Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7488,2,Mod(1,7488)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7488, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7488.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7488 = 2^{6} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7488.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: | \(59.7919810335\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1248) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7488.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.23607 | −0.552786 | −0.276393 | − | 0.961045i | \(-0.589139\pi\) | ||||
−0.276393 | + | 0.961045i | \(0.589139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23607 | 0.467190 | 0.233595 | − | 0.972334i | \(-0.424951\pi\) | ||||
0.233595 | + | 0.972334i | \(0.424951\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.23607 | 1.20124 | 0.600618 | − | 0.799536i | \(-0.294921\pi\) | ||||
0.600618 | + | 0.799536i | \(0.294921\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.47214 | −0.515476 | −0.257738 | − | 0.966215i | \(-0.582977\pi\) | ||||
−0.257738 | + | 0.966215i | \(0.582977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.70820 | −1.38443 | −0.692217 | − | 0.721689i | \(-0.743366\pi\) | ||||
−0.692217 | + | 0.721689i | \(0.743366\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.52786 | −0.258256 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.472136 | −0.0776187 | −0.0388093 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388093 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.23607 | −0.193041 | −0.0965207 | − | 0.995331i | \(-0.530771\pi\) | ||||
−0.0965207 | + | 0.995331i | \(0.530771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.47214 | 0.986991 | 0.493496 | − | 0.869748i | \(-0.335719\pi\) | ||||
0.493496 | + | 0.869748i | \(0.335719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.94427 | 1.01293 | 0.506463 | − | 0.862262i | \(-0.330953\pi\) | ||||
0.506463 | + | 0.862262i | \(0.330953\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.47214 | 0.333343 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.47214 | −1.10298 | −0.551489 | − | 0.834182i | \(-0.685940\pi\) | ||||
−0.551489 | + | 0.834182i | \(0.685940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4721 | 1.59689 | 0.798447 | − | 0.602066i | \(-0.205655\pi\) | ||||
0.798447 | + | 0.602066i | \(0.205655\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.23607 | −0.153315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.76393 | 0.826346 | 0.413173 | − | 0.910653i | \(-0.364421\pi\) | ||||
0.413173 | + | 0.910653i | \(0.364421\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.47214 | 0.530745 | 0.265372 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265372 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.472136 | 0.0552593 | 0.0276297 | − | 0.999618i | \(-0.491204\pi\) | ||||
0.0276297 | + | 0.999618i | \(0.491204\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.47214 | −0.281726 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.94427 | 1.00631 | 0.503155 | − | 0.864196i | \(-0.332173\pi\) | ||||
0.503155 | + | 0.864196i | \(0.332173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.52786 | −0.826290 | −0.413145 | − | 0.910665i | \(-0.635570\pi\) | ||||
−0.413145 | + | 0.910665i | \(0.635570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.52786 | 0.599581 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.1803 | 1.07911 | 0.539557 | − | 0.841949i | \(-0.318592\pi\) | ||||
0.539557 | + | 0.841949i | \(0.318592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23607 | 0.129575 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.47214 | −0.664027 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.47214 | −0.454077 | −0.227038 | − | 0.973886i | \(-0.572904\pi\) | ||||
−0.227038 | + | 0.973886i | \(0.572904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.94427 | −0.292966 | −0.146483 | − | 0.989213i | \(-0.546795\pi\) | ||||
−0.146483 | + | 0.989213i | \(0.546795\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.52786 | 0.150545 | 0.0752725 | − | 0.997163i | \(-0.476017\pi\) | ||||
0.0752725 | + | 0.997163i | \(0.476017\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.4721 | −1.39907 | −0.699537 | − | 0.714596i | \(-0.746610\pi\) | ||||
−0.699537 | + | 0.714596i | \(0.746610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.05573 | 0.101120 | 0.0505602 | − | 0.998721i | \(-0.483899\pi\) | ||||
0.0505602 | + | 0.998721i | \(0.483899\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.05573 | 0.284948 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.52786 | −0.506738 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.47214 | −0.574309 | −0.287155 | − | 0.957884i | \(-0.592709\pi\) | ||||
−0.287155 | + | 0.957884i | \(0.592709\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4164 | 0.997456 | 0.498728 | − | 0.866758i | \(-0.333801\pi\) | ||||
0.498728 | + | 0.866758i | \(0.333801\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.47214 | 0.561205 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.76393 | 0.577882 | 0.288941 | − | 0.957347i | \(-0.406697\pi\) | ||||
0.288941 | + | 0.957347i | \(0.406697\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8885 | −1.17801 | −0.589005 | − | 0.808129i | \(-0.700480\pi\) | ||||
−0.589005 | + | 0.808129i | \(0.700480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | −0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.52786 | −0.459064 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.29180 | 0.679290 | 0.339645 | − | 0.940554i | \(-0.389693\pi\) | ||||
0.339645 | + | 0.940554i | \(0.389693\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.7639 | 1.52699 | 0.763494 | − | 0.645815i | \(-0.223482\pi\) | ||||
0.763494 | + | 0.645815i | \(0.223482\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.52786 | 0.765296 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4164 | 1.07075 | 0.535373 | − | 0.844616i | \(-0.320171\pi\) | ||||
0.535373 | + | 0.844616i | \(0.320171\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.05573 | −0.240825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.76393 | 0.216488 | 0.108244 | − | 0.994124i | \(-0.465477\pi\) | ||||
0.108244 | + | 0.994124i | \(0.465477\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.8885 | −1.22949 | −0.614746 | − | 0.788725i | \(-0.710742\pi\) | ||||
−0.614746 | + | 0.788725i | \(0.710742\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000 | 0.152057 | 0.0760286 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760286 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.29180 | −0.324429 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.41641 | −0.554328 | −0.277164 | − | 0.960823i | \(-0.589395\pi\) | ||||
−0.277164 | + | 0.960823i | \(0.589395\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.41641 | −0.699916 | −0.349958 | − | 0.936765i | \(-0.613804\pi\) | ||||
−0.349958 | + | 0.936765i | \(0.613804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.583592 | 0.0429065 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.94427 | 0.654070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.52786 | −0.110552 | −0.0552762 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552762 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.8885 | 1.43161 | 0.715804 | − | 0.698301i | \(-0.246060\pi\) | ||||
0.715804 | + | 0.698301i | \(0.246060\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.7639 | 1.62186 | 0.810932 | − | 0.585141i | \(-0.198961\pi\) | ||||
0.810932 | + | 0.585141i | \(0.198961\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.52786 | 0.675412 | 0.337706 | − | 0.941252i | \(-0.390349\pi\) | ||||
0.337706 | + | 0.941252i | \(0.390349\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.52786 | 0.387980 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.52786 | 0.106711 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.4721 | −0.724373 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9443 | 1.16649 | 0.583246 | − | 0.812296i | \(-0.301782\pi\) | ||||
0.583246 | + | 0.812296i | \(0.301782\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.52786 | −0.646794 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.47214 | −0.300828 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.65248 | −0.311553 | −0.155776 | − | 0.987792i | \(-0.549788\pi\) | ||||
−0.155776 | + | 0.987792i | \(0.549788\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.9443 | −0.726397 | −0.363198 | − | 0.931712i | \(-0.618315\pi\) | ||||
−0.363198 | + | 0.931712i | \(0.618315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.4164 | 1.14099 | 0.570493 | − | 0.821302i | \(-0.306752\pi\) | ||||
0.570493 | + | 0.821302i | \(0.306752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.58359 | −0.559932 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.4721 | 0.806755 | 0.403378 | − | 0.915034i | \(-0.367836\pi\) | ||||
0.403378 | + | 0.915034i | \(0.367836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.3607 | −1.44038 | −0.720189 | − | 0.693778i | \(-0.755945\pi\) | ||||
−0.720189 | + | 0.693778i | \(0.755945\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.76393 | 0.432132 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.23607 | 0.333163 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.9443 | 1.82695 | 0.913473 | − | 0.406899i | \(-0.133390\pi\) | ||||
0.913473 | + | 0.406899i | \(0.133390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.94427 | 0.310844 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.4721 | 0.777990 | 0.388995 | − | 0.921240i | \(-0.372822\pi\) | ||||
0.388995 | + | 0.921240i | \(0.372822\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.583592 | −0.0362627 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.94427 | −0.551527 | −0.275764 | − | 0.961225i | \(-0.588931\pi\) | ||||
−0.275764 | + | 0.961225i | \(0.588931\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4721 | −0.643298 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.4721 | 1.24821 | 0.624104 | − | 0.781341i | \(-0.285464\pi\) | ||||
0.624104 | + | 0.781341i | \(0.285464\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1246 | 1.16174 | 0.580869 | − | 0.813997i | \(-0.302713\pi\) | ||||
0.580869 | + | 0.813997i | \(0.302713\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.94427 | 0.418755 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.9443 | 0.897914 | 0.448957 | − | 0.893553i | \(-0.351796\pi\) | ||||
0.448957 | + | 0.893553i | \(0.351796\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.70820 | 0.221213 | 0.110606 | − | 0.993864i | \(-0.464721\pi\) | ||||
0.110606 | + | 0.993864i | \(0.464721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.4721 | −1.33583 | −0.667915 | − | 0.744238i | \(-0.732813\pi\) | ||||
−0.667915 | + | 0.744238i | \(0.732813\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.52786 | −0.0901870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1803 | 0.594742 | 0.297371 | − | 0.954762i | \(-0.403890\pi\) | ||||
0.297371 | + | 0.954762i | \(0.403890\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.4721 | 0.609711 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.47214 | −0.142967 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.4164 | −0.882741 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.76393 | −0.386038 | −0.193019 | − | 0.981195i | \(-0.561828\pi\) | ||||
−0.193019 | + | 0.981195i | \(0.561828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.583592 | −0.0330925 | −0.0165462 | − | 0.999863i | \(-0.505267\pi\) | ||||
−0.0165462 | + | 0.999863i | \(0.505267\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.8885 | 1.80245 | 0.901224 | − | 0.433355i | \(-0.142670\pi\) | ||||
0.901224 | + | 0.433355i | \(0.142670\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.23607 | −0.518749 | −0.259375 | − | 0.965777i | \(-0.583516\pi\) | ||||
−0.259375 | + | 0.965777i | \(0.583516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.94427 | −0.500783 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.4164 | −1.30292 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.47214 | −0.192599 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.58359 | 0.473229 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1803 | −0.779422 | −0.389711 | − | 0.920937i | \(-0.627425\pi\) | ||||
−0.389711 | + | 0.920937i | \(0.627425\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.36068 | −0.456793 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.94427 | −0.378279 | −0.189139 | − | 0.981950i | \(-0.560570\pi\) | ||||
−0.189139 | + | 0.981950i | \(0.560570\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.4164 | 0.834845 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.4164 | −0.832408 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.0000 | 1.07366 | 0.536828 | − | 0.843692i | \(-0.319622\pi\) | ||||
0.536828 | + | 0.843692i | \(0.319622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3607 | 0.768710 | 0.384355 | − | 0.923185i | \(-0.374424\pi\) | ||||
0.384355 | + | 0.923185i | \(0.374424\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.5967 | 1.14948 | 0.574739 | − | 0.818336i | \(-0.305103\pi\) | ||||
0.574739 | + | 0.818336i | \(0.305103\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.52786 | −0.293389 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.8328 | −1.94396 | −0.971981 | − | 0.235060i | \(-0.924471\pi\) | ||||
−0.971981 | + | 0.235060i | \(0.924471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.41641 | 0.442969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.583592 | −0.0305466 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.0000 | −1.46159 | −0.730794 | − | 0.682598i | \(-0.760850\pi\) | ||||
−0.730794 | + | 0.682598i | \(0.760850\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4721 | 0.543686 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0557 | 0.883112 | 0.441556 | − | 0.897234i | \(-0.354427\pi\) | ||||
0.441556 | + | 0.897234i | \(0.354427\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.47214 | 0.230327 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.5967 | −1.31482 | −0.657408 | − | 0.753535i | \(-0.728347\pi\) | ||||
−0.657408 | + | 0.753535i | \(0.728347\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.0000 | 1.53293 | 0.766464 | − | 0.642287i | \(-0.222014\pi\) | ||||
0.766464 | + | 0.642287i | \(0.222014\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.05573 | 0.155734 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.8885 | 1.21120 | 0.605599 | − | 0.795770i | \(-0.292934\pi\) | ||||
0.605599 | + | 0.795770i | \(0.292934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0557 | 0.559112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.0557 | −0.556274 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.52786 | 0.377813 | 0.188906 | − | 0.981995i | \(-0.439506\pi\) | ||||
0.188906 | + | 0.981995i | \(0.439506\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.1803 | 0.907883 | 0.453941 | − | 0.891032i | \(-0.350018\pi\) | ||||
0.453941 | + | 0.891032i | \(0.350018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.70820 | −0.383973 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.944272 | 0.0468058 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.3607 | 1.69903 | 0.849513 | − | 0.527567i | \(-0.176896\pi\) | ||||
0.849513 | + | 0.527567i | \(0.176896\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.4721 | −0.515300 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.30495 | 0.456762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38.4721 | −1.87949 | −0.939743 | − | 0.341881i | \(-0.888936\pi\) | ||||
−0.939743 | + | 0.341881i | \(0.888936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9443 | 1.31318 | 0.656592 | − | 0.754246i | \(-0.271997\pi\) | ||||
0.656592 | + | 0.754246i | \(0.271997\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.5279 | 0.753212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.4164 | 0.746052 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.0000 | −0.481683 | −0.240842 | − | 0.970564i | \(-0.577423\pi\) | ||||
−0.240842 | + | 0.970564i | \(0.577423\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.47214 | −0.407145 | −0.203572 | − | 0.979060i | \(-0.565255\pi\) | ||||
−0.203572 | + | 0.979060i | \(0.565255\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.9443 | −0.619208 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.4721 | −1.07254 | −0.536268 | − | 0.844048i | \(-0.680166\pi\) | ||||
−0.536268 | + | 0.844048i | \(0.680166\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.4721 | 1.44777 | 0.723887 | − | 0.689918i | \(-0.242353\pi\) | ||||
0.723887 | + | 0.689918i | \(0.242353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.5836 | −0.596519 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.5410 | −1.44132 | −0.720660 | − | 0.693289i | \(-0.756161\pi\) | ||||
−0.720660 | + | 0.693289i | \(0.756161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.47214 | 0.116408 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.52786 | −0.0716274 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.3607 | 0.484652 | 0.242326 | − | 0.970195i | \(-0.422090\pi\) | ||||
0.242326 | + | 0.970195i | \(0.422090\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.65248 | 0.402986 | 0.201493 | − | 0.979490i | \(-0.435421\pi\) | ||||
0.201493 | + | 0.979490i | \(0.435421\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.29180 | 0.199457 | 0.0997283 | − | 0.995015i | \(-0.468203\pi\) | ||||
0.0997283 | + | 0.995015i | \(0.468203\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.8885 | 1.56817 | 0.784087 | − | 0.620650i | \(-0.213131\pi\) | ||||
0.784087 | + | 0.620650i | \(0.213131\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.36068 | 0.386060 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.9443 | −0.595178 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.1803 | −0.834171 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.3050 | 1.79589 | 0.897945 | − | 0.440109i | \(-0.145060\pi\) | ||||
0.897945 | + | 0.440109i | \(0.145060\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.472136 | −0.0215275 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.52786 | 0.251007 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.7082 | −1.79935 | −0.899675 | − | 0.436560i | \(-0.856197\pi\) | ||||
−0.899675 | + | 0.436560i | \(0.856197\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.9443 | 1.30624 | 0.653118 | − | 0.757256i | \(-0.273460\pi\) | ||||
0.653118 | + | 0.757256i | \(0.273460\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0000 | −0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.52786 | 0.247959 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.8197 | 0.797718 | 0.398859 | − | 0.917012i | \(-0.369406\pi\) | ||||
0.398859 | + | 0.917012i | \(0.369406\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.7771 | 1.41687 | 0.708435 | − | 0.705776i | \(-0.249401\pi\) | ||||
0.708435 | + | 0.705776i | \(0.249401\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.63932 | 0.161948 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.18034 | −0.273939 | −0.136969 | − | 0.990575i | \(-0.543736\pi\) | ||||
−0.136969 | + | 0.990575i | \(0.543736\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.583592 | 0.0258166 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.88854 | −0.0832192 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.8885 | −0.610817 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.05573 | −0.0462523 | −0.0231261 | − | 0.999733i | \(-0.507362\pi\) | ||||
−0.0231261 | + | 0.999733i | \(0.507362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.9443 | 1.79037 | 0.895184 | − | 0.445697i | \(-0.147044\pi\) | ||||
0.895184 | + | 0.445697i | \(0.147044\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.4721 | 1.50163 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.23607 | −0.0535400 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.8885 | 0.773389 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.9443 | 0.471403 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.30495 | −0.0558980 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.9443 | −0.724485 | −0.362242 | − | 0.932084i | \(-0.617989\pi\) | ||||
−0.362242 | + | 0.932084i | \(0.617989\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.4164 | 0.997573 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.0557 | 0.470137 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.291796 | 0.0123638 | 0.00618190 | − | 0.999981i | \(-0.498032\pi\) | ||||
0.00618190 | + | 0.999981i | \(0.498032\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.47214 | 0.273742 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.4721 | −0.441348 | −0.220674 | − | 0.975348i | \(-0.570826\pi\) | ||||
−0.220674 | + | 0.975348i | \(0.570826\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.47214 | −0.104004 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.3607 | 0.602031 | 0.301016 | − | 0.953619i | \(-0.402674\pi\) | ||||
0.301016 | + | 0.953619i | \(0.402674\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.5279 | −1.06831 | −0.534154 | − | 0.845387i | \(-0.679370\pi\) | ||||
−0.534154 | + | 0.845387i | \(0.679370\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.58359 | 0.357961 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.05573 | −0.0439505 | −0.0219753 | − | 0.999759i | \(-0.506996\pi\) | ||||
−0.0219753 | + | 0.999759i | \(0.506996\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.30495 | −0.386034 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9443 | −0.701760 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.4164 | −1.37924 | −0.689621 | − | 0.724170i | \(-0.742223\pi\) | ||||
−0.689621 | + | 0.724170i | \(0.742223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.3607 | −1.66303 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.7639 | −0.442022 | −0.221011 | − | 0.975271i | \(-0.570936\pi\) | ||||
−0.221011 | + | 0.975271i | \(0.570936\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.83282 | 0.280118 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.05573 | −0.288289 | −0.144145 | − | 0.989557i | \(-0.546043\pi\) | ||||
−0.144145 | + | 0.989557i | \(0.546043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.1115 | 0.494037 | 0.247018 | − | 0.969011i | \(-0.420549\pi\) | ||||
0.247018 | + | 0.969011i | \(0.420549\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.65248 | 0.351773 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.0000 | −1.13648 | −0.568242 | − | 0.822861i | \(-0.692376\pi\) | ||||
−0.568242 | + | 0.822861i | \(0.692376\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.94427 | 0.280935 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3607 | 0.580022 | 0.290011 | − | 0.957023i | \(-0.406341\pi\) | ||||
0.290011 | + | 0.957023i | \(0.406341\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 45.5967 | 1.83566 | 0.917828 | − | 0.396978i | \(-0.129941\pi\) | ||||
0.917828 | + | 0.396978i | \(0.129941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.34752 | 0.295322 | 0.147661 | − | 0.989038i | \(-0.452826\pi\) | ||||
0.147661 | + | 0.989038i | \(0.452826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.5836 | 0.504151 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.11146 | 0.0841893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6525 | 0.503687 | 0.251844 | − | 0.967768i | \(-0.418963\pi\) | ||||
0.251844 | + | 0.967768i | \(0.418963\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.00000 | 0.317470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.47214 | −0.216814 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.41641 | 0.213935 | 0.106968 | − | 0.994263i | \(-0.465886\pi\) | ||||
0.106968 | + | 0.994263i | \(0.465886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.1246 | −0.438712 | −0.219356 | − | 0.975645i | \(-0.570396\pi\) | ||||
−0.219356 | + | 0.975645i | \(0.570396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.0000 | 1.25805 | 0.629025 | − | 0.777385i | \(-0.283454\pi\) | ||||
0.629025 | + | 0.777385i | \(0.283454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.9443 | 0.665121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.3607 | −1.34464 | −0.672319 | − | 0.740262i | \(-0.734702\pi\) | ||||
−0.672319 | + | 0.740262i | \(0.734702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.1115 | −0.551380 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8328 | 0.733622 | 0.366811 | − | 0.930295i | \(-0.380450\pi\) | ||||
0.366811 | + | 0.930295i | \(0.380450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.2492 | −1.72110 | −0.860548 | − | 0.509370i | \(-0.829879\pi\) | ||||
−0.860548 | + | 0.509370i | \(0.829879\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.0557 | −0.428080 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.9443 | −0.962963 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.4164 | 1.75067 | 0.875337 | − | 0.483513i | \(-0.160640\pi\) | ||||
0.875337 | + | 0.483513i | \(0.160640\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3607 | 0.398193 | 0.199097 | − | 0.979980i | \(-0.436199\pi\) | ||||
0.199097 | + | 0.979980i | \(0.436199\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.52786 | −0.212140 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.0000 | −0.382639 | −0.191320 | − | 0.981528i | \(-0.561277\pi\) | ||||
−0.191320 | + | 0.981528i | \(0.561277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.36068 | −0.319445 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.47214 | 0.322763 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.5967 | 0.821579 | 0.410790 | − | 0.911730i | \(-0.365253\pi\) | ||||
0.410790 | + | 0.911730i | \(0.365253\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.1672 | 0.651188 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.52786 | 0.209383 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.47214 | −0.0932384 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.63932 | −0.136871 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0000 | 0.525781 | 0.262891 | − | 0.964826i | \(-0.415324\pi\) | ||||
0.262891 | + | 0.964826i | \(0.415324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.0557 | 0.713643 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.47214 | 0.0924526 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.47214 | −0.0921951 | −0.0460976 | − | 0.998937i | \(-0.514679\pi\) | ||||
−0.0460976 | + | 0.998937i | \(0.514679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.88854 | 0.0703330 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.5279 | −0.576690 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.52786 | −0.0566653 | −0.0283327 | − | 0.999599i | \(-0.509020\pi\) | ||||
−0.0283327 | + | 0.999599i | \(0.509020\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.9443 | −1.07054 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.8885 | −1.03009 | −0.515043 | − | 0.857164i | \(-0.672224\pi\) | ||||
−0.515043 | + | 0.857164i | \(0.672224\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.5279 | −0.498305 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.1803 | 1.69877 | 0.849386 | − | 0.527773i | \(-0.176973\pi\) | ||||
0.849386 | + | 0.527773i | \(0.176973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.4721 | −0.604304 | −0.302152 | − | 0.953260i | \(-0.597705\pi\) | ||||
−0.302152 | + | 0.953260i | \(0.597705\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.2492 | −0.375502 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.8885 | −0.653633 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.3607 | −1.18086 | −0.590429 | − | 0.807090i | \(-0.701041\pi\) | ||||
−0.590429 | + | 0.807090i | \(0.701041\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.1935 | −0.844098 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.4164 | −1.35992 | −0.679961 | − | 0.733248i | \(-0.738003\pi\) | ||||
−0.679961 | + | 0.733248i | \(0.738003\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.81966 | 0.355962 | 0.177981 | − | 0.984034i | \(-0.443043\pi\) | ||||
0.177981 | + | 0.984034i | \(0.443043\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.30495 | 0.0472424 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.47214 | −0.305911 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.8328 | −1.90520 | −0.952600 | − | 0.304226i | \(-0.901602\pi\) | ||||
−0.952600 | + | 0.304226i | \(0.901602\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.29180 | 0.298235 | 0.149118 | − | 0.988819i | \(-0.452357\pi\) | ||||
0.149118 | + | 0.988819i | \(0.452357\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.7639 | 0.961389 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.47214 | −0.231888 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.94427 | −0.320051 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.5836 | −0.591894 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.29180 | 0.152986 | 0.0764930 | − | 0.997070i | \(-0.475628\pi\) | ||||
0.0764930 | + | 0.997070i | \(0.475628\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.47214 | 0.0878990 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.4721 | 0.442899 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.0000 | −1.20434 | −0.602171 | − | 0.798367i | \(-0.705697\pi\) | ||||
−0.602171 | + | 0.798367i | \(0.705697\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.0557 | −1.09867 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.944272 | −0.0333226 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.77709 | 0.133125 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.9443 | 1.08794 | 0.543971 | − | 0.839104i | \(-0.316920\pi\) | ||||
0.543971 | + | 0.839104i | \(0.316920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.1803 | 0.919316 | 0.459658 | − | 0.888096i | \(-0.347972\pi\) | ||||
0.459658 | + | 0.888096i | \(0.347972\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.41641 | −0.119672 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.8885 | 1.18561 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.1246 | 1.08626 | 0.543128 | − | 0.839650i | \(-0.317240\pi\) | ||||
0.543128 | + | 0.839650i | \(0.317240\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.3050 | 1.57923 | 0.789616 | − | 0.613602i | \(-0.210280\pi\) | ||||
0.789616 | + | 0.613602i | \(0.210280\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.7771 | 1.17454 | 0.587272 | − | 0.809389i | \(-0.300202\pi\) | ||||
0.587272 | + | 0.809389i | \(0.300202\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.4721 | −1.68351 | −0.841753 | − | 0.539862i | \(-0.818476\pi\) | ||||
−0.841753 | + | 0.539862i | \(0.818476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.4721 | 0.847909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.6393 | 0.679647 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.3607 | −1.04817 | −0.524084 | − | 0.851667i | \(-0.675592\pi\) | ||||
−0.524084 | + | 0.851667i | \(0.675592\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.23607 | −0.0425220 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.65248 | −0.297303 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.16718 | 0.0400106 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.4721 | 0.700953 | 0.350476 | − | 0.936572i | \(-0.386020\pi\) | ||||
0.350476 | + | 0.936572i | \(0.386020\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.5836 | 0.361529 | 0.180764 | − | 0.983526i | \(-0.442143\pi\) | ||||
0.180764 | + | 0.983526i | \(0.442143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.0557 | −0.513695 | −0.256847 | − | 0.966452i | \(-0.582684\pi\) | ||||
−0.256847 | + | 0.966452i | \(0.582684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.1115 | 0.412279 | 0.206139 | − | 0.978523i | \(-0.433910\pi\) | ||||
0.206139 | + | 0.978523i | \(0.433910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.47214 | −0.0840551 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.8885 | −0.606827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.76393 | 0.229187 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.9443 | 0.437596 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.3050 | 1.19216 | 0.596082 | − | 0.802924i | \(-0.296723\pi\) | ||||
0.596082 | + | 0.802924i | \(0.296723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.3607 | −1.69669 | −0.848347 | − | 0.529440i | \(-0.822402\pi\) | ||||
−0.848347 | + | 0.529440i | \(0.822402\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.3607 | −1.62747 | −0.813733 | − | 0.581239i | \(-0.802568\pi\) | ||||
−0.813733 | + | 0.581239i | \(0.802568\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.3050 | 1.52119 | 0.760596 | − | 0.649226i | \(-0.224907\pi\) | ||||
0.760596 | + | 0.649226i | \(0.224907\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.3607 | 1.21676 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.16718 | 0.306425 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.4721 | −1.14971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.8885 | −1.26225 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.6393 | 0.386904 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.3607 | −0.808883 | −0.404442 | − | 0.914564i | \(-0.632534\pi\) | ||||
−0.404442 | + | 0.914564i | \(0.632534\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.4721 | −1.80474 | −0.902371 | − | 0.430960i | \(-0.858175\pi\) | ||||
−0.902371 | + | 0.430960i | \(0.858175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.0557 | 0.498272 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.1115 | 0.466001 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.8885 | −0.722036 | −0.361018 | − | 0.932559i | \(-0.617571\pi\) | ||||
−0.361018 | + | 0.932559i | \(0.617571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.47214 | 0.147202 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.63932 | 0.0539005 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 58.5410 | 1.92067 | 0.960334 | − | 0.278851i | \(-0.0899537\pi\) | ||||
0.960334 | + | 0.278851i | \(0.0899537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.6525 | −0.939047 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.0557 | −0.361561 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.3050 | −1.02269 | −0.511344 | − | 0.859376i | \(-0.670852\pi\) | ||||
−0.511344 | + | 0.859376i | \(0.670852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.7639 | −0.872479 | −0.436240 | − | 0.899831i | \(-0.643690\pi\) | ||||
−0.436240 | + | 0.899831i | \(0.643690\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.05573 | 0.0995082 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.5836 | −0.473903 | −0.236952 | − | 0.971521i | \(-0.576148\pi\) | ||||
−0.236952 | + | 0.971521i | \(0.576148\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.472136 | 0.0153262 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.4721 | −1.31102 | −0.655511 | − | 0.755186i | \(-0.727547\pi\) | ||||
−0.655511 | + | 0.755186i | \(0.727547\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.88854 | 0.0611118 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.36068 | 0.269980 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.4164 | 0.916658 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.5836 | −0.791374 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.7639 | −0.346145 | −0.173072 | − | 0.984909i | \(-0.555369\pi\) | ||||
−0.173072 | + | 0.984909i | \(0.555369\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.83282 | −0.0909094 | −0.0454547 | − | 0.998966i | \(-0.514474\pi\) | ||||
−0.0454547 | + | 0.998966i | \(0.514474\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.1672 | −0.550355 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.291796 | 0.00933538 | 0.00466769 | − | 0.999989i | \(-0.498514\pi\) | ||||
0.00466769 | + | 0.999989i | \(0.498514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.3607 | −0.650730 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −49.4164 | −1.57614 | −0.788069 | − | 0.615587i | \(-0.788919\pi\) | ||||
−0.788069 | + | 0.615587i | \(0.788919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.1378 | −0.896544 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0000 | −0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.0557 | 0.732389 | 0.366195 | − | 0.930538i | \(-0.380660\pi\) | ||||
0.366195 | + | 0.930538i | \(0.380660\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.7771 | −0.373359 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.1115 | 0.763617 | 0.381809 | − | 0.924241i | \(-0.375301\pi\) | ||||
0.381809 | + | 0.924241i | \(0.375301\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 7488.2.a.cs.1.1 | 2 | ||
3.2 | odd | 2 | 2496.2.a.bh.1.2 | 2 | |||
4.3 | odd | 2 | 7488.2.a.ct.1.1 | 2 | |||
8.3 | odd | 2 | 3744.2.a.s.1.2 | 2 | |||
8.5 | even | 2 | 3744.2.a.r.1.2 | 2 | |||
12.11 | even | 2 | 2496.2.a.be.1.2 | 2 | |||
24.5 | odd | 2 | 1248.2.a.l.1.1 | ✓ | 2 | ||
24.11 | even | 2 | 1248.2.a.n.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1248.2.a.l.1.1 | ✓ | 2 | 24.5 | odd | 2 | ||
1248.2.a.n.1.1 | yes | 2 | 24.11 | even | 2 | ||
2496.2.a.be.1.2 | 2 | 12.11 | even | 2 | |||
2496.2.a.bh.1.2 | 2 | 3.2 | odd | 2 | |||
3744.2.a.r.1.2 | 2 | 8.5 | even | 2 | |||
3744.2.a.s.1.2 | 2 | 8.3 | odd | 2 | |||
7488.2.a.cs.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7488.2.a.ct.1.1 | 2 | 4.3 | odd | 2 |