Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(1,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(53.8889634572\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 336.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −64.0000 | −1.14487 | −0.572433 | − | 0.819951i | \(-0.694000\pi\) | ||||
−0.572433 | + | 0.819951i | \(0.694000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 54.0000 | 0.134559 | 0.0672794 | − | 0.997734i | \(-0.478568\pi\) | ||||
0.0672794 | + | 0.997734i | \(0.478568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 738.000 | 1.21115 | 0.605575 | − | 0.795788i | \(-0.292943\pi\) | ||||
0.605575 | + | 0.795788i | \(0.292943\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 576.000 | 0.660989 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −848.000 | −0.711662 | −0.355831 | − | 0.934550i | \(-0.615802\pi\) | ||||
−0.355831 | + | 0.934550i | \(0.615802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1604.00 | 1.01934 | 0.509672 | − | 0.860369i | \(-0.329767\pi\) | ||||
0.509672 | + | 0.860369i | \(0.329767\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 441.000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3670.00 | 1.44659 | 0.723297 | − | 0.690537i | \(-0.242626\pi\) | ||||
0.723297 | + | 0.690537i | \(0.242626\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 971.000 | 0.310720 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4330.00 | −0.956077 | −0.478039 | − | 0.878339i | \(-0.658652\pi\) | ||||
−0.478039 | + | 0.878339i | \(0.658652\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4760.00 | 0.889616 | 0.444808 | − | 0.895626i | \(-0.353272\pi\) | ||||
0.444808 | + | 0.895626i | \(0.353272\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −486.000 | −0.0776875 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3136.00 | 0.432719 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2094.00 | −0.251462 | −0.125731 | − | 0.992064i | \(-0.540128\pi\) | ||||
−0.125731 | + | 0.992064i | \(0.540128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6642.00 | −0.699258 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6116.00 | −0.568209 | −0.284104 | − | 0.958793i | \(-0.591696\pi\) | ||||
−0.284104 | + | 0.958793i | \(0.591696\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7916.00 | −0.652882 | −0.326441 | − | 0.945218i | \(-0.605849\pi\) | ||||
−0.326441 | + | 0.945218i | \(0.605849\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5184.00 | −0.381622 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6572.00 | −0.433963 | −0.216982 | − | 0.976176i | \(-0.569621\pi\) | ||||
−0.216982 | + | 0.976176i | \(0.569621\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7632.00 | 0.410878 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7894.00 | −0.386018 | −0.193009 | − | 0.981197i | \(-0.561825\pi\) | ||||
−0.193009 | + | 0.981197i | \(0.561825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3456.00 | −0.154052 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14436.0 | −0.588518 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 41664.0 | 1.55823 | 0.779114 | − | 0.626882i | \(-0.215669\pi\) | ||||
0.779114 | + | 0.626882i | \(0.215669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −26570.0 | −0.914254 | −0.457127 | − | 0.889401i | \(-0.651122\pi\) | ||||
−0.457127 | + | 0.889401i | \(0.651122\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −47232.0 | −1.38661 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 41736.0 | 1.13586 | 0.567929 | − | 0.823078i | \(-0.307745\pi\) | ||||
0.567929 | + | 0.823078i | \(0.307745\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −33030.0 | −0.835191 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −83574.0 | −1.96755 | −0.983774 | − | 0.179412i | \(-0.942580\pi\) | ||||
−0.983774 | + | 0.179412i | \(0.942580\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −42314.0 | −0.929345 | −0.464672 | − | 0.885483i | \(-0.653828\pi\) | ||||
−0.464672 | + | 0.885483i | \(0.653828\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8739.00 | −0.179394 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2646.00 | −0.0508584 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −508.000 | −0.00915790 | −0.00457895 | − | 0.999990i | \(-0.501458\pi\) | ||||
−0.00457895 | + | 0.999990i | \(0.501458\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8364.00 | 0.133266 | 0.0666329 | − | 0.997778i | \(-0.478774\pi\) | ||||
0.0666329 | + | 0.997778i | \(0.478774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54272.0 | 0.814758 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 38970.0 | 0.551991 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −49220.0 | −0.658668 | −0.329334 | − | 0.944213i | \(-0.606824\pi\) | ||||
−0.329334 | + | 0.944213i | \(0.606824\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −36162.0 | −0.457772 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −42840.0 | −0.513620 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −102656. | −1.16701 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 159670. | 1.72303 | 0.861517 | − | 0.507728i | \(-0.169515\pi\) | ||||
0.861517 | + | 0.507728i | \(0.169515\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4374.00 | 0.0448529 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −67020.0 | −0.653734 | −0.326867 | − | 0.945070i | \(-0.605993\pi\) | ||||
−0.326867 | + | 0.945070i | \(0.605993\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −165768. | −1.53960 | −0.769800 | − | 0.638286i | \(-0.779644\pi\) | ||||
−0.769800 | + | 0.638286i | \(0.779644\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −28224.0 | −0.249830 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −103146. | −0.870949 | −0.435475 | − | 0.900201i | \(-0.643419\pi\) | ||||
−0.435475 | + | 0.900201i | \(0.643419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 60094.0 | 0.484468 | 0.242234 | − | 0.970218i | \(-0.422120\pi\) | ||||
0.242234 | + | 0.970218i | \(0.422120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18846.0 | 0.145182 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −126246. | −0.930083 | −0.465041 | − | 0.885289i | \(-0.653961\pi\) | ||||
−0.465041 | + | 0.885289i | \(0.653961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −234880. | −1.65616 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 59778.0 | 0.403717 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 41552.0 | 0.268983 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −158135. | −0.981894 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 55044.0 | 0.328055 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 137856. | 0.789134 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −308636. | −1.69800 | −0.848999 | − | 0.528394i | \(-0.822794\pi\) | ||||
−0.848999 | + | 0.528394i | \(0.822794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 71244.0 | 0.376942 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 61012.0 | 0.310625 | 0.155313 | − | 0.987865i | \(-0.450361\pi\) | ||||
0.155313 | + | 0.987865i | \(0.450361\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −78596.0 | −0.385275 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 46656.0 | 0.220330 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −317242. | −1.44407 | −0.722037 | − | 0.691855i | \(-0.756794\pi\) | ||||
−0.722037 | + | 0.691855i | \(0.756794\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7236.00 | 0.0317659 | 0.0158830 | − | 0.999874i | \(-0.494944\pi\) | ||||
0.0158830 | + | 0.999874i | \(0.494944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 59148.0 | 0.250549 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 39852.0 | 0.162971 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 277120. | 1.09458 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −21609.0 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 126058. | 0.465163 | 0.232581 | − | 0.972577i | \(-0.425283\pi\) | ||||
0.232581 | + | 0.972577i | \(0.425283\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −200296. | −0.714875 | −0.357437 | − | 0.933937i | \(-0.616349\pi\) | ||||
−0.357437 | + | 0.933937i | \(0.616349\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −68688.0 | −0.237221 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −304640. | −1.01849 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 510894. | 1.65418 | 0.827088 | − | 0.562073i | \(-0.189996\pi\) | ||||
0.827088 | + | 0.562073i | \(0.189996\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 71046.0 | 0.222868 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −179830. | −0.546761 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21184.0 | −0.0624509 | −0.0312255 | − | 0.999512i | \(-0.509941\pi\) | ||||
−0.0312255 | + | 0.999512i | \(0.509941\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 31104.0 | 0.0889419 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 267180. | 0.741332 | 0.370666 | − | 0.928766i | \(-0.379129\pi\) | ||||
0.370666 | + | 0.928766i | \(0.379129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 173351. | 0.466885 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 129924. | 0.339781 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −91948.0 | −0.233575 | −0.116788 | − | 0.993157i | \(-0.537260\pi\) | ||||
−0.116788 | + | 0.993157i | \(0.537260\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −47579.0 | −0.117441 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −374976. | −0.899643 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 402826. | 0.939691 | 0.469845 | − | 0.882749i | \(-0.344310\pi\) | ||||
0.469845 | + | 0.882749i | \(0.344310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −796222. | −1.80650 | −0.903250 | − | 0.429116i | \(-0.858825\pi\) | ||||
−0.903250 | + | 0.429116i | \(0.858825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 239130. | 0.527845 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 134016. | 0.287890 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −45792.0 | −0.0957603 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 35721.0 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −474934. | −0.941998 | −0.470999 | − | 0.882134i | \(-0.656106\pi\) | ||||
−0.470999 | + | 0.882134i | \(0.656106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 716022. | 1.38367 | 0.691836 | − | 0.722055i | \(-0.256802\pi\) | ||||
0.691836 | + | 0.722055i | \(0.256802\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 425088. | 0.800557 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −221814. | −0.407215 | −0.203607 | − | 0.979053i | \(-0.565267\pi\) | ||||
−0.203607 | + | 0.979053i | \(0.565267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 333616. | 0.597192 | 0.298596 | − | 0.954380i | \(-0.403482\pi\) | ||||
0.298596 | + | 0.954380i | \(0.403482\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −375624. | −0.655788 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 212170. | 0.361363 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 391424. | 0.650523 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 297270. | 0.482198 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 86616.0 | 0.137162 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 176404. | 0.272774 | 0.136387 | − | 0.990656i | \(-0.456451\pi\) | ||||
0.136387 | + | 0.990656i | \(0.456451\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 752166. | 1.13596 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 506624. | 0.747463 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −233240. | −0.336243 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 380826. | 0.536558 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −625824. | −0.861929 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 125016. | 0.168346 | 0.0841731 | − | 0.996451i | \(-0.473175\pi\) | ||||
0.0841731 | + | 0.996451i | \(0.473175\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 78651.0 | 0.103573 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 272104. | 0.350486 | 0.175243 | − | 0.984525i | \(-0.443929\pi\) | ||||
0.175243 | + | 0.984525i | \(0.443929\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −325822. | −0.410574 | −0.205287 | − | 0.978702i | \(-0.565813\pi\) | ||||
−0.205287 | + | 0.978702i | \(0.565813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23814.0 | 0.0293631 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −534682. | −0.645217 | −0.322608 | − | 0.946533i | \(-0.604560\pi\) | ||||
−0.322608 | + | 0.946533i | \(0.604560\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 420608. | 0.496830 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4572.00 | 0.00528732 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.48512e6 | −1.68177 | −0.840887 | − | 0.541211i | \(-0.817966\pi\) | ||||
−0.840887 | + | 0.541211i | \(0.817966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.17689e6 | 1.30524 | 0.652622 | − | 0.757684i | \(-0.273669\pi\) | ||||
0.652622 | + | 0.757684i | \(0.273669\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −153664. | −0.163552 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.18375e6 | 1.23458 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −75276.0 | −0.0769411 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14080.0 | −0.0141065 | −0.00705324 | − | 0.999975i | \(-0.502245\pi\) | ||||
−0.00705324 | + | 0.999975i | \(0.502245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 198180. | 0.194652 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −488448. | −0.470401 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.86851e6 | −1.76466 | −0.882332 | − | 0.470627i | \(-0.844028\pi\) | ||||
−0.882332 | + | 0.470627i | \(0.844028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 102606. | 0.0950437 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −350730. | −0.318692 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −802890. | −0.715759 | −0.357879 | − | 0.933768i | \(-0.616500\pi\) | ||||
−0.357879 | + | 0.933768i | \(0.616500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 505216. | 0.441939 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 442980. | 0.380282 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −197448. | −0.166369 | −0.0831844 | − | 0.996534i | \(-0.526509\pi\) | ||||
−0.0831844 | + | 0.996534i | \(0.526509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.01928e6 | 1.67022 | 0.835109 | − | 0.550084i | \(-0.185404\pi\) | ||||
0.835109 | + | 0.550084i | \(0.185404\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 325458. | 0.264295 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 52434.0 | 0.0418101 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.57993e6 | 1.23720 | 0.618598 | − | 0.785708i | \(-0.287701\pi\) | ||||
0.618598 | + | 0.785708i | \(0.287701\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 385560. | 0.296539 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.44392e6 | 1.09088 | 0.545440 | − | 0.838150i | \(-0.316363\pi\) | ||||
0.545440 | + | 0.838150i | \(0.316363\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.68046e6 | 1.24727 | 0.623637 | − | 0.781714i | \(-0.285654\pi\) | ||||
0.623637 | + | 0.781714i | \(0.285654\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 923904. | 0.673775 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 299684. | 0.214763 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −700753. | −0.493538 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.43703e6 | −0.994794 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.31092e6 | −1.57259 | −0.786297 | − | 0.617849i | \(-0.788004\pi\) | ||||
−0.786297 | + | 0.617849i | \(0.788004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.66650e6 | −1.78396 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −39366.0 | −0.0258958 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.70846e6 | 1.75204 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 387884. | 0.246766 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 603180. | 0.377433 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.70048e6 | 1.04670 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 793964. | 0.480789 | 0.240395 | − | 0.970675i | \(-0.422723\pi\) | ||||
0.240395 | + | 0.970675i | \(0.422723\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.49191e6 | 0.888888 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.18376e6 | −0.694007 | −0.347004 | − | 0.937864i | \(-0.612801\pi\) | ||||
−0.347004 | + | 0.937864i | \(0.612801\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 994970. | 0.574049 | 0.287025 | − | 0.957923i | \(-0.407334\pi\) | ||||
0.287025 | + | 0.957923i | \(0.407334\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 254016. | 0.144240 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.84619e6 | 1.03188 | 0.515940 | − | 0.856625i | \(-0.327443\pi\) | ||||
0.515940 | + | 0.856625i | \(0.327443\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −233820. | −0.128649 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 928314. | 0.502843 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.36019e6 | −0.725427 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 716598. | 0.376329 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −540846. | −0.279708 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 322028. | 0.164023 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.55801e6 | 0.781629 | 0.390815 | − | 0.920469i | \(-0.372193\pi\) | ||||
0.390815 | + | 0.920469i | \(0.372193\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −169614. | −0.0838207 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.67110e6 | −1.30041 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.28798e6 | 1.57708 | 0.788541 | − | 0.614982i | \(-0.210837\pi\) | ||||
0.788541 | + | 0.614982i | \(0.210837\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.13621e6 | 0.536983 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 257040. | 0.119706 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.11392e6 | 0.956183 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.66137e6 | −1.63238 | −0.816188 | − | 0.577786i | \(-0.803917\pi\) | ||||
−0.816188 | + | 0.577786i | \(0.803917\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.76811e6 | −1.65600 | −0.827998 | − | 0.560730i | \(-0.810520\pi\) | ||||
−0.827998 | + | 0.560730i | \(0.810520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −538002. | −0.233086 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.97794e6 | 0.844842 | 0.422421 | − | 0.906400i | \(-0.361180\pi\) | ||||
0.422421 | + | 0.906400i | \(0.361180\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.34874e6 | 2.25258 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −373968. | −0.155297 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.17410e6 | −1.29982 | −0.649912 | − | 0.760009i | \(-0.725194\pi\) | ||||
−0.649912 | + | 0.760009i | \(0.725194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 96717.0 | 0.0390602 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.42321e6 | 0.566897 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.70810e6 | 1.06398 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.62163e6 | −1.40359 | −0.701793 | − | 0.712381i | \(-0.747617\pi\) | ||||
−0.701793 | + | 0.712381i | \(0.747617\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −495396. | −0.189403 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 386806. | 0.145901 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.65737e6 | −1.36112 | −0.680561 | − | 0.732692i | \(-0.738264\pi\) | ||||
−0.680561 | + | 0.732692i | \(0.738264\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.24070e6 | −0.455607 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.19554e6 | −1.15795 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.07802e6 | −0.385504 | −0.192752 | − | 0.981248i | \(-0.561741\pi\) | ||||
−0.192752 | + | 0.981248i | \(0.561741\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.77772e6 | 0.980340 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.86954e6 | −1.34792 | −0.673958 | − | 0.738770i | \(-0.735407\pi\) | ||||
−0.673958 | + | 0.738770i | \(0.735407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 169344. | 0.0582261 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −641196. | −0.217627 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.75845e6 | −1.25932 | −0.629658 | − | 0.776872i | \(-0.716805\pi\) | ||||
−0.629658 | + | 0.776872i | \(0.716805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.11216e6 | −1.02948 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −549108. | −0.179340 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 32512.0 | 0.0104846 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.47106e6 | −0.468440 | −0.234220 | − | 0.972184i | \(-0.575254\pi\) | ||||
−0.234220 | + | 0.972184i | \(0.575254\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 707364. | 0.222439 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.30313e6 | −1.64692 | −0.823458 | − | 0.567378i | \(-0.807958\pi\) | ||||
−0.823458 | + | 0.567378i | \(0.807958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.51288e6 | 1.07746 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −419904. | −0.127207 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −113076. | −0.0338364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.46984e6 | −1.91243 | −0.956215 | − | 0.292666i | \(-0.905458\pi\) | ||||
−0.956215 | + | 0.292666i | \(0.905458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.85518e6 | 0.833736 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.04154e6 | −0.588955 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −535296. | −0.152572 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −65124.0 | −0.0183401 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −554024. | −0.154168 | −0.0770839 | − | 0.997025i | \(-0.524561\pi\) | ||||
−0.0770839 | + | 0.997025i | \(0.524561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.37900e6 | −0.929143 | −0.464572 | − | 0.885536i | \(-0.653792\pi\) | ||||
−0.464572 | + | 0.885536i | \(0.653792\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −532332. | −0.144654 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −823408. | −0.221128 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.30193e6 | 0.345556 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −358668. | −0.0940913 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.90338e6 | −0.752854 | −0.376427 | − | 0.926446i | \(-0.622848\pi\) | ||||
−0.376427 | + | 0.926446i | \(0.622848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.05684e6 | −1.29616 | −0.648081 | − | 0.761571i | \(-0.724428\pi\) | ||||
−0.648081 | + | 0.761571i | \(0.724428\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.49408e6 | −0.631957 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.88668e6 | 1.47457 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.43257e6 | 0.602426 | 0.301213 | − | 0.953557i | \(-0.402608\pi\) | ||||
0.301213 | + | 0.953557i | \(0.402608\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.35832e6 | 0.570944 | 0.285472 | − | 0.958387i | \(-0.407850\pi\) | ||||
0.285472 | + | 0.958387i | \(0.407850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.15008e6 | 0.754087 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.13452e6 | −0.268562 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 798466. | 0.186913 | 0.0934567 | − | 0.995623i | \(-0.470208\pi\) | ||||
0.0934567 | + | 0.995623i | \(0.470208\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −330264. | −0.0764575 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.80266e6 | 0.412733 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.31437e6 | 0.524088 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.53337e6 | −0.791404 | −0.395702 | − | 0.918379i | \(-0.629499\pi\) | ||||
−0.395702 | + | 0.918379i | \(0.629499\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 618192. | 0.136959 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.98709e6 | −0.435477 | −0.217739 | − | 0.976007i | \(-0.569868\pi\) | ||||
−0.217739 | + | 0.976007i | \(0.569868\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.33175e6 | −1.37269 | −0.686343 | − | 0.727278i | \(-0.740785\pi\) | ||||
−0.686343 | + | 0.727278i | \(0.740785\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.74176e6 | 0.588027 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −274560. | −0.0582566 | −0.0291283 | − | 0.999576i | \(-0.509273\pi\) | ||||
−0.0291283 | + | 0.999576i | \(0.509273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.04506e6 | −0.429314 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.59805e6 | −0.955039 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −427464. | −0.0878510 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.55748e6 | 0.316730 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −639414. | −0.128673 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −933460. | −0.185890 | −0.0929452 | − | 0.995671i | \(-0.529628\pi\) | ||||
−0.0929452 | + | 0.995671i | \(0.529628\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.54537e6 | −0.304558 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.61847e6 | 0.315673 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.02189e7 | −1.97265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.05600e6 | 1.15708 | 0.578540 | − | 0.815654i | \(-0.303623\pi\) | ||||
0.578540 | + | 0.815654i | \(0.303623\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 190656. | 0.0360561 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.65757e6 | −0.310290 | −0.155145 | − | 0.987892i | \(-0.549584\pi\) | ||||
−0.155145 | + | 0.987892i | \(0.549584\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.67184e6 | 0.680403 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −279936. | −0.0513506 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.09513e6 | 0.743663 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.08804e6 | −0.734961 | −0.367480 | − | 0.930031i | \(-0.619780\pi\) | ||||
−0.367480 | + | 0.930031i | \(0.619780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.40462e6 | −0.428008 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.43036e6 | 1.30945 | 0.654726 | − | 0.755866i | \(-0.272784\pi\) | ||||
0.654726 | + | 0.755866i | \(0.272784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.28928e6 | 0.748438 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.56016e6 | −0.269556 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.51290e6 | −0.600996 | −0.300498 | − | 0.953782i | \(-0.597153\pi\) | ||||
−0.300498 | + | 0.953782i | \(0.597153\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.07339e6 | 0.351259 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.16932e6 | −0.196173 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.06092e7 | 1.76264 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −354888. | −0.0583936 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 827532. | 0.134855 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.81406e6 | 0.776994 | 0.388497 | − | 0.921450i | \(-0.372994\pi\) | ||||
0.388497 | + | 0.921450i | \(0.372994\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.42660e6 | 0.387921 | 0.193960 | − | 0.981009i | \(-0.437867\pi\) | ||||
0.193960 | + | 0.981009i | \(0.437867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 428211. | 0.0678047 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.03648e6 | −0.633106 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.03256e6 | 1.09263 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.37478e6 | 0.519409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.51361e6 | −0.688186 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.60134e6 | 0.997121 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.62543e6 | −0.542531 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 129654. | 0.0192227 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.82543e6 | 0.708831 | 0.354415 | − | 0.935088i | \(-0.384680\pi\) | ||||
0.354415 | + | 0.935088i | \(0.384680\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.16600e6 | 1.04298 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.84602e6 | −0.554651 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.34543e6 | −0.192262 | −0.0961310 | − | 0.995369i | \(-0.530647\pi\) | ||||
−0.0961310 | + | 0.995369i | \(0.530647\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.15217e6 | −0.304751 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.94532e6 | −0.974571 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24892.0 | 0.00346136 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.20614e6 | −0.166214 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −938438. | −0.128164 | −0.0640822 | − | 0.997945i | \(-0.520412\pi\) | ||||
−0.0640822 | + | 0.997945i | \(0.520412\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.84201e6 | −0.790738 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 412128. | 0.0552872 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.16124e7 | −1.54402 | −0.772008 | − | 0.635613i | \(-0.780747\pi\) | ||||
−0.772008 | + | 0.635613i | \(0.780747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.07974e6 | 1.06482 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.94876e6 | −0.899760 | −0.449880 | − | 0.893089i | \(-0.648533\pi\) | ||||
−0.449880 | + | 0.893089i | \(0.648533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.59412e6 | −0.332966 | −0.166483 | − | 0.986044i | \(-0.553241\pi\) | ||||
−0.166483 | + | 0.986044i | \(0.553241\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.27441e6 | 0.543863 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.56357e6 | 0.449485 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.51612e7 | −1.89581 | −0.947906 | − | 0.318551i | \(-0.896804\pi\) | ||||
−0.947906 | + | 0.318551i | \(0.896804\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.44420e6 | −0.798863 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −409836. | −0.0503697 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −426276. | −0.0519421 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.82579e6 | −0.462202 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.29826e6 | 0.155513 | 0.0777567 | − | 0.996972i | \(-0.475224\pi\) | ||||
0.0777567 | + | 0.996972i | \(0.475224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.63504e6 | 0.906824 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.99633e6 | 0.235105 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.15002e7 | 1.34298 | 0.671490 | − | 0.741014i | \(-0.265655\pi\) | ||||
0.671490 | + | 0.741014i | \(0.265655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.65933e6 | −0.307949 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.00254e6 | −0.344789 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.99854e6 | −1.13860 | −0.569298 | − | 0.822131i | \(-0.692785\pi\) | ||||
−0.569298 | + | 0.822131i | \(0.692785\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.05405e6 | 0.909553 | 0.454777 | − | 0.890606i | \(-0.349719\pi\) | ||||
0.454777 | + | 0.890606i | \(0.349719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.38062e6 | 0.378619 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.01206e7 | 1.12414 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.03667e6 | −0.444684 | −0.222342 | − | 0.974969i | \(-0.571370\pi\) | ||||
−0.222342 | + | 0.974969i | \(0.571370\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.90953e6 | −0.208633 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.85014e6 | −0.525595 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.60521e7 | 1.72536 | 0.862681 | − | 0.505748i | \(-0.168784\pi\) | ||||
0.862681 | + | 0.505748i | \(0.168784\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.52282e6 | −0.375580 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.34770e7 | 1.42522 | 0.712609 | − | 0.701561i | \(-0.247513\pi\) | ||||
0.712609 | + | 0.701561i | \(0.247513\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.73797e7 | 1.82312 | 0.911559 | − | 0.411170i | \(-0.134880\pi\) | ||||
0.911559 | + | 0.411170i | \(0.134880\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.67543e6 | −0.278397 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.41178e6 | 0.248953 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.18572e7 | −1.21417 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −779544. | −0.0791903 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.77571e6 | 0.178956 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.46908e7 | −1.46883 | −0.734416 | − | 0.678700i | \(-0.762544\pi\) | ||||
−0.734416 | + | 0.678700i | \(0.762544\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.58764e6 | −0.157486 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.97527e7 | 1.94398 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.77194e6 | 0.173021 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.76949e6 | −0.655849 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.60166e7 | 1.53966 | 0.769830 | − | 0.638249i | \(-0.220341\pi\) | ||||
0.769830 | + | 0.638249i | \(0.220341\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.48624e6 | −0.809446 | −0.404723 | − | 0.914439i | \(-0.632632\pi\) | ||||
−0.404723 | + | 0.914439i | \(0.632632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.55962e6 | −0.431548 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.85487e7 | 1.74202 | 0.871008 | − | 0.491269i | \(-0.163467\pi\) | ||||
0.871008 | + | 0.491269i | \(0.163467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.24986e6 | 0.209673 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.09916e6 | 0.194130 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.01271e6 | −0.276486 | −0.138243 | − | 0.990398i | \(-0.544146\pi\) | ||||
−0.138243 | + | 0.990398i | \(0.544146\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.90477e6 | −0.355625 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.42743e6 | −0.309782 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.06060e6 | 0.543628 | 0.271814 | − | 0.962350i | \(-0.412376\pi\) | ||||
0.271814 | + | 0.962350i | \(0.412376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.42899e7 | 1.27211 | 0.636057 | − | 0.771642i | \(-0.280564\pi\) | ||||
0.636057 | + | 0.771642i | \(0.280564\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.63242e6 | 0.497635 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.03014e6 | 0.441089 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.58911e7 | −1.38305 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.12514e6 | −0.0971948 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.43478e6 | −0.123021 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.29680e6 | −0.450792 | −0.225396 | − | 0.974267i | \(-0.572368\pi\) | ||||
−0.225396 | + | 0.974267i | \(0.572368\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −707859. | −0.0597981 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.18550e7 | 0.994096 | 0.497048 | − | 0.867723i | \(-0.334417\pi\) | ||||
0.497048 | + | 0.867723i | \(0.334417\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.82383e6 | −0.651246 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.44894e6 | −0.202353 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.65625e7 | 1.35854 | 0.679272 | − | 0.733886i | \(-0.262296\pi\) | ||||
0.679272 | + | 0.733886i | \(0.262296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.03035e7 | 1.65327 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.93240e6 | 0.237045 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.82577e6 | −0.467526 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.69748e6 | 0.374257 | 0.187128 | − | 0.982335i | \(-0.440082\pi\) | ||||
0.187128 | + | 0.982335i | \(0.440082\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −214326. | −0.0169528 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −463104. | −0.0363678 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.18637e6 | 0.404372 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.81214e6 | 0.372516 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.10890e7 | −1.62092 | −0.810458 | − | 0.585797i | \(-0.800781\pi\) | ||||
−0.810458 | + | 0.585797i | \(0.800781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.35878e6 | −0.256326 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.78547e6 | −0.286845 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.28398e6 | 0.247088 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.68683e7 | −1.26025 | −0.630123 | − | 0.776495i | \(-0.716996\pi\) | ||||
−0.630123 | + | 0.776495i | \(0.716996\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41148.0 | −0.00305263 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.74692e7 | 1.28691 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.55053e6 | −0.186580 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.33661e7 | 0.970972 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.19606e7 | 0.862844 | 0.431422 | − | 0.902150i | \(-0.358012\pi\) | ||||
0.431422 | + | 0.902150i | \(0.358012\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.12263e6 | 0.581914 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.05920e7 | −0.753583 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.20443e6 | −0.297072 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.20722e6 | 0.154885 | 0.0774427 | − | 0.996997i | \(-0.475325\pi\) | ||||
0.0774427 | + | 0.996997i | \(0.475325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.71277e6 | 0.464631 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −384494. | −0.0264320 | −0.0132160 | − | 0.999913i | \(-0.504207\pi\) | ||||
−0.0132160 | + | 0.999913i | \(0.504207\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.38298e6 | 0.0944270 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.25374e6 | 0.152840 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.04242e6 | −0.541721 | −0.270860 | − | 0.962619i | \(-0.587308\pi\) | ||||
−0.270860 | + | 0.962619i | \(0.587308\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.06538e7 | −0.712784 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.85291e6 | 0.123135 | 0.0615675 | − | 0.998103i | \(-0.480390\pi\) | ||||
0.0615675 | + | 0.998103i | \(0.480390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.06771e6 | −0.532549 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 677484. | 0.0444219 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.05415e6 | 0.329188 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.19326e7 | −0.772034 | −0.386017 | − | 0.922492i | \(-0.626149\pi\) | ||||
−0.386017 | + | 0.922492i | \(0.626149\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 126720. | 0.00814437 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.28189e7 | 0.818436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.55886e6 | −0.352570 | −0.176285 | − | 0.984339i | \(-0.556408\pi\) | ||||
−0.176285 | + | 0.984339i | \(0.556408\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.78362e6 | −0.112382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.71599e7 | 1.70007 | 0.850033 | − | 0.526730i | \(-0.176582\pi\) | ||||
0.850033 | + | 0.526730i | \(0.176582\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.94461e6 | −0.183112 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.39603e6 | 0.271586 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.07480e7 | 1.88725 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.75668e6 | −0.533978 | −0.266989 | − | 0.963700i | \(-0.586029\pi\) | ||||
−0.266989 | + | 0.963700i | \(0.586029\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.68166e7 | 1.01883 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.96856e6 | −0.238883 | −0.119441 | − | 0.992841i | \(-0.538110\pi\) | ||||
−0.119441 | + | 0.992841i | \(0.538110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.62196e6 | 0.276422 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −923454. | −0.0548735 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.81006e6 | −0.579200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.51300e6 | −0.264751 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.15657e6 | 0.183997 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.26972e7 | −1.89381 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.11112e7 | 1.21500 | 0.607501 | − | 0.794319i | \(-0.292172\pi\) | ||||
0.607501 | + | 0.794319i | \(0.292172\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.22601e6 | 0.413244 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.18605e6 | 0.351538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.96087e7 | −1.10730 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.54694e6 | −0.255154 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.95085e7 | −1.64552 | −0.822758 | − | 0.568392i | \(-0.807566\pi\) | ||||
−0.822758 | + | 0.568392i | \(0.807566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.57306e6 | 0.308835 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.98682e6 | −0.219556 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.28496e6 | −0.125052 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.15091e7 | 0.625968 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.77703e6 | 0.0960531 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13002.0 | 0.000698456 0 | 0.000349228 | − | 1.00000i | \(-0.499889\pi\) | ||||
0.000349228 | 1.00000i | \(0.499889\pi\) | ||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.61790e7 | −1.39766 | −0.698829 | − | 0.715289i | \(-0.746295\pi\) | ||||
−0.698829 | + | 0.715289i | \(0.746295\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.81735e7 | −0.964301 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.35578e6 | 0.0714980 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.26973e7 | −0.665511 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.92912e6 | −0.152591 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.21209e7 | 1.66314 | 0.831572 | − | 0.555417i | \(-0.187441\pi\) | ||||
0.831572 | + | 0.555417i | \(0.187441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.49758e7 | 1.28535 | 0.642674 | − | 0.766140i | \(-0.277825\pi\) | ||||
0.642674 | + | 0.766140i | \(0.277825\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −471906. | −0.0241391 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.09229e7 | 1.57223 | 0.786116 | − | 0.618079i | \(-0.212089\pi\) | ||||
0.786116 | + | 0.618079i | \(0.212089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.69047e7 | −0.854319 | −0.427160 | − | 0.904176i | \(-0.640486\pi\) | ||||
−0.427160 | + | 0.904176i | \(0.640486\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.42194e7 | −0.714295 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.03605e6 | −0.101666 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.70995e7 | −0.848726 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.47004e6 | −0.171207 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.77783e7 | −1.36239 | −0.681194 | − | 0.732103i | \(-0.738539\pi\) | ||||
−0.681194 | + | 0.732103i | \(0.738539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.76225e6 | −0.0859166 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.29953e7 | −0.629820 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.10945e7 | −0.534521 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.74862e6 | 0.371121 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.51241e7 | −0.720114 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.68498e6 | −0.363763 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.77504e7 | −0.835289 | −0.417645 | − | 0.908611i | \(-0.637144\pi\) | ||||
−0.417645 | + | 0.908611i | \(0.637144\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.31514e6 | −0.389004 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.50040e7 | 0.697838 | 0.348919 | − | 0.937153i | \(-0.386549\pi\) | ||||
0.348919 | + | 0.937153i | \(0.386549\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −910972. | −0.0421233 | −0.0210616 | − | 0.999778i | \(-0.506705\pi\) | ||||
−0.0210616 | + | 0.999778i | \(0.506705\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.69716e6 | −0.123993 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.48837e7 | −0.680275 | −0.340138 | − | 0.940376i | \(-0.610474\pi\) | ||||
−0.340138 | + | 0.940376i | \(0.610474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.88467e6 | 0.267413 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.30678e6 | 0.284944 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27432.0 | −0.00123228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.08012e7 | 1.37569 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.29333e7 | 0.574345 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.75494e6 | −0.298265 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.39951e7 | −1.05348 | −0.526738 | − | 0.850028i | \(-0.676585\pi\) | ||||
−0.526738 | + | 0.850028i | \(0.676585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.07983e7 | 0.907938 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.85879e6 | 0.341127 | 0.170563 | − | 0.985347i | \(-0.445441\pi\) | ||||
0.170563 | + | 0.985347i | \(0.445441\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.74586e7 | 0.753541 | 0.376771 | − | 0.926307i | \(-0.377034\pi\) | ||||
0.376771 | + | 0.926307i | \(0.377034\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.39985e7 | 1.02997 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 700092. | 0.0298776 | 0.0149388 | − | 0.999888i | \(-0.495245\pi\) | ||||
0.0149388 | + | 0.999888i | \(0.495245\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.51232e7 | 0.641783 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 354294. | 0.0149510 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.05415e7 | −0.442357 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.57809e7 | −1.07582 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.43761e7 | −1.01154 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.06108e7 | −0.850542 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.69411e6 | 0.274714 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.49096e6 | −0.142471 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.09582e7 | 2.06820 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.72979e7 | −1.50545 | −0.752724 | − | 0.658336i | \(-0.771261\pi\) | ||||
−0.752724 | + | 0.658336i | \(0.771261\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.42862e6 | −0.217911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.99873e7 | 1.19713 | 0.598564 | − | 0.801075i | \(-0.295738\pi\) | ||||
0.598564 | + | 0.801075i | \(0.295738\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 451656. | 0.0179321 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.53043e7 | −0.604312 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.98959e6 | −0.117405 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.78316e7 | 1.08705 | 0.543525 | − | 0.839393i | \(-0.317089\pi\) | ||||
0.543525 | + | 0.839393i | \(0.317089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.14568e6 | −0.277584 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.16776e7 | −2.38300 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.03327e6 | −0.0781343 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.34272e7 | −0.513200 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.88191e7 | 0.715418 | 0.357709 | − | 0.933833i | \(-0.383558\pi\) | ||||
0.357709 | + | 0.933833i | \(0.383558\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.85120e6 | 0.145620 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.06539e7 | 0.400685 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.93069e6 | 0.109633 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.39613e6 | 0.200786 | 0.100393 | − | 0.994948i | \(-0.467990\pi\) | ||||
0.100393 | + | 0.994948i | \(0.467990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.95473e6 | −0.331427 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.99942e7 | 1.47239 | 0.736194 | − | 0.676770i | \(-0.236621\pi\) | ||||
0.736194 | + | 0.676770i | \(0.236621\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.24457e7 | −0.821967 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.28614e6 | −0.0832768 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.09314e7 | −1.12079 | −0.560395 | − | 0.828225i | \(-0.689351\pi\) | ||||
−0.560395 | + | 0.828225i | \(0.689351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.12277e7 | −1.12558 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.66157e7 | −0.595756 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.55848e7 | −0.555865 | −0.277933 | − | 0.960601i | \(-0.589649\pi\) | ||||
−0.277933 | + | 0.960601i | \(0.589649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.03958e7 | 1.07846 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.10438e6 | 0.0742753 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.55449e7 | 0.545808 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.97155e6 | −0.208583 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.35483e6 | −0.290316 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.58254e7 | −1.58412 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.60131e7 | 0.894593 | 0.447297 | − | 0.894386i | \(-0.352387\pi\) | ||||
0.447297 | + | 0.894386i | \(0.352387\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.22417e7 | 0.418826 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.84316e6 | 0.300995 | 0.150497 | − | 0.988610i | \(-0.451912\pi\) | ||||
0.150497 | + | 0.988610i | \(0.451912\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −354564. | −0.0120064 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.44938e6 | −0.217273 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.70010e7 | −0.904988 | −0.452494 | − | 0.891768i | \(-0.649466\pi\) | ||||
−0.452494 | + | 0.891768i | \(0.649466\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.65788e6 | −0.0886296 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.86761e6 | 0.161489 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.69892e7 | 0.560775 | 0.280387 | − | 0.959887i | \(-0.409537\pi\) | ||||
0.280387 | + | 0.959887i | \(0.409537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.41961e7 | 0.466207 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.89825e6 | −0.0946985 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.90517e7 | −0.944455 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.77922e7 | −1.22241 | −0.611207 | − | 0.791470i | \(-0.709316\pi\) | ||||
−0.611207 | + | 0.791470i | \(0.709316\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.40221e7 | −0.451274 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.13514e7 | −0.683706 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.16921e7 | −1.64697 | −0.823487 | − | 0.567336i | \(-0.807974\pi\) | ||||
−0.823487 | + | 0.567336i | \(0.807974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.52653e6 | 0.0483939 |
(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 | 336.6.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 1008.6.a.z.1.1 | 1 | |||
4.3 | odd | 2 | 168.6.a.d.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 504.6.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.6.a.d.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
336.6.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
504.6.a.h.1.1 | 1 | 12.11 | even | 2 | |||
1008.6.a.z.1.1 | 1 | 3.2 | odd | 2 |