Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.7 | ||
Root | \(1.84692 + 1.06632i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.6.c.c.146.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.13264i | − | 0.377001i | −0.982073 | − | 0.188501i | \(-0.939637\pi\) | ||
0.982073 | − | 0.188501i | \(-0.0603628\pi\) | |||||||
\(3\) | −9.16236 | + | 12.6115i | −0.587766 | + | 0.809031i | ||||
\(4\) | 27.4518 | 0.857870 | ||||||||
\(5\) | −95.0525 | −1.70035 | −0.850175 | − | 0.526500i | \(-0.823504\pi\) | ||||
−0.850175 | + | 0.526500i | \(0.823504\pi\) | |||||||
\(6\) | 26.8959 | + | 19.5400i | 0.305006 | + | 0.221589i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 126.790i | − | 0.700420i | ||||||
\(9\) | −75.1022 | − | 231.103i | −0.309063 | − | 0.951042i | ||||
\(10\) | 202.713i | 0.641035i | ||||||||
\(11\) | − | 130.679i | − | 0.325630i | −0.986657 | − | 0.162815i | \(-0.947943\pi\) | ||
0.986657 | − | 0.162815i | \(-0.0520573\pi\) | |||||||
\(12\) | −251.524 | + | 346.210i | −0.504227 | + | 0.694043i | ||||
\(13\) | − | 14.6710i | − | 0.0240769i | −0.999928 | − | 0.0120385i | \(-0.996168\pi\) | ||
0.999928 | − | 0.0120385i | \(-0.00383205\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 870.905 | − | 1198.76i | 0.999408 | − | 1.37564i | ||||
\(16\) | 608.062 | 0.593811 | ||||||||
\(17\) | 640.492 | 0.537516 | 0.268758 | − | 0.963208i | \(-0.413387\pi\) | ||||
0.268758 | + | 0.963208i | \(0.413387\pi\) | |||||||
\(18\) | −492.860 | + | 160.166i | −0.358544 | + | 0.116517i | ||||
\(19\) | − | 542.677i | − | 0.344872i | −0.985021 | − | 0.172436i | \(-0.944836\pi\) | ||
0.985021 | − | 0.172436i | \(-0.0551637\pi\) | |||||||
\(20\) | −2609.37 | −1.45868 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −278.692 | −0.122763 | ||||||||
\(23\) | 4094.31i | 1.61384i | 0.590659 | + | 0.806922i | \(0.298868\pi\) | ||||
−0.590659 | + | 0.806922i | \(0.701132\pi\) | |||||||
\(24\) | 1599.01 | + | 1161.69i | 0.566661 | + | 0.411683i | ||||
\(25\) | 5909.98 | 1.89119 | ||||||||
\(26\) | −31.2880 | −0.00907703 | ||||||||
\(27\) | 3602.68 | + | 1170.29i | 0.951079 | + | 0.308948i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3594.70i | 0.793721i | 0.917879 | + | 0.396861i | \(0.129900\pi\) | ||||
−0.917879 | + | 0.396861i | \(0.870100\pi\) | |||||||
\(30\) | −2556.52 | − | 1857.33i | −0.518617 | − | 0.376778i | ||||
\(31\) | 2900.94i | 0.542168i | 0.962556 | + | 0.271084i | \(0.0873821\pi\) | ||||
−0.962556 | + | 0.271084i | \(0.912618\pi\) | |||||||
\(32\) | − | 5354.04i | − | 0.924287i | ||||||
\(33\) | 1648.06 | + | 1197.33i | 0.263445 | + | 0.191394i | ||||
\(34\) | − | 1365.94i | − | 0.202644i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2061.69 | − | 6344.20i | −0.265136 | − | 0.815870i | ||||
\(37\) | −4342.05 | −0.521423 | −0.260712 | − | 0.965417i | \(-0.583957\pi\) | ||||
−0.260712 | + | 0.965417i | \(0.583957\pi\) | |||||||
\(38\) | −1157.34 | −0.130017 | ||||||||
\(39\) | 185.024 | + | 134.421i | 0.0194790 | + | 0.0141516i | ||||
\(40\) | 12051.7i | 1.19096i | ||||||||
\(41\) | 10945.3 | 1.01687 | 0.508436 | − | 0.861100i | \(-0.330224\pi\) | ||||
0.508436 | + | 0.861100i | \(0.330224\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20541.6 | 1.69419 | 0.847096 | − | 0.531440i | \(-0.178349\pi\) | ||||
0.847096 | + | 0.531440i | \(0.178349\pi\) | |||||||
\(44\) | − | 3587.38i | − | 0.279348i | ||||||
\(45\) | 7138.66 | + | 21966.9i | 0.525515 | + | 1.61710i | ||||
\(46\) | 8731.70 | 0.608421 | ||||||||
\(47\) | 8816.03 | 0.582141 | 0.291071 | − | 0.956702i | \(-0.405989\pi\) | ||||
0.291071 | + | 0.956702i | \(0.405989\pi\) | |||||||
\(48\) | −5571.28 | + | 7668.60i | −0.349022 | + | 0.480411i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 12603.9i | − | 0.712982i | ||||||
\(51\) | −5868.42 | + | 8077.60i | −0.315934 | + | 0.434867i | ||||
\(52\) | − | 402.745i | − | 0.0206549i | ||||||
\(53\) | − | 6977.45i | − | 0.341198i | −0.985341 | − | 0.170599i | \(-0.945430\pi\) | ||
0.985341 | − | 0.170599i | \(-0.0545703\pi\) | |||||||
\(54\) | 2495.82 | − | 7683.23i | 0.116474 | − | 0.358558i | ||||
\(55\) | 12421.4i | 0.553685i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6844.00 | + | 4972.20i | 0.279012 | + | 0.202704i | ||||
\(58\) | 7666.22 | 0.299234 | ||||||||
\(59\) | 40020.1 | 1.49675 | 0.748373 | − | 0.663278i | \(-0.230835\pi\) | ||||
0.748373 | + | 0.663278i | \(0.230835\pi\) | |||||||
\(60\) | 23908.0 | − | 32908.1i | 0.857362 | − | 1.18012i | ||||
\(61\) | − | 33210.2i | − | 1.14274i | −0.820693 | − | 0.571370i | \(-0.806412\pi\) | ||
0.820693 | − | 0.571370i | \(-0.193588\pi\) | |||||||
\(62\) | 6186.66 | 0.204398 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8039.72 | 0.245353 | ||||||||
\(65\) | 1394.51i | 0.0409392i | ||||||||
\(66\) | 2553.47 | − | 3514.73i | 0.0721558 | − | 0.0993190i | ||||
\(67\) | 6436.18 | 0.175163 | 0.0875813 | − | 0.996157i | \(-0.472086\pi\) | ||||
0.0875813 | + | 0.996157i | \(0.472086\pi\) | |||||||
\(68\) | 17582.7 | 0.461119 | ||||||||
\(69\) | −51635.6 | − | 37513.6i | −1.30565 | − | 0.948562i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 32493.9i | − | 0.764990i | −0.923958 | − | 0.382495i | \(-0.875065\pi\) | ||
0.923958 | − | 0.382495i | \(-0.124935\pi\) | |||||||
\(72\) | −29301.5 | + | 9522.18i | −0.666128 | + | 0.216474i | ||||
\(73\) | 12737.8i | 0.279761i | 0.990168 | + | 0.139880i | \(0.0446718\pi\) | ||||
−0.990168 | + | 0.139880i | \(0.955328\pi\) | |||||||
\(74\) | 9260.03i | 0.196577i | ||||||||
\(75\) | −54149.3 | + | 74533.9i | −1.11158 | + | 1.53003i | ||||
\(76\) | − | 14897.5i | − | 0.295855i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 286.672 | − | 394.590i | 0.00533517 | − | 0.00734360i | ||||
\(79\) | 8597.89 | 0.154997 | 0.0774986 | − | 0.996992i | \(-0.475307\pi\) | ||||
0.0774986 | + | 0.996992i | \(0.475307\pi\) | |||||||
\(80\) | −57797.8 | −1.00969 | ||||||||
\(81\) | −47768.3 | + | 34712.7i | −0.808960 | + | 0.587863i | ||||
\(82\) | − | 23342.3i | − | 0.383362i | ||||||
\(83\) | 31669.6 | 0.504601 | 0.252300 | − | 0.967649i | \(-0.418813\pi\) | ||||
0.252300 | + | 0.967649i | \(0.418813\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −60880.4 | −0.913966 | ||||||||
\(86\) | − | 43807.8i | − | 0.638713i | ||||||
\(87\) | −45334.8 | − | 32936.0i | −0.642145 | − | 0.466522i | ||||
\(88\) | −16568.7 | −0.228077 | ||||||||
\(89\) | −31945.9 | −0.427504 | −0.213752 | − | 0.976888i | \(-0.568568\pi\) | ||||
−0.213752 | + | 0.976888i | \(0.568568\pi\) | |||||||
\(90\) | 46847.6 | − | 15224.2i | 0.609651 | − | 0.198120i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 112396.i | 1.38447i | ||||||||
\(93\) | −36585.3 | − | 26579.4i | −0.438631 | − | 0.318668i | ||||
\(94\) | − | 18801.4i | − | 0.219468i | ||||||
\(95\) | 51582.8i | 0.586403i | ||||||||
\(96\) | 67522.8 | + | 49055.7i | 0.747777 | + | 0.543264i | ||||
\(97\) | 143107.i | 1.54430i | 0.635441 | + | 0.772149i | \(0.280818\pi\) | ||||
−0.635441 | + | 0.772149i | \(0.719182\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −30200.3 | + | 9814.28i | −0.309687 | + | 0.100640i | ||||
\(100\) | 162240. | 1.62240 | ||||||||
\(101\) | −53587.7 | −0.522711 | −0.261355 | − | 0.965243i | \(-0.584169\pi\) | ||||
−0.261355 | + | 0.965243i | \(0.584169\pi\) | |||||||
\(102\) | 17226.6 | + | 12515.2i | 0.163946 | + | 0.119107i | ||||
\(103\) | − | 153816.i | − | 1.42860i | −0.699842 | − | 0.714298i | \(-0.746746\pi\) | ||
0.699842 | − | 0.714298i | \(-0.253254\pi\) | |||||||
\(104\) | −1860.13 | −0.0168639 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14880.4 | −0.128632 | ||||||||
\(107\) | 153413.i | 1.29540i | 0.761897 | + | 0.647698i | \(0.224268\pi\) | ||||
−0.761897 | + | 0.647698i | \(0.775732\pi\) | |||||||
\(108\) | 98900.2 | + | 32126.7i | 0.815902 | + | 0.265038i | ||||
\(109\) | −127739. | −1.02981 | −0.514907 | − | 0.857246i | \(-0.672174\pi\) | ||||
−0.514907 | + | 0.857246i | \(0.672174\pi\) | |||||||
\(110\) | 26490.3 | 0.208740 | ||||||||
\(111\) | 39783.4 | − | 54759.9i | 0.306475 | − | 0.421847i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 90418.2i | 0.666131i | 0.942904 | + | 0.333066i | \(0.108083\pi\) | ||||
−0.942904 | + | 0.333066i | \(0.891917\pi\) | |||||||
\(114\) | 10603.9 | − | 14595.8i | 0.0764196 | − | 0.105188i | ||||
\(115\) | − | 389175.i | − | 2.74410i | ||||||
\(116\) | 98681.2i | 0.680910i | ||||||||
\(117\) | −3390.51 | + | 1101.82i | −0.0228981 | + | 0.00744128i | ||||
\(118\) | − | 85348.6i | − | 0.564276i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −151990. | − | 110422.i | −0.963523 | − | 0.700005i | ||||
\(121\) | 143974. | 0.893965 | ||||||||
\(122\) | −70825.5 | −0.430814 | ||||||||
\(123\) | −100284. | + | 138037.i | −0.597683 | + | 0.822681i | ||||
\(124\) | 79636.0i | 0.465110i | ||||||||
\(125\) | −264719. | −1.51534 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 132321. | 0.727982 | 0.363991 | − | 0.931402i | \(-0.381414\pi\) | ||||
0.363991 | + | 0.931402i | \(0.381414\pi\) | |||||||
\(128\) | − | 188475.i | − | 1.01679i | ||||||
\(129\) | −188209. | + | 259061.i | −0.995788 | + | 1.37065i | ||||
\(130\) | 2974.00 | 0.0154341 | ||||||||
\(131\) | −147778. | −0.752368 | −0.376184 | − | 0.926545i | \(-0.622764\pi\) | ||||
−0.376184 | + | 0.926545i | \(0.622764\pi\) | |||||||
\(132\) | 45242.4 | + | 32868.8i | 0.226001 | + | 0.164191i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 13726.1i | − | 0.0660366i | ||||||
\(135\) | −342444. | − | 111239.i | −1.61717 | − | 0.525321i | ||||
\(136\) | − | 81207.7i | − | 0.376487i | ||||||
\(137\) | − | 226682.i | − | 1.03185i | −0.856634 | − | 0.515925i | \(-0.827448\pi\) | ||
0.856634 | − | 0.515925i | \(-0.172552\pi\) | |||||||
\(138\) | −80003.0 | + | 110120.i | −0.357609 | + | 0.492232i | ||||
\(139\) | − | 230678.i | − | 1.01267i | −0.862335 | − | 0.506337i | \(-0.830999\pi\) | ||
0.862335 | − | 0.506337i | \(-0.169001\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −80775.7 | + | 111184.i | −0.342163 | + | 0.470971i | ||||
\(142\) | −69297.8 | −0.288402 | ||||||||
\(143\) | −1917.19 | −0.00784016 | ||||||||
\(144\) | −45666.8 | − | 140525.i | −0.183525 | − | 0.564739i | ||||
\(145\) | − | 341685.i | − | 1.34960i | ||||||
\(146\) | 27165.1 | 0.105470 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −119197. | −0.447313 | ||||||||
\(149\) | − | 9357.83i | − | 0.0345310i | −0.999851 | − | 0.0172655i | \(-0.994504\pi\) | ||
0.999851 | − | 0.0172655i | \(-0.00549605\pi\) | |||||||
\(150\) | 158954. | + | 115481.i | 0.576825 | + | 0.419067i | ||||
\(151\) | 138457. | 0.494166 | 0.247083 | − | 0.968994i | \(-0.420528\pi\) | ||||
0.247083 | + | 0.968994i | \(0.420528\pi\) | |||||||
\(152\) | −68805.8 | −0.241555 | ||||||||
\(153\) | −48102.4 | − | 148020.i | −0.166126 | − | 0.511200i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 275741.i | − | 0.921876i | ||||||
\(156\) | 5079.24 | + | 3690.10i | 0.0167104 | + | 0.0121402i | ||||
\(157\) | 15464.9i | 0.0500724i | 0.999687 | + | 0.0250362i | \(0.00797010\pi\) | ||||
−0.999687 | + | 0.0250362i | \(0.992030\pi\) | |||||||
\(158\) | − | 18336.2i | − | 0.0584342i | ||||||
\(159\) | 87996.4 | + | 63929.9i | 0.276040 | + | 0.200545i | ||||
\(160\) | 508915.i | 1.57161i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 74029.8 | + | 101873.i | 0.221625 | + | 0.304979i | ||||
\(163\) | 289645. | 0.853880 | 0.426940 | − | 0.904280i | \(-0.359592\pi\) | ||||
0.426940 | + | 0.904280i | \(0.359592\pi\) | |||||||
\(164\) | 300467. | 0.872344 | ||||||||
\(165\) | −156653. | − | 113809.i | −0.447948 | − | 0.325437i | ||||
\(166\) | − | 67540.0i | − | 0.190235i | ||||||
\(167\) | 347837. | 0.965128 | 0.482564 | − | 0.875861i | \(-0.339706\pi\) | ||||
0.482564 | + | 0.875861i | \(0.339706\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 371078. | 0.999420 | ||||||||
\(170\) | 129836.i | 0.344567i | ||||||||
\(171\) | −125414. | + | 40756.3i | −0.327987 | + | 0.106587i | ||||
\(172\) | 563904. | 1.45340 | ||||||||
\(173\) | 508138. | 1.29082 | 0.645411 | − | 0.763836i | \(-0.276686\pi\) | ||||
0.645411 | + | 0.763836i | \(0.276686\pi\) | |||||||
\(174\) | −70240.7 | + | 96682.9i | −0.175880 | + | 0.242090i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 79460.9i | − | 0.193362i | ||||||
\(177\) | −366679. | + | 504716.i | −0.879736 | + | 1.21091i | ||||
\(178\) | 68129.1i | 0.161169i | ||||||||
\(179\) | 400409.i | 0.934053i | 0.884243 | + | 0.467026i | \(0.154675\pi\) | ||||
−0.884243 | + | 0.467026i | \(0.845325\pi\) | |||||||
\(180\) | 195969. | + | 603032.i | 0.450824 | + | 1.38727i | ||||
\(181\) | 10694.7i | 0.0242646i | 0.999926 | + | 0.0121323i | \(0.00386192\pi\) | ||||
−0.999926 | + | 0.0121323i | \(0.996138\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 418832. | + | 304284.i | 0.924511 | + | 0.671663i | ||||
\(184\) | 519116. | 1.13037 | ||||||||
\(185\) | 412722. | 0.886602 | ||||||||
\(186\) | −56684.4 | + | 78023.3i | −0.120138 | + | 0.165364i | ||||
\(187\) | − | 83698.9i | − | 0.175031i | ||||||
\(188\) | 242016. | 0.499402 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 110008. | 0.221075 | ||||||||
\(191\) | − | 197252.i | − | 0.391236i | −0.980680 | − | 0.195618i | \(-0.937329\pi\) | ||
0.980680 | − | 0.195618i | \(-0.0626712\pi\) | |||||||
\(192\) | −73662.9 | + | 101393.i | −0.144210 | + | 0.198498i | ||||
\(193\) | −125511. | −0.242542 | −0.121271 | − | 0.992619i | \(-0.538697\pi\) | ||||
−0.121271 | + | 0.992619i | \(0.538697\pi\) | |||||||
\(194\) | 305196. | 0.582203 | ||||||||
\(195\) | −17587.0 | − | 12777.0i | −0.0331211 | − | 0.0240627i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 631690.i | − | 1.15968i | −0.814730 | − | 0.579841i | \(-0.803115\pi\) | ||
0.814730 | − | 0.579841i | \(-0.196885\pi\) | |||||||
\(198\) | 20930.4 | + | 64406.5i | 0.0379414 | + | 0.116753i | ||||
\(199\) | 622380.i | 1.11410i | 0.830480 | + | 0.557049i | \(0.188066\pi\) | ||||
−0.830480 | + | 0.557049i | \(0.811934\pi\) | |||||||
\(200\) | − | 749323.i | − | 1.32463i | ||||||
\(201\) | −58970.6 | + | 81170.2i | −0.102955 | + | 0.141712i | ||||
\(202\) | 114283.i | 0.197063i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −161099. | + | 221745.i | −0.271030 | + | 0.373060i | ||||
\(205\) | −1.04037e6 | −1.72904 | ||||||||
\(206\) | −328035. | −0.538583 | ||||||||
\(207\) | 946208. | − | 307492.i | 1.53483 | − | 0.498779i | ||||
\(208\) | − | 8920.87i | − | 0.0142971i | ||||||
\(209\) | −70916.5 | −0.112300 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −271742. | −0.420195 | −0.210098 | − | 0.977680i | \(-0.567378\pi\) | ||||
−0.210098 | + | 0.977680i | \(0.567378\pi\) | |||||||
\(212\) | − | 191544.i | − | 0.292704i | ||||||
\(213\) | 409798. | + | 297721.i | 0.618900 | + | 0.449635i | ||||
\(214\) | 327175. | 0.488366 | ||||||||
\(215\) | −1.95253e6 | −2.88072 | ||||||||
\(216\) | 148381. | − | 456782.i | 0.216394 | − | 0.666154i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 272423.i | 0.388241i | ||||||||
\(219\) | −160643. | − | 116708.i | −0.226335 | − | 0.164434i | ||||
\(220\) | 340989.i | 0.474989i | ||||||||
\(221\) | − | 9396.65i | − | 0.0129417i | ||||||
\(222\) | −116783. | − | 84843.8i | −0.159037 | − | 0.115541i | ||||
\(223\) | 256397.i | 0.345264i | 0.984986 | + | 0.172632i | \(0.0552271\pi\) | ||||
−0.984986 | + | 0.172632i | \(0.944773\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −443852. | − | 1.36581e6i | −0.584497 | − | 1.79860i | ||||
\(226\) | 192830. | 0.251133 | ||||||||
\(227\) | −117895. | −0.151856 | −0.0759278 | − | 0.997113i | \(-0.524192\pi\) | ||||
−0.0759278 | + | 0.997113i | \(0.524192\pi\) | |||||||
\(228\) | 187880. | + | 136496.i | 0.239356 | + | 0.173893i | ||||
\(229\) | 373781.i | 0.471008i | 0.971873 | + | 0.235504i | \(0.0756741\pi\) | ||||
−0.971873 | + | 0.235504i | \(0.924326\pi\) | |||||||
\(230\) | −829970. | −1.03453 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 455771. | 0.555938 | ||||||||
\(233\) | 1.26480e6i | 1.52627i | 0.646240 | + | 0.763134i | \(0.276340\pi\) | ||||
−0.646240 | + | 0.763134i | \(0.723660\pi\) | |||||||
\(234\) | 2349.80 | + | 7230.74i | 0.00280537 | + | 0.00863264i | ||||
\(235\) | −837986. | −0.989845 | ||||||||
\(236\) | 1.09863e6 | 1.28401 | ||||||||
\(237\) | −78776.9 | + | 108433.i | −0.0911021 | + | 0.125398i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 520817.i | 0.589780i | 0.955531 | + | 0.294890i | \(0.0952830\pi\) | ||||
−0.955531 | + | 0.294890i | \(0.904717\pi\) | |||||||
\(240\) | 529564. | − | 728920.i | 0.593459 | − | 0.816868i | ||||
\(241\) | − | 954289.i | − | 1.05837i | −0.848507 | − | 0.529185i | \(-0.822498\pi\) | ||
0.848507 | − | 0.529185i | \(-0.177502\pi\) | |||||||
\(242\) | − | 307045.i | − | 0.337026i | ||||||
\(243\) | −110.689 | − | 920483.i | −0.000120251 | − | 1.00000i | ||||
\(244\) | − | 911681.i | − | 0.980321i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 294383. | + | 213871.i | 0.310152 | + | 0.225327i | ||||
\(247\) | −7961.60 | −0.00830344 | ||||||||
\(248\) | 367808. | 0.379745 | ||||||||
\(249\) | −290169. | + | 399403.i | −0.296587 | + | 0.408238i | ||||
\(250\) | 564551.i | 0.571285i | ||||||||
\(251\) | −789792. | −0.791277 | −0.395638 | − | 0.918406i | \(-0.629477\pi\) | ||||
−0.395638 | + | 0.918406i | \(0.629477\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 535040. | 0.525515 | ||||||||
\(254\) | − | 282194.i | − | 0.274450i | ||||||
\(255\) | 557808. | − | 767796.i | 0.537198 | − | 0.739427i | ||||
\(256\) | −144679. | −0.137977 | ||||||||
\(257\) | 1.10769e6 | 1.04613 | 0.523064 | − | 0.852293i | \(-0.324789\pi\) | ||||
0.523064 | + | 0.852293i | \(0.324789\pi\) | |||||||
\(258\) | 552485. | + | 401383.i | 0.516739 | + | 0.375414i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 38281.9i | 0.0351205i | ||||||||
\(261\) | 830747. | − | 269970.i | 0.754862 | − | 0.245310i | ||||
\(262\) | 315157.i | 0.283644i | ||||||||
\(263\) | 1.05399e6i | 0.939608i | 0.882771 | + | 0.469804i | \(0.155675\pi\) | ||||
−0.882771 | + | 0.469804i | \(0.844325\pi\) | |||||||
\(264\) | 151809. | − | 208957.i | 0.134056 | − | 0.184522i | ||||
\(265\) | 663224.i | 0.580157i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 292700. | − | 402887.i | 0.251272 | − | 0.345864i | ||||
\(268\) | 176685. | 0.150267 | ||||||||
\(269\) | −459896. | −0.387507 | −0.193753 | − | 0.981050i | \(-0.562066\pi\) | ||||
−0.193753 | + | 0.981050i | \(0.562066\pi\) | |||||||
\(270\) | −237234. | + | 730310.i | −0.198047 | + | 0.609675i | ||||
\(271\) | − | 885691.i | − | 0.732586i | −0.930499 | − | 0.366293i | \(-0.880627\pi\) | ||
0.930499 | − | 0.366293i | \(-0.119373\pi\) | |||||||
\(272\) | 389459. | 0.319183 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −483433. | −0.389009 | ||||||||
\(275\) | − | 772310.i | − | 0.615828i | ||||||
\(276\) | −1.41749e6 | − | 1.02982e6i | −1.12008 | − | 0.813743i | ||||
\(277\) | −770456. | −0.603321 | −0.301660 | − | 0.953415i | \(-0.597541\pi\) | ||||
−0.301660 | + | 0.953415i | \(0.597541\pi\) | |||||||
\(278\) | −491955. | −0.381780 | ||||||||
\(279\) | 670415. | − | 217867.i | 0.515624 | − | 0.167564i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.25084e6i | 1.70051i | 0.526374 | + | 0.850253i | \(0.323551\pi\) | ||||
−0.526374 | + | 0.850253i | \(0.676449\pi\) | |||||||
\(282\) | 237115. | + | 172266.i | 0.177557 | + | 0.128996i | ||||
\(283\) | − | 5068.25i | − | 0.00376177i | −0.999998 | − | 0.00188088i | \(-0.999401\pi\) | ||
0.999998 | − | 0.00188088i | \(-0.000598704\pi\) | |||||||
\(284\) | − | 892016.i | − | 0.656262i | ||||||
\(285\) | −650539. | − | 472620.i | −0.474418 | − | 0.344667i | ||||
\(286\) | 4088.68i | 0.00295575i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.23734e6 | + | 402101.i | −0.879036 | + | 0.285663i | ||||
\(289\) | −1.00963e6 | −0.711076 | ||||||||
\(290\) | −728693. | −0.508803 | ||||||||
\(291\) | −1.80480e6 | − | 1.31120e6i | −1.24939 | − | 0.907686i | ||||
\(292\) | 349675.i | 0.239998i | ||||||||
\(293\) | 2.51767e6 | 1.71329 | 0.856643 | − | 0.515909i | \(-0.172546\pi\) | ||||
0.856643 | + | 0.515909i | \(0.172546\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.80401e6 | −2.54499 | ||||||||
\(296\) | 550526.i | 0.365215i | ||||||||
\(297\) | 152933. | − | 470795.i | 0.100603 | − | 0.309699i | ||||
\(298\) | −19956.9 | −0.0130182 | ||||||||
\(299\) | 60067.6 | 0.0388564 | ||||||||
\(300\) | −1.48650e6 | + | 2.04609e6i | −0.953589 | + | 1.31257i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 295280.i | − | 0.186301i | ||||||
\(303\) | 490989. | − | 675823.i | 0.307231 | − | 0.422889i | ||||
\(304\) | − | 329981.i | − | 0.204788i | ||||||
\(305\) | 3.15671e6i | 1.94306i | ||||||||
\(306\) | −315673. | + | 102585.i | −0.192723 | + | 0.0626299i | ||||
\(307\) | − | 2.31011e6i | − | 1.39890i | −0.714681 | − | 0.699451i | \(-0.753428\pi\) | ||
0.714681 | − | 0.699451i | \(-0.246572\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.93986e6 | + | 1.40932e6i | 1.15578 | + | 0.839680i | ||||
\(310\) | −588057. | −0.347549 | ||||||||
\(311\) | −2.35286e6 | −1.37941 | −0.689707 | − | 0.724089i | \(-0.742261\pi\) | ||||
−0.689707 | + | 0.724089i | \(0.742261\pi\) | |||||||
\(312\) | 17043.2 | − | 23459.1i | 0.00991205 | − | 0.0136435i | ||||
\(313\) | 1.99117e6i | 1.14881i | 0.818572 | + | 0.574404i | \(0.194766\pi\) | ||||
−0.818572 | + | 0.574404i | \(0.805234\pi\) | |||||||
\(314\) | 32981.1 | 0.0188774 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 236028. | 0.132967 | ||||||||
\(317\) | − | 2.09384e6i | − | 1.17029i | −0.810927 | − | 0.585147i | \(-0.801037\pi\) | ||
0.810927 | − | 0.585147i | \(-0.198963\pi\) | |||||||
\(318\) | 136340. | − | 187665.i | 0.0756056 | − | 0.104068i | ||||
\(319\) | 469752. | 0.258459 | ||||||||
\(320\) | −764196. | −0.417186 | ||||||||
\(321\) | −1.93478e6 | − | 1.40563e6i | −1.04802 | − | 0.761390i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 347581.i | − | 0.185374i | ||||||
\(324\) | −1.31133e6 | + | 952928.i | −0.693983 | + | 0.504310i | ||||
\(325\) | − | 86705.1i | − | 0.0455341i | ||||||
\(326\) | − | 617709.i | − | 0.321914i | ||||||
\(327\) | 1.17040e6 | − | 1.61099e6i | 0.605289 | − | 0.833152i | ||||
\(328\) | − | 1.38774e6i | − | 0.712237i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −242714. | + | 334084.i | −0.122690 | + | 0.168877i | ||||
\(331\) | 275243. | 0.138085 | 0.0690426 | − | 0.997614i | \(-0.478006\pi\) | ||||
0.0690426 | + | 0.997614i | \(0.478006\pi\) | |||||||
\(332\) | 869390. | 0.432882 | ||||||||
\(333\) | 326097. | + | 1.00346e6i | 0.161152 | + | 0.495895i | ||||
\(334\) | − | 741812.i | − | 0.363855i | ||||||
\(335\) | −611775. | −0.297838 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 455651. | 0.218553 | 0.109277 | − | 0.994011i | \(-0.465147\pi\) | ||||
0.109277 | + | 0.994011i | \(0.465147\pi\) | |||||||
\(338\) | − | 791376.i | − | 0.376783i | ||||||
\(339\) | −1.14031e6 | − | 828445.i | −0.538921 | − | 0.391529i | ||||
\(340\) | −1.67128e6 | −0.784064 | ||||||||
\(341\) | 379091. | 0.176546 | ||||||||
\(342\) | 86918.5 | + | 267464.i | 0.0401834 | + | 0.123652i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 2.60446e6i | − | 1.18665i | ||||||
\(345\) | 4.90809e6 | + | 3.56576e6i | 2.22006 | + | 1.61289i | ||||
\(346\) | − | 1.08368e6i | − | 0.486642i | ||||||
\(347\) | − | 1.71199e6i | − | 0.763271i | −0.924313 | − | 0.381636i | \(-0.875361\pi\) | ||
0.924313 | − | 0.381636i | \(-0.124639\pi\) | |||||||
\(348\) | −1.24452e6 | − | 904153.i | −0.550877 | − | 0.400215i | ||||
\(349\) | 1.94736e6i | 0.855822i | 0.903821 | + | 0.427911i | \(0.140750\pi\) | ||||
−0.903821 | + | 0.427911i | \(0.859250\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17169.4 | − | 52854.9i | 0.00743852 | − | 0.0228990i | ||||
\(352\) | −699661. | −0.300975 | ||||||||
\(353\) | 3.59350e6 | 1.53490 | 0.767452 | − | 0.641106i | \(-0.221524\pi\) | ||||
0.767452 | + | 0.641106i | \(0.221524\pi\) | |||||||
\(354\) | 1.07638e6 | + | 781995.i | 0.456517 | + | 0.331662i | ||||
\(355\) | 3.08862e6i | 1.30075i | ||||||||
\(356\) | −876973. | −0.366742 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 853930. | 0.352139 | ||||||||
\(359\) | 2.58351e6i | 1.05797i | 0.848630 | + | 0.528987i | \(0.177428\pi\) | ||||
−0.848630 | + | 0.528987i | \(0.822572\pi\) | |||||||
\(360\) | 2.78518e6 | − | 905107.i | 1.13265 | − | 0.368081i | ||||
\(361\) | 2.18160e6 | 0.881064 | ||||||||
\(362\) | 22808.0 | 0.00914779 | ||||||||
\(363\) | −1.31914e6 | + | 1.81574e6i | −0.525442 | + | 0.723246i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.21076e6i | − | 0.475691i | ||||||
\(366\) | 648929. | − | 893219.i | 0.253218 | − | 0.348542i | ||||
\(367\) | 3.76563e6i | 1.45939i | 0.683772 | + | 0.729696i | \(0.260338\pi\) | ||||
−0.683772 | + | 0.729696i | \(0.739662\pi\) | |||||||
\(368\) | 2.48960e6i | 0.958317i | ||||||||
\(369\) | −822014. | − | 2.52948e6i | −0.314277 | − | 0.967088i | ||||
\(370\) | − | 880189.i | − | 0.334250i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.00433e6 | − | 729654.i | −0.376288 | − | 0.273376i | ||||
\(373\) | −1.93722e6 | −0.720952 | −0.360476 | − | 0.932768i | \(-0.617386\pi\) | ||||
−0.360476 | + | 0.932768i | \(0.617386\pi\) | |||||||
\(374\) | −178500. | −0.0659870 | ||||||||
\(375\) | 2.42545e6 | − | 3.33852e6i | 0.890665 | − | 1.22596i | ||||
\(376\) | − | 1.11778e6i | − | 0.407743i | ||||||
\(377\) | 52737.8 | 0.0191104 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.04113e6 | 0.729917 | 0.364959 | − | 0.931024i | \(-0.381083\pi\) | ||||
0.364959 | + | 0.931024i | \(0.381083\pi\) | |||||||
\(380\) | 1.41604e6i | 0.503057i | ||||||||
\(381\) | −1.21238e6 | + | 1.66878e6i | −0.427883 | + | 0.588960i | ||||
\(382\) | −420668. | −0.147496 | ||||||||
\(383\) | −470701. | −0.163964 | −0.0819819 | − | 0.996634i | \(-0.526125\pi\) | ||||
−0.0819819 | + | 0.996634i | \(0.526125\pi\) | |||||||
\(384\) | 2.37696e6 | + | 1.72688e6i | 0.822611 | + | 0.597632i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 267670.i | 0.0914388i | ||||||||
\(387\) | −1.54272e6 | − | 4.74722e6i | −0.523612 | − | 1.61125i | ||||
\(388\) | 3.92855e6i | 1.32481i | ||||||||
\(389\) | − | 4.59134e6i | − | 1.53839i | −0.639017 | − | 0.769193i | \(-0.720659\pi\) | ||
0.639017 | − | 0.769193i | \(-0.279341\pi\) | |||||||
\(390\) | −27248.8 | + | 37506.7i | −0.00907166 | + | 0.0124867i | ||||
\(391\) | 2.62238e6i | 0.867467i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.35399e6 | − | 1.86371e6i | 0.442216 | − | 0.608690i | ||||
\(394\) | −1.34717e6 | −0.437202 | ||||||||
\(395\) | −817250. | −0.263550 | ||||||||
\(396\) | −829054. | + | 269420.i | −0.265671 | + | 0.0863360i | ||||
\(397\) | 4.55566e6i | 1.45069i | 0.688384 | + | 0.725346i | \(0.258320\pi\) | ||||
−0.688384 | + | 0.725346i | \(0.741680\pi\) | |||||||
\(398\) | 1.32731e6 | 0.420016 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.59363e6 | 1.12301 | ||||||||
\(401\) | − | 2.41750e6i | − | 0.750766i | −0.926870 | − | 0.375383i | \(-0.877511\pi\) | ||
0.926870 | − | 0.375383i | \(-0.122489\pi\) | |||||||
\(402\) | 173107. | + | 125763.i | 0.0534256 | + | 0.0388140i | ||||
\(403\) | 42559.6 | 0.0130537 | ||||||||
\(404\) | −1.47108e6 | −0.448418 | ||||||||
\(405\) | 4.54050e6 | − | 3.29953e6i | 1.37552 | − | 0.999573i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 567414.i | 0.169791i | ||||||||
\(408\) | 1.02415e6 | + | 744054.i | 0.304590 | + | 0.221286i | ||||
\(409\) | − | 64985.1i | − | 0.0192090i | −0.999954 | − | 0.00960452i | \(-0.996943\pi\) | ||
0.999954 | − | 0.00960452i | \(-0.00305726\pi\) | |||||||
\(410\) | 2.21875e6i | 0.651851i | ||||||||
\(411\) | 2.85882e6 | + | 2.07695e6i | 0.834798 | + | 0.606486i | ||||
\(412\) | − | 4.22254e6i | − | 1.22555i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −655771. | − | 2.01792e6i | −0.188040 | − | 0.578634i | ||||
\(415\) | −3.01028e6 | −0.857998 | ||||||||
\(416\) | −78549.1 | −0.0222540 | ||||||||
\(417\) | 2.90921e6 | + | 2.11356e6i | 0.819285 | + | 0.595216i | ||||
\(418\) | 151239.i | 0.0423374i | ||||||||
\(419\) | −4.52870e6 | −1.26020 | −0.630098 | − | 0.776515i | \(-0.716985\pi\) | ||||
−0.630098 | + | 0.776515i | \(0.716985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.77935e6 | −1.03923 | −0.519615 | − | 0.854401i | \(-0.673925\pi\) | ||||
−0.519615 | + | 0.854401i | \(0.673925\pi\) | |||||||
\(422\) | 579529.i | 0.158414i | ||||||||
\(423\) | −662104. | − | 2.03741e6i | −0.179918 | − | 0.553641i | ||||
\(424\) | −884667. | −0.238982 | ||||||||
\(425\) | 3.78529e6 | 1.01655 | ||||||||
\(426\) | 634932. | − | 873953.i | 0.169513 | − | 0.233326i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.21147e6i | 1.11128i | ||||||||
\(429\) | 17566.0 | − | 24178.7i | 0.00460818 | − | 0.00634293i | ||||
\(430\) | 4.16404e6i | 1.08604i | ||||||||
\(431\) | − | 6.61895e6i | − | 1.71631i | −0.513391 | − | 0.858155i | \(-0.671611\pi\) | ||
0.513391 | − | 0.858155i | \(-0.328389\pi\) | |||||||
\(432\) | 2.19065e6 | + | 711612.i | 0.564761 | + | 0.183457i | ||||
\(433\) | 5.25855e6i | 1.34786i | 0.738794 | + | 0.673932i | \(0.235396\pi\) | ||||
−0.738794 | + | 0.673932i | \(0.764604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.30918e6 | + | 3.13065e6i | 1.09187 | + | 0.793251i | ||||
\(436\) | −3.50668e6 | −0.883446 | ||||||||
\(437\) | 2.22189e6 | 0.556569 | ||||||||
\(438\) | −248897. | + | 342594.i | −0.0619917 | + | 0.0853286i | ||||
\(439\) | − | 416451.i | − | 0.103134i | −0.998670 | − | 0.0515671i | \(-0.983578\pi\) | ||
0.998670 | − | 0.0515671i | \(-0.0164216\pi\) | |||||||
\(440\) | 1.57490e6 | 0.387812 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20039.7 | −0.00487905 | ||||||||
\(443\) | 7.00727e6i | 1.69644i | 0.529641 | + | 0.848222i | \(0.322327\pi\) | ||||
−0.529641 | + | 0.848222i | \(0.677673\pi\) | |||||||
\(444\) | 1.09213e6 | − | 1.50326e6i | 0.262915 | − | 0.361890i | ||||
\(445\) | 3.03653e6 | 0.726906 | ||||||||
\(446\) | 546803. | 0.130165 | ||||||||
\(447\) | 118017. | + | 85739.8i | 0.0279367 | + | 0.0202961i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.63032e6i | − | 0.381643i | −0.981625 | − | 0.190822i | \(-0.938885\pi\) | ||
0.981625 | − | 0.190822i | \(-0.0611152\pi\) | |||||||
\(450\) | −2.91279e6 | + | 946579.i | −0.678076 | + | 0.220356i | ||||
\(451\) | − | 1.43032e6i | − | 0.331124i | ||||||
\(452\) | 2.48215e6i | 0.571454i | ||||||||
\(453\) | −1.26860e6 | + | 1.74616e6i | −0.290454 | + | 0.399796i | ||||
\(454\) | 251428.i | 0.0572498i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 630423. | − | 867747.i | 0.141978 | − | 0.195425i | ||||
\(457\) | 8.38895e6 | 1.87896 | 0.939479 | − | 0.342606i | \(-0.111310\pi\) | ||||
0.939479 | + | 0.342606i | \(0.111310\pi\) | |||||||
\(458\) | 797141. | 0.177571 | ||||||||
\(459\) | 2.30749e6 | + | 749565.i | 0.511220 | + | 0.166065i | ||||
\(460\) | − | 1.06836e7i | − | 2.35408i | ||||||
\(461\) | −186426. | −0.0408560 | −0.0204280 | − | 0.999791i | \(-0.506503\pi\) | ||||
−0.0204280 | + | 0.999791i | \(0.506503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.23908e6 | −1.13580 | −0.567901 | − | 0.823097i | \(-0.692244\pi\) | ||||
−0.567901 | + | 0.823097i | \(0.692244\pi\) | |||||||
\(464\) | 2.18580e6i | 0.471320i | ||||||||
\(465\) | 3.47752e6 | + | 2.52644e6i | 0.745826 | + | 0.541847i | ||||
\(466\) | 2.69736e6 | 0.575405 | ||||||||
\(467\) | 564223. | 0.119718 | 0.0598589 | − | 0.998207i | \(-0.480935\pi\) | ||||
0.0598589 | + | 0.998207i | \(0.480935\pi\) | |||||||
\(468\) | −93075.7 | + | 30247.1i | −0.0196436 | + | 0.00638365i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.78712e6i | 0.373173i | ||||||||
\(471\) | −195036. | − | 141695.i | −0.0405101 | − | 0.0294308i | ||||
\(472\) | − | 5.07413e6i | − | 1.04835i | ||||||
\(473\) | − | 2.68435e6i | − | 0.551679i | ||||||
\(474\) | 231248. | + | 168003.i | 0.0472751 | + | 0.0343456i | ||||
\(475\) | − | 3.20721e6i | − | 0.652219i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.61251e6 | + | 524022.i | −0.324494 | + | 0.105452i | ||||
\(478\) | 1.11072e6 | 0.222348 | ||||||||
\(479\) | 2.69727e6 | 0.537137 | 0.268568 | − | 0.963261i | \(-0.413449\pi\) | ||||
0.268568 | + | 0.963261i | \(0.413449\pi\) | |||||||
\(480\) | −6.41821e6 | − | 4.66286e6i | −1.27148 | − | 0.923740i | ||||
\(481\) | 63702.1i | 0.0125543i | ||||||||
\(482\) | −2.03516e6 | −0.399007 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.95235e6 | 0.766906 | ||||||||
\(485\) | − | 1.36027e7i | − | 2.62585i | ||||||
\(486\) | −1.96306e6 | + | 236.061i | −0.377001 | + | 4.53350e-5i | ||||
\(487\) | −2.84365e6 | −0.543317 | −0.271658 | − | 0.962394i | \(-0.587572\pi\) | ||||
−0.271658 | + | 0.962394i | \(0.587572\pi\) | |||||||
\(488\) | −4.21071e6 | −0.800397 | ||||||||
\(489\) | −2.65383e6 | + | 3.65287e6i | −0.501881 | + | 0.690815i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.38962e6i | − | 1.38331i | −0.722229 | − | 0.691654i | \(-0.756882\pi\) | ||
0.722229 | − | 0.691654i | \(-0.243118\pi\) | |||||||
\(492\) | −2.75299e6 | + | 3.78936e6i | −0.512734 | + | 0.705754i | ||||
\(493\) | 2.30238e6i | 0.426638i | ||||||||
\(494\) | 16979.3i | 0.00313041i | ||||||||
\(495\) | 2.87062e6 | − | 932872.i | 0.526577 | − | 0.171123i | ||||
\(496\) | 1.76395e6i | 0.321945i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 851784. | + | 618826.i | 0.153906 | + | 0.111814i | ||||
\(499\) | 2.13675e6 | 0.384152 | 0.192076 | − | 0.981380i | \(-0.438478\pi\) | ||||
0.192076 | + | 0.981380i | \(0.438478\pi\) | |||||||
\(500\) | −7.26702e6 | −1.29996 | ||||||||
\(501\) | −3.18701e6 | + | 4.38677e6i | −0.567269 | + | 0.780818i | ||||
\(502\) | 1.68434e6i | 0.298313i | ||||||||
\(503\) | 2.60933e6 | 0.459842 | 0.229921 | − | 0.973209i | \(-0.426153\pi\) | ||||
0.229921 | + | 0.973209i | \(0.426153\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.09364e6 | 0.888791 | ||||||||
\(506\) | − | 1.14105e6i | − | 0.198120i | ||||||
\(507\) | −3.39995e6 | + | 4.67986e6i | −0.587425 | + | 0.808562i | ||||
\(508\) | 3.63246e6 | 0.624514 | ||||||||
\(509\) | −5.78866e6 | −0.990338 | −0.495169 | − | 0.868797i | \(-0.664894\pi\) | ||||
−0.495169 | + | 0.868797i | \(0.664894\pi\) | |||||||
\(510\) | −1.63743e6 | − | 1.18961e6i | −0.278765 | − | 0.202524i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 5.72266e6i | − | 0.964768i | ||||||
\(513\) | 635092. | − | 1.95509e6i | 0.106548 | − | 0.328000i | ||||
\(514\) | − | 2.36231e6i | − | 0.394392i | ||||||
\(515\) | 1.46206e7i | 2.42911i | ||||||||
\(516\) | −5.16669e6 | + | 7.11170e6i | −0.854257 | + | 1.17584i | ||||
\(517\) | − | 1.15207e6i | − | 0.189563i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.65574e6 | + | 6.40840e6i | −0.758701 | + | 1.04431i | ||||
\(520\) | 176810. | 0.0286746 | ||||||||
\(521\) | −306226. | −0.0494250 | −0.0247125 | − | 0.999695i | \(-0.507867\pi\) | ||||
−0.0247125 | + | 0.999695i | \(0.507867\pi\) | |||||||
\(522\) | −575750. | − | 1.77169e6i | −0.0924821 | − | 0.284584i | ||||
\(523\) | 7.18513e6i | 1.14863i | 0.818634 | + | 0.574315i | \(0.194732\pi\) | ||||
−0.818634 | + | 0.574315i | \(0.805268\pi\) | |||||||
\(524\) | −4.05677e6 | −0.645434 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.24778e6 | 0.354234 | ||||||||
\(527\) | 1.85803e6i | 0.291424i | ||||||||
\(528\) | 1.00213e6 | + | 728050.i | 0.156436 | + | 0.113652i | ||||
\(529\) | −1.03270e7 | −1.60449 | ||||||||
\(530\) | 1.41442e6 | 0.218720 | ||||||||
\(531\) | −3.00560e6 | − | 9.24877e6i | −0.462589 | − | 1.42347i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 160578.i | − | 0.0244831i | ||||||
\(534\) | −859214. | − | 624224.i | −0.130391 | − | 0.0947299i | ||||
\(535\) | − | 1.45823e7i | − | 2.20263i | ||||||
\(536\) | − | 816040.i | − | 0.122687i | ||||||
\(537\) | −5.04978e6 | − | 3.66869e6i | −0.755678 | − | 0.549004i | ||||
\(538\) | 980795.i | 0.146091i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.40071e6 | − | 3.05373e6i | −1.38732 | − | 0.450657i | ||||
\(541\) | 7.76483e6 | 1.14061 | 0.570307 | − | 0.821431i | \(-0.306824\pi\) | ||||
0.570307 | + | 0.821431i | \(0.306824\pi\) | |||||||
\(542\) | −1.88886e6 | −0.276186 | ||||||||
\(543\) | −134877. | − | 97988.9i | −0.0196308 | − | 0.0142619i | ||||
\(544\) | − | 3.42922e6i | − | 0.496819i | ||||||
\(545\) | 1.21420e7 | 1.75104 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.87821e6 | −1.12580 | −0.562898 | − | 0.826527i | \(-0.690313\pi\) | ||||
−0.562898 | + | 0.826527i | \(0.690313\pi\) | |||||||
\(548\) | − | 6.22285e6i | − | 0.885193i | ||||||
\(549\) | −7.67498e6 | + | 2.49416e6i | −1.08679 | + | 0.353178i | ||||
\(550\) | −1.64706e6 | −0.232168 | ||||||||
\(551\) | 1.95076e6 | 0.273732 | ||||||||
\(552\) | −4.75633e6 | + | 6.54685e6i | −0.664391 | + | 0.914503i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.64311e6i | 0.227453i | ||||||||
\(555\) | −3.78151e6 | + | 5.20507e6i | −0.521114 | + | 0.717289i | ||||
\(556\) | − | 6.33255e6i | − | 0.868743i | ||||||
\(557\) | − | 4.59766e6i | − | 0.627913i | −0.949437 | − | 0.313956i | \(-0.898345\pi\) | ||
0.949437 | − | 0.313956i | \(-0.101655\pi\) | |||||||
\(558\) | −464632. | − | 1.42976e6i | −0.0631719 | − | 0.194391i | ||||
\(559\) | − | 301365.i | − | 0.0407909i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.05557e6 | + | 766879.i | 0.141606 | + | 0.102877i | ||||
\(562\) | 4.80023e6 | 0.641094 | ||||||||
\(563\) | 2.72419e6 | 0.362215 | 0.181107 | − | 0.983463i | \(-0.442032\pi\) | ||||
0.181107 | + | 0.983463i | \(0.442032\pi\) | |||||||
\(564\) | −2.21744e6 | + | 3.05220e6i | −0.293531 | + | 0.404031i | ||||
\(565\) | − | 8.59448e6i | − | 1.13266i | ||||||
\(566\) | −10808.8 | −0.00141819 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.11988e6 | −0.535814 | ||||||||
\(569\) | 8.67813e6i | 1.12369i | 0.827243 | + | 0.561844i | \(0.189908\pi\) | ||||
−0.827243 | + | 0.561844i | \(0.810092\pi\) | |||||||
\(570\) | −1.00793e6 | + | 1.38737e6i | −0.129940 | + | 0.178856i | ||||
\(571\) | 1.07384e7 | 1.37832 | 0.689161 | − | 0.724608i | \(-0.257979\pi\) | ||||
0.689161 | + | 0.724608i | \(0.257979\pi\) | |||||||
\(572\) | −52630.3 | −0.00672583 | ||||||||
\(573\) | 2.48765e6 | + | 1.80730e6i | 0.316522 | + | 0.229955i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.41973e7i | 3.05209i | ||||||||
\(576\) | −603801. | − | 1.85801e6i | −0.0758294 | − | 0.233341i | ||||
\(577\) | − | 7.06870e6i | − | 0.883894i | −0.897041 | − | 0.441947i | \(-0.854288\pi\) | ||
0.897041 | − | 0.441947i | \(-0.145712\pi\) | |||||||
\(578\) | 2.15317e6i | 0.268077i | ||||||||
\(579\) | 1.14997e6 | − | 1.58288e6i | 0.142558 | − | 0.196224i | ||||
\(580\) | − | 9.37989e6i | − | 1.15779i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.79631e6 | + | 3.84899e6i | −0.342199 | + | 0.471020i | ||||
\(583\) | −911805. | −0.111104 | ||||||||
\(584\) | 1.61502e6 | 0.195950 | ||||||||
\(585\) | 322276. | − | 104731.i | 0.0389349 | − | 0.0126528i | ||||
\(586\) | − | 5.36929e6i | − | 0.645911i | ||||||
\(587\) | −3.96818e6 | −0.475331 | −0.237666 | − | 0.971347i | \(-0.576382\pi\) | ||||
−0.237666 | + | 0.971347i | \(0.576382\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.57427e6 | 0.186978 | ||||||||
\(590\) | 8.11260e6i | 0.959467i | ||||||||
\(591\) | 7.96659e6 | + | 5.78777e6i | 0.938218 | + | 0.681621i | ||||
\(592\) | −2.64023e6 | −0.309626 | ||||||||
\(593\) | 1.67421e7 | 1.95512 | 0.977562 | − | 0.210649i | \(-0.0675576\pi\) | ||||
0.977562 | + | 0.210649i | \(0.0675576\pi\) | |||||||
\(594\) | −1.00404e6 | − | 326151.i | −0.116757 | − | 0.0379274i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 256889.i | − | 0.0296231i | ||||||
\(597\) | −7.84918e6 | − | 5.70247e6i | −0.901339 | − | 0.654828i | ||||
\(598\) | − | 128103.i | − | 0.0146489i | ||||||
\(599\) | 1.08814e7i | 1.23913i | 0.784944 | + | 0.619567i | \(0.212692\pi\) | ||||
−0.784944 | + | 0.619567i | \(0.787308\pi\) | |||||||
\(600\) | 9.45012e6 | + | 6.86557e6i | 1.07167 | + | 0.778571i | ||||
\(601\) | 1.72048e7i | 1.94296i | 0.237128 | + | 0.971478i | \(0.423794\pi\) | ||||
−0.237128 | + | 0.971478i | \(0.576206\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −483372. | − | 1.48742e6i | −0.0541362 | − | 0.166587i | ||||
\(604\) | 3.80090e6 | 0.423930 | ||||||||
\(605\) | −1.36851e7 | −1.52005 | ||||||||
\(606\) | −1.44129e6 | − | 1.04711e6i | −0.159430 | − | 0.115827i | ||||
\(607\) | − | 5.56535e6i | − | 0.613085i | −0.951857 | − | 0.306543i | \(-0.900828\pi\) | ||
0.951857 | − | 0.306543i | \(-0.0991722\pi\) | |||||||
\(608\) | −2.90552e6 | −0.318760 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.73214e6 | 0.732535 | ||||||||
\(611\) | − | 129340.i | − | 0.0140162i | ||||||
\(612\) | −1.32050e6 | − | 4.06341e6i | −0.142515 | − | 0.438543i | ||||
\(613\) | −1.18075e7 | −1.26914 | −0.634568 | − | 0.772867i | \(-0.718822\pi\) | ||||
−0.634568 | + | 0.772867i | \(0.718822\pi\) | |||||||
\(614\) | −4.92664e6 | −0.527388 | ||||||||
\(615\) | 9.53229e6 | − | 1.31207e7i | 1.01627 | − | 1.39885i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 5.91582e6i | − | 0.625608i | −0.949818 | − | 0.312804i | \(-0.898732\pi\) | ||
0.949818 | − | 0.312804i | \(-0.101268\pi\) | |||||||
\(618\) | 3.00558e6 | − | 4.13703e6i | 0.316560 | − | 0.435730i | ||||
\(619\) | − | 2.82876e6i | − | 0.296736i | −0.988932 | − | 0.148368i | \(-0.952598\pi\) | ||
0.988932 | − | 0.148368i | \(-0.0474020\pi\) | |||||||
\(620\) | − | 7.56960e6i | − | 0.790849i | ||||||
\(621\) | −4.79155e6 | + | 1.47505e7i | −0.498594 | + | 1.53489i | ||||
\(622\) | 5.01780e6i | 0.520041i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 112506. | + | 81736.2i | 0.0115668 | + | 0.00840336i | ||||
\(625\) | 6.69352e6 | 0.685416 | ||||||||
\(626\) | 4.24646e6 | 0.433103 | ||||||||
\(627\) | 649762. | − | 894366.i | 0.0660063 | − | 0.0908545i | ||||
\(628\) | 424540.i | 0.0429556i | ||||||||
\(629\) | −2.78105e6 | −0.280273 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.60301e6 | −0.960139 | −0.480069 | − | 0.877231i | \(-0.659389\pi\) | ||||
−0.480069 | + | 0.877231i | \(0.659389\pi\) | |||||||
\(632\) | − | 1.09012e6i | − | 0.108563i | ||||||
\(633\) | 2.48980e6 | − | 3.42709e6i | 0.246976 | − | 0.339951i | ||||
\(634\) | −4.46541e6 | −0.441203 | ||||||||
\(635\) | −1.25775e7 | −1.23782 | ||||||||
\(636\) | 2.41566e6 | + | 1.75499e6i | 0.236806 | + | 0.172041i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 1.00181e6i | − | 0.0974395i | ||||||
\(639\) | −7.50943e6 | + | 2.44036e6i | −0.727537 | + | 0.236430i | ||||
\(640\) | 1.79150e7i | 1.72889i | ||||||||
\(641\) | − | 9.00157e6i | − | 0.865312i | −0.901559 | − | 0.432656i | \(-0.857576\pi\) | ||
0.901559 | − | 0.432656i | \(-0.142424\pi\) | |||||||
\(642\) | −2.99770e6 | + | 4.12618e6i | −0.287045 | + | 0.395104i | ||||
\(643\) | − | 6.92082e6i | − | 0.660131i | −0.943958 | − | 0.330065i | \(-0.892929\pi\) | ||
0.943958 | − | 0.330065i | \(-0.107071\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.78898e7 | − | 2.46244e7i | 1.69319 | − | 2.33059i | ||||
\(646\) | −741265. | −0.0698863 | ||||||||
\(647\) | −1.66850e6 | −0.156699 | −0.0783495 | − | 0.996926i | \(-0.524965\pi\) | ||||
−0.0783495 | + | 0.996926i | \(0.524965\pi\) | |||||||
\(648\) | 4.40121e6 | + | 6.05652e6i | 0.411751 | + | 0.566612i | ||||
\(649\) | − | 5.22979e6i | − | 0.487385i | ||||||
\(650\) | −184911. | −0.0171664 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.95128e6 | 0.732518 | ||||||||
\(653\) | − | 1.81810e7i | − | 1.66853i | −0.551364 | − | 0.834265i | \(-0.685892\pi\) | ||
0.551364 | − | 0.834265i | \(-0.314108\pi\) | |||||||
\(654\) | −3.43567e6 | − | 2.49603e6i | −0.314099 | − | 0.228195i | ||||
\(655\) | 1.40466e7 | 1.27929 | ||||||||
\(656\) | 6.65540e6 | 0.603830 | ||||||||
\(657\) | 2.94374e6 | − | 956635.i | 0.266064 | − | 0.0864635i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.58660e6i | − | 0.501111i | −0.968102 | − | 0.250556i | \(-0.919387\pi\) | ||
0.968102 | − | 0.250556i | \(-0.0806133\pi\) | |||||||
\(660\) | −4.30040e6 | − | 3.12427e6i | −0.384281 | − | 0.279182i | ||||
\(661\) | 1.30855e7i | 1.16489i | 0.812870 | + | 0.582445i | \(0.197904\pi\) | ||||
−0.812870 | + | 0.582445i | \(0.802096\pi\) | |||||||
\(662\) | − | 586996.i | − | 0.0520583i | ||||||
\(663\) | 118506. | + | 86095.5i | 0.0104703 | + | 0.00760671i | ||||
\(664\) | − | 4.01538e6i | − | 0.353432i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.14002e6 | − | 695449.i | 0.186953 | − | 0.0607547i | ||||
\(667\) | −1.47178e7 | −1.28094 | ||||||||
\(668\) | 9.54877e6 | 0.827954 | ||||||||
\(669\) | −3.23356e6 | − | 2.34920e6i | −0.279329 | − | 0.202934i | ||||
\(670\) | 1.30470e6i | 0.112285i | ||||||||
\(671\) | −4.33988e6 | −0.372110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.79316e6 | 0.833461 | 0.416730 | − | 0.909030i | \(-0.363176\pi\) | ||||
0.416730 | + | 0.909030i | \(0.363176\pi\) | |||||||
\(674\) | − | 971740.i | − | 0.0823949i | ||||||
\(675\) | 2.12918e7 | + | 6.91642e6i | 1.79867 | + | 0.584281i | ||||
\(676\) | 1.01868e7 | 0.857373 | ||||||||
\(677\) | −8.00917e6 | −0.671608 | −0.335804 | − | 0.941932i | \(-0.609008\pi\) | ||||
−0.335804 | + | 0.941932i | \(0.609008\pi\) | |||||||
\(678\) | −1.76678e6 | + | 2.43188e6i | −0.147607 | + | 0.203174i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.71900e6i | 0.640160i | ||||||||
\(681\) | 1.08020e6 | − | 1.48684e6i | 0.0892555 | − | 0.122856i | ||||
\(682\) | − | 808466.i | − | 0.0665581i | ||||||
\(683\) | − | 2.00990e7i | − | 1.64863i | −0.566133 | − | 0.824314i | \(-0.691561\pi\) | ||
0.566133 | − | 0.824314i | \(-0.308439\pi\) | |||||||
\(684\) | −3.44285e6 | + | 1.11883e6i | −0.281370 | + | 0.0914377i | ||||
\(685\) | 2.15467e7i | 1.75451i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.71395e6 | − | 3.42471e6i | −0.381060 | − | 0.276842i | ||||
\(688\) | 1.24906e7 | 1.00603 | ||||||||
\(689\) | −102366. | −0.00821500 | ||||||||
\(690\) | 7.60449e6 | − | 1.04672e7i | 0.608061 | − | 0.836967i | ||||
\(691\) | − | 7.78435e6i | − | 0.620193i | −0.950705 | − | 0.310097i | \(-0.899639\pi\) | ||
0.950705 | − | 0.310097i | \(-0.100361\pi\) | |||||||
\(692\) | 1.39493e7 | 1.10736 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.65107e6 | −0.287754 | ||||||||
\(695\) | 2.19266e7i | 1.72190i | ||||||||
\(696\) | −4.17594e6 | + | 5.74797e6i | −0.326761 | + | 0.449771i | ||||
\(697\) | 7.01036e6 | 0.546586 | ||||||||
\(698\) | 4.15303e6 | 0.322646 | ||||||||
\(699\) | −1.59510e7 | − | 1.15885e7i | −1.23480 | − | 0.897088i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.12400e7i | − | 0.863912i | −0.901895 | − | 0.431956i | \(-0.857824\pi\) | ||
0.901895 | − | 0.431956i | \(-0.142176\pi\) | |||||||
\(702\) | −112721. | − | 36616.1i | −0.00863297 | − | 0.00280433i | ||||
\(703\) | 2.35633e6i | 0.179824i | ||||||||
\(704\) | − | 1.05062e6i | − | 0.0798942i | ||||||
\(705\) | 7.67793e6 | − | 1.05683e7i | 0.581797 | − | 0.800815i | ||||
\(706\) | − | 7.66366e6i | − | 0.578661i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.00660e7 | + | 1.38554e7i | −0.754699 | + | 1.03881i | ||||
\(709\) | −1.15696e7 | −0.864376 | −0.432188 | − | 0.901783i | \(-0.642258\pi\) | ||||
−0.432188 | + | 0.901783i | \(0.642258\pi\) | |||||||
\(710\) | 6.58693e6 | 0.490385 | ||||||||
\(711\) | −645721. | − | 1.98700e6i | −0.0479039 | − | 0.147409i | ||||
\(712\) | 4.05040e6i | 0.299432i | ||||||||
\(713\) | −1.18773e7 | −0.874974 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 182234. | 0.0133310 | ||||||||
\(716\) | 1.09920e7i | 0.801296i | ||||||||
\(717\) | −6.56830e6 | − | 4.77191e6i | −0.477150 | − | 0.346653i | ||||
\(718\) | 5.50971e6 | 0.398857 | ||||||||
\(719\) | 461291. | 0.0332777 | 0.0166388 | − | 0.999862i | \(-0.494703\pi\) | ||||
0.0166388 | + | 0.999862i | \(0.494703\pi\) | |||||||
\(720\) | 4.34075e6 | + | 1.33573e7i | 0.312056 | + | 0.960254i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 4.65257e6i | − | 0.332162i | ||||||
\(723\) | 1.20351e7 | + | 8.74354e6i | 0.856254 | + | 0.622073i | ||||
\(724\) | 293590.i | 0.0208159i | ||||||||
\(725\) | 2.12446e7i | 1.50108i | ||||||||
\(726\) | 3.87231e6 | + | 2.81326e6i | 0.272665 | + | 0.198093i | ||||
\(727\) | − | 2.83046e6i | − | 0.198619i | −0.995057 | − | 0.0993096i | \(-0.968337\pi\) | ||
0.995057 | − | 0.0993096i | \(-0.0316634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.16097e7 | + | 8.43240e6i | 0.809102 | + | 0.587669i | ||||
\(730\) | −2.58211e6 | −0.179336 | ||||||||
\(731\) | 1.31567e7 | 0.910656 | ||||||||
\(732\) | 1.14977e7 | + | 8.35315e6i | 0.793111 | + | 0.576199i | ||||
\(733\) | 2.05309e7i | 1.41140i | 0.708513 | + | 0.705698i | \(0.249366\pi\) | ||||
−0.708513 | + | 0.705698i | \(0.750634\pi\) | |||||||
\(734\) | 8.03073e6 | 0.550193 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.19211e7 | 1.49165 | ||||||||
\(737\) | − | 841074.i | − | 0.0570381i | ||||||
\(738\) | −5.39448e6 | + | 1.75306e6i | −0.364594 | + | 0.118483i | ||||
\(739\) | −1.51479e7 | −1.02033 | −0.510167 | − | 0.860075i | \(-0.670416\pi\) | ||||
−0.510167 | + | 0.860075i | \(0.670416\pi\) | |||||||
\(740\) | 1.13300e7 | 0.760589 | ||||||||
\(741\) | 72947.1 | − | 100408.i | 0.00488048 | − | 0.00671774i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.14063e6i | − | 0.208711i | −0.994540 | − | 0.104355i | \(-0.966722\pi\) | ||
0.994540 | − | 0.104355i | \(-0.0332779\pi\) | |||||||
\(744\) | −3.36999e6 | + | 4.63863e6i | −0.223201 | + | 0.307226i | ||||
\(745\) | 889485.i | 0.0587148i | ||||||||
\(746\) | 4.13140e6i | 0.271800i | ||||||||
\(747\) | −2.37846e6 | − | 7.31895e6i | −0.155953 | − | 0.479896i | ||||
\(748\) | − | 2.29769e6i | − | 0.150154i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.11986e6 | − | 5.17262e6i | −0.462188 | − | 0.335782i | ||||
\(751\) | −1.43376e6 | −0.0927634 | −0.0463817 | − | 0.998924i | \(-0.514769\pi\) | ||||
−0.0463817 | + | 0.998924i | \(0.514769\pi\) | |||||||
\(752\) | 5.36069e6 | 0.345682 | ||||||||
\(753\) | 7.23636e6 | − | 9.96050e6i | 0.465085 | − | 0.640168i | ||||
\(754\) | − | 112471.i | − | 0.00720463i | ||||||
\(755\) | −1.31607e7 | −0.840256 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.81110e6 | −0.431994 | −0.215997 | − | 0.976394i | \(-0.569300\pi\) | ||||
−0.215997 | + | 0.976394i | \(0.569300\pi\) | |||||||
\(758\) | − | 4.35301e6i | − | 0.275180i | ||||||
\(759\) | −4.90223e6 | + | 6.74769e6i | −0.308880 | + | 0.425158i | ||||
\(760\) | 6.54016e6 | 0.410728 | ||||||||
\(761\) | 110270. | 0.00690235 | 0.00345117 | − | 0.999994i | \(-0.498901\pi\) | ||||
0.00345117 | + | 0.999994i | \(0.498901\pi\) | |||||||
\(762\) | 3.55890e6 | + | 2.58557e6i | 0.222039 | + | 0.161313i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 5.41493e6i | − | 0.335629i | ||||||
\(765\) | 4.57225e6 | + | 1.40696e7i | 0.282473 | + | 0.869220i | ||||
\(766\) | 1.00384e6i | 0.0618146i | ||||||||
\(767\) | − | 587134.i | − | 0.0360370i | ||||||
\(768\) | 1.32560e6 | − | 1.82463e6i | 0.0810980 | − | 0.111628i | ||||
\(769\) | − | 1.61688e7i | − | 0.985968i | −0.870038 | − | 0.492984i | \(-0.835906\pi\) | ||
0.870038 | − | 0.492984i | \(-0.164094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.01491e7 | + | 1.39697e7i | −0.614879 | + | 0.846351i | ||||
\(772\) | −3.44550e6 | −0.208070 | ||||||||
\(773\) | −1.67611e7 | −1.00892 | −0.504458 | − | 0.863436i | \(-0.668308\pi\) | ||||
−0.504458 | + | 0.863436i | \(0.668308\pi\) | |||||||
\(774\) | −1.01241e7 | + | 3.29007e6i | −0.607443 | + | 0.197402i | ||||
\(775\) | 1.71445e7i | 1.02534i | ||||||||
\(776\) | 1.81445e7 | 1.08166 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.79168e6 | −0.579974 | ||||||||
\(779\) | − | 5.93974e6i | − | 0.350690i | ||||||
\(780\) | −482795. | − | 350753.i | −0.0284136 | − | 0.0206426i | ||||
\(781\) | −4.24627e6 | −0.249103 | ||||||||
\(782\) | 5.59259e6 | 0.327036 | ||||||||
\(783\) | −4.20686e6 | + | 1.29506e7i | −0.245219 | + | 0.754891i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.46998e6i | − | 0.0851406i | ||||||
\(786\) | −3.97462e6 | − | 2.88758e6i | −0.229477 | − | 0.166716i | ||||
\(787\) | − | 2.06482e7i | − | 1.18836i | −0.804334 | − | 0.594178i | \(-0.797478\pi\) | ||
0.804334 | − | 0.594178i | \(-0.202522\pi\) | |||||||
\(788\) | − | 1.73411e7i | − | 0.994856i | ||||||
\(789\) | −1.32924e7 | − | 9.65703e6i | −0.760172 | − | 0.552270i | ||||
\(790\) | 1.74290e6i | 0.0993586i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.24435e6 | + | 3.82908e6i | 0.0704902 | + | 0.216911i | ||||
\(793\) | −487226. | −0.0275136 | ||||||||
\(794\) | 9.71560e6 | 0.546913 | ||||||||
\(795\) | −8.36428e6 | − | 6.07670e6i | −0.469365 | − | 0.340996i | ||||
\(796\) | 1.70855e7i | 0.955751i | ||||||||
\(797\) | 2.91426e7 | 1.62511 | 0.812556 | − | 0.582884i | \(-0.198076\pi\) | ||||
0.812556 | + | 0.582884i | \(0.198076\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.64660e6 | 0.312911 | ||||||||
\(800\) | − | 3.16423e7i | − | 1.74800i | ||||||
\(801\) | 2.39921e6 | + | 7.38279e6i | 0.132125 | + | 0.406574i | ||||
\(802\) | −5.15565e6 | −0.283040 | ||||||||
\(803\) | 1.66456e6 | 0.0910983 | ||||||||
\(804\) | −1.61885e6 | + | 2.22827e6i | −0.0883216 | + | 0.121570i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 90764.4i | − | 0.00492128i | ||||||
\(807\) | 4.21374e6 | − | 5.80000e6i | 0.227763 | − | 0.313505i | ||||
\(808\) | 6.79435e6i | 0.366117i | ||||||||
\(809\) | 2.18383e7i | 1.17313i | 0.809901 | + | 0.586567i | \(0.199521\pi\) | ||||
−0.809901 | + | 0.586567i | \(0.800479\pi\) | |||||||
\(810\) | −7.03672e6 | − | 9.68326e6i | −0.376841 | − | 0.518572i | ||||
\(811\) | 2.56638e6i | 0.137015i | 0.997651 | + | 0.0685077i | \(0.0218238\pi\) | ||||
−0.997651 | + | 0.0685077i | \(0.978176\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.11699e7 | + | 8.11502e6i | 0.592685 | + | 0.430589i | ||||
\(814\) | 1.21009e6 | 0.0640114 | ||||||||
\(815\) | −2.75315e7 | −1.45190 | ||||||||
\(816\) | −3.56837e6 | + | 4.91168e6i | −0.187605 | + | 0.258229i | ||||
\(817\) | − | 1.11474e7i | − | 0.584279i | ||||||
\(818\) | −138590. | −0.00724184 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.85602e7 | −1.48329 | ||||||||
\(821\) | − | 965227.i | − | 0.0499771i | −0.999688 | − | 0.0249886i | \(-0.992045\pi\) | ||
0.999688 | − | 0.0249886i | \(-0.00795494\pi\) | |||||||
\(822\) | 4.42938e6 | − | 6.09683e6i | 0.228646 | − | 0.314720i | ||||
\(823\) | 2.07808e7 | 1.06945 | 0.534726 | − | 0.845025i | \(-0.320415\pi\) | ||||
0.534726 | + | 0.845025i | \(0.320415\pi\) | |||||||
\(824\) | −1.95023e7 | −1.00062 | ||||||||
\(825\) | 9.74002e6 | + | 7.07618e6i | 0.498224 | + | 0.361963i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.06026e6i | 0.257282i | 0.991691 | + | 0.128641i | \(0.0410615\pi\) | ||||
−0.991691 | + | 0.128641i | \(0.958939\pi\) | |||||||
\(828\) | 2.59752e7 | − | 8.44122e6i | 1.31669 | − | 0.427887i | ||||
\(829\) | 1.66931e7i | 0.843627i | 0.906683 | + | 0.421814i | \(0.138606\pi\) | ||||
−0.906683 | + | 0.421814i | \(0.861394\pi\) | |||||||
\(830\) | 6.41985e6i | 0.323467i | ||||||||
\(831\) | 7.05919e6 | − | 9.71664e6i | 0.354611 | − | 0.488105i | ||||
\(832\) | − | 117951.i | − | 0.00590734i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.50747e6 | − | 6.20431e6i | 0.224397 | − | 0.308872i | ||||
\(835\) | −3.30628e7 | −1.64106 | ||||||||
\(836\) | −1.94679e6 | −0.0963392 | ||||||||
\(837\) | −3.39495e6 | + | 1.04511e7i | −0.167502 | + | 0.515644i | ||||
\(838\) | 9.65809e6i | 0.475096i | ||||||||
\(839\) | −1.76055e7 | −0.863461 | −0.431731 | − | 0.902003i | \(-0.642097\pi\) | ||||
−0.431731 | + | 0.902003i | \(0.642097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.58926e6 | 0.370007 | ||||||||
\(842\) | 8.06000e6i | 0.391791i | ||||||||
\(843\) | −2.83865e7 | − | 2.06230e7i | −1.37576 | − | 0.999500i | ||||
\(844\) | −7.45982e6 | −0.360473 | ||||||||
\(845\) | −3.52719e7 | −1.69936 | ||||||||
\(846\) | −4.34507e6 | + | 1.41203e6i | −0.208723 | + | 0.0678294i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 4.24272e6i | − | 0.202607i | ||||||
\(849\) | 63918.5 | + | 46437.1i | 0.00304339 | + | 0.00221104i | ||||
\(850\) | − | 8.07268e6i | − | 0.383240i | ||||||
\(851\) | − | 1.77777e7i | − | 0.841495i | ||||||
\(852\) | 1.12497e7 | + | 8.17298e6i | 0.530936 | + | 0.385728i | ||||
\(853\) | − | 5.38585e6i | − | 0.253444i | −0.991938 | − | 0.126722i | \(-0.959554\pi\) | ||
0.991938 | − | 0.126722i | \(-0.0404456\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.19209e7 | − | 3.87398e6i | 0.557693 | − | 0.181235i | ||||
\(856\) | 1.94512e7 | 0.907321 | ||||||||
\(857\) | 2.24902e7 | 1.04602 | 0.523011 | − | 0.852326i | \(-0.324809\pi\) | ||||
0.523011 | + | 0.852326i | \(0.324809\pi\) | |||||||
\(858\) | −51564.6 | − | 37461.9i | −0.00239129 | − | 0.00173729i | ||||
\(859\) | − | 3.12962e7i | − | 1.44713i | −0.690255 | − | 0.723566i | \(-0.742502\pi\) | ||
0.690255 | − | 0.723566i | \(-0.257498\pi\) | |||||||
\(860\) | −5.36005e7 | −2.47128 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.41158e7 | −0.647051 | ||||||||
\(863\) | 1.79759e7i | 0.821604i | 0.911725 | + | 0.410802i | \(0.134751\pi\) | ||||
−0.911725 | + | 0.410802i | \(0.865249\pi\) | |||||||
\(864\) | 6.26581e6 | − | 1.92889e7i | 0.285557 | − | 0.879070i | ||||
\(865\) | −4.82998e7 | −2.19485 | ||||||||
\(866\) | 1.12146e7 | 0.508146 | ||||||||
\(867\) | 9.25056e6 | − | 1.27330e7i | 0.417946 | − | 0.575283i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.12356e6i | − | 0.0504717i | ||||||
\(870\) | 6.67655e6 | − | 9.18995e6i | 0.299057 | − | 0.411637i | ||||
\(871\) | − | 94425.1i | − | 0.00421737i | ||||||
\(872\) | 1.61960e7i | 0.721302i | ||||||||
\(873\) | 3.30724e7 | − | 1.07476e7i | 1.46869 | − | 0.477285i | ||||
\(874\) | − | 4.73850e6i | − | 0.209827i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.40995e6 | − | 3.20385e6i | −0.194166 | − | 0.141063i | ||||
\(877\) | 2.11950e7 | 0.930540 | 0.465270 | − | 0.885169i | \(-0.345957\pi\) | ||||
0.465270 | + | 0.885169i | \(0.345957\pi\) | |||||||
\(878\) | −888141. | −0.0388817 | ||||||||
\(879\) | −2.30678e7 | + | 3.17517e7i | −1.00701 | + | 1.38610i | ||||
\(880\) | 7.55296e6i | 0.328784i | ||||||||
\(881\) | −6.16325e6 | −0.267529 | −0.133764 | − | 0.991013i | \(-0.542707\pi\) | ||||
−0.133764 | + | 0.991013i | \(0.542707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.51180e7 | −0.652519 | −0.326260 | − | 0.945280i | \(-0.605788\pi\) | ||||
−0.326260 | + | 0.945280i | \(0.605788\pi\) | |||||||
\(884\) | − | 257955.i | − | 0.0111023i | ||||||
\(885\) | 3.48537e7 | − | 4.79745e7i | 1.49586 | − | 2.05898i | ||||
\(886\) | 1.49440e7 | 0.639562 | ||||||||
\(887\) | 2.42779e7 | 1.03610 | 0.518051 | − | 0.855350i | \(-0.326658\pi\) | ||||
0.518051 | + | 0.855350i | \(0.326658\pi\) | |||||||
\(888\) | −6.94298e6 | − | 5.04412e6i | −0.295470 | − | 0.214661i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 6.47584e6i | − | 0.274045i | ||||||
\(891\) | 4.53622e6 | + | 6.24231e6i | 0.191426 | + | 0.263422i | ||||
\(892\) | 7.03857e6i | 0.296191i | ||||||||
\(893\) | − | 4.78426e6i | − | 0.200764i | ||||||
\(894\) | 182852. | − | 251687.i | 0.00765168 | − | 0.0105322i | ||||
\(895\) | − | 3.80599e7i | − | 1.58822i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −550361. | + | 757545.i | −0.0228384 | + | 0.0314360i | ||||
\(898\) | −3.47689e6 | −0.143880 | ||||||||
\(899\) | −1.04280e7 | −0.430330 | ||||||||
\(900\) | −1.21846e7 | − | 3.74941e7i | −0.501422 | − | 1.54297i | ||||
\(901\) | − | 4.46900e6i | − | 0.183400i | ||||||
\(902\) | −3.05035e6 | −0.124834 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.14641e7 | 0.466572 | ||||||||
\(905\) | − | 1.01656e6i | − | 0.0412583i | ||||||
\(906\) | 3.72393e6 | + | 2.70546e6i | 0.150724 | + | 0.109502i | ||||
\(907\) | −2.06772e7 | −0.834591 | −0.417295 | − | 0.908771i | \(-0.637022\pi\) | ||||
−0.417295 | + | 0.908771i | \(0.637022\pi\) | |||||||
\(908\) | −3.23643e6 | −0.130272 | ||||||||
\(909\) | 4.02455e6 | + | 1.23843e7i | 0.161550 | + | 0.497120i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.74564e7i | 1.89452i | 0.320466 | + | 0.947260i | \(0.396161\pi\) | ||||
−0.320466 | + | 0.947260i | \(0.603839\pi\) | |||||||
\(912\) | 4.16157e6 | + | 3.02341e6i | 0.165680 | + | 0.120368i | ||||
\(913\) | − | 4.13856e6i | − | 0.164313i | ||||||
\(914\) | − | 1.78906e7i | − | 0.708370i | ||||||
\(915\) | −3.98110e7 | − | 2.89230e7i | −1.57199 | − | 1.14206i | ||||
\(916\) | 1.02610e7i | 0.404063i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.59855e6 | − | 4.92105e6i | 0.0626067 | − | 0.192731i | ||||
\(919\) | −4.98420e7 | −1.94674 | −0.973368 | − | 0.229249i | \(-0.926373\pi\) | ||||
−0.973368 | + | 0.229249i | \(0.926373\pi\) | |||||||
\(920\) | −4.93433e7 | −1.92202 | ||||||||
\(921\) | 2.91341e7 | + | 2.11661e7i | 1.13176 | + | 0.822227i | ||||
\(922\) | 397581.i | 0.0154028i | ||||||||
\(923\) | −476717. | −0.0184186 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.56614e7 | −0.986111 | ||||||||
\(926\) | 1.11731e7i | 0.428199i | ||||||||
\(927\) | −3.55474e7 | + | 1.15519e7i | −1.35865 | + | 0.441526i | ||||
\(928\) | 1.92462e7 | 0.733626 | ||||||||
\(929\) | 98732.8 | 0.00375338 | 0.00187669 | − | 0.999998i | \(-0.499403\pi\) | ||||
0.00187669 | + | 0.999998i | \(0.499403\pi\) | |||||||
\(930\) | 5.38799e6 | − | 7.41631e6i | 0.204277 | − | 0.281178i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.47210e7i | 1.30934i | ||||||||
\(933\) | 2.15577e7 | − | 2.96732e7i | 0.810772 | − | 1.11599i | ||||
\(934\) | − | 1.20329e6i | − | 0.0451338i | ||||||
\(935\) | 7.95579e6i | 0.297615i | ||||||||
\(936\) | 139700. | + | 429881.i | 0.00521202 | + | 0.0160383i | ||||
\(937\) | 2.17619e7i | 0.809743i | 0.914373 | + | 0.404872i | \(0.132684\pi\) | ||||
−0.914373 | + | 0.404872i | \(0.867316\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.51118e7 | − | 1.82438e7i | −0.929422 | − | 0.675231i | ||||
\(940\) | −2.30042e7 | −0.849158 | ||||||||
\(941\) | 2.89614e7 | 1.06622 | 0.533109 | − | 0.846046i | \(-0.321023\pi\) | ||||
0.533109 | + | 0.846046i | \(0.321023\pi\) | |||||||
\(942\) | −302185. | + | 415943.i | −0.0110955 | + | 0.0152724i | ||||
\(943\) | 4.48133e7i | 1.64107i | ||||||||
\(944\) | 2.43347e7 | 0.888784 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.72476e6 | −0.207984 | ||||||||
\(947\) | − | 3.11506e7i | − | 1.12873i | −0.825524 | − | 0.564367i | \(-0.809120\pi\) | ||
0.825524 | − | 0.564367i | \(-0.190880\pi\) | |||||||
\(948\) | −2.16257e6 | + | 2.97667e6i | −0.0781537 | + | 0.107575i | ||||
\(949\) | 186876. | 0.00673577 | ||||||||
\(950\) | −6.83983e6 | −0.245887 | ||||||||
\(951\) | 2.64065e7 | + | 1.91845e7i | 0.946804 | + | 0.687859i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.07840e6i | − | 0.216799i | −0.994107 | − | 0.108399i | \(-0.965427\pi\) | ||
0.994107 | − | 0.108399i | \(-0.0345725\pi\) | |||||||
\(954\) | 1.11755e6 | + | 3.43891e6i | 0.0397554 | + | 0.122335i | ||||
\(955\) | 1.87493e7i | 0.665238i | ||||||||
\(956\) | 1.42974e7i | 0.505955i | ||||||||
\(957\) | −4.30404e6 | + | 5.92430e6i | −0.151913 | + | 0.209102i | ||||
\(958\) | − | 5.75230e6i | − | 0.202501i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 7.00184e6 | − | 9.63769e6i | 0.245208 | − | 0.337516i | ||||
\(961\) | 2.02137e7 | 0.706054 | ||||||||
\(962\) | 135854. | 0.00473297 | ||||||||
\(963\) | 3.54542e7 | − | 1.15217e7i | 1.23198 | − | 0.400359i | ||||
\(964\) | − | 2.61970e7i | − | 0.907943i | ||||||
\(965\) | 1.19301e7 | 0.412407 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 412575. | 0.0141885 | 0.00709426 | − | 0.999975i | \(-0.497742\pi\) | ||||
0.00709426 | + | 0.999975i | \(0.497742\pi\) | |||||||
\(968\) | − | 1.82544e7i | − | 0.626151i | ||||||
\(969\) | 4.38353e6 | + | 3.18466e6i | 0.149973 | + | 0.108957i | ||||
\(970\) | −2.90096e7 | −0.989949 | ||||||||
\(971\) | −2.34602e7 | −0.798516 | −0.399258 | − | 0.916839i | \(-0.630732\pi\) | ||||
−0.399258 | + | 0.916839i | \(0.630732\pi\) | |||||||
\(972\) | −3038.63 | − | 2.52689e7i | −0.000103160 | − | 0.857870i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.06448e6i | 0.204831i | ||||||||
\(975\) | 1.09349e6 | + | 794424.i | 0.0368385 | + | 0.0267634i | ||||
\(976\) | − | 2.01939e7i | − | 0.678571i | ||||||
\(977\) | 1.56531e7i | 0.524643i | 0.964981 | + | 0.262322i | \(0.0844881\pi\) | ||||
−0.964981 | + | 0.262322i | \(0.915512\pi\) | |||||||
\(978\) | 7.79026e6 | + | 5.65967e6i | 0.260438 | + | 0.189210i | ||||
\(979\) | 4.17465e6i | 0.139208i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.59352e6 | + | 2.95210e7i | 0.318277 | + | 0.979396i | ||||
\(982\) | −1.57594e7 | −0.521509 | ||||||||
\(983\) | −6.11410e6 | −0.201813 | −0.100906 | − | 0.994896i | \(-0.532174\pi\) | ||||
−0.100906 | + | 0.994896i | \(0.532174\pi\) | |||||||
\(984\) | 1.75016e7 | + | 1.27150e7i | 0.576222 | + | 0.418629i | ||||
\(985\) | 6.00437e7i | 1.97186i | ||||||||
\(986\) | 4.91015e6 | 0.160843 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −218561. | −0.00712327 | ||||||||
\(989\) | 8.41036e7i | 2.73416i | ||||||||
\(990\) | −1.98948e6 | − | 6.12200e6i | −0.0645137 | − | 0.198520i | ||||
\(991\) | −3.56283e7 | −1.15242 | −0.576211 | − | 0.817301i | \(-0.695469\pi\) | ||||
−0.576211 | + | 0.817301i | \(0.695469\pi\) | |||||||
\(992\) | 1.55317e7 | 0.501119 | ||||||||
\(993\) | −2.52188e6 | + | 3.47125e6i | −0.0811617 | + | 0.111715i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.91588e7i | − | 1.89436i | ||||||
\(996\) | −7.96567e6 | + | 1.09644e7i | −0.254433 | + | 0.350215i | ||||
\(997\) | 5.76360e7i | 1.83635i | 0.396171 | + | 0.918177i | \(0.370339\pi\) | ||||
−0.396171 | + | 0.918177i | \(0.629661\pi\) | |||||||
\(998\) | − | 4.55693e6i | − | 0.144826i | ||||||
\(999\) | −1.56430e7 | − | 5.08148e6i | −0.495914 | − | 0.161093i |
(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 | 147.6.c.c.146.7 | 16 | ||
3.2 | odd | 2 | inner | 147.6.c.c.146.10 | 16 | ||
7.2 | even | 3 | 21.6.g.c.17.4 | yes | 16 | ||
7.3 | odd | 6 | 21.6.g.c.5.5 | yes | 16 | ||
7.6 | odd | 2 | inner | 147.6.c.c.146.8 | 16 | ||
21.2 | odd | 6 | 21.6.g.c.17.5 | yes | 16 | ||
21.17 | even | 6 | 21.6.g.c.5.4 | ✓ | 16 | ||
21.20 | even | 2 | inner | 147.6.c.c.146.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.g.c.5.4 | ✓ | 16 | 21.17 | even | 6 | ||
21.6.g.c.5.5 | yes | 16 | 7.3 | odd | 6 | ||
21.6.g.c.17.4 | yes | 16 | 7.2 | even | 3 | ||
21.6.g.c.17.5 | yes | 16 | 21.2 | odd | 6 | ||
147.6.c.c.146.7 | 16 | 1.1 | even | 1 | trivial | ||
147.6.c.c.146.8 | 16 | 7.6 | odd | 2 | inner | ||
147.6.c.c.146.9 | 16 | 21.20 | even | 2 | inner | ||
147.6.c.c.146.10 | 16 | 3.2 | odd | 2 | inner |