Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(137,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("552.137");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.m (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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.1 | ||
Root | \(-0.437016 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 552.137 |
Dual form | 552.2.m.a.137.3 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.61803 | − | 0.618034i | −0.934172 | − | 0.356822i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.874032 | −0.390879 | −0.195440 | − | 0.980716i | \(-0.562613\pi\) | ||||
−0.195440 | + | 0.980716i | \(0.562613\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.41421i | − | 0.534522i | −0.963624 | − | 0.267261i | \(-0.913881\pi\) | ||
0.963624 | − | 0.267261i | \(-0.0861187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | + | 2.00000i | 0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.11667 | 1.54273 | 0.771367 | − | 0.636390i | \(-0.219573\pi\) | ||||
0.771367 | + | 0.636390i | \(0.219573\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.23607 | −0.897524 | −0.448762 | − | 0.893651i | \(-0.648135\pi\) | ||||
−0.448762 | + | 0.893651i | \(0.648135\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | + | 0.540182i | 0.365148 | + | 0.139474i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.91034 | −1.19093 | −0.595466 | − | 0.803380i | \(-0.703033\pi\) | ||||
−0.595466 | + | 0.803380i | \(0.703033\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 8.27895i | − | 1.89932i | −0.313280 | − | 0.949661i | \(-0.601428\pi\) | ||
0.313280 | − | 0.949661i | \(-0.398572\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.874032 | + | 2.28825i | −0.190729 | + | 0.499336i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.24264 | − | 2.23607i | −0.884652 | − | 0.466252i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.23607 | −0.847214 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.38197 | − | 4.61803i | −0.458410 | − | 0.888741i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.23607i | 0.972313i | 0.873872 | + | 0.486157i | \(0.161602\pi\) | ||||
−0.873872 | + | 0.486157i | \(0.838398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.27895 | − | 3.16228i | −1.44118 | − | 0.550482i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.23607i | 0.208934i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.7735i | − | 1.77116i | −0.464490 | − | 0.885578i | \(-0.653762\pi\) | ||
0.464490 | − | 0.885578i | \(-0.346238\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.23607 | + | 2.00000i | 0.838442 | + | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.472136i | − | 0.0737352i | −0.999320 | − | 0.0368676i | \(-0.988262\pi\) | ||
0.999320 | − | 0.0368676i | \(-0.0117380\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.0270i | − | 1.52911i | −0.644561 | − | 0.764553i | \(-0.722960\pi\) | ||
0.644561 | − | 0.764553i | \(-0.277040\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.95440 | − | 1.74806i | −0.291344 | − | 0.260586i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7082i | 1.70782i | 0.520423 | + | 0.853909i | \(0.325774\pi\) | ||||
−0.520423 | + | 0.853909i | \(0.674226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.94510 | + | 3.03476i | 1.11254 | + | 0.424951i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.874032 | 0.120058 | 0.0600288 | − | 0.998197i | \(-0.480881\pi\) | ||||
0.0600288 | + | 0.998197i | \(0.480881\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.47214 | −0.603023 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.11667 | + | 13.3956i | −0.677720 | + | 1.77429i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.00000i | − | 1.04151i | −0.853706 | − | 0.520756i | \(-0.825650\pi\) | ||
0.853706 | − | 0.520756i | \(-0.174350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.20788i | 0.154654i | 0.997006 | + | 0.0773268i | \(0.0246385\pi\) | ||||
−0.997006 | + | 0.0773268i | \(0.975362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | − | 3.16228i | 0.356348 | − | 0.398410i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.82843 | 0.350823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.53089i | 0.797875i | 0.916978 | + | 0.398937i | \(0.130621\pi\) | ||||
−0.916978 | + | 0.398937i | \(0.869379\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.48277 | + | 6.24013i | 0.660048 | + | 0.751223i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.1803i | − | 1.44554i | −0.691088 | − | 0.722770i | \(-0.742869\pi\) | ||
0.691088 | − | 0.722770i | \(-0.257131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.23607 | −0.846918 | −0.423459 | − | 0.905915i | \(-0.639184\pi\) | ||||
−0.423459 | + | 0.905915i | \(0.639184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.85410 | + | 2.61803i | 0.791444 | + | 0.302305i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 7.23607i | − | 0.824626i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.65841i | 0.749129i | 0.927201 | + | 0.374565i | \(0.122208\pi\) | ||||
−0.927201 | + | 0.374565i | \(0.877792\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.94510 | −0.872088 | −0.436044 | − | 0.899925i | \(-0.643621\pi\) | ||||
−0.436044 | + | 0.899925i | \(0.643621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.29180 | 0.465511 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.23607 | − | 8.47214i | 0.346943 | − | 0.908308i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.333851 | 0.0353881 | 0.0176940 | − | 0.999843i | \(-0.494368\pi\) | ||||
0.0176940 | + | 0.999843i | \(0.494368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.57649i | 0.479747i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.70820 | + | 3.70820i | 1.00669 | + | 0.384523i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.23607i | 0.742405i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.41577i | 0.245284i | 0.992451 | + | 0.122642i | \(0.0391367\pi\) | ||||
−0.992451 | + | 0.122642i | \(0.960863\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.4412 | + | 10.2333i | 1.14989 | + | 1.02849i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.47214i | − | 0.843009i | −0.906826 | − | 0.421505i | \(-0.861502\pi\) | ||
0.906826 | − | 0.421505i | \(-0.138498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 7.07107i | − | 0.696733i | −0.937358 | − | 0.348367i | \(-0.886736\pi\) | ||
0.937358 | − | 0.348367i | \(-0.113264\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.763932 | − | 2.00000i | 0.0745521 | − | 0.195180i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.28050 | 0.897180 | 0.448590 | − | 0.893738i | \(-0.351926\pi\) | ||||
0.448590 | + | 0.893738i | \(0.351926\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.03631i | 0.386608i | 0.981139 | + | 0.193304i | \(0.0619204\pi\) | ||||
−0.981139 | + | 0.193304i | \(0.938080\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.65841 | + | 17.4319i | −0.631988 | + | 1.65457i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.89949 | 0.931266 | 0.465633 | − | 0.884978i | \(-0.345827\pi\) | ||||
0.465633 | + | 0.884978i | \(0.345827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.70820 | + | 1.95440i | 0.345792 | + | 0.182248i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.23607 | − | 6.47214i | −0.668975 | − | 0.598349i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.94427i | 0.636580i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.1803 | 1.38003 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.291796 | + | 0.763932i | −0.0263104 | + | 0.0688814i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.07262 | 0.722037 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.19704 | + | 16.2241i | −0.545619 | + | 1.42845i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.76393i | − | 0.241486i | −0.992684 | − | 0.120743i | \(-0.961472\pi\) | ||
0.992684 | − | 0.120743i | \(-0.0385277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.7082 | −1.01523 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.08191 | + | 4.03631i | 0.179183 | + | 0.347390i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.3044 | 1.47842 | 0.739208 | − | 0.673477i | \(-0.235200\pi\) | ||||
0.739208 | + | 0.673477i | \(0.235200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.47214 | 0.548959 | 0.274480 | − | 0.961593i | \(-0.411494\pi\) | ||||
0.274480 | + | 0.961593i | \(0.411494\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.23607 | − | 18.9443i | 0.609387 | − | 1.59540i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.5579 | −1.38464 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.57649i | − | 0.380057i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.09017 | − | 3.09017i | −0.667266 | − | 0.254873i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.35931 | −0.766745 | −0.383372 | − | 0.923594i | \(-0.625237\pi\) | ||||
−0.383372 | + | 0.923594i | \(0.625237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.05573 | 0.0859139 | 0.0429570 | − | 0.999077i | \(-0.486322\pi\) | ||||
0.0429570 | + | 0.999077i | \(0.486322\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.9799 | − | 9.82068i | −0.887669 | − | 0.793955i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.24419 | 0.421224 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.952843i | 0.0760452i | 0.999277 | + | 0.0380226i | \(0.0121059\pi\) | ||||
−0.999277 | + | 0.0380226i | \(0.987894\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.41421 | − | 0.540182i | −0.112154 | − | 0.0428392i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.16228 | + | 6.00000i | −0.249222 | + | 0.472866i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.9443 | −1.01387 | −0.506937 | − | 0.861983i | \(-0.669222\pi\) | ||||
−0.506937 | + | 0.861983i | \(0.669222\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.23607 | + | 2.76393i | 0.563327 | + | 0.215172i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.1246i | 1.32514i | 0.748999 | + | 0.662571i | \(0.230535\pi\) | ||||
−0.748999 | + | 0.662571i | \(0.769465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.5579 | − | 18.5123i | 1.26621 | − | 1.41567i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.1803i | 0.773997i | 0.922080 | + | 0.386998i | \(0.126488\pi\) | ||||
−0.922080 | + | 0.386998i | \(0.873512\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.99070i | 0.452855i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.94427 | + | 12.9443i | −0.371634 | + | 0.972951i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.94427i | − | 0.668526i | −0.942480 | − | 0.334263i | \(-0.891513\pi\) | ||
0.942480 | − | 0.334263i | \(-0.108487\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.78437i | 0.429949i | 0.976620 | + | 0.214975i | \(0.0689669\pi\) | ||||
−0.976620 | + | 0.214975i | \(0.931033\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.746512 | − | 1.95440i | 0.0551838 | − | 0.144473i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.41641i | 0.692308i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.1246 | −1.83729 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.53089 | + | 3.36861i | −0.475052 | + | 0.245030i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.0432 | −1.81206 | −0.906031 | − | 0.423212i | \(-0.860902\pi\) | ||||
−0.906031 | + | 0.423212i | \(0.860902\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.41641 | 0.245918 | 0.122959 | − | 0.992412i | \(-0.460762\pi\) | ||||
0.122959 | + | 0.992412i | \(0.460762\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.57649 | − | 1.74806i | −0.327729 | − | 0.125181i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.52786i | 0.536338i | 0.963372 | + | 0.268169i | \(0.0864186\pi\) | ||||
−0.963372 | + | 0.268169i | \(0.913581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.9799i | − | 0.778341i | −0.921166 | − | 0.389171i | \(-0.872762\pi\) | ||
0.921166 | − | 0.389171i | \(-0.127238\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.03631 | − | 10.5672i | 0.284699 | − | 0.745353i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.40492 | 0.519723 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.412662i | 0.0288216i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.01470 | − | 13.4853i | −0.348546 | − | 0.937292i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 42.3607i | − | 2.93015i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.6525 | 1.00872 | 0.504359 | − | 0.863494i | \(-0.331729\pi\) | ||||
0.504359 | + | 0.863494i | \(0.331729\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.52786 | + | 19.7082i | −0.515801 | + | 1.35038i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.76393i | 0.597695i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.48528i | 0.576018i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.7082 | + | 4.47214i | 0.791167 | + | 0.302199i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.8902 | 1.06889 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.9443 | 1.26860 | 0.634301 | − | 0.773086i | \(-0.281288\pi\) | ||||
0.634301 | + | 0.773086i | \(0.281288\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.47214 | − | 8.47214i | −0.631476 | − | 0.564809i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.20788 | −0.0801700 | −0.0400850 | − | 0.999196i | \(-0.512763\pi\) | ||||
−0.0400850 | + | 0.999196i | \(0.512763\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.02546i | 0.596419i | 0.954500 | + | 0.298210i | \(0.0963895\pi\) | ||||
−0.954500 | + | 0.298210i | \(0.903611\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.47214 | + | 11.7082i | −0.294245 | + | 0.770343i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 21.8885i | − | 1.43397i | −0.697091 | − | 0.716983i | \(-0.745522\pi\) | ||
0.697091 | − | 0.716983i | \(-0.254478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 10.2333i | − | 0.667550i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.11512 | − | 10.7735i | 0.267306 | − | 0.699816i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.00000i | − | 0.129369i | −0.997906 | − | 0.0646846i | \(-0.979396\pi\) | ||
0.997906 | − | 0.0646846i | \(-0.0206041\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 22.2148i | − | 1.43098i | −0.698624 | − | 0.715489i | \(-0.746204\pi\) | ||
0.698624 | − | 0.715489i | \(-0.253796\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.90983 | − | 15.0902i | 0.250816 | − | 0.968035i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.37016 | −0.279199 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.7912i | 1.70469i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.8554 | + | 4.91034i | 0.814681 | + | 0.311180i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.70091 | 0.170480 | 0.0852399 | − | 0.996360i | \(-0.472834\pi\) | ||||
0.0852399 | + | 0.996360i | \(0.472834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.7082 | − | 11.4412i | −1.36478 | − | 0.719304i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.94427 | − | 2.65248i | −0.434867 | − | 0.166104i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.5279i | 0.968602i | 0.874902 | + | 0.484301i | \(0.160926\pi\) | ||||
−0.874902 | + | 0.484301i | \(0.839074\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.2361 | −0.946723 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.4721 | + | 11.7082i | −0.648209 | + | 0.724720i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.2874 | −1.86760 | −0.933800 | − | 0.357796i | \(-0.883528\pi\) | ||||
−0.933800 | + | 0.357796i | \(0.883528\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.763932 | −0.0469280 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.540182 | − | 0.206331i | −0.0330586 | − | 0.0126273i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 7.52786i | − | 0.458982i | −0.973311 | − | 0.229491i | \(-0.926294\pi\) | ||
0.973311 | − | 0.229491i | \(-0.0737061\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | −0.242983 | −0.121491 | − | 0.992592i | \(-0.538768\pi\) | ||||
−0.121491 | + | 0.992592i | \(0.538768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.82843 | − | 7.40492i | 0.171184 | − | 0.448166i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.6746 | −1.30703 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.3607 | 1.34352 | 0.671762 | − | 0.740767i | \(-0.265538\pi\) | ||||
0.671762 | + | 0.740767i | \(0.265538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.4164 | − | 12.0000i | −0.803219 | − | 0.718421i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.5378 | 1.64276 | 0.821382 | − | 0.570378i | \(-0.193203\pi\) | ||||
0.821382 | + | 0.570378i | \(0.193203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9.61435i | − | 0.571514i | −0.958302 | − | 0.285757i | \(-0.907755\pi\) | ||
0.958302 | − | 0.285757i | \(-0.0922450\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.47214 | − | 11.7082i | 0.264906 | − | 0.693534i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.667701 | −0.0394131 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.11146 | 0.418321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.49302 | − | 3.90879i | 0.0875227 | − | 0.229137i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.78282 | 0.279415 | 0.139708 | − | 0.990193i | \(-0.455384\pi\) | ||||
0.139708 | + | 0.990193i | \(0.455384\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.99226i | 0.407105i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.1877 | − | 23.6290i | −0.707204 | − | 1.37109i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.7295 | + | 7.23607i | 0.793996 | + | 0.418473i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.1803 | −0.817341 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.23607 | + | 13.7082i | −0.300804 | + | 0.787516i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.05573i | − | 0.0604508i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.3607 | 1.16205 | 0.581023 | − | 0.813887i | \(-0.302653\pi\) | ||||
0.581023 | + | 0.813887i | \(0.302653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.37016 | + | 11.4412i | −0.248610 | + | 0.650869i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0000i | 1.13410i | 0.823685 | + | 0.567048i | \(0.191915\pi\) | ||||
−0.823685 | + | 0.567048i | \(0.808085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.8933i | − | 1.01139i | −0.862713 | − | 0.505695i | \(-0.831236\pi\) | ||
0.862713 | − | 0.505695i | \(-0.168764\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.47214 | + | 2.76393i | −0.139289 | + | 0.155730i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.70820i | − | 0.208273i | −0.994563 | − | 0.104137i | \(-0.966792\pi\) | ||
0.994563 | − | 0.104137i | \(-0.0332080\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.7912i | 1.50002i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0162 | − | 5.73567i | −0.838121 | − | 0.320134i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.6525i | 2.26196i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.7082 | 0.760394 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.49458 | − | 6.53089i | 0.137950 | − | 0.361159i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.5579 | 0.912867 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.6525 | −0.805373 | −0.402686 | − | 0.915338i | \(-0.631923\pi\) | ||||
−0.402686 | + | 0.915338i | \(0.631923\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.5471 | − | 24.0903i | 1.18077 | − | 1.32014i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.70820i | − | 0.311872i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9706i | 0.924445i | 0.886764 | + | 0.462223i | \(0.152948\pi\) | ||||
−0.886764 | + | 0.462223i | \(0.847052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.0177 | − | 6.11822i | −0.869963 | − | 0.332296i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.7000 | −1.66250 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.79212 | − | 5.45407i | −0.257999 | − | 0.293637i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 26.8328i | − | 1.44046i | −0.693735 | − | 0.720231i | \(-0.744036\pi\) | ||
0.693735 | − | 0.720231i | \(-0.255964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.7082 | 0.733783 | 0.366892 | − | 0.930264i | \(-0.380422\pi\) | ||||
0.366892 | + | 0.930264i | \(0.380422\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.70820 | + | 14.9443i | 0.411433 | + | 0.797666i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.4721i | 0.983173i | 0.870829 | + | 0.491586i | \(0.163583\pi\) | ||||
−0.870829 | + | 0.491586i | \(0.836417\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.6460i | 0.565031i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.29180 | − | 11.2361i | 0.227146 | − | 0.594676i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.8825 | 1.20769 | 0.603845 | − | 0.797102i | \(-0.293635\pi\) | ||||
0.603845 | + | 0.797102i | \(0.293635\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −49.5410 | −2.60742 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.5623 | − | 9.38197i | −1.28919 | − | 0.492426i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.32456 | 0.331042 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.0370i | − | 1.72452i | −0.506469 | − | 0.862258i | \(-0.669049\pi\) | ||
0.506469 | − | 0.862258i | \(-0.330951\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.944272 | − | 1.05573i | 0.0491568 | − | 0.0549590i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.23607i | − | 0.0641735i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.1862i | 0.579199i | 0.957148 | + | 0.289599i | \(0.0935221\pi\) | ||||
−0.957148 | + | 0.289599i | \(0.906478\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.0618 | − | 4.98915i | −0.674507 | − | 0.257639i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 16.9443i | − | 0.872674i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.0084i | 1.13050i | 0.824921 | + | 0.565248i | \(0.191220\pi\) | ||||
−0.824921 | + | 0.565248i | \(0.808780\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.4164 | − | 7.41641i | −0.994733 | − | 0.379954i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.1266 | −1.43720 | −0.718602 | − | 0.695421i | \(-0.755218\pi\) | ||||
−0.718602 | + | 0.695421i | \(0.755218\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.32456i | 0.322329i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.0540 | − | 22.4211i | 1.01940 | − | 1.13973i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.6544 | −1.65565 | −0.827823 | − | 0.560990i | \(-0.810421\pi\) | ||||
−0.827823 | + | 0.560990i | \(0.810421\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.8328 | + | 10.9799i | 1.05356 | + | 0.555275i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.70820 | + | 4.47214i | −0.0861675 | + | 0.225589i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 5.81966i | − | 0.292819i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.3050 | 1.57115 | 0.785575 | − | 0.618766i | \(-0.212367\pi\) | ||||
0.785575 | + | 0.618766i | \(0.212367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.9443 | + | 7.23607i | 0.948400 | + | 0.362257i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.48683 | 0.473750 | 0.236875 | − | 0.971540i | \(-0.423877\pi\) | ||||
0.236875 | + | 0.971540i | \(0.423877\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.4164 | 0.967200 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.874032 | − | 7.81758i | −0.0434310 | − | 0.388459i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 55.1246i | − | 2.73243i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.47214 | 0.122239 | 0.0611196 | − | 0.998130i | \(-0.480533\pi\) | ||||
0.0611196 | + | 0.998130i | \(0.480533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.9991 | − | 10.6947i | −1.38110 | − | 0.527531i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.3137 | −0.556711 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.94427 | 0.340881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.4721 | − | 4.00000i | −0.512823 | − | 0.195881i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.11978 | 0.347824 | 0.173912 | − | 0.984761i | \(-0.444359\pi\) | ||||
0.173912 | + | 0.984761i | \(0.444359\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.29135i | 0.209148i | 0.994517 | + | 0.104574i | \(0.0333478\pi\) | ||||
−0.994517 | + | 0.104574i | \(0.966652\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.4164 | + | 26.1803i | −1.13854 | + | 1.27293i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.8005 | 1.00897 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.70820 | 0.0826658 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.7912 | + | 10.2333i | 1.29349 | + | 0.494071i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.41577 | −0.116363 | −0.0581817 | − | 0.998306i | \(-0.518530\pi\) | ||||
−0.0581817 | + | 0.998306i | \(0.518530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7.40492i | − | 0.355858i | −0.984043 | − | 0.177929i | \(-0.943060\pi\) | ||
0.984043 | − | 0.177929i | \(-0.0569397\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.82843 | + | 7.40492i | −0.135613 | + | 0.355039i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.5123 | + | 35.1246i | −0.885563 | + | 1.68024i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.41641 | −0.163056 | −0.0815281 | − | 0.996671i | \(-0.525980\pi\) | ||||
−0.0815281 | + | 0.996671i | \(0.525980\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.1803 | + | 10.0000i | 0.532397 | + | 0.476190i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.1246i | 0.908638i | 0.890839 | + | 0.454319i | \(0.150117\pi\) | ||||
−0.890839 | + | 0.454319i | \(0.849883\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.291796 | −0.0138325 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.1437 | + | 5.78437i | 0.716272 | + | 0.273591i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.8328i | 1.36070i | 0.732885 | + | 0.680352i | \(0.238173\pi\) | ||||
−0.732885 | + | 0.680352i | \(0.761827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.41577i | − | 0.113754i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.70820 | − | 0.652476i | −0.0802584 | − | 0.0306560i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 4.00000i | − | 0.187523i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.07262i | 0.377621i | 0.982014 | + | 0.188811i | \(0.0604632\pi\) | ||||
−0.982014 | + | 0.188811i | \(0.939537\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.6963 | + | 22.6761i | 0.545935 | + | 1.05843i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.8885i | 1.29890i | 0.760405 | + | 0.649449i | \(0.225001\pi\) | ||||
−0.760405 | + | 0.649449i | \(0.774999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.3607 | −0.574450 | −0.287225 | − | 0.957863i | \(-0.592733\pi\) | ||||
−0.287225 | + | 0.957863i | \(0.592733\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.48528 | − | 3.24109i | −0.393496 | − | 0.150302i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.8353 | 1.10297 | 0.551483 | − | 0.834186i | \(-0.314062\pi\) | ||||
0.551483 | + | 0.834186i | \(0.314062\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.23607 | 0.426482 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.588890 | − | 1.54173i | 0.0271346 | − | 0.0710393i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 51.3050i | − | 2.35900i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.0702i | 1.60913i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.95440 | + | 1.74806i | 0.0894856 | + | 0.0800384i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.33540 | 0.0610161 | 0.0305080 | − | 0.999535i | \(-0.490287\pi\) | ||||
0.0305080 | + | 0.999535i | \(0.490287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.8639i | 1.58966i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.82488 | − | 7.75381i | 0.401546 | − | 0.352811i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.11146i | − | 0.0958763i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.9443 | −0.949076 | −0.474538 | − | 0.880235i | \(-0.657385\pi\) | ||||
−0.474538 | + | 0.880235i | \(0.657385\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.9443 | + | 8.00000i | 0.947133 | + | 0.361773i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.5279i | − | 0.971539i | −0.874087 | − | 0.485769i | \(-0.838539\pi\) | ||
0.874087 | − | 0.485769i | \(-0.161461\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 25.7109i | − | 1.15796i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.0000 | − | 8.94427i | −0.449467 | − | 0.402015i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.2256 | −0.772674 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.4721 | 1.00599 | 0.502995 | − | 0.864289i | \(-0.332231\pi\) | ||||
0.502995 | + | 0.864289i | \(0.332231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.5836 | − | 27.7082i | 0.472840 | − | 1.23791i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.5471 | 0.960736 | 0.480368 | − | 0.877067i | \(-0.340503\pi\) | ||||
0.480368 | + | 0.877067i | \(0.340503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.40492i | 0.329515i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.09017 | + | 1.56231i | 0.181651 | + | 0.0693844i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 9.59675i | − | 0.425368i | −0.977121 | − | 0.212684i | \(-0.931779\pi\) | ||
0.977121 | − | 0.212684i | \(-0.0682205\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2333i | 0.452697i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −38.2325 | + | 19.7202i | −1.68800 | + | 0.870667i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.18034i | 0.272338i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 59.9070i | 2.63471i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.29180 | − | 16.4721i | 0.276179 | − | 0.723047i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.57804 | −0.244378 | −0.122189 | − | 0.992507i | \(-0.538991\pi\) | ||||
−0.122189 | + | 0.992507i | \(0.538991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 26.3299i | − | 1.15133i | −0.817687 | − | 0.575663i | \(-0.804744\pi\) | ||
0.817687 | − | 0.575663i | \(-0.195256\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.70246 | − | 9.69316i | 0.161589 | − | 0.423044i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.4621 | 1.28339 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | + | 18.9737i | 0.565217 | + | 0.824942i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.0000 | − | 17.8885i | 0.694341 | − | 0.776297i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.52786i | 0.0661791i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.11146 | −0.350689 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.52786 | + | 14.4721i | −0.238545 | + | 0.624519i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.5834 | 1.10195 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.23607 | −0.311103 | −0.155551 | − | 0.987828i | \(-0.549715\pi\) | ||||
−0.155551 | + | 0.987828i | \(0.549715\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.57494 | − | 9.35931i | 0.153415 | − | 0.401647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 3.52786i | − | 0.151117i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.81966 | 0.163317 | 0.0816584 | − | 0.996660i | \(-0.473978\pi\) | ||||
0.0816584 | + | 0.996660i | \(0.473978\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.41577 | + | 2.70091i | −0.103102 | + | 0.115272i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.3491 | 1.84674 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.41641 | 0.400426 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.81966 | − | 15.2361i | 0.247031 | − | 0.646735i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.4288 | −0.653740 | −0.326870 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326870 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.4481i | 1.37241i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.6525 | + | 15.5279i | 1.71635 | + | 0.655587i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.03631 | −0.170110 | −0.0850551 | − | 0.996376i | \(-0.527107\pi\) | ||||
−0.0850551 | + | 0.996376i | \(0.527107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.65248 | −0.364012 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.6491 | − | 1.41421i | 0.531213 | − | 0.0593914i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.3987 | 0.645548 | 0.322774 | − | 0.946476i | \(-0.395385\pi\) | ||||
0.322774 | + | 0.946476i | \(0.395385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 6.78593i | − | 0.283982i | −0.989868 | − | 0.141991i | \(-0.954650\pi\) | ||
0.989868 | − | 0.141991i | \(-0.0453504\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.5207 | + | 15.4775i | 1.69278 | + | 0.646583i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.9721 | + | 9.47214i | 0.749489 | + | 0.395015i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.3475 | 0.472404 | 0.236202 | − | 0.971704i | \(-0.424097\pi\) | ||||
0.236202 | + | 0.971704i | \(0.424097\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.52786 | − | 2.11146i | −0.229730 | − | 0.0877491i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.2361i | 0.466151i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.47214 | 0.185217 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.32456 | + | 5.65685i | 0.261488 | + | 0.233882i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7.12461i | − | 0.294064i | −0.989132 | − | 0.147032i | \(-0.953028\pi\) | ||
0.989132 | − | 0.147032i | \(-0.0469721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.6737i | 2.04677i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.65248 | − | 12.1803i | 0.191377 | − | 0.501032i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.0557i | 0.864655i | 0.901717 | + | 0.432328i | \(0.142308\pi\) | ||||
−0.901717 | + | 0.432328i | \(0.857692\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6.06952i | − | 0.248826i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.78593 | + | 17.7658i | −0.277729 | + | 0.727105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5279i | 0.634451i | 0.948350 | + | 0.317226i | \(0.102751\pi\) | ||||
−0.948350 | + | 0.317226i | \(0.897249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.7082 | 0.640751 | 0.320376 | − | 0.947291i | \(-0.396191\pi\) | ||||
0.320376 | + | 0.947291i | \(0.396191\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0618 | + | 14.6035i | −0.531917 | + | 0.594701i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.2681 | −0.539425 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.0000 | 0.405887 | 0.202944 | − | 0.979190i | \(-0.434949\pi\) | ||||
0.202944 | + | 0.979190i | \(0.434949\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.9814 | − | 4.57649i | −0.485511 | − | 0.185449i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 37.8885i | − | 1.53281i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 33.4009i | − | 1.34905i | −0.738251 | − | 0.674526i | \(-0.764348\pi\) | ||
0.738251 | − | 0.674526i | \(-0.235652\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.255039 | − | 0.667701i | 0.0102842 | − | 0.0269243i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.5300 | −1.39013 | −0.695063 | − | 0.718949i | \(-0.744624\pi\) | ||||
−0.695063 | + | 0.718949i | \(0.744624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 11.1074i | − | 0.446443i | −0.974768 | − | 0.223222i | \(-0.928343\pi\) | ||
0.974768 | − | 0.223222i | \(-0.0716574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.220412 | + | 24.9189i | −0.00884483 | + | 0.999961i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 0.472136i | − | 0.0189157i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.1246 | 0.564984 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −26.1803 | + | 68.5410i | −1.04554 | + | 2.73726i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 52.9017i | 2.10933i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31.7016i | − | 1.26202i | −0.775775 | − | 0.631010i | \(-0.782641\pi\) | ||
0.775775 | − | 0.631010i | \(-0.217359\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.7082 | − | 9.05573i | −0.942317 | − | 0.359933i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.4884 | −0.416219 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.1803 | −0.641088 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.3607 | − | 27.2361i | 0.963694 | − | 1.07744i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.4605 | −1.12412 | −0.562061 | − | 0.827096i | \(-0.689991\pi\) | ||||
−0.562061 | + | 0.827096i | \(0.689991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.7751i | 0.464364i | 0.972672 | + | 0.232182i | \(0.0745865\pi\) | ||||
−0.972672 | + | 0.232182i | \(0.925414\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.41641 | − | 14.1803i | 0.213271 | − | 0.558350i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 20.9443i | − | 0.823404i | −0.911318 | − | 0.411702i | \(-0.864934\pi\) | ||
0.911318 | − | 0.411702i | \(-0.135066\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 40.9334i | − | 1.60678i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.24419 | − | 13.7295i | 0.205536 | − | 0.538100i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 34.0000i | − | 1.33052i | −0.746611 | − | 0.665261i | \(-0.768320\pi\) | ||
0.746611 | − | 0.665261i | \(-0.231680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.41577i | 0.0943918i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.1803 | − | 14.4721i | −0.631255 | − | 0.564612i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.7766 | 0.497707 | 0.248853 | − | 0.968541i | \(-0.419946\pi\) | ||||
0.248853 | + | 0.968541i | \(0.419946\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 31.2402i | − | 1.21510i | −0.794280 | − | 0.607552i | \(-0.792152\pi\) | ||
0.794280 | − | 0.607552i | \(-0.207848\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.7109 | − | 9.82068i | −0.998528 | − | 0.381404i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.2333 | 0.396832 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7082 | − | 22.2148i | 0.453343 | − | 0.860159i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.6525 | − | 11.7082i | −1.18509 | − | 0.452665i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.18034i | 0.238589i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6525 | 0.950283 | 0.475142 | − | 0.879909i | \(-0.342397\pi\) | ||||
0.475142 | + | 0.879909i | \(0.342397\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0902 | + | 19.5623i | 0.388371 | + | 0.752954i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5046 | −0.980220 | −0.490110 | − | 0.871661i | \(-0.663043\pi\) | ||||
−0.490110 | + | 0.871661i | \(0.663043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.41641 | 0.131110 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.95440 | + | 0.746512i | 0.0748926 | + | 0.0286064i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 33.0132i | − | 1.26321i | −0.775289 | − | 0.631607i | \(-0.782396\pi\) | ||
0.775289 | − | 0.631607i | \(-0.217604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.1246 | −0.577882 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.57804 | − | 14.6035i | 0.212816 | − | 0.557158i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.82843 | −0.107754 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.2361 | −1.03611 | −0.518054 | − | 0.855348i | \(-0.673344\pi\) | ||||
−0.518054 | + | 0.855348i | \(0.673344\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.4721 | − | 16.1803i | 0.549751 | − | 0.614640i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.65685 | −0.214577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.31835i | 0.0878137i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.5279 | + | 35.4164i | −0.511671 | + | 1.33957i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.3994 | −1.22371 | −0.611854 | − | 0.790971i | \(-0.709576\pi\) | ||||
−0.611854 | + | 0.790971i | \(0.709576\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −89.1935 | −3.36400 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.32456 | + | 16.5579i | −0.238197 | + | 0.623607i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.9814 | −0.450607 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.6777i | 0.889234i | 0.895721 | + | 0.444617i | \(0.146660\pi\) | ||||
−0.895721 | + | 0.444617i | \(0.853340\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.3168 | + | 14.8886i | −0.499419 | + | 0.558368i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.4558 | + | 13.4164i | 0.953329 | + | 0.502448i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.4721 | 0.541227 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.23607 | + | 3.23607i | −0.0461618 | + | 0.120853i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 28.0000i | − | 1.04422i | −0.852877 | − | 0.522112i | \(-0.825144\pi\) | ||
0.852877 | − | 0.522112i | \(-0.174856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | −0.372419 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.7295 | + | 35.9442i | −0.510605 | + | 1.33678i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 22.1803i | − | 0.823757i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.0664i | − | 0.595871i | −0.954586 | − | 0.297935i | \(-0.903702\pi\) | ||
0.954586 | − | 0.297935i | \(-0.0962980\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.6525 | + | 22.0000i | −0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.2361i | 1.82106i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 37.8198i | − | 1.39691i | −0.715656 | − | 0.698453i | \(-0.753872\pi\) | ||
0.715656 | − | 0.698453i | \(-0.246128\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.07107 | + | 2.70091i | 0.260820 | + | 0.0996245i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.4164i | 1.23091i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.4853 | −1.67320 | −0.836602 | − | 0.547812i | \(-0.815461\pi\) | ||||
−0.836602 | + | 0.547812i | \(0.815461\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.5579 | − | 43.3491i | 0.608270 | − | 1.59247i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.2843 | 1.03765 | 0.518825 | − | 0.854881i | \(-0.326370\pi\) | ||||
0.518825 | + | 0.854881i | \(0.326370\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.18034 | 0.299704 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.7658 | − | 15.8902i | −0.650016 | − | 0.581392i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 13.1246i | − | 0.479563i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.89639i | 0.288143i | 0.989567 | + | 0.144072i | \(0.0460196\pi\) | ||||
−0.989567 | + | 0.144072i | \(0.953980\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.37016 | − | 1.66925i | −0.159257 | − | 0.0608309i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.922740 | −0.0335820 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 49.2911i | − | 1.79152i | −0.444541 | − | 0.895759i | \(-0.646633\pi\) | ||
0.444541 | − | 0.895759i | \(-0.353367\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.0535 | + | 31.9287i | 1.01828 | + | 1.15894i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7.05573i | − | 0.255770i | −0.991789 | − | 0.127885i | \(-0.959181\pi\) | ||
0.991789 | − | 0.127885i | \(-0.0408188\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.70820 | 0.206651 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.59675 | + | 8.58359i | 0.346971 | + | 0.310340i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.8885i | 0.934781i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 11.7264i | − | 0.422864i | −0.977393 | − | 0.211432i | \(-0.932187\pi\) | ||
0.977393 | − | 0.211432i | \(-0.0678126\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.59675 | − | 25.1246i | 0.345618 | − | 0.904841i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.5123 | −0.665841 | −0.332921 | − | 0.942955i | \(-0.608034\pi\) | ||||
−0.332921 | + | 0.942955i | \(0.608034\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.4164 | 0.912984 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.6525 | + | 9.41641i | 0.884403 | + | 0.337812i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.90879 | −0.140047 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 62.3228i | − | 2.23009i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.1803 | − | 12.4721i | 0.864135 | − | 0.445718i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 0.832816i | − | 0.0297245i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.3516i | 0.582871i | 0.956591 | + | 0.291435i | \(0.0941328\pi\) | ||||
−0.956591 | + | 0.291435i | \(0.905867\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 49.0060 | + | 18.7186i | 1.74466 | + | 0.666401i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 14.0000i | − | 0.497783i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.90879i | − | 0.138805i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.23607 | + | 0.472136i | 0.0438388 | + | 0.0167449i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.4428 | 0.440746 | 0.220373 | − | 0.975416i | \(-0.429273\pi\) | ||||
0.220373 | + | 0.975416i | \(0.429273\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 57.4913i | − | 2.03390i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.746512 | + | 0.667701i | 0.0263767 | + | 0.0235921i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.0246 | −1.30657 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.76393 | − | 5.24419i | 0.0974158 | − | 0.184833i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.65248 | + | 12.1803i | −0.163775 | + | 0.428768i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.00000i | 0.281265i | 0.990062 | + | 0.140633i | \(0.0449136\pi\) | ||||
−0.990062 | + | 0.140633i | \(0.955086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.6525 | −0.514518 | −0.257259 | − | 0.966342i | \(-0.582819\pi\) | ||||
−0.257259 | + | 0.966342i | \(0.582819\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.47214 | + | 2.47214i | 0.226988 | + | 0.0867016i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.3137 | 0.396302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −83.0132 | −2.90426 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.15298 | + | 10.2333i | −0.319831 | + | 0.357582i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 27.8885i | − | 0.973317i | −0.873592 | − | 0.486658i | \(-0.838216\pi\) | ||
0.873592 | − | 0.486658i | \(-0.161784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.4721 | 0.992476 | 0.496238 | − | 0.868186i | \(-0.334714\pi\) | ||||
0.496238 | + | 0.868186i | \(0.334714\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 35.0702 | + | 13.3956i | 1.22099 | + | 0.466376i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.1738 | −0.944926 | −0.472463 | − | 0.881351i | \(-0.656635\pi\) | ||||
−0.472463 | + | 0.881351i | \(0.656635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.8197 | −0.549440 | −0.274720 | − | 0.961524i | \(-0.588585\pi\) | ||||
−0.274720 | + | 0.961524i | \(0.588585\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.1803 | − | 13.8197i | −1.25508 | − | 0.479399i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.5517 | −0.850666 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 14.9675i | − | 0.517970i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.2918 | + | 27.7082i | 0.493997 | + | 0.957736i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.81758 | 0.269893 | 0.134946 | − | 0.990853i | \(-0.456914\pi\) | ||||
0.134946 | + | 0.990853i | \(0.456914\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.58359 | 0.0546066 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44.5570 | − | 17.0193i | −1.53463 | − | 0.586175i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.20943 | 0.0760068 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 21.4682i | − | 0.737658i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.94200 | + | 15.5563i | −0.203929 | + | 0.533893i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.0903 | + | 45.7082i | −0.825806 | + | 1.56686i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.7214 | −1.32579 | −0.662897 | − | 0.748711i | \(-0.730673\pi\) | ||||
−0.662897 | + | 0.748711i | \(0.730673\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.4721 | + | 16.1803i | −0.494937 | + | 0.553356i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 15.4164i | − | 0.526614i | −0.964712 | − | 0.263307i | \(-0.915187\pi\) | ||
0.964712 | − | 0.263307i | \(-0.0848133\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.5967 | 1.62398 | 0.811990 | − | 0.583671i | \(-0.198384\pi\) | ||||
0.811990 | + | 0.583671i | \(0.198384\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.08036 | + | 0.412662i | 0.0368187 | + | 0.0140635i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.11146i | 0.0718748i | 0.999354 | + | 0.0359374i | \(0.0114417\pi\) | ||||
−0.999354 | + | 0.0359374i | \(0.988558\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 8.89794i | − | 0.302539i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.5066 | − | 4.39512i | −0.390784 | − | 0.149266i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.0689i | 1.15571i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 21.1344i | − | 0.716112i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.83153 | + | 5.40182i | −0.163523 | + | 0.182824i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 11.4164i | − | 0.385945i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.4164 | 0.723181 | 0.361590 | − | 0.932337i | \(-0.382234\pi\) | ||||
0.361590 | + | 0.932337i | \(0.382234\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.73877 | − | 2.95595i | −0.261022 | − | 0.0997016i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.2132 | −0.714691 | −0.357345 | − | 0.933972i | \(-0.616318\pi\) | ||||
−0.357345 | + | 0.933972i | \(0.616318\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.5967 | −0.524872 | −0.262436 | − | 0.964949i | \(-0.584526\pi\) | ||||
−0.262436 | + | 0.964949i | \(0.584526\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.32145 | − | 11.3137i | 0.145264 | − | 0.380306i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 15.1246i | − | 0.507835i | −0.967226 | − | 0.253917i | \(-0.918281\pi\) | ||
0.967226 | − | 0.253917i | \(-0.0817191\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 16.9706i | − | 0.569174i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.11667 | + | 45.7649i | 0.171415 | + | 1.53318i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 96.9316 | 3.24369 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.81758i | 0.261313i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.7426 | − | 20.1935i | −0.592409 | − | 0.674241i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 31.4164i | − | 1.04780i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.29180 | −0.142980 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.9443 | + | 8.76393i | 0.763538 | + | 0.291645i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 5.05573i | − | 0.168058i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5.60815i | − | 0.186215i | −0.995656 | − | 0.0931077i | \(-0.970320\pi\) | ||
0.995656 | − | 0.0931077i | \(-0.0296801\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.9443 | − | 18.9443i | 0.562006 | − | 0.628342i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.2333 | 0.339046 | 0.169523 | − | 0.985526i | \(-0.445777\pi\) | ||||
0.169523 | + | 0.985526i | \(0.445777\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40.6525 | −1.34540 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.652476 | + | 1.70820i | −0.0215702 | + | 0.0564715i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.90879 | −0.129080 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.8763i | 1.01851i | 0.860615 | + | 0.509257i | \(0.170080\pi\) | ||||
−0.860615 | + | 0.509257i | \(0.829920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.9443 | − | 12.5836i | −1.08555 | − | 0.414643i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.4164i | 1.29741i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.6374i | 1.50055i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.1421 | − | 15.8114i | 0.464489 | − | 0.519314i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 34.3607i | − | 1.12734i | −0.826001 | − | 0.563669i | \(-0.809389\pi\) | ||
0.826001 | − | 0.563669i | \(-0.190611\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 41.3948i | − | 1.35666i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.3607 | − | 32.3607i | 0.404670 | − | 1.05944i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.9597 | 0.718160 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.7510i | 1.59262i | 0.604886 | + | 0.796312i | \(0.293219\pi\) | ||||
−0.604886 | + | 0.796312i | \(0.706781\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.0587 | + | 28.9520i | −0.360886 | + | 0.944812i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.03165 | 0.0336310 | 0.0168155 | − | 0.999859i | \(-0.494647\pi\) | ||||
0.0168155 | + | 0.999859i | \(0.494647\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.05573 | + | 2.00310i | −0.0343792 | + | 0.0652300i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.70820 | − | 2.94427i | 0.185688 | − | 0.0957772i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.2492i | 0.723003i | 0.932372 | + | 0.361501i | \(0.117736\pi\) | ||||
−0.932372 | + | 0.361501i | \(0.882264\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.4164 | 0.760129 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.29180 | + | 6.00000i | −0.0743166 | + | 0.194563i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.32611 | −0.237316 | −0.118658 | − | 0.992935i | \(-0.537859\pi\) | ||||
−0.118658 | + | 0.992935i | \(0.537859\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.8885 | 0.708297 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.5579 | − | 43.3491i | 0.535241 | − | 1.40128i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 24.4721i | − | 0.790246i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.7518 | + | 18.5610i | 0.668718 | + | 0.598120i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.98605 | −0.0961243 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1115 | −0.389478 | −0.194739 | − | 0.980855i | \(-0.562386\pi\) | ||||
−0.194739 | + | 0.980855i | \(0.562386\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.1246 | − | 65.7771i | 0.807119 | − | 2.11306i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.6529 | 1.01579 | 0.507895 | − | 0.861419i | \(-0.330424\pi\) | ||||
0.507895 | + | 0.861419i | \(0.330424\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 9.15298i | − | 0.293431i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.1803 | − | 8.47214i | −0.710339 | − | 0.271325i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.1946 | 1.06199 | 0.530995 | − | 0.847375i | \(-0.321818\pi\) | ||||
0.530995 | + | 0.847375i | \(0.321818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.70820 | 0.0545944 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.07262 | + | 9.02546i | −0.257739 | + | 0.288161i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.2364 | −0.390282 | −0.195141 | − | 0.980775i | \(-0.562516\pi\) | ||||
−0.195141 | + | 0.980775i | \(0.562516\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.57959i | − | 0.209643i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.7912 | − | 10.2333i | −0.852775 | − | 0.325731i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.4211 | + | 42.5410i | −0.712949 | + | 1.35273i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.4164 | 0.934443 | 0.467221 | − | 0.884140i | \(-0.345255\pi\) | ||||
0.467221 | + | 0.884140i | \(0.345255\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.7082 | + | 9.05573i | 0.752357 | + | 0.287375i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.59675i | 0.304237i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.5967 | −0.620635 | −0.310318 | − | 0.950633i | \(-0.600435\pi\) | ||||
−0.310318 | + | 0.950633i | \(0.600435\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.7525 | + | 25.6622i | −1.57410 | + | 0.811915i |
(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 | 552.2.m.a.137.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 552.2.m.a.137.4 | yes | 8 | |
4.3 | odd | 2 | 1104.2.m.c.689.7 | 8 | |||
12.11 | even | 2 | 1104.2.m.c.689.6 | 8 | |||
23.22 | odd | 2 | inner | 552.2.m.a.137.2 | yes | 8 | |
69.68 | even | 2 | inner | 552.2.m.a.137.3 | yes | 8 | |
92.91 | even | 2 | 1104.2.m.c.689.8 | 8 | |||
276.275 | odd | 2 | 1104.2.m.c.689.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.m.a.137.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
552.2.m.a.137.2 | yes | 8 | 23.22 | odd | 2 | inner | |
552.2.m.a.137.3 | yes | 8 | 69.68 | even | 2 | inner | |
552.2.m.a.137.4 | yes | 8 | 3.2 | odd | 2 | inner | |
1104.2.m.c.689.5 | 8 | 276.275 | odd | 2 | |||
1104.2.m.c.689.6 | 8 | 12.11 | even | 2 | |||
1104.2.m.c.689.7 | 8 | 4.3 | odd | 2 | |||
1104.2.m.c.689.8 | 8 | 92.91 | even | 2 |