Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,8,Mod(49,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.49");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(187.431015290\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.49 |
Dual form | 600.8.f.d.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 27.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 504.000i | 0.555376i | 0.960671 | + | 0.277688i | \(0.0895682\pi\) | ||||
−0.960671 | + | 0.277688i | \(0.910432\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3812.00 | 0.863532 | 0.431766 | − | 0.901986i | \(-0.357891\pi\) | ||||
0.431766 | + | 0.901986i | \(0.357891\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 9574.00i | − 1.20863i | −0.796747 | − | 0.604313i | \(-0.793448\pi\) | ||||
0.796747 | − | 0.604313i | \(-0.206552\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26098.0i | 1.28836i | 0.764875 | + | 0.644178i | \(0.222800\pi\) | ||||
−0.764875 | + | 0.644178i | \(0.777200\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38308.0 | 1.28130 | 0.640652 | − | 0.767832i | \(-0.278664\pi\) | ||||
0.640652 | + | 0.767832i | \(0.278664\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13608.0 | 0.320647 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 71128.0i | 1.21897i | 0.792797 | + | 0.609485i | \(0.208624\pi\) | ||||
−0.792797 | + | 0.609485i | \(0.791376\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −74262.0 | −0.565423 | −0.282712 | − | 0.959205i | \(-0.591234\pi\) | ||||
−0.282712 | + | 0.959205i | \(0.591234\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −275680. | −1.66203 | −0.831016 | − | 0.556249i | \(-0.812240\pi\) | ||||
−0.831016 | + | 0.556249i | \(0.812240\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 102924.i | − 0.498560i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 266610.i | − 0.865307i | −0.901560 | − | 0.432654i | \(-0.857577\pi\) | ||||
0.901560 | − | 0.432654i | \(-0.142423\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −258498. | −0.697800 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 684762. | 1.55166 | 0.775829 | − | 0.630943i | \(-0.217332\pi\) | ||||
0.775829 | + | 0.630943i | \(0.217332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 245956.i | − 0.471756i | −0.971783 | − | 0.235878i | \(-0.924203\pi\) | ||||
0.971783 | − | 0.235878i | \(-0.0757966\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 478800.i | 0.672685i | 0.941740 | + | 0.336342i | \(0.109190\pi\) | ||||
−0.941740 | + | 0.336342i | \(0.890810\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 569527. | 0.691557 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 704646. | 0.743833 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 569410.i | 0.525363i | 0.964883 | + | 0.262682i | \(0.0846069\pi\) | ||||
−0.964883 | + | 0.262682i | \(0.915393\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 1.03432e6i | − 0.739761i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.52532e6 | 0.966897 | 0.483448 | − | 0.875373i | \(-0.339384\pi\) | ||||
0.483448 | + | 0.875373i | \(0.339384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.64046e6 | −1.48945 | −0.744723 | − | 0.667374i | \(-0.767418\pi\) | ||||
−0.744723 | + | 0.667374i | \(0.767418\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 367416.i | − 0.185125i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.41624e6i | 0.575273i | 0.957740 | + | 0.287636i | \(0.0928695\pi\) | ||||
−0.957740 | + | 0.287636i | \(0.907131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.92046e6 | 0.703773 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.51130e6 | −1.16430 | −0.582149 | − | 0.813082i | \(-0.697788\pi\) | ||||
−0.582149 | + | 0.813082i | \(0.697788\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 4.73862e6i | − 1.42568i | −0.701327 | − | 0.712839i | \(-0.747409\pi\) | ||||
0.701327 | − | 0.712839i | \(-0.252591\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.92125e6i | 0.479585i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.66149e6 | −1.06373 | −0.531863 | − | 0.846830i | \(-0.678508\pi\) | ||||
−0.531863 | + | 0.846830i | \(0.678508\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.72925e6i | 1.09983i | 0.835221 | + | 0.549914i | \(0.185339\pi\) | ||||
−0.835221 | + | 0.549914i | \(0.814661\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00507e6i | 0.326447i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.19935e7 | −1.80336 | −0.901678 | − | 0.432408i | \(-0.857664\pi\) | ||||
−0.901678 | + | 0.432408i | \(0.857664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.82530e6 | 0.671242 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.44336e6i | 0.959575i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.15075e6i | 0.795519i | 0.917490 | + | 0.397760i | \(0.130212\pi\) | ||||
−0.917490 | + | 0.397760i | \(0.869788\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.77895e6 | −0.287844 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.78373e6 | −0.848309 | −0.424155 | − | 0.905590i | \(-0.639429\pi\) | ||||
−0.424155 | + | 0.905590i | \(0.639429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.01610e6i | 0.722825i | 0.932406 | + | 0.361412i | \(0.117705\pi\) | ||||
−0.932406 | + | 0.361412i | \(0.882295\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 5.15123e6i | − 0.406507i | −0.979126 | − | 0.203253i | \(-0.934849\pi\) | ||||
0.979126 | − | 0.203253i | \(-0.0651515\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.41280e7 | 1.78455 | 0.892274 | − | 0.451493i | \(-0.149109\pi\) | ||||
0.892274 | + | 0.451493i | \(0.149109\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.19847e6 | −0.499585 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.04827e6i | − 0.133541i | −0.997768 | − | 0.0667703i | \(-0.978731\pi\) | ||||
0.997768 | − | 0.0667703i | \(-0.0212695\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.97945e6i | 0.402875i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.31534e7 | −0.715523 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.95583e6 | −0.254312 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.84886e7i | − 0.895850i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.36634e6i | 0.0591895i | 0.999562 | + | 0.0295947i | \(0.00942167\pi\) | ||||
−0.999562 | + | 0.0295947i | \(0.990578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.64081e6 | −0.272369 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.84645e7 | 1.49489 | 0.747447 | − | 0.664321i | \(-0.231279\pi\) | ||||
0.747447 | + | 0.664321i | \(0.231279\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.93072e7i | 0.711605i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.62585e6i | 0.253376i | 0.991943 | + | 0.126688i | \(0.0404348\pi\) | ||||
−0.991943 | + | 0.126688i | \(0.959565\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.32324e6 | −0.168122 | −0.0840609 | − | 0.996461i | \(-0.526789\pi\) | ||||
−0.0840609 | + | 0.996461i | \(0.526789\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.29276e7 | 0.388375 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 3.64961e7i | − 1.04369i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.53772e7i | − 0.399271i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.61366e6 | −0.188557 | −0.0942783 | − | 0.995546i | \(-0.530054\pi\) | ||||
−0.0942783 | + | 0.995546i | \(0.530054\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50221e7 | −0.591432 | −0.295716 | − | 0.955276i | \(-0.595558\pi\) | ||||
−0.295716 | + | 0.955276i | \(0.595558\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 1.90254e7i | − 0.429452i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.93145e7i | 0.810782i | 0.914143 | + | 0.405391i | \(0.132865\pi\) | ||||
−0.914143 | + | 0.405391i | \(0.867135\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.53741e7 | 0.303319 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.58485e7 | −0.676987 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.28387e7i | 1.13650i | 0.822855 | + | 0.568252i | \(0.192380\pi\) | ||||
−0.822855 | + | 0.568252i | \(0.807620\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.04133e7i | 0.173014i | 0.996251 | + | 0.0865072i | \(0.0275706\pi\) | ||||
−0.996251 | + | 0.0865072i | \(0.972429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.89130e7 | −0.460775 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.79265e7 | −0.427101 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.03551e7i | 1.17992i | 0.807433 | + | 0.589959i | \(0.200856\pi\) | ||||
−0.807433 | + | 0.589959i | \(0.799144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 4.11837e7i | − 0.558238i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.40084e7 | 1.09481 | 0.547403 | − | 0.836869i | \(-0.315617\pi\) | ||||
0.547403 | + | 0.836869i | \(0.315617\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.15469e8 | 1.44741 | 0.723703 | − | 0.690112i | \(-0.242439\pi\) | ||||
0.723703 | + | 0.690112i | \(0.242439\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.12924e7i | 0.859932i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.94856e7i | 1.11254i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.92023e6 | −0.106882 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.97154e7 | 1.03549 | 0.517744 | − | 0.855535i | \(-0.326772\pi\) | ||||
0.517744 | + | 0.855535i | \(0.326772\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.86157e7i | 0.186393i | 0.995648 | + | 0.0931965i | \(0.0297085\pi\) | ||||
−0.995648 | + | 0.0931965i | \(0.970292\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.30384e7i | 0.867022i | 0.901148 | + | 0.433511i | \(0.142726\pi\) | ||||
−0.901148 | + | 0.433511i | \(0.857274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.39686e7 | −0.665367 | −0.332684 | − | 0.943038i | \(-0.607954\pi\) | ||||
−0.332684 | + | 0.943038i | \(0.607954\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.82384e7 | 0.332134 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3.74280e7i | − 0.314023i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 5.18523e7i | − 0.406323i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.46030e8 | 1.10645 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.85163e8 | 1.35695 | 0.678476 | − | 0.734623i | \(-0.262641\pi\) | ||||
0.678476 | + | 0.734623i | \(0.262641\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.48052e7i | 0.672208i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1.38943e8i | − 0.923053i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.27943e8 | −0.823116 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.49862e8 | 1.55714 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.20862e8i | 0.729830i | 0.931041 | + | 0.364915i | \(0.118902\pi\) | ||||
−0.931041 | + | 0.364915i | \(0.881098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.82315e8i | − 1.60193i | −0.598710 | − | 0.800966i | \(-0.704320\pi\) | ||||
0.598710 | − | 0.800966i | \(-0.295680\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.91913e7 | 0.490793 | 0.245397 | − | 0.969423i | \(-0.421082\pi\) | ||||
0.245397 | + | 0.969423i | \(0.421082\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.18737e7 | 0.276889 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.32240e8i | 1.20279i | 0.798951 | + | 0.601396i | \(0.205389\pi\) | ||||
−0.798951 | + | 0.601396i | \(0.794611\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.25860e8i | 0.614142i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.21986e8 | −1.52561 | −0.762807 | − | 0.646626i | \(-0.776179\pi\) | ||||
−0.762807 | + | 0.646626i | \(0.776179\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00366e8 | −0.922072 | −0.461036 | − | 0.887381i | \(-0.652522\pi\) | ||||
−0.461036 | + | 0.887381i | \(0.652522\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.43489e7i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3.66761e8i | − 1.54862i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.54690e8 | 0.634986 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.70560e7 | −0.347489 | −0.173744 | − | 0.984791i | \(-0.555587\pi\) | ||||
−0.173744 | + | 0.984791i | \(0.555587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.71140e8i | 1.05262i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.22879e8i | 1.92148i | 0.277457 | + | 0.960738i | \(0.410509\pi\) | ||||
−0.277457 | + | 0.960738i | \(0.589491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.34371e8 | 0.480571 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.41370e7 | 0.188474 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.06215e8i | 1.37693i | 0.725270 | + | 0.688464i | \(0.241715\pi\) | ||||
−0.725270 | + | 0.688464i | \(0.758285\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.23825e8i | 1.04117i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.82347e8 | −1.19764 | −0.598818 | − | 0.800885i | \(-0.704363\pi\) | ||||
−0.598818 | + | 0.800885i | \(0.704363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.84165e8 | 0.867317 | 0.433658 | − | 0.901077i | \(-0.357222\pi\) | ||||
0.433658 | + | 0.901077i | \(0.357222\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 1.30283e8i | − 0.387542i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.93752e8i | 0.830427i | 0.909724 | + | 0.415213i | \(0.136293\pi\) | ||||
−0.909724 | + | 0.415213i | \(0.863707\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00971e8 | 0.554011 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.15399e8 | 1.11685 | 0.558424 | − | 0.829556i | \(-0.311406\pi\) | ||||
0.558424 | + | 0.829556i | \(0.311406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5.06429e7i | − 0.132821i | −0.997792 | − | 0.0664104i | \(-0.978845\pi\) | ||||
0.997792 | − | 0.0664104i | \(-0.0211547\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.45120e8i | 0.861754i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.70767e8 | −0.659862 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.93070e8 | 0.459293 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7.47714e7i | − 0.173660i | −0.996223 | − | 0.0868298i | \(-0.972326\pi\) | ||||
0.996223 | − | 0.0868298i | \(-0.0276736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.50316e7i | 0.166187i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.80979e8 | 1.47328 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.23962e8 | 0.262002 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.37161e8i | 0.489772i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.52577e7i | 0.168170i | 0.996459 | + | 0.0840851i | \(0.0267968\pi\) | ||||
−0.996459 | + | 0.0840851i | \(0.973203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.16435e8 | 0.417323 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.39129e8 | 1.77037 | 0.885184 | − | 0.465240i | \(-0.154032\pi\) | ||||
0.885184 | + | 0.465240i | \(0.154032\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.43040e8i | 0.632323i | 0.948705 | + | 0.316162i | \(0.102394\pi\) | ||||
−0.948705 | + | 0.316162i | \(0.897606\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.03960e9i | − 1.83298i | −0.400054 | − | 0.916492i | \(-0.631009\pi\) | ||||
0.400054 | − | 0.916492i | \(-0.368991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.83087e8 | −0.488261 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.39083e8 | −0.234697 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.99762e8i | 1.65077i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 6.51456e8i | − 1.03031i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.41315e8 | −0.373593 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.10022e9 | 1.66756 | 0.833779 | − | 0.552098i | \(-0.186173\pi\) | ||||
0.833779 | + | 0.552098i | \(0.186173\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.94359e8i | 0.288436i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.28272e9i | 1.82569i | 0.408302 | + | 0.912847i | \(0.366121\pi\) | ||||
−0.408302 | + | 0.912847i | \(0.633879\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.53034e7 | −0.0770997 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.05089e9 | −1.43522 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.02107e8i | 0.939451i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.25822e9i | 1.61660i | 0.588770 | + | 0.808301i | \(0.299612\pi\) | ||||
−0.588770 | + | 0.808301i | \(0.700388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.35371e8 | −0.170465 | −0.0852327 | − | 0.996361i | \(-0.527163\pi\) | ||||
−0.0852327 | + | 0.996361i | \(0.527163\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.88445e8 | 0.232600 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.49221e8i | 1.02756i | 0.857921 | + | 0.513782i | \(0.171756\pi\) | ||||
−0.857921 | + | 0.513782i | \(0.828244\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.55142e8i | 0.413107i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.20121e8 | −0.251091 | −0.125546 | − | 0.992088i | \(-0.540068\pi\) | ||||
−0.125546 | + | 0.992088i | \(0.540068\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.73631e8 | 0.641738 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.33807e8i | 0.146827i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.66505e8i | 0.492635i | 0.969189 | + | 0.246317i | \(0.0792205\pi\) | ||||
−0.969189 | + | 0.246317i | \(0.920779\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.99191e8 | −0.517220 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.86983e8 | −0.291774 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.98453e8i | 0.297780i | 0.988854 | + | 0.148890i | \(0.0475700\pi\) | ||||
−0.988854 | + | 0.148890i | \(0.952430\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.10984e8i | 0.683385i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.46218e9 | −1.37964 | −0.689818 | − | 0.723983i | \(-0.742309\pi\) | ||||
−0.689818 | + | 0.723983i | \(0.742309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.68911e7 | 0.0341731 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 1.58702e9i | − 1.44340i | −0.692206 | − | 0.721700i | \(-0.743361\pi\) | ||||
0.692206 | − | 0.721700i | \(-0.256639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.79302e8i | 0.157252i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.14439e8 | 0.270840 | 0.135420 | − | 0.990788i | \(-0.456762\pi\) | ||||
0.135420 | + | 0.990788i | \(0.456762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.85630e9 | −1.57047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1.03854e9i | − 0.863078i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8.52757e8i | − 0.684004i | −0.939699 | − | 0.342002i | \(-0.888895\pi\) | ||||
0.939699 | − | 0.342002i | \(-0.111105\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.21295e8 | 0.410846 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.92522e8 | 0.536325 | 0.268163 | − | 0.963374i | \(-0.413584\pi\) | ||||
0.268163 | + | 0.963374i | \(0.413584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.63936e9i | 2.00877i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.01632e9i | − 0.747221i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.17357e8 | −0.446174 | −0.223087 | − | 0.974799i | \(-0.571613\pi\) | ||||
−0.223087 | + | 0.974799i | \(0.571613\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.05898e8 | 0.146287 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.68763e8i | 0.536992i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.43727e8i | 0.0970651i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.65512e9 | 1.09921 | 0.549604 | − | 0.835425i | \(-0.314779\pi\) | ||||
0.549604 | + | 0.835425i | \(0.314779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.01472e7 | 0.0458166 | 0.0229083 | − | 0.999738i | \(-0.492707\pi\) | ||||
0.0229083 | + | 0.999738i | \(0.492707\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 3.49045e8i | − 0.224228i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.33079e9i | − 0.827203i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.85394e8 | −0.602573 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.81387e9 | 1.09128 | 0.545640 | − | 0.838020i | \(-0.316287\pi\) | ||||
0.545640 | + | 0.838020i | \(0.316287\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.59970e9i | 1.53892i | 0.638695 | + | 0.769460i | \(0.279475\pi\) | ||||
−0.638695 | + | 0.769460i | \(0.720525\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.72477e9i | 1.56187i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.67431e9 | 0.944517 | 0.472258 | − | 0.881460i | \(-0.343439\pi\) | ||||
0.472258 | + | 0.881460i | \(0.343439\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.15185e8 | −0.230519 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.52711e8i | 0.138105i | 0.997613 | + | 0.0690527i | \(0.0219977\pi\) | ||||
−0.997613 | + | 0.0690527i | \(0.978002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.05569e8i | 0.108863i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.55311e8 | −0.393789 | −0.196895 | − | 0.980425i | \(-0.563086\pi\) | ||||
−0.196895 | + | 0.980425i | \(0.563086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.61031e9 | 1.33991 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.75597e8i | 0.341463i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 1.51584e8i | − 0.0742928i | −0.999310 | − | 0.0371464i | \(-0.988173\pi\) | ||||
0.999310 | − | 0.0371464i | \(-0.0118268\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.13687e8 | −0.247944 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.78405e8 | −0.370043 | −0.185022 | − | 0.982734i | \(-0.559236\pi\) | ||||
−0.185022 | + | 0.982734i | \(0.559236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.41052e9i | − 1.12870i | −0.825536 | − | 0.564349i | \(-0.809127\pi\) | ||||
0.825536 | − | 0.564349i | \(-0.190873\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.76192e9i | − 0.800527i | −0.916400 | − | 0.400264i | \(-0.868919\pi\) | ||||
0.916400 | − | 0.400264i | \(-0.131081\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.13783e8 | −0.319493 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.06149e9 | 0.468105 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.37584e8i | − 0.407377i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 4.15100e8i | − 0.175121i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.43811e8 | −0.267661 | −0.133830 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133830 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.55252e9 | −1.04583 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.67910e8i | 0.390859i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.16421e9i | 1.24141i | 0.784045 | + | 0.620704i | \(0.213153\pi\) | ||||
−0.784045 | + | 0.620704i | \(0.786847\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.69665e9 | 0.656160 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.62406e9 | 1.38169 | 0.690844 | − | 0.723004i | \(-0.257239\pi\) | ||||
0.690844 | + | 0.723004i | \(0.257239\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.93809e9i | − 0.728467i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1.76970e9i | − 0.646624i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.35483e9 | 0.488128 | 0.244064 | − | 0.969759i | \(-0.421519\pi\) | ||||
0.244064 | + | 0.969759i | \(0.421519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.81160e8 | 0.0998899 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.66389e9i | 1.63403i | 0.576616 | + | 0.817015i | \(0.304373\pi\) | ||||
−0.576616 | + | 0.817015i | \(0.695627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.80650e8i | 0.266029i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.34292e9 | 0.451376 | 0.225688 | − | 0.974200i | \(-0.427537\pi\) | ||||
0.225688 | + | 0.974200i | \(0.427537\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.38826e9 | 0.791788 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.54016e8i | 0.246587i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.82519e9i | 0.580885i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.16959e9 | 0.681226 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.45400e9 | −0.450435 | −0.225217 | − | 0.974309i | \(-0.572309\pi\) | ||||
−0.225217 | + | 0.974309i | \(0.572309\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4.90309e8i | − 0.149870i | −0.997188 | − | 0.0749349i | \(-0.976125\pi\) | ||||
0.997188 | − | 0.0749349i | \(-0.0238749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 7.19470e9i | − 2.14129i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.65437e9 | −0.485889 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.11196e9 | −0.322299 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 6.55591e9i | − 1.87537i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 2.26823e9i | − 0.632086i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.17104e9 | 0.597182 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.82889e9 | −1.31116 | −0.655582 | − | 0.755124i | \(-0.727577\pi\) | ||||
−0.655582 | + | 0.755124i | \(0.727577\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 3.11766e9i | − 0.835660i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.08793e9i | − 0.806698i | −0.915046 | − | 0.403349i | \(-0.867846\pi\) | ||||
0.915046 | − | 0.403349i | \(-0.132154\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.92489e9 | 0.496482 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.84483e9 | −0.724479 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 2.34939e9i | − 0.590768i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.09889e9i | 1.00502i | 0.864573 | + | 0.502508i | \(0.167589\pi\) | ||||
−0.864573 | + | 0.502508i | \(0.832411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.35478e9 | −0.570177 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.68611e9 | 0.642324 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 4.97105e9i | − 1.17400i | −0.809587 | − | 0.587001i | \(-0.800309\pi\) | ||||
0.809587 | − | 0.587001i | \(-0.199691\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.67846e8i | 0.0617085i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.71316e9 | −0.844988 | −0.422494 | − | 0.906366i | \(-0.638845\pi\) | ||||
−0.422494 | + | 0.906366i | \(0.638845\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.36205e9 | −0.530961 | −0.265481 | − | 0.964116i | \(-0.585531\pi\) | ||||
−0.265481 | + | 0.964116i | \(0.585531\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.69232e9i | − 0.597840i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1.81146e8i | − 0.0392566i | −0.999807 | − | 0.0196283i | \(-0.993752\pi\) | ||||
0.999807 | − | 0.0196283i | \(-0.00624828\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.02625e8 | 0.107614 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.88754e9 | −0.610818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.17059e9i | 0.453668i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.31976e9i | 0.473380i | 0.971585 | + | 0.236690i | \(0.0760626\pi\) | ||||
−0.971585 | + | 0.236690i | \(0.923937\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.05607e10 | −2.12957 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.51204e9 | 0.500576 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 2.27806e9i | − 0.448615i | −0.974518 | − | 0.224308i | \(-0.927988\pi\) | ||||
0.974518 | − | 0.224308i | \(-0.0720120\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.99715e9i | 0.384150i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.88253e9 | 0.928220 | 0.464110 | − | 0.885778i | \(-0.346374\pi\) | ||||
0.464110 | + | 0.885778i | \(0.346374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.74758e9 | −1.26791 | −0.633954 | − | 0.773371i | \(-0.718569\pi\) | ||||
−0.633954 | + | 0.773371i | \(0.718569\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.03244e9i | − 0.191758i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 9.05928e9i | − 1.64412i | −0.569401 | − | 0.822060i | \(-0.692825\pi\) | ||||
0.569401 | − | 0.822060i | \(-0.307175\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.01056e9 | −0.181301 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.58403e9 | 0.813024 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.48777e9i | 1.48827i | 0.668029 | + | 0.744135i | \(0.267138\pi\) | ||||
−0.668029 | + | 0.744135i | \(0.732862\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.34407e9i | 0.401766i | 0.979615 | + | 0.200883i | \(0.0643810\pi\) | ||||
−0.979615 | + | 0.200883i | \(0.935619\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.01541e9 | 0.172077 | 0.0860384 | − | 0.996292i | \(-0.472579\pi\) | ||||
0.0860384 | + | 0.996292i | \(0.472579\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.40001e9 | −0.234591 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 6.04473e9i | − 1.00154i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.94281e9i | − 0.638807i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.95799e9 | 1.11482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.01911e9 | 1.11219 | 0.556095 | − | 0.831119i | \(-0.312299\pi\) | ||||
0.556095 | + | 0.831119i | \(0.312299\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 4.99939e9i | − 0.783437i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 5.45265e9i | − 0.835833i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.55974e9 | 0.388099 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.52776e9 | −0.679016 | −0.339508 | − | 0.940603i | \(-0.610261\pi\) | ||||
−0.339508 | + | 0.940603i | \(0.610261\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.63094e9i | 1.28032i | 0.768240 | + | 0.640162i | \(0.221133\pi\) | ||||
−0.768240 | + | 0.640162i | \(0.778867\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.57401e9i | 0.373632i | 0.982395 | + | 0.186816i | \(0.0598169\pi\) | ||||
−0.982395 | + | 0.186816i | \(0.940183\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.81454e9 | 0.834946 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.75145e9 | −0.532925 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.31827e9i | 1.30960i | 0.755802 | + | 0.654800i | \(0.227247\pi\) | ||||
−0.755802 | + | 0.654800i | \(0.772753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.45445e9i | 0.475226i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.04422e10 | −1.42133 | −0.710663 | − | 0.703532i | \(-0.751605\pi\) | ||||
−0.710663 | + | 0.703532i | \(0.751605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.04761e10 | −1.41090 | −0.705449 | − | 0.708761i | \(-0.749254\pi\) | ||||
−0.705449 | + | 0.708761i | \(0.749254\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 6.74628e9i | − 0.899015i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 5.28211e9i | − 0.689234i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.26327e9 | 0.421368 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.00654e10 | −1.28618 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 1.38891e10i | − 1.75639i | −0.478299 | − | 0.878197i | \(-0.658746\pi\) | ||||
0.478299 | − | 0.878197i | \(-0.341254\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 7.48893e8i | − 0.0927598i | −0.998924 | − | 0.0463799i | \(-0.985232\pi\) | ||||
0.998924 | − | 0.0463799i | \(-0.0147685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.60398e9 | −0.441813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.62251e9 | −0.924875 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.15581e10i | − 1.38808i | −0.719938 | − | 0.694038i | \(-0.755830\pi\) | ||||
0.719938 | − | 0.694038i | \(-0.244170\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 2.40817e9i | − 0.283360i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.45153e9 | 0.634967 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.34337e8 | 0.0385489 | 0.0192744 | − | 0.999814i | \(-0.493864\pi\) | ||||
0.0192744 | + | 0.999814i | \(0.493864\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.40059e9i | − 0.159862i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.78709e10i | 1.99909i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.27047e9 | 0.694433 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.55383e9 | −0.608948 | −0.304474 | − | 0.952521i | \(-0.598481\pi\) | ||||
−0.304474 | + | 0.952521i | \(0.598481\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.02133e10i | − 1.10872i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.42700e9i | − 0.471131i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.30817e10 | −1.37849 | −0.689243 | − | 0.724530i | \(-0.742057\pi\) | ||||
−0.689243 | + | 0.724530i | \(0.742057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.39822e9 | 0.354575 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.96086e10i | − 2.02597i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.69363e9i | 0.880814i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.10847e10 | 1.11217 | 0.556085 | − | 0.831125i | \(-0.312303\pi\) | ||||
0.556085 | + | 0.831125i | \(0.312303\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.04012e9 | −0.401440 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.40989e9i | 0.532358i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7.79416e9i | − 0.752314i | −0.926556 | − | 0.376157i | \(-0.877245\pi\) | ||||
0.926556 | − | 0.376157i | \(-0.122755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.41896e9 | 0.607790 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 6.83552e9i | − 0.641073i | −0.947236 | − | 0.320537i | \(-0.896137\pi\) | ||||
0.947236 | − | 0.320537i | \(-0.103863\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.39869e9i | 0.496767i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.73862e10 | −1.58471 | −0.792356 | − | 0.610059i | \(-0.791146\pi\) | ||||
−0.792356 | + | 0.610059i | \(0.791146\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.90254e9 | −0.894094 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 2.25537e9i | − 0.201724i | −0.994900 | − | 0.100862i | \(-0.967840\pi\) | ||||
0.994900 | − | 0.100862i | \(-0.0321600\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.17662e9i | − 0.366609i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.59622e9 | 0.225764 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.05027e10 | −1.76632 | −0.883162 | − | 0.469068i | \(-0.844590\pi\) | ||||
−0.883162 | + | 0.469068i | \(0.844590\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.35051e9i | 0.200623i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 2.57872e8i | − 0.0216057i | −0.999942 | − | 0.0108029i | \(-0.996561\pi\) | ||||
0.999942 | − | 0.0108029i | \(-0.00343872\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.32078e9 | 0.607731 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.34452e10 | −1.10591 | −0.552957 | − | 0.833210i | \(-0.686501\pi\) | ||||
−0.552957 | + | 0.833210i | \(0.686501\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.21605e10i | 0.991096i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.46035e10i | − 1.16862i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.28541e9 | −0.657009 | −0.328505 | − | 0.944502i | \(-0.606545\pi\) | ||||
−0.328505 | + | 0.944502i | \(0.606545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.41177e10 | 1.10936 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.43430e10i | − 1.11689i | −0.829540 | − | 0.558447i | \(-0.811397\pi\) | ||||
0.829540 | − | 0.558447i | \(-0.188603\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 3.62803e9i | − 0.277458i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.62319e10 | 1.98814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.33851e10 | −1.00541 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 1.46170e9i | − 0.108816i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.83137e9i | − 0.280184i | −0.990139 | − | 0.140092i | \(-0.955260\pi\) | ||||
0.990139 | − | 0.140092i | \(-0.0447398\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.09678e10 | 0.794970 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.03233e9 | 0.0741653 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.52797e10i | 1.80018i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.95859e9i | − 0.137038i | −0.997650 | − | 0.0685188i | \(-0.978173\pi\) | ||||
0.997650 | − | 0.0685188i | \(-0.0218273\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.24957e10 | −0.866658 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.74327e9 | 0.601119 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.80636e10i | − 1.23112i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.03234e10i | 0.691455i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.07415e9 | −0.137727 | −0.0688637 | − | 0.997626i | \(-0.521937\pi\) | ||||
−0.0688637 | + | 0.997626i | \(0.521937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.71508e9 | −0.376227 | −0.188113 | − | 0.982147i | \(-0.560237\pi\) | ||||
−0.188113 | + | 0.982147i | \(0.560237\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.67245e9i | − 0.500746i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 9.42208e9i | − 0.604463i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.51764e9 | −0.223747 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.82748e10 | 1.78319 | 0.891596 | − | 0.452832i | \(-0.149586\pi\) | ||||
0.891596 | + | 0.452832i | \(0.149586\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.09283e9i | 0.130868i | 0.997857 | + | 0.0654342i | \(0.0208432\pi\) | ||||
−0.997857 | + | 0.0654342i | \(0.979157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.71453e9i | − 0.228368i | −0.993460 | − | 0.114184i | \(-0.963575\pi\) | ||||
0.993460 | − | 0.114184i | \(-0.0364253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.37924e9 | −0.206005 | −0.103003 | − | 0.994681i | \(-0.532845\pi\) | ||||
−0.103003 | + | 0.994681i | \(0.532845\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.93130e9 | 0.479447 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.48635e10i | 0.890972i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 5.42621e9i | − 0.319858i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.64907e10 | −0.963990 | −0.481995 | − | 0.876174i | \(-0.660088\pi\) | ||||
−0.481995 | + | 0.876174i | \(0.660088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.17350e10 | −0.680297 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.12158e10i | − 0.644812i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.49774e9i | − 0.141239i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.36736e9 | −0.0766841 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.89634e10 | 1.05478 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.77028e9i | 0.263162i | 0.991305 | + | 0.131581i | \(0.0420053\pi\) | ||||
−0.991305 | + | 0.131581i | \(0.957995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.61514e10i | 0.876554i | 0.898840 | + | 0.438277i | \(0.144411\pi\) | ||||
−0.898840 | + | 0.438277i | \(0.855589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.41593e8 | 0.0183879 | 0.00919397 | − | 0.999958i | \(-0.497073\pi\) | ||||
0.00919397 | + | 0.999958i | \(0.497073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.31824e9 | 0.497534 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 6.07878e9i | − 0.321943i | −0.986959 | − | 0.160971i | \(-0.948537\pi\) | ||||
0.986959 | − | 0.160971i | \(-0.0514627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.31071e9i | 0.380972i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.77696e10 | −0.918562 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.35590e10 | 0.695289 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 5.21290e9i | − 0.265173i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.23852e10i | 0.620020i | 0.950733 | + | 0.310010i | \(0.100332\pi\) | ||||
−0.950733 | + | 0.310010i | \(0.899668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.01883e9 | −0.100262 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.37801e10 | −0.678949 | −0.339475 | − | 0.940615i | \(-0.610249\pi\) | ||||
−0.339475 | + | 0.940615i | \(0.610249\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.89296e9i | − 0.0925292i | −0.998929 | − | 0.0462646i | \(-0.985268\pi\) | ||||
0.998929 | − | 0.0462646i | \(-0.0147317\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.23912e9i | 0.203959i | 0.994787 | + | 0.101979i | \(0.0325176\pi\) | ||||
−0.994787 | + | 0.101979i | \(0.967482\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.88633e8 | −0.0328724 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.02585e9 | 0.0959480 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.83419e10i | 0.861913i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1.83864e10i | − 0.850598i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.04725e10 | 0.939751 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.48605e10 | −0.676855 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3.34697e9i | − 0.151267i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 9.51367e9i | − 0.423372i | −0.977338 | − | 0.211686i | \(-0.932105\pi\) | ||||
0.977338 | − | 0.211686i | \(-0.0678955\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.40334e9 | 0.282770 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.16235e10 | −0.509359 | −0.254680 | − | 0.967025i | \(-0.581970\pi\) | ||||
−0.254680 | + | 0.967025i | \(0.581970\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.18399e10i | 0.949736i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.93861e10i | 0.830229i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.22943e9 | 0.392257 | 0.196128 | − | 0.980578i | \(-0.437163\pi\) | ||||
0.196128 | + | 0.980578i | \(0.437163\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.30196e9 | 0.0970931 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.36172e10i | 1.40720i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 5.84374e9i | − 0.240942i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.09353e10 | 1.67511 | 0.837555 | − | 0.546353i | \(-0.183984\pi\) | ||||
0.837555 | + | 0.546353i | \(0.183984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.18174e10 | 0.886094 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.53565e10i | − 1.02212i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1.75085e9i | − 0.0695281i | −0.999396 | − | 0.0347641i | \(-0.988932\pi\) | ||||
0.999396 | − | 0.0347641i | \(-0.0110680\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.26207e9 | 0.365072 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.91102e9 | 0.231259 | 0.115630 | − | 0.993292i | \(-0.463111\pi\) | ||||
0.115630 | + | 0.993292i | \(0.463111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.87058e10i | 1.89143i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.26089e10i | − 0.865077i | −0.901616 | − | 0.432538i | \(-0.857618\pi\) | ||||
0.901616 | − | 0.432538i | \(-0.142382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.53675e10 | −1.72311 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.80692e10 | −1.05827 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1.11773e10i | − 0.418322i | −0.977881 | − | 0.209161i | \(-0.932927\pi\) | ||||
0.977881 | − | 0.209161i | \(-0.0670733\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.64334e9i | 0.281898i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.84343e9 | −0.140719 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.84868e10 | 1.76235 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.75525e9i | 0.135502i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.55518e10i | 0.553078i | 0.961003 | + | 0.276539i | \(0.0891875\pi\) | ||||
−0.961003 | + | 0.276539i | \(0.910812\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.69936e10 | 0.953075 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.34508e9 | 0.292525 | 0.146263 | − | 0.989246i | \(-0.453276\pi\) | ||||
0.146263 | + | 0.989246i | \(0.453276\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.68291e9i | − 0.0933709i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 9.85180e9i | − 0.337975i | −0.985618 | − | 0.168988i | \(-0.945950\pi\) | ||||
0.985618 | − | 0.168988i | \(-0.0540498\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.57193e10 | −1.55726 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.75893e10 | −0.594850 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 3.70884e10i | − 1.24538i | −0.782470 | − | 0.622688i | \(-0.786041\pi\) | ||||
0.782470 | − | 0.622688i | \(-0.213959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.51551e9i | 0.215694i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.74944e10 | 0.575057 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.43526e9 | 0.210043 | 0.105022 | − | 0.994470i | \(-0.466509\pi\) | ||||
0.105022 | + | 0.994470i | \(0.466509\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 2.97059e10i | − 0.962765i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.23071e10i | − 0.393299i | −0.980474 | − | 0.196650i | \(-0.936994\pi\) | ||||
0.980474 | − | 0.196650i | \(-0.0630062\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.24768e9 | 0.166528 |
(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 | 600.8.f.d.49.1 | 2 | ||
5.2 | odd | 4 | 600.8.a.a.1.1 | 1 | |||
5.3 | odd | 4 | 24.8.a.c.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 600.8.f.d.49.2 | 2 | ||
15.8 | even | 4 | 72.8.a.b.1.1 | 1 | |||
20.3 | even | 4 | 48.8.a.c.1.1 | 1 | |||
40.3 | even | 4 | 192.8.a.k.1.1 | 1 | |||
40.13 | odd | 4 | 192.8.a.c.1.1 | 1 | |||
60.23 | odd | 4 | 144.8.a.d.1.1 | 1 | |||
120.53 | even | 4 | 576.8.a.t.1.1 | 1 | |||
120.83 | odd | 4 | 576.8.a.s.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.8.a.c.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
48.8.a.c.1.1 | 1 | 20.3 | even | 4 | |||
72.8.a.b.1.1 | 1 | 15.8 | even | 4 | |||
144.8.a.d.1.1 | 1 | 60.23 | odd | 4 | |||
192.8.a.c.1.1 | 1 | 40.13 | odd | 4 | |||
192.8.a.k.1.1 | 1 | 40.3 | even | 4 | |||
576.8.a.s.1.1 | 1 | 120.83 | odd | 4 | |||
576.8.a.t.1.1 | 1 | 120.53 | even | 4 | |||
600.8.a.a.1.1 | 1 | 5.2 | odd | 4 | |||
600.8.f.d.49.1 | 2 | 1.1 | even | 1 | trivial | ||
600.8.f.d.49.2 | 2 | 5.4 | even | 2 | inner |