Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(1,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.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: | \(14.3091920422\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 896) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.765367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1 |
$q$-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 | ||||||||
\(3\) | 1.08239 | 0.624919 | 0.312460 | − | 0.949931i | \(-0.398847\pi\) | ||||
0.312460 | + | 0.949931i | \(0.398847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.08239 | −0.484061 | −0.242030 | − | 0.970269i | \(-0.577813\pi\) | ||||
−0.242030 | + | 0.970269i | \(0.577813\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.82843 | −0.609476 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.22625 | 1.57577 | 0.787887 | − | 0.615820i | \(-0.211175\pi\) | ||||
0.787887 | + | 0.615820i | \(0.211175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.30864 | −1.74970 | −0.874852 | − | 0.484391i | \(-0.839041\pi\) | ||||
−0.874852 | + | 0.484391i | \(0.839041\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.17157 | −0.302499 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.65685 | 0.886917 | 0.443459 | − | 0.896295i | \(-0.353751\pi\) | ||||
0.443459 | + | 0.896295i | \(0.353751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.14386 | −0.950667 | −0.475333 | − | 0.879806i | \(-0.657673\pi\) | ||||
−0.475333 | + | 0.879806i | \(0.657673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.08239 | −0.236197 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.17157 | −0.244290 | −0.122145 | − | 0.992512i | \(-0.538977\pi\) | ||||
−0.122145 | + | 0.992512i | \(0.538977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.82843 | −0.765685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.22625 | −1.00579 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.28772 | 1.53899 | 0.769495 | − | 0.638652i | \(-0.220508\pi\) | ||||
0.769495 | + | 0.638652i | \(0.220508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.65685 | −1.01600 | −0.508001 | − | 0.861357i | \(-0.669615\pi\) | ||||
−0.508001 | + | 0.861357i | \(0.669615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.65685 | 0.984732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.08239 | 0.182958 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.16478 | −0.355888 | −0.177944 | − | 0.984041i | \(-0.556945\pi\) | ||||
−0.177944 | + | 0.984041i | \(0.556945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.82843 | −1.09342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.65685 | −1.19580 | −0.597900 | − | 0.801571i | \(-0.703998\pi\) | ||||
−0.597900 | + | 0.801571i | \(0.703998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.22625 | −0.796996 | −0.398498 | − | 0.917169i | \(-0.630468\pi\) | ||||
−0.398498 | + | 0.917169i | \(0.630468\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.97908 | 0.295023 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.95815 | 0.554252 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.32957 | 0.594712 | 0.297356 | − | 0.954767i | \(-0.403895\pi\) | ||||
0.297356 | + | 0.954767i | \(0.403895\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.48528 | −0.594090 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.30864 | 0.821315 | 0.410658 | − | 0.911790i | \(-0.365299\pi\) | ||||
0.410658 | + | 0.911790i | \(0.365299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.20533 | −0.922548 | −0.461274 | − | 0.887258i | \(-0.652607\pi\) | ||||
−0.461274 | + | 0.887258i | \(0.652607\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.82843 | 0.230360 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.82843 | 0.846962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.39104 | 0.902959 | 0.451479 | − | 0.892282i | \(-0.350896\pi\) | ||||
0.451479 | + | 0.892282i | \(0.350896\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.26810 | −0.152661 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6569 | −1.62077 | −0.810385 | − | 0.585897i | \(-0.800742\pi\) | ||||
−0.810385 | + | 0.585897i | \(0.800742\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.343146 | −0.0401622 | −0.0200811 | − | 0.999798i | \(-0.506392\pi\) | ||||
−0.0200811 | + | 0.999798i | \(0.506392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.14386 | −0.478492 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.22625 | −0.595587 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.6569 | −1.53652 | −0.768258 | − | 0.640140i | \(-0.778876\pi\) | ||||
−0.768258 | + | 0.640140i | \(0.778876\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.171573 | −0.0190637 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.41196 | −0.594040 | −0.297020 | − | 0.954871i | \(-0.595993\pi\) | ||||
−0.297020 | + | 0.954871i | \(0.595993\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.95815 | −0.429322 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.97056 | 0.961745 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.30864 | 0.661326 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.12293 | −0.634919 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.48528 | 0.460180 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.55582 | −0.960396 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.14386 | −0.412329 | −0.206165 | − | 0.978517i | \(-0.566098\pi\) | ||||
−0.206165 | + | 0.978517i | \(0.566098\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.34315 | −0.230877 | −0.115439 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115439 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.17157 | 0.114334 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.7206 | −1.13307 | −0.566537 | − | 0.824036i | \(-0.691717\pi\) | ||||
−0.566537 | + | 0.824036i | \(0.691717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.9469 | 1.62321 | 0.811607 | − | 0.584203i | \(-0.198593\pi\) | ||||
0.811607 | + | 0.584203i | \(0.198593\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.34315 | −0.222402 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.17157 | 0.298356 | 0.149178 | − | 0.988810i | \(-0.452337\pi\) | ||||
0.149178 | + | 0.988810i | \(0.452337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.26810 | 0.118251 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.5349 | 1.06640 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.65685 | −0.335223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.3137 | 1.48306 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.28772 | −0.747278 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.55582 | 0.854699 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4853 | 1.10789 | 0.553945 | − | 0.832553i | \(-0.313122\pi\) | ||||
0.553945 | + | 0.832553i | \(0.313122\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.65685 | −0.498058 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.57675 | 0.661983 | 0.330992 | − | 0.943634i | \(-0.392617\pi\) | ||||
0.330992 | + | 0.943634i | \(0.392617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.14386 | 0.359318 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.2668 | 0.870818 | 0.435409 | − | 0.900233i | \(-0.356604\pi\) | ||||
0.435409 | + | 0.900233i | \(0.356604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.65914 | −0.729231 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −32.9706 | −2.75714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.97056 | −0.744965 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.08239 | 0.0892742 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.1116 | 1.56569 | 0.782843 | − | 0.622219i | \(-0.213769\pi\) | ||||
0.782843 | + | 0.622219i | \(0.213769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.1421 | −0.825355 | −0.412678 | − | 0.910877i | \(-0.635406\pi\) | ||||
−0.412678 | + | 0.910877i | \(0.635406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.68629 | −0.540555 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.12293 | 0.491806 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.14386 | 0.330716 | 0.165358 | − | 0.986234i | \(-0.447122\pi\) | ||||
0.165358 | + | 0.986234i | \(0.447122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.68629 | 0.371647 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.17157 | 0.0923329 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.0083 | −1.56717 | −0.783586 | − | 0.621283i | \(-0.786612\pi\) | ||||
−0.783586 | + | 0.621283i | \(0.786612\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.12293 | −0.476670 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0000 | −1.23812 | −0.619059 | − | 0.785345i | \(-0.712486\pi\) | ||||
−0.619059 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.7990 | 2.06146 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.57675 | 0.579408 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8030 | 0.973394 | 0.486697 | − | 0.873571i | \(-0.338202\pi\) | ||||
0.486697 | + | 0.873571i | \(0.338202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.82843 | 0.289402 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.82843 | 0.513256 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.18440 | −0.686474 | −0.343237 | − | 0.939249i | \(-0.611523\pi\) | ||||
−0.343237 | + | 0.939249i | \(0.611523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.08239 | 0.0804536 | 0.0402268 | − | 0.999191i | \(-0.487192\pi\) | ||||
0.0402268 | + | 0.999191i | \(0.487192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.79899 | −0.576518 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.34315 | 0.172272 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.1116 | 1.39758 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.22625 | 0.380154 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.31371 | −0.239772 | −0.119886 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.7990 | −1.85705 | −0.928526 | − | 0.371267i | \(-0.878923\pi\) | ||||
−0.928526 | + | 0.371267i | \(0.878923\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.39104 | 0.529283 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.7821 | −1.05318 | −0.526590 | − | 0.850120i | \(-0.676530\pi\) | ||||
−0.526590 | + | 0.850120i | \(0.676530\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.9706 | 1.77012 | 0.885058 | − | 0.465481i | \(-0.154118\pi\) | ||||
0.885058 | + | 0.465481i | \(0.154118\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.28772 | −0.581684 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.28772 | 0.578839 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.14214 | 0.148889 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.6569 | −1.49804 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.1731 | 1.52646 | 0.763230 | − | 0.646127i | \(-0.223612\pi\) | ||||
0.763230 | + | 0.646127i | \(0.223612\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.7821 | −1.01285 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.65685 | 0.385794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.65685 | 0.384012 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.371418 | −0.0250981 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.0698 | −1.55184 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.9706 | 1.67215 | 0.836076 | − | 0.548613i | \(-0.184844\pi\) | ||||
0.836076 | + | 0.548613i | \(0.184844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4316 | 0.825113 | 0.412556 | − | 0.910932i | \(-0.364636\pi\) | ||||
0.412556 | + | 0.910932i | \(0.364636\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.47343 | 0.559940 | 0.279970 | − | 0.960009i | \(-0.409675\pi\) | ||||
0.279970 | + | 0.960009i | \(0.409675\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.65914 | 0.564860 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7821 | −0.960199 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.1421 | 0.656040 | 0.328020 | − | 0.944671i | \(-0.393619\pi\) | ||||
0.328020 | + | 0.944671i | \(0.393619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.3137 | −1.37294 | −0.686468 | − | 0.727160i | \(-0.740840\pi\) | ||||
−0.686468 | + | 0.727160i | \(0.740840\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4930 | 0.993879 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.08239 | −0.0691515 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.1421 | 1.66338 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.85786 | −0.371227 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.1522 | −1.52447 | −0.762236 | − | 0.647299i | \(-0.775899\pi\) | ||||
−0.762236 | + | 0.647299i | \(0.775899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.12293 | −0.384946 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.28427 | −0.268291 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.3137 | 0.830486 | 0.415243 | − | 0.909710i | \(-0.363696\pi\) | ||||
0.415243 | + | 0.909710i | \(0.363696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.16478 | 0.134513 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.1535 | −0.937978 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.6569 | −0.842118 | −0.421059 | − | 0.907033i | \(-0.638341\pi\) | ||||
−0.421059 | + | 0.907033i | \(0.638341\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.68629 | −0.287877 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.16478 | 0.132483 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.2137 | −1.65925 | −0.829623 | − | 0.558324i | \(-0.811445\pi\) | ||||
−0.829623 | + | 0.558324i | \(0.811445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6569 | −0.829595 | −0.414797 | − | 0.909914i | \(-0.636148\pi\) | ||||
−0.414797 | + | 0.909914i | \(0.636148\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.82843 | 0.413275 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.0083 | −1.20655 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.12293 | 0.367892 | 0.183946 | − | 0.982936i | \(-0.441113\pi\) | ||||
0.183946 | + | 0.982936i | \(0.441113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.3431 | 0.619228 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.1103 | −1.67099 | −0.835493 | − | 0.549501i | \(-0.814818\pi\) | ||||
−0.835493 | + | 0.549501i | \(0.814818\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.85483 | 0.287576 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.65685 | 0.451970 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.8239 | −0.634510 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.6382 | 0.621491 | 0.310746 | − | 0.950493i | \(-0.399421\pi\) | ||||
0.310746 | + | 0.950493i | \(0.399421\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.82843 | −0.397566 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −27.3137 | −1.58490 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.39104 | 0.427435 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.22625 | 0.301236 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.48528 | −0.257673 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.79899 | 0.446569 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.8645 | −0.905433 | −0.452716 | − | 0.891655i | \(-0.649545\pi\) | ||||
−0.452716 | + | 0.891655i | \(0.649545\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.53620 | −0.144280 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.6274 | 1.73672 | 0.868361 | − | 0.495933i | \(-0.165174\pi\) | ||||
0.868361 | + | 0.495933i | \(0.165174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.6569 | 1.11107 | 0.555536 | − | 0.831493i | \(-0.312513\pi\) | ||||
0.555536 | + | 0.831493i | \(0.312513\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.97908 | −0.111508 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.9050 | 1.17414 | 0.587071 | − | 0.809535i | \(-0.300281\pi\) | ||||
0.587071 | + | 0.809535i | \(0.300281\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43.3137 | 2.42510 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.6863 | −0.708080 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.1535 | −0.843163 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.1522 | 1.33972 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.3431 | 1.01438 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.8854 | −0.763210 | −0.381605 | − | 0.924325i | \(-0.624629\pi\) | ||||
−0.381605 | + | 0.924325i | \(0.624629\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.95815 | 0.216905 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8284 | 0.916703 | 0.458351 | − | 0.888771i | \(-0.348440\pi\) | ||||
0.458351 | + | 0.888771i | \(0.348440\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.43289 | 0.186449 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.5641 | −1.60099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.37258 | 0.0738974 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.896683 | 0.0481365 | 0.0240682 | − | 0.999710i | \(-0.492338\pi\) | ||||
0.0240682 | + | 0.999710i | \(0.492338\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.87576 | 0.153936 | 0.0769679 | − | 0.997034i | \(-0.475476\pi\) | ||||
0.0769679 | + | 0.997034i | \(0.475476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.9706 | 1.75984 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.34315 | 0.231162 | 0.115581 | − | 0.993298i | \(-0.463127\pi\) | ||||
0.115581 | + | 0.993298i | \(0.463127\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.7821 | 0.784551 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.95815 | −0.209488 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.17157 | −0.0618333 | −0.0309166 | − | 0.999522i | \(-0.509843\pi\) | ||||
−0.0309166 | + | 0.999522i | \(0.509843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.82843 | −0.0962330 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.6578 | 0.926796 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.371418 | 0.0194409 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.97056 | −0.468260 | −0.234130 | − | 0.972205i | \(-0.575224\pi\) | ||||
−0.234130 | + | 0.972205i | \(0.575224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.0000 | 0.728811 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.32957 | −0.224780 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.6984 | −1.17528 | −0.587639 | − | 0.809124i | \(-0.699942\pi\) | ||||
−0.587639 | + | 0.809124i | \(0.699942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.3431 | 0.534118 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −52.2843 | −2.69278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.43289 | −0.176335 | −0.0881677 | − | 0.996106i | \(-0.528101\pi\) | ||||
−0.0881677 | + | 0.996106i | \(0.528101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.5140 | 0.692342 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.31371 | 0.169323 | 0.0846613 | − | 0.996410i | \(-0.473019\pi\) | ||||
0.0846613 | + | 0.996410i | \(0.473019\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.65685 | 0.288300 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.55582 | 0.485750 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.95815 | 0.200686 | 0.100343 | − | 0.994953i | \(-0.468006\pi\) | ||||
0.100343 | + | 0.994953i | \(0.468006\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.28427 | −0.216665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.20101 | 0.413686 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.7821 | 0.743767 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.57675 | −0.380266 | −0.190133 | − | 0.981758i | \(-0.560892\pi\) | ||||
−0.190133 | + | 0.981758i | \(0.560892\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.48528 | 0.224545 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.4853 | 1.32261 | 0.661306 | − | 0.750116i | \(-0.270003\pi\) | ||||
0.661306 | + | 0.750116i | \(0.270003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.6871 | 1.77770 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.185709 | 0.00922796 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.3137 | −0.560800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3137 | 0.856108 | 0.428054 | − | 0.903753i | \(-0.359199\pi\) | ||||
0.428054 | + | 0.903753i | \(0.359199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.16478 | −0.106781 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.30864 | −0.310428 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.85786 | 0.287551 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.1127 | 0.544191 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.41196 | 0.264392 | 0.132196 | − | 0.991224i | \(-0.457797\pi\) | ||||
0.132196 | + | 0.991224i | \(0.457797\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.6871 | 1.73928 | 0.869641 | − | 0.493685i | \(-0.164350\pi\) | ||||
0.869641 | + | 0.493685i | \(0.164350\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.6274 | 0.711209 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.0000 | −0.679100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.20533 | 0.348690 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −35.6871 | −1.72299 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.17157 | 0.0564327 | 0.0282163 | − | 0.999602i | \(-0.491017\pi\) | ||||
0.0282163 | + | 0.999602i | \(0.491017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6569 | −1.13688 | −0.568438 | − | 0.822726i | \(-0.692452\pi\) | ||||
−0.568438 | + | 0.822726i | \(0.692452\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.70967 | −0.465543 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.85483 | 0.232238 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.9706 | 1.57360 | 0.786800 | − | 0.617209i | \(-0.211737\pi\) | ||||
0.786800 | + | 0.617209i | \(0.211737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.82843 | −0.0870680 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.1731 | 1.05348 | 0.526738 | − | 0.850028i | \(-0.323415\pi\) | ||||
0.526738 | + | 0.850028i | \(0.323415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.16478 | −0.102621 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.6863 | 0.978428 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.6274 | 0.973468 | 0.486734 | − | 0.873550i | \(-0.338188\pi\) | ||||
0.486734 | + | 0.873550i | \(0.338188\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40.0166 | −1.88431 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.9778 | −0.515781 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.82843 | −0.320122 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.48528 | −0.303369 | −0.151684 | − | 0.988429i | \(-0.548470\pi\) | ||||
−0.151684 | + | 0.988429i | \(0.548470\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.1116 | −0.892055 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.4399 | 1.51088 | 0.755438 | − | 0.655220i | \(-0.227424\pi\) | ||||
0.755438 | + | 0.655220i | \(0.227424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.62742 | 0.307339 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.9259 | −0.875788 | −0.437894 | − | 0.899027i | \(-0.644275\pi\) | ||||
−0.437894 | + | 0.899027i | \(0.644275\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.39104 | −0.341286 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.48528 | 0.206671 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.3137 | −1.25589 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.8645 | 0.727912 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.91630 | −0.362463 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.65685 | −0.258468 | −0.129234 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129234 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.6569 | 0.622699 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.26810 | 0.0577006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.8239 | 0.491489 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.79899 | −0.353406 | −0.176703 | − | 0.984264i | \(-0.556543\pi\) | ||||
−0.176703 | + | 0.984264i | \(0.556543\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.6569 | −0.979357 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.85483 | −0.219096 | −0.109548 | − | 0.993982i | \(-0.534940\pi\) | ||||
−0.109548 | + | 0.993982i | \(0.534940\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.3070 | 1.36496 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.3431 | 0.464890 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.6569 | 0.612594 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.5140 | 0.604968 | 0.302484 | − | 0.953154i | \(-0.402184\pi\) | ||||
0.302484 | + | 0.953154i | \(0.402184\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3183 | −0.773723 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.65685 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.48528 | 0.199592 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.0070 | 1.28825 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.6997 | −0.607228 | −0.303614 | − | 0.952795i | \(-0.598193\pi\) | ||||
−0.303614 | + | 0.952795i | \(0.598193\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.343146 | 0.0151799 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.6569 | 0.956173 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.53620 | 0.111758 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.8100 | −1.83880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.8579 | 0.608293 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.3137 | −1.63474 | −0.817372 | − | 0.576111i | \(-0.804570\pi\) | ||||
−0.817372 | + | 0.576111i | \(0.804570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.7080 | −1.47395 | −0.736974 | − | 0.675921i | \(-0.763746\pi\) | ||||
−0.736974 | + | 0.675921i | \(0.763746\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.14386 | 0.180853 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.6863 | −0.901109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6274 | −0.940322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.5349 | −0.500572 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.3044 | 2.09229 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6863 | 0.548476 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.94113 | −0.428991 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.22625 | 0.225111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.9887 | −0.558428 | −0.279214 | − | 0.960229i | \(-0.590074\pi\) | ||||
−0.279214 | + | 0.960229i | \(0.590074\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.17157 | 0.0502770 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.3431 | −0.785734 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0920 | −0.517018 | −0.258509 | − | 0.966009i | \(-0.583231\pi\) | ||||
−0.258509 | + | 0.966009i | \(0.583231\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.1744 | 0.562270 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.3431 | −1.46307 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.6569 | 0.580749 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.53620 | 0.107656 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.12293 | −0.259437 | −0.129719 | − | 0.991551i | \(-0.541407\pi\) | ||||
−0.129719 | + | 0.991551i | \(0.541407\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.9706 | 1.39451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.6863 | 0.873376 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.5014 | 1.49620 | 0.748102 | − | 0.663584i | \(-0.230965\pi\) | ||||
0.748102 | + | 0.663584i | \(0.230965\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.43289 | −0.144423 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.171573 | 0.00720538 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.4853 | 1.44570 | 0.722849 | − | 0.691006i | \(-0.242832\pi\) | ||||
0.722849 | + | 0.691006i | \(0.242832\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8854 | 0.581085 | 0.290543 | − | 0.956862i | \(-0.406164\pi\) | ||||
0.290543 | + | 0.956862i | \(0.406164\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.58673 | −0.149838 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.48528 | 0.187049 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9706 | 0.456711 | 0.228355 | − | 0.973578i | \(-0.426665\pi\) | ||||
0.228355 | + | 0.973578i | \(0.426665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.9246 | −1.16051 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.41196 | 0.224526 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.6274 | 0.937132 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.4853 | −0.516203 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.0070 | −1.19725 | −0.598624 | − | 0.801030i | \(-0.704286\pi\) | ||||
−0.598624 | + | 0.801030i | \(0.704286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.4412 | 0.965878 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.0000 | −0.658152 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.68629 | −0.110313 | −0.0551564 | − | 0.998478i | \(-0.517566\pi\) | ||||
−0.0551564 | + | 0.998478i | \(0.517566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.95815 | 0.162268 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.0279 | 1.10618 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.6863 | −0.762230 | −0.381115 | − | 0.924528i | \(-0.624460\pi\) | ||||
−0.381115 | + | 0.924528i | \(0.624460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.5140 | −0.550331 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.6578 | −0.717893 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.68629 | 0.190211 | 0.0951054 | − | 0.995467i | \(-0.469681\pi\) | ||||
0.0951054 | + | 0.995467i | \(0.469681\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.97056 | −0.363506 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.4692 | 2.04176 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.8239 | 0.437174 | 0.218587 | − | 0.975817i | \(-0.429855\pi\) | ||||
0.218587 | + | 0.975817i | \(0.429855\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.97056 | 0.361728 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.20101 | 0.0886093 | 0.0443047 | − | 0.999018i | \(-0.485893\pi\) | ||||
0.0443047 | + | 0.999018i | \(0.485893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0711 | −0.565565 | −0.282783 | − | 0.959184i | \(-0.591257\pi\) | ||||
−0.282783 | + | 0.959184i | \(0.591257\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.12293 | 0.245705 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.00000 | −0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.79899 | 0.351960 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −23.4412 | −0.936152 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.91630 | −0.315644 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.6274 | 0.582308 | 0.291154 | − | 0.956676i | \(-0.405961\pi\) | ||||
0.291154 | + | 0.956676i | \(0.405961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.0000 | 0.953914 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.5140 | −0.536286 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.30864 | −0.249958 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.9706 | 0.987820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.4558 | −0.926450 | −0.463225 | − | 0.886241i | \(-0.653308\pi\) | ||||
−0.463225 | + | 0.886241i | \(0.653308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.3784 | 1.15857 | 0.579286 | − | 0.815124i | \(-0.303331\pi\) | ||||
0.579286 | + | 0.815124i | \(0.303331\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.12293 | 0.241090 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.3431 | −0.721143 | −0.360572 | − | 0.932731i | \(-0.617418\pi\) | ||||
−0.360572 | + | 0.932731i | \(0.617418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.9706 | 1.29421 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.12293 | 0.239977 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.6452 | 1.55144 | 0.775719 | − | 0.631079i | \(-0.217387\pi\) | ||||
0.775719 | + | 0.631079i | \(0.217387\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.20101 | −0.320440 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.627417 | 0.0244779 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.7904 | 1.35524 | 0.677621 | − | 0.735412i | \(-0.263011\pi\) | ||||
0.677621 | + | 0.735412i | \(0.263011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.30864 | 0.245378 | 0.122689 | − | 0.992445i | \(-0.460848\pi\) | ||||
0.122689 | + | 0.992445i | \(0.460848\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.9706 | −0.969776 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.48528 | −0.173932 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.70967 | −0.375960 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.0279 | 1.04496 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.6569 | −1.45373 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.6274 | −0.640940 | −0.320470 | − | 0.947259i | \(-0.603841\pi\) | ||||
−0.320470 | + | 0.947259i | \(0.603841\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.0083 | 0.770121 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8645 | 0.609721 | 0.304860 | − | 0.952397i | \(-0.401390\pi\) | ||||
0.304860 | + | 0.952397i | \(0.401390\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000 | 0.383765 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.4558 | 0.515629 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.2960 | 1.08272 | 0.541359 | − | 0.840792i | \(-0.317910\pi\) | ||||
0.541359 | + | 0.840792i | \(0.317910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.16478 | 0.0827122 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.17157 | 0.349917 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.3137 | −1.04057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.3057 | −1.49526 | −0.747629 | − | 0.664116i | \(-0.768808\pi\) | ||||
−0.747629 | + | 0.664116i | \(0.768808\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.55582 | 0.362996 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.1127 | −0.421529 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0000 | −1.06058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.8239 | 0.409398 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.70099 | −0.177554 | −0.0887769 | − | 0.996052i | \(-0.528296\pi\) | ||||
−0.0887769 | + | 0.996052i | \(0.528296\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.97056 | 0.338331 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.37258 | 0.352992 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.14386 | 0.155846 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.7289 | −1.19160 | −0.595802 | − | 0.803131i | \(-0.703166\pi\) | ||||
−0.595802 | + | 0.803131i | \(0.703166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.9706 | 0.936469 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.62742 | 0.248199 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.6871 | 1.33462 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.9778 | 0.409972 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.3137 | −0.720280 | −0.360140 | − | 0.932898i | \(-0.617271\pi\) | ||||
−0.360140 | + | 0.932898i | \(0.617271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.34315 | 0.0872633 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.0698 | −0.857975 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −31.7289 | −1.17838 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.3137 | −1.60642 | −0.803208 | − | 0.595698i | \(-0.796875\pi\) | ||||
−0.803208 | + | 0.595698i | \(0.796875\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.2843 | 0.640158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.1116 | −0.706870 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.4930 | 0.572249 | 0.286124 | − | 0.958192i | \(-0.407633\pi\) | ||||
0.286124 | + | 0.958192i | \(0.407633\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.17157 | −0.0432141 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38.6274 | 1.42286 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.6675 | −1.05455 | −0.527275 | − | 0.849695i | \(-0.676786\pi\) | ||||
−0.527275 | + | 0.849695i | \(0.676786\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.2960 | 1.03948 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.4853 | −1.63201 | −0.816003 | − | 0.578047i | \(-0.803815\pi\) | ||||
−0.816003 | + | 0.578047i | \(0.803815\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.6863 | −0.757887 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.89538 | 0.362053 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.7206 | 0.428262 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.45584 | −0.199087 | −0.0995433 | − | 0.995033i | \(-0.531738\pi\) | ||||
−0.0995433 | + | 0.995033i | \(0.531738\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.1421 | −0.952672 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.9778 | 0.399522 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.6452 | −1.44093 | −0.720465 | − | 0.693491i | \(-0.756072\pi\) | ||||
−0.720465 | + | 0.693491i | \(0.756072\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.62742 | −0.240560 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9706 | 0.542682 | 0.271341 | − | 0.962483i | \(-0.412533\pi\) | ||||
0.271341 | + | 0.962483i | \(0.412533\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.9469 | −0.613517 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.23719 | 0.261661 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −39.7990 | −1.43706 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −55.2548 | −1.99254 | −0.996270 | − | 0.0862891i | \(-0.972499\pi\) | ||||
−0.996270 | + | 0.0862891i | \(0.972499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.4107 | 0.518987 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.8645 | −0.570605 | −0.285303 | − | 0.958438i | \(-0.592094\pi\) | ||||
−0.285303 | + | 0.958438i | \(0.592094\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.6569 | 0.777937 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.34315 | 0.0840599 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.7289 | 1.13681 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.3742 | −2.55397 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −43.3137 | −1.54791 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.48528 | −0.160087 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.7080 | −1.20156 | −0.600780 | − | 0.799414i | \(-0.705143\pi\) | ||||
−0.600780 | + | 0.799414i | \(0.705143\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.7821 | −0.526256 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.17157 | −0.112768 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.4558 | 1.61418 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.07241 | −0.179900 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.7499 | −1.05379 | −0.526897 | − | 0.849929i | \(-0.676645\pi\) | ||||
−0.526897 | + | 0.849929i | \(0.676645\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.2548 | −1.03496 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.65685 | −0.129209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.79337 | −0.0632865 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.26810 | −0.0446947 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.4558 | −1.03689 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.8284 | 1.29482 | 0.647409 | − | 0.762143i | \(-0.275852\pi\) | ||||
0.647409 | + | 0.762143i | \(0.275852\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.4286 | −1.59521 | −0.797607 | − | 0.603177i | \(-0.793901\pi\) | ||||
−0.797607 | + | 0.603177i | \(0.793901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.7821 | −0.518430 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.6569 | 0.758607 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.6569 | 0.757677 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.5349 | −0.403062 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.9050 | −0.729590 | −0.364795 | − | 0.931088i | \(-0.618861\pi\) | ||||
−0.364795 | + | 0.931088i | \(0.618861\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.02944 | −0.245031 | −0.122515 | − | 0.992467i | \(-0.539096\pi\) | ||||
−0.122515 | + | 0.992467i | \(0.539096\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.6569 | −0.753995 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.4077 | −1.64853 | −0.824263 | − | 0.566207i | \(-0.808410\pi\) | ||||
−0.824263 | + | 0.566207i | \(0.808410\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.5515 | −1.79046 | −0.895230 | − | 0.445605i | \(-0.852989\pi\) | ||||
−0.895230 | + | 0.445605i | \(0.852989\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.62742 | 0.229903 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.65685 | 0.126702 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.3183 | 0.599324 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.5641 | 1.02189 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.2843 | 0.700291 | 0.350145 | − | 0.936695i | \(-0.386132\pi\) | ||||
0.350145 | + | 0.936695i | \(0.386132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.6863 | 1.36849 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.16478 | 0.0745591 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.0070 | −0.997872 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.3137 | −0.560546 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.4264 | −1.04423 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.53620 | 0.0869399 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.7472 | 1.63483 | 0.817417 | − | 0.576046i | \(-0.195405\pi\) | ||||
0.817417 | + | 0.576046i | \(0.195405\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.20101 | −0.280469 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.6274 | 1.52444 | 0.762222 | − | 0.647316i | \(-0.224109\pi\) | ||||
0.762222 | + | 0.647316i | \(0.224109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.6997 | −0.467427 | −0.233714 | − | 0.972306i | \(-0.575088\pi\) | ||||
−0.233714 | + | 0.972306i | \(0.575088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.28772 | 0.282445 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.6863 | −0.976493 | −0.488246 | − | 0.872706i | \(-0.662363\pi\) | ||||
−0.488246 | + | 0.872706i | \(0.662363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.8579 | −0.471182 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.92629 | −0.133344 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −71.3742 | −2.42120 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.6274 | −1.57991 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.2843 | 0.618829 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.55582 | −0.323046 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.6060 | −0.864653 | −0.432326 | − | 0.901717i | \(-0.642307\pi\) | ||||
−0.432326 | + | 0.901717i | \(0.642307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.5147 | 0.388382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.9706 | −0.773898 | −0.386949 | − | 0.922101i | \(-0.626471\pi\) | ||||
−0.386949 | + | 0.922101i | \(0.626471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.4303 | −0.721186 | −0.360593 | − | 0.932723i | \(-0.617426\pi\) | ||||
−0.360593 | + | 0.932723i | \(0.617426\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.39104 | −0.248447 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6274 | −0.759754 | −0.379877 | − | 0.925037i | \(-0.624034\pi\) | ||||
−0.379877 | + | 0.925037i | \(0.624034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.4853 | −0.418743 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.896683 | −0.0300400 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.1509 | 1.10935 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.94113 | 0.332295 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.00000 | 0.267112 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.8824 | −1.56362 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.8326 | 0.527460 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.65685 | 0.188248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.17157 | −0.0389444 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.8435 | −0.592485 | −0.296243 | − | 0.955113i | \(-0.595734\pi\) | ||||
−0.296243 | + | 0.955113i | \(0.595734\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.57675 | 0.251305 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.1716 | −1.09902 | −0.549512 | − | 0.835486i | \(-0.685186\pi\) | ||||
−0.549512 | + | 0.835486i | \(0.685186\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.2843 | −0.936073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.44157 | 0.279070 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.57675 | −0.250206 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6569 | −0.450498 | −0.225249 | − | 0.974301i | \(-0.572320\pi\) | ||||
−0.225249 | + | 0.974301i | \(0.572320\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.1716 | −0.565823 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 86.1562 | 2.83587 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.28772 | 0.272499 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.28427 | 0.140714 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.2843 | −1.51854 | −0.759269 | − | 0.650777i | \(-0.774443\pi\) | ||||
−0.759269 | + | 0.650777i | \(0.774443\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.14386 | −0.135810 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.1509 | 1.08531 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.6863 | −0.676514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.2843 | −0.597321 | −0.298661 | − | 0.954359i | \(-0.596540\pi\) | ||||
−0.298661 | + | 0.954359i | \(0.596540\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.2764 | 0.694330 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.4595 | 1.28634 | 0.643172 | − | 0.765722i | \(-0.277618\pi\) | ||||
0.643172 | + | 0.765722i | \(0.277618\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.97056 | 0.292122 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.65685 | −0.184017 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.63952 | 0.0532772 | 0.0266386 | − | 0.999645i | \(-0.491520\pi\) | ||||
0.0266386 | + | 0.999645i | \(0.491520\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.16478 | 0.0702719 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.6274 | 0.733744 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.6863 | −0.475736 | −0.237868 | − | 0.971298i | \(-0.576449\pi\) | ||||
−0.237868 | + | 0.971298i | \(0.576449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.58673 | 0.116064 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 46.8824 | 1.51549 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.00000 | 0.0645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.4303 | 0.690581 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.9246 | 0.898925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.1421 | 1.86973 | 0.934863 | − | 0.355010i | \(-0.115523\pi\) | ||||
0.934863 | + | 0.355010i | \(0.115523\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.4020 | −0.526909 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.5825 | 1.46281 | 0.731405 | − | 0.681943i | \(-0.238865\pi\) | ||||
0.731405 | + | 0.681943i | \(0.238865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.2668 | −0.329138 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.1421 | 0.837218 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.0000 | 0.959785 | 0.479893 | − | 0.877327i | \(-0.340676\pi\) | ||||
0.479893 | + | 0.877327i | \(0.340676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.4525 | 0.334063 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.9861 | −0.989310 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.9706 | −1.81708 | −0.908539 | − | 0.417799i | \(-0.862802\pi\) | ||||
−0.908539 | + | 0.417799i | \(0.862802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | 0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.65914 | 0.275623 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.12293 | 0.194698 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.3431 | −0.582689 | −0.291345 | − | 0.956618i | \(-0.594103\pi\) | ||||
−0.291345 | + | 0.956618i | \(0.594103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.0294 | −0.476945 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.0279 | −0.856843 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.7695 | −1.16450 | −0.582250 | − | 0.813009i | \(-0.697828\pi\) | ||||
−0.582250 | + | 0.813009i | \(0.697828\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.3137 | 0.357950 |
(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 | 1792.2.a.u.1.3 | 4 | ||
4.3 | odd | 2 | 1792.2.a.w.1.2 | 4 | |||
8.3 | odd | 2 | 1792.2.a.w.1.3 | 4 | |||
8.5 | even | 2 | inner | 1792.2.a.u.1.2 | 4 | ||
16.3 | odd | 4 | 896.2.b.f.449.2 | ✓ | 4 | ||
16.5 | even | 4 | 896.2.b.h.449.2 | yes | 4 | ||
16.11 | odd | 4 | 896.2.b.f.449.3 | yes | 4 | ||
16.13 | even | 4 | 896.2.b.h.449.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.b.f.449.2 | ✓ | 4 | 16.3 | odd | 4 | ||
896.2.b.f.449.3 | yes | 4 | 16.11 | odd | 4 | ||
896.2.b.h.449.2 | yes | 4 | 16.5 | even | 4 | ||
896.2.b.h.449.3 | yes | 4 | 16.13 | even | 4 | ||
1792.2.a.u.1.2 | 4 | 8.5 | even | 2 | inner | ||
1792.2.a.u.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1792.2.a.w.1.2 | 4 | 4.3 | odd | 2 | |||
1792.2.a.w.1.3 | 4 | 8.3 | odd | 2 |