Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 31 x^{10} + 82 x^{9} + 334 x^{8} - 684 x^{7} - 1561 x^{6} + 1551 x^{5} + 3573 x^{4} + 345 x^{3} - 1607 x^{2} - 594 x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.28984\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.28984 | −0.576836 | −0.288418 | − | 0.957505i | \(-0.593129\pi\) | ||||
−0.288418 | + | 0.957505i | \(0.593129\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.20787 | 1.21246 | 0.606230 | − | 0.795290i | \(-0.292681\pi\) | ||||
0.606230 | + | 0.795290i | \(0.292681\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.28984 | 0.407885 | ||||||||
\(11\) | 3.26304 | 0.983844 | 0.491922 | − | 0.870639i | \(-0.336294\pi\) | ||||
0.491922 | + | 0.870639i | \(0.336294\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.85048 | −1.06793 | −0.533966 | − | 0.845506i | \(-0.679299\pi\) | ||||
−0.533966 | + | 0.845506i | \(0.679299\pi\) | |||||||
\(14\) | −3.20787 | −0.857338 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.41773 | 1.31399 | 0.656996 | − | 0.753894i | \(-0.271827\pi\) | ||||
0.656996 | + | 0.753894i | \(0.271827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.39994 | −1.00941 | −0.504707 | − | 0.863290i | \(-0.668400\pi\) | ||||
−0.504707 | + | 0.863290i | \(0.668400\pi\) | |||||||
\(20\) | −1.28984 | −0.288418 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.26304 | −0.695683 | ||||||||
\(23\) | −0.544759 | −0.113590 | −0.0567951 | − | 0.998386i | \(-0.518088\pi\) | ||||
−0.0567951 | + | 0.998386i | \(0.518088\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.33630 | −0.667260 | ||||||||
\(26\) | 3.85048 | 0.755141 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.20787 | 0.606230 | ||||||||
\(29\) | 5.75789 | 1.06921 | 0.534606 | − | 0.845101i | \(-0.320460\pi\) | ||||
0.534606 | + | 0.845101i | \(0.320460\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.11583 | 1.09844 | 0.549218 | − | 0.835679i | \(-0.314926\pi\) | ||||
0.549218 | + | 0.835679i | \(0.314926\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.41773 | −0.929133 | ||||||||
\(35\) | −4.13765 | −0.699390 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.67003 | −0.767749 | −0.383874 | − | 0.923385i | \(-0.625410\pi\) | ||||
−0.383874 | + | 0.923385i | \(0.625410\pi\) | |||||||
\(38\) | 4.39994 | 0.713764 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.28984 | 0.203942 | ||||||||
\(41\) | −9.17084 | −1.43224 | −0.716122 | − | 0.697975i | \(-0.754085\pi\) | ||||
−0.716122 | + | 0.697975i | \(0.754085\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.38737 | 0.821566 | 0.410783 | − | 0.911733i | \(-0.365255\pi\) | ||||
0.410783 | + | 0.911733i | \(0.365255\pi\) | |||||||
\(44\) | 3.26304 | 0.491922 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.544759 | 0.0803203 | ||||||||
\(47\) | 12.5824 | 1.83534 | 0.917668 | − | 0.397348i | \(-0.130070\pi\) | ||||
0.917668 | + | 0.397348i | \(0.130070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.29040 | 0.470058 | ||||||||
\(50\) | 3.33630 | 0.471824 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.85048 | −0.533966 | ||||||||
\(53\) | 10.7984 | 1.48328 | 0.741639 | − | 0.670799i | \(-0.234049\pi\) | ||||
0.741639 | + | 0.670799i | \(0.234049\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.20882 | −0.567517 | ||||||||
\(56\) | −3.20787 | −0.428669 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.75789 | −0.756048 | ||||||||
\(59\) | −3.15039 | −0.410145 | −0.205073 | − | 0.978747i | \(-0.565743\pi\) | ||||
−0.205073 | + | 0.978747i | \(0.565743\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.9696 | −1.78863 | −0.894313 | − | 0.447442i | \(-0.852335\pi\) | ||||
−0.894313 | + | 0.447442i | \(0.852335\pi\) | |||||||
\(62\) | −6.11583 | −0.776711 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.96652 | 0.616021 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.06275 | −1.10719 | −0.553595 | − | 0.832786i | \(-0.686745\pi\) | ||||
−0.553595 | + | 0.832786i | \(0.686745\pi\) | |||||||
\(68\) | 5.41773 | 0.656996 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.13765 | 0.494544 | ||||||||
\(71\) | 5.97564 | 0.709178 | 0.354589 | − | 0.935022i | \(-0.384621\pi\) | ||||
0.354589 | + | 0.935022i | \(0.384621\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.92590 | 0.693574 | 0.346787 | − | 0.937944i | \(-0.387273\pi\) | ||||
0.346787 | + | 0.937944i | \(0.387273\pi\) | |||||||
\(74\) | 4.67003 | 0.542881 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.39994 | −0.504707 | ||||||||
\(77\) | 10.4674 | 1.19287 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.21363 | 0.699088 | 0.349544 | − | 0.936920i | \(-0.386337\pi\) | ||||
0.349544 | + | 0.936920i | \(0.386337\pi\) | |||||||
\(80\) | −1.28984 | −0.144209 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.17084 | 1.01275 | ||||||||
\(83\) | 0.323107 | 0.0354656 | 0.0177328 | − | 0.999843i | \(-0.494355\pi\) | ||||
0.0177328 | + | 0.999843i | \(0.494355\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.98803 | −0.757958 | ||||||||
\(86\) | −5.38737 | −0.580935 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.26304 | −0.347841 | ||||||||
\(89\) | −4.91999 | −0.521518 | −0.260759 | − | 0.965404i | \(-0.583973\pi\) | ||||
−0.260759 | + | 0.965404i | \(0.583973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.3518 | −1.29482 | ||||||||
\(92\) | −0.544759 | −0.0567951 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.5824 | −1.29778 | ||||||||
\(95\) | 5.67524 | 0.582267 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0890 | 1.63359 | 0.816796 | − | 0.576927i | \(-0.195748\pi\) | ||||
0.816796 | + | 0.576927i | \(0.195748\pi\) | |||||||
\(98\) | −3.29040 | −0.332381 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.33630 | −0.333630 | ||||||||
\(101\) | 11.4226 | 1.13659 | 0.568294 | − | 0.822825i | \(-0.307603\pi\) | ||||
0.568294 | + | 0.822825i | \(0.307603\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.09261 | 0.304723 | 0.152362 | − | 0.988325i | \(-0.451312\pi\) | ||||
0.152362 | + | 0.988325i | \(0.451312\pi\) | |||||||
\(104\) | 3.85048 | 0.377571 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.7984 | −1.04884 | ||||||||
\(107\) | 5.60796 | 0.542142 | 0.271071 | − | 0.962559i | \(-0.412622\pi\) | ||||
0.271071 | + | 0.962559i | \(0.412622\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.52073 | −0.337225 | −0.168612 | − | 0.985682i | \(-0.553929\pi\) | ||||
−0.168612 | + | 0.985682i | \(0.553929\pi\) | |||||||
\(110\) | 4.20882 | 0.401295 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.20787 | 0.303115 | ||||||||
\(113\) | 6.78189 | 0.637987 | 0.318993 | − | 0.947757i | \(-0.396655\pi\) | ||||
0.318993 | + | 0.947757i | \(0.396655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.702655 | 0.0655229 | ||||||||
\(116\) | 5.75789 | 0.534606 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.15039 | 0.290017 | ||||||||
\(119\) | 17.3794 | 1.59316 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.352555 | −0.0320504 | ||||||||
\(122\) | 13.9696 | 1.26475 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.11583 | 0.549218 | ||||||||
\(125\) | 10.7525 | 0.961736 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6435 | 1.38814 | 0.694070 | − | 0.719908i | \(-0.255816\pi\) | ||||
0.694070 | + | 0.719908i | \(0.255816\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.96652 | −0.435593 | ||||||||
\(131\) | 6.07893 | 0.531119 | 0.265559 | − | 0.964094i | \(-0.414443\pi\) | ||||
0.265559 | + | 0.964094i | \(0.414443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.1144 | −1.22387 | ||||||||
\(134\) | 9.06275 | 0.782902 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.41773 | −0.464567 | ||||||||
\(137\) | −16.0391 | −1.37032 | −0.685158 | − | 0.728395i | \(-0.740267\pi\) | ||||
−0.685158 | + | 0.728395i | \(0.740267\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.6387 | −0.902362 | −0.451181 | − | 0.892432i | \(-0.648997\pi\) | ||||
−0.451181 | + | 0.892432i | \(0.648997\pi\) | |||||||
\(140\) | −4.13765 | −0.349695 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.97564 | −0.501465 | ||||||||
\(143\) | −12.5643 | −1.05068 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.42678 | −0.616761 | ||||||||
\(146\) | −5.92590 | −0.490431 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.67003 | −0.383874 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.15112 | 0.500571 | 0.250285 | − | 0.968172i | \(-0.419476\pi\) | ||||
0.250285 | + | 0.968172i | \(0.419476\pi\) | |||||||
\(152\) | 4.39994 | 0.356882 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.4674 | −0.843487 | ||||||||
\(155\) | −7.88847 | −0.633617 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4628 | −1.31387 | −0.656937 | − | 0.753945i | \(-0.728148\pi\) | ||||
−0.656937 | + | 0.753945i | \(0.728148\pi\) | |||||||
\(158\) | −6.21363 | −0.494330 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.28984 | 0.101971 | ||||||||
\(161\) | −1.74751 | −0.137723 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.94721 | 0.700800 | 0.350400 | − | 0.936600i | \(-0.386046\pi\) | ||||
0.350400 | + | 0.936600i | \(0.386046\pi\) | |||||||
\(164\) | −9.17084 | −0.716122 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.323107 | −0.0250780 | ||||||||
\(167\) | 0.565153 | 0.0437329 | 0.0218664 | − | 0.999761i | \(-0.493039\pi\) | ||||
0.0218664 | + | 0.999761i | \(0.493039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.82620 | 0.140477 | ||||||||
\(170\) | 6.98803 | 0.535958 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.38737 | 0.410783 | ||||||||
\(173\) | 6.52301 | 0.495935 | 0.247968 | − | 0.968768i | \(-0.420237\pi\) | ||||
0.247968 | + | 0.968768i | \(0.420237\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.7024 | −0.809026 | ||||||||
\(176\) | 3.26304 | 0.245961 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.91999 | 0.368769 | ||||||||
\(179\) | −17.3901 | −1.29979 | −0.649897 | − | 0.760022i | \(-0.725188\pi\) | ||||
−0.649897 | + | 0.760022i | \(0.725188\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5623 | −0.859421 | −0.429711 | − | 0.902967i | \(-0.641384\pi\) | ||||
−0.429711 | + | 0.902967i | \(0.641384\pi\) | |||||||
\(182\) | 12.3518 | 0.915578 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.544759 | 0.0401602 | ||||||||
\(185\) | 6.02362 | 0.442865 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.6783 | 1.29276 | ||||||||
\(188\) | 12.5824 | 0.917668 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.67524 | −0.411725 | ||||||||
\(191\) | −1.42498 | −0.103108 | −0.0515539 | − | 0.998670i | \(-0.516417\pi\) | ||||
−0.0515539 | + | 0.998670i | \(0.516417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.56918 | −0.328897 | −0.164449 | − | 0.986386i | \(-0.552584\pi\) | ||||
−0.164449 | + | 0.986386i | \(0.552584\pi\) | |||||||
\(194\) | −16.0890 | −1.15512 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.29040 | 0.235029 | ||||||||
\(197\) | −4.57007 | −0.325604 | −0.162802 | − | 0.986659i | \(-0.552053\pi\) | ||||
−0.162802 | + | 0.986659i | \(0.552053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.4721 | 1.80567 | 0.902833 | − | 0.429991i | \(-0.141483\pi\) | ||||
0.902833 | + | 0.429991i | \(0.141483\pi\) | |||||||
\(200\) | 3.33630 | 0.235912 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.4226 | −0.803690 | ||||||||
\(203\) | 18.4705 | 1.29638 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.8290 | 0.826170 | ||||||||
\(206\) | −3.09261 | −0.215472 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.85048 | −0.266983 | ||||||||
\(209\) | −14.3572 | −0.993107 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.7505 | 1.77274 | 0.886369 | − | 0.462979i | \(-0.153220\pi\) | ||||
0.886369 | + | 0.462979i | \(0.153220\pi\) | |||||||
\(212\) | 10.7984 | 0.741639 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.60796 | −0.383352 | ||||||||
\(215\) | −6.94887 | −0.473909 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.6188 | 1.33181 | ||||||||
\(218\) | 3.52073 | 0.238454 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.20882 | −0.283758 | ||||||||
\(221\) | −20.8609 | −1.40325 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3557 | 0.827398 | 0.413699 | − | 0.910414i | \(-0.364237\pi\) | ||||
0.413699 | + | 0.910414i | \(0.364237\pi\) | |||||||
\(224\) | −3.20787 | −0.214335 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.78189 | −0.451125 | ||||||||
\(227\) | −8.06407 | −0.535231 | −0.267615 | − | 0.963526i | \(-0.586236\pi\) | ||||
−0.267615 | + | 0.963526i | \(0.586236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0700 | 1.39235 | 0.696173 | − | 0.717874i | \(-0.254885\pi\) | ||||
0.696173 | + | 0.717874i | \(0.254885\pi\) | |||||||
\(230\) | −0.702655 | −0.0463317 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.75789 | −0.378024 | ||||||||
\(233\) | −15.8020 | −1.03522 | −0.517612 | − | 0.855615i | \(-0.673179\pi\) | ||||
−0.517612 | + | 0.855615i | \(0.673179\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.2294 | −1.05869 | ||||||||
\(236\) | −3.15039 | −0.205073 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −17.3794 | −1.12654 | ||||||||
\(239\) | 4.53148 | 0.293117 | 0.146559 | − | 0.989202i | \(-0.453180\pi\) | ||||
0.146559 | + | 0.989202i | \(0.453180\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.04690 | 0.518347 | 0.259173 | − | 0.965831i | \(-0.416550\pi\) | ||||
0.259173 | + | 0.965831i | \(0.416550\pi\) | |||||||
\(242\) | 0.352555 | 0.0226631 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.9696 | −0.894313 | ||||||||
\(245\) | −4.24411 | −0.271146 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.9419 | 1.07799 | ||||||||
\(248\) | −6.11583 | −0.388356 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.7525 | −0.680050 | ||||||||
\(251\) | −1.18604 | −0.0748623 | −0.0374312 | − | 0.999299i | \(-0.511917\pi\) | ||||
−0.0374312 | + | 0.999299i | \(0.511917\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.77757 | −0.111755 | ||||||||
\(254\) | −15.6435 | −0.981563 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.9570 | −1.30726 | −0.653632 | − | 0.756813i | \(-0.726756\pi\) | ||||
−0.653632 | + | 0.756813i | \(0.726756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.9808 | −0.930864 | ||||||||
\(260\) | 4.96652 | 0.308011 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.07893 | −0.375558 | ||||||||
\(263\) | 27.9860 | 1.72569 | 0.862844 | − | 0.505470i | \(-0.168681\pi\) | ||||
0.862844 | + | 0.505470i | \(0.168681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.9283 | −0.855609 | ||||||||
\(266\) | 14.1144 | 0.865410 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.06275 | −0.553595 | ||||||||
\(269\) | 16.7221 | 1.01956 | 0.509782 | − | 0.860304i | \(-0.329726\pi\) | ||||
0.509782 | + | 0.860304i | \(0.329726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.1645 | −1.52863 | −0.764316 | − | 0.644842i | \(-0.776923\pi\) | ||||
−0.764316 | + | 0.644842i | \(0.776923\pi\) | |||||||
\(272\) | 5.41773 | 0.328498 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.0391 | 0.968959 | ||||||||
\(275\) | −10.8865 | −0.656480 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.5995 | −1.89863 | −0.949315 | − | 0.314328i | \(-0.898221\pi\) | ||||
−0.949315 | + | 0.314328i | \(0.898221\pi\) | |||||||
\(278\) | 10.6387 | 0.638066 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.13765 | 0.247272 | ||||||||
\(281\) | 11.3652 | 0.677989 | 0.338995 | − | 0.940788i | \(-0.389913\pi\) | ||||
0.338995 | + | 0.940788i | \(0.389913\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.901374 | 0.0535811 | 0.0267906 | − | 0.999641i | \(-0.491471\pi\) | ||||
0.0267906 | + | 0.999641i | \(0.491471\pi\) | |||||||
\(284\) | 5.97564 | 0.354589 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.5643 | 0.742942 | ||||||||
\(287\) | −29.4188 | −1.73654 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.3518 | 0.726577 | ||||||||
\(290\) | 7.42678 | 0.436116 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.92590 | 0.346787 | ||||||||
\(293\) | 14.2554 | 0.832808 | 0.416404 | − | 0.909180i | \(-0.363290\pi\) | ||||
0.416404 | + | 0.909180i | \(0.363290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.06351 | 0.236587 | ||||||||
\(296\) | 4.67003 | 0.271440 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | 2.09758 | 0.121306 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.2820 | 0.996115 | ||||||||
\(302\) | −6.15112 | −0.353957 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.39994 | −0.252354 | ||||||||
\(305\) | 18.0186 | 1.03174 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.2188 | −1.43931 | −0.719656 | − | 0.694331i | \(-0.755701\pi\) | ||||
−0.719656 | + | 0.694331i | \(0.755701\pi\) | |||||||
\(308\) | 10.4674 | 0.596436 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.88847 | 0.448035 | ||||||||
\(311\) | −1.85525 | −0.105202 | −0.0526008 | − | 0.998616i | \(-0.516751\pi\) | ||||
−0.0526008 | + | 0.998616i | \(0.516751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.47705 | 0.422628 | 0.211314 | − | 0.977418i | \(-0.432226\pi\) | ||||
0.211314 | + | 0.977418i | \(0.432226\pi\) | |||||||
\(314\) | 16.4628 | 0.929049 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.21363 | 0.349544 | ||||||||
\(317\) | −30.7715 | −1.72830 | −0.864150 | − | 0.503234i | \(-0.832143\pi\) | ||||
−0.864150 | + | 0.503234i | \(0.832143\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.7882 | 1.05194 | ||||||||
\(320\) | −1.28984 | −0.0721045 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.74751 | 0.0973852 | ||||||||
\(323\) | −23.8377 | −1.32636 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8464 | 0.712588 | ||||||||
\(326\) | −8.94721 | −0.495540 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.17084 | 0.506375 | ||||||||
\(329\) | 40.3627 | 2.22527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9574 | 1.37178 | 0.685891 | − | 0.727704i | \(-0.259413\pi\) | ||||
0.685891 | + | 0.727704i | \(0.259413\pi\) | |||||||
\(332\) | 0.323107 | 0.0177328 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.565153 | −0.0309238 | ||||||||
\(335\) | 11.6895 | 0.638668 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0767 | 0.766805 | 0.383402 | − | 0.923581i | \(-0.374752\pi\) | ||||
0.383402 | + | 0.923581i | \(0.374752\pi\) | |||||||
\(338\) | −1.82620 | −0.0993324 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.98803 | −0.378979 | ||||||||
\(341\) | 19.9562 | 1.08069 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.8999 | −0.642533 | ||||||||
\(344\) | −5.38737 | −0.290467 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.52301 | −0.350679 | ||||||||
\(347\) | 0.244603 | 0.0131310 | 0.00656549 | − | 0.999978i | \(-0.497910\pi\) | ||||
0.00656549 | + | 0.999978i | \(0.497910\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.0705 | −1.50258 | −0.751289 | − | 0.659973i | \(-0.770568\pi\) | ||||
−0.751289 | + | 0.659973i | \(0.770568\pi\) | |||||||
\(350\) | 10.7024 | 0.572068 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.26304 | −0.173921 | ||||||||
\(353\) | −13.8962 | −0.739618 | −0.369809 | − | 0.929108i | \(-0.620577\pi\) | ||||
−0.369809 | + | 0.929108i | \(0.620577\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.70765 | −0.409079 | ||||||||
\(356\) | −4.91999 | −0.260759 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.3901 | 0.919093 | ||||||||
\(359\) | 28.8648 | 1.52342 | 0.761712 | − | 0.647915i | \(-0.224359\pi\) | ||||
0.761712 | + | 0.647915i | \(0.224359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.359449 | 0.0189184 | ||||||||
\(362\) | 11.5623 | 0.607703 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.3518 | −0.647412 | ||||||||
\(365\) | −7.64349 | −0.400078 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.27469 | −0.170937 | −0.0854686 | − | 0.996341i | \(-0.527239\pi\) | ||||
−0.0854686 | + | 0.996341i | \(0.527239\pi\) | |||||||
\(368\) | −0.544759 | −0.0283975 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.02362 | −0.313153 | ||||||||
\(371\) | 34.6399 | 1.79842 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.5287 | 0.752267 | 0.376134 | − | 0.926565i | \(-0.377253\pi\) | ||||
0.376134 | + | 0.926565i | \(0.377253\pi\) | |||||||
\(374\) | −17.6783 | −0.914122 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.5824 | −0.648889 | ||||||||
\(377\) | −22.1706 | −1.14185 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.92973 | 0.150490 | 0.0752449 | − | 0.997165i | \(-0.476026\pi\) | ||||
0.0752449 | + | 0.997165i | \(0.476026\pi\) | |||||||
\(380\) | 5.67524 | 0.291133 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.42498 | 0.0729082 | ||||||||
\(383\) | 6.14540 | 0.314015 | 0.157008 | − | 0.987597i | \(-0.449815\pi\) | ||||
0.157008 | + | 0.987597i | \(0.449815\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.5013 | −0.688091 | ||||||||
\(386\) | 4.56918 | 0.232565 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.0890 | 0.816796 | ||||||||
\(389\) | −18.2567 | −0.925650 | −0.462825 | − | 0.886450i | \(-0.653164\pi\) | ||||
−0.462825 | + | 0.886450i | \(0.653164\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.95136 | −0.149257 | ||||||||
\(392\) | −3.29040 | −0.166191 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.57007 | 0.230237 | ||||||||
\(395\) | −8.01461 | −0.403259 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.5588 | 0.931438 | 0.465719 | − | 0.884933i | \(-0.345796\pi\) | ||||
0.465719 | + | 0.884933i | \(0.345796\pi\) | |||||||
\(398\) | −25.4721 | −1.27680 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.33630 | −0.166815 | ||||||||
\(401\) | 22.3568 | 1.11645 | 0.558223 | − | 0.829691i | \(-0.311483\pi\) | ||||
0.558223 | + | 0.829691i | \(0.311483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.5489 | −1.17305 | ||||||||
\(404\) | 11.4226 | 0.568294 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.4705 | −0.916677 | ||||||||
\(407\) | −15.2385 | −0.755345 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.42743 | 0.317816 | 0.158908 | − | 0.987293i | \(-0.449203\pi\) | ||||
0.158908 | + | 0.987293i | \(0.449203\pi\) | |||||||
\(410\) | −11.8290 | −0.584191 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.09261 | 0.152362 | ||||||||
\(413\) | −10.1060 | −0.497285 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.416758 | −0.0204578 | ||||||||
\(416\) | 3.85048 | 0.188785 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.3572 | 0.702233 | ||||||||
\(419\) | 31.2114 | 1.52477 | 0.762387 | − | 0.647121i | \(-0.224027\pi\) | ||||
0.762387 | + | 0.647121i | \(0.224027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1359 | 0.786414 | 0.393207 | − | 0.919450i | \(-0.371366\pi\) | ||||
0.393207 | + | 0.919450i | \(0.371366\pi\) | |||||||
\(422\) | −25.7505 | −1.25352 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.7984 | −0.524418 | ||||||||
\(425\) | −18.0752 | −0.876775 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −44.8127 | −2.16864 | ||||||||
\(428\) | 5.60796 | 0.271071 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.94887 | 0.335104 | ||||||||
\(431\) | −5.79223 | −0.279002 | −0.139501 | − | 0.990222i | \(-0.544550\pi\) | ||||
−0.139501 | + | 0.990222i | \(0.544550\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.81723 | −0.0873305 | −0.0436653 | − | 0.999046i | \(-0.513904\pi\) | ||||
−0.0436653 | + | 0.999046i | \(0.513904\pi\) | |||||||
\(434\) | −19.6188 | −0.941731 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.52073 | −0.168612 | ||||||||
\(437\) | 2.39691 | 0.114660 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.0055 | 1.00254 | 0.501268 | − | 0.865292i | \(-0.332867\pi\) | ||||
0.501268 | + | 0.865292i | \(0.332867\pi\) | |||||||
\(440\) | 4.20882 | 0.200647 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.8609 | 0.992250 | ||||||||
\(443\) | 37.1284 | 1.76402 | 0.882011 | − | 0.471229i | \(-0.156189\pi\) | ||||
0.882011 | + | 0.471229i | \(0.156189\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.34602 | 0.300830 | ||||||||
\(446\) | −12.3557 | −0.585058 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.20787 | 0.151557 | ||||||||
\(449\) | 26.8067 | 1.26509 | 0.632543 | − | 0.774525i | \(-0.282011\pi\) | ||||
0.632543 | + | 0.774525i | \(0.282011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.9248 | −1.40911 | ||||||||
\(452\) | 6.78189 | 0.318993 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.06407 | 0.378465 | ||||||||
\(455\) | 15.9319 | 0.746901 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.8431 | 0.881443 | 0.440721 | − | 0.897644i | \(-0.354723\pi\) | ||||
0.440721 | + | 0.897644i | \(0.354723\pi\) | |||||||
\(458\) | −21.0700 | −0.984537 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.702655 | 0.0327614 | ||||||||
\(461\) | 0.774819 | 0.0360869 | 0.0180435 | − | 0.999837i | \(-0.494256\pi\) | ||||
0.0180435 | + | 0.999837i | \(0.494256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.87804 | 0.0872799 | 0.0436400 | − | 0.999047i | \(-0.486105\pi\) | ||||
0.0436400 | + | 0.999047i | \(0.486105\pi\) | |||||||
\(464\) | 5.75789 | 0.267303 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.8020 | 0.732014 | ||||||||
\(467\) | 12.1725 | 0.563276 | 0.281638 | − | 0.959521i | \(-0.409122\pi\) | ||||
0.281638 | + | 0.959521i | \(0.409122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.0721 | −1.34242 | ||||||||
\(470\) | 16.2294 | 0.748605 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.15039 | 0.145008 | ||||||||
\(473\) | 17.5792 | 0.808293 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.6795 | 0.673542 | ||||||||
\(476\) | 17.3794 | 0.796581 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.53148 | −0.207265 | ||||||||
\(479\) | 17.2910 | 0.790048 | 0.395024 | − | 0.918671i | \(-0.370736\pi\) | ||||
0.395024 | + | 0.918671i | \(0.370736\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.9819 | 0.819903 | ||||||||
\(482\) | −8.04690 | −0.366526 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.352555 | −0.0160252 | ||||||||
\(485\) | −20.7523 | −0.942315 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.7705 | −0.805257 | −0.402628 | − | 0.915364i | \(-0.631903\pi\) | ||||
−0.402628 | + | 0.915364i | \(0.631903\pi\) | |||||||
\(488\) | 13.9696 | 0.632375 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.24411 | 0.191729 | ||||||||
\(491\) | 21.3837 | 0.965033 | 0.482517 | − | 0.875887i | \(-0.339723\pi\) | ||||
0.482517 | + | 0.875887i | \(0.339723\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.1947 | 1.40494 | ||||||||
\(494\) | −16.9419 | −0.762251 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.11583 | 0.274609 | ||||||||
\(497\) | 19.1691 | 0.859850 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.9564 | 1.60963 | 0.804814 | − | 0.593528i | \(-0.202265\pi\) | ||||
0.804814 | + | 0.593528i | \(0.202265\pi\) | |||||||
\(500\) | 10.7525 | 0.480868 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.18604 | 0.0529356 | ||||||||
\(503\) | 4.49120 | 0.200253 | 0.100126 | − | 0.994975i | \(-0.468075\pi\) | ||||
0.100126 | + | 0.994975i | \(0.468075\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.7333 | −0.655625 | ||||||||
\(506\) | 1.77757 | 0.0790227 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.6435 | 0.694070 | ||||||||
\(509\) | 35.6812 | 1.58154 | 0.790770 | − | 0.612113i | \(-0.209680\pi\) | ||||
0.790770 | + | 0.612113i | \(0.209680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.0095 | 0.840930 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.9570 | 0.924375 | ||||||||
\(515\) | −3.98898 | −0.175775 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.0570 | 1.80568 | ||||||||
\(518\) | 14.9808 | 0.658221 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.96652 | −0.217796 | ||||||||
\(521\) | −26.0613 | −1.14177 | −0.570883 | − | 0.821031i | \(-0.693399\pi\) | ||||
−0.570883 | + | 0.821031i | \(0.693399\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.9756 | 1.87919 | 0.939596 | − | 0.342287i | \(-0.111201\pi\) | ||||
0.939596 | + | 0.342287i | \(0.111201\pi\) | |||||||
\(524\) | 6.07893 | 0.265559 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.9860 | −1.22025 | ||||||||
\(527\) | 33.1339 | 1.44334 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7032 | −0.987097 | ||||||||
\(530\) | 13.9283 | 0.605007 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.1144 | −0.611937 | ||||||||
\(533\) | 35.3122 | 1.52954 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.23339 | −0.312727 | ||||||||
\(536\) | 9.06275 | 0.391451 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.7221 | −0.720940 | ||||||||
\(539\) | 10.7367 | 0.462464 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.5023 | −0.881462 | −0.440731 | − | 0.897639i | \(-0.645281\pi\) | ||||
−0.440731 | + | 0.897639i | \(0.645281\pi\) | |||||||
\(542\) | 25.1645 | 1.08091 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.41773 | −0.232283 | ||||||||
\(545\) | 4.54119 | 0.194523 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.7695 | 1.82869 | 0.914345 | − | 0.404935i | \(-0.132706\pi\) | ||||
0.914345 | + | 0.404935i | \(0.132706\pi\) | |||||||
\(548\) | −16.0391 | −0.685158 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.8865 | 0.464202 | ||||||||
\(551\) | −25.3343 | −1.07928 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.9325 | 0.847616 | ||||||||
\(554\) | 31.5995 | 1.34253 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.6387 | −0.451181 | ||||||||
\(557\) | −41.5046 | −1.75861 | −0.879303 | − | 0.476263i | \(-0.841991\pi\) | ||||
−0.879303 | + | 0.476263i | \(0.841991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.7440 | −0.877376 | ||||||||
\(560\) | −4.13765 | −0.174848 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.3652 | −0.479411 | ||||||||
\(563\) | −11.8254 | −0.498382 | −0.249191 | − | 0.968454i | \(-0.580165\pi\) | ||||
−0.249191 | + | 0.968454i | \(0.580165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.74758 | −0.368014 | ||||||||
\(566\) | −0.901374 | −0.0378876 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.97564 | −0.250732 | ||||||||
\(569\) | 4.19085 | 0.175690 | 0.0878448 | − | 0.996134i | \(-0.472002\pi\) | ||||
0.0878448 | + | 0.996134i | \(0.472002\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.5467 | −0.566912 | −0.283456 | − | 0.958985i | \(-0.591481\pi\) | ||||
−0.283456 | + | 0.958985i | \(0.591481\pi\) | |||||||
\(572\) | −12.5643 | −0.525339 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 29.4188 | 1.22792 | ||||||||
\(575\) | 1.81748 | 0.0757942 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.9881 | −1.29005 | −0.645025 | − | 0.764162i | \(-0.723153\pi\) | ||||
−0.645025 | + | 0.764162i | \(0.723153\pi\) | |||||||
\(578\) | −12.3518 | −0.513768 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.42678 | −0.308380 | ||||||||
\(581\) | 1.03648 | 0.0430006 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.2357 | 1.45932 | ||||||||
\(584\) | −5.92590 | −0.245215 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.2554 | −0.588884 | ||||||||
\(587\) | −11.8328 | −0.488391 | −0.244196 | − | 0.969726i | \(-0.578524\pi\) | ||||
−0.244196 | + | 0.969726i | \(0.578524\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.9093 | −1.10878 | ||||||||
\(590\) | −4.06351 | −0.167292 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.67003 | −0.191937 | ||||||||
\(593\) | 26.1799 | 1.07508 | 0.537539 | − | 0.843239i | \(-0.319354\pi\) | ||||
0.537539 | + | 0.843239i | \(0.319354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.4167 | −0.918994 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.09758 | −0.0857766 | ||||||||
\(599\) | 28.2031 | 1.15235 | 0.576174 | − | 0.817327i | \(-0.304545\pi\) | ||||
0.576174 | + | 0.817327i | \(0.304545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.54747 | 0.307868 | 0.153934 | − | 0.988081i | \(-0.450806\pi\) | ||||
0.153934 | + | 0.988081i | \(0.450806\pi\) | |||||||
\(602\) | −17.2820 | −0.704360 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.15112 | 0.250285 | ||||||||
\(605\) | 0.454740 | 0.0184878 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.6119 | 0.552490 | 0.276245 | − | 0.961087i | \(-0.410910\pi\) | ||||
0.276245 | + | 0.961087i | \(0.410910\pi\) | |||||||
\(608\) | 4.39994 | 0.178441 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.0186 | −0.729553 | ||||||||
\(611\) | −48.4484 | −1.96001 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.2099 | −0.493155 | −0.246578 | − | 0.969123i | \(-0.579306\pi\) | ||||
−0.246578 | + | 0.969123i | \(0.579306\pi\) | |||||||
\(614\) | 25.2188 | 1.01775 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.4674 | −0.421744 | ||||||||
\(617\) | 17.9612 | 0.723090 | 0.361545 | − | 0.932355i | \(-0.382249\pi\) | ||||
0.361545 | + | 0.932355i | \(0.382249\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.78344 | −0.353036 | −0.176518 | − | 0.984297i | \(-0.556483\pi\) | ||||
−0.176518 | + | 0.984297i | \(0.556483\pi\) | |||||||
\(620\) | −7.88847 | −0.316809 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.85525 | 0.0743888 | ||||||||
\(623\) | −15.7827 | −0.632319 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.81241 | 0.112496 | ||||||||
\(626\) | −7.47705 | −0.298843 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.4628 | −0.656937 | ||||||||
\(629\) | −25.3010 | −1.00882 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.6453 | −1.53845 | −0.769223 | − | 0.638980i | \(-0.779357\pi\) | ||||
−0.769223 | + | 0.638980i | \(0.779357\pi\) | |||||||
\(632\) | −6.21363 | −0.247165 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.7715 | 1.22209 | ||||||||
\(635\) | −20.1777 | −0.800729 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.6696 | −0.501989 | ||||||||
\(638\) | −18.7882 | −0.743833 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.28984 | 0.0509856 | ||||||||
\(641\) | 6.71131 | 0.265081 | 0.132540 | − | 0.991178i | \(-0.457687\pi\) | ||||
0.132540 | + | 0.991178i | \(0.457687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.6962 | −1.40772 | −0.703859 | − | 0.710339i | \(-0.748542\pi\) | ||||
−0.703859 | + | 0.710339i | \(0.748542\pi\) | |||||||
\(644\) | −1.74751 | −0.0688617 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.8377 | 0.937881 | ||||||||
\(647\) | 19.7034 | 0.774621 | 0.387311 | − | 0.921949i | \(-0.373404\pi\) | ||||
0.387311 | + | 0.921949i | \(0.373404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2798 | −0.403519 | ||||||||
\(650\) | −12.8464 | −0.503876 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.94721 | 0.350400 | ||||||||
\(653\) | 1.14695 | 0.0448836 | 0.0224418 | − | 0.999748i | \(-0.492856\pi\) | ||||
0.0224418 | + | 0.999748i | \(0.492856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.84088 | −0.306368 | ||||||||
\(656\) | −9.17084 | −0.358061 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −40.3627 | −1.57350 | ||||||||
\(659\) | 41.4619 | 1.61513 | 0.807563 | − | 0.589781i | \(-0.200786\pi\) | ||||
0.807563 | + | 0.589781i | \(0.200786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.79426 | −0.342057 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(662\) | −24.9574 | −0.969997 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.323107 | −0.0125390 | ||||||||
\(665\) | 18.2054 | 0.705975 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.13666 | −0.121452 | ||||||||
\(668\) | 0.565153 | 0.0218664 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.6895 | −0.451606 | ||||||||
\(671\) | −45.5835 | −1.75973 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.42888 | 0.286362 | 0.143181 | − | 0.989697i | \(-0.454267\pi\) | ||||
0.143181 | + | 0.989697i | \(0.454267\pi\) | |||||||
\(674\) | −14.0767 | −0.542213 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.82620 | 0.0702386 | ||||||||
\(677\) | 2.76346 | 0.106209 | 0.0531043 | − | 0.998589i | \(-0.483088\pi\) | ||||
0.0531043 | + | 0.998589i | \(0.483088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 51.6114 | 1.98066 | ||||||||
\(680\) | 6.98803 | 0.267979 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −19.9562 | −0.764163 | ||||||||
\(683\) | 49.1142 | 1.87930 | 0.939652 | − | 0.342133i | \(-0.111149\pi\) | ||||
0.939652 | + | 0.342133i | \(0.111149\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.6880 | 0.790447 | ||||||||
\(686\) | 11.8999 | 0.454340 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.38737 | 0.205391 | ||||||||
\(689\) | −41.5792 | −1.58404 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1678 | −0.424843 | −0.212421 | − | 0.977178i | \(-0.568135\pi\) | ||||
−0.212421 | + | 0.977178i | \(0.568135\pi\) | |||||||
\(692\) | 6.52301 | 0.247968 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.244603 | −0.00928500 | ||||||||
\(695\) | 13.7223 | 0.520515 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.6852 | −1.88196 | ||||||||
\(698\) | 28.0705 | 1.06248 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.7024 | −0.404513 | ||||||||
\(701\) | 9.04525 | 0.341635 | 0.170817 | − | 0.985303i | \(-0.445359\pi\) | ||||
0.170817 | + | 0.985303i | \(0.445359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.5479 | 0.774977 | ||||||||
\(704\) | 3.26304 | 0.122981 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.8962 | 0.522989 | ||||||||
\(707\) | 36.6421 | 1.37807 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8659 | 1.42208 | 0.711042 | − | 0.703150i | \(-0.248224\pi\) | ||||
0.711042 | + | 0.703150i | \(0.248224\pi\) | |||||||
\(710\) | 7.70765 | 0.289263 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.91999 | 0.184384 | ||||||||
\(713\) | −3.33165 | −0.124771 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.2060 | 0.606069 | ||||||||
\(716\) | −17.3901 | −0.649897 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.8648 | −1.07722 | ||||||||
\(719\) | −36.3141 | −1.35429 | −0.677143 | − | 0.735852i | \(-0.736782\pi\) | ||||
−0.677143 | + | 0.735852i | \(0.736782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.92066 | 0.369465 | ||||||||
\(722\) | −0.359449 | −0.0133773 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.5623 | −0.429711 | ||||||||
\(725\) | −19.2100 | −0.713443 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.32073 | −0.345687 | −0.172843 | − | 0.984949i | \(-0.555295\pi\) | ||||
−0.172843 | + | 0.984949i | \(0.555295\pi\) | |||||||
\(728\) | 12.3518 | 0.457789 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.64349 | 0.282898 | ||||||||
\(731\) | 29.1873 | 1.07953 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.6052 | −0.724134 | −0.362067 | − | 0.932152i | \(-0.617929\pi\) | ||||
−0.362067 | + | 0.932152i | \(0.617929\pi\) | |||||||
\(734\) | 3.27469 | 0.120871 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.544759 | 0.0200801 | ||||||||
\(737\) | −29.5721 | −1.08930 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.7365 | 0.726020 | 0.363010 | − | 0.931785i | \(-0.381749\pi\) | ||||
0.363010 | + | 0.931785i | \(0.381749\pi\) | |||||||
\(740\) | 6.02362 | 0.221433 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −34.6399 | −1.27167 | ||||||||
\(743\) | 4.87522 | 0.178854 | 0.0894272 | − | 0.995993i | \(-0.471496\pi\) | ||||
0.0894272 | + | 0.995993i | \(0.471496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.28984 | 0.0472562 | ||||||||
\(746\) | −14.5287 | −0.531933 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.6783 | 0.646382 | ||||||||
\(749\) | 17.9896 | 0.657325 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.8776 | −1.30919 | −0.654596 | − | 0.755979i | \(-0.727161\pi\) | ||||
−0.654596 | + | 0.755979i | \(0.727161\pi\) | |||||||
\(752\) | 12.5824 | 0.458834 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.1706 | 0.807407 | ||||||||
\(755\) | −7.93399 | −0.288747 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.5845 | 1.40238 | 0.701189 | − | 0.712975i | \(-0.252653\pi\) | ||||
0.701189 | + | 0.712975i | \(0.252653\pi\) | |||||||
\(758\) | −2.92973 | −0.106412 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.67524 | −0.205862 | ||||||||
\(761\) | 8.51702 | 0.308742 | 0.154371 | − | 0.988013i | \(-0.450665\pi\) | ||||
0.154371 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2940 | −0.408871 | ||||||||
\(764\) | −1.42498 | −0.0515539 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.14540 | −0.222042 | ||||||||
\(767\) | 12.1305 | 0.438007 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.2406 | 1.01838 | 0.509191 | − | 0.860654i | \(-0.329945\pi\) | ||||
0.509191 | + | 0.860654i | \(0.329945\pi\) | |||||||
\(770\) | 13.5013 | 0.486554 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.56918 | −0.164449 | ||||||||
\(773\) | −53.0040 | −1.90642 | −0.953210 | − | 0.302308i | \(-0.902243\pi\) | ||||
−0.953210 | + | 0.302308i | \(0.902243\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.4042 | −0.732942 | ||||||||
\(776\) | −16.0890 | −0.577562 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.2567 | 0.654533 | ||||||||
\(779\) | 40.3511 | 1.44573 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.4988 | 0.697721 | ||||||||
\(782\) | 2.95136 | 0.105540 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.29040 | 0.117514 | ||||||||
\(785\) | 21.2344 | 0.757890 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.39006 | −0.192135 | −0.0960674 | − | 0.995375i | \(-0.530626\pi\) | ||||
−0.0960674 | + | 0.995375i | \(0.530626\pi\) | |||||||
\(788\) | −4.57007 | −0.162802 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.01461 | 0.285147 | ||||||||
\(791\) | 21.7554 | 0.773533 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.7897 | 1.91013 | ||||||||
\(794\) | −18.5588 | −0.658626 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.4721 | 0.902833 | ||||||||
\(797\) | −5.93084 | −0.210081 | −0.105041 | − | 0.994468i | \(-0.533497\pi\) | ||||
−0.105041 | + | 0.994468i | \(0.533497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 68.1682 | 2.41162 | ||||||||
\(800\) | 3.33630 | 0.117956 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.3568 | −0.789447 | ||||||||
\(803\) | 19.3365 | 0.682369 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.25402 | 0.0794438 | ||||||||
\(806\) | 23.5489 | 0.829474 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.4226 | −0.401845 | ||||||||
\(809\) | 44.5550 | 1.56647 | 0.783236 | − | 0.621725i | \(-0.213568\pi\) | ||||
0.783236 | + | 0.621725i | \(0.213568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.8980 | 0.944518 | 0.472259 | − | 0.881460i | \(-0.343439\pi\) | ||||
0.472259 | + | 0.881460i | \(0.343439\pi\) | |||||||
\(812\) | 18.4705 | 0.648189 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.2385 | 0.534110 | ||||||||
\(815\) | −11.5405 | −0.404247 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.7041 | −0.829301 | ||||||||
\(818\) | −6.42743 | −0.224730 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.8290 | 0.413085 | ||||||||
\(821\) | −17.4081 | −0.607547 | −0.303773 | − | 0.952744i | \(-0.598247\pi\) | ||||
−0.303773 | + | 0.952744i | \(0.598247\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.0176 | −0.732628 | −0.366314 | − | 0.930491i | \(-0.619380\pi\) | ||||
−0.366314 | + | 0.930491i | \(0.619380\pi\) | |||||||
\(824\) | −3.09261 | −0.107736 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.1060 | 0.351633 | ||||||||
\(827\) | 6.58525 | 0.228992 | 0.114496 | − | 0.993424i | \(-0.463475\pi\) | ||||
0.114496 | + | 0.993424i | \(0.463475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.68704 | −0.301713 | −0.150857 | − | 0.988556i | \(-0.548203\pi\) | ||||
−0.150857 | + | 0.988556i | \(0.548203\pi\) | |||||||
\(830\) | 0.416758 | 0.0144659 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.85048 | −0.133491 | ||||||||
\(833\) | 17.8265 | 0.617653 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.728960 | −0.0252267 | ||||||||
\(836\) | −14.3572 | −0.496554 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.2114 | −1.07818 | ||||||||
\(839\) | 41.3804 | 1.42861 | 0.714305 | − | 0.699834i | \(-0.246743\pi\) | ||||
0.714305 | + | 0.699834i | \(0.246743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.15328 | 0.143216 | ||||||||
\(842\) | −16.1359 | −0.556079 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 25.7505 | 0.886369 | ||||||||
\(845\) | −2.35552 | −0.0810323 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.13095 | −0.0388598 | ||||||||
\(848\) | 10.7984 | 0.370820 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.0752 | 0.619974 | ||||||||
\(851\) | 2.54404 | 0.0872087 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.8146 | 1.08931 | 0.544656 | − | 0.838660i | \(-0.316660\pi\) | ||||
0.544656 | + | 0.838660i | \(0.316660\pi\) | |||||||
\(854\) | 44.8127 | 1.53346 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.60796 | −0.191676 | ||||||||
\(857\) | −42.9083 | −1.46572 | −0.732860 | − | 0.680379i | \(-0.761815\pi\) | ||||
−0.732860 | + | 0.680379i | \(0.761815\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.2701 | 1.27164 | 0.635820 | − | 0.771838i | \(-0.280662\pi\) | ||||
0.635820 | + | 0.771838i | \(0.280662\pi\) | |||||||
\(860\) | −6.94887 | −0.236954 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.79223 | 0.197284 | ||||||||
\(863\) | 8.20579 | 0.279328 | 0.139664 | − | 0.990199i | \(-0.455398\pi\) | ||||
0.139664 | + | 0.990199i | \(0.455398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.41367 | −0.286073 | ||||||||
\(866\) | 1.81723 | 0.0617520 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 19.6188 | 0.665904 | ||||||||
\(869\) | 20.2753 | 0.687794 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.8959 | 1.18240 | ||||||||
\(872\) | 3.52073 | 0.119227 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.39691 | −0.0810766 | ||||||||
\(875\) | 34.4927 | 1.16607 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.5804 | −1.64044 | −0.820222 | − | 0.572045i | \(-0.806150\pi\) | ||||
−0.820222 | + | 0.572045i | \(0.806150\pi\) | |||||||
\(878\) | −21.0055 | −0.708900 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.20882 | −0.141879 | ||||||||
\(881\) | −36.4874 | −1.22929 | −0.614645 | − | 0.788804i | \(-0.710701\pi\) | ||||
−0.614645 | + | 0.788804i | \(0.710701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.4845 | −0.891273 | −0.445637 | − | 0.895214i | \(-0.647023\pi\) | ||||
−0.445637 | + | 0.895214i | \(0.647023\pi\) | |||||||
\(884\) | −20.8609 | −0.701627 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −37.1284 | −1.24735 | ||||||||
\(887\) | 52.1259 | 1.75022 | 0.875108 | − | 0.483928i | \(-0.160790\pi\) | ||||
0.875108 | + | 0.483928i | \(0.160790\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.1824 | 1.68306 | ||||||||
\(890\) | −6.34602 | −0.212719 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.3557 | 0.413699 | ||||||||
\(893\) | −55.3619 | −1.85262 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.4305 | 0.749768 | ||||||||
\(896\) | −3.20787 | −0.107167 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.8067 | −0.894551 | ||||||||
\(899\) | 35.2143 | 1.17446 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.5030 | 1.94902 | ||||||||
\(902\) | 29.9248 | 0.996388 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.78189 | −0.225562 | ||||||||
\(905\) | 14.9136 | 0.495745 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.3037 | 0.375332 | 0.187666 | − | 0.982233i | \(-0.439908\pi\) | ||||
0.187666 | + | 0.982233i | \(0.439908\pi\) | |||||||
\(908\) | −8.06407 | −0.267615 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15.9319 | −0.528139 | ||||||||
\(911\) | −42.3928 | −1.40453 | −0.702267 | − | 0.711913i | \(-0.747829\pi\) | ||||
−0.702267 | + | 0.711913i | \(0.747829\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.05431 | 0.0348926 | ||||||||
\(914\) | −18.8431 | −0.623274 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.0700 | 0.696173 | ||||||||
\(917\) | 19.5004 | 0.643960 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.6300 | −0.350651 | −0.175326 | − | 0.984510i | \(-0.556098\pi\) | ||||
−0.175326 | + | 0.984510i | \(0.556098\pi\) | |||||||
\(920\) | −0.702655 | −0.0231658 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.774819 | −0.0255173 | ||||||||
\(923\) | −23.0091 | −0.757354 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.5806 | 0.512288 | ||||||||
\(926\) | −1.87804 | −0.0617162 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.75789 | −0.189012 | ||||||||
\(929\) | −4.08682 | −0.134084 | −0.0670421 | − | 0.997750i | \(-0.521356\pi\) | ||||
−0.0670421 | + | 0.997750i | \(0.521356\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.4776 | −0.474483 | ||||||||
\(932\) | −15.8020 | −0.517612 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.1725 | −0.398296 | ||||||||
\(935\) | −22.8022 | −0.745713 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.3617 | −1.18788 | −0.593942 | − | 0.804508i | \(-0.702429\pi\) | ||||
−0.593942 | + | 0.804508i | \(0.702429\pi\) | |||||||
\(938\) | 29.0721 | 0.949237 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.2294 | −0.529344 | ||||||||
\(941\) | −55.3089 | −1.80302 | −0.901509 | − | 0.432761i | \(-0.857540\pi\) | ||||
−0.901509 | + | 0.432761i | \(0.857540\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.99590 | 0.162689 | ||||||||
\(944\) | −3.15039 | −0.102536 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.5792 | −0.571549 | ||||||||
\(947\) | 34.5292 | 1.12205 | 0.561025 | − | 0.827799i | \(-0.310407\pi\) | ||||
0.561025 | + | 0.827799i | \(0.310407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.8176 | −0.740689 | ||||||||
\(950\) | −14.6795 | −0.476266 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.3794 | −0.563268 | ||||||||
\(953\) | 59.7894 | 1.93677 | 0.968385 | − | 0.249462i | \(-0.0802538\pi\) | ||||
0.968385 | + | 0.249462i | \(0.0802538\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.83800 | 0.0594763 | ||||||||
\(956\) | 4.53148 | 0.146559 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.2910 | −0.558648 | ||||||||
\(959\) | −51.4514 | −1.66145 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.40336 | 0.206560 | ||||||||
\(962\) | −17.9819 | −0.579759 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.04690 | 0.259173 | ||||||||
\(965\) | 5.89354 | 0.189720 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.362252 | −0.0116492 | −0.00582461 | − | 0.999983i | \(-0.501854\pi\) | ||||
−0.00582461 | + | 0.999983i | \(0.501854\pi\) | |||||||
\(968\) | 0.352555 | 0.0113315 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20.7523 | 0.666317 | ||||||||
\(971\) | −1.80116 | −0.0578021 | −0.0289011 | − | 0.999582i | \(-0.509201\pi\) | ||||
−0.0289011 | + | 0.999582i | \(0.509201\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.1275 | −1.09408 | ||||||||
\(974\) | 17.7705 | 0.569402 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.9696 | −0.447157 | ||||||||
\(977\) | 6.43661 | 0.205925 | 0.102963 | − | 0.994685i | \(-0.467168\pi\) | ||||
0.102963 | + | 0.994685i | \(0.467168\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.0541 | −0.513092 | ||||||||
\(980\) | −4.24411 | −0.135573 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.3837 | −0.682382 | ||||||||
\(983\) | −51.5087 | −1.64287 | −0.821437 | − | 0.570299i | \(-0.806827\pi\) | ||||
−0.821437 | + | 0.570299i | \(0.806827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.89468 | 0.187820 | ||||||||
\(986\) | −31.1947 | −0.993441 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.9419 | 0.538993 | ||||||||
\(989\) | −2.93482 | −0.0933218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.4457 | 0.427118 | 0.213559 | − | 0.976930i | \(-0.431494\pi\) | ||||
0.213559 | + | 0.976930i | \(0.431494\pi\) | |||||||
\(992\) | −6.11583 | −0.194178 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −19.1691 | −0.608006 | ||||||||
\(995\) | −32.8550 | −1.04157 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.77372 | 0.119515 | 0.0597575 | − | 0.998213i | \(-0.480967\pi\) | ||||
0.0597575 | + | 0.998213i | \(0.480967\pi\) | |||||||
\(998\) | −35.9564 | −1.13818 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.k.1.3 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.n.1.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.k.1.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.n.1.10 | yes | 12 | 3.2 | odd | 2 |