Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7350,2,Mod(1,7350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7350.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7350.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: | \(58.6900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1470) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.69230\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7350.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.979056 | 0.295197 | 0.147598 | − | 0.989047i | \(-0.452846\pi\) | ||||
0.147598 | + | 0.989047i | \(0.452846\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.435157 | 0.120691 | 0.0603455 | − | 0.998178i | \(-0.480780\pi\) | ||||
0.0603455 | + | 0.998178i | \(0.480780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.79881 | −0.678811 | −0.339405 | − | 0.940640i | \(-0.610226\pi\) | ||||
−0.339405 | + | 0.940640i | \(0.610226\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 7.34271 | 1.68453 | 0.842266 | − | 0.539062i | \(-0.181221\pi\) | ||||
0.842266 | + | 0.539062i | \(0.181221\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.979056 | 0.208735 | ||||||||
\(23\) | −3.34271 | −0.697003 | −0.348501 | − | 0.937308i | \(-0.613309\pi\) | ||||
−0.348501 | + | 0.937308i | \(0.613309\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.435157 | 0.0853414 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.74825 | 0.696032 | 0.348016 | − | 0.937489i | \(-0.386856\pi\) | ||||
0.348016 | + | 0.937489i | \(0.386856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.97906 | 0.894265 | 0.447132 | − | 0.894468i | \(-0.352445\pi\) | ||||
0.447132 | + | 0.894468i | \(0.352445\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.979056 | 0.170432 | ||||||||
\(34\) | −2.79881 | −0.479992 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.63591 | 0.762139 | 0.381069 | − | 0.924546i | \(-0.375556\pi\) | ||||
0.381069 | + | 0.924546i | \(0.375556\pi\) | |||||||
\(38\) | 7.34271 | 1.19114 | ||||||||
\(39\) | 0.435157 | 0.0696809 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.94944 | 0.772972 | 0.386486 | − | 0.922295i | \(-0.373689\pi\) | ||||
0.386486 | + | 0.922295i | \(0.373689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.97862 | −1.52172 | −0.760862 | − | 0.648913i | \(-0.775224\pi\) | ||||
−0.760862 | + | 0.648913i | \(0.775224\pi\) | |||||||
\(44\) | 0.979056 | 0.147598 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.34271 | −0.492855 | ||||||||
\(47\) | 4.40554 | 0.642614 | 0.321307 | − | 0.946975i | \(-0.395878\pi\) | ||||
0.321307 | + | 0.946975i | \(0.395878\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.79881 | −0.391912 | ||||||||
\(52\) | 0.435157 | 0.0603455 | ||||||||
\(53\) | 0.657293 | 0.0902861 | 0.0451431 | − | 0.998981i | \(-0.485626\pi\) | ||||
0.0451431 | + | 0.998981i | \(0.485626\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.34271 | 0.972565 | ||||||||
\(58\) | 3.74825 | 0.492169 | ||||||||
\(59\) | 8.27226 | 1.07696 | 0.538478 | − | 0.842639i | \(-0.318999\pi\) | ||||
0.538478 | + | 0.842639i | \(0.318999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3336 | −1.45112 | −0.725559 | − | 0.688160i | \(-0.758419\pi\) | ||||
−0.725559 | + | 0.688160i | \(0.758419\pi\) | |||||||
\(62\) | 4.97906 | 0.632341 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.979056 | 0.120513 | ||||||||
\(67\) | 2.36365 | 0.288766 | 0.144383 | − | 0.989522i | \(-0.453880\pi\) | ||||
0.144383 | + | 0.989522i | \(0.453880\pi\) | |||||||
\(68\) | −2.79881 | −0.339405 | ||||||||
\(69\) | −3.34271 | −0.402415 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1119 | −1.67477 | −0.837387 | − | 0.546610i | \(-0.815918\pi\) | ||||
−0.837387 | + | 0.546610i | \(0.815918\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −15.3928 | −1.80159 | −0.900797 | − | 0.434240i | \(-0.857017\pi\) | ||||
−0.900797 | + | 0.434240i | \(0.857017\pi\) | |||||||
\(74\) | 4.63591 | 0.538914 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.34271 | 0.842266 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.435157 | 0.0492719 | ||||||||
\(79\) | −2.88767 | −0.324888 | −0.162444 | − | 0.986718i | \(-0.551938\pi\) | ||||
−0.162444 | + | 0.986718i | \(0.551938\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.94944 | 0.546574 | ||||||||
\(83\) | 14.3842 | 1.57887 | 0.789433 | − | 0.613837i | \(-0.210375\pi\) | ||||
0.789433 | + | 0.613837i | \(0.210375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.97862 | −1.07602 | ||||||||
\(87\) | 3.74825 | 0.401854 | ||||||||
\(88\) | 0.979056 | 0.104368 | ||||||||
\(89\) | 10.1210 | 1.07282 | 0.536412 | − | 0.843956i | \(-0.319779\pi\) | ||||
0.536412 | + | 0.843956i | \(0.319779\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.34271 | −0.348501 | ||||||||
\(93\) | 4.97906 | 0.516304 | ||||||||
\(94\) | 4.40554 | 0.454397 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 10.6655 | 1.08292 | 0.541460 | − | 0.840726i | \(-0.317872\pi\) | ||||
0.541460 | + | 0.840726i | \(0.317872\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.979056 | 0.0983989 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0328 | 1.39631 | 0.698157 | − | 0.715945i | \(-0.254004\pi\) | ||||
0.698157 | + | 0.715945i | \(0.254004\pi\) | |||||||
\(102\) | −2.79881 | −0.277123 | ||||||||
\(103\) | −10.3842 | −1.02318 | −0.511591 | − | 0.859229i | \(-0.670944\pi\) | ||||
−0.511591 | + | 0.859229i | \(0.670944\pi\) | |||||||
\(104\) | 0.435157 | 0.0426707 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.657293 | 0.0638419 | ||||||||
\(107\) | 20.0410 | 1.93744 | 0.968719 | − | 0.248161i | \(-0.0798262\pi\) | ||||
0.968719 | + | 0.248161i | \(0.0798262\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 18.6564 | 1.78696 | 0.893480 | − | 0.449102i | \(-0.148256\pi\) | ||||
0.893480 | + | 0.449102i | \(0.148256\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.63591 | 0.440021 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.4132 | 0.979587 | 0.489794 | − | 0.871838i | \(-0.337072\pi\) | ||||
0.489794 | + | 0.871838i | \(0.337072\pi\) | |||||||
\(114\) | 7.34271 | 0.687708 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.74825 | 0.348016 | ||||||||
\(117\) | 0.435157 | 0.0402303 | ||||||||
\(118\) | 8.27226 | 0.761523 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0414 | −0.912859 | ||||||||
\(122\) | −11.3336 | −1.02610 | ||||||||
\(123\) | 4.94944 | 0.446276 | ||||||||
\(124\) | 4.97906 | 0.447132 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6987 | −1.03810 | −0.519048 | − | 0.854745i | \(-0.673713\pi\) | ||||
−0.519048 | + | 0.854745i | \(0.673713\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.97862 | −0.878568 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.38459 | 0.470454 | 0.235227 | − | 0.971940i | \(-0.424417\pi\) | ||||
0.235227 | + | 0.971940i | \(0.424417\pi\) | |||||||
\(132\) | 0.979056 | 0.0852159 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.36365 | 0.204188 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.79881 | −0.239996 | ||||||||
\(137\) | 3.68585 | 0.314904 | 0.157452 | − | 0.987527i | \(-0.449672\pi\) | ||||
0.157452 | + | 0.987527i | \(0.449672\pi\) | |||||||
\(138\) | −3.34271 | −0.284550 | ||||||||
\(139\) | 8.15378 | 0.691595 | 0.345797 | − | 0.938309i | \(-0.387608\pi\) | ||||
0.345797 | + | 0.938309i | \(0.387608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.40554 | 0.371013 | ||||||||
\(142\) | −14.1119 | −1.18424 | ||||||||
\(143\) | 0.426043 | 0.0356275 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.3928 | −1.27392 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.63591 | 0.381069 | ||||||||
\(149\) | −15.6774 | −1.28434 | −0.642170 | − | 0.766563i | \(-0.721966\pi\) | ||||
−0.642170 | + | 0.766563i | \(0.721966\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.27226 | 0.347672 | 0.173836 | − | 0.984775i | \(-0.444384\pi\) | ||||
0.173836 | + | 0.984775i | \(0.444384\pi\) | |||||||
\(152\) | 7.34271 | 0.595572 | ||||||||
\(153\) | −2.79881 | −0.226270 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.435157 | 0.0348405 | ||||||||
\(157\) | 15.2498 | 1.21707 | 0.608534 | − | 0.793528i | \(-0.291758\pi\) | ||||
0.608534 | + | 0.793528i | \(0.291758\pi\) | |||||||
\(158\) | −2.88767 | −0.229730 | ||||||||
\(159\) | 0.657293 | 0.0521267 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −7.47599 | −0.585564 | −0.292782 | − | 0.956179i | \(-0.594581\pi\) | ||||
−0.292782 | + | 0.956179i | \(0.594581\pi\) | |||||||
\(164\) | 4.94944 | 0.386486 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.3842 | 1.11643 | ||||||||
\(167\) | −12.6640 | −0.979972 | −0.489986 | − | 0.871730i | \(-0.662998\pi\) | ||||
−0.489986 | + | 0.871730i | \(0.662998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8106 | −0.985434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.34271 | 0.561511 | ||||||||
\(172\) | −9.97862 | −0.760862 | ||||||||
\(173\) | 7.12057 | 0.541367 | 0.270684 | − | 0.962668i | \(-0.412750\pi\) | ||||
0.270684 | + | 0.962668i | \(0.412750\pi\) | |||||||
\(174\) | 3.74825 | 0.284154 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.979056 | 0.0737991 | ||||||||
\(177\) | 8.27226 | 0.621781 | ||||||||
\(178\) | 10.1210 | 0.758602 | ||||||||
\(179\) | 3.26420 | 0.243978 | 0.121989 | − | 0.992531i | \(-0.461073\pi\) | ||||
0.121989 | + | 0.992531i | \(0.461073\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.93823 | 0.144067 | 0.0720337 | − | 0.997402i | \(-0.477051\pi\) | ||||
0.0720337 | + | 0.997402i | \(0.477051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3336 | −0.837803 | ||||||||
\(184\) | −3.34271 | −0.246428 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.97906 | 0.365082 | ||||||||
\(187\) | −2.74019 | −0.200383 | ||||||||
\(188\) | 4.40554 | 0.321307 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.07001 | 0.583925 | 0.291963 | − | 0.956430i | \(-0.405692\pi\) | ||||
0.291963 | + | 0.956430i | \(0.405692\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 1.95811 | 0.140948 | 0.0704740 | − | 0.997514i | \(-0.477549\pi\) | ||||
0.0704740 | + | 0.997514i | \(0.477549\pi\) | |||||||
\(194\) | 10.6655 | 0.765740 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.3418 | −1.23555 | −0.617777 | − | 0.786353i | \(-0.711967\pi\) | ||||
−0.617777 | + | 0.786353i | \(0.711967\pi\) | |||||||
\(198\) | 0.979056 | 0.0695785 | ||||||||
\(199\) | 2.59490 | 0.183948 | 0.0919738 | − | 0.995761i | \(-0.470682\pi\) | ||||
0.0919738 | + | 0.995761i | \(0.470682\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.36365 | 0.166719 | ||||||||
\(202\) | 14.0328 | 0.987343 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.79881 | −0.195956 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.3842 | −0.723498 | ||||||||
\(207\) | −3.34271 | −0.232334 | ||||||||
\(208\) | 0.435157 | 0.0301727 | ||||||||
\(209\) | 7.18892 | 0.497268 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4127 | 1.06106 | 0.530528 | − | 0.847668i | \(-0.321994\pi\) | ||||
0.530528 | + | 0.847668i | \(0.321994\pi\) | |||||||
\(212\) | 0.657293 | 0.0451431 | ||||||||
\(213\) | −14.1119 | −0.966931 | ||||||||
\(214\) | 20.0410 | 1.36998 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.6564 | 1.26357 | ||||||||
\(219\) | −15.3928 | −1.04015 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.21792 | −0.0819263 | ||||||||
\(222\) | 4.63591 | 0.311142 | ||||||||
\(223\) | 7.61497 | 0.509936 | 0.254968 | − | 0.966950i | \(-0.417935\pi\) | ||||
0.254968 | + | 0.966950i | \(0.417935\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.4132 | 0.692673 | ||||||||
\(227\) | −8.34227 | −0.553696 | −0.276848 | − | 0.960914i | \(-0.589290\pi\) | ||||
−0.276848 | + | 0.960914i | \(0.589290\pi\) | |||||||
\(228\) | 7.34271 | 0.486283 | ||||||||
\(229\) | 18.6901 | 1.23507 | 0.617537 | − | 0.786542i | \(-0.288131\pi\) | ||||
0.617537 | + | 0.786542i | \(0.288131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.74825 | 0.246084 | ||||||||
\(233\) | 20.0829 | 1.31567 | 0.657837 | − | 0.753160i | \(-0.271471\pi\) | ||||
0.657837 | + | 0.753160i | \(0.271471\pi\) | |||||||
\(234\) | 0.435157 | 0.0284471 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.27226 | 0.538478 | ||||||||
\(237\) | −2.88767 | −0.187574 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.2714 | −1.44062 | −0.720308 | − | 0.693654i | \(-0.756000\pi\) | ||||
−0.720308 | + | 0.693654i | \(0.756000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.20075 | −0.399426 | −0.199713 | − | 0.979854i | \(-0.564001\pi\) | ||||
−0.199713 | + | 0.979854i | \(0.564001\pi\) | |||||||
\(242\) | −10.0414 | −0.645489 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.3336 | −0.725559 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.94944 | 0.315565 | ||||||||
\(247\) | 3.19523 | 0.203308 | ||||||||
\(248\) | 4.97906 | 0.316170 | ||||||||
\(249\) | 14.3842 | 0.911559 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.6560 | −1.74563 | −0.872815 | − | 0.488051i | \(-0.837708\pi\) | ||||
−0.872815 | + | 0.488051i | \(0.837708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.27270 | −0.205753 | ||||||||
\(254\) | −11.6987 | −0.734044 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.7681 | −0.734076 | −0.367038 | − | 0.930206i | \(-0.619628\pi\) | ||||
−0.367038 | + | 0.930206i | \(0.619628\pi\) | |||||||
\(258\) | −9.97862 | −0.621242 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.74825 | 0.232011 | ||||||||
\(262\) | 5.38459 | 0.332661 | ||||||||
\(263\) | −0.455042 | −0.0280591 | −0.0140295 | − | 0.999902i | \(-0.504466\pi\) | ||||
−0.0140295 | + | 0.999902i | \(0.504466\pi\) | |||||||
\(264\) | 0.979056 | 0.0602567 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.1210 | 0.619396 | ||||||||
\(268\) | 2.36365 | 0.144383 | ||||||||
\(269\) | 26.1375 | 1.59363 | 0.796815 | − | 0.604223i | \(-0.206516\pi\) | ||||
0.796815 | + | 0.604223i | \(0.206516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.7768 | 1.01912 | 0.509559 | − | 0.860436i | \(-0.329808\pi\) | ||||
0.509559 | + | 0.860436i | \(0.329808\pi\) | |||||||
\(272\) | −2.79881 | −0.169703 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.68585 | 0.222671 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.34271 | −0.201207 | ||||||||
\(277\) | −20.7478 | −1.24661 | −0.623307 | − | 0.781977i | \(-0.714211\pi\) | ||||
−0.623307 | + | 0.781977i | \(0.714211\pi\) | |||||||
\(278\) | 8.15378 | 0.489031 | ||||||||
\(279\) | 4.97906 | 0.298088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.3141 | −1.09253 | −0.546265 | − | 0.837612i | \(-0.683951\pi\) | ||||
−0.546265 | + | 0.837612i | \(0.683951\pi\) | |||||||
\(282\) | 4.40554 | 0.262346 | ||||||||
\(283\) | −11.8525 | −0.704560 | −0.352280 | − | 0.935895i | \(-0.614593\pi\) | ||||
−0.352280 | + | 0.935895i | \(0.614593\pi\) | |||||||
\(284\) | −14.1119 | −0.837387 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.426043 | 0.0251925 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −9.16667 | −0.539216 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.6655 | 0.625224 | ||||||||
\(292\) | −15.3928 | −0.900797 | ||||||||
\(293\) | −14.4770 | −0.845758 | −0.422879 | − | 0.906186i | \(-0.638980\pi\) | ||||
−0.422879 | + | 0.906186i | \(0.638980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.63591 | 0.269457 | ||||||||
\(297\) | 0.979056 | 0.0568106 | ||||||||
\(298\) | −15.6774 | −0.908165 | ||||||||
\(299\) | −1.45460 | −0.0841219 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.27226 | 0.245841 | ||||||||
\(303\) | 14.0328 | 0.806162 | ||||||||
\(304\) | 7.34271 | 0.421133 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.79881 | −0.159997 | ||||||||
\(307\) | 30.4252 | 1.73646 | 0.868228 | − | 0.496165i | \(-0.165259\pi\) | ||||
0.868228 | + | 0.496165i | \(0.165259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.3842 | −0.590734 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.02856 | −0.511963 | −0.255981 | − | 0.966682i | \(-0.582399\pi\) | ||||
−0.255981 | + | 0.966682i | \(0.582399\pi\) | |||||||
\(312\) | 0.435157 | 0.0246359 | ||||||||
\(313\) | 17.1732 | 0.970688 | 0.485344 | − | 0.874323i | \(-0.338694\pi\) | ||||
0.485344 | + | 0.874323i | \(0.338694\pi\) | |||||||
\(314\) | 15.2498 | 0.860597 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.88767 | −0.162444 | ||||||||
\(317\) | 2.61541 | 0.146896 | 0.0734479 | − | 0.997299i | \(-0.476600\pi\) | ||||
0.0734479 | + | 0.997299i | \(0.476600\pi\) | |||||||
\(318\) | 0.657293 | 0.0368592 | ||||||||
\(319\) | 3.66974 | 0.205466 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.0410 | 1.11858 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.5508 | −1.14348 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.47599 | −0.414057 | ||||||||
\(327\) | 18.6564 | 1.03170 | ||||||||
\(328\) | 4.94944 | 0.273287 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.7559 | −0.975950 | −0.487975 | − | 0.872857i | \(-0.662264\pi\) | ||||
−0.487975 | + | 0.872857i | \(0.662264\pi\) | |||||||
\(332\) | 14.3842 | 0.789433 | ||||||||
\(333\) | 4.63591 | 0.254046 | ||||||||
\(334\) | −12.6640 | −0.692945 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2304 | −1.31991 | −0.659956 | − | 0.751304i | \(-0.729425\pi\) | ||||
−0.659956 | + | 0.751304i | \(0.729425\pi\) | |||||||
\(338\) | −12.8106 | −0.696807 | ||||||||
\(339\) | 10.4132 | 0.565565 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.87478 | 0.263984 | ||||||||
\(342\) | 7.34271 | 0.397048 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.97862 | −0.538011 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.12057 | 0.382804 | ||||||||
\(347\) | 30.4252 | 1.63331 | 0.816654 | − | 0.577127i | \(-0.195826\pi\) | ||||
0.816654 | + | 0.577127i | \(0.195826\pi\) | |||||||
\(348\) | 3.74825 | 0.200927 | ||||||||
\(349\) | 30.2623 | 1.61990 | 0.809951 | − | 0.586497i | \(-0.199494\pi\) | ||||
0.809951 | + | 0.586497i | \(0.199494\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.435157 | 0.0232270 | ||||||||
\(352\) | 0.979056 | 0.0521839 | ||||||||
\(353\) | 4.37189 | 0.232692 | 0.116346 | − | 0.993209i | \(-0.462882\pi\) | ||||
0.116346 | + | 0.993209i | \(0.462882\pi\) | |||||||
\(354\) | 8.27226 | 0.439666 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.1210 | 0.536412 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.26420 | 0.172519 | ||||||||
\(359\) | −15.6850 | −0.827821 | −0.413911 | − | 0.910318i | \(-0.635837\pi\) | ||||
−0.413911 | + | 0.910318i | \(0.635837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.9153 | 1.83765 | ||||||||
\(362\) | 1.93823 | 0.101871 | ||||||||
\(363\) | −10.0414 | −0.527039 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −11.3336 | −0.592416 | ||||||||
\(367\) | −4.94478 | −0.258116 | −0.129058 | − | 0.991637i | \(-0.541195\pi\) | ||||
−0.129058 | + | 0.991637i | \(0.541195\pi\) | |||||||
\(368\) | −3.34271 | −0.174251 | ||||||||
\(369\) | 4.94944 | 0.257657 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.97906 | 0.258152 | ||||||||
\(373\) | −6.02138 | −0.311775 | −0.155888 | − | 0.987775i | \(-0.549824\pi\) | ||||
−0.155888 | + | 0.987775i | \(0.549824\pi\) | |||||||
\(374\) | −2.74019 | −0.141692 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.40554 | 0.227198 | ||||||||
\(377\) | 1.63108 | 0.0840047 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.8030 | −1.89044 | −0.945222 | − | 0.326429i | \(-0.894155\pi\) | ||||
−0.945222 | + | 0.326429i | \(0.894155\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.6987 | −0.599345 | ||||||||
\(382\) | 8.07001 | 0.412898 | ||||||||
\(383\) | 9.03383 | 0.461607 | 0.230804 | − | 0.973000i | \(-0.425864\pi\) | ||||
0.230804 | + | 0.973000i | \(0.425864\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.95811 | 0.0996653 | ||||||||
\(387\) | −9.97862 | −0.507242 | ||||||||
\(388\) | 10.6655 | 0.541460 | ||||||||
\(389\) | 33.5646 | 1.70179 | 0.850896 | − | 0.525334i | \(-0.176060\pi\) | ||||
0.850896 | + | 0.525334i | \(0.176060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.35560 | 0.473133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.38459 | 0.271617 | ||||||||
\(394\) | −17.3418 | −0.873669 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.979056 | 0.0491994 | ||||||||
\(397\) | −33.9792 | −1.70537 | −0.852685 | − | 0.522426i | \(-0.825027\pi\) | ||||
−0.852685 | + | 0.522426i | \(0.825027\pi\) | |||||||
\(398\) | 2.59490 | 0.130071 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.27226 | −0.213346 | −0.106673 | − | 0.994294i | \(-0.534020\pi\) | ||||
−0.106673 | + | 0.994294i | \(0.534020\pi\) | |||||||
\(402\) | 2.36365 | 0.117888 | ||||||||
\(403\) | 2.16667 | 0.107930 | ||||||||
\(404\) | 14.0328 | 0.698157 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.53882 | 0.224981 | ||||||||
\(408\) | −2.79881 | −0.138562 | ||||||||
\(409\) | 3.63888 | 0.179931 | 0.0899656 | − | 0.995945i | \(-0.471324\pi\) | ||||
0.0899656 | + | 0.995945i | \(0.471324\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.68585 | 0.181810 | ||||||||
\(412\) | −10.3842 | −0.511591 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.34271 | −0.164285 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.435157 | 0.0213353 | ||||||||
\(417\) | 8.15378 | 0.399293 | ||||||||
\(418\) | 7.18892 | 0.351622 | ||||||||
\(419\) | −26.6274 | −1.30083 | −0.650417 | − | 0.759577i | \(-0.725406\pi\) | ||||
−0.650417 | + | 0.759577i | \(0.725406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1880 | −0.740220 | −0.370110 | − | 0.928988i | \(-0.620680\pi\) | ||||
−0.370110 | + | 0.928988i | \(0.620680\pi\) | |||||||
\(422\) | 15.4127 | 0.750279 | ||||||||
\(423\) | 4.40554 | 0.214205 | ||||||||
\(424\) | 0.657293 | 0.0319210 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.1119 | −0.683724 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 20.0410 | 0.968719 | ||||||||
\(429\) | 0.426043 | 0.0205696 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.23125 | −0.203812 | −0.101906 | − | 0.994794i | \(-0.532494\pi\) | ||||
−0.101906 | + | 0.994794i | \(0.532494\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −33.9352 | −1.63082 | −0.815412 | − | 0.578882i | \(-0.803489\pi\) | ||||
−0.815412 | + | 0.578882i | \(0.803489\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.6564 | 0.893480 | ||||||||
\(437\) | −24.5445 | −1.17412 | ||||||||
\(438\) | −15.3928 | −0.735498 | ||||||||
\(439\) | 5.48257 | 0.261669 | 0.130834 | − | 0.991404i | \(-0.458234\pi\) | ||||
0.130834 | + | 0.991404i | \(0.458234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.21792 | −0.0579306 | ||||||||
\(443\) | 1.23081 | 0.0584776 | 0.0292388 | − | 0.999572i | \(-0.490692\pi\) | ||||
0.0292388 | + | 0.999572i | \(0.490692\pi\) | |||||||
\(444\) | 4.63591 | 0.220011 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.61497 | 0.360579 | ||||||||
\(447\) | −15.6774 | −0.741514 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6435 | 0.691071 | 0.345535 | − | 0.938406i | \(-0.387697\pi\) | ||||
0.345535 | + | 0.938406i | \(0.387697\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.84578 | 0.228179 | ||||||||
\(452\) | 10.4132 | 0.489794 | ||||||||
\(453\) | 4.27226 | 0.200728 | ||||||||
\(454\) | −8.34227 | −0.391522 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.34271 | 0.343854 | ||||||||
\(457\) | −31.3289 | −1.46551 | −0.732753 | − | 0.680495i | \(-0.761765\pi\) | ||||
−0.732753 | + | 0.680495i | \(0.761765\pi\) | |||||||
\(458\) | 18.6901 | 0.873329 | ||||||||
\(459\) | −2.79881 | −0.130637 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.7667 | −0.594602 | −0.297301 | − | 0.954784i | \(-0.596087\pi\) | ||||
−0.297301 | + | 0.954784i | \(0.596087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.7112 | −1.24137 | −0.620687 | − | 0.784058i | \(-0.713146\pi\) | ||||
−0.620687 | + | 0.784058i | \(0.713146\pi\) | |||||||
\(464\) | 3.74825 | 0.174008 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.0829 | 0.930322 | ||||||||
\(467\) | 37.6141 | 1.74057 | 0.870286 | − | 0.492546i | \(-0.163934\pi\) | ||||
0.870286 | + | 0.492546i | \(0.163934\pi\) | |||||||
\(468\) | 0.435157 | 0.0201152 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.2498 | 0.702675 | ||||||||
\(472\) | 8.27226 | 0.380762 | ||||||||
\(473\) | −9.76963 | −0.449208 | ||||||||
\(474\) | −2.88767 | −0.132635 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.657293 | 0.0300954 | ||||||||
\(478\) | −22.2714 | −1.01867 | ||||||||
\(479\) | 23.8235 | 1.08852 | 0.544262 | − | 0.838915i | \(-0.316810\pi\) | ||||
0.544262 | + | 0.838915i | \(0.316810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.01735 | 0.0919833 | ||||||||
\(482\) | −6.20075 | −0.282437 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0414 | −0.456429 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −3.75674 | −0.170234 | −0.0851170 | − | 0.996371i | \(-0.527126\pi\) | ||||
−0.0851170 | + | 0.996371i | \(0.527126\pi\) | |||||||
\(488\) | −11.3336 | −0.513048 | ||||||||
\(489\) | −7.47599 | −0.338076 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00762 | 0.0906025 | 0.0453012 | − | 0.998973i | \(-0.485575\pi\) | ||||
0.0453012 | + | 0.998973i | \(0.485575\pi\) | |||||||
\(492\) | 4.94944 | 0.223138 | ||||||||
\(493\) | −10.4906 | −0.472474 | ||||||||
\(494\) | 3.19523 | 0.143760 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.97906 | 0.223566 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.3842 | 0.644569 | ||||||||
\(499\) | −0.628294 | −0.0281263 | −0.0140632 | − | 0.999901i | \(-0.504477\pi\) | ||||
−0.0140632 | + | 0.999901i | \(0.504477\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.6640 | −0.565787 | ||||||||
\(502\) | −27.6560 | −1.23435 | ||||||||
\(503\) | −28.9911 | −1.29265 | −0.646324 | − | 0.763063i | \(-0.723695\pi\) | ||||
−0.646324 | + | 0.763063i | \(0.723695\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.27270 | −0.145489 | ||||||||
\(507\) | −12.8106 | −0.568940 | ||||||||
\(508\) | −11.6987 | −0.519048 | ||||||||
\(509\) | 15.5056 | 0.687274 | 0.343637 | − | 0.939103i | \(-0.388341\pi\) | ||||
0.343637 | + | 0.939103i | \(0.388341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.34271 | 0.324188 | ||||||||
\(514\) | −11.7681 | −0.519070 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.97862 | −0.439284 | ||||||||
\(517\) | 4.31327 | 0.189697 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.12057 | 0.312558 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.5532 | 0.593776 | 0.296888 | − | 0.954912i | \(-0.404051\pi\) | ||||
0.296888 | + | 0.954912i | \(0.404051\pi\) | |||||||
\(522\) | 3.74825 | 0.164056 | ||||||||
\(523\) | −22.4542 | −0.981852 | −0.490926 | − | 0.871201i | \(-0.663341\pi\) | ||||
−0.490926 | + | 0.871201i | \(0.663341\pi\) | |||||||
\(524\) | 5.38459 | 0.235227 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.455042 | −0.0198408 | ||||||||
\(527\) | −13.9354 | −0.607037 | ||||||||
\(528\) | 0.979056 | 0.0426080 | ||||||||
\(529\) | −11.8263 | −0.514187 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.27226 | 0.358985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.15378 | 0.0932907 | ||||||||
\(534\) | 10.1210 | 0.437979 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.36365 | 0.102094 | ||||||||
\(537\) | 3.26420 | 0.140861 | ||||||||
\(538\) | 26.1375 | 1.12687 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.8111 | 0.464804 | 0.232402 | − | 0.972620i | \(-0.425341\pi\) | ||||
0.232402 | + | 0.972620i | \(0.425341\pi\) | |||||||
\(542\) | 16.7768 | 0.720625 | ||||||||
\(543\) | 1.93823 | 0.0831773 | ||||||||
\(544\) | −2.79881 | −0.119998 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.1881 | −1.03421 | −0.517103 | − | 0.855923i | \(-0.672990\pi\) | ||||
−0.517103 | + | 0.855923i | \(0.672990\pi\) | |||||||
\(548\) | 3.68585 | 0.157452 | ||||||||
\(549\) | −11.3336 | −0.483706 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.5223 | 1.17249 | ||||||||
\(552\) | −3.34271 | −0.142275 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −20.7478 | −0.881490 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.15378 | 0.345797 | ||||||||
\(557\) | −26.1529 | −1.10813 | −0.554067 | − | 0.832472i | \(-0.686925\pi\) | ||||
−0.554067 | + | 0.832472i | \(0.686925\pi\) | |||||||
\(558\) | 4.97906 | 0.210780 | ||||||||
\(559\) | −4.34227 | −0.183658 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.74019 | −0.115691 | ||||||||
\(562\) | −18.3141 | −0.772536 | ||||||||
\(563\) | −10.5864 | −0.446164 | −0.223082 | − | 0.974800i | \(-0.571612\pi\) | ||||
−0.223082 | + | 0.974800i | \(0.571612\pi\) | |||||||
\(564\) | 4.40554 | 0.185507 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.8525 | −0.498199 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.1119 | −0.592122 | ||||||||
\(569\) | 15.6440 | 0.655829 | 0.327915 | − | 0.944707i | \(-0.393654\pi\) | ||||
0.327915 | + | 0.944707i | \(0.393654\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.50982 | 0.356125 | 0.178062 | − | 0.984019i | \(-0.443017\pi\) | ||||
0.178062 | + | 0.984019i | \(0.443017\pi\) | |||||||
\(572\) | 0.426043 | 0.0178138 | ||||||||
\(573\) | 8.07001 | 0.337129 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 9.67798 | 0.402900 | 0.201450 | − | 0.979499i | \(-0.435435\pi\) | ||||
0.201450 | + | 0.979499i | \(0.435435\pi\) | |||||||
\(578\) | −9.16667 | −0.381283 | ||||||||
\(579\) | 1.95811 | 0.0813764 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.6655 | 0.442100 | ||||||||
\(583\) | 0.643527 | 0.0266522 | ||||||||
\(584\) | −15.3928 | −0.636960 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.4770 | −0.598041 | ||||||||
\(587\) | −16.3013 | −0.672825 | −0.336412 | − | 0.941715i | \(-0.609214\pi\) | ||||
−0.336412 | + | 0.941715i | \(0.609214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.5598 | 1.50642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.3418 | −0.713348 | ||||||||
\(592\) | 4.63591 | 0.190535 | ||||||||
\(593\) | −12.4802 | −0.512500 | −0.256250 | − | 0.966610i | \(-0.582487\pi\) | ||||
−0.256250 | + | 0.966610i | \(0.582487\pi\) | |||||||
\(594\) | 0.979056 | 0.0401712 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.6774 | −0.642170 | ||||||||
\(597\) | 2.59490 | 0.106202 | ||||||||
\(598\) | −1.45460 | −0.0594832 | ||||||||
\(599\) | 40.7545 | 1.66519 | 0.832593 | − | 0.553886i | \(-0.186856\pi\) | ||||
0.832593 | + | 0.553886i | \(0.186856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.94541 | −0.201727 | −0.100864 | − | 0.994900i | \(-0.532161\pi\) | ||||
−0.100864 | + | 0.994900i | \(0.532161\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.36365 | 0.0962553 | ||||||||
\(604\) | 4.27226 | 0.173836 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.0328 | 0.570042 | ||||||||
\(607\) | −0.871555 | −0.0353753 | −0.0176877 | − | 0.999844i | \(-0.505630\pi\) | ||||
−0.0176877 | + | 0.999844i | \(0.505630\pi\) | |||||||
\(608\) | 7.34271 | 0.297786 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.91710 | 0.0775577 | ||||||||
\(612\) | −2.79881 | −0.113135 | ||||||||
\(613\) | 36.9007 | 1.49041 | 0.745203 | − | 0.666838i | \(-0.232353\pi\) | ||||
0.745203 | + | 0.666838i | \(0.232353\pi\) | |||||||
\(614\) | 30.4252 | 1.22786 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.6911 | 1.15506 | 0.577530 | − | 0.816369i | \(-0.304016\pi\) | ||||
0.577530 | + | 0.816369i | \(0.304016\pi\) | |||||||
\(618\) | −10.3842 | −0.417712 | ||||||||
\(619\) | 6.31415 | 0.253787 | 0.126894 | − | 0.991916i | \(-0.459499\pi\) | ||||
0.126894 | + | 0.991916i | \(0.459499\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.34271 | −0.134138 | ||||||||
\(622\) | −9.02856 | −0.362012 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.435157 | 0.0174202 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.1732 | 0.686380 | ||||||||
\(627\) | 7.18892 | 0.287098 | ||||||||
\(628\) | 15.2498 | 0.608534 | ||||||||
\(629\) | −12.9750 | −0.517348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.237559 | −0.00945707 | −0.00472853 | − | 0.999989i | \(-0.501505\pi\) | ||||
−0.00472853 | + | 0.999989i | \(0.501505\pi\) | |||||||
\(632\) | −2.88767 | −0.114865 | ||||||||
\(633\) | 15.4127 | 0.612600 | ||||||||
\(634\) | 2.61541 | 0.103871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.657293 | 0.0260634 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.66974 | 0.145287 | ||||||||
\(639\) | −14.1119 | −0.558258 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.3490 | −0.606250 | −0.303125 | − | 0.952951i | \(-0.598030\pi\) | ||||
−0.303125 | + | 0.952951i | \(0.598030\pi\) | |||||||
\(642\) | 20.0410 | 0.790956 | ||||||||
\(643\) | −8.77577 | −0.346083 | −0.173041 | − | 0.984915i | \(-0.555359\pi\) | ||||
−0.173041 | + | 0.984915i | \(0.555359\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.5508 | −0.808562 | ||||||||
\(647\) | 19.2504 | 0.756813 | 0.378406 | − | 0.925640i | \(-0.376472\pi\) | ||||
0.378406 | + | 0.925640i | \(0.376472\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 8.09901 | 0.317914 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.47599 | −0.292782 | ||||||||
\(653\) | 7.45460 | 0.291721 | 0.145861 | − | 0.989305i | \(-0.453405\pi\) | ||||
0.145861 | + | 0.989305i | \(0.453405\pi\) | |||||||
\(654\) | 18.6564 | 0.729524 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.94944 | 0.193243 | ||||||||
\(657\) | −15.3928 | −0.600532 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.93717 | 0.114416 | 0.0572079 | − | 0.998362i | \(-0.481780\pi\) | ||||
0.0572079 | + | 0.998362i | \(0.481780\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.6361 | −0.919337 | −0.459669 | − | 0.888090i | \(-0.652032\pi\) | ||||
−0.459669 | + | 0.888090i | \(0.652032\pi\) | |||||||
\(662\) | −17.7559 | −0.690101 | ||||||||
\(663\) | −1.21792 | −0.0473002 | ||||||||
\(664\) | 14.3842 | 0.558214 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.63591 | 0.179638 | ||||||||
\(667\) | −12.5293 | −0.485136 | ||||||||
\(668\) | −12.6640 | −0.489986 | ||||||||
\(669\) | 7.61497 | 0.294412 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.0962 | −0.428365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.9568 | −1.96424 | −0.982120 | − | 0.188256i | \(-0.939717\pi\) | ||||
−0.982120 | + | 0.188256i | \(0.939717\pi\) | |||||||
\(674\) | −24.2304 | −0.933319 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8106 | −0.492717 | ||||||||
\(677\) | −5.23992 | −0.201387 | −0.100693 | − | 0.994918i | \(-0.532106\pi\) | ||||
−0.100693 | + | 0.994918i | \(0.532106\pi\) | |||||||
\(678\) | 10.4132 | 0.399915 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.34227 | −0.319676 | ||||||||
\(682\) | 4.87478 | 0.186665 | ||||||||
\(683\) | 32.2648 | 1.23458 | 0.617289 | − | 0.786736i | \(-0.288231\pi\) | ||||
0.617289 | + | 0.786736i | \(0.288231\pi\) | |||||||
\(684\) | 7.34271 | 0.280755 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.6901 | 0.713071 | ||||||||
\(688\) | −9.97862 | −0.380431 | ||||||||
\(689\) | 0.286026 | 0.0108967 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.4470 | −0.777840 | −0.388920 | − | 0.921272i | \(-0.627152\pi\) | ||||
−0.388920 | + | 0.921272i | \(0.627152\pi\) | |||||||
\(692\) | 7.12057 | 0.270684 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.4252 | 1.15492 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.74825 | 0.142077 | ||||||||
\(697\) | −13.8525 | −0.524702 | ||||||||
\(698\) | 30.2623 | 1.14544 | ||||||||
\(699\) | 20.0829 | 0.759605 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.4969 | −0.585311 | −0.292655 | − | 0.956218i | \(-0.594539\pi\) | ||||
−0.292655 | + | 0.956218i | \(0.594539\pi\) | |||||||
\(702\) | 0.435157 | 0.0164240 | ||||||||
\(703\) | 34.0401 | 1.28385 | ||||||||
\(704\) | 0.979056 | 0.0368996 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.37189 | 0.164538 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.27226 | 0.310891 | ||||||||
\(709\) | 38.9212 | 1.46172 | 0.730859 | − | 0.682529i | \(-0.239120\pi\) | ||||
0.730859 | + | 0.682529i | \(0.239120\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.88767 | −0.108296 | ||||||||
\(712\) | 10.1210 | 0.379301 | ||||||||
\(713\) | −16.6435 | −0.623305 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.26420 | 0.121989 | ||||||||
\(717\) | −22.2714 | −0.831740 | ||||||||
\(718\) | −15.6850 | −0.585358 | ||||||||
\(719\) | 3.53119 | 0.131691 | 0.0658456 | − | 0.997830i | \(-0.479026\pi\) | ||||
0.0658456 | + | 0.997830i | \(0.479026\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 34.9153 | 1.29941 | ||||||||
\(723\) | −6.20075 | −0.230608 | ||||||||
\(724\) | 1.93823 | 0.0720337 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.0414 | −0.372673 | ||||||||
\(727\) | −45.2934 | −1.67984 | −0.839919 | − | 0.542712i | \(-0.817398\pi\) | ||||
−0.839919 | + | 0.542712i | \(0.817398\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.9282 | 1.03296 | ||||||||
\(732\) | −11.3336 | −0.418902 | ||||||||
\(733\) | −48.5462 | −1.79309 | −0.896547 | − | 0.442949i | \(-0.853932\pi\) | ||||
−0.896547 | + | 0.442949i | \(0.853932\pi\) | |||||||
\(734\) | −4.94478 | −0.182515 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.34271 | −0.123214 | ||||||||
\(737\) | 2.31415 | 0.0852427 | ||||||||
\(738\) | 4.94944 | 0.182191 | ||||||||
\(739\) | 25.7969 | 0.948953 | 0.474477 | − | 0.880268i | \(-0.342637\pi\) | ||||
0.474477 | + | 0.880268i | \(0.342637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.19523 | 0.117380 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.7192 | −1.05361 | −0.526803 | − | 0.849987i | \(-0.676610\pi\) | ||||
−0.526803 | + | 0.849987i | \(0.676610\pi\) | |||||||
\(744\) | 4.97906 | 0.182541 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.02138 | −0.220458 | ||||||||
\(747\) | 14.3842 | 0.526289 | ||||||||
\(748\) | −2.74019 | −0.100191 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.1876 | −1.24752 | −0.623762 | − | 0.781615i | \(-0.714396\pi\) | ||||
−0.623762 | + | 0.781615i | \(0.714396\pi\) | |||||||
\(752\) | 4.40554 | 0.160653 | ||||||||
\(753\) | −27.6560 | −1.00784 | ||||||||
\(754\) | 1.63108 | 0.0594003 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.4622 | −1.50697 | −0.753485 | − | 0.657465i | \(-0.771629\pi\) | ||||
−0.753485 | + | 0.657465i | \(0.771629\pi\) | |||||||
\(758\) | −36.8030 | −1.33675 | ||||||||
\(759\) | −3.27270 | −0.118791 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.6941 | −1.00391 | −0.501955 | − | 0.864894i | \(-0.667386\pi\) | ||||
−0.501955 | + | 0.864894i | \(0.667386\pi\) | |||||||
\(762\) | −11.6987 | −0.423801 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.07001 | 0.291963 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.03383 | 0.326406 | ||||||||
\(767\) | 3.59973 | 0.129979 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −9.74001 | −0.351234 | −0.175617 | − | 0.984459i | \(-0.556192\pi\) | ||||
−0.175617 | + | 0.984459i | \(0.556192\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.7681 | −0.423819 | ||||||||
\(772\) | 1.95811 | 0.0704740 | ||||||||
\(773\) | −30.6171 | −1.10122 | −0.550610 | − | 0.834763i | \(-0.685605\pi\) | ||||
−0.550610 | + | 0.834763i | \(0.685605\pi\) | |||||||
\(774\) | −9.97862 | −0.358674 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.6655 | 0.382870 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.5646 | 1.20335 | ||||||||
\(779\) | 36.3423 | 1.30210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8163 | −0.494388 | ||||||||
\(782\) | 9.35560 | 0.334555 | ||||||||
\(783\) | 3.74825 | 0.133951 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.38459 | 0.192062 | ||||||||
\(787\) | −15.7977 | −0.563129 | −0.281564 | − | 0.959542i | \(-0.590853\pi\) | ||||
−0.281564 | + | 0.959542i | \(0.590853\pi\) | |||||||
\(788\) | −17.3418 | −0.617777 | ||||||||
\(789\) | −0.455042 | −0.0161999 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.979056 | 0.0347892 | ||||||||
\(793\) | −4.93190 | −0.175137 | ||||||||
\(794\) | −33.9792 | −1.20588 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.59490 | 0.0919738 | ||||||||
\(797\) | −47.6651 | −1.68838 | −0.844192 | − | 0.536041i | \(-0.819919\pi\) | ||||
−0.844192 | + | 0.536041i | \(0.819919\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.3303 | −0.436213 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.1210 | 0.357608 | ||||||||
\(802\) | −4.27226 | −0.150859 | ||||||||
\(803\) | −15.0704 | −0.531825 | ||||||||
\(804\) | 2.36365 | 0.0833595 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.16667 | 0.0763178 | ||||||||
\(807\) | 26.1375 | 0.920083 | ||||||||
\(808\) | 14.0328 | 0.493671 | ||||||||
\(809\) | −17.2709 | −0.607214 | −0.303607 | − | 0.952797i | \(-0.598191\pi\) | ||||
−0.303607 | + | 0.952797i | \(0.598191\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.7901 | 0.519351 | 0.259676 | − | 0.965696i | \(-0.416384\pi\) | ||||
0.259676 | + | 0.965696i | \(0.416384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.7768 | 0.588388 | ||||||||
\(814\) | 4.53882 | 0.159085 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.79881 | −0.0979779 | ||||||||
\(817\) | −73.2701 | −2.56340 | ||||||||
\(818\) | 3.63888 | 0.127231 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.6917 | −1.59465 | −0.797326 | − | 0.603549i | \(-0.793753\pi\) | ||||
−0.797326 | + | 0.603549i | \(0.793753\pi\) | |||||||
\(822\) | 3.68585 | 0.128559 | ||||||||
\(823\) | −4.99386 | −0.174075 | −0.0870375 | − | 0.996205i | \(-0.527740\pi\) | ||||
−0.0870375 | + | 0.996205i | \(0.527740\pi\) | |||||||
\(824\) | −10.3842 | −0.361749 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.5946 | 1.86367 | 0.931834 | − | 0.362885i | \(-0.118208\pi\) | ||||
0.931834 | + | 0.362885i | \(0.118208\pi\) | |||||||
\(828\) | −3.34271 | −0.116167 | ||||||||
\(829\) | 1.16692 | 0.0405288 | 0.0202644 | − | 0.999795i | \(-0.493549\pi\) | ||||
0.0202644 | + | 0.999795i | \(0.493549\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.7478 | −0.719733 | ||||||||
\(832\) | 0.435157 | 0.0150864 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.15378 | 0.282342 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.18892 | 0.248634 | ||||||||
\(837\) | 4.97906 | 0.172101 | ||||||||
\(838\) | −26.6274 | −0.919829 | ||||||||
\(839\) | −31.2709 | −1.07959 | −0.539796 | − | 0.841796i | \(-0.681499\pi\) | ||||
−0.539796 | + | 0.841796i | \(0.681499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.9507 | −0.515540 | ||||||||
\(842\) | −15.1880 | −0.523415 | ||||||||
\(843\) | −18.3141 | −0.630773 | ||||||||
\(844\) | 15.4127 | 0.530528 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.40554 | 0.151466 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.657293 | 0.0225715 | ||||||||
\(849\) | −11.8525 | −0.406778 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.4965 | −0.531213 | ||||||||
\(852\) | −14.1119 | −0.483466 | ||||||||
\(853\) | 11.3154 | 0.387431 | 0.193715 | − | 0.981058i | \(-0.437946\pi\) | ||||
0.193715 | + | 0.981058i | \(0.437946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.0410 | 0.684988 | ||||||||
\(857\) | −36.8572 | −1.25902 | −0.629508 | − | 0.776994i | \(-0.716744\pi\) | ||||
−0.629508 | + | 0.776994i | \(0.716744\pi\) | |||||||
\(858\) | 0.426043 | 0.0145449 | ||||||||
\(859\) | 18.6974 | 0.637948 | 0.318974 | − | 0.947763i | \(-0.396662\pi\) | ||||
0.318974 | + | 0.947763i | \(0.396662\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.23125 | −0.144117 | ||||||||
\(863\) | 29.5384 | 1.00550 | 0.502749 | − | 0.864432i | \(-0.332322\pi\) | ||||
0.502749 | + | 0.864432i | \(0.332322\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −33.9352 | −1.15317 | ||||||||
\(867\) | −9.16667 | −0.311317 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.82719 | −0.0959057 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.02856 | 0.0348514 | ||||||||
\(872\) | 18.6564 | 0.631786 | ||||||||
\(873\) | 10.6655 | 0.360973 | ||||||||
\(874\) | −24.5445 | −0.830231 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.3928 | −0.520076 | ||||||||
\(877\) | −14.2581 | −0.481461 | −0.240730 | − | 0.970592i | \(-0.577387\pi\) | ||||
−0.240730 | + | 0.970592i | \(0.577387\pi\) | |||||||
\(878\) | 5.48257 | 0.185028 | ||||||||
\(879\) | −14.4770 | −0.488299 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.2744 | 1.05366 | 0.526830 | − | 0.849971i | \(-0.323380\pi\) | ||||
0.526830 | + | 0.849971i | \(0.323380\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.3566 | 1.12254 | 0.561270 | − | 0.827633i | \(-0.310313\pi\) | ||||
0.561270 | + | 0.827633i | \(0.310313\pi\) | |||||||
\(884\) | −1.21792 | −0.0409631 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.23081 | 0.0413499 | ||||||||
\(887\) | 42.1444 | 1.41507 | 0.707535 | − | 0.706678i | \(-0.249807\pi\) | ||||
0.707535 | + | 0.706678i | \(0.249807\pi\) | |||||||
\(888\) | 4.63591 | 0.155571 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.979056 | 0.0327996 | ||||||||
\(892\) | 7.61497 | 0.254968 | ||||||||
\(893\) | 32.3486 | 1.08250 | ||||||||
\(894\) | −15.6774 | −0.524329 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.45460 | −0.0485678 | ||||||||
\(898\) | 14.6435 | 0.488661 | ||||||||
\(899\) | 18.6627 | 0.622437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.83964 | −0.0612872 | ||||||||
\(902\) | 4.84578 | 0.161347 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.4132 | 0.346336 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.27226 | 0.141936 | ||||||||
\(907\) | 55.9840 | 1.85892 | 0.929460 | − | 0.368923i | \(-0.120273\pi\) | ||||
0.929460 | + | 0.368923i | \(0.120273\pi\) | |||||||
\(908\) | −8.34227 | −0.276848 | ||||||||
\(909\) | 14.0328 | 0.465438 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4389 | 1.00849 | 0.504243 | − | 0.863562i | \(-0.331771\pi\) | ||||
0.504243 | + | 0.863562i | \(0.331771\pi\) | |||||||
\(912\) | 7.34271 | 0.243141 | ||||||||
\(913\) | 14.0829 | 0.466076 | ||||||||
\(914\) | −31.3289 | −1.03627 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.6901 | 0.617537 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.79881 | −0.0923744 | ||||||||
\(919\) | −28.1538 | −0.928708 | −0.464354 | − | 0.885650i | \(-0.653713\pi\) | ||||
−0.464354 | + | 0.885650i | \(0.653713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.4252 | 1.00254 | ||||||||
\(922\) | −12.7667 | −0.420447 | ||||||||
\(923\) | −6.14089 | −0.202130 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −26.7112 | −0.877784 | ||||||||
\(927\) | −10.3842 | −0.341060 | ||||||||
\(928\) | 3.74825 | 0.123042 | ||||||||
\(929\) | −25.8955 | −0.849603 | −0.424801 | − | 0.905287i | \(-0.639656\pi\) | ||||
−0.424801 | + | 0.905287i | \(0.639656\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.0829 | 0.657837 | ||||||||
\(933\) | −9.02856 | −0.295582 | ||||||||
\(934\) | 37.6141 | 1.23077 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.435157 | 0.0142236 | ||||||||
\(937\) | 48.1184 | 1.57196 | 0.785979 | − | 0.618253i | \(-0.212159\pi\) | ||||
0.785979 | + | 0.618253i | \(0.212159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.1732 | 0.560427 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.2066 | 1.70189 | 0.850944 | − | 0.525257i | \(-0.176031\pi\) | ||||
0.850944 | + | 0.525257i | \(0.176031\pi\) | |||||||
\(942\) | 15.2498 | 0.496866 | ||||||||
\(943\) | −16.5445 | −0.538764 | ||||||||
\(944\) | 8.27226 | 0.269239 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.76963 | −0.317638 | ||||||||
\(947\) | −20.2995 | −0.659645 | −0.329823 | − | 0.944043i | \(-0.606989\pi\) | ||||
−0.329823 | + | 0.944043i | \(0.606989\pi\) | |||||||
\(948\) | −2.88767 | −0.0937870 | ||||||||
\(949\) | −6.69830 | −0.217436 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.61541 | 0.0848103 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.9511 | −0.549100 | −0.274550 | − | 0.961573i | \(-0.588529\pi\) | ||||
−0.274550 | + | 0.961573i | \(0.588529\pi\) | |||||||
\(954\) | 0.657293 | 0.0212806 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.2714 | −0.720308 | ||||||||
\(957\) | 3.66974 | 0.118626 | ||||||||
\(958\) | 23.8235 | 0.769703 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.20900 | −0.200290 | ||||||||
\(962\) | 2.01735 | 0.0650420 | ||||||||
\(963\) | 20.0410 | 0.645813 | ||||||||
\(964\) | −6.20075 | −0.199713 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.0294 | −0.740577 | −0.370288 | − | 0.928917i | \(-0.620741\pi\) | ||||
−0.370288 | + | 0.928917i | \(0.620741\pi\) | |||||||
\(968\) | −10.0414 | −0.322744 | ||||||||
\(969\) | −20.5508 | −0.660188 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.3770 | 0.397196 | 0.198598 | − | 0.980081i | \(-0.436361\pi\) | ||||
0.198598 | + | 0.980081i | \(0.436361\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.75674 | −0.120374 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.3336 | −0.362779 | ||||||||
\(977\) | −1.00614 | −0.0321893 | −0.0160946 | − | 0.999870i | \(-0.505123\pi\) | ||||
−0.0160946 | + | 0.999870i | \(0.505123\pi\) | |||||||
\(978\) | −7.47599 | −0.239056 | ||||||||
\(979\) | 9.90904 | 0.316694 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.6564 | 0.595654 | ||||||||
\(982\) | 2.00762 | 0.0640656 | ||||||||
\(983\) | −42.1444 | −1.34420 | −0.672099 | − | 0.740461i | \(-0.734607\pi\) | ||||
−0.672099 | + | 0.740461i | \(0.734607\pi\) | |||||||
\(984\) | 4.94944 | 0.157782 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.4906 | −0.334089 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.19523 | 0.101654 | ||||||||
\(989\) | 33.3556 | 1.06065 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.0691 | −1.08224 | −0.541121 | − | 0.840945i | \(-0.682000\pi\) | ||||
−0.541121 | + | 0.840945i | \(0.682000\pi\) | |||||||
\(992\) | 4.97906 | 0.158085 | ||||||||
\(993\) | −17.7559 | −0.563465 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.3842 | 0.455779 | ||||||||
\(997\) | −6.02076 | −0.190679 | −0.0953397 | − | 0.995445i | \(-0.530394\pi\) | ||||
−0.0953397 | + | 0.995445i | \(0.530394\pi\) | |||||||
\(998\) | −0.628294 | −0.0198883 | ||||||||
\(999\) | 4.63591 | 0.146674 |
(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 | 7350.2.a.du.1.3 | 4 | ||
5.2 | odd | 4 | 1470.2.g.k.589.5 | yes | 8 | ||
5.3 | odd | 4 | 1470.2.g.k.589.1 | yes | 8 | ||
5.4 | even | 2 | 7350.2.a.dr.1.3 | 4 | |||
7.6 | odd | 2 | 7350.2.a.dt.1.3 | 4 | |||
35.2 | odd | 12 | 1470.2.n.k.949.7 | 16 | |||
35.3 | even | 12 | 1470.2.n.l.79.6 | 16 | |||
35.12 | even | 12 | 1470.2.n.l.949.6 | 16 | |||
35.13 | even | 4 | 1470.2.g.j.589.4 | ✓ | 8 | ||
35.17 | even | 12 | 1470.2.n.l.79.1 | 16 | |||
35.18 | odd | 12 | 1470.2.n.k.79.7 | 16 | |||
35.23 | odd | 12 | 1470.2.n.k.949.4 | 16 | |||
35.27 | even | 4 | 1470.2.g.j.589.8 | yes | 8 | ||
35.32 | odd | 12 | 1470.2.n.k.79.4 | 16 | |||
35.33 | even | 12 | 1470.2.n.l.949.1 | 16 | |||
35.34 | odd | 2 | 7350.2.a.ds.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.g.j.589.4 | ✓ | 8 | 35.13 | even | 4 | ||
1470.2.g.j.589.8 | yes | 8 | 35.27 | even | 4 | ||
1470.2.g.k.589.1 | yes | 8 | 5.3 | odd | 4 | ||
1470.2.g.k.589.5 | yes | 8 | 5.2 | odd | 4 | ||
1470.2.n.k.79.4 | 16 | 35.32 | odd | 12 | |||
1470.2.n.k.79.7 | 16 | 35.18 | odd | 12 | |||
1470.2.n.k.949.4 | 16 | 35.23 | odd | 12 | |||
1470.2.n.k.949.7 | 16 | 35.2 | odd | 12 | |||
1470.2.n.l.79.1 | 16 | 35.17 | even | 12 | |||
1470.2.n.l.79.6 | 16 | 35.3 | even | 12 | |||
1470.2.n.l.949.1 | 16 | 35.33 | even | 12 | |||
1470.2.n.l.949.6 | 16 | 35.12 | even | 12 | |||
7350.2.a.dr.1.3 | 4 | 5.4 | even | 2 | |||
7350.2.a.ds.1.3 | 4 | 35.34 | odd | 2 | |||
7350.2.a.dt.1.3 | 4 | 7.6 | odd | 2 | |||
7350.2.a.du.1.3 | 4 | 1.1 | even | 1 | trivial |