | ||||
0.431002 | + | 0.902351i | \(0.358160\pi\) | |||||||
\(410\) | 25.8974 | 1.27898 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.8116 | 0.926782 | ||||||||
\(413\) | −11.2620 | −0.554169 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.28621 | 0.161314 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.14914 | 0.105118 | ||||||||
\(419\) | −9.97584 | −0.487352 | −0.243676 | − | 0.969857i | \(-0.578353\pi\) | ||||
−0.243676 | + | 0.969857i | \(0.578353\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.615957 | −0.0300199 | −0.0150100 | − | 0.999887i | \(-0.504778\pi\) | ||||
−0.0150100 | + | 0.999887i | \(0.504778\pi\) | |||||||
\(422\) | −25.0465 | −1.21925 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.38404 | 0.164344 | ||||||||
\(425\) | −47.6142 | −2.30963 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.487991 | −0.0236156 | ||||||||
\(428\) | −18.0519 | −0.872572 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.85862 | −0.0896308 | ||||||||
\(431\) | −14.7922 | −0.712518 | −0.356259 | − | 0.934387i | \(-0.615948\pi\) | ||||
−0.356259 | + | 0.934387i | \(0.615948\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.5321 | 0.794483 | 0.397242 | − | 0.917714i | \(-0.369968\pi\) | ||||
0.397242 | + | 0.917714i | \(0.369968\pi\) | |||||||
\(434\) | 9.42758 | 0.452538 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.09783 | 0.292033 | ||||||||
\(437\) | −3.08575 | −0.147612 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.50125 | 0.167106 | 0.0835529 | − | 0.996503i | \(-0.473373\pi\) | ||||
0.0835529 | + | 0.996503i | \(0.473373\pi\) | |||||||
\(440\) | 8.49396 | 0.404934 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.4077 | −0.827066 | −0.413533 | − | 0.910489i | \(-0.635705\pi\) | ||||
−0.413533 | + | 0.910489i | \(0.635705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.5168 | −0.640758 | ||||||||
\(446\) | 12.9879 | 0.614996 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.10992 | 0.0524386 | ||||||||
\(449\) | 34.1497 | 1.61163 | 0.805813 | − | 0.592170i | \(-0.201729\pi\) | ||||
0.805813 | + | 0.592170i | \(0.201729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.9366 | 0.797514 | ||||||||
\(452\) | 12.2010 | 0.573889 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.8049 | 0.647897 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.40342 | −0.439873 | −0.219937 | − | 0.975514i | \(-0.570585\pi\) | ||||
−0.219937 | + | 0.975514i | \(0.570585\pi\) | |||||||
\(458\) | −11.5603 | −0.540179 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.1957 | −0.568626 | ||||||||
\(461\) | −0.733169 | −0.0341471 | −0.0170735 | − | 0.999854i | \(-0.505435\pi\) | ||||
−0.0170735 | + | 0.999854i | \(0.505435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.24267 | −0.336595 | −0.168298 | − | 0.985736i | \(-0.553827\pi\) | ||||
−0.168298 | + | 0.985736i | \(0.553827\pi\) | |||||||
\(464\) | 3.78017 | 0.175490 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.77479 | −0.452808 | ||||||||
\(467\) | −30.2446 | −1.39955 | −0.699776 | − | 0.714362i | \(-0.746717\pi\) | ||||
−0.699776 | + | 0.714362i | \(0.746717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.38271 | 0.110024 | ||||||||
\(470\) | −25.1836 | −1.16163 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.1468 | −0.467042 | ||||||||
\(473\) | −1.21552 | −0.0558897 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.28382 | 0.334204 | ||||||||
\(476\) | −6.61596 | −0.303242 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.944378 | 0.0431948 | ||||||||
\(479\) | −36.7198 | −1.67777 | −0.838884 | − | 0.544310i | \(-0.816792\pi\) | ||||
−0.838884 | + | 0.544310i | \(0.816792\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.219833 | −0.0100131 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.44504 | −0.247502 | ||||||||
\(485\) | −52.8853 | −2.40140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.6547 | 1.29847 | 0.649234 | − | 0.760588i | \(-0.275089\pi\) | ||||
0.649234 | + | 0.760588i | \(0.275089\pi\) | |||||||
\(488\) | −0.439665 | −0.0199027 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −20.7875 | −0.939082 | ||||||||
\(491\) | −30.4295 | −1.37326 | −0.686632 | − | 0.727005i | \(-0.740912\pi\) | ||||
−0.686632 | + | 0.727005i | \(0.740912\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.5327 | −1.01482 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.49396 | 0.381390 | ||||||||
\(497\) | −0.683661 | −0.0306664 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.9715 | −0.714984 | −0.357492 | − | 0.933916i | \(-0.616368\pi\) | ||||
−0.357492 | + | 0.933916i | \(0.616368\pi\) | |||||||
\(500\) | 10.7681 | 0.481563 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.2543 | −0.725464 | ||||||||
\(503\) | 41.9711 | 1.87140 | 0.935698 | − | 0.352801i | \(-0.114771\pi\) | ||||
0.935698 | + | 0.352801i | \(0.114771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.5991 | −1.40614 | ||||||||
\(506\) | −7.97584 | −0.354569 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.4276 | 0.507017 | ||||||||
\(509\) | 0.914247 | 0.0405233 | 0.0202616 | − | 0.999795i | \(-0.493550\pi\) | ||||
0.0202616 | + | 0.999795i | \(0.493550\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.01805 | 0.310460 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.4373 | 0.989666 | ||||||||
\(515\) | 67.7948 | 2.98739 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.4698 | −0.724341 | ||||||||
\(518\) | 5.42758 | 0.238474 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.31096 | 0.145056 | 0.0725279 | − | 0.997366i | \(-0.476893\pi\) | ||||
0.0725279 | + | 0.997366i | \(0.476893\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.850855 | −0.0372053 | −0.0186026 | − | 0.999827i | \(-0.505922\pi\) | ||||
−0.0186026 | + | 0.999827i | \(0.505922\pi\) | |||||||
\(524\) | −2.29590 | −0.100297 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.4940 | 0.457558 | ||||||||
\(527\) | −50.6305 | −2.20550 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5483 | −0.502098 | ||||||||
\(530\) | 12.1957 | 0.529746 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.01208 | 0.0438793 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −65.0568 | −2.81265 | ||||||||
\(536\) | 2.14675 | 0.0927256 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.4155 | −1.13885 | ||||||||
\(539\) | −13.5948 | −0.585569 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.8853 | 1.75780 | 0.878898 | − | 0.477010i | \(-0.158279\pi\) | ||||
0.878898 | + | 0.477010i | \(0.158279\pi\) | |||||||
\(542\) | −22.0301 | −0.946275 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.96077 | −0.255566 | ||||||||
\(545\) | 21.9758 | 0.941341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.39075 | −0.102221 | −0.0511105 | − | 0.998693i | \(-0.516276\pi\) | ||||
−0.0511105 | + | 0.998693i | \(0.516276\pi\) | |||||||
\(548\) | −9.08038 | −0.387894 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.8267 | 0.802773 | ||||||||
\(551\) | 3.44696 | 0.146845 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.1836 | −0.730720 | ||||||||
\(554\) | 2.17629 | 0.0924618 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.9051 | 0.801757 | ||||||||
\(557\) | 27.1508 | 1.15042 | 0.575208 | − | 0.818007i | \(-0.304921\pi\) | ||||
0.575208 | + | 0.818007i | \(0.304921\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.0030 | −1.05469 | ||||||||
\(563\) | 6.52409 | 0.274958 | 0.137479 | − | 0.990505i | \(-0.456100\pi\) | ||||
0.137479 | + | 0.990505i | \(0.456100\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 43.9711 | 1.84988 | ||||||||
\(566\) | −16.3153 | −0.685782 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.615957 | −0.0258450 | ||||||||
\(569\) | −7.30021 | −0.306041 | −0.153020 | − | 0.988223i | \(-0.548900\pi\) | ||||
−0.153020 | + | 0.988223i | \(0.548900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.6722 | −1.82762 | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.97584 | 0.332905 | ||||||||
\(575\) | −27.0315 | −1.12729 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.8528 | −0.701590 | −0.350795 | − | 0.936452i | \(-0.614089\pi\) | ||||
−0.350795 | + | 0.936452i | \(0.614089\pi\) | |||||||
\(578\) | 18.5308 | 0.770779 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.6233 | 0.565675 | ||||||||
\(581\) | 1.01208 | 0.0419882 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.97584 | 0.330325 | ||||||||
\(584\) | 6.32304 | 0.261649 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.87800 | 0.0775796 | ||||||||
\(587\) | −22.1825 | −0.915571 | −0.457785 | − | 0.889063i | \(-0.651357\pi\) | ||||
−0.457785 | + | 0.889063i | \(0.651357\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.74525 | 0.319137 | ||||||||
\(590\) | −36.5676 | −1.50547 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.89008 | 0.200981 | ||||||||
\(593\) | 3.98493 | 0.163642 | 0.0818208 | − | 0.996647i | \(-0.473926\pi\) | ||||
0.0818208 | + | 0.996647i | \(0.473926\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.8431 | −0.977471 | ||||||||
\(596\) | −18.6896 | −0.765557 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.2379 | −1.35806 | −0.679032 | − | 0.734109i | \(-0.737600\pi\) | ||||
−0.679032 | + | 0.734109i | \(0.737600\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.79715 | 0.399634 | 0.199817 | − | 0.979833i | \(-0.435965\pi\) | ||||
0.199817 | + | 0.979833i | \(0.435965\pi\) | |||||||
\(602\) | −0.572417 | −0.0233300 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.317667 | −0.0129257 | ||||||||
\(605\) | −19.6233 | −0.797799 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.2258 | −0.983295 | −0.491647 | − | 0.870794i | \(-0.663605\pi\) | ||||
−0.491647 | + | 0.870794i | \(0.663605\pi\) | |||||||
\(608\) | 0.911854 | 0.0369806 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.58450 | −0.0641545 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.0556 | 0.608091 | 0.304045 | − | 0.952658i | \(-0.401663\pi\) | ||||
0.304045 | + | 0.952658i | \(0.401663\pi\) | |||||||
\(614\) | −23.9801 | −0.967760 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.61596 | 0.105400 | ||||||||
\(617\) | −2.01879 | −0.0812733 | −0.0406366 | − | 0.999174i | \(-0.512939\pi\) | ||||
−0.0406366 | + | 0.999174i | \(0.512939\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.84309 | 0.315240 | 0.157620 | − | 0.987500i | \(-0.449618\pi\) | ||||
0.157620 | + | 0.987500i | \(0.449618\pi\) | |||||||
\(620\) | 30.6112 | 1.22937 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.38404 | 0.215880 | ||||||||
\(623\) | −4.16288 | −0.166782 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.13275 | −0.0453101 | ||||||||
\(626\) | 18.9487 | 0.757342 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.8901 | 0.753796 | ||||||||
\(629\) | −29.1487 | −1.16223 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.5327 | −0.976632 | −0.488316 | − | 0.872667i | \(-0.662389\pi\) | ||||
−0.488316 | + | 0.872667i | \(0.662389\pi\) | |||||||
\(632\) | −15.4819 | −0.615836 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.5013 | 0.456773 | ||||||||
\(635\) | 41.1836 | 1.63432 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.90946 | 0.352729 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.60388 | 0.142456 | ||||||||
\(641\) | 41.6015 | 1.64316 | 0.821580 | − | 0.570093i | \(-0.193093\pi\) | ||||
0.821580 | + | 0.570093i | \(0.193093\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −45.4118 | −1.79087 | −0.895433 | − | 0.445196i | \(-0.853134\pi\) | ||||
−0.895433 | + | 0.445196i | \(0.853134\pi\) | |||||||
\(644\) | −3.75600 | −0.148007 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.43535 | −0.213851 | ||||||||
\(647\) | −35.8345 | −1.40880 | −0.704399 | − | 0.709804i | \(-0.748783\pi\) | ||||
−0.704399 | + | 0.709804i | \(0.748783\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.9148 | −0.938740 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.33273 | −0.169683 | ||||||||
\(653\) | −18.5590 | −0.726270 | −0.363135 | − | 0.931737i | \(-0.618294\pi\) | ||||
−0.363135 | + | 0.931737i | \(0.618294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.27413 | −0.323297 | ||||||||
\(656\) | 7.18598 | 0.280565 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.75600 | −0.302361 | ||||||||
\(659\) | 3.97525 | 0.154854 | 0.0774268 | − | 0.996998i | \(-0.475330\pi\) | ||||
0.0774268 | + | 0.996998i | \(0.475330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.23191 | −0.0479159 | −0.0239580 | − | 0.999713i | \(-0.507627\pi\) | ||||
−0.0239580 | + | 0.999713i | \(0.507627\pi\) | |||||||
\(662\) | −34.6112 | −1.34520 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.911854 | 0.0353868 | ||||||||
\(665\) | 3.64742 | 0.141441 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.7922 | −0.495318 | ||||||||
\(668\) | −14.0000 | −0.541676 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.73663 | 0.298892 | ||||||||
\(671\) | −1.03624 | −0.0400038 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.8256 | −1.41952 | −0.709762 | − | 0.704442i | \(-0.751197\pi\) | ||||
−0.709762 | + | 0.704442i | \(0.751197\pi\) | |||||||
\(674\) | 1.95407 | 0.0752678 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.9215 | 0.996246 | 0.498123 | − | 0.867106i | \(-0.334023\pi\) | ||||
0.498123 | + | 0.867106i | \(0.334023\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.2875 | −0.625058 | ||||||||
\(680\) | −21.4819 | −0.823792 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20.0194 | 0.766582 | ||||||||
\(683\) | 37.5472 | 1.43670 | 0.718352 | − | 0.695680i | \(-0.244897\pi\) | ||||
0.718352 | + | 0.695680i | \(0.244897\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.7245 | −1.25034 | ||||||||
\(686\) | −14.1715 | −0.541071 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.515729 | −0.0196620 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.2549 | −1.72158 | −0.860788 | − | 0.508963i | \(-0.830029\pi\) | ||||
−0.860788 | + | 0.508963i | \(0.830029\pi\) | |||||||
\(692\) | 10.9879 | 0.417698 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.41550 | 0.243529 | ||||||||
\(695\) | 68.1318 | 2.58439 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.8340 | −1.62245 | ||||||||
\(698\) | −1.08575 | −0.0410964 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.86592 | 0.335100 | ||||||||
\(701\) | −36.0823 | −1.36281 | −0.681405 | − | 0.731907i | \(-0.738631\pi\) | ||||
−0.681405 | + | 0.731907i | \(0.738631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.45904 | 0.168176 | ||||||||
\(704\) | 2.35690 | 0.0888289 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.28919 | 0.161426 | ||||||||
\(707\) | −9.73184 | −0.366004 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0664 | 0.716053 | 0.358026 | − | 0.933711i | \(-0.383450\pi\) | ||||
0.358026 | + | 0.933711i | \(0.383450\pi\) | |||||||
\(710\) | −2.21983 | −0.0833088 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.75063 | −0.140561 | ||||||||
\(713\) | −28.7439 | −1.07647 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.65519 | −0.173972 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.5060 | −0.578680 | ||||||||
\(719\) | 15.3056 | 0.570802 | 0.285401 | − | 0.958408i | \(-0.407873\pi\) | ||||
0.285401 | + | 0.958408i | \(0.407873\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.8793 | 0.777587 | ||||||||
\(722\) | −18.1685 | −0.676162 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.06638 | −0.0396315 | ||||||||
\(725\) | 30.1957 | 1.12144 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.46250 | 0.128417 | 0.0642085 | − | 0.997937i | \(-0.479548\pi\) | ||||
0.0642085 | + | 0.997937i | \(0.479548\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 22.7875 | 0.843402 | ||||||||
\(731\) | 3.07415 | 0.113701 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0930 | 0.963769 | 0.481884 | − | 0.876235i | \(-0.339953\pi\) | ||||
0.481884 | + | 0.876235i | \(0.339953\pi\) | |||||||
\(734\) | 17.4276 | 0.643264 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.38404 | −0.124737 | ||||||||
\(737\) | 5.05967 | 0.186375 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.4993 | 0.974794 | 0.487397 | − | 0.873181i | \(-0.337946\pi\) | ||||
0.487397 | + | 0.873181i | \(0.337946\pi\) | |||||||
\(740\) | 17.6233 | 0.647844 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.75600 | 0.137887 | ||||||||
\(743\) | −0.415502 | −0.0152433 | −0.00762164 | − | 0.999971i | \(-0.502426\pi\) | ||||
−0.00762164 | + | 0.999971i | \(0.502426\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −67.3551 | −2.46770 | ||||||||
\(746\) | 8.19567 | 0.300065 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.0489 | −0.513679 | ||||||||
\(749\) | −20.0361 | −0.732103 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.90946 | 0.106168 | 0.0530839 | − | 0.998590i | \(-0.483095\pi\) | ||||
0.0530839 | + | 0.998590i | \(0.483095\pi\) | |||||||
\(752\) | −6.98792 | −0.254823 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.14483 | −0.0416647 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.3720 | 0.449667 | 0.224833 | − | 0.974397i | \(-0.427816\pi\) | ||||
0.224833 | + | 0.974397i | \(0.427816\pi\) | |||||||
\(758\) | 15.0476 | 0.546553 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.28621 | 0.119203 | ||||||||
\(761\) | 42.4306 | 1.53811 | 0.769053 | − | 0.639184i | \(-0.220728\pi\) | ||||
0.769053 | + | 0.639184i | \(0.220728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.76809 | 0.245021 | ||||||||
\(764\) | −0.890084 | −0.0322021 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.1207 | −0.401806 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.3341 | −0.480839 | −0.240419 | − | 0.970669i | \(-0.577285\pi\) | ||||
−0.240419 | + | 0.970669i | \(0.577285\pi\) | |||||||
\(770\) | 9.42758 | 0.339747 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.2174 | 0.583678 | ||||||||
\(773\) | −5.85384 | −0.210548 | −0.105274 | − | 0.994443i | \(-0.533572\pi\) | ||||
−0.105274 | + | 0.994443i | \(0.533572\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 67.8491 | 2.43721 | ||||||||
\(776\) | −14.6746 | −0.526786 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.04354 | 0.288375 | ||||||||
\(779\) | 6.55257 | 0.234770 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.45175 | −0.0519476 | ||||||||
\(782\) | 20.1715 | 0.721332 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.76809 | −0.206003 | ||||||||
\(785\) | 68.0775 | 2.42979 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.2965 | 0.830430 | 0.415215 | − | 0.909723i | \(-0.363706\pi\) | ||||
0.415215 | + | 0.909723i | \(0.363706\pi\) | |||||||
\(788\) | 11.4711 | 0.408642 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −55.7948 | −1.98509 | ||||||||
\(791\) | 13.5421 | 0.481503 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 21.9081 | 0.777491 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.79954 | −0.134671 | ||||||||
\(797\) | −35.8103 | −1.26847 | −0.634233 | − | 0.773142i | \(-0.718684\pi\) | ||||
−0.634233 | + | 0.773142i | \(0.718684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.6534 | 1.47359 | ||||||||
\(800\) | 7.98792 | 0.282416 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.4426 | 0.615921 | ||||||||
\(803\) | 14.9028 | 0.525907 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.5362 | −0.477087 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.76809 | −0.308460 | ||||||||
\(809\) | −28.3744 | −0.997589 | −0.498795 | − | 0.866720i | \(-0.666224\pi\) | ||||
−0.498795 | + | 0.866720i | \(0.666224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.20344 | −0.182717 | −0.0913587 | − | 0.995818i | \(-0.529121\pi\) | ||||
−0.0913587 | + | 0.995818i | \(0.529121\pi\) | |||||||
\(812\) | 4.19567 | 0.147239 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.5254 | 0.403966 | ||||||||
\(815\) | −15.6146 | −0.546957 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.470270 | −0.0164527 | ||||||||
\(818\) | 17.4330 | 0.609529 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25.8974 | 0.904376 | ||||||||
\(821\) | −5.65338 | −0.197304 | −0.0986522 | − | 0.995122i | \(-0.531453\pi\) | ||||
−0.0986522 | + | 0.995122i | \(0.531453\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.0616 | 1.36160 | 0.680801 | − | 0.732469i | \(-0.261632\pi\) | ||||
0.680801 | + | 0.732469i | \(0.261632\pi\) | |||||||
\(824\) | 18.8116 | 0.655334 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.2620 | −0.391857 | ||||||||
\(827\) | −5.40283 | −0.187875 | −0.0939374 | − | 0.995578i | \(-0.529945\pi\) | ||||
−0.0939374 | + | 0.995578i | \(0.529945\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.38537 | −0.291236 | −0.145618 | − | 0.989341i | \(-0.546517\pi\) | ||||
−0.145618 | + | 0.989341i | \(0.546517\pi\) | |||||||
\(830\) | 3.28621 | 0.114066 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.3822 | 1.19127 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −50.4543 | −1.74604 | ||||||||
\(836\) | 2.14914 | 0.0743297 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.97584 | −0.344610 | ||||||||
\(839\) | −3.98062 | −0.137426 | −0.0687132 | − | 0.997636i | \(-0.521889\pi\) | ||||
−0.0687132 | + | 0.997636i | \(0.521889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7103 | −0.507253 | ||||||||
\(842\) | −0.615957 | −0.0212273 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.0465 | −0.862137 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.04354 | −0.207659 | ||||||||
\(848\) | 3.38404 | 0.116209 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −47.6142 | −1.63315 | ||||||||
\(851\) | −16.5483 | −0.567267 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.29350 | −0.215485 | −0.107743 | − | 0.994179i | \(-0.534362\pi\) | ||||
−0.107743 | + | 0.994179i | \(0.534362\pi\) | |||||||
\(854\) | −0.487991 | −0.0166987 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.0519 | −0.617001 | ||||||||
\(857\) | −4.37627 | −0.149491 | −0.0747453 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747453 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0261 | 0.512683 | 0.256342 | − | 0.966586i | \(-0.417483\pi\) | ||||
0.256342 | + | 0.966586i | \(0.417483\pi\) | |||||||
\(860\) | −1.85862 | −0.0633786 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.7922 | −0.503826 | ||||||||
\(863\) | 6.21121 | 0.211432 | 0.105716 | − | 0.994396i | \(-0.466287\pi\) | ||||
0.105716 | + | 0.994396i | \(0.466287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.5991 | 1.34641 | ||||||||
\(866\) | 16.5321 | 0.561784 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.42758 | 0.319993 | ||||||||
\(869\) | −36.4892 | −1.23781 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.09783 | 0.206499 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.08575 | −0.104377 | ||||||||
\(875\) | 11.9517 | 0.404040 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.2198 | −1.29059 | −0.645296 | − | 0.763933i | \(-0.723266\pi\) | ||||
−0.645296 | + | 0.763933i | \(0.723266\pi\) | |||||||
\(878\) | 3.50125 | 0.118162 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.49396 | 0.286331 | ||||||||
\(881\) | −26.7832 | −0.902347 | −0.451174 | − | 0.892436i | \(-0.648994\pi\) | ||||
−0.451174 | + | 0.892436i | \(0.648994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.4956 | −1.16087 | −0.580435 | − | 0.814307i | \(-0.697117\pi\) | ||||
−0.580435 | + | 0.814307i | \(0.697117\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.4077 | −0.584824 | ||||||||
\(887\) | 23.9866 | 0.805391 | 0.402695 | − | 0.915334i | \(-0.368073\pi\) | ||||
0.402695 | + | 0.915334i | \(0.368073\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.6837 | 0.425396 | ||||||||
\(890\) | −13.5168 | −0.453084 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.9879 | 0.434868 | ||||||||
\(893\) | −6.37196 | −0.213230 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.7767 | −0.560784 | ||||||||
\(896\) | 1.10992 | 0.0370797 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.1497 | 1.13959 | ||||||||
\(899\) | 32.1086 | 1.07088 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.1715 | −0.672010 | ||||||||
\(902\) | 16.9366 | 0.563927 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.2010 | 0.405801 | ||||||||
\(905\) | −3.84309 | −0.127748 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.9269 | 0.794480 | 0.397240 | − | 0.917715i | \(-0.369968\pi\) | ||||
0.397240 | + | 0.917715i | \(0.369968\pi\) | |||||||
\(908\) | 13.8049 | 0.458132 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.8866 | 1.18898 | 0.594488 | − | 0.804104i | \(-0.297355\pi\) | ||||
0.594488 | + | 0.804104i | \(0.297355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.14914 | 0.0711263 | ||||||||
\(914\) | −9.40342 | −0.311037 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.5603 | −0.381964 | ||||||||
\(917\) | −2.54825 | −0.0841507 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.2465 | 1.09670 | 0.548351 | − | 0.836249i | \(-0.315256\pi\) | ||||
0.548351 | + | 0.836249i | \(0.315256\pi\) | |||||||
\(920\) | −12.1957 | −0.402079 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.733169 | −0.0241456 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.0616 | 1.28434 | ||||||||
\(926\) | −7.24267 | −0.238009 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.78017 | 0.124090 | ||||||||
\(929\) | 54.2583 | 1.78016 | 0.890079 | − | 0.455806i | \(-0.150649\pi\) | ||||
0.890079 | + | 0.455806i | \(0.150649\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.25965 | −0.172378 | ||||||||
\(932\) | −9.77479 | −0.320184 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −30.2446 | −0.989633 | ||||||||
\(935\) | −50.6305 | −1.65580 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5265 | 0.539897 | 0.269948 | − | 0.962875i | \(-0.412993\pi\) | ||||
0.269948 | + | 0.962875i | \(0.412993\pi\) | |||||||
\(938\) | 2.38271 | 0.0777984 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −25.1836 | −0.821398 | ||||||||
\(941\) | 41.7017 | 1.35944 | 0.679718 | − | 0.733473i | \(-0.262102\pi\) | ||||
0.679718 | + | 0.733473i | \(0.262102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.3177 | −0.791892 | ||||||||
\(944\) | −10.1468 | −0.330249 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.21552 | −0.0395200 | ||||||||
\(947\) | −3.00106 | −0.0975215 | −0.0487608 | − | 0.998810i | \(-0.515527\pi\) | ||||
−0.0487608 | + | 0.998810i | \(0.515527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.28382 | 0.236318 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.61596 | −0.214424 | ||||||||
\(953\) | −38.1450 | −1.23564 | −0.617818 | − | 0.786321i | \(-0.711983\pi\) | ||||
−0.617818 | + | 0.786321i | \(0.711983\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.20775 | −0.103800 | ||||||||
\(956\) | 0.944378 | 0.0305434 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.7198 | −1.18636 | ||||||||
\(959\) | −10.0785 | −0.325450 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.1473 | 1.32733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.219833 | −0.00708033 | ||||||||
\(965\) | 58.4456 | 1.88143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.8793 | −0.864381 | −0.432190 | − | 0.901782i | \(-0.642259\pi\) | ||||
−0.432190 | + | 0.901782i | \(0.642259\pi\) | |||||||
\(968\) | −5.44504 | −0.175010 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −52.8853 | −1.69804 | ||||||||
\(971\) | −3.13647 | −0.100654 | −0.0503271 | − | 0.998733i | \(-0.516026\pi\) | ||||
−0.0503271 | + | 0.998733i | \(0.516026\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.9831 | 0.672688 | ||||||||
\(974\) | 28.6547 | 0.918156 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.439665 | −0.0140733 | ||||||||
\(977\) | −35.8864 | −1.14811 | −0.574053 | − | 0.818818i | \(-0.694630\pi\) | ||||
−0.574053 | + | 0.818818i | \(0.694630\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.83984 | −0.282522 | ||||||||
\(980\) | −20.7875 | −0.664031 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.4295 | −0.971044 | ||||||||
\(983\) | 30.4370 | 0.970790 | 0.485395 | − | 0.874295i | \(-0.338676\pi\) | ||||
0.485395 | + | 0.874295i | \(0.338676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.3405 | 1.31722 | ||||||||
\(986\) | −22.5327 | −0.717588 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.74525 | 0.0554957 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.4470 | 0.998946 | 0.499473 | − | 0.866330i | \(-0.333527\pi\) | ||||
0.499473 | + | 0.866330i | \(0.333527\pi\) | |||||||
\(992\) | 8.49396 | 0.269683 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.683661 | −0.0216844 | ||||||||
\(995\) | −13.6931 | −0.434100 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.1099 | 0.605217 | 0.302609 | − | 0.953115i | \(-0.402143\pi\) | ||||
0.302609 | + | 0.953115i | \(0.402143\pi\) | |||||||
\(998\) | −15.9715 | −0.505570 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3042.2.a.bi.1.3 | 3 | ||
3.2 | odd | 2 | 338.2.a.g.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 2704.2.a.v.1.3 | 3 | |||
13.5 | odd | 4 | 3042.2.b.n.1351.1 | 6 | |||
13.8 | odd | 4 | 3042.2.b.n.1351.6 | 6 | |||
13.12 | even | 2 | 3042.2.a.z.1.1 | 3 | |||
15.14 | odd | 2 | 8450.2.a.bx.1.3 | 3 | |||
39.2 | even | 12 | 338.2.e.e.147.3 | 12 | |||
39.5 | even | 4 | 338.2.b.d.337.4 | 6 | |||
39.8 | even | 4 | 338.2.b.d.337.1 | 6 | |||
39.11 | even | 12 | 338.2.e.e.147.6 | 12 | |||
39.17 | odd | 6 | 338.2.c.h.315.3 | 6 | |||
39.20 | even | 12 | 338.2.e.e.23.3 | 12 | |||
39.23 | odd | 6 | 338.2.c.h.191.3 | 6 | |||
39.29 | odd | 6 | 338.2.c.i.191.3 | 6 | |||
39.32 | even | 12 | 338.2.e.e.23.6 | 12 | |||
39.35 | odd | 6 | 338.2.c.i.315.3 | 6 | |||
39.38 | odd | 2 | 338.2.a.h.1.1 | yes | 3 | ||
156.47 | odd | 4 | 2704.2.f.m.337.5 | 6 | |||
156.83 | odd | 4 | 2704.2.f.m.337.6 | 6 | |||
156.155 | even | 2 | 2704.2.a.w.1.3 | 3 | |||
195.194 | odd | 2 | 8450.2.a.bn.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
338.2.a.g.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
338.2.a.h.1.1 | yes | 3 | 39.38 | odd | 2 | ||
338.2.b.d.337.1 | 6 | 39.8 | even | 4 | |||
338.2.b.d.337.4 | 6 | 39.5 | even | 4 | |||
338.2.c.h.191.3 | 6 | 39.23 | odd | 6 | |||
338.2.c.h.315.3 | 6 | 39.17 | odd | 6 | |||
338.2.c.i.191.3 | 6 | 39.29 | odd | 6 | |||
338.2.c.i.315.3 | 6 | 39.35 | odd | 6 | |||
338.2.e.e.23.3 | 12 | 39.20 | even | 12 | |||
338.2.e.e.23.6 | 12 | 39.32 | even | 12 | |||
338.2.e.e.147.3 | 12 | 39.2 | even | 12 | |||
338.2.e.e.147.6 | 12 | 39.11 | even | 12 | |||
2704.2.a.v.1.3 | 3 | 12.11 | even | 2 | |||
2704.2.a.w.1.3 | 3 | 156.155 | even | 2 | |||
2704.2.f.m.337.5 | 6 | 156.47 | odd | 4 | |||
2704.2.f.m.337.6 | 6 | 156.83 | odd | 4 | |||
3042.2.a.z.1.1 | 3 | 13.12 | even | 2 | |||
3042.2.a.bi.1.3 | 3 | 1.1 | even | 1 | trivial | ||
3042.2.b.n.1351.1 | 6 | 13.5 | odd | 4 | |||
3042.2.b.n.1351.6 | 6 | 13.8 | odd | 4 | |||
8450.2.a.bn.1.3 | 3 | 195.194 | odd | 2 | |||
8450.2.a.bx.1.3 | 3 | 15.14 | odd | 2 |