Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8400,2,Mod(1,8400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8400.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(67.0743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 840) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.41855 | −1.63375 | −0.816877 | − | 0.576812i | \(-0.804297\pi\) | ||||
−0.816877 | + | 0.576812i | \(0.804297\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.34017 | 1.20375 | 0.601874 | − | 0.798591i | \(-0.294421\pi\) | ||||
0.601874 | + | 0.798591i | \(0.294421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.07838 | 0.261545 | 0.130773 | − | 0.991412i | \(-0.458254\pi\) | ||||
0.130773 | + | 0.991412i | \(0.458254\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34017 | −0.995704 | −0.497852 | − | 0.867262i | \(-0.665878\pi\) | ||||
−0.497852 | + | 0.867262i | \(0.665878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.34017 | −1.32202 | −0.661009 | − | 0.750378i | \(-0.729871\pi\) | ||||
−0.661009 | + | 0.750378i | \(0.729871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.83710 | −1.64101 | −0.820504 | − | 0.571640i | \(-0.806307\pi\) | ||||
−0.820504 | + | 0.571640i | \(0.806307\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.34017 | 0.779518 | 0.389759 | − | 0.920917i | \(-0.372558\pi\) | ||||
0.389759 | + | 0.920917i | \(0.372558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.41855 | 0.943249 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.68035 | −1.42704 | −0.713520 | − | 0.700635i | \(-0.752900\pi\) | ||||
−0.713520 | + | 0.700635i | \(0.752900\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.34017 | −0.694984 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.34017 | 1.30252 | 0.651258 | − | 0.758856i | \(-0.274242\pi\) | ||||
0.651258 | + | 0.758856i | \(0.274242\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.15676 | −0.938896 | −0.469448 | − | 0.882960i | \(-0.655547\pi\) | ||||
−0.469448 | + | 0.882960i | \(0.655547\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.83710 | 0.997294 | 0.498647 | − | 0.866805i | \(-0.333830\pi\) | ||||
0.498647 | + | 0.866805i | \(0.333830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.07838 | −0.151003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.18342 | 0.849358 | 0.424679 | − | 0.905344i | \(-0.360387\pi\) | ||||
0.424679 | + | 0.905344i | \(0.360387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.34017 | 0.574870 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.83710 | 0.890115 | 0.445057 | − | 0.895502i | \(-0.353183\pi\) | ||||
0.445057 | + | 0.895502i | \(0.353183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.52359 | −0.579186 | −0.289593 | − | 0.957150i | \(-0.593520\pi\) | ||||
−0.289593 | + | 0.957150i | \(0.593520\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.34017 | 0.763267 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0989 | 1.67323 | 0.836616 | − | 0.547790i | \(-0.184531\pi\) | ||||
0.836616 | + | 0.547790i | \(0.184531\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1773 | −1.30820 | −0.654101 | − | 0.756408i | \(-0.726953\pi\) | ||||
−0.654101 | + | 0.756408i | \(0.726953\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.41855 | 0.617501 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.680346 | −0.0765449 | −0.0382724 | − | 0.999267i | \(-0.512185\pi\) | ||||
−0.0382724 | + | 0.999267i | \(0.512185\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.83710 | 0.750469 | 0.375235 | − | 0.926930i | \(-0.377562\pi\) | ||||
0.375235 | + | 0.926930i | \(0.377562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.83710 | 0.947437 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.49693 | 0.688673 | 0.344337 | − | 0.938846i | \(-0.388104\pi\) | ||||
0.344337 | + | 0.938846i | \(0.388104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.34017 | −0.454974 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.34017 | −0.450055 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.4969 | −1.06580 | −0.532901 | − | 0.846178i | \(-0.678898\pi\) | ||||
−0.532901 | + | 0.846178i | \(0.678898\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.41855 | −0.544585 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.8638 | 1.87701 | 0.938507 | − | 0.345259i | \(-0.112209\pi\) | ||||
0.938507 | + | 0.345259i | \(0.112209\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.1568 | −1.00077 | −0.500387 | − | 0.865802i | \(-0.666809\pi\) | ||||
−0.500387 | + | 0.865802i | \(0.666809\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.6537 | −1.41663 | −0.708313 | − | 0.705899i | \(-0.750543\pi\) | ||||
−0.708313 | + | 0.705899i | \(0.750543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.8371 | −1.22957 | −0.614786 | − | 0.788694i | \(-0.710757\pi\) | ||||
−0.614786 | + | 0.788694i | \(0.710757\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.68035 | 0.823902 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.50307 | 0.141397 | 0.0706985 | − | 0.997498i | \(-0.477477\pi\) | ||||
0.0706985 | + | 0.997498i | \(0.477477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.34017 | 0.401249 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.07838 | −0.0988547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3607 | 1.66915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.34017 | −0.752008 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.2039 | −1.70407 | −0.852037 | − | 0.523482i | \(-0.824633\pi\) | ||||
−0.852037 | + | 0.523482i | \(0.824633\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.15676 | 0.542072 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.34017 | 0.376341 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.65368 | 0.739334 | 0.369667 | − | 0.929164i | \(-0.379472\pi\) | ||||
0.369667 | + | 0.929164i | \(0.379472\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.18342 | 0.524471 | 0.262235 | − | 0.965004i | \(-0.415540\pi\) | ||||
0.262235 | + | 0.965004i | \(0.415540\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.83710 | −0.575788 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.5174 | −1.96663 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.2039 | −1.08171 | −0.540854 | − | 0.841116i | \(-0.681899\pi\) | ||||
−0.540854 | + | 0.841116i | \(0.681899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1568 | 1.47758 | 0.738788 | − | 0.673938i | \(-0.235399\pi\) | ||||
0.738788 | + | 0.673938i | \(0.235399\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.07838 | 0.0871817 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.1773 | 1.21128 | 0.605639 | − | 0.795739i | \(-0.292917\pi\) | ||||
0.605639 | + | 0.795739i | \(0.292917\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.18342 | −0.490377 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.34017 | 0.499676 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.83710 | 0.222219 | 0.111109 | − | 0.993808i | \(-0.464560\pi\) | ||||
0.111109 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.3607 | −1.03388 | −0.516941 | − | 0.856021i | \(-0.672929\pi\) | ||||
−0.516941 | + | 0.856021i | \(0.672929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.83710 | 0.449008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.34017 | −0.331901 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.55479 | 0.194237 | 0.0971184 | − | 0.995273i | \(-0.469037\pi\) | ||||
0.0971184 | + | 0.995273i | \(0.469037\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.83710 | −0.513908 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9421 | 0.892598 | 0.446299 | − | 0.894884i | \(-0.352742\pi\) | ||||
0.446299 | + | 0.894884i | \(0.352742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.15676 | 0.308969 | 0.154485 | − | 0.987995i | \(-0.450628\pi\) | ||||
0.154485 | + | 0.987995i | \(0.450628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.52359 | 0.334393 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.84324 | −0.427300 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.09890 | −0.441301 | −0.220650 | − | 0.975353i | \(-0.570818\pi\) | ||||
−0.220650 | + | 0.975353i | \(0.570818\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6803 | 0.912751 | 0.456376 | − | 0.889787i | \(-0.349147\pi\) | ||||
0.456376 | + | 0.889787i | \(0.349147\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.8576 | −0.844820 | −0.422410 | − | 0.906405i | \(-0.638816\pi\) | ||||
−0.422410 | + | 0.906405i | \(0.638816\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.50307 | 0.390102 | 0.195051 | − | 0.980793i | \(-0.437513\pi\) | ||||
0.195051 | + | 0.980793i | \(0.437513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.83710 | 0.620243 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.34017 | −0.440672 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.5174 | 1.62674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.1506 | 1.31838 | 0.659191 | − | 0.751975i | \(-0.270899\pi\) | ||||
0.659191 | + | 0.751975i | \(0.270899\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.0989 | −0.966040 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.34017 | −0.294630 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.1773 | 0.755290 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.68035 | 0.314834 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.3135 | −0.824574 | −0.412287 | − | 0.911054i | \(-0.635270\pi\) | ||||
−0.412287 | + | 0.911054i | \(0.635270\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.2039 | 1.00912 | 0.504560 | − | 0.863376i | \(-0.331655\pi\) | ||||
0.504560 | + | 0.863376i | \(0.331655\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.20394 | 0.343886 | 0.171943 | − | 0.985107i | \(-0.444996\pi\) | ||||
0.171943 | + | 0.985107i | \(0.444996\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.41855 | −0.356514 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.6598 | 0.763861 | 0.381930 | − | 0.924191i | \(-0.375259\pi\) | ||||
0.381930 | + | 0.924191i | \(0.375259\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.680346 | 0.0441932 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.6225 | −1.33396 | −0.666979 | − | 0.745077i | \(-0.732413\pi\) | ||||
−0.666979 | + | 0.745077i | \(0.732413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3545 | −1.31115 | −0.655576 | − | 0.755129i | \(-0.727574\pi\) | ||||
−0.655576 | + | 0.755129i | \(0.727574\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.8371 | −1.19858 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.83710 | −0.433284 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5236 | −0.664243 | −0.332122 | − | 0.943237i | \(-0.607764\pi\) | ||||
−0.332122 | + | 0.943237i | \(0.607764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.3545 | 2.15985 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.8059 | 1.42259 | 0.711297 | − | 0.702892i | \(-0.248108\pi\) | ||||
0.711297 | + | 0.702892i | \(0.248108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.68035 | 0.539370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.83710 | −0.547003 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.0144 | 1.72744 | 0.863720 | − | 0.503972i | \(-0.168128\pi\) | ||||
0.863720 | + | 0.503972i | \(0.168128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.49693 | −0.397606 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.4969 | 1.12778 | 0.563889 | − | 0.825851i | \(-0.309305\pi\) | ||||
0.563889 | + | 0.825851i | \(0.309305\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.0205 | 1.76287 | 0.881435 | − | 0.472304i | \(-0.156578\pi\) | ||||
0.881435 | + | 0.472304i | \(0.156578\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.34017 | 0.262679 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.68035 | −0.521551 | −0.260776 | − | 0.965399i | \(-0.583978\pi\) | ||||
−0.260776 | + | 0.965399i | \(0.583978\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.34017 | 0.259839 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.63317 | 0.336046 | 0.168023 | − | 0.985783i | \(-0.446262\pi\) | ||||
0.168023 | + | 0.985783i | \(0.446262\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.47027 | 0.146842 | 0.0734210 | − | 0.997301i | \(-0.476608\pi\) | ||||
0.0734210 | + | 0.997301i | \(0.476608\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.34017 | −0.492305 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8371 | −0.931594 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.4969 | 0.615341 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.60197 | −0.444112 | −0.222056 | − | 0.975034i | \(-0.571277\pi\) | ||||
−0.222056 | + | 0.975034i | \(0.571277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.41855 | 0.314416 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.5174 | −1.59138 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.15676 | 0.354869 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.8638 | −1.08369 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.15676 | −0.351385 | −0.175692 | − | 0.984445i | \(-0.556216\pi\) | ||||
−0.175692 | + | 0.984445i | \(0.556216\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.1568 | 0.577798 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.52973 | 0.0867432 | 0.0433716 | − | 0.999059i | \(-0.486190\pi\) | ||||
0.0433716 | + | 0.999059i | \(0.486190\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9733 | 0.676773 | 0.338387 | − | 0.941007i | \(-0.390119\pi\) | ||||
0.338387 | + | 0.941007i | \(0.390119\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.5441 | 1.32237 | 0.661184 | − | 0.750223i | \(-0.270054\pi\) | ||||
0.661184 | + | 0.750223i | \(0.270054\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 47.8843 | 2.68101 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.6537 | 0.817889 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.68035 | −0.260421 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.8371 | 0.709893 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.83710 | −0.376942 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.16290 | 0.503638 | 0.251819 | − | 0.967774i | \(-0.418971\pi\) | ||||
0.251819 | + | 0.967774i | \(0.418971\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.68035 | −0.475680 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0000 | 0.871576 | 0.435788 | − | 0.900049i | \(-0.356470\pi\) | ||||
0.435788 | + | 0.900049i | \(0.356470\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.50307 | −0.0816356 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.5174 | −1.27354 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.0205 | 1.23581 | 0.617903 | − | 0.786254i | \(-0.287982\pi\) | ||||
0.617903 | + | 0.786254i | \(0.287982\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.78992 | −0.202870 | −0.101435 | − | 0.994842i | \(-0.532343\pi\) | ||||
−0.101435 | + | 0.994842i | \(0.532343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.34017 | −0.231661 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.5958 | 1.52200 | 0.761001 | − | 0.648751i | \(-0.224708\pi\) | ||||
0.761001 | + | 0.648751i | \(0.224708\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.07838 | 0.0570738 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.2618 | 0.594375 | 0.297187 | − | 0.954819i | \(-0.403951\pi\) | ||||
0.297187 | + | 0.954819i | \(0.403951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.162899 | −0.00857361 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.3607 | −0.963686 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.3607 | 1.32382 | 0.661909 | − | 0.749584i | \(-0.269747\pi\) | ||||
0.661909 | + | 0.749584i | \(0.269747\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.34017 | 0.434172 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.18342 | −0.321027 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.3074 | −1.10325 | −0.551627 | − | 0.834091i | \(-0.685993\pi\) | ||||
−0.551627 | + | 0.834091i | \(0.685993\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −38.3545 | −1.97536 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.84324 | 0.0946811 | 0.0473406 | − | 0.998879i | \(-0.484925\pi\) | ||||
0.0473406 | + | 0.998879i | \(0.484925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.2039 | 0.983847 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.99386 | −0.255174 | −0.127587 | − | 0.991827i | \(-0.540723\pi\) | ||||
−0.127587 | + | 0.991827i | \(0.540723\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.15676 | −0.312965 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.8371 | 0.853675 | 0.426837 | − | 0.904328i | \(-0.359628\pi\) | ||||
0.426837 | + | 0.904328i | \(0.359628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.83710 | −0.345767 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.8515 | −1.84952 | −0.924761 | − | 0.380548i | \(-0.875736\pi\) | ||||
−0.924761 | + | 0.380548i | \(0.875736\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.34017 | −0.217280 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.3545 | −1.21621 | −0.608104 | − | 0.793857i | \(-0.708070\pi\) | ||||
−0.608104 | + | 0.793857i | \(0.708070\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.8371 | 0.938343 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 47.0349 | 2.33143 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.0410 | −1.38654 | −0.693270 | − | 0.720678i | \(-0.743831\pi\) | ||||
−0.693270 | + | 0.720678i | \(0.743831\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.65368 | −0.426855 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.83710 | −0.336432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.18342 | −0.302803 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.482553 | −0.0235742 | −0.0117871 | − | 0.999931i | \(-0.503752\pi\) | ||||
−0.0117871 | + | 0.999931i | \(0.503752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.1506 | 1.03082 | 0.515409 | − | 0.856944i | \(-0.327640\pi\) | ||||
0.515409 | + | 0.856944i | \(0.327640\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.83710 | 0.332431 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.52359 | 0.218912 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.5174 | 1.13543 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.7382 | 1.38427 | 0.692135 | − | 0.721768i | \(-0.256670\pi\) | ||||
0.692135 | + | 0.721768i | \(0.256670\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.02052 | 0.433498 | 0.216749 | − | 0.976227i | \(-0.430455\pi\) | ||||
0.216749 | + | 0.976227i | \(0.430455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.5174 | 1.31634 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.8166 | 0.850339 | 0.425170 | − | 0.905114i | \(-0.360214\pi\) | ||||
0.425170 | + | 0.905114i | \(0.360214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.7009 | −0.555925 | −0.277962 | − | 0.960592i | \(-0.589659\pi\) | ||||
−0.277962 | + | 0.960592i | \(0.589659\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.2039 | 0.624525 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.7337 | 0.506553 | 0.253277 | − | 0.967394i | \(-0.418492\pi\) | ||||
0.253277 | + | 0.967394i | \(0.418492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −45.1917 | −2.12799 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.1568 | −0.853079 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.9939 | 0.982051 | 0.491026 | − | 0.871145i | \(-0.336622\pi\) | ||||
0.491026 | + | 0.871145i | \(0.336622\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.07838 | −0.0503344 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3751 | −0.716088 | −0.358044 | − | 0.933705i | \(-0.616556\pi\) | ||||
−0.358044 | + | 0.933705i | \(0.616556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.1917 | 1.35665 | 0.678326 | − | 0.734762i | \(-0.262706\pi\) | ||||
0.678326 | + | 0.734762i | \(0.262706\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.2039 | −0.703554 | −0.351777 | − | 0.936084i | \(-0.614423\pi\) | ||||
−0.351777 | + | 0.936084i | \(0.614423\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.1773 | −0.699332 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.3607 | 1.53393 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.18342 | 0.283119 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.7838 | 0.858253 | 0.429126 | − | 0.903244i | \(-0.358822\pi\) | ||||
0.429126 | + | 0.903244i | \(0.358822\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.6742 | −1.71780 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.34017 | −0.288488 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.5113 | −0.748199 | −0.374099 | − | 0.927389i | \(-0.622048\pi\) | ||||
−0.374099 | + | 0.927389i | \(0.622048\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.83710 | −0.128298 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.4063 | −1.77838 | −0.889190 | − | 0.457538i | \(-0.848731\pi\) | ||||
−0.889190 | + | 0.457538i | \(0.848731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.52973 | −0.429198 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.0989 | −0.632422 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.5174 | 1.41091 | 0.705457 | − | 0.708752i | \(-0.250742\pi\) | ||||
0.705457 | + | 0.708752i | \(0.250742\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.3607 | 0.596912 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.3668 | 0.908112 | 0.454056 | − | 0.890973i | \(-0.349977\pi\) | ||||
0.454056 | + | 0.890973i | \(0.349977\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.83710 | −0.259235 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1773 | 0.495424 | 0.247712 | − | 0.968834i | \(-0.420321\pi\) | ||||
0.247712 | + | 0.968834i | \(0.420321\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1773 | 0.494454 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.34017 | 0.191623 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.0472 | −1.62933 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.55479 | −0.112143 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.6537 | 1.43058 | 0.715292 | − | 0.698826i | \(-0.246294\pi\) | ||||
0.715292 | + | 0.698826i | \(0.246294\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.6865 | −0.685922 | −0.342961 | − | 0.939350i | \(-0.611430\pi\) | ||||
−0.342961 | + | 0.939350i | \(0.611430\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.68035 | 0.203879 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.1978 | 0.747730 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.83710 | 0.296705 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.1978 | 1.56790 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.9421 | −0.515341 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.41855 | −0.233394 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.1978 | 1.29830 | 0.649152 | − | 0.760658i | \(-0.275124\pi\) | ||||
0.649152 | + | 0.760658i | \(0.275124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.15676 | −0.178383 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.36069 | −0.400234 | −0.200117 | − | 0.979772i | \(-0.564132\pi\) | ||||
−0.200117 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.52359 | −0.193062 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.3545 | 1.63396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.680346 | 0.0289313 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.49079 | −0.317395 | −0.158697 | − | 0.987327i | \(-0.550729\pi\) | ||||
−0.158697 | + | 0.987327i | \(0.550729\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.7214 | −1.13019 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.84324 | 0.246702 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.7152 | −1.33664 | −0.668319 | − | 0.743875i | \(-0.732986\pi\) | ||||
−0.668319 | + | 0.743875i | \(0.732986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.6803 | 1.28619 | 0.643094 | − | 0.765788i | \(-0.277651\pi\) | ||||
0.643094 | + | 0.765788i | \(0.277651\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.6393 | 0.445241 | 0.222621 | − | 0.974905i | \(-0.428539\pi\) | ||||
0.222621 | + | 0.974905i | \(0.428539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.09890 | 0.254785 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.0677 | 1.25173 | 0.625867 | − | 0.779930i | \(-0.284745\pi\) | ||||
0.625867 | + | 0.779930i | \(0.284745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6803 | −0.526977 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.83710 | −0.283651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.5052 | −1.38764 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.0410 | −0.414438 | −0.207219 | − | 0.978295i | \(-0.566441\pi\) | ||||
−0.207219 | + | 0.978295i | \(0.566441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.8371 | −0.776169 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.8576 | 0.487757 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.2823 | −0.997155 | −0.498578 | − | 0.866845i | \(-0.666144\pi\) | ||||
−0.498578 | + | 0.866845i | \(0.666144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.50307 | −0.225226 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.90110 | 0.404548 | 0.202274 | − | 0.979329i | \(-0.435167\pi\) | ||||
0.202274 | + | 0.979329i | \(0.435167\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.6865 | 0.721447 | 0.360723 | − | 0.932673i | \(-0.382530\pi\) | ||||
0.360723 | + | 0.932673i | \(0.382530\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.3135 | −1.14921 | −0.574605 | − | 0.818431i | \(-0.694844\pi\) | ||||
−0.574605 | + | 0.818431i | \(0.694844\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.83710 | −0.358097 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.6742 | 1.20049 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.6865 | −0.956688 | −0.478344 | − | 0.878172i | \(-0.658763\pi\) | ||||
−0.478344 | + | 0.878172i | \(0.658763\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7009 | −0.551576 | −0.275788 | − | 0.961218i | \(-0.588939\pi\) | ||||
−0.275788 | + | 0.961218i | \(0.588939\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.49693 | 0.100360 | 0.0501800 | − | 0.998740i | \(-0.484020\pi\) | ||||
0.0501800 | + | 0.998740i | \(0.484020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.34017 | 0.254422 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.49693 | −0.260294 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −23.5174 | −0.939196 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.36069 | −0.373235 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.68035 | −0.345559 | −0.172780 | − | 0.984961i | \(-0.555275\pi\) | ||||
−0.172780 | + | 0.984961i | \(0.555275\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.1506 | −0.761169 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.34017 | 0.171964 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.0989 | 0.557744 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.30737 | 0.130633 | 0.0653166 | − | 0.997865i | \(-0.479194\pi\) | ||||
0.0653166 | + | 0.997865i | \(0.479194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.15676 | 0.242799 | 0.121399 | − | 0.992604i | \(-0.461262\pi\) | ||||
0.121399 | + | 0.992604i | \(0.461262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.95282 | 0.273344 | 0.136672 | − | 0.990616i | \(-0.456359\pi\) | ||||
0.136672 | + | 0.990616i | \(0.456359\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.0472 | −1.45423 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.34017 | 0.170105 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −38.7480 | −1.51633 | −0.758164 | − | 0.652064i | \(-0.773903\pi\) | ||||
−0.758164 | + | 0.652064i | \(0.773903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.1773 | −0.436067 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.22076 | −0.359190 | −0.179595 | − | 0.983741i | \(-0.557479\pi\) | ||||
−0.179595 | + | 0.983741i | \(0.557479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.8843 | 1.00678 | 0.503391 | − | 0.864059i | \(-0.332086\pi\) | ||||
0.503391 | + | 0.864059i | \(0.332086\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.68035 | −0.181770 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.0288 | 2.16944 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.3135 | 0.476068 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.5113 | 0.946248 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0821 | −1.54505 | −0.772525 | − | 0.634984i | \(-0.781007\pi\) | ||||
−0.772525 | + | 0.634984i | \(0.781007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.5897 | 1.29096 | 0.645478 | − | 0.763779i | \(-0.276658\pi\) | ||||
0.645478 | + | 0.763779i | \(0.276658\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.4969 | 0.402835 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.2039 | −0.582616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.7070 | 0.715804 | 0.357902 | − | 0.933759i | \(-0.383492\pi\) | ||||
0.357902 | + | 0.933759i | \(0.383492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.20394 | −0.198543 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.8371 | 1.02241 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1773 | 0.729538 | 0.364769 | − | 0.931098i | \(-0.381148\pi\) | ||||
0.364769 | + | 0.931098i | \(0.381148\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.41855 | 0.205834 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.99386 | 0.340667 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.6598 | −0.441015 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.4641 | 0.810689 | 0.405344 | − | 0.914164i | \(-0.367152\pi\) | ||||
0.405344 | + | 0.914164i | \(0.367152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.6742 | 1.42091 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.8638 | −0.709445 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.62702 | 0.0986599 | 0.0493299 | − | 0.998783i | \(-0.484291\pi\) | ||||
0.0493299 | + | 0.998783i | \(0.484291\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.680346 | −0.0255150 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.5174 | −1.03054 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.6225 | 0.770161 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.36683 | 0.162855 | 0.0814277 | − | 0.996679i | \(-0.474052\pi\) | ||||
0.0814277 | + | 0.996679i | \(0.474052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.1568 | 0.378257 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.3545 | 0.756994 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.1445 | 1.04382 | 0.521910 | − | 0.853000i | \(-0.325220\pi\) | ||||
0.521910 | + | 0.853000i | \(0.325220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.63931 | −0.245564 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.7480 | 0.987962 | 0.493981 | − | 0.869473i | \(-0.335541\pi\) | ||||
0.493981 | + | 0.869473i | \(0.335541\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0349 | −0.700210 | −0.350105 | − | 0.936710i | \(-0.613854\pi\) | ||||
−0.350105 | + | 0.936710i | \(0.613854\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.8371 | 0.691998 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.6598 | 1.23486 | 0.617430 | − | 0.786626i | \(-0.288174\pi\) | ||||
0.617430 | + | 0.786626i | \(0.288174\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.83710 | 0.250156 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.6537 | 0.535434 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.8720 | 1.81985 | 0.909927 | − | 0.414767i | \(-0.136137\pi\) | ||||
0.909927 | + | 0.414767i | \(0.136137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.5236 | 0.383501 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.63317 | 0.277432 | 0.138716 | − | 0.990332i | \(-0.455702\pi\) | ||||
0.138716 | + | 0.990332i | \(0.455702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.3545 | −1.24699 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.5974 | 0.710406 | 0.355203 | − | 0.934789i | \(-0.384412\pi\) | ||||
0.355203 | + | 0.934789i | \(0.384412\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.8371 | 0.464734 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.6742 | 1.07147 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.4079 | −1.16866 | −0.584329 | − | 0.811517i | \(-0.698642\pi\) | ||||
−0.584329 | + | 0.811517i | \(0.698642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.8059 | −0.821335 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0845 | 0.434650 | 0.217325 | − | 0.976099i | \(-0.430267\pi\) | ||||
0.217325 | + | 0.976099i | \(0.430267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.68035 | −0.311406 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.1978 | −1.29692 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −76.3956 | −2.73365 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.83710 | 0.315812 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.0472 | 0.892836 | 0.446418 | − | 0.894825i | \(-0.352700\pi\) | ||||
0.446418 | + | 0.894825i | \(0.352700\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.0144 | −0.997338 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.50307 | −0.0534431 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.6332 | −0.697194 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.2762 | 0.753641 | 0.376820 | − | 0.926286i | \(-0.377017\pi\) | ||||
0.376820 | + | 0.926286i | \(0.377017\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.37298 | 0.260837 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.49693 | 0.229558 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 60.5646 | 2.13728 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.4969 | −0.651123 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.6619 | −1.74602 | −0.873010 | − | 0.487702i | \(-0.837835\pi\) | ||||
−0.873010 | + | 0.487702i | \(0.837835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.8166 | −0.906543 | −0.453271 | − | 0.891373i | \(-0.649743\pi\) | ||||
−0.453271 | + | 0.891373i | \(0.649743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.0205 | −1.01779 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.7214 | 0.934863 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.34017 | −0.151658 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.8904 | 0.868682 | 0.434341 | − | 0.900749i | \(-0.356981\pi\) | ||||
0.434341 | + | 0.900749i | \(0.356981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.4703 | 0.643833 | 0.321917 | − | 0.946768i | \(-0.395673\pi\) | ||||
0.321917 | + | 0.946768i | \(0.395673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.6886 | −0.754186 | −0.377093 | − | 0.926175i | \(-0.623076\pi\) | ||||
−0.377093 | + | 0.926175i | \(0.623076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.5052 | 1.64992 | 0.824961 | − | 0.565189i | \(-0.191197\pi\) | ||||
0.824961 | + | 0.565189i | \(0.191197\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.68035 | 0.301118 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.07838 | 0.0373636 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.34017 | −0.150018 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.4641 | −0.395785 | −0.197893 | − | 0.980224i | \(-0.563410\pi\) | ||||
−0.197893 | + | 0.980224i | \(0.563410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.0944 | 1.69291 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.63317 | −0.194017 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3607 | −0.630881 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.47027 | −0.0847793 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 55.0349 | 1.88657 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.8043 | −1.36287 | −0.681437 | − | 0.731877i | \(-0.738644\pi\) | ||||
−0.681437 | + | 0.731877i | \(0.738644\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.9627 | −0.579433 | −0.289717 | − | 0.957112i | \(-0.593561\pi\) | ||||
−0.289717 | + | 0.957112i | \(0.593561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.0493 | 1.40058 | 0.700292 | − | 0.713857i | \(-0.253053\pi\) | ||||
0.700292 | + | 0.713857i | \(0.253053\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.34017 | 0.284232 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 50.0554 | 1.70391 | 0.851953 | − | 0.523618i | \(-0.175418\pi\) | ||||
0.851953 | + | 0.523618i | \(0.175418\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.8371 | 0.537856 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.68649 | 0.125056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.4969 | −0.355267 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.32580 | −0.213607 | −0.106803 | − | 0.994280i | \(-0.534062\pi\) | ||||
−0.106803 | + | 0.994280i | \(0.534062\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.60197 | 0.256408 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.5380 | 0.691942 | 0.345971 | − | 0.938245i | \(-0.387550\pi\) | ||||
0.345971 | + | 0.938245i | \(0.387550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.30737 | −0.178607 | −0.0893036 | − | 0.996004i | \(-0.528464\pi\) | ||||
−0.0893036 | + | 0.996004i | \(0.528464\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.15061 | −0.105787 | −0.0528936 | − | 0.998600i | \(-0.516844\pi\) | ||||
−0.0528936 | + | 0.998600i | \(0.516844\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.2039 | 0.644079 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.41855 | −0.181528 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.6742 | −0.993009 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.5174 | 0.918781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.3545 | −1.27920 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.66806 | 0.222145 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.15676 | −0.204884 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.9467 | 0.396683 | 0.198341 | − | 0.980133i | \(-0.436445\pi\) | ||||
0.198341 | + | 0.980133i | \(0.436445\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.8638 | 0.625672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.0989 | −1.52732 | −0.763662 | − | 0.645616i | \(-0.776601\pi\) | ||||
−0.763662 | + | 0.645616i | \(0.776601\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37.0472 | −1.22608 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.25726 | −0.239395 | −0.119697 | − | 0.992810i | \(-0.538192\pi\) | ||||
−0.119697 | + | 0.992810i | \(0.538192\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.15676 | 0.202872 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61.1917 | 2.01415 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.1568 | −0.333592 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.9048 | −1.47328 | −0.736639 | − | 0.676286i | \(-0.763588\pi\) | ||||
−0.736639 | + | 0.676286i | \(0.763588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.34017 | −0.142243 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.52973 | −0.0500812 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.6886 | 1.42724 | 0.713622 | − | 0.700531i | \(-0.247054\pi\) | ||||
0.713622 | + | 0.700531i | \(0.247054\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.9733 | −0.390735 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.6660 | 0.478097 | 0.239048 | − | 0.971008i | \(-0.423165\pi\) | ||||
0.239048 | + | 0.971008i | \(0.423165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −52.8781 | −1.72195 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.96719 | 0.0964209 | 0.0482104 | − | 0.998837i | \(-0.484648\pi\) | ||||
0.0482104 | + | 0.998837i | \(0.484648\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.5113 | −1.57474 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.5441 | −0.763470 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.5851 | 1.47665 | 0.738324 | − | 0.674446i | \(-0.235618\pi\) | ||||
0.738324 | + | 0.674446i | \(0.235618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.8843 | −1.54788 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.65368 | −0.279442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1629 | −0.392352 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.6537 | −0.472208 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3668 | 1.04085 | 0.520424 | − | 0.853908i | \(-0.325774\pi\) | ||||
0.520424 | + | 0.853908i | \(0.325774\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.68035 | 0.150354 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3197 | 0.363265 | 0.181632 | − | 0.983366i | \(-0.441862\pi\) | ||||
0.181632 | + | 0.983366i | \(0.441862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.18342 | −0.198231 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.6886 | −1.26975 | −0.634875 | − | 0.772615i | \(-0.718948\pi\) | ||||
−0.634875 | + | 0.772615i | \(0.718948\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.2039 | −1.12512 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.8371 | −0.409857 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.5174 | 1.38799 | 0.693996 | − | 0.719979i | \(-0.255849\pi\) | ||||
0.693996 | + | 0.719979i | \(0.255849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.83710 | 0.217627 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39.0349 | 1.24124 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.80221 | 0.120781 | 0.0603905 | − | 0.998175i | \(-0.480765\pi\) | ||||
0.0603905 | + | 0.998175i | \(0.480765\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.16290 | −0.290776 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.8043 | −0.753890 | −0.376945 | − | 0.926236i | \(-0.623025\pi\) | ||||
−0.376945 | + | 0.926236i | \(0.623025\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.68035 | 0.274634 |
(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 | 8400.2.a.dh.1.1 | 3 | ||
4.3 | odd | 2 | 4200.2.a.bq.1.3 | 3 | |||
5.2 | odd | 4 | 1680.2.t.i.1009.4 | 6 | |||
5.3 | odd | 4 | 1680.2.t.i.1009.1 | 6 | |||
5.4 | even | 2 | 8400.2.a.dk.1.1 | 3 | |||
15.2 | even | 4 | 5040.2.t.ba.1009.5 | 6 | |||
15.8 | even | 4 | 5040.2.t.ba.1009.6 | 6 | |||
20.3 | even | 4 | 840.2.t.e.169.4 | yes | 6 | ||
20.7 | even | 4 | 840.2.t.e.169.1 | ✓ | 6 | ||
20.19 | odd | 2 | 4200.2.a.bo.1.3 | 3 | |||
60.23 | odd | 4 | 2520.2.t.j.1009.6 | 6 | |||
60.47 | odd | 4 | 2520.2.t.j.1009.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.e.169.1 | ✓ | 6 | 20.7 | even | 4 | ||
840.2.t.e.169.4 | yes | 6 | 20.3 | even | 4 | ||
1680.2.t.i.1009.1 | 6 | 5.3 | odd | 4 | |||
1680.2.t.i.1009.4 | 6 | 5.2 | odd | 4 | |||
2520.2.t.j.1009.5 | 6 | 60.47 | odd | 4 | |||
2520.2.t.j.1009.6 | 6 | 60.23 | odd | 4 | |||
4200.2.a.bo.1.3 | 3 | 20.19 | odd | 2 | |||
4200.2.a.bq.1.3 | 3 | 4.3 | odd | 2 | |||
5040.2.t.ba.1009.5 | 6 | 15.2 | even | 4 | |||
5040.2.t.ba.1009.6 | 6 | 15.8 | even | 4 | |||
8400.2.a.dh.1.1 | 3 | 1.1 | even | 1 | trivial | ||
8400.2.a.dk.1.1 | 3 | 5.4 | even | 2 |