Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(401,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.g (of order \(2\), degree \(1\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} - x^{12} - 27x^{10} + 88x^{8} - 243x^{6} - 81x^{4} - 729x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Root | \(-1.72824 - 0.114788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.401 |
Dual form | 804.2.g.c.401.2 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.72824 | − | 0.114788i | −0.997802 | − | 0.0662726i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.40477 | −1.07544 | −0.537722 | − | 0.843122i | \(-0.680715\pi\) | ||||
−0.537722 | + | 0.843122i | \(0.680715\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.48008i | − | 1.31535i | −0.753303 | − | 0.657674i | \(-0.771540\pi\) | ||
0.753303 | − | 0.657674i | \(-0.228460\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.97365 | + | 0.396761i | 0.991216 | + | 0.132254i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00557 | 0.303190 | 0.151595 | − | 0.988443i | \(-0.451559\pi\) | ||||
0.151595 | + | 0.988443i | \(0.451559\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.58879i | − | 0.440652i | −0.975426 | − | 0.220326i | \(-0.929288\pi\) | ||
0.975426 | − | 0.220326i | \(-0.0707122\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.15602 | + | 0.276037i | 1.07308 | + | 0.0712725i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.02716i | 0.734194i | 0.930183 | + | 0.367097i | \(0.119648\pi\) | ||||
−0.930183 | + | 0.367097i | \(0.880352\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.52914 | −0.809640 | −0.404820 | − | 0.914396i | \(-0.632666\pi\) | ||||
−0.404820 | + | 0.914396i | \(0.632666\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.399470 | + | 6.01443i | −0.0871715 | + | 1.31246i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.89371i | − | 1.22892i | −0.788947 | − | 0.614461i | \(-0.789373\pi\) | ||
0.788947 | − | 0.614461i | \(-0.210627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.782904 | 0.156581 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.09364 | − | 1.02704i | −0.980272 | − | 0.197654i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.29577i | 1.16909i | 0.811360 | + | 0.584547i | \(0.198728\pi\) | ||||
−0.811360 | + | 0.584547i | \(0.801272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0710i | 1.80880i | 0.426686 | + | 0.904400i | \(0.359681\pi\) | ||||
−0.426686 | + | 0.904400i | \(0.640319\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.73787 | − | 0.115427i | −0.302524 | − | 0.0200932i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.36879i | 1.41458i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.52914 | −1.07338 | −0.536692 | − | 0.843778i | \(-0.680326\pi\) | ||||
−0.536692 | + | 0.843778i | \(0.680326\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.182374 | + | 2.74582i | −0.0292032 | + | 0.439684i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.16073 | −0.649796 | −0.324898 | − | 0.945749i | \(-0.605330\pi\) | ||||
−0.324898 | + | 0.945749i | \(0.605330\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.62403i | 0.857656i | 0.903386 | + | 0.428828i | \(0.141073\pi\) | ||||
−0.903386 | + | 0.428828i | \(0.858927\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.15093 | − | 0.954119i | −1.06600 | − | 0.142232i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.23364i | − | 0.325809i | −0.986642 | − | 0.162905i | \(-0.947914\pi\) | ||
0.986642 | − | 0.162905i | \(-0.0520863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.11098 | −0.730140 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.347480 | − | 5.23167i | 0.0486569 | − | 0.732580i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.1411 | −1.39299 | −0.696496 | − | 0.717561i | \(-0.745259\pi\) | ||||
−0.696496 | + | 0.717561i | \(0.745259\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.41816 | −0.326064 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.09921 | + | 0.405101i | 0.807860 | + | 0.0536570i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2.62510i | − | 0.341759i | −0.985292 | − | 0.170879i | \(-0.945339\pi\) | ||
0.985292 | − | 0.170879i | \(-0.0546609\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.1980i | 1.56179i | 0.624663 | + | 0.780895i | \(0.285236\pi\) | ||||
−0.624663 | + | 0.780895i | \(0.714764\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.38076 | − | 10.3485i | 0.173960 | − | 1.30379i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.82068i | 0.473897i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.94730 | + | 5.62403i | 0.726578 | + | 0.687084i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.676524 | + | 10.1858i | −0.0814439 | + | 1.22622i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.00170i | − | 1.06831i | −0.845388 | − | 0.534153i | \(-0.820631\pi\) | ||
0.845388 | − | 0.534153i | \(-0.179369\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.635252 | −0.0743507 | −0.0371753 | − | 0.999309i | \(-0.511836\pi\) | ||||
−0.0371753 | + | 0.999309i | \(0.511836\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.35305 | − | 0.0898676i | −0.156236 | − | 0.0103770i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.49946i | − | 0.398800i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.44903i | − | 1.06310i | −0.847027 | − | 0.531550i | \(-0.821610\pi\) | ||
0.847027 | − | 0.531550i | \(-0.178390\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.68516 | + | 2.35966i | 0.965018 | + | 0.262184i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.80612i | 0.856833i | 0.903581 | + | 0.428417i | \(0.140928\pi\) | ||||
−0.903581 | + | 0.428417i | \(0.859072\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7.27961i | − | 0.789585i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.722675 | − | 10.8806i | 0.0774789 | − | 1.16652i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8389i | 1.67893i | 0.543418 | + | 0.839463i | \(0.317130\pi\) | ||||
−0.543418 | + | 0.839463i | \(0.682870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.52914 | −0.579611 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.15602 | − | 17.4051i | 0.119874 | − | 1.80482i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.48676 | 0.870723 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.49912i | 0.862955i | 0.902124 | + | 0.431478i | \(0.142008\pi\) | ||||
−0.902124 | + | 0.431478i | \(0.857992\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.99020 | + | 0.398970i | 0.300527 | + | 0.0400980i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.4979 | −1.04458 | −0.522290 | − | 0.852768i | \(-0.674922\pi\) | ||||
−0.522290 | + | 0.852768i | \(0.674922\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.32808 | 0.229392 | 0.114696 | − | 0.993401i | \(-0.463411\pi\) | ||||
0.114696 | + | 0.993401i | \(0.463411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.960633 | − | 14.4633i | 0.0937481 | − | 1.41147i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.21877i | − | 0.794539i | −0.917702 | − | 0.397269i | \(-0.869958\pi\) | ||
0.917702 | − | 0.397269i | \(-0.130042\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.41330i | − | 0.326934i | −0.986549 | − | 0.163467i | \(-0.947732\pi\) | ||
0.986549 | − | 0.163467i | \(-0.0522678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.2839 | + | 0.749464i | 1.07102 | + | 0.0711359i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.57663 | 0.806821 | 0.403411 | − | 0.915019i | \(-0.367825\pi\) | ||||
0.403411 | + | 0.915019i | \(0.367825\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.1730i | 1.32164i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.630373 | − | 4.72452i | 0.0582780 | − | 0.436782i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.5348 | 0.965720 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.98883 | −0.908076 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.19074 | + | 0.477599i | 0.648368 | + | 0.0430637i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.1411 | 0.907051 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.05757 | 0.803730 | 0.401865 | − | 0.915699i | \(-0.368362\pi\) | ||||
0.401865 | + | 0.915699i | \(0.368362\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.645568 | − | 9.71969i | 0.0568391 | − | 0.855771i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8439i | 0.947434i | 0.880677 | + | 0.473717i | \(0.157088\pi\) | ||||
−0.880677 | + | 0.473717i | \(0.842912\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.2817i | 1.06496i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.2490 | + | 2.46979i | 1.05423 | + | 0.212565i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9395 | −1.10550 | −0.552749 | − | 0.833348i | \(-0.686421\pi\) | ||||
−0.552749 | + | 0.833348i | \(0.686421\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.57394i | − | 0.557594i | −0.960350 | − | 0.278797i | \(-0.910064\pi\) | ||
0.960350 | − | 0.278797i | \(-0.0899357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.256393 | + | 3.86026i | −0.0215922 | + | 0.325093i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.59764i | − | 0.133601i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 15.1398i | − | 1.25730i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.83302 | + | 0.586677i | 0.728535 | + | 0.0483883i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.60639i | − | 0.541217i | −0.962690 | − | 0.270608i | \(-0.912775\pi\) | ||
0.962690 | − | 0.270608i | \(-0.0872248\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.3127 | −1.32751 | −0.663756 | − | 0.747949i | \(-0.731039\pi\) | ||||
−0.663756 | + | 0.747949i | \(0.731039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.20106 | + | 9.00170i | −0.0970999 | + | 0.727745i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 24.2183i | − | 1.94526i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.74624 | −0.298982 | −0.149491 | − | 0.988763i | \(-0.547764\pi\) | ||||
−0.149491 | + | 0.988763i | \(0.547764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.5263 | + | 1.16408i | 1.38993 | + | 0.0923172i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.5106 | −1.61646 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.98467 | −0.782059 | −0.391030 | − | 0.920378i | \(-0.627881\pi\) | ||||
−0.391030 | + | 0.920378i | \(0.627881\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.17916 | + | 0.277574i | 0.325347 | + | 0.0216091i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18.2438i | − | 1.41175i | −0.708338 | − | 0.705873i | \(-0.750555\pi\) | ||
0.708338 | − | 0.705873i | \(-0.249445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4757 | 0.805825 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.4944 | − | 1.40023i | −0.802528 | − | 0.107078i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.94236i | − | 0.527817i | −0.964548 | − | 0.263909i | \(-0.914988\pi\) | ||
0.964548 | − | 0.263909i | \(-0.0850118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.72457i | − | 0.205958i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.301329 | + | 4.53681i | −0.0226492 | + | 0.341007i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.92683 | −0.218762 | −0.109381 | − | 0.994000i | \(-0.534887\pi\) | ||||
−0.109381 | + | 0.994000i | \(0.534887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.5180 | −1.30210 | −0.651050 | − | 0.759035i | \(-0.725671\pi\) | ||||
−0.651050 | + | 0.759035i | \(0.725671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.40017 | − | 21.0810i | 0.103504 | − | 1.55836i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.7011 | 1.15436 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.04401i | 0.222600i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.57418 | + | 17.7263i | −0.259983 | + | 1.28940i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6602 | 1.63963 | 0.819817 | − | 0.572626i | \(-0.194075\pi\) | ||||
0.819817 | + | 0.572626i | \(0.194075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.84048 | 0.636352 | 0.318176 | − | 0.948032i | \(-0.396930\pi\) | ||||
0.318176 | + | 0.948032i | \(0.396930\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.438566 | − | 6.60307i | 0.0314064 | − | 0.472855i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1411 | 0.722526 | 0.361263 | − | 0.932464i | \(-0.382346\pi\) | ||||
0.361263 | + | 0.932464i | \(0.382346\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.7142 | −0.759507 | −0.379753 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379753 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.63280 | − | 10.4024i | −0.679446 | − | 0.733726i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.9098 | 1.53777 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0056 | 0.698820 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.33840 | − | 17.5258i | 0.162530 | − | 1.21813i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.54879 | −0.245475 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.48690 | −0.171205 | −0.0856025 | − | 0.996329i | \(-0.527282\pi\) | ||||
−0.0856025 | + | 0.996329i | \(0.527282\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.03328 | + | 15.5571i | −0.0707994 | + | 1.06596i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 13.5245i | − | 0.922361i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.0478 | 2.37920 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.09787 | + | 0.0729190i | 0.0741872 | + | 0.00492741i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.80953 | 0.323524 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0845 | −1.61282 | −0.806408 | − | 0.591359i | \(-0.798591\pi\) | ||||
−0.806408 | + | 0.591359i | \(0.798591\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.32808 | + | 0.310626i | 0.155205 | + | 0.0207084i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.95692i | 0.196257i | 0.995174 | + | 0.0981287i | \(0.0312857\pi\) | ||||
−0.995174 | + | 0.0981287i | \(0.968714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.7369i | − | 0.907761i | −0.891063 | − | 0.453881i | \(-0.850039\pi\) | ||
0.891063 | − | 0.453881i | \(-0.149961\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.401694 | + | 6.04792i | −0.0264295 | + | 0.397924i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.12443 | 0.466737 | 0.233368 | − | 0.972388i | \(-0.425025\pi\) | ||||
0.233368 | + | 0.972388i | \(0.425025\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.37137i | 0.350390i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.08463 | + | 16.3302i | −0.0704543 | + | 1.06076i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.3019 | 0.925110 | 0.462555 | − | 0.886591i | \(-0.346933\pi\) | ||||
0.462555 | + | 0.886591i | \(0.346933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.0216 | −1.54737 | −0.773684 | − | 0.633572i | \(-0.781588\pi\) | ||||
−0.773684 | + | 0.633572i | \(0.781588\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7392 | − | 5.07501i | −0.945521 | − | 0.325562i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.2907 | 0.785225 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.60708i | 0.356770i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.896045 | − | 13.4909i | 0.0567846 | − | 0.854949i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.2823 | −1.28021 | −0.640103 | − | 0.768289i | \(-0.721108\pi\) | ||||
−0.640103 | + | 0.768289i | \(0.721108\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.92652i | − | 0.372597i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.835608 | + | 12.5809i | −0.0523278 | + | 0.787849i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.7121i | 1.41674i | 0.705840 | + | 0.708372i | \(0.250570\pi\) | ||||
−0.705840 | + | 0.708372i | \(0.749430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.7220i | 1.41187i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.49792 | + | 18.7214i | −0.154617 | + | 1.15882i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.80612i | 0.481346i | 0.970606 | + | 0.240673i | \(0.0773681\pi\) | ||||
−0.970606 | + | 0.240673i | \(0.922632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.3871 | 1.49809 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.81811 | − | 27.3735i | 0.111267 | − | 1.67523i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.7210i | 0.836585i | 0.908312 | + | 0.418293i | \(0.137371\pi\) | ||||
−0.908312 | + | 0.418293i | \(0.862629\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.56307i | 0.155695i | 0.996965 | + | 0.0778476i | \(0.0248047\pi\) | ||||
−0.996965 | + | 0.0778476i | \(0.975195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.55570 | + | 0.634676i | 0.578337 | + | 0.0384123i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.787263 | 0.0474737 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1525 | −0.790258 | −0.395129 | − | 0.918626i | \(-0.629300\pi\) | ||||
−0.395129 | + | 0.918626i | \(0.629300\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.99577 | + | 29.9475i | −0.239221 | + | 1.79291i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.0052 | −1.37238 | −0.686188 | − | 0.727424i | \(-0.740717\pi\) | ||||
−0.686188 | + | 0.727424i | \(0.740717\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.852349 | −0.0506669 | −0.0253334 | − | 0.999679i | \(-0.508065\pi\) | ||||
−0.0253334 | + | 0.999679i | \(0.508065\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.6672 | − | 0.974174i | −0.868809 | − | 0.0577051i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.4797i | 0.854708i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.83631 | 0.460960 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.975593 | − | 14.6885i | 0.0571903 | − | 0.861058i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 32.7235i | − | 1.91172i | −0.293814 | − | 0.955862i | \(-0.594925\pi\) | ||
0.293814 | − | 0.955862i | \(-0.405075\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.31275i | 0.367543i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.12200 | − | 1.03276i | −0.297209 | − | 0.0599266i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.36389 | −0.541528 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.5721 | 1.12812 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.1429 | + | 1.20503i | 1.04228 | + | 0.0692270i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 29.3333i | − | 1.67962i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.2802 | −1.21453 | −0.607264 | − | 0.794500i | \(-0.707733\pi\) | ||||
−0.607264 | + | 0.794500i | \(0.707733\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.02349 | − | 0.267234i | −0.228888 | − | 0.0152024i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.70337 | 0.493523 | 0.246761 | − | 0.969076i | \(-0.420634\pi\) | ||||
0.246761 | + | 0.969076i | \(0.420634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.72237i | − | 0.0973542i | −0.998815 | − | 0.0486771i | \(-0.984499\pi\) | ||
0.998815 | − | 0.0486771i | \(-0.0155005\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.32041 | + | 24.8858i | −0.187084 | + | 1.40216i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.30281i | 0.129339i | 0.997907 | + | 0.0646694i | \(0.0205993\pi\) | ||||
−0.997907 | + | 0.0646694i | \(0.979401\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.33082i | 0.354458i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.943413 | + | 14.2040i | −0.0526562 | + | 0.792792i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.6833i | − | 0.594433i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.24387i | − | 0.0689977i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.391804 | + | 5.89900i | −0.0216668 | + | 0.326216i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.77324 | −0.428553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.75771i | 0.0966126i | 0.998833 | + | 0.0483063i | \(0.0153824\pi\) | ||||
−0.998833 | + | 0.0483063i | \(0.984618\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.4154 | − | 2.59051i | −1.06396 | − | 0.141959i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.3019 | − | 13.5245i | −0.781394 | − | 0.738921i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 32.4978i | − | 1.77027i | −0.465334 | − | 0.885135i | \(-0.654066\pi\) | ||
0.465334 | − | 0.885135i | \(-0.345934\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.8225 | − | 0.984490i | −0.805047 | − | 0.0534701i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.1270i | 0.548410i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.57394i | − | 0.354959i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.62688 | − | 24.4944i | 0.0875884 | − | 1.31873i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.0665 | −1.77510 | −0.887552 | − | 0.460708i | \(-0.847595\pi\) | ||||
−0.887552 | + | 0.460708i | \(0.847595\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.6663 | 1.53447 | 0.767237 | − | 0.641364i | \(-0.221631\pi\) | ||||
0.767237 | + | 0.641364i | \(0.221631\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.63175 | + | 8.09275i | −0.0870965 | + | 0.431959i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.8641 | 0.684687 | 0.342343 | − | 0.939575i | \(-0.388779\pi\) | ||||
0.342343 | + | 0.939575i | \(0.388779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.6470i | 1.14890i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.2066 | − | 1.20926i | −0.963597 | − | 0.0640008i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.1184i | 0.903477i | 0.892150 | + | 0.451739i | \(0.149196\pi\) | ||||
−0.892150 | + | 0.451739i | \(0.850804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.54518 | −0.344483 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.2631 | + | 1.14659i | 0.906079 | + | 0.0601805i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.52763 | 0.0799600 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.8981i | − | 0.986471i | −0.869896 | − | 0.493235i | \(-0.835814\pi\) | ||
0.869896 | − | 0.493235i | \(-0.164186\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.3725 | − | 1.65082i | −0.644088 | − | 0.0859380i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.2920i | 1.83227i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.0000i | 1.39801i | 0.715119 | + | 0.699003i | \(0.246373\pi\) | ||||
−0.715119 | + | 0.699003i | \(0.753627\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.5263 | − | 1.16408i | −0.905056 | − | 0.0601126i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.0027 | 0.515164 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.7259i | − | 0.705054i | −0.935802 | − | 0.352527i | \(-0.885322\pi\) | ||
0.935802 | − | 0.352527i | \(-0.114678\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.6537 | − | 1.03970i | −0.801963 | − | 0.0532653i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6233 | −1.15600 | −0.577999 | − | 0.816038i | \(-0.696166\pi\) | ||||
−0.577999 | + | 0.816038i | \(0.696166\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.41539i | 0.428888i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.23140 | + | 16.7239i | −0.113428 | + | 0.850122i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.3306i | 1.08150i | 0.841182 | + | 0.540752i | \(0.181860\pi\) | ||||
−0.841182 | + | 0.540752i | \(0.818140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8412 | 0.902267 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.24474 | − | 18.7408i | 0.0627889 | − | 0.945351i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.7227i | 1.14330i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.3023 | 1.77177 | 0.885885 | − | 0.463904i | \(-0.153552\pi\) | ||||
0.885885 | + | 0.463904i | \(0.153552\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.40979 | − | 21.2258i | 0.0705776 | − | 1.06262i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.4019 | −0.569383 | −0.284691 | − | 0.958619i | \(-0.591891\pi\) | ||||
−0.284691 | + | 0.958619i | \(0.591891\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.0007 | 0.797052 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.8858 | − | 5.67443i | −1.03782 | − | 0.281964i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.56549 | −0.325439 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1479i | 0.650120i | 0.945693 | + | 0.325060i | \(0.105385\pi\) | ||||
−0.945693 | + | 0.325060i | \(0.894615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.3627 | + | 1.48530i | 1.10307 | + | 0.0732643i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.13557 | −0.449532 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 18.7719i | − | 0.921476i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.754606 | + | 11.3614i | −0.0369532 | + | 0.556368i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 13.1614i | − | 0.642978i | −0.946913 | − | 0.321489i | \(-0.895817\pi\) | ||
0.946913 | − | 0.321489i | \(-0.104183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.94589 | 0.241048 | 0.120524 | − | 0.992710i | \(-0.461543\pi\) | ||||
0.120524 | + | 0.992710i | \(0.461543\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.886220 | − | 6.64205i | 0.0430895 | − | 0.322947i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.36997i | 0.114961i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 42.4499 | 2.05430 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.183389 | + | 2.76111i | −0.00885412 | + | 0.133308i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.6698i | 1.71815i | 0.511847 | + | 0.859076i | \(0.328961\pi\) | ||||
−0.511847 | + | 0.859076i | \(0.671039\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.6992i | − | 1.23502i | −0.786562 | − | 0.617512i | \(-0.788141\pi\) | ||
0.786562 | − | 0.617512i | \(-0.211859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.73787 | + | 26.1653i | −0.0833243 | + | 1.25453i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.7997i | 0.994985i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.6879 | −1.84647 | −0.923237 | − | 0.384230i | \(-0.874467\pi\) | ||||
−0.923237 | + | 0.384230i | \(0.874467\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.1983 | − | 2.02784i | −0.723727 | − | 0.0965639i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.0310 | −0.999211 | −0.499606 | − | 0.866253i | \(-0.666522\pi\) | ||||
−0.499606 | + | 0.866253i | \(0.666522\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 38.0890i | − | 1.80559i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.758331 | + | 11.4174i | −0.0358678 | + | 0.540027i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.1427i | − | 0.809015i | −0.914535 | − | 0.404508i | \(-0.867443\pi\) | ||
0.914535 | − | 0.404508i | \(-0.132557\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.18389 | −0.197012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.1924 | + | 1.87250i | 1.32459 | + | 0.0879777i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.2963 | 0.623340 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.76687 | −0.410097 | −0.205048 | − | 0.978752i | \(-0.565735\pi\) | ||||
−0.205048 | + | 0.978752i | \(0.565735\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.10901 | − | 15.4193i | 0.145116 | − | 0.719710i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.4969i | 0.861486i | 0.902475 | + | 0.430743i | \(0.141749\pi\) | ||||
−0.902475 | + | 0.430743i | \(0.858251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 27.2710i | − | 1.26739i | −0.773582 | − | 0.633696i | \(-0.781537\pi\) | ||
0.773582 | − | 0.633696i | \(-0.218463\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.77996 | + | 41.8552i | −0.128918 | + | 1.94099i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.3387i | 1.40391i | 0.712221 | + | 0.701955i | \(0.247689\pi\) | ||||
−0.712221 | + | 0.701955i | \(0.752311\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.5721 | − | 20.6971i | 0.903755 | − | 0.955703i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.47441 | + | 0.430021i | 0.298325 | + | 0.0198143i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.65534i | 0.260033i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.76298 | −0.126774 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.1562 | − | 4.02361i | −1.38076 | − | 0.184228i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 32.1159i | − | 1.46741i | −0.679467 | − | 0.733706i | \(-0.737789\pi\) | ||
0.679467 | − | 0.733706i | \(-0.262211\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3735i | 0.472989i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 35.4473 | + | 2.35436i | 1.61291 | + | 0.107127i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 20.4384i | − | 0.928060i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.2926i | 0.738287i | 0.929372 | + | 0.369143i | \(0.120349\pi\) | ||||
−0.929372 | + | 0.369143i | \(0.879651\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.2559 | + | 1.14612i | 0.780340 | + | 0.0518291i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4705i | 0.833562i | 0.909007 | + | 0.416781i | \(0.136842\pi\) | ||||
−0.909007 | + | 0.416781i | \(0.863158\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.0583 | −0.858342 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.19074 | − | 0.959431i | −0.323200 | − | 0.0431232i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.3267 | −1.40519 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 42.7473i | − | 1.91363i | −0.290697 | − | 0.956815i | \(-0.593887\pi\) | ||
0.290697 | − | 0.956815i | \(-0.406113\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.09416 | + | 31.5297i | −0.0935601 | + | 1.40864i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.4077 | 1.44499 | 0.722494 | − | 0.691378i | \(-0.242996\pi\) | ||||
0.722494 | + | 0.691378i | \(0.242996\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.2450 | 1.12339 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.1046 | − | 1.20248i | −0.804054 | − | 0.0534041i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 13.0680i | − | 0.579228i | −0.957144 | − | 0.289614i | \(-0.906473\pi\) | ||
0.957144 | − | 0.289614i | \(-0.0935269\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.21073i | 0.0977970i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.9762 | + | 3.62456i | 0.793667 | + | 0.160028i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.59849 | −0.246699 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.24607i | − | 0.0987821i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.796896 | + | 11.9981i | −0.0349798 | + | 0.526657i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.74750 | −0.427046 | −0.213523 | − | 0.976938i | \(-0.568494\pi\) | ||||
−0.213523 | + | 0.976938i | \(0.568494\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.59858 | 0.332263 | 0.166131 | − | 0.986104i | \(-0.446872\pi\) | ||||
0.166131 | + | 0.986104i | \(0.446872\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.312747 | + | 4.70872i | −0.0136494 | + | 0.205505i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.4864 | −1.32801 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7358 | −0.510251 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.04154 | − | 7.80612i | 0.0451989 | − | 0.338757i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.61054i | 0.286334i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.7642i | 0.854482i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.05828 | + | 0.335964i | 0.218281 | + | 0.0144979i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.13944 | −0.221371 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.4590i | 0.707629i | 0.935316 | + | 0.353815i | \(0.115116\pi\) | ||||
−0.935316 | + | 0.353815i | \(0.884884\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.2753 | + | 2.01084i | 1.29924 | + | 0.0862936i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.20818i | 0.351600i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.9269i | − | 0.509958i | −0.966947 | − | 0.254979i | \(-0.917931\pi\) | ||
0.966947 | − | 0.254979i | \(-0.0820686\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.83968 | + | 36.2724i | −0.206553 | + | 1.54807i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 22.2186i | − | 0.946546i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.8834 | −1.39835 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27.1352 | − | 1.80229i | −1.15183 | − | 0.0765028i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 8.04650i | − | 0.340941i | −0.985363 | − | 0.170471i | \(-0.945471\pi\) | ||
0.985363 | − | 0.170471i | \(-0.0545288\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.93543 | 0.377928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.349415 | − | 5.26079i | 0.0147523 | − | 0.222111i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.0248 | −0.717511 | −0.358755 | − | 0.933432i | \(-0.616799\pi\) | ||||
−0.358755 | + | 0.933432i | \(0.616799\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.6248 | −0.867691 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.21181 | − | 30.2251i | 0.344863 | − | 1.26933i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 18.1503i | − | 0.760902i | −0.924801 | − | 0.380451i | \(-0.875769\pi\) | ||
0.924801 | − | 0.380451i | \(-0.124231\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.8258 | 1.41557 | 0.707784 | − | 0.706429i | \(-0.249695\pi\) | ||||
0.707784 | + | 0.706429i | \(0.249695\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.1623 | − | 2.60111i | −1.63603 | − | 0.108663i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.61420i | − | 0.192426i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.1979i | 1.63183i | 0.578171 | + | 0.815916i | \(0.303767\pi\) | ||||
−0.578171 | + | 0.815916i | \(0.696233\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.2785 | − | 1.01478i | −0.634953 | − | 0.0421727i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.1660 | 1.12703 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.1976 | −0.422341 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.51590 | + | 11.3614i | −0.0626747 | + | 0.469734i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.34104 | 0.0966251 | 0.0483126 | − | 0.998832i | \(-0.484616\pi\) | ||||
0.0483126 | + | 0.998832i | \(0.484616\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 35.5419i | − | 1.46448i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.5263 | − | 1.16408i | −0.720937 | − | 0.0478837i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.6039 | 0.599711 | 0.299856 | − | 0.953985i | \(-0.403061\pi\) | ||||
0.299856 | + | 0.953985i | \(0.403061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.3337 | −1.03858 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.5167 | + | 1.22985i | 0.757837 | + | 0.0503345i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.4218 | −0.916131 | −0.458066 | − | 0.888918i | \(-0.651458\pi\) | ||||
−0.458066 | + | 0.888918i | \(0.651458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6824 | −0.802860 | −0.401430 | − | 0.915890i | \(-0.631487\pi\) | ||||
−0.401430 | + | 0.915890i | \(0.631487\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.4538 | + | 19.0835i | 0.629326 | + | 0.777141i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.0208 | 0.976585 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.47227 | 0.181524 | 0.0907619 | − | 0.995873i | \(-0.471070\pi\) | ||||
0.0907619 | + | 0.995873i | \(0.471070\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −37.8654 | − | 2.51497i | −1.53439 | − | 0.101912i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.54879 | −0.143569 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.2817 | 0.980727 | 0.490363 | − | 0.871518i | \(-0.336864\pi\) | ||||
0.490363 | + | 0.871518i | \(0.336864\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.2921 | − | 1.14851i | −0.697283 | − | 0.0463126i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.63721i | − | 0.307463i | −0.988113 | − | 0.153731i | \(-0.950871\pi\) | ||
0.988113 | − | 0.153731i | \(-0.0491290\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.1700 | 0.810699 | 0.405350 | − | 0.914162i | \(-0.367150\pi\) | ||||
0.405350 | + | 0.914162i | \(0.367150\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.05306 | + | 30.0204i | −0.242901 | + | 1.20468i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55.1209 | 2.20837 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.3016 | −1.13206 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.13317 | + | 0.407357i | 0.244935 | + | 0.0162683i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 19.7647i | − | 0.788072i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.9970i | 1.63206i | 0.578007 | + | 0.816032i | \(0.303831\pi\) | ||||
−0.578007 | + | 0.816032i | \(0.696169\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.29796 | + | 0.285465i | 0.170829 | + | 0.0113462i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.7814 | −0.864367 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.12030i | 0.321738i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.57153 | − | 26.7679i | 0.141287 | − | 1.05892i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.20160 | 0.0869581 | 0.0434790 | − | 0.999054i | \(-0.486156\pi\) | ||||
0.0434790 | + | 0.999054i | \(0.486156\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.5553 | −1.20499 | −0.602493 | − | 0.798124i | \(-0.705826\pi\) | ||||
−0.602493 | + | 0.798124i | \(0.705826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.55244 | + | 23.3736i | −0.0611273 | + | 0.920334i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.9608 | −0.470228 | −0.235114 | − | 0.971968i | \(-0.575546\pi\) | ||||
−0.235114 | + | 0.971968i | \(0.575546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.63972i | − | 0.103618i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −60.5711 | − | 4.02305i | −2.37397 | − | 0.157676i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.5043 | 1.35026 | 0.675128 | − | 0.737700i | \(-0.264088\pi\) | ||||
0.675128 | + | 0.737700i | \(0.264088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 26.0770i | − | 1.01891i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.88902 | − | 0.252044i | −0.0736976 | − | 0.00983316i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.85950i | 0.267208i | 0.991035 | + | 0.133604i | \(0.0426550\pi\) | ||||
−0.991035 | + | 0.133604i | \(0.957345\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 38.1922i | − | 1.48551i | −0.669566 | − | 0.742753i | \(-0.733520\pi\) | ||
0.669566 | − | 0.742753i | \(-0.266480\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.31204 | − | 0.552074i | −0.322813 | − | 0.0214408i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 29.5346i | − | 1.14530i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.1054 | 1.43673 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 41.6238 | + | 2.76460i | 1.60927 | + | 0.106886i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.2659i | 0.473519i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.3366i | 1.20794i | 0.797008 | + | 0.603968i | \(0.206415\pi\) | ||||
−0.797008 | + | 0.603968i | \(0.793585\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.98783 | − | 0.804072i | −0.153492 | − | 0.0309487i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.2747 | 1.39415 | 0.697074 | − | 0.716999i | \(-0.254485\pi\) | ||||
0.697074 | + | 0.716999i | \(0.254485\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.5777 | 1.13509 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.339417 | − | 5.11027i | 0.0130065 | − | 0.195826i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.72296 | −0.104191 | −0.0520956 | − | 0.998642i | \(-0.516590\pi\) | ||||
−0.0520956 | + | 0.998642i | \(0.516590\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.1166 | 1.18890 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.57683 | + | 23.7407i | −0.0601597 | + | 0.905765i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.1122i | 0.613825i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.92666 | −0.149377 | −0.0746887 | − | 0.997207i | \(-0.523796\pi\) | ||||
−0.0746887 | + | 0.997207i | \(0.523796\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.38845 | − | 10.4062i | 0.0527429 | − | 0.395297i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.8088i | 0.599661i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.5952i | − | 0.477076i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.3127 | − | 0.817796i | −0.465711 | − | 0.0309319i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.06182 | 0.342260 | 0.171130 | − | 0.985248i | \(-0.445258\pi\) | ||||
0.171130 | + | 0.985248i | \(0.445258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.0422 | 0.869055 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.616567 | − | 9.28304i | 0.0232212 | − | 0.349619i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.5335i | 1.37399i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.7100 | −0.552445 | −0.276223 | − | 0.961094i | \(-0.589083\pi\) | ||||
−0.276223 | + | 0.961094i | \(0.589083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.74901 | − | 28.0981i | 0.140599 | − | 1.05376i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 59.3553 | 2.22287 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.84195i | 0.143681i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.7171 | − | 1.64167i | −0.923077 | − | 0.0613095i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 35.0485i | − | 1.30709i | −0.756888 | − | 0.653545i | \(-0.773281\pi\) | ||
0.756888 | − | 0.653545i | \(-0.226719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 8.10191i | − | 0.301731i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 41.5152 | + | 2.75738i | 1.54397 | + | 0.102548i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.92898i | 0.183058i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.9711i | 1.25992i | 0.776628 | + | 0.629960i | \(0.216929\pi\) | ||||
−0.776628 | + | 0.629960i | \(0.783071\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.8904 | + | 10.4627i | 0.921866 | + | 0.387508i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.0248 | −0.629686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.9611i | − | 1.18051i | −0.807217 | − | 0.590255i | \(-0.799027\pi\) | ||
0.807217 | − | 0.590255i | \(-0.200973\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.2414 | − | 1.41082i | −0.783499 | − | 0.0520389i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.98041 | + | 5.65534i | 0.220291 | + | 0.208317i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.52798i | − | 0.0562075i | −0.999605 | − | 0.0281037i | \(-0.991053\pi\) | ||
0.999605 | − | 0.0281037i | \(-0.00894688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.643623 | − | 9.69039i | 0.0236441 | − | 0.355986i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 40.0113i | − | 1.46787i | −0.679218 | − | 0.733936i | \(-0.737681\pi\) | ||
0.679218 | − | 0.733936i | \(-0.262319\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.8868i | 0.582048i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.09717 | + | 23.2127i | −0.113319 | + | 0.849307i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.6020 | −1.04510 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8586 | 0.578689 | 0.289345 | − | 0.957225i | \(-0.406563\pi\) | ||||
0.289345 | + | 0.957225i | \(0.406563\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 35.0527 | + | 2.32815i | 1.27739 | + | 0.0848425i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.2284 | 1.42767 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 0.529669i | − | 0.0192512i | −0.999954 | − | 0.00962558i | \(-0.996936\pi\) | ||
0.999954 | − | 0.00962558i | \(-0.00306396\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.680291 | + | 10.2425i | −0.0246930 | + | 0.371778i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 32.3498i | − | 1.17268i | −0.810065 | − | 0.586340i | \(-0.800568\pi\) | ||
0.810065 | − | 0.586340i | \(-0.199432\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.8786 | −0.430033 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.88827 | − | 21.6470i | 0.104426 | − | 0.782649i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.17074 | −0.150597 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.9970i | − | 0.504744i | −0.967630 | − | 0.252372i | \(-0.918789\pi\) | ||
0.967630 | − | 0.252372i | \(-0.0812107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.60707 | − | 39.2521i | 0.0938913 | − | 1.41363i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 33.3659i | − | 1.20009i | −0.799967 | − | 0.600044i | \(-0.795150\pi\) | ||
0.799967 | − | 0.600044i | \(-0.204850\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.88460i | 0.283223i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.60820 | − | 39.2691i | 0.0935685 | − | 1.40877i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.6838 | 0.526101 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 9.05182i | − | 0.323900i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.46599 | − | 32.0684i | 0.231076 | − | 1.14603i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.00882 | 0.321539 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 10.9770i | − | 0.391288i | −0.980675 | − | 0.195644i | \(-0.937320\pi\) | ||
0.980675 | − | 0.195644i | \(-0.0626797\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.896045 | − | 13.4909i | 0.0319001 | − | 0.480288i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 29.8474i | − | 1.06125i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.3801 | 0.688206 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −42.1468 | − | 2.79933i | −1.49479 | − | 0.0992820i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.0974i | − | 1.17237i | −0.810178 | − | 0.586185i | \(-0.800629\pi\) | ||
0.810178 | − | 0.586185i | \(-0.199371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.76157 | 0.239207 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.28428 | + | 47.0994i | −0.222044 | + | 1.66418i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.638789 | −0.0225424 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 49.3232 | 1.73841 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.57500 | − | 23.7133i | 0.0554427 | − | 0.834746i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.19372 | 0.112285 | 0.0561426 | − | 0.998423i | \(-0.482120\pi\) | ||||
0.0561426 | + | 0.998423i | \(0.482120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.3729i | − | 1.24211i | −0.783766 | − | 0.621056i | \(-0.786704\pi\) | ||
0.783766 | − | 0.621056i | \(-0.213296\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.294208 | − | 4.42960i | 0.0103183 | − | 0.155353i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0108 | 0.841062 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 19.8480i | − | 0.694393i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.4417 | − | 2.19375i | −0.574520 | − | 0.0766558i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 19.0763i | − | 0.665768i | −0.942968 | − | 0.332884i | \(-0.891978\pi\) | ||
0.942968 | − | 0.332884i | \(-0.108022\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.8258 | −0.412223 | −0.206112 | − | 0.978528i | \(-0.566081\pi\) | ||||
−0.206112 | + | 0.978528i | \(0.566081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.36058 | − | 0.0903679i | −0.0473694 | − | 0.00314621i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.52199i | − | 0.331112i | −0.986200 | − | 0.165556i | \(-0.947058\pi\) | ||
0.986200 | − | 0.165556i | \(-0.0529419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6367 | 0.543084 | 0.271542 | − | 0.962427i | \(-0.412466\pi\) | ||||
0.271542 | + | 0.962427i | \(0.412466\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.7308 | + | 1.50975i | 0.788521 | + | 0.0523725i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 15.4718i | − | 0.536065i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.8721i | 1.51826i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.3433 | − | 51.2979i | 0.357516 | − | 1.77312i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 13.3597i | − | 0.461229i | −0.973045 | − | 0.230614i | \(-0.925926\pi\) | ||
0.973045 | − | 0.230614i | \(-0.0740736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6367 | −0.366781 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 39.7586 | + | 2.64071i | 1.36936 | + | 0.0909510i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.1917 | −0.866620 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.7620i | 1.19444i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.47307 | + | 0.0978390i | 0.0505555 | + | 0.00335783i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.4808i | 1.31911i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.2956 | 0.455232 | 0.227616 | − | 0.973751i | \(-0.426907\pi\) | ||||
0.227616 | + | 0.973751i | \(0.426907\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.2366 | + | 3.36722i | 0.863074 | + | 0.115156i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.70395 | 0.229002 | 0.114501 | − | 0.993423i | \(-0.463473\pi\) | ||||
0.114501 | + | 0.993423i | \(0.463473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.4223 | −0.389725 | −0.194862 | − | 0.980831i | \(-0.562426\pi\) | ||||
−0.194862 | + | 0.980831i | \(0.562426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.66209 | − | 25.0244i | 0.0566437 | − | 0.852829i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 47.1153i | − | 1.60382i | −0.597442 | − | 0.801912i | \(-0.703816\pi\) | ||
0.597442 | − | 0.801912i | \(-0.296184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6947i | 0.567638i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.5431 | − | 0.899511i | −0.459946 | − | 0.0305490i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.50164i | − | 0.322321i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.93543 | − | 9.44903i | 0.302765 | − | 0.320168i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.37212 | + | 25.2734i | −0.114129 | + | 0.855375i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 35.2920i | − | 1.19309i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.66733 | 0.326442 | 0.163221 | − | 0.986589i | \(-0.447812\pi\) | ||||
0.163221 | + | 0.986589i | \(0.447812\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.75624 | + | 56.5541i | −0.126695 | + | 1.90752i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.1873i | 1.89300i | 0.322707 | + | 0.946499i | \(0.395407\pi\) | ||||
−0.322707 | + | 0.946499i | \(0.604593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7.92106i | − | 0.266565i | −0.991078 | − | 0.133282i | \(-0.957448\pi\) | ||
0.991078 | − | 0.133282i | \(-0.0425517\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.724625 | − | 10.9100i | 0.0243580 | − | 0.366735i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.3663i | 0.583105i | 0.956555 | + | 0.291552i | \(0.0941718\pi\) | ||||
−0.956555 | + | 0.291552i | \(0.905828\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 31.5211i | − | 1.05718i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.73352 | + | 2.37280i | 0.292584 | + | 0.0794916i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.88281i | 0.263788i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.03835 | 0.235266 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.1831 | + | 1.07486i | 0.540337 | + | 0.0358885i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −63.4045 | −2.11466 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 30.6988i | − | 1.02273i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −33.8253 | − | 2.24663i | −1.12564 | − | 0.0747632i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 42.1266 | 1.40034 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.2484 | −1.40284 | −0.701418 | − | 0.712750i | \(-0.747449\pi\) | ||||
−0.701418 | + | 0.712750i | \(0.747449\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.2170 | − | 4.16516i | −1.03540 | − | 0.138150i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.6141i | 1.27934i | 0.768649 | + | 0.639671i | \(0.220929\pi\) | ||||
−0.768649 | + | 0.639671i | \(0.779071\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.84958i | 0.259783i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.36709 | + | 50.6950i | −0.111313 | + | 1.67592i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.7376 | 1.24621 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 6.07220i | − | 0.200303i | −0.994972 | − | 0.100152i | \(-0.968067\pi\) | ||
0.994972 | − | 0.100152i | \(-0.0319328\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.7774 | + | 2.44271i | 1.21186 | + | 0.0804899i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.3019 | −0.470751 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.11169 | −0.168071 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.92289 | + | 0.923692i | 0.227377 | + | 0.0303380i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.1838 | −1.02311 | −0.511554 | − | 0.859251i | \(-0.670930\pi\) | ||||
−0.511554 | + | 0.859251i | \(0.670930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0374 | 0.591151 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.0415 | − | 0.999038i | −0.492438 | − | 0.0327070i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 7.32014i | − | 0.239394i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.03365i | 0.0337678i | 0.999857 | + | 0.0168839i | \(0.00537456\pi\) | ||||
−0.999857 | + | 0.0168839i | \(0.994625\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.197707 | + | 2.97668i | −0.00645192 | + | 0.0971402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55.6144 | −1.81298 | −0.906489 | − | 0.422230i | \(-0.861247\pi\) | ||||
−0.906489 | + | 0.422230i | \(0.861247\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.5221i | 0.798549i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.59506 | − | 42.6276i | 0.279597 | − | 1.38668i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 45.9267i | − | 1.49242i | −0.665712 | − | 0.746209i | \(-0.731872\pi\) | ||
0.665712 | − | 0.746209i | \(-0.268128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00929i | 0.0327628i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.264334 | − | 3.97982i | 0.00857162 | − | 0.129055i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.1738i | 0.750674i | 0.926888 | + | 0.375337i | \(0.122473\pi\) | ||||
−0.926888 | + | 0.375337i | \(0.877527\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −54.4925 | −1.76333 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.726699 | − | 10.9412i | 0.0234908 | − | 0.353679i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.0307i | 1.45412i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −70.4244 | −2.27176 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.26089 | − | 24.4397i | 0.105081 | − | 0.787560i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.2593 | −0.684361 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.8732 | −1.82892 | −0.914460 | − | 0.404676i | \(-0.867384\pi\) | ||||
−0.914460 | + | 0.404676i | \(0.867384\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.22631 | + | 18.4633i | −0.0393946 | + | 0.593126i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.5301i | 1.78205i | 0.453958 | + | 0.891023i | \(0.350011\pi\) | ||||
−0.453958 | + | 0.891023i | \(0.649989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.8779 | −0.733430 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.142781 | + | 2.14972i | −0.00457266 | + | 0.0688460i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.1001i | 1.02697i | 0.858098 | + | 0.513486i | \(0.171646\pi\) | ||||
−0.858098 | + | 0.513486i | \(0.828354\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.9271i | 0.509033i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.35426 | − | 10.1499i | 0.0432383 | − | 0.324063i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.0273 | 1.43615 | 0.718074 | − | 0.695966i | \(-0.245024\pi\) | ||||
0.718074 | + | 0.695966i | \(0.245024\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.3871 | −0.777036 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.4340 | + | 0.892271i | 0.427610 | + | 0.0284013i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.1464 | 1.05399 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 14.3808i | − | 0.456820i | −0.973565 | − | 0.228410i | \(-0.926647\pi\) | ||
0.973565 | − | 0.228410i | \(-0.0733527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.201763 | − | 3.03775i | 0.00640277 | − | 0.0964002i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.7651 | 0.816807 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.8426 | −0.723432 | −0.361716 | − | 0.932288i | \(-0.617809\pi\) | ||||
−0.361716 | + | 0.932288i | \(0.617809\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.2571 | + | 6.70567i | 1.05221 | + | 0.212158i |
(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 | 804.2.g.c.401.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 804.2.g.c.401.15 | yes | 16 | |
67.66 | odd | 2 | inner | 804.2.g.c.401.16 | yes | 16 | |
201.200 | even | 2 | inner | 804.2.g.c.401.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.g.c.401.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
804.2.g.c.401.2 | yes | 16 | 201.200 | even | 2 | inner | |
804.2.g.c.401.15 | yes | 16 | 3.2 | odd | 2 | inner | |
804.2.g.c.401.16 | yes | 16 | 67.66 | odd | 2 | inner |