Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [90,6,Mod(1,90)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(90, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("90.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.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: | \(14.4345437832\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 90.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −118.000 | −0.910200 | −0.455100 | − | 0.890440i | \(-0.650397\pi\) | ||||
−0.455100 | + | 0.890440i | \(0.650397\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | −192.000 | −0.478431 | −0.239216 | − | 0.970966i | \(-0.576890\pi\) | ||||
−0.239216 | + | 0.970966i | \(0.576890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1106.00 | 1.81508 | 0.907542 | − | 0.419961i | \(-0.137956\pi\) | ||||
0.907542 | + | 0.419961i | \(0.137956\pi\) | |||||||
\(14\) | 472.000 | 0.643609 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −762.000 | −0.639488 | −0.319744 | − | 0.947504i | \(-0.603597\pi\) | ||||
−0.319744 | + | 0.947504i | \(0.603597\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2740.00 | −1.74127 | −0.870636 | − | 0.491928i | \(-0.836292\pi\) | ||||
−0.870636 | + | 0.491928i | \(0.836292\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 768.000 | 0.338302 | ||||||||
\(23\) | −1566.00 | −0.617266 | −0.308633 | − | 0.951181i | \(-0.599871\pi\) | ||||
−0.308633 | + | 0.951181i | \(0.599871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −4424.00 | −1.28346 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1888.00 | −0.455100 | ||||||||
\(29\) | −5910.00 | −1.30495 | −0.652473 | − | 0.757812i | \(-0.726268\pi\) | ||||
−0.652473 | + | 0.757812i | \(0.726268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6868.00 | −1.28359 | −0.641795 | − | 0.766877i | \(-0.721810\pi\) | ||||
−0.641795 | + | 0.766877i | \(0.721810\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3048.00 | 0.452187 | ||||||||
\(35\) | −2950.00 | −0.407054 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5518.00 | −0.662640 | −0.331320 | − | 0.943519i | \(-0.607494\pi\) | ||||
−0.331320 | + | 0.943519i | \(0.607494\pi\) | |||||||
\(38\) | 10960.0 | 1.23127 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | 378.000 | 0.0351182 | 0.0175591 | − | 0.999846i | \(-0.494410\pi\) | ||||
0.0175591 | + | 0.999846i | \(0.494410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2434.00 | −0.200747 | −0.100374 | − | 0.994950i | \(-0.532004\pi\) | ||||
−0.100374 | + | 0.994950i | \(0.532004\pi\) | |||||||
\(44\) | −3072.00 | −0.239216 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6264.00 | 0.436473 | ||||||||
\(47\) | −13122.0 | −0.866474 | −0.433237 | − | 0.901280i | \(-0.642629\pi\) | ||||
−0.433237 | + | 0.901280i | \(0.642629\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2883.00 | −0.171536 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 17696.0 | 0.907542 | ||||||||
\(53\) | 9174.00 | 0.448610 | 0.224305 | − | 0.974519i | \(-0.427989\pi\) | ||||
0.224305 | + | 0.974519i | \(0.427989\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4800.00 | −0.213961 | ||||||||
\(56\) | 7552.00 | 0.321804 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 23640.0 | 0.922736 | ||||||||
\(59\) | 34980.0 | 1.30825 | 0.654124 | − | 0.756388i | \(-0.273038\pi\) | ||||
0.654124 | + | 0.756388i | \(0.273038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9838.00 | −0.338518 | −0.169259 | − | 0.985572i | \(-0.554137\pi\) | ||||
−0.169259 | + | 0.985572i | \(0.554137\pi\) | |||||||
\(62\) | 27472.0 | 0.907635 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 27650.0 | 0.811730 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 33722.0 | 0.917754 | 0.458877 | − | 0.888500i | \(-0.348252\pi\) | ||||
0.458877 | + | 0.888500i | \(0.348252\pi\) | |||||||
\(68\) | −12192.0 | −0.319744 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11800.0 | 0.287831 | ||||||||
\(71\) | −70212.0 | −1.65297 | −0.826486 | − | 0.562957i | \(-0.809664\pi\) | ||||
−0.826486 | + | 0.562957i | \(0.809664\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 21986.0 | 0.482880 | 0.241440 | − | 0.970416i | \(-0.422380\pi\) | ||||
0.241440 | + | 0.970416i | \(0.422380\pi\) | |||||||
\(74\) | 22072.0 | 0.468557 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −43840.0 | −0.870636 | ||||||||
\(77\) | 22656.0 | 0.435468 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4520.00 | 0.0814837 | 0.0407418 | − | 0.999170i | \(-0.487028\pi\) | ||||
0.0407418 | + | 0.999170i | \(0.487028\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1512.00 | −0.0248323 | ||||||||
\(83\) | 109074. | 1.73790 | 0.868952 | − | 0.494896i | \(-0.164794\pi\) | ||||
0.868952 | + | 0.494896i | \(0.164794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19050.0 | −0.285988 | ||||||||
\(86\) | 9736.00 | 0.141950 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12288.0 | 0.169151 | ||||||||
\(89\) | −38490.0 | −0.515078 | −0.257539 | − | 0.966268i | \(-0.582912\pi\) | ||||
−0.257539 | + | 0.966268i | \(0.582912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −130508. | −1.65209 | ||||||||
\(92\) | −25056.0 | −0.308633 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 52488.0 | 0.612689 | ||||||||
\(95\) | −68500.0 | −0.778720 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1918.00 | −0.0206976 | −0.0103488 | − | 0.999946i | \(-0.503294\pi\) | ||||
−0.0103488 | + | 0.999946i | \(0.503294\pi\) | |||||||
\(98\) | 11532.0 | 0.121294 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −77622.0 | −0.757149 | −0.378575 | − | 0.925571i | \(-0.623586\pi\) | ||||
−0.378575 | + | 0.925571i | \(0.623586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −46714.0 | −0.433864 | −0.216932 | − | 0.976187i | \(-0.569605\pi\) | ||||
−0.216932 | + | 0.976187i | \(0.569605\pi\) | |||||||
\(104\) | −70784.0 | −0.641729 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −36696.0 | −0.317215 | ||||||||
\(107\) | 1038.00 | 0.00876472 | 0.00438236 | − | 0.999990i | \(-0.498605\pi\) | ||||
0.00438236 | + | 0.999990i | \(0.498605\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 206930. | 1.66823 | 0.834117 | − | 0.551587i | \(-0.185977\pi\) | ||||
0.834117 | + | 0.551587i | \(0.185977\pi\) | |||||||
\(110\) | 19200.0 | 0.151293 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −30208.0 | −0.227550 | ||||||||
\(113\) | −139386. | −1.02689 | −0.513444 | − | 0.858123i | \(-0.671631\pi\) | ||||
−0.513444 | + | 0.858123i | \(0.671631\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −39150.0 | −0.276050 | ||||||||
\(116\) | −94560.0 | −0.652473 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −139920. | −0.925070 | ||||||||
\(119\) | 89916.0 | 0.582062 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −124187. | −0.771104 | ||||||||
\(122\) | 39352.0 | 0.239369 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −109888. | −0.641795 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 299882. | 1.64984 | 0.824919 | − | 0.565252i | \(-0.191221\pi\) | ||||
0.824919 | + | 0.565252i | \(0.191221\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −110600. | −0.573980 | ||||||||
\(131\) | −7872.00 | −0.0400781 | −0.0200390 | − | 0.999799i | \(-0.506379\pi\) | ||||
−0.0200390 | + | 0.999799i | \(0.506379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 323320. | 1.58491 | ||||||||
\(134\) | −134888. | −0.648950 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 48768.0 | 0.226093 | ||||||||
\(137\) | 164238. | 0.747605 | 0.373803 | − | 0.927508i | \(-0.378054\pi\) | ||||
0.373803 | + | 0.927508i | \(0.378054\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −282100. | −1.23841 | −0.619207 | − | 0.785228i | \(-0.712546\pi\) | ||||
−0.619207 | + | 0.785228i | \(0.712546\pi\) | |||||||
\(140\) | −47200.0 | −0.203527 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 280848. | 1.16883 | ||||||||
\(143\) | −212352. | −0.868393 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −147750. | −0.583590 | ||||||||
\(146\) | −87944.0 | −0.341448 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −88288.0 | −0.331320 | ||||||||
\(149\) | 388950. | 1.43525 | 0.717626 | − | 0.696429i | \(-0.245229\pi\) | ||||
0.717626 | + | 0.696429i | \(0.245229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −97948.0 | −0.349585 | −0.174793 | − | 0.984605i | \(-0.555926\pi\) | ||||
−0.174793 | + | 0.984605i | \(0.555926\pi\) | |||||||
\(152\) | 175360. | 0.615633 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −90624.0 | −0.307923 | ||||||||
\(155\) | −171700. | −0.574039 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3718.00 | −0.0120382 | −0.00601908 | − | 0.999982i | \(-0.501916\pi\) | ||||
−0.00601908 | + | 0.999982i | \(0.501916\pi\) | |||||||
\(158\) | −18080.0 | −0.0576177 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | 184788. | 0.561835 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −43234.0 | −0.127455 | −0.0637274 | − | 0.997967i | \(-0.520299\pi\) | ||||
−0.0637274 | + | 0.997967i | \(0.520299\pi\) | |||||||
\(164\) | 6048.00 | 0.0175591 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −436296. | −1.22888 | ||||||||
\(167\) | −186522. | −0.517534 | −0.258767 | − | 0.965940i | \(-0.583316\pi\) | ||||
−0.258767 | + | 0.965940i | \(0.583316\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 851943. | 2.29453 | ||||||||
\(170\) | 76200.0 | 0.202224 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −38944.0 | −0.100374 | ||||||||
\(173\) | 374454. | 0.951225 | 0.475612 | − | 0.879655i | \(-0.342226\pi\) | ||||
0.475612 | + | 0.879655i | \(0.342226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −73750.0 | −0.182040 | ||||||||
\(176\) | −49152.0 | −0.119608 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 153960. | 0.364215 | ||||||||
\(179\) | −272100. | −0.634740 | −0.317370 | − | 0.948302i | \(-0.602800\pi\) | ||||
−0.317370 | + | 0.948302i | \(0.602800\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −75418.0 | −0.171111 | −0.0855556 | − | 0.996333i | \(-0.527267\pi\) | ||||
−0.0855556 | + | 0.996333i | \(0.527267\pi\) | |||||||
\(182\) | 522032. | 1.16820 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 100224. | 0.218236 | ||||||||
\(185\) | −137950. | −0.296341 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 146304. | 0.305951 | ||||||||
\(188\) | −209952. | −0.433237 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 274000. | 0.550638 | ||||||||
\(191\) | 356988. | 0.708060 | 0.354030 | − | 0.935234i | \(-0.384811\pi\) | ||||
0.354030 | + | 0.935234i | \(0.384811\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −438694. | −0.847751 | −0.423876 | − | 0.905720i | \(-0.639331\pi\) | ||||
−0.423876 | + | 0.905720i | \(0.639331\pi\) | |||||||
\(194\) | 7672.00 | 0.0146354 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −46128.0 | −0.0857678 | ||||||||
\(197\) | 156798. | 0.287856 | 0.143928 | − | 0.989588i | \(-0.454027\pi\) | ||||
0.143928 | + | 0.989588i | \(0.454027\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −162520. | −0.290920 | −0.145460 | − | 0.989364i | \(-0.546466\pi\) | ||||
−0.145460 | + | 0.989364i | \(0.546466\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 310488. | 0.535385 | ||||||||
\(203\) | 697380. | 1.18776 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9450.00 | 0.0157053 | ||||||||
\(206\) | 186856. | 0.306788 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 283136. | 0.453771 | ||||||||
\(209\) | 526080. | 0.833079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −181648. | −0.280882 | −0.140441 | − | 0.990089i | \(-0.544852\pi\) | ||||
−0.140441 | + | 0.990089i | \(0.544852\pi\) | |||||||
\(212\) | 146784. | 0.224305 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4152.00 | −0.00619759 | ||||||||
\(215\) | −60850.0 | −0.0897769 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 810424. | 1.16832 | ||||||||
\(218\) | −827720. | −1.17962 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −76800.0 | −0.106980 | ||||||||
\(221\) | −842772. | −1.16073 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −288274. | −0.388189 | −0.194095 | − | 0.980983i | \(-0.562177\pi\) | ||||
−0.194095 | + | 0.980983i | \(0.562177\pi\) | |||||||
\(224\) | 120832. | 0.160902 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 557544. | 0.726119 | ||||||||
\(227\) | −1.12552e6 | −1.44974 | −0.724869 | − | 0.688887i | \(-0.758100\pi\) | ||||
−0.724869 | + | 0.688887i | \(0.758100\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −415810. | −0.523970 | −0.261985 | − | 0.965072i | \(-0.584377\pi\) | ||||
−0.261985 | + | 0.965072i | \(0.584377\pi\) | |||||||
\(230\) | 156600. | 0.195197 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 378240. | 0.461368 | ||||||||
\(233\) | −770586. | −0.929889 | −0.464945 | − | 0.885340i | \(-0.653926\pi\) | ||||
−0.464945 | + | 0.885340i | \(0.653926\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −328050. | −0.387499 | ||||||||
\(236\) | 559680. | 0.654124 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −359664. | −0.411580 | ||||||||
\(239\) | 595320. | 0.674149 | 0.337074 | − | 0.941478i | \(-0.390563\pi\) | ||||
0.337074 | + | 0.941478i | \(0.390563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 273902. | 0.303775 | 0.151888 | − | 0.988398i | \(-0.451465\pi\) | ||||
0.151888 | + | 0.988398i | \(0.451465\pi\) | |||||||
\(242\) | 496748. | 0.545253 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −157408. | −0.169259 | ||||||||
\(245\) | −72075.0 | −0.0767131 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.03044e6 | −3.16055 | ||||||||
\(248\) | 439552. | 0.453817 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −850752. | −0.852351 | −0.426176 | − | 0.904640i | \(-0.640139\pi\) | ||||
−0.426176 | + | 0.904640i | \(0.640139\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 300672. | 0.295319 | ||||||||
\(254\) | −1.19953e6 | −1.16661 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −825402. | −0.779530 | −0.389765 | − | 0.920914i | \(-0.627444\pi\) | ||||
−0.389765 | + | 0.920914i | \(0.627444\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 651124. | 0.603135 | ||||||||
\(260\) | 442400. | 0.405865 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 31488.0 | 0.0283395 | ||||||||
\(263\) | −1.36465e6 | −1.21655 | −0.608276 | − | 0.793726i | \(-0.708139\pi\) | ||||
−0.608276 | + | 0.793726i | \(0.708139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 229350. | 0.200625 | ||||||||
\(266\) | −1.29328e6 | −1.12070 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 539552. | 0.458877 | ||||||||
\(269\) | 113310. | 0.0954745 | 0.0477373 | − | 0.998860i | \(-0.484799\pi\) | ||||
0.0477373 | + | 0.998860i | \(0.484799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −849628. | −0.702758 | −0.351379 | − | 0.936233i | \(-0.614287\pi\) | ||||
−0.351379 | + | 0.936233i | \(0.614287\pi\) | |||||||
\(272\) | −195072. | −0.159872 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −656952. | −0.528637 | ||||||||
\(275\) | −120000. | −0.0956862 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 438602. | 0.343456 | 0.171728 | − | 0.985144i | \(-0.445065\pi\) | ||||
0.171728 | + | 0.985144i | \(0.445065\pi\) | |||||||
\(278\) | 1.12840e6 | 0.875691 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 188800. | 0.143915 | ||||||||
\(281\) | 1.45670e6 | 1.10053 | 0.550267 | − | 0.834989i | \(-0.314526\pi\) | ||||
0.550267 | + | 0.834989i | \(0.314526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −120394. | −0.0893591 | −0.0446795 | − | 0.999001i | \(-0.514227\pi\) | ||||
−0.0446795 | + | 0.999001i | \(0.514227\pi\) | |||||||
\(284\) | −1.12339e6 | −0.826486 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 849408. | 0.614047 | ||||||||
\(287\) | −44604.0 | −0.0319646 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −839213. | −0.591055 | ||||||||
\(290\) | 591000. | 0.412660 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 351776. | 0.241440 | ||||||||
\(293\) | 2.64209e6 | 1.79796 | 0.898978 | − | 0.437993i | \(-0.144311\pi\) | ||||
0.898978 | + | 0.437993i | \(0.144311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 874500. | 0.585066 | ||||||||
\(296\) | 353152. | 0.234278 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.55580e6 | −1.01488 | ||||||||
\(299\) | −1.73200e6 | −1.12039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 287212. | 0.182720 | ||||||||
\(302\) | 391792. | 0.247194 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −701440. | −0.435318 | ||||||||
\(305\) | −245950. | −0.151390 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.44756e6 | −0.876577 | −0.438288 | − | 0.898834i | \(-0.644415\pi\) | ||||
−0.438288 | + | 0.898834i | \(0.644415\pi\) | |||||||
\(308\) | 362496. | 0.217734 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 686800. | 0.405907 | ||||||||
\(311\) | 928068. | 0.544100 | 0.272050 | − | 0.962283i | \(-0.412298\pi\) | ||||
0.272050 | + | 0.962283i | \(0.412298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.29563e6 | 1.32446 | 0.662232 | − | 0.749299i | \(-0.269609\pi\) | ||||
0.662232 | + | 0.749299i | \(0.269609\pi\) | |||||||
\(314\) | 14872.0 | 0.00851227 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 72320.0 | 0.0407418 | ||||||||
\(317\) | −2.73652e6 | −1.52950 | −0.764752 | − | 0.644324i | \(-0.777139\pi\) | ||||
−0.764752 | + | 0.644324i | \(0.777139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.13472e6 | 0.624327 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −739152. | −0.397278 | ||||||||
\(323\) | 2.08788e6 | 1.11352 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 691250. | 0.363017 | ||||||||
\(326\) | 172936. | 0.0901242 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −24192.0 | −0.0124162 | ||||||||
\(329\) | 1.54840e6 | 0.788665 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.81879e6 | 1.91583 | 0.957913 | − | 0.287059i | \(-0.0926776\pi\) | ||||
0.957913 | + | 0.287059i | \(0.0926776\pi\) | |||||||
\(332\) | 1.74518e6 | 0.868952 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 746088. | 0.365952 | ||||||||
\(335\) | 843050. | 0.410432 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.21088e6 | −1.06045 | −0.530225 | − | 0.847857i | \(-0.677892\pi\) | ||||
−0.530225 | + | 0.847857i | \(0.677892\pi\) | |||||||
\(338\) | −3.40777e6 | −1.62248 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −304800. | −0.142994 | ||||||||
\(341\) | 1.31866e6 | 0.614109 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.32342e6 | 1.06633 | ||||||||
\(344\) | 155776. | 0.0709748 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.49782e6 | −0.672618 | ||||||||
\(347\) | 2.32724e6 | 1.03757 | 0.518785 | − | 0.854905i | \(-0.326385\pi\) | ||||
0.518785 | + | 0.854905i | \(0.326385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −311290. | −0.136805 | −0.0684024 | − | 0.997658i | \(-0.521790\pi\) | ||||
−0.0684024 | + | 0.997658i | \(0.521790\pi\) | |||||||
\(350\) | 295000. | 0.128722 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 196608. | 0.0845755 | ||||||||
\(353\) | 3.08657e6 | 1.31838 | 0.659189 | − | 0.751977i | \(-0.270900\pi\) | ||||
0.659189 | + | 0.751977i | \(0.270900\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.75530e6 | −0.739232 | ||||||||
\(356\) | −615840. | −0.257539 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.08840e6 | 0.448829 | ||||||||
\(359\) | 3.53076e6 | 1.44588 | 0.722940 | − | 0.690911i | \(-0.242790\pi\) | ||||
0.722940 | + | 0.690911i | \(0.242790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.03150e6 | 2.03203 | ||||||||
\(362\) | 301672. | 0.120994 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.08813e6 | −0.826045 | ||||||||
\(365\) | 549650. | 0.215950 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35762.0 | 0.0138598 | 0.00692989 | − | 0.999976i | \(-0.497794\pi\) | ||||
0.00692989 | + | 0.999976i | \(0.497794\pi\) | |||||||
\(368\) | −400896. | −0.154316 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 551800. | 0.209545 | ||||||||
\(371\) | −1.08253e6 | −0.408325 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.71525e6 | −0.638346 | −0.319173 | − | 0.947696i | \(-0.603405\pi\) | ||||
−0.319173 | + | 0.947696i | \(0.603405\pi\) | |||||||
\(374\) | −585216. | −0.216340 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 839808. | 0.306345 | ||||||||
\(377\) | −6.53646e6 | −2.36859 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.10174e6 | −1.10919 | −0.554597 | − | 0.832119i | \(-0.687127\pi\) | ||||
−0.554597 | + | 0.832119i | \(0.687127\pi\) | |||||||
\(380\) | −1.09600e6 | −0.389360 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.42795e6 | −0.500674 | ||||||||
\(383\) | −5.31949e6 | −1.85299 | −0.926494 | − | 0.376309i | \(-0.877193\pi\) | ||||
−0.926494 | + | 0.376309i | \(0.877193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 566400. | 0.194747 | ||||||||
\(386\) | 1.75478e6 | 0.599451 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −30688.0 | −0.0103488 | ||||||||
\(389\) | −1.16145e6 | −0.389158 | −0.194579 | − | 0.980887i | \(-0.562334\pi\) | ||||
−0.194579 | + | 0.980887i | \(0.562334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.19329e6 | 0.394734 | ||||||||
\(392\) | 184512. | 0.0606470 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −627192. | −0.203545 | ||||||||
\(395\) | 113000. | 0.0364406 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 628562. | 0.200157 | 0.100079 | − | 0.994980i | \(-0.468091\pi\) | ||||
0.100079 | + | 0.994980i | \(0.468091\pi\) | |||||||
\(398\) | 650080. | 0.205712 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 2.72432e6 | 0.846052 | 0.423026 | − | 0.906118i | \(-0.360968\pi\) | ||||
0.423026 | + | 0.906118i | \(0.360968\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.59601e6 | −2.32982 | ||||||||
\(404\) | −1.24195e6 | −0.378575 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.78952e6 | −0.839875 | ||||||||
\(407\) | 1.05946e6 | 0.317027 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.78019e6 | 0.526209 | 0.263104 | − | 0.964767i | \(-0.415254\pi\) | ||||
0.263104 | + | 0.964767i | \(0.415254\pi\) | |||||||
\(410\) | −37800.0 | −0.0111053 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −747424. | −0.216932 | ||||||||
\(413\) | −4.12764e6 | −1.19077 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.72685e6 | 0.777215 | ||||||||
\(416\) | −1.13254e6 | −0.320865 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.10432e6 | −0.589076 | ||||||||
\(419\) | −650580. | −0.181036 | −0.0905181 | − | 0.995895i | \(-0.528852\pi\) | ||||
−0.0905181 | + | 0.995895i | \(0.528852\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.54060e6 | −0.973579 | −0.486790 | − | 0.873519i | \(-0.661832\pi\) | ||||
−0.486790 | + | 0.873519i | \(0.661832\pi\) | |||||||
\(422\) | 726592. | 0.198614 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −587136. | −0.158608 | ||||||||
\(425\) | −476250. | −0.127898 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.16088e6 | 0.308119 | ||||||||
\(428\) | 16608.0 | 0.00438236 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 243400. | 0.0634818 | ||||||||
\(431\) | 548748. | 0.142292 | 0.0711459 | − | 0.997466i | \(-0.477334\pi\) | ||||
0.0711459 | + | 0.997466i | \(0.477334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.49241e6 | −0.382534 | −0.191267 | − | 0.981538i | \(-0.561260\pi\) | ||||
−0.191267 | + | 0.981538i | \(0.561260\pi\) | |||||||
\(434\) | −3.24170e6 | −0.826129 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.31088e6 | 0.834117 | ||||||||
\(437\) | 4.29084e6 | 1.07483 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.86212e6 | 1.20411 | 0.602053 | − | 0.798456i | \(-0.294350\pi\) | ||||
0.602053 | + | 0.798456i | \(0.294350\pi\) | |||||||
\(440\) | 307200. | 0.0756466 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.37109e6 | 0.820757 | ||||||||
\(443\) | 1.86155e6 | 0.450678 | 0.225339 | − | 0.974280i | \(-0.427651\pi\) | ||||
0.225339 | + | 0.974280i | \(0.427651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −962250. | −0.230350 | ||||||||
\(446\) | 1.15310e6 | 0.274491 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −483328. | −0.113775 | ||||||||
\(449\) | −3.73719e6 | −0.874841 | −0.437421 | − | 0.899257i | \(-0.644108\pi\) | ||||
−0.437421 | + | 0.899257i | \(0.644108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −72576.0 | −0.0168016 | ||||||||
\(452\) | −2.23018e6 | −0.513444 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.50209e6 | 1.02512 | ||||||||
\(455\) | −3.26270e6 | −0.738837 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.48276e6 | −1.45201 | −0.726005 | − | 0.687690i | \(-0.758625\pi\) | ||||
−0.726005 | + | 0.687690i | \(0.758625\pi\) | |||||||
\(458\) | 1.66324e6 | 0.370503 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −626400. | −0.138025 | ||||||||
\(461\) | −1.50910e6 | −0.330724 | −0.165362 | − | 0.986233i | \(-0.552879\pi\) | ||||
−0.165362 | + | 0.986233i | \(0.552879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.68401e6 | 1.88264 | 0.941321 | − | 0.337513i | \(-0.109586\pi\) | ||||
0.941321 | + | 0.337513i | \(0.109586\pi\) | |||||||
\(464\) | −1.51296e6 | −0.326236 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.08234e6 | 0.657531 | ||||||||
\(467\) | −6.96412e6 | −1.47766 | −0.738829 | − | 0.673893i | \(-0.764621\pi\) | ||||
−0.738829 | + | 0.673893i | \(0.764621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.97920e6 | −0.835340 | ||||||||
\(470\) | 1.31220e6 | 0.274003 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.23872e6 | −0.462535 | ||||||||
\(473\) | 467328. | 0.0960437 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.71250e6 | −0.348254 | ||||||||
\(476\) | 1.43866e6 | 0.291031 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.38128e6 | −0.476695 | ||||||||
\(479\) | 5.51052e6 | 1.09737 | 0.548686 | − | 0.836029i | \(-0.315128\pi\) | ||||
0.548686 | + | 0.836029i | \(0.315128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.10291e6 | −1.20275 | ||||||||
\(482\) | −1.09561e6 | −0.214802 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.98699e6 | −0.385552 | ||||||||
\(485\) | −47950.0 | −0.00925623 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.51808e6 | 1.05430 | 0.527152 | − | 0.849771i | \(-0.323260\pi\) | ||||
0.527152 | + | 0.849771i | \(0.323260\pi\) | |||||||
\(488\) | 629632. | 0.119684 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 288300. | 0.0542443 | ||||||||
\(491\) | 1.51277e6 | 0.283184 | 0.141592 | − | 0.989925i | \(-0.454778\pi\) | ||||
0.141592 | + | 0.989925i | \(0.454778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.50342e6 | 0.834498 | ||||||||
\(494\) | 1.21218e7 | 2.23485 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.75821e6 | −0.320897 | ||||||||
\(497\) | 8.28502e6 | 1.50454 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.93042e6 | −0.347057 | −0.173528 | − | 0.984829i | \(-0.555517\pi\) | ||||
−0.173528 | + | 0.984829i | \(0.555517\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.40301e6 | 0.602703 | ||||||||
\(503\) | −6.73105e6 | −1.18621 | −0.593106 | − | 0.805124i | \(-0.702099\pi\) | ||||
−0.593106 | + | 0.805124i | \(0.702099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.94055e6 | −0.338607 | ||||||||
\(506\) | −1.20269e6 | −0.208822 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.79811e6 | 0.824919 | ||||||||
\(509\) | 556650. | 0.0952331 | 0.0476165 | − | 0.998866i | \(-0.484837\pi\) | ||||
0.0476165 | + | 0.998866i | \(0.484837\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.59435e6 | −0.439517 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.30161e6 | 0.551211 | ||||||||
\(515\) | −1.16785e6 | −0.194030 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.51942e6 | 0.414548 | ||||||||
\(518\) | −2.60450e6 | −0.426481 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.76960e6 | −0.286990 | ||||||||
\(521\) | −1.01110e7 | −1.63192 | −0.815962 | − | 0.578106i | \(-0.803792\pi\) | ||||
−0.815962 | + | 0.578106i | \(0.803792\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.03719e6 | −1.12498 | −0.562491 | − | 0.826804i | \(-0.690157\pi\) | ||||
−0.562491 | + | 0.826804i | \(0.690157\pi\) | |||||||
\(524\) | −125952. | −0.0200390 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.45858e6 | 0.860232 | ||||||||
\(527\) | 5.23342e6 | 0.820840 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.98399e6 | −0.618983 | ||||||||
\(530\) | −917400. | −0.141863 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.17312e6 | 0.792453 | ||||||||
\(533\) | 418068. | 0.0637425 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25950.0 | 0.00391970 | ||||||||
\(536\) | −2.15821e6 | −0.324475 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −453240. | −0.0675107 | ||||||||
\(539\) | 553536. | 0.0820680 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.23114e6 | −0.621533 | −0.310766 | − | 0.950486i | \(-0.600586\pi\) | ||||
−0.310766 | + | 0.950486i | \(0.600586\pi\) | |||||||
\(542\) | 3.39851e6 | 0.496925 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 780288. | 0.113047 | ||||||||
\(545\) | 5.17325e6 | 0.746057 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.44024e6 | 0.634510 | 0.317255 | − | 0.948340i | \(-0.397239\pi\) | ||||
0.317255 | + | 0.948340i | \(0.397239\pi\) | |||||||
\(548\) | 2.62781e6 | 0.373803 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 480000. | 0.0676604 | ||||||||
\(551\) | 1.61934e7 | 2.27227 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −533360. | −0.0741665 | ||||||||
\(554\) | −1.75441e6 | −0.242860 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.51360e6 | −0.619207 | ||||||||
\(557\) | 9.01448e6 | 1.23113 | 0.615563 | − | 0.788088i | \(-0.288929\pi\) | ||||
0.615563 | + | 0.788088i | \(0.288929\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.69200e6 | −0.364373 | ||||||||
\(560\) | −755200. | −0.101763 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.82679e6 | −0.778196 | ||||||||
\(563\) | 9.81287e6 | 1.30474 | 0.652372 | − | 0.757899i | \(-0.273774\pi\) | ||||
0.652372 | + | 0.757899i | \(0.273774\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.48465e6 | −0.459238 | ||||||||
\(566\) | 481576. | 0.0631864 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.49357e6 | 0.584414 | ||||||||
\(569\) | −1.33152e7 | −1.72412 | −0.862061 | − | 0.506804i | \(-0.830827\pi\) | ||||
−0.862061 | + | 0.506804i | \(0.830827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.95895e6 | 1.27827 | 0.639136 | − | 0.769094i | \(-0.279292\pi\) | ||||
0.639136 | + | 0.769094i | \(0.279292\pi\) | |||||||
\(572\) | −3.39763e6 | −0.434196 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 178416. | 0.0226024 | ||||||||
\(575\) | −978750. | −0.123453 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.50372e6 | 0.563160 | 0.281580 | − | 0.959538i | \(-0.409141\pi\) | ||||
0.281580 | + | 0.959538i | \(0.409141\pi\) | |||||||
\(578\) | 3.35685e6 | 0.417939 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.36400e6 | −0.291795 | ||||||||
\(581\) | −1.28707e7 | −1.58184 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.76141e6 | −0.214629 | ||||||||
\(584\) | −1.40710e6 | −0.170724 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.05684e7 | −1.27135 | ||||||||
\(587\) | −625842. | −0.0749669 | −0.0374834 | − | 0.999297i | \(-0.511934\pi\) | ||||
−0.0374834 | + | 0.999297i | \(0.511934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.88183e7 | 2.23508 | ||||||||
\(590\) | −3.49800e6 | −0.413704 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.41261e6 | −0.165660 | ||||||||
\(593\) | 2.50385e6 | 0.292397 | 0.146198 | − | 0.989255i | \(-0.453296\pi\) | ||||
0.146198 | + | 0.989255i | \(0.453296\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.24790e6 | 0.260306 | ||||||||
\(596\) | 6.22320e6 | 0.717626 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.92798e6 | 0.792235 | ||||||||
\(599\) | 756480. | 0.0861451 | 0.0430725 | − | 0.999072i | \(-0.486285\pi\) | ||||
0.0430725 | + | 0.999072i | \(0.486285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.38565e7 | −1.56483 | −0.782413 | − | 0.622760i | \(-0.786011\pi\) | ||||
−0.782413 | + | 0.622760i | \(0.786011\pi\) | |||||||
\(602\) | −1.14885e6 | −0.129203 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.56717e6 | −0.174793 | ||||||||
\(605\) | −3.10468e6 | −0.344848 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.13772e7 | 1.25333 | 0.626663 | − | 0.779291i | \(-0.284420\pi\) | ||||
0.626663 | + | 0.779291i | \(0.284420\pi\) | |||||||
\(608\) | 2.80576e6 | 0.307816 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 983800. | 0.107049 | ||||||||
\(611\) | −1.45129e7 | −1.57272 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.00161e6 | −0.752570 | −0.376285 | − | 0.926504i | \(-0.622799\pi\) | ||||
−0.376285 | + | 0.926504i | \(0.622799\pi\) | |||||||
\(614\) | 5.79023e6 | 0.619833 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.44998e6 | −0.153961 | ||||||||
\(617\) | −7.90300e6 | −0.835755 | −0.417878 | − | 0.908503i | \(-0.637226\pi\) | ||||
−0.417878 | + | 0.908503i | \(0.637226\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.02362e6 | 0.422076 | 0.211038 | − | 0.977478i | \(-0.432316\pi\) | ||||
0.211038 | + | 0.977478i | \(0.432316\pi\) | |||||||
\(620\) | −2.74720e6 | −0.287019 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.71227e6 | −0.384737 | ||||||||
\(623\) | 4.54182e6 | 0.468824 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −9.18250e6 | −0.936538 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −59488.0 | −0.00601908 | ||||||||
\(629\) | 4.20472e6 | 0.423750 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00227e7 | −1.00210 | −0.501049 | − | 0.865419i | \(-0.667052\pi\) | ||||
−0.501049 | + | 0.865419i | \(0.667052\pi\) | |||||||
\(632\) | −289280. | −0.0288088 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.09461e7 | 1.08152 | ||||||||
\(635\) | 7.49705e6 | 0.737830 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.18860e6 | −0.311352 | ||||||||
\(638\) | −4.53888e6 | −0.441466 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | −6.37390e6 | −0.612718 | −0.306359 | − | 0.951916i | \(-0.599111\pi\) | ||||
−0.306359 | + | 0.951916i | \(0.599111\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.00457e6 | 0.477352 | 0.238676 | − | 0.971099i | \(-0.423287\pi\) | ||||
0.238676 | + | 0.971099i | \(0.423287\pi\) | |||||||
\(644\) | 2.95661e6 | 0.280918 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.35152e6 | −0.787380 | ||||||||
\(647\) | 8.71928e6 | 0.818879 | 0.409440 | − | 0.912337i | \(-0.365724\pi\) | ||||
0.409440 | + | 0.912337i | \(0.365724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.71616e6 | −0.625906 | ||||||||
\(650\) | −2.76500e6 | −0.256692 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −691744. | −0.0637274 | ||||||||
\(653\) | 1.58477e6 | 0.145440 | 0.0727201 | − | 0.997352i | \(-0.476832\pi\) | ||||
0.0727201 | + | 0.997352i | \(0.476832\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −196800. | −0.0179235 | ||||||||
\(656\) | 96768.0 | 0.00877955 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.19358e6 | −0.557670 | ||||||||
\(659\) | −1.26410e7 | −1.13388 | −0.566940 | − | 0.823759i | \(-0.691873\pi\) | ||||
−0.566940 | + | 0.823759i | \(0.691873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.61572e6 | −0.321878 | −0.160939 | − | 0.986964i | \(-0.551452\pi\) | ||||
−0.160939 | + | 0.986964i | \(0.551452\pi\) | |||||||
\(662\) | −1.52752e7 | −1.35469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.98074e6 | −0.614442 | ||||||||
\(665\) | 8.08300e6 | 0.708791 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.25506e6 | 0.805498 | ||||||||
\(668\) | −2.98435e6 | −0.258767 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.37220e6 | −0.290219 | ||||||||
\(671\) | 1.88890e6 | 0.161958 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.11313e7 | 0.947349 | 0.473675 | − | 0.880700i | \(-0.342927\pi\) | ||||
0.473675 | + | 0.880700i | \(0.342927\pi\) | |||||||
\(674\) | 8.84351e6 | 0.749851 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.36311e7 | 1.14727 | ||||||||
\(677\) | 235518. | 0.0197493 | 0.00987467 | − | 0.999951i | \(-0.496857\pi\) | ||||
0.00987467 | + | 0.999951i | \(0.496857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 226324. | 0.0188389 | ||||||||
\(680\) | 1.21920e6 | 0.101112 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.27462e6 | −0.434241 | ||||||||
\(683\) | −2.05830e7 | −1.68833 | −0.844164 | − | 0.536084i | \(-0.819903\pi\) | ||||
−0.844164 | + | 0.536084i | \(0.819903\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.10595e6 | 0.334339 | ||||||||
\(686\) | −9.29368e6 | −0.754011 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −623104. | −0.0501868 | ||||||||
\(689\) | 1.01464e7 | 0.814265 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.54825e6 | −0.760727 | −0.380363 | − | 0.924837i | \(-0.624201\pi\) | ||||
−0.380363 | + | 0.924837i | \(0.624201\pi\) | |||||||
\(692\) | 5.99126e6 | 0.475612 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.30895e6 | −0.733672 | ||||||||
\(695\) | −7.05250e6 | −0.553836 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −288036. | −0.0224577 | ||||||||
\(698\) | 1.24516e6 | 0.0967357 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.18000e6 | −0.0910200 | ||||||||
\(701\) | −1.29304e6 | −0.0993843 | −0.0496921 | − | 0.998765i | \(-0.515824\pi\) | ||||
−0.0496921 | + | 0.998765i | \(0.515824\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.51193e7 | 1.15384 | ||||||||
\(704\) | −786432. | −0.0598039 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.23463e7 | −0.932234 | ||||||||
\(707\) | 9.15940e6 | 0.689157 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.12720e7 | −1.58926 | −0.794628 | − | 0.607097i | \(-0.792334\pi\) | ||||
−0.794628 | + | 0.607097i | \(0.792334\pi\) | |||||||
\(710\) | 7.02120e6 | 0.522716 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.46336e6 | 0.182108 | ||||||||
\(713\) | 1.07553e7 | 0.792316 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.30880e6 | −0.388357 | ||||||||
\(716\) | −4.35360e6 | −0.317370 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.41230e7 | −1.02239 | ||||||||
\(719\) | −8.31732e6 | −0.600014 | −0.300007 | − | 0.953937i | \(-0.596989\pi\) | ||||
−0.300007 | + | 0.953937i | \(0.596989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.51225e6 | 0.394903 | ||||||||
\(722\) | −2.01260e7 | −1.43686 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.20669e6 | −0.0855556 | ||||||||
\(725\) | −3.69375e6 | −0.260989 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.36740e6 | −0.306469 | −0.153235 | − | 0.988190i | \(-0.548969\pi\) | ||||
−0.153235 | + | 0.988190i | \(0.548969\pi\) | |||||||
\(728\) | 8.35251e6 | 0.584102 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.19860e6 | −0.152700 | ||||||||
\(731\) | 1.85471e6 | 0.128375 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.05645e6 | −0.278860 | −0.139430 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139430 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(734\) | −143048. | −0.00980035 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.60358e6 | 0.109118 | ||||||||
\(737\) | −6.47462e6 | −0.439082 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 768260. | 0.0517484 | 0.0258742 | − | 0.999665i | \(-0.491763\pi\) | ||||
0.0258742 | + | 0.999665i | \(0.491763\pi\) | |||||||
\(740\) | −2.20720e6 | −0.148171 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.33013e6 | 0.288729 | ||||||||
\(743\) | −6.18781e6 | −0.411211 | −0.205605 | − | 0.978635i | \(-0.565916\pi\) | ||||
−0.205605 | + | 0.978635i | \(0.565916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.72375e6 | 0.641864 | ||||||||
\(746\) | 6.86102e6 | 0.451379 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.34086e6 | 0.152976 | ||||||||
\(749\) | −122484. | −0.00797765 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.81698e7 | 1.17557 | 0.587787 | − | 0.809016i | \(-0.299999\pi\) | ||||
0.587787 | + | 0.809016i | \(0.299999\pi\) | |||||||
\(752\) | −3.35923e6 | −0.216618 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.61458e7 | 1.67484 | ||||||||
\(755\) | −2.44870e6 | −0.156339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.93494e7 | 1.22724 | 0.613618 | − | 0.789603i | \(-0.289714\pi\) | ||||
0.613618 | + | 0.789603i | \(0.289714\pi\) | |||||||
\(758\) | 1.24070e7 | 0.784318 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.38400e6 | 0.275319 | ||||||||
\(761\) | 3.01992e7 | 1.89031 | 0.945155 | − | 0.326621i | \(-0.105910\pi\) | ||||
0.945155 | + | 0.326621i | \(0.105910\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.44177e7 | −1.51843 | ||||||||
\(764\) | 5.71181e6 | 0.354030 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.12779e7 | 1.31026 | ||||||||
\(767\) | 3.86879e7 | 2.37458 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.15854e7 | 1.31627 | 0.658134 | − | 0.752901i | \(-0.271346\pi\) | ||||
0.658134 | + | 0.752901i | \(0.271346\pi\) | |||||||
\(770\) | −2.26560e6 | −0.137707 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.01910e6 | −0.423876 | ||||||||
\(773\) | −3.90895e6 | −0.235294 | −0.117647 | − | 0.993055i | \(-0.537535\pi\) | ||||
−0.117647 | + | 0.993055i | \(0.537535\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.29250e6 | −0.256718 | ||||||||
\(776\) | 122752. | 0.00731769 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.64580e6 | 0.275177 | ||||||||
\(779\) | −1.03572e6 | −0.0611503 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.34807e7 | 0.790833 | ||||||||
\(782\) | −4.77317e6 | −0.279119 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −738048. | −0.0428839 | ||||||||
\(785\) | −92950.0 | −0.00538363 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.65082e7 | −1.52561 | −0.762806 | − | 0.646628i | \(-0.776179\pi\) | ||||
−0.762806 | + | 0.646628i | \(0.776179\pi\) | |||||||
\(788\) | 2.50877e6 | 0.143928 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −452000. | −0.0257674 | ||||||||
\(791\) | 1.64475e7 | 0.934674 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.08808e7 | −0.614439 | ||||||||
\(794\) | −2.51425e6 | −0.141533 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.60032e6 | −0.145460 | ||||||||
\(797\) | −1.07940e7 | −0.601919 | −0.300960 | − | 0.953637i | \(-0.597307\pi\) | ||||
−0.300960 | + | 0.953637i | \(0.597307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.99896e6 | 0.554100 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.08973e7 | −0.598249 | ||||||||
\(803\) | −4.22131e6 | −0.231025 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.61970e6 | 0.251260 | ||||||||
\(806\) | 3.03840e7 | 1.64743 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.96781e6 | 0.267693 | ||||||||
\(809\) | 1.11446e7 | 0.598675 | 0.299338 | − | 0.954147i | \(-0.403234\pi\) | ||||
0.299338 | + | 0.954147i | \(0.403234\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.14866e7 | −0.613253 | −0.306626 | − | 0.951830i | \(-0.599200\pi\) | ||||
−0.306626 | + | 0.951830i | \(0.599200\pi\) | |||||||
\(812\) | 1.11581e7 | 0.593881 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.23782e6 | −0.224172 | ||||||||
\(815\) | −1.08085e6 | −0.0569995 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.66916e6 | 0.349555 | ||||||||
\(818\) | −7.12076e6 | −0.372086 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 151200. | 0.00785267 | ||||||||
\(821\) | −3.04347e7 | −1.57584 | −0.787918 | − | 0.615781i | \(-0.788841\pi\) | ||||
−0.787918 | + | 0.615781i | \(0.788841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.09773e6 | 0.210884 | 0.105442 | − | 0.994425i | \(-0.466374\pi\) | ||||
0.105442 | + | 0.994425i | \(0.466374\pi\) | |||||||
\(824\) | 2.98970e6 | 0.153394 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.65106e7 | 0.841999 | ||||||||
\(827\) | 1.70652e7 | 0.867654 | 0.433827 | − | 0.900996i | \(-0.357163\pi\) | ||||
0.433827 | + | 0.900996i | \(0.357163\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.47617e7 | −1.25139 | −0.625697 | − | 0.780066i | \(-0.715185\pi\) | ||||
−0.625697 | + | 0.780066i | \(0.715185\pi\) | |||||||
\(830\) | −1.09074e7 | −0.549574 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.53018e6 | 0.226886 | ||||||||
\(833\) | 2.19685e6 | 0.109695 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.66305e6 | −0.231448 | ||||||||
\(836\) | 8.41728e6 | 0.416539 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.60232e6 | 0.128012 | ||||||||
\(839\) | −3.16529e7 | −1.55242 | −0.776208 | − | 0.630476i | \(-0.782860\pi\) | ||||
−0.776208 | + | 0.630476i | \(0.782860\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.44170e7 | 0.702884 | ||||||||
\(842\) | 1.41624e7 | 0.688425 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.90637e6 | −0.140441 | ||||||||
\(845\) | 2.12986e7 | 1.02615 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.46541e7 | 0.701859 | ||||||||
\(848\) | 2.34854e6 | 0.112153 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.90500e6 | 0.0904373 | ||||||||
\(851\) | 8.64119e6 | 0.409025 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.82671e7 | 1.33017 | 0.665087 | − | 0.746765i | \(-0.268394\pi\) | ||||
0.665087 | + | 0.746765i | \(0.268394\pi\) | |||||||
\(854\) | −4.64354e6 | −0.217873 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −66432.0 | −0.00309880 | ||||||||
\(857\) | −2.60870e7 | −1.21331 | −0.606655 | − | 0.794966i | \(-0.707489\pi\) | ||||
−0.606655 | + | 0.794966i | \(0.707489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.38111e7 | −1.56342 | −0.781710 | − | 0.623642i | \(-0.785652\pi\) | ||||
−0.781710 | + | 0.623642i | \(0.785652\pi\) | |||||||
\(860\) | −973600. | −0.0448884 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.19499e6 | −0.100615 | ||||||||
\(863\) | −2.22817e7 | −1.01841 | −0.509204 | − | 0.860646i | \(-0.670060\pi\) | ||||
−0.509204 | + | 0.860646i | \(0.670060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.36135e6 | 0.425401 | ||||||||
\(866\) | 5.96966e6 | 0.270492 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.29668e7 | 0.584162 | ||||||||
\(869\) | −867840. | −0.0389843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.72965e7 | 1.66580 | ||||||||
\(872\) | −1.32435e7 | −0.589810 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.71634e7 | −0.760018 | ||||||||
\(875\) | −1.84375e6 | −0.0814108 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.46748e7 | −1.52235 | −0.761177 | − | 0.648545i | \(-0.775378\pi\) | ||||
−0.761177 | + | 0.648545i | \(0.775378\pi\) | |||||||
\(878\) | −1.94485e7 | −0.851431 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.22880e6 | −0.0534902 | ||||||||
\(881\) | −1.42603e7 | −0.618998 | −0.309499 | − | 0.950900i | \(-0.600161\pi\) | ||||
−0.309499 | + | 0.950900i | \(0.600161\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.75177e7 | −1.61933 | −0.809663 | − | 0.586895i | \(-0.800350\pi\) | ||||
−0.809663 | + | 0.586895i | \(0.800350\pi\) | |||||||
\(884\) | −1.34844e7 | −0.580363 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.44622e6 | −0.318677 | ||||||||
\(887\) | −4.07657e7 | −1.73975 | −0.869873 | − | 0.493275i | \(-0.835800\pi\) | ||||
−0.869873 | + | 0.493275i | \(0.835800\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.53861e7 | −1.50168 | ||||||||
\(890\) | 3.84900e6 | 0.162882 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.61238e6 | −0.194095 | ||||||||
\(893\) | 3.59543e7 | 1.50877 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.80250e6 | −0.283864 | ||||||||
\(896\) | 1.93331e6 | 0.0804511 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.49488e7 | 0.618606 | ||||||||
\(899\) | 4.05899e7 | 1.67501 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.99059e6 | −0.286881 | ||||||||
\(902\) | 290304. | 0.0118806 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.92070e6 | 0.363060 | ||||||||
\(905\) | −1.88545e6 | −0.0765233 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.57116e7 | −1.44142 | −0.720712 | − | 0.693235i | \(-0.756185\pi\) | ||||
−0.720712 | + | 0.693235i | \(0.756185\pi\) | |||||||
\(908\) | −1.80084e7 | −0.724869 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.30508e7 | 0.522437 | ||||||||
\(911\) | 2.11389e7 | 0.843893 | 0.421947 | − | 0.906621i | \(-0.361347\pi\) | ||||
0.421947 | + | 0.906621i | \(0.361347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.09422e7 | −0.831468 | ||||||||
\(914\) | 2.59310e7 | 1.02673 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.65296e6 | −0.261985 | ||||||||
\(917\) | 928896. | 0.0364791 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.85996e7 | 0.726465 | 0.363233 | − | 0.931698i | \(-0.381673\pi\) | ||||
0.363233 | + | 0.931698i | \(0.381673\pi\) | |||||||
\(920\) | 2.50560e6 | 0.0975983 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.03641e6 | 0.233857 | ||||||||
\(923\) | −7.76545e7 | −3.00028 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.44875e6 | −0.132528 | ||||||||
\(926\) | −3.47360e7 | −1.33123 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.05184e6 | 0.230684 | ||||||||
\(929\) | −4.45110e7 | −1.69211 | −0.846055 | − | 0.533096i | \(-0.821028\pi\) | ||||
−0.846055 | + | 0.533096i | \(0.821028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.89942e6 | 0.298690 | ||||||||
\(932\) | −1.23294e7 | −0.464945 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.78565e7 | 1.04486 | ||||||||
\(935\) | 3.65760e6 | 0.136826 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.19419e7 | −0.816441 | −0.408221 | − | 0.912883i | \(-0.633851\pi\) | ||||
−0.408221 | + | 0.912883i | \(0.633851\pi\) | |||||||
\(938\) | 1.59168e7 | 0.590675 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.24880e6 | −0.193749 | ||||||||
\(941\) | 7.77722e6 | 0.286319 | 0.143160 | − | 0.989700i | \(-0.454274\pi\) | ||||
0.143160 | + | 0.989700i | \(0.454274\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −591948. | −0.0216773 | ||||||||
\(944\) | 8.95488e6 | 0.327062 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.86931e6 | −0.0679132 | ||||||||
\(947\) | −3.17199e7 | −1.14936 | −0.574681 | − | 0.818378i | \(-0.694874\pi\) | ||||
−0.574681 | + | 0.818378i | \(0.694874\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.43165e7 | 0.876468 | ||||||||
\(950\) | 6.85000e6 | 0.246253 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.75462e6 | −0.205790 | ||||||||
\(953\) | 5.60285e6 | 0.199838 | 0.0999188 | − | 0.994996i | \(-0.468142\pi\) | ||||
0.0999188 | + | 0.994996i | \(0.468142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.92470e6 | 0.316654 | ||||||||
\(956\) | 9.52512e6 | 0.337074 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.20421e7 | −0.775959 | ||||||||
\(959\) | −1.93801e7 | −0.680470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.85403e7 | 0.647601 | ||||||||
\(962\) | 2.44116e7 | 0.850470 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.38243e6 | 0.151888 | ||||||||
\(965\) | −1.09674e7 | −0.379126 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.03532e7 | −0.699949 | −0.349975 | − | 0.936759i | \(-0.613810\pi\) | ||||
−0.349975 | + | 0.936759i | \(0.613810\pi\) | |||||||
\(968\) | 7.94797e6 | 0.272626 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 191800. | 0.00654514 | ||||||||
\(971\) | 2.34306e7 | 0.797510 | 0.398755 | − | 0.917057i | \(-0.369442\pi\) | ||||
0.398755 | + | 0.917057i | \(0.369442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.32878e7 | 1.12721 | ||||||||
\(974\) | −2.20723e7 | −0.745505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.51853e6 | −0.0846296 | ||||||||
\(977\) | 4.30412e7 | 1.44261 | 0.721303 | − | 0.692619i | \(-0.243543\pi\) | ||||
0.721303 | + | 0.692619i | \(0.243543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.39008e6 | 0.246429 | ||||||||
\(980\) | −1.15320e6 | −0.0383565 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.05107e6 | −0.200241 | ||||||||
\(983\) | 4.75003e7 | 1.56788 | 0.783940 | − | 0.620837i | \(-0.213207\pi\) | ||||
0.783940 | + | 0.620837i | \(0.213207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.91995e6 | 0.128733 | ||||||||
\(986\) | −1.80137e7 | −0.590079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.84870e7 | −1.58028 | ||||||||
\(989\) | 3.81164e6 | 0.123914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.09231e7 | 0.676770 | 0.338385 | − | 0.941008i | \(-0.390119\pi\) | ||||
0.338385 | + | 0.941008i | \(0.390119\pi\) | |||||||
\(992\) | 7.03283e6 | 0.226909 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.31401e7 | −1.06387 | ||||||||
\(995\) | −4.06300e6 | −0.130104 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.96332e7 | 0.944148 | 0.472074 | − | 0.881559i | \(-0.343505\pi\) | ||||
0.472074 | + | 0.881559i | \(0.343505\pi\) | |||||||
\(998\) | 7.72168e6 | 0.245406 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 90.6.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 10.6.a.c.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 720.6.a.v.1.1 | 1 | |||
5.2 | odd | 4 | 450.6.c.f.199.1 | 2 | |||
5.3 | odd | 4 | 450.6.c.f.199.2 | 2 | |||
5.4 | even | 2 | 450.6.a.u.1.1 | 1 | |||
12.11 | even | 2 | 80.6.a.c.1.1 | 1 | |||
15.2 | even | 4 | 50.6.b.b.49.2 | 2 | |||
15.8 | even | 4 | 50.6.b.b.49.1 | 2 | |||
15.14 | odd | 2 | 50.6.a.b.1.1 | 1 | |||
21.20 | even | 2 | 490.6.a.k.1.1 | 1 | |||
24.5 | odd | 2 | 320.6.a.f.1.1 | 1 | |||
24.11 | even | 2 | 320.6.a.k.1.1 | 1 | |||
60.23 | odd | 4 | 400.6.c.i.49.1 | 2 | |||
60.47 | odd | 4 | 400.6.c.i.49.2 | 2 | |||
60.59 | even | 2 | 400.6.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.c.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
50.6.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
50.6.b.b.49.1 | 2 | 15.8 | even | 4 | |||
50.6.b.b.49.2 | 2 | 15.2 | even | 4 | |||
80.6.a.c.1.1 | 1 | 12.11 | even | 2 | |||
90.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
320.6.a.f.1.1 | 1 | 24.5 | odd | 2 | |||
320.6.a.k.1.1 | 1 | 24.11 | even | 2 | |||
400.6.a.i.1.1 | 1 | 60.59 | even | 2 | |||
400.6.c.i.49.1 | 2 | 60.23 | odd | 4 | |||
400.6.c.i.49.2 | 2 | 60.47 | odd | 4 | |||
450.6.a.u.1.1 | 1 | 5.4 | even | 2 | |||
450.6.c.f.199.1 | 2 | 5.2 | odd | 4 | |||
450.6.c.f.199.2 | 2 | 5.3 | odd | 4 | |||
490.6.a.k.1.1 | 1 | 21.20 | even | 2 | |||
720.6.a.v.1.1 | 1 | 4.3 | odd | 2 |