Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [40,6,Mod(1,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("40.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.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: | \(6.41535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 40.1 |
$q$-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 | ||||||||
\(3\) | −18.0000 | −1.15470 | −0.577350 | − | 0.816497i | \(-0.695913\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 242.000 | 1.86668 | 0.933341 | − | 0.358991i | \(-0.116879\pi\) | ||||
0.933341 | + | 0.358991i | \(0.116879\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 656.000 | 1.63464 | 0.817320 | − | 0.576184i | \(-0.195459\pi\) | ||||
0.817320 | + | 0.576184i | \(0.195459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −206.000 | −0.338072 | −0.169036 | − | 0.985610i | \(-0.554065\pi\) | ||||
−0.169036 | + | 0.985610i | \(0.554065\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 450.000 | 0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1690.00 | 1.41829 | 0.709144 | − | 0.705064i | \(-0.249082\pi\) | ||||
0.709144 | + | 0.705064i | \(0.249082\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1364.00 | −0.866823 | −0.433411 | − | 0.901196i | \(-0.642690\pi\) | ||||
−0.433411 | + | 0.901196i | \(0.642690\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4356.00 | −2.15546 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2198.00 | 0.866379 | 0.433190 | − | 0.901303i | \(-0.357388\pi\) | ||||
0.433190 | + | 0.901303i | \(0.357388\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2916.00 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2218.00 | −0.489741 | −0.244871 | − | 0.969556i | \(-0.578745\pi\) | ||||
−0.244871 | + | 0.969556i | \(0.578745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1700.00 | −0.317720 | −0.158860 | − | 0.987301i | \(-0.550782\pi\) | ||||
−0.158860 | + | 0.987301i | \(0.550782\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11808.0 | −1.88752 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6050.00 | −0.834805 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −846.000 | −0.101594 | −0.0507968 | − | 0.998709i | \(-0.516176\pi\) | ||||
−0.0507968 | + | 0.998709i | \(0.516176\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3708.00 | 0.390372 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1818.00 | −0.168902 | −0.0844509 | − | 0.996428i | \(-0.526914\pi\) | ||||
−0.0844509 | + | 0.996428i | \(0.526914\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10534.0 | 0.868805 | 0.434402 | − | 0.900719i | \(-0.356960\pi\) | ||||
0.434402 | + | 0.900719i | \(0.356960\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12074.0 | 0.797272 | 0.398636 | − | 0.917109i | \(-0.369484\pi\) | ||||
0.398636 | + | 0.917109i | \(0.369484\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41757.0 | 2.48450 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −30420.0 | −1.63770 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 32586.0 | 1.59346 | 0.796730 | − | 0.604335i | \(-0.206561\pi\) | ||||
0.796730 | + | 0.604335i | \(0.206561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16400.0 | −0.731033 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24552.0 | 1.00092 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8668.00 | 0.324182 | 0.162091 | − | 0.986776i | \(-0.448176\pi\) | ||||
0.162091 | + | 0.986776i | \(0.448176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34670.0 | −1.19297 | −0.596485 | − | 0.802624i | \(-0.703436\pi\) | ||||
−0.596485 | + | 0.802624i | \(0.703436\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19602.0 | 0.622227 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5150.00 | 0.151190 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −47566.0 | −1.29452 | −0.647261 | − | 0.762268i | \(-0.724086\pi\) | ||||
−0.647261 | + | 0.762268i | \(0.724086\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −39564.0 | −1.00041 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 948.000 | 0.0223184 | 0.0111592 | − | 0.999938i | \(-0.496448\pi\) | ||||
0.0111592 | + | 0.999938i | \(0.496448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −63102.0 | −1.38591 | −0.692957 | − | 0.720979i | \(-0.743692\pi\) | ||||
−0.692957 | + | 0.720979i | \(0.743692\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11250.0 | −0.230940 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 158752. | 3.05135 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 46536.0 | 0.838921 | 0.419461 | − | 0.907773i | \(-0.362219\pi\) | ||||
0.419461 | + | 0.907773i | \(0.362219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −72171.0 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −88778.0 | −1.41452 | −0.707262 | − | 0.706952i | \(-0.750070\pi\) | ||||
−0.707262 | + | 0.706952i | \(0.750070\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −42250.0 | −0.634278 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 39924.0 | 0.565504 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −104934. | −1.40424 | −0.702120 | − | 0.712059i | \(-0.747763\pi\) | ||||
−0.702120 | + | 0.712059i | \(0.747763\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −49852.0 | −0.631072 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 30600.0 | 0.366872 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 34100.0 | 0.387655 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −36254.0 | −0.391225 | −0.195612 | − | 0.980681i | \(-0.562669\pi\) | ||||
−0.195612 | + | 0.980681i | \(0.562669\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 53136.0 | 0.544880 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 42486.0 | 0.414422 | 0.207211 | − | 0.978296i | \(-0.433561\pi\) | ||||
0.207211 | + | 0.978296i | \(0.433561\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 147934. | 1.37396 | 0.686981 | − | 0.726675i | \(-0.258935\pi\) | ||||
0.686981 | + | 0.726675i | \(0.258935\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 108900. | 0.963950 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18390.0 | −0.155282 | −0.0776412 | − | 0.996981i | \(-0.524739\pi\) | ||||
−0.0776412 | + | 0.996981i | \(0.524739\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −145006. | −1.16901 | −0.584507 | − | 0.811389i | \(-0.698712\pi\) | ||||
−0.584507 | + | 0.811389i | \(0.698712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15228.0 | 0.117310 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 82746.0 | 0.609608 | 0.304804 | − | 0.952415i | \(-0.401409\pi\) | ||||
0.304804 | + | 0.952415i | \(0.401409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −54950.0 | −0.387457 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16686.0 | −0.112691 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 408980. | 2.64749 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 269285. | 1.67205 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 32724.0 | 0.195031 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −274446. | −1.50990 | −0.754949 | − | 0.655784i | \(-0.772338\pi\) | ||||
−0.754949 | + | 0.655784i | \(0.772338\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −189612. | −1.00321 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 202608. | 1.03152 | 0.515761 | − | 0.856733i | \(-0.327509\pi\) | ||||
0.515761 | + | 0.856733i | \(0.327509\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −330088. | −1.61808 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −72900.0 | −0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −48142.0 | −0.219141 | −0.109570 | − | 0.993979i | \(-0.534947\pi\) | ||||
−0.109570 | + | 0.993979i | \(0.534947\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −111156. | −0.487973 | −0.243987 | − | 0.969779i | \(-0.578455\pi\) | ||||
−0.243987 | + | 0.969779i | \(0.578455\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −217332. | −0.920610 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −135136. | −0.552626 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 55450.0 | 0.219019 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −751626. | −2.86885 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 243178. | 0.897343 | 0.448672 | − | 0.893697i | \(-0.351897\pi\) | ||||
0.448672 | + | 0.893697i | \(0.351897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 368852. | 1.31647 | 0.658233 | − | 0.752814i | \(-0.271304\pi\) | ||||
0.658233 | + | 0.752814i | \(0.271304\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 136890. | 0.472763 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42500.0 | 0.142089 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 319546. | 1.03463 | 0.517314 | − | 0.855796i | \(-0.326932\pi\) | ||||
0.517314 | + | 0.855796i | \(0.326932\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −586548. | −1.83997 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 531916. | 1.61725 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 69862.0 | 0.205955 | 0.102977 | − | 0.994684i | \(-0.467163\pi\) | ||||
0.102977 | + | 0.994684i | \(0.467163\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 295200. | 0.844124 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −343422. | −0.952877 | −0.476439 | − | 0.879208i | \(-0.658073\pi\) | ||||
−0.476439 | + | 0.879208i | \(0.658073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −328857. | −0.885708 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −110484. | −0.288941 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1142.00 | −0.00290102 | −0.00145051 | − | 0.999999i | \(-0.500462\pi\) | ||||
−0.00145051 | + | 0.999999i | \(0.500462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 151250. | 0.373336 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −156024. | −0.374333 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −86684.0 | −0.202212 | −0.101106 | − | 0.994876i | \(-0.532238\pi\) | ||||
−0.101106 | + | 0.994876i | \(0.532238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −651418. | −1.47796 | −0.738981 | − | 0.673726i | \(-0.764693\pi\) | ||||
−0.738981 | + | 0.673726i | \(0.764693\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 624060. | 1.37752 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21150.0 | 0.0454340 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.10864e6 | 2.31839 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 705672. | 1.43697 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 29140.0 | 0.0577971 | 0.0288986 | − | 0.999582i | \(-0.490800\pi\) | ||||
0.0288986 | + | 0.999582i | \(0.490800\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −646406. | −1.24914 | −0.624571 | − | 0.780968i | \(-0.714726\pi\) | ||||
−0.624571 | + | 0.780968i | \(0.714726\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −92700.0 | −0.174579 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 431138. | 0.791500 | 0.395750 | − | 0.918358i | \(-0.370485\pi\) | ||||
0.395750 | + | 0.918358i | \(0.370485\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −131608. | −0.235586 | −0.117793 | − | 0.993038i | \(-0.537582\pi\) | ||||
−0.117793 | + | 0.993038i | \(0.537582\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 856188. | 1.49479 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −536756. | −0.914191 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 45450.0 | 0.0755352 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 178038. | 0.288793 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −894784. | −1.41694 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.21078e6 | 1.87224 | 0.936118 | − | 0.351686i | \(-0.114392\pi\) | ||||
0.936118 | + | 0.351686i | \(0.114392\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17064.0 | −0.0257710 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −263350. | −0.388541 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −411400. | −0.593082 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.13584e6 | 1.60031 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −348140. | −0.479483 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 34886.0 | 0.0469774 | 0.0234887 | − | 0.999724i | \(-0.492523\pi\) | ||||
0.0234887 | + | 0.999724i | \(0.492523\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −124182. | −0.159954 | −0.0799768 | − | 0.996797i | \(-0.525485\pi\) | ||||
−0.0799768 | + | 0.996797i | \(0.525485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −456386. | −0.575100 | −0.287550 | − | 0.957766i | \(-0.592841\pi\) | ||||
−0.287550 | + | 0.957766i | \(0.592841\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.85754e6 | −3.52340 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 252666. | 0.304900 | 0.152450 | − | 0.988311i | \(-0.451284\pi\) | ||||
0.152450 | + | 0.988311i | \(0.451284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −301850. | −0.356551 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −837648. | −0.968703 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 65064.0 | 0.0736794 | 0.0368397 | − | 0.999321i | \(-0.488271\pi\) | ||||
0.0368397 | + | 0.999321i | \(0.488271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.40600e6 | −1.55935 | −0.779675 | − | 0.626185i | \(-0.784615\pi\) | ||||
−0.779675 | + | 0.626185i | \(0.784615\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 590490. | 0.641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.04392e6 | −1.11110 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 280984. | 0.293048 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.59800e6 | 1.63335 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −548400. | −0.549431 | −0.274715 | − | 0.961526i | \(-0.588584\pi\) | ||||
−0.274715 | + | 0.961526i | \(0.588584\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.44189e6 | 1.41622 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 760500. | 0.732401 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −493830. | −0.466385 | −0.233193 | − | 0.972431i | \(-0.574917\pi\) | ||||
−0.233193 | + | 0.972431i | \(0.574917\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −204732. | −0.189643 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −179658. | −0.163247 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.07181e6 | −0.955495 | −0.477748 | − | 0.878497i | \(-0.658547\pi\) | ||||
−0.477748 | + | 0.878497i | \(0.658547\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −814650. | −0.712617 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.88881e6 | 1.62148 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 999394. | 0.842085 | 0.421043 | − | 0.907041i | \(-0.361664\pi\) | ||||
0.421043 | + | 0.907041i | \(0.361664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.00760e6 | 0.833425 | 0.416713 | − | 0.909038i | \(-0.363182\pi\) | ||||
0.416713 | + | 0.909038i | \(0.363182\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 897336. | 0.728700 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 410000. | 0.326928 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.02286e6 | 0.800969 | 0.400485 | − | 0.916303i | \(-0.368842\pi\) | ||||
0.400485 | + | 0.916303i | \(0.368842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −137700. | −0.105907 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.18172e6 | −0.892790 | −0.446395 | − | 0.894836i | \(-0.647292\pi\) | ||||
−0.446395 | + | 0.894836i | \(0.647292\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −917506. | −0.680993 | −0.340497 | − | 0.940246i | \(-0.610595\pi\) | ||||
−0.340497 | + | 0.940246i | \(0.610595\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −613800. | −0.447625 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −439956. | −0.315286 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.43624e6 | 1.01154 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 652572. | 0.451748 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −512302. | −0.348624 | −0.174312 | − | 0.984690i | \(-0.555770\pi\) | ||||
−0.174312 | + | 0.984690i | \(0.555770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −216700. | −0.144979 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.91290e6 | 1.25835 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −452788. | −0.292898 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.54923e6 | 1.62178 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −764748. | −0.478533 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 866750. | 0.533512 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.40946e6 | 0.853505 | 0.426753 | − | 0.904368i | \(-0.359658\pi\) | ||||
0.426753 | + | 0.904368i | \(0.359658\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.66281e6 | −1.58652 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.78604e6 | −1.63337 | −0.816687 | − | 0.577081i | \(-0.804192\pi\) | ||||
−0.816687 | + | 0.577081i | \(0.804192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.55086e6 | 0.894770 | 0.447385 | − | 0.894342i | \(-0.352355\pi\) | ||||
0.447385 | + | 0.894342i | \(0.352355\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −490050. | −0.278268 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 377322. | 0.210894 | 0.105447 | − | 0.994425i | \(-0.466373\pi\) | ||||
0.105447 | + | 0.994425i | \(0.466373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.45501e6 | −0.800550 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 331020. | 0.179305 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.30516e6 | −1.22940 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −128750. | −0.0676143 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.61011e6 | 1.34986 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.92191e6 | 1.48825 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.63063e6 | −0.818062 | −0.409031 | − | 0.912521i | \(-0.634133\pi\) | ||||
−0.409031 | + | 0.912521i | \(0.634133\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −68526.0 | −0.0338645 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.18915e6 | 0.578928 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.36717e6 | −1.61506 | −0.807532 | − | 0.589824i | \(-0.799197\pi\) | ||||
−0.807532 | + | 0.589824i | \(0.799197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.48943e6 | −0.703915 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.11520e6 | −0.519358 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.03790e6 | 2.77109 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 989100. | 0.447396 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 837202. | 0.373256 | 0.186628 | − | 0.982431i | \(-0.440244\pi\) | ||||
0.186628 | + | 0.982431i | \(0.440244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.51910e6 | −0.667609 | −0.333805 | − | 0.942642i | \(-0.608333\pi\) | ||||
−0.333805 | + | 0.942642i | \(0.608333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −600696. | −0.260248 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.51851e6 | −1.50287 | −0.751436 | − | 0.659806i | \(-0.770638\pi\) | ||||
−0.751436 | + | 0.659806i | \(0.770638\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23700.0 | −0.00998108 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.36164e6 | −3.05706 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.57089e6 | −1.46231 | −0.731156 | − | 0.682210i | \(-0.761019\pi\) | ||||
−0.731156 | + | 0.682210i | \(0.761019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −615603. | −0.248618 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.84713e6 | −1.93071 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.57755e6 | 0.619799 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.58231e6 | −1.38835 | −0.694173 | − | 0.719808i | \(-0.744230\pi\) | ||||
−0.694173 | + | 0.719808i | \(0.744230\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −147258. | −0.0563006 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.88581e6 | 2.97448 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 635530. | 0.236518 | 0.118259 | − | 0.992983i | \(-0.462269\pi\) | ||||
0.118259 | + | 0.992983i | \(0.462269\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 281250. | 0.103280 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 456908. | 0.165568 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 67060.0 | 0.0239809 | 0.0119905 | − | 0.999928i | \(-0.496183\pi\) | ||||
0.0119905 | + | 0.999928i | \(0.496183\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.94003e6 | 1.74348 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.45129e6 | 1.55056 | 0.775280 | − | 0.631618i | \(-0.217609\pi\) | ||||
0.775280 | + | 0.631618i | \(0.217609\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.96880e6 | −1.36461 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 853254. | 0.289602 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.79825e6 | 1.94278 | 0.971388 | − | 0.237496i | \(-0.0763267\pi\) | ||||
0.971388 | + | 0.237496i | \(0.0763267\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.71462e6 | 1.22878 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.64694e6 | −1.19110 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.16340e6 | −0.375177 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 333874. | 0.106318 | 0.0531589 | − | 0.998586i | \(-0.483071\pi\) | ||||
0.0531589 | + | 0.998586i | \(0.483071\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.94158e6 | 1.86840 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.55689e6 | −0.794057 | −0.397029 | − | 0.917806i | \(-0.629959\pi\) | ||||
−0.397029 | + | 0.917806i | \(0.629959\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 350200. | 0.107412 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.80428e6 | 0.546594 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −554976. | −0.166069 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.05511e6 | −0.903063 | −0.451531 | − | 0.892255i | \(-0.649122\pi\) | ||||
−0.451531 | + | 0.892255i | \(0.649122\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 866556. | 0.253042 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.09766e6 | 0.605145 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.21945e6 | 0.632594 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.00081e6 | 0.563463 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.54347e6 | −0.986038 | −0.493019 | − | 0.870019i | \(-0.664107\pi\) | ||||
−0.493019 | + | 0.870019i | \(0.664107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.97294e6 | 0.542511 | 0.271255 | − | 0.962507i | \(-0.412561\pi\) | ||||
0.271255 | + | 0.962507i | \(0.412561\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 977994. | 0.265757 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.05625e6 | 0.283658 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.39014e6 | −2.22689 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.43245e6 | 0.638117 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.37396e6 | 0.356270 | 0.178135 | − | 0.984006i | \(-0.442994\pi\) | ||||
0.178135 | + | 0.984006i | \(0.442994\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.18813e6 | 1.32981 | 0.664907 | − | 0.746926i | \(-0.268471\pi\) | ||||
0.664907 | + | 0.746926i | \(0.268471\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −998100. | −0.252901 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.99807e6 | −0.750997 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.94082e6 | −0.728296 | −0.364148 | − | 0.931341i | \(-0.618640\pi\) | ||||
−0.364148 | + | 0.931341i | \(0.618640\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.38232e6 | 0.828167 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.28347e6 | −0.310724 | −0.155362 | − | 0.987858i | \(-0.549654\pi\) | ||||
−0.155362 | + | 0.987858i | \(0.549654\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.62335e6 | 0.627995 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.37720e6 | −1.03616 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.95263e6 | −1.15937 | −0.579683 | − | 0.814842i | \(-0.696824\pi\) | ||||
−0.579683 | + | 0.814842i | \(0.696824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.19261e6 | −0.276094 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.63934e6 | −1.52012 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.24630e6 | 0.282224 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.91315e6 | 1.77239 | 0.886194 | − | 0.463315i | \(-0.153340\pi\) | ||||
0.886194 | + | 0.463315i | \(0.153340\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.92804e6 | 1.09180 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.18530e6 | −1.35553 | −0.677764 | − | 0.735280i | \(-0.737051\pi\) | ||||
−0.677764 | + | 0.735280i | \(0.737051\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 491934. | 0.106648 | 0.0533242 | − | 0.998577i | \(-0.483018\pi\) | ||||
0.0533242 | + | 0.998577i | \(0.483018\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −765000. | −0.164070 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 447442. | 0.0949390 | 0.0474695 | − | 0.998873i | \(-0.484884\pi\) | ||||
0.0474695 | + | 0.998873i | \(0.484884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.15110e7 | −2.41646 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.75183e6 | −1.19469 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.91030e6 | 1.42018 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −852500. | −0.173365 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.63947e6 | 0.531154 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.18487e6 | 1.62995 | 0.814973 | − | 0.579499i | \(-0.196752\pi\) | ||||
0.814973 | + | 0.579499i | \(0.196752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 174276. | 0.0343459 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.57449e6 | −1.86744 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 906350. | 0.174961 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.21524e6 | 1.18751 | 0.593753 | − | 0.804648i | \(-0.297646\pi\) | ||||
0.593753 | + | 0.804648i | \(0.297646\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.25752e6 | −0.237816 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 827856. | 0.154971 | 0.0774856 | − | 0.996993i | \(-0.475311\pi\) | ||||
0.0774856 | + | 0.996993i | \(0.475311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.74842e6 | −0.694594 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.32840e6 | −0.243678 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 229416. | 0.0416613 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.04004e7 | −1.86982 | −0.934908 | − | 0.354890i | \(-0.884518\pi\) | ||||
−0.934908 | + | 0.354890i | \(0.884518\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.18160e6 | 1.10029 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.03821e6 | 0.359193 | 0.179597 | − | 0.983740i | \(-0.442521\pi\) | ||||
0.179597 | + | 0.983740i | \(0.442521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.06215e6 | −0.185335 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.91943e6 | 1.02273 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.66133e6 | 0.626390 | 0.313195 | − | 0.949689i | \(-0.398601\pi\) | ||||
0.313195 | + | 0.949689i | \(0.398601\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.52707e7 | −2.58706 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.97742e6 | −0.667281 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.69835e6 | −0.614455 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.92054e6 | 1.30325 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20556.0 | 0.00334981 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.24713e6 | 0.524089 | 0.262045 | − | 0.965056i | \(-0.415603\pi\) | ||||
0.262045 | + | 0.965056i | \(0.415603\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.97357e6 | −0.795086 | −0.397543 | − | 0.917584i | \(-0.630137\pi\) | ||||
−0.397543 | + | 0.917584i | \(0.630137\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.72250e6 | −0.431092 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.87300e6 | −0.450619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.60514e6 | −0.249387 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 702108. | 0.108061 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 374508. | 0.0571009 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 459750. | 0.0694444 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.56031e6 | 0.233494 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.73926e7 | 4.06126 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.42544e6 | 0.356285 | 0.178142 | − | 0.984005i | \(-0.442991\pi\) | ||||
0.178142 | + | 0.984005i | \(0.442991\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.17255e7 | 1.70660 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.62515e6 | 0.522799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −731254. | −0.104496 | −0.0522480 | − | 0.998634i | \(-0.516639\pi\) | ||||
−0.0522480 | + | 0.998634i | \(0.516639\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.80827e6 | −0.397656 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.02535e6 | 0.424519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.12617e7 | 1.56600 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −380700. | −0.0524627 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.71992e6 | 1.05433 | 0.527163 | − | 0.849764i | \(-0.323256\pi\) | ||||
0.527163 | + | 0.849764i | \(0.323256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.17000e6 | −0.293718 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.99555e7 | −2.67705 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.10576e6 | 0.412949 | 0.206475 | − | 0.978452i | \(-0.433801\pi\) | ||||
0.206475 | + | 0.978452i | \(0.433801\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.06865e6 | −0.272625 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.74654e7 | −2.28150 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −482498. | −0.0624762 | −0.0312381 | − | 0.999512i | \(-0.509945\pi\) | ||||
−0.0312381 | + | 0.999512i | \(0.509945\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.38502e7 | 1.77773 | 0.888865 | − | 0.458169i | \(-0.151495\pi\) | ||||
0.888865 | + | 0.458169i | \(0.151495\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −524520. | −0.0667384 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.37375e6 | 0.173276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.09764e6 | 0.887513 | 0.443756 | − | 0.896147i | \(-0.353646\pi\) | ||||
0.443756 | + | 0.896147i | \(0.353646\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.16353e7 | 1.44239 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.14843e7 | −2.64046 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.13764e7 | 2.60473 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 417150. | 0.0503968 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.56926e6 | 0.187975 | 0.0939873 | − | 0.995573i | \(-0.470039\pi\) | ||||
0.0939873 | + | 0.995573i | \(0.470039\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.31880e6 | 0.275407 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.76048e6 | −0.913945 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.30477e7 | −1.52370 | −0.761848 | − | 0.647756i | \(-0.775707\pi\) | ||||
−0.761848 | + | 0.647756i | \(0.775707\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.02245e7 | −1.18399 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.36894e6 | 0.272031 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.24688e6 | −0.597495 | −0.298747 | − | 0.954332i | \(-0.596569\pi\) | ||||
−0.298747 | + | 0.954332i | \(0.596569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.57316e6 | −0.629384 | −0.314692 | − | 0.949194i | \(-0.601901\pi\) | ||||
−0.314692 | + | 0.949194i | \(0.601901\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.85285e6 | −0.431508 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.73212e6 | −0.747763 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.98249e6 | 0.218393 | 0.109197 | − | 0.994020i | \(-0.465172\pi\) | ||||
0.109197 | + | 0.994020i | \(0.465172\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.66161e6 | 1.05562 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.48724e6 | −0.269535 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 969810. | 0.104240 | 0.0521201 | − | 0.998641i | \(-0.483402\pi\) | ||||
0.0521201 | + | 0.998641i | \(0.483402\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −818100. | −0.0872205 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.12946e7 | −1.19442 | −0.597211 | − | 0.802084i | \(-0.703725\pi\) | ||||
−0.597211 | + | 0.802084i | \(0.703725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.80728e7 | −1.89583 | −0.947914 | − | 0.318528i | \(-0.896812\pi\) | ||||
−0.947914 | + | 0.318528i | \(0.896812\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.40937e6 | 0.666939 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.53940e7 | −2.62127 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.61061e7 | 1.63615 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.42974e6 | −0.144089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.62634e6 | 0.462556 | 0.231278 | − | 0.972888i | \(-0.425709\pi\) | ||||
0.231278 | + | 0.972888i | \(0.425709\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.17941e7 | −2.16187 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.86115e6 | 0.675247 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.60194e6 | −0.839939 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 76788.0 | 0.00743946 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.99058e7 | 1.91352 | 0.956762 | − | 0.290871i | \(-0.0939452\pi\) | ||||
0.956762 | + | 0.290871i | \(0.0939452\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.21078e7 | 1.15489 | 0.577443 | − | 0.816431i | \(-0.304051\pi\) | ||||
0.577443 | + | 0.816431i | \(0.304051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.74030e6 | 0.448649 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.53124e6 | −0.237724 | −0.118862 | − | 0.992911i | \(-0.537925\pi\) | ||||
−0.118862 | + | 0.992911i | \(0.537925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.68621e6 | 0.529921 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.40520e6 | 0.684832 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.37043e7 | 1.25770 | 0.628848 | − | 0.777529i | \(-0.283527\pi\) | ||||
0.628848 | + | 0.777529i | \(0.283527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.06520e6 | −0.461311 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.11126e6 | −0.461971 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.83320e6 | −0.882026 | −0.441013 | − | 0.897501i | \(-0.645381\pi\) | ||||
−0.441013 | + | 0.897501i | \(0.645381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.68687e6 | 0.595278 | 0.297639 | − | 0.954679i | \(-0.403801\pi\) | ||||
0.297639 | + | 0.954679i | \(0.403801\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.26652e6 | 0.553659 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.25220e6 | 0.723628 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.87516e6 | −0.424302 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −627948. | −0.0542448 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.27435e7 | −1.95008 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −727566. | −0.0619205 | −0.0309603 | − | 0.999521i | \(-0.509857\pi\) | ||||
−0.0309603 | + | 0.999521i | \(0.509857\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.82250e6 | 0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.86951e7 | 1.56768 | 0.783839 | − | 0.620964i | \(-0.213259\pi\) | ||||
0.783839 | + | 0.620964i | \(0.213259\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.77347e6 | −0.730293 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.23528e6 | 0.184699 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.79850e7 | −1.47523 | −0.737614 | − | 0.675223i | \(-0.764048\pi\) | ||||
−0.737614 | + | 0.675223i | \(0.764048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.20355e6 | 0.0980026 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.21495e6 | 0.664069 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.71272e6 | −0.538704 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.20006e6 | 0.0956107 | 0.0478053 | − | 0.998857i | \(-0.484777\pi\) | ||||
0.0478053 | + | 0.998857i | \(0.484777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.28589e7 | 1.01712 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.77890e6 | 0.218228 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.07242e6 | −0.239551 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.54799e6 | −0.352068 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.15194e7 | −0.885393 | −0.442697 | − | 0.896671i | \(-0.645978\pi\) | ||||
−0.442697 | + | 0.896671i | \(0.645978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.15394e6 | 0.0880636 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.43330e6 | 0.411710 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.02816e7 | 0.773593 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −610738. | −0.0456288 | −0.0228144 | − | 0.999740i | \(-0.507263\pi\) | ||||
−0.0228144 | + | 0.999740i | \(0.507263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.76942e6 | 0.279640 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.73660e6 | −0.275266 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.37840e6 | 0.247142 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.17115e6 | −0.0850776 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.97278e6 | 0.286597 | 0.143299 | − | 0.989680i | \(-0.454229\pi\) | ||||
0.143299 | + | 0.989680i | \(0.454229\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.58000e7 | 2.56475 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.53080e7 | 1.80058 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.38625e6 | −0.0979482 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.23220e7 | −0.864658 | −0.432329 | − | 0.901716i | \(-0.642308\pi\) | ||||
−0.432329 | + | 0.901716i | \(0.642308\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.90873e6 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.78025e7 | 1.23222 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.14579e6 | 0.559981 | 0.279990 | − | 0.960003i | \(-0.409669\pi\) | ||||
0.279990 | + | 0.960003i | \(0.409669\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.87906e7 | 1.28299 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.12033e7 | −2.11608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.16653e6 | 0.482723 | 0.241361 | − | 0.970435i | \(-0.422406\pi\) | ||||
0.241361 | + | 0.970435i | \(0.422406\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.05771e6 | −0.338383 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.65041e6 | −0.375498 | −0.187749 | − | 0.982217i | \(-0.560119\pi\) | ||||
−0.187749 | + | 0.982217i | \(0.560119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.07945e6 | −0.401304 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.19102e6 | −0.471508 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.45038e6 | −0.289863 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.09500e6 | 0.588441 | 0.294221 | − | 0.955738i | \(-0.404940\pi\) | ||||
0.294221 | + | 0.955738i | \(0.404940\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.87120e6 | 0.634428 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.22130e6 | −0.588742 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.12880e7 | −0.715944 | −0.357972 | − | 0.933732i | \(-0.616532\pi\) | ||||
−0.357972 | + | 0.933732i | \(0.616532\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.59540e7 | −1.63531 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.52933e7 | 0.957283 | 0.478641 | − | 0.878011i | \(-0.341129\pi\) | ||||
0.478641 | + | 0.878011i | \(0.341129\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.50915e7 | −2.18218 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.42225e6 | −0.211426 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.78561e6 | −0.109597 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.77402e6 | 0.108179 | 0.0540894 | − | 0.998536i | \(-0.482774\pi\) | ||||
0.0540894 | + | 0.998536i | \(0.482774\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.88894e6 | 0.538535 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.46441e7 | −0.881484 | −0.440742 | − | 0.897634i | \(-0.645285\pi\) | ||||
−0.440742 | + | 0.897634i | \(0.645285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.06250e6 | −0.0635440 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.68518e6 | 0.218981 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.47975e6 | 0.146408 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 621888. | 0.0364825 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.46769e6 | −0.377003 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.98865e6 | −0.462700 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.97074e6 | −0.343630 | −0.171815 | − | 0.985129i | \(-0.554963\pi\) | ||||
−0.171815 | + | 0.985129i | \(0.554963\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.92926e7 | 1.10331 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00245e7 | 1.13794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.14202e6 | 0.403309 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.46637e7 | 0.822860 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.40500e7 | −1.89876 | −0.949382 | − | 0.314125i | \(-0.898289\pi\) | ||||
−0.949382 | + | 0.314125i | \(0.898289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.04051e7 | 1.13076 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.49965e6 | −0.468080 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.13949e7 | −2.26547 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.32979e7 | −0.723258 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.79891e7 | −0.972356 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.63540e7 | −1.41571 | −0.707857 | − | 0.706356i | \(-0.750338\pi\) | ||||
−0.707857 | + | 0.706356i | \(0.750338\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.49658e6 | −0.507008 | −0.253504 | − | 0.967334i | \(-0.581583\pi\) | ||||
−0.253504 | + | 0.967334i | \(0.581583\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.81369e7 | −0.962357 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.74655e6 | −0.0921058 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.43684e7 | −0.753100 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.03801e6 | −0.210357 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.59887e7 | −0.827856 | −0.413928 | − | 0.910310i | \(-0.635843\pi\) | ||||
−0.413928 | + | 0.910310i | \(0.635843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.18347e7 | 1.63833 | 0.819164 | − | 0.573559i | \(-0.194438\pi\) | ||||
0.819164 | + | 0.573559i | \(0.194438\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.38000e6 | −0.377504 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.27575e7 | 0.648635 | 0.324317 | − | 0.945948i | \(-0.394865\pi\) | ||||
0.324317 | + | 0.945948i | \(0.394865\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.18613e6 | 0.312631 | 0.156316 | − | 0.987707i | \(-0.450038\pi\) | ||||
0.156316 | + | 0.987707i | \(0.450038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.84114e7 | −0.924880 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.05693e7 | 3.52374 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.58555e6 | 0.426140 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.95720e6 | −0.244581 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.66754e6 | −0.277965 | −0.138982 | − | 0.990295i | \(-0.544383\pi\) | ||||
−0.138982 | + | 0.990295i | \(0.544383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.55916e7 | −0.760154 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.12710e7 | 1.03091 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.22142e6 | 0.396100 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.51670e7 | 3.12118 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.65151e7 | 0.786343 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.85951e6 | −0.0880185 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.76010e7 | −0.828257 | −0.414129 | − | 0.910218i | \(-0.635914\pi\) | ||||
−0.414129 | + | 0.910218i | \(0.635914\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.76210e6 | 0.129218 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 162162. | 0.00754218 | 0.00377109 | − | 0.999993i | \(-0.498800\pi\) | ||||
0.00377109 | + | 0.999993i | \(0.498800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.10520e6 | −0.328544 | −0.164272 | − | 0.986415i | \(-0.552527\pi\) | ||||
−0.164272 | + | 0.986415i | \(0.552527\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.91921e6 | 0.364061 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.08956e6 | 0.186917 | 0.0934586 | − | 0.995623i | \(-0.470208\pi\) | ||||
0.0934586 | + | 0.995623i | \(0.470208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28550.0 | 0.00129738 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.58524e7 | −1.16803 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.05276e7 | 1.37133 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.79860e6 | 0.437641 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.93657e6 | −0.130408 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.78125e6 | −0.166961 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 809194. | 0.0355266 | 0.0177633 | − | 0.999842i | \(-0.494345\pi\) | ||||
0.0177633 | + | 0.999842i | \(0.494345\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.22144e6 | 0.402556 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.90411e6 | 0.169466 | 0.0847329 | − | 0.996404i | \(-0.472996\pi\) | ||||
0.0847329 | + | 0.996404i | \(0.472996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.58290e7 | 1.54644 | 0.773220 | − | 0.634138i | \(-0.218645\pi\) | ||||
0.773220 | + | 0.634138i | \(0.218645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.90060e6 | 0.167407 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.77571e7 | 1.18458 | 0.592290 | − | 0.805725i | \(-0.298224\pi\) | ||||
0.592290 | + | 0.805725i | \(0.298224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.64159e7 | −2.81850 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.73442e7 | −1.99789 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.64689e7 | −0.691094 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.16710e6 | 0.0904318 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.15018e6 | 0.338210 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.77060e6 | 0.155601 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.50703e7 | 2.25999 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.58861e7 | −1.87267 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.62855e7 | 0.660965 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.01914e7 | 0.814981 | 0.407490 | − | 0.913209i | \(-0.366404\pi\) | ||||
0.407490 | + | 0.913209i | \(0.366404\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.44137e6 | 0.138141 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.75179e7 | 1.09855 | 0.549274 | − | 0.835642i | \(-0.314904\pi\) | ||||
0.549274 | + | 0.835642i | \(0.314904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.82384e7 | −2.31224 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.56015e7 | −0.616047 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.90311e7 | 1.92552 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.31786e7 | 0.514730 | 0.257365 | − | 0.966314i | \(-0.417146\pi\) | ||||
0.257365 | + | 0.966314i | \(0.417146\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.53702e7 | −0.985543 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −195288. | −0.00754521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −528750. | −0.0203187 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.19827e7 | 0.457988 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.00688e7 | 1.52323 | 0.761617 | − | 0.648027i | \(-0.224406\pi\) | ||||
0.761617 | + | 0.648027i | \(0.224406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.69565e7 | −2.15362 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.01486e7 | 1.88606 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.77160e7 | −1.03682 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.04258e7 | 1.13212 | 0.566060 | − | 0.824364i | \(-0.308467\pi\) | ||||
0.566060 | + | 0.824364i | \(0.308467\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.79154e7 | −1.03319 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.26349e7 | −1.20146 | −0.600729 | − | 0.799452i | \(-0.705123\pi\) | ||||
−0.600729 | + | 0.799452i | \(0.705123\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.99596e6 | −0.146333 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.76418e7 | −0.642634 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.01534e7 | 1.09260 | 0.546300 | − | 0.837589i | \(-0.316036\pi\) | ||||
0.546300 | + | 0.837589i | \(0.316036\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.29990e7 | 0.468538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.79180e6 | −0.243519 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 303066. | 0.0108095 | 0.00540474 | − | 0.999985i | \(-0.498280\pi\) | ||||
0.00540474 | + | 0.999985i | \(0.498280\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −728500. | −0.0258477 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.61901e7 | 0.924396 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.16504e7 | −0.409066 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.57392e7 | −0.899054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.48959e6 | −0.0517608 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.61601e7 | 0.558634 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.39863e6 | −0.254440 | −0.127220 | − | 0.991875i | \(-0.540605\pi\) | ||||
−0.127220 | + | 0.991875i | \(0.540605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.14929e7 | 1.41959 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.18414e6 | −0.210490 | −0.105245 | − | 0.994446i | \(-0.533563\pi\) | ||||
−0.105245 | + | 0.994446i | \(0.533563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.68998e7 | −0.910891 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.31750e6 | 0.0780743 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.63928e6 | 0.0549436 | 0.0274718 | − | 0.999623i | \(-0.491254\pi\) | ||||
0.0274718 | + | 0.999623i | \(0.491254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.88367e7 | −2.29543 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.17455e7 | −0.389671 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.13020e7 | −0.373052 | −0.186526 | − | 0.982450i | \(-0.559723\pi\) | ||||
−0.186526 | + | 0.982450i | \(0.559723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.07784e7 | −0.353969 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.25943e7 | −1.71849 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.31537e7 | 0.752714 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.12643e6 | 0.101126 | 0.0505632 | − | 0.998721i | \(-0.483898\pi\) | ||||
0.0505632 | + | 0.998721i | \(0.483898\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.93514e7 | 0.944616 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.29020e6 | 0.105357 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.55827e7 | −1.13371 | −0.566854 | − | 0.823818i | \(-0.691840\pi\) | ||||
−0.566854 | + | 0.823818i | \(0.691840\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.46694e6 | −0.0782067 |
(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 | 40.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 360.6.a.i.1.1 | 1 | |||
4.3 | odd | 2 | 80.6.a.g.1.1 | 1 | |||
5.2 | odd | 4 | 200.6.c.b.49.2 | 2 | |||
5.3 | odd | 4 | 200.6.c.b.49.1 | 2 | |||
5.4 | even | 2 | 200.6.a.d.1.1 | 1 | |||
8.3 | odd | 2 | 320.6.a.d.1.1 | 1 | |||
8.5 | even | 2 | 320.6.a.m.1.1 | 1 | |||
12.11 | even | 2 | 720.6.a.k.1.1 | 1 | |||
20.3 | even | 4 | 400.6.c.e.49.2 | 2 | |||
20.7 | even | 4 | 400.6.c.e.49.1 | 2 | |||
20.19 | odd | 2 | 400.6.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
80.6.a.g.1.1 | 1 | 4.3 | odd | 2 | |||
200.6.a.d.1.1 | 1 | 5.4 | even | 2 | |||
200.6.c.b.49.1 | 2 | 5.3 | odd | 4 | |||
200.6.c.b.49.2 | 2 | 5.2 | odd | 4 | |||
320.6.a.d.1.1 | 1 | 8.3 | odd | 2 | |||
320.6.a.m.1.1 | 1 | 8.5 | even | 2 | |||
360.6.a.i.1.1 | 1 | 3.2 | odd | 2 | |||
400.6.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
400.6.c.e.49.1 | 2 | 20.7 | even | 4 | |||
400.6.c.e.49.2 | 2 | 20.3 | even | 4 | |||
720.6.a.k.1.1 | 1 | 12.11 | even | 2 |