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 | 1.3 | ||
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 | ||||||||
\(5\) | −10.8102 | −0.193379 | −0.0966896 | − | 0.995315i | \(-0.530825\pi\) | ||||
−0.0966896 | + | 0.995315i | \(0.530825\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 229.182 | 1.76781 | 0.883905 | − | 0.467666i | \(-0.154905\pi\) | ||||
0.883905 | + | 0.467666i | \(0.154905\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 43.2409 | 0.136740 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | −903.518 | −1.48279 | −0.741393 | − | 0.671072i | \(-0.765834\pi\) | ||||
−0.741393 | + | 0.671072i | \(0.765834\pi\) | |||||||
\(14\) | −916.728 | −1.25003 | ||||||||
\(15\) | −97.2921 | −0.111648 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −763.758 | −0.640964 | −0.320482 | − | 0.947255i | \(-0.603845\pi\) | ||||
−0.320482 | + | 0.947255i | \(0.603845\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | 2270.29 | 1.44277 | 0.721384 | − | 0.692535i | \(-0.243506\pi\) | ||||
0.721384 | + | 0.692535i | \(0.243506\pi\) | |||||||
\(20\) | −172.964 | −0.0966896 | ||||||||
\(21\) | 2062.64 | 1.02065 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2828.01 | 1.11471 | 0.557355 | − | 0.830274i | \(-0.311816\pi\) | ||||
0.557355 | + | 0.830274i | \(0.311816\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | −3008.14 | −0.962604 | ||||||||
\(26\) | 3614.07 | 1.04849 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 3666.91 | 0.883905 | ||||||||
\(29\) | −6972.21 | −1.53949 | −0.769743 | − | 0.638354i | \(-0.779615\pi\) | ||||
−0.769743 | + | 0.638354i | \(0.779615\pi\) | |||||||
\(30\) | 389.168 | 0.0789468 | ||||||||
\(31\) | −7337.38 | −1.37131 | −0.685657 | − | 0.727925i | \(-0.740485\pi\) | ||||
−0.685657 | + | 0.727925i | \(0.740485\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3055.03 | 0.453230 | ||||||||
\(35\) | −2477.51 | −0.341858 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −10540.9 | −1.26583 | −0.632914 | − | 0.774222i | \(-0.718141\pi\) | ||||
−0.632914 | + | 0.774222i | \(0.718141\pi\) | |||||||
\(38\) | −9081.14 | −1.02019 | ||||||||
\(39\) | −8131.66 | −0.856086 | ||||||||
\(40\) | 691.855 | 0.0683699 | ||||||||
\(41\) | −6102.66 | −0.566969 | −0.283484 | − | 0.958977i | \(-0.591490\pi\) | ||||
−0.283484 | + | 0.958977i | \(0.591490\pi\) | |||||||
\(42\) | −8250.56 | −0.721705 | ||||||||
\(43\) | 2029.16 | 0.167358 | 0.0836789 | − | 0.996493i | \(-0.473333\pi\) | ||||
0.0836789 | + | 0.996493i | \(0.473333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −875.629 | −0.0644598 | ||||||||
\(46\) | −11312.1 | −0.788219 | ||||||||
\(47\) | −20218.0 | −1.33504 | −0.667519 | − | 0.744592i | \(-0.732644\pi\) | ||||
−0.667519 | + | 0.744592i | \(0.732644\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | 35717.4 | 2.12515 | ||||||||
\(50\) | 12032.6 | 0.680664 | ||||||||
\(51\) | −6873.82 | −0.370061 | ||||||||
\(52\) | −14456.3 | −0.741393 | ||||||||
\(53\) | −18442.2 | −0.901828 | −0.450914 | − | 0.892567i | \(-0.648902\pi\) | ||||
−0.450914 | + | 0.892567i | \(0.648902\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14667.7 | −0.625015 | ||||||||
\(57\) | 20432.6 | 0.832982 | ||||||||
\(58\) | 27888.8 | 1.08858 | ||||||||
\(59\) | 8759.93 | 0.327620 | 0.163810 | − | 0.986492i | \(-0.447622\pi\) | ||||
0.163810 | + | 0.986492i | \(0.447622\pi\) | |||||||
\(60\) | −1556.67 | −0.0558238 | ||||||||
\(61\) | 25412.8 | 0.874436 | 0.437218 | − | 0.899356i | \(-0.355964\pi\) | ||||
0.437218 | + | 0.899356i | \(0.355964\pi\) | |||||||
\(62\) | 29349.5 | 0.969665 | ||||||||
\(63\) | 18563.8 | 0.589270 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 9767.23 | 0.286740 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −44383.4 | −1.20791 | −0.603953 | − | 0.797020i | \(-0.706409\pi\) | ||||
−0.603953 | + | 0.797020i | \(0.706409\pi\) | |||||||
\(68\) | −12220.1 | −0.320482 | ||||||||
\(69\) | 25452.1 | 0.643578 | ||||||||
\(70\) | 9910.04 | 0.241730 | ||||||||
\(71\) | −80387.8 | −1.89254 | −0.946268 | − | 0.323382i | \(-0.895180\pi\) | ||||
−0.946268 | + | 0.323382i | \(0.895180\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 74385.0 | 1.63372 | 0.816861 | − | 0.576834i | \(-0.195712\pi\) | ||||
0.816861 | + | 0.576834i | \(0.195712\pi\) | |||||||
\(74\) | 42163.7 | 0.895075 | ||||||||
\(75\) | −27073.3 | −0.555760 | ||||||||
\(76\) | 36324.6 | 0.721384 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 32526.6 | 0.605345 | ||||||||
\(79\) | 29426.2 | 0.530477 | 0.265238 | − | 0.964183i | \(-0.414549\pi\) | ||||
0.265238 | + | 0.964183i | \(0.414549\pi\) | |||||||
\(80\) | −2767.42 | −0.0483448 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 24410.6 | 0.400908 | ||||||||
\(83\) | −2401.93 | −0.0382707 | −0.0191353 | − | 0.999817i | \(-0.506091\pi\) | ||||
−0.0191353 | + | 0.999817i | \(0.506091\pi\) | |||||||
\(84\) | 33002.2 | 0.510323 | ||||||||
\(85\) | 8256.40 | 0.123949 | ||||||||
\(86\) | −8116.66 | −0.118340 | ||||||||
\(87\) | −62749.9 | −0.888822 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −36838.3 | −0.492974 | −0.246487 | − | 0.969146i | \(-0.579276\pi\) | ||||
−0.246487 | + | 0.969146i | \(0.579276\pi\) | |||||||
\(90\) | 3502.51 | 0.0455799 | ||||||||
\(91\) | −207070. | −2.62128 | ||||||||
\(92\) | 45248.2 | 0.557355 | ||||||||
\(93\) | −66036.4 | −0.791729 | ||||||||
\(94\) | 80872.1 | 0.944015 | ||||||||
\(95\) | −24542.3 | −0.279001 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | −63691.6 | −0.687311 | −0.343655 | − | 0.939096i | \(-0.611665\pi\) | ||||
−0.343655 | + | 0.939096i | \(0.611665\pi\) | |||||||
\(98\) | −142870. | −1.50271 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −48130.2 | −0.481302 | ||||||||
\(101\) | −28724.5 | −0.280188 | −0.140094 | − | 0.990138i | \(-0.544741\pi\) | ||||
−0.140094 | + | 0.990138i | \(0.544741\pi\) | |||||||
\(102\) | 27495.3 | 0.261672 | ||||||||
\(103\) | 72496.2 | 0.673321 | 0.336660 | − | 0.941626i | \(-0.390703\pi\) | ||||
0.336660 | + | 0.941626i | \(0.390703\pi\) | |||||||
\(104\) | 57825.1 | 0.524244 | ||||||||
\(105\) | −22297.6 | −0.197372 | ||||||||
\(106\) | 73768.9 | 0.637689 | ||||||||
\(107\) | 27700.3 | 0.233897 | 0.116949 | − | 0.993138i | \(-0.462689\pi\) | ||||
0.116949 | + | 0.993138i | \(0.462689\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | 53898.2 | 0.434518 | 0.217259 | − | 0.976114i | \(-0.430288\pi\) | ||||
0.217259 | + | 0.976114i | \(0.430288\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −94868.4 | −0.730826 | ||||||||
\(112\) | 58670.6 | 0.441953 | ||||||||
\(113\) | 120624. | 0.888665 | 0.444332 | − | 0.895862i | \(-0.353441\pi\) | ||||
0.444332 | + | 0.895862i | \(0.353441\pi\) | |||||||
\(114\) | −81730.3 | −0.589007 | ||||||||
\(115\) | −30571.5 | −0.215562 | ||||||||
\(116\) | −111555. | −0.769743 | ||||||||
\(117\) | −73184.9 | −0.494262 | ||||||||
\(118\) | −35039.7 | −0.231663 | ||||||||
\(119\) | −175040. | −1.13310 | ||||||||
\(120\) | 6226.69 | 0.0394734 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −101651. | −0.618320 | ||||||||
\(123\) | −54923.9 | −0.327340 | ||||||||
\(124\) | −117398. | −0.685657 | ||||||||
\(125\) | 66300.6 | 0.379527 | ||||||||
\(126\) | −74255.0 | −0.416677 | ||||||||
\(127\) | 72961.2 | 0.401405 | 0.200703 | − | 0.979652i | \(-0.435678\pi\) | ||||
0.200703 | + | 0.979652i | \(0.435678\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 18262.5 | 0.0966241 | ||||||||
\(130\) | −39068.9 | −0.202756 | ||||||||
\(131\) | 87861.7 | 0.447323 | 0.223662 | − | 0.974667i | \(-0.428199\pi\) | ||||
0.223662 | + | 0.974667i | \(0.428199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 520309. | 2.55054 | ||||||||
\(134\) | 177533. | 0.854119 | ||||||||
\(135\) | −7880.66 | −0.0372159 | ||||||||
\(136\) | 48880.5 | 0.226615 | ||||||||
\(137\) | 181912. | 0.828055 | 0.414027 | − | 0.910264i | \(-0.364122\pi\) | ||||
0.414027 | + | 0.910264i | \(0.364122\pi\) | |||||||
\(138\) | −101809. | −0.455079 | ||||||||
\(139\) | 130282. | 0.571937 | 0.285968 | − | 0.958239i | \(-0.407685\pi\) | ||||
0.285968 | + | 0.958239i | \(0.407685\pi\) | |||||||
\(140\) | −39640.2 | −0.170929 | ||||||||
\(141\) | −181962. | −0.770785 | ||||||||
\(142\) | 321551. | 1.33823 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 75371.2 | 0.297705 | ||||||||
\(146\) | −297540. | −1.15522 | ||||||||
\(147\) | 321457. | 1.22696 | ||||||||
\(148\) | −168655. | −0.632914 | ||||||||
\(149\) | −510763. | −1.88475 | −0.942375 | − | 0.334558i | \(-0.891413\pi\) | ||||
−0.942375 | + | 0.334558i | \(0.891413\pi\) | |||||||
\(150\) | 108293. | 0.392982 | ||||||||
\(151\) | 156912. | 0.560035 | 0.280017 | − | 0.959995i | \(-0.409660\pi\) | ||||
0.280017 | + | 0.959995i | \(0.409660\pi\) | |||||||
\(152\) | −145298. | −0.510095 | ||||||||
\(153\) | −61864.4 | −0.213655 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 79318.8 | 0.265184 | ||||||||
\(156\) | −130107. | −0.428043 | ||||||||
\(157\) | −95113.5 | −0.307959 | −0.153980 | − | 0.988074i | \(-0.549209\pi\) | ||||
−0.153980 | + | 0.988074i | \(0.549209\pi\) | |||||||
\(158\) | −117705. | −0.375104 | ||||||||
\(159\) | −165980. | −0.520670 | ||||||||
\(160\) | 11069.7 | 0.0341849 | ||||||||
\(161\) | 648130. | 1.97060 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −167377. | −0.493432 | −0.246716 | − | 0.969088i | \(-0.579352\pi\) | ||||
−0.246716 | + | 0.969088i | \(0.579352\pi\) | |||||||
\(164\) | −97642.5 | −0.283484 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9607.74 | 0.0270614 | ||||||||
\(167\) | −336730. | −0.934310 | −0.467155 | − | 0.884175i | \(-0.654721\pi\) | ||||
−0.467155 | + | 0.884175i | \(0.654721\pi\) | |||||||
\(168\) | −132009. | −0.360853 | ||||||||
\(169\) | 445051. | 1.19865 | ||||||||
\(170\) | −33025.6 | −0.0876452 | ||||||||
\(171\) | 183893. | 0.480923 | ||||||||
\(172\) | 32466.6 | 0.0836789 | ||||||||
\(173\) | −560330. | −1.42340 | −0.711702 | − | 0.702481i | \(-0.752076\pi\) | ||||
−0.711702 | + | 0.702481i | \(0.752076\pi\) | |||||||
\(174\) | 251000. | 0.628492 | ||||||||
\(175\) | −689412. | −1.70170 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 78839.4 | 0.189152 | ||||||||
\(178\) | 147353. | 0.348585 | ||||||||
\(179\) | −95541.3 | −0.222874 | −0.111437 | − | 0.993772i | \(-0.535545\pi\) | ||||
−0.111437 | + | 0.993772i | \(0.535545\pi\) | |||||||
\(180\) | −14010.1 | −0.0322299 | ||||||||
\(181\) | −83262.0 | −0.188908 | −0.0944540 | − | 0.995529i | \(-0.530111\pi\) | ||||
−0.0944540 | + | 0.995529i | \(0.530111\pi\) | |||||||
\(182\) | 828280. | 1.85353 | ||||||||
\(183\) | 228715. | 0.504856 | ||||||||
\(184\) | −180993. | −0.394110 | ||||||||
\(185\) | 113950. | 0.244785 | ||||||||
\(186\) | 264146. | 0.559837 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −323488. | −0.667519 | ||||||||
\(189\) | 167074. | 0.340215 | ||||||||
\(190\) | 98169.2 | 0.197284 | ||||||||
\(191\) | −664980. | −1.31894 | −0.659470 | − | 0.751730i | \(-0.729219\pi\) | ||||
−0.659470 | + | 0.751730i | \(0.729219\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | 157126. | 0.303637 | 0.151819 | − | 0.988408i | \(-0.451487\pi\) | ||||
0.151819 | + | 0.988408i | \(0.451487\pi\) | |||||||
\(194\) | 254767. | 0.486002 | ||||||||
\(195\) | 87905.1 | 0.165549 | ||||||||
\(196\) | 571479. | 1.06258 | ||||||||
\(197\) | −297052. | −0.545339 | −0.272669 | − | 0.962108i | \(-0.587907\pi\) | ||||
−0.272669 | + | 0.962108i | \(0.587907\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −384778. | −0.688774 | −0.344387 | − | 0.938828i | \(-0.611913\pi\) | ||||
−0.344387 | + | 0.938828i | \(0.611913\pi\) | |||||||
\(200\) | 192521. | 0.340332 | ||||||||
\(201\) | −399450. | −0.697385 | ||||||||
\(202\) | 114898. | 0.198123 | ||||||||
\(203\) | −1.59791e6 | −2.72152 | ||||||||
\(204\) | −109981. | −0.185030 | ||||||||
\(205\) | 65971.1 | 0.109640 | ||||||||
\(206\) | −289985. | −0.476110 | ||||||||
\(207\) | 229069. | 0.371570 | ||||||||
\(208\) | −231301. | −0.370696 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 89190.4 | 0.139563 | ||||||||
\(211\) | 244133. | 0.377503 | 0.188751 | − | 0.982025i | \(-0.439556\pi\) | ||||
0.188751 | + | 0.982025i | \(0.439556\pi\) | |||||||
\(212\) | −295076. | −0.450914 | ||||||||
\(213\) | −723490. | −1.09266 | ||||||||
\(214\) | −110801. | −0.165390 | ||||||||
\(215\) | −21935.7 | −0.0323635 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | −1.68160e6 | −2.42422 | ||||||||
\(218\) | −215593. | −0.307251 | ||||||||
\(219\) | 669465. | 0.943230 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 690069. | 0.950412 | ||||||||
\(222\) | 379473. | 0.516772 | ||||||||
\(223\) | 47797.2 | 0.0643636 | 0.0321818 | − | 0.999482i | \(-0.489754\pi\) | ||||
0.0321818 | + | 0.999482i | \(0.489754\pi\) | |||||||
\(224\) | −234682. | −0.312508 | ||||||||
\(225\) | −243659. | −0.320868 | ||||||||
\(226\) | −482496. | −0.628381 | ||||||||
\(227\) | 604310. | 0.778387 | 0.389193 | − | 0.921156i | \(-0.372754\pi\) | ||||
0.389193 | + | 0.921156i | \(0.372754\pi\) | |||||||
\(228\) | 326921. | 0.416491 | ||||||||
\(229\) | −984859. | −1.24104 | −0.620519 | − | 0.784191i | \(-0.713078\pi\) | ||||
−0.620519 | + | 0.784191i | \(0.713078\pi\) | |||||||
\(230\) | 122286. | 0.152425 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 446222. | 0.544290 | ||||||||
\(233\) | 777885. | 0.938698 | 0.469349 | − | 0.883013i | \(-0.344489\pi\) | ||||
0.469349 | + | 0.883013i | \(0.344489\pi\) | |||||||
\(234\) | 292740. | 0.349496 | ||||||||
\(235\) | 218561. | 0.258169 | ||||||||
\(236\) | 140159. | 0.163810 | ||||||||
\(237\) | 264836. | 0.306271 | ||||||||
\(238\) | 700159. | 0.801224 | ||||||||
\(239\) | −846574. | −0.958672 | −0.479336 | − | 0.877631i | \(-0.659123\pi\) | ||||
−0.479336 | + | 0.877631i | \(0.659123\pi\) | |||||||
\(240\) | −24906.8 | −0.0279119 | ||||||||
\(241\) | −1.04323e6 | −1.15702 | −0.578508 | − | 0.815677i | \(-0.696365\pi\) | ||||
−0.578508 | + | 0.815677i | \(0.696365\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 406605. | 0.437218 | ||||||||
\(245\) | −386114. | −0.410960 | ||||||||
\(246\) | 219696. | 0.231464 | ||||||||
\(247\) | −2.05124e6 | −2.13931 | ||||||||
\(248\) | 469592. | 0.484833 | ||||||||
\(249\) | −21617.4 | −0.0220956 | ||||||||
\(250\) | −265203. | −0.268366 | ||||||||
\(251\) | 515862. | 0.516832 | 0.258416 | − | 0.966034i | \(-0.416800\pi\) | ||||
0.258416 | + | 0.966034i | \(0.416800\pi\) | |||||||
\(252\) | 297020. | 0.294635 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −291845. | −0.283836 | ||||||||
\(255\) | 74307.6 | 0.0715620 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 547492. | 0.517065 | 0.258532 | − | 0.966003i | \(-0.416761\pi\) | ||||
0.258532 | + | 0.966003i | \(0.416761\pi\) | |||||||
\(258\) | −73049.9 | −0.0683235 | ||||||||
\(259\) | −2.41579e6 | −2.23774 | ||||||||
\(260\) | 156276. | 0.143370 | ||||||||
\(261\) | −564749. | −0.513162 | ||||||||
\(262\) | −351447. | −0.316305 | ||||||||
\(263\) | −349065. | −0.311184 | −0.155592 | − | 0.987821i | \(-0.549728\pi\) | ||||
−0.155592 | + | 0.987821i | \(0.549728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 199365. | 0.174395 | ||||||||
\(266\) | −2.08123e6 | −1.80350 | ||||||||
\(267\) | −331544. | −0.284619 | ||||||||
\(268\) | −710134. | −0.603953 | ||||||||
\(269\) | 749494. | 0.631520 | 0.315760 | − | 0.948839i | \(-0.397741\pi\) | ||||
0.315760 | + | 0.948839i | \(0.397741\pi\) | |||||||
\(270\) | 31522.6 | 0.0263156 | ||||||||
\(271\) | −1.52749e6 | −1.26344 | −0.631720 | − | 0.775197i | \(-0.717651\pi\) | ||||
−0.631720 | + | 0.775197i | \(0.717651\pi\) | |||||||
\(272\) | −195522. | −0.160241 | ||||||||
\(273\) | −1.86363e6 | −1.51340 | ||||||||
\(274\) | −727646. | −0.585523 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 407234. | 0.321789 | ||||||||
\(277\) | 1.31031e6 | 1.02607 | 0.513033 | − | 0.858369i | \(-0.328522\pi\) | ||||
0.513033 | + | 0.858369i | \(0.328522\pi\) | |||||||
\(278\) | −521129. | −0.404420 | ||||||||
\(279\) | −594328. | −0.457105 | ||||||||
\(280\) | 158561. | 0.120865 | ||||||||
\(281\) | 1.40135e6 | 1.05872 | 0.529361 | − | 0.848397i | \(-0.322432\pi\) | ||||
0.529361 | + | 0.848397i | \(0.322432\pi\) | |||||||
\(282\) | 727849. | 0.545027 | ||||||||
\(283\) | 581548. | 0.431638 | 0.215819 | − | 0.976433i | \(-0.430758\pi\) | ||||
0.215819 | + | 0.976433i | \(0.430758\pi\) | |||||||
\(284\) | −1.28621e6 | −0.946268 | ||||||||
\(285\) | −220881. | −0.161082 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.39862e6 | −1.00229 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −836531. | −0.589165 | ||||||||
\(290\) | −301485. | −0.210509 | ||||||||
\(291\) | −573225. | −0.396819 | ||||||||
\(292\) | 1.19016e6 | 0.816861 | ||||||||
\(293\) | −1.86180e6 | −1.26697 | −0.633483 | − | 0.773756i | \(-0.718375\pi\) | ||||
−0.633483 | + | 0.773756i | \(0.718375\pi\) | |||||||
\(294\) | −1.28583e6 | −0.867590 | ||||||||
\(295\) | −94696.9 | −0.0633550 | ||||||||
\(296\) | 674619. | 0.447538 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.04305e6 | 1.33272 | ||||||||
\(299\) | −2.55516e6 | −1.65288 | ||||||||
\(300\) | −433172. | −0.277880 | ||||||||
\(301\) | 465048. | 0.295857 | ||||||||
\(302\) | −627650. | −0.396004 | ||||||||
\(303\) | −258521. | −0.161767 | ||||||||
\(304\) | 581193. | 0.360692 | ||||||||
\(305\) | −274718. | −0.169098 | ||||||||
\(306\) | 247458. | 0.151077 | ||||||||
\(307\) | −1.39974e6 | −0.847620 | −0.423810 | − | 0.905751i | \(-0.639308\pi\) | ||||
−0.423810 | + | 0.905751i | \(0.639308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 652466. | 0.388742 | ||||||||
\(310\) | −317275. | −0.187513 | ||||||||
\(311\) | −832541. | −0.488095 | −0.244048 | − | 0.969763i | \(-0.578475\pi\) | ||||
−0.244048 | + | 0.969763i | \(0.578475\pi\) | |||||||
\(312\) | 520426. | 0.302672 | ||||||||
\(313\) | −2.60734e6 | −1.50431 | −0.752155 | − | 0.658986i | \(-0.770986\pi\) | ||||
−0.752155 | + | 0.658986i | \(0.770986\pi\) | |||||||
\(314\) | 380454. | 0.217760 | ||||||||
\(315\) | −200678. | −0.113953 | ||||||||
\(316\) | 470819. | 0.265238 | ||||||||
\(317\) | −35395.8 | −0.0197835 | −0.00989175 | − | 0.999951i | \(-0.503149\pi\) | ||||
−0.00989175 | + | 0.999951i | \(0.503149\pi\) | |||||||
\(318\) | 663920. | 0.368170 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −44278.7 | −0.0241724 | ||||||||
\(321\) | 249303. | 0.135041 | ||||||||
\(322\) | −2.59252e6 | −1.39342 | ||||||||
\(323\) | −1.73395e6 | −0.924762 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 2.71791e6 | 1.42734 | ||||||||
\(326\) | 669509. | 0.348909 | ||||||||
\(327\) | 485083. | 0.250869 | ||||||||
\(328\) | 390570. | 0.200454 | ||||||||
\(329\) | −4.63361e6 | −2.36009 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 125174. | 0.0627978 | 0.0313989 | − | 0.999507i | \(-0.490004\pi\) | ||||
0.0313989 | + | 0.999507i | \(0.490004\pi\) | |||||||
\(332\) | −38431.0 | −0.0191353 | ||||||||
\(333\) | −853815. | −0.421943 | ||||||||
\(334\) | 1.34692e6 | 0.660657 | ||||||||
\(335\) | 479794. | 0.233584 | ||||||||
\(336\) | 528036. | 0.255161 | ||||||||
\(337\) | −607149. | −0.291220 | −0.145610 | − | 0.989342i | \(-0.546514\pi\) | ||||
−0.145610 | + | 0.989342i | \(0.546514\pi\) | |||||||
\(338\) | −1.78020e6 | −0.847575 | ||||||||
\(339\) | 1.08562e6 | 0.513071 | ||||||||
\(340\) | 132102. | 0.0619745 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −735572. | −0.340064 | ||||||||
\(343\) | 4.33393e6 | 1.98906 | ||||||||
\(344\) | −129867. | −0.0591699 | ||||||||
\(345\) | −275143. | −0.124455 | ||||||||
\(346\) | 2.24132e6 | 1.00650 | ||||||||
\(347\) | −2.76192e6 | −1.23137 | −0.615683 | − | 0.787994i | \(-0.711120\pi\) | ||||
−0.615683 | + | 0.787994i | \(0.711120\pi\) | |||||||
\(348\) | −1.00400e6 | −0.444411 | ||||||||
\(349\) | 1.52151e6 | 0.668670 | 0.334335 | − | 0.942454i | \(-0.391488\pi\) | ||||
0.334335 | + | 0.942454i | \(0.391488\pi\) | |||||||
\(350\) | 2.75765e6 | 1.20328 | ||||||||
\(351\) | −658664. | −0.285362 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −529162. | −0.226022 | −0.113011 | − | 0.993594i | \(-0.536050\pi\) | ||||
−0.113011 | + | 0.993594i | \(0.536050\pi\) | |||||||
\(354\) | −315358. | −0.133750 | ||||||||
\(355\) | 869011. | 0.365977 | ||||||||
\(356\) | −589412. | −0.246487 | ||||||||
\(357\) | −1.57536e6 | −0.654197 | ||||||||
\(358\) | 382165. | 0.157595 | ||||||||
\(359\) | 2.68712e6 | 1.10040 | 0.550201 | − | 0.835032i | \(-0.314551\pi\) | ||||
0.550201 | + | 0.835032i | \(0.314551\pi\) | |||||||
\(360\) | 56040.2 | 0.0227900 | ||||||||
\(361\) | 2.67810e6 | 1.08158 | ||||||||
\(362\) | 333048. | 0.133578 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.31312e6 | −1.31064 | ||||||||
\(365\) | −804119. | −0.315928 | ||||||||
\(366\) | −914861. | −0.356987 | ||||||||
\(367\) | 2.26817e6 | 0.879042 | 0.439521 | − | 0.898232i | \(-0.355148\pi\) | ||||
0.439521 | + | 0.898232i | \(0.355148\pi\) | |||||||
\(368\) | 723972. | 0.278678 | ||||||||
\(369\) | −494315. | −0.188990 | ||||||||
\(370\) | −455799. | −0.173089 | ||||||||
\(371\) | −4.22663e6 | −1.59426 | ||||||||
\(372\) | −1.05658e6 | −0.395864 | ||||||||
\(373\) | 2.70420e6 | 1.00639 | 0.503195 | − | 0.864173i | \(-0.332158\pi\) | ||||
0.503195 | + | 0.864173i | \(0.332158\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 596706. | 0.219120 | ||||||||
\(376\) | 1.29395e6 | 0.472007 | ||||||||
\(377\) | 6.29952e6 | 2.28273 | ||||||||
\(378\) | −668295. | −0.240568 | ||||||||
\(379\) | 2.32153e6 | 0.830186 | 0.415093 | − | 0.909779i | \(-0.363749\pi\) | ||||
0.415093 | + | 0.909779i | \(0.363749\pi\) | |||||||
\(380\) | −392677. | −0.139501 | ||||||||
\(381\) | 656651. | 0.231751 | ||||||||
\(382\) | 2.65992e6 | 0.932632 | ||||||||
\(383\) | −5.16764e6 | −1.80009 | −0.900047 | − | 0.435792i | \(-0.856468\pi\) | ||||
−0.900047 | + | 0.435792i | \(0.856468\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −628504. | −0.214704 | ||||||||
\(387\) | 164362. | 0.0557859 | ||||||||
\(388\) | −1.01907e6 | −0.343655 | ||||||||
\(389\) | −126727. | −0.0424616 | −0.0212308 | − | 0.999775i | \(-0.506758\pi\) | ||||
−0.0212308 | + | 0.999775i | \(0.506758\pi\) | |||||||
\(390\) | −351620. | −0.117061 | ||||||||
\(391\) | −2.15992e6 | −0.714489 | ||||||||
\(392\) | −2.28592e6 | −0.751355 | ||||||||
\(393\) | 790755. | 0.258262 | ||||||||
\(394\) | 1.18821e6 | 0.385613 | ||||||||
\(395\) | −318104. | −0.102583 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.95769e6 | −0.623402 | −0.311701 | − | 0.950180i | \(-0.600899\pi\) | ||||
−0.311701 | + | 0.950180i | \(0.600899\pi\) | |||||||
\(398\) | 1.53911e6 | 0.487037 | ||||||||
\(399\) | 4.68278e6 | 1.47255 | ||||||||
\(400\) | −770084. | −0.240651 | ||||||||
\(401\) | 1.30000e6 | 0.403721 | 0.201861 | − | 0.979414i | \(-0.435301\pi\) | ||||
0.201861 | + | 0.979414i | \(0.435301\pi\) | |||||||
\(402\) | 1.59780e6 | 0.493126 | ||||||||
\(403\) | 6.62945e6 | 2.03336 | ||||||||
\(404\) | −459593. | −0.140094 | ||||||||
\(405\) | −70925.9 | −0.0214866 | ||||||||
\(406\) | 6.39162e6 | 1.92440 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 439925. | 0.130836 | ||||||||
\(409\) | 294959. | 0.0871873 | 0.0435936 | − | 0.999049i | \(-0.486119\pi\) | ||||
0.0435936 | + | 0.999049i | \(0.486119\pi\) | |||||||
\(410\) | −263884. | −0.0775272 | ||||||||
\(411\) | 1.63720e6 | 0.478078 | ||||||||
\(412\) | 1.15994e6 | 0.336660 | ||||||||
\(413\) | 2.00762e6 | 0.579170 | ||||||||
\(414\) | −916277. | −0.262740 | ||||||||
\(415\) | 25965.5 | 0.00740075 | ||||||||
\(416\) | 925202. | 0.262122 | ||||||||
\(417\) | 1.17254e6 | 0.330208 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.46469e6 | −0.407578 | −0.203789 | − | 0.979015i | \(-0.565326\pi\) | ||||
−0.203789 | + | 0.979015i | \(0.565326\pi\) | |||||||
\(420\) | −356762. | −0.0986858 | ||||||||
\(421\) | −1.15202e6 | −0.316779 | −0.158389 | − | 0.987377i | \(-0.550630\pi\) | ||||
−0.158389 | + | 0.987377i | \(0.550630\pi\) | |||||||
\(422\) | −976532. | −0.266935 | ||||||||
\(423\) | −1.63766e6 | −0.445013 | ||||||||
\(424\) | 1.18030e6 | 0.318844 | ||||||||
\(425\) | 2.29749e6 | 0.616995 | ||||||||
\(426\) | 2.89396e6 | 0.772625 | ||||||||
\(427\) | 5.82416e6 | 1.54584 | ||||||||
\(428\) | 443205. | 0.116949 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 87742.9 | 0.0228845 | ||||||||
\(431\) | 4.31164e6 | 1.11802 | 0.559009 | − | 0.829161i | \(-0.311182\pi\) | ||||
0.559009 | + | 0.829161i | \(0.311182\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | 6.53482e6 | 1.67500 | 0.837498 | − | 0.546441i | \(-0.184018\pi\) | ||||
0.837498 | + | 0.546441i | \(0.184018\pi\) | |||||||
\(434\) | 6.72639e6 | 1.71418 | ||||||||
\(435\) | 678341. | 0.171880 | ||||||||
\(436\) | 862370. | 0.217259 | ||||||||
\(437\) | 6.42040e6 | 1.60827 | ||||||||
\(438\) | −2.67786e6 | −0.666965 | ||||||||
\(439\) | −6.84390e6 | −1.69489 | −0.847446 | − | 0.530881i | \(-0.821861\pi\) | ||||
−0.847446 | + | 0.530881i | \(0.821861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.89311e6 | 0.708384 | ||||||||
\(442\) | −2.76028e6 | −0.672042 | ||||||||
\(443\) | −597201. | −0.144581 | −0.0722906 | − | 0.997384i | \(-0.523031\pi\) | ||||
−0.0722906 | + | 0.997384i | \(0.523031\pi\) | |||||||
\(444\) | −1.51789e6 | −0.365413 | ||||||||
\(445\) | 398230. | 0.0953309 | ||||||||
\(446\) | −191189. | −0.0455119 | ||||||||
\(447\) | −4.59687e6 | −1.08816 | ||||||||
\(448\) | 938730. | 0.220976 | ||||||||
\(449\) | −6.49320e6 | −1.52000 | −0.759999 | − | 0.649924i | \(-0.774801\pi\) | ||||
−0.759999 | + | 0.649924i | \(0.774801\pi\) | |||||||
\(450\) | 974637. | 0.226888 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.92999e6 | 0.444332 | ||||||||
\(453\) | 1.41221e6 | 0.323336 | ||||||||
\(454\) | −2.41724e6 | −0.550403 | ||||||||
\(455\) | 2.23847e6 | 0.506902 | ||||||||
\(456\) | −1.30768e6 | −0.294504 | ||||||||
\(457\) | −5.26873e6 | −1.18009 | −0.590046 | − | 0.807370i | \(-0.700890\pi\) | ||||
−0.590046 | + | 0.807370i | \(0.700890\pi\) | |||||||
\(458\) | 3.93943e6 | 0.877546 | ||||||||
\(459\) | −556780. | −0.123354 | ||||||||
\(460\) | −489144. | −0.107781 | ||||||||
\(461\) | 467971. | 0.102557 | 0.0512786 | − | 0.998684i | \(-0.483670\pi\) | ||||
0.0512786 | + | 0.998684i | \(0.483670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.63233e6 | 0.570674 | 0.285337 | − | 0.958427i | \(-0.407894\pi\) | ||||
0.285337 | + | 0.958427i | \(0.407894\pi\) | |||||||
\(464\) | −1.78489e6 | −0.384871 | ||||||||
\(465\) | 713869. | 0.153104 | ||||||||
\(466\) | −3.11154e6 | −0.663759 | ||||||||
\(467\) | −8.65002e6 | −1.83538 | −0.917688 | − | 0.397302i | \(-0.869947\pi\) | ||||
−0.917688 | + | 0.397302i | \(0.869947\pi\) | |||||||
\(468\) | −1.17096e6 | −0.247131 | ||||||||
\(469\) | −1.01719e7 | −2.13535 | ||||||||
\(470\) | −874245. | −0.182553 | ||||||||
\(471\) | −856021. | −0.177800 | ||||||||
\(472\) | −560636. | −0.115831 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.05934e6 | −0.216566 | ||||||||
\(475\) | −6.82933e6 | −1.38881 | ||||||||
\(476\) | −2.80063e6 | −0.566551 | ||||||||
\(477\) | −1.49382e6 | −0.300609 | ||||||||
\(478\) | 3.38630e6 | 0.677884 | ||||||||
\(479\) | −2.99462e6 | −0.596353 | −0.298177 | − | 0.954511i | \(-0.596378\pi\) | ||||
−0.298177 | + | 0.954511i | \(0.596378\pi\) | |||||||
\(480\) | 99627.1 | 0.0197367 | ||||||||
\(481\) | 9.52391e6 | 1.87695 | ||||||||
\(482\) | 4.17294e6 | 0.818134 | ||||||||
\(483\) | 5.83317e6 | 1.13772 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 688521. | 0.132912 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | 6.18023e6 | 1.18082 | 0.590408 | − | 0.807105i | \(-0.298967\pi\) | ||||
0.590408 | + | 0.807105i | \(0.298967\pi\) | |||||||
\(488\) | −1.62642e6 | −0.309160 | ||||||||
\(489\) | −1.50640e6 | −0.284883 | ||||||||
\(490\) | 1.54445e6 | 0.290593 | ||||||||
\(491\) | −1.00918e7 | −1.88915 | −0.944575 | − | 0.328296i | \(-0.893526\pi\) | ||||
−0.944575 | + | 0.328296i | \(0.893526\pi\) | |||||||
\(492\) | −878782. | −0.163670 | ||||||||
\(493\) | 5.32508e6 | 0.986754 | ||||||||
\(494\) | 8.20497e6 | 1.51272 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.87837e6 | −0.342829 | ||||||||
\(497\) | −1.84234e7 | −3.34565 | ||||||||
\(498\) | 86469.6 | 0.0156239 | ||||||||
\(499\) | −958506. | −0.172323 | −0.0861615 | − | 0.996281i | \(-0.527460\pi\) | ||||
−0.0861615 | + | 0.996281i | \(0.527460\pi\) | |||||||
\(500\) | 1.06081e6 | 0.189763 | ||||||||
\(501\) | −3.03057e6 | −0.539424 | ||||||||
\(502\) | −2.06345e6 | −0.365455 | ||||||||
\(503\) | 2.90590e6 | 0.512106 | 0.256053 | − | 0.966663i | \(-0.417578\pi\) | ||||
0.256053 | + | 0.966663i | \(0.417578\pi\) | |||||||
\(504\) | −1.18808e6 | −0.208338 | ||||||||
\(505\) | 310519. | 0.0541826 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.00546e6 | 0.692042 | ||||||||
\(508\) | 1.16738e6 | 0.200703 | ||||||||
\(509\) | 1.03221e7 | 1.76594 | 0.882968 | − | 0.469433i | \(-0.155542\pi\) | ||||
0.882968 | + | 0.469433i | \(0.155542\pi\) | |||||||
\(510\) | −297230. | −0.0506020 | ||||||||
\(511\) | 1.70477e7 | 2.88811 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 1.65504e6 | 0.277661 | ||||||||
\(514\) | −2.18997e6 | −0.365620 | ||||||||
\(515\) | −783700. | −0.130206 | ||||||||
\(516\) | 292200. | 0.0483120 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 9.66317e6 | 1.58232 | ||||||||
\(519\) | −5.04297e6 | −0.821803 | ||||||||
\(520\) | −625103. | −0.101378 | ||||||||
\(521\) | −1.17658e6 | −0.189901 | −0.0949507 | − | 0.995482i | \(-0.530269\pi\) | ||||
−0.0949507 | + | 0.995482i | \(0.530269\pi\) | |||||||
\(522\) | 2.25900e6 | 0.362860 | ||||||||
\(523\) | −4.16140e6 | −0.665251 | −0.332626 | − | 0.943059i | \(-0.607935\pi\) | ||||
−0.332626 | + | 0.943059i | \(0.607935\pi\) | |||||||
\(524\) | 1.40579e6 | 0.223662 | ||||||||
\(525\) | −6.20470e6 | −0.982478 | ||||||||
\(526\) | 1.39626e6 | 0.220040 | ||||||||
\(527\) | 5.60398e6 | 0.878963 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.56132e6 | 0.242579 | ||||||||
\(530\) | −797459. | −0.123316 | ||||||||
\(531\) | 709555. | 0.109207 | ||||||||
\(532\) | 8.32494e6 | 1.27527 | ||||||||
\(533\) | 5.51386e6 | 0.840693 | ||||||||
\(534\) | 1.32618e6 | 0.201256 | ||||||||
\(535\) | −299447. | −0.0452309 | ||||||||
\(536\) | 2.84054e6 | 0.427059 | ||||||||
\(537\) | −859871. | −0.128676 | ||||||||
\(538\) | −2.99798e6 | −0.446552 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −126091. | −0.0186079 | ||||||||
\(541\) | 1.14751e7 | 1.68564 | 0.842819 | − | 0.538198i | \(-0.180895\pi\) | ||||
0.842819 | + | 0.538198i | \(0.180895\pi\) | |||||||
\(542\) | 6.10995e6 | 0.893386 | ||||||||
\(543\) | −749358. | −0.109066 | ||||||||
\(544\) | 782088. | 0.113307 | ||||||||
\(545\) | −582651. | −0.0840267 | ||||||||
\(546\) | 7.45452e6 | 1.07013 | ||||||||
\(547\) | 9.28056e6 | 1.32619 | 0.663095 | − | 0.748535i | \(-0.269243\pi\) | ||||
0.663095 | + | 0.748535i | \(0.269243\pi\) | |||||||
\(548\) | 2.91059e6 | 0.414027 | ||||||||
\(549\) | 2.05844e6 | 0.291479 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.58289e7 | −2.22112 | ||||||||
\(552\) | −1.62894e6 | −0.227539 | ||||||||
\(553\) | 6.74396e6 | 0.937782 | ||||||||
\(554\) | −5.24124e6 | −0.725538 | ||||||||
\(555\) | 1.02555e6 | 0.141327 | ||||||||
\(556\) | 2.08452e6 | 0.285968 | ||||||||
\(557\) | −5.49440e6 | −0.750382 | −0.375191 | − | 0.926947i | \(-0.622423\pi\) | ||||
−0.375191 | + | 0.926947i | \(0.622423\pi\) | |||||||
\(558\) | 2.37731e6 | 0.323222 | ||||||||
\(559\) | −1.83339e6 | −0.248156 | ||||||||
\(560\) | −634243. | −0.0854644 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.60541e6 | −0.748629 | ||||||||
\(563\) | 3.37210e6 | 0.448363 | 0.224181 | − | 0.974547i | \(-0.428029\pi\) | ||||
0.224181 | + | 0.974547i | \(0.428029\pi\) | |||||||
\(564\) | −2.91139e6 | −0.385392 | ||||||||
\(565\) | −1.30397e6 | −0.171849 | ||||||||
\(566\) | −2.32619e6 | −0.305214 | ||||||||
\(567\) | 1.50366e6 | 0.196423 | ||||||||
\(568\) | 5.14482e6 | 0.669113 | ||||||||
\(569\) | 6.21502e6 | 0.804752 | 0.402376 | − | 0.915475i | \(-0.368185\pi\) | ||||
0.402376 | + | 0.915475i | \(0.368185\pi\) | |||||||
\(570\) | 883523. | 0.113902 | ||||||||
\(571\) | 947370. | 0.121599 | 0.0607994 | − | 0.998150i | \(-0.480635\pi\) | ||||
0.0607994 | + | 0.998150i | \(0.480635\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.98482e6 | −0.761491 | ||||||||
\(574\) | 5.59448e6 | 0.708728 | ||||||||
\(575\) | −8.50706e6 | −1.07303 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −5.75469e6 | −0.719585 | −0.359793 | − | 0.933032i | \(-0.617153\pi\) | ||||
−0.359793 | + | 0.933032i | \(0.617153\pi\) | |||||||
\(578\) | 3.34612e6 | 0.416603 | ||||||||
\(579\) | 1.41413e6 | 0.175305 | ||||||||
\(580\) | 1.20594e6 | 0.148852 | ||||||||
\(581\) | −550480. | −0.0676553 | ||||||||
\(582\) | 2.29290e6 | 0.280593 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −4.76064e6 | −0.577608 | ||||||||
\(585\) | 791146. | 0.0955800 | ||||||||
\(586\) | 7.44722e6 | 0.895881 | ||||||||
\(587\) | −6.28253e6 | −0.752556 | −0.376278 | − | 0.926507i | \(-0.622796\pi\) | ||||
−0.376278 | + | 0.926507i | \(0.622796\pi\) | |||||||
\(588\) | 5.14331e6 | 0.613479 | ||||||||
\(589\) | −1.66580e7 | −1.97849 | ||||||||
\(590\) | 378788. | 0.0447987 | ||||||||
\(591\) | −2.67347e6 | −0.314852 | ||||||||
\(592\) | −2.69848e6 | −0.316457 | ||||||||
\(593\) | 1.02214e7 | 1.19364 | 0.596818 | − | 0.802377i | \(-0.296431\pi\) | ||||
0.596818 | + | 0.802377i | \(0.296431\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.89222e6 | 0.219118 | ||||||||
\(596\) | −8.17221e6 | −0.942375 | ||||||||
\(597\) | −3.46300e6 | −0.397664 | ||||||||
\(598\) | 1.02206e7 | 1.16876 | ||||||||
\(599\) | 1.50081e7 | 1.70907 | 0.854534 | − | 0.519395i | \(-0.173843\pi\) | ||||
0.854534 | + | 0.519395i | \(0.173843\pi\) | |||||||
\(600\) | 1.73269e6 | 0.196491 | ||||||||
\(601\) | −2.81933e6 | −0.318391 | −0.159195 | − | 0.987247i | \(-0.550890\pi\) | ||||
−0.159195 | + | 0.987247i | \(0.550890\pi\) | |||||||
\(602\) | −1.86019e6 | −0.209202 | ||||||||
\(603\) | −3.59505e6 | −0.402635 | ||||||||
\(604\) | 2.51060e6 | 0.280017 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.03408e6 | 0.114386 | ||||||||
\(607\) | 1.42538e7 | 1.57022 | 0.785108 | − | 0.619359i | \(-0.212607\pi\) | ||||
0.785108 | + | 0.619359i | \(0.212607\pi\) | |||||||
\(608\) | −2.32477e6 | −0.255048 | ||||||||
\(609\) | −1.43812e7 | −1.57127 | ||||||||
\(610\) | 1.09887e6 | 0.119570 | ||||||||
\(611\) | 1.82673e7 | 1.97958 | ||||||||
\(612\) | −989830. | −0.106827 | ||||||||
\(613\) | 2.51664e6 | 0.270501 | 0.135251 | − | 0.990811i | \(-0.456816\pi\) | ||||
0.135251 | + | 0.990811i | \(0.456816\pi\) | |||||||
\(614\) | 5.59896e6 | 0.599358 | ||||||||
\(615\) | 593740. | 0.0633007 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.72075e6 | 0.816482 | 0.408241 | − | 0.912874i | \(-0.366142\pi\) | ||||
0.408241 | + | 0.912874i | \(0.366142\pi\) | |||||||
\(618\) | −2.60986e6 | −0.274882 | ||||||||
\(619\) | 5.49668e6 | 0.576599 | 0.288300 | − | 0.957540i | \(-0.406910\pi\) | ||||
0.288300 | + | 0.957540i | \(0.406910\pi\) | |||||||
\(620\) | 1.26910e6 | 0.132592 | ||||||||
\(621\) | 2.06162e6 | 0.214526 | ||||||||
\(622\) | 3.33016e6 | 0.345136 | ||||||||
\(623\) | −8.44267e6 | −0.871484 | ||||||||
\(624\) | −2.08170e6 | −0.214022 | ||||||||
\(625\) | 8.68371e6 | 0.889212 | ||||||||
\(626\) | 1.04294e7 | 1.06371 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.52182e6 | −0.153980 | ||||||||
\(629\) | 8.05072e6 | 0.811350 | ||||||||
\(630\) | 802714. | 0.0805767 | ||||||||
\(631\) | 1.88580e7 | 1.88548 | 0.942742 | − | 0.333523i | \(-0.108237\pi\) | ||||
0.942742 | + | 0.333523i | \(0.108237\pi\) | |||||||
\(632\) | −1.88328e6 | −0.187552 | ||||||||
\(633\) | 2.19720e6 | 0.217951 | ||||||||
\(634\) | 141583. | 0.0139890 | ||||||||
\(635\) | −788728. | −0.0776234 | ||||||||
\(636\) | −2.65568e6 | −0.260335 | ||||||||
\(637\) | −3.22713e7 | −3.15114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.51141e6 | −0.630846 | ||||||||
\(640\) | 177115. | 0.0170925 | ||||||||
\(641\) | 5.03974e6 | 0.484465 | 0.242233 | − | 0.970218i | \(-0.422120\pi\) | ||||
0.242233 | + | 0.970218i | \(0.422120\pi\) | |||||||
\(642\) | −997212. | −0.0954882 | ||||||||
\(643\) | −6.29875e6 | −0.600796 | −0.300398 | − | 0.953814i | \(-0.597119\pi\) | ||||
−0.300398 | + | 0.953814i | \(0.597119\pi\) | |||||||
\(644\) | 1.03701e7 | 0.985298 | ||||||||
\(645\) | −197422. | −0.0186851 | ||||||||
\(646\) | 6.93579e6 | 0.653905 | ||||||||
\(647\) | 1.09807e7 | 1.03126 | 0.515632 | − | 0.856810i | \(-0.327557\pi\) | ||||
0.515632 | + | 0.856810i | \(0.327557\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.08716e7 | −1.00928 | ||||||||
\(651\) | −1.51344e7 | −1.39963 | ||||||||
\(652\) | −2.67804e6 | −0.246716 | ||||||||
\(653\) | −7.84121e6 | −0.719615 | −0.359808 | − | 0.933027i | \(-0.617158\pi\) | ||||
−0.359808 | + | 0.933027i | \(0.617158\pi\) | |||||||
\(654\) | −1.94033e6 | −0.177391 | ||||||||
\(655\) | −949805. | −0.0865030 | ||||||||
\(656\) | −1.56228e6 | −0.141742 | ||||||||
\(657\) | 6.02519e6 | 0.544574 | ||||||||
\(658\) | 1.85344e7 | 1.66884 | ||||||||
\(659\) | −1.28457e7 | −1.15224 | −0.576121 | − | 0.817364i | \(-0.695434\pi\) | ||||
−0.576121 | + | 0.817364i | \(0.695434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.16392e6 | −0.459701 | −0.229851 | − | 0.973226i | \(-0.573824\pi\) | ||||
−0.229851 | + | 0.973226i | \(0.573824\pi\) | |||||||
\(662\) | −500696. | −0.0444047 | ||||||||
\(663\) | 6.21062e6 | 0.548720 | ||||||||
\(664\) | 153724. | 0.0135307 | ||||||||
\(665\) | −5.62466e6 | −0.493221 | ||||||||
\(666\) | 3.41526e6 | 0.298358 | ||||||||
\(667\) | −1.97175e7 | −1.71608 | ||||||||
\(668\) | −5.38768e6 | −0.467155 | ||||||||
\(669\) | 430175. | 0.0371603 | ||||||||
\(670\) | −1.91918e6 | −0.165169 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.11214e6 | −0.180426 | ||||||||
\(673\) | 6.97138e6 | 0.593309 | 0.296654 | − | 0.954985i | \(-0.404129\pi\) | ||||
0.296654 | + | 0.954985i | \(0.404129\pi\) | |||||||
\(674\) | 2.42860e6 | 0.205923 | ||||||||
\(675\) | −2.19293e6 | −0.185253 | ||||||||
\(676\) | 7.12082e6 | 0.599326 | ||||||||
\(677\) | −1.41142e7 | −1.18354 | −0.591771 | − | 0.806106i | \(-0.701571\pi\) | ||||
−0.591771 | + | 0.806106i | \(0.701571\pi\) | |||||||
\(678\) | −4.34247e6 | −0.362796 | ||||||||
\(679\) | −1.45970e7 | −1.21503 | ||||||||
\(680\) | −528410. | −0.0438226 | ||||||||
\(681\) | 5.43879e6 | 0.449402 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.62086e7 | 1.32952 | 0.664759 | − | 0.747058i | \(-0.268534\pi\) | ||||
0.664759 | + | 0.747058i | \(0.268534\pi\) | |||||||
\(684\) | 2.94229e6 | 0.240461 | ||||||||
\(685\) | −1.96651e6 | −0.160129 | ||||||||
\(686\) | −1.73357e7 | −1.40647 | ||||||||
\(687\) | −8.86373e6 | −0.716514 | ||||||||
\(688\) | 519466. | 0.0418395 | ||||||||
\(689\) | 1.66629e7 | 1.33722 | ||||||||
\(690\) | 1.10057e6 | 0.0880028 | ||||||||
\(691\) | 1.15076e7 | 0.916831 | 0.458415 | − | 0.888738i | \(-0.348417\pi\) | ||||
0.458415 | + | 0.888738i | \(0.348417\pi\) | |||||||
\(692\) | −8.96528e6 | −0.711702 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.10477e7 | 0.870707 | ||||||||
\(695\) | −1.40838e6 | −0.110601 | ||||||||
\(696\) | 4.01599e6 | 0.314246 | ||||||||
\(697\) | 4.66095e6 | 0.363406 | ||||||||
\(698\) | −6.08604e6 | −0.472821 | ||||||||
\(699\) | 7.00097e6 | 0.541957 | ||||||||
\(700\) | −1.10306e7 | −0.850851 | ||||||||
\(701\) | 9.75656e6 | 0.749897 | 0.374949 | − | 0.927046i | \(-0.377660\pi\) | ||||
0.374949 | + | 0.927046i | \(0.377660\pi\) | |||||||
\(702\) | 2.63466e6 | 0.201782 | ||||||||
\(703\) | −2.39309e7 | −1.82630 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.96705e6 | 0.149054 | ||||||||
\(706\) | 2.11665e6 | 0.159822 | ||||||||
\(707\) | −6.58315e6 | −0.495319 | ||||||||
\(708\) | 1.26143e6 | 0.0945758 | ||||||||
\(709\) | 4.92386e6 | 0.367867 | 0.183933 | − | 0.982939i | \(-0.441117\pi\) | ||||
0.183933 | + | 0.982939i | \(0.441117\pi\) | |||||||
\(710\) | −3.47604e6 | −0.258785 | ||||||||
\(711\) | 2.38352e6 | 0.176826 | ||||||||
\(712\) | 2.35765e6 | 0.174293 | ||||||||
\(713\) | −2.07502e7 | −1.52862 | ||||||||
\(714\) | 6.30143e6 | 0.462587 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.52866e6 | −0.111437 | ||||||||
\(717\) | −7.61917e6 | −0.553490 | ||||||||
\(718\) | −1.07485e7 | −0.778102 | ||||||||
\(719\) | 2.10739e7 | 1.52027 | 0.760137 | − | 0.649763i | \(-0.225132\pi\) | ||||
0.760137 | + | 0.649763i | \(0.225132\pi\) | |||||||
\(720\) | −224161. | −0.0161149 | ||||||||
\(721\) | 1.66148e7 | 1.19030 | ||||||||
\(722\) | −1.07124e7 | −0.764792 | ||||||||
\(723\) | −9.38911e6 | −0.668003 | ||||||||
\(724\) | −1.33219e6 | −0.0944540 | ||||||||
\(725\) | 2.09734e7 | 1.48192 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.02370e7 | 0.718348 | 0.359174 | − | 0.933271i | \(-0.383058\pi\) | ||||
0.359174 | + | 0.933271i | \(0.383058\pi\) | |||||||
\(728\) | 1.32525e7 | 0.926763 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 3.21648e6 | 0.223395 | ||||||||
\(731\) | −1.54979e6 | −0.107270 | ||||||||
\(732\) | 3.65944e6 | 0.252428 | ||||||||
\(733\) | −2.13623e7 | −1.46855 | −0.734275 | − | 0.678853i | \(-0.762478\pi\) | ||||
−0.734275 | + | 0.678853i | \(0.762478\pi\) | |||||||
\(734\) | −9.07266e6 | −0.621576 | ||||||||
\(735\) | −3.47502e6 | −0.237268 | ||||||||
\(736\) | −2.89589e6 | −0.197055 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.97726e6 | 0.133636 | ||||||||
\(739\) | −1.69237e7 | −1.13995 | −0.569973 | − | 0.821663i | \(-0.693047\pi\) | ||||
−0.569973 | + | 0.821663i | \(0.693047\pi\) | |||||||
\(740\) | 1.82320e6 | 0.122392 | ||||||||
\(741\) | −1.84612e7 | −1.23513 | ||||||||
\(742\) | 1.69065e7 | 1.12731 | ||||||||
\(743\) | −2.82700e7 | −1.87869 | −0.939343 | − | 0.342979i | \(-0.888564\pi\) | ||||
−0.939343 | + | 0.342979i | \(0.888564\pi\) | |||||||
\(744\) | 4.22633e6 | 0.279918 | ||||||||
\(745\) | 5.52147e6 | 0.364472 | ||||||||
\(746\) | −1.08168e7 | −0.711625 | ||||||||
\(747\) | −194557. | −0.0127569 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.34842e6 | 0.413486 | ||||||||
\(750\) | −2.38682e6 | −0.154941 | ||||||||
\(751\) | −8.90168e6 | −0.575933 | −0.287966 | − | 0.957640i | \(-0.592979\pi\) | ||||
−0.287966 | + | 0.957640i | \(0.592979\pi\) | |||||||
\(752\) | −5.17581e6 | −0.333760 | ||||||||
\(753\) | 4.64276e6 | 0.298393 | ||||||||
\(754\) | −2.51981e7 | −1.61413 | ||||||||
\(755\) | −1.69626e6 | −0.108299 | ||||||||
\(756\) | 2.67318e6 | 0.170108 | ||||||||
\(757\) | −5.08557e6 | −0.322552 | −0.161276 | − | 0.986909i | \(-0.551561\pi\) | ||||
−0.161276 | + | 0.986909i | \(0.551561\pi\) | |||||||
\(758\) | −9.28610e6 | −0.587030 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.57071e6 | 0.0986419 | ||||||||
\(761\) | −9.65849e6 | −0.604571 | −0.302286 | − | 0.953217i | \(-0.597750\pi\) | ||||
−0.302286 | + | 0.953217i | \(0.597750\pi\) | |||||||
\(762\) | −2.62660e6 | −0.163873 | ||||||||
\(763\) | 1.23525e7 | 0.768145 | ||||||||
\(764\) | −1.06397e7 | −0.659470 | ||||||||
\(765\) | 668768. | 0.0413164 | ||||||||
\(766\) | 2.06706e7 | 1.27286 | ||||||||
\(767\) | −7.91475e6 | −0.485791 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | 6.05284e6 | 0.369100 | 0.184550 | − | 0.982823i | \(-0.440917\pi\) | ||||
0.184550 | + | 0.982823i | \(0.440917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.92743e6 | 0.298527 | ||||||||
\(772\) | 2.51402e6 | 0.151819 | ||||||||
\(773\) | 5.07914e6 | 0.305732 | 0.152866 | − | 0.988247i | \(-0.451150\pi\) | ||||
0.152866 | + | 0.988247i | \(0.451150\pi\) | |||||||
\(774\) | −657449. | −0.0394466 | ||||||||
\(775\) | 2.20719e7 | 1.32003 | ||||||||
\(776\) | 4.07627e6 | 0.243001 | ||||||||
\(777\) | −2.17421e7 | −1.29196 | ||||||||
\(778\) | 506910. | 0.0300249 | ||||||||
\(779\) | −1.38548e7 | −0.818004 | ||||||||
\(780\) | 1.40648e6 | 0.0827747 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 8.63967e6 | 0.505220 | ||||||||
\(783\) | −5.08274e6 | −0.296274 | ||||||||
\(784\) | 9.14366e6 | 0.531288 | ||||||||
\(785\) | 1.02820e6 | 0.0595529 | ||||||||
\(786\) | −3.16302e6 | −0.182619 | ||||||||
\(787\) | 2.23661e7 | 1.28722 | 0.643611 | − | 0.765353i | \(-0.277436\pi\) | ||||
0.643611 | + | 0.765353i | \(0.277436\pi\) | |||||||
\(788\) | −4.75283e6 | −0.272669 | ||||||||
\(789\) | −3.14158e6 | −0.179662 | ||||||||
\(790\) | 1.27242e6 | 0.0725373 | ||||||||
\(791\) | 2.76449e7 | 1.57099 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.29609e7 | −1.29660 | ||||||||
\(794\) | 7.83076e6 | 0.440811 | ||||||||
\(795\) | 1.79428e6 | 0.100687 | ||||||||
\(796\) | −6.15644e6 | −0.344387 | ||||||||
\(797\) | −3.57436e7 | −1.99321 | −0.996604 | − | 0.0823487i | \(-0.973758\pi\) | ||||
−0.996604 | + | 0.0823487i | \(0.973758\pi\) | |||||||
\(798\) | −1.87311e7 | −1.04125 | ||||||||
\(799\) | 1.54417e7 | 0.855711 | ||||||||
\(800\) | 3.08033e6 | 0.170166 | ||||||||
\(801\) | −2.98390e6 | −0.164325 | ||||||||
\(802\) | −5.19999e6 | −0.285474 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −6.39120e6 | −0.348692 | ||||||||
\(805\) | −7.00644e6 | −0.381072 | ||||||||
\(806\) | −2.65178e7 | −1.43781 | ||||||||
\(807\) | 6.74544e6 | 0.364608 | ||||||||
\(808\) | 1.83837e6 | 0.0990615 | ||||||||
\(809\) | −3.75852e6 | −0.201904 | −0.100952 | − | 0.994891i | \(-0.532189\pi\) | ||||
−0.100952 | + | 0.994891i | \(0.532189\pi\) | |||||||
\(810\) | 283704. | 0.0151933 | ||||||||
\(811\) | −1.27989e7 | −0.683314 | −0.341657 | − | 0.939825i | \(-0.610988\pi\) | ||||
−0.341657 | + | 0.939825i | \(0.610988\pi\) | |||||||
\(812\) | −2.55665e7 | −1.36076 | ||||||||
\(813\) | −1.37474e7 | −0.729447 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.80939e6 | 0.0954196 | ||||||||
\(816\) | −1.75970e6 | −0.0925151 | ||||||||
\(817\) | 4.60678e6 | 0.241458 | ||||||||
\(818\) | −1.17984e6 | −0.0616507 | ||||||||
\(819\) | −1.67727e7 | −0.873761 | ||||||||
\(820\) | 1.05554e6 | 0.0548200 | ||||||||
\(821\) | 2.48541e7 | 1.28689 | 0.643444 | − | 0.765493i | \(-0.277505\pi\) | ||||
0.643444 | + | 0.765493i | \(0.277505\pi\) | |||||||
\(822\) | −6.54882e6 | −0.338052 | ||||||||
\(823\) | 2.53059e7 | 1.30233 | 0.651167 | − | 0.758934i | \(-0.274280\pi\) | ||||
0.651167 | + | 0.758934i | \(0.274280\pi\) | |||||||
\(824\) | −4.63976e6 | −0.238055 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.03048e6 | −0.409535 | ||||||||
\(827\) | 2.36753e7 | 1.20374 | 0.601868 | − | 0.798596i | \(-0.294424\pi\) | ||||
0.601868 | + | 0.798596i | \(0.294424\pi\) | |||||||
\(828\) | 3.66511e6 | 0.185785 | ||||||||
\(829\) | −7.08170e6 | −0.357891 | −0.178946 | − | 0.983859i | \(-0.557269\pi\) | ||||
−0.178946 | + | 0.983859i | \(0.557269\pi\) | |||||||
\(830\) | −103862. | −0.00523312 | ||||||||
\(831\) | 1.17928e7 | 0.592399 | ||||||||
\(832\) | −3.70081e6 | −0.185348 | ||||||||
\(833\) | −2.72795e7 | −1.36215 | ||||||||
\(834\) | −4.69016e6 | −0.233492 | ||||||||
\(835\) | 3.64013e6 | 0.180676 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.34895e6 | −0.263910 | ||||||||
\(838\) | 5.85876e6 | 0.288201 | ||||||||
\(839\) | 8.52065e6 | 0.417896 | 0.208948 | − | 0.977927i | \(-0.432996\pi\) | ||||
0.208948 | + | 0.977927i | \(0.432996\pi\) | |||||||
\(840\) | 1.42705e6 | 0.0697814 | ||||||||
\(841\) | 2.81006e7 | 1.37002 | ||||||||
\(842\) | 4.60809e6 | 0.223996 | ||||||||
\(843\) | 1.26122e7 | 0.611253 | ||||||||
\(844\) | 3.90613e6 | 0.188751 | ||||||||
\(845\) | −4.81110e6 | −0.231794 | ||||||||
\(846\) | 6.55064e6 | 0.314672 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.72121e6 | −0.225457 | ||||||||
\(849\) | 5.23393e6 | 0.249206 | ||||||||
\(850\) | −9.18996e6 | −0.436281 | ||||||||
\(851\) | −2.98099e7 | −1.41103 | ||||||||
\(852\) | −1.15758e7 | −0.546328 | ||||||||
\(853\) | 1.79912e7 | 0.846618 | 0.423309 | − | 0.905985i | \(-0.360868\pi\) | ||||
0.423309 | + | 0.905985i | \(0.360868\pi\) | |||||||
\(854\) | −2.32966e7 | −1.09307 | ||||||||
\(855\) | −1.98793e6 | −0.0930004 | ||||||||
\(856\) | −1.77282e6 | −0.0826952 | ||||||||
\(857\) | −2.30359e7 | −1.07140 | −0.535702 | − | 0.844407i | \(-0.679953\pi\) | ||||
−0.535702 | + | 0.844407i | \(0.679953\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.53653e6 | −0.440968 | −0.220484 | − | 0.975391i | \(-0.570764\pi\) | ||||
−0.220484 | + | 0.975391i | \(0.570764\pi\) | |||||||
\(860\) | −350972. | −0.0161818 | ||||||||
\(861\) | −1.25876e7 | −0.578674 | ||||||||
\(862\) | −1.72465e7 | −0.790559 | ||||||||
\(863\) | −3.36705e7 | −1.53894 | −0.769471 | − | 0.638681i | \(-0.779480\pi\) | ||||
−0.769471 | + | 0.638681i | \(0.779480\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | 6.05729e6 | 0.275257 | ||||||||
\(866\) | −2.61393e7 | −1.18440 | ||||||||
\(867\) | −7.52878e6 | −0.340155 | ||||||||
\(868\) | −2.69055e7 | −1.21211 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.71336e6 | −0.121537 | ||||||||
\(871\) | 4.01011e7 | 1.79107 | ||||||||
\(872\) | −3.44948e6 | −0.153625 | ||||||||
\(873\) | −5.15902e6 | −0.229104 | ||||||||
\(874\) | −2.56816e7 | −1.13722 | ||||||||
\(875\) | 1.51949e7 | 0.670932 | ||||||||
\(876\) | 1.07114e7 | 0.471615 | ||||||||
\(877\) | −2.50783e7 | −1.10103 | −0.550515 | − | 0.834826i | \(-0.685568\pi\) | ||||
−0.550515 | + | 0.834826i | \(0.685568\pi\) | |||||||
\(878\) | 2.73756e7 | 1.19847 | ||||||||
\(879\) | −1.67562e7 | −0.731483 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.09068e7 | 1.34157 | 0.670786 | − | 0.741651i | \(-0.265957\pi\) | ||||
0.670786 | + | 0.741651i | \(0.265957\pi\) | |||||||
\(882\) | −1.15724e7 | −0.500903 | ||||||||
\(883\) | −2.17837e7 | −0.940221 | −0.470111 | − | 0.882607i | \(-0.655786\pi\) | ||||
−0.470111 | + | 0.882607i | \(0.655786\pi\) | |||||||
\(884\) | 1.10411e7 | 0.475206 | ||||||||
\(885\) | −852272. | −0.0365780 | ||||||||
\(886\) | 2.38881e6 | 0.102234 | ||||||||
\(887\) | 3.71753e7 | 1.58652 | 0.793260 | − | 0.608884i | \(-0.208382\pi\) | ||||
0.793260 | + | 0.608884i | \(0.208382\pi\) | |||||||
\(888\) | 6.07158e6 | 0.258386 | ||||||||
\(889\) | 1.67214e7 | 0.709608 | ||||||||
\(890\) | −1.59292e6 | −0.0674092 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 764755. | 0.0321818 | ||||||||
\(893\) | −4.59007e7 | −1.92615 | ||||||||
\(894\) | 1.83875e7 | 0.769446 | ||||||||
\(895\) | 1.03282e6 | 0.0430991 | ||||||||
\(896\) | −3.75492e6 | −0.156254 | ||||||||
\(897\) | −2.29964e7 | −0.954288 | ||||||||
\(898\) | 2.59728e7 | 1.07480 | ||||||||
\(899\) | 5.11578e7 | 2.11112 | ||||||||
\(900\) | −3.89855e6 | −0.160434 | ||||||||
\(901\) | 1.40854e7 | 0.578039 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.18543e6 | 0.170813 | ||||||||
\(904\) | −7.71994e6 | −0.314190 | ||||||||
\(905\) | 900081. | 0.0365309 | ||||||||
\(906\) | −5.64885e6 | −0.228633 | ||||||||
\(907\) | −3.88968e7 | −1.56998 | −0.784992 | − | 0.619506i | \(-0.787333\pi\) | ||||
−0.784992 | + | 0.619506i | \(0.787333\pi\) | |||||||
\(908\) | 9.66897e6 | 0.389193 | ||||||||
\(909\) | −2.32669e6 | −0.0933961 | ||||||||
\(910\) | −8.95390e6 | −0.358434 | ||||||||
\(911\) | 4.24797e7 | 1.69584 | 0.847920 | − | 0.530124i | \(-0.177855\pi\) | ||||
0.847920 | + | 0.530124i | \(0.177855\pi\) | |||||||
\(912\) | 5.23074e6 | 0.208246 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 2.10749e7 | 0.834451 | ||||||||
\(915\) | −2.47246e6 | −0.0976286 | ||||||||
\(916\) | −1.57577e7 | −0.620519 | ||||||||
\(917\) | 2.01363e7 | 0.790782 | ||||||||
\(918\) | 2.22712e6 | 0.0872241 | ||||||||
\(919\) | −2.29560e7 | −0.896618 | −0.448309 | − | 0.893879i | \(-0.647974\pi\) | ||||
−0.448309 | + | 0.893879i | \(0.647974\pi\) | |||||||
\(920\) | 1.95657e6 | 0.0762126 | ||||||||
\(921\) | −1.25977e7 | −0.489374 | ||||||||
\(922\) | −1.87188e6 | −0.0725189 | ||||||||
\(923\) | 7.26318e7 | 2.80623 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.17086e7 | 1.21849 | ||||||||
\(926\) | −1.05293e7 | −0.403527 | ||||||||
\(927\) | 5.87219e6 | 0.224440 | ||||||||
\(928\) | 7.13954e6 | 0.272145 | ||||||||
\(929\) | 527354. | 0.0200476 | 0.0100238 | − | 0.999950i | \(-0.496809\pi\) | ||||
0.0100238 | + | 0.999950i | \(0.496809\pi\) | |||||||
\(930\) | −2.85548e6 | −0.108261 | ||||||||
\(931\) | 8.10888e7 | 3.06610 | ||||||||
\(932\) | 1.24462e7 | 0.469349 | ||||||||
\(933\) | −7.49287e6 | −0.281802 | ||||||||
\(934\) | 3.46001e7 | 1.29781 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.68384e6 | 0.174748 | ||||||||
\(937\) | 2.91096e7 | 1.08315 | 0.541574 | − | 0.840653i | \(-0.317829\pi\) | ||||
0.541574 | + | 0.840653i | \(0.317829\pi\) | |||||||
\(938\) | 4.06875e7 | 1.50992 | ||||||||
\(939\) | −2.34661e7 | −0.868514 | ||||||||
\(940\) | 3.49698e6 | 0.129084 | ||||||||
\(941\) | 3.08431e7 | 1.13549 | 0.567746 | − | 0.823204i | \(-0.307815\pi\) | ||||
0.567746 | + | 0.823204i | \(0.307815\pi\) | |||||||
\(942\) | 3.42408e6 | 0.125724 | ||||||||
\(943\) | −1.72584e7 | −0.632006 | ||||||||
\(944\) | 2.24254e6 | 0.0819051 | ||||||||
\(945\) | −1.80611e6 | −0.0657906 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.07297e7 | −1.11348 | −0.556741 | − | 0.830686i | \(-0.687948\pi\) | ||||
−0.556741 | + | 0.830686i | \(0.687948\pi\) | |||||||
\(948\) | 4.23737e6 | 0.153135 | ||||||||
\(949\) | −6.72082e7 | −2.42246 | ||||||||
\(950\) | 2.73173e7 | 0.982040 | ||||||||
\(951\) | −318562. | −0.0114220 | ||||||||
\(952\) | 1.12025e7 | 0.400612 | ||||||||
\(953\) | 6.93181e6 | 0.247237 | 0.123619 | − | 0.992330i | \(-0.460550\pi\) | ||||
0.123619 | + | 0.992330i | \(0.460550\pi\) | |||||||
\(954\) | 5.97528e6 | 0.212563 | ||||||||
\(955\) | 7.18859e6 | 0.255056 | ||||||||
\(956\) | −1.35452e7 | −0.479336 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.19785e7 | 0.421685 | ||||||||
\(959\) | 4.16909e7 | 1.46384 | ||||||||
\(960\) | −398508. | −0.0139559 | ||||||||
\(961\) | 2.52080e7 | 0.880502 | ||||||||
\(962\) | −3.80957e7 | −1.32720 | ||||||||
\(963\) | 2.24373e6 | 0.0779658 | ||||||||
\(964\) | −1.66918e7 | −0.578508 | ||||||||
\(965\) | −1.69857e6 | −0.0587171 | ||||||||
\(966\) | −2.33327e7 | −0.804492 | ||||||||
\(967\) | −1.01604e7 | −0.349416 | −0.174708 | − | 0.984620i | \(-0.555898\pi\) | ||||
−0.174708 | + | 0.984620i | \(0.555898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.56055e7 | −0.533911 | ||||||||
\(970\) | −2.75409e6 | −0.0939827 | ||||||||
\(971\) | −5.18278e7 | −1.76407 | −0.882033 | − | 0.471187i | \(-0.843826\pi\) | ||||
−0.882033 | + | 0.471187i | \(0.843826\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 2.98584e7 | 1.01108 | ||||||||
\(974\) | −2.47209e7 | −0.834963 | ||||||||
\(975\) | 2.44612e7 | 0.824073 | ||||||||
\(976\) | 6.50568e6 | 0.218609 | ||||||||
\(977\) | −3.30445e7 | −1.10755 | −0.553774 | − | 0.832667i | \(-0.686813\pi\) | ||||
−0.553774 | + | 0.832667i | \(0.686813\pi\) | |||||||
\(978\) | 6.02558e6 | 0.201443 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.17782e6 | −0.205480 | ||||||||
\(981\) | 4.36575e6 | 0.144839 | ||||||||
\(982\) | 4.03673e7 | 1.33583 | ||||||||
\(983\) | −1.81291e7 | −0.598402 | −0.299201 | − | 0.954190i | \(-0.596720\pi\) | ||||
−0.299201 | + | 0.954190i | \(0.596720\pi\) | |||||||
\(984\) | 3.51513e6 | 0.115732 | ||||||||
\(985\) | 3.21120e6 | 0.105457 | ||||||||
\(986\) | −2.13003e7 | −0.697741 | ||||||||
\(987\) | −4.17025e7 | −1.36260 | ||||||||
\(988\) | −3.28199e7 | −1.06966 | ||||||||
\(989\) | 5.73850e6 | 0.186555 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.24023e7 | −1.69499 | −0.847493 | − | 0.530806i | \(-0.821889\pi\) | ||||
−0.847493 | + | 0.530806i | \(0.821889\pi\) | |||||||
\(992\) | 7.51348e6 | 0.242416 | ||||||||
\(993\) | 1.12657e6 | 0.0362563 | ||||||||
\(994\) | 7.36938e7 | 2.36573 | ||||||||
\(995\) | 4.15953e6 | 0.133195 | ||||||||
\(996\) | −345879. | −0.0110478 | ||||||||
\(997\) | 4.86084e6 | 0.154872 | 0.0774361 | − | 0.996997i | \(-0.475327\pi\) | ||||
0.0774361 | + | 0.996997i | \(0.475327\pi\) | |||||||
\(998\) | 3.83402e6 | 0.121851 | ||||||||
\(999\) | −7.68434e6 | −0.243609 |
(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.bb.1.3 | 4 | ||
11.7 | odd | 10 | 66.6.e.a.49.2 | yes | 8 | ||
11.8 | odd | 10 | 66.6.e.a.31.2 | ✓ | 8 | ||
11.10 | odd | 2 | 726.6.a.be.1.3 | 4 | |||
33.8 | even | 10 | 198.6.f.c.163.1 | 8 | |||
33.29 | even | 10 | 198.6.f.c.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
66.6.e.a.31.2 | ✓ | 8 | 11.8 | odd | 10 | ||
66.6.e.a.49.2 | yes | 8 | 11.7 | odd | 10 | ||
198.6.f.c.163.1 | 8 | 33.8 | even | 10 | |||
198.6.f.c.181.1 | 8 | 33.29 | even | 10 | |||
726.6.a.bb.1.3 | 4 | 1.1 | even | 1 | trivial | ||
726.6.a.be.1.3 | 4 | 11.10 | odd | 2 |