Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,8,Mod(1,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.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: | \(22.4917218349\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{46}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 46 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.78233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −213.552 | −0.764026 | −0.382013 | − | 0.924157i | \(-0.624769\pi\) | ||||
−0.382013 | + | 0.924157i | \(0.624769\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −882.207 | −0.972137 | −0.486069 | − | 0.873921i | \(-0.661569\pi\) | ||||
−0.486069 | + | 0.873921i | \(0.661569\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3586.62 | 0.812477 | 0.406239 | − | 0.913767i | \(-0.366840\pi\) | ||||
0.406239 | + | 0.913767i | \(0.366840\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3778.83 | 0.477041 | 0.238520 | − | 0.971137i | \(-0.423338\pi\) | ||||
0.238520 | + | 0.971137i | \(0.423338\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1610.41 | 0.0794996 | 0.0397498 | − | 0.999210i | \(-0.487344\pi\) | ||||
0.0397498 | + | 0.999210i | \(0.487344\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5686.07 | 0.190184 | 0.0950922 | − | 0.995468i | \(-0.469685\pi\) | ||||
0.0950922 | + | 0.995468i | \(0.469685\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72030.1 | 1.23443 | 0.617215 | − | 0.786795i | \(-0.288261\pi\) | ||||
0.617215 | + | 0.786795i | \(0.288261\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −32520.6 | −0.416264 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 255258. | 1.94351 | 0.971753 | − | 0.236000i | \(-0.0758366\pi\) | ||||
0.971753 | + | 0.236000i | \(0.0758366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −80295.2 | −0.484087 | −0.242044 | − | 0.970265i | \(-0.577818\pi\) | ||||
−0.242044 | + | 0.970265i | \(0.577818\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 188397. | 0.742738 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 438408. | 1.42289 | 0.711446 | − | 0.702741i | \(-0.248041\pi\) | ||||
0.711446 | + | 0.702741i | \(0.248041\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 541078. | 1.22607 | 0.613037 | − | 0.790054i | \(-0.289948\pi\) | ||||
0.613037 | + | 0.790054i | \(0.289948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −430715. | −0.826133 | −0.413066 | − | 0.910701i | \(-0.635542\pi\) | ||||
−0.413066 | + | 0.910701i | \(0.635542\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.28648e6 | 1.80742 | 0.903710 | − | 0.428145i | \(-0.140833\pi\) | ||||
0.903710 | + | 0.428145i | \(0.140833\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −45253.2 | −0.0549494 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −229708. | −0.211939 | −0.105969 | − | 0.994369i | \(-0.533795\pi\) | ||||
−0.105969 | + | 0.994369i | \(0.533795\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −765930. | −0.620754 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.31873e6 | −0.835939 | −0.417970 | − | 0.908461i | \(-0.637258\pi\) | ||||
−0.417970 | + | 0.908461i | \(0.637258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.37915e6 | 1.34205 | 0.671023 | − | 0.741436i | \(-0.265855\pi\) | ||||
0.671023 | + | 0.741436i | \(0.265855\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −806976. | −0.364472 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.92673e6 | −1.18883 | −0.594416 | − | 0.804158i | \(-0.702617\pi\) | ||||
−0.594416 | + | 0.804158i | \(0.702617\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.10039e6 | −0.696459 | −0.348229 | − | 0.937409i | \(-0.613217\pi\) | ||||
−0.348229 | + | 0.937409i | \(0.613217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.34873e6 | 1.60924 | 0.804620 | − | 0.593790i | \(-0.202369\pi\) | ||||
0.804620 | + | 0.593790i | \(0.202369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.16414e6 | −0.789839 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.77873e6 | −1.31867 | −0.659337 | − | 0.751848i | \(-0.729163\pi\) | ||||
−0.659337 | + | 0.751848i | \(0.729163\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.84724e6 | −1.50641 | −0.753206 | − | 0.657785i | \(-0.771494\pi\) | ||||
−0.753206 | + | 0.657785i | \(0.771494\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −343906. | −0.0607398 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.48134e6 | −0.974540 | −0.487270 | − | 0.873251i | \(-0.662007\pi\) | ||||
−0.487270 | + | 0.873251i | \(0.662007\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.33371e6 | −0.463749 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.21427e6 | −0.145306 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.50626e6 | 0.946320 | 0.473160 | − | 0.880977i | \(-0.343113\pi\) | ||||
0.473160 | + | 0.880977i | \(0.343113\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 902665. | 0.0871770 | 0.0435885 | − | 0.999050i | \(-0.486121\pi\) | ||||
0.0435885 | + | 0.999050i | \(0.486121\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.87862e6 | 0.439913 | 0.219957 | − | 0.975510i | \(-0.429408\pi\) | ||||
0.219957 | + | 0.975510i | \(0.429408\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.74994e7 | 1.38095 | 0.690477 | − | 0.723354i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723354i | \(0.257401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.34534e6 | 0.0995034 | 0.0497517 | − | 0.998762i | \(-0.484157\pi\) | ||||
0.0497517 | + | 0.998762i | \(0.484157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.60631e6 | 0.235119 | 0.117560 | − | 0.993066i | \(-0.462493\pi\) | ||||
0.117560 | + | 0.993066i | \(0.462493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.53822e7 | −0.943137 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.42071e6 | −0.0772845 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.62331e6 | −0.339881 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.36286e7 | 1.08206 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.12919e6 | 0.395475 | 0.197738 | − | 0.980255i | \(-0.436641\pi\) | ||||
0.197738 | + | 0.980255i | \(0.436641\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.94755e7 | 0.756902 | 0.378451 | − | 0.925621i | \(-0.376457\pi\) | ||||
0.378451 | + | 0.925621i | \(0.376457\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.01630e6 | −0.184885 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.70078e7 | 1.89414 | 0.947071 | − | 0.321025i | \(-0.104027\pi\) | ||||
0.947071 | + | 0.321025i | \(0.104027\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.21649e7 | 1.01585 | 0.507927 | − | 0.861400i | \(-0.330412\pi\) | ||||
0.507927 | + | 0.861400i | \(0.330412\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.35532e7 | 0.387585 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.45108e7 | −1.48489 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.93507e7 | −0.726888 | −0.363444 | − | 0.931616i | \(-0.618399\pi\) | ||||
−0.363444 | + | 0.931616i | \(0.618399\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.51159e7 | 1.77547 | 0.887734 | − | 0.460357i | \(-0.152279\pi\) | ||||
0.887734 | + | 0.460357i | \(0.152279\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.71472e7 | 0.369855 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.49260e7 | −0.307818 | −0.153909 | − | 0.988085i | \(-0.549186\pi\) | ||||
−0.153909 | + | 0.988085i | \(0.549186\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.35455e7 | −1.20004 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.98084e7 | −0.539116 | −0.269558 | − | 0.962984i | \(-0.586878\pi\) | ||||
−0.269558 | + | 0.962984i | \(0.586878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.93495e7 | −0.653780 | −0.326890 | − | 0.945062i | \(-0.606001\pi\) | ||||
−0.326890 | + | 0.945062i | \(0.606001\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.84690e7 | −0.772432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.43294e7 | 0.210410 | 0.105205 | − | 0.994451i | \(-0.466450\pi\) | ||||
0.105205 | + | 0.994451i | \(0.466450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.86899e7 | 0.404666 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.41674e7 | −0.836235 | −0.418118 | − | 0.908393i | \(-0.637310\pi\) | ||||
−0.418118 | + | 0.908393i | \(0.637310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.41695e7 | −0.302965 | −0.151483 | − | 0.988460i | \(-0.548405\pi\) | ||||
−0.151483 | + | 0.988460i | \(0.548405\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.36227e7 | −1.08713 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.77593e6 | 0.0645916 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.60596e7 | −0.166770 | −0.0833852 | − | 0.996517i | \(-0.526573\pi\) | ||||
−0.0833852 | + | 0.996517i | \(0.526573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.52440e7 | 0.453013 | 0.226506 | − | 0.974010i | \(-0.427270\pi\) | ||||
0.226506 | + | 0.974010i | \(0.427270\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.29152e7 | −0.586305 | −0.293152 | − | 0.956066i | \(-0.594704\pi\) | ||||
−0.293152 | + | 0.956066i | \(0.594704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.09010e8 | 1.88010 | 0.940052 | − | 0.341032i | \(-0.110776\pi\) | ||||
0.940052 | + | 0.341032i | \(0.110776\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.25190e8 | −1.88935 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.15548e8 | −0.936752 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.03938e7 | 0.154520 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.36673e8 | −1.73444 | −0.867221 | − | 0.497924i | \(-0.834096\pi\) | ||||
−0.867221 | + | 0.497924i | \(0.834096\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.19799e7 | 0.631187 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.08370e7 | 0.470599 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.08546e6 | 0.0379245 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.18342e7 | 0.131847 | 0.0659234 | − | 0.997825i | \(-0.479001\pi\) | ||||
0.0659234 | + | 0.997825i | \(0.479001\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.89067e8 | 1.07281 | 0.536407 | − | 0.843960i | \(-0.319781\pi\) | ||||
0.536407 | + | 0.843960i | \(0.319781\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.96027e7 | 0.493057 | 0.246528 | − | 0.969136i | \(-0.420710\pi\) | ||||
0.246528 | + | 0.969136i | \(0.420710\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.49996e8 | 1.29476 | 0.647378 | − | 0.762169i | \(-0.275865\pi\) | ||||
0.647378 | + | 0.762169i | \(0.275865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.74729e8 | −1.38092 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.90127e7 | 0.0900847 | 0.0450424 | − | 0.998985i | \(-0.485658\pi\) | ||||
0.0450424 | + | 0.998985i | \(0.485658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.44479e8 | 1.12508 | 0.562539 | − | 0.826771i | \(-0.309825\pi\) | ||||
0.562539 | + | 0.826771i | \(0.309825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.66390e6 | 0.0419828 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.14867e7 | 0.0907257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.51370e8 | 1.00336 | 0.501678 | − | 0.865054i | \(-0.332716\pi\) | ||||
0.501678 | + | 0.865054i | \(0.332716\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.58345e8 | 1.00295 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.74901e8 | −0.642728 | −0.321364 | − | 0.946956i | \(-0.604141\pi\) | ||||
−0.321364 | + | 0.946956i | \(0.604141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.86766e8 | −1.38325 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.23893e8 | 1.43685 | 0.718425 | − | 0.695605i | \(-0.244863\pi\) | ||||
0.718425 | + | 0.695605i | \(0.244863\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.90545e7 | 0.161927 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.58706e8 | 1.43682 | 0.718409 | − | 0.695621i | \(-0.244871\pi\) | ||||
0.718409 | + | 0.695621i | \(0.244871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.84831e8 | 0.869350 | 0.434675 | − | 0.900587i | \(-0.356863\pi\) | ||||
0.434675 | + | 0.900587i | \(0.356863\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.16639e8 | −0.338205 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.63864e8 | 0.463239 | 0.231619 | − | 0.972807i | \(-0.425598\pi\) | ||||
0.231619 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.19587e8 | 1.39697 | 0.698484 | − | 0.715626i | \(-0.253858\pi\) | ||||
0.698484 | + | 0.715626i | \(0.253858\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.17681e8 | −1.61999 | −0.809994 | − | 0.586438i | \(-0.800530\pi\) | ||||
−0.809994 | + | 0.586438i | \(0.800530\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.77343e8 | −1.19191 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.07745e8 | −0.993680 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.21804e8 | −0.979657 | −0.489828 | − | 0.871819i | \(-0.662941\pi\) | ||||
−0.489828 | + | 0.871819i | \(0.662941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.81618e8 | 0.638679 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.72189e8 | 0.588873 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.79980e8 | 0.803114 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.08072e8 | −1.02536 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.22691e8 | −0.833755 | −0.416878 | − | 0.908963i | \(-0.636876\pi\) | ||||
−0.416878 | + | 0.908963i | \(0.636876\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.52256e8 | −1.79512 | −0.897558 | − | 0.440896i | \(-0.854661\pi\) | ||||
−0.897558 | + | 0.440896i | \(0.854661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.10919e8 | 0.757445 | 0.378723 | − | 0.925510i | \(-0.376363\pi\) | ||||
0.378723 | + | 0.925510i | \(0.376363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.81546e7 | 0.0672728 | 0.0336364 | − | 0.999434i | \(-0.489291\pi\) | ||||
0.0336364 | + | 0.999434i | \(0.489291\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.15513e8 | 1.57905 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.15690e6 | 0.0151196 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.22890e8 | −0.198575 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.13494e9 | −1.75706 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.15640e8 | −1.23623 | −0.618117 | − | 0.786086i | \(-0.712104\pi\) | ||||
−0.618117 | + | 0.786086i | \(0.712104\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.25008e8 | 0.908299 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.53882e8 | −0.503679 | −0.251840 | − | 0.967769i | \(-0.581036\pi\) | ||||
−0.251840 | + | 0.967769i | \(0.581036\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.87988e8 | −0.393310 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.66458e8 | 1.02556 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.06402e9 | −1.36709 | −0.683544 | − | 0.729909i | \(-0.739562\pi\) | ||||
−0.683544 | + | 0.729909i | \(0.739562\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.15671e9 | −1.45659 | −0.728293 | − | 0.685266i | \(-0.759686\pi\) | ||||
−0.728293 | + | 0.685266i | \(0.759686\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.55384e8 | 0.672020 | 0.336010 | − | 0.941858i | \(-0.390922\pi\) | ||||
0.336010 | + | 0.941858i | \(0.390922\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.48542e8 | 0.532113 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.51190e8 | −0.514670 | −0.257335 | − | 0.966322i | \(-0.582844\pi\) | ||||
−0.257335 | + | 0.966322i | \(0.582844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.61540e8 | −0.963830 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.14223e9 | −1.22950 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.45006e9 | 1.53128 | 0.765641 | − | 0.643268i | \(-0.222422\pi\) | ||||
0.765641 | + | 0.643268i | \(0.222422\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.02650e8 | 0.206033 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.45233e8 | −0.544003 | −0.272002 | − | 0.962297i | \(-0.587686\pi\) | ||||
−0.272002 | + | 0.962297i | \(0.587686\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.64575e8 | 0.927132 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.48717e8 | 0.234676 | 0.117338 | − | 0.993092i | \(-0.462564\pi\) | ||||
0.117338 | + | 0.993092i | \(0.462564\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.72764e8 | 0.339030 | 0.169515 | − | 0.985528i | \(-0.445780\pi\) | ||||
0.169515 | + | 0.985528i | \(0.445780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.75709e8 | 0.603458 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.35373e9 | 1.16603 | 0.583013 | − | 0.812463i | \(-0.301874\pi\) | ||||
0.583013 | + | 0.812463i | \(0.301874\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.15998e8 | 0.0981366 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.23406e9 | 1.00750 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.56136e8 | −0.686714 | −0.343357 | − | 0.939205i | \(-0.611564\pi\) | ||||
−0.343357 | + | 0.939205i | \(0.611564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.10560e8 | 0.627740 | 0.313870 | − | 0.949466i | \(-0.398374\pi\) | ||||
0.313870 | + | 0.949466i | \(0.398374\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.03422e8 | −0.230929 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.57240e9 | 1.15607 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.01646e8 | 0.434820 | 0.217410 | − | 0.976080i | \(-0.430239\pi\) | ||||
0.217410 | + | 0.976080i | \(0.430239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.16340e9 | 0.812647 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.67579e9 | 1.15094 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.70669e9 | −1.13346 | −0.566728 | − | 0.823905i | \(-0.691791\pi\) | ||||
−0.566728 | + | 0.823905i | \(0.691791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.92228e8 | −0.256183 | −0.128092 | − | 0.991762i | \(-0.540885\pi\) | ||||
−0.128092 | + | 0.991762i | \(0.540885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.23715e7 | −0.0330928 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.09890e9 | −1.30465 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.71724e9 | 1.03314 | 0.516572 | − | 0.856244i | \(-0.327208\pi\) | ||||
0.516572 | + | 0.856244i | \(0.327208\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.18342e9 | −1.29250 | −0.646248 | − | 0.763127i | \(-0.723663\pi\) | ||||
−0.646248 | + | 0.763127i | \(0.723663\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.09568e8 | 0.234769 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.46917e7 | 0.00828793 | 0.00414396 | − | 0.999991i | \(-0.498681\pi\) | ||||
0.00414396 | + | 0.999991i | \(0.498681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.17753e9 | 0.643515 | 0.321758 | − | 0.946822i | \(-0.395726\pi\) | ||||
0.321758 | + | 0.946822i | \(0.395726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.38410e9 | 0.744574 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.08778e9 | −0.567126 | −0.283563 | − | 0.958954i | \(-0.591517\pi\) | ||||
−0.283563 | + | 0.958954i | \(0.591517\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.94064e9 | 0.996157 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.11920e8 | 0.354317 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00353e8 | 0.147206 | 0.0736030 | − | 0.997288i | \(-0.476550\pi\) | ||||
0.0736030 | + | 0.997288i | \(0.476550\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.39237e8 | 0.256346 | 0.128173 | − | 0.991752i | \(-0.459089\pi\) | ||||
0.128173 | + | 0.991752i | \(0.459089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.84582e9 | −0.864284 | −0.432142 | − | 0.901806i | \(-0.642242\pi\) | ||||
−0.432142 | + | 0.901806i | \(0.642242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.19642e9 | 0.543595 | 0.271797 | − | 0.962355i | \(-0.412382\pi\) | ||||
0.271797 | + | 0.962355i | \(0.412382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.58198e9 | 1.15571 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.54481e9 | −0.671214 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.84915e8 | −0.0791669 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.02670e9 | −1.67407 | −0.837037 | − | 0.547147i | \(-0.815714\pi\) | ||||
−0.837037 | + | 0.547147i | \(0.815714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.65667e9 | 0.678778 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.81653e9 | −0.723013 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.69600e8 | −0.301935 | −0.150968 | − | 0.988539i | \(-0.548239\pi\) | ||||
−0.150968 | + | 0.988539i | \(0.548239\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.56564e9 | −0.978163 | −0.489082 | − | 0.872238i | \(-0.662668\pi\) | ||||
−0.489082 | + | 0.872238i | \(0.662668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.11069e8 | 0.154508 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.85298e9 | 0.677053 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.77120e9 | −1.71900 | −0.859499 | − | 0.511138i | \(-0.829224\pi\) | ||||
−0.859499 | + | 0.511138i | \(0.829224\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.57359e9 | −1.25204 | −0.626018 | − | 0.779808i | \(-0.715316\pi\) | ||||
−0.626018 | + | 0.779808i | \(0.715316\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.92766e8 | −0.0666055 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.35215e9 | −1.46282 | −0.731411 | − | 0.681937i | \(-0.761138\pi\) | ||||
−0.731411 | + | 0.681937i | \(0.761138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.71869e9 | −1.56440 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.04184e9 | −0.336105 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.61410e9 | 1.46849 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.03350e9 | −0.320168 | −0.160084 | − | 0.987103i | \(-0.551176\pi\) | ||||
−0.160084 | + | 0.987103i | \(0.551176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.96154e9 | 1.21090 | 0.605449 | − | 0.795884i | \(-0.292993\pi\) | ||||
0.605449 | + | 0.795884i | \(0.292993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.29308e8 | −0.0384847 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.78351e9 | 0.523817 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.04464e9 | 0.584887 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.73702e9 | −1.05509 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.62306e8 | −0.0446451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.85497e9 | −1.04672 | −0.523360 | − | 0.852112i | \(-0.675322\pi\) | ||||
−0.523360 | + | 0.852112i | \(0.675322\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.87299e8 | −0.0760232 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.73287e9 | 0.713941 | 0.356971 | − | 0.934116i | \(-0.383810\pi\) | ||||
0.356971 | + | 0.934116i | \(0.383810\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.45141e9 | 0.369625 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.09804e9 | 1.28193 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.18376e9 | −0.780632 | −0.390316 | − | 0.920681i | \(-0.627634\pi\) | ||||
−0.390316 | + | 0.920681i | \(0.627634\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.62760e9 | −0.394099 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.51193e9 | 1.30174 | 0.650870 | − | 0.759189i | \(-0.274404\pi\) | ||||
0.650870 | + | 0.759189i | \(0.274404\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.70133e8 | −0.179637 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.03959e9 | −1.14684 | −0.573419 | − | 0.819262i | \(-0.694383\pi\) | ||||
−0.573419 | + | 0.819262i | \(0.694383\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.21837e9 | 0.948241 | 0.474120 | − | 0.880460i | \(-0.342766\pi\) | ||||
0.474120 | + | 0.880460i | \(0.342766\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.34246e9 | −0.513849 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.68975e9 | −1.01633 | −0.508165 | − | 0.861260i | \(-0.669676\pi\) | ||||
−0.508165 | + | 0.861260i | \(0.669676\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.92289e9 | 1.46444 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.23875e8 | −0.172195 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.84274e8 | −0.0376037 | −0.0188019 | − | 0.999823i | \(-0.505985\pi\) | ||||
−0.0188019 | + | 0.999823i | \(0.505985\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.56564e8 | −0.0920658 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.28613e9 | 1.63178 | 0.815888 | − | 0.578211i | \(-0.196249\pi\) | ||||
0.815888 | + | 0.578211i | \(0.196249\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.03396e8 | 0.0590474 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.93413e9 | 0.938031 | 0.469015 | − | 0.883190i | \(-0.344609\pi\) | ||||
0.469015 | + | 0.883190i | \(0.344609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.42246e9 | 0.831005 | 0.415502 | − | 0.909592i | \(-0.363606\pi\) | ||||
0.415502 | + | 0.909592i | \(0.363606\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.41442e9 | 0.259678 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.15596e9 | −1.29870 | −0.649348 | − | 0.760491i | \(-0.724958\pi\) | ||||
−0.649348 | + | 0.760491i | \(0.724958\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.86137e9 | 0.862213 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.20601e9 | −1.08818 | −0.544090 | − | 0.839027i | \(-0.683125\pi\) | ||||
−0.544090 | + | 0.839027i | \(0.683125\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.96991e9 | 1.02322 | 0.511611 | − | 0.859217i | \(-0.329049\pi\) | ||||
0.511611 | + | 0.859217i | \(0.329049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.23494e9 | 0.717678 | 0.358839 | − | 0.933399i | \(-0.383173\pi\) | ||||
0.358839 | + | 0.933399i | \(0.383173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.71789e9 | 0.947387 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.50525e9 | −0.410461 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.06015e8 | 0.113119 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.03786e9 | 0.798258 | 0.399129 | − | 0.916895i | \(-0.369313\pi\) | ||||
0.399129 | + | 0.916895i | \(0.369313\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.94956e9 | −0.302153 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.71004e8 | −0.0262131 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.73075e9 | −1.00939 | −0.504697 | − | 0.863297i | \(-0.668396\pi\) | ||||
−0.504697 | + | 0.863297i | \(0.668396\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.23218e10 | 1.82783 | 0.913917 | − | 0.405901i | \(-0.133042\pi\) | ||||
0.913917 | + | 0.405901i | \(0.133042\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.30782e8 | −0.135109 | −0.0675543 | − | 0.997716i | \(-0.521520\pi\) | ||||
−0.0675543 | + | 0.997716i | \(0.521520\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.72979e9 | −0.679181 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.06457e10 | 1.49617 | 0.748083 | − | 0.663605i | \(-0.230975\pi\) | ||||
0.748083 | + | 0.663605i | \(0.230975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.15903e9 | −0.578293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.34030e10 | −1.82433 | −0.912167 | − | 0.409819i | \(-0.865592\pi\) | ||||
−0.912167 | + | 0.409819i | \(0.865592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.12505e9 | 0.286196 | 0.143098 | − | 0.989709i | \(-0.454294\pi\) | ||||
0.143098 | + | 0.989709i | \(0.454294\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.07124e9 | 0.141257 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.83862e10 | 2.39912 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.53311e9 | 1.09038 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.32323e10 | −1.67334 | −0.836669 | − | 0.547709i | \(-0.815500\pi\) | ||||
−0.836669 | + | 0.547709i | \(0.815500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.29518e10 | −1.60424 | −0.802121 | − | 0.597162i | \(-0.796295\pi\) | ||||
−0.802121 | + | 0.597162i | \(0.796295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.50429e9 | −0.919952 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.10069e9 | 0.492475 | 0.246237 | − | 0.969210i | \(-0.420806\pi\) | ||||
0.246237 | + | 0.969210i | \(0.420806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.21741e10 | −1.44717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.68027e8 | −0.101103 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.09622e8 | −0.0702891 | −0.0351445 | − | 0.999382i | \(-0.511189\pi\) | ||||
−0.0351445 | + | 0.999382i | \(0.511189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.86888e9 | −0.776139 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.71357e8 | 0.0974723 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.28579e9 | −0.469914 | −0.234957 | − | 0.972006i | \(-0.575495\pi\) | ||||
−0.234957 | + | 0.972006i | \(0.575495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.49282e9 | 0.270612 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.96338e8 | −0.0847480 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.41237e10 | 1.48829 | 0.744144 | − | 0.668019i | \(-0.232858\pi\) | ||||
0.744144 | + | 0.668019i | \(0.232858\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.78367e9 | −0.597572 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.89432e9 | −0.296125 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.37470e10 | −1.37930 | −0.689648 | − | 0.724144i | \(-0.742235\pi\) | ||||
−0.689648 | + | 0.724144i | \(0.742235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.30396e9 | −0.427656 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.30114e9 | −0.809011 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.00341e9 | −0.675989 | −0.337994 | − | 0.941148i | \(-0.609748\pi\) | ||||
−0.337994 | + | 0.941148i | \(0.609748\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.93626e8 | −0.0656772 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.55094e8 | 0.0239241 | 0.0119621 | − | 0.999928i | \(-0.496192\pi\) | ||||
0.0119621 | + | 0.999928i | \(0.496192\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.04971e10 | −0.965899 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.46183e10 | 1.33242 | 0.666210 | − | 0.745764i | \(-0.267915\pi\) | ||||
0.666210 | + | 0.745764i | \(0.267915\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.75022e9 | 0.514309 | 0.257154 | − | 0.966370i | \(-0.417215\pi\) | ||||
0.257154 | + | 0.966370i | \(0.417215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.26791e9 | 0.555361 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.54381e10 | −1.34248 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.03937e10 | −0.895425 | −0.447713 | − | 0.894178i | \(-0.647761\pi\) | ||||
−0.447713 | + | 0.894178i | \(0.647761\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.60411e10 | −1.35650 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.09130e9 | 0.342788 | 0.171394 | − | 0.985203i | \(-0.445173\pi\) | ||||
0.171394 | + | 0.985203i | \(0.445173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.80339e10 | 1.48335 | 0.741673 | − | 0.670761i | \(-0.234032\pi\) | ||||
0.741673 | + | 0.670761i | \(0.234032\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.18687e9 | −0.0967310 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.98326e9 | −0.398777 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.13253e9 | 0.248401 | 0.124200 | − | 0.992257i | \(-0.460363\pi\) | ||||
0.124200 | + | 0.992257i | \(0.460363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.60791e10 | 1.25208 | 0.626042 | − | 0.779789i | \(-0.284674\pi\) | ||||
0.626042 | + | 0.779789i | \(0.284674\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.61125e9 | 0.201508 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.07661e9 | 0.233180 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.53330e9 | −0.565857 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.18747e9 | 0.235181 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.43551e10 | −1.04977 | −0.524884 | − | 0.851174i | \(-0.675891\pi\) | ||||
−0.524884 | + | 0.851174i | \(0.675891\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.18151e9 | −0.228568 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.99040e9 | 0.640211 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.06182e10 | 1.44260 | 0.721300 | − | 0.692623i | \(-0.243545\pi\) | ||||
0.721300 | + | 0.692623i | \(0.243545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.07175e9 | 0.143689 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.91839e10 | 1.30747 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.35703e10 | 0.916858 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.33465e10 | −1.55025 | −0.775126 | − | 0.631806i | \(-0.782314\pi\) | ||||
−0.775126 | + | 0.631806i | \(0.782314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.30392e10 | −0.858375 | −0.429188 | − | 0.903215i | \(-0.641200\pi\) | ||||
−0.429188 | + | 0.903215i | \(0.641200\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.36564e9 | 0.411899 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.44907e9 | −0.157118 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.70882e9 | 0.296969 | 0.148484 | − | 0.988915i | \(-0.452561\pi\) | ||||
0.148484 | + | 0.988915i | \(0.452561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.30346e10 | −1.44039 | −0.720197 | − | 0.693769i | \(-0.755949\pi\) | ||||
−0.720197 | + | 0.693769i | \(0.755949\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.77049e10 | 1.08849 | 0.544246 | − | 0.838926i | \(-0.316816\pi\) | ||||
0.544246 | + | 0.838926i | \(0.316816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.17131e10 | −1.32367 | −0.661837 | − | 0.749648i | \(-0.730223\pi\) | ||||
−0.661837 | + | 0.749648i | \(0.730223\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.28761e7 | −0.00436845 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.40316e9 | 0.499505 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.94676e10 | −1.13801 | −0.569004 | − | 0.822335i | \(-0.692671\pi\) | ||||
−0.569004 | + | 0.822335i | \(0.692671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.79066e10 | 2.77722 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.03506e10 | 0.590158 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.84314e9 | 0.330411 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.15785e10 | 1.75646 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.38137e10 | 1.31373 | 0.656864 | − | 0.754009i | \(-0.271882\pi\) | ||||
0.656864 | + | 0.754009i | \(0.271882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.13645e10 | 1.70218 | 0.851089 | − | 0.525022i | \(-0.175943\pi\) | ||||
0.851089 | + | 0.525022i | \(0.175943\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.82276e10 | −0.981189 | −0.490594 | − | 0.871388i | \(-0.663220\pi\) | ||||
−0.490594 | + | 0.871388i | \(0.663220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.55094e10 | 1.88064 | 0.940321 | − | 0.340289i | \(-0.110525\pi\) | ||||
0.940321 | + | 0.340289i | \(0.110525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.06007e9 | −0.160759 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.07261e10 | −1.07139 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.10596e10 | −0.567121 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.08453e10 | −1.05191 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.20103e9 | 0.360492 | 0.180246 | − | 0.983622i | \(-0.442311\pi\) | ||||
0.180246 | + | 0.983622i | \(0.442311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.40025e10 | 0.689905 | 0.344953 | − | 0.938620i | \(-0.387895\pi\) | ||||
0.344953 | + | 0.938620i | \(0.387895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.63228e9 | −0.275310 | −0.137655 | − | 0.990480i | \(-0.543957\pi\) | ||||
−0.137655 | + | 0.990480i | \(0.543957\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.43622e10 | 0.691016 | 0.345508 | − | 0.938416i | \(-0.387707\pi\) | ||||
0.345508 | + | 0.938416i | \(0.387707\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.05384e9 | −0.384456 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.31500e9 | 0.343743 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.37031e10 | 0.638906 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.04960e10 | −0.940826 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.69923e8 | −0.0168490 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.16144e9 | 0.231473 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.39756e10 | −1.06695 | −0.533475 | − | 0.845816i | \(-0.679114\pi\) | ||||
−0.533475 | + | 0.845816i | \(0.679114\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.02762e10 | −0.888531 | −0.444265 | − | 0.895895i | \(-0.646535\pi\) | ||||
−0.444265 | + | 0.895895i | \(0.646535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.81451e10 | −1.22393 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.71814e10 | −0.735812 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.05393e10 | 0.872935 | 0.436468 | − | 0.899720i | \(-0.356229\pi\) | ||||
0.436468 | + | 0.899720i | \(0.356229\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.93701e9 | −0.332239 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.42573e10 | −0.592299 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.80619e10 | −1.55753 | −0.778763 | − | 0.627318i | \(-0.784153\pi\) | ||||
−0.778763 | + | 0.627318i | \(0.784153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.57313e8 | −0.0104505 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.23346e9 | −0.0493497 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.78785e8 | −0.0190130 | −0.00950652 | − | 0.999955i | \(-0.503026\pi\) | ||||
−0.00950652 | + | 0.999955i | \(0.503026\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.37933e9 | 0.327828 | 0.163914 | − | 0.986475i | \(-0.447588\pi\) | ||||
0.163914 | + | 0.986475i | \(0.447588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.89739e10 | 1.51350 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.33599e9 | −0.165907 | −0.0829533 | − | 0.996553i | \(-0.526435\pi\) | ||||
−0.0829533 | + | 0.996553i | \(0.526435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.02119e10 | 0.767673 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.07549e9 | 0.302234 | 0.151117 | − | 0.988516i | \(-0.451713\pi\) | ||||
0.151117 | + | 0.988516i | \(0.451713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.42957e9 | 0.127417 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.02927e10 | −1.84137 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.10653e10 | −0.765660 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.66194e9 | −0.346114 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.14315e10 | 0.762182 | 0.381091 | − | 0.924537i | \(-0.375548\pi\) | ||||
0.381091 | + | 0.924537i | \(0.375548\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.81424e9 | −0.203810 | −0.101905 | − | 0.994794i | \(-0.532494\pi\) | ||||
−0.101905 | + | 0.994794i | \(0.532494\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.83762e10 | −0.987549 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.46503e10 | −0.502592 | −0.251296 | − | 0.967910i | \(-0.580857\pi\) | ||||
−0.251296 | + | 0.967910i | \(0.580857\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.32461e10 | −0.791792 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.29782e10 | 1.44315 | 0.721575 | − | 0.692337i | \(-0.243419\pi\) | ||||
0.721575 | + | 0.692337i | \(0.243419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.34356e10 | 0.447952 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.10244e10 | −1.01980 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.24661e10 | 0.406888 | 0.203444 | − | 0.979087i | \(-0.434787\pi\) | ||||
0.203444 | + | 0.979087i | \(0.434787\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.46345e10 | −1.43645 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.82605e10 | 1.22269 | 0.611346 | − | 0.791363i | \(-0.290628\pi\) | ||||
0.611346 | + | 0.791363i | \(0.290628\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 72.8.a.g.1.1 | yes | 2 | |
3.2 | odd | 2 | 72.8.a.f.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 144.8.a.n.1.1 | 2 | |||
8.3 | odd | 2 | 576.8.a.bc.1.2 | 2 | |||
8.5 | even | 2 | 576.8.a.bd.1.2 | 2 | |||
12.11 | even | 2 | 144.8.a.l.1.2 | 2 | |||
24.5 | odd | 2 | 576.8.a.bq.1.1 | 2 | |||
24.11 | even | 2 | 576.8.a.bp.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.8.a.f.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
72.8.a.g.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
144.8.a.l.1.2 | 2 | 12.11 | even | 2 | |||
144.8.a.n.1.1 | 2 | 4.3 | odd | 2 | |||
576.8.a.bc.1.2 | 2 | 8.3 | odd | 2 | |||
576.8.a.bd.1.2 | 2 | 8.5 | even | 2 | |||
576.8.a.bp.1.1 | 2 | 24.11 | even | 2 | |||
576.8.a.bq.1.1 | 2 | 24.5 | odd | 2 |