Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,6,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(84.2015054018\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-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 | \(0.322068\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.125000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 54.0000 | 0.612372 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | −168.000 | −0.928078 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 444.000 | 1.10637 | 0.553186 | − | 0.833058i | \(-0.313412\pi\) | ||||
0.553186 | + | 0.833058i | \(0.313412\pi\) | |||||||
\(12\) | 36.0000 | 0.0721688 | ||||||||
\(13\) | 442.000 | 0.725377 | 0.362689 | − | 0.931910i | \(-0.381859\pi\) | ||||
0.362689 | + | 0.931910i | \(0.381859\pi\) | |||||||
\(14\) | −294.000 | −0.400892 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1136.00 | −1.10938 | ||||||||
\(17\) | 126.000 | 0.105742 | 0.0528711 | − | 0.998601i | \(-0.483163\pi\) | ||||
0.0528711 | + | 0.998601i | \(0.483163\pi\) | |||||||
\(18\) | 486.000 | 0.353553 | ||||||||
\(19\) | 2684.00 | 1.70568 | 0.852842 | − | 0.522169i | \(-0.174877\pi\) | ||||
0.852842 | + | 0.522169i | \(0.174877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −441.000 | −0.218218 | ||||||||
\(22\) | 2664.00 | 1.17348 | ||||||||
\(23\) | −4200.00 | −1.65550 | −0.827751 | − | 0.561096i | \(-0.810380\pi\) | ||||
−0.827751 | + | 0.561096i | \(0.810380\pi\) | |||||||
\(24\) | −1512.00 | −0.535826 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2652.00 | 0.769379 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −196.000 | −0.0472456 | ||||||||
\(29\) | −5442.00 | −1.20161 | −0.600805 | − | 0.799396i | \(-0.705153\pi\) | ||||
−0.600805 | + | 0.799396i | \(0.705153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 80.0000 | 0.0149515 | 0.00747577 | − | 0.999972i | \(-0.497620\pi\) | ||||
0.00747577 | + | 0.999972i | \(0.497620\pi\) | |||||||
\(32\) | −1440.00 | −0.248592 | ||||||||
\(33\) | 3996.00 | 0.638764 | ||||||||
\(34\) | 756.000 | 0.112157 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 324.000 | 0.0416667 | ||||||||
\(37\) | 5434.00 | 0.652552 | 0.326276 | − | 0.945274i | \(-0.394206\pi\) | ||||
0.326276 | + | 0.945274i | \(0.394206\pi\) | |||||||
\(38\) | 16104.0 | 1.80915 | ||||||||
\(39\) | 3978.00 | 0.418797 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7962.00 | 0.739712 | 0.369856 | − | 0.929089i | \(-0.379407\pi\) | ||||
0.369856 | + | 0.929089i | \(0.379407\pi\) | |||||||
\(42\) | −2646.00 | −0.231455 | ||||||||
\(43\) | 11524.0 | 0.950456 | 0.475228 | − | 0.879863i | \(-0.342366\pi\) | ||||
0.475228 | + | 0.879863i | \(0.342366\pi\) | |||||||
\(44\) | 1776.00 | 0.138297 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −25200.0 | −1.75592 | ||||||||
\(47\) | 13920.0 | 0.919167 | 0.459584 | − | 0.888134i | \(-0.347999\pi\) | ||||
0.459584 | + | 0.888134i | \(0.347999\pi\) | |||||||
\(48\) | −10224.0 | −0.640498 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1134.00 | 0.0610503 | ||||||||
\(52\) | 1768.00 | 0.0906721 | ||||||||
\(53\) | 9594.00 | 0.469148 | 0.234574 | − | 0.972098i | \(-0.424630\pi\) | ||||
0.234574 | + | 0.972098i | \(0.424630\pi\) | |||||||
\(54\) | 4374.00 | 0.204124 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8232.00 | 0.350780 | ||||||||
\(57\) | 24156.0 | 0.984777 | ||||||||
\(58\) | −32652.0 | −1.27450 | ||||||||
\(59\) | 27492.0 | 1.02820 | 0.514098 | − | 0.857731i | \(-0.328127\pi\) | ||||
0.514098 | + | 0.857731i | \(0.328127\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 49478.0 | 1.70250 | 0.851251 | − | 0.524759i | \(-0.175845\pi\) | ||||
0.851251 | + | 0.524759i | \(0.175845\pi\) | |||||||
\(62\) | 480.000 | 0.0158585 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | 27712.0 | 0.845703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 23976.0 | 0.677512 | ||||||||
\(67\) | 59356.0 | 1.61539 | 0.807695 | − | 0.589600i | \(-0.200715\pi\) | ||||
0.807695 | + | 0.589600i | \(0.200715\pi\) | |||||||
\(68\) | 504.000 | 0.0132178 | ||||||||
\(69\) | −37800.0 | −0.955805 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 32040.0 | 0.754304 | 0.377152 | − | 0.926151i | \(-0.376903\pi\) | ||||
0.377152 | + | 0.926151i | \(0.376903\pi\) | |||||||
\(72\) | −13608.0 | −0.309359 | ||||||||
\(73\) | 61846.0 | 1.35833 | 0.679164 | − | 0.733987i | \(-0.262343\pi\) | ||||
0.679164 | + | 0.733987i | \(0.262343\pi\) | |||||||
\(74\) | 32604.0 | 0.692136 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10736.0 | 0.213210 | ||||||||
\(77\) | −21756.0 | −0.418169 | ||||||||
\(78\) | 23868.0 | 0.444201 | ||||||||
\(79\) | −65776.0 | −1.18577 | −0.592884 | − | 0.805288i | \(-0.702011\pi\) | ||||
−0.592884 | + | 0.805288i | \(0.702011\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 47772.0 | 0.784583 | ||||||||
\(83\) | −40188.0 | −0.640326 | −0.320163 | − | 0.947362i | \(-0.603738\pi\) | ||||
−0.320163 | + | 0.947362i | \(0.603738\pi\) | |||||||
\(84\) | −1764.00 | −0.0272772 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 69144.0 | 1.00811 | ||||||||
\(87\) | −48978.0 | −0.693750 | ||||||||
\(88\) | −74592.0 | −1.02680 | ||||||||
\(89\) | −7974.00 | −0.106709 | −0.0533545 | − | 0.998576i | \(-0.516991\pi\) | ||||
−0.0533545 | + | 0.998576i | \(0.516991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21658.0 | −0.274167 | ||||||||
\(92\) | −16800.0 | −0.206938 | ||||||||
\(93\) | 720.000 | 0.00863227 | ||||||||
\(94\) | 83520.0 | 0.974924 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −12960.0 | −0.143525 | ||||||||
\(97\) | 143662. | 1.55029 | 0.775144 | − | 0.631784i | \(-0.217677\pi\) | ||||
0.775144 | + | 0.631784i | \(0.217677\pi\) | |||||||
\(98\) | 14406.0 | 0.151523 | ||||||||
\(99\) | 35964.0 | 0.368791 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2706.00 | −0.0263952 | −0.0131976 | − | 0.999913i | \(-0.504201\pi\) | ||||
−0.0131976 | + | 0.999913i | \(0.504201\pi\) | |||||||
\(102\) | 6804.00 | 0.0647536 | ||||||||
\(103\) | −131768. | −1.22382 | −0.611909 | − | 0.790928i | \(-0.709598\pi\) | ||||
−0.611909 | + | 0.790928i | \(0.709598\pi\) | |||||||
\(104\) | −74256.0 | −0.673206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 57564.0 | 0.497607 | ||||||||
\(107\) | 128916. | 1.08855 | 0.544274 | − | 0.838908i | \(-0.316805\pi\) | ||||
0.544274 | + | 0.838908i | \(0.316805\pi\) | |||||||
\(108\) | 2916.00 | 0.0240563 | ||||||||
\(109\) | −100978. | −0.814068 | −0.407034 | − | 0.913413i | \(-0.633437\pi\) | ||||
−0.407034 | + | 0.913413i | \(0.633437\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 48906.0 | 0.376751 | ||||||||
\(112\) | 55664.0 | 0.419304 | ||||||||
\(113\) | −220146. | −1.62186 | −0.810932 | − | 0.585140i | \(-0.801040\pi\) | ||||
−0.810932 | + | 0.585140i | \(0.801040\pi\) | |||||||
\(114\) | 144936. | 1.04451 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −21768.0 | −0.150201 | ||||||||
\(117\) | 35802.0 | 0.241792 | ||||||||
\(118\) | 164952. | 1.09057 | ||||||||
\(119\) | −6174.00 | −0.0399668 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 36085.0 | 0.224059 | ||||||||
\(122\) | 296868. | 1.80578 | ||||||||
\(123\) | 71658.0 | 0.427073 | ||||||||
\(124\) | 320.000 | 0.00186894 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −23814.0 | −0.133631 | ||||||||
\(127\) | 74320.0 | 0.408880 | 0.204440 | − | 0.978879i | \(-0.434463\pi\) | ||||
0.204440 | + | 0.978879i | \(0.434463\pi\) | |||||||
\(128\) | 212352. | 1.14560 | ||||||||
\(129\) | 103716. | 0.548746 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −155316. | −0.790748 | −0.395374 | − | 0.918520i | \(-0.629385\pi\) | ||||
−0.395374 | + | 0.918520i | \(0.629385\pi\) | |||||||
\(132\) | 15984.0 | 0.0798455 | ||||||||
\(133\) | −131516. | −0.644688 | ||||||||
\(134\) | 356136. | 1.71338 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −21168.0 | −0.0981369 | ||||||||
\(137\) | 264246. | 1.20284 | 0.601419 | − | 0.798934i | \(-0.294602\pi\) | ||||
0.601419 | + | 0.798934i | \(0.294602\pi\) | |||||||
\(138\) | −226800. | −1.01378 | ||||||||
\(139\) | 224612. | 0.986043 | 0.493022 | − | 0.870017i | \(-0.335892\pi\) | ||||
0.493022 | + | 0.870017i | \(0.335892\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 125280. | 0.530682 | ||||||||
\(142\) | 192240. | 0.800061 | ||||||||
\(143\) | 196248. | 0.802537 | ||||||||
\(144\) | −92016.0 | −0.369792 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 371076. | 1.44072 | ||||||||
\(147\) | 21609.0 | 0.0824786 | ||||||||
\(148\) | 21736.0 | 0.0815690 | ||||||||
\(149\) | −82074.0 | −0.302859 | −0.151429 | − | 0.988468i | \(-0.548388\pi\) | ||||
−0.151429 | + | 0.988468i | \(0.548388\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −287032. | −1.02444 | −0.512222 | − | 0.858853i | \(-0.671177\pi\) | ||||
−0.512222 | + | 0.858853i | \(0.671177\pi\) | |||||||
\(152\) | −450912. | −1.58301 | ||||||||
\(153\) | 10206.0 | 0.0352474 | ||||||||
\(154\) | −130536. | −0.443536 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 15912.0 | 0.0523496 | ||||||||
\(157\) | −129878. | −0.420520 | −0.210260 | − | 0.977646i | \(-0.567431\pi\) | ||||
−0.210260 | + | 0.977646i | \(0.567431\pi\) | |||||||
\(158\) | −394656. | −1.25770 | ||||||||
\(159\) | 86346.0 | 0.270863 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 205800. | 0.625721 | ||||||||
\(162\) | 39366.0 | 0.117851 | ||||||||
\(163\) | −555284. | −1.63699 | −0.818495 | − | 0.574513i | \(-0.805191\pi\) | ||||
−0.818495 | + | 0.574513i | \(0.805191\pi\) | |||||||
\(164\) | 31848.0 | 0.0924640 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −241128. | −0.679168 | ||||||||
\(167\) | −43512.0 | −0.120731 | −0.0603654 | − | 0.998176i | \(-0.519227\pi\) | ||||
−0.0603654 | + | 0.998176i | \(0.519227\pi\) | |||||||
\(168\) | 74088.0 | 0.202523 | ||||||||
\(169\) | −175929. | −0.473828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 217404. | 0.568561 | ||||||||
\(172\) | 46096.0 | 0.118807 | ||||||||
\(173\) | 18330.0 | 0.0465637 | 0.0232818 | − | 0.999729i | \(-0.492588\pi\) | ||||
0.0232818 | + | 0.999729i | \(0.492588\pi\) | |||||||
\(174\) | −293868. | −0.735833 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −504384. | −1.22738 | ||||||||
\(177\) | 247428. | 0.593630 | ||||||||
\(178\) | −47844.0 | −0.113182 | ||||||||
\(179\) | −153324. | −0.357666 | −0.178833 | − | 0.983879i | \(-0.557232\pi\) | ||||
−0.178833 | + | 0.983879i | \(0.557232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −382066. | −0.866846 | −0.433423 | − | 0.901191i | \(-0.642694\pi\) | ||||
−0.433423 | + | 0.901191i | \(0.642694\pi\) | |||||||
\(182\) | −129948. | −0.290798 | ||||||||
\(183\) | 445302. | 0.982940 | ||||||||
\(184\) | 705600. | 1.53643 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4320.00 | 0.00915591 | ||||||||
\(187\) | 55944.0 | 0.116990 | ||||||||
\(188\) | 55680.0 | 0.114896 | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −273408. | −0.542285 | −0.271143 | − | 0.962539i | \(-0.587402\pi\) | ||||
−0.271143 | + | 0.962539i | \(0.587402\pi\) | |||||||
\(192\) | 249408. | 0.488267 | ||||||||
\(193\) | −153602. | −0.296827 | −0.148414 | − | 0.988925i | \(-0.547417\pi\) | ||||
−0.148414 | + | 0.988925i | \(0.547417\pi\) | |||||||
\(194\) | 861972. | 1.64433 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9604.00 | 0.0178571 | ||||||||
\(197\) | −154422. | −0.283494 | −0.141747 | − | 0.989903i | \(-0.545272\pi\) | ||||
−0.141747 | + | 0.989903i | \(0.545272\pi\) | |||||||
\(198\) | 215784. | 0.391162 | ||||||||
\(199\) | −366856. | −0.656694 | −0.328347 | − | 0.944557i | \(-0.606492\pi\) | ||||
−0.328347 | + | 0.944557i | \(0.606492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 534204. | 0.932646 | ||||||||
\(202\) | −16236.0 | −0.0279963 | ||||||||
\(203\) | 266658. | 0.454166 | ||||||||
\(204\) | 4536.00 | 0.00763128 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −790608. | −1.29806 | ||||||||
\(207\) | −340200. | −0.551834 | ||||||||
\(208\) | −502112. | −0.804715 | ||||||||
\(209\) | 1.19170e6 | 1.88712 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 520244. | 0.804453 | 0.402227 | − | 0.915540i | \(-0.368236\pi\) | ||||
0.402227 | + | 0.915540i | \(0.368236\pi\) | |||||||
\(212\) | 38376.0 | 0.0586435 | ||||||||
\(213\) | 288360. | 0.435498 | ||||||||
\(214\) | 773496. | 1.15458 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −122472. | −0.178609 | ||||||||
\(217\) | −3920.00 | −0.00565115 | ||||||||
\(218\) | −605868. | −0.863449 | ||||||||
\(219\) | 556614. | 0.784231 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 55692.0 | 0.0767030 | ||||||||
\(222\) | 293436. | 0.399605 | ||||||||
\(223\) | −304736. | −0.410357 | −0.205178 | − | 0.978725i | \(-0.565777\pi\) | ||||
−0.205178 | + | 0.978725i | \(0.565777\pi\) | |||||||
\(224\) | 70560.0 | 0.0939590 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.32088e6 | −1.72025 | ||||||||
\(227\) | −288588. | −0.371718 | −0.185859 | − | 0.982576i | \(-0.559507\pi\) | ||||
−0.185859 | + | 0.982576i | \(0.559507\pi\) | |||||||
\(228\) | 96624.0 | 0.123097 | ||||||||
\(229\) | 772190. | 0.973051 | 0.486525 | − | 0.873666i | \(-0.338264\pi\) | ||||
0.486525 | + | 0.873666i | \(0.338264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −195804. | −0.241430 | ||||||||
\(232\) | 914256. | 1.11519 | ||||||||
\(233\) | −252234. | −0.304378 | −0.152189 | − | 0.988351i | \(-0.548632\pi\) | ||||
−0.152189 | + | 0.988351i | \(0.548632\pi\) | |||||||
\(234\) | 214812. | 0.256460 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 109968. | 0.128525 | ||||||||
\(237\) | −591984. | −0.684603 | ||||||||
\(238\) | −37044.0 | −0.0423912 | ||||||||
\(239\) | −1.45114e6 | −1.64329 | −0.821643 | − | 0.570002i | \(-0.806942\pi\) | ||||
−0.821643 | + | 0.570002i | \(0.806942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −146398. | −0.162365 | −0.0811825 | − | 0.996699i | \(-0.525870\pi\) | ||||
−0.0811825 | + | 0.996699i | \(0.525870\pi\) | |||||||
\(242\) | 216510. | 0.237651 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 197912. | 0.212813 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 429948. | 0.452979 | ||||||||
\(247\) | 1.18633e6 | 1.23726 | ||||||||
\(248\) | −13440.0 | −0.0138762 | ||||||||
\(249\) | −361692. | −0.369692 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 607860. | 0.609003 | 0.304501 | − | 0.952512i | \(-0.401510\pi\) | ||||
0.304501 | + | 0.952512i | \(0.401510\pi\) | |||||||
\(252\) | −15876.0 | −0.0157485 | ||||||||
\(253\) | −1.86480e6 | −1.83160 | ||||||||
\(254\) | 445920. | 0.433683 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 387328. | 0.369385 | ||||||||
\(257\) | −95586.0 | −0.0902737 | −0.0451369 | − | 0.998981i | \(-0.514372\pi\) | ||||
−0.0451369 | + | 0.998981i | \(0.514372\pi\) | |||||||
\(258\) | 622296. | 0.582033 | ||||||||
\(259\) | −266266. | −0.246642 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −440802. | −0.400537 | ||||||||
\(262\) | −931896. | −0.838715 | ||||||||
\(263\) | 2.20034e6 | 1.96156 | 0.980779 | − | 0.195121i | \(-0.0625100\pi\) | ||||
0.980779 | + | 0.195121i | \(0.0625100\pi\) | |||||||
\(264\) | −671328. | −0.592823 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −789096. | −0.683795 | ||||||||
\(267\) | −71766.0 | −0.0616085 | ||||||||
\(268\) | 237424. | 0.201924 | ||||||||
\(269\) | 1.77025e6 | 1.49160 | 0.745801 | − | 0.666169i | \(-0.232067\pi\) | ||||
0.745801 | + | 0.666169i | \(0.232067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −223504. | −0.184868 | −0.0924341 | − | 0.995719i | \(-0.529465\pi\) | ||||
−0.0924341 | + | 0.995719i | \(0.529465\pi\) | |||||||
\(272\) | −143136. | −0.117308 | ||||||||
\(273\) | −194922. | −0.158290 | ||||||||
\(274\) | 1.58548e6 | 1.27580 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −151200. | −0.119476 | ||||||||
\(277\) | 342778. | 0.268419 | 0.134210 | − | 0.990953i | \(-0.457150\pi\) | ||||
0.134210 | + | 0.990953i | \(0.457150\pi\) | |||||||
\(278\) | 1.34767e6 | 1.04586 | ||||||||
\(279\) | 6480.00 | 0.00498384 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 480378. | 0.362925 | 0.181463 | − | 0.983398i | \(-0.441917\pi\) | ||||
0.181463 | + | 0.983398i | \(0.441917\pi\) | |||||||
\(282\) | 751680. | 0.562873 | ||||||||
\(283\) | 29980.0 | 0.0222518 | 0.0111259 | − | 0.999938i | \(-0.496458\pi\) | ||||
0.0111259 | + | 0.999938i | \(0.496458\pi\) | |||||||
\(284\) | 128160. | 0.0942880 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.17749e6 | 0.851219 | ||||||||
\(287\) | −390138. | −0.279585 | ||||||||
\(288\) | −116640. | −0.0828641 | ||||||||
\(289\) | −1.40398e6 | −0.988819 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.29296e6 | 0.895060 | ||||||||
\(292\) | 247384. | 0.169791 | ||||||||
\(293\) | 198066. | 0.134785 | 0.0673924 | − | 0.997727i | \(-0.478532\pi\) | ||||
0.0673924 | + | 0.997727i | \(0.478532\pi\) | |||||||
\(294\) | 129654. | 0.0874818 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −912912. | −0.605619 | ||||||||
\(297\) | 323676. | 0.212921 | ||||||||
\(298\) | −492444. | −0.321230 | ||||||||
\(299\) | −1.85640e6 | −1.20086 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −564676. | −0.359239 | ||||||||
\(302\) | −1.72219e6 | −1.08659 | ||||||||
\(303\) | −24354.0 | −0.0152393 | ||||||||
\(304\) | −3.04902e6 | −1.89224 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 61236.0 | 0.0373855 | ||||||||
\(307\) | 1.04564e6 | 0.633191 | 0.316595 | − | 0.948561i | \(-0.397460\pi\) | ||||
0.316595 | + | 0.948561i | \(0.397460\pi\) | |||||||
\(308\) | −87024.0 | −0.0522712 | ||||||||
\(309\) | −1.18591e6 | −0.706572 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.83718e6 | 1.07708 | 0.538542 | − | 0.842598i | \(-0.318975\pi\) | ||||
0.538542 | + | 0.842598i | \(0.318975\pi\) | |||||||
\(312\) | −668304. | −0.388676 | ||||||||
\(313\) | 365494. | 0.210872 | 0.105436 | − | 0.994426i | \(-0.466376\pi\) | ||||
0.105436 | + | 0.994426i | \(0.466376\pi\) | |||||||
\(314\) | −779268. | −0.446029 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −263104. | −0.148221 | ||||||||
\(317\) | 28338.0 | 0.0158388 | 0.00791938 | − | 0.999969i | \(-0.497479\pi\) | ||||
0.00791938 | + | 0.999969i | \(0.497479\pi\) | |||||||
\(318\) | 518076. | 0.287293 | ||||||||
\(319\) | −2.41625e6 | −1.32943 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.16024e6 | 0.628473 | ||||||||
\(322\) | 1.23480e6 | 0.663677 | ||||||||
\(323\) | 338184. | 0.180363 | ||||||||
\(324\) | 26244.0 | 0.0138889 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.33170e6 | −1.73629 | ||||||||
\(327\) | −908802. | −0.470002 | ||||||||
\(328\) | −1.33762e6 | −0.686510 | ||||||||
\(329\) | −682080. | −0.347413 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.93392e6 | 0.970214 | 0.485107 | − | 0.874455i | \(-0.338781\pi\) | ||||
0.485107 | + | 0.874455i | \(0.338781\pi\) | |||||||
\(332\) | −160752. | −0.0800408 | ||||||||
\(333\) | 440154. | 0.217517 | ||||||||
\(334\) | −261072. | −0.128054 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 500976. | 0.242085 | ||||||||
\(337\) | 1.88817e6 | 0.905664 | 0.452832 | − | 0.891596i | \(-0.350414\pi\) | ||||
0.452832 | + | 0.891596i | \(0.350414\pi\) | |||||||
\(338\) | −1.05557e6 | −0.502570 | ||||||||
\(339\) | −1.98131e6 | −0.936384 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35520.0 | 0.0165420 | ||||||||
\(342\) | 1.30442e6 | 0.603050 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | −1.93603e6 | −0.882097 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 109980. | 0.0493882 | ||||||||
\(347\) | −2.91937e6 | −1.30156 | −0.650782 | − | 0.759264i | \(-0.725559\pi\) | ||||
−0.650782 | + | 0.759264i | \(0.725559\pi\) | |||||||
\(348\) | −195912. | −0.0867187 | ||||||||
\(349\) | −780682. | −0.343092 | −0.171546 | − | 0.985176i | \(-0.554876\pi\) | ||||
−0.171546 | + | 0.985176i | \(0.554876\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 322218. | 0.139599 | ||||||||
\(352\) | −639360. | −0.275036 | ||||||||
\(353\) | −1.33437e6 | −0.569954 | −0.284977 | − | 0.958534i | \(-0.591986\pi\) | ||||
−0.284977 | + | 0.958534i | \(0.591986\pi\) | |||||||
\(354\) | 1.48457e6 | 0.629639 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −31896.0 | −0.0133386 | ||||||||
\(357\) | −55566.0 | −0.0230748 | ||||||||
\(358\) | −919944. | −0.379362 | ||||||||
\(359\) | 1.01743e6 | 0.416648 | 0.208324 | − | 0.978060i | \(-0.433199\pi\) | ||||
0.208324 | + | 0.978060i | \(0.433199\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.72776e6 | 1.90936 | ||||||||
\(362\) | −2.29240e6 | −0.919429 | ||||||||
\(363\) | 324765. | 0.129361 | ||||||||
\(364\) | −86632.0 | −0.0342709 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.67181e6 | 1.04257 | ||||||||
\(367\) | −837680. | −0.324648 | −0.162324 | − | 0.986737i | \(-0.551899\pi\) | ||||
−0.162324 | + | 0.986737i | \(0.551899\pi\) | |||||||
\(368\) | 4.77120e6 | 1.83657 | ||||||||
\(369\) | 644922. | 0.246571 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −470106. | −0.177321 | ||||||||
\(372\) | 2880.00 | 0.00107903 | ||||||||
\(373\) | 1.51993e6 | 0.565655 | 0.282827 | − | 0.959171i | \(-0.408728\pi\) | ||||
0.282827 | + | 0.959171i | \(0.408728\pi\) | |||||||
\(374\) | 335664. | 0.124087 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.33856e6 | −0.853059 | ||||||||
\(377\) | −2.40536e6 | −0.871620 | ||||||||
\(378\) | −214326. | −0.0771517 | ||||||||
\(379\) | 2.64465e6 | 0.945737 | 0.472869 | − | 0.881133i | \(-0.343219\pi\) | ||||
0.472869 | + | 0.881133i | \(0.343219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 668880. | 0.236067 | ||||||||
\(382\) | −1.64045e6 | −0.575180 | ||||||||
\(383\) | −2.01336e6 | −0.701333 | −0.350667 | − | 0.936500i | \(-0.614045\pi\) | ||||
−0.350667 | + | 0.936500i | \(0.614045\pi\) | |||||||
\(384\) | 1.91117e6 | 0.661410 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −921612. | −0.314833 | ||||||||
\(387\) | 933444. | 0.316819 | ||||||||
\(388\) | 574648. | 0.193786 | ||||||||
\(389\) | −726234. | −0.243334 | −0.121667 | − | 0.992571i | \(-0.538824\pi\) | ||||
−0.121667 | + | 0.992571i | \(0.538824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −529200. | −0.175056 | ||||||||
\(392\) | −403368. | −0.132583 | ||||||||
\(393\) | −1.39784e6 | −0.456538 | ||||||||
\(394\) | −926532. | −0.300691 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 143856. | 0.0460988 | ||||||||
\(397\) | −4.57578e6 | −1.45710 | −0.728549 | − | 0.684993i | \(-0.759805\pi\) | ||||
−0.728549 | + | 0.684993i | \(0.759805\pi\) | |||||||
\(398\) | −2.20114e6 | −0.696529 | ||||||||
\(399\) | −1.18364e6 | −0.372211 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33870.0 | −0.0105185 | −0.00525926 | − | 0.999986i | \(-0.501674\pi\) | ||||
−0.00525926 | + | 0.999986i | \(0.501674\pi\) | |||||||
\(402\) | 3.20522e6 | 0.989221 | ||||||||
\(403\) | 35360.0 | 0.0108455 | ||||||||
\(404\) | −10824.0 | −0.00329940 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.59995e6 | 0.481716 | ||||||||
\(407\) | 2.41270e6 | 0.721966 | ||||||||
\(408\) | −190512. | −0.0566594 | ||||||||
\(409\) | −5.86178e6 | −1.73269 | −0.866346 | − | 0.499444i | \(-0.833538\pi\) | ||||
−0.866346 | + | 0.499444i | \(0.833538\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.37821e6 | 0.694459 | ||||||||
\(412\) | −527072. | −0.152977 | ||||||||
\(413\) | −1.34711e6 | −0.388622 | ||||||||
\(414\) | −2.04120e6 | −0.585308 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −636480. | −0.180323 | ||||||||
\(417\) | 2.02151e6 | 0.569292 | ||||||||
\(418\) | 7.15018e6 | 2.00159 | ||||||||
\(419\) | 302748. | 0.0842454 | 0.0421227 | − | 0.999112i | \(-0.486588\pi\) | ||||
0.0421227 | + | 0.999112i | \(0.486588\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.36708e6 | −1.47582 | −0.737909 | − | 0.674900i | \(-0.764187\pi\) | ||||
−0.737909 | + | 0.674900i | \(0.764187\pi\) | |||||||
\(422\) | 3.12146e6 | 0.853252 | ||||||||
\(423\) | 1.12752e6 | 0.306389 | ||||||||
\(424\) | −1.61179e6 | −0.435406 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.73016e6 | 0.461915 | ||||||||
\(427\) | −2.42442e6 | −0.643485 | ||||||||
\(428\) | 515664. | 0.136068 | ||||||||
\(429\) | 1.76623e6 | 0.463345 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.17706e6 | 0.305214 | 0.152607 | − | 0.988287i | \(-0.451233\pi\) | ||||
0.152607 | + | 0.988287i | \(0.451233\pi\) | |||||||
\(432\) | −828144. | −0.213499 | ||||||||
\(433\) | 3.66249e6 | 0.938766 | 0.469383 | − | 0.882995i | \(-0.344476\pi\) | ||||
0.469383 | + | 0.882995i | \(0.344476\pi\) | |||||||
\(434\) | −23520.0 | −0.00599395 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −403912. | −0.101758 | ||||||||
\(437\) | −1.12728e7 | −2.82376 | ||||||||
\(438\) | 3.33968e6 | 0.831802 | ||||||||
\(439\) | −2.53674e6 | −0.628225 | −0.314113 | − | 0.949386i | \(-0.601707\pi\) | ||||
−0.314113 | + | 0.949386i | \(0.601707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 334152. | 0.0813558 | ||||||||
\(443\) | −6.01504e6 | −1.45623 | −0.728113 | − | 0.685457i | \(-0.759603\pi\) | ||||
−0.728113 | + | 0.685457i | \(0.759603\pi\) | |||||||
\(444\) | 195624. | 0.0470939 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.82842e6 | −0.435249 | ||||||||
\(447\) | −738666. | −0.174856 | ||||||||
\(448\) | −1.35789e6 | −0.319646 | ||||||||
\(449\) | 5.65965e6 | 1.32487 | 0.662436 | − | 0.749119i | \(-0.269523\pi\) | ||||
0.662436 | + | 0.749119i | \(0.269523\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.53513e6 | 0.818397 | ||||||||
\(452\) | −880584. | −0.202733 | ||||||||
\(453\) | −2.58329e6 | −0.591463 | ||||||||
\(454\) | −1.73153e6 | −0.394267 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.05821e6 | −0.913949 | ||||||||
\(457\) | 6.46159e6 | 1.44727 | 0.723634 | − | 0.690184i | \(-0.242470\pi\) | ||||
0.723634 | + | 0.690184i | \(0.242470\pi\) | |||||||
\(458\) | 4.63314e6 | 1.03208 | ||||||||
\(459\) | 91854.0 | 0.0203501 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.37353e6 | −0.739320 | −0.369660 | − | 0.929167i | \(-0.620526\pi\) | ||||
−0.369660 | + | 0.929167i | \(0.620526\pi\) | |||||||
\(462\) | −1.17482e6 | −0.256075 | ||||||||
\(463\) | 4.54974e6 | 0.986358 | 0.493179 | − | 0.869928i | \(-0.335835\pi\) | ||||
0.493179 | + | 0.869928i | \(0.335835\pi\) | |||||||
\(464\) | 6.18211e6 | 1.33304 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.51340e6 | −0.322842 | ||||||||
\(467\) | −2.01136e6 | −0.426773 | −0.213386 | − | 0.976968i | \(-0.568449\pi\) | ||||
−0.213386 | + | 0.976968i | \(0.568449\pi\) | |||||||
\(468\) | 143208. | 0.0302240 | ||||||||
\(469\) | −2.90844e6 | −0.610560 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.16890e6 | −0.242787 | ||||||||
\(472\) | −4.61866e6 | −0.954247 | ||||||||
\(473\) | 5.11666e6 | 1.05156 | ||||||||
\(474\) | −3.55190e6 | −0.726132 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −24696.0 | −0.00499585 | ||||||||
\(477\) | 777114. | 0.156383 | ||||||||
\(478\) | −8.70682e6 | −1.74297 | ||||||||
\(479\) | −7.60402e6 | −1.51427 | −0.757137 | − | 0.653257i | \(-0.773402\pi\) | ||||
−0.757137 | + | 0.653257i | \(0.773402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.40183e6 | 0.473347 | ||||||||
\(482\) | −878388. | −0.172214 | ||||||||
\(483\) | 1.85220e6 | 0.361260 | ||||||||
\(484\) | 144340. | 0.0280074 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 354294. | 0.0680414 | ||||||||
\(487\) | −673112. | −0.128607 | −0.0643035 | − | 0.997930i | \(-0.520483\pi\) | ||||
−0.0643035 | + | 0.997930i | \(0.520483\pi\) | |||||||
\(488\) | −8.31230e6 | −1.58005 | ||||||||
\(489\) | −4.99756e6 | −0.945117 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.47170e6 | −0.462692 | −0.231346 | − | 0.972872i | \(-0.574313\pi\) | ||||
−0.231346 | + | 0.972872i | \(0.574313\pi\) | |||||||
\(492\) | 286632. | 0.0533841 | ||||||||
\(493\) | −685692. | −0.127061 | ||||||||
\(494\) | 7.11797e6 | 1.31232 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −90880.0 | −0.0165869 | ||||||||
\(497\) | −1.56996e6 | −0.285100 | ||||||||
\(498\) | −2.17015e6 | −0.392118 | ||||||||
\(499\) | 6.08152e6 | 1.09335 | 0.546677 | − | 0.837343i | \(-0.315892\pi\) | ||||
0.546677 | + | 0.837343i | \(0.315892\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −391608. | −0.0697039 | ||||||||
\(502\) | 3.64716e6 | 0.645945 | ||||||||
\(503\) | 846216. | 0.149129 | 0.0745644 | − | 0.997216i | \(-0.476243\pi\) | ||||
0.0745644 | + | 0.997216i | \(0.476243\pi\) | |||||||
\(504\) | 666792. | 0.116927 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.11888e7 | −1.94271 | ||||||||
\(507\) | −1.58336e6 | −0.273565 | ||||||||
\(508\) | 297280. | 0.0511101 | ||||||||
\(509\) | −7.66785e6 | −1.31183 | −0.655917 | − | 0.754833i | \(-0.727718\pi\) | ||||
−0.655917 | + | 0.754833i | \(0.727718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.03045e6 | −0.513400 | ||||||||
\(512\) | −4.47130e6 | −0.753804 | ||||||||
\(513\) | 1.95664e6 | 0.328259 | ||||||||
\(514\) | −573516. | −0.0957498 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 414864. | 0.0685933 | ||||||||
\(517\) | 6.18048e6 | 1.01694 | ||||||||
\(518\) | −1.59760e6 | −0.261603 | ||||||||
\(519\) | 164970. | 0.0268835 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.68938e6 | −1.56387 | −0.781937 | − | 0.623357i | \(-0.785768\pi\) | ||||
−0.781937 | + | 0.623357i | \(0.785768\pi\) | |||||||
\(522\) | −2.64481e6 | −0.424833 | ||||||||
\(523\) | 7.51678e6 | 1.20165 | 0.600824 | − | 0.799381i | \(-0.294839\pi\) | ||||
0.600824 | + | 0.799381i | \(0.294839\pi\) | |||||||
\(524\) | −621264. | −0.0988435 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.32021e7 | 2.08055 | ||||||||
\(527\) | 10080.0 | 0.00158101 | ||||||||
\(528\) | −4.53946e6 | −0.708629 | ||||||||
\(529\) | 1.12037e7 | 1.74069 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.22685e6 | 0.342732 | ||||||||
\(532\) | −526064. | −0.0805860 | ||||||||
\(533\) | 3.51920e6 | 0.536570 | ||||||||
\(534\) | −430596. | −0.0653457 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.97181e6 | −1.49921 | ||||||||
\(537\) | −1.37992e6 | −0.206499 | ||||||||
\(538\) | 1.06215e7 | 1.58208 | ||||||||
\(539\) | 1.06604e6 | 0.158053 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.34325e6 | 1.07869 | 0.539343 | − | 0.842086i | \(-0.318673\pi\) | ||||
0.539343 | + | 0.842086i | \(0.318673\pi\) | |||||||
\(542\) | −1.34102e6 | −0.196082 | ||||||||
\(543\) | −3.43859e6 | −0.500474 | ||||||||
\(544\) | −181440. | −0.0262867 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.16953e6 | −0.167892 | ||||||||
\(547\) | −2.18296e6 | −0.311945 | −0.155973 | − | 0.987761i | \(-0.549851\pi\) | ||||
−0.155973 | + | 0.987761i | \(0.549851\pi\) | |||||||
\(548\) | 1.05698e6 | 0.150355 | ||||||||
\(549\) | 4.00772e6 | 0.567501 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.46063e7 | −2.04957 | ||||||||
\(552\) | 6.35040e6 | 0.887061 | ||||||||
\(553\) | 3.22302e6 | 0.448178 | ||||||||
\(554\) | 2.05667e6 | 0.284702 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 898448. | 0.123255 | ||||||||
\(557\) | −1.25466e7 | −1.71351 | −0.856755 | − | 0.515724i | \(-0.827523\pi\) | ||||
−0.856755 | + | 0.515724i | \(0.827523\pi\) | |||||||
\(558\) | 38880.0 | 0.00528617 | ||||||||
\(559\) | 5.09361e6 | 0.689439 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 503496. | 0.0675443 | ||||||||
\(562\) | 2.88227e6 | 0.384940 | ||||||||
\(563\) | −5.15972e6 | −0.686050 | −0.343025 | − | 0.939326i | \(-0.611451\pi\) | ||||
−0.343025 | + | 0.939326i | \(0.611451\pi\) | |||||||
\(564\) | 501120. | 0.0663352 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 179880. | 0.0236016 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | −5.38272e6 | −0.700053 | ||||||||
\(569\) | 1.17452e7 | 1.52083 | 0.760414 | − | 0.649439i | \(-0.224996\pi\) | ||||
0.760414 | + | 0.649439i | \(0.224996\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.54728e6 | −0.968725 | −0.484362 | − | 0.874867i | \(-0.660948\pi\) | ||||
−0.484362 | + | 0.874867i | \(0.660948\pi\) | |||||||
\(572\) | 784992. | 0.100317 | ||||||||
\(573\) | −2.46067e6 | −0.313089 | ||||||||
\(574\) | −2.34083e6 | −0.296544 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.24467e6 | 0.281901 | ||||||||
\(577\) | −9.28483e6 | −1.16101 | −0.580503 | − | 0.814258i | \(-0.697144\pi\) | ||||
−0.580503 | + | 0.814258i | \(0.697144\pi\) | |||||||
\(578\) | −8.42389e6 | −1.04880 | ||||||||
\(579\) | −1.38242e6 | −0.171373 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.96921e6 | 0.242020 | ||||||||
\(582\) | 7.75775e6 | 0.949354 | ||||||||
\(583\) | 4.25974e6 | 0.519053 | ||||||||
\(584\) | −1.03901e7 | −1.26063 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.18840e6 | 0.142961 | ||||||||
\(587\) | −1.47623e6 | −0.176831 | −0.0884155 | − | 0.996084i | \(-0.528180\pi\) | ||||
−0.0884155 | + | 0.996084i | \(0.528180\pi\) | |||||||
\(588\) | 86436.0 | 0.0103098 | ||||||||
\(589\) | 214720. | 0.0255026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.38980e6 | −0.163675 | ||||||||
\(592\) | −6.17302e6 | −0.723925 | ||||||||
\(593\) | 1.24007e7 | 1.44813 | 0.724067 | − | 0.689729i | \(-0.242270\pi\) | ||||
0.724067 | + | 0.689729i | \(0.242270\pi\) | |||||||
\(594\) | 1.94206e6 | 0.225837 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −328296. | −0.0378573 | ||||||||
\(597\) | −3.30170e6 | −0.379142 | ||||||||
\(598\) | −1.11384e7 | −1.27371 | ||||||||
\(599\) | −3.69127e6 | −0.420348 | −0.210174 | − | 0.977664i | \(-0.567403\pi\) | ||||
−0.210174 | + | 0.977664i | \(0.567403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.12223e6 | 1.03018 | 0.515092 | − | 0.857135i | \(-0.327758\pi\) | ||||
0.515092 | + | 0.857135i | \(0.327758\pi\) | |||||||
\(602\) | −3.38806e6 | −0.381030 | ||||||||
\(603\) | 4.80784e6 | 0.538464 | ||||||||
\(604\) | −1.14813e6 | −0.128055 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −146124. | −0.0161637 | ||||||||
\(607\) | 5.67914e6 | 0.625620 | 0.312810 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312810 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(608\) | −3.86496e6 | −0.424020 | ||||||||
\(609\) | 2.39992e6 | 0.262213 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.15264e6 | 0.666743 | ||||||||
\(612\) | 40824.0 | 0.00440592 | ||||||||
\(613\) | 1.40106e7 | 1.50593 | 0.752966 | − | 0.658060i | \(-0.228623\pi\) | ||||
0.752966 | + | 0.658060i | \(0.228623\pi\) | |||||||
\(614\) | 6.27382e6 | 0.671600 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.65501e6 | 0.388094 | ||||||||
\(617\) | 253686. | 0.0268277 | 0.0134139 | − | 0.999910i | \(-0.495730\pi\) | ||||
0.0134139 | + | 0.999910i | \(0.495730\pi\) | |||||||
\(618\) | −7.11547e6 | −0.749433 | ||||||||
\(619\) | 4.30034e6 | 0.451103 | 0.225552 | − | 0.974231i | \(-0.427582\pi\) | ||||
0.225552 | + | 0.974231i | \(0.427582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.06180e6 | −0.318602 | ||||||||
\(622\) | 1.10231e7 | 1.14242 | ||||||||
\(623\) | 390726. | 0.0403322 | ||||||||
\(624\) | −4.51901e6 | −0.464603 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.19296e6 | 0.223664 | ||||||||
\(627\) | 1.07253e7 | 1.08953 | ||||||||
\(628\) | −519512. | −0.0525650 | ||||||||
\(629\) | 684684. | 0.0690023 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.04150e7 | 1.04132 | 0.520662 | − | 0.853763i | \(-0.325685\pi\) | ||||
0.520662 | + | 0.853763i | \(0.325685\pi\) | |||||||
\(632\) | 1.10504e7 | 1.10048 | ||||||||
\(633\) | 4.68220e6 | 0.464451 | ||||||||
\(634\) | 170028. | 0.0167995 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 345384. | 0.0338579 | ||||||||
\(637\) | 1.06124e6 | 0.103625 | ||||||||
\(638\) | −1.44975e7 | −1.41007 | ||||||||
\(639\) | 2.59524e6 | 0.251435 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.52714e6 | 0.435190 | 0.217595 | − | 0.976039i | \(-0.430179\pi\) | ||||
0.217595 | + | 0.976039i | \(0.430179\pi\) | |||||||
\(642\) | 6.96146e6 | 0.666596 | ||||||||
\(643\) | −1.49687e7 | −1.42776 | −0.713882 | − | 0.700266i | \(-0.753065\pi\) | ||||
−0.713882 | + | 0.700266i | \(0.753065\pi\) | |||||||
\(644\) | 823200. | 0.0782151 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.02910e6 | 0.191304 | ||||||||
\(647\) | 1.73020e7 | 1.62493 | 0.812465 | − | 0.583010i | \(-0.198125\pi\) | ||||
0.812465 | + | 0.583010i | \(0.198125\pi\) | |||||||
\(648\) | −1.10225e6 | −0.103120 | ||||||||
\(649\) | 1.22064e7 | 1.13757 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35280.0 | −0.00326269 | ||||||||
\(652\) | −2.22114e6 | −0.204624 | ||||||||
\(653\) | −4.07470e6 | −0.373949 | −0.186975 | − | 0.982365i | \(-0.559868\pi\) | ||||
−0.186975 | + | 0.982365i | \(0.559868\pi\) | |||||||
\(654\) | −5.45281e6 | −0.498513 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.04483e6 | −0.820618 | ||||||||
\(657\) | 5.00953e6 | 0.452776 | ||||||||
\(658\) | −4.09248e6 | −0.368487 | ||||||||
\(659\) | −3.79475e6 | −0.340384 | −0.170192 | − | 0.985411i | \(-0.554439\pi\) | ||||
−0.170192 | + | 0.985411i | \(0.554439\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.64261e7 | 1.46228 | 0.731142 | − | 0.682225i | \(-0.238988\pi\) | ||||
0.731142 | + | 0.682225i | \(0.238988\pi\) | |||||||
\(662\) | 1.16035e7 | 1.02907 | ||||||||
\(663\) | 501228. | 0.0442845 | ||||||||
\(664\) | 6.75158e6 | 0.594272 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.64092e6 | 0.230712 | ||||||||
\(667\) | 2.28564e7 | 1.98927 | ||||||||
\(668\) | −174048. | −0.0150913 | ||||||||
\(669\) | −2.74262e6 | −0.236920 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.19682e7 | 1.88360 | ||||||||
\(672\) | 635040. | 0.0542473 | ||||||||
\(673\) | −5.50675e6 | −0.468660 | −0.234330 | − | 0.972157i | \(-0.575290\pi\) | ||||
−0.234330 | + | 0.972157i | \(0.575290\pi\) | |||||||
\(674\) | 1.13290e7 | 0.960602 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −703716. | −0.0592285 | ||||||||
\(677\) | −1.83957e7 | −1.54257 | −0.771286 | − | 0.636488i | \(-0.780386\pi\) | ||||
−0.771286 | + | 0.636488i | \(0.780386\pi\) | |||||||
\(678\) | −1.18879e7 | −0.993185 | ||||||||
\(679\) | −7.03944e6 | −0.585954 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.59729e6 | −0.214612 | ||||||||
\(682\) | 213120. | 0.0175454 | ||||||||
\(683\) | −1.75835e6 | −0.144229 | −0.0721146 | − | 0.997396i | \(-0.522975\pi\) | ||||
−0.0721146 | + | 0.997396i | \(0.522975\pi\) | |||||||
\(684\) | 869616. | 0.0710702 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −705894. | −0.0572703 | ||||||||
\(687\) | 6.94971e6 | 0.561791 | ||||||||
\(688\) | −1.30913e7 | −1.05441 | ||||||||
\(689\) | 4.24055e6 | 0.340309 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.36314e6 | −0.427291 | −0.213646 | − | 0.976911i | \(-0.568534\pi\) | ||||
−0.213646 | + | 0.976911i | \(0.568534\pi\) | |||||||
\(692\) | 73320.0 | 0.00582046 | ||||||||
\(693\) | −1.76224e6 | −0.139390 | ||||||||
\(694\) | −1.75162e7 | −1.38052 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.22830e6 | 0.643854 | ||||||||
\(697\) | 1.00321e6 | 0.0782187 | ||||||||
\(698\) | −4.68409e6 | −0.363904 | ||||||||
\(699\) | −2.27011e6 | −0.175733 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.12606e7 | −1.63411 | −0.817054 | − | 0.576561i | \(-0.804394\pi\) | ||||
−0.817054 | + | 0.576561i | \(0.804394\pi\) | |||||||
\(702\) | 1.93331e6 | 0.148067 | ||||||||
\(703\) | 1.45849e7 | 1.11305 | ||||||||
\(704\) | 1.23041e7 | 0.935662 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.00622e6 | −0.604527 | ||||||||
\(707\) | 132594. | 0.00997643 | ||||||||
\(708\) | 989712. | 0.0742037 | ||||||||
\(709\) | 2.07729e6 | 0.155196 | 0.0775980 | − | 0.996985i | \(-0.475275\pi\) | ||||
0.0775980 | + | 0.996985i | \(0.475275\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.32786e6 | −0.395256 | ||||||||
\(712\) | 1.33963e6 | 0.0990343 | ||||||||
\(713\) | −336000. | −0.0247523 | ||||||||
\(714\) | −333396. | −0.0244746 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −613296. | −0.0447082 | ||||||||
\(717\) | −1.30602e7 | −0.948752 | ||||||||
\(718\) | 6.10459e6 | 0.441922 | ||||||||
\(719\) | 4.23619e6 | 0.305600 | 0.152800 | − | 0.988257i | \(-0.451171\pi\) | ||||
0.152800 | + | 0.988257i | \(0.451171\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.45663e6 | 0.462560 | ||||||||
\(722\) | 2.83665e7 | 2.02518 | ||||||||
\(723\) | −1.31758e6 | −0.0937415 | ||||||||
\(724\) | −1.52826e6 | −0.108356 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.94859e6 | 0.137208 | ||||||||
\(727\) | −2.14524e7 | −1.50536 | −0.752678 | − | 0.658389i | \(-0.771238\pi\) | ||||
−0.752678 | + | 0.658389i | \(0.771238\pi\) | |||||||
\(728\) | 3.63854e6 | 0.254448 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.45202e6 | 0.100503 | ||||||||
\(732\) | 1.78121e6 | 0.122867 | ||||||||
\(733\) | 1.48892e7 | 1.02355 | 0.511777 | − | 0.859118i | \(-0.328987\pi\) | ||||
0.511777 | + | 0.859118i | \(0.328987\pi\) | |||||||
\(734\) | −5.02608e6 | −0.344341 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.04800e6 | 0.411545 | ||||||||
\(737\) | 2.63541e7 | 1.78722 | ||||||||
\(738\) | 3.86953e6 | 0.261528 | ||||||||
\(739\) | 6.99324e6 | 0.471050 | 0.235525 | − | 0.971868i | \(-0.424319\pi\) | ||||
0.235525 | + | 0.971868i | \(0.424319\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.06770e7 | 0.714335 | ||||||||
\(742\) | −2.82064e6 | −0.188078 | ||||||||
\(743\) | −1.90428e6 | −0.126549 | −0.0632745 | − | 0.997996i | \(-0.520154\pi\) | ||||
−0.0632745 | + | 0.997996i | \(0.520154\pi\) | |||||||
\(744\) | −120960. | −0.00801142 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.11958e6 | 0.599968 | ||||||||
\(747\) | −3.25523e6 | −0.213442 | ||||||||
\(748\) | 223776. | 0.0146238 | ||||||||
\(749\) | −6.31688e6 | −0.411432 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.95361e7 | 1.26398 | 0.631988 | − | 0.774978i | \(-0.282239\pi\) | ||||
0.631988 | + | 0.774978i | \(0.282239\pi\) | |||||||
\(752\) | −1.58131e7 | −1.01970 | ||||||||
\(753\) | 5.47074e6 | 0.351608 | ||||||||
\(754\) | −1.44322e7 | −0.924493 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −142884. | −0.00909241 | ||||||||
\(757\) | −1.25183e6 | −0.0793973 | −0.0396986 | − | 0.999212i | \(-0.512640\pi\) | ||||
−0.0396986 | + | 0.999212i | \(0.512640\pi\) | |||||||
\(758\) | 1.58679e7 | 1.00311 | ||||||||
\(759\) | −1.67832e7 | −1.05748 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.04472e7 | 1.27989 | 0.639944 | − | 0.768422i | \(-0.278958\pi\) | ||||
0.639944 | + | 0.768422i | \(0.278958\pi\) | |||||||
\(762\) | 4.01328e6 | 0.250387 | ||||||||
\(763\) | 4.94792e6 | 0.307689 | ||||||||
\(764\) | −1.09363e6 | −0.0677857 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.20802e7 | −0.743876 | ||||||||
\(767\) | 1.21515e7 | 0.745831 | ||||||||
\(768\) | 3.48595e6 | 0.213264 | ||||||||
\(769\) | 2.21064e6 | 0.134804 | 0.0674020 | − | 0.997726i | \(-0.478529\pi\) | ||||
0.0674020 | + | 0.997726i | \(0.478529\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −860274. | −0.0521196 | ||||||||
\(772\) | −614408. | −0.0371034 | ||||||||
\(773\) | −1.29151e7 | −0.777405 | −0.388703 | − | 0.921363i | \(-0.627077\pi\) | ||||
−0.388703 | + | 0.921363i | \(0.627077\pi\) | |||||||
\(774\) | 5.60066e6 | 0.336037 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.41352e7 | −1.43879 | ||||||||
\(777\) | −2.39639e6 | −0.142399 | ||||||||
\(778\) | −4.35740e6 | −0.258095 | ||||||||
\(779\) | 2.13700e7 | 1.26171 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.42258e7 | 0.834541 | ||||||||
\(782\) | −3.17520e6 | −0.185675 | ||||||||
\(783\) | −3.96722e6 | −0.231250 | ||||||||
\(784\) | −2.72754e6 | −0.158482 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.38706e6 | −0.484232 | ||||||||
\(787\) | 1.35499e7 | 0.779830 | 0.389915 | − | 0.920851i | \(-0.372504\pi\) | ||||
0.389915 | + | 0.920851i | \(0.372504\pi\) | |||||||
\(788\) | −617688. | −0.0354367 | ||||||||
\(789\) | 1.98031e7 | 1.13251 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.07872e7 | 0.613007 | ||||||||
\(792\) | −6.04195e6 | −0.342266 | ||||||||
\(793\) | 2.18693e7 | 1.23496 | ||||||||
\(794\) | −2.74547e7 | −1.54549 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.46742e6 | −0.0820867 | ||||||||
\(797\) | 2.45956e7 | 1.37155 | 0.685776 | − | 0.727813i | \(-0.259463\pi\) | ||||
0.685776 | + | 0.727813i | \(0.259463\pi\) | |||||||
\(798\) | −7.10186e6 | −0.394789 | ||||||||
\(799\) | 1.75392e6 | 0.0971948 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −645894. | −0.0355697 | ||||||||
\(802\) | −203220. | −0.0111566 | ||||||||
\(803\) | 2.74596e7 | 1.50282 | ||||||||
\(804\) | 2.13682e6 | 0.116581 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 212160. | 0.0115034 | ||||||||
\(807\) | 1.59322e7 | 0.861177 | ||||||||
\(808\) | 454608. | 0.0244968 | ||||||||
\(809\) | 1.55237e7 | 0.833920 | 0.416960 | − | 0.908925i | \(-0.363095\pi\) | ||||
0.416960 | + | 0.908925i | \(0.363095\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.66262e7 | −1.42153 | −0.710766 | − | 0.703429i | \(-0.751651\pi\) | ||||
−0.710766 | + | 0.703429i | \(0.751651\pi\) | |||||||
\(812\) | 1.06663e6 | 0.0567707 | ||||||||
\(813\) | −2.01154e6 | −0.106734 | ||||||||
\(814\) | 1.44762e7 | 0.765760 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.28822e6 | −0.0677276 | ||||||||
\(817\) | 3.09304e7 | 1.62118 | ||||||||
\(818\) | −3.51707e7 | −1.83780 | ||||||||
\(819\) | −1.75430e6 | −0.0913889 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.23891e7 | −0.641477 | −0.320739 | − | 0.947168i | \(-0.603931\pi\) | ||||
−0.320739 | + | 0.947168i | \(0.603931\pi\) | |||||||
\(822\) | 1.42693e7 | 0.736585 | ||||||||
\(823\) | 3.65630e6 | 0.188166 | 0.0940831 | − | 0.995564i | \(-0.470008\pi\) | ||||
0.0940831 | + | 0.995564i | \(0.470008\pi\) | |||||||
\(824\) | 2.21370e7 | 1.13580 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.08265e6 | −0.412196 | ||||||||
\(827\) | −2.80463e7 | −1.42597 | −0.712987 | − | 0.701178i | \(-0.752658\pi\) | ||||
−0.712987 | + | 0.701178i | \(0.752658\pi\) | |||||||
\(828\) | −1.36080e6 | −0.0689792 | ||||||||
\(829\) | 2.11153e7 | 1.06712 | 0.533558 | − | 0.845763i | \(-0.320855\pi\) | ||||
0.533558 | + | 0.845763i | \(0.320855\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.08500e6 | 0.154972 | ||||||||
\(832\) | 1.22487e7 | 0.613454 | ||||||||
\(833\) | 302526. | 0.0151060 | ||||||||
\(834\) | 1.21290e7 | 0.603826 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.76678e6 | 0.235890 | ||||||||
\(837\) | 58320.0 | 0.00287742 | ||||||||
\(838\) | 1.81649e6 | 0.0893557 | ||||||||
\(839\) | 1.33947e7 | 0.656944 | 0.328472 | − | 0.944514i | \(-0.393466\pi\) | ||||
0.328472 | + | 0.944514i | \(0.393466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.10422e6 | 0.443867 | ||||||||
\(842\) | −3.22025e7 | −1.56534 | ||||||||
\(843\) | 4.32340e6 | 0.209535 | ||||||||
\(844\) | 2.08098e6 | 0.100557 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.76512e6 | 0.324975 | ||||||||
\(847\) | −1.76816e6 | −0.0846865 | ||||||||
\(848\) | −1.08988e7 | −0.520461 | ||||||||
\(849\) | 269820. | 0.0128471 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.28228e7 | −1.08030 | ||||||||
\(852\) | 1.15344e6 | 0.0544372 | ||||||||
\(853\) | −3.01513e7 | −1.41884 | −0.709420 | − | 0.704786i | \(-0.751043\pi\) | ||||
−0.709420 | + | 0.704786i | \(0.751043\pi\) | |||||||
\(854\) | −1.45465e7 | −0.682519 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.16579e7 | −1.01026 | ||||||||
\(857\) | −2.39894e7 | −1.11575 | −0.557875 | − | 0.829925i | \(-0.688383\pi\) | ||||
−0.557875 | + | 0.829925i | \(0.688383\pi\) | |||||||
\(858\) | 1.05974e7 | 0.491452 | ||||||||
\(859\) | −8.87576e6 | −0.410414 | −0.205207 | − | 0.978719i | \(-0.565787\pi\) | ||||
−0.205207 | + | 0.978719i | \(0.565787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.51124e6 | −0.161418 | ||||||||
\(862\) | 7.06234e6 | 0.323728 | ||||||||
\(863\) | 8.71286e6 | 0.398230 | 0.199115 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199115 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(864\) | −1.04976e6 | −0.0478416 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.19750e7 | 0.995711 | ||||||||
\(867\) | −1.26358e7 | −0.570895 | ||||||||
\(868\) | −15680.0 | −0.000706394 0 | ||||||||
\(869\) | −2.92045e7 | −1.31190 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.62354e7 | 1.17177 | ||||||||
\(872\) | 1.69643e7 | 0.755518 | ||||||||
\(873\) | 1.16366e7 | 0.516763 | ||||||||
\(874\) | −6.76368e7 | −2.99505 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.22646e6 | 0.0980288 | ||||||||
\(877\) | 2.95788e7 | 1.29862 | 0.649310 | − | 0.760524i | \(-0.275058\pi\) | ||||
0.649310 | + | 0.760524i | \(0.275058\pi\) | |||||||
\(878\) | −1.52205e7 | −0.666333 | ||||||||
\(879\) | 1.78259e6 | 0.0778180 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.45670e7 | 1.06638 | 0.533190 | − | 0.845995i | \(-0.320993\pi\) | ||||
0.533190 | + | 0.845995i | \(0.320993\pi\) | |||||||
\(882\) | 1.16689e6 | 0.0505076 | ||||||||
\(883\) | −1.45682e7 | −0.628788 | −0.314394 | − | 0.949293i | \(-0.601801\pi\) | ||||
−0.314394 | + | 0.949293i | \(0.601801\pi\) | |||||||
\(884\) | 222768. | 0.00958787 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.60902e7 | −1.54456 | ||||||||
\(887\) | −1.61714e7 | −0.690141 | −0.345070 | − | 0.938577i | \(-0.612145\pi\) | ||||
−0.345070 | + | 0.938577i | \(0.612145\pi\) | |||||||
\(888\) | −8.21621e6 | −0.349654 | ||||||||
\(889\) | −3.64168e6 | −0.154542 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.91308e6 | 0.122930 | ||||||||
\(892\) | −1.21894e6 | −0.0512946 | ||||||||
\(893\) | 3.73613e7 | 1.56781 | ||||||||
\(894\) | −4.43200e6 | −0.185462 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.04052e7 | −0.432995 | ||||||||
\(897\) | −1.67076e7 | −0.693319 | ||||||||
\(898\) | 3.39579e7 | 1.40524 | ||||||||
\(899\) | −435360. | −0.0179659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.20884e6 | 0.0496087 | ||||||||
\(902\) | 2.12108e7 | 0.868041 | ||||||||
\(903\) | −5.08208e6 | −0.207407 | ||||||||
\(904\) | 3.69845e7 | 1.50522 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.54997e7 | −0.627341 | ||||||||
\(907\) | −3.14446e7 | −1.26919 | −0.634596 | − | 0.772844i | \(-0.718833\pi\) | ||||
−0.634596 | + | 0.772844i | \(0.718833\pi\) | |||||||
\(908\) | −1.15435e6 | −0.0464648 | ||||||||
\(909\) | −219186. | −0.00879839 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.51427e7 | 0.604514 | 0.302257 | − | 0.953227i | \(-0.402260\pi\) | ||||
0.302257 | + | 0.953227i | \(0.402260\pi\) | |||||||
\(912\) | −2.74412e7 | −1.09249 | ||||||||
\(913\) | −1.78435e7 | −0.708439 | ||||||||
\(914\) | 3.87695e7 | 1.53506 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.08876e6 | 0.121631 | ||||||||
\(917\) | 7.61048e6 | 0.298875 | ||||||||
\(918\) | 551124. | 0.0215845 | ||||||||
\(919\) | 4.14876e7 | 1.62043 | 0.810214 | − | 0.586134i | \(-0.199351\pi\) | ||||
0.810214 | + | 0.586134i | \(0.199351\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.41072e6 | 0.365573 | ||||||||
\(922\) | −2.02412e7 | −0.784167 | ||||||||
\(923\) | 1.41617e7 | 0.547155 | ||||||||
\(924\) | −783216. | −0.0301788 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.72985e7 | 1.04619 | ||||||||
\(927\) | −1.06732e7 | −0.407939 | ||||||||
\(928\) | 7.83648e6 | 0.298711 | ||||||||
\(929\) | −1.78495e7 | −0.678556 | −0.339278 | − | 0.940686i | \(-0.610183\pi\) | ||||
−0.339278 | + | 0.940686i | \(0.610183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.44428e6 | 0.243669 | ||||||||
\(932\) | −1.00894e6 | −0.0380473 | ||||||||
\(933\) | 1.65346e7 | 0.621855 | ||||||||
\(934\) | −1.20681e7 | −0.452661 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.01474e6 | −0.224402 | ||||||||
\(937\) | −2.96399e7 | −1.10288 | −0.551439 | − | 0.834215i | \(-0.685921\pi\) | ||||
−0.551439 | + | 0.834215i | \(0.685921\pi\) | |||||||
\(938\) | −1.74507e7 | −0.647597 | ||||||||
\(939\) | 3.28945e6 | 0.121747 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.22282e7 | −1.18648 | −0.593242 | − | 0.805024i | \(-0.702152\pi\) | ||||
−0.593242 | + | 0.805024i | \(0.702152\pi\) | |||||||
\(942\) | −7.01341e6 | −0.257515 | ||||||||
\(943\) | −3.34404e7 | −1.22459 | ||||||||
\(944\) | −3.12309e7 | −1.14066 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.06999e7 | 1.11535 | ||||||||
\(947\) | −4.84885e7 | −1.75697 | −0.878484 | − | 0.477772i | \(-0.841444\pi\) | ||||
−0.878484 | + | 0.477772i | \(0.841444\pi\) | |||||||
\(948\) | −2.36794e6 | −0.0855754 | ||||||||
\(949\) | 2.73359e7 | 0.985300 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 255042. | 0.00914451 | ||||||||
\(952\) | 1.03723e6 | 0.0370923 | ||||||||
\(953\) | 2.03264e7 | 0.724983 | 0.362491 | − | 0.931987i | \(-0.381926\pi\) | ||||
0.362491 | + | 0.931987i | \(0.381926\pi\) | |||||||
\(954\) | 4.66268e6 | 0.165869 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.80454e6 | −0.205411 | ||||||||
\(957\) | −2.17462e7 | −0.767546 | ||||||||
\(958\) | −4.56241e7 | −1.60613 | ||||||||
\(959\) | −1.29481e7 | −0.454630 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86228e7 | −0.999776 | ||||||||
\(962\) | 1.44110e7 | 0.502060 | ||||||||
\(963\) | 1.04422e7 | 0.362849 | ||||||||
\(964\) | −585592. | −0.0202956 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.11132e7 | 0.383174 | ||||||||
\(967\) | 3.66292e6 | 0.125968 | 0.0629841 | − | 0.998015i | \(-0.479938\pi\) | ||||
0.0629841 | + | 0.998015i | \(0.479938\pi\) | |||||||
\(968\) | −6.06228e6 | −0.207945 | ||||||||
\(969\) | 3.04366e6 | 0.104132 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.48741e6 | 0.0506271 | 0.0253136 | − | 0.999680i | \(-0.491942\pi\) | ||||
0.0253136 | + | 0.999680i | \(0.491942\pi\) | |||||||
\(972\) | 236196. | 0.00801875 | ||||||||
\(973\) | −1.10060e7 | −0.372689 | ||||||||
\(974\) | −4.03867e6 | −0.136408 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.62070e7 | −1.88871 | ||||||||
\(977\) | −4.07930e7 | −1.36725 | −0.683627 | − | 0.729831i | \(-0.739599\pi\) | ||||
−0.683627 | + | 0.729831i | \(0.739599\pi\) | |||||||
\(978\) | −2.99853e7 | −1.00245 | ||||||||
\(979\) | −3.54046e6 | −0.118060 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.17922e6 | −0.271356 | ||||||||
\(982\) | −1.48302e7 | −0.490759 | ||||||||
\(983\) | 9.26326e6 | 0.305759 | 0.152880 | − | 0.988245i | \(-0.451145\pi\) | ||||
0.152880 | + | 0.988245i | \(0.451145\pi\) | |||||||
\(984\) | −1.20385e7 | −0.396357 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.11415e6 | −0.134768 | ||||||||
\(987\) | −6.13872e6 | −0.200579 | ||||||||
\(988\) | 4.74531e6 | 0.154658 | ||||||||
\(989\) | −4.84008e7 | −1.57348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.22051e7 | −1.68861 | −0.844303 | − | 0.535866i | \(-0.819985\pi\) | ||||
−0.844303 | + | 0.535866i | \(0.819985\pi\) | |||||||
\(992\) | −115200. | −0.00371684 | ||||||||
\(993\) | 1.74052e7 | 0.560153 | ||||||||
\(994\) | −9.41976e6 | −0.302394 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.44677e6 | −0.0462116 | ||||||||
\(997\) | 1.86609e7 | 0.594560 | 0.297280 | − | 0.954790i | \(-0.403921\pi\) | ||||
0.297280 | + | 0.954790i | \(0.403921\pi\) | |||||||
\(998\) | 3.64891e7 | 1.15968 | ||||||||
\(999\) | 3.96139e6 | 0.125584 |
(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 | 525.6.a.d.1.1 | 1 | ||
5.2 | odd | 4 | 525.6.d.b.274.2 | 2 | |||
5.3 | odd | 4 | 525.6.d.b.274.1 | 2 | |||
5.4 | even | 2 | 21.6.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 63.6.a.d.1.1 | 1 | |||
20.19 | odd | 2 | 336.6.a.r.1.1 | 1 | |||
35.4 | even | 6 | 147.6.e.j.79.1 | 2 | |||
35.9 | even | 6 | 147.6.e.j.67.1 | 2 | |||
35.19 | odd | 6 | 147.6.e.i.67.1 | 2 | |||
35.24 | odd | 6 | 147.6.e.i.79.1 | 2 | |||
35.34 | odd | 2 | 147.6.a.b.1.1 | 1 | |||
60.59 | even | 2 | 1008.6.a.c.1.1 | 1 | |||
105.104 | even | 2 | 441.6.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
63.6.a.d.1.1 | 1 | 15.14 | odd | 2 | |||
147.6.a.b.1.1 | 1 | 35.34 | odd | 2 | |||
147.6.e.i.67.1 | 2 | 35.19 | odd | 6 | |||
147.6.e.i.79.1 | 2 | 35.24 | odd | 6 | |||
147.6.e.j.67.1 | 2 | 35.9 | even | 6 | |||
147.6.e.j.79.1 | 2 | 35.4 | even | 6 | |||
336.6.a.r.1.1 | 1 | 20.19 | odd | 2 | |||
441.6.a.j.1.1 | 1 | 105.104 | even | 2 | |||
525.6.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
525.6.d.b.274.1 | 2 | 5.3 | odd | 4 | |||
525.6.d.b.274.2 | 2 | 5.2 | odd | 4 | |||
1008.6.a.c.1.1 | 1 | 60.59 | even | 2 |