Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(577,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.s (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.2696112.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1873.3 | ||
Root | \(1.17146 - 2.02903i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1873 |
Dual form | 2736.2.s.y.577.3 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.17146 | − | 2.02903i | 0.523894 | − | 0.907410i | −0.475720 | − | 0.879597i | \(-0.657812\pi\) |
0.999613 | − | 0.0278132i | \(-0.00885437\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.83221 | −1.44844 | −0.724220 | − | 0.689569i | \(-0.757800\pi\) | ||||
−0.724220 | + | 0.689569i | \(0.757800\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.34292 | 1.00793 | 0.503965 | − | 0.863724i | \(-0.331874\pi\) | ||||
0.503965 | + | 0.863724i | \(0.331874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.08757 | − | 5.34782i | −0.856337 | − | 1.48322i | −0.875399 | − | 0.483401i | \(-0.839401\pi\) |
0.0190619 | − | 0.999818i | \(-0.493932\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.59828 | − | 4.50035i | 0.630175 | − | 1.09150i | −0.357340 | − | 0.933974i | \(-0.616316\pi\) |
0.987516 | − | 0.157521i | \(-0.0503503\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.01438 | + | 3.14857i | 0.691547 | + | 0.722331i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.17146 | − | 2.02903i | −0.244267 | − | 0.423082i | 0.717659 | − | 0.696395i | \(-0.245214\pi\) |
−0.961925 | + | 0.273313i | \(0.911881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.244644 | − | 0.423736i | −0.0489289 | − | 0.0847473i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0250961 | + | 0.0434676i | 0.00466022 | + | 0.00807174i | 0.868346 | − | 0.495959i | \(-0.165183\pi\) |
−0.863686 | + | 0.504030i | \(0.831850\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.43910 | 0.617680 | 0.308840 | − | 0.951114i | \(-0.400059\pi\) | ||||
0.308840 | + | 0.951114i | \(0.400059\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.48929 | + | 7.77568i | −0.758828 | + | 1.31433i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.43910 | −0.894182 | −0.447091 | − | 0.894488i | \(-0.647540\pi\) | ||||
−0.447091 | + | 0.894488i | \(0.647540\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.64637 | + | 6.31569i | −0.569467 | + | 0.986345i | 0.427152 | + | 0.904180i | \(0.359517\pi\) |
−0.996619 | + | 0.0821653i | \(0.973816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.43049 | + | 7.67383i | −0.675643 | + | 1.17025i | 0.300637 | + | 0.953739i | \(0.402801\pi\) |
−0.976280 | + | 0.216510i | \(0.930533\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.36802 | − | 9.29768i | −0.783006 | − | 1.35621i | −0.930183 | − | 0.367096i | \(-0.880352\pi\) |
0.147177 | − | 0.989110i | \(-0.452981\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.68585 | 1.09798 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.59828 | − | 2.76830i | −0.219540 | − | 0.380255i | 0.735127 | − | 0.677929i | \(-0.237122\pi\) |
−0.954668 | + | 0.297674i | \(0.903789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.91611 | − | 6.78289i | 0.528048 | − | 0.914605i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.92682 | + | 3.33735i | −0.250850 | + | 0.434485i | −0.963760 | − | 0.266770i | \(-0.914044\pi\) |
0.712910 | + | 0.701256i | \(0.247377\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.46419 | − | 2.53606i | −0.187471 | − | 0.324709i | 0.756936 | − | 0.653489i | \(-0.226696\pi\) |
−0.944406 | + | 0.328781i | \(0.893362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.4679 | −1.79452 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.75903 | − | 9.97493i | −0.703577 | − | 1.21863i | −0.967203 | − | 0.254007i | \(-0.918252\pi\) |
0.263625 | − | 0.964625i | \(-0.415082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.744644 | + | 1.28976i | −0.0883730 | + | 0.153067i | −0.906824 | − | 0.421510i | \(-0.861500\pi\) |
0.818451 | + | 0.574577i | \(0.194833\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.84292 | − | 6.65614i | 0.449780 | − | 0.779042i | −0.548591 | − | 0.836091i | \(-0.684836\pi\) |
0.998371 | + | 0.0570486i | \(0.0181690\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.8108 | −1.45992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0875674 | − | 0.151671i | 0.00985210 | − | 0.0170643i | −0.861057 | − | 0.508508i | \(-0.830197\pi\) |
0.870909 | + | 0.491444i | \(0.163531\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.00735 | −0.769156 | −0.384578 | − | 0.923092i | \(-0.625653\pi\) | ||||
−0.384578 | + | 0.923092i | \(0.625653\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.08757 | − | 10.5440i | −0.660289 | − | 1.14365i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.77341 | − | 11.7319i | −0.717980 | − | 1.24358i | −0.961799 | − | 0.273758i | \(-0.911733\pi\) |
0.243818 | − | 0.969821i | \(-0.421600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.8322 | + | 20.4940i | 1.24035 | + | 2.14835i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.91978 | − | 2.42785i | 1.01775 | − | 0.249092i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.84292 | − | 3.19204i | 0.187120 | − | 0.324102i | −0.757169 | − | 0.653220i | \(-0.773418\pi\) |
0.944289 | + | 0.329117i | \(0.106751\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.80712 | − | 6.59412i | −0.378822 | − | 0.656139i | 0.612069 | − | 0.790804i | \(-0.290337\pi\) |
−0.990891 | + | 0.134665i | \(0.957004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6430 | −1.63988 | −0.819942 | − | 0.572447i | \(-0.805994\pi\) | ||||
−0.819942 | + | 0.572447i | \(0.805994\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.29273 | −0.608341 | −0.304171 | − | 0.952618i | \(-0.598379\pi\) | ||||
−0.304171 | + | 0.952618i | \(0.598379\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.57686 | + | 9.65940i | −0.534166 | + | 0.925203i | 0.465037 | + | 0.885291i | \(0.346041\pi\) |
−0.999203 | + | 0.0399114i | \(0.987292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.7606 | 1.67078 | 0.835388 | − | 0.549660i | \(-0.185243\pi\) | ||||
0.835388 | + | 0.549660i | \(0.185243\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.48929 | −0.511879 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.95715 | + | 17.2463i | −0.912771 | + | 1.58097i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.175135 | 0.0159213 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.5682 | 0.945253 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.21251 | + | 15.9565i | 0.817478 | + | 1.41591i | 0.907535 | + | 0.419977i | \(0.137962\pi\) |
−0.0900567 | + | 0.995937i | \(0.528705\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.61266 | − | 2.79321i | 0.140899 | − | 0.244044i | −0.786936 | − | 0.617034i | \(-0.788334\pi\) |
0.927835 | + | 0.372990i | \(0.121667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.5518 | − | 12.0660i | −1.00166 | − | 1.04625i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.98929 | − | 5.17760i | −0.255392 | − | 0.442352i | 0.709610 | − | 0.704595i | \(-0.248871\pi\) |
−0.965002 | + | 0.262243i | \(0.915538\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.58389 | − | 7.93954i | −0.388801 | − | 0.673423i | 0.603488 | − | 0.797372i | \(-0.293777\pi\) |
−0.992289 | + | 0.123950i | \(0.960444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.3215 | − | 17.8774i | −0.863127 | − | 1.49498i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.117596 | 0.00976584 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.07529 | − | 5.32656i | 0.251937 | − | 0.436368i | −0.712122 | − | 0.702056i | \(-0.752266\pi\) |
0.964059 | + | 0.265688i | \(0.0855990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.14637 | −0.418805 | −0.209403 | − | 0.977830i | \(-0.567152\pi\) | ||||
−0.209403 | + | 0.977830i | \(0.567152\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.02877 | − | 6.97803i | 0.323599 | − | 0.560489i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.20516 | + | 3.81946i | −0.175991 | + | 0.304826i | −0.940504 | − | 0.339783i | \(-0.889646\pi\) |
0.764513 | + | 0.644609i | \(0.222980\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.48929 | + | 7.77568i | 0.353806 | + | 0.612809i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3215 | −0.965094 | −0.482547 | − | 0.875870i | \(-0.660288\pi\) | ||||
−0.482547 | + | 0.875870i | \(0.660288\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.89101 | − | 5.00738i | −0.223713 | − | 0.387482i | 0.732220 | − | 0.681069i | \(-0.238485\pi\) |
−0.955933 | + | 0.293586i | \(0.905151\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5661 | + | 21.7652i | −0.966627 | + | 1.67425i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.912433 | + | 1.58038i | −0.0693710 | + | 0.120154i | −0.898625 | − | 0.438718i | \(-0.855433\pi\) |
0.829254 | + | 0.558872i | \(0.188766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.937529 | + | 1.62385i | 0.0708705 | + | 0.122751i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.26396 | 0.617678 | 0.308839 | − | 0.951114i | \(-0.400060\pi\) | ||||
0.308839 | + | 0.951114i | \(0.400060\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.8573 | + | 18.8054i | 0.807017 | + | 1.39780i | 0.914921 | + | 0.403634i | \(0.132253\pi\) |
−0.107903 | + | 0.994161i | \(0.534414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.37169 | + | 11.0361i | −0.468456 | + | 0.811390i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.68585 | − | 15.0443i | 0.635172 | − | 1.10015i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.58546 | −0.331792 | −0.165896 | − | 0.986143i | \(-0.553052\pi\) | ||||
−0.165896 | + | 0.986143i | \(0.553052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.08757 | − | 10.5440i | 0.438193 | − | 0.758972i | −0.559357 | − | 0.828927i | \(-0.688952\pi\) |
0.997550 | + | 0.0699545i | \(0.0222854\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.26817 | 0.304095 | 0.152047 | − | 0.988373i | \(-0.451413\pi\) | ||||
0.152047 | + | 0.988373i | \(0.451413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.43049 | − | 2.47768i | −0.101405 | − | 0.175638i | 0.810859 | − | 0.585242i | \(-0.199000\pi\) |
−0.912264 | + | 0.409604i | \(0.865667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0961734 | − | 0.166577i | −0.00675005 | − | 0.0116914i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.54315 | + | 14.7972i | 0.596680 | + | 1.03348i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0769 | + | 10.5254i | 0.697031 | + | 0.728059i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.13776 | − | 15.8271i | 0.629069 | − | 1.08958i | −0.358670 | − | 0.933465i | \(-0.616769\pi\) |
0.987739 | − | 0.156115i | \(-0.0498972\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.3803 | + | 17.9792i | 0.707930 | + | 1.22617i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.1793 | −0.894672 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.0894 | −2.15857 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.02510 | + | 10.4358i | −0.403470 | + | 0.698831i | −0.994142 | − | 0.108081i | \(-0.965529\pi\) |
0.590672 | + | 0.806912i | \(0.298863\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.71462 | −0.578409 | −0.289205 | − | 0.957267i | \(-0.593391\pi\) | ||||
−0.289205 | + | 0.957267i | \(0.593391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5640 | 1.02850 | 0.514250 | − | 0.857640i | \(-0.328070\pi\) | ||||
0.514250 | + | 0.857640i | \(0.328070\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.2146 | + | 19.4243i | −0.734694 | + | 1.27253i | 0.220164 | + | 0.975463i | \(0.429341\pi\) |
−0.954858 | + | 0.297064i | \(0.903992\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.1537 | −1.64085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.7434 | 1.98862 | 0.994312 | − | 0.106505i | \(-0.0339662\pi\) | ||||
0.994312 | + | 0.106505i | \(0.0339662\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.47858 | − | 4.29302i | −0.159659 | − | 0.276538i | 0.775087 | − | 0.631855i | \(-0.217706\pi\) |
−0.934746 | + | 0.355317i | \(0.884373\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.00367 | − | 15.5948i | 0.575224 | − | 0.996316i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.53087 | − | 25.8418i | 0.479178 | − | 1.64428i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.7664 | − | 23.8441i | −0.868926 | − | 1.50502i | −0.863095 | − | 0.505041i | \(-0.831477\pi\) |
−0.00583044 | − | 0.999983i | \(-0.501856\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.91611 | − | 6.78289i | −0.246203 | − | 0.426437i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.94331 | − | 10.2941i | −0.370733 | − | 0.642129i | 0.618945 | − | 0.785434i | \(-0.287560\pi\) |
−0.989679 | + | 0.143305i | \(0.954227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.8438 | 1.29517 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.71094 | + | 16.8198i | −0.598802 | + | 1.03716i | 0.394196 | + | 0.919026i | \(0.371023\pi\) |
−0.992998 | + | 0.118130i | \(0.962310\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.48929 | −0.460063 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.24128 | − | 16.0064i | 0.563451 | − | 0.975925i | −0.433741 | − | 0.901037i | \(-0.642807\pi\) |
0.997192 | − | 0.0748878i | \(-0.0238599\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.17146 | − | 14.1534i | 0.496381 | − | 0.859757i | −0.503610 | − | 0.863931i | \(-0.667995\pi\) |
0.999991 | + | 0.00417390i | \(0.00132860\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.817827 | − | 1.41652i | −0.0493168 | − | 0.0854192i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7894 | 0.948691 | 0.474346 | − | 0.880339i | \(-0.342685\pi\) | ||||
0.474346 | + | 0.880339i | \(0.342685\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.21462 | + | 7.29993i | 0.251423 | + | 0.435477i | 0.963918 | − | 0.266200i | \(-0.0857682\pi\) |
−0.712495 | + | 0.701677i | \(0.752435\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.905394 | − | 1.56819i | 0.0538201 | − | 0.0932192i | −0.837860 | − | 0.545885i | \(-0.816194\pi\) |
0.891680 | + | 0.452666i | \(0.149527\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.9736 | − | 24.2031i | 0.824838 | − | 1.42866i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00211 | − | 8.66390i | −0.294241 | − | 0.509641i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.2400 | −1.41612 | −0.708059 | − | 0.706154i | \(-0.750429\pi\) | ||||
−0.708059 | + | 0.706154i | \(0.750429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.51438 | + | 7.81914i | 0.262838 | + | 0.455248i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.23393 | + | 12.5295i | −0.418349 | + | 0.724602i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.9786 | − | 29.4078i | 0.978629 | − | 1.69504i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.86098 | −0.392859 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0016 | − | 19.0553i | 0.627893 | − | 1.08754i | −0.360081 | − | 0.932921i | \(-0.617251\pi\) |
0.987974 | − | 0.154621i | \(-0.0494156\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.4752 | −1.84150 | −0.920750 | − | 0.390153i | \(-0.872422\pi\) | ||||
−0.920750 | + | 0.390153i | \(0.872422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.62494 | + | 8.01064i | 0.261417 | + | 0.452788i | 0.966619 | − | 0.256219i | \(-0.0824768\pi\) |
−0.705202 | + | 0.709007i | \(0.749143\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.08757 | + | 5.34782i | 0.173415 | + | 0.300364i | 0.939612 | − | 0.342243i | \(-0.111186\pi\) |
−0.766197 | + | 0.642606i | \(0.777853\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0838942 | + | 0.145309i | 0.00469717 | + | 0.00813574i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.0019 | − | 5.38493i | 1.22422 | − | 0.299625i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.51071 | + | 2.61663i | −0.0837992 | + | 0.145144i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.5714 | + | 35.6307i | 1.13414 | + | 1.96438i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3643 | 0.569676 | 0.284838 | − | 0.958576i | \(-0.408060\pi\) | ||||
0.284838 | + | 0.958576i | \(0.408060\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.9859 | −1.47440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.3108 | + | 17.8588i | −0.561664 | + | 0.972831i | 0.435687 | + | 0.900098i | \(0.356505\pi\) |
−0.997351 | + | 0.0727331i | \(0.976828\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.4966 | 0.622578 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.62831 | −0.141915 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.9054 | − | 24.0848i | 0.746481 | − | 1.29294i | −0.203019 | − | 0.979175i | \(-0.565075\pi\) |
0.949500 | − | 0.313768i | \(-0.101591\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.60688 | 0.300130 | 0.150065 | − | 0.988676i | \(-0.452052\pi\) | ||||
0.150065 | + | 0.988676i | \(0.452052\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.0105 | 1.59730 | 0.798648 | − | 0.601798i | \(-0.205549\pi\) | ||||
0.798648 | + | 0.601798i | \(0.205549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.74464 | + | 3.02181i | 0.0925961 | + | 0.160381i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.48562 | − | 7.76931i | 0.236742 | − | 0.410049i | −0.723036 | − | 0.690811i | \(-0.757254\pi\) |
0.959777 | + | 0.280762i | \(0.0905871\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.826971 | + | 18.9820i | −0.0435248 | + | 0.999052i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.00367 | − | 15.5948i | −0.471274 | − | 0.816270i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.24621 | − | 9.08671i | −0.273850 | − | 0.474322i | 0.695994 | − | 0.718047i | \(-0.254964\pi\) |
−0.969844 | + | 0.243725i | \(0.921631\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.12494 | + | 10.6087i | 0.317991 | + | 0.550777i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.3074 | −0.947922 | −0.473961 | − | 0.880546i | \(-0.657176\pi\) | ||||
−0.473961 | + | 0.880546i | \(0.657176\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.154972 | − | 0.268419i | 0.00798144 | − | 0.0138243i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.8438 | −1.27614 | −0.638069 | − | 0.769979i | \(-0.720267\pi\) | ||||
−0.638069 | + | 0.769979i | \(0.720267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.58600 | + | 2.74703i | −0.0810408 | + | 0.140367i | −0.903697 | − | 0.428172i | \(-0.859158\pi\) |
0.822656 | + | 0.568539i | \(0.192491\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.0073 | + | 25.9935i | −0.764845 | + | 1.32475i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.69445 | − | 9.86308i | −0.288720 | − | 0.500078i | 0.684784 | − | 0.728746i | \(-0.259896\pi\) |
−0.973505 | + | 0.228668i | \(0.926563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.1751 | −0.615723 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.205164 | − | 0.355354i | −0.0103229 | − | 0.0178798i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.44277 | − | 16.3554i | 0.473919 | − | 0.820852i | −0.525635 | − | 0.850710i | \(-0.676172\pi\) |
0.999554 | + | 0.0298583i | \(0.00950560\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.0107 | + | 17.3391i | −0.499911 | + | 0.865871i | −1.00000 | 0.000102681i | \(-0.999967\pi\) | |
0.500089 | + | 0.865974i | \(0.333301\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.6184 | − | 18.3917i | −0.528942 | − | 0.916155i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.1825 | −0.901272 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.45715 | − | 9.45207i | −0.269839 | − | 0.467375i | 0.698981 | − | 0.715140i | \(-0.253637\pi\) |
−0.968820 | + | 0.247765i | \(0.920304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.38397 | − | 12.7894i | 0.363341 | − | 0.629326i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.20884 | + | 14.2181i | −0.402956 | + | 0.697940i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.4145 | −0.753049 | −0.376525 | − | 0.926407i | \(-0.622881\pi\) | ||||
−0.376525 | + | 0.926407i | \(0.622881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.98225 | − | 5.16541i | 0.145346 | − | 0.251747i | −0.784156 | − | 0.620564i | \(-0.786904\pi\) |
0.929502 | + | 0.368817i | \(0.120237\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.54262 | −0.123335 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.61110 | + | 9.71870i | 0.271540 | + | 0.470321i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5095 | + | 25.1311i | 0.698896 | + | 1.21052i | 0.968850 | + | 0.247650i | \(0.0796582\pi\) |
−0.269954 | + | 0.962873i | \(0.587008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.19109 | + | 15.9194i | 0.441695 | + | 0.765039i | 0.997815 | − | 0.0660630i | \(-0.0210438\pi\) |
−0.556120 | + | 0.831102i | \(0.687711\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.85731 | − | 9.80471i | 0.136684 | − | 0.469023i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.80712 | − | 6.59412i | 0.181704 | − | 0.314720i | −0.760757 | − | 0.649037i | \(-0.775172\pi\) |
0.942461 | + | 0.334317i | \(0.108505\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.75168 | − | 6.49810i | −0.178248 | − | 0.308734i | 0.763033 | − | 0.646360i | \(-0.223710\pi\) |
−0.941280 | + | 0.337626i | \(0.890376\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.7392 | −1.50458 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.31836 | −0.439761 | −0.219880 | − | 0.975527i | \(-0.570567\pi\) | ||||
−0.219880 | + | 0.975527i | \(0.570567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.1895 | + | 21.1129i | −0.573982 | + | 0.994166i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 55.4439 | 2.59925 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.4893 | 1.05200 | 0.526002 | − | 0.850483i | \(-0.323690\pi\) | ||||
0.526002 | + | 0.850483i | \(0.323690\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.67303 | − | 2.89777i | 0.0779207 | − | 0.134963i | −0.824432 | − | 0.565961i | \(-0.808505\pi\) |
0.902353 | + | 0.430998i | \(0.141839\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0147 | 1.20901 | 0.604503 | − | 0.796603i | \(-0.293372\pi\) | ||||
0.604503 | + | 0.796603i | \(0.293372\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.3429 | −0.524888 | −0.262444 | − | 0.964947i | \(-0.584528\pi\) | ||||
−0.262444 | + | 0.964947i | \(0.584528\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.0698 | + | 38.2260i | 1.01909 | + | 1.76511i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.8108 | + | 25.6530i | −0.681001 | + | 1.17953i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.596711 | − | 2.04758i | 0.0273790 | − | 0.0939496i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.75199 | + | 9.96274i | 0.262815 | + | 0.455209i | 0.966989 | − | 0.254818i | \(-0.0820157\pi\) |
−0.704174 | + | 0.710028i | \(0.748682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.7936 | + | 29.0873i | 0.765721 | + | 1.32627i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.31783 | − | 7.47870i | −0.196062 | − | 0.339590i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.3832 | −1.01428 | −0.507141 | − | 0.861863i | \(-0.669298\pi\) | ||||
−0.507141 | + | 0.861863i | \(0.669298\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0160 | − | 19.0802i | 0.497143 | − | 0.861077i | −0.502852 | − | 0.864373i | \(-0.667716\pi\) |
0.999995 | + | 0.00329588i | \(0.00104911\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.260826 | 0.0117470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.85363 | − | 4.94264i | 0.128003 | − | 0.221708i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.605317 | + | 1.04844i | −0.0270977 | + | 0.0469346i | −0.879256 | − | 0.476349i | \(-0.841960\pi\) |
0.852159 | + | 0.523284i | \(0.175293\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.2462 | + | 26.4072i | 0.679795 | + | 1.17744i | 0.975042 | + | 0.222019i | \(0.0712646\pi\) |
−0.295247 | + | 0.955421i | \(0.595402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.8396 | −0.793850 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.423144 | − | 0.732907i | −0.0187555 | − | 0.0324855i | 0.856495 | − | 0.516155i | \(-0.172637\pi\) |
−0.875251 | + | 0.483669i | \(0.839304\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.7269 | + | 25.5077i | −0.651479 | + | 1.12840i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.4966 | + | 33.7692i | −0.859124 | + | 1.48805i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.9449 | − | 31.0814i | −0.789215 | − | 1.36696i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.6044 | 1.86653 | 0.933266 | − | 0.359187i | \(-0.116946\pi\) | ||||
0.933266 | + | 0.359187i | \(0.116946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.86224 | − | 10.1537i | −0.256338 | − | 0.443990i | 0.708920 | − | 0.705289i | \(-0.249183\pi\) |
−0.965258 | + | 0.261299i | \(0.915849\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.93573 | − | 15.4771i | 0.389247 | − | 0.674195i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.75536 | − | 15.1647i | 0.380668 | − | 0.659336i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45.0336 | 1.95062 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.37169 | + | 12.7681i | −0.318706 | + | 0.552015i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.6932 | 1.10668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.06614 | + | 15.7030i | 0.389784 | + | 0.675126i | 0.992420 | − | 0.122890i | \(-0.0392163\pi\) |
−0.602636 | + | 0.798016i | \(0.705883\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.0661 | + | 22.6312i | 0.559692 | + | 0.969415i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.7018 | + | 37.5886i | 0.927902 | + | 1.60717i | 0.786826 | + | 0.617174i | \(0.211723\pi\) |
0.141076 | + | 0.989999i | \(0.454944\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0612117 | + | 0.210045i | −0.00260771 | + | 0.00894821i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.335577 | + | 0.581236i | −0.0142702 | + | 0.0247167i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.59828 | + | 7.96445i | 0.194835 | + | 0.337465i | 0.946847 | − | 0.321686i | \(-0.104249\pi\) |
−0.752011 | + | 0.659150i | \(0.770916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54.7178 | 2.31431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.3576 | 1.74302 | 0.871508 | − | 0.490382i | \(-0.163143\pi\) | ||||
0.871508 | + | 0.490382i | \(0.163143\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.8059 | − | 36.0368i | 0.875309 | − | 1.51608i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.22219 | −0.0512369 | −0.0256185 | − | 0.999672i | \(-0.508156\pi\) | ||||
−0.0256185 | + | 0.999672i | \(0.508156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.32150 | 0.180849 | 0.0904246 | − | 0.995903i | \(-0.471178\pi\) | ||||
0.0904246 | + | 0.995903i | \(0.471178\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.573183 | + | 0.992782i | −0.0239034 | + | 0.0414019i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.03863 | 0.0848695 | 0.0424347 | − | 0.999099i | \(-0.486489\pi\) | ||||
0.0424347 | + | 0.999099i | \(0.486489\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.8536 | 1.11408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.34292 | − | 9.25421i | −0.221281 | − | 0.383270i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.33011 | − | 7.49996i | 0.178723 | − | 0.309557i | −0.762721 | − | 0.646728i | \(-0.776137\pi\) |
0.941443 | + | 0.337171i | \(0.109470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.3668 | + | 10.8282i | 0.427155 | + | 0.446170i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.48592 | + | 9.50190i | 0.225280 | + | 0.390196i | 0.956403 | − | 0.292049i | \(-0.0943370\pi\) |
−0.731123 | + | 0.682245i | \(0.761004\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.3288 | + | 40.4067i | 0.956389 | + | 1.65652i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.7109 | − | 39.3365i | −0.927944 | − | 1.60725i | −0.786757 | − | 0.617263i | \(-0.788241\pi\) |
−0.141187 | − | 0.989983i | \(-0.545092\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.8757 | 1.21865 | 0.609327 | − | 0.792919i | \(-0.291440\pi\) | ||||
0.609327 | + | 0.792919i | \(0.291440\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.205164 | − | 0.355354i | 0.00834109 | − | 0.0144472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.7764 | 1.41153 | 0.705765 | − | 0.708446i | \(-0.250604\pi\) | ||||
0.705765 | + | 0.708446i | \(0.250604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.1482 | + | 57.4144i | −1.34103 | + | 2.32274i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.38030 | + | 12.7831i | −0.298087 | + | 0.516303i | −0.975698 | − | 0.219118i | \(-0.929682\pi\) |
0.677611 | + | 0.735421i | \(0.263015\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.0181 | − | 22.5479i | −0.524087 | − | 0.907746i | −0.999607 | − | 0.0280406i | \(-0.991073\pi\) |
0.475520 | − | 0.879705i | \(-0.342260\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.7497 | 1.63787 | 0.818933 | − | 0.573888i | \(-0.194566\pi\) | ||||
0.818933 | + | 0.573888i | \(0.194566\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.9572 | + | 44.9591i | 1.03995 | + | 1.80125i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.6035 | − | 23.5620i | 0.544141 | − | 0.942479i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.1323 | + | 24.4778i | −0.563491 | + | 0.975996i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.9106 | + | 27.5580i | 0.633392 | + | 1.09707i | 0.986853 | + | 0.161619i | \(0.0516714\pi\) |
−0.353461 | + | 0.935449i | \(0.614995\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 43.1684 | 1.71309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.7306 | − | 41.1025i | −0.940239 | − | 1.62854i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.08233 | + | 7.07080i | −0.161242 | + | 0.279280i | −0.935314 | − | 0.353818i | \(-0.884883\pi\) |
0.774072 | + | 0.633097i | \(0.218217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.29851 | − | 5.71319i | 0.130081 | − | 0.225306i | −0.793627 | − | 0.608405i | \(-0.791810\pi\) |
0.923707 | + | 0.383099i | \(0.125143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.60015 | 0.102223 | 0.0511113 | − | 0.998693i | \(-0.483724\pi\) | ||||
0.0511113 | + | 0.998693i | \(0.483724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.44120 | + | 11.1565i | −0.252839 | + | 0.437930i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.39312 | 0.0936498 | 0.0468249 | − | 0.998903i | \(-0.485090\pi\) | ||||
0.0468249 | + | 0.998903i | \(0.485090\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.77835 | − | 6.54429i | −0.147632 | − | 0.255706i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.3417 | − | 19.6443i | −0.441808 | − | 0.765235i | 0.556015 | − | 0.831172i | \(-0.312330\pi\) |
−0.997824 | + | 0.0659373i | \(0.978996\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.2750 | − | 35.1173i | −0.788605 | − | 1.36590i | −0.926821 | − | 0.375502i | \(-0.877470\pi\) |
0.138216 | − | 0.990402i | \(-0.455863\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −38.0147 | + | 9.30404i | −1.47415 | + | 0.360795i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0587981 | − | 0.101841i | 0.00227667 | − | 0.00394331i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.89468 | − | 8.47784i | −0.188957 | − | 0.327283i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1004 | −0.774813 | −0.387406 | − | 0.921909i | \(-0.626629\pi\) | ||||
−0.387406 | + | 0.921909i | \(0.626629\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.3717 | 0.744515 | 0.372257 | − | 0.928130i | \(-0.378584\pi\) | ||||
0.372257 | + | 0.928130i | \(0.378584\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.06247 | + | 12.2326i | −0.271033 | + | 0.469443i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.1151 | −0.616626 | −0.308313 | − | 0.951285i | \(-0.599764\pi\) | ||||
−0.308313 | + | 0.951285i | \(0.599764\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0073 | −0.535193 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.86959 | + | 17.0946i | −0.376001 | + | 0.651253i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.4145 | −0.586397 | −0.293198 | − | 0.956052i | \(-0.594720\pi\) | ||||
−0.293198 | + | 0.956052i | \(0.594720\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.4794 | −0.814761 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.9485 | + | 32.8198i | 0.717727 | + | 1.24314i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.9148 | − | 31.0294i | 0.676634 | − | 1.17197i | −0.299354 | − | 0.954142i | \(-0.596771\pi\) |
0.975988 | − | 0.217823i | \(-0.0698956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.3955 | − | 17.1254i | −0.618369 | − | 0.645896i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.5897 | + | 25.2701i | 0.548701 | + | 0.950378i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.41400 | − | 7.64527i | −0.165771 | − | 0.287124i | 0.771158 | − | 0.636644i | \(-0.219678\pi\) |
−0.936929 | + | 0.349520i | \(0.886345\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.02877 | − | 6.97803i | −0.150879 | − | 0.261329i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −48.3650 | −1.80875 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.13355 | − | 14.0877i | 0.303330 | − | 0.525383i | −0.673558 | − | 0.739134i | \(-0.735235\pi\) |
0.976888 | + | 0.213751i | \(0.0685682\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 63.7795 | 2.37527 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.0122792 | − | 0.0212682i | 0.000456038 | − | 0.000789882i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.3803 | − | 35.2997i | 0.755863 | − | 1.30919i | −0.189081 | − | 0.981962i | \(-0.560551\pi\) |
0.944944 | − | 0.327232i | \(-0.106116\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.0233 | + | 39.8775i | 0.851547 | + | 1.47492i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.6827 | 0.726998 | 0.363499 | − | 0.931595i | \(-0.381582\pi\) | ||||
0.363499 | + | 0.931595i | \(0.381582\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.2520 | − | 33.3454i | −0.709156 | − | 1.22829i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.3775 | + | 37.0269i | −0.786383 | + | 1.36206i | 0.141786 | + | 0.989897i | \(0.454715\pi\) |
−0.928169 | + | 0.372158i | \(0.878618\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.34239 | − | 14.4494i | 0.306052 | − | 0.530098i | −0.671443 | − | 0.741057i | \(-0.734325\pi\) |
0.977495 | + | 0.210958i | \(0.0676584\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.20516 | − | 12.4797i | −0.263977 | − | 0.457221i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.1151 | 0.881146 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.4305 | − | 26.7264i | −0.563067 | − | 0.975260i | −0.997227 | − | 0.0744242i | \(-0.976288\pi\) |
0.434160 | − | 0.900836i | \(-0.357045\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.02877 | + | 10.4421i | −0.219409 | + | 0.380028i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.99139 | − | 13.8415i | 0.290452 | − | 0.503078i | −0.683465 | − | 0.729984i | \(-0.739528\pi\) |
0.973917 | + | 0.226906i | \(0.0728610\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.9975 | −0.833658 | −0.416829 | − | 0.908985i | \(-0.636859\pi\) | ||||
−0.416829 | + | 0.908985i | \(0.636859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.3717 | − | 37.0169i | 0.773707 | − | 1.34010i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.7967 | 0.859249 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.9731 | − | 25.9342i | −0.539944 | − | 0.935211i | −0.998906 | − | 0.0467548i | \(-0.985112\pi\) |
0.458962 | − | 0.888456i | \(-0.348221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.75379 | + | 4.76970i | 0.0990469 | + | 0.171554i | 0.911290 | − | 0.411764i | \(-0.135087\pi\) |
−0.812244 | + | 0.583318i | \(0.801754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.841355 | − | 1.45727i | −0.0302224 | − | 0.0523467i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.8769 | + | 7.55709i | −1.10628 | + | 0.270761i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.48929 | + | 4.31157i | −0.0890737 | + | 0.154280i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.16653 | + | 8.94869i | 0.184401 | + | 0.319392i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.40719 | 0.299684 | 0.149842 | − | 0.988710i | \(-0.452123\pi\) | ||||
0.149842 | + | 0.988710i | \(0.452123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −68.0624 | −2.42002 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.04159 | + | 15.6605i | −0.321076 | + | 0.556120i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.2186 | −1.17666 | −0.588332 | − | 0.808620i | \(-0.700215\pi\) | ||||
−0.588332 | + | 0.808620i | \(0.700215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.7904 | −1.97372 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.8466 | − | 22.2510i | 0.453347 | − | 0.785219i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.0361 | 0.741426 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.8971 | −0.453438 | −0.226719 | − | 0.973960i | \(-0.572800\pi\) | ||||
−0.226719 | + | 0.973960i | \(0.572800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.33432 | − | 2.31110i | −0.0468542 | − | 0.0811539i | 0.841647 | − | 0.540028i | \(-0.181586\pi\) |
−0.888501 | + | 0.458874i | \(0.848253\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.4342 | + | 25.0007i | −0.505607 | + | 0.875736i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.5168 | + | 9.18219i | −1.31255 | + | 0.321244i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.8267 | − | 29.1448i | −0.587257 | − | 1.01716i | −0.994590 | − | 0.103880i | \(-0.966874\pi\) |
0.407333 | − | 0.913280i | \(-0.366459\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.91978 | + | 15.4495i | 0.310924 | + | 0.538536i | 0.978563 | − | 0.205949i | \(-0.0660282\pi\) |
−0.667639 | + | 0.744485i | \(0.732695\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.87663 | − | 3.25041i | −0.0652567 | − | 0.113028i | 0.831551 | − | 0.555448i | \(-0.187453\pi\) |
−0.896808 | + | 0.442420i | \(0.854120\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.77781 | 0.0964773 | 0.0482386 | − | 0.998836i | \(-0.484639\pi\) | ||||
0.0482386 | + | 0.998836i | \(0.484639\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.9700 | − | 34.5890i | 0.691918 | − | 1.19844i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.5468 | −0.468807 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.1114 | − | 48.6904i | 0.970513 | − | 1.68098i | 0.276504 | − | 0.961013i | \(-0.410824\pi\) |
0.694010 | − | 0.719966i | \(-0.255843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4987 | − | 25.1126i | 0.499957 | − | 0.865950i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.4415 | + | 50.9942i | 1.01282 | + | 1.75425i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.671153 | −0.0230611 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.37169 | + | 11.0361i | 0.218419 | + | 0.378312i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.16232 | − | 8.94140i | 0.176754 | − | 0.306148i | −0.764013 | − | 0.645201i | \(-0.776774\pi\) |
0.940767 | + | 0.339054i | \(0.110107\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.5894 | − | 46.0543i | 0.908278 | − | 1.57318i | 0.0918226 | − | 0.995775i | \(-0.470731\pi\) |
0.816455 | − | 0.577408i | \(-0.195936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.12651 | − | 8.87938i | −0.174914 | − | 0.302960i | 0.765217 | − | 0.643772i | \(-0.222631\pi\) |
−0.940132 | + | 0.340812i | \(0.889298\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.7679 | −0.366545 | −0.183273 | − | 0.983062i | \(-0.558669\pi\) | ||||
−0.183273 | + | 0.983062i | \(0.558669\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.13776 | + | 3.70271i | 0.0726860 | + | 0.125896i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.292731 | − | 0.507025i | 0.00993022 | − | 0.0171996i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.5628 | + | 61.5965i | −1.20500 | + | 2.08712i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −40.4998 | −1.36914 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.3638 | + | 19.6827i | −0.383729 | + | 0.664637i | −0.991592 | − | 0.129404i | \(-0.958693\pi\) |
0.607863 | + | 0.794042i | \(0.292027\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.44644 | 0.284568 | 0.142284 | − | 0.989826i | \(-0.454555\pi\) | ||||
0.142284 | + | 0.989826i | \(0.454555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.5196 | + | 39.0051i | 0.757846 | + | 1.31263i | 0.943947 | + | 0.330097i | \(0.107081\pi\) |
−0.186101 | + | 0.982531i | \(0.559585\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.4231 | + | 18.0534i | 0.349975 | + | 0.606174i | 0.986245 | − | 0.165292i | \(-0.0528568\pi\) |
−0.636270 | + | 0.771467i | \(0.719523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.3043 | − | 61.1488i | −1.18407 | − | 2.05087i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.0931 | − | 44.9284i | 0.438144 | − | 1.50347i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.68091 | − | 16.7678i | 0.323597 | − | 0.560487i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0863077 | + | 0.149489i | 0.00287852 | + | 0.00498575i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.6111 | −0.553396 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.8757 | 1.69116 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2055 | − | 21.1405i | 0.405276 | − | 0.701959i | −0.589078 | − | 0.808077i | \(-0.700509\pi\) |
0.994354 | + | 0.106118i | \(0.0338421\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.2744 | 0.804248 | 0.402124 | − | 0.915585i | \(-0.368272\pi\) | ||||
0.402124 | + | 0.915585i | \(0.368272\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.4250 | −0.775255 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.18007 | + | 10.7042i | −0.204084 | + | 0.353484i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.8568 | 1.05086 | 0.525429 | − | 0.850837i | \(-0.323905\pi\) | ||||
0.525429 | + | 0.850837i | \(0.323905\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.19656 | 0.302708 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.33064 | + | 2.30474i | 0.0437513 | + | 0.0757795i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.1044 | + | 43.4820i | −0.823648 | + | 1.42660i | 0.0793010 | + | 0.996851i | \(0.474731\pi\) |
−0.902949 | + | 0.429749i | \(0.858602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.1681 | + | 24.1994i | 0.759304 | + | 0.793104i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.3503 | − | 35.2477i | −0.665525 | − | 1.15272i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.32800 | + | 4.03222i | 0.0760525 | + | 0.131727i | 0.901543 | − | 0.432689i | \(-0.142435\pi\) |
−0.825491 | + | 0.564415i | \(0.809102\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6987 | − | 20.2627i | −0.381366 | − | 0.660544i | 0.609892 | − | 0.792484i | \(-0.291213\pi\) |
−0.991258 | + | 0.131940i | \(0.957879\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.0863 | 0.556407 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.7134 | − | 49.7330i | 0.933059 | − | 1.61611i | 0.154999 | − | 0.987915i | \(-0.450463\pi\) |
0.778060 | − | 0.628190i | \(-0.216204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.4611 | −1.54065 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.9966 | + | 34.6352i | −0.647755 | + | 1.12194i | 0.335903 | + | 0.941896i | \(0.390958\pi\) |
−0.983658 | + | 0.180047i | \(0.942375\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.37169 | + | 9.30404i | −0.173824 | + | 0.301072i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.4556 | + | 19.8417i | 0.369920 | + | 0.640721i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.1726 | −0.618471 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.2627 | − | 24.7037i | −0.459133 | − | 0.795241i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.94120 | + | 3.36226i | −0.0624248 | + | 0.108123i | −0.895549 | − | 0.444963i | \(-0.853217\pi\) |
0.833124 | + | 0.553086i | \(0.186550\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.687414 | − | 1.19064i | 0.0220602 | − | 0.0382093i | −0.854785 | − | 0.518983i | \(-0.826311\pi\) |
0.876845 | + | 0.480774i | \(0.159644\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.5665 | + | 30.4260i | 0.563155 | + | 0.975412i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.2541 | −0.647986 | −0.323993 | − | 0.946059i | \(-0.605025\pi\) | ||||
−0.323993 | + | 0.946059i | \(0.605025\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.6430 | − | 39.2188i | −0.723673 | − | 1.25344i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.38030 | + | 11.0510i | −0.203500 | + | 0.352472i | −0.949654 | − | 0.313301i | \(-0.898565\pi\) |
0.746154 | + | 0.665774i | \(0.231898\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.00000 | − | 8.66025i | 0.159313 | − | 0.275939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.7606 | 0.660149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.47647 | + | 16.4137i | −0.301030 | + | 0.521399i | −0.976370 | − | 0.216108i | \(-0.930664\pi\) |
0.675339 | + | 0.737507i | \(0.263997\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.70306 | −0.212501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.03244 | + | 10.4485i | 0.191049 | + | 0.330907i | 0.945598 | − | 0.325337i | \(-0.105478\pi\) |
−0.754549 | + | 0.656244i | \(0.772144\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.2.s.y.1873.3 | 6 | ||
3.2 | odd | 2 | 304.2.i.f.49.2 | 6 | |||
4.3 | odd | 2 | 1368.2.s.k.505.3 | 6 | |||
12.11 | even | 2 | 152.2.i.c.49.2 | ✓ | 6 | ||
19.7 | even | 3 | inner | 2736.2.s.y.577.3 | 6 | ||
24.5 | odd | 2 | 1216.2.i.m.961.2 | 6 | |||
24.11 | even | 2 | 1216.2.i.n.961.2 | 6 | |||
57.8 | even | 6 | 5776.2.a.bq.1.2 | 3 | |||
57.11 | odd | 6 | 5776.2.a.bk.1.2 | 3 | |||
57.26 | odd | 6 | 304.2.i.f.273.2 | 6 | |||
76.7 | odd | 6 | 1368.2.s.k.577.3 | 6 | |||
228.11 | even | 6 | 2888.2.a.r.1.2 | 3 | |||
228.83 | even | 6 | 152.2.i.c.121.2 | yes | 6 | ||
228.179 | odd | 6 | 2888.2.a.n.1.2 | 3 | |||
456.83 | even | 6 | 1216.2.i.n.577.2 | 6 | |||
456.197 | odd | 6 | 1216.2.i.m.577.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.i.c.49.2 | ✓ | 6 | 12.11 | even | 2 | ||
152.2.i.c.121.2 | yes | 6 | 228.83 | even | 6 | ||
304.2.i.f.49.2 | 6 | 3.2 | odd | 2 | |||
304.2.i.f.273.2 | 6 | 57.26 | odd | 6 | |||
1216.2.i.m.577.2 | 6 | 456.197 | odd | 6 | |||
1216.2.i.m.961.2 | 6 | 24.5 | odd | 2 | |||
1216.2.i.n.577.2 | 6 | 456.83 | even | 6 | |||
1216.2.i.n.961.2 | 6 | 24.11 | even | 2 | |||
1368.2.s.k.505.3 | 6 | 4.3 | odd | 2 | |||
1368.2.s.k.577.3 | 6 | 76.7 | odd | 6 | |||
2736.2.s.y.577.3 | 6 | 19.7 | even | 3 | inner | ||
2736.2.s.y.1873.3 | 6 | 1.1 | even | 1 | trivial | ||
2888.2.a.n.1.2 | 3 | 228.179 | odd | 6 | |||
2888.2.a.r.1.2 | 3 | 228.11 | even | 6 | |||
5776.2.a.bk.1.2 | 3 | 57.11 | odd | 6 | |||
5776.2.a.bq.1.2 | 3 | 57.8 | even | 6 |