Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,6,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(1.44345437832\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.00000 | 1.06066 | 0.530330 | − | 0.847791i | \(-0.322068\pi\) | ||||
0.530330 | + | 0.847791i | \(0.322068\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.125000 | ||||||||
\(5\) | −6.00000 | −0.107331 | −0.0536656 | − | 0.998559i | \(-0.517091\pi\) | ||||
−0.0536656 | + | 0.998559i | \(0.517091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −40.0000 | −0.308542 | −0.154271 | − | 0.988029i | \(-0.549303\pi\) | ||||
−0.154271 | + | 0.988029i | \(0.549303\pi\) | |||||||
\(8\) | −168.000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −36.0000 | −0.113842 | ||||||||
\(11\) | 564.000 | 1.40539 | 0.702696 | − | 0.711490i | \(-0.251979\pi\) | ||||
0.702696 | + | 0.711490i | \(0.251979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 638.000 | 1.04704 | 0.523519 | − | 0.852014i | \(-0.324619\pi\) | ||||
0.523519 | + | 0.852014i | \(0.324619\pi\) | |||||||
\(14\) | −240.000 | −0.327259 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1136.00 | −1.10938 | ||||||||
\(17\) | −882.000 | −0.740195 | −0.370098 | − | 0.928993i | \(-0.620676\pi\) | ||||
−0.370098 | + | 0.928993i | \(0.620676\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −556.000 | −0.353338 | −0.176669 | − | 0.984270i | \(-0.556532\pi\) | ||||
−0.176669 | + | 0.984270i | \(0.556532\pi\) | |||||||
\(20\) | −24.0000 | −0.0134164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3384.00 | 1.49064 | ||||||||
\(23\) | 840.000 | 0.331100 | 0.165550 | − | 0.986201i | \(-0.447060\pi\) | ||||
0.165550 | + | 0.986201i | \(0.447060\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3089.00 | −0.988480 | ||||||||
\(26\) | 3828.00 | 1.11055 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −160.000 | −0.0385678 | ||||||||
\(29\) | −4638.00 | −1.02408 | −0.512042 | − | 0.858960i | \(-0.671111\pi\) | ||||
−0.512042 | + | 0.858960i | \(0.671111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4400.00 | 0.822334 | 0.411167 | − | 0.911560i | \(-0.365121\pi\) | ||||
0.411167 | + | 0.911560i | \(0.365121\pi\) | |||||||
\(32\) | −1440.00 | −0.248592 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5292.00 | −0.785096 | ||||||||
\(35\) | 240.000 | 0.0331162 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2410.00 | −0.289409 | −0.144705 | − | 0.989475i | \(-0.546223\pi\) | ||||
−0.144705 | + | 0.989475i | \(0.546223\pi\) | |||||||
\(38\) | −3336.00 | −0.374772 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1008.00 | 0.0996117 | ||||||||
\(41\) | 6870.00 | 0.638259 | 0.319130 | − | 0.947711i | \(-0.396609\pi\) | ||||
0.319130 | + | 0.947711i | \(0.396609\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9644.00 | 0.795401 | 0.397700 | − | 0.917515i | \(-0.369808\pi\) | ||||
0.397700 | + | 0.917515i | \(0.369808\pi\) | |||||||
\(44\) | 2256.00 | 0.175674 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5040.00 | 0.351185 | ||||||||
\(47\) | 18672.0 | 1.23295 | 0.616476 | − | 0.787374i | \(-0.288560\pi\) | ||||
0.616476 | + | 0.787374i | \(0.288560\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15207.0 | −0.904802 | ||||||||
\(50\) | −18534.0 | −1.04844 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2552.00 | 0.130880 | ||||||||
\(53\) | −33750.0 | −1.65038 | −0.825190 | − | 0.564855i | \(-0.808932\pi\) | ||||
−0.825190 | + | 0.564855i | \(0.808932\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3384.00 | −0.150842 | ||||||||
\(56\) | 6720.00 | 0.286351 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −27828.0 | −1.08621 | ||||||||
\(59\) | 18084.0 | 0.676339 | 0.338170 | − | 0.941085i | \(-0.390192\pi\) | ||||
0.338170 | + | 0.941085i | \(0.390192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39758.0 | 1.36804 | 0.684022 | − | 0.729462i | \(-0.260229\pi\) | ||||
0.684022 | + | 0.729462i | \(0.260229\pi\) | |||||||
\(62\) | 26400.0 | 0.872217 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 27712.0 | 0.845703 | ||||||||
\(65\) | −3828.00 | −0.112380 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −23068.0 | −0.627802 | −0.313901 | − | 0.949456i | \(-0.601636\pi\) | ||||
−0.313901 | + | 0.949456i | \(0.601636\pi\) | |||||||
\(68\) | −3528.00 | −0.0925244 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1440.00 | 0.0351251 | ||||||||
\(71\) | 4248.00 | 0.100009 | 0.0500044 | − | 0.998749i | \(-0.484076\pi\) | ||||
0.0500044 | + | 0.998749i | \(0.484076\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −41110.0 | −0.902901 | −0.451451 | − | 0.892296i | \(-0.649093\pi\) | ||||
−0.451451 | + | 0.892296i | \(0.649093\pi\) | |||||||
\(74\) | −14460.0 | −0.306965 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2224.00 | −0.0441673 | ||||||||
\(77\) | −22560.0 | −0.433623 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 21920.0 | 0.395160 | 0.197580 | − | 0.980287i | \(-0.436692\pi\) | ||||
0.197580 | + | 0.980287i | \(0.436692\pi\) | |||||||
\(80\) | 6816.00 | 0.119071 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 41220.0 | 0.676976 | ||||||||
\(83\) | −82452.0 | −1.31373 | −0.656865 | − | 0.754008i | \(-0.728118\pi\) | ||||
−0.656865 | + | 0.754008i | \(0.728118\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5292.00 | 0.0794461 | ||||||||
\(86\) | 57864.0 | 0.843650 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −94752.0 | −1.30431 | ||||||||
\(89\) | 94086.0 | 1.25907 | 0.629535 | − | 0.776972i | \(-0.283245\pi\) | ||||
0.629535 | + | 0.776972i | \(0.283245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25520.0 | −0.323056 | ||||||||
\(92\) | 3360.00 | 0.0413875 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 112032. | 1.30774 | ||||||||
\(95\) | 3336.00 | 0.0379243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 49442.0 | 0.533540 | 0.266770 | − | 0.963760i | \(-0.414044\pi\) | ||||
0.266770 | + | 0.963760i | \(0.414044\pi\) | |||||||
\(98\) | −91242.0 | −0.959687 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12356.0 | −0.123560 | ||||||||
\(101\) | 143034. | 1.39520 | 0.697599 | − | 0.716488i | \(-0.254252\pi\) | ||||
0.697599 | + | 0.716488i | \(0.254252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 53144.0 | 0.493584 | 0.246792 | − | 0.969068i | \(-0.420624\pi\) | ||||
0.246792 | + | 0.969068i | \(0.420624\pi\) | |||||||
\(104\) | −107184. | −0.971732 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −202500. | −1.75049 | ||||||||
\(107\) | −90828.0 | −0.766938 | −0.383469 | − | 0.923554i | \(-0.625271\pi\) | ||||
−0.383469 | + | 0.923554i | \(0.625271\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −61666.0 | −0.497141 | −0.248570 | − | 0.968614i | \(-0.579961\pi\) | ||||
−0.248570 | + | 0.968614i | \(0.579961\pi\) | |||||||
\(110\) | −20304.0 | −0.159993 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 45440.0 | 0.342289 | ||||||||
\(113\) | −10482.0 | −0.0772232 | −0.0386116 | − | 0.999254i | \(-0.512294\pi\) | ||||
−0.0386116 | + | 0.999254i | \(0.512294\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5040.00 | −0.0355374 | ||||||||
\(116\) | −18552.0 | −0.128011 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 108504. | 0.717366 | ||||||||
\(119\) | 35280.0 | 0.228382 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 157045. | 0.975126 | ||||||||
\(122\) | 238548. | 1.45103 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17600.0 | 0.102792 | ||||||||
\(125\) | 37284.0 | 0.213426 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −171088. | −0.941261 | −0.470631 | − | 0.882330i | \(-0.655974\pi\) | ||||
−0.470631 | + | 0.882330i | \(0.655974\pi\) | |||||||
\(128\) | 212352. | 1.14560 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −22968.0 | −0.119197 | ||||||||
\(131\) | −258468. | −1.31592 | −0.657959 | − | 0.753054i | \(-0.728580\pi\) | ||||
−0.657959 | + | 0.753054i | \(0.728580\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22240.0 | 0.109020 | ||||||||
\(134\) | −138408. | −0.665885 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 148176. | 0.686959 | ||||||||
\(137\) | −300234. | −1.36665 | −0.683327 | − | 0.730113i | \(-0.739468\pi\) | ||||
−0.683327 | + | 0.730113i | \(0.739468\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −350164. | −1.53721 | −0.768607 | − | 0.639721i | \(-0.779050\pi\) | ||||
−0.768607 | + | 0.639721i | \(0.779050\pi\) | |||||||
\(140\) | 960.000 | 0.00413953 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25488.0 | 0.106075 | ||||||||
\(143\) | 359832. | 1.47150 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27828.0 | 0.109916 | ||||||||
\(146\) | −246660. | −0.957672 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9640.00 | −0.0361762 | ||||||||
\(149\) | 105258. | 0.388409 | 0.194205 | − | 0.980961i | \(-0.437787\pi\) | ||||
0.194205 | + | 0.980961i | \(0.437787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 396392. | 1.41476 | 0.707380 | − | 0.706834i | \(-0.249877\pi\) | ||||
0.707380 | + | 0.706834i | \(0.249877\pi\) | |||||||
\(152\) | 93408.0 | 0.327925 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −135360. | −0.459927 | ||||||||
\(155\) | −26400.0 | −0.0882622 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −137746. | −0.445995 | −0.222997 | − | 0.974819i | \(-0.571584\pi\) | ||||
−0.222997 | + | 0.974819i | \(0.571584\pi\) | |||||||
\(158\) | 131520. | 0.419130 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8640.00 | 0.0266817 | ||||||||
\(161\) | −33600.0 | −0.102159 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 352676. | 1.03970 | 0.519849 | − | 0.854258i | \(-0.325988\pi\) | ||||
0.519849 | + | 0.854258i | \(0.325988\pi\) | |||||||
\(164\) | 27480.0 | 0.0797824 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −494712. | −1.39342 | ||||||||
\(167\) | 217560. | 0.603654 | 0.301827 | − | 0.953363i | \(-0.402404\pi\) | ||||
0.301827 | + | 0.953363i | \(0.402404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35751.0 | 0.0962878 | ||||||||
\(170\) | 31752.0 | 0.0842653 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 38576.0 | 0.0994251 | ||||||||
\(173\) | 163698. | 0.415842 | 0.207921 | − | 0.978146i | \(-0.433330\pi\) | ||||
0.207921 | + | 0.978146i | \(0.433330\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 123560. | 0.304988 | ||||||||
\(176\) | −640704. | −1.55911 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 564516. | 1.33545 | ||||||||
\(179\) | −358740. | −0.836849 | −0.418425 | − | 0.908252i | \(-0.637418\pi\) | ||||
−0.418425 | + | 0.908252i | \(0.637418\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −507130. | −1.15060 | −0.575298 | − | 0.817944i | \(-0.695114\pi\) | ||||
−0.575298 | + | 0.817944i | \(0.695114\pi\) | |||||||
\(182\) | −153120. | −0.342652 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −141120. | −0.307287 | ||||||||
\(185\) | 14460.0 | 0.0310627 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −497448. | −1.04026 | ||||||||
\(188\) | 74688.0 | 0.154119 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 20016.0 | 0.0402247 | ||||||||
\(191\) | 648384. | 1.28602 | 0.643012 | − | 0.765856i | \(-0.277685\pi\) | ||||
0.643012 | + | 0.765856i | \(0.277685\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −27838.0 | −0.0537954 | −0.0268977 | − | 0.999638i | \(-0.508563\pi\) | ||||
−0.0268977 | + | 0.999638i | \(0.508563\pi\) | |||||||
\(194\) | 296652. | 0.565904 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −60828.0 | −0.113100 | ||||||||
\(197\) | −611046. | −1.12178 | −0.560891 | − | 0.827890i | \(-0.689541\pi\) | ||||
−0.560891 | + | 0.827890i | \(0.689541\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 879032. | 1.57352 | 0.786760 | − | 0.617260i | \(-0.211757\pi\) | ||||
0.786760 | + | 0.617260i | \(0.211757\pi\) | |||||||
\(200\) | 518952. | 0.917386 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 858204. | 1.47983 | ||||||||
\(203\) | 185520. | 0.315973 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −41220.0 | −0.0685052 | ||||||||
\(206\) | 318864. | 0.523525 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −724768. | −1.16156 | ||||||||
\(209\) | −313584. | −0.496579 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 48500.0 | 0.0749956 | 0.0374978 | − | 0.999297i | \(-0.488061\pi\) | ||||
0.0374978 | + | 0.999297i | \(0.488061\pi\) | |||||||
\(212\) | −135000. | −0.206298 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −544968. | −0.813461 | ||||||||
\(215\) | −57864.0 | −0.0853714 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −176000. | −0.253725 | ||||||||
\(218\) | −369996. | −0.527298 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13536.0 | −0.0188553 | ||||||||
\(221\) | −562716. | −0.775012 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −999472. | −1.34589 | −0.672943 | − | 0.739694i | \(-0.734970\pi\) | ||||
−0.672943 | + | 0.739694i | \(0.734970\pi\) | |||||||
\(224\) | 57600.0 | 0.0767012 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −62892.0 | −0.0819076 | ||||||||
\(227\) | −606180. | −0.780795 | −0.390397 | − | 0.920646i | \(-0.627662\pi\) | ||||
−0.390397 | + | 0.920646i | \(0.627662\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.35993e6 | 1.71367 | 0.856834 | − | 0.515593i | \(-0.172428\pi\) | ||||
0.856834 | + | 0.515593i | \(0.172428\pi\) | |||||||
\(230\) | −30240.0 | −0.0376931 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 779184. | 0.950430 | ||||||||
\(233\) | 392886. | 0.474107 | 0.237054 | − | 0.971497i | \(-0.423818\pi\) | ||||
0.237054 | + | 0.971497i | \(0.423818\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −112032. | −0.132334 | ||||||||
\(236\) | 72336.0 | 0.0845424 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 211680. | 0.242235 | ||||||||
\(239\) | 1.32514e6 | 1.50060 | 0.750301 | − | 0.661096i | \(-0.229908\pi\) | ||||
0.750301 | + | 0.661096i | \(0.229908\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −990094. | −1.09808 | −0.549040 | − | 0.835796i | \(-0.685006\pi\) | ||||
−0.549040 | + | 0.835796i | \(0.685006\pi\) | |||||||
\(242\) | 942270. | 1.03428 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 159032. | 0.171005 | ||||||||
\(245\) | 91242.0 | 0.0971135 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −354728. | −0.369959 | ||||||||
\(248\) | −739200. | −0.763190 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 223704. | 0.226373 | ||||||||
\(251\) | −147132. | −0.147409 | −0.0737043 | − | 0.997280i | \(-0.523482\pi\) | ||||
−0.0737043 | + | 0.997280i | \(0.523482\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 473760. | 0.465326 | ||||||||
\(254\) | −1.02653e6 | −0.998358 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 387328. | 0.369385 | ||||||||
\(257\) | 483582. | 0.456707 | 0.228353 | − | 0.973578i | \(-0.426666\pi\) | ||||
0.228353 | + | 0.973578i | \(0.426666\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 96400.0 | 0.0892951 | ||||||||
\(260\) | −15312.0 | −0.0140475 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.55081e6 | −1.39574 | ||||||||
\(263\) | −813576. | −0.725285 | −0.362643 | − | 0.931928i | \(-0.618125\pi\) | ||||
−0.362643 | + | 0.931928i | \(0.618125\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 202500. | 0.177137 | ||||||||
\(266\) | 133440. | 0.115633 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −92272.0 | −0.0784753 | ||||||||
\(269\) | 461106. | 0.388526 | 0.194263 | − | 0.980949i | \(-0.437768\pi\) | ||||
0.194263 | + | 0.980949i | \(0.437768\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.67514e6 | 1.38556 | 0.692782 | − | 0.721147i | \(-0.256385\pi\) | ||||
0.692782 | + | 0.721147i | \(0.256385\pi\) | |||||||
\(272\) | 1.00195e6 | 0.821154 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.80140e6 | −1.44956 | ||||||||
\(275\) | −1.74220e6 | −1.38920 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 401126. | 0.314110 | 0.157055 | − | 0.987590i | \(-0.449800\pi\) | ||||
0.157055 | + | 0.987590i | \(0.449800\pi\) | |||||||
\(278\) | −2.10098e6 | −1.63046 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −40320.0 | −0.0307344 | ||||||||
\(281\) | 2.30977e6 | 1.74503 | 0.872514 | − | 0.488590i | \(-0.162489\pi\) | ||||
0.872514 | + | 0.488590i | \(0.162489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.12877e6 | −0.837800 | −0.418900 | − | 0.908032i | \(-0.637584\pi\) | ||||
−0.418900 | + | 0.908032i | \(0.637584\pi\) | |||||||
\(284\) | 16992.0 | 0.0125011 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.15899e6 | 1.56076 | ||||||||
\(287\) | −274800. | −0.196930 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −641933. | −0.452111 | ||||||||
\(290\) | 166968. | 0.116584 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −164440. | −0.112863 | ||||||||
\(293\) | 938874. | 0.638908 | 0.319454 | − | 0.947602i | \(-0.396501\pi\) | ||||
0.319454 | + | 0.947602i | \(0.396501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −108504. | −0.0725923 | ||||||||
\(296\) | 404880. | 0.268594 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 631548. | 0.411970 | ||||||||
\(299\) | 535920. | 0.346675 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −385760. | −0.245415 | ||||||||
\(302\) | 2.37835e6 | 1.50058 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 631616. | 0.391985 | ||||||||
\(305\) | −238548. | −0.146834 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 692948. | 0.419619 | 0.209809 | − | 0.977742i | \(-0.432716\pi\) | ||||
0.209809 | + | 0.977742i | \(0.432716\pi\) | |||||||
\(308\) | −90240.0 | −0.0542029 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −158400. | −0.0936162 | ||||||||
\(311\) | −2.94310e6 | −1.72545 | −0.862727 | − | 0.505670i | \(-0.831245\pi\) | ||||
−0.862727 | + | 0.505670i | \(0.831245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 885146. | 0.510686 | 0.255343 | − | 0.966851i | \(-0.417812\pi\) | ||||
0.255343 | + | 0.966851i | \(0.417812\pi\) | |||||||
\(314\) | −826476. | −0.473049 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 87680.0 | 0.0493950 | ||||||||
\(317\) | −2.50880e6 | −1.40222 | −0.701112 | − | 0.713051i | \(-0.747313\pi\) | ||||
−0.701112 | + | 0.713051i | \(0.747313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.61583e6 | −1.43924 | ||||||||
\(320\) | −166272. | −0.0907704 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −201600. | −0.108355 | ||||||||
\(323\) | 490392. | 0.261539 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.97078e6 | −1.03498 | ||||||||
\(326\) | 2.11606e6 | 1.10277 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.15416e6 | −0.592354 | ||||||||
\(329\) | −746880. | −0.380418 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −216148. | −0.108438 | −0.0542190 | − | 0.998529i | \(-0.517267\pi\) | ||||
−0.0542190 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(332\) | −329808. | −0.164216 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.30536e6 | 0.640271 | ||||||||
\(335\) | 138408. | 0.0673828 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.25263e6 | 1.56012 | 0.780062 | − | 0.625702i | \(-0.215187\pi\) | ||||
0.780062 | + | 0.625702i | \(0.215187\pi\) | |||||||
\(338\) | 214506. | 0.102129 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 21168.0 | 0.00993076 | ||||||||
\(341\) | 2.48160e6 | 1.15570 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.28056e6 | 0.587712 | ||||||||
\(344\) | −1.62019e6 | −0.738194 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 982188. | 0.441067 | ||||||||
\(347\) | 2.93207e6 | 1.30723 | 0.653613 | − | 0.756829i | \(-0.273253\pi\) | ||||
0.653613 | + | 0.756829i | \(0.273253\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 905198. | 0.397814 | 0.198907 | − | 0.980018i | \(-0.436261\pi\) | ||||
0.198907 | + | 0.980018i | \(0.436261\pi\) | |||||||
\(350\) | 741360. | 0.323489 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −812160. | −0.349369 | ||||||||
\(353\) | −1.91786e6 | −0.819181 | −0.409590 | − | 0.912270i | \(-0.634328\pi\) | ||||
−0.409590 | + | 0.912270i | \(0.634328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25488.0 | −0.0107341 | ||||||||
\(356\) | 376344. | 0.157384 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.15244e6 | −0.887613 | ||||||||
\(359\) | 2.43698e6 | 0.997968 | 0.498984 | − | 0.866611i | \(-0.333707\pi\) | ||||
0.498984 | + | 0.866611i | \(0.333707\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.16696e6 | −0.875152 | ||||||||
\(362\) | −3.04278e6 | −1.22039 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −102080. | −0.0403819 | ||||||||
\(365\) | 246660. | 0.0969095 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −984064. | −0.381380 | −0.190690 | − | 0.981650i | \(-0.561073\pi\) | ||||
−0.190690 | + | 0.981650i | \(0.561073\pi\) | |||||||
\(368\) | −954240. | −0.367314 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 86760.0 | 0.0329470 | ||||||||
\(371\) | 1.35000e6 | 0.509212 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.70365e6 | 0.634029 | 0.317015 | − | 0.948421i | \(-0.397320\pi\) | ||||
0.317015 | + | 0.948421i | \(0.397320\pi\) | |||||||
\(374\) | −2.98469e6 | −1.10337 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.13690e6 | −1.14428 | ||||||||
\(377\) | −2.95904e6 | −1.07225 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.75654e6 | 0.985749 | 0.492874 | − | 0.870100i | \(-0.335946\pi\) | ||||
0.492874 | + | 0.870100i | \(0.335946\pi\) | |||||||
\(380\) | 13344.0 | 0.00474053 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.89030e6 | 1.36403 | ||||||||
\(383\) | −456576. | −0.159044 | −0.0795218 | − | 0.996833i | \(-0.525339\pi\) | ||||
−0.0795218 | + | 0.996833i | \(0.525339\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 135360. | 0.0465413 | ||||||||
\(386\) | −167028. | −0.0570586 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 197768. | 0.0666925 | ||||||||
\(389\) | 2.00639e6 | 0.672268 | 0.336134 | − | 0.941814i | \(-0.390881\pi\) | ||||
0.336134 | + | 0.941814i | \(0.390881\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −740880. | −0.245079 | ||||||||
\(392\) | 2.55478e6 | 0.839726 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.66628e6 | −1.18983 | ||||||||
\(395\) | −131520. | −0.0424130 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.77040e6 | −1.83751 | −0.918755 | − | 0.394828i | \(-0.870804\pi\) | ||||
−0.918755 | + | 0.394828i | \(0.870804\pi\) | |||||||
\(398\) | 5.27419e6 | 1.66897 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.50910e6 | 1.09659 | ||||||||
\(401\) | −3.00626e6 | −0.933610 | −0.466805 | − | 0.884360i | \(-0.654595\pi\) | ||||
−0.466805 | + | 0.884360i | \(0.654595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.80720e6 | 0.861015 | ||||||||
\(404\) | 572136. | 0.174400 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.11312e6 | 0.335140 | ||||||||
\(407\) | −1.35924e6 | −0.406734 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.53363e6 | 0.453327 | 0.226663 | − | 0.973973i | \(-0.427218\pi\) | ||||
0.226663 | + | 0.973973i | \(0.427218\pi\) | |||||||
\(410\) | −247320. | −0.0726607 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 212576. | 0.0616980 | ||||||||
\(413\) | −723360. | −0.208679 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 494712. | 0.141004 | ||||||||
\(416\) | −918720. | −0.260285 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.88150e6 | −0.526701 | ||||||||
\(419\) | 3.87376e6 | 1.07795 | 0.538973 | − | 0.842323i | \(-0.318812\pi\) | ||||
0.538973 | + | 0.842323i | \(0.318812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.33307e6 | −0.366561 | −0.183281 | − | 0.983061i | \(-0.558672\pi\) | ||||
−0.183281 | + | 0.983061i | \(0.558672\pi\) | |||||||
\(422\) | 291000. | 0.0795448 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.67000e6 | 1.53168 | ||||||||
\(425\) | 2.72450e6 | 0.731668 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.59032e6 | −0.422099 | ||||||||
\(428\) | −363312. | −0.0958673 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −347184. | −0.0905500 | ||||||||
\(431\) | −6.45192e6 | −1.67300 | −0.836500 | − | 0.547967i | \(-0.815402\pi\) | ||||
−0.836500 | + | 0.547967i | \(0.815402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.16577e6 | −1.06777 | −0.533883 | − | 0.845558i | \(-0.679268\pi\) | ||||
−0.533883 | + | 0.845558i | \(0.679268\pi\) | |||||||
\(434\) | −1.05600e6 | −0.269116 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −246664. | −0.0621426 | ||||||||
\(437\) | −467040. | −0.116990 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 792680. | 0.196307 | 0.0981537 | − | 0.995171i | \(-0.468706\pi\) | ||||
0.0981537 | + | 0.995171i | \(0.468706\pi\) | |||||||
\(440\) | 568512. | 0.139994 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.37630e6 | −0.822025 | ||||||||
\(443\) | 1.39981e6 | 0.338891 | 0.169446 | − | 0.985540i | \(-0.445802\pi\) | ||||
0.169446 | + | 0.985540i | \(0.445802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −564516. | −0.135138 | ||||||||
\(446\) | −5.99683e6 | −1.42753 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.10848e6 | −0.260935 | ||||||||
\(449\) | −2.99248e6 | −0.700512 | −0.350256 | − | 0.936654i | \(-0.613905\pi\) | ||||
−0.350256 | + | 0.936654i | \(0.613905\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.87468e6 | 0.897004 | ||||||||
\(452\) | −41928.0 | −0.00965291 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.63708e6 | −0.828158 | ||||||||
\(455\) | 153120. | 0.0346740 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.29969e6 | 1.41101 | 0.705503 | − | 0.708707i | \(-0.250721\pi\) | ||||
0.705503 | + | 0.708707i | \(0.250721\pi\) | |||||||
\(458\) | 8.15956e6 | 1.81762 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −20160.0 | −0.00444218 | ||||||||
\(461\) | −3.40318e6 | −0.745818 | −0.372909 | − | 0.927868i | \(-0.621640\pi\) | ||||
−0.372909 | + | 0.927868i | \(0.621640\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.23034e6 | −0.483524 | −0.241762 | − | 0.970336i | \(-0.577725\pi\) | ||||
−0.241762 | + | 0.970336i | \(0.577725\pi\) | |||||||
\(464\) | 5.26877e6 | 1.13609 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.35732e6 | 0.502867 | ||||||||
\(467\) | 6.51409e6 | 1.38217 | 0.691085 | − | 0.722773i | \(-0.257133\pi\) | ||||
0.691085 | + | 0.722773i | \(0.257133\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 922720. | 0.193704 | ||||||||
\(470\) | −672192. | −0.140362 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.03811e6 | −0.627695 | ||||||||
\(473\) | 5.43922e6 | 1.11785 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.71748e6 | 0.349268 | ||||||||
\(476\) | 141120. | 0.0285477 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.95082e6 | 1.59163 | ||||||||
\(479\) | −2.39232e6 | −0.476410 | −0.238205 | − | 0.971215i | \(-0.576559\pi\) | ||||
−0.238205 | + | 0.971215i | \(0.576559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.53758e6 | −0.303023 | ||||||||
\(482\) | −5.94056e6 | −1.16469 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 628180. | 0.121891 | ||||||||
\(485\) | −296652. | −0.0572655 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.13089e6 | −1.17139 | −0.585694 | − | 0.810532i | \(-0.699178\pi\) | ||||
−0.585694 | + | 0.810532i | \(0.699178\pi\) | |||||||
\(488\) | −6.67934e6 | −1.26965 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 547452. | 0.103004 | ||||||||
\(491\) | 1.23589e6 | 0.231354 | 0.115677 | − | 0.993287i | \(-0.463096\pi\) | ||||
0.115677 | + | 0.993287i | \(0.463096\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.09072e6 | 0.758022 | ||||||||
\(494\) | −2.12837e6 | −0.392400 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.99840e6 | −0.912277 | ||||||||
\(497\) | −169920. | −0.0308570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.85496e6 | −1.77175 | −0.885877 | − | 0.463921i | \(-0.846442\pi\) | ||||
−0.885877 | + | 0.463921i | \(0.846442\pi\) | |||||||
\(500\) | 149136. | 0.0266783 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −882792. | −0.156350 | ||||||||
\(503\) | −1.16777e6 | −0.205796 | −0.102898 | − | 0.994692i | \(-0.532812\pi\) | ||||
−0.102898 | + | 0.994692i | \(0.532812\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −858204. | −0.149748 | ||||||||
\(506\) | 2.84256e6 | 0.493552 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −684352. | −0.117658 | ||||||||
\(509\) | −1.04941e6 | −0.179535 | −0.0897675 | − | 0.995963i | \(-0.528612\pi\) | ||||
−0.0897675 | + | 0.995963i | \(0.528612\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.64440e6 | 0.278583 | ||||||||
\(512\) | −4.47130e6 | −0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.90149e6 | 0.484411 | ||||||||
\(515\) | −318864. | −0.0529770 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.05310e7 | 1.73278 | ||||||||
\(518\) | 578400. | 0.0947118 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 643104. | 0.104297 | ||||||||
\(521\) | 9.61407e6 | 1.55172 | 0.775859 | − | 0.630906i | \(-0.217317\pi\) | ||||
0.775859 | + | 0.630906i | \(0.217317\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.96148e6 | 1.11288 | 0.556439 | − | 0.830888i | \(-0.312167\pi\) | ||||
0.556439 | + | 0.830888i | \(0.312167\pi\) | |||||||
\(524\) | −1.03387e6 | −0.164490 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.88146e6 | −0.769281 | ||||||||
\(527\) | −3.88080e6 | −0.608688 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.73074e6 | −0.890373 | ||||||||
\(530\) | 1.21500e6 | 0.187883 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 88960.0 | 0.0136275 | ||||||||
\(533\) | 4.38306e6 | 0.668281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 544968. | 0.0823164 | ||||||||
\(536\) | 3.87542e6 | 0.582649 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.76664e6 | 0.412094 | ||||||||
\(539\) | −8.57675e6 | −1.27160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −712690. | −0.104691 | −0.0523453 | − | 0.998629i | \(-0.516670\pi\) | ||||
−0.0523453 | + | 0.998629i | \(0.516670\pi\) | |||||||
\(542\) | 1.00508e7 | 1.46961 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.27008e6 | 0.184007 | ||||||||
\(545\) | 369996. | 0.0533588 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.62614e6 | −0.518175 | −0.259087 | − | 0.965854i | \(-0.583422\pi\) | ||||
−0.259087 | + | 0.965854i | \(0.583422\pi\) | |||||||
\(548\) | −1.20094e6 | −0.170832 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.04532e7 | −1.47347 | ||||||||
\(551\) | 2.57873e6 | 0.361848 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −876800. | −0.121924 | ||||||||
\(554\) | 2.40676e6 | 0.333164 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.40066e6 | −0.192152 | ||||||||
\(557\) | −4.84846e6 | −0.662165 | −0.331082 | − | 0.943602i | \(-0.607414\pi\) | ||||
−0.331082 | + | 0.943602i | \(0.607414\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.15287e6 | 0.832815 | ||||||||
\(560\) | −272640. | −0.0367383 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.38586e7 | 1.85088 | ||||||||
\(563\) | −8.50405e6 | −1.13072 | −0.565360 | − | 0.824844i | \(-0.691263\pi\) | ||||
−0.565360 | + | 0.824844i | \(0.691263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 62892.0 | 0.00828847 | ||||||||
\(566\) | −6.77263e6 | −0.888621 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −713664. | −0.0928160 | ||||||||
\(569\) | −362874. | −0.0469867 | −0.0234934 | − | 0.999724i | \(-0.507479\pi\) | ||||
−0.0234934 | + | 0.999724i | \(0.507479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.11024e6 | 0.527566 | 0.263783 | − | 0.964582i | \(-0.415030\pi\) | ||||
0.263783 | + | 0.964582i | \(0.415030\pi\) | |||||||
\(572\) | 1.43933e6 | 0.183937 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.64880e6 | −0.208876 | ||||||||
\(575\) | −2.59476e6 | −0.327286 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.87680e6 | −0.984941 | −0.492470 | − | 0.870329i | \(-0.663906\pi\) | ||||
−0.492470 | + | 0.870329i | \(0.663906\pi\) | |||||||
\(578\) | −3.85160e6 | −0.479536 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 111312. | 0.0137395 | ||||||||
\(581\) | 3.29808e6 | 0.405341 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.90350e7 | −2.31943 | ||||||||
\(584\) | 6.90648e6 | 0.837963 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.63324e6 | 0.677664 | ||||||||
\(587\) | −603948. | −0.0723443 | −0.0361721 | − | 0.999346i | \(-0.511516\pi\) | ||||
−0.0361721 | + | 0.999346i | \(0.511516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.44640e6 | −0.290562 | ||||||||
\(590\) | −651024. | −0.0769958 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.73776e6 | 0.321064 | ||||||||
\(593\) | 5.39077e6 | 0.629526 | 0.314763 | − | 0.949170i | \(-0.398075\pi\) | ||||
0.314763 | + | 0.949170i | \(0.398075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −211680. | −0.0245125 | ||||||||
\(596\) | 421032. | 0.0485511 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.21552e6 | 0.367704 | ||||||||
\(599\) | −4.27999e6 | −0.487389 | −0.243695 | − | 0.969852i | \(-0.578359\pi\) | ||||
−0.243695 | + | 0.969852i | \(0.578359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.02483e6 | 0.115735 | 0.0578674 | − | 0.998324i | \(-0.481570\pi\) | ||||
0.0578674 | + | 0.998324i | \(0.481570\pi\) | |||||||
\(602\) | −2.31456e6 | −0.260302 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.58557e6 | 0.176845 | ||||||||
\(605\) | −942270. | −0.104661 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.24342e7 | 1.36976 | 0.684882 | − | 0.728654i | \(-0.259854\pi\) | ||||
0.684882 | + | 0.728654i | \(0.259854\pi\) | |||||||
\(608\) | 800640. | 0.0878372 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.43129e6 | −0.155741 | ||||||||
\(611\) | 1.19127e7 | 1.29095 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.21506e6 | 0.453057 | 0.226528 | − | 0.974005i | \(-0.427262\pi\) | ||||
0.226528 | + | 0.974005i | \(0.427262\pi\) | |||||||
\(614\) | 4.15769e6 | 0.445073 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.79008e6 | 0.402436 | ||||||||
\(617\) | 4.40665e6 | 0.466010 | 0.233005 | − | 0.972476i | \(-0.425144\pi\) | ||||
0.233005 | + | 0.972476i | \(0.425144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.80168e6 | 0.503693 | 0.251847 | − | 0.967767i | \(-0.418962\pi\) | ||||
0.251847 | + | 0.967767i | \(0.418962\pi\) | |||||||
\(620\) | −105600. | −0.0110328 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.76586e7 | −1.83012 | ||||||||
\(623\) | −3.76344e6 | −0.388477 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.42942e6 | 0.965573 | ||||||||
\(626\) | 5.31088e6 | 0.541664 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −550984. | −0.0557494 | ||||||||
\(629\) | 2.12562e6 | 0.214220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.30727e6 | 0.830587 | 0.415293 | − | 0.909688i | \(-0.363679\pi\) | ||||
0.415293 | + | 0.909688i | \(0.363679\pi\) | |||||||
\(632\) | −3.68256e6 | −0.366739 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.50528e7 | −1.48728 | ||||||||
\(635\) | 1.02653e6 | 0.101027 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.70207e6 | −0.947361 | ||||||||
\(638\) | −1.56950e7 | −1.52654 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.27411e6 | −0.122958 | ||||||||
\(641\) | −1.76956e7 | −1.70107 | −0.850534 | − | 0.525921i | \(-0.823721\pi\) | ||||
−0.850534 | + | 0.525921i | \(0.823721\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.28394e7 | −1.22466 | −0.612330 | − | 0.790602i | \(-0.709768\pi\) | ||||
−0.612330 | + | 0.790602i | \(0.709768\pi\) | |||||||
\(644\) | −134400. | −0.0127698 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.94235e6 | 0.277404 | ||||||||
\(647\) | 2.08468e7 | 1.95785 | 0.978924 | − | 0.204226i | \(-0.0654678\pi\) | ||||
0.978924 | + | 0.204226i | \(0.0654678\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.01994e7 | 0.950521 | ||||||||
\(650\) | −1.18247e7 | −1.09776 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.41070e6 | 0.129962 | ||||||||
\(653\) | −1.29632e7 | −1.18968 | −0.594841 | − | 0.803843i | \(-0.702785\pi\) | ||||
−0.594841 | + | 0.803843i | \(0.702785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.55081e6 | 0.141239 | ||||||||
\(656\) | −7.80432e6 | −0.708069 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.48128e6 | −0.403494 | ||||||||
\(659\) | 5.66862e6 | 0.508468 | 0.254234 | − | 0.967143i | \(-0.418177\pi\) | ||||
0.254234 | + | 0.967143i | \(0.418177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.11430e6 | −0.277240 | −0.138620 | − | 0.990346i | \(-0.544267\pi\) | ||||
−0.138620 | + | 0.990346i | \(0.544267\pi\) | |||||||
\(662\) | −1.29689e6 | −0.115016 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.38519e7 | 1.21924 | ||||||||
\(665\) | −133440. | −0.0117012 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.89592e6 | −0.339075 | ||||||||
\(668\) | 870240. | 0.0754567 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 830448. | 0.0714703 | ||||||||
\(671\) | 2.24235e7 | 1.92264 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 105890. | 0.00901192 | 0.00450596 | − | 0.999990i | \(-0.498566\pi\) | ||||
0.00450596 | + | 0.999990i | \(0.498566\pi\) | |||||||
\(674\) | 1.95158e7 | 1.65476 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 143004. | 0.0120360 | ||||||||
\(677\) | 1.60910e7 | 1.34931 | 0.674656 | − | 0.738132i | \(-0.264292\pi\) | ||||
0.674656 | + | 0.738132i | \(0.264292\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.97768e6 | −0.164620 | ||||||||
\(680\) | −889056. | −0.0737321 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.48896e7 | 1.22581 | ||||||||
\(683\) | −1.60780e7 | −1.31880 | −0.659402 | − | 0.751791i | \(-0.729190\pi\) | ||||
−0.659402 | + | 0.751791i | \(0.729190\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.80140e6 | 0.146685 | ||||||||
\(686\) | 7.68336e6 | 0.623363 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.09556e7 | −0.882398 | ||||||||
\(689\) | −2.15325e7 | −1.72801 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −165964. | −0.0132227 | −0.00661133 | − | 0.999978i | \(-0.502104\pi\) | ||||
−0.00661133 | + | 0.999978i | \(0.502104\pi\) | |||||||
\(692\) | 654792. | 0.0519802 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.75924e7 | 1.38652 | ||||||||
\(695\) | 2.10098e6 | 0.164991 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.05934e6 | −0.472436 | ||||||||
\(698\) | 5.43119e6 | 0.421945 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 494240. | 0.0381235 | ||||||||
\(701\) | −1.77248e7 | −1.36234 | −0.681171 | − | 0.732124i | \(-0.738529\pi\) | ||||
−0.681171 | + | 0.732124i | \(0.738529\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.33996e6 | 0.102259 | ||||||||
\(704\) | 1.56296e7 | 1.18854 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.15071e7 | −0.868872 | ||||||||
\(707\) | −5.72136e6 | −0.430478 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.06023e7 | −0.792112 | −0.396056 | − | 0.918226i | \(-0.629621\pi\) | ||||
−0.396056 | + | 0.918226i | \(0.629621\pi\) | |||||||
\(710\) | −152928. | −0.0113852 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.58064e7 | −1.16852 | ||||||||
\(713\) | 3.69600e6 | 0.272275 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.15899e6 | −0.157938 | ||||||||
\(716\) | −1.43496e6 | −0.104606 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.46219e7 | 1.05850 | ||||||||
\(719\) | −9.03211e6 | −0.651579 | −0.325790 | − | 0.945442i | \(-0.605630\pi\) | ||||
−0.325790 | + | 0.945442i | \(0.605630\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.12576e6 | −0.152292 | ||||||||
\(722\) | −1.30018e7 | −0.928239 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.02852e6 | −0.143825 | ||||||||
\(725\) | 1.43268e7 | 1.01229 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.87575e7 | 1.31625 | 0.658127 | − | 0.752907i | \(-0.271349\pi\) | ||||
0.658127 | + | 0.752907i | \(0.271349\pi\) | |||||||
\(728\) | 4.28736e6 | 0.299821 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.47996e6 | 0.102788 | ||||||||
\(731\) | −8.50601e6 | −0.588752 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.17773e7 | −0.809626 | −0.404813 | − | 0.914399i | \(-0.632663\pi\) | ||||
−0.404813 | + | 0.914399i | \(0.632663\pi\) | |||||||
\(734\) | −5.90438e6 | −0.404515 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.20960e6 | −0.0823090 | ||||||||
\(737\) | −1.30104e7 | −0.882308 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.88948e6 | 0.396703 | 0.198352 | − | 0.980131i | \(-0.436441\pi\) | ||||
0.198352 | + | 0.980131i | \(0.436441\pi\) | |||||||
\(740\) | 57840.0 | 0.00388284 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.10000e6 | 0.540101 | ||||||||
\(743\) | 1.00476e7 | 0.667712 | 0.333856 | − | 0.942624i | \(-0.391650\pi\) | ||||
0.333856 | + | 0.942624i | \(0.391650\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −631548. | −0.0416884 | ||||||||
\(746\) | 1.02219e7 | 0.672490 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.98979e6 | −0.130033 | ||||||||
\(749\) | 3.63312e6 | 0.236633 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.81530e6 | 0.311547 | 0.155773 | − | 0.987793i | \(-0.450213\pi\) | ||||
0.155773 | + | 0.987793i | \(0.450213\pi\) | |||||||
\(752\) | −2.12114e7 | −1.36781 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.77543e7 | −1.13730 | ||||||||
\(755\) | −2.37835e6 | −0.151848 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.12973e6 | 0.198503 | 0.0992516 | − | 0.995062i | \(-0.468355\pi\) | ||||
0.0992516 | + | 0.995062i | \(0.468355\pi\) | |||||||
\(758\) | 1.65392e7 | 1.04554 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −560448. | −0.0351967 | ||||||||
\(761\) | 1.17773e7 | 0.737197 | 0.368599 | − | 0.929589i | \(-0.379838\pi\) | ||||
0.368599 | + | 0.929589i | \(0.379838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.46664e6 | 0.153389 | ||||||||
\(764\) | 2.59354e6 | 0.160753 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.73946e6 | −0.168691 | ||||||||
\(767\) | 1.15376e7 | 0.708152 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.49376e6 | −0.0910887 | −0.0455443 | − | 0.998962i | \(-0.514502\pi\) | ||||
−0.0455443 | + | 0.998962i | \(0.514502\pi\) | |||||||
\(770\) | 812160. | 0.0493645 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −111352. | −0.00672442 | ||||||||
\(773\) | 2.25125e7 | 1.35511 | 0.677555 | − | 0.735472i | \(-0.263040\pi\) | ||||
0.677555 | + | 0.735472i | \(0.263040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.35916e7 | −0.812861 | ||||||||
\(776\) | −8.30626e6 | −0.495166 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.20384e7 | 0.713048 | ||||||||
\(779\) | −3.81972e6 | −0.225521 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.39587e6 | 0.140552 | ||||||||
\(782\) | −4.44528e6 | −0.259945 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.72752e7 | 1.00376 | ||||||||
\(785\) | 826476. | 0.0478692 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.19547e7 | 0.688022 | 0.344011 | − | 0.938966i | \(-0.388214\pi\) | ||||
0.344011 | + | 0.938966i | \(0.388214\pi\) | |||||||
\(788\) | −2.44418e6 | −0.140223 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −789120. | −0.0449858 | ||||||||
\(791\) | 419280. | 0.0238266 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.53656e7 | 1.43239 | ||||||||
\(794\) | −3.46224e7 | −1.94897 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.51613e6 | 0.196690 | ||||||||
\(797\) | −540798. | −0.0301571 | −0.0150785 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150785 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.64687e7 | −0.912625 | ||||||||
\(800\) | 4.44816e6 | 0.245728 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.80375e7 | −0.990243 | ||||||||
\(803\) | −2.31860e7 | −1.26893 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 201600. | 0.0109648 | ||||||||
\(806\) | 1.68432e7 | 0.913244 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.40297e7 | −1.29485 | ||||||||
\(809\) | 6.14223e6 | 0.329955 | 0.164978 | − | 0.986297i | \(-0.447245\pi\) | ||||
0.164978 | + | 0.986297i | \(0.447245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.16734e7 | −1.69100 | −0.845499 | − | 0.533977i | \(-0.820697\pi\) | ||||
−0.845499 | + | 0.533977i | \(0.820697\pi\) | |||||||
\(812\) | 742080. | 0.0394967 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.15544e6 | −0.431406 | ||||||||
\(815\) | −2.11606e6 | −0.111592 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.36206e6 | −0.281046 | ||||||||
\(818\) | 9.20176e6 | 0.480825 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −164880. | −0.00856315 | ||||||||
\(821\) | −2.66175e7 | −1.37819 | −0.689095 | − | 0.724671i | \(-0.741992\pi\) | ||||
−0.689095 | + | 0.724671i | \(0.741992\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.62817e7 | 1.86719 | 0.933593 | − | 0.358335i | \(-0.116655\pi\) | ||||
0.933593 | + | 0.358335i | \(0.116655\pi\) | |||||||
\(824\) | −8.92819e6 | −0.458084 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.34016e6 | −0.221338 | ||||||||
\(827\) | −1.09033e6 | −0.0554364 | −0.0277182 | − | 0.999616i | \(-0.508824\pi\) | ||||
−0.0277182 | + | 0.999616i | \(0.508824\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.03016e7 | −0.520620 | −0.260310 | − | 0.965525i | \(-0.583825\pi\) | ||||
−0.260310 | + | 0.965525i | \(0.583825\pi\) | |||||||
\(830\) | 2.96827e6 | 0.149558 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.76803e7 | 0.885483 | ||||||||
\(833\) | 1.34126e7 | 0.669730 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.30536e6 | −0.0647909 | ||||||||
\(836\) | −1.25434e6 | −0.0620724 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.32425e7 | 1.14333 | ||||||||
\(839\) | 1.96134e7 | 0.961940 | 0.480970 | − | 0.876737i | \(-0.340285\pi\) | ||||
0.480970 | + | 0.876737i | \(0.340285\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 999895. | 0.0487489 | ||||||||
\(842\) | −7.99840e6 | −0.388797 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 194000. | 0.00937445 | ||||||||
\(845\) | −214506. | −0.0103347 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.28180e6 | −0.300868 | ||||||||
\(848\) | 3.83400e7 | 1.83089 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.63470e7 | 0.776051 | ||||||||
\(851\) | −2.02440e6 | −0.0958236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.27565e7 | 1.54143 | 0.770717 | − | 0.637178i | \(-0.219898\pi\) | ||||
0.770717 | + | 0.637178i | \(0.219898\pi\) | |||||||
\(854\) | −9.54192e6 | −0.447704 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.52591e7 | 0.711778 | ||||||||
\(857\) | 2.57953e7 | 1.19974 | 0.599872 | − | 0.800096i | \(-0.295218\pi\) | ||||
0.599872 | + | 0.800096i | \(0.295218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.98548e7 | −0.918085 | −0.459043 | − | 0.888414i | \(-0.651807\pi\) | ||||
−0.459043 | + | 0.888414i | \(0.651807\pi\) | |||||||
\(860\) | −231456. | −0.0106714 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.87115e7 | −1.77448 | ||||||||
\(863\) | 673056. | 0.0307627 | 0.0153813 | − | 0.999882i | \(-0.495104\pi\) | ||||
0.0153813 | + | 0.999882i | \(0.495104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −982188. | −0.0446328 | ||||||||
\(866\) | −2.49946e7 | −1.13254 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −704000. | −0.0317156 | ||||||||
\(869\) | 1.23629e7 | 0.555354 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.47174e7 | −0.657333 | ||||||||
\(872\) | 1.03599e7 | 0.461385 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.80224e6 | −0.124087 | ||||||||
\(875\) | −1.49136e6 | −0.0658510 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.32115e6 | 0.233618 | 0.116809 | − | 0.993154i | \(-0.462733\pi\) | ||||
0.116809 | + | 0.993154i | \(0.462733\pi\) | |||||||
\(878\) | 4.75608e6 | 0.208215 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.84422e6 | 0.167341 | ||||||||
\(881\) | −2.78891e7 | −1.21058 | −0.605291 | − | 0.796004i | \(-0.706943\pi\) | ||||
−0.605291 | + | 0.796004i | \(0.706943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.83786e7 | −1.22487 | −0.612435 | − | 0.790521i | \(-0.709810\pi\) | ||||
−0.612435 | + | 0.790521i | \(0.709810\pi\) | |||||||
\(884\) | −2.25086e6 | −0.0968765 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.39887e6 | 0.359448 | ||||||||
\(887\) | −4.22678e7 | −1.80385 | −0.901925 | − | 0.431893i | \(-0.857846\pi\) | ||||
−0.901925 | + | 0.431893i | \(0.857846\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.84352e6 | 0.290419 | ||||||||
\(890\) | −3.38710e6 | −0.143335 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.99789e6 | −0.168236 | ||||||||
\(893\) | −1.03816e7 | −0.435649 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.15244e6 | 0.0898201 | ||||||||
\(896\) | −8.49408e6 | −0.353465 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.79549e7 | −0.743005 | ||||||||
\(899\) | −2.04072e7 | −0.842140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.97675e7 | 1.22160 | ||||||||
\(902\) | 2.32481e7 | 0.951417 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.76098e6 | 0.0716692 | ||||||||
\(905\) | 3.04278e6 | 0.123495 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.19526e7 | 1.28970 | 0.644849 | − | 0.764310i | \(-0.276920\pi\) | ||||
0.644849 | + | 0.764310i | \(0.276920\pi\) | |||||||
\(908\) | −2.42472e6 | −0.0975994 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 918720. | 0.0367773 | ||||||||
\(911\) | 1.16429e7 | 0.464800 | 0.232400 | − | 0.972620i | \(-0.425342\pi\) | ||||
0.232400 | + | 0.972620i | \(0.425342\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.65029e7 | −1.84630 | ||||||||
\(914\) | 3.77981e7 | 1.49660 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.43970e6 | 0.214208 | ||||||||
\(917\) | 1.03387e7 | 0.406016 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.39844e6 | 0.0546204 | 0.0273102 | − | 0.999627i | \(-0.491306\pi\) | ||||
0.0273102 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(920\) | 846720. | 0.0329815 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.04191e7 | −0.791059 | ||||||||
\(923\) | 2.71022e6 | 0.104713 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.44449e6 | 0.286075 | ||||||||
\(926\) | −1.33820e7 | −0.512854 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.67872e6 | 0.254579 | ||||||||
\(929\) | 1.66792e7 | 0.634067 | 0.317033 | − | 0.948414i | \(-0.397313\pi\) | ||||
0.317033 | + | 0.948414i | \(0.397313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.45509e6 | 0.319701 | ||||||||
\(932\) | 1.57154e6 | 0.0592634 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.90846e7 | 1.46601 | ||||||||
\(935\) | 2.98469e6 | 0.111653 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.47956e7 | −0.922625 | −0.461312 | − | 0.887238i | \(-0.652621\pi\) | ||||
−0.461312 | + | 0.887238i | \(0.652621\pi\) | |||||||
\(938\) | 5.53632e6 | 0.205454 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −448128. | −0.0165418 | ||||||||
\(941\) | −2.79574e7 | −1.02925 | −0.514627 | − | 0.857414i | \(-0.672070\pi\) | ||||
−0.514627 | + | 0.857414i | \(0.672070\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.77080e6 | 0.211328 | ||||||||
\(944\) | −2.05434e7 | −0.750314 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.26353e7 | 1.18566 | ||||||||
\(947\) | −7.64936e6 | −0.277173 | −0.138586 | − | 0.990350i | \(-0.544256\pi\) | ||||
−0.138586 | + | 0.990350i | \(0.544256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.62282e7 | −0.945372 | ||||||||
\(950\) | 1.03049e7 | 0.370455 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.92704e6 | −0.211956 | ||||||||
\(953\) | 4.62179e7 | 1.64846 | 0.824228 | − | 0.566257i | \(-0.191609\pi\) | ||||
0.824228 | + | 0.566257i | \(0.191609\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.89030e6 | −0.138031 | ||||||||
\(956\) | 5.30054e6 | 0.187575 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.43539e7 | −0.505309 | ||||||||
\(959\) | 1.20094e7 | 0.421671 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.26915e6 | −0.323766 | ||||||||
\(962\) | −9.22548e6 | −0.321404 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.96038e6 | −0.137260 | ||||||||
\(965\) | 167028. | 0.00577392 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.08557e7 | 0.717229 | 0.358615 | − | 0.933486i | \(-0.383249\pi\) | ||||
0.358615 | + | 0.933486i | \(0.383249\pi\) | |||||||
\(968\) | −2.63836e7 | −0.904993 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.77991e6 | −0.0607392 | ||||||||
\(971\) | 4.58152e7 | 1.55941 | 0.779707 | − | 0.626144i | \(-0.215368\pi\) | ||||
0.779707 | + | 0.626144i | \(0.215368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.40066e7 | 0.474296 | ||||||||
\(974\) | −3.67853e7 | −1.24245 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.51651e7 | −1.51767 | ||||||||
\(977\) | 1.09544e6 | 0.0367157 | 0.0183578 | − | 0.999831i | \(-0.494156\pi\) | ||||
0.0183578 | + | 0.999831i | \(0.494156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.30645e7 | 1.76949 | ||||||||
\(980\) | 364968. | 0.0121392 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.41535e6 | 0.245388 | ||||||||
\(983\) | −5.25817e7 | −1.73561 | −0.867803 | − | 0.496909i | \(-0.834468\pi\) | ||||
−0.867803 | + | 0.496909i | \(0.834468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.66628e6 | 0.120402 | ||||||||
\(986\) | 2.45443e7 | 0.804004 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.41891e6 | −0.0462448 | ||||||||
\(989\) | 8.10096e6 | 0.263358 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.90389e7 | −1.58620 | −0.793098 | − | 0.609094i | \(-0.791533\pi\) | ||||
−0.793098 | + | 0.609094i | \(0.791533\pi\) | |||||||
\(992\) | −6.33600e6 | −0.204426 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.01952e6 | −0.0327288 | ||||||||
\(995\) | −5.27419e6 | −0.168888 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.05461e6 | 0.0973237 | 0.0486618 | − | 0.998815i | \(-0.484504\pi\) | ||||
0.0486618 | + | 0.998815i | \(0.484504\pi\) | |||||||
\(998\) | −5.91297e7 | −1.87923 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9.6.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 3.6.a.a.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 144.6.a.f.1.1 | 1 | |||
5.2 | odd | 4 | 225.6.b.b.199.2 | 2 | |||
5.3 | odd | 4 | 225.6.b.b.199.1 | 2 | |||
5.4 | even | 2 | 225.6.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 441.6.a.i.1.1 | 1 | |||
8.3 | odd | 2 | 576.6.a.t.1.1 | 1 | |||
8.5 | even | 2 | 576.6.a.s.1.1 | 1 | |||
9.2 | odd | 6 | 81.6.c.c.28.1 | 2 | |||
9.4 | even | 3 | 81.6.c.a.55.1 | 2 | |||
9.5 | odd | 6 | 81.6.c.c.55.1 | 2 | |||
9.7 | even | 3 | 81.6.c.a.28.1 | 2 | |||
11.10 | odd | 2 | 1089.6.a.b.1.1 | 1 | |||
12.11 | even | 2 | 48.6.a.a.1.1 | 1 | |||
15.2 | even | 4 | 75.6.b.b.49.1 | 2 | |||
15.8 | even | 4 | 75.6.b.b.49.2 | 2 | |||
15.14 | odd | 2 | 75.6.a.e.1.1 | 1 | |||
21.2 | odd | 6 | 147.6.e.h.67.1 | 2 | |||
21.5 | even | 6 | 147.6.e.k.67.1 | 2 | |||
21.11 | odd | 6 | 147.6.e.h.79.1 | 2 | |||
21.17 | even | 6 | 147.6.e.k.79.1 | 2 | |||
21.20 | even | 2 | 147.6.a.a.1.1 | 1 | |||
24.5 | odd | 2 | 192.6.a.d.1.1 | 1 | |||
24.11 | even | 2 | 192.6.a.l.1.1 | 1 | |||
33.32 | even | 2 | 363.6.a.d.1.1 | 1 | |||
39.38 | odd | 2 | 507.6.a.b.1.1 | 1 | |||
48.5 | odd | 4 | 768.6.d.k.385.1 | 2 | |||
48.11 | even | 4 | 768.6.d.h.385.2 | 2 | |||
48.29 | odd | 4 | 768.6.d.k.385.2 | 2 | |||
48.35 | even | 4 | 768.6.d.h.385.1 | 2 | |||
51.50 | odd | 2 | 867.6.a.a.1.1 | 1 | |||
57.56 | even | 2 | 1083.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.6.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
9.6.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
48.6.a.a.1.1 | 1 | 12.11 | even | 2 | |||
75.6.a.e.1.1 | 1 | 15.14 | odd | 2 | |||
75.6.b.b.49.1 | 2 | 15.2 | even | 4 | |||
75.6.b.b.49.2 | 2 | 15.8 | even | 4 | |||
81.6.c.a.28.1 | 2 | 9.7 | even | 3 | |||
81.6.c.a.55.1 | 2 | 9.4 | even | 3 | |||
81.6.c.c.28.1 | 2 | 9.2 | odd | 6 | |||
81.6.c.c.55.1 | 2 | 9.5 | odd | 6 | |||
144.6.a.f.1.1 | 1 | 4.3 | odd | 2 | |||
147.6.a.a.1.1 | 1 | 21.20 | even | 2 | |||
147.6.e.h.67.1 | 2 | 21.2 | odd | 6 | |||
147.6.e.h.79.1 | 2 | 21.11 | odd | 6 | |||
147.6.e.k.67.1 | 2 | 21.5 | even | 6 | |||
147.6.e.k.79.1 | 2 | 21.17 | even | 6 | |||
192.6.a.d.1.1 | 1 | 24.5 | odd | 2 | |||
192.6.a.l.1.1 | 1 | 24.11 | even | 2 | |||
225.6.a.a.1.1 | 1 | 5.4 | even | 2 | |||
225.6.b.b.199.1 | 2 | 5.3 | odd | 4 | |||
225.6.b.b.199.2 | 2 | 5.2 | odd | 4 | |||
363.6.a.d.1.1 | 1 | 33.32 | even | 2 | |||
441.6.a.i.1.1 | 1 | 7.6 | odd | 2 | |||
507.6.a.b.1.1 | 1 | 39.38 | odd | 2 | |||
576.6.a.s.1.1 | 1 | 8.5 | even | 2 | |||
576.6.a.t.1.1 | 1 | 8.3 | odd | 2 | |||
768.6.d.h.385.1 | 2 | 48.35 | even | 4 | |||
768.6.d.h.385.2 | 2 | 48.11 | even | 4 | |||
768.6.d.k.385.1 | 2 | 48.5 | odd | 4 | |||
768.6.d.k.385.2 | 2 | 48.29 | odd | 4 | |||
867.6.a.a.1.1 | 1 | 51.50 | odd | 2 | |||
1083.6.a.c.1.1 | 1 | 57.56 | even | 2 | |||
1089.6.a.b.1.1 | 1 | 11.10 | odd | 2 |