Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [726,6,Mod(1,726)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(726, 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("726.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 726 = 2 \cdot 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 726.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: | \(116.438653184\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8052400.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 288x^{2} + 20131 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 11 \) |
Twist minimal: | no (minimal twist has level 66) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-12.9845\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 726.1 |
$q$-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 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −30.6488 | −0.548262 | −0.274131 | − | 0.961692i | \(-0.588390\pi\) | ||||
−0.274131 | + | 0.961692i | \(0.588390\pi\) | |||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | −1.59188 | −0.0122791 | −0.00613954 | − | 0.999981i | \(-0.501954\pi\) | ||||
−0.00613954 | + | 0.999981i | \(0.501954\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −122.595 | −0.387679 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | −935.937 | −1.53599 | −0.767995 | − | 0.640456i | \(-0.778745\pi\) | ||||
−0.767995 | + | 0.640456i | \(0.778745\pi\) | |||||||
\(14\) | −6.36753 | −0.00868262 | ||||||||
\(15\) | −275.839 | −0.316539 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 394.404 | 0.330993 | 0.165496 | − | 0.986210i | \(-0.447077\pi\) | ||||
0.165496 | + | 0.986210i | \(0.447077\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | 2138.65 | 1.35911 | 0.679557 | − | 0.733623i | \(-0.262172\pi\) | ||||
0.679557 | + | 0.733623i | \(0.262172\pi\) | |||||||
\(20\) | −490.380 | −0.274131 | ||||||||
\(21\) | −14.3269 | −0.00708933 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −90.5594 | −0.0356955 | −0.0178478 | − | 0.999841i | \(-0.505681\pi\) | ||||
−0.0178478 | + | 0.999841i | \(0.505681\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | −2185.65 | −0.699409 | ||||||||
\(26\) | −3743.75 | −1.08611 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −25.4701 | −0.00613954 | ||||||||
\(29\) | −1055.69 | −0.233101 | −0.116550 | − | 0.993185i | \(-0.537184\pi\) | ||||
−0.116550 | + | 0.993185i | \(0.537184\pi\) | |||||||
\(30\) | −1103.36 | −0.223827 | ||||||||
\(31\) | −4176.06 | −0.780482 | −0.390241 | − | 0.920713i | \(-0.627608\pi\) | ||||
−0.390241 | + | 0.920713i | \(0.627608\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1577.61 | 0.234047 | ||||||||
\(35\) | 48.7892 | 0.00673215 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 11518.7 | 1.38325 | 0.691625 | − | 0.722257i | \(-0.256895\pi\) | ||||
0.691625 | + | 0.722257i | \(0.256895\pi\) | |||||||
\(38\) | 8554.60 | 0.961038 | ||||||||
\(39\) | −8423.43 | −0.886804 | ||||||||
\(40\) | −1961.52 | −0.193840 | ||||||||
\(41\) | −1330.00 | −0.123564 | −0.0617818 | − | 0.998090i | \(-0.519678\pi\) | ||||
−0.0617818 | + | 0.998090i | \(0.519678\pi\) | |||||||
\(42\) | −57.3077 | −0.00501291 | ||||||||
\(43\) | −17727.1 | −1.46206 | −0.731032 | − | 0.682343i | \(-0.760961\pi\) | ||||
−0.731032 | + | 0.682343i | \(0.760961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2482.55 | −0.182754 | ||||||||
\(46\) | −362.237 | −0.0252405 | ||||||||
\(47\) | −9985.30 | −0.659351 | −0.329675 | − | 0.944094i | \(-0.606939\pi\) | ||||
−0.329675 | + | 0.944094i | \(0.606939\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | −16804.5 | −0.999849 | ||||||||
\(50\) | −8742.62 | −0.494557 | ||||||||
\(51\) | 3549.63 | 0.191099 | ||||||||
\(52\) | −14975.0 | −0.767995 | ||||||||
\(53\) | −25413.3 | −1.24272 | −0.621358 | − | 0.783527i | \(-0.713419\pi\) | ||||
−0.621358 | + | 0.783527i | \(0.713419\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −101.880 | −0.00434131 | ||||||||
\(57\) | 19247.8 | 0.784684 | ||||||||
\(58\) | −4222.78 | −0.164827 | ||||||||
\(59\) | −8581.00 | −0.320928 | −0.160464 | − | 0.987042i | \(-0.551299\pi\) | ||||
−0.160464 | + | 0.987042i | \(0.551299\pi\) | |||||||
\(60\) | −4413.42 | −0.158269 | ||||||||
\(61\) | −39347.3 | −1.35391 | −0.676956 | − | 0.736023i | \(-0.736701\pi\) | ||||
−0.676956 | + | 0.736023i | \(0.736701\pi\) | |||||||
\(62\) | −16704.3 | −0.551884 | ||||||||
\(63\) | −128.942 | −0.00409303 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 28685.3 | 0.842124 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6661.08 | 0.181283 | 0.0906417 | − | 0.995884i | \(-0.471108\pi\) | ||||
0.0906417 | + | 0.995884i | \(0.471108\pi\) | |||||||
\(68\) | 6310.46 | 0.165496 | ||||||||
\(69\) | −815.034 | −0.0206088 | ||||||||
\(70\) | 195.157 | 0.00476035 | ||||||||
\(71\) | 29210.4 | 0.687689 | 0.343844 | − | 0.939027i | \(-0.388271\pi\) | ||||
0.343844 | + | 0.939027i | \(0.388271\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | 384.834 | 0.00845214 | 0.00422607 | − | 0.999991i | \(-0.498655\pi\) | ||||
0.00422607 | + | 0.999991i | \(0.498655\pi\) | |||||||
\(74\) | 46075.0 | 0.978105 | ||||||||
\(75\) | −19670.9 | −0.403804 | ||||||||
\(76\) | 34218.4 | 0.679557 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −33693.7 | −0.627065 | ||||||||
\(79\) | −25707.5 | −0.463439 | −0.231720 | − | 0.972783i | \(-0.574435\pi\) | ||||
−0.231720 | + | 0.972783i | \(0.574435\pi\) | |||||||
\(80\) | −7846.08 | −0.137065 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −5319.98 | −0.0873727 | ||||||||
\(83\) | 101629. | 1.61928 | 0.809642 | − | 0.586924i | \(-0.199661\pi\) | ||||
0.809642 | + | 0.586924i | \(0.199661\pi\) | |||||||
\(84\) | −229.231 | −0.00354466 | ||||||||
\(85\) | −12088.0 | −0.181471 | ||||||||
\(86\) | −70908.4 | −1.03384 | ||||||||
\(87\) | −9501.25 | −0.134581 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −55800.4 | −0.746728 | −0.373364 | − | 0.927685i | \(-0.621796\pi\) | ||||
−0.373364 | + | 0.927685i | \(0.621796\pi\) | |||||||
\(90\) | −9930.20 | −0.129226 | ||||||||
\(91\) | 1489.90 | 0.0188605 | ||||||||
\(92\) | −1448.95 | −0.0178478 | ||||||||
\(93\) | −37584.6 | −0.450611 | ||||||||
\(94\) | −39941.2 | −0.466231 | ||||||||
\(95\) | −65546.9 | −0.745149 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −167341. | −1.80582 | −0.902909 | − | 0.429832i | \(-0.858573\pi\) | ||||
−0.902909 | + | 0.429832i | \(0.858573\pi\) | |||||||
\(98\) | −67217.9 | −0.707000 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −34970.5 | −0.349705 | ||||||||
\(101\) | −37006.3 | −0.360971 | −0.180485 | − | 0.983578i | \(-0.557767\pi\) | ||||
−0.180485 | + | 0.983578i | \(0.557767\pi\) | |||||||
\(102\) | 14198.5 | 0.135127 | ||||||||
\(103\) | 79070.2 | 0.734378 | 0.367189 | − | 0.930146i | \(-0.380320\pi\) | ||||
0.367189 | + | 0.930146i | \(0.380320\pi\) | |||||||
\(104\) | −59900.0 | −0.543054 | ||||||||
\(105\) | 439.103 | 0.00388681 | ||||||||
\(106\) | −101653. | −0.878733 | ||||||||
\(107\) | −177733. | −1.50075 | −0.750376 | − | 0.661011i | \(-0.770128\pi\) | ||||
−0.750376 | + | 0.661011i | \(0.770128\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | 19984.5 | 0.161112 | 0.0805560 | − | 0.996750i | \(-0.474330\pi\) | ||||
0.0805560 | + | 0.996750i | \(0.474330\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 103669. | 0.798620 | ||||||||
\(112\) | −407.522 | −0.00306977 | ||||||||
\(113\) | −209615. | −1.54428 | −0.772139 | − | 0.635454i | \(-0.780813\pi\) | ||||
−0.772139 | + | 0.635454i | \(0.780813\pi\) | |||||||
\(114\) | 76991.4 | 0.554856 | ||||||||
\(115\) | 2775.53 | 0.0195705 | ||||||||
\(116\) | −16891.1 | −0.116550 | ||||||||
\(117\) | −75810.9 | −0.511997 | ||||||||
\(118\) | −34324.0 | −0.226930 | ||||||||
\(119\) | −627.844 | −0.00406429 | ||||||||
\(120\) | −17653.7 | −0.111913 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −157389. | −0.957361 | ||||||||
\(123\) | −11970.0 | −0.0713395 | ||||||||
\(124\) | −66817.0 | −0.390241 | ||||||||
\(125\) | 162765. | 0.931721 | ||||||||
\(126\) | −515.770 | −0.00289421 | ||||||||
\(127\) | 113445. | 0.624132 | 0.312066 | − | 0.950060i | \(-0.398979\pi\) | ||||
0.312066 | + | 0.950060i | \(0.398979\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | −159544. | −0.844123 | ||||||||
\(130\) | 114741. | 0.595472 | ||||||||
\(131\) | 30840.5 | 0.157015 | 0.0785077 | − | 0.996914i | \(-0.474984\pi\) | ||||
0.0785077 | + | 0.996914i | \(0.474984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3404.48 | −0.0166887 | ||||||||
\(134\) | 26644.3 | 0.128187 | ||||||||
\(135\) | −22342.9 | −0.105513 | ||||||||
\(136\) | 25241.8 | 0.117024 | ||||||||
\(137\) | −280642. | −1.27747 | −0.638736 | − | 0.769426i | \(-0.720542\pi\) | ||||
−0.638736 | + | 0.769426i | \(0.720542\pi\) | |||||||
\(138\) | −3260.14 | −0.0145726 | ||||||||
\(139\) | −204032. | −0.895696 | −0.447848 | − | 0.894110i | \(-0.647809\pi\) | ||||
−0.447848 | + | 0.894110i | \(0.647809\pi\) | |||||||
\(140\) | 780.627 | 0.00336607 | ||||||||
\(141\) | −89867.7 | −0.380676 | ||||||||
\(142\) | 116842. | 0.486269 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 32355.7 | 0.127800 | ||||||||
\(146\) | 1539.34 | 0.00597657 | ||||||||
\(147\) | −151240. | −0.577263 | ||||||||
\(148\) | 184300. | 0.691625 | ||||||||
\(149\) | −239826. | −0.884975 | −0.442488 | − | 0.896775i | \(-0.645904\pi\) | ||||
−0.442488 | + | 0.896775i | \(0.645904\pi\) | |||||||
\(150\) | −78683.5 | −0.285533 | ||||||||
\(151\) | 479338. | 1.71080 | 0.855400 | − | 0.517968i | \(-0.173311\pi\) | ||||
0.855400 | + | 0.517968i | \(0.173311\pi\) | |||||||
\(152\) | 136874. | 0.480519 | ||||||||
\(153\) | 31946.7 | 0.110331 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 127991. | 0.427908 | ||||||||
\(156\) | −134775. | −0.443402 | ||||||||
\(157\) | −137336. | −0.444669 | −0.222334 | − | 0.974970i | \(-0.571368\pi\) | ||||
−0.222334 | + | 0.974970i | \(0.571368\pi\) | |||||||
\(158\) | −102830. | −0.327701 | ||||||||
\(159\) | −228720. | −0.717482 | ||||||||
\(160\) | −31384.3 | −0.0969199 | ||||||||
\(161\) | 144.160 | 0.000438308 0 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −199958. | −0.589482 | −0.294741 | − | 0.955577i | \(-0.595233\pi\) | ||||
−0.294741 | + | 0.955577i | \(0.595233\pi\) | |||||||
\(164\) | −21279.9 | −0.0617818 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 406517. | 1.14501 | ||||||||
\(167\) | −62887.3 | −0.174490 | −0.0872452 | − | 0.996187i | \(-0.527806\pi\) | ||||
−0.0872452 | + | 0.996187i | \(0.527806\pi\) | |||||||
\(168\) | −916.924 | −0.00250646 | ||||||||
\(169\) | 504685. | 1.35926 | ||||||||
\(170\) | −48351.9 | −0.128319 | ||||||||
\(171\) | 173231. | 0.453038 | ||||||||
\(172\) | −283634. | −0.731032 | ||||||||
\(173\) | 599918. | 1.52397 | 0.761985 | − | 0.647595i | \(-0.224225\pi\) | ||||
0.761985 | + | 0.647595i | \(0.224225\pi\) | |||||||
\(174\) | −38005.0 | −0.0951629 | ||||||||
\(175\) | 3479.30 | 0.00858810 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −77229.0 | −0.185288 | ||||||||
\(178\) | −223202. | −0.528016 | ||||||||
\(179\) | −106737. | −0.248991 | −0.124496 | − | 0.992220i | \(-0.539731\pi\) | ||||
−0.124496 | + | 0.992220i | \(0.539731\pi\) | |||||||
\(180\) | −39720.8 | −0.0913769 | ||||||||
\(181\) | −181668. | −0.412176 | −0.206088 | − | 0.978534i | \(-0.566073\pi\) | ||||
−0.206088 | + | 0.978534i | \(0.566073\pi\) | |||||||
\(182\) | 5959.61 | 0.0133364 | ||||||||
\(183\) | −354126. | −0.781682 | ||||||||
\(184\) | −5795.80 | −0.0126203 | ||||||||
\(185\) | −353035. | −0.758383 | ||||||||
\(186\) | −150338. | −0.318630 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −159765. | −0.329675 | ||||||||
\(189\) | −1160.48 | −0.00236311 | ||||||||
\(190\) | −262188. | −0.526900 | ||||||||
\(191\) | −370816. | −0.735487 | −0.367743 | − | 0.929927i | \(-0.619869\pi\) | ||||
−0.367743 | + | 0.929927i | \(0.619869\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | 201284. | 0.388971 | 0.194485 | − | 0.980905i | \(-0.437696\pi\) | ||||
0.194485 | + | 0.980905i | \(0.437696\pi\) | |||||||
\(194\) | −669365. | −1.27691 | ||||||||
\(195\) | 258168. | 0.486201 | ||||||||
\(196\) | −268871. | −0.499925 | ||||||||
\(197\) | 329001. | 0.603992 | 0.301996 | − | 0.953309i | \(-0.402347\pi\) | ||||
0.301996 | + | 0.953309i | \(0.402347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 729463. | 1.30578 | 0.652891 | − | 0.757452i | \(-0.273556\pi\) | ||||
0.652891 | + | 0.757452i | \(0.273556\pi\) | |||||||
\(200\) | −139882. | −0.247279 | ||||||||
\(201\) | 59949.8 | 0.104664 | ||||||||
\(202\) | −148025. | −0.255245 | ||||||||
\(203\) | 1680.54 | 0.00286226 | ||||||||
\(204\) | 56794.1 | 0.0955494 | ||||||||
\(205\) | 40762.7 | 0.0677452 | ||||||||
\(206\) | 316281. | 0.519284 | ||||||||
\(207\) | −7335.31 | −0.0118985 | ||||||||
\(208\) | −239600. | −0.383997 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1756.41 | 0.00274839 | ||||||||
\(211\) | −591312. | −0.914347 | −0.457173 | − | 0.889378i | \(-0.651138\pi\) | ||||
−0.457173 | + | 0.889378i | \(0.651138\pi\) | |||||||
\(212\) | −406613. | −0.621358 | ||||||||
\(213\) | 262894. | 0.397037 | ||||||||
\(214\) | −710932. | −1.06119 | ||||||||
\(215\) | 543313. | 0.801594 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 6647.80 | 0.00958360 | ||||||||
\(218\) | 79938.1 | 0.113923 | ||||||||
\(219\) | 3463.51 | 0.00487985 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −369137. | −0.508402 | ||||||||
\(222\) | 414675. | 0.564709 | ||||||||
\(223\) | −641078. | −0.863274 | −0.431637 | − | 0.902047i | \(-0.642064\pi\) | ||||
−0.431637 | + | 0.902047i | \(0.642064\pi\) | |||||||
\(224\) | −1630.09 | −0.00217065 | ||||||||
\(225\) | −177038. | −0.233136 | ||||||||
\(226\) | −838458. | −1.09197 | ||||||||
\(227\) | −401846. | −0.517601 | −0.258800 | − | 0.965931i | \(-0.583327\pi\) | ||||
−0.258800 | + | 0.965931i | \(0.583327\pi\) | |||||||
\(228\) | 307966. | 0.392342 | ||||||||
\(229\) | 338688. | 0.426786 | 0.213393 | − | 0.976966i | \(-0.431548\pi\) | ||||
0.213393 | + | 0.976966i | \(0.431548\pi\) | |||||||
\(230\) | 11102.1 | 0.0138384 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −67564.5 | −0.0824135 | ||||||||
\(233\) | 1.16272e6 | 1.40309 | 0.701543 | − | 0.712627i | \(-0.252495\pi\) | ||||
0.701543 | + | 0.712627i | \(0.252495\pi\) | |||||||
\(234\) | −303244. | −0.362036 | ||||||||
\(235\) | 306037. | 0.361497 | ||||||||
\(236\) | −137296. | −0.160464 | ||||||||
\(237\) | −231368. | −0.267567 | ||||||||
\(238\) | −2511.38 | −0.00287389 | ||||||||
\(239\) | 1.07347e6 | 1.21561 | 0.607805 | − | 0.794087i | \(-0.292050\pi\) | ||||
0.607805 | + | 0.794087i | \(0.292050\pi\) | |||||||
\(240\) | −70614.7 | −0.0791347 | ||||||||
\(241\) | 859568. | 0.953318 | 0.476659 | − | 0.879088i | \(-0.341848\pi\) | ||||
0.476659 | + | 0.879088i | \(0.341848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −629557. | −0.676956 | ||||||||
\(245\) | 515036. | 0.548179 | ||||||||
\(246\) | −47879.8 | −0.0504446 | ||||||||
\(247\) | −2.00164e6 | −2.08758 | ||||||||
\(248\) | −267268. | −0.275942 | ||||||||
\(249\) | 914663. | 0.934894 | ||||||||
\(250\) | 651060. | 0.658826 | ||||||||
\(251\) | −850739. | −0.852338 | −0.426169 | − | 0.904644i | \(-0.640137\pi\) | ||||
−0.426169 | + | 0.904644i | \(0.640137\pi\) | |||||||
\(252\) | −2063.08 | −0.00204651 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 453781. | 0.441328 | ||||||||
\(255\) | −108792. | −0.104772 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.94444e6 | −1.83638 | −0.918188 | − | 0.396144i | \(-0.870348\pi\) | ||||
−0.918188 | + | 0.396144i | \(0.870348\pi\) | |||||||
\(258\) | −638176. | −0.596885 | ||||||||
\(259\) | −18336.5 | −0.0169850 | ||||||||
\(260\) | 458965. | 0.421062 | ||||||||
\(261\) | −85511.3 | −0.0777002 | ||||||||
\(262\) | 123362. | 0.111027 | ||||||||
\(263\) | 2.00871e6 | 1.79072 | 0.895360 | − | 0.445342i | \(-0.146918\pi\) | ||||
0.895360 | + | 0.445342i | \(0.146918\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 778887. | 0.681333 | ||||||||
\(266\) | −13617.9 | −0.0118007 | ||||||||
\(267\) | −502204. | −0.431123 | ||||||||
\(268\) | 106577. | 0.0906417 | ||||||||
\(269\) | −1.77751e6 | −1.49772 | −0.748862 | − | 0.662726i | \(-0.769400\pi\) | ||||
−0.748862 | + | 0.662726i | \(0.769400\pi\) | |||||||
\(270\) | −89371.8 | −0.0746089 | ||||||||
\(271\) | 184785. | 0.152842 | 0.0764210 | − | 0.997076i | \(-0.475651\pi\) | ||||
0.0764210 | + | 0.997076i | \(0.475651\pi\) | |||||||
\(272\) | 100967. | 0.0827482 | ||||||||
\(273\) | 13409.1 | 0.0108891 | ||||||||
\(274\) | −1.12257e6 | −0.903309 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13040.5 | −0.0103044 | ||||||||
\(277\) | −1.43700e6 | −1.12527 | −0.562637 | − | 0.826704i | \(-0.690213\pi\) | ||||
−0.562637 | + | 0.826704i | \(0.690213\pi\) | |||||||
\(278\) | −816127. | −0.633353 | ||||||||
\(279\) | −338261. | −0.260161 | ||||||||
\(280\) | 3122.51 | 0.00238017 | ||||||||
\(281\) | −199179. | −0.150479 | −0.0752397 | − | 0.997165i | \(-0.523972\pi\) | ||||
−0.0752397 | + | 0.997165i | \(0.523972\pi\) | |||||||
\(282\) | −359471. | −0.269179 | ||||||||
\(283\) | 1.38955e6 | 1.03136 | 0.515679 | − | 0.856782i | \(-0.327540\pi\) | ||||
0.515679 | + | 0.856782i | \(0.327540\pi\) | |||||||
\(284\) | 467367. | 0.343844 | ||||||||
\(285\) | −589922. | −0.430212 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2117.20 | 0.00151725 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | −1.26430e6 | −0.890444 | ||||||||
\(290\) | 129423. | 0.0903683 | ||||||||
\(291\) | −1.50607e6 | −1.04259 | ||||||||
\(292\) | 6157.35 | 0.00422607 | ||||||||
\(293\) | −2.27270e6 | −1.54658 | −0.773290 | − | 0.634052i | \(-0.781390\pi\) | ||||
−0.773290 | + | 0.634052i | \(0.781390\pi\) | |||||||
\(294\) | −604961. | −0.408187 | ||||||||
\(295\) | 262997. | 0.175953 | ||||||||
\(296\) | 737199. | 0.489053 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −959305. | −0.625772 | ||||||||
\(299\) | 84757.9 | 0.0548280 | ||||||||
\(300\) | −314734. | −0.201902 | ||||||||
\(301\) | 28219.4 | 0.0179528 | ||||||||
\(302\) | 1.91735e6 | 1.20972 | ||||||||
\(303\) | −333057. | −0.208407 | ||||||||
\(304\) | 547494. | 0.339778 | ||||||||
\(305\) | 1.20595e6 | 0.742298 | ||||||||
\(306\) | 127787. | 0.0780158 | ||||||||
\(307\) | 2.98610e6 | 1.80825 | 0.904125 | − | 0.427268i | \(-0.140524\pi\) | ||||
0.904125 | + | 0.427268i | \(0.140524\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 711632. | 0.423993 | ||||||||
\(310\) | 511965. | 0.302577 | ||||||||
\(311\) | 873086. | 0.511866 | 0.255933 | − | 0.966695i | \(-0.417617\pi\) | ||||
0.255933 | + | 0.966695i | \(0.417617\pi\) | |||||||
\(312\) | −539100. | −0.313533 | ||||||||
\(313\) | 497931. | 0.287282 | 0.143641 | − | 0.989630i | \(-0.454119\pi\) | ||||
0.143641 | + | 0.989630i | \(0.454119\pi\) | |||||||
\(314\) | −549345. | −0.314428 | ||||||||
\(315\) | 3951.92 | 0.00224405 | ||||||||
\(316\) | −411321. | −0.231720 | ||||||||
\(317\) | −2.74182e6 | −1.53247 | −0.766234 | − | 0.642562i | \(-0.777872\pi\) | ||||
−0.766234 | + | 0.642562i | \(0.777872\pi\) | |||||||
\(318\) | −914880. | −0.507337 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −125537. | −0.0685327 | ||||||||
\(321\) | −1.59960e6 | −0.866460 | ||||||||
\(322\) | 576.639 | 0.000309931 0 | ||||||||
\(323\) | 843491. | 0.449857 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 2.04563e6 | 1.07429 | ||||||||
\(326\) | −799834. | −0.416827 | ||||||||
\(327\) | 179861. | 0.0930180 | ||||||||
\(328\) | −85119.7 | −0.0436863 | ||||||||
\(329\) | 15895.4 | 0.00809622 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.59901e6 | −1.80557 | −0.902783 | − | 0.430097i | \(-0.858479\pi\) | ||||
−0.902783 | + | 0.430097i | \(0.858479\pi\) | |||||||
\(332\) | 1.62607e6 | 0.809642 | ||||||||
\(333\) | 933018. | 0.461083 | ||||||||
\(334\) | −251549. | −0.123383 | ||||||||
\(335\) | −204154. | −0.0993907 | ||||||||
\(336\) | −3667.70 | −0.00177233 | ||||||||
\(337\) | −1.38633e6 | −0.664956 | −0.332478 | − | 0.943111i | \(-0.607885\pi\) | ||||
−0.332478 | + | 0.943111i | \(0.607885\pi\) | |||||||
\(338\) | 2.01874e6 | 0.961145 | ||||||||
\(339\) | −1.88653e6 | −0.891589 | ||||||||
\(340\) | −193408. | −0.0907353 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 692922. | 0.320346 | ||||||||
\(343\) | 53505.5 | 0.0245563 | ||||||||
\(344\) | −1.13453e6 | −0.516918 | ||||||||
\(345\) | 24979.8 | 0.0112990 | ||||||||
\(346\) | 2.39967e6 | 1.07761 | ||||||||
\(347\) | −1.31626e6 | −0.586838 | −0.293419 | − | 0.955984i | \(-0.594793\pi\) | ||||
−0.293419 | + | 0.955984i | \(0.594793\pi\) | |||||||
\(348\) | −152020. | −0.0672903 | ||||||||
\(349\) | −2.01266e6 | −0.884520 | −0.442260 | − | 0.896887i | \(-0.645823\pi\) | ||||
−0.442260 | + | 0.896887i | \(0.645823\pi\) | |||||||
\(350\) | 13917.2 | 0.00607270 | ||||||||
\(351\) | −682298. | −0.295601 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.49229e6 | −0.637407 | −0.318703 | − | 0.947854i | \(-0.603247\pi\) | ||||
−0.318703 | + | 0.947854i | \(0.603247\pi\) | |||||||
\(354\) | −308916. | −0.131018 | ||||||||
\(355\) | −895263. | −0.377033 | ||||||||
\(356\) | −892806. | −0.373364 | ||||||||
\(357\) | −5650.60 | −0.00234652 | ||||||||
\(358\) | −426949. | −0.176063 | ||||||||
\(359\) | 4.23116e6 | 1.73270 | 0.866351 | − | 0.499436i | \(-0.166460\pi\) | ||||
0.866351 | + | 0.499436i | \(0.166460\pi\) | |||||||
\(360\) | −158883. | −0.0646132 | ||||||||
\(361\) | 2.09772e6 | 0.847189 | ||||||||
\(362\) | −726672. | −0.291452 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 23838.4 | 0.00943027 | ||||||||
\(365\) | −11794.7 | −0.00463398 | ||||||||
\(366\) | −1.41650e6 | −0.552732 | ||||||||
\(367\) | 3.40149e6 | 1.31827 | 0.659134 | − | 0.752026i | \(-0.270923\pi\) | ||||
0.659134 | + | 0.752026i | \(0.270923\pi\) | |||||||
\(368\) | −23183.2 | −0.00892388 | ||||||||
\(369\) | −107730. | −0.0411879 | ||||||||
\(370\) | −1.41214e6 | −0.536258 | ||||||||
\(371\) | 40455.0 | 0.0152594 | ||||||||
\(372\) | −601353. | −0.225306 | ||||||||
\(373\) | 3.01172e6 | 1.12084 | 0.560418 | − | 0.828210i | \(-0.310640\pi\) | ||||
0.560418 | + | 0.828210i | \(0.310640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.46488e6 | 0.537929 | ||||||||
\(376\) | −639059. | −0.233116 | ||||||||
\(377\) | 988064. | 0.358040 | ||||||||
\(378\) | −4641.93 | −0.00167097 | ||||||||
\(379\) | −1.78261e6 | −0.637470 | −0.318735 | − | 0.947844i | \(-0.603258\pi\) | ||||
−0.318735 | + | 0.947844i | \(0.603258\pi\) | |||||||
\(380\) | −1.04875e6 | −0.372575 | ||||||||
\(381\) | 1.02101e6 | 0.360343 | ||||||||
\(382\) | −1.48326e6 | −0.520068 | ||||||||
\(383\) | 5.43959e6 | 1.89483 | 0.947413 | − | 0.320013i | \(-0.103687\pi\) | ||||
0.947413 | + | 0.320013i | \(0.103687\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 805138. | 0.275044 | ||||||||
\(387\) | −1.43590e6 | −0.487355 | ||||||||
\(388\) | −2.67746e6 | −0.902909 | ||||||||
\(389\) | 3.58835e6 | 1.20232 | 0.601161 | − | 0.799128i | \(-0.294705\pi\) | ||||
0.601161 | + | 0.799128i | \(0.294705\pi\) | |||||||
\(390\) | 1.03267e6 | 0.343796 | ||||||||
\(391\) | −35716.9 | −0.0118150 | ||||||||
\(392\) | −1.07549e6 | −0.353500 | ||||||||
\(393\) | 277564. | 0.0906529 | ||||||||
\(394\) | 1.31600e6 | 0.427087 | ||||||||
\(395\) | 787904. | 0.254086 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.21167e6 | 1.65959 | 0.829795 | − | 0.558069i | \(-0.188457\pi\) | ||||
0.829795 | + | 0.558069i | \(0.188457\pi\) | |||||||
\(398\) | 2.91785e6 | 0.923328 | ||||||||
\(399\) | −30640.3 | −0.00963520 | ||||||||
\(400\) | −559527. | −0.174852 | ||||||||
\(401\) | −641775. | −0.199307 | −0.0996533 | − | 0.995022i | \(-0.531773\pi\) | ||||
−0.0996533 | + | 0.995022i | \(0.531773\pi\) | |||||||
\(402\) | 239799. | 0.0740086 | ||||||||
\(403\) | 3.90853e6 | 1.19881 | ||||||||
\(404\) | −592101. | −0.180485 | ||||||||
\(405\) | −201086. | −0.0609179 | ||||||||
\(406\) | 6722.17 | 0.00202392 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 227177. | 0.0675636 | ||||||||
\(409\) | −5.08445e6 | −1.50292 | −0.751460 | − | 0.659778i | \(-0.770650\pi\) | ||||
−0.751460 | + | 0.659778i | \(0.770650\pi\) | |||||||
\(410\) | 163051. | 0.0479031 | ||||||||
\(411\) | −2.52578e6 | −0.737548 | ||||||||
\(412\) | 1.26512e6 | 0.367189 | ||||||||
\(413\) | 13659.9 | 0.00394070 | ||||||||
\(414\) | −29341.2 | −0.00841352 | ||||||||
\(415\) | −3.11481e6 | −0.887791 | ||||||||
\(416\) | −958400. | −0.271527 | ||||||||
\(417\) | −1.83629e6 | −0.517130 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.44419e6 | −0.680143 | −0.340072 | − | 0.940400i | \(-0.610451\pi\) | ||||
−0.340072 | + | 0.940400i | \(0.610451\pi\) | |||||||
\(420\) | 7025.64 | 0.00194340 | ||||||||
\(421\) | 5.36407e6 | 1.47499 | 0.737495 | − | 0.675353i | \(-0.236009\pi\) | ||||
0.737495 | + | 0.675353i | \(0.236009\pi\) | |||||||
\(422\) | −2.36525e6 | −0.646541 | ||||||||
\(423\) | −808809. | −0.219784 | ||||||||
\(424\) | −1.62645e6 | −0.439366 | ||||||||
\(425\) | −862030. | −0.231500 | ||||||||
\(426\) | 1.05158e6 | 0.280748 | ||||||||
\(427\) | 62636.3 | 0.0166248 | ||||||||
\(428\) | −2.84373e6 | −0.750376 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.17325e6 | 0.566812 | ||||||||
\(431\) | 5.49234e6 | 1.42418 | 0.712089 | − | 0.702089i | \(-0.247749\pi\) | ||||
0.712089 | + | 0.702089i | \(0.247749\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | −106167. | −0.0272126 | −0.0136063 | − | 0.999907i | \(-0.504331\pi\) | ||||
−0.0136063 | + | 0.999907i | \(0.504331\pi\) | |||||||
\(434\) | 26591.2 | 0.00677663 | ||||||||
\(435\) | 291202. | 0.0737854 | ||||||||
\(436\) | 319753. | 0.0805560 | ||||||||
\(437\) | −193675. | −0.0485143 | ||||||||
\(438\) | 13854.0 | 0.00345057 | ||||||||
\(439\) | −4.59366e6 | −1.13762 | −0.568811 | − | 0.822469i | \(-0.692596\pi\) | ||||
−0.568811 | + | 0.822469i | \(0.692596\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.36116e6 | −0.333283 | ||||||||
\(442\) | −1.47655e6 | −0.359494 | ||||||||
\(443\) | 4.98339e6 | 1.20647 | 0.603234 | − | 0.797564i | \(-0.293878\pi\) | ||||
0.603234 | + | 0.797564i | \(0.293878\pi\) | |||||||
\(444\) | 1.65870e6 | 0.399310 | ||||||||
\(445\) | 1.71021e6 | 0.409402 | ||||||||
\(446\) | −2.56431e6 | −0.610427 | ||||||||
\(447\) | −2.15844e6 | −0.510941 | ||||||||
\(448\) | −6520.35 | −0.00153488 | ||||||||
\(449\) | −6.30470e6 | −1.47587 | −0.737935 | − | 0.674872i | \(-0.764199\pi\) | ||||
−0.737935 | + | 0.674872i | \(0.764199\pi\) | |||||||
\(450\) | −708152. | −0.164852 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.35383e6 | −0.772139 | ||||||||
\(453\) | 4.31404e6 | 0.987731 | ||||||||
\(454\) | −1.60738e6 | −0.365999 | ||||||||
\(455\) | −45663.6 | −0.0103405 | ||||||||
\(456\) | 1.23186e6 | 0.277428 | ||||||||
\(457\) | 8.04543e6 | 1.80202 | 0.901008 | − | 0.433802i | \(-0.142828\pi\) | ||||
0.901008 | + | 0.433802i | \(0.142828\pi\) | |||||||
\(458\) | 1.35475e6 | 0.301784 | ||||||||
\(459\) | 287520. | 0.0636996 | ||||||||
\(460\) | 44408.5 | 0.00978524 | ||||||||
\(461\) | 1.76141e6 | 0.386018 | 0.193009 | − | 0.981197i | \(-0.438175\pi\) | ||||
0.193009 | + | 0.981197i | \(0.438175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.64405e6 | −0.573214 | −0.286607 | − | 0.958048i | \(-0.592527\pi\) | ||||
−0.286607 | + | 0.958048i | \(0.592527\pi\) | |||||||
\(464\) | −270258. | −0.0582751 | ||||||||
\(465\) | 1.15192e6 | 0.247053 | ||||||||
\(466\) | 4.65087e6 | 0.992132 | ||||||||
\(467\) | 8.12766e6 | 1.72454 | 0.862270 | − | 0.506448i | \(-0.169042\pi\) | ||||
0.862270 | + | 0.506448i | \(0.169042\pi\) | |||||||
\(468\) | −1.21297e6 | −0.255998 | ||||||||
\(469\) | −10603.7 | −0.00222599 | ||||||||
\(470\) | 1.22415e6 | 0.255617 | ||||||||
\(471\) | −1.23603e6 | −0.256729 | ||||||||
\(472\) | −549184. | −0.113465 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −925472. | −0.189198 | ||||||||
\(475\) | −4.67435e6 | −0.950576 | ||||||||
\(476\) | −10045.5 | −0.00203214 | ||||||||
\(477\) | −2.05848e6 | −0.414239 | ||||||||
\(478\) | 4.29387e6 | 0.859566 | ||||||||
\(479\) | 5.61347e6 | 1.11787 | 0.558937 | − | 0.829210i | \(-0.311209\pi\) | ||||
0.558937 | + | 0.829210i | \(0.311209\pi\) | |||||||
\(480\) | −282459. | −0.0559567 | ||||||||
\(481\) | −1.07808e7 | −2.12466 | ||||||||
\(482\) | 3.43827e6 | 0.674098 | ||||||||
\(483\) | 1297.44 | 0.000253057 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.12880e6 | 0.990060 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 4.81250e6 | 0.919494 | 0.459747 | − | 0.888050i | \(-0.347940\pi\) | ||||
0.459747 | + | 0.888050i | \(0.347940\pi\) | |||||||
\(488\) | −2.51823e6 | −0.478680 | ||||||||
\(489\) | −1.79963e6 | −0.340338 | ||||||||
\(490\) | 2.06014e6 | 0.387621 | ||||||||
\(491\) | −3.89670e6 | −0.729446 | −0.364723 | − | 0.931116i | \(-0.618836\pi\) | ||||
−0.364723 | + | 0.931116i | \(0.618836\pi\) | |||||||
\(492\) | −191519. | −0.0356697 | ||||||||
\(493\) | −416370. | −0.0771546 | ||||||||
\(494\) | −8.00657e6 | −1.47614 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.06907e6 | −0.195120 | ||||||||
\(497\) | −46499.5 | −0.00844419 | ||||||||
\(498\) | 3.65865e6 | 0.661070 | ||||||||
\(499\) | 8.26693e6 | 1.48625 | 0.743126 | − | 0.669151i | \(-0.233342\pi\) | ||||
0.743126 | + | 0.669151i | \(0.233342\pi\) | |||||||
\(500\) | 2.60424e6 | 0.465860 | ||||||||
\(501\) | −565985. | −0.100742 | ||||||||
\(502\) | −3.40295e6 | −0.602694 | ||||||||
\(503\) | −5.42357e6 | −0.955797 | −0.477899 | − | 0.878415i | \(-0.658601\pi\) | ||||
−0.477899 | + | 0.878415i | \(0.658601\pi\) | |||||||
\(504\) | −8252.32 | −0.00144710 | ||||||||
\(505\) | 1.13420e6 | 0.197906 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.54217e6 | 0.784772 | ||||||||
\(508\) | 1.81512e6 | 0.312066 | ||||||||
\(509\) | 4.13731e6 | 0.707821 | 0.353910 | − | 0.935279i | \(-0.384852\pi\) | ||||
0.353910 | + | 0.935279i | \(0.384852\pi\) | |||||||
\(510\) | −435167. | −0.0740851 | ||||||||
\(511\) | −612.611 | −0.000103785 0 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 1.55908e6 | 0.261561 | ||||||||
\(514\) | −7.77776e6 | −1.29851 | ||||||||
\(515\) | −2.42340e6 | −0.402631 | ||||||||
\(516\) | −2.55270e6 | −0.422062 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −73345.9 | −0.0120102 | ||||||||
\(519\) | 5.39926e6 | 0.879865 | ||||||||
\(520\) | 1.83586e6 | 0.297736 | ||||||||
\(521\) | −5.96732e6 | −0.963130 | −0.481565 | − | 0.876411i | \(-0.659931\pi\) | ||||
−0.481565 | + | 0.876411i | \(0.659931\pi\) | |||||||
\(522\) | −342045. | −0.0549423 | ||||||||
\(523\) | 5.74212e6 | 0.917947 | 0.458974 | − | 0.888450i | \(-0.348217\pi\) | ||||
0.458974 | + | 0.888450i | \(0.348217\pi\) | |||||||
\(524\) | 493447. | 0.0785077 | ||||||||
\(525\) | 31313.7 | 0.00495834 | ||||||||
\(526\) | 8.03484e6 | 1.26623 | ||||||||
\(527\) | −1.64706e6 | −0.258334 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.42814e6 | −0.998726 | ||||||||
\(530\) | 3.11555e6 | 0.481775 | ||||||||
\(531\) | −695061. | −0.106976 | ||||||||
\(532\) | −54471.6 | −0.00834433 | ||||||||
\(533\) | 1.24479e6 | 0.189792 | ||||||||
\(534\) | −2.00881e6 | −0.304850 | ||||||||
\(535\) | 5.44730e6 | 0.822805 | ||||||||
\(536\) | 426309. | 0.0640933 | ||||||||
\(537\) | −960636. | −0.143755 | ||||||||
\(538\) | −7.11005e6 | −1.05905 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −357487. | −0.0527565 | ||||||||
\(541\) | 5.87557e6 | 0.863092 | 0.431546 | − | 0.902091i | \(-0.357968\pi\) | ||||
0.431546 | + | 0.902091i | \(0.357968\pi\) | |||||||
\(542\) | 739139. | 0.108076 | ||||||||
\(543\) | −1.63501e6 | −0.237970 | ||||||||
\(544\) | 403869. | 0.0585118 | ||||||||
\(545\) | −612501. | −0.0883315 | ||||||||
\(546\) | 53636.4 | 0.00769978 | ||||||||
\(547\) | 7.35228e6 | 1.05064 | 0.525320 | − | 0.850905i | \(-0.323946\pi\) | ||||
0.525320 | + | 0.850905i | \(0.323946\pi\) | |||||||
\(548\) | −4.49027e6 | −0.638736 | ||||||||
\(549\) | −3.18713e6 | −0.451304 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.25776e6 | −0.316810 | ||||||||
\(552\) | −52162.2 | −0.00728632 | ||||||||
\(553\) | 40923.4 | 0.00569061 | ||||||||
\(554\) | −5.74801e6 | −0.795689 | ||||||||
\(555\) | −3.17731e6 | −0.437852 | ||||||||
\(556\) | −3.26451e6 | −0.447848 | ||||||||
\(557\) | 8.20787e6 | 1.12097 | 0.560483 | − | 0.828166i | \(-0.310616\pi\) | ||||
0.560483 | + | 0.828166i | \(0.310616\pi\) | |||||||
\(558\) | −1.35304e6 | −0.183961 | ||||||||
\(559\) | 1.65915e7 | 2.24572 | ||||||||
\(560\) | 12490.0 | 0.00168304 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −796715. | −0.106405 | ||||||||
\(563\) | 701186. | 0.0932314 | 0.0466157 | − | 0.998913i | \(-0.485156\pi\) | ||||
0.0466157 | + | 0.998913i | \(0.485156\pi\) | |||||||
\(564\) | −1.43788e6 | −0.190338 | ||||||||
\(565\) | 6.42442e6 | 0.846668 | ||||||||
\(566\) | 5.55822e6 | 0.729280 | ||||||||
\(567\) | −10444.3 | −0.00136434 | ||||||||
\(568\) | 1.86947e6 | 0.243135 | ||||||||
\(569\) | −7.70015e6 | −0.997053 | −0.498527 | − | 0.866874i | \(-0.666125\pi\) | ||||
−0.498527 | + | 0.866874i | \(0.666125\pi\) | |||||||
\(570\) | −2.35969e6 | −0.304206 | ||||||||
\(571\) | 9.38506e6 | 1.20461 | 0.602306 | − | 0.798266i | \(-0.294249\pi\) | ||||
0.602306 | + | 0.798266i | \(0.294249\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.33734e6 | −0.424633 | ||||||||
\(574\) | 8468.78 | 0.00107286 | ||||||||
\(575\) | 197931. | 0.0249658 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 1.15237e7 | 1.44096 | 0.720481 | − | 0.693474i | \(-0.243921\pi\) | ||||
0.720481 | + | 0.693474i | \(0.243921\pi\) | |||||||
\(578\) | −5.05721e6 | −0.629639 | ||||||||
\(579\) | 1.81156e6 | 0.224572 | ||||||||
\(580\) | 517692. | 0.0639000 | ||||||||
\(581\) | −161782. | −0.0198833 | ||||||||
\(582\) | −6.02429e6 | −0.737222 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 24629.4 | 0.00298828 | ||||||||
\(585\) | 2.32351e6 | 0.280708 | ||||||||
\(586\) | −9.09079e6 | −1.09360 | ||||||||
\(587\) | −1.30019e7 | −1.55744 | −0.778721 | − | 0.627371i | \(-0.784131\pi\) | ||||
−0.778721 | + | 0.627371i | \(0.784131\pi\) | |||||||
\(588\) | −2.41984e6 | −0.288632 | ||||||||
\(589\) | −8.93114e6 | −1.06076 | ||||||||
\(590\) | 1.05199e6 | 0.124417 | ||||||||
\(591\) | 2.96100e6 | 0.348715 | ||||||||
\(592\) | 2.94880e6 | 0.345812 | ||||||||
\(593\) | −5.36206e6 | −0.626173 | −0.313087 | − | 0.949725i | \(-0.601363\pi\) | ||||
−0.313087 | + | 0.949725i | \(0.601363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19242.6 | 0.00222829 | ||||||||
\(596\) | −3.83722e6 | −0.442488 | ||||||||
\(597\) | 6.56517e6 | 0.753894 | ||||||||
\(598\) | 339031. | 0.0387692 | ||||||||
\(599\) | −7.35088e6 | −0.837090 | −0.418545 | − | 0.908196i | \(-0.637460\pi\) | ||||
−0.418545 | + | 0.908196i | \(0.637460\pi\) | |||||||
\(600\) | −1.25894e6 | −0.142766 | ||||||||
\(601\) | 1.36159e7 | 1.53766 | 0.768832 | − | 0.639451i | \(-0.220838\pi\) | ||||
0.768832 | + | 0.639451i | \(0.220838\pi\) | |||||||
\(602\) | 112878. | 0.0126945 | ||||||||
\(603\) | 539548. | 0.0604278 | ||||||||
\(604\) | 7.66940e6 | 0.855400 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.33223e6 | −0.147366 | ||||||||
\(607\) | −224378. | −0.0247177 | −0.0123589 | − | 0.999924i | \(-0.503934\pi\) | ||||
−0.0123589 | + | 0.999924i | \(0.503934\pi\) | |||||||
\(608\) | 2.18998e6 | 0.240260 | ||||||||
\(609\) | 15124.9 | 0.00165253 | ||||||||
\(610\) | 4.82378e6 | 0.524884 | ||||||||
\(611\) | 9.34561e6 | 1.01276 | ||||||||
\(612\) | 511147. | 0.0551655 | ||||||||
\(613\) | −1.03984e7 | −1.11767 | −0.558836 | − | 0.829278i | \(-0.688752\pi\) | ||||
−0.558836 | + | 0.829278i | \(0.688752\pi\) | |||||||
\(614\) | 1.19444e7 | 1.27863 | ||||||||
\(615\) | 366864. | 0.0391127 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.76529e6 | −0.609688 | −0.304844 | − | 0.952402i | \(-0.598604\pi\) | ||||
−0.304844 | + | 0.952402i | \(0.598604\pi\) | |||||||
\(618\) | 2.84653e6 | 0.299809 | ||||||||
\(619\) | 1.18149e7 | 1.23937 | 0.619686 | − | 0.784850i | \(-0.287260\pi\) | ||||
0.619686 | + | 0.784850i | \(0.287260\pi\) | |||||||
\(620\) | 2.04786e6 | 0.213954 | ||||||||
\(621\) | −66017.8 | −0.00686961 | ||||||||
\(622\) | 3.49235e6 | 0.361944 | ||||||||
\(623\) | 88827.6 | 0.00916913 | ||||||||
\(624\) | −2.15640e6 | −0.221701 | ||||||||
\(625\) | 1.84163e6 | 0.188583 | ||||||||
\(626\) | 1.99172e6 | 0.203139 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.19738e6 | −0.222334 | ||||||||
\(629\) | 4.54303e6 | 0.457846 | ||||||||
\(630\) | 15807.7 | 0.00158678 | ||||||||
\(631\) | 1.00792e7 | 1.00775 | 0.503877 | − | 0.863775i | \(-0.331906\pi\) | ||||
0.503877 | + | 0.863775i | \(0.331906\pi\) | |||||||
\(632\) | −1.64528e6 | −0.163851 | ||||||||
\(633\) | −5.32181e6 | −0.527898 | ||||||||
\(634\) | −1.09673e7 | −1.08362 | ||||||||
\(635\) | −3.47695e6 | −0.342188 | ||||||||
\(636\) | −3.65952e6 | −0.358741 | ||||||||
\(637\) | 1.57279e7 | 1.53576 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.36604e6 | 0.229230 | ||||||||
\(640\) | −502149. | −0.0484599 | ||||||||
\(641\) | 549446. | 0.0528178 | 0.0264089 | − | 0.999651i | \(-0.491593\pi\) | ||||
0.0264089 | + | 0.999651i | \(0.491593\pi\) | |||||||
\(642\) | −6.39839e6 | −0.612679 | ||||||||
\(643\) | 1.60686e7 | 1.53268 | 0.766338 | − | 0.642437i | \(-0.222077\pi\) | ||||
0.766338 | + | 0.642437i | \(0.222077\pi\) | |||||||
\(644\) | 2306.56 | 0.000219154 0 | ||||||||
\(645\) | 4.88982e6 | 0.462800 | ||||||||
\(646\) | 3.37397e6 | 0.318097 | ||||||||
\(647\) | −1.35520e7 | −1.27275 | −0.636373 | − | 0.771381i | \(-0.719566\pi\) | ||||
−0.636373 | + | 0.771381i | \(0.719566\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 8.18254e6 | 0.759635 | ||||||||
\(651\) | 59830.2 | 0.00553309 | ||||||||
\(652\) | −3.19934e6 | −0.294741 | ||||||||
\(653\) | 3.99537e6 | 0.366669 | 0.183334 | − | 0.983051i | \(-0.441311\pi\) | ||||
0.183334 | + | 0.983051i | \(0.441311\pi\) | |||||||
\(654\) | 719443. | 0.0657737 | ||||||||
\(655\) | −945221. | −0.0860855 | ||||||||
\(656\) | −340479. | −0.0308909 | ||||||||
\(657\) | 31171.6 | 0.00281738 | ||||||||
\(658\) | 63581.7 | 0.00572489 | ||||||||
\(659\) | −2.14695e7 | −1.92578 | −0.962892 | − | 0.269889i | \(-0.913013\pi\) | ||||
−0.962892 | + | 0.269889i | \(0.913013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.17516e6 | 0.549724 | 0.274862 | − | 0.961484i | \(-0.411368\pi\) | ||||
0.274862 | + | 0.961484i | \(0.411368\pi\) | |||||||
\(662\) | −1.43960e7 | −1.27673 | ||||||||
\(663\) | −3.32223e6 | −0.293526 | ||||||||
\(664\) | 6.50427e6 | 0.572504 | ||||||||
\(665\) | 104343. | 0.00914975 | ||||||||
\(666\) | 3.73207e6 | 0.326035 | ||||||||
\(667\) | 95603.0 | 0.00832065 | ||||||||
\(668\) | −1.00620e6 | −0.0872452 | ||||||||
\(669\) | −5.76970e6 | −0.498412 | ||||||||
\(670\) | −816616. | −0.0702798 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −14670.8 | −0.00125323 | ||||||||
\(673\) | −2.32597e7 | −1.97955 | −0.989776 | − | 0.142632i | \(-0.954444\pi\) | ||||
−0.989776 | + | 0.142632i | \(0.954444\pi\) | |||||||
\(674\) | −5.54533e6 | −0.470195 | ||||||||
\(675\) | −1.59334e6 | −0.134601 | ||||||||
\(676\) | 8.07496e6 | 0.679632 | ||||||||
\(677\) | −1.77561e6 | −0.148894 | −0.0744470 | − | 0.997225i | \(-0.523719\pi\) | ||||
−0.0744470 | + | 0.997225i | \(0.523719\pi\) | |||||||
\(678\) | −7.54612e6 | −0.630448 | ||||||||
\(679\) | 266388. | 0.0221738 | ||||||||
\(680\) | −773631. | −0.0641596 | ||||||||
\(681\) | −3.61661e6 | −0.298837 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.78941e6 | 0.392853 | 0.196426 | − | 0.980519i | \(-0.437066\pi\) | ||||
0.196426 | + | 0.980519i | \(0.437066\pi\) | |||||||
\(684\) | 2.77169e6 | 0.226519 | ||||||||
\(685\) | 8.60132e6 | 0.700388 | ||||||||
\(686\) | 214022. | 0.0173639 | ||||||||
\(687\) | 3.04819e6 | 0.246405 | ||||||||
\(688\) | −4.53814e6 | −0.365516 | ||||||||
\(689\) | 2.37853e7 | 1.90880 | ||||||||
\(690\) | 99919.1 | 0.00798962 | ||||||||
\(691\) | 5.00709e6 | 0.398924 | 0.199462 | − | 0.979906i | \(-0.436081\pi\) | ||||
0.199462 | + | 0.979906i | \(0.436081\pi\) | |||||||
\(692\) | 9.59868e6 | 0.761985 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.26504e6 | −0.414957 | ||||||||
\(695\) | 6.25332e6 | 0.491076 | ||||||||
\(696\) | −608080. | −0.0475815 | ||||||||
\(697\) | −524555. | −0.0408987 | ||||||||
\(698\) | −8.05066e6 | −0.625450 | ||||||||
\(699\) | 1.04645e7 | 0.810072 | ||||||||
\(700\) | 55668.8 | 0.00429405 | ||||||||
\(701\) | 3.77795e6 | 0.290376 | 0.145188 | − | 0.989404i | \(-0.453621\pi\) | ||||
0.145188 | + | 0.989404i | \(0.453621\pi\) | |||||||
\(702\) | −2.72919e6 | −0.209022 | ||||||||
\(703\) | 2.46345e7 | 1.87999 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.75433e6 | 0.208710 | ||||||||
\(706\) | −5.96916e6 | −0.450715 | ||||||||
\(707\) | 58909.6 | 0.00443239 | ||||||||
\(708\) | −1.23566e6 | −0.0926440 | ||||||||
\(709\) | 1.99946e6 | 0.149381 | 0.0746907 | − | 0.997207i | \(-0.476203\pi\) | ||||
0.0746907 | + | 0.997207i | \(0.476203\pi\) | |||||||
\(710\) | −3.58105e6 | −0.266603 | ||||||||
\(711\) | −2.08231e6 | −0.154480 | ||||||||
\(712\) | −3.57123e6 | −0.264008 | ||||||||
\(713\) | 378182. | 0.0278597 | ||||||||
\(714\) | −22602.4 | −0.00165924 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.70780e6 | −0.124496 | ||||||||
\(717\) | 9.66121e6 | 0.701832 | ||||||||
\(718\) | 1.69247e7 | 1.22520 | ||||||||
\(719\) | 9.72481e6 | 0.701551 | 0.350775 | − | 0.936460i | \(-0.385918\pi\) | ||||
0.350775 | + | 0.936460i | \(0.385918\pi\) | |||||||
\(720\) | −635533. | −0.0456885 | ||||||||
\(721\) | −125870. | −0.00901749 | ||||||||
\(722\) | 8.39089e6 | 0.599053 | ||||||||
\(723\) | 7.73611e6 | 0.550398 | ||||||||
\(724\) | −2.90669e6 | −0.206088 | ||||||||
\(725\) | 2.30738e6 | 0.163033 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.16302e6 | −0.292127 | −0.146064 | − | 0.989275i | \(-0.546660\pi\) | ||||
−0.146064 | + | 0.989275i | \(0.546660\pi\) | |||||||
\(728\) | 95353.7 | 0.00666821 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −47178.8 | −0.00327672 | ||||||||
\(731\) | −6.99163e6 | −0.483933 | ||||||||
\(732\) | −5.66601e6 | −0.390841 | ||||||||
\(733\) | 9.11162e6 | 0.626377 | 0.313188 | − | 0.949691i | \(-0.398603\pi\) | ||||
0.313188 | + | 0.949691i | \(0.398603\pi\) | |||||||
\(734\) | 1.36059e7 | 0.932156 | ||||||||
\(735\) | 4.63532e6 | 0.316491 | ||||||||
\(736\) | −92732.8 | −0.00631014 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −430919. | −0.0291242 | ||||||||
\(739\) | −1.13353e7 | −0.763523 | −0.381762 | − | 0.924261i | \(-0.624683\pi\) | ||||
−0.381762 | + | 0.924261i | \(0.624683\pi\) | |||||||
\(740\) | −5.64856e6 | −0.379191 | ||||||||
\(741\) | −1.80148e7 | −1.20527 | ||||||||
\(742\) | 161820. | 0.0107900 | ||||||||
\(743\) | −1.22060e7 | −0.811150 | −0.405575 | − | 0.914062i | \(-0.632929\pi\) | ||||
−0.405575 | + | 0.914062i | \(0.632929\pi\) | |||||||
\(744\) | −2.40541e6 | −0.159315 | ||||||||
\(745\) | 7.35038e6 | 0.485198 | ||||||||
\(746\) | 1.20469e7 | 0.792551 | ||||||||
\(747\) | 8.23196e6 | 0.539762 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 282930. | 0.0184278 | ||||||||
\(750\) | 5.85954e6 | 0.380373 | ||||||||
\(751\) | −2.07578e7 | −1.34301 | −0.671507 | − | 0.740998i | \(-0.734353\pi\) | ||||
−0.671507 | + | 0.740998i | \(0.734353\pi\) | |||||||
\(752\) | −2.55624e6 | −0.164838 | ||||||||
\(753\) | −7.65665e6 | −0.492098 | ||||||||
\(754\) | 3.95226e6 | 0.253173 | ||||||||
\(755\) | −1.46911e7 | −0.937966 | ||||||||
\(756\) | −18567.7 | −0.00118155 | ||||||||
\(757\) | 1.79946e7 | 1.14131 | 0.570653 | − | 0.821192i | \(-0.306690\pi\) | ||||
0.570653 | + | 0.821192i | \(0.306690\pi\) | |||||||
\(758\) | −7.13046e6 | −0.450759 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.19500e6 | −0.263450 | ||||||||
\(761\) | 1.66788e7 | 1.04401 | 0.522003 | − | 0.852943i | \(-0.325185\pi\) | ||||
0.522003 | + | 0.852943i | \(0.325185\pi\) | |||||||
\(762\) | 4.08403e6 | 0.254801 | ||||||||
\(763\) | −31813.0 | −0.00197831 | ||||||||
\(764\) | −5.93305e6 | −0.367743 | ||||||||
\(765\) | −979126. | −0.0604902 | ||||||||
\(766\) | 2.17584e7 | 1.33984 | ||||||||
\(767\) | 8.03127e6 | 0.492942 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | 1.10319e7 | 0.672718 | 0.336359 | − | 0.941734i | \(-0.390804\pi\) | ||||
0.336359 | + | 0.941734i | \(0.390804\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.75000e7 | −1.06023 | ||||||||
\(772\) | 3.22055e6 | 0.194485 | ||||||||
\(773\) | −3.43596e6 | −0.206823 | −0.103412 | − | 0.994639i | \(-0.532976\pi\) | ||||
−0.103412 | + | 0.994639i | \(0.532976\pi\) | |||||||
\(774\) | −5.74358e6 | −0.344612 | ||||||||
\(775\) | 9.12743e6 | 0.545876 | ||||||||
\(776\) | −1.07098e7 | −0.638453 | ||||||||
\(777\) | −165028. | −0.00980631 | ||||||||
\(778\) | 1.43534e7 | 0.850170 | ||||||||
\(779\) | −2.84439e6 | −0.167937 | ||||||||
\(780\) | 4.13068e6 | 0.243100 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −142868. | −0.00835444 | ||||||||
\(783\) | −769601. | −0.0448602 | ||||||||
\(784\) | −4.30194e6 | −0.249962 | ||||||||
\(785\) | 4.20919e6 | 0.243795 | ||||||||
\(786\) | 1.11026e6 | 0.0641013 | ||||||||
\(787\) | 1.14455e7 | 0.658717 | 0.329359 | − | 0.944205i | \(-0.393168\pi\) | ||||
0.329359 | + | 0.944205i | \(0.393168\pi\) | |||||||
\(788\) | 5.26401e6 | 0.301996 | ||||||||
\(789\) | 1.80784e7 | 1.03387 | ||||||||
\(790\) | 3.15162e6 | 0.179666 | ||||||||
\(791\) | 333682. | 0.0189623 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.68266e7 | 2.07960 | ||||||||
\(794\) | 2.08467e7 | 1.17351 | ||||||||
\(795\) | 7.00998e6 | 0.393368 | ||||||||
\(796\) | 1.16714e7 | 0.652891 | ||||||||
\(797\) | −3.15709e7 | −1.76052 | −0.880259 | − | 0.474493i | \(-0.842631\pi\) | ||||
−0.880259 | + | 0.474493i | \(0.842631\pi\) | |||||||
\(798\) | −122561. | −0.00681312 | ||||||||
\(799\) | −3.93824e6 | −0.218240 | ||||||||
\(800\) | −2.23811e6 | −0.123639 | ||||||||
\(801\) | −4.51983e6 | −0.248909 | ||||||||
\(802\) | −2.56710e6 | −0.140931 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 959196. | 0.0523320 | ||||||||
\(805\) | −4418.32 | −0.000240307 0 | ||||||||
\(806\) | 1.56341e7 | 0.847688 | ||||||||
\(807\) | −1.59976e7 | −0.864712 | ||||||||
\(808\) | −2.36840e6 | −0.127622 | ||||||||
\(809\) | −3.31409e6 | −0.178030 | −0.0890148 | − | 0.996030i | \(-0.528372\pi\) | ||||
−0.0890148 | + | 0.996030i | \(0.528372\pi\) | |||||||
\(810\) | −804346. | −0.0430755 | ||||||||
\(811\) | −7.61602e6 | −0.406608 | −0.203304 | − | 0.979116i | \(-0.565168\pi\) | ||||
−0.203304 | + | 0.979116i | \(0.565168\pi\) | |||||||
\(812\) | 26888.7 | 0.00143113 | ||||||||
\(813\) | 1.66306e6 | 0.0882434 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.12848e6 | 0.323190 | ||||||||
\(816\) | 908706. | 0.0477747 | ||||||||
\(817\) | −3.79121e7 | −1.98711 | ||||||||
\(818\) | −2.03378e7 | −1.06273 | ||||||||
\(819\) | 120682. | 0.00628685 | ||||||||
\(820\) | 652203. | 0.0338726 | ||||||||
\(821\) | −3.12518e7 | −1.61815 | −0.809073 | − | 0.587708i | \(-0.800030\pi\) | ||||
−0.809073 | + | 0.587708i | \(0.800030\pi\) | |||||||
\(822\) | −1.01031e7 | −0.521525 | ||||||||
\(823\) | 1.24276e7 | 0.639570 | 0.319785 | − | 0.947490i | \(-0.396389\pi\) | ||||
0.319785 | + | 0.947490i | \(0.396389\pi\) | |||||||
\(824\) | 5.06049e6 | 0.259642 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 54639.7 | 0.00278650 | ||||||||
\(827\) | −2.78542e7 | −1.41621 | −0.708104 | − | 0.706108i | \(-0.750449\pi\) | ||||
−0.708104 | + | 0.706108i | \(0.750449\pi\) | |||||||
\(828\) | −117365. | −0.00594925 | ||||||||
\(829\) | 727915. | 0.0367870 | 0.0183935 | − | 0.999831i | \(-0.494145\pi\) | ||||
0.0183935 | + | 0.999831i | \(0.494145\pi\) | |||||||
\(830\) | −1.24592e7 | −0.627763 | ||||||||
\(831\) | −1.29330e7 | −0.649677 | ||||||||
\(832\) | −3.83360e6 | −0.191999 | ||||||||
\(833\) | −6.62774e6 | −0.330943 | ||||||||
\(834\) | −7.34514e6 | −0.365666 | ||||||||
\(835\) | 1.92742e6 | 0.0956664 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.04435e6 | −0.150204 | ||||||||
\(838\) | −9.77677e6 | −0.480934 | ||||||||
\(839\) | −1.25803e7 | −0.617000 | −0.308500 | − | 0.951224i | \(-0.599827\pi\) | ||||
−0.308500 | + | 0.951224i | \(0.599827\pi\) | |||||||
\(840\) | 28102.6 | 0.00137419 | ||||||||
\(841\) | −1.93967e7 | −0.945664 | ||||||||
\(842\) | 2.14563e7 | 1.04297 | ||||||||
\(843\) | −1.79261e6 | −0.0868793 | ||||||||
\(844\) | −9.46100e6 | −0.457173 | ||||||||
\(845\) | −1.54680e7 | −0.745232 | ||||||||
\(846\) | −3.23524e6 | −0.155410 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.50581e6 | −0.310679 | ||||||||
\(849\) | 1.25060e7 | 0.595455 | ||||||||
\(850\) | −3.44812e6 | −0.163695 | ||||||||
\(851\) | −1.04313e6 | −0.0493758 | ||||||||
\(852\) | 4.20630e6 | 0.198519 | ||||||||
\(853\) | 2.47398e6 | 0.116419 | 0.0582095 | − | 0.998304i | \(-0.481461\pi\) | ||||
0.0582095 | + | 0.998304i | \(0.481461\pi\) | |||||||
\(854\) | 250545. | 0.0117555 | ||||||||
\(855\) | −5.30930e6 | −0.248383 | ||||||||
\(856\) | −1.13749e7 | −0.530596 | ||||||||
\(857\) | −3.29116e7 | −1.53072 | −0.765362 | − | 0.643600i | \(-0.777440\pi\) | ||||
−0.765362 | + | 0.643600i | \(0.777440\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.12463e7 | −0.520028 | −0.260014 | − | 0.965605i | \(-0.583727\pi\) | ||||
−0.260014 | + | 0.965605i | \(0.583727\pi\) | |||||||
\(860\) | 8.69302e6 | 0.400797 | ||||||||
\(861\) | 19054.8 | 0.000875983 0 | ||||||||
\(862\) | 2.19694e7 | 1.00705 | ||||||||
\(863\) | −2.01704e7 | −0.921910 | −0.460955 | − | 0.887424i | \(-0.652493\pi\) | ||||
−0.460955 | + | 0.887424i | \(0.652493\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | −1.83867e7 | −0.835534 | ||||||||
\(866\) | −424669. | −0.0192422 | ||||||||
\(867\) | −1.13787e7 | −0.514098 | ||||||||
\(868\) | 106365. | 0.00479180 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.16481e6 | 0.0521742 | ||||||||
\(871\) | −6.23436e6 | −0.278449 | ||||||||
\(872\) | 1.27901e6 | 0.0569617 | ||||||||
\(873\) | −1.35546e7 | −0.601939 | ||||||||
\(874\) | −774699. | −0.0343048 | ||||||||
\(875\) | −259103. | −0.0114407 | ||||||||
\(876\) | 55416.2 | 0.00243992 | ||||||||
\(877\) | 2.04223e7 | 0.896613 | 0.448307 | − | 0.893880i | \(-0.352027\pi\) | ||||
0.448307 | + | 0.893880i | \(0.352027\pi\) | |||||||
\(878\) | −1.83746e7 | −0.804420 | ||||||||
\(879\) | −2.04543e7 | −0.892919 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.49818e6 | 0.195253 | 0.0976263 | − | 0.995223i | \(-0.468875\pi\) | ||||
0.0976263 | + | 0.995223i | \(0.468875\pi\) | |||||||
\(882\) | −5.44465e6 | −0.235667 | ||||||||
\(883\) | 3.81825e6 | 0.164802 | 0.0824009 | − | 0.996599i | \(-0.473741\pi\) | ||||
0.0824009 | + | 0.996599i | \(0.473741\pi\) | |||||||
\(884\) | −5.90619e6 | −0.254201 | ||||||||
\(885\) | 2.36697e6 | 0.101586 | ||||||||
\(886\) | 1.99336e7 | 0.853102 | ||||||||
\(887\) | −2.15429e7 | −0.919380 | −0.459690 | − | 0.888080i | \(-0.652039\pi\) | ||||
−0.459690 | + | 0.888080i | \(0.652039\pi\) | |||||||
\(888\) | 6.63479e6 | 0.282355 | ||||||||
\(889\) | −180591. | −0.00766377 | ||||||||
\(890\) | 6.84085e6 | 0.289491 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.02573e7 | −0.431637 | ||||||||
\(893\) | −2.13551e7 | −0.896132 | ||||||||
\(894\) | −8.63375e6 | −0.361290 | ||||||||
\(895\) | 3.27137e6 | 0.136512 | ||||||||
\(896\) | −26081.4 | −0.00108533 | ||||||||
\(897\) | 762821. | 0.0316549 | ||||||||
\(898\) | −2.52188e7 | −1.04360 | ||||||||
\(899\) | 4.40865e6 | 0.181931 | ||||||||
\(900\) | −2.83261e6 | −0.116568 | ||||||||
\(901\) | −1.00231e7 | −0.411330 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 253975. | 0.0103651 | ||||||||
\(904\) | −1.34153e7 | −0.545984 | ||||||||
\(905\) | 5.56790e6 | 0.225980 | ||||||||
\(906\) | 1.72562e7 | 0.698431 | ||||||||
\(907\) | −6.62481e6 | −0.267396 | −0.133698 | − | 0.991022i | \(-0.542685\pi\) | ||||
−0.133698 | + | 0.991022i | \(0.542685\pi\) | |||||||
\(908\) | −6.42954e6 | −0.258800 | ||||||||
\(909\) | −2.99751e6 | −0.120324 | ||||||||
\(910\) | −182654. | −0.00731184 | ||||||||
\(911\) | −3.05177e7 | −1.21830 | −0.609152 | − | 0.793053i | \(-0.708490\pi\) | ||||
−0.609152 | + | 0.793053i | \(0.708490\pi\) | |||||||
\(912\) | 4.92745e6 | 0.196171 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.21817e7 | 1.27422 | ||||||||
\(915\) | 1.08535e7 | 0.428566 | ||||||||
\(916\) | 5.41900e6 | 0.213393 | ||||||||
\(917\) | −49094.4 | −0.00192801 | ||||||||
\(918\) | 1.15008e6 | 0.0450424 | ||||||||
\(919\) | −1.55296e7 | −0.606556 | −0.303278 | − | 0.952902i | \(-0.598081\pi\) | ||||
−0.303278 | + | 0.952902i | \(0.598081\pi\) | |||||||
\(920\) | 177634. | 0.00691921 | ||||||||
\(921\) | 2.68749e7 | 1.04399 | ||||||||
\(922\) | 7.04564e6 | 0.272956 | ||||||||
\(923\) | −2.73391e7 | −1.05628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.51760e7 | −0.967458 | ||||||||
\(926\) | −1.05762e7 | −0.405324 | ||||||||
\(927\) | 6.40469e6 | 0.244793 | ||||||||
\(928\) | −1.08103e6 | −0.0412068 | ||||||||
\(929\) | 4.76935e7 | 1.81309 | 0.906546 | − | 0.422108i | \(-0.138710\pi\) | ||||
0.906546 | + | 0.422108i | \(0.138710\pi\) | |||||||
\(930\) | 4.60768e6 | 0.174693 | ||||||||
\(931\) | −3.59389e7 | −1.35891 | ||||||||
\(932\) | 1.86035e7 | 0.701543 | ||||||||
\(933\) | 7.85778e6 | 0.295526 | ||||||||
\(934\) | 3.25106e7 | 1.21943 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.85190e6 | −0.181018 | ||||||||
\(937\) | 1.43460e7 | 0.533805 | 0.266902 | − | 0.963724i | \(-0.414000\pi\) | ||||
0.266902 | + | 0.963724i | \(0.414000\pi\) | |||||||
\(938\) | −42414.6 | −0.00157401 | ||||||||
\(939\) | 4.48138e6 | 0.165862 | ||||||||
\(940\) | 4.89659e6 | 0.180748 | ||||||||
\(941\) | 2.95359e7 | 1.08737 | 0.543683 | − | 0.839291i | \(-0.317029\pi\) | ||||
0.543683 | + | 0.839291i | \(0.317029\pi\) | |||||||
\(942\) | −4.94411e6 | −0.181535 | ||||||||
\(943\) | 120444. | 0.00441067 | ||||||||
\(944\) | −2.19674e6 | −0.0802320 | ||||||||
\(945\) | 35567.3 | 0.00129560 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.69481e7 | 0.614109 | 0.307054 | − | 0.951692i | \(-0.400657\pi\) | ||||
0.307054 | + | 0.951692i | \(0.400657\pi\) | |||||||
\(948\) | −3.70189e6 | −0.133783 | ||||||||
\(949\) | −360181. | −0.0129824 | ||||||||
\(950\) | −1.86974e7 | −0.672159 | ||||||||
\(951\) | −2.46764e7 | −0.884771 | ||||||||
\(952\) | −40182.0 | −0.00143694 | ||||||||
\(953\) | −3.48842e7 | −1.24422 | −0.622109 | − | 0.782930i | \(-0.713724\pi\) | ||||
−0.622109 | + | 0.782930i | \(0.713724\pi\) | |||||||
\(954\) | −8.23392e6 | −0.292911 | ||||||||
\(955\) | 1.13650e7 | 0.403239 | ||||||||
\(956\) | 1.71755e7 | 0.607805 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.24539e7 | 0.790456 | ||||||||
\(959\) | 446749. | 0.0156862 | ||||||||
\(960\) | −1.12984e6 | −0.0395674 | ||||||||
\(961\) | −1.11896e7 | −0.390848 | ||||||||
\(962\) | −4.31233e7 | −1.50236 | ||||||||
\(963\) | −1.43964e7 | −0.500251 | ||||||||
\(964\) | 1.37531e7 | 0.476659 | ||||||||
\(965\) | −6.16912e6 | −0.213258 | ||||||||
\(966\) | 5189.75 | 0.000178939 0 | ||||||||
\(967\) | 4.59896e6 | 0.158159 | 0.0790794 | − | 0.996868i | \(-0.474802\pi\) | ||||
0.0790794 | + | 0.996868i | \(0.474802\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.59142e6 | 0.259725 | ||||||||
\(970\) | 2.05152e7 | 0.700078 | ||||||||
\(971\) | −2.43140e7 | −0.827578 | −0.413789 | − | 0.910373i | \(-0.635795\pi\) | ||||
−0.413789 | + | 0.910373i | \(0.635795\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 324794. | 0.0109983 | ||||||||
\(974\) | 1.92500e7 | 0.650180 | ||||||||
\(975\) | 1.84107e7 | 0.620239 | ||||||||
\(976\) | −1.00729e7 | −0.338478 | ||||||||
\(977\) | 4.17905e6 | 0.140069 | 0.0700344 | − | 0.997545i | \(-0.477689\pi\) | ||||
0.0700344 | + | 0.997545i | \(0.477689\pi\) | |||||||
\(978\) | −7.19850e6 | −0.240655 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 8.24057e6 | 0.274089 | ||||||||
\(981\) | 1.61875e6 | 0.0537040 | ||||||||
\(982\) | −1.55868e7 | −0.515796 | ||||||||
\(983\) | 3.74303e7 | 1.23549 | 0.617746 | − | 0.786378i | \(-0.288046\pi\) | ||||
0.617746 | + | 0.786378i | \(0.288046\pi\) | |||||||
\(984\) | −766078. | −0.0252223 | ||||||||
\(985\) | −1.00835e7 | −0.331145 | ||||||||
\(986\) | −1.66548e6 | −0.0545566 | ||||||||
\(987\) | 143059. | 0.00467435 | ||||||||
\(988\) | −3.20263e7 | −1.04379 | ||||||||
\(989\) | 1.60535e6 | 0.0521892 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.60166e7 | −1.48844 | −0.744218 | − | 0.667937i | \(-0.767178\pi\) | ||||
−0.744218 | + | 0.667937i | \(0.767178\pi\) | |||||||
\(992\) | −4.27629e6 | −0.137971 | ||||||||
\(993\) | −3.23911e7 | −1.04244 | ||||||||
\(994\) | −185998. | −0.00597094 | ||||||||
\(995\) | −2.23571e7 | −0.715910 | ||||||||
\(996\) | 1.46346e7 | 0.467447 | ||||||||
\(997\) | 2.49411e7 | 0.794652 | 0.397326 | − | 0.917677i | \(-0.369938\pi\) | ||||
0.397326 | + | 0.917677i | \(0.369938\pi\) | |||||||
\(998\) | 3.30677e7 | 1.05094 | ||||||||
\(999\) | 8.39716e6 | 0.266207 |
(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 | 726.6.a.be.1.2 | 4 | ||
11.3 | even | 5 | 66.6.e.a.31.1 | ✓ | 8 | ||
11.4 | even | 5 | 66.6.e.a.49.1 | yes | 8 | ||
11.10 | odd | 2 | 726.6.a.bb.1.2 | 4 | |||
33.14 | odd | 10 | 198.6.f.c.163.2 | 8 | |||
33.26 | odd | 10 | 198.6.f.c.181.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
66.6.e.a.31.1 | ✓ | 8 | 11.3 | even | 5 | ||
66.6.e.a.49.1 | yes | 8 | 11.4 | even | 5 | ||
198.6.f.c.163.2 | 8 | 33.14 | odd | 10 | |||
198.6.f.c.181.2 | 8 | 33.26 | odd | 10 | |||
726.6.a.bb.1.2 | 4 | 11.10 | odd | 2 | |||
726.6.a.be.1.2 | 4 | 1.1 | even | 1 | trivial |