Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(703,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.703");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.g (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.7 | ||
Root | \(0.500000 + 0.564882i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.703 |
Dual form | 1728.3.g.m.703.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.42091 | 1.28418 | 0.642091 | − | 0.766628i | \(-0.278067\pi\) | ||||
0.642091 | + | 0.766628i | \(0.278067\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 13.8102i | − 1.97289i | −0.164102 | − | 0.986443i | \(-0.552473\pi\) | ||||
0.164102 | − | 0.986443i | \(-0.447527\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.0350i | 1.18500i | 0.805572 | + | 0.592498i | \(0.201858\pi\) | ||||
−0.805572 | + | 0.592498i | \(0.798142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.16454 | −0.551118 | −0.275559 | − | 0.961284i | \(-0.588863\pi\) | ||||
−0.275559 | + | 0.961284i | \(0.588863\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −31.5918 | −1.85834 | −0.929171 | − | 0.369651i | \(-0.879477\pi\) | ||||
−0.929171 | + | 0.369651i | \(0.879477\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 16.4875i | − 0.867763i | −0.900970 | − | 0.433881i | \(-0.857144\pi\) | ||||
0.900970 | − | 0.433881i | \(-0.142856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.9778i | 0.738163i | 0.929397 | + | 0.369082i | \(0.120328\pi\) | ||||
−0.929397 | + | 0.369082i | \(0.879672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 16.2281 | 0.649124 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −42.4562 | −1.46401 | −0.732004 | − | 0.681301i | \(-0.761415\pi\) | ||||
−0.732004 | + | 0.681301i | \(0.761415\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 29.6836i | − 0.957537i | −0.877941 | − | 0.478769i | \(-0.841083\pi\) | ||||
0.877941 | − | 0.478769i | \(-0.158917\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 88.6741i | − 2.53355i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −39.3037 | −1.06226 | −0.531131 | − | 0.847289i | \(-0.678233\pi\) | ||||
−0.531131 | + | 0.847289i | \(0.678233\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −39.8856 | −0.972819 | −0.486409 | − | 0.873731i | \(-0.661694\pi\) | ||||
−0.486409 | + | 0.873731i | \(0.661694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 16.3291i | − 0.379746i | −0.981809 | − | 0.189873i | \(-0.939192\pi\) | ||||
0.981809 | − | 0.189873i | \(-0.0608076\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 57.8888i | 1.23168i | 0.787872 | + | 0.615839i | \(0.211183\pi\) | ||||
−0.787872 | + | 0.615839i | \(0.788817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −141.722 | −2.89228 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 46.4110 | 0.875680 | 0.437840 | − | 0.899053i | \(-0.355744\pi\) | ||||
0.437840 | + | 0.899053i | \(0.355744\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 83.6964i | 1.52175i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 14.2179i | − 0.240981i | −0.992714 | − | 0.120491i | \(-0.961553\pi\) | ||||
0.992714 | − | 0.120491i | \(-0.0384468\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 63.7479 | 1.04505 | 0.522524 | − | 0.852625i | \(-0.324991\pi\) | ||||
0.522524 | + | 0.852625i | \(0.324991\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −46.0028 | −0.707736 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 32.5634i | 0.486022i | 0.970024 | + | 0.243011i | \(0.0781350\pi\) | ||||
−0.970024 | + | 0.243011i | \(0.921865\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 22.4738i | 0.316532i | 0.987397 | + | 0.158266i | \(0.0505904\pi\) | ||||
−0.987397 | + | 0.158266i | \(0.949410\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24.9252 | 0.341441 | 0.170721 | − | 0.985319i | \(-0.445390\pi\) | ||||
0.170721 | + | 0.985319i | \(0.445390\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 180.016 | 2.33786 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61.9501i | 0.784178i | 0.919927 | + | 0.392089i | \(0.128247\pi\) | ||||
−0.919927 | + | 0.392089i | \(0.871753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 44.7901i | − 0.539640i | −0.962911 | − | 0.269820i | \(-0.913036\pi\) | ||||
0.962911 | − | 0.269820i | \(-0.0869642\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −202.848 | −2.38645 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.95333 | 0.0219475 | 0.0109738 | − | 0.999940i | \(-0.496507\pi\) | ||||
0.0109738 | + | 0.999940i | \(0.496507\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 98.9437i | 1.08729i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 105.865i | − 1.11437i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −44.5813 | −0.459601 | −0.229800 | − | 0.973238i | \(-0.573807\pi\) | ||||
−0.229800 | + | 0.973238i | \(0.573807\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 138.393 | 1.37022 | 0.685112 | − | 0.728438i | \(-0.259753\pi\) | ||||
0.685112 | + | 0.728438i | \(0.259753\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.5698i | 0.189998i | 0.995477 | + | 0.0949991i | \(0.0302848\pi\) | ||||
−0.995477 | + | 0.0949991i | \(0.969715\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 39.6245i | 0.370323i | 0.982708 | + | 0.185161i | \(0.0592808\pi\) | ||||
−0.982708 | + | 0.185161i | \(0.940719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −45.2012 | −0.414690 | −0.207345 | − | 0.978268i | \(-0.566482\pi\) | ||||
−0.207345 | + | 0.978268i | \(0.566482\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −111.845 | −0.989776 | −0.494888 | − | 0.868957i | \(-0.664791\pi\) | ||||
−0.494888 | + | 0.868957i | \(0.664791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 109.013i | 0.947936i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 436.289i | 3.66630i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −48.9103 | −0.404218 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −56.3235 | −0.450588 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 110.064i | − 0.866642i | −0.901240 | − | 0.433321i | \(-0.857342\pi\) | ||||
0.901240 | − | 0.433321i | \(-0.142658\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 14.3672i | − 0.109673i | −0.998495 | − | 0.0548367i | \(-0.982536\pi\) | ||||
0.998495 | − | 0.0548367i | \(-0.0174638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −227.696 | −1.71200 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 170.048 | 1.24123 | 0.620613 | − | 0.784117i | \(-0.286884\pi\) | ||||
0.620613 | + | 0.784117i | \(0.286884\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 213.171i | − 1.53360i | −0.641884 | − | 0.766802i | \(-0.721847\pi\) | ||||
0.641884 | − | 0.766802i | \(-0.278153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 93.3895i | − 0.653073i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −272.608 | −1.88005 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −84.5143 | −0.567210 | −0.283605 | − | 0.958941i | \(-0.591530\pi\) | ||||
−0.283605 | + | 0.958941i | \(0.591530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 180.407i | − 1.19475i | −0.801962 | − | 0.597376i | \(-0.796210\pi\) | ||||
0.801962 | − | 0.597376i | \(-0.203790\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 190.596i | − 1.22965i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −49.7071 | −0.316605 | −0.158303 | − | 0.987391i | \(-0.550602\pi\) | ||||
−0.158303 | + | 0.987391i | \(0.550602\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 234.466 | 1.45631 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 49.3718i | 0.302894i | 0.988465 | + | 0.151447i | \(0.0483933\pi\) | ||||
−0.988465 | + | 0.151447i | \(0.951607\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 161.617i | − 0.967766i | −0.875133 | − | 0.483883i | \(-0.839226\pi\) | ||||
0.875133 | − | 0.483883i | \(-0.160774\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −117.669 | −0.696269 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −63.6058 | −0.367664 | −0.183832 | − | 0.982958i | \(-0.558850\pi\) | ||||
−0.183832 | + | 0.982958i | \(0.558850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 224.114i | − 1.28065i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 203.780i | − 1.13844i | −0.822186 | − | 0.569219i | \(-0.807246\pi\) | ||||
0.822186 | − | 0.569219i | \(-0.192754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.1886 | −0.128114 | −0.0640570 | − | 0.997946i | \(-0.520404\pi\) | ||||
−0.0640570 | + | 0.997946i | \(0.520404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −252.366 | −1.36414 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 411.798i | − 2.20213i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 247.017i | − 1.29328i | −0.762793 | − | 0.646642i | \(-0.776173\pi\) | ||||
0.762793 | − | 0.646642i | \(-0.223827\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 126.813 | 0.657063 | 0.328531 | − | 0.944493i | \(-0.393446\pi\) | ||||
0.328531 | + | 0.944493i | \(0.393446\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 47.1824 | 0.239505 | 0.119752 | − | 0.992804i | \(-0.461790\pi\) | ||||
0.119752 | + | 0.992804i | \(0.461790\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 298.835i | 1.50168i | 0.660482 | + | 0.750842i | \(0.270352\pi\) | ||||
−0.660482 | + | 0.750842i | \(0.729648\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 586.329i | 2.88832i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −256.102 | −1.24928 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 214.914 | 1.02830 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 270.034i | − 1.27978i | −0.768466 | − | 0.639891i | \(-0.778980\pi\) | ||||
0.768466 | − | 0.639891i | \(-0.221020\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 104.848i | − 0.487663i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −409.937 | −1.88911 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 226.341 | 1.02417 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 171.763i | 0.770237i | 0.922867 | + | 0.385118i | \(0.125839\pi\) | ||||
−0.922867 | + | 0.385118i | \(0.874161\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 146.057i | 0.643424i | 0.946838 | + | 0.321712i | \(0.104258\pi\) | ||||
−0.946838 | + | 0.321712i | \(0.895742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 325.016 | 1.41928 | 0.709641 | − | 0.704563i | \(-0.248857\pi\) | ||||
0.709641 | + | 0.704563i | \(0.248857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −405.093 | −1.73860 | −0.869299 | − | 0.494286i | \(-0.835430\pi\) | ||||
−0.869299 | + | 0.494286i | \(0.835430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 371.699i | 1.58170i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 85.3071i | − 0.356933i | −0.983946 | − | 0.178467i | \(-0.942886\pi\) | ||||
0.983946 | − | 0.178467i | \(-0.0571137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −357.900 | −1.48506 | −0.742532 | − | 0.669811i | \(-0.766375\pi\) | ||||
−0.742532 | + | 0.669811i | \(0.766375\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −909.983 | −3.71422 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 118.125i | 0.478240i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 88.8097i | 0.353823i | 0.984227 | + | 0.176912i | \(0.0566107\pi\) | ||||
−0.984227 | + | 0.176912i | \(0.943389\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −221.304 | −0.874721 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −237.843 | −0.925460 | −0.462730 | − | 0.886499i | \(-0.653130\pi\) | ||||
−0.462730 | + | 0.886499i | \(0.653130\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 542.793i | 2.09572i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 309.702i | − 1.17757i | −0.808289 | − | 0.588786i | \(-0.799606\pi\) | ||||
0.808289 | − | 0.588786i | \(-0.200394\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 298.001 | 1.12453 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −490.940 | −1.82505 | −0.912527 | − | 0.409016i | \(-0.865872\pi\) | ||||
−0.912527 | + | 0.409016i | \(0.865872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 0.493459i | − 0.00182088i | −1.00000 | 0.000910442i | \(-0.999710\pi\) | |||||
1.00000 | 0.000910442i | \(-0.000289803\pi\) | ||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 211.533i | 0.769210i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.8497 | 0.0391686 | 0.0195843 | − | 0.999808i | \(-0.493766\pi\) | ||||
0.0195843 | + | 0.999808i | \(0.493766\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 351.417 | 1.25059 | 0.625297 | − | 0.780387i | \(-0.284978\pi\) | ||||
0.625297 | + | 0.780387i | \(0.284978\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 62.5357i | 0.220974i | 0.993878 | + | 0.110487i | \(0.0352411\pi\) | ||||
−0.993878 | + | 0.110487i | \(0.964759\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 550.828i | 1.91926i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 709.042 | 2.45343 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 74.3035 | 0.253596 | 0.126798 | − | 0.991929i | \(-0.459530\pi\) | ||||
0.126798 | + | 0.991929i | \(0.459530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 91.2919i | − 0.309464i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 121.638i | − 0.406815i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −225.508 | −0.749195 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 409.320 | 1.34203 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 460.555i | 1.50018i | 0.661336 | + | 0.750089i | \(0.269990\pi\) | ||||
−0.661336 | + | 0.750089i | \(0.730010\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 433.687i | − 1.39449i | −0.716832 | − | 0.697246i | \(-0.754409\pi\) | ||||
0.716832 | − | 0.697246i | \(-0.245591\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −434.686 | −1.38877 | −0.694387 | − | 0.719602i | \(-0.744324\pi\) | ||||
−0.694387 | + | 0.719602i | \(0.744324\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −212.120 | −0.669149 | −0.334574 | − | 0.942369i | \(-0.608593\pi\) | ||||
−0.334574 | + | 0.942369i | \(0.608593\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 553.415i | − 1.73484i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 520.870i | 1.61260i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −116.267 | −0.357744 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 799.457 | 2.42996 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 578.614i | − 1.74808i | −0.485854 | − | 0.874040i | \(-0.661491\pi\) | ||||
0.485854 | − | 0.874040i | \(-0.338509\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 209.087i | 0.624140i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −214.736 | −0.637198 | −0.318599 | − | 0.947890i | \(-0.603212\pi\) | ||||
−0.318599 | + | 0.947890i | \(0.603212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 386.925 | 1.13468 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1280.51i | 3.73326i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 280.616i | − 0.808692i | −0.914606 | − | 0.404346i | \(-0.867499\pi\) | ||||
0.914606 | − | 0.404346i | \(-0.132501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −232.447 | −0.666036 | −0.333018 | − | 0.942920i | \(-0.608067\pi\) | ||||
−0.333018 | + | 0.942920i | \(0.608067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 97.0279 | 0.274866 | 0.137433 | − | 0.990511i | \(-0.456115\pi\) | ||||
0.137433 | + | 0.990511i | \(0.456115\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 144.302i | 0.406485i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 37.7190i | 0.105067i | 0.998619 | + | 0.0525334i | \(0.0167296\pi\) | ||||
−0.998619 | + | 0.0525334i | \(0.983270\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 89.1625 | 0.246988 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 160.043 | 0.438473 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 303.506i | − 0.826991i | −0.910506 | − | 0.413496i | \(-0.864308\pi\) | ||||
0.910506 | − | 0.413496i | \(-0.135692\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 640.946i | − 1.72762i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 576.215 | 1.54481 | 0.772406 | − | 0.635129i | \(-0.219053\pi\) | ||||
0.772406 | + | 0.635129i | \(0.219053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 304.179 | 0.806841 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 36.0808i | − 0.0952001i | −0.998866 | − | 0.0476000i | \(-0.984843\pi\) | ||||
0.998866 | − | 0.0476000i | \(-0.0151573\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 521.053i | − 1.36045i | −0.733003 | − | 0.680225i | \(-0.761882\pi\) | ||||
0.733003 | − | 0.680225i | \(-0.238118\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1155.86 | 3.00224 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 472.918 | 1.21573 | 0.607864 | − | 0.794041i | \(-0.292027\pi\) | ||||
0.607864 | + | 0.794041i | \(0.292027\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 536.358i | − 1.37176i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 397.776i | 1.00703i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 209.784 | 0.528423 | 0.264212 | − | 0.964465i | \(-0.414888\pi\) | ||||
0.264212 | + | 0.964465i | \(0.414888\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −664.907 | −1.65812 | −0.829062 | − | 0.559157i | \(-0.811125\pi\) | ||||
−0.829062 | + | 0.559157i | \(0.811125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 212.670i | 0.527716i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 512.323i | − 1.25878i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −573.373 | −1.40189 | −0.700945 | − | 0.713215i | \(-0.747238\pi\) | ||||
−0.700945 | + | 0.713215i | \(0.747238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −196.352 | −0.475429 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 287.594i | − 0.692996i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 672.621i | 1.60530i | 0.596450 | + | 0.802651i | \(0.296578\pi\) | ||||
−0.596450 | + | 0.802651i | \(0.703422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 659.810 | 1.56724 | 0.783622 | − | 0.621238i | \(-0.213370\pi\) | ||||
0.783622 | + | 0.621238i | \(0.213370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −512.675 | −1.20629 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 880.372i | − 2.06176i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 360.903i | − 0.837361i | −0.908134 | − | 0.418681i | \(-0.862493\pi\) | ||||
0.908134 | − | 0.418681i | \(-0.137507\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −319.790 | −0.738546 | −0.369273 | − | 0.929321i | \(-0.620393\pi\) | ||||
−0.369273 | + | 0.929321i | \(0.620393\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 279.921 | 0.640551 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 80.6635i | 0.183744i | 0.995771 | + | 0.0918719i | \(0.0292850\pi\) | ||||
−0.995771 | + | 0.0918719i | \(0.970715\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 551.362i | − 1.24461i | −0.782775 | − | 0.622305i | \(-0.786197\pi\) | ||||
0.782775 | − | 0.622305i | \(-0.213803\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.5422 | 0.0281847 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 43.0735 | 0.0959321 | 0.0479661 | − | 0.998849i | \(-0.484726\pi\) | ||||
0.0479661 | + | 0.998849i | \(0.484726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 519.907i | − 1.15279i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 635.309i | 1.39628i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 205.936 | 0.450626 | 0.225313 | − | 0.974286i | \(-0.427659\pi\) | ||||
0.225313 | + | 0.974286i | \(0.427659\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 650.729 | 1.41156 | 0.705780 | − | 0.708431i | \(-0.250597\pi\) | ||||
0.705780 | + | 0.708431i | \(0.250597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 333.871i | − 0.721103i | −0.932739 | − | 0.360552i | \(-0.882588\pi\) | ||||
0.932739 | − | 0.360552i | \(-0.117412\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 359.357i | 0.769502i | 0.923020 | + | 0.384751i | \(0.125713\pi\) | ||||
−0.923020 | + | 0.384751i | \(0.874287\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 449.708 | 0.958865 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 212.849 | 0.449998 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 267.561i | − 0.563286i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 635.502i | 1.32673i | 0.748297 | + | 0.663363i | \(0.230872\pi\) | ||||
−0.748297 | + | 0.663363i | \(0.769128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 281.593 | 0.585432 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −286.252 | −0.590211 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 233.959i | 0.480409i | 0.970722 | + | 0.240205i | \(0.0772146\pi\) | ||||
−0.970722 | + | 0.240205i | \(0.922785\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 494.173i | − 1.00646i | −0.864152 | − | 0.503231i | \(-0.832145\pi\) | ||||
0.864152 | − | 0.503231i | \(-0.167855\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1341.27 | 2.72063 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 310.368 | 0.624482 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 468.260i | − 0.938396i | −0.883093 | − | 0.469198i | \(-0.844543\pi\) | ||||
0.883093 | − | 0.469198i | \(-0.155457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 59.2449i | 0.117783i | 0.998264 | + | 0.0588916i | \(0.0187566\pi\) | ||||
−0.998264 | + | 0.0588916i | \(0.981243\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 888.607 | 1.75962 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −161.243 | −0.316784 | −0.158392 | − | 0.987376i | \(-0.550631\pi\) | ||||
−0.158392 | + | 0.987376i | \(0.550631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 344.222i | − 0.673625i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 125.656i | 0.243992i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −754.579 | −1.45953 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −350.872 | −0.673458 | −0.336729 | − | 0.941602i | \(-0.609321\pi\) | ||||
−0.336729 | + | 0.941602i | \(0.609321\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 729.342i | 1.39454i | 0.716811 | + | 0.697268i | \(0.245601\pi\) | ||||
−0.716811 | + | 0.697268i | \(0.754399\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 937.760i | 1.77943i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 240.756 | 0.455115 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 285.762 | 0.536138 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 254.426i | 0.475562i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1847.34i | − 3.42734i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 365.728 | 0.676021 | 0.338011 | − | 0.941142i | \(-0.390246\pi\) | ||||
0.338011 | + | 0.941142i | \(0.390246\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −290.233 | −0.532537 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 468.636i | 0.856738i | 0.903604 | + | 0.428369i | \(0.140912\pi\) | ||||
−0.903604 | + | 0.428369i | \(0.859088\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 699.997i | 1.27041i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 855.543 | 1.54709 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 288.006 | 0.517066 | 0.258533 | − | 0.966002i | \(-0.416761\pi\) | ||||
0.258533 | + | 0.966002i | \(0.416761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 116.990i | 0.209285i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 158.644i | − 0.281783i | −0.990025 | − | 0.140892i | \(-0.955003\pi\) | ||||
0.990025 | − | 0.140892i | \(-0.0449969\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −718.145 | −1.27105 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −438.309 | −0.770315 | −0.385157 | − | 0.922851i | \(-0.625853\pi\) | ||||
−0.385157 | + | 0.922851i | \(0.625853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 683.282i | − 1.19664i | −0.801257 | − | 0.598321i | \(-0.795835\pi\) | ||||
0.801257 | − | 0.598321i | \(-0.204165\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 275.517i | 0.479160i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −166.370 | −0.288337 | −0.144168 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144168 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −618.561 | −1.06465 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 604.966i | 1.03768i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1095.17i | 1.86570i | 0.360265 | + | 0.932850i | \(0.382686\pi\) | ||||
−0.360265 | + | 0.932850i | \(0.617314\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −489.409 | −0.830915 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −131.905 | −0.222437 | −0.111218 | − | 0.993796i | \(-0.535475\pi\) | ||||
−0.111218 | + | 0.993796i | \(0.535475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2801.38i | 4.70819i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 228.590i | − 0.381619i | −0.981627 | − | 0.190809i | \(-0.938889\pi\) | ||||
0.981627 | − | 0.190809i | \(-0.0611112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 945.987 | 1.57402 | 0.787010 | − | 0.616940i | \(-0.211628\pi\) | ||||
0.787010 | + | 0.616940i | \(0.211628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −314.049 | −0.519089 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 539.641i | − 0.889029i | −0.895772 | − | 0.444514i | \(-0.853376\pi\) | ||||
0.895772 | − | 0.444514i | \(-0.146624\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 414.747i | − 0.678800i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 305.962 | 0.499123 | 0.249561 | − | 0.968359i | \(-0.419714\pi\) | ||||
0.249561 | + | 0.968359i | \(0.419714\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −409.095 | −0.663038 | −0.331519 | − | 0.943449i | \(-0.607561\pi\) | ||||
−0.331519 | + | 0.943449i | \(0.607561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 453.938i | − 0.733341i | −0.930351 | − | 0.366670i | \(-0.880498\pi\) | ||||
0.930351 | − | 0.366670i | \(-0.119502\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 26.9759i | − 0.0433000i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −767.351 | −1.22776 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1241.68 | 1.97405 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 393.383i | 0.623428i | 0.950176 | + | 0.311714i | \(0.100903\pi\) | ||||
−0.950176 | + | 0.311714i | \(0.899097\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 706.709i | − 1.11293i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1015.37 | 1.59399 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −982.724 | −1.53311 | −0.766555 | − | 0.642179i | \(-0.778031\pi\) | ||||
−0.766555 | + | 0.642179i | \(0.778031\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1078.21i | 1.67684i | 0.545025 | + | 0.838420i | \(0.316520\pi\) | ||||
−0.545025 | + | 0.838420i | \(0.683480\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 38.4217i | − 0.0593844i | −0.999559 | − | 0.0296922i | \(-0.990547\pi\) | ||||
0.999559 | − | 0.0296922i | \(-0.00945271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 185.330 | 0.285562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −317.953 | −0.486911 | −0.243456 | − | 0.969912i | \(-0.578281\pi\) | ||||
−0.243456 | + | 0.969912i | \(0.578281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 92.2507i | − 0.140841i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 792.921i | 1.20322i | 0.798790 | + | 0.601609i | \(0.205474\pi\) | ||||
−0.798790 | + | 0.601609i | \(0.794526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1029.55 | 1.55757 | 0.778786 | − | 0.627290i | \(-0.215836\pi\) | ||||
0.778786 | + | 0.627290i | \(0.215836\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1462.01 | −2.19852 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 720.811i | − 1.08068i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 830.952i | 1.23838i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.46119 | −0.00960059 | −0.00480029 | − | 0.999988i | \(-0.501528\pi\) | ||||
−0.00480029 | + | 0.999988i | \(0.501528\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.6650 | 0.0320015 | 0.0160008 | − | 0.999872i | \(-0.494907\pi\) | ||||
0.0160008 | + | 0.999872i | \(0.494907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 615.676i | 0.906740i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 503.008i | 0.736469i | 0.929733 | + | 0.368234i | \(0.120038\pi\) | ||||
−0.929733 | + | 0.368234i | \(0.879962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1091.86 | 1.59396 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −332.514 | −0.482603 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 514.362i | − 0.744374i | −0.928158 | − | 0.372187i | \(-0.878608\pi\) | ||||
0.928158 | − | 0.372187i | \(-0.121392\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1368.75i | − 1.96943i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1260.06 | 1.80783 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 457.404 | 0.652502 | 0.326251 | − | 0.945283i | \(-0.394214\pi\) | ||||
0.326251 | + | 0.945283i | \(0.394214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 648.020i | 0.921792i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1911.23i | − 2.70330i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −390.207 | −0.550363 | −0.275182 | − | 0.961392i | \(-0.588738\pi\) | ||||
−0.275182 | + | 0.961392i | \(0.588738\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 503.962 | 0.706819 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 599.646i | − 0.838665i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 979.508i | − 1.36232i | −0.732134 | − | 0.681160i | \(-0.761476\pi\) | ||||
0.732134 | − | 0.681160i | \(-0.238524\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 270.263 | 0.374845 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −688.984 | −0.950323 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 553.802i | 0.761764i | 0.924624 | + | 0.380882i | \(0.124380\pi\) | ||||
−0.924624 | + | 0.380882i | \(0.875620\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 515.865i | 0.705697i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −250.392 | −0.341599 | −0.170800 | − | 0.985306i | \(-0.554635\pi\) | ||||
−0.170800 | + | 0.985306i | \(0.554635\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −424.463 | −0.575934 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 403.959i | − 0.546630i | −0.961925 | − | 0.273315i | \(-0.911880\pi\) | ||||
0.961925 | − | 0.273315i | \(-0.0881201\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 142.091i | − 0.191240i | −0.995418 | − | 0.0956201i | \(-0.969517\pi\) | ||||
0.995418 | − | 0.0956201i | \(-0.0304834\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −542.659 | −0.728401 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 547.223 | 0.730605 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 667.242i | − 0.888471i | −0.895910 | − | 0.444235i | \(-0.853475\pi\) | ||||
0.895910 | − | 0.444235i | \(-0.146525\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1158.38i | − 1.53428i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −970.866 | −1.28252 | −0.641259 | − | 0.767325i | \(-0.721587\pi\) | ||||
−0.641259 | + | 0.767325i | \(0.721587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 295.323 | 0.388072 | 0.194036 | − | 0.980994i | \(-0.437842\pi\) | ||||
0.194036 | + | 0.980994i | \(0.437842\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 624.238i | 0.818136i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 101.865i | 0.132809i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −552.240 | −0.718128 | −0.359064 | − | 0.933313i | \(-0.616904\pi\) | ||||
−0.359064 | + | 0.933313i | \(0.616904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −797.819 | −1.03211 | −0.516053 | − | 0.856556i | \(-0.672599\pi\) | ||||
−0.516053 | + | 0.856556i | \(0.672599\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 481.709i | − 0.621561i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 657.613i | 0.844176i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −292.945 | −0.375090 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −319.165 | −0.406579 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1140.72i | − 1.44946i | −0.689033 | − | 0.724730i | \(-0.741965\pi\) | ||||
0.689033 | − | 0.724730i | \(-0.258035\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1544.60i | 1.95272i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −456.724 | −0.575945 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1453.75 | 1.82403 | 0.912016 | − | 0.410154i | \(-0.134525\pi\) | ||||
0.912016 | + | 0.410154i | \(0.134525\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1828.81i | − 2.28888i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 324.899i | 0.404607i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1505.49 | 1.87017 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 981.664 | 1.21343 | 0.606714 | − | 0.794920i | \(-0.292487\pi\) | ||||
0.606714 | + | 0.794920i | \(0.292487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1090.81i | − 1.34502i | −0.740087 | − | 0.672511i | \(-0.765216\pi\) | ||||
0.740087 | − | 0.672511i | \(-0.234784\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 317.012i | 0.388972i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −269.225 | −0.329529 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 282.456 | 0.344039 | 0.172019 | − | 0.985094i | \(-0.444971\pi\) | ||||
0.172019 | + | 0.985094i | \(0.444971\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 497.382i | 0.604352i | 0.953252 | + | 0.302176i | \(0.0977131\pi\) | ||||
−0.953252 | + | 0.302176i | \(0.902287\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1159.09i | 1.40156i | 0.713379 | + | 0.700778i | \(0.247164\pi\) | ||||
−0.713379 | + | 0.700778i | \(0.752836\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 806.908 | 0.973351 | 0.486675 | − | 0.873583i | \(-0.338209\pi\) | ||||
0.486675 | + | 0.873583i | \(0.338209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4477.25 | 5.37485 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1037.73i | − 1.24279i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1045.71i | 1.24638i | 0.782071 | + | 0.623189i | \(0.214163\pi\) | ||||
−0.782071 | + | 0.623189i | \(0.785837\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 961.530 | 1.14332 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −755.545 | −0.894136 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 675.462i | 0.797476i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 667.289i | − 0.784123i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1126.10 | −1.32017 | −0.660083 | − | 0.751193i | \(-0.729479\pi\) | ||||
−0.660083 | + | 0.751193i | \(0.729479\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 112.853 | 0.131684 | 0.0658419 | − | 0.997830i | \(-0.479027\pi\) | ||||
0.0658419 | + | 0.997830i | \(0.479027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 679.360i | − 0.790873i | −0.918493 | − | 0.395437i | \(-0.870593\pi\) | ||||
0.918493 | − | 0.395437i | \(-0.129407\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 560.002i | − 0.648901i | −0.945903 | − | 0.324451i | \(-0.894821\pi\) | ||||
0.945903 | − | 0.324451i | \(-0.105179\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −408.408 | −0.472147 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −807.517 | −0.929249 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 233.302i | − 0.267855i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 777.840i | 0.888960i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 775.431 | 0.884186 | 0.442093 | − | 0.896969i | \(-0.354236\pi\) | ||||
0.442093 | + | 0.896969i | \(0.354236\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1024.25 | 1.16260 | 0.581298 | − | 0.813691i | \(-0.302545\pi\) | ||||
0.581298 | + | 0.813691i | \(0.302545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1301.28i | 1.47370i | 0.676057 | + | 0.736850i | \(0.263687\pi\) | ||||
−0.676057 | + | 0.736850i | \(0.736313\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1284.02i | 1.44760i | 0.690010 | + | 0.723800i | \(0.257606\pi\) | ||||
−0.690010 | + | 0.723800i | \(0.742394\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1520.00 | −1.70979 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 954.442 | 1.06880 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1308.46i | − 1.46196i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1260.26i | 1.40184i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1466.21 | −1.62731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −148.892 | −0.164522 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1042.84i | 1.14976i | 0.818236 | + | 0.574882i | \(0.194952\pi\) | ||||
−0.818236 | + | 0.574882i | \(0.805048\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 857.109i | − 0.940844i | −0.882442 | − | 0.470422i | \(-0.844102\pi\) | ||||
0.882442 | − | 0.470422i | \(-0.155898\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 583.838 | 0.639472 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −198.414 | −0.216373 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 451.721i | 0.491536i | 0.969329 | + | 0.245768i | \(0.0790401\pi\) | ||||
−0.969329 | + | 0.245768i | \(0.920960\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 161.014i | − 0.174447i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −637.825 | −0.689541 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1826.21 | −1.96578 | −0.982890 | − | 0.184191i | \(-0.941033\pi\) | ||||
−0.982890 | + | 0.184191i | \(0.941033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2336.64i | 2.50981i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 2644.12i | − 2.82794i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −264.729 | −0.282529 | −0.141264 | − | 0.989972i | \(-0.545117\pi\) | ||||
−0.141264 | + | 0.989972i | \(0.545117\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1401.16 | −1.48901 | −0.744505 | − | 0.667616i | \(-0.767315\pi\) | ||||
−0.744505 | + | 0.667616i | \(0.767315\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 677.167i | − 0.718099i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 389.952i | − 0.411776i | −0.978576 | − | 0.205888i | \(-0.933992\pi\) | ||||
0.978576 | − | 0.205888i | \(-0.0660082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −178.578 | −0.188175 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1291.61 | 1.35531 | 0.677656 | − | 0.735379i | \(-0.262996\pi\) | ||||
0.677656 | + | 0.735379i | \(0.262996\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1586.08i | − 1.66081i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2348.40i | − 2.44880i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79.8811 | 0.0831229 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 814.256 | 0.843789 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1802.57i | − 1.86408i | −0.362349 | − | 0.932042i | \(-0.618025\pi\) | ||||
0.362349 | − | 0.932042i | \(-0.381975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 473.260i | − 0.487395i | −0.969851 | − | 0.243697i | \(-0.921640\pi\) | ||||
0.969851 | − | 0.243697i | \(-0.0783603\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2943.93 | −3.02563 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −656.147 | −0.671594 | −0.335797 | − | 0.941934i | \(-0.609006\pi\) | ||||
−0.335797 | + | 0.941934i | \(0.609006\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.4616i | 0.0260078i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 267.000i | 0.271617i | 0.990735 | + | 0.135809i | \(0.0433632\pi\) | ||||
−0.990735 | + | 0.135809i | \(0.956637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 302.954 | 0.307568 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 277.231 | 0.280314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 549.499i | − 0.554489i | −0.960799 | − | 0.277245i | \(-0.910579\pi\) | ||||
0.960799 | − | 0.277245i | \(-0.0894213\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1918.79i | 1.92844i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −546.254 | −0.547898 | −0.273949 | − | 0.961744i | \(-0.588330\pi\) | ||||
−0.273949 | + | 0.961744i | \(0.588330\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.g.m.703.7 | 8 | ||
3.2 | odd | 2 | 1728.3.g.j.703.1 | 8 | |||
4.3 | odd | 2 | inner | 1728.3.g.m.703.8 | 8 | ||
8.3 | odd | 2 | 864.3.g.b.703.2 | yes | 8 | ||
8.5 | even | 2 | 864.3.g.b.703.1 | ✓ | 8 | ||
12.11 | even | 2 | 1728.3.g.j.703.2 | 8 | |||
24.5 | odd | 2 | 864.3.g.d.703.7 | yes | 8 | ||
24.11 | even | 2 | 864.3.g.d.703.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.g.b.703.1 | ✓ | 8 | 8.5 | even | 2 | ||
864.3.g.b.703.2 | yes | 8 | 8.3 | odd | 2 | ||
864.3.g.d.703.7 | yes | 8 | 24.5 | odd | 2 | ||
864.3.g.d.703.8 | yes | 8 | 24.11 | even | 2 | ||
1728.3.g.j.703.1 | 8 | 3.2 | odd | 2 | |||
1728.3.g.j.703.2 | 8 | 12.11 | even | 2 | |||
1728.3.g.m.703.7 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.g.m.703.8 | 8 | 4.3 | odd | 2 | inner |