Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,6,Mod(1,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, 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("280.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.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: | \(44.9074695476\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 1151x^{3} - 5642x^{2} + 193596x + 1258056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-27.3320\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.1 |
$q$-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 | ||||||||
\(3\) | 30.3320 | 1.94580 | 0.972900 | − | 0.231227i | \(-0.0742739\pi\) | ||||
0.972900 | + | 0.231227i | \(0.0742739\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 677.031 | 2.78614 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 604.346 | 1.50593 | 0.752963 | − | 0.658063i | \(-0.228624\pi\) | ||||
0.752963 | + | 0.658063i | \(0.228624\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 383.964 | 0.630133 | 0.315067 | − | 0.949070i | \(-0.397973\pi\) | ||||
0.315067 | + | 0.949070i | \(0.397973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 758.300 | 0.870188 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −791.640 | −0.664363 | −0.332181 | − | 0.943216i | \(-0.607785\pi\) | ||||
−0.332181 | + | 0.943216i | \(0.607785\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2078.78 | −1.32107 | −0.660533 | − | 0.750797i | \(-0.729670\pi\) | ||||
−0.660533 | + | 0.750797i | \(0.729670\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1486.27 | 0.735443 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2523.45 | −0.994660 | −0.497330 | − | 0.867561i | \(-0.665686\pi\) | ||||
−0.497330 | + | 0.867561i | \(0.665686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13165.0 | 3.47546 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 372.040 | 0.0821475 | 0.0410737 | − | 0.999156i | \(-0.486922\pi\) | ||||
0.0410737 | + | 0.999156i | \(0.486922\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2484.87 | −0.464408 | −0.232204 | − | 0.972667i | \(-0.574594\pi\) | ||||
−0.232204 | + | 0.972667i | \(0.574594\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18331.0 | 2.93023 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6552.46 | −0.786865 | −0.393433 | − | 0.919354i | \(-0.628712\pi\) | ||||
−0.393433 | + | 0.919354i | \(0.628712\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11646.4 | 1.22611 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −16194.7 | −1.50458 | −0.752289 | − | 0.658834i | \(-0.771050\pi\) | ||||
−0.752289 | + | 0.658834i | \(0.771050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 15433.1 | 1.27287 | 0.636433 | − | 0.771332i | \(-0.280409\pi\) | ||||
0.636433 | + | 0.771332i | \(0.280409\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16925.8 | 1.24600 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 22278.8 | 1.47112 | 0.735559 | − | 0.677460i | \(-0.236919\pi\) | ||||
0.735559 | + | 0.677460i | \(0.236919\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −24012.0 | −1.29272 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −26272.4 | −1.28472 | −0.642362 | − | 0.766401i | \(-0.722046\pi\) | ||||
−0.642362 | + | 0.766401i | \(0.722046\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15108.6 | 0.673471 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −63053.6 | −2.57053 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 39869.1 | 1.49110 | 0.745549 | − | 0.666451i | \(-0.232187\pi\) | ||||
0.745549 | + | 0.666451i | \(0.232187\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5893.86 | 0.202804 | 0.101402 | − | 0.994846i | \(-0.467667\pi\) | ||||
0.101402 | + | 0.994846i | \(0.467667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 33174.5 | 1.05306 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9599.11 | 0.281804 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −32074.7 | −0.872922 | −0.436461 | − | 0.899723i | \(-0.643768\pi\) | ||||
−0.436461 | + | 0.899723i | \(0.643768\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −76541.3 | −1.93541 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −57992.0 | −1.36528 | −0.682641 | − | 0.730754i | \(-0.739169\pi\) | ||||
−0.682641 | + | 0.730754i | \(0.739169\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 39480.1 | 0.867103 | 0.433552 | − | 0.901129i | \(-0.357260\pi\) | ||||
0.433552 | + | 0.901129i | \(0.357260\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18957.5 | 0.389160 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 29612.9 | 0.569187 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8987.90 | −0.162028 | −0.0810141 | − | 0.996713i | \(-0.525816\pi\) | ||||
−0.0810141 | + | 0.996713i | \(0.525816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 234804. | 3.97642 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −52523.4 | −0.836870 | −0.418435 | − | 0.908247i | \(-0.637421\pi\) | ||||
−0.418435 | + | 0.908247i | \(0.637421\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19791.0 | −0.297112 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11284.7 | 0.159843 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 52068.7 | 0.696790 | 0.348395 | − | 0.937348i | \(-0.386727\pi\) | ||||
0.348395 | + | 0.937348i | \(0.386727\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18814.3 | 0.238168 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −75371.1 | −0.903645 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −51969.5 | −0.590799 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14928.3 | 0.161094 | 0.0805472 | − | 0.996751i | \(-0.474333\pi\) | ||||
0.0805472 | + | 0.996751i | \(0.474333\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 409161. | 4.19572 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −137155. | −1.33785 | −0.668927 | − | 0.743328i | \(-0.733246\pi\) | ||||
−0.668927 | + | 0.743328i | \(0.733246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −112201. | −1.04208 | −0.521041 | − | 0.853532i | \(-0.674456\pi\) | ||||
−0.521041 | + | 0.853532i | \(0.674456\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 37156.7 | 0.328900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 195834. | 1.65360 | 0.826798 | − | 0.562499i | \(-0.190160\pi\) | ||||
0.826798 | + | 0.562499i | \(0.190160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 220762. | 1.77974 | 0.889872 | − | 0.456210i | \(-0.150793\pi\) | ||||
0.889872 | + | 0.456210i | \(0.150793\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −198749. | −1.53108 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −51394.7 | −0.378636 | −0.189318 | − | 0.981916i | \(-0.560628\pi\) | ||||
−0.189318 | + | 0.981916i | \(0.560628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −63086.2 | −0.444826 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 259956. | 1.75564 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −38790.4 | −0.251106 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 204183. | 1.26781 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −491219. | −2.92761 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −35496.6 | −0.195289 | −0.0976445 | − | 0.995221i | \(-0.531131\pi\) | ||||
−0.0976445 | + | 0.995221i | \(0.531131\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 468118. | 2.47674 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 130196. | 0.662857 | 0.331428 | − | 0.943480i | \(-0.392469\pi\) | ||||
0.331428 | + | 0.943480i | \(0.392469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −101860. | −0.499316 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 329126. | 1.55427 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −260457. | −1.18559 | −0.592795 | − | 0.805353i | \(-0.701976\pi\) | ||||
−0.592795 | + | 0.805353i | \(0.701976\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 91256.3 | 0.400614 | 0.200307 | − | 0.979733i | \(-0.435806\pi\) | ||||
0.200307 | + | 0.979733i | \(0.435806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 675762. | 2.86250 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 232047. | 0.948935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9300.99 | 0.0367375 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 72827.2 | 0.277971 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 450638. | 1.66289 | 0.831443 | − | 0.555610i | \(-0.187515\pi\) | ||||
0.831443 | + | 0.555610i | \(0.187515\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −322713. | −1.15179 | −0.575896 | − | 0.817523i | \(-0.695347\pi\) | ||||
−0.575896 | + | 0.817523i | \(0.695347\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −535965. | −1.85101 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −62121.8 | −0.207690 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −106359. | −0.344371 | −0.172186 | − | 0.985065i | \(-0.555083\pi\) | ||||
−0.172186 | + | 0.985065i | \(0.555083\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −796895. | −2.49982 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −123649. | −0.375946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −134910. | −0.397719 | −0.198860 | − | 0.980028i | \(-0.563724\pi\) | ||||
−0.198860 | + | 0.980028i | \(0.563724\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 458276. | 1.31044 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −232478. | −0.645047 | −0.322523 | − | 0.946561i | \(-0.604531\pi\) | ||||
−0.322523 | + | 0.946561i | \(0.604531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −223864. | −0.602932 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.40740e6 | −3.68067 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −150150. | −0.381427 | −0.190713 | − | 0.981646i | \(-0.561080\pi\) | ||||
−0.190713 | + | 0.981646i | \(0.561080\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30625.0 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.20931e6 | 2.90138 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −537663. | −1.25423 | −0.627115 | − | 0.778926i | \(-0.715765\pi\) | ||||
−0.627115 | + | 0.778926i | \(0.715765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −474105. | −1.07567 | −0.537834 | − | 0.843051i | \(-0.680757\pi\) | ||||
−0.537834 | + | 0.843051i | \(0.680757\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 178773. | 0.394615 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −163812. | −0.351897 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −478424. | −1.00048 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 645087. | 1.31360 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −991261. | −1.96610 | −0.983048 | − | 0.183348i | \(-0.941306\pi\) | ||||
−0.983048 | + | 0.183348i | \(0.941306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −398252. | −0.769598 | −0.384799 | − | 0.923000i | \(-0.625729\pi\) | ||||
−0.384799 | + | 0.923000i | \(0.625729\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 291160. | 0.548335 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 424086. | 0.778553 | 0.389277 | − | 0.921121i | \(-0.372725\pi\) | ||||
0.389277 | + | 0.921121i | \(0.372725\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −178201. | −0.318991 | −0.159495 | − | 0.987199i | \(-0.550987\pi\) | ||||
−0.159495 | + | 0.987199i | \(0.550987\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −972890. | −1.69853 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18229.9 | 0.0310488 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −404869. | −0.672867 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.70845e6 | −2.77126 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.25630e6 | −1.98943 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 837166. | 1.29451 | 0.647255 | − | 0.762273i | \(-0.275917\pi\) | ||||
0.647255 | + | 0.762273i | \(0.275917\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.75901e6 | −2.65656 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 385828. | 0.569243 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −121759. | −0.175530 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.19751e6 | 1.68721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −303961. | −0.418637 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −545816. | −0.734995 | −0.367497 | − | 0.930025i | \(-0.619785\pi\) | ||||
−0.367497 | + | 0.930025i | \(0.619785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 423145. | 0.557227 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.12689e6 | 1.45151 | 0.725753 | − | 0.687956i | \(-0.241492\pi\) | ||||
0.725753 | + | 0.687956i | \(0.241492\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.35322e6 | 1.70522 | 0.852610 | − | 0.522547i | \(-0.175018\pi\) | ||||
0.852610 | + | 0.522547i | \(0.175018\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 898220. | 1.10752 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.17172e6 | 1.41395 | 0.706975 | − | 0.707238i | \(-0.250059\pi\) | ||||
0.706975 | + | 0.707238i | \(0.250059\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 556971. | 0.657904 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −272621. | −0.315274 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.63077e6 | −1.84671 | −0.923355 | − | 0.383946i | \(-0.874565\pi\) | ||||
−0.923355 | + | 0.383946i | \(0.874565\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −459984. | −0.510153 | −0.255076 | − | 0.966921i | \(-0.582101\pi\) | ||||
−0.255076 | + | 0.966921i | \(0.582101\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.92296e6 | 4.26185 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −798178. | −0.832448 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.59314e6 | −1.62838 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26214.6 | −0.0262639 | −0.0131319 | − | 0.999914i | \(-0.504180\pi\) | ||||
−0.0131319 | + | 0.999914i | \(0.504180\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.52504e6 | −1.49789 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −600301. | −0.578121 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.10412e6 | −1.04275 | −0.521377 | − | 0.853326i | \(-0.674582\pi\) | ||||
−0.521377 | + | 0.853326i | \(0.674582\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −321071. | −0.297407 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 251882. | 0.228874 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 219876. | 0.196015 | 0.0980074 | − | 0.995186i | \(-0.468753\pi\) | ||||
0.0980074 | + | 0.995186i | \(0.468753\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −656810. | −0.574546 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.57935e6 | 1.35581 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.85329e6 | 1.56157 | 0.780786 | − | 0.624799i | \(-0.214819\pi\) | ||||
0.780786 | + | 0.624799i | \(0.214819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.70884e6 | 1.41344 | 0.706722 | − | 0.707492i | \(-0.250173\pi\) | ||||
0.706722 | + | 0.707492i | \(0.250173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 570674. | 0.463427 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 377716. | 0.301185 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 188853. | 0.147885 | 0.0739424 | − | 0.997263i | \(-0.476442\pi\) | ||||
0.0739424 | + | 0.997263i | \(0.476442\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.68233e6 | −1.29390 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.77467e6 | 1.34076 | 0.670380 | − | 0.742018i | \(-0.266131\pi\) | ||||
0.670380 | + | 0.742018i | \(0.266131\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 472156. | 0.350445 | 0.175222 | − | 0.984529i | \(-0.443936\pi\) | ||||
0.175222 | + | 0.984529i | \(0.443936\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.57634e6 | −1.14958 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −793543. | −0.568677 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −793163. | −0.558622 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 452805. | 0.313458 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −642119. | −0.436965 | −0.218482 | − | 0.975841i | \(-0.570111\pi\) | ||||
−0.218482 | + | 0.975841i | \(0.570111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 996727. | 0.666839 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.95624e6 | 5.23379 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −968914. | −0.626769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 756223. | 0.481098 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.16019e6 | −2.60320 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 147347. | 0.0906965 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.54290e6 | −1.53987 | −0.769935 | − | 0.638123i | \(-0.779711\pi\) | ||||
−0.769935 | + | 0.638123i | \(0.779711\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.40327e6 | −2.02768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.97181e6 | −1.74229 | −0.871143 | − | 0.491029i | \(-0.836621\pi\) | ||||
−0.871143 | + | 0.491029i | \(0.836621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 41506.6 | 0.0239473 | 0.0119736 | − | 0.999928i | \(-0.496189\pi\) | ||||
0.0119736 | + | 0.999928i | \(0.496189\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 829363. | 0.470943 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 762636. | 0.426254 | 0.213127 | − | 0.977024i | \(-0.431635\pi\) | ||||
0.213127 | + | 0.977024i | \(0.431635\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 224841. | 0.123708 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.94005e6 | 3.21757 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.64565e6 | 0.877668 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 239978. | 0.126027 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.69615e6 | 3.46303 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.09166e6 | 0.556031 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.07851e6 | −1.54444 | −0.772219 | − | 0.635356i | \(-0.780853\pi\) | ||||
−0.772219 | + | 0.635356i | \(0.780853\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.43622e6 | −2.19231 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −801867. | −0.390383 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.44180e6 | 0.691560 | 0.345780 | − | 0.938316i | \(-0.387614\pi\) | ||||
0.345780 | + | 0.938316i | \(0.387614\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.55891e6 | −0.736751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.50172e6 | −0.699364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.91353e6 | −0.865542 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.48182e6 | −0.660649 | −0.330324 | − | 0.943868i | \(-0.607158\pi\) | ||||
−0.330324 | + | 0.943868i | \(0.607158\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.90464e6 | −0.837046 | −0.418523 | − | 0.908206i | \(-0.637452\pi\) | ||||
−0.418523 | + | 0.908206i | \(0.637452\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.05491e6 | 2.19001 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −298729. | −0.127597 | −0.0637986 | − | 0.997963i | \(-0.520322\pi\) | ||||
−0.0637986 | + | 0.997963i | \(0.520322\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.44980e6 | −0.610573 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.17659e6 | −0.488601 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.36818e6 | −1.37930 | −0.689651 | − | 0.724142i | \(-0.742236\pi\) | ||||
−0.689651 | + | 0.724142i | \(0.742236\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.84523e6 | 0.745217 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.19327e6 | 2.46691 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 987002. | 0.387780 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23037.2 | −0.00892820 | −0.00446410 | − | 0.999990i | \(-0.501421\pi\) | ||||
−0.00446410 | + | 0.999990i | \(0.501421\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.09643e7 | −4.19196 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.28735e6 | −0.485580 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.71485e6 | −0.638195 | −0.319097 | − | 0.947722i | \(-0.603380\pi\) | ||||
−0.319097 | + | 0.947722i | \(0.603380\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 473938. | 0.174038 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 142850. | 0.0517639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.90452e6 | −0.681064 | −0.340532 | − | 0.940233i | \(-0.610607\pi\) | ||||
−0.340532 | + | 0.940233i | \(0.610607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.07668e6 | −0.379993 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.77535e6 | 0.618424 | 0.309212 | − | 0.950993i | \(-0.399935\pi\) | ||||
0.309212 | + | 0.950993i | \(0.399935\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 740323. | 0.254548 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.04487e7 | 3.54638 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.47325e6 | −0.828693 | −0.414346 | − | 0.910119i | \(-0.635990\pi\) | ||||
−0.414346 | + | 0.910119i | \(0.635990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.99766e6 | 0.660815 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.94911e6 | 1.28979 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −224697. | −0.0724612 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 298950. | 0.0951968 | 0.0475984 | − | 0.998867i | \(-0.484843\pi\) | ||||
0.0475984 | + | 0.998867i | \(0.484843\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.08963e6 | −0.971569 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.60863e6 | 1.12068 | 0.560340 | − | 0.828263i | \(-0.310671\pi\) | ||||
0.560340 | + | 0.828263i | \(0.310671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −954102. | −0.292639 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.87009e6 | 1.77831 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.95995e6 | −1.18496 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −431739. | −0.127618 | −0.0638092 | − | 0.997962i | \(-0.520325\pi\) | ||||
−0.0638092 | + | 0.997962i | \(0.520325\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.90019e6 | −2.30692 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.95358e6 | 0.563582 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.31309e6 | −0.374260 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.76799e6 | 0.779514 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.10143e6 | 1.69784 | 0.848920 | − | 0.528522i | \(-0.177253\pi\) | ||||
0.848920 | + | 0.528522i | \(0.177253\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 768074. | 0.211202 | 0.105601 | − | 0.994409i | \(-0.466323\pi\) | ||||
0.105601 | + | 0.994409i | \(0.466323\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.50835e7 | 4.09874 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −494775. | −0.132873 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 288799. | 0.0766525 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.03846e6 | 1.84644 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.21891e6 | −0.316067 | −0.158034 | − | 0.987434i | \(-0.550515\pi\) | ||||
−0.158034 | + | 0.987434i | \(0.550515\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.44392e6 | 0.626423 | 0.313211 | − | 0.949683i | \(-0.398595\pi\) | ||||
0.313211 | + | 0.949683i | \(0.398595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 282118. | 0.0714838 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.24570e6 | 1.31401 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 495858. | 0.122799 | 0.0613997 | − | 0.998113i | \(-0.480444\pi\) | ||||
0.0613997 | + | 0.998113i | \(0.480444\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.62555e6 | 0.398020 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.75805e6 | 1.39401 | 0.697006 | − | 0.717066i | \(-0.254515\pi\) | ||||
0.697006 | + | 0.717066i | \(0.254515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.30172e6 | 0.311614 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.36688e7 | 3.23564 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.74045e6 | 1.10970 | 0.554848 | − | 0.831952i | \(-0.312777\pi\) | ||||
0.554848 | + | 0.831952i | \(0.312777\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.78723e6 | −2.26578 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.78853e6 | −2.24116 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 470356. | 0.106512 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.61547e6 | −0.585814 | −0.292907 | − | 0.956141i | \(-0.594623\pi\) | ||||
−0.292907 | + | 0.956141i | \(0.594623\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.04220e7 | −2.30897 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −110237. | −0.0241588 | −0.0120794 | − | 0.999927i | \(-0.503845\pi\) | ||||
−0.0120794 | + | 0.999927i | \(0.503845\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.53603e6 | −0.333003 | −0.166501 | − | 0.986041i | \(-0.553247\pi\) | ||||
−0.166501 | + | 0.986041i | \(0.553247\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.88428e6 | −0.404122 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.37245e6 | 0.927753 | 0.463877 | − | 0.885900i | \(-0.346458\pi\) | ||||
0.463877 | + | 0.885900i | \(0.346458\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.57166e6 | −0.329933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.22610e6 | −0.670078 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.32694e6 | 1.91684 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.29924e6 | −0.264213 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.77872e7 | −3.57942 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.50712e6 | 0.499271 | 0.249635 | − | 0.968340i | \(-0.419689\pi\) | ||||
0.249635 | + | 0.968340i | \(0.419689\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.51591e6 | −0.495830 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.75052e6 | −0.731516 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 373207. | 0.0720436 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.35121e6 | −0.640295 | −0.320147 | − | 0.947368i | \(-0.603732\pi\) | ||||
−0.320147 | + | 0.947368i | \(0.603732\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.09211e6 | −0.773882 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.04673e6 | 1.31912 | 0.659559 | − | 0.751652i | \(-0.270743\pi\) | ||||
0.659559 | + | 0.751652i | \(0.270743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −294521. | −0.0545757 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.02290e7 | 1.87638 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.84161e6 | −0.516028 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.36969e6 | −1.50473 | −0.752364 | − | 0.658747i | \(-0.771087\pi\) | ||||
−0.752364 | + | 0.658747i | \(0.771087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.05153e6 | −1.25513 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.04525e6 | 0.536665 | 0.268333 | − | 0.963326i | \(-0.413527\pi\) | ||||
0.268333 | + | 0.963326i | \(0.413527\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.42888e6 | −0.598307 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.79026e6 | −1.17318 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 564309. | 0.0965434 | 0.0482717 | − | 0.998834i | \(-0.484629\pi\) | ||||
0.0482717 | + | 0.998834i | \(0.484629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.93452e6 | 0.327734 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.73672e7 | −4.59132 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.80501e6 | −0.466033 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.34641e7 | 2.21540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.55436e6 | −0.742180 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.99644e6 | −0.645029 | −0.322515 | − | 0.946564i | \(-0.604528\pi\) | ||||
−0.322515 | + | 0.946564i | \(0.604528\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.52509e6 | −0.723391 | −0.361695 | − | 0.932296i | \(-0.617802\pi\) | ||||
−0.361695 | + | 0.932296i | \(0.617802\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 928918. | 0.147089 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.96712e6 | 0.308535 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −68550.6 | −0.0106505 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.69926e7 | 4.15440 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.21821e6 | −0.948085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.89586e6 | 0.739511 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.63084e7 | −2.44048 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.45103e6 | 0.215132 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.68445e6 | −0.835018 | −0.417509 | − | 0.908673i | \(-0.637097\pi\) | ||||
−0.417509 | + | 0.908673i | \(0.637097\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.43806e7 | −2.09304 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.51904e6 | 0.795926 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.82153e6 | 1.11770 | 0.558848 | − | 0.829270i | \(-0.311244\pi\) | ||||
0.558848 | + | 0.829270i | \(0.311244\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.99033e6 | 0.565038 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −773389. | −0.108522 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −440407. | −0.0612409 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.96874e6 | −0.684721 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.04122e6 | 0.961634 | 0.480817 | − | 0.876821i | \(-0.340340\pi\) | ||||
0.480817 | + | 0.876821i | \(0.340340\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.92577e6 | 0.802076 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.45116e7 | −1.94674 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.83612e6 | −1.04191 | −0.520955 | − | 0.853584i | \(-0.674424\pi\) | ||||
−0.520955 | + | 0.853584i | \(0.674424\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.28487e6 | −0.169331 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.15054e7 | 1.50295 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.57277e6 | 0.851075 | 0.425537 | − | 0.904941i | \(-0.360085\pi\) | ||||
0.425537 | + | 0.904941i | \(0.360085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −881273. | −0.113115 | −0.0565575 | − | 0.998399i | \(-0.518012\pi\) | ||||
−0.0565575 | + | 0.998399i | \(0.518012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.00670e7 | −3.82563 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.57716e6 | −0.198932 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.35985e7 | 1.70041 | 0.850203 | − | 0.526455i | \(-0.176479\pi\) | ||||
0.850203 | + | 0.526455i | \(0.176479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.20798e7 | −1.49748 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.57365e6 | −0.316307 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.58776e7 | −1.93470 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.49890e6 | 0.785145 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.56764e6 | −0.666923 | −0.333462 | − | 0.942764i | \(-0.608217\pi\) | ||||
−0.333462 | + | 0.942764i | \(0.608217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.16550e6 | 0.613514 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.28634e7 | 1.51491 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.27729e6 | 0.499496 | 0.249748 | − | 0.968311i | \(-0.419652\pi\) | ||||
0.249748 | + | 0.968311i | \(0.419652\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −969759. | −0.112298 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.40520e6 | −0.620692 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.53192e6 | 0.743830 | 0.371915 | − | 0.928267i | \(-0.378701\pi\) | ||||
0.371915 | + | 0.928267i | \(0.378701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.26670e6 | −0.368913 | −0.184456 | − | 0.982841i | \(-0.559052\pi\) | ||||
−0.184456 | + | 0.982841i | \(0.559052\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.17156e7 | −2.43208 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.10457e6 | 0.566984 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.17041e6 | −0.239094 | −0.119547 | − | 0.992829i | \(-0.538144\pi\) | ||||
−0.119547 | + | 0.992829i | \(0.538144\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 552951. | 0.0604148 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.55427e6 | 0.927001 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.89798e6 | 1.06389 | 0.531943 | − | 0.846780i | \(-0.321462\pi\) | ||||
0.531943 | + | 0.846780i | \(0.321462\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.22805e7 | −1.30927 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.68570e7 | 1.78266 | 0.891329 | − | 0.453357i | \(-0.149774\pi\) | ||||
0.891329 | + | 0.453357i | \(0.149774\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.38025e7 | 1.44787 | 0.723935 | − | 0.689868i | \(-0.242331\pi\) | ||||
0.723935 | + | 0.689868i | \(0.242331\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.32213e7 | −3.45691 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.55137e6 | 0.263362 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.81062e7 | −3.87103 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.18719e6 | 0.522764 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.76100e6 | −0.975935 | −0.487967 | − | 0.872862i | \(-0.662262\pi\) | ||||
−0.487967 | + | 0.872862i | \(0.662262\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.53929e7 | 2.51886 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −887415. | −0.0873359 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 921898. | 0.0900191 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.92624e7 | −3.80386 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.72746e7 | −1.66059 | −0.830295 | − | 0.557324i | \(-0.811828\pi\) | ||||
−0.830295 | + | 0.557324i | \(0.811828\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.88097e6 | −0.370180 | −0.185090 | − | 0.982722i | \(-0.559258\pi\) | ||||
−0.185090 | + | 0.982722i | \(0.559258\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.17029e7 | 1.10763 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.53463e7 | 1.44126 | 0.720632 | − | 0.693318i | \(-0.243852\pi\) | ||||
0.720632 | + | 0.693318i | \(0.243852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.40947e7 | 2.24548 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.69319e6 | −0.341546 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −436146. | −0.0400266 | −0.0200133 | − | 0.999800i | \(-0.506371\pi\) | ||||
−0.0200133 | + | 0.999800i | \(0.506371\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.25490e6 | 0.296439 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.67292e7 | 2.41587 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.04128e6 | −0.541895 | −0.270948 | − | 0.962594i | \(-0.587337\pi\) | ||||
−0.270948 | + | 0.962594i | \(0.587337\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.67242e6 | 0.504969 | 0.252485 | − | 0.967601i | \(-0.418752\pi\) | ||||
0.252485 | + | 0.967601i | \(0.418752\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.21977e6 | −0.814584 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.54651e6 | −0.223301 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −938823. | −0.0817088 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.65557e7 | −1.43015 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.56193e6 | 0.305407 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −585604. | −0.0498387 | −0.0249193 | − | 0.999689i | \(-0.507933\pi\) | ||||
−0.0249193 | + | 0.999689i | \(0.507933\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.22815e6 | 0.695093 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.94361e6 | 0.330691 | 0.165346 | − | 0.986236i | \(-0.447126\pi\) | ||||
0.165346 | + | 0.986236i | \(0.447126\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 731486. | 0.0608880 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.41810e7 | 2.82434 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.30389e7 | 1.06952 | 0.534761 | − | 0.845003i | \(-0.320402\pi\) | ||||
0.534761 | + | 0.845003i | \(0.320402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.51143e6 | −0.530212 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.10460e7 | 3.31802 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.00877e7 | −0.809548 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.39341e7 | 1.11016 | 0.555079 | − | 0.831798i | \(-0.312688\pi\) | ||||
0.555079 | + | 0.831798i | \(0.312688\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.00489e7 | 1.58583 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.28141e6 | 0.179160 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.28204e7 | 0.999585 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.55406e7 | 2.75126 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.17868e7 | 1.67455 | 0.837277 | − | 0.546779i | \(-0.184146\pi\) | ||||
0.837277 | + | 0.546779i | \(0.184146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.36211e7 | 1.03950 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.68940e7 | 1.28015 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.72060e6 | −0.505661 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.10065e6 | 0.679919 | 0.339959 | − | 0.940440i | \(-0.389587\pi\) | ||||
0.339959 | + | 0.940440i | \(0.389587\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.08509e6 | −0.451432 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.27044e6 | 0.461928 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.80118e6 | 0.424376 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.94646e7 | −3.59333 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.49384e7 | 1.79906 | 0.899532 | − | 0.436854i | \(-0.143907\pi\) | ||||
0.899532 | + | 0.436854i | \(0.143907\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.49783e6 | −0.393870 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.39522e7 | −0.992655 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 232525. | 0.0164295 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.51596e7 | −1.76550 | −0.882750 | − | 0.469843i | \(-0.844310\pi\) | ||||
−0.882750 | + | 0.469843i | \(0.844310\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.19341e7 | 4.31629 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.22175e7 | −0.845645 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.35013e6 | 0.299049 | 0.149524 | − | 0.988758i | \(-0.452226\pi\) | ||||
0.149524 | + | 0.988758i | \(0.452226\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.82068e6 | 0.124313 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.93842e7 | −1.31456 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.16737e7 | −1.45990 | −0.729948 | − | 0.683502i | \(-0.760456\pi\) | ||||
−0.729948 | + | 0.683502i | \(0.760456\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.42103e7 | −1.61978 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.05226e7 | −0.699281 | −0.349641 | − | 0.936884i | \(-0.613696\pi\) | ||||
−0.349641 | + | 0.936884i | \(0.613696\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.12660e7 | 0.743665 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.55600e7 | −2.33163 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.59588e6 | 0.625001 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.04846e7 | 1.32534 | 0.662670 | − | 0.748912i | \(-0.269423\pi\) | ||||
0.662670 | + | 0.748912i | \(0.269423\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −795142. | −0.0511042 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.06782e6 | −0.515097 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.48469e6 | 0.284441 | 0.142221 | − | 0.989835i | \(-0.454576\pi\) | ||||
0.142221 | + | 0.989835i | \(0.454576\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.62574e7 | −2.91458 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.92897e6 | −0.245933 | −0.122967 | − | 0.992411i | \(-0.539241\pi\) | ||||
−0.122967 | + | 0.992411i | \(0.539241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.08173e7 | 0.672680 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.33991e7 | −0.827795 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.53083e7 | 0.939590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.23798e6 | 0.0754915 | 0.0377458 | − | 0.999287i | \(-0.487982\pi\) | ||||
0.0377458 | + | 0.999287i | \(0.487982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.34901e7 | −2.02899 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.21618e6 | −0.253788 | −0.126894 | − | 0.991916i | \(-0.540501\pi\) | ||||
−0.126894 | + | 0.991916i | \(0.540501\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.55304e6 | −0.0928816 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.73872e6 | −0.578695 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.36653e7 | 1.98765 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.50472e7 | −2.05601 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.89792e6 | 0.285501 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.65899e6 | −0.154008 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.70556e7 | −1.55711 | −0.778557 | − | 0.627574i | \(-0.784048\pi\) | ||||
−0.778557 | + | 0.627574i | \(0.784048\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.66929e6 | 0.381406 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.51834e6 | −0.143111 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.26303e6 | 0.127793 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.99224e7 | −1.11795 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.70075e7 | 1.50605 | 0.753024 | − | 0.657993i | \(-0.228594\pi\) | ||||
0.753024 | + | 0.657993i | \(0.228594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.76368e7 | −0.977356 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.52522e7 | 1.94135 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.38596e7 | 1.30579 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.09122e6 | −0.168128 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.62139e7 | 3.03850 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.12425e7 | −0.603937 | −0.301969 | − | 0.953318i | \(-0.597644\pi\) | ||||
−0.301969 | + | 0.953318i | \(0.597644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.73965e7 | −1.46266 | −0.731331 | − | 0.682023i | \(-0.761100\pi\) | ||||
−0.731331 | + | 0.682023i | \(0.761100\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.18326e7 | 2.75028 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.37276e6 | −0.177865 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.20821e7 | −1.68154 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.27378e7 | 0.663569 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.83040e7 | 1.46551 | 0.732756 | − | 0.680491i | \(-0.238233\pi\) | ||||
0.732756 | + | 0.680491i | \(0.238233\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.63941e7 | −0.843701 | −0.421850 | − | 0.906665i | \(-0.638619\pi\) | ||||
−0.421850 | + | 0.906665i | \(0.638619\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.14569e7 | 0.586046 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.47958e7 | 1.76914 | 0.884570 | − | 0.466407i | \(-0.154452\pi\) | ||||
0.884570 | + | 0.466407i | \(0.154452\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.57884e7 | −0.797905 | −0.398952 | − | 0.916972i | \(-0.630626\pi\) | ||||
−0.398952 | + | 0.916972i | \(0.630626\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.72828e6 | 0.287754 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.90073e6 | −0.0949090 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.81196e6 | −0.288474 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.27134e7 | −1.61403 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.22890e7 | −0.602714 | −0.301357 | − | 0.953511i | \(-0.597440\pi\) | ||||
−0.301357 | + | 0.953511i | \(0.597440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.03727e7 | −0.993252 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.38292e7 | 2.60885 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.59661e6 | −0.269639 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00050e7 | 0.479189 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.43214e7 | 0.681895 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.65348e7 | 0.782664 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.39815e7 | 1.59908 | 0.799539 | − | 0.600615i | \(-0.205077\pi\) | ||||
0.799539 | + | 0.600615i | \(0.205077\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.51850e7 | −1.64605 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.74121e6 | 0.360045 | 0.180022 | − | 0.983662i | \(-0.442383\pi\) | ||||
0.180022 | + | 0.983662i | \(0.442383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.03603e7 | −1.40386 | −0.701930 | − | 0.712246i | \(-0.747678\pi\) | ||||
−0.701930 | + | 0.712246i | \(0.747678\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.40697e7 | −1.10653 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.02445e7 | −1.38235 | −0.691177 | − | 0.722686i | \(-0.742907\pi\) | ||||
−0.691177 | + | 0.722686i | \(0.742907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.75376e6 | −0.170579 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.40582e7 | −1.08697 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.43180e6 | −0.244002 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.23155e7 | −0.550057 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.01069e7 | 0.448831 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.48236e7 | 1.08985 | 0.544924 | − | 0.838485i | \(-0.316558\pi\) | ||||
0.544924 | + | 0.838485i | \(0.316558\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.94768e7 | −0.850246 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.40667e7 | 1.91281 | 0.956403 | − | 0.292050i | \(-0.0943374\pi\) | ||||
0.956403 | + | 0.292050i | \(0.0943374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.46407e6 | −0.149515 | −0.0747574 | − | 0.997202i | \(-0.523818\pi\) | ||||
−0.0747574 | + | 0.997202i | \(0.523818\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.02327e7 | 1.29754 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.67314e7 | 0.714039 | 0.357020 | − | 0.934097i | \(-0.383793\pi\) | ||||
0.357020 | + | 0.934097i | \(0.383793\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.73933e6 | −0.0738123 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.41903e8 | 5.98820 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.63128e7 | −1.94345 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.34416e7 | −0.560909 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.93891e7 | −1.21957 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −924470. | −0.0381499 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.07983e7 | 0.853523 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.29378e7 | 0.936121 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.18526e7 | −0.481054 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.76952e7 | 0.714227 | 0.357114 | − | 0.934061i | \(-0.383761\pi\) | ||||
0.357114 | + | 0.934061i | \(0.383761\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.28583e7 | −3.72744 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.39235e6 | 0.175348 | 0.0876740 | − | 0.996149i | \(-0.472057\pi\) | ||||
0.0876740 | + | 0.996149i | \(0.472057\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.17423e7 | −1.26026 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.46932e6 | 0.176477 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.37961e6 | 0.250536 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.35758e7 | 0.920825 | 0.460412 | − | 0.887705i | \(-0.347702\pi\) | ||||
0.460412 | + | 0.887705i | \(0.347702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.71314e7 | −2.99628 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.22669e7 | −0.860310 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.09529e6 | −0.157373 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.59633e7 | −2.90338 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.38326e7 | 0.906007 | 0.453004 | − | 0.891509i | \(-0.350352\pi\) | ||||
0.453004 | + | 0.891509i | \(0.350352\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.99115e6 | −0.188724 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.01409e7 | −3.39014 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.19606e7 | −0.447429 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.52434e6 | 0.0939288 | 0.0469644 | − | 0.998897i | \(-0.485045\pi\) | ||||
0.0469644 | + | 0.998897i | \(0.485045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.25898e6 | 0.0465966 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.95629e7 | 1.45651 | 0.728257 | − | 0.685305i | \(-0.240331\pi\) | ||||
0.728257 | + | 0.685305i | \(0.240331\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.08666e7 | 1.49654 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.61272e7 | 0.587461 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.96005e7 | −0.710218 | −0.355109 | − | 0.934825i | \(-0.615556\pi\) | ||||
−0.355109 | + | 0.934825i | \(0.615556\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.51589e7 | 0.546391 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.31323e7 | 0.829406 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.69856e7 | 0.605828 | 0.302914 | − | 0.953018i | \(-0.402041\pi\) | ||||
0.302914 | + | 0.953018i | \(0.402041\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.47815e7 | −0.879265 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.81987e6 | 0.240711 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.27624e7 | −0.448111 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.24546e7 | −0.784325 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.32586e8 | 4.60715 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.95629e6 | −0.344175 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.70160e7 | 0.585184 | 0.292592 | − | 0.956237i | \(-0.405482\pi\) | ||||
0.292592 | + | 0.956237i | \(0.405482\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.99158e7 | 1.70777 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.53215e7 | −0.521499 | −0.260750 | − | 0.965406i | \(-0.583970\pi\) | ||||
−0.260750 | + | 0.965406i | \(0.583970\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.47156e6 | 0.151418 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.27901e6 | 0.245223 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.60455e7 | 0.537795 | 0.268898 | − | 0.963169i | \(-0.413341\pi\) | ||||
0.268898 | + | 0.963169i | \(0.413341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.14675e7 | 1.04931 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.49463e8 | 4.95861 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.45298e7 | 1.46983 | 0.734914 | − | 0.678160i | \(-0.237222\pi\) | ||||
0.734914 | + | 0.678160i | \(0.237222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.06021e7 | 0.348180 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.31123e7 | 1.08192 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.89447e7 | −1.26607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.31862e6 | −0.301417 | −0.150708 | − | 0.988578i | \(-0.548155\pi\) | ||||
−0.150708 | + | 0.988578i | \(0.548155\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.33774e7 | −3.00517 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.45503e6 | −0.142657 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.78418e7 | −1.52430 | −0.762149 | − | 0.647402i | \(-0.775856\pi\) | ||||
−0.762149 | + | 0.647402i | \(0.775856\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.62634e7 | −2.73472 |
(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 | 280.6.a.j.1.5 | ✓ | 5 | |
4.3 | odd | 2 | 560.6.a.y.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.6.a.j.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
560.6.a.y.1.1 | 5 | 4.3 | odd | 2 |