Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,6,Mod(1,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, 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("325.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.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: | \(52.1247414392\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 257 x^{9} + 1165 x^{8} + 22234 x^{7} - 90282 x^{6} - 751180 x^{5} + 2564400 x^{4} + \cdots + 44115200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.89241\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.89241 | −0.511311 | −0.255656 | − | 0.966768i | \(-0.582291\pi\) | ||||
−0.255656 | + | 0.966768i | \(0.582291\pi\) | |||||||
\(3\) | 3.45730 | 0.221786 | 0.110893 | − | 0.993832i | \(-0.464629\pi\) | ||||
0.110893 | + | 0.993832i | \(0.464629\pi\) | |||||||
\(4\) | −23.6340 | −0.738561 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −9.99993 | −0.113402 | ||||||||
\(7\) | 148.288 | 1.14383 | 0.571914 | − | 0.820313i | \(-0.306201\pi\) | ||||
0.571914 | + | 0.820313i | \(0.306201\pi\) | |||||||
\(8\) | 160.916 | 0.888945 | ||||||||
\(9\) | −231.047 | −0.950811 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −712.658 | −1.77582 | −0.887912 | − | 0.460014i | \(-0.847844\pi\) | ||||
−0.887912 | + | 0.460014i | \(0.847844\pi\) | |||||||
\(12\) | −81.7096 | −0.163802 | ||||||||
\(13\) | −169.000 | −0.277350 | ||||||||
\(14\) | −428.910 | −0.584852 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 290.850 | 0.284033 | ||||||||
\(17\) | 1131.92 | 0.949935 | 0.474968 | − | 0.880003i | \(-0.342460\pi\) | ||||
0.474968 | + | 0.880003i | \(0.342460\pi\) | |||||||
\(18\) | 668.283 | 0.486160 | ||||||||
\(19\) | 1400.39 | 0.889947 | 0.444974 | − | 0.895544i | \(-0.353213\pi\) | ||||
0.444974 | + | 0.895544i | \(0.353213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 512.676 | 0.253685 | ||||||||
\(22\) | 2061.30 | 0.907998 | ||||||||
\(23\) | −897.571 | −0.353793 | −0.176896 | − | 0.984229i | \(-0.556606\pi\) | ||||
−0.176896 | + | 0.984229i | \(0.556606\pi\) | |||||||
\(24\) | 556.336 | 0.197156 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 488.818 | 0.141812 | ||||||||
\(27\) | −1638.92 | −0.432662 | ||||||||
\(28\) | −3504.63 | −0.844787 | ||||||||
\(29\) | 3238.07 | 0.714975 | 0.357488 | − | 0.933918i | \(-0.383633\pi\) | ||||
0.357488 | + | 0.933918i | \(0.383633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7976.53 | −1.49077 | −0.745383 | − | 0.666636i | \(-0.767733\pi\) | ||||
−0.745383 | + | 0.666636i | \(0.767733\pi\) | |||||||
\(32\) | −5990.58 | −1.03417 | ||||||||
\(33\) | −2463.87 | −0.393852 | ||||||||
\(34\) | −3273.98 | −0.485712 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5460.56 | 0.702232 | ||||||||
\(37\) | −4978.35 | −0.597835 | −0.298917 | − | 0.954279i | \(-0.596626\pi\) | ||||
−0.298917 | + | 0.954279i | \(0.596626\pi\) | |||||||
\(38\) | −4050.50 | −0.455040 | ||||||||
\(39\) | −584.284 | −0.0615123 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15559.9 | −1.44560 | −0.722800 | − | 0.691057i | \(-0.757145\pi\) | ||||
−0.722800 | + | 0.691057i | \(0.757145\pi\) | |||||||
\(42\) | −1482.87 | −0.129712 | ||||||||
\(43\) | 2308.61 | 0.190405 | 0.0952026 | − | 0.995458i | \(-0.469650\pi\) | ||||
0.0952026 | + | 0.995458i | \(0.469650\pi\) | |||||||
\(44\) | 16842.9 | 1.31155 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2596.15 | 0.180898 | ||||||||
\(47\) | 7602.52 | 0.502011 | 0.251005 | − | 0.967986i | \(-0.419239\pi\) | ||||
0.251005 | + | 0.967986i | \(0.419239\pi\) | |||||||
\(48\) | 1005.56 | 0.0629946 | ||||||||
\(49\) | 5182.35 | 0.308344 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3913.39 | 0.210682 | ||||||||
\(52\) | 3994.14 | 0.204840 | ||||||||
\(53\) | 14138.1 | 0.691357 | 0.345678 | − | 0.938353i | \(-0.387649\pi\) | ||||
0.345678 | + | 0.938353i | \(0.387649\pi\) | |||||||
\(54\) | 4740.44 | 0.221225 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 23862.0 | 1.01680 | ||||||||
\(57\) | 4841.56 | 0.197378 | ||||||||
\(58\) | −9365.83 | −0.365575 | ||||||||
\(59\) | 49808.7 | 1.86284 | 0.931419 | − | 0.363948i | \(-0.118572\pi\) | ||||
0.931419 | + | 0.363948i | \(0.118572\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2516.69 | −0.0865973 | −0.0432986 | − | 0.999062i | \(-0.513787\pi\) | ||||
−0.0432986 | + | 0.999062i | \(0.513787\pi\) | |||||||
\(62\) | 23071.4 | 0.762245 | ||||||||
\(63\) | −34261.5 | −1.08757 | ||||||||
\(64\) | 8020.03 | 0.244752 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7126.54 | 0.201381 | ||||||||
\(67\) | 38549.3 | 1.04913 | 0.524566 | − | 0.851370i | \(-0.324228\pi\) | ||||
0.524566 | + | 0.851370i | \(0.324228\pi\) | |||||||
\(68\) | −26751.8 | −0.701585 | ||||||||
\(69\) | −3103.17 | −0.0784663 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 68008.5 | 1.60110 | 0.800548 | − | 0.599269i | \(-0.204542\pi\) | ||||
0.800548 | + | 0.599269i | \(0.204542\pi\) | |||||||
\(72\) | −37179.2 | −0.845219 | ||||||||
\(73\) | 21305.2 | 0.467927 | 0.233963 | − | 0.972245i | \(-0.424830\pi\) | ||||
0.233963 | + | 0.972245i | \(0.424830\pi\) | |||||||
\(74\) | 14399.4 | 0.305680 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −33096.7 | −0.657280 | ||||||||
\(77\) | −105679. | −2.03124 | ||||||||
\(78\) | 1689.99 | 0.0314519 | ||||||||
\(79\) | 3984.60 | 0.0718318 | 0.0359159 | − | 0.999355i | \(-0.488565\pi\) | ||||
0.0359159 | + | 0.999355i | \(0.488565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 50478.2 | 0.854853 | ||||||||
\(82\) | 45005.8 | 0.739152 | ||||||||
\(83\) | 13876.6 | 0.221100 | 0.110550 | − | 0.993871i | \(-0.464739\pi\) | ||||
0.110550 | + | 0.993871i | \(0.464739\pi\) | |||||||
\(84\) | −12116.6 | −0.187362 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6677.44 | −0.0973563 | ||||||||
\(87\) | 11195.0 | 0.158571 | ||||||||
\(88\) | −114678. | −1.57861 | ||||||||
\(89\) | 89289.8 | 1.19489 | 0.597443 | − | 0.801911i | \(-0.296183\pi\) | ||||
0.597443 | + | 0.801911i | \(0.296183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25060.7 | −0.317241 | ||||||||
\(92\) | 21213.1 | 0.261298 | ||||||||
\(93\) | −27577.2 | −0.330631 | ||||||||
\(94\) | −21989.6 | −0.256684 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −20711.2 | −0.229365 | ||||||||
\(97\) | 147549. | 1.59223 | 0.796116 | − | 0.605145i | \(-0.206885\pi\) | ||||
0.796116 | + | 0.605145i | \(0.206885\pi\) | |||||||
\(98\) | −14989.5 | −0.157660 | ||||||||
\(99\) | 164658. | 1.68847 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10084.2 | −0.0983642 | −0.0491821 | − | 0.998790i | \(-0.515661\pi\) | ||||
−0.0491821 | + | 0.998790i | \(0.515661\pi\) | |||||||
\(102\) | −11319.1 | −0.107724 | ||||||||
\(103\) | −175080. | −1.62608 | −0.813041 | − | 0.582206i | \(-0.802190\pi\) | ||||
−0.813041 | + | 0.582206i | \(0.802190\pi\) | |||||||
\(104\) | −27194.9 | −0.246549 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −40893.3 | −0.353498 | ||||||||
\(107\) | 225117. | 1.90086 | 0.950428 | − | 0.310946i | \(-0.100646\pi\) | ||||
0.950428 | + | 0.310946i | \(0.100646\pi\) | |||||||
\(108\) | 38734.2 | 0.319547 | ||||||||
\(109\) | 25083.5 | 0.202219 | 0.101109 | − | 0.994875i | \(-0.467761\pi\) | ||||
0.101109 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17211.6 | −0.132591 | ||||||||
\(112\) | 43129.6 | 0.324885 | ||||||||
\(113\) | 39258.9 | 0.289229 | 0.144615 | − | 0.989488i | \(-0.453806\pi\) | ||||
0.144615 | + | 0.989488i | \(0.453806\pi\) | |||||||
\(114\) | −14003.8 | −0.100921 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −76528.3 | −0.528053 | ||||||||
\(117\) | 39047.0 | 0.263708 | ||||||||
\(118\) | −144067. | −0.952490 | ||||||||
\(119\) | 167850. | 1.08656 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 346831. | 2.15355 | ||||||||
\(122\) | 7279.29 | 0.0442782 | ||||||||
\(123\) | −53795.4 | −0.320614 | ||||||||
\(124\) | 188517. | 1.10102 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 99098.4 | 0.556084 | ||||||||
\(127\) | 267258. | 1.47035 | 0.735177 | − | 0.677875i | \(-0.237099\pi\) | ||||
0.735177 | + | 0.677875i | \(0.237099\pi\) | |||||||
\(128\) | 168501. | 0.909031 | ||||||||
\(129\) | 7981.55 | 0.0422292 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −157114. | −0.799903 | −0.399952 | − | 0.916536i | \(-0.630973\pi\) | ||||
−0.399952 | + | 0.916536i | \(0.630973\pi\) | |||||||
\(132\) | 58231.1 | 0.290884 | ||||||||
\(133\) | 207661. | 1.01795 | ||||||||
\(134\) | −111501. | −0.536433 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 182145. | 0.844441 | ||||||||
\(137\) | −132383. | −0.602603 | −0.301302 | − | 0.953529i | \(-0.597421\pi\) | ||||
−0.301302 | + | 0.953529i | \(0.597421\pi\) | |||||||
\(138\) | 8975.65 | 0.0401207 | ||||||||
\(139\) | −285040. | −1.25132 | −0.625661 | − | 0.780095i | \(-0.715171\pi\) | ||||
−0.625661 | + | 0.780095i | \(0.715171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26284.2 | 0.111339 | ||||||||
\(142\) | −196709. | −0.818658 | ||||||||
\(143\) | 120439. | 0.492525 | ||||||||
\(144\) | −67200.1 | −0.270062 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −61623.4 | −0.239256 | ||||||||
\(147\) | 17916.9 | 0.0683864 | ||||||||
\(148\) | 117658. | 0.441537 | ||||||||
\(149\) | −156686. | −0.578180 | −0.289090 | − | 0.957302i | \(-0.593353\pi\) | ||||
−0.289090 | + | 0.957302i | \(0.593353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 422557. | 1.50814 | 0.754072 | − | 0.656792i | \(-0.228087\pi\) | ||||
0.754072 | + | 0.656792i | \(0.228087\pi\) | |||||||
\(152\) | 225345. | 0.791115 | ||||||||
\(153\) | −261527. | −0.903209 | ||||||||
\(154\) | 305666. | 1.03859 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13808.9 | 0.0454306 | ||||||||
\(157\) | 129540. | 0.419427 | 0.209713 | − | 0.977763i | \(-0.432747\pi\) | ||||
0.209713 | + | 0.977763i | \(0.432747\pi\) | |||||||
\(158\) | −11525.1 | −0.0367284 | ||||||||
\(159\) | 48879.7 | 0.153333 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −133099. | −0.404679 | ||||||||
\(162\) | −146004. | −0.437096 | ||||||||
\(163\) | −616763. | −1.81823 | −0.909116 | − | 0.416542i | \(-0.863242\pi\) | ||||
−0.909116 | + | 0.416542i | \(0.863242\pi\) | |||||||
\(164\) | 367743. | 1.06766 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −40136.9 | −0.113051 | ||||||||
\(167\) | −512670. | −1.42248 | −0.711241 | − | 0.702948i | \(-0.751867\pi\) | ||||
−0.711241 | + | 0.702948i | \(0.751867\pi\) | |||||||
\(168\) | 82498.0 | 0.225512 | ||||||||
\(169\) | 28561.0 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −323556. | −0.846172 | ||||||||
\(172\) | −54561.5 | −0.140626 | ||||||||
\(173\) | 462817. | 1.17569 | 0.587846 | − | 0.808973i | \(-0.299976\pi\) | ||||
0.587846 | + | 0.808973i | \(0.299976\pi\) | |||||||
\(174\) | −32380.5 | −0.0810793 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −207277. | −0.504393 | ||||||||
\(177\) | 172204. | 0.413151 | ||||||||
\(178\) | −258263. | −0.610959 | ||||||||
\(179\) | 413926. | 0.965584 | 0.482792 | − | 0.875735i | \(-0.339623\pi\) | ||||
0.482792 | + | 0.875735i | \(0.339623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −167089. | −0.379099 | −0.189549 | − | 0.981871i | \(-0.560703\pi\) | ||||
−0.189549 | + | 0.981871i | \(0.560703\pi\) | |||||||
\(182\) | 72485.8 | 0.162209 | ||||||||
\(183\) | −8700.93 | −0.0192061 | ||||||||
\(184\) | −144434. | −0.314503 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 79764.7 | 0.169055 | ||||||||
\(187\) | −806673. | −1.68692 | ||||||||
\(188\) | −179678. | −0.370766 | ||||||||
\(189\) | −243033. | −0.494892 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 30723.8 | 0.0609385 | 0.0304692 | − | 0.999536i | \(-0.490300\pi\) | ||||
0.0304692 | + | 0.999536i | \(0.490300\pi\) | |||||||
\(192\) | 27727.6 | 0.0542825 | ||||||||
\(193\) | 1.01259e6 | 1.95677 | 0.978387 | − | 0.206784i | \(-0.0662996\pi\) | ||||
0.978387 | + | 0.206784i | \(0.0662996\pi\) | |||||||
\(194\) | −426772. | −0.814125 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −122479. | −0.227731 | ||||||||
\(197\) | 422275. | 0.775229 | 0.387614 | − | 0.921822i | \(-0.373299\pi\) | ||||
0.387614 | + | 0.921822i | \(0.373299\pi\) | |||||||
\(198\) | −476258. | −0.863335 | ||||||||
\(199\) | 553506. | 0.990808 | 0.495404 | − | 0.868663i | \(-0.335020\pi\) | ||||
0.495404 | + | 0.868663i | \(0.335020\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 133277. | 0.232683 | ||||||||
\(202\) | 29167.6 | 0.0502947 | ||||||||
\(203\) | 480167. | 0.817809 | ||||||||
\(204\) | −92488.9 | −0.155602 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 506402. | 0.831434 | ||||||||
\(207\) | 207381. | 0.336390 | ||||||||
\(208\) | −49153.7 | −0.0787767 | ||||||||
\(209\) | −997998. | −1.58039 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −758171. | −1.17236 | −0.586180 | − | 0.810181i | \(-0.699369\pi\) | ||||
−0.586180 | + | 0.810181i | \(0.699369\pi\) | |||||||
\(212\) | −334140. | −0.510609 | ||||||||
\(213\) | 235126. | 0.355100 | ||||||||
\(214\) | −651132. | −0.971928 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −263729. | −0.384613 | ||||||||
\(217\) | −1.18282e6 | −1.70518 | ||||||||
\(218\) | −72551.8 | −0.103397 | ||||||||
\(219\) | 73658.4 | 0.103780 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −191295. | −0.263465 | ||||||||
\(222\) | 49783.2 | 0.0677954 | ||||||||
\(223\) | 142765. | 0.192247 | 0.0961236 | − | 0.995369i | \(-0.469356\pi\) | ||||
0.0961236 | + | 0.995369i | \(0.469356\pi\) | |||||||
\(224\) | −888332. | −1.18292 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −113553. | −0.147886 | ||||||||
\(227\) | −578969. | −0.745746 | −0.372873 | − | 0.927882i | \(-0.621627\pi\) | ||||
−0.372873 | + | 0.927882i | \(0.621627\pi\) | |||||||
\(228\) | −114425. | −0.145775 | ||||||||
\(229\) | −242404. | −0.305457 | −0.152729 | − | 0.988268i | \(-0.548806\pi\) | ||||
−0.152729 | + | 0.988268i | \(0.548806\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −365363. | −0.450500 | ||||||||
\(232\) | 521058. | 0.635574 | ||||||||
\(233\) | 540278. | 0.651970 | 0.325985 | − | 0.945375i | \(-0.394304\pi\) | ||||
0.325985 | + | 0.945375i | \(0.394304\pi\) | |||||||
\(234\) | −112940. | −0.134837 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.17718e6 | −1.37582 | ||||||||
\(237\) | 13776.0 | 0.0159313 | ||||||||
\(238\) | −485493. | −0.555572 | ||||||||
\(239\) | −223034. | −0.252567 | −0.126284 | − | 0.991994i | \(-0.540305\pi\) | ||||
−0.126284 | + | 0.991994i | \(0.540305\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.31596e6 | 1.45948 | 0.729742 | − | 0.683723i | \(-0.239640\pi\) | ||||
0.729742 | + | 0.683723i | \(0.239640\pi\) | |||||||
\(242\) | −1.00318e6 | −1.10113 | ||||||||
\(243\) | 572776. | 0.622256 | ||||||||
\(244\) | 59479.2 | 0.0639574 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 155598. | 0.163933 | ||||||||
\(247\) | −236666. | −0.246827 | ||||||||
\(248\) | −1.28355e6 | −1.32521 | ||||||||
\(249\) | 47975.6 | 0.0490368 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 475886. | 0.476781 | 0.238390 | − | 0.971169i | \(-0.423380\pi\) | ||||
0.238390 | + | 0.971169i | \(0.423380\pi\) | |||||||
\(252\) | 809735. | 0.803233 | ||||||||
\(253\) | 639661. | 0.628274 | ||||||||
\(254\) | −773021. | −0.751808 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −744016. | −0.709549 | ||||||||
\(257\) | 184678. | 0.174415 | 0.0872074 | − | 0.996190i | \(-0.472206\pi\) | ||||
0.0872074 | + | 0.996190i | \(0.472206\pi\) | |||||||
\(258\) | −23085.9 | −0.0215923 | ||||||||
\(259\) | −738230. | −0.683821 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −748146. | −0.679806 | ||||||||
\(262\) | 454439. | 0.408999 | ||||||||
\(263\) | −541222. | −0.482487 | −0.241244 | − | 0.970465i | \(-0.577555\pi\) | ||||
−0.241244 | + | 0.970465i | \(0.577555\pi\) | |||||||
\(264\) | −396477. | −0.350113 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −600641. | −0.520488 | ||||||||
\(267\) | 308702. | 0.265009 | ||||||||
\(268\) | −911073. | −0.774848 | ||||||||
\(269\) | 198419. | 0.167187 | 0.0835934 | − | 0.996500i | \(-0.473360\pi\) | ||||
0.0835934 | + | 0.996500i | \(0.473360\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −258403. | −0.213734 | −0.106867 | − | 0.994273i | \(-0.534082\pi\) | ||||
−0.106867 | + | 0.994273i | \(0.534082\pi\) | |||||||
\(272\) | 329219. | 0.269813 | ||||||||
\(273\) | −86642.3 | −0.0703596 | ||||||||
\(274\) | 382907. | 0.308118 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 73340.2 | 0.0579521 | ||||||||
\(277\) | −2.19835e6 | −1.72146 | −0.860729 | − | 0.509063i | \(-0.829992\pi\) | ||||
−0.860729 | + | 0.509063i | \(0.829992\pi\) | |||||||
\(278\) | 824454. | 0.639815 | ||||||||
\(279\) | 1.84295e6 | 1.41744 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −842.387 | −0.000636423 0 | −0.000318211 | − | 1.00000i | \(-0.500101\pi\) | ||||
−0.000318211 | 1.00000i | \(0.500101\pi\) | ||||||||
\(282\) | −76024.7 | −0.0569288 | ||||||||
\(283\) | 1.93205e6 | 1.43401 | 0.717006 | − | 0.697067i | \(-0.245512\pi\) | ||||
0.717006 | + | 0.697067i | \(0.245512\pi\) | |||||||
\(284\) | −1.60731e6 | −1.18251 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −348360. | −0.251833 | ||||||||
\(287\) | −2.30735e6 | −1.65352 | ||||||||
\(288\) | 1.38411e6 | 0.983305 | ||||||||
\(289\) | −138611. | −0.0976230 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 510120. | 0.353134 | ||||||||
\(292\) | −503526. | −0.345593 | ||||||||
\(293\) | 1.01321e6 | 0.689493 | 0.344747 | − | 0.938696i | \(-0.387965\pi\) | ||||
0.344747 | + | 0.938696i | \(0.387965\pi\) | |||||||
\(294\) | −51823.1 | −0.0349667 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −801098. | −0.531443 | ||||||||
\(297\) | 1.16799e6 | 0.768332 | ||||||||
\(298\) | 453199. | 0.295630 | ||||||||
\(299\) | 151689. | 0.0981245 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 342339. | 0.217791 | ||||||||
\(302\) | −1.22221e6 | −0.771131 | ||||||||
\(303\) | −34864.0 | −0.0218158 | ||||||||
\(304\) | 407303. | 0.252775 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 756444. | 0.461821 | ||||||||
\(307\) | 386274. | 0.233910 | 0.116955 | − | 0.993137i | \(-0.462687\pi\) | ||||
0.116955 | + | 0.993137i | \(0.462687\pi\) | |||||||
\(308\) | 2.49761e6 | 1.50019 | ||||||||
\(309\) | −605303. | −0.360642 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.37666e6 | 0.807099 | 0.403550 | − | 0.914958i | \(-0.367776\pi\) | ||||
0.403550 | + | 0.914958i | \(0.367776\pi\) | |||||||
\(312\) | −94020.8 | −0.0546811 | ||||||||
\(313\) | −541373. | −0.312346 | −0.156173 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156173 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(314\) | −374684. | −0.214458 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −94171.8 | −0.0530522 | ||||||||
\(317\) | 1.91853e6 | 1.07231 | 0.536154 | − | 0.844120i | \(-0.319876\pi\) | ||||
0.536154 | + | 0.844120i | \(0.319876\pi\) | |||||||
\(318\) | −141380. | −0.0784009 | ||||||||
\(319\) | −2.30764e6 | −1.26967 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 778297. | 0.421583 | ||||||||
\(322\) | 384977. | 0.206917 | ||||||||
\(323\) | 1.58513e6 | 0.845392 | ||||||||
\(324\) | −1.19300e6 | −0.631361 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.78393e6 | 0.929683 | ||||||||
\(327\) | 86721.2 | 0.0448493 | ||||||||
\(328\) | −2.50385e6 | −1.28506 | ||||||||
\(329\) | 1.12736e6 | 0.574215 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.40144e6 | −1.20477 | −0.602383 | − | 0.798207i | \(-0.705782\pi\) | ||||
−0.602383 | + | 0.798207i | \(0.705782\pi\) | |||||||
\(332\) | −327959. | −0.163296 | ||||||||
\(333\) | 1.15023e6 | 0.568428 | ||||||||
\(334\) | 1.48285e6 | 0.727331 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 149112. | 0.0720550 | ||||||||
\(337\) | 3.84325e6 | 1.84342 | 0.921709 | − | 0.387882i | \(-0.126793\pi\) | ||||
0.921709 | + | 0.387882i | \(0.126793\pi\) | |||||||
\(338\) | −82610.2 | −0.0393316 | ||||||||
\(339\) | 135730. | 0.0641469 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.68454e6 | 2.64734 | ||||||||
\(342\) | 935856. | 0.432657 | ||||||||
\(343\) | −1.72380e6 | −0.791136 | ||||||||
\(344\) | 371493. | 0.169260 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.33866e6 | −0.601144 | ||||||||
\(347\) | −1.02696e6 | −0.457858 | −0.228929 | − | 0.973443i | \(-0.573522\pi\) | ||||
−0.228929 | + | 0.973443i | \(0.573522\pi\) | |||||||
\(348\) | −264581. | −0.117115 | ||||||||
\(349\) | 1.24908e6 | 0.548944 | 0.274472 | − | 0.961595i | \(-0.411497\pi\) | ||||
0.274472 | + | 0.961595i | \(0.411497\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 276978. | 0.119999 | ||||||||
\(352\) | 4.26924e6 | 1.83651 | ||||||||
\(353\) | −3.13090e6 | −1.33731 | −0.668654 | − | 0.743573i | \(-0.733129\pi\) | ||||
−0.668654 | + | 0.743573i | \(0.733129\pi\) | |||||||
\(354\) | −498084. | −0.211249 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.11027e6 | −0.882497 | ||||||||
\(357\) | 580309. | 0.240984 | ||||||||
\(358\) | −1.19724e6 | −0.493714 | ||||||||
\(359\) | −2.63535e6 | −1.07920 | −0.539600 | − | 0.841921i | \(-0.681425\pi\) | ||||
−0.539600 | + | 0.841921i | \(0.681425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −515013. | −0.207994 | ||||||||
\(362\) | 483291. | 0.193837 | ||||||||
\(363\) | 1.19910e6 | 0.477626 | ||||||||
\(364\) | 592283. | 0.234302 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25166.7 | 0.00982027 | ||||||||
\(367\) | −2.23239e6 | −0.865175 | −0.432588 | − | 0.901592i | \(-0.642399\pi\) | ||||
−0.432588 | + | 0.901592i | \(0.642399\pi\) | |||||||
\(368\) | −261059. | −0.100489 | ||||||||
\(369\) | 3.59508e6 | 1.37449 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.09651e6 | 0.790794 | ||||||||
\(372\) | 651759. | 0.244191 | ||||||||
\(373\) | −3.72332e6 | −1.38566 | −0.692832 | − | 0.721099i | \(-0.743637\pi\) | ||||
−0.692832 | + | 0.721099i | \(0.743637\pi\) | |||||||
\(374\) | 2.33323e6 | 0.862539 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.22337e6 | 0.446260 | ||||||||
\(377\) | −547233. | −0.198298 | ||||||||
\(378\) | 702951. | 0.253044 | ||||||||
\(379\) | −2.11153e6 | −0.755089 | −0.377545 | − | 0.925991i | \(-0.623232\pi\) | ||||
−0.377545 | + | 0.925991i | \(0.623232\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 923992. | 0.326104 | ||||||||
\(382\) | −88865.9 | −0.0311585 | ||||||||
\(383\) | −414336. | −0.144330 | −0.0721648 | − | 0.997393i | \(-0.522991\pi\) | ||||
−0.0721648 | + | 0.997393i | \(0.522991\pi\) | |||||||
\(384\) | 582560. | 0.201610 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.92883e6 | −1.00052 | ||||||||
\(387\) | −533397. | −0.181039 | ||||||||
\(388\) | −3.48716e6 | −1.17596 | ||||||||
\(389\) | 4.10572e6 | 1.37567 | 0.687837 | − | 0.725865i | \(-0.258560\pi\) | ||||
0.687837 | + | 0.725865i | \(0.258560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.01598e6 | −0.336080 | ||||||||
\(392\) | 833924. | 0.274101 | ||||||||
\(393\) | −543191. | −0.177407 | ||||||||
\(394\) | −1.22139e6 | −0.396383 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.89151e6 | −1.24704 | ||||||||
\(397\) | −5.78249e6 | −1.84136 | −0.920681 | − | 0.390317i | \(-0.872365\pi\) | ||||
−0.920681 | + | 0.390317i | \(0.872365\pi\) | |||||||
\(398\) | −1.60097e6 | −0.506611 | ||||||||
\(399\) | 717945. | 0.225766 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.48722e6 | −1.08298 | −0.541488 | − | 0.840708i | \(-0.682139\pi\) | ||||
−0.541488 | + | 0.840708i | \(0.682139\pi\) | |||||||
\(402\) | −385491. | −0.118973 | ||||||||
\(403\) | 1.34803e6 | 0.413464 | ||||||||
\(404\) | 238329. | 0.0726479 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.38884e6 | −0.418155 | ||||||||
\(407\) | 3.54786e6 | 1.06165 | ||||||||
\(408\) | 629729. | 0.187285 | ||||||||
\(409\) | −3.23381e6 | −0.955886 | −0.477943 | − | 0.878391i | \(-0.658618\pi\) | ||||
−0.477943 | + | 0.878391i | \(0.658618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −457688. | −0.133649 | ||||||||
\(412\) | 4.13782e6 | 1.20096 | ||||||||
\(413\) | 7.38603e6 | 2.13077 | ||||||||
\(414\) | −599832. | −0.172000 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.01241e6 | 0.286829 | ||||||||
\(417\) | −985470. | −0.277526 | ||||||||
\(418\) | 2.88662e6 | 0.808070 | ||||||||
\(419\) | 3.63720e6 | 1.01212 | 0.506060 | − | 0.862498i | \(-0.331101\pi\) | ||||
0.506060 | + | 0.862498i | \(0.331101\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.11596e6 | 0.581839 | 0.290920 | − | 0.956747i | \(-0.406039\pi\) | ||||
0.290920 | + | 0.956747i | \(0.406039\pi\) | |||||||
\(422\) | 2.19294e6 | 0.599441 | ||||||||
\(423\) | −1.75654e6 | −0.477318 | ||||||||
\(424\) | 2.27505e6 | 0.614578 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −680081. | −0.181567 | ||||||||
\(427\) | −373194. | −0.0990525 | ||||||||
\(428\) | −5.32041e6 | −1.40390 | ||||||||
\(429\) | 416395. | 0.109235 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.14425e6 | 1.59322 | 0.796609 | − | 0.604495i | \(-0.206625\pi\) | ||||
0.796609 | + | 0.604495i | \(0.206625\pi\) | |||||||
\(432\) | −476681. | −0.122890 | ||||||||
\(433\) | −6.08667e6 | −1.56013 | −0.780064 | − | 0.625700i | \(-0.784813\pi\) | ||||
−0.780064 | + | 0.625700i | \(0.784813\pi\) | |||||||
\(434\) | 3.42121e6 | 0.871878 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −592822. | −0.149351 | ||||||||
\(437\) | −1.25695e6 | −0.314857 | ||||||||
\(438\) | −213050. | −0.0530636 | ||||||||
\(439\) | 5.46357e6 | 1.35305 | 0.676527 | − | 0.736418i | \(-0.263484\pi\) | ||||
0.676527 | + | 0.736418i | \(0.263484\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.19737e6 | −0.293177 | ||||||||
\(442\) | 553303. | 0.134712 | ||||||||
\(443\) | −4.25637e6 | −1.03046 | −0.515229 | − | 0.857052i | \(-0.672293\pi\) | ||||
−0.515229 | + | 0.857052i | \(0.672293\pi\) | |||||||
\(444\) | 406779. | 0.0979268 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −412935. | −0.0982981 | ||||||||
\(447\) | −541709. | −0.128232 | ||||||||
\(448\) | 1.18927e6 | 0.279954 | ||||||||
\(449\) | 3.07736e6 | 0.720382 | 0.360191 | − | 0.932879i | \(-0.382712\pi\) | ||||
0.360191 | + | 0.932879i | \(0.382712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.10889e7 | 2.56713 | ||||||||
\(452\) | −927843. | −0.213613 | ||||||||
\(453\) | 1.46091e6 | 0.334485 | ||||||||
\(454\) | 1.67462e6 | 0.381308 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 779086. | 0.175458 | ||||||||
\(457\) | −1.92830e6 | −0.431901 | −0.215951 | − | 0.976404i | \(-0.569285\pi\) | ||||
−0.215951 | + | 0.976404i | \(0.569285\pi\) | |||||||
\(458\) | 701132. | 0.156184 | ||||||||
\(459\) | −1.85513e6 | −0.411001 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.53125e6 | 0.335578 | 0.167789 | − | 0.985823i | \(-0.446337\pi\) | ||||
0.167789 | + | 0.985823i | \(0.446337\pi\) | |||||||
\(462\) | 1.05678e6 | 0.230346 | ||||||||
\(463\) | −2.13296e6 | −0.462412 | −0.231206 | − | 0.972905i | \(-0.574267\pi\) | ||||
−0.231206 | + | 0.972905i | \(0.574267\pi\) | |||||||
\(464\) | 941792. | 0.203077 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.56271e6 | −0.333359 | ||||||||
\(467\) | −2.47557e6 | −0.525270 | −0.262635 | − | 0.964895i | \(-0.584592\pi\) | ||||
−0.262635 | + | 0.964895i | \(0.584592\pi\) | |||||||
\(468\) | −922834. | −0.194764 | ||||||||
\(469\) | 5.71641e6 | 1.20003 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 447860. | 0.0930230 | ||||||||
\(472\) | 8.01503e6 | 1.65596 | ||||||||
\(473\) | −1.64525e6 | −0.338126 | ||||||||
\(474\) | −39845.7 | −0.00814584 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.96697e6 | −0.802493 | ||||||||
\(477\) | −3.26657e6 | −0.657349 | ||||||||
\(478\) | 645108. | 0.129140 | ||||||||
\(479\) | 6.52504e6 | 1.29940 | 0.649702 | − | 0.760189i | \(-0.274894\pi\) | ||||
0.649702 | + | 0.760189i | \(0.274894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 841341. | 0.165810 | ||||||||
\(482\) | −3.80629e6 | −0.746250 | ||||||||
\(483\) | −460163. | −0.0897520 | ||||||||
\(484\) | −8.19699e6 | −1.59053 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.65671e6 | −0.318167 | ||||||||
\(487\) | 5.50061e6 | 1.05097 | 0.525483 | − | 0.850804i | \(-0.323885\pi\) | ||||
0.525483 | + | 0.850804i | \(0.323885\pi\) | |||||||
\(488\) | −404976. | −0.0769803 | ||||||||
\(489\) | −2.13233e6 | −0.403258 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.54562e6 | 1.59970 | 0.799852 | − | 0.600197i | \(-0.204911\pi\) | ||||
0.799852 | + | 0.600197i | \(0.204911\pi\) | |||||||
\(492\) | 1.27140e6 | 0.236793 | ||||||||
\(493\) | 3.66524e6 | 0.679180 | ||||||||
\(494\) | 684534. | 0.126205 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.31997e6 | −0.423427 | ||||||||
\(497\) | 1.00848e7 | 1.83138 | ||||||||
\(498\) | −138765. | −0.0250730 | ||||||||
\(499\) | 2.98189e6 | 0.536094 | 0.268047 | − | 0.963406i | \(-0.413622\pi\) | ||||
0.268047 | + | 0.963406i | \(0.413622\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.77245e6 | −0.315486 | ||||||||
\(502\) | −1.37646e6 | −0.243783 | ||||||||
\(503\) | 4.24939e6 | 0.748871 | 0.374436 | − | 0.927253i | \(-0.377836\pi\) | ||||
0.374436 | + | 0.927253i | \(0.377836\pi\) | |||||||
\(504\) | −5.51324e6 | −0.966786 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.85016e6 | −0.321243 | ||||||||
\(507\) | 98743.9 | 0.0170604 | ||||||||
\(508\) | −6.31637e6 | −1.08595 | ||||||||
\(509\) | −1.22747e6 | −0.209999 | −0.105000 | − | 0.994472i | \(-0.533484\pi\) | ||||
−0.105000 | + | 0.994472i | \(0.533484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.15930e6 | 0.535228 | ||||||||
\(512\) | −3.24004e6 | −0.546230 | ||||||||
\(513\) | −2.29513e6 | −0.385047 | ||||||||
\(514\) | −534166. | −0.0891802 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −188635. | −0.0311888 | ||||||||
\(517\) | −5.41800e6 | −0.891483 | ||||||||
\(518\) | 2.13527e6 | 0.349645 | ||||||||
\(519\) | 1.60010e6 | 0.260752 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.91981e6 | −1.27826 | −0.639131 | − | 0.769097i | \(-0.720706\pi\) | ||||
−0.639131 | + | 0.769097i | \(0.720706\pi\) | |||||||
\(522\) | 2.16395e6 | 0.347592 | ||||||||
\(523\) | 4.76548e6 | 0.761821 | 0.380910 | − | 0.924612i | \(-0.375611\pi\) | ||||
0.380910 | + | 0.924612i | \(0.375611\pi\) | |||||||
\(524\) | 3.71323e6 | 0.590777 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.56544e6 | 0.246701 | ||||||||
\(527\) | −9.02880e6 | −1.41613 | ||||||||
\(528\) | −716618. | −0.111867 | ||||||||
\(529\) | −5.63071e6 | −0.874831 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.15082e7 | −1.77121 | ||||||||
\(532\) | −4.90784e6 | −0.751816 | ||||||||
\(533\) | 2.62963e6 | 0.400938 | ||||||||
\(534\) | −892892. | −0.135502 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.20322e6 | 0.932621 | ||||||||
\(537\) | 1.43107e6 | 0.214153 | ||||||||
\(538\) | −573909. | −0.0854845 | ||||||||
\(539\) | −3.69324e6 | −0.547565 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.85407e6 | −0.859934 | −0.429967 | − | 0.902845i | \(-0.641475\pi\) | ||||
−0.429967 | + | 0.902845i | \(0.641475\pi\) | |||||||
\(542\) | 747408. | 0.109285 | ||||||||
\(543\) | −577678. | −0.0840787 | ||||||||
\(544\) | −6.78087e6 | −0.982399 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 250605. | 0.0359756 | ||||||||
\(547\) | 587042. | 0.0838882 | 0.0419441 | − | 0.999120i | \(-0.486645\pi\) | ||||
0.0419441 | + | 0.999120i | \(0.486645\pi\) | |||||||
\(548\) | 3.12874e6 | 0.445059 | ||||||||
\(549\) | 581473. | 0.0823377 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.53455e6 | 0.636290 | ||||||||
\(552\) | −499351. | −0.0697522 | ||||||||
\(553\) | 590868. | 0.0821633 | ||||||||
\(554\) | 6.35852e6 | 0.880201 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.73663e6 | 0.924178 | ||||||||
\(557\) | −3.23702e6 | −0.442086 | −0.221043 | − | 0.975264i | \(-0.570946\pi\) | ||||
−0.221043 | + | 0.975264i | \(0.570946\pi\) | |||||||
\(558\) | −5.33058e6 | −0.724751 | ||||||||
\(559\) | −390155. | −0.0528089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.78891e6 | −0.374134 | ||||||||
\(562\) | 2436.53 | 0.000325410 0 | ||||||||
\(563\) | 1.09630e7 | 1.45767 | 0.728835 | − | 0.684689i | \(-0.240062\pi\) | ||||
0.728835 | + | 0.684689i | \(0.240062\pi\) | |||||||
\(564\) | −621200. | −0.0822306 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.58829e6 | −0.733226 | ||||||||
\(567\) | 7.48531e6 | 0.977805 | ||||||||
\(568\) | 1.09437e7 | 1.42329 | ||||||||
\(569\) | 4.35413e6 | 0.563795 | 0.281897 | − | 0.959445i | \(-0.409036\pi\) | ||||
0.281897 | + | 0.959445i | \(0.409036\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.59961e6 | 0.590379 | 0.295189 | − | 0.955439i | \(-0.404617\pi\) | ||||
0.295189 | + | 0.955439i | \(0.404617\pi\) | |||||||
\(572\) | −2.84646e6 | −0.363760 | ||||||||
\(573\) | 106221. | 0.0135153 | ||||||||
\(574\) | 6.67382e6 | 0.845463 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.85300e6 | −0.232713 | ||||||||
\(577\) | −7.57061e6 | −0.946654 | −0.473327 | − | 0.880887i | \(-0.656947\pi\) | ||||
−0.473327 | + | 0.880887i | \(0.656947\pi\) | |||||||
\(578\) | 400919. | 0.0499157 | ||||||||
\(579\) | 3.50083e6 | 0.433985 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.05773e6 | 0.252900 | ||||||||
\(582\) | −1.47548e6 | −0.180561 | ||||||||
\(583\) | −1.00757e7 | −1.22773 | ||||||||
\(584\) | 3.42835e6 | 0.415962 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.93062e6 | −0.352546 | ||||||||
\(587\) | 1.48215e7 | 1.77541 | 0.887703 | − | 0.460416i | \(-0.152300\pi\) | ||||
0.887703 | + | 0.460416i | \(0.152300\pi\) | |||||||
\(588\) | −423448. | −0.0505076 | ||||||||
\(589\) | −1.11702e7 | −1.32670 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.45993e6 | 0.171935 | ||||||||
\(592\) | −1.44795e6 | −0.169805 | ||||||||
\(593\) | 1.00021e6 | 0.116803 | 0.0584017 | − | 0.998293i | \(-0.481400\pi\) | ||||
0.0584017 | + | 0.998293i | \(0.481400\pi\) | |||||||
\(594\) | −3.37831e6 | −0.392856 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.70310e6 | 0.427021 | ||||||||
\(597\) | 1.91363e6 | 0.219747 | ||||||||
\(598\) | −438749. | −0.0501721 | ||||||||
\(599\) | −8.35745e6 | −0.951715 | −0.475857 | − | 0.879522i | \(-0.657862\pi\) | ||||
−0.475857 | + | 0.879522i | \(0.657862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.04104e6 | −0.682222 | −0.341111 | − | 0.940023i | \(-0.610803\pi\) | ||||
−0.341111 | + | 0.940023i | \(0.610803\pi\) | |||||||
\(602\) | −990185. | −0.111359 | ||||||||
\(603\) | −8.90671e6 | −0.997526 | ||||||||
\(604\) | −9.98669e6 | −1.11386 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 100841. | 0.0111547 | ||||||||
\(607\) | −137224. | −0.0151168 | −0.00755838 | − | 0.999971i | \(-0.502406\pi\) | ||||
−0.00755838 | + | 0.999971i | \(0.502406\pi\) | |||||||
\(608\) | −8.38914e6 | −0.920361 | ||||||||
\(609\) | 1.66008e6 | 0.181378 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.28483e6 | −0.139233 | ||||||||
\(612\) | 6.18092e6 | 0.667075 | ||||||||
\(613\) | 1.09895e7 | 1.18121 | 0.590606 | − | 0.806960i | \(-0.298889\pi\) | ||||
0.590606 | + | 0.806960i | \(0.298889\pi\) | |||||||
\(614\) | −1.11726e6 | −0.119601 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.70054e7 | −1.80566 | ||||||||
\(617\) | 3.42268e6 | 0.361954 | 0.180977 | − | 0.983487i | \(-0.442074\pi\) | ||||
0.180977 | + | 0.983487i | \(0.442074\pi\) | |||||||
\(618\) | 1.75078e6 | 0.184400 | ||||||||
\(619\) | −1.22543e7 | −1.28547 | −0.642736 | − | 0.766088i | \(-0.722201\pi\) | ||||
−0.642736 | + | 0.766088i | \(0.722201\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.47105e6 | 0.153073 | ||||||||
\(622\) | −3.98188e6 | −0.412679 | ||||||||
\(623\) | 1.32406e7 | 1.36675 | ||||||||
\(624\) | −169939. | −0.0174715 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.56587e6 | 0.159706 | ||||||||
\(627\) | −3.45038e6 | −0.350508 | ||||||||
\(628\) | −3.06155e6 | −0.309772 | ||||||||
\(629\) | −5.63510e6 | −0.567904 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.99788e6 | 0.799653 | 0.399827 | − | 0.916591i | \(-0.369070\pi\) | ||||
0.399827 | + | 0.916591i | \(0.369070\pi\) | |||||||
\(632\) | 641187. | 0.0638546 | ||||||||
\(633\) | −2.62122e6 | −0.260013 | ||||||||
\(634\) | −5.54917e6 | −0.548283 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.15522e6 | −0.113246 | ||||||||
\(637\) | −875816. | −0.0855194 | ||||||||
\(638\) | 6.67463e6 | 0.649196 | ||||||||
\(639\) | −1.57132e7 | −1.52234 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.18872e6 | 0.787175 | 0.393587 | − | 0.919287i | \(-0.371234\pi\) | ||||
0.393587 | + | 0.919287i | \(0.371234\pi\) | |||||||
\(642\) | −2.25116e6 | −0.215560 | ||||||||
\(643\) | −1.64743e7 | −1.57137 | −0.785686 | − | 0.618626i | \(-0.787690\pi\) | ||||
−0.785686 | + | 0.618626i | \(0.787690\pi\) | |||||||
\(644\) | 3.14566e6 | 0.298880 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.58485e6 | −0.432258 | ||||||||
\(647\) | −3.65606e6 | −0.343362 | −0.171681 | − | 0.985153i | \(-0.554920\pi\) | ||||
−0.171681 | + | 0.985153i | \(0.554920\pi\) | |||||||
\(648\) | 8.12277e6 | 0.759917 | ||||||||
\(649\) | −3.54966e7 | −3.30807 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.08938e6 | −0.378185 | ||||||||
\(652\) | 1.45766e7 | 1.34288 | ||||||||
\(653\) | 1.22553e7 | 1.12471 | 0.562355 | − | 0.826896i | \(-0.309896\pi\) | ||||
0.562355 | + | 0.826896i | \(0.309896\pi\) | |||||||
\(654\) | −250833. | −0.0229319 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.52561e6 | −0.410599 | ||||||||
\(657\) | −4.92250e6 | −0.444910 | ||||||||
\(658\) | −3.26080e6 | −0.293602 | ||||||||
\(659\) | 708926. | 0.0635898 | 0.0317949 | − | 0.999494i | \(-0.489878\pi\) | ||||
0.0317949 | + | 0.999494i | \(0.489878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.69284e7 | 1.50700 | 0.753500 | − | 0.657448i | \(-0.228364\pi\) | ||||
0.753500 | + | 0.657448i | \(0.228364\pi\) | |||||||
\(662\) | 6.94597e6 | 0.616010 | ||||||||
\(663\) | −661363. | −0.0584327 | ||||||||
\(664\) | 2.23297e6 | 0.196546 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.32695e6 | −0.290644 | ||||||||
\(667\) | −2.90639e6 | −0.252953 | ||||||||
\(668\) | 1.21164e7 | 1.05059 | ||||||||
\(669\) | 493582. | 0.0426377 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.79354e6 | 0.153781 | ||||||||
\(672\) | −3.07123e6 | −0.262355 | ||||||||
\(673\) | −1.00330e7 | −0.853873 | −0.426937 | − | 0.904281i | \(-0.640407\pi\) | ||||
−0.426937 | + | 0.904281i | \(0.640407\pi\) | |||||||
\(674\) | −1.11163e7 | −0.942560 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −675009. | −0.0568124 | ||||||||
\(677\) | −1.54623e7 | −1.29659 | −0.648296 | − | 0.761388i | \(-0.724518\pi\) | ||||
−0.648296 | + | 0.761388i | \(0.724518\pi\) | |||||||
\(678\) | −392586. | −0.0327990 | ||||||||
\(679\) | 2.18797e7 | 1.82124 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.00167e6 | −0.165396 | ||||||||
\(682\) | −1.64420e7 | −1.35361 | ||||||||
\(683\) | 9.19066e6 | 0.753868 | 0.376934 | − | 0.926240i | \(-0.376978\pi\) | ||||
0.376934 | + | 0.926240i | \(0.376978\pi\) | |||||||
\(684\) | 7.64689e6 | 0.624949 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.98593e6 | 0.404516 | ||||||||
\(687\) | −838062. | −0.0677461 | ||||||||
\(688\) | 671459. | 0.0540814 | ||||||||
\(689\) | −2.38934e6 | −0.191748 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.38192e7 | −1.10100 | −0.550502 | − | 0.834834i | \(-0.685564\pi\) | ||||
−0.550502 | + | 0.834834i | \(0.685564\pi\) | |||||||
\(692\) | −1.09382e7 | −0.868320 | ||||||||
\(693\) | 2.44168e7 | 1.93132 | ||||||||
\(694\) | 2.97040e6 | 0.234108 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.80145e6 | 0.140961 | ||||||||
\(697\) | −1.76126e7 | −1.37323 | ||||||||
\(698\) | −3.61286e6 | −0.280681 | ||||||||
\(699\) | 1.86790e6 | 0.144598 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.58946e7 | 1.22167 | 0.610834 | − | 0.791758i | \(-0.290834\pi\) | ||||
0.610834 | + | 0.791758i | \(0.290834\pi\) | |||||||
\(702\) | −801134. | −0.0613568 | ||||||||
\(703\) | −6.97162e6 | −0.532041 | ||||||||
\(704\) | −5.71554e6 | −0.434636 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.05584e6 | 0.683781 | ||||||||
\(707\) | −1.49536e6 | −0.112512 | ||||||||
\(708\) | −4.06985e6 | −0.305137 | ||||||||
\(709\) | 1.20549e7 | 0.900635 | 0.450317 | − | 0.892869i | \(-0.351311\pi\) | ||||
0.450317 | + | 0.892869i | \(0.351311\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −920630. | −0.0682985 | ||||||||
\(712\) | 1.43682e7 | 1.06219 | ||||||||
\(713\) | 7.15950e6 | 0.527423 | ||||||||
\(714\) | −1.67849e6 | −0.123218 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.78271e6 | −0.713143 | ||||||||
\(717\) | −771097. | −0.0560159 | ||||||||
\(718\) | 7.62252e6 | 0.551807 | ||||||||
\(719\) | 1.21480e7 | 0.876357 | 0.438178 | − | 0.898888i | \(-0.355624\pi\) | ||||
0.438178 | + | 0.898888i | \(0.355624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.59622e7 | −1.85996 | ||||||||
\(722\) | 1.48963e6 | 0.106350 | ||||||||
\(723\) | 4.54966e6 | 0.323693 | ||||||||
\(724\) | 3.94898e6 | 0.279988 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.46829e6 | −0.244216 | ||||||||
\(727\) | 1.37550e7 | 0.965215 | 0.482607 | − | 0.875837i | \(-0.339690\pi\) | ||||
0.482607 | + | 0.875837i | \(0.339690\pi\) | |||||||
\(728\) | −4.03267e6 | −0.282010 | ||||||||
\(729\) | −1.02859e7 | −0.716845 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.61316e6 | 0.180873 | ||||||||
\(732\) | 205637. | 0.0141848 | ||||||||
\(733\) | −5.10914e6 | −0.351227 | −0.175614 | − | 0.984459i | \(-0.556191\pi\) | ||||
−0.175614 | + | 0.984459i | \(0.556191\pi\) | |||||||
\(734\) | 6.45698e6 | 0.442374 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.37697e6 | 0.365884 | ||||||||
\(737\) | −2.74725e7 | −1.86307 | ||||||||
\(738\) | −1.03985e7 | −0.702794 | ||||||||
\(739\) | 4.07246e6 | 0.274312 | 0.137156 | − | 0.990549i | \(-0.456204\pi\) | ||||
0.137156 | + | 0.990549i | \(0.456204\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −818224. | −0.0547427 | ||||||||
\(742\) | −6.06398e6 | −0.404342 | ||||||||
\(743\) | −1.86637e7 | −1.24029 | −0.620147 | − | 0.784485i | \(-0.712927\pi\) | ||||
−0.620147 | + | 0.784485i | \(0.712927\pi\) | |||||||
\(744\) | −4.43763e6 | −0.293913 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.07694e7 | 0.708505 | ||||||||
\(747\) | −3.20615e6 | −0.210224 | ||||||||
\(748\) | 1.90649e7 | 1.24589 | ||||||||
\(749\) | 3.33822e7 | 2.17425 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.20898e7 | −1.42919 | −0.714597 | − | 0.699536i | \(-0.753390\pi\) | ||||
−0.714597 | + | 0.699536i | \(0.753390\pi\) | |||||||
\(752\) | 2.21119e6 | 0.142588 | ||||||||
\(753\) | 1.64528e6 | 0.105743 | ||||||||
\(754\) | 1.58282e6 | 0.101392 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.74382e6 | 0.365508 | ||||||||
\(757\) | 2.27912e7 | 1.44553 | 0.722765 | − | 0.691094i | \(-0.242871\pi\) | ||||
0.722765 | + | 0.691094i | \(0.242871\pi\) | |||||||
\(758\) | 6.10740e6 | 0.386085 | ||||||||
\(759\) | 2.21150e6 | 0.139342 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.05216e7 | 1.28455 | 0.642274 | − | 0.766475i | \(-0.277991\pi\) | ||||
0.642274 | + | 0.766475i | \(0.277991\pi\) | |||||||
\(762\) | −2.67257e6 | −0.166740 | ||||||||
\(763\) | 3.71958e6 | 0.231304 | ||||||||
\(764\) | −726125. | −0.0450068 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.19843e6 | 0.0737973 | ||||||||
\(767\) | −8.41767e6 | −0.516658 | ||||||||
\(768\) | −2.57229e6 | −0.157368 | ||||||||
\(769\) | −2.11516e7 | −1.28982 | −0.644908 | − | 0.764260i | \(-0.723104\pi\) | ||||
−0.644908 | + | 0.764260i | \(0.723104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 638488. | 0.0386827 | ||||||||
\(772\) | −2.39315e7 | −1.44520 | ||||||||
\(773\) | 6.75134e6 | 0.406389 | 0.203194 | − | 0.979138i | \(-0.434868\pi\) | ||||
0.203194 | + | 0.979138i | \(0.434868\pi\) | |||||||
\(774\) | 1.54280e6 | 0.0925675 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.37430e7 | 1.41541 | ||||||||
\(777\) | −2.55228e6 | −0.151662 | ||||||||
\(778\) | −1.18754e7 | −0.703398 | ||||||||
\(779\) | −2.17900e7 | −1.28651 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.84668e7 | −2.84326 | ||||||||
\(782\) | 2.93863e6 | 0.171842 | ||||||||
\(783\) | −5.30694e6 | −0.309343 | ||||||||
\(784\) | 1.50729e6 | 0.0875801 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.57113e6 | 0.0907103 | ||||||||
\(787\) | 1.78318e7 | 1.02626 | 0.513132 | − | 0.858310i | \(-0.328485\pi\) | ||||
0.513132 | + | 0.858310i | \(0.328485\pi\) | |||||||
\(788\) | −9.98003e6 | −0.572554 | ||||||||
\(789\) | −1.87117e6 | −0.107009 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.82163e6 | 0.330829 | ||||||||
\(792\) | 2.64961e7 | 1.50096 | ||||||||
\(793\) | 425320. | 0.0240178 | ||||||||
\(794\) | 1.67254e7 | 0.941508 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.30815e7 | −0.731772 | ||||||||
\(797\) | −1.22612e7 | −0.683732 | −0.341866 | − | 0.939749i | \(-0.611059\pi\) | ||||
−0.341866 | + | 0.939749i | \(0.611059\pi\) | |||||||
\(798\) | −2.07659e6 | −0.115437 | ||||||||
\(799\) | 8.60546e6 | 0.476878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.06301e7 | −1.13611 | ||||||||
\(802\) | 1.00865e7 | 0.553738 | ||||||||
\(803\) | −1.51833e7 | −0.830956 | ||||||||
\(804\) | −3.14985e6 | −0.171850 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.89907e6 | −0.211409 | ||||||||
\(807\) | 685993. | 0.0370797 | ||||||||
\(808\) | −1.62271e6 | −0.0874404 | ||||||||
\(809\) | −1.86542e7 | −1.00208 | −0.501042 | − | 0.865423i | \(-0.667050\pi\) | ||||
−0.501042 | + | 0.865423i | \(0.667050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.65131e6 | 0.141550 | 0.0707748 | − | 0.997492i | \(-0.477453\pi\) | ||||
0.0707748 | + | 0.997492i | \(0.477453\pi\) | |||||||
\(812\) | −1.13482e7 | −0.604002 | ||||||||
\(813\) | −893377. | −0.0474033 | ||||||||
\(814\) | −1.02619e7 | −0.542833 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.13821e6 | 0.0598408 | ||||||||
\(817\) | 3.23295e6 | 0.169451 | ||||||||
\(818\) | 9.35351e6 | 0.488755 | ||||||||
\(819\) | 5.79020e6 | 0.301636 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.04948e7 | 1.06117 | 0.530587 | − | 0.847630i | \(-0.321972\pi\) | ||||
0.530587 | + | 0.847630i | \(0.321972\pi\) | |||||||
\(822\) | 1.32382e6 | 0.0683361 | ||||||||
\(823\) | −1.26841e7 | −0.652768 | −0.326384 | − | 0.945237i | \(-0.605830\pi\) | ||||
−0.326384 | + | 0.945237i | \(0.605830\pi\) | |||||||
\(824\) | −2.81732e7 | −1.44550 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.13635e7 | −1.08949 | ||||||||
\(827\) | −9.90644e6 | −0.503679 | −0.251839 | − | 0.967769i | \(-0.581035\pi\) | ||||
−0.251839 | + | 0.967769i | \(0.581035\pi\) | |||||||
\(828\) | −4.90124e6 | −0.248445 | ||||||||
\(829\) | 8.05866e6 | 0.407265 | 0.203632 | − | 0.979047i | \(-0.434725\pi\) | ||||
0.203632 | + | 0.979047i | \(0.434725\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.60034e6 | −0.381795 | ||||||||
\(832\) | −1.35538e6 | −0.0678819 | ||||||||
\(833\) | 5.86601e6 | 0.292907 | ||||||||
\(834\) | 2.85039e6 | 0.141902 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.35866e7 | 1.16721 | ||||||||
\(837\) | 1.30729e7 | 0.644998 | ||||||||
\(838\) | −1.05203e7 | −0.517508 | ||||||||
\(839\) | 2.15392e7 | 1.05639 | 0.528196 | − | 0.849122i | \(-0.322869\pi\) | ||||
0.528196 | + | 0.849122i | \(0.322869\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00261e7 | −0.488811 | ||||||||
\(842\) | −6.12024e6 | −0.297501 | ||||||||
\(843\) | −2912.38 | −0.000141150 0 | ||||||||
\(844\) | 1.79186e7 | 0.865860 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.08064e6 | 0.244058 | ||||||||
\(847\) | 5.14309e7 | 2.46329 | ||||||||
\(848\) | 4.11207e6 | 0.196368 | ||||||||
\(849\) | 6.67968e6 | 0.318044 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.46842e6 | 0.211510 | ||||||||
\(852\) | −5.55695e6 | −0.262263 | ||||||||
\(853\) | −1.55629e7 | −0.732351 | −0.366175 | − | 0.930546i | \(-0.619333\pi\) | ||||
−0.366175 | + | 0.930546i | \(0.619333\pi\) | |||||||
\(854\) | 1.07943e6 | 0.0506466 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.62250e7 | 1.68976 | ||||||||
\(857\) | 3.66500e7 | 1.70460 | 0.852299 | − | 0.523055i | \(-0.175208\pi\) | ||||
0.852299 | + | 0.523055i | \(0.175208\pi\) | |||||||
\(858\) | −1.20438e6 | −0.0558531 | ||||||||
\(859\) | 3.16288e7 | 1.46251 | 0.731257 | − | 0.682102i | \(-0.238934\pi\) | ||||
0.731257 | + | 0.682102i | \(0.238934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.97721e6 | −0.366727 | ||||||||
\(862\) | −1.77717e7 | −0.814630 | ||||||||
\(863\) | −1.63149e7 | −0.745691 | −0.372845 | − | 0.927894i | \(-0.621618\pi\) | ||||
−0.372845 | + | 0.927894i | \(0.621618\pi\) | |||||||
\(864\) | 9.81810e6 | 0.447448 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.76052e7 | 0.797710 | ||||||||
\(867\) | −479219. | −0.0216514 | ||||||||
\(868\) | 2.79548e7 | 1.25938 | ||||||||
\(869\) | −2.83966e6 | −0.127561 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.51484e6 | −0.290977 | ||||||||
\(872\) | 4.03634e6 | 0.179762 | ||||||||
\(873\) | −3.40907e7 | −1.51391 | ||||||||
\(874\) | 3.63561e6 | 0.160990 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.74084e6 | −0.0766475 | ||||||||
\(877\) | 2.64601e7 | 1.16170 | 0.580848 | − | 0.814012i | \(-0.302721\pi\) | ||||
0.580848 | + | 0.814012i | \(0.302721\pi\) | |||||||
\(878\) | −1.58029e7 | −0.691831 | ||||||||
\(879\) | 3.50297e6 | 0.152920 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.51155e7 | 0.656119 | 0.328059 | − | 0.944657i | \(-0.393605\pi\) | ||||
0.328059 | + | 0.944657i | \(0.393605\pi\) | |||||||
\(882\) | 3.46328e6 | 0.149905 | ||||||||
\(883\) | 2.08156e7 | 0.898437 | 0.449218 | − | 0.893422i | \(-0.351703\pi\) | ||||
0.449218 | + | 0.893422i | \(0.351703\pi\) | |||||||
\(884\) | 4.52105e6 | 0.194585 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.23112e7 | 0.526885 | ||||||||
\(887\) | 1.01116e7 | 0.431529 | 0.215764 | − | 0.976445i | \(-0.430776\pi\) | ||||
0.215764 | + | 0.976445i | \(0.430776\pi\) | |||||||
\(888\) | −2.76964e6 | −0.117866 | ||||||||
\(889\) | 3.96312e7 | 1.68183 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.59737e7 | −1.51807 | ||||||||
\(892\) | −3.37410e6 | −0.141986 | ||||||||
\(893\) | 1.06465e7 | 0.446763 | ||||||||
\(894\) | 1.56684e6 | 0.0655665 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.49867e7 | 1.03978 | ||||||||
\(897\) | 524436. | 0.0217626 | ||||||||
\(898\) | −8.90100e6 | −0.368339 | ||||||||
\(899\) | −2.58285e7 | −1.06586 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.60032e7 | 0.656744 | ||||||||
\(902\) | −3.20737e7 | −1.31260 | ||||||||
\(903\) | 1.18357e6 | 0.0483030 | ||||||||
\(904\) | 6.31740e6 | 0.257109 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.22554e6 | −0.171026 | ||||||||
\(907\) | −3.04365e6 | −0.122850 | −0.0614251 | − | 0.998112i | \(-0.519565\pi\) | ||||
−0.0614251 | + | 0.998112i | \(0.519565\pi\) | |||||||
\(908\) | 1.36833e7 | 0.550779 | ||||||||
\(909\) | 2.32992e6 | 0.0935257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.90597e7 | −1.16010 | −0.580050 | − | 0.814581i | \(-0.696967\pi\) | ||||
−0.580050 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(912\) | 1.40817e6 | 0.0560618 | ||||||||
\(913\) | −9.88928e6 | −0.392634 | ||||||||
\(914\) | 5.57744e6 | 0.220836 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.72896e6 | 0.225599 | ||||||||
\(917\) | −2.32982e7 | −0.914952 | ||||||||
\(918\) | 5.36581e6 | 0.210149 | ||||||||
\(919\) | 3.38583e7 | 1.32244 | 0.661220 | − | 0.750192i | \(-0.270039\pi\) | ||||
0.661220 | + | 0.750192i | \(0.270039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.33546e6 | 0.0518780 | ||||||||
\(922\) | −4.42900e6 | −0.171585 | ||||||||
\(923\) | −1.14934e7 | −0.444064 | ||||||||
\(924\) | 8.63497e6 | 0.332722 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.16939e6 | 0.236437 | ||||||||
\(927\) | 4.04516e7 | 1.54610 | ||||||||
\(928\) | −1.93979e7 | −0.739409 | ||||||||
\(929\) | 3.78136e7 | 1.43750 | 0.718751 | − | 0.695267i | \(-0.244714\pi\) | ||||
0.718751 | + | 0.695267i | \(0.244714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.25729e6 | 0.274410 | ||||||||
\(932\) | −1.27689e7 | −0.481519 | ||||||||
\(933\) | 4.75954e6 | 0.179003 | ||||||||
\(934\) | 7.16037e6 | 0.268577 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.28329e6 | 0.234422 | ||||||||
\(937\) | 2.00563e7 | 0.746281 | 0.373140 | − | 0.927775i | \(-0.378281\pi\) | ||||
0.373140 | + | 0.927775i | \(0.378281\pi\) | |||||||
\(938\) | −1.65342e7 | −0.613587 | ||||||||
\(939\) | −1.87169e6 | −0.0692739 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.54644e7 | −0.937473 | −0.468737 | − | 0.883338i | \(-0.655291\pi\) | ||||
−0.468737 | + | 0.883338i | \(0.655291\pi\) | |||||||
\(942\) | −1.29540e6 | −0.0475637 | ||||||||
\(943\) | 1.39662e7 | 0.511443 | ||||||||
\(944\) | 1.44869e7 | 0.529108 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.75874e6 | 0.172888 | ||||||||
\(947\) | −1.42435e7 | −0.516110 | −0.258055 | − | 0.966130i | \(-0.583082\pi\) | ||||
−0.258055 | + | 0.966130i | \(0.583082\pi\) | |||||||
\(948\) | −325580. | −0.0117662 | ||||||||
\(949\) | −3.60058e6 | −0.129780 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.63292e6 | 0.237823 | ||||||||
\(952\) | 2.70099e7 | 0.965896 | ||||||||
\(953\) | 3.95389e7 | 1.41024 | 0.705119 | − | 0.709089i | \(-0.250894\pi\) | ||||
0.705119 | + | 0.709089i | \(0.250894\pi\) | |||||||
\(954\) | 9.44827e6 | 0.336110 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.27119e6 | 0.186536 | ||||||||
\(957\) | −7.97819e6 | −0.281595 | ||||||||
\(958\) | −1.88731e7 | −0.664399 | ||||||||
\(959\) | −1.96308e7 | −0.689275 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.49958e7 | 1.22238 | ||||||||
\(962\) | −2.43351e6 | −0.0847803 | ||||||||
\(963\) | −5.20127e7 | −1.80735 | ||||||||
\(964\) | −3.11013e7 | −1.07792 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.33098e6 | 0.0458912 | ||||||||
\(967\) | −4.28774e7 | −1.47456 | −0.737279 | − | 0.675588i | \(-0.763890\pi\) | ||||
−0.737279 | + | 0.675588i | \(0.763890\pi\) | |||||||
\(968\) | 5.58108e7 | 1.91439 | ||||||||
\(969\) | 5.48027e6 | 0.187496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.56895e7 | 0.534023 | 0.267011 | − | 0.963693i | \(-0.413964\pi\) | ||||
0.267011 | + | 0.963693i | \(0.413964\pi\) | |||||||
\(972\) | −1.35370e7 | −0.459574 | ||||||||
\(973\) | −4.22681e7 | −1.43130 | ||||||||
\(974\) | −1.59100e7 | −0.537370 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −731978. | −0.0245965 | ||||||||
\(977\) | 2.22874e7 | 0.747004 | 0.373502 | − | 0.927629i | \(-0.378157\pi\) | ||||
0.373502 | + | 0.927629i | \(0.378157\pi\) | |||||||
\(978\) | 6.16759e6 | 0.206190 | ||||||||
\(979\) | −6.36331e7 | −2.12191 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.79547e6 | −0.192272 | ||||||||
\(982\) | −2.47174e7 | −0.817946 | ||||||||
\(983\) | −2.46890e6 | −0.0814929 | −0.0407465 | − | 0.999170i | \(-0.512974\pi\) | ||||
−0.0407465 | + | 0.999170i | \(0.512974\pi\) | |||||||
\(984\) | −8.65656e6 | −0.285008 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.06014e7 | −0.347272 | ||||||||
\(987\) | 3.89763e6 | 0.127353 | ||||||||
\(988\) | 5.59334e6 | 0.182297 | ||||||||
\(989\) | −2.07214e6 | −0.0673640 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.73304e7 | 0.560563 | 0.280281 | − | 0.959918i | \(-0.409572\pi\) | ||||
0.280281 | + | 0.959918i | \(0.409572\pi\) | |||||||
\(992\) | 4.77840e7 | 1.54171 | ||||||||
\(993\) | −8.30251e6 | −0.267200 | ||||||||
\(994\) | −2.91695e7 | −0.936405 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.13385e6 | −0.0362166 | ||||||||
\(997\) | 5.90647e7 | 1.88187 | 0.940936 | − | 0.338586i | \(-0.109948\pi\) | ||||
0.940936 | + | 0.338586i | \(0.109948\pi\) | |||||||
\(998\) | −8.62487e6 | −0.274111 | ||||||||
\(999\) | 8.15913e6 | 0.258661 |
(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 | 325.6.a.j.1.5 | ✓ | 11 | |
5.2 | odd | 4 | 325.6.b.i.274.9 | 22 | |||
5.3 | odd | 4 | 325.6.b.i.274.14 | 22 | |||
5.4 | even | 2 | 325.6.a.k.1.7 | yes | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.6.a.j.1.5 | ✓ | 11 | 1.1 | even | 1 | trivial | |
325.6.a.k.1.7 | yes | 11 | 5.4 | even | 2 | ||
325.6.b.i.274.9 | 22 | 5.2 | odd | 4 | |||
325.6.b.i.274.14 | 22 | 5.3 | odd | 4 |