Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(1,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.12489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.60975 | 1.36436 | 0.682178 | − | 0.731186i | \(-0.261033\pi\) | ||||
0.682178 | + | 0.731186i | \(0.261033\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.60975 | 0.485357 | 0.242679 | − | 0.970107i | \(-0.421974\pi\) | ||||
0.242679 | + | 0.970107i | \(0.421974\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.640023 | 0.177511 | 0.0887553 | − | 0.996053i | \(-0.471711\pi\) | ||||
0.0887553 | + | 0.996053i | \(0.471711\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.28005 | 1.28060 | 0.640300 | − | 0.768125i | \(-0.278810\pi\) | ||||
0.640300 | + | 0.768125i | \(0.278810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.60975 | 0.787711 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.24977 | 1.72020 | 0.860098 | − | 0.510129i | \(-0.170402\pi\) | ||||
0.860098 | + | 0.510129i | \(0.170402\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.88979 | −0.908012 | −0.454006 | − | 0.890999i | \(-0.650006\pi\) | ||||
−0.454006 | + | 0.890999i | \(0.650006\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.28005 | 1.30754 | 0.653768 | − | 0.756695i | \(-0.273187\pi\) | ||||
0.653768 | + | 0.756695i | \(0.273187\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.60975 | 0.280221 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.60975 | −0.610159 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.92007 | −1.63085 | −0.815425 | − | 0.578863i | \(-0.803497\pi\) | ||||
−0.815425 | + | 0.578863i | \(0.803497\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.640023 | 0.102486 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.57947 | 0.715193 | 0.357597 | − | 0.933876i | \(-0.383596\pi\) | ||||
0.357597 | + | 0.933876i | \(0.383596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.92007 | −1.20780 | −0.603900 | − | 0.797060i | \(-0.706387\pi\) | ||||
−0.603900 | + | 0.797060i | \(0.706387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.249771 | −0.0364328 | −0.0182164 | − | 0.999834i | \(-0.505799\pi\) | ||||
−0.0182164 | + | 0.999834i | \(0.505799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.03028 | 0.861468 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.28005 | 0.739354 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.75023 | 0.240412 | 0.120206 | − | 0.992749i | \(-0.461644\pi\) | ||||
0.120206 | + | 0.992749i | \(0.461644\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.60975 | −0.217058 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.3103 | −1.60267 | −0.801334 | − | 0.598218i | \(-0.795876\pi\) | ||||
−0.801334 | + | 0.598218i | \(0.795876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5298 | 1.47624 | 0.738121 | − | 0.674668i | \(-0.235713\pi\) | ||||
0.738121 | + | 0.674668i | \(0.235713\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.60975 | 0.454785 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.640023 | −0.0793851 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.4995 | −1.52706 | −0.763531 | − | 0.645771i | \(-0.776536\pi\) | ||||
−0.763531 | + | 0.645771i | \(0.776536\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.24977 | 0.993156 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.7796 | −1.63534 | −0.817668 | − | 0.575690i | \(-0.804734\pi\) | ||||
−0.817668 | + | 0.575690i | \(0.804734\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.93945 | 0.461077 | 0.230539 | − | 0.973063i | \(-0.425951\pi\) | ||||
0.230539 | + | 0.973063i | \(0.425951\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.81078 | 0.662200 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.03028 | 0.340933 | 0.170466 | − | 0.985363i | \(-0.445473\pi\) | ||||
0.170466 | + | 0.985363i | \(0.445473\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.4995 | 1.15247 | 0.576237 | − | 0.817282i | \(-0.304520\pi\) | ||||
0.576237 | + | 0.817282i | \(0.304520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.28005 | −0.572701 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.88979 | −0.524241 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.9201 | 1.68752 | 0.843762 | − | 0.536717i | \(-0.180336\pi\) | ||||
0.843762 | + | 0.536717i | \(0.180336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.31032 | 0.242188 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.28005 | 0.754906 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.92007 | −1.00723 | −0.503615 | − | 0.863928i | \(-0.667997\pi\) | ||||
−0.503615 | + | 0.863928i | \(0.667997\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.60975 | 0.161786 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.2195 | 1.71340 | 0.856702 | − | 0.515812i | \(-0.172510\pi\) | ||||
0.856702 | + | 0.515812i | \(0.172510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4995 | −1.23162 | −0.615808 | − | 0.787896i | \(-0.711170\pi\) | ||||
−0.615808 | + | 0.787896i | \(0.711170\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.60975 | −0.352275 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.5601 | 1.02088 | 0.510441 | − | 0.859913i | \(-0.329482\pi\) | ||||
0.510441 | + | 0.859913i | \(0.329482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3103 | 0.987550 | 0.493775 | − | 0.869590i | \(-0.335617\pi\) | ||||
0.493775 | + | 0.869590i | \(0.335617\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.92007 | −0.941571 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.470182 | 0.0442310 | 0.0221155 | − | 0.999755i | \(-0.492960\pi\) | ||||
0.0221155 | + | 0.999755i | \(0.492960\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.24977 | −0.769295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.640023 | 0.0591702 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.0596 | 1.74719 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.40871 | −0.764428 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.57947 | 0.412917 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4995 | 1.10915 | 0.554577 | − | 0.832132i | \(-0.312880\pi\) | ||||
0.554577 | + | 0.832132i | \(0.312880\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.92007 | −0.697323 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.32970 | −0.378288 | −0.189144 | − | 0.981949i | \(-0.560571\pi\) | ||||
−0.189144 | + | 0.981949i | \(0.560571\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.60975 | −0.313005 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.03028 | 0.429765 | 0.214883 | − | 0.976640i | \(-0.431063\pi\) | ||||
0.214883 | + | 0.976640i | \(0.431063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.77959 | 0.829494 | 0.414747 | − | 0.909937i | \(-0.363870\pi\) | ||||
0.414747 | + | 0.909937i | \(0.363870\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.249771 | −0.0210345 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.03028 | 0.0861560 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.88979 | 0.406075 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.03028 | 0.497369 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.0000 | 1.14692 | 0.573462 | − | 0.819232i | \(-0.305600\pi\) | ||||
0.573462 | + | 0.819232i | \(0.305600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.34060 | −0.109096 | −0.0545482 | − | 0.998511i | \(-0.517372\pi\) | ||||
−0.0545482 | + | 0.998511i | \(0.517372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.28005 | 0.426866 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.28005 | −0.584747 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1892 | −0.813188 | −0.406594 | − | 0.913609i | \(-0.633284\pi\) | ||||
−0.406594 | + | 0.913609i | \(0.633284\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.75023 | 0.138802 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 29.7796 | 2.34696 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.7990 | −1.23747 | −0.618735 | − | 0.785600i | \(-0.712355\pi\) | ||||
−0.618735 | + | 0.785600i | \(0.712355\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.60975 | −0.125319 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.52982 | −0.737439 | −0.368720 | − | 0.929541i | \(-0.620204\pi\) | ||||
−0.368720 | + | 0.929541i | \(0.620204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5904 | −0.968490 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.4693 | 1.02405 | 0.512025 | − | 0.858971i | \(-0.328896\pi\) | ||||
0.512025 | + | 0.858971i | \(0.328896\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.60975 | 0.272871 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.3103 | −0.925301 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.1892 | −1.50901 | −0.754507 | − | 0.656293i | \(-0.772124\pi\) | ||||
−0.754507 | + | 0.656293i | \(0.772124\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.75023 | −0.576070 | −0.288035 | − | 0.957620i | \(-0.593002\pi\) | ||||
−0.288035 | + | 0.957620i | \(0.593002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5298 | 0.852309 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.92007 | 0.729338 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.49954 | 0.621548 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.60975 | 0.262570 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.39025 | 0.172953 | 0.0864763 | − | 0.996254i | \(-0.472439\pi\) | ||||
0.0864763 | + | 0.996254i | \(0.472439\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.640023 | −0.0460699 | −0.0230349 | − | 0.999735i | \(-0.507333\pi\) | ||||
−0.0230349 | + | 0.999735i | \(0.507333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.640023 | −0.0458330 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.7493 | −1.05085 | −0.525423 | − | 0.850841i | \(-0.676093\pi\) | ||||
−0.525423 | + | 0.850841i | \(0.676093\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.8401 | −1.40643 | −0.703215 | − | 0.710977i | \(-0.748253\pi\) | ||||
−0.703215 | + | 0.710977i | \(0.748253\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4995 | −0.881650 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.6509 | −1.23885 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.57947 | −0.319844 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.24977 | 0.573399 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.60975 | −0.111349 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.06055 | 0.141854 | 0.0709271 | − | 0.997481i | \(-0.477404\pi\) | ||||
0.0709271 | + | 0.997481i | \(0.477404\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.7796 | −0.944162 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.92007 | 0.540144 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.2791 | 1.78394 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.93945 | 0.266203 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.37935 | 0.227320 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.5601 | 1.77860 | 0.889298 | − | 0.457329i | \(-0.151194\pi\) | ||||
0.889298 | + | 0.457329i | \(0.151194\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.03028 | 0.333871 | 0.166936 | − | 0.985968i | \(-0.446613\pi\) | ||||
0.166936 | + | 0.985968i | \(0.446613\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.5298 | 1.55489 | 0.777447 | − | 0.628948i | \(-0.216514\pi\) | ||||
0.777447 | + | 0.628948i | \(0.216514\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.81078 | 0.382321 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9688 | 1.04615 | 0.523076 | − | 0.852286i | \(-0.324785\pi\) | ||||
0.523076 | + | 0.852286i | \(0.324785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.249771 | 0.0162933 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.03028 | 0.196838 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6703 | −1.01363 | −0.506814 | − | 0.862056i | \(-0.669177\pi\) | ||||
−0.506814 | + | 0.862056i | \(0.669177\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.4390 | −1.83192 | −0.915958 | − | 0.401274i | \(-0.868568\pi\) | ||||
−0.915958 | + | 0.401274i | \(0.868568\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.03028 | −0.385260 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.640023 | −0.0407237 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.4995 | 0.665381 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.8292 | 1.56721 | 0.783604 | − | 0.621261i | \(-0.213379\pi\) | ||||
0.783604 | + | 0.621261i | \(0.213379\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.2800 | 0.834909 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.28005 | −0.330649 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.46927 | −0.590677 | −0.295338 | − | 0.955393i | \(-0.595432\pi\) | ||||
−0.295338 | + | 0.955393i | \(0.595432\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −35.8089 | −2.22506 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.88979 | −0.302671 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5298 | 0.834284 | 0.417142 | − | 0.908841i | \(-0.363032\pi\) | ||||
0.417142 | + | 0.908841i | \(0.363032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.75023 | −0.107516 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.9201 | 0.974292 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.8889 | 1.57847 | 0.789236 | − | 0.614090i | \(-0.210477\pi\) | ||||
0.789236 | + | 0.614090i | \(0.210477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.6585 | 1.80162 | 0.900812 | − | 0.434209i | \(-0.142972\pi\) | ||||
0.900812 | + | 0.434209i | \(0.142972\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.31032 | 0.139827 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.60975 | 0.0970714 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.03028 | 0.0619033 | 0.0309516 | − | 0.999521i | \(-0.490146\pi\) | ||||
0.0309516 | + | 0.999521i | \(0.490146\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.28005 | 0.435845 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0799 | 0.720628 | 0.360314 | − | 0.932831i | \(-0.382670\pi\) | ||||
0.360314 | + | 0.932831i | \(0.382670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.2001 | 0.784666 | 0.392333 | − | 0.919823i | \(-0.371668\pi\) | ||||
0.392333 | + | 0.919823i | \(0.371668\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.5307 | 0.975778 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8789 | 0.639935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.92007 | −0.581525 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.0303 | 0.644396 | 0.322198 | − | 0.946672i | \(-0.395578\pi\) | ||||
0.322198 | + | 0.946672i | \(0.395578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.3103 | 0.716735 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.60975 | 0.0934070 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.28005 | 0.305353 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.5895 | −1.64787 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.2195 | 0.989234 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.5298 | −0.660195 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.7796 | −1.01473 | −0.507367 | − | 0.861730i | \(-0.669381\pi\) | ||||
−0.507367 | + | 0.861730i | \(0.669381\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4995 | −0.711074 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.88979 | −0.163865 | −0.0819326 | − | 0.996638i | \(-0.526109\pi\) | ||||
−0.0819326 | + | 0.996638i | \(0.526109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.40115 | −0.192244 | −0.0961222 | − | 0.995370i | \(-0.530644\pi\) | ||||
−0.0961222 | + | 0.995370i | \(0.530644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.60975 | −0.203386 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.18922 | 0.235290 | 0.117645 | − | 0.993056i | \(-0.462466\pi\) | ||||
0.117645 | + | 0.993056i | \(0.462466\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.87133 | −0.440710 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.5601 | 0.589407 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.28005 | −0.293790 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.640023 | 0.0355021 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.3103 | 0.570162 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.901610 | −0.0497073 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3103 | −0.566707 | −0.283353 | − | 0.959016i | \(-0.591447\pi\) | ||||
−0.283353 | + | 0.959016i | \(0.591447\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.92007 | −0.543617 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.4995 | 0.682923 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.6400 | −0.906440 | −0.453220 | − | 0.891399i | \(-0.649725\pi\) | ||||
−0.453220 | + | 0.891399i | \(0.649725\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.470182 | 0.0255368 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7190 | 0.634621 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.50046 | −0.189007 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.24977 | −0.444153 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.0606 | 0.862176 | 0.431088 | − | 0.902310i | \(-0.358130\pi\) | ||||
0.431088 | + | 0.902310i | \(0.358130\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0606 | −0.645587 | −0.322793 | − | 0.946469i | \(-0.604622\pi\) | ||||
−0.322793 | + | 0.946469i | \(0.604622\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.640023 | 0.0341619 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.5298 | 0.720120 | 0.360060 | − | 0.932929i | \(-0.382756\pi\) | ||||
0.360060 | + | 0.932929i | \(0.382756\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.7796 | 0.731345 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.0596 | 1.00874 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.6097 | −1.56274 | −0.781371 | − | 0.624066i | \(-0.785479\pi\) | ||||
−0.781371 | + | 0.624066i | \(0.785479\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.40871 | −0.441343 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.93945 | −0.206200 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4886 | 0.599702 | 0.299851 | − | 0.953986i | \(-0.403063\pi\) | ||||
0.299851 | + | 0.953986i | \(0.403063\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.57947 | 0.238398 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.31789 | 0.328008 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.20012 | 0.372808 | 0.186404 | − | 0.982473i | \(-0.440317\pi\) | ||||
0.186404 | + | 0.982473i | \(0.440317\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.12958 | −0.161182 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.68968 | −0.497725 | −0.248863 | − | 0.968539i | \(-0.580057\pi\) | ||||
−0.248863 | + | 0.968539i | \(0.580057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4995 | 0.640371 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.9385 | −1.17210 | −0.586052 | − | 0.810273i | \(-0.699319\pi\) | ||||
−0.586052 | + | 0.810273i | \(0.699319\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.81078 | −0.296145 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.92007 | −0.402600 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.5592 | −1.09309 | −0.546547 | − | 0.837429i | \(-0.684058\pi\) | ||||
−0.546547 | + | 0.837429i | \(0.684058\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.5592 | 2.20288 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.32970 | −0.218404 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.03028 | −0.152470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0294 | 1.10562 | 0.552811 | − | 0.833307i | \(-0.313555\pi\) | ||||
0.552811 | + | 0.833307i | \(0.313555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.60975 | −0.180713 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.0790 | −0.852885 | −0.426443 | − | 0.904515i | \(-0.640233\pi\) | ||||
−0.426443 | + | 0.904515i | \(0.640233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.65940 | 0.232101 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.9688 | −0.791544 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.6585 | −1.16984 | −0.584918 | − | 0.811092i | \(-0.698873\pi\) | ||||
−0.584918 | + | 0.811092i | \(0.698873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.03028 | 0.248125 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −44.4372 | −2.18661 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.4995 | −0.515402 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.77959 | 0.478909 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.7687 | −1.11232 | −0.556162 | − | 0.831074i | \(-0.687726\pi\) | ||||
−0.556162 | + | 0.831074i | \(0.687726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.47018 | −0.120389 | −0.0601947 | − | 0.998187i | \(-0.519172\pi\) | ||||
−0.0601947 | + | 0.998187i | \(0.519172\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.249771 | −0.0121443 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.28005 | 0.256120 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.6197 | 2.01412 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.03028 | 0.0497422 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.40115 | 0.452838 | 0.226419 | − | 0.974030i | \(-0.427298\pi\) | ||||
0.226419 | + | 0.974030i | \(0.427298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.4802 | 1.75312 | 0.876562 | − | 0.481288i | \(-0.159831\pi\) | ||||
0.876562 | + | 0.481288i | \(0.159831\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.88979 | 0.234448 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.24977 | −0.394640 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.5895 | 1.45995 | 0.729977 | − | 0.683471i | \(-0.239531\pi\) | ||||
0.729977 | + | 0.683471i | \(0.239531\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.03028 | 0.287156 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.9612 | −1.04341 | −0.521705 | − | 0.853126i | \(-0.674704\pi\) | ||||
−0.521705 | + | 0.853126i | \(0.674704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.9201 | −0.754684 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0000 | 0.662177 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.3212 | 0.628667 | 0.314334 | − | 0.949313i | \(-0.398219\pi\) | ||||
0.314334 | + | 0.949313i | \(0.398219\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.37179 | 0.347124 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.34060 | −0.0629868 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.31032 | −0.108310 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9612 | −0.840192 | −0.420096 | − | 0.907480i | \(-0.638004\pi\) | ||||
−0.420096 | + | 0.907480i | \(0.638004\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.28005 | 0.246451 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.5592 | 1.37671 | 0.688354 | − | 0.725375i | \(-0.258334\pi\) | ||||
0.688354 | + | 0.725375i | \(0.258334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.3288 | −0.526493 | −0.263247 | − | 0.964729i | \(-0.584793\pi\) | ||||
−0.263247 | + | 0.964729i | \(0.584793\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.28005 | −0.337604 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.84014 | 0.0851516 | 0.0425758 | − | 0.999093i | \(-0.486444\pi\) | ||||
0.0425758 | + | 0.999093i | \(0.486444\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −45.1202 | −2.08346 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.1892 | −0.469494 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.7493 | −0.586214 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.75023 | 0.0801375 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.51044 | −0.343161 | −0.171580 | − | 0.985170i | \(-0.554887\pi\) | ||||
−0.171580 | + | 0.985170i | \(0.554887\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.34908 | −0.289493 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.7796 | 1.35502 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.92007 | 0.450447 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.2791 | −0.828306 | −0.414153 | − | 0.910207i | \(-0.635922\pi\) | ||||
−0.414153 | + | 0.910207i | \(0.635922\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.7990 | −0.714454 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.7678 | 1.61418 | 0.807089 | − | 0.590430i | \(-0.201042\pi\) | ||||
0.807089 | + | 0.590430i | \(0.201042\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.8183 | −1.16280 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.60975 | −0.0723528 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −49.7408 | −2.23118 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.65848 | 0.253309 | 0.126654 | − | 0.991947i | \(-0.459576\pi\) | ||||
0.126654 | + | 0.991947i | \(0.459576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.52982 | −0.425761 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.4078 | −1.71252 | −0.856260 | − | 0.516546i | \(-0.827218\pi\) | ||||
−0.856260 | + | 0.516546i | \(0.827218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.2195 | −0.766257 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.5904 | −0.559158 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.1093 | −0.714032 | −0.357016 | − | 0.934098i | \(-0.616206\pi\) | ||||
−0.357016 | + | 0.934098i | \(0.616206\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.2204 | 0.629074 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.4995 | 0.550796 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.402068 | −0.0176829 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.4693 | 0.591235 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.9182 | −1.83647 | −0.918236 | − | 0.396034i | \(-0.870386\pi\) | ||||
−0.918236 | + | 0.396034i | \(0.870386\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.5979 | −1.20677 | −0.603387 | − | 0.797449i | \(-0.706182\pi\) | ||||
−0.603387 | + | 0.797449i | \(0.706182\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.60975 | 0.157542 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 38.4390 | 1.67443 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 45.0587 | 1.95907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.3103 | −0.534223 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.93097 | 0.126954 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.5601 | −0.456553 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.1892 | −0.871229 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.70722 | 0.418120 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.9991 | 1.67670 | 0.838351 | − | 0.545131i | \(-0.183520\pi\) | ||||
0.838351 | + | 0.545131i | \(0.183520\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.75023 | −0.332594 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.3103 | −0.441646 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.21949 | 0.308683 | 0.154342 | − | 0.988018i | \(-0.450674\pi\) | ||||
0.154342 | + | 0.988018i | \(0.450674\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.5298 | 0.492081 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.88979 | 0.208312 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.9385 | 0.465154 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.92007 | 0.421084 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.3179 | 0.521926 | 0.260963 | − | 0.965349i | \(-0.415960\pi\) | ||||
0.260963 | + | 0.965349i | \(0.415960\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.06903 | −0.214397 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.49954 | 0.358851 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.2110 | 1.35753 | 0.678766 | − | 0.734354i | \(-0.262515\pi\) | ||||
0.678766 | + | 0.734354i | \(0.262515\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.470182 | −0.0197807 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.60975 | 0.151595 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.9201 | −1.17047 | −0.585235 | − | 0.810864i | \(-0.698998\pi\) | ||||
−0.585235 | + | 0.810864i | \(0.698998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.9603 | −1.71414 | −0.857068 | − | 0.515203i | \(-0.827717\pi\) | ||||
−0.857068 | + | 0.515203i | \(0.827717\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.39025 | 0.0998542 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.24977 | 0.344039 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.6585 | −1.65100 | −0.825502 | − | 0.564399i | \(-0.809108\pi\) | ||||
−0.825502 | + | 0.564399i | \(0.809108\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.640023 | −0.0265985 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.9007 | 1.57239 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.81743 | 0.116686 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.640023 | −0.0264617 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.3388 | −1.78878 | −0.894391 | − | 0.447286i | \(-0.852391\pi\) | ||||
−0.894391 | + | 0.447286i | \(0.852391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.28005 | −0.299969 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.7493 | −0.606706 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.5895 | −1.33829 | −0.669144 | − | 0.743133i | \(-0.733339\pi\) | ||||
−0.669144 | + | 0.743133i | \(0.733339\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.0596 | −0.781369 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.8401 | −0.812003 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.1807 | 1.11057 | 0.555287 | − | 0.831658i | \(-0.312608\pi\) | ||||
0.555287 | + | 0.831658i | \(0.312608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.71904 | −0.396448 | −0.198224 | − | 0.980157i | \(-0.563517\pi\) | ||||
−0.198224 | + | 0.980157i | \(0.563517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.4995 | −0.509021 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.40871 | 0.341863 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.7796 | 0.721651 | 0.360826 | − | 0.932633i | \(-0.382495\pi\) | ||||
0.360826 | + | 0.932633i | \(0.382495\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.6509 | −0.715251 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.159859 | −0.00646721 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.9915 | −0.686281 | −0.343141 | − | 0.939284i | \(-0.611491\pi\) | ||||
−0.343141 | + | 0.939284i | \(0.611491\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.57947 | −0.184662 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.3406 | 1.10069 | 0.550346 | − | 0.834937i | \(-0.314496\pi\) | ||||
0.550346 | + | 0.834937i | \(0.314496\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.2800 | −1.65919 | −0.829593 | − | 0.558369i | \(-0.811427\pi\) | ||||
−0.829593 | + | 0.558369i | \(0.811427\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.24977 | 0.331052 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 57.4674 | 2.30238 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.60975 | −0.0642871 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.3784 | −2.08847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.5601 | 1.05734 | 0.528670 | − | 0.848827i | \(-0.322691\pi\) | ||||
0.528670 | + | 0.848827i | \(0.322691\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.06055 | 0.0818996 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.4995 | −0.496029 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.85952 | 0.152920 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.7796 | −0.545112 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.01846 | −0.119222 | −0.0596110 | − | 0.998222i | \(-0.518986\pi\) | ||||
−0.0596110 | + | 0.998222i | \(0.518986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.7990 | 0.465306 | 0.232653 | − | 0.972560i | \(-0.425259\pi\) | ||||
0.232653 | + | 0.972560i | \(0.425259\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.92007 | 0.311852 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.46927 | 0.293647 | 0.146824 | − | 0.989163i | \(-0.453095\pi\) | ||||
0.146824 | + | 0.989163i | \(0.453095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.8165 | −0.777866 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.2791 | 1.02996 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 41.8089 | 1.63611 | 0.818055 | − | 0.575140i | \(-0.195052\pi\) | ||||
0.818055 | + | 0.575140i | \(0.195052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.32970 | 0.169175 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.93945 | 0.153692 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.8477 | −1.16270 | −0.581351 | − | 0.813653i | \(-0.697476\pi\) | ||||
−0.581351 | + | 0.813653i | \(0.697476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.5677 | 0.722198 | 0.361099 | − | 0.932527i | \(-0.382402\pi\) | ||||
0.361099 | + | 0.932527i | \(0.382402\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.37935 | 0.131243 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.60975 | 0.139980 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −40.3397 | −1.56196 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.5601 | 1.02687 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.5601 | 0.716504 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.64002 | −0.178860 | −0.0894299 | − | 0.995993i | \(-0.528504\pi\) | ||||
−0.0894299 | + | 0.995993i | \(0.528504\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.3709 | 0.706050 | 0.353025 | − | 0.935614i | \(-0.385153\pi\) | ||||
0.353025 | + | 0.935614i | \(0.385153\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.8089 | −1.37422 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.03028 | 0.192761 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.9385 | −0.724663 | −0.362331 | − | 0.932049i | \(-0.618019\pi\) | ||||
−0.362331 | + | 0.932049i | \(0.618019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.03028 | −0.192197 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.5298 | 0.897719 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.12019 | 0.0426758 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.1580 | −1.45160 | −0.725800 | − | 0.687906i | \(-0.758530\pi\) | ||||
−0.725800 | + | 0.687906i | \(0.758530\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.81078 | 0.220733 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.77959 | −0.370961 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.1798 | 0.915876 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.9688 | 0.603996 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.9394 | 0.904180 | 0.452090 | − | 0.891972i | \(-0.350678\pi\) | ||||
0.452090 | + | 0.891972i | \(0.350678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.92007 | 0.374143 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.249771 | 0.00940691 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 62.1580 | 2.33769 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0908 | −0.491636 | −0.245818 | − | 0.969316i | \(-0.579057\pi\) | ||||
−0.245818 | + | 0.969316i | \(0.579057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.03028 | 0.113644 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 60.0587 | 2.24922 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.03028 | −0.0385301 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.6703 | −0.585218 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6088 | −0.843167 | −0.421584 | − | 0.906790i | \(-0.638526\pi\) | ||||
−0.421584 | + | 0.906790i | \(0.638526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.1202 | −1.68036 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.4390 | −1.05766 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.88979 | −0.181602 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.10929 | −0.152405 | −0.0762025 | − | 0.997092i | \(-0.524280\pi\) | ||||
−0.0762025 | + | 0.997092i | \(0.524280\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.8183 | −1.54671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.52890 | −0.241150 | −0.120575 | − | 0.992704i | \(-0.538474\pi\) | ||||
−0.120575 | + | 0.992704i | \(0.538474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.03028 | −0.222430 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.1211 | −0.741170 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.8780 | −1.20944 | −0.604718 | − | 0.796440i | \(-0.706714\pi\) | ||||
−0.604718 | + | 0.796440i | \(0.706714\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.640023 | −0.0235118 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.06055 | −0.0755943 | −0.0377972 | − | 0.999285i | \(-0.512034\pi\) | ||||
−0.0377972 | + | 0.999285i | \(0.512034\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.0000 | −0.512920 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.4995 | 0.384158 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.1193 | 1.39285 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.7787 | −0.466300 | −0.233150 | − | 0.972441i | \(-0.574903\pi\) | ||||
−0.233150 | + | 0.972441i | \(0.574903\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.8292 | 0.904828 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.34060 | 0.0487894 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.3094 | −0.411047 | −0.205524 | − | 0.978652i | \(-0.565890\pi\) | ||||
−0.205524 | + | 0.978652i | \(0.565890\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.2800 | 0.482035 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.2177 | 1.34737 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.28005 | −0.190900 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.87890 | −0.284490 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.6206 | 0.382990 | 0.191495 | − | 0.981494i | \(-0.438666\pi\) | ||||
0.191495 | + | 0.981494i | \(0.438666\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.46927 | −0.341027 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.8695 | −1.00240 | −0.501198 | − | 0.865333i | \(-0.667107\pi\) | ||||
−0.501198 | + | 0.865333i | \(0.667107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.28005 | 0.261507 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −35.8089 | −1.28464 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.57947 | −0.164077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.1817 | −0.793722 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.88979 | −0.174747 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.1892 | 0.363669 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.2782 | 1.54270 | 0.771351 | − | 0.636410i | \(-0.219581\pi\) | ||||
0.771351 | + | 0.636410i | \(0.219581\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.5298 | 0.481674 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.69724 | 0.0603469 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.37935 | 0.262049 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.75023 | −0.0620742 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.53073 | 0.0896432 | 0.0448216 | − | 0.998995i | \(-0.485728\pi\) | ||||
0.0448216 | + | 0.998995i | \(0.485728\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.31880 | −0.0466559 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.9201 | 0.562508 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.34152 | 0.223787 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.7796 | −1.04959 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.8889 | 0.911332 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.99908 | −0.105442 | −0.0527211 | − | 0.998609i | \(-0.516789\pi\) | ||||
−0.0527211 | + | 0.998609i | \(0.516789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.3784 | −1.27742 | −0.638710 | − | 0.769448i | \(-0.720532\pi\) | ||||
−0.638710 | + | 0.769448i | \(0.720532\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.6585 | 1.04017 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.7990 | 0.553414 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.92007 | 0.277088 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.31032 | 0.0807292 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.7181 | 0.932469 | 0.466234 | − | 0.884661i | \(-0.345610\pi\) | ||||
0.466234 | + | 0.884661i | \(0.345610\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.8292 | −0.377484 | −0.188742 | − | 0.982027i | \(-0.560441\pi\) | ||||
−0.188742 | + | 0.982027i | \(0.560441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.60975 | 0.0560442 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.0303 | 0.592201 | 0.296100 | − | 0.955157i | \(-0.404314\pi\) | ||||
0.296100 | + | 0.955157i | \(0.404314\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.8695 | −1.87097 | −0.935483 | − | 0.353373i | \(-0.885035\pi\) | ||||
−0.935483 | + | 0.353373i | \(0.885035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.03028 | 0.0357399 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.8401 | 1.10320 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.52982 | 0.329793 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.28005 | 0.251635 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.4608 | −1.25877 | −0.629383 | − | 0.777095i | \(-0.716692\pi\) | ||||
−0.629383 | + | 0.777095i | \(0.716692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.08991 | −0.175514 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0799 | 0.416055 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.5904 | 0.433122 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.3533 | −1.04295 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.2001 | 0.453027 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −81.8383 | −2.80538 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.6888 | −1.18772 | −0.593860 | − | 0.804568i | \(-0.702397\pi\) | ||||
−0.593860 | + | 0.804568i | \(0.702397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.2498 | −1.57986 | −0.789931 | − | 0.613196i | \(-0.789884\pi\) | ||||
−0.789931 | + | 0.613196i | \(0.789884\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.0596 | 0.786785 | 0.393392 | − | 0.919371i | \(-0.371301\pi\) | ||||
0.393392 | + | 0.919371i | \(0.371301\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.5307 | 0.563366 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.9385 | −0.780837 | −0.390418 | − | 0.920638i | \(-0.627670\pi\) | ||||
−0.390418 | + | 0.920638i | \(0.627670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.4693 | −0.457969 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.8789 | 0.369467 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.87798 | 0.165474 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.92007 | −0.335744 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.60975 | −0.122032 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.42053 | 0.0479678 | 0.0239839 | − | 0.999712i | \(-0.492365\pi\) | ||||
0.0239839 | + | 0.999712i | \(0.492365\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.0303 | 0.372042 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.90161 | −0.232521 | −0.116261 | − | 0.993219i | \(-0.537091\pi\) | ||||
−0.116261 | + | 0.993219i | \(0.537091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.98062 | −0.0666533 | −0.0333266 | − | 0.999445i | \(-0.510610\pi\) | ||||
−0.0333266 | + | 0.999445i | \(0.510610\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.3103 | 0.413807 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.56101 | 0.321027 | 0.160514 | − | 0.987034i | \(-0.448685\pi\) | ||||
0.160514 | + | 0.987034i | \(0.448685\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.1202 | 1.51328 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.60975 | 0.0539286 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.249771 | 0.00835826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.1892 | 0.674851 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.28005 | 0.176296 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −35.5979 | −1.18726 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.24129 | 0.307872 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28.5895 | −0.951397 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.75023 | 0.257626 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.2195 | 0.505355 | 0.252678 | − | 0.967551i | \(-0.418689\pi\) | ||||
0.252678 | + | 0.967551i | \(0.418689\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.2195 | 0.571135 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.9991 | 1.49089 | 0.745443 | − | 0.666569i | \(-0.232238\pi\) | ||||
0.745443 | + | 0.666569i | \(0.232238\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.9016 | 0.559362 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.5298 | −0.381164 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.6291 | −0.516119 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.3775 | −1.49687 | −0.748433 | − | 0.663210i | \(-0.769194\pi\) | ||||
−0.748433 | + | 0.663210i | \(0.769194\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.7796 | −0.585857 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.81926 | −0.290289 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.92007 | −0.326170 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.4995 | −0.410539 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.3406 | −0.700162 | −0.350081 | − | 0.936719i | \(-0.613846\pi\) | ||||
−0.350081 | + | 0.936719i | \(0.613846\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.03028 | −0.197634 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.88979 | −0.0946076 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.49954 | −0.277965 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.9007 | 0.650127 | 0.325064 | − | 0.945692i | \(-0.394614\pi\) | ||||
0.325064 | + | 0.945692i | \(0.394614\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.40115 | −0.110992 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.70905 | 0.186110 | 0.0930549 | − | 0.995661i | \(-0.470337\pi\) | ||||
0.0930549 | + | 0.995661i | \(0.470337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.7796 | 1.23027 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.60975 | −0.117425 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.3179 | 0.920208 | 0.460104 | − | 0.887865i | \(-0.347812\pi\) | ||||
0.460104 | + | 0.887865i | \(0.347812\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.52134 | 0.0818461 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.18922 | 0.135845 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.97064 | 0.128622 | 0.0643108 | − | 0.997930i | \(-0.479515\pi\) | ||||
0.0643108 | + | 0.997930i | \(0.479515\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.39025 | −0.0773468 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.87133 | −0.254444 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.1580 | 0.586353 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.9991 | 0.709648 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5601 | 0.340294 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.640023 | 0.0206031 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.55011 | −0.146322 | −0.0731609 | − | 0.997320i | \(-0.523309\pi\) | ||||
−0.0731609 | + | 0.997320i | \(0.523309\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.28005 | −0.169620 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.5298 | −0.370009 | −0.185005 | − | 0.982738i | \(-0.559230\pi\) | ||||
−0.185005 | + | 0.982738i | \(0.559230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.3018 | 1.13173 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.640023 | 0.0204972 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.4920 | 0.335668 | 0.167834 | − | 0.985815i | \(-0.446323\pi\) | ||||
0.167834 | + | 0.985815i | \(0.446323\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.6273 | 0.819052 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.3103 | 0.329183 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.40871 | 0.172511 | 0.0862556 | − | 0.996273i | \(-0.472510\pi\) | ||||
0.0862556 | + | 0.996273i | \(0.472510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.7493 | 0.469952 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.901610 | −0.0286986 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −65.3388 | −2.07765 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.0890 | 0.860510 | 0.430255 | − | 0.902707i | \(-0.358424\pi\) | ||||
0.430255 | + | 0.902707i | \(0.358424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.3103 | −0.327188 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.8401 | 0.628975 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.8099 | 0.722396 | 0.361198 | − | 0.932489i | \(-0.382368\pi\) | ||||
0.361198 | + | 0.932489i | \(0.382368\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.92007 | −0.313857 |
(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 | 4560.2.a.bt.1.3 | 3 | ||
4.3 | odd | 2 | 2280.2.a.r.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 6840.2.a.bk.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.r.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
4560.2.a.bt.1.3 | 3 | 1.1 | even | 1 | trivial | ||
6840.2.a.bk.1.1 | 3 | 12.11 | even | 2 |