Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.42048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 13x^{2} + 8x + 34 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.94433\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(5\) | 3.82843 | 1.71212 | 0.856062 | − | 0.516873i | \(-0.172904\pi\) | ||||
0.856062 | + | 0.516873i | \(0.172904\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.82843 | 1.21065 | ||||||||
\(11\) | 5.27981 | 1.59192 | 0.795962 | − | 0.605347i | \(-0.206966\pi\) | ||||
0.795962 | + | 0.605347i | \(0.206966\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.35854 | −1.20884 | −0.604421 | − | 0.796665i | \(-0.706596\pi\) | ||||
−0.604421 | + | 0.796665i | \(0.706596\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.82843 | −0.988496 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.46988 | 0.599035 | 0.299517 | − | 0.954091i | \(-0.403174\pi\) | ||||
0.299517 | + | 0.954091i | \(0.403174\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.92127 | 0.440770 | 0.220385 | − | 0.975413i | \(-0.429269\pi\) | ||||
0.220385 | + | 0.975413i | \(0.429269\pi\) | |||||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.27981 | 1.12566 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 9.65685 | 1.93137 | ||||||||
\(26\) | −4.35854 | −0.854781 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.35854 | −0.252275 | −0.126138 | − | 0.992013i | \(-0.540258\pi\) | ||||
−0.126138 | + | 0.992013i | \(0.540258\pi\) | |||||||
\(30\) | −3.82843 | −0.698972 | ||||||||
\(31\) | 1.43727 | 0.258142 | 0.129071 | − | 0.991635i | \(-0.458801\pi\) | ||||
0.129071 | + | 0.991635i | \(0.458801\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.27981 | −0.919098 | ||||||||
\(34\) | 2.46988 | 0.423582 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.63836 | 1.09134 | 0.545670 | − | 0.838000i | \(-0.316275\pi\) | ||||
0.545670 | + | 0.838000i | \(0.316275\pi\) | |||||||
\(38\) | 1.92127 | 0.311671 | ||||||||
\(39\) | 4.35854 | 0.697926 | ||||||||
\(40\) | 3.82843 | 0.605327 | ||||||||
\(41\) | −1.92127 | −0.300052 | −0.150026 | − | 0.988682i | \(-0.547936\pi\) | ||||
−0.150026 | + | 0.988682i | \(0.547936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.21648 | −1.25300 | −0.626501 | − | 0.779421i | \(-0.715514\pi\) | ||||
−0.626501 | + | 0.779421i | \(0.715514\pi\) | |||||||
\(44\) | 5.27981 | 0.795962 | ||||||||
\(45\) | 3.82843 | 0.570708 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 6.99690 | 1.02060 | 0.510301 | − | 0.859996i | \(-0.329534\pi\) | ||||
0.510301 | + | 0.859996i | \(0.329534\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.65685 | 1.36569 | ||||||||
\(51\) | −2.46988 | −0.345853 | ||||||||
\(52\) | −4.35854 | −0.604421 | ||||||||
\(53\) | −2.88866 | −0.396788 | −0.198394 | − | 0.980122i | \(-0.563573\pi\) | ||||
−0.198394 | + | 0.980122i | \(0.563573\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 20.2134 | 2.72557 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.92127 | −0.254479 | ||||||||
\(58\) | −1.35854 | −0.178385 | ||||||||
\(59\) | −4.29831 | −0.559592 | −0.279796 | − | 0.960059i | \(-0.590267\pi\) | ||||
−0.279796 | + | 0.960059i | \(0.590267\pi\) | |||||||
\(60\) | −3.82843 | −0.494248 | ||||||||
\(61\) | −11.4342 | −1.46400 | −0.731998 | − | 0.681307i | \(-0.761412\pi\) | ||||
−0.731998 | + | 0.681307i | \(0.761412\pi\) | |||||||
\(62\) | 1.43727 | 0.182534 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −16.6864 | −2.06969 | ||||||||
\(66\) | −5.27981 | −0.649900 | ||||||||
\(67\) | 5.33092 | 0.651276 | 0.325638 | − | 0.945495i | \(-0.394421\pi\) | ||||
0.325638 | + | 0.945495i | \(0.394421\pi\) | |||||||
\(68\) | 2.46988 | 0.299517 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.64146 | 0.906874 | 0.453437 | − | 0.891288i | \(-0.350198\pi\) | ||||
0.453437 | + | 0.891288i | \(0.350198\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.437273 | 0.0511789 | 0.0255895 | − | 0.999673i | \(-0.491854\pi\) | ||||
0.0255895 | + | 0.999673i | \(0.491854\pi\) | |||||||
\(74\) | 6.63836 | 0.771693 | ||||||||
\(75\) | −9.65685 | −1.11508 | ||||||||
\(76\) | 1.92127 | 0.220385 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.35854 | 0.493508 | ||||||||
\(79\) | 1.35854 | 0.152848 | 0.0764240 | − | 0.997075i | \(-0.475650\pi\) | ||||
0.0764240 | + | 0.997075i | \(0.475650\pi\) | |||||||
\(80\) | 3.82843 | 0.428031 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.92127 | −0.212169 | ||||||||
\(83\) | 4.37704 | 0.480443 | 0.240221 | − | 0.970718i | \(-0.422780\pi\) | ||||
0.240221 | + | 0.970718i | \(0.422780\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.45577 | 1.02562 | ||||||||
\(86\) | −8.21648 | −0.886006 | ||||||||
\(87\) | 1.35854 | 0.145651 | ||||||||
\(88\) | 5.27981 | 0.562830 | ||||||||
\(89\) | 12.2952 | 1.30329 | 0.651645 | − | 0.758524i | \(-0.274079\pi\) | ||||
0.651645 | + | 0.758524i | \(0.274079\pi\) | |||||||
\(90\) | 3.82843 | 0.403552 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −1.43727 | −0.149038 | ||||||||
\(94\) | 6.99690 | 0.721675 | ||||||||
\(95\) | 7.35544 | 0.754653 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −0.298311 | −0.0302889 | −0.0151444 | − | 0.999885i | \(-0.504821\pi\) | ||||
−0.0151444 | + | 0.999885i | \(0.504821\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.27981 | 0.530641 | ||||||||
\(100\) | 9.65685 | 0.965685 | ||||||||
\(101\) | −18.0590 | −1.79694 | −0.898470 | − | 0.439035i | \(-0.855320\pi\) | ||||
−0.898470 | + | 0.439035i | \(0.855320\pi\) | |||||||
\(102\) | −2.46988 | −0.244555 | ||||||||
\(103\) | 0.669078 | 0.0659263 | 0.0329631 | − | 0.999457i | \(-0.489506\pi\) | ||||
0.0329631 | + | 0.999457i | \(0.489506\pi\) | |||||||
\(104\) | −4.35854 | −0.427390 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.88866 | −0.280571 | ||||||||
\(107\) | −18.4361 | −1.78228 | −0.891141 | − | 0.453727i | \(-0.850094\pi\) | ||||
−0.891141 | + | 0.453727i | \(0.850094\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 16.5314 | 1.58342 | 0.791710 | − | 0.610896i | \(-0.209191\pi\) | ||||
0.791710 | + | 0.610896i | \(0.209191\pi\) | |||||||
\(110\) | 20.2134 | 1.92727 | ||||||||
\(111\) | −6.63836 | −0.630085 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.7466 | 1.85760 | 0.928802 | − | 0.370577i | \(-0.120840\pi\) | ||||
0.928802 | + | 0.370577i | \(0.120840\pi\) | |||||||
\(114\) | −1.92127 | −0.179943 | ||||||||
\(115\) | 3.82843 | 0.357003 | ||||||||
\(116\) | −1.35854 | −0.126138 | ||||||||
\(117\) | −4.35854 | −0.402947 | ||||||||
\(118\) | −4.29831 | −0.395692 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.82843 | −0.349486 | ||||||||
\(121\) | 16.8764 | 1.53422 | ||||||||
\(122\) | −11.4342 | −1.03520 | ||||||||
\(123\) | 1.92127 | 0.173235 | ||||||||
\(124\) | 1.43727 | 0.129071 | ||||||||
\(125\) | 17.8284 | 1.59462 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.9367 | 1.68036 | 0.840179 | − | 0.542310i | \(-0.182450\pi\) | ||||
0.840179 | + | 0.542310i | \(0.182450\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.21648 | 0.723421 | ||||||||
\(130\) | −16.6864 | −1.46349 | ||||||||
\(131\) | −16.3554 | −1.42898 | −0.714491 | − | 0.699645i | \(-0.753342\pi\) | ||||
−0.714491 | + | 0.699645i | \(0.753342\pi\) | |||||||
\(132\) | −5.27981 | −0.459549 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.33092 | 0.460521 | ||||||||
\(135\) | −3.82843 | −0.329499 | ||||||||
\(136\) | 2.46988 | 0.211791 | ||||||||
\(137\) | −5.10824 | −0.436426 | −0.218213 | − | 0.975901i | \(-0.570023\pi\) | ||||
−0.218213 | + | 0.975901i | \(0.570023\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −9.31371 | −0.789978 | −0.394989 | − | 0.918686i | \(-0.629252\pi\) | ||||
−0.394989 | + | 0.918686i | \(0.629252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.99690 | −0.589245 | ||||||||
\(142\) | 7.64146 | 0.641257 | ||||||||
\(143\) | −23.0123 | −1.92439 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −5.20108 | −0.431927 | ||||||||
\(146\) | 0.437273 | 0.0361890 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.63836 | 0.545670 | ||||||||
\(149\) | 2.23370 | 0.182991 | 0.0914957 | − | 0.995805i | \(-0.470835\pi\) | ||||
0.0914957 | + | 0.995805i | \(0.470835\pi\) | |||||||
\(150\) | −9.65685 | −0.788479 | ||||||||
\(151\) | −22.2134 | −1.80770 | −0.903850 | − | 0.427850i | \(-0.859271\pi\) | ||||
−0.903850 | + | 0.427850i | \(0.859271\pi\) | |||||||
\(152\) | 1.92127 | 0.155836 | ||||||||
\(153\) | 2.46988 | 0.199678 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.50249 | 0.441971 | ||||||||
\(156\) | 4.35854 | 0.348963 | ||||||||
\(157\) | −10.5731 | −0.843828 | −0.421914 | − | 0.906636i | \(-0.638642\pi\) | ||||
−0.421914 | + | 0.906636i | \(0.638642\pi\) | |||||||
\(158\) | 1.35854 | 0.108080 | ||||||||
\(159\) | 2.88866 | 0.229086 | ||||||||
\(160\) | 3.82843 | 0.302664 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 19.7294 | 1.54532 | 0.772662 | − | 0.634817i | \(-0.218925\pi\) | ||||
0.772662 | + | 0.634817i | \(0.218925\pi\) | |||||||
\(164\) | −1.92127 | −0.150026 | ||||||||
\(165\) | −20.2134 | −1.57361 | ||||||||
\(166\) | 4.37704 | 0.339724 | ||||||||
\(167\) | −10.6907 | −0.827275 | −0.413637 | − | 0.910442i | \(-0.635742\pi\) | ||||
−0.413637 | + | 0.910442i | \(0.635742\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.99690 | 0.461300 | ||||||||
\(170\) | 9.45577 | 0.725224 | ||||||||
\(171\) | 1.92127 | 0.146923 | ||||||||
\(172\) | −8.21648 | −0.626501 | ||||||||
\(173\) | −22.0308 | −1.67497 | −0.837485 | − | 0.546460i | \(-0.815975\pi\) | ||||
−0.837485 | + | 0.546460i | \(0.815975\pi\) | |||||||
\(174\) | 1.35854 | 0.102991 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.27981 | 0.397981 | ||||||||
\(177\) | 4.29831 | 0.323081 | ||||||||
\(178\) | 12.2952 | 0.921565 | ||||||||
\(179\) | −16.9969 | −1.27041 | −0.635204 | − | 0.772344i | \(-0.719084\pi\) | ||||
−0.635204 | + | 0.772344i | \(0.719084\pi\) | |||||||
\(180\) | 3.82843 | 0.285354 | ||||||||
\(181\) | 12.4022 | 0.921846 | 0.460923 | − | 0.887440i | \(-0.347518\pi\) | ||||
0.460923 | + | 0.887440i | \(0.347518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.4342 | 0.845238 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 25.4145 | 1.86851 | ||||||||
\(186\) | −1.43727 | −0.105386 | ||||||||
\(187\) | 13.0405 | 0.953618 | ||||||||
\(188\) | 6.99690 | 0.510301 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.35544 | 0.533620 | ||||||||
\(191\) | −16.6384 | −1.20391 | −0.601955 | − | 0.798530i | \(-0.705611\pi\) | ||||
−0.601955 | + | 0.798530i | \(0.705611\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 25.2165 | 1.81512 | 0.907561 | − | 0.419920i | \(-0.137942\pi\) | ||||
0.907561 | + | 0.419920i | \(0.137942\pi\) | |||||||
\(194\) | −0.298311 | −0.0214175 | ||||||||
\(195\) | 16.6864 | 1.19494 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.6199 | 0.970375 | 0.485187 | − | 0.874410i | \(-0.338751\pi\) | ||||
0.485187 | + | 0.874410i | \(0.338751\pi\) | |||||||
\(198\) | 5.27981 | 0.375220 | ||||||||
\(199\) | 0.902774 | 0.0639959 | 0.0319980 | − | 0.999488i | \(-0.489813\pi\) | ||||
0.0319980 | + | 0.999488i | \(0.489813\pi\) | |||||||
\(200\) | 9.65685 | 0.682843 | ||||||||
\(201\) | −5.33092 | −0.376014 | ||||||||
\(202\) | −18.0590 | −1.27063 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.46988 | −0.172926 | ||||||||
\(205\) | −7.35544 | −0.513727 | ||||||||
\(206\) | 0.669078 | 0.0466169 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −4.35854 | −0.302211 | ||||||||
\(209\) | 10.1440 | 0.701672 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.8131 | −1.57052 | −0.785259 | − | 0.619167i | \(-0.787470\pi\) | ||||
−0.785259 | + | 0.619167i | \(0.787470\pi\) | |||||||
\(212\) | −2.88866 | −0.198394 | ||||||||
\(213\) | −7.64146 | −0.523584 | ||||||||
\(214\) | −18.4361 | −1.26026 | ||||||||
\(215\) | −31.4562 | −2.14530 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.5314 | 1.11965 | ||||||||
\(219\) | −0.437273 | −0.0295482 | ||||||||
\(220\) | 20.2134 | 1.36279 | ||||||||
\(221\) | −10.7651 | −0.724139 | ||||||||
\(222\) | −6.63836 | −0.445537 | ||||||||
\(223\) | 0.942867 | 0.0631390 | 0.0315695 | − | 0.999502i | \(-0.489949\pi\) | ||||
0.0315695 | + | 0.999502i | \(0.489949\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.65685 | 0.643790 | ||||||||
\(226\) | 19.7466 | 1.31352 | ||||||||
\(227\) | −15.3106 | −1.01620 | −0.508100 | − | 0.861298i | \(-0.669652\pi\) | ||||
−0.508100 | + | 0.861298i | \(0.669652\pi\) | |||||||
\(228\) | −1.92127 | −0.127239 | ||||||||
\(229\) | 6.07873 | 0.401694 | 0.200847 | − | 0.979623i | \(-0.435631\pi\) | ||||
0.200847 | + | 0.979623i | \(0.435631\pi\) | |||||||
\(230\) | 3.82843 | 0.252439 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.35854 | −0.0891927 | ||||||||
\(233\) | −7.57812 | −0.496459 | −0.248230 | − | 0.968701i | \(-0.579849\pi\) | ||||
−0.248230 | + | 0.968701i | \(0.579849\pi\) | |||||||
\(234\) | −4.35854 | −0.284927 | ||||||||
\(235\) | 26.7871 | 1.74740 | ||||||||
\(236\) | −4.29831 | −0.279796 | ||||||||
\(237\) | −1.35854 | −0.0882469 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.4330 | −1.06296 | −0.531480 | − | 0.847071i | \(-0.678364\pi\) | ||||
−0.531480 | + | 0.847071i | \(0.678364\pi\) | |||||||
\(240\) | −3.82843 | −0.247124 | ||||||||
\(241\) | 13.2319 | 0.852340 | 0.426170 | − | 0.904643i | \(-0.359862\pi\) | ||||
0.426170 | + | 0.904643i | \(0.359862\pi\) | |||||||
\(242\) | 16.8764 | 1.08486 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.4342 | −0.731998 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.92127 | 0.122496 | ||||||||
\(247\) | −8.37394 | −0.532821 | ||||||||
\(248\) | 1.43727 | 0.0912669 | ||||||||
\(249\) | −4.37704 | −0.277384 | ||||||||
\(250\) | 17.8284 | 1.12757 | ||||||||
\(251\) | −9.87644 | −0.623395 | −0.311698 | − | 0.950181i | \(-0.600898\pi\) | ||||
−0.311698 | + | 0.950181i | \(0.600898\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.27981 | 0.331939 | ||||||||
\(254\) | 18.9367 | 1.18819 | ||||||||
\(255\) | −9.45577 | −0.592143 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.3554 | 1.33212 | 0.666058 | − | 0.745900i | \(-0.267980\pi\) | ||||
0.666058 | + | 0.745900i | \(0.267980\pi\) | |||||||
\(258\) | 8.21648 | 0.511536 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −16.6864 | −1.03484 | ||||||||
\(261\) | −1.35854 | −0.0840917 | ||||||||
\(262\) | −16.3554 | −1.01044 | ||||||||
\(263\) | 8.68009 | 0.535237 | 0.267619 | − | 0.963525i | \(-0.413763\pi\) | ||||
0.267619 | + | 0.963525i | \(0.413763\pi\) | |||||||
\(264\) | −5.27981 | −0.324950 | ||||||||
\(265\) | −11.0590 | −0.679350 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.2952 | −0.752455 | ||||||||
\(268\) | 5.33092 | 0.325638 | ||||||||
\(269\) | 26.0142 | 1.58611 | 0.793057 | − | 0.609148i | \(-0.208488\pi\) | ||||
0.793057 | + | 0.609148i | \(0.208488\pi\) | |||||||
\(270\) | −3.82843 | −0.232991 | ||||||||
\(271\) | −1.43727 | −0.0873081 | −0.0436541 | − | 0.999047i | \(-0.513900\pi\) | ||||
−0.0436541 | + | 0.999047i | \(0.513900\pi\) | |||||||
\(272\) | 2.46988 | 0.149759 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.10824 | −0.308600 | ||||||||
\(275\) | 50.9864 | 3.07460 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 18.0289 | 1.08325 | 0.541626 | − | 0.840620i | \(-0.317809\pi\) | ||||
0.541626 | + | 0.840620i | \(0.317809\pi\) | |||||||
\(278\) | −9.31371 | −0.558599 | ||||||||
\(279\) | 1.43727 | 0.0860473 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.9643 | 1.48924 | 0.744622 | − | 0.667486i | \(-0.232630\pi\) | ||||
0.744622 | + | 0.667486i | \(0.232630\pi\) | |||||||
\(282\) | −6.99690 | −0.416659 | ||||||||
\(283\) | −2.73430 | −0.162537 | −0.0812686 | − | 0.996692i | \(-0.525897\pi\) | ||||
−0.0812686 | + | 0.996692i | \(0.525897\pi\) | |||||||
\(284\) | 7.64146 | 0.453437 | ||||||||
\(285\) | −7.35544 | −0.435699 | ||||||||
\(286\) | −23.0123 | −1.36075 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −10.8997 | −0.641157 | ||||||||
\(290\) | −5.20108 | −0.305418 | ||||||||
\(291\) | 0.298311 | 0.0174873 | ||||||||
\(292\) | 0.437273 | 0.0255895 | ||||||||
\(293\) | 14.5147 | 0.847959 | 0.423979 | − | 0.905672i | \(-0.360633\pi\) | ||||
0.423979 | + | 0.905672i | \(0.360633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.4558 | −0.958092 | ||||||||
\(296\) | 6.63836 | 0.385847 | ||||||||
\(297\) | −5.27981 | −0.306366 | ||||||||
\(298\) | 2.23370 | 0.129394 | ||||||||
\(299\) | −4.35854 | −0.252061 | ||||||||
\(300\) | −9.65685 | −0.557539 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22.2134 | −1.27824 | ||||||||
\(303\) | 18.0590 | 1.03746 | ||||||||
\(304\) | 1.92127 | 0.110192 | ||||||||
\(305\) | −43.7749 | −2.50654 | ||||||||
\(306\) | 2.46988 | 0.141194 | ||||||||
\(307\) | −31.9521 | −1.82360 | −0.911800 | − | 0.410634i | \(-0.865307\pi\) | ||||
−0.911800 | + | 0.410634i | \(0.865307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.669078 | −0.0380625 | ||||||||
\(310\) | 5.50249 | 0.312521 | ||||||||
\(311\) | −31.0142 | −1.75865 | −0.879327 | − | 0.476219i | \(-0.842007\pi\) | ||||
−0.879327 | + | 0.476219i | \(0.842007\pi\) | |||||||
\(312\) | 4.35854 | 0.246754 | ||||||||
\(313\) | 6.57623 | 0.371711 | 0.185855 | − | 0.982577i | \(-0.440494\pi\) | ||||
0.185855 | + | 0.982577i | \(0.440494\pi\) | |||||||
\(314\) | −10.5731 | −0.596677 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.35854 | 0.0764240 | ||||||||
\(317\) | −28.0142 | −1.57343 | −0.786717 | − | 0.617314i | \(-0.788221\pi\) | ||||
−0.786717 | + | 0.617314i | \(0.788221\pi\) | |||||||
\(318\) | 2.88866 | 0.161988 | ||||||||
\(319\) | −7.17286 | −0.401603 | ||||||||
\(320\) | 3.82843 | 0.214016 | ||||||||
\(321\) | 18.4361 | 1.02900 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.74531 | 0.264036 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −42.0898 | −2.33472 | ||||||||
\(326\) | 19.7294 | 1.09271 | ||||||||
\(327\) | −16.5314 | −0.914189 | ||||||||
\(328\) | −1.92127 | −0.106084 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −20.2134 | −1.11271 | ||||||||
\(331\) | 24.8266 | 1.36459 | 0.682297 | − | 0.731075i | \(-0.260981\pi\) | ||||
0.682297 | + | 0.731075i | \(0.260981\pi\) | |||||||
\(332\) | 4.37704 | 0.240221 | ||||||||
\(333\) | 6.63836 | 0.363780 | ||||||||
\(334\) | −10.6907 | −0.584972 | ||||||||
\(335\) | 20.4090 | 1.11507 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.4176 | 0.948795 | 0.474398 | − | 0.880311i | \(-0.342666\pi\) | ||||
0.474398 | + | 0.880311i | \(0.342666\pi\) | |||||||
\(338\) | 5.99690 | 0.326188 | ||||||||
\(339\) | −19.7466 | −1.07249 | ||||||||
\(340\) | 9.45577 | 0.512811 | ||||||||
\(341\) | 7.58853 | 0.410942 | ||||||||
\(342\) | 1.92127 | 0.103890 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.21648 | −0.443003 | ||||||||
\(345\) | −3.82843 | −0.206116 | ||||||||
\(346\) | −22.0308 | −1.18438 | ||||||||
\(347\) | −9.87145 | −0.529927 | −0.264964 | − | 0.964258i | \(-0.585360\pi\) | ||||
−0.264964 | + | 0.964258i | \(0.585360\pi\) | |||||||
\(348\) | 1.35854 | 0.0728256 | ||||||||
\(349\) | −33.9170 | −1.81553 | −0.907767 | − | 0.419475i | \(-0.862214\pi\) | ||||
−0.907767 | + | 0.419475i | \(0.862214\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.35854 | 0.232642 | ||||||||
\(352\) | 5.27981 | 0.281415 | ||||||||
\(353\) | 7.35544 | 0.391491 | 0.195745 | − | 0.980655i | \(-0.437287\pi\) | ||||
0.195745 | + | 0.980655i | \(0.437287\pi\) | |||||||
\(354\) | 4.29831 | 0.228453 | ||||||||
\(355\) | 29.2548 | 1.55268 | ||||||||
\(356\) | 12.2952 | 0.651645 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.9969 | −0.898314 | ||||||||
\(359\) | 15.1932 | 0.801869 | 0.400934 | − | 0.916107i | \(-0.368686\pi\) | ||||
0.400934 | + | 0.916107i | \(0.368686\pi\) | |||||||
\(360\) | 3.82843 | 0.201776 | ||||||||
\(361\) | −15.3087 | −0.805722 | ||||||||
\(362\) | 12.4022 | 0.651844 | ||||||||
\(363\) | −16.8764 | −0.885783 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.67407 | 0.0876247 | ||||||||
\(366\) | 11.4342 | 0.597674 | ||||||||
\(367\) | −8.34632 | −0.435674 | −0.217837 | − | 0.975985i | \(-0.569900\pi\) | ||||
−0.217837 | + | 0.975985i | \(0.569900\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −1.92127 | −0.100017 | ||||||||
\(370\) | 25.4145 | 1.32124 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.43727 | −0.0745191 | ||||||||
\(373\) | 20.5596 | 1.06454 | 0.532269 | − | 0.846576i | \(-0.321340\pi\) | ||||
0.532269 | + | 0.846576i | \(0.321340\pi\) | |||||||
\(374\) | 13.0405 | 0.674310 | ||||||||
\(375\) | −17.8284 | −0.920656 | ||||||||
\(376\) | 6.99690 | 0.360838 | ||||||||
\(377\) | 5.92127 | 0.304961 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.45139 | −0.0745527 | −0.0372764 | − | 0.999305i | \(-0.511868\pi\) | ||||
−0.0372764 | + | 0.999305i | \(0.511868\pi\) | |||||||
\(380\) | 7.35544 | 0.377326 | ||||||||
\(381\) | −18.9367 | −0.970155 | ||||||||
\(382\) | −16.6384 | −0.851292 | ||||||||
\(383\) | 29.4145 | 1.50301 | 0.751505 | − | 0.659728i | \(-0.229328\pi\) | ||||
0.751505 | + | 0.659728i | \(0.229328\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.2165 | 1.28349 | ||||||||
\(387\) | −8.21648 | −0.417667 | ||||||||
\(388\) | −0.298311 | −0.0151444 | ||||||||
\(389\) | 22.1513 | 1.12311 | 0.561557 | − | 0.827438i | \(-0.310203\pi\) | ||||
0.561557 | + | 0.827438i | \(0.310203\pi\) | |||||||
\(390\) | 16.6864 | 0.844947 | ||||||||
\(391\) | 2.46988 | 0.124907 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.3554 | 0.825023 | ||||||||
\(394\) | 13.6199 | 0.686159 | ||||||||
\(395\) | 5.20108 | 0.261695 | ||||||||
\(396\) | 5.27981 | 0.265321 | ||||||||
\(397\) | 20.8567 | 1.04677 | 0.523385 | − | 0.852097i | \(-0.324669\pi\) | ||||
0.523385 | + | 0.852097i | \(0.324669\pi\) | |||||||
\(398\) | 0.902774 | 0.0452520 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.65685 | 0.482843 | ||||||||
\(401\) | −15.0430 | −0.751213 | −0.375606 | − | 0.926779i | \(-0.622565\pi\) | ||||
−0.375606 | + | 0.926779i | \(0.622565\pi\) | |||||||
\(402\) | −5.33092 | −0.265882 | ||||||||
\(403\) | −6.26442 | −0.312053 | ||||||||
\(404\) | −18.0590 | −0.898470 | ||||||||
\(405\) | 3.82843 | 0.190236 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.0493 | 1.73733 | ||||||||
\(408\) | −2.46988 | −0.122277 | ||||||||
\(409\) | 19.0960 | 0.944237 | 0.472119 | − | 0.881535i | \(-0.343489\pi\) | ||||
0.472119 | + | 0.881535i | \(0.343489\pi\) | |||||||
\(410\) | −7.35544 | −0.363259 | ||||||||
\(411\) | 5.10824 | 0.251971 | ||||||||
\(412\) | 0.669078 | 0.0329631 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 16.7572 | 0.822578 | ||||||||
\(416\) | −4.35854 | −0.213695 | ||||||||
\(417\) | 9.31371 | 0.456094 | ||||||||
\(418\) | 10.1440 | 0.496157 | ||||||||
\(419\) | 20.2165 | 0.987640 | 0.493820 | − | 0.869564i | \(-0.335600\pi\) | ||||
0.493820 | + | 0.869564i | \(0.335600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.59662 | 0.418974 | 0.209487 | − | 0.977811i | \(-0.432821\pi\) | ||||
0.209487 | + | 0.977811i | \(0.432821\pi\) | |||||||
\(422\) | −22.8131 | −1.11052 | ||||||||
\(423\) | 6.99690 | 0.340201 | ||||||||
\(424\) | −2.88866 | −0.140286 | ||||||||
\(425\) | 23.8513 | 1.15696 | ||||||||
\(426\) | −7.64146 | −0.370230 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −18.4361 | −0.891141 | ||||||||
\(429\) | 23.0123 | 1.11104 | ||||||||
\(430\) | −31.4562 | −1.51695 | ||||||||
\(431\) | 36.0616 | 1.73703 | 0.868513 | − | 0.495667i | \(-0.165076\pi\) | ||||
0.868513 | + | 0.495667i | \(0.165076\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −7.56462 | −0.363532 | −0.181766 | − | 0.983342i | \(-0.558181\pi\) | ||||
−0.181766 | + | 0.983342i | \(0.558181\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.20108 | 0.249373 | ||||||||
\(436\) | 16.5314 | 0.791710 | ||||||||
\(437\) | 1.92127 | 0.0919068 | ||||||||
\(438\) | −0.437273 | −0.0208937 | ||||||||
\(439\) | −35.1470 | −1.67747 | −0.838736 | − | 0.544538i | \(-0.816705\pi\) | ||||
−0.838736 | + | 0.544538i | \(0.816705\pi\) | |||||||
\(440\) | 20.2134 | 0.963635 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.7651 | −0.512043 | ||||||||
\(443\) | −6.35544 | −0.301956 | −0.150978 | − | 0.988537i | \(-0.548242\pi\) | ||||
−0.150978 | + | 0.988537i | \(0.548242\pi\) | |||||||
\(444\) | −6.63836 | −0.315043 | ||||||||
\(445\) | 47.0713 | 2.23139 | ||||||||
\(446\) | 0.942867 | 0.0446460 | ||||||||
\(447\) | −2.23370 | −0.105650 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.36043 | −0.205782 | −0.102891 | − | 0.994693i | \(-0.532809\pi\) | ||||
−0.102891 | + | 0.994693i | \(0.532809\pi\) | |||||||
\(450\) | 9.65685 | 0.455228 | ||||||||
\(451\) | −10.1440 | −0.477660 | ||||||||
\(452\) | 19.7466 | 0.928802 | ||||||||
\(453\) | 22.2134 | 1.04368 | ||||||||
\(454\) | −15.3106 | −0.718563 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.92127 | −0.0899717 | ||||||||
\(457\) | −33.8567 | −1.58375 | −0.791876 | − | 0.610683i | \(-0.790895\pi\) | ||||
−0.791876 | + | 0.610683i | \(0.790895\pi\) | |||||||
\(458\) | 6.07873 | 0.284040 | ||||||||
\(459\) | −2.46988 | −0.115284 | ||||||||
\(460\) | 3.82843 | 0.178501 | ||||||||
\(461\) | 17.6851 | 0.823676 | 0.411838 | − | 0.911257i | \(-0.364887\pi\) | ||||
0.411838 | + | 0.911257i | \(0.364887\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.5954 | 1.65426 | 0.827130 | − | 0.562011i | \(-0.189972\pi\) | ||||
0.827130 | + | 0.562011i | \(0.189972\pi\) | |||||||
\(464\) | −1.35854 | −0.0630688 | ||||||||
\(465\) | −5.50249 | −0.255172 | ||||||||
\(466\) | −7.57812 | −0.351050 | ||||||||
\(467\) | 14.4022 | 0.666453 | 0.333226 | − | 0.942847i | \(-0.391863\pi\) | ||||
0.333226 | + | 0.942847i | \(0.391863\pi\) | |||||||
\(468\) | −4.35854 | −0.201474 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 26.7871 | 1.23560 | ||||||||
\(471\) | 10.5731 | 0.487184 | ||||||||
\(472\) | −4.29831 | −0.197846 | ||||||||
\(473\) | −43.3815 | −1.99468 | ||||||||
\(474\) | −1.35854 | −0.0624000 | ||||||||
\(475\) | 18.5534 | 0.851290 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.88866 | −0.132263 | ||||||||
\(478\) | −16.4330 | −0.751626 | ||||||||
\(479\) | 38.3542 | 1.75245 | 0.876225 | − | 0.481902i | \(-0.160054\pi\) | ||||
0.876225 | + | 0.481902i | \(0.160054\pi\) | |||||||
\(480\) | −3.82843 | −0.174743 | ||||||||
\(481\) | −28.9336 | −1.31926 | ||||||||
\(482\) | 13.2319 | 0.602696 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.8764 | 0.767111 | ||||||||
\(485\) | −1.14206 | −0.0518583 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 20.2504 | 0.917632 | 0.458816 | − | 0.888531i | \(-0.348274\pi\) | ||||
0.458816 | + | 0.888531i | \(0.348274\pi\) | |||||||
\(488\) | −11.4342 | −0.517601 | ||||||||
\(489\) | −19.7294 | −0.892194 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.6459 | −1.20251 | −0.601257 | − | 0.799056i | \(-0.705333\pi\) | ||||
−0.601257 | + | 0.799056i | \(0.705333\pi\) | |||||||
\(492\) | 1.92127 | 0.0866176 | ||||||||
\(493\) | −3.35544 | −0.151122 | ||||||||
\(494\) | −8.37394 | −0.376761 | ||||||||
\(495\) | 20.2134 | 0.908524 | ||||||||
\(496\) | 1.43727 | 0.0645355 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.37704 | −0.196140 | ||||||||
\(499\) | −13.0602 | −0.584656 | −0.292328 | − | 0.956318i | \(-0.594430\pi\) | ||||
−0.292328 | + | 0.956318i | \(0.594430\pi\) | |||||||
\(500\) | 17.8284 | 0.797311 | ||||||||
\(501\) | 10.6907 | 0.477627 | ||||||||
\(502\) | −9.87644 | −0.440807 | ||||||||
\(503\) | 11.1525 | 0.497264 | 0.248632 | − | 0.968598i | \(-0.420019\pi\) | ||||
0.248632 | + | 0.968598i | \(0.420019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −69.1377 | −3.07659 | ||||||||
\(506\) | 5.27981 | 0.234716 | ||||||||
\(507\) | −5.99690 | −0.266332 | ||||||||
\(508\) | 18.9367 | 0.840179 | ||||||||
\(509\) | 11.8874 | 0.526899 | 0.263449 | − | 0.964673i | \(-0.415140\pi\) | ||||
0.263449 | + | 0.964673i | \(0.415140\pi\) | |||||||
\(510\) | −9.45577 | −0.418709 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.92127 | −0.0848262 | ||||||||
\(514\) | 21.3554 | 0.941948 | ||||||||
\(515\) | 2.56152 | 0.112874 | ||||||||
\(516\) | 8.21648 | 0.361710 | ||||||||
\(517\) | 36.9423 | 1.62472 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.0308 | 0.967045 | ||||||||
\(520\) | −16.6864 | −0.731746 | ||||||||
\(521\) | −25.4452 | −1.11477 | −0.557387 | − | 0.830253i | \(-0.688196\pi\) | ||||
−0.557387 | + | 0.830253i | \(0.688196\pi\) | |||||||
\(522\) | −1.35854 | −0.0594618 | ||||||||
\(523\) | 24.5424 | 1.07316 | 0.536582 | − | 0.843848i | \(-0.319715\pi\) | ||||
0.536582 | + | 0.843848i | \(0.319715\pi\) | |||||||
\(524\) | −16.3554 | −0.714491 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.68009 | 0.378470 | ||||||||
\(527\) | 3.54990 | 0.154636 | ||||||||
\(528\) | −5.27981 | −0.229774 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −11.0590 | −0.480373 | ||||||||
\(531\) | −4.29831 | −0.186531 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.37394 | 0.362716 | ||||||||
\(534\) | −12.2952 | −0.532066 | ||||||||
\(535\) | −70.5811 | −3.05149 | ||||||||
\(536\) | 5.33092 | 0.230261 | ||||||||
\(537\) | 16.9969 | 0.733470 | ||||||||
\(538\) | 26.0142 | 1.12155 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.82843 | −0.164749 | ||||||||
\(541\) | −29.9909 | −1.28941 | −0.644706 | − | 0.764431i | \(-0.723020\pi\) | ||||
−0.644706 | + | 0.764431i | \(0.723020\pi\) | |||||||
\(542\) | −1.43727 | −0.0617362 | ||||||||
\(543\) | −12.4022 | −0.532228 | ||||||||
\(544\) | 2.46988 | 0.105895 | ||||||||
\(545\) | 63.2893 | 2.71101 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.6986 | −1.52636 | −0.763181 | − | 0.646185i | \(-0.776363\pi\) | ||||
−0.763181 | + | 0.646185i | \(0.776363\pi\) | |||||||
\(548\) | −5.10824 | −0.218213 | ||||||||
\(549\) | −11.4342 | −0.487999 | ||||||||
\(550\) | 50.9864 | 2.17407 | ||||||||
\(551\) | −2.61013 | −0.111195 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 18.0289 | 0.765975 | ||||||||
\(555\) | −25.4145 | −1.07878 | ||||||||
\(556\) | −9.31371 | −0.394989 | ||||||||
\(557\) | −34.3426 | −1.45514 | −0.727572 | − | 0.686032i | \(-0.759351\pi\) | ||||
−0.727572 | + | 0.686032i | \(0.759351\pi\) | |||||||
\(558\) | 1.43727 | 0.0608446 | ||||||||
\(559\) | 35.8119 | 1.51468 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.0405 | −0.550571 | ||||||||
\(562\) | 24.9643 | 1.05306 | ||||||||
\(563\) | 32.4078 | 1.36583 | 0.682914 | − | 0.730499i | \(-0.260712\pi\) | ||||
0.682914 | + | 0.730499i | \(0.260712\pi\) | |||||||
\(564\) | −6.99690 | −0.294623 | ||||||||
\(565\) | 75.5984 | 3.18045 | ||||||||
\(566\) | −2.73430 | −0.114931 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.64146 | 0.320628 | ||||||||
\(569\) | −19.4884 | −0.816995 | −0.408498 | − | 0.912759i | \(-0.633947\pi\) | ||||
−0.408498 | + | 0.912759i | \(0.633947\pi\) | |||||||
\(570\) | −7.35544 | −0.308086 | ||||||||
\(571\) | −9.13173 | −0.382151 | −0.191075 | − | 0.981575i | \(-0.561198\pi\) | ||||
−0.191075 | + | 0.981575i | \(0.561198\pi\) | |||||||
\(572\) | −23.0123 | −0.962193 | ||||||||
\(573\) | 16.6384 | 0.695077 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.65685 | 0.402719 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −34.9957 | −1.45689 | −0.728445 | − | 0.685104i | \(-0.759757\pi\) | ||||
−0.728445 | + | 0.685104i | \(0.759757\pi\) | |||||||
\(578\) | −10.8997 | −0.453367 | ||||||||
\(579\) | −25.2165 | −1.04796 | ||||||||
\(580\) | −5.20108 | −0.215963 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.298311 | 0.0123654 | ||||||||
\(583\) | −15.2516 | −0.631656 | ||||||||
\(584\) | 0.437273 | 0.0180945 | ||||||||
\(585\) | −16.6864 | −0.689896 | ||||||||
\(586\) | 14.5147 | 0.599597 | ||||||||
\(587\) | 3.60136 | 0.148644 | 0.0743221 | − | 0.997234i | \(-0.476321\pi\) | ||||
0.0743221 | + | 0.997234i | \(0.476321\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.76139 | 0.113781 | ||||||||
\(590\) | −16.4558 | −0.677473 | ||||||||
\(591\) | −13.6199 | −0.560246 | ||||||||
\(592\) | 6.63836 | 0.272835 | ||||||||
\(593\) | −7.65066 | −0.314175 | −0.157087 | − | 0.987585i | \(-0.550210\pi\) | ||||
−0.157087 | + | 0.987585i | \(0.550210\pi\) | |||||||
\(594\) | −5.27981 | −0.216633 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.23370 | 0.0914957 | ||||||||
\(597\) | −0.902774 | −0.0369481 | ||||||||
\(598\) | −4.35854 | −0.178234 | ||||||||
\(599\) | −19.7030 | −0.805045 | −0.402522 | − | 0.915410i | \(-0.631866\pi\) | ||||
−0.402522 | + | 0.915410i | \(0.631866\pi\) | |||||||
\(600\) | −9.65685 | −0.394239 | ||||||||
\(601\) | 22.3094 | 0.910019 | 0.455010 | − | 0.890486i | \(-0.349636\pi\) | ||||
0.455010 | + | 0.890486i | \(0.349636\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.33092 | 0.217092 | ||||||||
\(604\) | −22.2134 | −0.903850 | ||||||||
\(605\) | 64.6102 | 2.62678 | ||||||||
\(606\) | 18.0590 | 0.733598 | ||||||||
\(607\) | −4.21958 | −0.171268 | −0.0856338 | − | 0.996327i | \(-0.527291\pi\) | ||||
−0.0856338 | + | 0.996327i | \(0.527291\pi\) | |||||||
\(608\) | 1.92127 | 0.0779178 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −43.7749 | −1.77239 | ||||||||
\(611\) | −30.4963 | −1.23375 | ||||||||
\(612\) | 2.46988 | 0.0998391 | ||||||||
\(613\) | −9.33816 | −0.377165 | −0.188582 | − | 0.982057i | \(-0.560389\pi\) | ||||
−0.188582 | + | 0.982057i | \(0.560389\pi\) | |||||||
\(614\) | −31.9521 | −1.28948 | ||||||||
\(615\) | 7.35544 | 0.296600 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.89055 | 0.0761107 | 0.0380553 | − | 0.999276i | \(-0.487884\pi\) | ||||
0.0380553 | + | 0.999276i | \(0.487884\pi\) | |||||||
\(618\) | −0.669078 | −0.0269143 | ||||||||
\(619\) | 15.3665 | 0.617630 | 0.308815 | − | 0.951122i | \(-0.400068\pi\) | ||||
0.308815 | + | 0.951122i | \(0.400068\pi\) | |||||||
\(620\) | 5.50249 | 0.220985 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −31.0142 | −1.24356 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.35854 | 0.174481 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 6.57623 | 0.262839 | ||||||||
\(627\) | −10.1440 | −0.405110 | ||||||||
\(628\) | −10.5731 | −0.421914 | ||||||||
\(629\) | 16.3960 | 0.653750 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.49622 | −0.0595636 | −0.0297818 | − | 0.999556i | \(-0.509481\pi\) | ||||
−0.0297818 | + | 0.999556i | \(0.509481\pi\) | |||||||
\(632\) | 1.35854 | 0.0540400 | ||||||||
\(633\) | 22.8131 | 0.906739 | ||||||||
\(634\) | −28.0142 | −1.11259 | ||||||||
\(635\) | 72.4977 | 2.87698 | ||||||||
\(636\) | 2.88866 | 0.114543 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.17286 | −0.283976 | ||||||||
\(639\) | 7.64146 | 0.302291 | ||||||||
\(640\) | 3.82843 | 0.151332 | ||||||||
\(641\) | −1.33566 | −0.0527555 | −0.0263778 | − | 0.999652i | \(-0.508397\pi\) | ||||
−0.0263778 | + | 0.999652i | \(0.508397\pi\) | |||||||
\(642\) | 18.4361 | 0.727613 | ||||||||
\(643\) | 17.5167 | 0.690791 | 0.345395 | − | 0.938457i | \(-0.387745\pi\) | ||||
0.345395 | + | 0.938457i | \(0.387745\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.4562 | 1.23859 | ||||||||
\(646\) | 4.74531 | 0.186702 | ||||||||
\(647\) | −22.1612 | −0.871248 | −0.435624 | − | 0.900129i | \(-0.643472\pi\) | ||||
−0.435624 | + | 0.900129i | \(0.643472\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −22.6943 | −0.890828 | ||||||||
\(650\) | −42.0898 | −1.65090 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.7294 | 0.772662 | ||||||||
\(653\) | −9.17286 | −0.358962 | −0.179481 | − | 0.983761i | \(-0.557442\pi\) | ||||
−0.179481 | + | 0.983761i | \(0.557442\pi\) | |||||||
\(654\) | −16.5314 | −0.646429 | ||||||||
\(655\) | −62.6156 | −2.44659 | ||||||||
\(656\) | −1.92127 | −0.0750130 | ||||||||
\(657\) | 0.437273 | 0.0170596 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.3419 | −0.909273 | −0.454636 | − | 0.890677i | \(-0.650231\pi\) | ||||
−0.454636 | + | 0.890677i | \(0.650231\pi\) | |||||||
\(660\) | −20.2134 | −0.786805 | ||||||||
\(661\) | 35.9632 | 1.39880 | 0.699402 | − | 0.714728i | \(-0.253450\pi\) | ||||
0.699402 | + | 0.714728i | \(0.253450\pi\) | |||||||
\(662\) | 24.8266 | 0.964914 | ||||||||
\(663\) | 10.7651 | 0.418082 | ||||||||
\(664\) | 4.37704 | 0.169862 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.63836 | 0.257231 | ||||||||
\(667\) | −1.35854 | −0.0526030 | ||||||||
\(668\) | −10.6907 | −0.413637 | ||||||||
\(669\) | −0.942867 | −0.0364533 | ||||||||
\(670\) | 20.4090 | 0.788470 | ||||||||
\(671\) | −60.3703 | −2.33057 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.9957 | 0.886419 | 0.443209 | − | 0.896418i | \(-0.353840\pi\) | ||||
0.443209 | + | 0.896418i | \(0.353840\pi\) | |||||||
\(674\) | 17.4176 | 0.670900 | ||||||||
\(675\) | −9.65685 | −0.371692 | ||||||||
\(676\) | 5.99690 | 0.230650 | ||||||||
\(677\) | −13.3648 | −0.513652 | −0.256826 | − | 0.966458i | \(-0.582677\pi\) | ||||
−0.256826 | + | 0.966458i | \(0.582677\pi\) | |||||||
\(678\) | −19.7466 | −0.758364 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.45577 | 0.362612 | ||||||||
\(681\) | 15.3106 | 0.586704 | ||||||||
\(682\) | 7.58853 | 0.290580 | ||||||||
\(683\) | −11.1660 | −0.427254 | −0.213627 | − | 0.976915i | \(-0.568528\pi\) | ||||
−0.213627 | + | 0.976915i | \(0.568528\pi\) | |||||||
\(684\) | 1.92127 | 0.0734616 | ||||||||
\(685\) | −19.5565 | −0.747217 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.07873 | −0.231918 | ||||||||
\(688\) | −8.21648 | −0.313250 | ||||||||
\(689\) | 12.5903 | 0.479654 | ||||||||
\(690\) | −3.82843 | −0.145746 | ||||||||
\(691\) | −43.9829 | −1.67319 | −0.836593 | − | 0.547824i | \(-0.815456\pi\) | ||||
−0.836593 | + | 0.547824i | \(0.815456\pi\) | |||||||
\(692\) | −22.0308 | −0.837485 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.87145 | −0.374715 | ||||||||
\(695\) | −35.6569 | −1.35254 | ||||||||
\(696\) | 1.35854 | 0.0514955 | ||||||||
\(697\) | −4.74531 | −0.179742 | ||||||||
\(698\) | −33.9170 | −1.28378 | ||||||||
\(699\) | 7.57812 | 0.286631 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.86043 | −0.108037 | −0.0540185 | − | 0.998540i | \(-0.517203\pi\) | ||||
−0.0540185 | + | 0.998540i | \(0.517203\pi\) | |||||||
\(702\) | 4.35854 | 0.164503 | ||||||||
\(703\) | 12.7541 | 0.481029 | ||||||||
\(704\) | 5.27981 | 0.198990 | ||||||||
\(705\) | −26.7871 | −1.00886 | ||||||||
\(706\) | 7.35544 | 0.276826 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.29831 | 0.161540 | ||||||||
\(709\) | −34.5795 | −1.29866 | −0.649330 | − | 0.760507i | \(-0.724951\pi\) | ||||
−0.649330 | + | 0.760507i | \(0.724951\pi\) | |||||||
\(710\) | 29.2548 | 1.09791 | ||||||||
\(711\) | 1.35854 | 0.0509494 | ||||||||
\(712\) | 12.2952 | 0.460783 | ||||||||
\(713\) | 1.43727 | 0.0538263 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −88.1009 | −3.29479 | ||||||||
\(716\) | −16.9969 | −0.635204 | ||||||||
\(717\) | 16.4330 | 0.613700 | ||||||||
\(718\) | 15.1932 | 0.567007 | ||||||||
\(719\) | −23.3991 | −0.872638 | −0.436319 | − | 0.899792i | \(-0.643718\pi\) | ||||
−0.436319 | + | 0.899792i | \(0.643718\pi\) | |||||||
\(720\) | 3.82843 | 0.142677 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.3087 | −0.569732 | ||||||||
\(723\) | −13.2319 | −0.492099 | ||||||||
\(724\) | 12.4022 | 0.460923 | ||||||||
\(725\) | −13.1193 | −0.487237 | ||||||||
\(726\) | −16.8764 | −0.626343 | ||||||||
\(727\) | −0.604463 | −0.0224183 | −0.0112091 | − | 0.999937i | \(-0.503568\pi\) | ||||
−0.0112091 | + | 0.999937i | \(0.503568\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.67407 | 0.0619600 | ||||||||
\(731\) | −20.2938 | −0.750592 | ||||||||
\(732\) | 11.4342 | 0.422619 | ||||||||
\(733\) | −20.2670 | −0.748578 | −0.374289 | − | 0.927312i | \(-0.622113\pi\) | ||||
−0.374289 | + | 0.927312i | \(0.622113\pi\) | |||||||
\(734\) | −8.34632 | −0.308068 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 28.1463 | 1.03678 | ||||||||
\(738\) | −1.92127 | −0.0707229 | ||||||||
\(739\) | −20.8376 | −0.766522 | −0.383261 | − | 0.923640i | \(-0.625199\pi\) | ||||
−0.383261 | + | 0.923640i | \(0.625199\pi\) | |||||||
\(740\) | 25.4145 | 0.934254 | ||||||||
\(741\) | 8.37394 | 0.307624 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.3222 | −1.07573 | −0.537864 | − | 0.843032i | \(-0.680769\pi\) | ||||
−0.537864 | + | 0.843032i | \(0.680769\pi\) | |||||||
\(744\) | −1.43727 | −0.0526930 | ||||||||
\(745\) | 8.55154 | 0.313304 | ||||||||
\(746\) | 20.5596 | 0.752741 | ||||||||
\(747\) | 4.37704 | 0.160148 | ||||||||
\(748\) | 13.0405 | 0.476809 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −17.8284 | −0.651002 | ||||||||
\(751\) | 3.60325 | 0.131485 | 0.0657423 | − | 0.997837i | \(-0.479058\pi\) | ||||
0.0657423 | + | 0.997837i | \(0.479058\pi\) | |||||||
\(752\) | 6.99690 | 0.255151 | ||||||||
\(753\) | 9.87644 | 0.359917 | ||||||||
\(754\) | 5.92127 | 0.215640 | ||||||||
\(755\) | −85.0423 | −3.09501 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.0161 | 1.85421 | 0.927105 | − | 0.374801i | \(-0.122289\pi\) | ||||
0.927105 | + | 0.374801i | \(0.122289\pi\) | |||||||
\(758\) | −1.45139 | −0.0527167 | ||||||||
\(759\) | −5.27981 | −0.191645 | ||||||||
\(760\) | 7.35544 | 0.266810 | ||||||||
\(761\) | −38.8524 | −1.40840 | −0.704200 | − | 0.710002i | \(-0.748694\pi\) | ||||
−0.704200 | + | 0.710002i | \(0.748694\pi\) | |||||||
\(762\) | −18.9367 | −0.686003 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.6384 | −0.601955 | ||||||||
\(765\) | 9.45577 | 0.341874 | ||||||||
\(766\) | 29.4145 | 1.06279 | ||||||||
\(767\) | 18.7344 | 0.676459 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 23.4176 | 0.844459 | 0.422230 | − | 0.906489i | \(-0.361248\pi\) | ||||
0.422230 | + | 0.906489i | \(0.361248\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.3554 | −0.769098 | ||||||||
\(772\) | 25.2165 | 0.907561 | ||||||||
\(773\) | −26.1685 | −0.941215 | −0.470607 | − | 0.882343i | \(-0.655965\pi\) | ||||
−0.470607 | + | 0.882343i | \(0.655965\pi\) | |||||||
\(774\) | −8.21648 | −0.295335 | ||||||||
\(775\) | 13.8795 | 0.498568 | ||||||||
\(776\) | −0.298311 | −0.0107087 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.1513 | 0.794161 | ||||||||
\(779\) | −3.69128 | −0.132254 | ||||||||
\(780\) | 16.6864 | 0.597468 | ||||||||
\(781\) | 40.3455 | 1.44367 | ||||||||
\(782\) | 2.46988 | 0.0883229 | ||||||||
\(783\) | 1.35854 | 0.0485504 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.4785 | −1.44474 | ||||||||
\(786\) | 16.3554 | 0.583379 | ||||||||
\(787\) | 12.4872 | 0.445120 | 0.222560 | − | 0.974919i | \(-0.428559\pi\) | ||||
0.222560 | + | 0.974919i | \(0.428559\pi\) | |||||||
\(788\) | 13.6199 | 0.485187 | ||||||||
\(789\) | −8.68009 | −0.309019 | ||||||||
\(790\) | 5.20108 | 0.185046 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.27981 | 0.187610 | ||||||||
\(793\) | 49.8363 | 1.76974 | ||||||||
\(794\) | 20.8567 | 0.740178 | ||||||||
\(795\) | 11.0590 | 0.392223 | ||||||||
\(796\) | 0.902774 | 0.0319980 | ||||||||
\(797\) | 15.2626 | 0.540629 | 0.270315 | − | 0.962772i | \(-0.412872\pi\) | ||||
0.270315 | + | 0.962772i | \(0.412872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.2815 | 0.611377 | ||||||||
\(800\) | 9.65685 | 0.341421 | ||||||||
\(801\) | 12.2952 | 0.434430 | ||||||||
\(802\) | −15.0430 | −0.531187 | ||||||||
\(803\) | 2.30872 | 0.0814729 | ||||||||
\(804\) | −5.33092 | −0.188007 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.26442 | −0.220655 | ||||||||
\(807\) | −26.0142 | −0.915743 | ||||||||
\(808\) | −18.0590 | −0.635314 | ||||||||
\(809\) | −21.3492 | −0.750600 | −0.375300 | − | 0.926903i | \(-0.622460\pi\) | ||||
−0.375300 | + | 0.926903i | \(0.622460\pi\) | |||||||
\(810\) | 3.82843 | 0.134517 | ||||||||
\(811\) | −2.14869 | −0.0754508 | −0.0377254 | − | 0.999288i | \(-0.512011\pi\) | ||||
−0.0377254 | + | 0.999288i | \(0.512011\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.43727 | 0.0504074 | ||||||||
\(814\) | 35.0493 | 1.22848 | ||||||||
\(815\) | 75.5325 | 2.64579 | ||||||||
\(816\) | −2.46988 | −0.0864632 | ||||||||
\(817\) | −15.7861 | −0.552285 | ||||||||
\(818\) | 19.0960 | 0.667677 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.35544 | −0.256863 | ||||||||
\(821\) | 23.5688 | 0.822558 | 0.411279 | − | 0.911510i | \(-0.365082\pi\) | ||||
0.411279 | + | 0.911510i | \(0.365082\pi\) | |||||||
\(822\) | 5.10824 | 0.178170 | ||||||||
\(823\) | −19.0948 | −0.665603 | −0.332802 | − | 0.942997i | \(-0.607994\pi\) | ||||
−0.332802 | + | 0.942997i | \(0.607994\pi\) | |||||||
\(824\) | 0.669078 | 0.0233084 | ||||||||
\(825\) | −50.9864 | −1.77512 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.2428 | −0.460498 | −0.230249 | − | 0.973132i | \(-0.573954\pi\) | ||||
−0.230249 | + | 0.973132i | \(0.573954\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −17.6218 | −0.612029 | −0.306014 | − | 0.952027i | \(-0.598996\pi\) | ||||
−0.306014 | + | 0.952027i | \(0.598996\pi\) | |||||||
\(830\) | 16.7572 | 0.581650 | ||||||||
\(831\) | −18.0289 | −0.625416 | ||||||||
\(832\) | −4.35854 | −0.151105 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.31371 | 0.322507 | ||||||||
\(835\) | −40.9288 | −1.41640 | ||||||||
\(836\) | 10.1440 | 0.350836 | ||||||||
\(837\) | −1.43727 | −0.0496794 | ||||||||
\(838\) | 20.2165 | 0.698367 | ||||||||
\(839\) | 5.89682 | 0.203581 | 0.101790 | − | 0.994806i | \(-0.467543\pi\) | ||||
0.101790 | + | 0.994806i | \(0.467543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1544 | −0.936357 | ||||||||
\(842\) | 8.59662 | 0.296259 | ||||||||
\(843\) | −24.9643 | −0.859816 | ||||||||
\(844\) | −22.8131 | −0.785259 | ||||||||
\(845\) | 22.9587 | 0.789803 | ||||||||
\(846\) | 6.99690 | 0.240558 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.88866 | −0.0991970 | ||||||||
\(849\) | 2.73430 | 0.0938409 | ||||||||
\(850\) | 23.8513 | 0.818093 | ||||||||
\(851\) | 6.63836 | 0.227560 | ||||||||
\(852\) | −7.64146 | −0.261792 | ||||||||
\(853\) | −26.1575 | −0.895614 | −0.447807 | − | 0.894130i | \(-0.647795\pi\) | ||||
−0.447807 | + | 0.894130i | \(0.647795\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.35544 | 0.251551 | ||||||||
\(856\) | −18.4361 | −0.630132 | ||||||||
\(857\) | 26.3825 | 0.901208 | 0.450604 | − | 0.892724i | \(-0.351209\pi\) | ||||
0.450604 | + | 0.892724i | \(0.351209\pi\) | |||||||
\(858\) | 23.0123 | 0.785627 | ||||||||
\(859\) | −40.4565 | −1.38036 | −0.690178 | − | 0.723640i | \(-0.742468\pi\) | ||||
−0.690178 | + | 0.723640i | \(0.742468\pi\) | |||||||
\(860\) | −31.4562 | −1.07265 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.0616 | 1.22826 | ||||||||
\(863\) | −20.2501 | −0.689322 | −0.344661 | − | 0.938727i | \(-0.612006\pi\) | ||||
−0.344661 | + | 0.938727i | \(0.612006\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −84.3433 | −2.86776 | ||||||||
\(866\) | −7.56462 | −0.257056 | ||||||||
\(867\) | 10.8997 | 0.370172 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.17286 | 0.243322 | ||||||||
\(870\) | 5.20108 | 0.176333 | ||||||||
\(871\) | −23.2351 | −0.787290 | ||||||||
\(872\) | 16.5314 | 0.559824 | ||||||||
\(873\) | −0.298311 | −0.0100963 | ||||||||
\(874\) | 1.92127 | 0.0649879 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.437273 | −0.0147741 | ||||||||
\(877\) | −9.88873 | −0.333919 | −0.166959 | − | 0.985964i | \(-0.553395\pi\) | ||||
−0.166959 | + | 0.985964i | \(0.553395\pi\) | |||||||
\(878\) | −35.1470 | −1.18615 | ||||||||
\(879\) | −14.5147 | −0.489569 | ||||||||
\(880\) | 20.2134 | 0.681393 | ||||||||
\(881\) | −4.39115 | −0.147942 | −0.0739709 | − | 0.997260i | \(-0.523567\pi\) | ||||
−0.0739709 | + | 0.997260i | \(0.523567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.05428 | −0.203743 | −0.101871 | − | 0.994798i | \(-0.532483\pi\) | ||||
−0.101871 | + | 0.994798i | \(0.532483\pi\) | |||||||
\(884\) | −10.7651 | −0.362069 | ||||||||
\(885\) | 16.4558 | 0.553155 | ||||||||
\(886\) | −6.35544 | −0.213515 | ||||||||
\(887\) | 44.4946 | 1.49398 | 0.746990 | − | 0.664835i | \(-0.231498\pi\) | ||||
0.746990 | + | 0.664835i | \(0.231498\pi\) | |||||||
\(888\) | −6.63836 | −0.222769 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 47.0713 | 1.57783 | ||||||||
\(891\) | 5.27981 | 0.176880 | ||||||||
\(892\) | 0.942867 | 0.0315695 | ||||||||
\(893\) | 13.4429 | 0.449851 | ||||||||
\(894\) | −2.23370 | −0.0747059 | ||||||||
\(895\) | −65.0714 | −2.17510 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.35854 | 0.145528 | ||||||||
\(898\) | −4.36043 | −0.145510 | ||||||||
\(899\) | −1.95260 | −0.0651228 | ||||||||
\(900\) | 9.65685 | 0.321895 | ||||||||
\(901\) | −7.13465 | −0.237690 | ||||||||
\(902\) | −10.1440 | −0.337757 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.7466 | 0.656762 | ||||||||
\(905\) | 47.4808 | 1.57832 | ||||||||
\(906\) | 22.2134 | 0.737990 | ||||||||
\(907\) | −20.0063 | −0.664297 | −0.332149 | − | 0.943227i | \(-0.607774\pi\) | ||||
−0.332149 | + | 0.943227i | \(0.607774\pi\) | |||||||
\(908\) | −15.3106 | −0.508100 | ||||||||
\(909\) | −18.0590 | −0.598980 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.4085 | 1.20627 | 0.603134 | − | 0.797640i | \(-0.293918\pi\) | ||||
0.603134 | + | 0.797640i | \(0.293918\pi\) | |||||||
\(912\) | −1.92127 | −0.0636196 | ||||||||
\(913\) | 23.1100 | 0.764828 | ||||||||
\(914\) | −33.8567 | −1.11988 | ||||||||
\(915\) | 43.7749 | 1.44715 | ||||||||
\(916\) | 6.07873 | 0.200847 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.46988 | −0.0815183 | ||||||||
\(919\) | −33.7883 | −1.11457 | −0.557287 | − | 0.830320i | \(-0.688158\pi\) | ||||
−0.557287 | + | 0.830320i | \(0.688158\pi\) | |||||||
\(920\) | 3.82843 | 0.126220 | ||||||||
\(921\) | 31.9521 | 1.05286 | ||||||||
\(922\) | 17.6851 | 0.582427 | ||||||||
\(923\) | −33.3056 | −1.09627 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 64.1056 | 2.10778 | ||||||||
\(926\) | 35.5954 | 1.16974 | ||||||||
\(927\) | 0.669078 | 0.0219754 | ||||||||
\(928\) | −1.35854 | −0.0445964 | ||||||||
\(929\) | 28.8610 | 0.946900 | 0.473450 | − | 0.880821i | \(-0.343008\pi\) | ||||
0.473450 | + | 0.880821i | \(0.343008\pi\) | |||||||
\(930\) | −5.50249 | −0.180434 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.57812 | −0.248230 | ||||||||
\(933\) | 31.0142 | 1.01536 | ||||||||
\(934\) | 14.4022 | 0.471253 | ||||||||
\(935\) | 49.9247 | 1.63271 | ||||||||
\(936\) | −4.35854 | −0.142463 | ||||||||
\(937\) | −15.6710 | −0.511951 | −0.255975 | − | 0.966683i | \(-0.582397\pi\) | ||||
−0.255975 | + | 0.966683i | \(0.582397\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.57623 | −0.214607 | ||||||||
\(940\) | 26.7871 | 0.873700 | ||||||||
\(941\) | −21.7460 | −0.708899 | −0.354450 | − | 0.935075i | \(-0.615332\pi\) | ||||
−0.354450 | + | 0.935075i | \(0.615332\pi\) | |||||||
\(942\) | 10.5731 | 0.344491 | ||||||||
\(943\) | −1.92127 | −0.0625652 | ||||||||
\(944\) | −4.29831 | −0.139898 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.3815 | −1.41045 | ||||||||
\(947\) | 24.3784 | 0.792192 | 0.396096 | − | 0.918209i | \(-0.370365\pi\) | ||||
0.396096 | + | 0.918209i | \(0.370365\pi\) | |||||||
\(948\) | −1.35854 | −0.0441234 | ||||||||
\(949\) | −1.90587 | −0.0618673 | ||||||||
\(950\) | 18.5534 | 0.601953 | ||||||||
\(951\) | 28.0142 | 0.908422 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.2178 | 1.33518 | 0.667588 | − | 0.744531i | \(-0.267327\pi\) | ||||
0.667588 | + | 0.744531i | \(0.267327\pi\) | |||||||
\(954\) | −2.88866 | −0.0935238 | ||||||||
\(955\) | −63.6987 | −2.06124 | ||||||||
\(956\) | −16.4330 | −0.531480 | ||||||||
\(957\) | 7.17286 | 0.231866 | ||||||||
\(958\) | 38.3542 | 1.23917 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.82843 | −0.123562 | ||||||||
\(961\) | −28.9342 | −0.933363 | ||||||||
\(962\) | −28.9336 | −0.932856 | ||||||||
\(963\) | −18.4361 | −0.594094 | ||||||||
\(964\) | 13.2319 | 0.426170 | ||||||||
\(965\) | 96.5395 | 3.10772 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.7730 | 1.18254 | 0.591270 | − | 0.806474i | \(-0.298627\pi\) | ||||
0.591270 | + | 0.806474i | \(0.298627\pi\) | |||||||
\(968\) | 16.8764 | 0.542429 | ||||||||
\(969\) | −4.74531 | −0.152441 | ||||||||
\(970\) | −1.14206 | −0.0366694 | ||||||||
\(971\) | −15.9661 | −0.512377 | −0.256188 | − | 0.966627i | \(-0.582467\pi\) | ||||
−0.256188 | + | 0.966627i | \(0.582467\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20.2504 | 0.648864 | ||||||||
\(975\) | 42.0898 | 1.34795 | ||||||||
\(976\) | −11.4342 | −0.365999 | ||||||||
\(977\) | 18.0392 | 0.577127 | 0.288563 | − | 0.957461i | \(-0.406822\pi\) | ||||
0.288563 | + | 0.957461i | \(0.406822\pi\) | |||||||
\(978\) | −19.7294 | −0.630876 | ||||||||
\(979\) | 64.9164 | 2.07474 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.5314 | 0.527807 | ||||||||
\(982\) | −26.6459 | −0.850305 | ||||||||
\(983\) | 14.0417 | 0.447862 | 0.223931 | − | 0.974605i | \(-0.428111\pi\) | ||||
0.223931 | + | 0.974605i | \(0.428111\pi\) | |||||||
\(984\) | 1.92127 | 0.0612479 | ||||||||
\(985\) | 52.1426 | 1.66140 | ||||||||
\(986\) | −3.35544 | −0.106859 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.37394 | −0.266411 | ||||||||
\(989\) | −8.21648 | −0.261269 | ||||||||
\(990\) | 20.2134 | 0.642423 | ||||||||
\(991\) | 14.1581 | 0.449748 | 0.224874 | − | 0.974388i | \(-0.427803\pi\) | ||||
0.224874 | + | 0.974388i | \(0.427803\pi\) | |||||||
\(992\) | 1.43727 | 0.0456335 | ||||||||
\(993\) | −24.8266 | −0.787849 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.45620 | 0.109569 | ||||||||
\(996\) | −4.37704 | −0.138692 | ||||||||
\(997\) | 25.1735 | 0.797254 | 0.398627 | − | 0.917113i | \(-0.369487\pi\) | ||||
0.398627 | + | 0.917113i | \(0.369487\pi\) | |||||||
\(998\) | −13.0602 | −0.413414 | ||||||||
\(999\) | −6.63836 | −0.210028 |
(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 | 6762.2.a.cm.1.4 | 4 | ||
7.3 | odd | 6 | 966.2.i.l.415.3 | yes | 8 | ||
7.5 | odd | 6 | 966.2.i.l.277.3 | ✓ | 8 | ||
7.6 | odd | 2 | 6762.2.a.cp.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.l.277.3 | ✓ | 8 | 7.5 | odd | 6 | ||
966.2.i.l.415.3 | yes | 8 | 7.3 | odd | 6 | ||
6762.2.a.cm.1.4 | 4 | 1.1 | even | 1 | trivial | ||
6762.2.a.cp.1.2 | 4 | 7.6 | odd | 2 |