Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,6,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, 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("3.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(0.481151459439\) |
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 | \(\chi\) | \(=\) | 3.1 |
$q$-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 | \(-0.677932\pi\) | ||||
−0.530330 | + | 0.847791i | \(0.677932\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.125000 | ||||||||
\(5\) | 6.00000 | 0.107331 | 0.0536656 | − | 0.998559i | \(-0.482909\pi\) | ||||
0.0536656 | + | 0.998559i | \(0.482909\pi\) | |||||||
\(6\) | −54.0000 | −0.612372 | ||||||||
\(7\) | −40.0000 | −0.308542 | −0.154271 | − | 0.988029i | \(-0.549303\pi\) | ||||
−0.154271 | + | 0.988029i | \(0.549303\pi\) | |||||||
\(8\) | 168.000 | 0.928078 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −36.0000 | −0.113842 | ||||||||
\(11\) | −564.000 | −1.40539 | −0.702696 | − | 0.711490i | \(-0.748021\pi\) | ||||
−0.702696 | + | 0.711490i | \(0.748021\pi\) | |||||||
\(12\) | 36.0000 | 0.0721688 | ||||||||
\(13\) | 638.000 | 1.04704 | 0.523519 | − | 0.852014i | \(-0.324619\pi\) | ||||
0.523519 | + | 0.852014i | \(0.324619\pi\) | |||||||
\(14\) | 240.000 | 0.327259 | ||||||||
\(15\) | 54.0000 | 0.0619677 | ||||||||
\(16\) | −1136.00 | −1.10938 | ||||||||
\(17\) | 882.000 | 0.740195 | 0.370098 | − | 0.928993i | \(-0.379324\pi\) | ||||
0.370098 | + | 0.928993i | \(0.379324\pi\) | |||||||
\(18\) | −486.000 | −0.353553 | ||||||||
\(19\) | −556.000 | −0.353338 | −0.176669 | − | 0.984270i | \(-0.556532\pi\) | ||||
−0.176669 | + | 0.984270i | \(0.556532\pi\) | |||||||
\(20\) | 24.0000 | 0.0134164 | ||||||||
\(21\) | −360.000 | −0.178137 | ||||||||
\(22\) | 3384.00 | 1.49064 | ||||||||
\(23\) | −840.000 | −0.331100 | −0.165550 | − | 0.986201i | \(-0.552940\pi\) | ||||
−0.165550 | + | 0.986201i | \(0.552940\pi\) | |||||||
\(24\) | 1512.00 | 0.535826 | ||||||||
\(25\) | −3089.00 | −0.988480 | ||||||||
\(26\) | −3828.00 | −1.11055 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −160.000 | −0.0385678 | ||||||||
\(29\) | 4638.00 | 1.02408 | 0.512042 | − | 0.858960i | \(-0.328889\pi\) | ||||
0.512042 | + | 0.858960i | \(0.328889\pi\) | |||||||
\(30\) | −324.000 | −0.0657267 | ||||||||
\(31\) | 4400.00 | 0.822334 | 0.411167 | − | 0.911560i | \(-0.365121\pi\) | ||||
0.411167 | + | 0.911560i | \(0.365121\pi\) | |||||||
\(32\) | 1440.00 | 0.248592 | ||||||||
\(33\) | −5076.00 | −0.811403 | ||||||||
\(34\) | −5292.00 | −0.785096 | ||||||||
\(35\) | −240.000 | −0.0331162 | ||||||||
\(36\) | 324.000 | 0.0416667 | ||||||||
\(37\) | −2410.00 | −0.289409 | −0.144705 | − | 0.989475i | \(-0.546223\pi\) | ||||
−0.144705 | + | 0.989475i | \(0.546223\pi\) | |||||||
\(38\) | 3336.00 | 0.374772 | ||||||||
\(39\) | 5742.00 | 0.604507 | ||||||||
\(40\) | 1008.00 | 0.0996117 | ||||||||
\(41\) | −6870.00 | −0.638259 | −0.319130 | − | 0.947711i | \(-0.603391\pi\) | ||||
−0.319130 | + | 0.947711i | \(0.603391\pi\) | |||||||
\(42\) | 2160.00 | 0.188943 | ||||||||
\(43\) | 9644.00 | 0.795401 | 0.397700 | − | 0.917515i | \(-0.369808\pi\) | ||||
0.397700 | + | 0.917515i | \(0.369808\pi\) | |||||||
\(44\) | −2256.00 | −0.175674 | ||||||||
\(45\) | 486.000 | 0.0357771 | ||||||||
\(46\) | 5040.00 | 0.351185 | ||||||||
\(47\) | −18672.0 | −1.23295 | −0.616476 | − | 0.787374i | \(-0.711440\pi\) | ||||
−0.616476 | + | 0.787374i | \(0.711440\pi\) | |||||||
\(48\) | −10224.0 | −0.640498 | ||||||||
\(49\) | −15207.0 | −0.904802 | ||||||||
\(50\) | 18534.0 | 1.04844 | ||||||||
\(51\) | 7938.00 | 0.427352 | ||||||||
\(52\) | 2552.00 | 0.130880 | ||||||||
\(53\) | 33750.0 | 1.65038 | 0.825190 | − | 0.564855i | \(-0.191068\pi\) | ||||
0.825190 | + | 0.564855i | \(0.191068\pi\) | |||||||
\(54\) | −4374.00 | −0.204124 | ||||||||
\(55\) | −3384.00 | −0.150842 | ||||||||
\(56\) | −6720.00 | −0.286351 | ||||||||
\(57\) | −5004.00 | −0.204000 | ||||||||
\(58\) | −27828.0 | −1.08621 | ||||||||
\(59\) | −18084.0 | −0.676339 | −0.338170 | − | 0.941085i | \(-0.609808\pi\) | ||||
−0.338170 | + | 0.941085i | \(0.609808\pi\) | |||||||
\(60\) | 216.000 | 0.00774597 | ||||||||
\(61\) | 39758.0 | 1.36804 | 0.684022 | − | 0.729462i | \(-0.260229\pi\) | ||||
0.684022 | + | 0.729462i | \(0.260229\pi\) | |||||||
\(62\) | −26400.0 | −0.872217 | ||||||||
\(63\) | −3240.00 | −0.102847 | ||||||||
\(64\) | 27712.0 | 0.845703 | ||||||||
\(65\) | 3828.00 | 0.112380 | ||||||||
\(66\) | 30456.0 | 0.860623 | ||||||||
\(67\) | −23068.0 | −0.627802 | −0.313901 | − | 0.949456i | \(-0.601636\pi\) | ||||
−0.313901 | + | 0.949456i | \(0.601636\pi\) | |||||||
\(68\) | 3528.00 | 0.0925244 | ||||||||
\(69\) | −7560.00 | −0.191161 | ||||||||
\(70\) | 1440.00 | 0.0351251 | ||||||||
\(71\) | −4248.00 | −0.100009 | −0.0500044 | − | 0.998749i | \(-0.515924\pi\) | ||||
−0.0500044 | + | 0.998749i | \(0.515924\pi\) | |||||||
\(72\) | 13608.0 | 0.309359 | ||||||||
\(73\) | −41110.0 | −0.902901 | −0.451451 | − | 0.892296i | \(-0.649093\pi\) | ||||
−0.451451 | + | 0.892296i | \(0.649093\pi\) | |||||||
\(74\) | 14460.0 | 0.306965 | ||||||||
\(75\) | −27801.0 | −0.570699 | ||||||||
\(76\) | −2224.00 | −0.0441673 | ||||||||
\(77\) | 22560.0 | 0.433623 | ||||||||
\(78\) | −34452.0 | −0.641177 | ||||||||
\(79\) | 21920.0 | 0.395160 | 0.197580 | − | 0.980287i | \(-0.436692\pi\) | ||||
0.197580 | + | 0.980287i | \(0.436692\pi\) | |||||||
\(80\) | −6816.00 | −0.119071 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 41220.0 | 0.676976 | ||||||||
\(83\) | 82452.0 | 1.31373 | 0.656865 | − | 0.754008i | \(-0.271882\pi\) | ||||
0.656865 | + | 0.754008i | \(0.271882\pi\) | |||||||
\(84\) | −1440.00 | −0.0222671 | ||||||||
\(85\) | 5292.00 | 0.0794461 | ||||||||
\(86\) | −57864.0 | −0.843650 | ||||||||
\(87\) | 41742.0 | 0.591255 | ||||||||
\(88\) | −94752.0 | −1.30431 | ||||||||
\(89\) | −94086.0 | −1.25907 | −0.629535 | − | 0.776972i | \(-0.716755\pi\) | ||||
−0.629535 | + | 0.776972i | \(0.716755\pi\) | |||||||
\(90\) | −2916.00 | −0.0379473 | ||||||||
\(91\) | −25520.0 | −0.323056 | ||||||||
\(92\) | −3360.00 | −0.0413875 | ||||||||
\(93\) | 39600.0 | 0.474775 | ||||||||
\(94\) | 112032. | 1.30774 | ||||||||
\(95\) | −3336.00 | −0.0379243 | ||||||||
\(96\) | 12960.0 | 0.143525 | ||||||||
\(97\) | 49442.0 | 0.533540 | 0.266770 | − | 0.963760i | \(-0.414044\pi\) | ||||
0.266770 | + | 0.963760i | \(0.414044\pi\) | |||||||
\(98\) | 91242.0 | 0.959687 | ||||||||
\(99\) | −45684.0 | −0.468464 | ||||||||
\(100\) | −12356.0 | −0.123560 | ||||||||
\(101\) | −143034. | −1.39520 | −0.697599 | − | 0.716488i | \(-0.745748\pi\) | ||||
−0.697599 | + | 0.716488i | \(0.745748\pi\) | |||||||
\(102\) | −47628.0 | −0.453275 | ||||||||
\(103\) | 53144.0 | 0.493584 | 0.246792 | − | 0.969068i | \(-0.420624\pi\) | ||||
0.246792 | + | 0.969068i | \(0.420624\pi\) | |||||||
\(104\) | 107184. | 0.971732 | ||||||||
\(105\) | −2160.00 | −0.0191197 | ||||||||
\(106\) | −202500. | −1.75049 | ||||||||
\(107\) | 90828.0 | 0.766938 | 0.383469 | − | 0.923554i | \(-0.374729\pi\) | ||||
0.383469 | + | 0.923554i | \(0.374729\pi\) | |||||||
\(108\) | 2916.00 | 0.0240563 | ||||||||
\(109\) | −61666.0 | −0.497141 | −0.248570 | − | 0.968614i | \(-0.579961\pi\) | ||||
−0.248570 | + | 0.968614i | \(0.579961\pi\) | |||||||
\(110\) | 20304.0 | 0.159993 | ||||||||
\(111\) | −21690.0 | −0.167091 | ||||||||
\(112\) | 45440.0 | 0.342289 | ||||||||
\(113\) | 10482.0 | 0.0772232 | 0.0386116 | − | 0.999254i | \(-0.487706\pi\) | ||||
0.0386116 | + | 0.999254i | \(0.487706\pi\) | |||||||
\(114\) | 30024.0 | 0.216375 | ||||||||
\(115\) | −5040.00 | −0.0355374 | ||||||||
\(116\) | 18552.0 | 0.128011 | ||||||||
\(117\) | 51678.0 | 0.349013 | ||||||||
\(118\) | 108504. | 0.717366 | ||||||||
\(119\) | −35280.0 | −0.228382 | ||||||||
\(120\) | 9072.00 | 0.0575109 | ||||||||
\(121\) | 157045. | 0.975126 | ||||||||
\(122\) | −238548. | −1.45103 | ||||||||
\(123\) | −61830.0 | −0.368499 | ||||||||
\(124\) | 17600.0 | 0.102792 | ||||||||
\(125\) | −37284.0 | −0.213426 | ||||||||
\(126\) | 19440.0 | 0.109086 | ||||||||
\(127\) | −171088. | −0.941261 | −0.470631 | − | 0.882330i | \(-0.655974\pi\) | ||||
−0.470631 | + | 0.882330i | \(0.655974\pi\) | |||||||
\(128\) | −212352. | −1.14560 | ||||||||
\(129\) | 86796.0 | 0.459225 | ||||||||
\(130\) | −22968.0 | −0.119197 | ||||||||
\(131\) | 258468. | 1.31592 | 0.657959 | − | 0.753054i | \(-0.271420\pi\) | ||||
0.657959 | + | 0.753054i | \(0.271420\pi\) | |||||||
\(132\) | −20304.0 | −0.101425 | ||||||||
\(133\) | 22240.0 | 0.109020 | ||||||||
\(134\) | 138408. | 0.665885 | ||||||||
\(135\) | 4374.00 | 0.0206559 | ||||||||
\(136\) | 148176. | 0.686959 | ||||||||
\(137\) | 300234. | 1.36665 | 0.683327 | − | 0.730113i | \(-0.260532\pi\) | ||||
0.683327 | + | 0.730113i | \(0.260532\pi\) | |||||||
\(138\) | 45360.0 | 0.202757 | ||||||||
\(139\) | −350164. | −1.53721 | −0.768607 | − | 0.639721i | \(-0.779050\pi\) | ||||
−0.768607 | + | 0.639721i | \(0.779050\pi\) | |||||||
\(140\) | −960.000 | −0.00413953 | ||||||||
\(141\) | −168048. | −0.711845 | ||||||||
\(142\) | 25488.0 | 0.106075 | ||||||||
\(143\) | −359832. | −1.47150 | ||||||||
\(144\) | −92016.0 | −0.369792 | ||||||||
\(145\) | 27828.0 | 0.109916 | ||||||||
\(146\) | 246660. | 0.957672 | ||||||||
\(147\) | −136863. | −0.522387 | ||||||||
\(148\) | −9640.00 | −0.0361762 | ||||||||
\(149\) | −105258. | −0.388409 | −0.194205 | − | 0.980961i | \(-0.562213\pi\) | ||||
−0.194205 | + | 0.980961i | \(0.562213\pi\) | |||||||
\(150\) | 166806. | 0.605318 | ||||||||
\(151\) | 396392. | 1.41476 | 0.707380 | − | 0.706834i | \(-0.249877\pi\) | ||||
0.707380 | + | 0.706834i | \(0.249877\pi\) | |||||||
\(152\) | −93408.0 | −0.327925 | ||||||||
\(153\) | 71442.0 | 0.246732 | ||||||||
\(154\) | −135360. | −0.459927 | ||||||||
\(155\) | 26400.0 | 0.0882622 | ||||||||
\(156\) | 22968.0 | 0.0755634 | ||||||||
\(157\) | −137746. | −0.445995 | −0.222997 | − | 0.974819i | \(-0.571584\pi\) | ||||
−0.222997 | + | 0.974819i | \(0.571584\pi\) | |||||||
\(158\) | −131520. | −0.419130 | ||||||||
\(159\) | 303750. | 0.952848 | ||||||||
\(160\) | 8640.00 | 0.0266817 | ||||||||
\(161\) | 33600.0 | 0.102159 | ||||||||
\(162\) | −39366.0 | −0.117851 | ||||||||
\(163\) | 352676. | 1.03970 | 0.519849 | − | 0.854258i | \(-0.325988\pi\) | ||||
0.519849 | + | 0.854258i | \(0.325988\pi\) | |||||||
\(164\) | −27480.0 | −0.0797824 | ||||||||
\(165\) | −30456.0 | −0.0870889 | ||||||||
\(166\) | −494712. | −1.39342 | ||||||||
\(167\) | −217560. | −0.603654 | −0.301827 | − | 0.953363i | \(-0.597596\pi\) | ||||
−0.301827 | + | 0.953363i | \(0.597596\pi\) | |||||||
\(168\) | −60480.0 | −0.165325 | ||||||||
\(169\) | 35751.0 | 0.0962878 | ||||||||
\(170\) | −31752.0 | −0.0842653 | ||||||||
\(171\) | −45036.0 | −0.117779 | ||||||||
\(172\) | 38576.0 | 0.0994251 | ||||||||
\(173\) | −163698. | −0.415842 | −0.207921 | − | 0.978146i | \(-0.566670\pi\) | ||||
−0.207921 | + | 0.978146i | \(0.566670\pi\) | |||||||
\(174\) | −250452. | −0.627121 | ||||||||
\(175\) | 123560. | 0.304988 | ||||||||
\(176\) | 640704. | 1.55911 | ||||||||
\(177\) | −162756. | −0.390485 | ||||||||
\(178\) | 564516. | 1.33545 | ||||||||
\(179\) | 358740. | 0.836849 | 0.418425 | − | 0.908252i | \(-0.362582\pi\) | ||||
0.418425 | + | 0.908252i | \(0.362582\pi\) | |||||||
\(180\) | 1944.00 | 0.00447214 | ||||||||
\(181\) | −507130. | −1.15060 | −0.575298 | − | 0.817944i | \(-0.695114\pi\) | ||||
−0.575298 | + | 0.817944i | \(0.695114\pi\) | |||||||
\(182\) | 153120. | 0.342652 | ||||||||
\(183\) | 357822. | 0.789840 | ||||||||
\(184\) | −141120. | −0.307287 | ||||||||
\(185\) | −14460.0 | −0.0310627 | ||||||||
\(186\) | −237600. | −0.503575 | ||||||||
\(187\) | −497448. | −1.04026 | ||||||||
\(188\) | −74688.0 | −0.154119 | ||||||||
\(189\) | −29160.0 | −0.0593790 | ||||||||
\(190\) | 20016.0 | 0.0402247 | ||||||||
\(191\) | −648384. | −1.28602 | −0.643012 | − | 0.765856i | \(-0.722315\pi\) | ||||
−0.643012 | + | 0.765856i | \(0.722315\pi\) | |||||||
\(192\) | 249408. | 0.488267 | ||||||||
\(193\) | −27838.0 | −0.0537954 | −0.0268977 | − | 0.999638i | \(-0.508563\pi\) | ||||
−0.0268977 | + | 0.999638i | \(0.508563\pi\) | |||||||
\(194\) | −296652. | −0.565904 | ||||||||
\(195\) | 34452.0 | 0.0648826 | ||||||||
\(196\) | −60828.0 | −0.113100 | ||||||||
\(197\) | 611046. | 1.12178 | 0.560891 | − | 0.827890i | \(-0.310459\pi\) | ||||
0.560891 | + | 0.827890i | \(0.310459\pi\) | |||||||
\(198\) | 274104. | 0.496881 | ||||||||
\(199\) | 879032. | 1.57352 | 0.786760 | − | 0.617260i | \(-0.211757\pi\) | ||||
0.786760 | + | 0.617260i | \(0.211757\pi\) | |||||||
\(200\) | −518952. | −0.917386 | ||||||||
\(201\) | −207612. | −0.362462 | ||||||||
\(202\) | 858204. | 1.47983 | ||||||||
\(203\) | −185520. | −0.315973 | ||||||||
\(204\) | 31752.0 | 0.0534190 | ||||||||
\(205\) | −41220.0 | −0.0685052 | ||||||||
\(206\) | −318864. | −0.523525 | ||||||||
\(207\) | −68040.0 | −0.110367 | ||||||||
\(208\) | −724768. | −1.16156 | ||||||||
\(209\) | 313584. | 0.496579 | ||||||||
\(210\) | 12960.0 | 0.0202795 | ||||||||
\(211\) | 48500.0 | 0.0749956 | 0.0374978 | − | 0.999297i | \(-0.488061\pi\) | ||||
0.0374978 | + | 0.999297i | \(0.488061\pi\) | |||||||
\(212\) | 135000. | 0.206298 | ||||||||
\(213\) | −38232.0 | −0.0577402 | ||||||||
\(214\) | −544968. | −0.813461 | ||||||||
\(215\) | 57864.0 | 0.0853714 | ||||||||
\(216\) | 122472. | 0.178609 | ||||||||
\(217\) | −176000. | −0.253725 | ||||||||
\(218\) | 369996. | 0.527298 | ||||||||
\(219\) | −369990. | −0.521290 | ||||||||
\(220\) | −13536.0 | −0.0188553 | ||||||||
\(221\) | 562716. | 0.775012 | ||||||||
\(222\) | 130140. | 0.177226 | ||||||||
\(223\) | −999472. | −1.34589 | −0.672943 | − | 0.739694i | \(-0.734970\pi\) | ||||
−0.672943 | + | 0.739694i | \(0.734970\pi\) | |||||||
\(224\) | −57600.0 | −0.0767012 | ||||||||
\(225\) | −250209. | −0.329493 | ||||||||
\(226\) | −62892.0 | −0.0819076 | ||||||||
\(227\) | 606180. | 0.780795 | 0.390397 | − | 0.920646i | \(-0.372338\pi\) | ||||
0.390397 | + | 0.920646i | \(0.372338\pi\) | |||||||
\(228\) | −20016.0 | −0.0255000 | ||||||||
\(229\) | 1.35993e6 | 1.71367 | 0.856834 | − | 0.515593i | \(-0.172428\pi\) | ||||
0.856834 | + | 0.515593i | \(0.172428\pi\) | |||||||
\(230\) | 30240.0 | 0.0376931 | ||||||||
\(231\) | 203040. | 0.250352 | ||||||||
\(232\) | 779184. | 0.950430 | ||||||||
\(233\) | −392886. | −0.474107 | −0.237054 | − | 0.971497i | \(-0.576182\pi\) | ||||
−0.237054 | + | 0.971497i | \(0.576182\pi\) | |||||||
\(234\) | −310068. | −0.370184 | ||||||||
\(235\) | −112032. | −0.132334 | ||||||||
\(236\) | −72336.0 | −0.0845424 | ||||||||
\(237\) | 197280. | 0.228146 | ||||||||
\(238\) | 211680. | 0.242235 | ||||||||
\(239\) | −1.32514e6 | −1.50060 | −0.750301 | − | 0.661096i | \(-0.770092\pi\) | ||||
−0.750301 | + | 0.661096i | \(0.770092\pi\) | |||||||
\(240\) | −61344.0 | −0.0687455 | ||||||||
\(241\) | −990094. | −1.09808 | −0.549040 | − | 0.835796i | \(-0.685006\pi\) | ||||
−0.549040 | + | 0.835796i | \(0.685006\pi\) | |||||||
\(242\) | −942270. | −1.03428 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 159032. | 0.171005 | ||||||||
\(245\) | −91242.0 | −0.0971135 | ||||||||
\(246\) | 370980. | 0.390852 | ||||||||
\(247\) | −354728. | −0.369959 | ||||||||
\(248\) | 739200. | 0.763190 | ||||||||
\(249\) | 742068. | 0.758482 | ||||||||
\(250\) | 223704. | 0.226373 | ||||||||
\(251\) | 147132. | 0.147409 | 0.0737043 | − | 0.997280i | \(-0.476518\pi\) | ||||
0.0737043 | + | 0.997280i | \(0.476518\pi\) | |||||||
\(252\) | −12960.0 | −0.0128559 | ||||||||
\(253\) | 473760. | 0.465326 | ||||||||
\(254\) | 1.02653e6 | 0.998358 | ||||||||
\(255\) | 47628.0 | 0.0458682 | ||||||||
\(256\) | 387328. | 0.369385 | ||||||||
\(257\) | −483582. | −0.456707 | −0.228353 | − | 0.973578i | \(-0.573334\pi\) | ||||
−0.228353 | + | 0.973578i | \(0.573334\pi\) | |||||||
\(258\) | −520776. | −0.487082 | ||||||||
\(259\) | 96400.0 | 0.0892951 | ||||||||
\(260\) | 15312.0 | 0.0140475 | ||||||||
\(261\) | 375678. | 0.341361 | ||||||||
\(262\) | −1.55081e6 | −1.39574 | ||||||||
\(263\) | 813576. | 0.725285 | 0.362643 | − | 0.931928i | \(-0.381875\pi\) | ||||
0.362643 | + | 0.931928i | \(0.381875\pi\) | |||||||
\(264\) | −852768. | −0.753045 | ||||||||
\(265\) | 202500. | 0.177137 | ||||||||
\(266\) | −133440. | −0.115633 | ||||||||
\(267\) | −846774. | −0.726925 | ||||||||
\(268\) | −92272.0 | −0.0784753 | ||||||||
\(269\) | −461106. | −0.388526 | −0.194263 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194263 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(270\) | −26244.0 | −0.0219089 | ||||||||
\(271\) | 1.67514e6 | 1.38556 | 0.692782 | − | 0.721147i | \(-0.256385\pi\) | ||||
0.692782 | + | 0.721147i | \(0.256385\pi\) | |||||||
\(272\) | −1.00195e6 | −0.821154 | ||||||||
\(273\) | −229680. | −0.186516 | ||||||||
\(274\) | −1.80140e6 | −1.44956 | ||||||||
\(275\) | 1.74220e6 | 1.38920 | ||||||||
\(276\) | −30240.0 | −0.0238951 | ||||||||
\(277\) | 401126. | 0.314110 | 0.157055 | − | 0.987590i | \(-0.449800\pi\) | ||||
0.157055 | + | 0.987590i | \(0.449800\pi\) | |||||||
\(278\) | 2.10098e6 | 1.63046 | ||||||||
\(279\) | 356400. | 0.274111 | ||||||||
\(280\) | −40320.0 | −0.0307344 | ||||||||
\(281\) | −2.30977e6 | −1.74503 | −0.872514 | − | 0.488590i | \(-0.837511\pi\) | ||||
−0.872514 | + | 0.488590i | \(0.837511\pi\) | |||||||
\(282\) | 1.00829e6 | 0.755026 | ||||||||
\(283\) | −1.12877e6 | −0.837800 | −0.418900 | − | 0.908032i | \(-0.637584\pi\) | ||||
−0.418900 | + | 0.908032i | \(0.637584\pi\) | |||||||
\(284\) | −16992.0 | −0.0125011 | ||||||||
\(285\) | −30024.0 | −0.0218956 | ||||||||
\(286\) | 2.15899e6 | 1.56076 | ||||||||
\(287\) | 274800. | 0.196930 | ||||||||
\(288\) | 116640. | 0.0828641 | ||||||||
\(289\) | −641933. | −0.452111 | ||||||||
\(290\) | −166968. | −0.116584 | ||||||||
\(291\) | 444978. | 0.308039 | ||||||||
\(292\) | −164440. | −0.112863 | ||||||||
\(293\) | −938874. | −0.638908 | −0.319454 | − | 0.947602i | \(-0.603499\pi\) | ||||
−0.319454 | + | 0.947602i | \(0.603499\pi\) | |||||||
\(294\) | 821178. | 0.554076 | ||||||||
\(295\) | −108504. | −0.0725923 | ||||||||
\(296\) | −404880. | −0.268594 | ||||||||
\(297\) | −411156. | −0.270468 | ||||||||
\(298\) | 631548. | 0.411970 | ||||||||
\(299\) | −535920. | −0.346675 | ||||||||
\(300\) | −111204. | −0.0713374 | ||||||||
\(301\) | −385760. | −0.245415 | ||||||||
\(302\) | −2.37835e6 | −1.50058 | ||||||||
\(303\) | −1.28731e6 | −0.805518 | ||||||||
\(304\) | 631616. | 0.391985 | ||||||||
\(305\) | 238548. | 0.146834 | ||||||||
\(306\) | −428652. | −0.261699 | ||||||||
\(307\) | 692948. | 0.419619 | 0.209809 | − | 0.977742i | \(-0.432716\pi\) | ||||
0.209809 | + | 0.977742i | \(0.432716\pi\) | |||||||
\(308\) | 90240.0 | 0.0542029 | ||||||||
\(309\) | 478296. | 0.284971 | ||||||||
\(310\) | −158400. | −0.0936162 | ||||||||
\(311\) | 2.94310e6 | 1.72545 | 0.862727 | − | 0.505670i | \(-0.168755\pi\) | ||||
0.862727 | + | 0.505670i | \(0.168755\pi\) | |||||||
\(312\) | 964656. | 0.561030 | ||||||||
\(313\) | 885146. | 0.510686 | 0.255343 | − | 0.966851i | \(-0.417812\pi\) | ||||
0.255343 | + | 0.966851i | \(0.417812\pi\) | |||||||
\(314\) | 826476. | 0.473049 | ||||||||
\(315\) | −19440.0 | −0.0110387 | ||||||||
\(316\) | 87680.0 | 0.0493950 | ||||||||
\(317\) | 2.50880e6 | 1.40222 | 0.701112 | − | 0.713051i | \(-0.252687\pi\) | ||||
0.701112 | + | 0.713051i | \(0.252687\pi\) | |||||||
\(318\) | −1.82250e6 | −1.01065 | ||||||||
\(319\) | −2.61583e6 | −1.43924 | ||||||||
\(320\) | 166272. | 0.0907704 | ||||||||
\(321\) | 817452. | 0.442792 | ||||||||
\(322\) | −201600. | −0.108355 | ||||||||
\(323\) | −490392. | −0.261539 | ||||||||
\(324\) | 26244.0 | 0.0138889 | ||||||||
\(325\) | −1.97078e6 | −1.03498 | ||||||||
\(326\) | −2.11606e6 | −1.10277 | ||||||||
\(327\) | −554994. | −0.287024 | ||||||||
\(328\) | −1.15416e6 | −0.592354 | ||||||||
\(329\) | 746880. | 0.380418 | ||||||||
\(330\) | 182736. | 0.0923718 | ||||||||
\(331\) | −216148. | −0.108438 | −0.0542190 | − | 0.998529i | \(-0.517267\pi\) | ||||
−0.0542190 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(332\) | 329808. | 0.164216 | ||||||||
\(333\) | −195210. | −0.0964698 | ||||||||
\(334\) | 1.30536e6 | 0.640271 | ||||||||
\(335\) | −138408. | −0.0673828 | ||||||||
\(336\) | 408960. | 0.197621 | ||||||||
\(337\) | 3.25263e6 | 1.56012 | 0.780062 | − | 0.625702i | \(-0.215187\pi\) | ||||
0.780062 | + | 0.625702i | \(0.215187\pi\) | |||||||
\(338\) | −214506. | −0.102129 | ||||||||
\(339\) | 94338.0 | 0.0445849 | ||||||||
\(340\) | 21168.0 | 0.00993076 | ||||||||
\(341\) | −2.48160e6 | −1.15570 | ||||||||
\(342\) | 270216. | 0.124924 | ||||||||
\(343\) | 1.28056e6 | 0.587712 | ||||||||
\(344\) | 1.62019e6 | 0.738194 | ||||||||
\(345\) | −45360.0 | −0.0205175 | ||||||||
\(346\) | 982188. | 0.441067 | ||||||||
\(347\) | −2.93207e6 | −1.30723 | −0.653613 | − | 0.756829i | \(-0.726747\pi\) | ||||
−0.653613 | + | 0.756829i | \(0.726747\pi\) | |||||||
\(348\) | 166968. | 0.0739069 | ||||||||
\(349\) | 905198. | 0.397814 | 0.198907 | − | 0.980018i | \(-0.436261\pi\) | ||||
0.198907 | + | 0.980018i | \(0.436261\pi\) | |||||||
\(350\) | −741360. | −0.323489 | ||||||||
\(351\) | 465102. | 0.201502 | ||||||||
\(352\) | −812160. | −0.349369 | ||||||||
\(353\) | 1.91786e6 | 0.819181 | 0.409590 | − | 0.912270i | \(-0.365672\pi\) | ||||
0.409590 | + | 0.912270i | \(0.365672\pi\) | |||||||
\(354\) | 976536. | 0.414171 | ||||||||
\(355\) | −25488.0 | −0.0107341 | ||||||||
\(356\) | −376344. | −0.157384 | ||||||||
\(357\) | −317520. | −0.131856 | ||||||||
\(358\) | −2.15244e6 | −0.887613 | ||||||||
\(359\) | −2.43698e6 | −0.997968 | −0.498984 | − | 0.866611i | \(-0.666293\pi\) | ||||
−0.498984 | + | 0.866611i | \(0.666293\pi\) | |||||||
\(360\) | 81648.0 | 0.0332039 | ||||||||
\(361\) | −2.16696e6 | −0.875152 | ||||||||
\(362\) | 3.04278e6 | 1.22039 | ||||||||
\(363\) | 1.41340e6 | 0.562989 | ||||||||
\(364\) | −102080. | −0.0403819 | ||||||||
\(365\) | −246660. | −0.0969095 | ||||||||
\(366\) | −2.14693e6 | −0.837752 | ||||||||
\(367\) | −984064. | −0.381380 | −0.190690 | − | 0.981650i | \(-0.561073\pi\) | ||||
−0.190690 | + | 0.981650i | \(0.561073\pi\) | |||||||
\(368\) | 954240. | 0.367314 | ||||||||
\(369\) | −556470. | −0.212753 | ||||||||
\(370\) | 86760.0 | 0.0329470 | ||||||||
\(371\) | −1.35000e6 | −0.509212 | ||||||||
\(372\) | 158400. | 0.0593469 | ||||||||
\(373\) | 1.70365e6 | 0.634029 | 0.317015 | − | 0.948421i | \(-0.397320\pi\) | ||||
0.317015 | + | 0.948421i | \(0.397320\pi\) | |||||||
\(374\) | 2.98469e6 | 1.10337 | ||||||||
\(375\) | −335556. | −0.123222 | ||||||||
\(376\) | −3.13690e6 | −1.14428 | ||||||||
\(377\) | 2.95904e6 | 1.07225 | ||||||||
\(378\) | 174960. | 0.0629810 | ||||||||
\(379\) | 2.75654e6 | 0.985749 | 0.492874 | − | 0.870100i | \(-0.335946\pi\) | ||||
0.492874 | + | 0.870100i | \(0.335946\pi\) | |||||||
\(380\) | −13344.0 | −0.00474053 | ||||||||
\(381\) | −1.53979e6 | −0.543438 | ||||||||
\(382\) | 3.89030e6 | 1.36403 | ||||||||
\(383\) | 456576. | 0.159044 | 0.0795218 | − | 0.996833i | \(-0.474661\pi\) | ||||
0.0795218 | + | 0.996833i | \(0.474661\pi\) | |||||||
\(384\) | −1.91117e6 | −0.661410 | ||||||||
\(385\) | 135360. | 0.0465413 | ||||||||
\(386\) | 167028. | 0.0570586 | ||||||||
\(387\) | 781164. | 0.265134 | ||||||||
\(388\) | 197768. | 0.0666925 | ||||||||
\(389\) | −2.00639e6 | −0.672268 | −0.336134 | − | 0.941814i | \(-0.609119\pi\) | ||||
−0.336134 | + | 0.941814i | \(0.609119\pi\) | |||||||
\(390\) | −206712. | −0.0688183 | ||||||||
\(391\) | −740880. | −0.245079 | ||||||||
\(392\) | −2.55478e6 | −0.839726 | ||||||||
\(393\) | 2.32621e6 | 0.759745 | ||||||||
\(394\) | −3.66628e6 | −1.18983 | ||||||||
\(395\) | 131520. | 0.0424130 | ||||||||
\(396\) | −182736. | −0.0585580 | ||||||||
\(397\) | −5.77040e6 | −1.83751 | −0.918755 | − | 0.394828i | \(-0.870804\pi\) | ||||
−0.918755 | + | 0.394828i | \(0.870804\pi\) | |||||||
\(398\) | −5.27419e6 | −1.66897 | ||||||||
\(399\) | 200160. | 0.0629427 | ||||||||
\(400\) | 3.50910e6 | 1.09659 | ||||||||
\(401\) | 3.00626e6 | 0.933610 | 0.466805 | − | 0.884360i | \(-0.345405\pi\) | ||||
0.466805 | + | 0.884360i | \(0.345405\pi\) | |||||||
\(402\) | 1.24567e6 | 0.384449 | ||||||||
\(403\) | 2.80720e6 | 0.861015 | ||||||||
\(404\) | −572136. | −0.174400 | ||||||||
\(405\) | 39366.0 | 0.0119257 | ||||||||
\(406\) | 1.11312e6 | 0.335140 | ||||||||
\(407\) | 1.35924e6 | 0.406734 | ||||||||
\(408\) | 1.33358e6 | 0.396616 | ||||||||
\(409\) | 1.53363e6 | 0.453327 | 0.226663 | − | 0.973973i | \(-0.427218\pi\) | ||||
0.226663 | + | 0.973973i | \(0.427218\pi\) | |||||||
\(410\) | 247320. | 0.0726607 | ||||||||
\(411\) | 2.70211e6 | 0.789038 | ||||||||
\(412\) | 212576. | 0.0616980 | ||||||||
\(413\) | 723360. | 0.208679 | ||||||||
\(414\) | 408240. | 0.117062 | ||||||||
\(415\) | 494712. | 0.141004 | ||||||||
\(416\) | 918720. | 0.260285 | ||||||||
\(417\) | −3.15148e6 | −0.887511 | ||||||||
\(418\) | −1.88150e6 | −0.526701 | ||||||||
\(419\) | −3.87376e6 | −1.07795 | −0.538973 | − | 0.842323i | \(-0.681188\pi\) | ||||
−0.538973 | + | 0.842323i | \(0.681188\pi\) | |||||||
\(420\) | −8640.00 | −0.00238996 | ||||||||
\(421\) | −1.33307e6 | −0.366561 | −0.183281 | − | 0.983061i | \(-0.558672\pi\) | ||||
−0.183281 | + | 0.983061i | \(0.558672\pi\) | |||||||
\(422\) | −291000. | −0.0795448 | ||||||||
\(423\) | −1.51243e6 | −0.410984 | ||||||||
\(424\) | 5.67000e6 | 1.53168 | ||||||||
\(425\) | −2.72450e6 | −0.731668 | ||||||||
\(426\) | 229392. | 0.0612427 | ||||||||
\(427\) | −1.59032e6 | −0.422099 | ||||||||
\(428\) | 363312. | 0.0958673 | ||||||||
\(429\) | −3.23849e6 | −0.849570 | ||||||||
\(430\) | −347184. | −0.0905500 | ||||||||
\(431\) | 6.45192e6 | 1.67300 | 0.836500 | − | 0.547967i | \(-0.184598\pi\) | ||||
0.836500 | + | 0.547967i | \(0.184598\pi\) | |||||||
\(432\) | −828144. | −0.213499 | ||||||||
\(433\) | −4.16577e6 | −1.06777 | −0.533883 | − | 0.845558i | \(-0.679268\pi\) | ||||
−0.533883 | + | 0.845558i | \(0.679268\pi\) | |||||||
\(434\) | 1.05600e6 | 0.269116 | ||||||||
\(435\) | 250452. | 0.0634602 | ||||||||
\(436\) | −246664. | −0.0621426 | ||||||||
\(437\) | 467040. | 0.116990 | ||||||||
\(438\) | 2.21994e6 | 0.552912 | ||||||||
\(439\) | 792680. | 0.196307 | 0.0981537 | − | 0.995171i | \(-0.468706\pi\) | ||||
0.0981537 | + | 0.995171i | \(0.468706\pi\) | |||||||
\(440\) | −568512. | −0.139994 | ||||||||
\(441\) | −1.23177e6 | −0.301601 | ||||||||
\(442\) | −3.37630e6 | −0.822025 | ||||||||
\(443\) | −1.39981e6 | −0.338891 | −0.169446 | − | 0.985540i | \(-0.554198\pi\) | ||||
−0.169446 | + | 0.985540i | \(0.554198\pi\) | |||||||
\(444\) | −86760.0 | −0.0208863 | ||||||||
\(445\) | −564516. | −0.135138 | ||||||||
\(446\) | 5.99683e6 | 1.42753 | ||||||||
\(447\) | −947322. | −0.224248 | ||||||||
\(448\) | −1.10848e6 | −0.260935 | ||||||||
\(449\) | 2.99248e6 | 0.700512 | 0.350256 | − | 0.936654i | \(-0.386095\pi\) | ||||
0.350256 | + | 0.936654i | \(0.386095\pi\) | |||||||
\(450\) | 1.50125e6 | 0.349480 | ||||||||
\(451\) | 3.87468e6 | 0.897004 | ||||||||
\(452\) | 41928.0 | 0.00965291 | ||||||||
\(453\) | 3.56753e6 | 0.816812 | ||||||||
\(454\) | −3.63708e6 | −0.828158 | ||||||||
\(455\) | −153120. | −0.0346740 | ||||||||
\(456\) | −840672. | −0.189328 | ||||||||
\(457\) | 6.29969e6 | 1.41101 | 0.705503 | − | 0.708707i | \(-0.250721\pi\) | ||||
0.705503 | + | 0.708707i | \(0.250721\pi\) | |||||||
\(458\) | −8.15956e6 | −1.81762 | ||||||||
\(459\) | 642978. | 0.142451 | ||||||||
\(460\) | −20160.0 | −0.00444218 | ||||||||
\(461\) | 3.40318e6 | 0.745818 | 0.372909 | − | 0.927868i | \(-0.378360\pi\) | ||||
0.372909 | + | 0.927868i | \(0.378360\pi\) | |||||||
\(462\) | −1.21824e6 | −0.265539 | ||||||||
\(463\) | −2.23034e6 | −0.483524 | −0.241762 | − | 0.970336i | \(-0.577725\pi\) | ||||
−0.241762 | + | 0.970336i | \(0.577725\pi\) | |||||||
\(464\) | −5.26877e6 | −1.13609 | ||||||||
\(465\) | 237600. | 0.0509582 | ||||||||
\(466\) | 2.35732e6 | 0.502867 | ||||||||
\(467\) | −6.51409e6 | −1.38217 | −0.691085 | − | 0.722773i | \(-0.742867\pi\) | ||||
−0.691085 | + | 0.722773i | \(0.742867\pi\) | |||||||
\(468\) | 206712. | 0.0436266 | ||||||||
\(469\) | 922720. | 0.193704 | ||||||||
\(470\) | 672192. | 0.140362 | ||||||||
\(471\) | −1.23971e6 | −0.257495 | ||||||||
\(472\) | −3.03811e6 | −0.627695 | ||||||||
\(473\) | −5.43922e6 | −1.11785 | ||||||||
\(474\) | −1.18368e6 | −0.241985 | ||||||||
\(475\) | 1.71748e6 | 0.349268 | ||||||||
\(476\) | −141120. | −0.0285477 | ||||||||
\(477\) | 2.73375e6 | 0.550127 | ||||||||
\(478\) | 7.95082e6 | 1.59163 | ||||||||
\(479\) | 2.39232e6 | 0.476410 | 0.238205 | − | 0.971215i | \(-0.423441\pi\) | ||||
0.238205 | + | 0.971215i | \(0.423441\pi\) | |||||||
\(480\) | 77760.0 | 0.0154047 | ||||||||
\(481\) | −1.53758e6 | −0.303023 | ||||||||
\(482\) | 5.94056e6 | 1.16469 | ||||||||
\(483\) | 302400. | 0.0589812 | ||||||||
\(484\) | 628180. | 0.121891 | ||||||||
\(485\) | 296652. | 0.0572655 | ||||||||
\(486\) | −354294. | −0.0680414 | ||||||||
\(487\) | −6.13089e6 | −1.17139 | −0.585694 | − | 0.810532i | \(-0.699178\pi\) | ||||
−0.585694 | + | 0.810532i | \(0.699178\pi\) | |||||||
\(488\) | 6.67934e6 | 1.26965 | ||||||||
\(489\) | 3.17408e6 | 0.600269 | ||||||||
\(490\) | 547452. | 0.103004 | ||||||||
\(491\) | −1.23589e6 | −0.231354 | −0.115677 | − | 0.993287i | \(-0.536904\pi\) | ||||
−0.115677 | + | 0.993287i | \(0.536904\pi\) | |||||||
\(492\) | −247320. | −0.0460624 | ||||||||
\(493\) | 4.09072e6 | 0.758022 | ||||||||
\(494\) | 2.12837e6 | 0.392400 | ||||||||
\(495\) | −274104. | −0.0502808 | ||||||||
\(496\) | −4.99840e6 | −0.912277 | ||||||||
\(497\) | 169920. | 0.0308570 | ||||||||
\(498\) | −4.45241e6 | −0.804492 | ||||||||
\(499\) | −9.85496e6 | −1.77175 | −0.885877 | − | 0.463921i | \(-0.846442\pi\) | ||||
−0.885877 | + | 0.463921i | \(0.846442\pi\) | |||||||
\(500\) | −149136. | −0.0266783 | ||||||||
\(501\) | −1.95804e6 | −0.348520 | ||||||||
\(502\) | −882792. | −0.156350 | ||||||||
\(503\) | 1.16777e6 | 0.205796 | 0.102898 | − | 0.994692i | \(-0.467188\pi\) | ||||
0.102898 | + | 0.994692i | \(0.467188\pi\) | |||||||
\(504\) | −544320. | −0.0954504 | ||||||||
\(505\) | −858204. | −0.149748 | ||||||||
\(506\) | −2.84256e6 | −0.493552 | ||||||||
\(507\) | 321759. | 0.0555918 | ||||||||
\(508\) | −684352. | −0.117658 | ||||||||
\(509\) | 1.04941e6 | 0.179535 | 0.0897675 | − | 0.995963i | \(-0.471388\pi\) | ||||
0.0897675 | + | 0.995963i | \(0.471388\pi\) | |||||||
\(510\) | −285768. | −0.0486506 | ||||||||
\(511\) | 1.64440e6 | 0.278583 | ||||||||
\(512\) | 4.47130e6 | 0.753804 | ||||||||
\(513\) | −405324. | −0.0680000 | ||||||||
\(514\) | 2.90149e6 | 0.484411 | ||||||||
\(515\) | 318864. | 0.0529770 | ||||||||
\(516\) | 347184. | 0.0574031 | ||||||||
\(517\) | 1.05310e7 | 1.73278 | ||||||||
\(518\) | −578400. | −0.0947118 | ||||||||
\(519\) | −1.47328e6 | −0.240086 | ||||||||
\(520\) | 643104. | 0.104297 | ||||||||
\(521\) | −9.61407e6 | −1.55172 | −0.775859 | − | 0.630906i | \(-0.782683\pi\) | ||||
−0.775859 | + | 0.630906i | \(0.782683\pi\) | |||||||
\(522\) | −2.25407e6 | −0.362069 | ||||||||
\(523\) | 6.96148e6 | 1.11288 | 0.556439 | − | 0.830888i | \(-0.312167\pi\) | ||||
0.556439 | + | 0.830888i | \(0.312167\pi\) | |||||||
\(524\) | 1.03387e6 | 0.164490 | ||||||||
\(525\) | 1.11204e6 | 0.176085 | ||||||||
\(526\) | −4.88146e6 | −0.769281 | ||||||||
\(527\) | 3.88080e6 | 0.608688 | ||||||||
\(528\) | 5.76634e6 | 0.900151 | ||||||||
\(529\) | −5.73074e6 | −0.890373 | ||||||||
\(530\) | −1.21500e6 | −0.187883 | ||||||||
\(531\) | −1.46480e6 | −0.225446 | ||||||||
\(532\) | 88960.0 | 0.0136275 | ||||||||
\(533\) | −4.38306e6 | −0.668281 | ||||||||
\(534\) | 5.08064e6 | 0.771020 | ||||||||
\(535\) | 544968. | 0.0823164 | ||||||||
\(536\) | −3.87542e6 | −0.582649 | ||||||||
\(537\) | 3.22866e6 | 0.483155 | ||||||||
\(538\) | 2.76664e6 | 0.412094 | ||||||||
\(539\) | 8.57675e6 | 1.27160 | ||||||||
\(540\) | 17496.0 | 0.00258199 | ||||||||
\(541\) | −712690. | −0.104691 | −0.0523453 | − | 0.998629i | \(-0.516670\pi\) | ||||
−0.0523453 | + | 0.998629i | \(0.516670\pi\) | |||||||
\(542\) | −1.00508e7 | −1.46961 | ||||||||
\(543\) | −4.56417e6 | −0.664297 | ||||||||
\(544\) | 1.27008e6 | 0.184007 | ||||||||
\(545\) | −369996. | −0.0533588 | ||||||||
\(546\) | 1.37808e6 | 0.197830 | ||||||||
\(547\) | −3.62614e6 | −0.518175 | −0.259087 | − | 0.965854i | \(-0.583422\pi\) | ||||
−0.259087 | + | 0.965854i | \(0.583422\pi\) | |||||||
\(548\) | 1.20094e6 | 0.170832 | ||||||||
\(549\) | 3.22040e6 | 0.456015 | ||||||||
\(550\) | −1.04532e7 | −1.47347 | ||||||||
\(551\) | −2.57873e6 | −0.361848 | ||||||||
\(552\) | −1.27008e6 | −0.177412 | ||||||||
\(553\) | −876800. | −0.121924 | ||||||||
\(554\) | −2.40676e6 | −0.333164 | ||||||||
\(555\) | −130140. | −0.0179340 | ||||||||
\(556\) | −1.40066e6 | −0.192152 | ||||||||
\(557\) | 4.84846e6 | 0.662165 | 0.331082 | − | 0.943602i | \(-0.392586\pi\) | ||||
0.331082 | + | 0.943602i | \(0.392586\pi\) | |||||||
\(558\) | −2.13840e6 | −0.290739 | ||||||||
\(559\) | 6.15287e6 | 0.832815 | ||||||||
\(560\) | 272640. | 0.0367383 | ||||||||
\(561\) | −4.47703e6 | −0.600597 | ||||||||
\(562\) | 1.38586e7 | 1.85088 | ||||||||
\(563\) | 8.50405e6 | 1.13072 | 0.565360 | − | 0.824844i | \(-0.308737\pi\) | ||||
0.565360 | + | 0.824844i | \(0.308737\pi\) | |||||||
\(564\) | −672192. | −0.0889807 | ||||||||
\(565\) | 62892.0 | 0.00828847 | ||||||||
\(566\) | 6.77263e6 | 0.888621 | ||||||||
\(567\) | −262440. | −0.0342825 | ||||||||
\(568\) | −713664. | −0.0928160 | ||||||||
\(569\) | 362874. | 0.0469867 | 0.0234934 | − | 0.999724i | \(-0.492521\pi\) | ||||
0.0234934 | + | 0.999724i | \(0.492521\pi\) | |||||||
\(570\) | 180144. | 0.0232238 | ||||||||
\(571\) | 4.11024e6 | 0.527566 | 0.263783 | − | 0.964582i | \(-0.415030\pi\) | ||||
0.263783 | + | 0.964582i | \(0.415030\pi\) | |||||||
\(572\) | −1.43933e6 | −0.183937 | ||||||||
\(573\) | −5.83546e6 | −0.742486 | ||||||||
\(574\) | −1.64880e6 | −0.208876 | ||||||||
\(575\) | 2.59476e6 | 0.327286 | ||||||||
\(576\) | 2.24467e6 | 0.281901 | ||||||||
\(577\) | −7.87680e6 | −0.984941 | −0.492470 | − | 0.870329i | \(-0.663906\pi\) | ||||
−0.492470 | + | 0.870329i | \(0.663906\pi\) | |||||||
\(578\) | 3.85160e6 | 0.479536 | ||||||||
\(579\) | −250542. | −0.0310588 | ||||||||
\(580\) | 111312. | 0.0137395 | ||||||||
\(581\) | −3.29808e6 | −0.405341 | ||||||||
\(582\) | −2.66987e6 | −0.326725 | ||||||||
\(583\) | −1.90350e7 | −2.31943 | ||||||||
\(584\) | −6.90648e6 | −0.837963 | ||||||||
\(585\) | 310068. | 0.0374600 | ||||||||
\(586\) | 5.63324e6 | 0.677664 | ||||||||
\(587\) | 603948. | 0.0723443 | 0.0361721 | − | 0.999346i | \(-0.488484\pi\) | ||||
0.0361721 | + | 0.999346i | \(0.488484\pi\) | |||||||
\(588\) | −547452. | −0.0652984 | ||||||||
\(589\) | −2.44640e6 | −0.290562 | ||||||||
\(590\) | 651024. | 0.0769958 | ||||||||
\(591\) | 5.49941e6 | 0.647661 | ||||||||
\(592\) | 2.73776e6 | 0.321064 | ||||||||
\(593\) | −5.39077e6 | −0.629526 | −0.314763 | − | 0.949170i | \(-0.601925\pi\) | ||||
−0.314763 | + | 0.949170i | \(0.601925\pi\) | |||||||
\(594\) | 2.46694e6 | 0.286874 | ||||||||
\(595\) | −211680. | −0.0245125 | ||||||||
\(596\) | −421032. | −0.0485511 | ||||||||
\(597\) | 7.91129e6 | 0.908472 | ||||||||
\(598\) | 3.21552e6 | 0.367704 | ||||||||
\(599\) | 4.27999e6 | 0.487389 | 0.243695 | − | 0.969852i | \(-0.421641\pi\) | ||||
0.243695 | + | 0.969852i | \(0.421641\pi\) | |||||||
\(600\) | −4.67057e6 | −0.529653 | ||||||||
\(601\) | 1.02483e6 | 0.115735 | 0.0578674 | − | 0.998324i | \(-0.481570\pi\) | ||||
0.0578674 | + | 0.998324i | \(0.481570\pi\) | |||||||
\(602\) | 2.31456e6 | 0.260302 | ||||||||
\(603\) | −1.86851e6 | −0.209267 | ||||||||
\(604\) | 1.58557e6 | 0.176845 | ||||||||
\(605\) | 942270. | 0.104661 | ||||||||
\(606\) | 7.72384e6 | 0.854381 | ||||||||
\(607\) | 1.24342e7 | 1.36976 | 0.684882 | − | 0.728654i | \(-0.259854\pi\) | ||||
0.684882 | + | 0.728654i | \(0.259854\pi\) | |||||||
\(608\) | −800640. | −0.0878372 | ||||||||
\(609\) | −1.66968e6 | −0.182427 | ||||||||
\(610\) | −1.43129e6 | −0.155741 | ||||||||
\(611\) | −1.19127e7 | −1.29095 | ||||||||
\(612\) | 285768. | 0.0308415 | ||||||||
\(613\) | 4.21506e6 | 0.453057 | 0.226528 | − | 0.974005i | \(-0.427262\pi\) | ||||
0.226528 | + | 0.974005i | \(0.427262\pi\) | |||||||
\(614\) | −4.15769e6 | −0.445073 | ||||||||
\(615\) | −370980. | −0.0395515 | ||||||||
\(616\) | 3.79008e6 | 0.402436 | ||||||||
\(617\) | −4.40665e6 | −0.466010 | −0.233005 | − | 0.972476i | \(-0.574856\pi\) | ||||
−0.233005 | + | 0.972476i | \(0.574856\pi\) | |||||||
\(618\) | −2.86978e6 | −0.302257 | ||||||||
\(619\) | 4.80168e6 | 0.503693 | 0.251847 | − | 0.967767i | \(-0.418962\pi\) | ||||
0.251847 | + | 0.967767i | \(0.418962\pi\) | |||||||
\(620\) | 105600. | 0.0110328 | ||||||||
\(621\) | −612360. | −0.0637203 | ||||||||
\(622\) | −1.76586e7 | −1.83012 | ||||||||
\(623\) | 3.76344e6 | 0.388477 | ||||||||
\(624\) | −6.52291e6 | −0.670625 | ||||||||
\(625\) | 9.42942e6 | 0.965573 | ||||||||
\(626\) | −5.31088e6 | −0.541664 | ||||||||
\(627\) | 2.82226e6 | 0.286700 | ||||||||
\(628\) | −550984. | −0.0557494 | ||||||||
\(629\) | −2.12562e6 | −0.214220 | ||||||||
\(630\) | 116640. | 0.0117084 | ||||||||
\(631\) | 8.30727e6 | 0.830587 | 0.415293 | − | 0.909688i | \(-0.363679\pi\) | ||||
0.415293 | + | 0.909688i | \(0.363679\pi\) | |||||||
\(632\) | 3.68256e6 | 0.366739 | ||||||||
\(633\) | 436500. | 0.0432987 | ||||||||
\(634\) | −1.50528e7 | −1.48728 | ||||||||
\(635\) | −1.02653e6 | −0.101027 | ||||||||
\(636\) | 1.21500e6 | 0.119106 | ||||||||
\(637\) | −9.70207e6 | −0.947361 | ||||||||
\(638\) | 1.56950e7 | 1.52654 | ||||||||
\(639\) | −344088. | −0.0333363 | ||||||||
\(640\) | −1.27411e6 | −0.122958 | ||||||||
\(641\) | 1.76956e7 | 1.70107 | 0.850534 | − | 0.525921i | \(-0.176279\pi\) | ||||
0.850534 | + | 0.525921i | \(0.176279\pi\) | |||||||
\(642\) | −4.90471e6 | −0.469652 | ||||||||
\(643\) | −1.28394e7 | −1.22466 | −0.612330 | − | 0.790602i | \(-0.709768\pi\) | ||||
−0.612330 | + | 0.790602i | \(0.709768\pi\) | |||||||
\(644\) | 134400. | 0.0127698 | ||||||||
\(645\) | 520776. | 0.0492892 | ||||||||
\(646\) | 2.94235e6 | 0.277404 | ||||||||
\(647\) | −2.08468e7 | −1.95785 | −0.978924 | − | 0.204226i | \(-0.934532\pi\) | ||||
−0.978924 | + | 0.204226i | \(0.934532\pi\) | |||||||
\(648\) | 1.10225e6 | 0.103120 | ||||||||
\(649\) | 1.01994e7 | 0.950521 | ||||||||
\(650\) | 1.18247e7 | 1.09776 | ||||||||
\(651\) | −1.58400e6 | −0.146488 | ||||||||
\(652\) | 1.41070e6 | 0.129962 | ||||||||
\(653\) | 1.29632e7 | 1.18968 | 0.594841 | − | 0.803843i | \(-0.297215\pi\) | ||||
0.594841 | + | 0.803843i | \(0.297215\pi\) | |||||||
\(654\) | 3.32996e6 | 0.304435 | ||||||||
\(655\) | 1.55081e6 | 0.141239 | ||||||||
\(656\) | 7.80432e6 | 0.708069 | ||||||||
\(657\) | −3.32991e6 | −0.300967 | ||||||||
\(658\) | −4.48128e6 | −0.403494 | ||||||||
\(659\) | −5.66862e6 | −0.508468 | −0.254234 | − | 0.967143i | \(-0.581823\pi\) | ||||
−0.254234 | + | 0.967143i | \(0.581823\pi\) | |||||||
\(660\) | −121824. | −0.0108861 | ||||||||
\(661\) | −3.11430e6 | −0.277240 | −0.138620 | − | 0.990346i | \(-0.544267\pi\) | ||||
−0.138620 | + | 0.990346i | \(0.544267\pi\) | |||||||
\(662\) | 1.29689e6 | 0.115016 | ||||||||
\(663\) | 5.06444e6 | 0.447454 | ||||||||
\(664\) | 1.38519e7 | 1.21924 | ||||||||
\(665\) | 133440. | 0.0117012 | ||||||||
\(666\) | 1.17126e6 | 0.102322 | ||||||||
\(667\) | −3.89592e6 | −0.339075 | ||||||||
\(668\) | −870240. | −0.0754567 | ||||||||
\(669\) | −8.99525e6 | −0.777048 | ||||||||
\(670\) | 830448. | 0.0714703 | ||||||||
\(671\) | −2.24235e7 | −1.92264 | ||||||||
\(672\) | −518400. | −0.0442835 | ||||||||
\(673\) | 105890. | 0.00901192 | 0.00450596 | − | 0.999990i | \(-0.498566\pi\) | ||||
0.00450596 | + | 0.999990i | \(0.498566\pi\) | |||||||
\(674\) | −1.95158e7 | −1.65476 | ||||||||
\(675\) | −2.25188e6 | −0.190233 | ||||||||
\(676\) | 143004. | 0.0120360 | ||||||||
\(677\) | −1.60910e7 | −1.34931 | −0.674656 | − | 0.738132i | \(-0.735708\pi\) | ||||
−0.674656 | + | 0.738132i | \(0.735708\pi\) | |||||||
\(678\) | −566028. | −0.0472894 | ||||||||
\(679\) | −1.97768e6 | −0.164620 | ||||||||
\(680\) | 889056. | 0.0737321 | ||||||||
\(681\) | 5.45562e6 | 0.450792 | ||||||||
\(682\) | 1.48896e7 | 1.22581 | ||||||||
\(683\) | 1.60780e7 | 1.31880 | 0.659402 | − | 0.751791i | \(-0.270810\pi\) | ||||
0.659402 | + | 0.751791i | \(0.270810\pi\) | |||||||
\(684\) | −180144. | −0.0147224 | ||||||||
\(685\) | 1.80140e6 | 0.146685 | ||||||||
\(686\) | −7.68336e6 | −0.623363 | ||||||||
\(687\) | 1.22393e7 | 0.989386 | ||||||||
\(688\) | −1.09556e7 | −0.882398 | ||||||||
\(689\) | 2.15325e7 | 1.72801 | ||||||||
\(690\) | 272160. | 0.0217621 | ||||||||
\(691\) | −165964. | −0.0132227 | −0.00661133 | − | 0.999978i | \(-0.502104\pi\) | ||||
−0.00661133 | + | 0.999978i | \(0.502104\pi\) | |||||||
\(692\) | −654792. | −0.0519802 | ||||||||
\(693\) | 1.82736e6 | 0.144541 | ||||||||
\(694\) | 1.75924e7 | 1.38652 | ||||||||
\(695\) | −2.10098e6 | −0.164991 | ||||||||
\(696\) | 7.01266e6 | 0.548731 | ||||||||
\(697\) | −6.05934e6 | −0.472436 | ||||||||
\(698\) | −5.43119e6 | −0.421945 | ||||||||
\(699\) | −3.53597e6 | −0.273726 | ||||||||
\(700\) | 494240. | 0.0381235 | ||||||||
\(701\) | 1.77248e7 | 1.36234 | 0.681171 | − | 0.732124i | \(-0.261471\pi\) | ||||
0.681171 | + | 0.732124i | \(0.261471\pi\) | |||||||
\(702\) | −2.79061e6 | −0.213726 | ||||||||
\(703\) | 1.33996e6 | 0.102259 | ||||||||
\(704\) | −1.56296e7 | −1.18854 | ||||||||
\(705\) | −1.00829e6 | −0.0764032 | ||||||||
\(706\) | −1.15071e7 | −0.868872 | ||||||||
\(707\) | 5.72136e6 | 0.430478 | ||||||||
\(708\) | −651024. | −0.0488106 | ||||||||
\(709\) | −1.06023e7 | −0.792112 | −0.396056 | − | 0.918226i | \(-0.629621\pi\) | ||||
−0.396056 | + | 0.918226i | \(0.629621\pi\) | |||||||
\(710\) | 152928. | 0.0113852 | ||||||||
\(711\) | 1.77552e6 | 0.131720 | ||||||||
\(712\) | −1.58064e7 | −1.16852 | ||||||||
\(713\) | −3.69600e6 | −0.272275 | ||||||||
\(714\) | 1.90512e6 | 0.139855 | ||||||||
\(715\) | −2.15899e6 | −0.157938 | ||||||||
\(716\) | 1.43496e6 | 0.104606 | ||||||||
\(717\) | −1.19262e7 | −0.866373 | ||||||||
\(718\) | 1.46219e7 | 1.05850 | ||||||||
\(719\) | 9.03211e6 | 0.651579 | 0.325790 | − | 0.945442i | \(-0.394370\pi\) | ||||
0.325790 | + | 0.945442i | \(0.394370\pi\) | |||||||
\(720\) | −552096. | −0.0396902 | ||||||||
\(721\) | −2.12576e6 | −0.152292 | ||||||||
\(722\) | 1.30018e7 | 0.928239 | ||||||||
\(723\) | −8.91085e6 | −0.633977 | ||||||||
\(724\) | −2.02852e6 | −0.143825 | ||||||||
\(725\) | −1.43268e7 | −1.01229 | ||||||||
\(726\) | −8.48043e6 | −0.597140 | ||||||||
\(727\) | 1.87575e7 | 1.31625 | 0.658127 | − | 0.752907i | \(-0.271349\pi\) | ||||
0.658127 | + | 0.752907i | \(0.271349\pi\) | |||||||
\(728\) | −4.28736e6 | −0.299821 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.47996e6 | 0.102788 | ||||||||
\(731\) | 8.50601e6 | 0.588752 | ||||||||
\(732\) | 1.43129e6 | 0.0987300 | ||||||||
\(733\) | −1.17773e7 | −0.809626 | −0.404813 | − | 0.914399i | \(-0.632663\pi\) | ||||
−0.404813 | + | 0.914399i | \(0.632663\pi\) | |||||||
\(734\) | 5.90438e6 | 0.404515 | ||||||||
\(735\) | −821178. | −0.0560685 | ||||||||
\(736\) | −1.20960e6 | −0.0823090 | ||||||||
\(737\) | 1.30104e7 | 0.882308 | ||||||||
\(738\) | 3.33882e6 | 0.225659 | ||||||||
\(739\) | 5.88948e6 | 0.396703 | 0.198352 | − | 0.980131i | \(-0.436441\pi\) | ||||
0.198352 | + | 0.980131i | \(0.436441\pi\) | |||||||
\(740\) | −57840.0 | −0.00388284 | ||||||||
\(741\) | −3.19255e6 | −0.213596 | ||||||||
\(742\) | 8.10000e6 | 0.540101 | ||||||||
\(743\) | −1.00476e7 | −0.667712 | −0.333856 | − | 0.942624i | \(-0.608350\pi\) | ||||
−0.333856 | + | 0.942624i | \(0.608350\pi\) | |||||||
\(744\) | 6.65280e6 | 0.440628 | ||||||||
\(745\) | −631548. | −0.0416884 | ||||||||
\(746\) | −1.02219e7 | −0.672490 | ||||||||
\(747\) | 6.67861e6 | 0.437910 | ||||||||
\(748\) | −1.98979e6 | −0.130033 | ||||||||
\(749\) | −3.63312e6 | −0.236633 | ||||||||
\(750\) | 2.01334e6 | 0.130696 | ||||||||
\(751\) | 4.81530e6 | 0.311547 | 0.155773 | − | 0.987793i | \(-0.450213\pi\) | ||||
0.155773 | + | 0.987793i | \(0.450213\pi\) | |||||||
\(752\) | 2.12114e7 | 1.36781 | ||||||||
\(753\) | 1.32419e6 | 0.0851064 | ||||||||
\(754\) | −1.77543e7 | −1.13730 | ||||||||
\(755\) | 2.37835e6 | 0.151848 | ||||||||
\(756\) | −116640. | −0.00742238 | ||||||||
\(757\) | 3.12973e6 | 0.198503 | 0.0992516 | − | 0.995062i | \(-0.468355\pi\) | ||||
0.0992516 | + | 0.995062i | \(0.468355\pi\) | |||||||
\(758\) | −1.65392e7 | −1.04554 | ||||||||
\(759\) | 4.26384e6 | 0.268656 | ||||||||
\(760\) | −560448. | −0.0351967 | ||||||||
\(761\) | −1.17773e7 | −0.737197 | −0.368599 | − | 0.929589i | \(-0.620162\pi\) | ||||
−0.368599 | + | 0.929589i | \(0.620162\pi\) | |||||||
\(762\) | 9.23875e6 | 0.576403 | ||||||||
\(763\) | 2.46664e6 | 0.153389 | ||||||||
\(764\) | −2.59354e6 | −0.160753 | ||||||||
\(765\) | 428652. | 0.0264820 | ||||||||
\(766\) | −2.73946e6 | −0.168691 | ||||||||
\(767\) | −1.15376e7 | −0.708152 | ||||||||
\(768\) | 3.48595e6 | 0.213264 | ||||||||
\(769\) | −1.49376e6 | −0.0910887 | −0.0455443 | − | 0.998962i | \(-0.514502\pi\) | ||||
−0.0455443 | + | 0.998962i | \(0.514502\pi\) | |||||||
\(770\) | −812160. | −0.0493645 | ||||||||
\(771\) | −4.35224e6 | −0.263680 | ||||||||
\(772\) | −111352. | −0.00672442 | ||||||||
\(773\) | −2.25125e7 | −1.35511 | −0.677555 | − | 0.735472i | \(-0.736960\pi\) | ||||
−0.677555 | + | 0.735472i | \(0.736960\pi\) | |||||||
\(774\) | −4.68698e6 | −0.281217 | ||||||||
\(775\) | −1.35916e7 | −0.812861 | ||||||||
\(776\) | 8.30626e6 | 0.495166 | ||||||||
\(777\) | 867600. | 0.0515545 | ||||||||
\(778\) | 1.20384e7 | 0.713048 | ||||||||
\(779\) | 3.81972e6 | 0.225521 | ||||||||
\(780\) | 137808. | 0.00811032 | ||||||||
\(781\) | 2.39587e6 | 0.140552 | ||||||||
\(782\) | 4.44528e6 | 0.259945 | ||||||||
\(783\) | 3.38110e6 | 0.197085 | ||||||||
\(784\) | 1.72752e7 | 1.00376 | ||||||||
\(785\) | −826476. | −0.0478692 | ||||||||
\(786\) | −1.39573e7 | −0.805831 | ||||||||
\(787\) | 1.19547e7 | 0.688022 | 0.344011 | − | 0.938966i | \(-0.388214\pi\) | ||||
0.344011 | + | 0.938966i | \(0.388214\pi\) | |||||||
\(788\) | 2.44418e6 | 0.140223 | ||||||||
\(789\) | 7.32218e6 | 0.418744 | ||||||||
\(790\) | −789120. | −0.0449858 | ||||||||
\(791\) | −419280. | −0.0238266 | ||||||||
\(792\) | −7.67491e6 | −0.434771 | ||||||||
\(793\) | 2.53656e7 | 1.43239 | ||||||||
\(794\) | 3.46224e7 | 1.94897 | ||||||||
\(795\) | 1.82250e6 | 0.102270 | ||||||||
\(796\) | 3.51613e6 | 0.196690 | ||||||||
\(797\) | 540798. | 0.0301571 | 0.0150785 | − | 0.999886i | \(-0.495200\pi\) | ||||
0.0150785 | + | 0.999886i | \(0.495200\pi\) | |||||||
\(798\) | −1.20096e6 | −0.0667608 | ||||||||
\(799\) | −1.64687e7 | −0.912625 | ||||||||
\(800\) | −4.44816e6 | −0.245728 | ||||||||
\(801\) | −7.62097e6 | −0.419690 | ||||||||
\(802\) | −1.80375e7 | −0.990243 | ||||||||
\(803\) | 2.31860e7 | 1.26893 | ||||||||
\(804\) | −830448. | −0.0453077 | ||||||||
\(805\) | 201600. | 0.0109648 | ||||||||
\(806\) | −1.68432e7 | −0.913244 | ||||||||
\(807\) | −4.14995e6 | −0.224316 | ||||||||
\(808\) | −2.40297e7 | −1.29485 | ||||||||
\(809\) | −6.14223e6 | −0.329955 | −0.164978 | − | 0.986297i | \(-0.552755\pi\) | ||||
−0.164978 | + | 0.986297i | \(0.552755\pi\) | |||||||
\(810\) | −236196. | −0.0126491 | ||||||||
\(811\) | −3.16734e7 | −1.69100 | −0.845499 | − | 0.533977i | \(-0.820697\pi\) | ||||
−0.845499 | + | 0.533977i | \(0.820697\pi\) | |||||||
\(812\) | −742080. | −0.0394967 | ||||||||
\(813\) | 1.50762e7 | 0.799956 | ||||||||
\(814\) | −8.15544e6 | −0.431406 | ||||||||
\(815\) | 2.11606e6 | 0.111592 | ||||||||
\(816\) | −9.01757e6 | −0.474094 | ||||||||
\(817\) | −5.36206e6 | −0.281046 | ||||||||
\(818\) | −9.20176e6 | −0.480825 | ||||||||
\(819\) | −2.06712e6 | −0.107685 | ||||||||
\(820\) | −164880. | −0.00856315 | ||||||||
\(821\) | 2.66175e7 | 1.37819 | 0.689095 | − | 0.724671i | \(-0.258008\pi\) | ||||
0.689095 | + | 0.724671i | \(0.258008\pi\) | |||||||
\(822\) | −1.62126e7 | −0.836901 | ||||||||
\(823\) | 3.62817e7 | 1.86719 | 0.933593 | − | 0.358335i | \(-0.116655\pi\) | ||||
0.933593 | + | 0.358335i | \(0.116655\pi\) | |||||||
\(824\) | 8.92819e6 | 0.458084 | ||||||||
\(825\) | 1.56798e7 | 0.802056 | ||||||||
\(826\) | −4.34016e6 | −0.221338 | ||||||||
\(827\) | 1.09033e6 | 0.0554364 | 0.0277182 | − | 0.999616i | \(-0.491176\pi\) | ||||
0.0277182 | + | 0.999616i | \(0.491176\pi\) | |||||||
\(828\) | −272160. | −0.0137958 | ||||||||
\(829\) | −1.03016e7 | −0.520620 | −0.260310 | − | 0.965525i | \(-0.583825\pi\) | ||||
−0.260310 | + | 0.965525i | \(0.583825\pi\) | |||||||
\(830\) | −2.96827e6 | −0.149558 | ||||||||
\(831\) | 3.61013e6 | 0.181351 | ||||||||
\(832\) | 1.76803e7 | 0.885483 | ||||||||
\(833\) | −1.34126e7 | −0.669730 | ||||||||
\(834\) | 1.89089e7 | 0.941348 | ||||||||
\(835\) | −1.30536e6 | −0.0647909 | ||||||||
\(836\) | 1.25434e6 | 0.0620724 | ||||||||
\(837\) | 3.20760e6 | 0.158258 | ||||||||
\(838\) | 2.32425e7 | 1.14333 | ||||||||
\(839\) | −1.96134e7 | −0.961940 | −0.480970 | − | 0.876737i | \(-0.659715\pi\) | ||||
−0.480970 | + | 0.876737i | \(0.659715\pi\) | |||||||
\(840\) | −362880. | −0.0177445 | ||||||||
\(841\) | 999895. | 0.0487489 | ||||||||
\(842\) | 7.99840e6 | 0.388797 | ||||||||
\(843\) | −2.07879e7 | −1.00749 | ||||||||
\(844\) | 194000. | 0.00937445 | ||||||||
\(845\) | 214506. | 0.0103347 | ||||||||
\(846\) | 9.07459e6 | 0.435914 | ||||||||
\(847\) | −6.28180e6 | −0.300868 | ||||||||
\(848\) | −3.83400e7 | −1.83089 | ||||||||
\(849\) | −1.01589e7 | −0.483704 | ||||||||
\(850\) | 1.63470e7 | 0.776051 | ||||||||
\(851\) | 2.02440e6 | 0.0958236 | ||||||||
\(852\) | −152928. | −0.00721752 | ||||||||
\(853\) | 3.27565e7 | 1.54143 | 0.770717 | − | 0.637178i | \(-0.219898\pi\) | ||||
0.770717 | + | 0.637178i | \(0.219898\pi\) | |||||||
\(854\) | 9.54192e6 | 0.447704 | ||||||||
\(855\) | −270216. | −0.0126414 | ||||||||
\(856\) | 1.52591e7 | 0.711778 | ||||||||
\(857\) | −2.57953e7 | −1.19974 | −0.599872 | − | 0.800096i | \(-0.704782\pi\) | ||||
−0.599872 | + | 0.800096i | \(0.704782\pi\) | |||||||
\(858\) | 1.94309e7 | 0.901105 | ||||||||
\(859\) | −1.98548e7 | −0.918085 | −0.459043 | − | 0.888414i | \(-0.651807\pi\) | ||||
−0.459043 | + | 0.888414i | \(0.651807\pi\) | |||||||
\(860\) | 231456. | 0.0106714 | ||||||||
\(861\) | 2.47320e6 | 0.113698 | ||||||||
\(862\) | −3.87115e7 | −1.77448 | ||||||||
\(863\) | −673056. | −0.0307627 | −0.0153813 | − | 0.999882i | \(-0.504896\pi\) | ||||
−0.0153813 | + | 0.999882i | \(0.504896\pi\) | |||||||
\(864\) | 1.04976e6 | 0.0478416 | ||||||||
\(865\) | −982188. | −0.0446328 | ||||||||
\(866\) | 2.49946e7 | 1.13254 | ||||||||
\(867\) | −5.77740e6 | −0.261026 | ||||||||
\(868\) | −704000. | −0.0317156 | ||||||||
\(869\) | −1.23629e7 | −0.555354 | ||||||||
\(870\) | −1.50271e6 | −0.0673097 | ||||||||
\(871\) | −1.47174e7 | −0.657333 | ||||||||
\(872\) | −1.03599e7 | −0.461385 | ||||||||
\(873\) | 4.00480e6 | 0.177847 | ||||||||
\(874\) | −2.80224e6 | −0.124087 | ||||||||
\(875\) | 1.49136e6 | 0.0658510 | ||||||||
\(876\) | −1.47996e6 | −0.0651613 | ||||||||
\(877\) | 5.32115e6 | 0.233618 | 0.116809 | − | 0.993154i | \(-0.462733\pi\) | ||||
0.116809 | + | 0.993154i | \(0.462733\pi\) | |||||||
\(878\) | −4.75608e6 | −0.208215 | ||||||||
\(879\) | −8.44987e6 | −0.368874 | ||||||||
\(880\) | 3.84422e6 | 0.167341 | ||||||||
\(881\) | 2.78891e7 | 1.21058 | 0.605291 | − | 0.796004i | \(-0.293057\pi\) | ||||
0.605291 | + | 0.796004i | \(0.293057\pi\) | |||||||
\(882\) | 7.39060e6 | 0.319896 | ||||||||
\(883\) | −2.83786e7 | −1.22487 | −0.612435 | − | 0.790521i | \(-0.709810\pi\) | ||||
−0.612435 | + | 0.790521i | \(0.709810\pi\) | |||||||
\(884\) | 2.25086e6 | 0.0968765 | ||||||||
\(885\) | −976536. | −0.0419112 | ||||||||
\(886\) | 8.39887e6 | 0.359448 | ||||||||
\(887\) | 4.22678e7 | 1.80385 | 0.901925 | − | 0.431893i | \(-0.142154\pi\) | ||||
0.901925 | + | 0.431893i | \(0.142154\pi\) | |||||||
\(888\) | −3.64392e6 | −0.155073 | ||||||||
\(889\) | 6.84352e6 | 0.290419 | ||||||||
\(890\) | 3.38710e6 | 0.143335 | ||||||||
\(891\) | −3.70040e6 | −0.156155 | ||||||||
\(892\) | −3.99789e6 | −0.168236 | ||||||||
\(893\) | 1.03816e7 | 0.435649 | ||||||||
\(894\) | 5.68393e6 | 0.237851 | ||||||||
\(895\) | 2.15244e6 | 0.0898201 | ||||||||
\(896\) | 8.49408e6 | 0.353465 | ||||||||
\(897\) | −4.82328e6 | −0.200153 | ||||||||
\(898\) | −1.79549e7 | −0.743005 | ||||||||
\(899\) | 2.04072e7 | 0.842140 | ||||||||
\(900\) | −1.00084e6 | −0.0411867 | ||||||||
\(901\) | 2.97675e7 | 1.22160 | ||||||||
\(902\) | −2.32481e7 | −0.951417 | ||||||||
\(903\) | −3.47184e6 | −0.141690 | ||||||||
\(904\) | 1.76098e6 | 0.0716692 | ||||||||
\(905\) | −3.04278e6 | −0.123495 | ||||||||
\(906\) | −2.14052e7 | −0.866360 | ||||||||
\(907\) | 3.19526e7 | 1.28970 | 0.644849 | − | 0.764310i | \(-0.276920\pi\) | ||||
0.644849 | + | 0.764310i | \(0.276920\pi\) | |||||||
\(908\) | 2.42472e6 | 0.0975994 | ||||||||
\(909\) | −1.15858e7 | −0.465066 | ||||||||
\(910\) | 918720. | 0.0367773 | ||||||||
\(911\) | −1.16429e7 | −0.464800 | −0.232400 | − | 0.972620i | \(-0.574658\pi\) | ||||
−0.232400 | + | 0.972620i | \(0.574658\pi\) | |||||||
\(912\) | 5.68454e6 | 0.226312 | ||||||||
\(913\) | −4.65029e7 | −1.84630 | ||||||||
\(914\) | −3.77981e7 | −1.49660 | ||||||||
\(915\) | 2.14693e6 | 0.0847746 | ||||||||
\(916\) | 5.43970e6 | 0.214208 | ||||||||
\(917\) | −1.03387e7 | −0.406016 | ||||||||
\(918\) | −3.85787e6 | −0.151092 | ||||||||
\(919\) | 1.39844e6 | 0.0546204 | 0.0273102 | − | 0.999627i | \(-0.491306\pi\) | ||||
0.0273102 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(920\) | −846720. | −0.0329815 | ||||||||
\(921\) | 6.23653e6 | 0.242267 | ||||||||
\(922\) | −2.04191e7 | −0.791059 | ||||||||
\(923\) | −2.71022e6 | −0.104713 | ||||||||
\(924\) | 812160. | 0.0312940 | ||||||||
\(925\) | 7.44449e6 | 0.286075 | ||||||||
\(926\) | 1.33820e7 | 0.512854 | ||||||||
\(927\) | 4.30466e6 | 0.164528 | ||||||||
\(928\) | 6.67872e6 | 0.254579 | ||||||||
\(929\) | −1.66792e7 | −0.634067 | −0.317033 | − | 0.948414i | \(-0.602687\pi\) | ||||
−0.317033 | + | 0.948414i | \(0.602687\pi\) | |||||||
\(930\) | −1.42560e6 | −0.0540493 | ||||||||
\(931\) | 8.45509e6 | 0.319701 | ||||||||
\(932\) | −1.57154e6 | −0.0592634 | ||||||||
\(933\) | 2.64879e7 | 0.996191 | ||||||||
\(934\) | 3.90846e7 | 1.46601 | ||||||||
\(935\) | −2.98469e6 | −0.111653 | ||||||||
\(936\) | 8.68190e6 | 0.323911 | ||||||||
\(937\) | −2.47956e7 | −0.922625 | −0.461312 | − | 0.887238i | \(-0.652621\pi\) | ||||
−0.461312 | + | 0.887238i | \(0.652621\pi\) | |||||||
\(938\) | −5.53632e6 | −0.205454 | ||||||||
\(939\) | 7.96631e6 | 0.294845 | ||||||||
\(940\) | −448128. | −0.0165418 | ||||||||
\(941\) | 2.79574e7 | 1.02925 | 0.514627 | − | 0.857414i | \(-0.327930\pi\) | ||||
0.514627 | + | 0.857414i | \(0.327930\pi\) | |||||||
\(942\) | 7.43828e6 | 0.273115 | ||||||||
\(943\) | 5.77080e6 | 0.211328 | ||||||||
\(944\) | 2.05434e7 | 0.750314 | ||||||||
\(945\) | −174960. | −0.00637322 | ||||||||
\(946\) | 3.26353e7 | 1.18566 | ||||||||
\(947\) | 7.64936e6 | 0.277173 | 0.138586 | − | 0.990350i | \(-0.455744\pi\) | ||||
0.138586 | + | 0.990350i | \(0.455744\pi\) | |||||||
\(948\) | 789120. | 0.0285182 | ||||||||
\(949\) | −2.62282e7 | −0.945372 | ||||||||
\(950\) | −1.03049e7 | −0.370455 | ||||||||
\(951\) | 2.25792e7 | 0.809575 | ||||||||
\(952\) | −5.92704e6 | −0.211956 | ||||||||
\(953\) | −4.62179e7 | −1.64846 | −0.824228 | − | 0.566257i | \(-0.808391\pi\) | ||||
−0.824228 | + | 0.566257i | \(0.808391\pi\) | |||||||
\(954\) | −1.64025e7 | −0.583498 | ||||||||
\(955\) | −3.89030e6 | −0.138031 | ||||||||
\(956\) | −5.30054e6 | −0.187575 | ||||||||
\(957\) | −2.35425e7 | −0.830945 | ||||||||
\(958\) | −1.43539e7 | −0.505309 | ||||||||
\(959\) | −1.20094e7 | −0.421671 | ||||||||
\(960\) | 1.49645e6 | 0.0524063 | ||||||||
\(961\) | −9.26915e6 | −0.323766 | ||||||||
\(962\) | 9.22548e6 | 0.321404 | ||||||||
\(963\) | 7.35707e6 | 0.255646 | ||||||||
\(964\) | −3.96038e6 | −0.137260 | ||||||||
\(965\) | −167028. | −0.00577392 | ||||||||
\(966\) | −1.81440e6 | −0.0625591 | ||||||||
\(967\) | 2.08557e7 | 0.717229 | 0.358615 | − | 0.933486i | \(-0.383249\pi\) | ||||
0.358615 | + | 0.933486i | \(0.383249\pi\) | |||||||
\(968\) | 2.63836e7 | 0.904993 | ||||||||
\(969\) | −4.41353e6 | −0.151000 | ||||||||
\(970\) | −1.77991e6 | −0.0607392 | ||||||||
\(971\) | −4.58152e7 | −1.55941 | −0.779707 | − | 0.626144i | \(-0.784632\pi\) | ||||
−0.779707 | + | 0.626144i | \(0.784632\pi\) | |||||||
\(972\) | 236196. | 0.00801875 | ||||||||
\(973\) | 1.40066e7 | 0.474296 | ||||||||
\(974\) | 3.67853e7 | 1.24245 | ||||||||
\(975\) | −1.77370e7 | −0.597544 | ||||||||
\(976\) | −4.51651e7 | −1.51767 | ||||||||
\(977\) | −1.09544e6 | −0.0367157 | −0.0183578 | − | 0.999831i | \(-0.505844\pi\) | ||||
−0.0183578 | + | 0.999831i | \(0.505844\pi\) | |||||||
\(978\) | −1.90445e7 | −0.636682 | ||||||||
\(979\) | 5.30645e7 | 1.76949 | ||||||||
\(980\) | −364968. | −0.0121392 | ||||||||
\(981\) | −4.99495e6 | −0.165714 | ||||||||
\(982\) | 7.41535e6 | 0.245388 | ||||||||
\(983\) | 5.25817e7 | 1.73561 | 0.867803 | − | 0.496909i | \(-0.165532\pi\) | ||||
0.867803 | + | 0.496909i | \(0.165532\pi\) | |||||||
\(984\) | −1.03874e7 | −0.341996 | ||||||||
\(985\) | 3.66628e6 | 0.120402 | ||||||||
\(986\) | −2.45443e7 | −0.804004 | ||||||||
\(987\) | 6.72192e6 | 0.219634 | ||||||||
\(988\) | −1.41891e6 | −0.0462448 | ||||||||
\(989\) | −8.10096e6 | −0.263358 | ||||||||
\(990\) | 1.64462e6 | 0.0533309 | ||||||||
\(991\) | −4.90389e7 | −1.58620 | −0.793098 | − | 0.609094i | \(-0.791533\pi\) | ||||
−0.793098 | + | 0.609094i | \(0.791533\pi\) | |||||||
\(992\) | 6.33600e6 | 0.204426 | ||||||||
\(993\) | −1.94533e6 | −0.0626067 | ||||||||
\(994\) | −1.01952e6 | −0.0327288 | ||||||||
\(995\) | 5.27419e6 | 0.168888 | ||||||||
\(996\) | 2.96827e6 | 0.0948103 | ||||||||
\(997\) | 3.05461e6 | 0.0973237 | 0.0486618 | − | 0.998815i | \(-0.484504\pi\) | ||||
0.0486618 | + | 0.998815i | \(0.484504\pi\) | |||||||
\(998\) | 5.91297e7 | 1.87923 | ||||||||
\(999\) | −1.75689e6 | −0.0556969 |
(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 | 3.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.6.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 48.6.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 75.6.b.b.49.1 | 2 | |||
5.3 | odd | 4 | 75.6.b.b.49.2 | 2 | |||
5.4 | even | 2 | 75.6.a.e.1.1 | 1 | |||
7.2 | even | 3 | 147.6.e.h.67.1 | 2 | |||
7.3 | odd | 6 | 147.6.e.k.79.1 | 2 | |||
7.4 | even | 3 | 147.6.e.h.79.1 | 2 | |||
7.5 | odd | 6 | 147.6.e.k.67.1 | 2 | |||
7.6 | odd | 2 | 147.6.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 192.6.a.l.1.1 | 1 | |||
8.5 | even | 2 | 192.6.a.d.1.1 | 1 | |||
9.2 | odd | 6 | 81.6.c.a.28.1 | 2 | |||
9.4 | even | 3 | 81.6.c.c.55.1 | 2 | |||
9.5 | odd | 6 | 81.6.c.a.55.1 | 2 | |||
9.7 | even | 3 | 81.6.c.c.28.1 | 2 | |||
11.10 | odd | 2 | 363.6.a.d.1.1 | 1 | |||
12.11 | even | 2 | 144.6.a.f.1.1 | 1 | |||
13.12 | even | 2 | 507.6.a.b.1.1 | 1 | |||
15.2 | even | 4 | 225.6.b.b.199.2 | 2 | |||
15.8 | even | 4 | 225.6.b.b.199.1 | 2 | |||
15.14 | odd | 2 | 225.6.a.a.1.1 | 1 | |||
16.3 | odd | 4 | 768.6.d.h.385.1 | 2 | |||
16.5 | even | 4 | 768.6.d.k.385.1 | 2 | |||
16.11 | odd | 4 | 768.6.d.h.385.2 | 2 | |||
16.13 | even | 4 | 768.6.d.k.385.2 | 2 | |||
17.16 | even | 2 | 867.6.a.a.1.1 | 1 | |||
19.18 | odd | 2 | 1083.6.a.c.1.1 | 1 | |||
21.20 | even | 2 | 441.6.a.i.1.1 | 1 | |||
24.5 | odd | 2 | 576.6.a.s.1.1 | 1 | |||
24.11 | even | 2 | 576.6.a.t.1.1 | 1 | |||
33.32 | even | 2 | 1089.6.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.6.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
48.6.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
75.6.a.e.1.1 | 1 | 5.4 | even | 2 | |||
75.6.b.b.49.1 | 2 | 5.2 | odd | 4 | |||
75.6.b.b.49.2 | 2 | 5.3 | odd | 4 | |||
81.6.c.a.28.1 | 2 | 9.2 | odd | 6 | |||
81.6.c.a.55.1 | 2 | 9.5 | odd | 6 | |||
81.6.c.c.28.1 | 2 | 9.7 | even | 3 | |||
81.6.c.c.55.1 | 2 | 9.4 | even | 3 | |||
144.6.a.f.1.1 | 1 | 12.11 | even | 2 | |||
147.6.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
147.6.e.h.67.1 | 2 | 7.2 | even | 3 | |||
147.6.e.h.79.1 | 2 | 7.4 | even | 3 | |||
147.6.e.k.67.1 | 2 | 7.5 | odd | 6 | |||
147.6.e.k.79.1 | 2 | 7.3 | odd | 6 | |||
192.6.a.d.1.1 | 1 | 8.5 | even | 2 | |||
192.6.a.l.1.1 | 1 | 8.3 | odd | 2 | |||
225.6.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
225.6.b.b.199.1 | 2 | 15.8 | even | 4 | |||
225.6.b.b.199.2 | 2 | 15.2 | even | 4 | |||
363.6.a.d.1.1 | 1 | 11.10 | odd | 2 | |||
441.6.a.i.1.1 | 1 | 21.20 | even | 2 | |||
507.6.a.b.1.1 | 1 | 13.12 | even | 2 | |||
576.6.a.s.1.1 | 1 | 24.5 | odd | 2 | |||
576.6.a.t.1.1 | 1 | 24.11 | even | 2 | |||
768.6.d.h.385.1 | 2 | 16.3 | odd | 4 | |||
768.6.d.h.385.2 | 2 | 16.11 | odd | 4 | |||
768.6.d.k.385.1 | 2 | 16.5 | even | 4 | |||
768.6.d.k.385.2 | 2 | 16.13 | even | 4 | |||
867.6.a.a.1.1 | 1 | 17.16 | even | 2 | |||
1083.6.a.c.1.1 | 1 | 19.18 | odd | 2 | |||
1089.6.a.b.1.1 | 1 | 33.32 | even | 2 |