Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,5,Mod(73,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("168.73");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.z (of order \(6\), degree \(2\), 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: | \(17.3661537981\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 99 x^{14} - 1810 x^{13} + 14212 x^{12} - 199882 x^{11} + 1800935 x^{10} + \cdots + 41390114348800 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{36}\cdot 7^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.3 | ||
Root | \(2.19101 + 3.06642i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.73 |
Dual form | 168.5.z.a.145.3 |
$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.50000 | − | 2.59808i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.72797 | + | 3.88439i | −0.269119 | + | 0.155376i | −0.628487 | − | 0.777820i | \(-0.716326\pi\) |
0.359368 | + | 0.933196i | \(0.382992\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −35.4710 | − | 33.8055i | −0.723897 | − | 0.689908i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.5000 | + | 23.3827i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.76101 | − | 11.7104i | 0.0558762 | − | 0.0967803i | −0.836734 | − | 0.547609i | \(-0.815538\pi\) |
0.892610 | + | 0.450829i | \(0.148871\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 75.5898i | 0.447277i | 0.974672 | + | 0.223638i | \(0.0717935\pi\) | ||||
−0.974672 | + | 0.223638i | \(0.928207\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 40.3678 | 0.179412 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 117.962 | + | 68.1055i | 0.408174 | + | 0.235659i | 0.690005 | − | 0.723805i | \(-0.257608\pi\) |
−0.281831 | + | 0.959464i | \(0.590942\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36.5610 | − | 21.1085i | 0.101277 | − | 0.0584723i | −0.448506 | − | 0.893780i | \(-0.648044\pi\) |
0.549783 | + | 0.835307i | \(0.314710\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 71.7902 | + | 244.281i | 0.162790 | + | 0.553925i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 185.061 | + | 320.535i | 0.349831 | + | 0.605926i | 0.986219 | − | 0.165443i | \(-0.0529055\pi\) |
−0.636388 | + | 0.771369i | \(0.719572\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −282.323 | + | 488.998i | −0.451717 | + | 0.782396i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 500.906 | 0.595607 | 0.297804 | − | 0.954627i | \(-0.403746\pi\) | ||||
0.297804 | + | 0.954627i | \(0.403746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 771.688 | + | 445.534i | 0.803006 | + | 0.463616i | 0.844521 | − | 0.535522i | \(-0.179885\pi\) |
−0.0415154 | + | 0.999138i | \(0.513219\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −60.8491 | + | 35.1313i | −0.0558762 | + | 0.0322601i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 369.961 | + | 89.6589i | 0.302009 | + | 0.0731909i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1143.66 | + | 1980.87i | 0.835395 | + | 1.44695i | 0.893709 | + | 0.448648i | \(0.148094\pi\) |
−0.0583137 | + | 0.998298i | \(0.518572\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 196.388 | − | 340.154i | 0.129118 | − | 0.223638i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1038.61i | 0.617853i | 0.951086 | + | 0.308927i | \(0.0999698\pi\) | ||||
−0.951086 | + | 0.308927i | \(0.900030\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1936.96 | 1.04757 | 0.523787 | − | 0.851849i | \(-0.324519\pi\) | ||||
0.523787 | + | 0.851849i | \(0.324519\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −181.655 | − | 104.879i | −0.0897062 | − | 0.0517919i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 668.768 | − | 386.113i | 0.302747 | − | 0.174791i | −0.340929 | − | 0.940089i | \(-0.610742\pi\) |
0.643676 | + | 0.765298i | \(0.277408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 115.380 | + | 2398.23i | 0.0480551 | + | 0.998845i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −353.886 | − | 612.949i | −0.136058 | − | 0.235659i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −370.015 | + | 640.885i | −0.131725 | + | 0.228154i | −0.924342 | − | 0.381566i | \(-0.875385\pi\) |
0.792617 | + | 0.609720i | \(0.208718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 105.050i | 0.0347272i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −219.366 | −0.0675180 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2540.86 | − | 1466.96i | −0.729922 | − | 0.421420i | 0.0884719 | − | 0.996079i | \(-0.471802\pi\) |
−0.818393 | + | 0.574658i | \(0.805135\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3016.80 | + | 1741.75i | −0.810750 | + | 0.468087i | −0.847216 | − | 0.531248i | \(-0.821723\pi\) |
0.0364661 | + | 0.999335i | \(0.488390\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 311.605 | − | 1285.78i | 0.0785096 | − | 0.323956i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −293.621 | − | 508.566i | −0.0694960 | − | 0.120371i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −844.320 | + | 1462.41i | −0.188086 | + | 0.325775i | −0.944612 | − | 0.328189i | \(-0.893562\pi\) |
0.756526 | + | 0.653964i | \(0.226895\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1923.21i | − | 0.403951i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2285.68 | 0.453417 | 0.226709 | − | 0.973963i | \(-0.427203\pi\) | ||||
0.226709 | + | 0.973963i | \(0.427203\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1222.01 | − | 705.526i | −0.229313 | − | 0.132394i | 0.380942 | − | 0.924599i | \(-0.375600\pi\) |
−0.610255 | + | 0.792205i | \(0.708933\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2540.91 | − | 1466.99i | 0.451717 | − | 0.260799i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −635.696 | + | 186.821i | −0.107218 | + | 0.0315097i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 365.793 | + | 633.573i | 0.0586113 | + | 0.101518i | 0.893842 | − | 0.448382i | \(-0.147999\pi\) |
−0.835231 | + | 0.549899i | \(0.814666\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −364.500 | + | 631.333i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10031.8i | − | 1.45620i | −0.685468 | − | 0.728102i | \(-0.740403\pi\) | ||
0.685468 | − | 0.728102i | \(-0.259597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1058.19 | −0.146463 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2254.08 | − | 1301.39i | −0.297804 | − | 0.171937i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1956.82 | − | 1129.77i | 0.247042 | − | 0.142630i | −0.371367 | − | 0.928486i | \(-0.621111\pi\) |
0.618409 | + | 0.785856i | \(0.287777\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2555.35 | − | 2681.24i | 0.308580 | − | 0.323783i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2315.07 | − | 4009.81i | −0.267669 | − | 0.463616i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −163.988 | + | 284.035i | −0.0181704 | + | 0.0314720i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7671.75i | 0.815363i | 0.913124 | + | 0.407681i | \(0.133663\pi\) | ||||
−0.913124 | + | 0.407681i | \(0.866337\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 365.095 | 0.0372508 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12570.9 | − | 7257.81i | −1.23232 | − | 0.711480i | −0.264807 | − | 0.964302i | \(-0.585308\pi\) |
−0.967513 | + | 0.252821i | \(0.918641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2354.59 | + | 1359.43i | −0.221943 | + | 0.128139i | −0.606850 | − | 0.794817i | \(-0.707567\pi\) |
0.384907 | + | 0.922956i | \(0.374234\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1431.89 | − | 1364.65i | −0.129876 | − | 0.123778i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7840.05 | − | 13579.4i | −0.684780 | − | 1.18607i | −0.973506 | − | 0.228662i | \(-0.926565\pi\) |
0.288726 | − | 0.957412i | \(-0.406768\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7883.54 | + | 13654.7i | −0.663541 | + | 1.14929i | 0.316137 | + | 0.948714i | \(0.397614\pi\) |
−0.979679 | + | 0.200574i | \(0.935719\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 11885.2i | − | 0.964631i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11151.6 | 0.873337 | 0.436669 | − | 0.899622i | \(-0.356158\pi\) | ||||
0.436669 | + | 0.899622i | \(0.356158\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2490.17 | − | 1437.70i | −0.188292 | − | 0.108711i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1767.49 | + | 1020.46i | −0.129118 | + | 0.0745462i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1881.89 | − | 6403.53i | −0.132893 | − | 0.452195i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7229.08 | + | 12521.1i | 0.493756 | + | 0.855210i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2698.39 | − | 4673.75i | 0.178359 | − | 0.308927i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 9242.11i | − | 0.591495i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14759.9 | 0.915114 | 0.457557 | − | 0.889180i | \(-0.348725\pi\) | ||||
0.457557 | + | 0.889180i | \(0.348725\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8716.33 | − | 5032.38i | −0.523787 | − | 0.302408i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13084.4 | + | 7554.29i | −0.762451 | + | 0.440201i | −0.830175 | − | 0.557503i | \(-0.811760\pi\) |
0.0677241 | + | 0.997704i | \(0.478426\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2010.44 | − | 487.223i | −0.113655 | − | 0.0275438i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 544.965 | + | 943.908i | 0.0299021 | + | 0.0517919i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6215.33 | − | 10765.3i | 0.331149 | − | 0.573567i | −0.651588 | − | 0.758573i | \(-0.725897\pi\) |
0.982737 | + | 0.185006i | \(0.0592304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4634.36i | 0.239861i | 0.992782 | + | 0.119931i | \(0.0382672\pi\) | ||||
−0.992782 | + | 0.119931i | \(0.961733\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4012.61 | −0.201831 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 885.188 | + | 511.064i | 0.0432876 | + | 0.0249921i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3370.08 | + | 1945.72i | −0.160289 | + | 0.0925430i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5711.56 | − | 11091.8i | 0.264314 | − | 0.513295i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2515.53 | + | 4357.03i | 0.113307 | + | 0.196254i | 0.917102 | − | 0.398653i | \(-0.130522\pi\) |
−0.803795 | + | 0.594907i | \(0.797189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17177.3 | + | 29752.0i | −0.753359 | + | 1.30486i | 0.192827 | + | 0.981233i | \(0.438234\pi\) |
−0.946186 | + | 0.323623i | \(0.895099\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3677.70i | 0.157106i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6922.53 | −0.288138 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4995.16 | − | 2883.96i | −0.202652 | − | 0.117001i | 0.395240 | − | 0.918578i | \(-0.370661\pi\) |
−0.597892 | + | 0.801577i | \(0.703995\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3330.13 | − | 1922.65i | 0.131725 | − | 0.0760514i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4271.54 | − | 17625.7i | 0.164791 | − | 0.679979i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6124.36 | + | 10607.7i | 0.230508 | + | 0.399251i | 0.957958 | − | 0.286910i | \(-0.0926279\pi\) |
−0.727450 | + | 0.686161i | \(0.759295\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 272.927 | − | 472.724i | 0.0100249 | − | 0.0173636i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 51247.9i | 1.83757i | 0.394762 | + | 0.918783i | \(0.370827\pi\) | ||||
−0.394762 | + | 0.918783i | \(0.629173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22847.2 | 0.799943 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 987.147 | + | 569.930i | 0.0337590 | + | 0.0194908i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 45699.5 | − | 26384.6i | 1.52693 | − | 0.881574i | 0.527442 | − | 0.849591i | \(-0.323151\pi\) |
0.999488 | − | 0.0319829i | \(-0.0101822\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26545.1 | − | 7801.17i | 0.866778 | − | 0.254732i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7622.57 | + | 13202.7i | 0.243307 | + | 0.421420i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24843.8 | + | 43030.8i | −0.775376 | + | 1.34299i | 0.159207 | + | 0.987245i | \(0.449106\pi\) |
−0.934583 | + | 0.355746i | \(0.884227\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21949.2i | 0.669980i | 0.942222 | + | 0.334990i | \(0.108733\pi\) | ||||
−0.942222 | + | 0.334990i | \(0.891267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18100.8 | 0.540500 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15389.0 | − | 8884.82i | −0.449641 | − | 0.259600i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1595.09 | − | 920.924i | 0.0456143 | − | 0.0263354i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4742.78 | + | 4976.44i | −0.132773 | + | 0.139314i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 30573.5 | + | 52954.9i | 0.838067 | + | 1.45157i | 0.891509 | + | 0.453003i | \(0.149647\pi\) |
−0.0534418 | + | 0.998571i | \(0.517019\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7496.00 | + | 12983.5i | −0.201240 | + | 0.348559i | −0.948928 | − | 0.315492i | \(-0.897831\pi\) |
0.747688 | + | 0.664050i | \(0.231164\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3051.39i | 0.0802471i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 69960.1 | 1.80268 | 0.901339 | − | 0.433114i | \(-0.142585\pi\) | ||||
0.901339 | + | 0.433114i | \(0.142585\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20926.9 | + | 12082.2i | 0.528444 | + | 0.305098i | 0.740383 | − | 0.672186i | \(-0.234644\pi\) |
−0.211938 | + | 0.977283i | \(0.567978\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7598.88 | − | 4387.22i | 0.188086 | − | 0.108592i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17767.6 | − | 16933.4i | −0.431159 | − | 0.410914i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4034.38 | − | 6987.75i | −0.0959995 | − | 0.166276i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4996.64 | + | 8654.44i | −0.116610 | + | 0.201975i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 570.860i | − | 0.0130688i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10962.5 | −0.246232 | −0.123116 | − | 0.992392i | \(-0.539289\pi\) | ||||
−0.123116 | + | 0.992392i | \(0.539289\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10285.5 | − | 5938.36i | −0.226709 | − | 0.130890i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13031.8 | + | 7523.93i | −0.281922 | + | 0.162768i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12311.0 | − | 41890.8i | −0.261442 | − | 0.889610i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3666.02 | + | 6349.74i | 0.0764376 | + | 0.132394i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5148.08 | + | 8916.74i | −0.105405 | + | 0.182567i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21364.5i | 0.429618i | 0.976656 | + | 0.214809i | \(0.0689129\pi\) | ||||
−0.976656 | + | 0.214809i | \(0.931087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15245.4 | −0.301144 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −49907.4 | − | 28814.1i | −0.968531 | − | 0.559182i | −0.0697428 | − | 0.997565i | \(-0.522218\pi\) |
−0.898788 | + | 0.438383i | \(0.855551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30360.2 | − | 17528.5i | 0.578940 | − | 0.334251i | −0.181772 | − | 0.983341i | \(-0.558183\pi\) |
0.760712 | + | 0.649090i | \(0.224850\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3346.01 | + | 810.893i | 0.0627051 | + | 0.0151964i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4261.59 | − | 7381.29i | −0.0784982 | − | 0.135963i | 0.824104 | − | 0.566439i | \(-0.191679\pi\) |
−0.902602 | + | 0.430476i | \(0.858346\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2999.63 | + | 5195.52i | −0.0543166 | + | 0.0940790i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 3801.44i | − | 0.0676785i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26435.0 | −0.462789 | −0.231395 | − | 0.972860i | \(-0.574329\pi\) | ||||
−0.231395 | + | 0.972860i | \(0.574329\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −66270.4 | − | 38261.2i | −1.14100 | − | 0.658756i | −0.194322 | − | 0.980938i | \(-0.562251\pi\) |
−0.946678 | + | 0.322181i | \(0.895584\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3280.50 | − | 1894.00i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10091.9 | − | 15687.0i | −0.168129 | − | 0.261341i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1595.59 | + | 2763.64i | 0.0261533 | + | 0.0452989i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −26063.4 | + | 45143.1i | −0.420370 | + | 0.728102i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 32807.4i | − | 0.520743i | −0.965508 | − | 0.260372i | \(-0.916155\pi\) | ||
0.965508 | − | 0.260372i | \(-0.0838451\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5004.80 | 0.0781889 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4761.87 | + | 2749.27i | 0.0732314 | + | 0.0422802i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 62322.5 | − | 35981.9i | 0.943579 | − | 0.544776i | 0.0524986 | − | 0.998621i | \(-0.483281\pi\) |
0.891080 | + | 0.453845i | \(0.149948\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26397.6 | − | 108925.i | 0.393519 | − | 1.62379i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6762.23 | + | 11712.5i | 0.0992679 | + | 0.171937i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −50349.3 | + | 87207.6i | −0.727917 | + | 1.26079i | 0.229845 | + | 0.973227i | \(0.426178\pi\) |
−0.957762 | + | 0.287562i | \(0.907155\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5749.14i | − | 0.0818674i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11740.9 | −0.164695 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −38269.8 | − | 22095.1i | −0.528874 | − | 0.305345i | 0.211684 | − | 0.977338i | \(-0.432105\pi\) |
−0.740558 | + | 0.671993i | \(0.765439\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32492.4 | − | 18759.5i | 0.442428 | − | 0.255436i | −0.262199 | − | 0.965014i | \(-0.584448\pi\) |
0.704627 | + | 0.709578i | \(0.251114\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18465.1 | + | 5426.61i | −0.247758 | + | 0.0728120i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3817.58 | + | 6612.24i | 0.0504804 | + | 0.0874346i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12551.1 | − | 21739.2i | 0.163577 | − | 0.283324i | −0.772572 | − | 0.634927i | \(-0.781030\pi\) |
0.936149 | + | 0.351603i | \(0.114363\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24058.9i | 0.309077i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22667.1 | 0.287067 | 0.143533 | − | 0.989645i | \(-0.454154\pi\) | ||||
0.143533 | + | 0.989645i | \(0.454154\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −119088. | − | 68755.7i | −1.48695 | − | 0.858491i | −0.487061 | − | 0.873368i | \(-0.661931\pi\) |
−0.999889 | + | 0.0148762i | \(0.995265\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1475.89 | − | 852.104i | 0.0181704 | − | 0.0104907i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35110.8 | − | 36840.6i | 0.426262 | − | 0.447263i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −32483.8 | − | 56263.6i | −0.388930 | − | 0.673646i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19931.8 | − | 34522.9i | 0.235375 | − | 0.407681i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 88726.2i | 1.03351i | 0.856132 | + | 0.516757i | \(0.172861\pi\) | ||||
−0.856132 | + | 0.516757i | \(0.827139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22793.1 | 0.261914 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1642.93 | − | 948.544i | −0.0186254 | − | 0.0107534i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24229.2 | + | 13988.7i | −0.271017 | + | 0.156472i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −68706.0 | − | 65479.9i | −0.758336 | − | 0.722729i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 37712.7 | + | 65320.3i | 0.410773 | + | 0.711480i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13531.3 | − | 23436.9i | 0.145459 | − | 0.251942i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 168464.i | − | 1.78744i | −0.448629 | − | 0.893718i | \(-0.648088\pi\) | ||
0.448629 | − | 0.893718i | \(-0.351912\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14127.6 | 0.147962 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −43728.1 | − | 25246.5i | −0.452106 | − | 0.261024i | 0.256613 | − | 0.966514i | \(-0.417393\pi\) |
−0.708719 | + | 0.705491i | \(0.750727\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −73627.9 | + | 42509.1i | −0.751543 | + | 0.433903i | −0.826251 | − | 0.563302i | \(-0.809531\pi\) |
0.0747084 | + | 0.997205i | \(0.476197\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2898.01 | + | 9861.09i | 0.0292065 | + | 0.0993811i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30813.9 | + | 53371.3i | 0.306640 | + | 0.531116i | 0.977625 | − | 0.210355i | \(-0.0674619\pi\) |
−0.670985 | + | 0.741471i | \(0.734129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3386.63 | − | 5865.82i | 0.0332803 | − | 0.0576431i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 81476.2i | 0.790716i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5750.42 | 0.0551181 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −36963.2 | − | 21340.7i | −0.349948 | − | 0.202042i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 70951.8 | − | 40964.1i | 0.663541 | − | 0.383096i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −36774.6 | − | 8912.19i | −0.339747 | − | 0.0823366i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −58966.7 | − | 102133.i | −0.538208 | − | 0.932204i | −0.999001 | − | 0.0446963i | \(-0.985768\pi\) |
0.460792 | − | 0.887508i | \(-0.347565\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −30878.7 | + | 53483.5i | −0.278465 | + | 0.482315i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 13118.7i | − | 0.116896i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 168112. | 1.48027 | 0.740134 | − | 0.672460i | \(-0.234762\pi\) | ||||
0.740134 | + | 0.672460i | \(0.234762\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −50182.4 | − | 28972.8i | −0.436669 | − | 0.252111i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10434.8 | − | 6024.53i | 0.0897377 | − | 0.0518101i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 76980.5 | − | 88967.9i | 0.654324 | − | 0.756215i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7470.50 | + | 12939.3i | 0.0627641 | + | 0.108711i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34494.3 | + | 59745.9i | −0.286476 | + | 0.496191i | −0.972966 | − | 0.230948i | \(-0.925817\pi\) |
0.686490 | + | 0.727139i | \(0.259151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 55130.4i | 0.452626i | 0.974055 | + | 0.226313i | \(0.0726673\pi\) | ||||
−0.974055 | + | 0.226313i | \(0.927333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10605.0 | 0.0860785 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −41940.6 | − | 24214.4i | −0.336578 | − | 0.194323i | 0.322180 | − | 0.946678i | \(-0.395584\pi\) |
−0.658758 | + | 0.752355i | \(0.728918\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15378.0 | + | 8878.47i | −0.122023 | + | 0.0704501i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8168.34 | + | 33705.2i | −0.0640911 | + | 0.264460i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 95322.9 | + | 165104.i | 0.739619 | + | 1.28106i | 0.952667 | + | 0.304016i | \(0.0983277\pi\) |
−0.213048 | + | 0.977042i | \(0.568339\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −64269.4 | + | 111318.i | −0.493162 | + | 0.854182i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 75126.8i | − | 0.570140i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10962.2 | 0.0822831 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 124732. | + | 72014.1i | 0.926075 | + | 0.534669i | 0.885568 | − | 0.464510i | \(-0.153769\pi\) |
0.0405067 | + | 0.999179i | \(0.487103\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24285.5 | + | 14021.3i | −0.178359 | + | 0.102976i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34790.2 | − | 10224.3i | 0.252760 | − | 0.0742822i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −43720.7 | − | 75726.5i | −0.314246 | − | 0.544290i | 0.665031 | − | 0.746816i | \(-0.268418\pi\) |
−0.979277 | + | 0.202526i | \(0.935085\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24011.7 | + | 41589.5i | −0.170750 | + | 0.295747i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37863.4i | 0.266401i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20646.4 | 0.143736 | 0.0718682 | − | 0.997414i | \(-0.477104\pi\) | ||||
0.0718682 | + | 0.997414i | \(0.477104\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −66419.4 | − | 38347.3i | −0.457557 | − | 0.264171i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 38723.4 | − | 22357.0i | 0.263983 | − | 0.152411i | −0.362167 | − | 0.932113i | \(-0.617963\pi\) |
0.626150 | + | 0.779702i | \(0.284630\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3551.26 | − | 3726.22i | 0.0239586 | − | 0.0251389i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26149.0 | + | 45291.4i | 0.174596 | + | 0.302408i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −51436.1 | + | 89090.0i | −0.339914 | + | 0.588749i | −0.984416 | − | 0.175854i | \(-0.943731\pi\) |
0.644502 | + | 0.764603i | \(0.277065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50414.6i | 0.329764i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 78506.5 | 0.508301 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4922.09 | − | 2841.77i | −0.0315468 | − | 0.0182136i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −57688.7 | + | 33306.6i | −0.366024 | + | 0.211324i | −0.671720 | − | 0.740805i | \(-0.734444\pi\) |
0.305696 | + | 0.952129i | \(0.401111\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7781.13 | + | 7415.77i | 0.0488761 | + | 0.0465812i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15514.3 | − | 26871.6i | −0.0964816 | − | 0.167111i | 0.813744 | − | 0.581223i | \(-0.197426\pi\) |
−0.910226 | + | 0.414112i | \(0.864092\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33677.9 | + | 58331.8i | −0.207365 | + | 0.359166i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 5663.45i | − | 0.0345279i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30929.1 | 0.186715 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 112001. | + | 64663.7i | 0.669537 | + | 0.386557i | 0.795901 | − | 0.605427i | \(-0.206998\pi\) |
−0.126364 | + | 0.991984i | \(0.540331\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −55938.0 | + | 32295.8i | −0.331149 | + | 0.191189i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40535.3 | + | 137930.i | 0.237647 | + | 0.808644i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38967.4 | + | 67493.6i | 0.226259 | + | 0.391892i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12040.4 | − | 20854.6i | 0.0692420 | − | 0.119931i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 226622.i | − | 1.29085i | −0.763826 | − | 0.645423i | \(-0.776681\pi\) | ||
0.763826 | − | 0.645423i | \(-0.223319\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 174587. | 0.985024 | 0.492512 | − | 0.870306i | \(-0.336079\pi\) | ||||
0.492512 | + | 0.870306i | \(0.336079\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18056.7 | + | 10425.1i | 0.100916 | + | 0.0582637i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −66606.8 | + | 38455.5i | −0.368758 | + | 0.212902i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 165890. | + | 40202.8i | 0.909837 | + | 0.220496i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2655.57 | − | 4599.57i | −0.0144292 | − | 0.0249921i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22934.0 | − | 39722.8i | 0.123459 | − | 0.213838i | −0.797670 | − | 0.603094i | \(-0.793934\pi\) |
0.921130 | + | 0.389256i | \(0.127268\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 278272.i | 1.48420i | 0.670287 | + | 0.742102i | \(0.266171\pi\) | ||||
−0.670287 | + | 0.742102i | \(0.733829\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20220.5 | 0.106859 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13532.0 | + | 7812.72i | 0.0708598 | + | 0.0409109i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −66629.0 | + | 38468.3i | −0.345728 | + | 0.199606i | −0.662802 | − | 0.748795i | \(-0.730633\pi\) |
0.317074 | + | 0.948401i | \(0.397300\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −54519.3 | + | 35074.0i | −0.280332 | + | 0.180346i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 43415.8 | + | 75198.4i | 0.221228 | + | 0.383178i | 0.955181 | − | 0.296022i | \(-0.0956601\pi\) |
−0.733953 | + | 0.679200i | \(0.762327\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8776.95 | + | 15202.1i | −0.0443225 | + | 0.0767687i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 26142.2i | − | 0.130836i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 238675. | 1.18390 | 0.591949 | − | 0.805976i | \(-0.298359\pi\) | ||||
0.591949 | + | 0.805976i | \(0.298359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12162.6 | + | 7022.07i | 0.0597961 | + | 0.0345233i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 154596. | − | 89256.1i | 0.753359 | − | 0.434952i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6777.30 | + | 27965.3i | −0.0327366 | + | 0.135082i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −72057.2 | − | 124807.i | −0.345021 | − | 0.597593i | 0.640337 | − | 0.768094i | \(-0.278795\pi\) |
−0.985358 | + | 0.170501i | \(0.945461\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9554.93 | − | 16549.6i | 0.0453526 | − | 0.0785530i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 195405.i | 0.919462i | 0.888058 | + | 0.459731i | \(0.152054\pi\) | ||||
−0.888058 | + | 0.459731i | \(0.847946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −155163. | −0.723813 | −0.361906 | − | 0.932214i | \(-0.617874\pi\) | ||||
−0.361906 | + | 0.932214i | \(0.617874\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31151.4 | + | 17985.3i | 0.144069 | + | 0.0831784i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 266635. | − | 153942.i | 1.22260 | − | 0.705866i | 0.257125 | − | 0.966378i | \(-0.417225\pi\) |
0.965471 | + | 0.260512i | \(0.0838914\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 79386.2 | − | 23330.3i | 0.360910 | − | 0.106066i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14985.5 | + | 25955.6i | 0.0675505 | + | 0.117001i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13095.8 | − | 22682.7i | 0.0585344 | − | 0.101385i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23837.7i | 0.105652i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19980.8 | −0.0878165 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 82401.4 | + | 47574.5i | 0.359140 | + | 0.207349i | 0.668703 | − | 0.743529i | \(-0.266850\pi\) |
−0.309564 | + | 0.950879i | \(0.600183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −149734. | + | 86448.7i | −0.647186 | + | 0.373653i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −65015.0 | + | 68218.1i | −0.278689 | + | 0.292419i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29800.1 | − | 51615.3i | −0.126688 | − | 0.219429i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −54230.5 | + | 93929.9i | −0.228657 | + | 0.396046i | −0.957410 | − | 0.288730i | \(-0.906767\pi\) |
0.728753 | + | 0.684777i | \(0.240100\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 63646.2i | − | 0.266167i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −328876. | −1.36417 | −0.682087 | − | 0.731271i | \(-0.738927\pi\) | ||||
−0.682087 | + | 0.731271i | \(0.738927\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 59087.9 | + | 34114.4i | 0.243111 | + | 0.140360i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2456.35 | + | 1418.17i | −0.0100249 | + | 0.00578787i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −81075.2 | − | 77268.4i | −0.328228 | − | 0.312816i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22002.2 | + | 38108.9i | 0.0883618 | + | 0.153047i | 0.906819 | − | 0.421521i | \(-0.138503\pi\) |
−0.818457 | + | 0.574568i | \(0.805170\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 133146. | − | 230616.i | 0.530460 | − | 0.918783i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 481813.i | − | 1.90433i | −0.305580 | − | 0.952166i | \(-0.598850\pi\) | ||
0.305580 | − | 0.952166i | \(-0.401150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 112769. | 0.442187 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −102812. | − | 59358.7i | −0.399972 | − | 0.230924i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −232170. | + | 134043.i | −0.896128 | + | 0.517380i | −0.875942 | − | 0.482416i | \(-0.839759\pi\) |
−0.0201862 | + | 0.999796i | \(0.506426\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19495.1 | + | 66336.2i | 0.0746594 | + | 0.254044i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2961.44 | − | 5129.37i | −0.0112530 | − | 0.0194908i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10561.1 | − | 18292.3i | 0.0398194 | − | 0.0689692i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10442.1i | − | 0.0390666i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −274197. | −1.01795 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −396125. | − | 228703.i | −1.45934 | − | 0.842552i | −0.460364 | − | 0.887730i | \(-0.652281\pi\) |
−0.998979 | + | 0.0451784i | \(0.985614\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −382306. | + | 220724.i | −1.39768 | + | 0.806951i | −0.994149 | − | 0.108015i | \(-0.965551\pi\) |
−0.403531 | + | 0.914966i | \(0.632217\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −139721. | − | 33860.9i | −0.506924 | − | 0.122851i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 60686.7 | + | 105112.i | 0.218510 | + | 0.378471i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 71425.5 | − | 123713.i | 0.255236 | − | 0.442082i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 79216.1i | − | 0.280947i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −78508.5 | −0.276352 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 105495. | + | 60907.7i | 0.368574 | + | 0.212797i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 223594. | − | 129092.i | 0.775376 | − | 0.447664i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28864.3 | + | 14863.3i | 0.0993537 | + | 0.0511608i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −234260. | − | 405750.i | −0.800394 | − | 1.38632i | −0.919357 | − | 0.393424i | \(-0.871290\pi\) |
0.118964 | − | 0.992899i | \(-0.462043\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 57025.7 | − | 98771.4i | 0.193406 | − | 0.334990i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 122491.i | − | 0.412393i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30223.3 | −0.101011 | −0.0505053 | − | 0.998724i | \(-0.516083\pi\) | ||||
−0.0505053 | + | 0.998724i | \(0.516083\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −81453.6 | − | 47027.3i | −0.270250 | − | 0.156029i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18313.6 | − | 10573.4i | 0.0603214 | − | 0.0348265i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8443.17 | − | 34839.3i | 0.0276093 | − | 0.113925i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 46166.9 | + | 79963.4i | 0.149880 | + | 0.259600i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 269643. | − | 467035.i | 0.869117 | − | 1.50535i | 0.00621580 | − | 0.999981i | \(-0.498021\pi\) |
0.862901 | − | 0.505373i | \(-0.168645\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 146415.i | 0.468555i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9570.53 | −0.0304096 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 69013.6 | + | 39845.0i | 0.217730 | + | 0.125706i | 0.604899 | − | 0.796302i | \(-0.293214\pi\) |
−0.387169 | + | 0.922009i | \(0.626547\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −75027.9 | + | 43317.4i | −0.235031 | + | 0.135695i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 34271.7 | − | 10071.9i | 0.106603 | − | 0.0313289i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −205774. | − | 356410.i | −0.635572 | − | 1.10084i | −0.986394 | − | 0.164401i | \(-0.947431\pi\) |
0.350821 | − | 0.936442i | \(-0.385902\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −164913. | + | 285637.i | −0.505803 | + | 0.876077i | 0.494174 | + | 0.869363i | \(0.335470\pi\) |
−0.999977 | + | 0.00671401i | \(0.997863\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 317729.i | − | 0.967716i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −208988. | −0.632099 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 492831. | + | 284536.i | 1.48029 | + | 0.854645i | 0.999751 | − | 0.0223281i | \(-0.00710786\pi\) |
0.480539 | + | 0.876974i | \(0.340441\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 67464.0 | − | 38950.4i | 0.201240 | − | 0.116186i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −339130. | + | 355838.i | −1.00465 | + | 1.05414i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5003.35 | + | 8666.06i | 0.0147206 | + | 0.0254967i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7927.76 | − | 13731.3i | 0.0231653 | − | 0.0401235i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 261714.i | − | 0.759540i | −0.925081 | − | 0.379770i | \(-0.876003\pi\) | ||
0.925081 | − | 0.379770i | \(-0.123997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37618.3 | 0.108435 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −314821. | − | 181762.i | −0.901339 | − | 0.520388i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 472133. | − | 272586.i | 1.34263 | − | 0.775165i | 0.355433 | − | 0.934702i | \(-0.384333\pi\) |
0.987192 | + | 0.159537i | \(0.0510000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37535.2 | + | 35772.7i | 0.106024 | + | 0.101046i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −62780.8 | − | 108739.i | −0.176148 | − | 0.305098i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24712.7 | − | 42803.7i | 0.0688759 | − | 0.119296i | −0.829531 | − | 0.558461i | \(-0.811392\pi\) |
0.898407 | + | 0.439164i | \(0.144725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 352114.i | 0.974843i | 0.873167 | + | 0.487422i | \(0.162063\pi\) | ||||
−0.873167 | + | 0.487422i | \(0.837937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −45593.3 | −0.125391 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −97274.0 | − | 56161.2i | −0.265758 | − | 0.153435i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −190770. | + | 110141.i | −0.517765 | + | 0.298932i | −0.736020 | − | 0.676960i | \(-0.763297\pi\) |
0.218255 | + | 0.975892i | \(0.429964\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 35960.1 | + | 122362.i | 0.0969587 | + | 0.329922i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29186.2 | + | 50552.0i | 0.0781800 | + | 0.135412i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 252311. | − | 437016.i | 0.671453 | − | 1.16299i | −0.306039 | − | 0.952019i | \(-0.599004\pi\) |
0.977492 | − | 0.210972i | \(-0.0676628\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 41926.5i | 0.110851i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −402406. | −1.05705 | −0.528524 | − | 0.848919i | \(-0.677254\pi\) | ||||
−0.528524 | + | 0.848919i | \(0.677254\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 578914. | + | 334236.i | 1.51089 | + | 0.872313i | 0.999919 | + | 0.0127147i | \(0.00404734\pi\) |
0.510971 | + | 0.859598i | \(0.329286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44969.8 | − | 25963.3i | 0.116610 | − | 0.0673251i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −107603. | − | 26077.2i | −0.277235 | − | 0.0671869i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −140552. | − | 243443.i | −0.359813 | − | 0.623214i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1483.14 | + | 2568.87i | −0.00377265 | + | 0.00653442i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 311557.i | 0.787474i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −703475. | −1.76681 | −0.883405 | − | 0.468610i | \(-0.844755\pi\) | ||||
−0.883405 | + | 0.468610i | \(0.844755\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 49331.3 | + | 28481.4i | 0.123116 | + | 0.0710811i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −99303.9 | + | 57333.1i | −0.246274 | + | 0.142186i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −181281. | + | 8721.58i | −0.446760 | + | 0.0214940i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30856.6 | + | 53445.3i | 0.0755696 | + | 0.130890i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 151858. | − | 263026.i | 0.369592 | − | 0.640152i | −0.619910 | − | 0.784673i | \(-0.712831\pi\) |
0.989502 | + | 0.144521i | \(0.0461642\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 73377.4i | 0.177476i | 0.996055 | + | 0.0887382i | \(0.0282834\pi\) | ||||
−0.996055 | + | 0.0887382i | \(0.971717\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 78191.0 | 0.187948 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 523716. | + | 302368.i | 1.25109 | + | 0.722316i | 0.971325 | − | 0.237754i | \(-0.0764111\pi\) |
0.279762 | + | 0.960069i | \(0.409744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34357.5 | + | 19836.3i | −0.0815704 | + | 0.0470947i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −53435.9 | + | 220494.i | −0.126087 | + | 0.520277i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 213363. | + | 369556.i | 0.500372 | + | 0.866669i | 1.00000 | 0.000429258i | \(0.000136637\pi\) | |
−0.499628 | + | 0.866240i | \(0.666530\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 58687.7 | − | 101650.i | 0.136793 | − | 0.236933i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 38098.4i | − | 0.0882625i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 108430. | 0.249678 | 0.124839 | − | 0.992177i | \(-0.460159\pi\) | ||||
0.124839 | + | 0.992177i | \(0.460159\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 544794. | + | 314537.i | 1.24689 | + | 0.719894i | 0.970489 | − | 0.241147i | \(-0.0775236\pi\) |
0.276405 | + | 0.961041i | \(0.410857\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 46332.7 | − | 26750.2i | 0.105405 | − | 0.0608555i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15418.7 | − | 4531.31i | 0.0348662 | − | 0.0102466i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 92698.0 | + | 160558.i | 0.208362 | + | 0.360894i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 55506.5 | − | 96140.1i | 0.124020 | − | 0.214809i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47104.0i | 0.104620i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 103653. | 0.228851 | 0.114425 | − | 0.993432i | \(-0.463497\pi\) | ||||
0.114425 | + | 0.993432i | \(0.463497\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 68604.5 | + | 39608.8i | 0.150572 | + | 0.0869329i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 98794.4 | − | 57039.0i | 0.215553 | − | 0.124450i | −0.388336 | − | 0.921518i | \(-0.626950\pi\) |
0.603890 | + | 0.797068i | \(0.293617\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 259347. | − | 272124.i | 0.562525 | − | 0.590239i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 149722. | + | 259327.i | 0.322844 | + | 0.559182i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 220633. | − | 382148.i | 0.472966 | − | 0.819201i | −0.526556 | − | 0.850141i | \(-0.676517\pi\) |
0.999521 | + | 0.0309401i | \(0.00985011\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 96571.2i | 0.205810i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −182161. | −0.385960 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −48444.4 | − | 27969.4i | −0.102048 | − | 0.0589175i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −557701. | + | 321989.i | −1.16801 | + | 0.674350i | −0.953210 | − | 0.302309i | \(-0.902243\pi\) |
−0.214798 | + | 0.976659i | \(0.568909\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12950.3 | − | 12342.2i | −0.0269657 | − | 0.0256996i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18001.7 | − | 31179.8i | −0.0372686 | − | 0.0645512i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −70735.1 | + | 122517.i | −0.145603 | + | 0.252191i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 44287.7i | 0.0906419i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −337689. | −0.687196 | −0.343598 | − | 0.939117i | \(-0.611646\pi\) | ||||
−0.343598 | + | 0.939117i | \(0.611646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 83626.4 | + | 48281.7i | 0.169213 | + | 0.0976950i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26996.7 | − | 15586.5i | 0.0543166 | − | 0.0313597i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 200548. | + | 682406.i | 0.401218 | + | 1.36523i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −214167. | − | 370949.i | −0.426050 | − | 0.737941i | 0.570468 | − | 0.821320i | \(-0.306762\pi\) |
−0.996518 | + | 0.0833795i | \(0.973429\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9876.42 | + | 17106.5i | −0.0195371 | + | 0.0338393i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 329804.i | 0.648749i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7940.69 | −0.0155327 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 118957. | + | 68680.1i | 0.231395 | + | 0.133596i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 858771. | − | 495812.i | 1.66119 | − | 0.959090i | 0.689044 | − | 0.724719i | \(-0.258030\pi\) |
0.972147 | − | 0.234370i | \(-0.0753029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 129476. | + | 31378.0i | 0.249068 | + | 0.0603608i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 198811. | + | 344351.i | 0.380333 | + | 0.658756i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −141417. | + | 244942.i | −0.269046 | + | 0.466001i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 88010.4i | 0.166519i | 0.996528 | + | 0.0832597i | \(0.0265331\pi\) | ||||
−0.996528 | + | 0.0832597i | \(0.973467\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 228488. | + | 131918.i | 0.427592 | + | 0.246870i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −280457. | + | 161922.i | −0.521986 | + | 0.301369i | −0.737747 | − | 0.675078i | \(-0.764110\pi\) |
0.215761 | + | 0.976446i | \(0.430777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4657.65 | + | 96811.1i | 0.00862169 | + | 0.179205i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11416.9 | + | 19774.7i | 0.0210191 | + | 0.0364061i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 182318. | − | 315784.i | 0.333841 | − | 0.578230i | −0.649420 | − | 0.760430i | \(-0.724988\pi\) |
0.983262 | + | 0.182200i | \(0.0583217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 16581.8i | − | 0.0301993i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −695021. | −1.25898 | −0.629492 | − | 0.777007i | \(-0.716737\pi\) | ||||
−0.629492 | + | 0.777007i | \(0.716737\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33848.8 | − | 19542.6i | −0.0609861 | − | 0.0352104i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 234570. | − | 135429.i | 0.420370 | − | 0.242701i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −180963. | + | 746710.i | −0.322571 | + | 1.33103i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −513684. | − | 889726.i | −0.910785 | − | 1.57753i | −0.812957 | − | 0.582323i | \(-0.802144\pi\) |
−0.0978278 | − | 0.995203i | \(-0.531189\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −85236.0 | + | 147633.i | −0.150326 | + | 0.260372i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 266894.i | − | 0.468215i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 419375. | 0.731832 | 0.365916 | − | 0.930648i | \(-0.380756\pi\) | ||||
0.365916 | + | 0.930648i | \(0.380756\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22521.6 | − | 13002.8i | −0.0390945 | − | 0.0225712i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −766840. | + | 442735.i | −1.32415 | + | 0.764496i | −0.984387 | − | 0.176017i | \(-0.943679\pi\) |
−0.339758 | + | 0.940513i | \(0.610345\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 741240. | − | 217838.i | 1.27324 | − | 0.374184i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14285.6 | − | 24743.4i | −0.0244105 | − | 0.0422802i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 110888. | − | 192063.i | 0.188492 | − | 0.326477i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 333255.i | 0.563540i | 0.959482 | + | 0.281770i | \(0.0909215\pi\) | ||||
−0.959482 | + | 0.281770i | \(0.909079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −373935. | −0.629053 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 787057. | + | 454408.i | 1.31719 | + | 0.760478i | 0.983275 | − | 0.182127i | \(-0.0582981\pi\) |
0.333911 | + | 0.942605i | \(0.391631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −435731. | + | 251569.i | −0.725462 | + | 0.418846i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −401785. | + | 421580.i | −0.665506 | + | 0.698294i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21923.5 | + | 37972.7i | 0.0361273 | + | 0.0625744i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15453.5 | − | 26766.2i | 0.0253352 | − | 0.0438819i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 70275.1i | − | 0.114625i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44809.7 | 0.0727165 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 703181. | + | 405982.i | 1.13532 | + | 0.655477i | 0.945267 | − | 0.326298i | \(-0.105801\pi\) |
0.190052 | + | 0.981774i | \(0.439134\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 453144. | − | 261623.i | 0.727917 | − | 0.420263i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −395560. | − | 376987.i | −0.632207 | − | 0.602522i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −131659. | − | 228039.i | −0.209364 | − | 0.362630i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14936.7 | + | 25871.1i | −0.0236331 | + | 0.0409337i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 918678.i | 1.44626i | 0.690711 | + | 0.723130i | \(0.257297\pi\) | ||||
−0.690711 | + | 0.723130i | \(0.742703\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 105186. | 0.164764 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 52834.2 | + | 30503.8i | 0.0823474 | + | 0.0475433i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16524.0 | + | 9540.15i | −0.0256262 | + | 0.0147953i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 39726.6 | + | 135178.i | 0.0613041 | + | 0.208600i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 114810. | + | 198856.i | 0.176291 | + | 0.305345i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 402027. | − | 696332.i | 0.614269 | − | 1.06395i | −0.376243 | − | 0.926521i | \(-0.622784\pi\) |
0.990512 | − | 0.137424i | \(-0.0438824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 308731.i | − | 0.469396i | −0.972068 | − | 0.234698i | \(-0.924590\pi\) | ||
0.972068 | − | 0.234698i | \(-0.0754100\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −194954. | −0.294952 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −82409.0 | − | 47578.9i | −0.124068 | − | 0.0716307i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 70817.3 | − | 40886.4i | 0.106095 | − | 0.0612540i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 97191.9 | + | 23554.1i | 0.144898 | + | 0.0351155i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 334029. | + | 578555.i | 0.495561 | + | 0.858337i | 0.999987 | − | 0.00511783i | \(-0.00162906\pi\) |
−0.504426 | + | 0.863455i | \(0.668296\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 457854. | − | 793026.i | 0.675969 | − | 1.17081i | −0.300215 | − | 0.953871i | \(-0.597059\pi\) |
0.976185 | − | 0.216942i | \(-0.0696081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 39673.5i | − | 0.0582897i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.04336e6 | 1.52554 | 0.762769 | − | 0.646672i | \(-0.223840\pi\) | ||||
0.762769 | + | 0.646672i | \(0.223840\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 462255. | + | 266883.i | 0.672625 | + | 0.388340i | 0.797070 | − | 0.603886i | \(-0.206382\pi\) |
−0.124446 | + | 0.992226i | \(0.539715\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −112960. | + | 65217.5i | −0.163577 | + | 0.0944414i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −149722. | + | 290758.i | −0.215772 | + | 0.419027i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −199067. | − | 344794.i | −0.285513 | − | 0.494524i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 62506.8 | − | 108265.i | 0.0892228 | − | 0.154539i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 657882.i | − | 0.934597i | −0.884100 | − | 0.467298i | \(-0.845227\pi\) | ||
0.884100 | − | 0.467298i | \(-0.154773\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −456374. | −0.645252 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −102002. | − | 58890.8i | −0.143533 | − | 0.0828690i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −153715. | + | 88747.5i | −0.215280 | + | 0.124292i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 166860. | − | 688519.i | 0.232587 | − | 0.959730i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 357265. | + | 618801.i | 0.495650 | + | 0.858491i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −423292. | + | 733163.i | −0.584495 | + | 1.01237i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 994103.i | − | 1.36626i | −0.730297 | − | 0.683130i | \(-0.760618\pi\) | ||
0.730297 | − | 0.683130i | \(-0.239382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8855.33 | −0.0121136 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.08942e6 | − | 628977.i | −1.48332 | − | 0.856393i | −0.483497 | − | 0.875346i | \(-0.660633\pi\) |
−0.999820 | + | 0.0189528i | \(0.993967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −267518. | + | 154452.i | −0.362549 | + | 0.209318i | −0.670199 | − | 0.742182i | \(-0.733791\pi\) |
0.307649 | + | 0.951500i | \(0.400458\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −253713. | + | 74562.1i | −0.342244 | + | 0.100580i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −156153. | − | 270466.i | −0.209667 | − | 0.363154i | 0.741943 | − | 0.670463i | \(-0.233905\pi\) |
−0.951610 | + | 0.307310i | \(0.900571\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −204977. | + | 355030.i | −0.273950 | + | 0.474496i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 337581.i | 0.449097i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9892.54 | 0.0130999 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −110543. | − | 63822.0i | −0.145712 | − | 0.0841267i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −179386. | + | 103569.i | −0.235375 | + | 0.135894i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −312434. | + | 327827.i | −0.408077 | + | 0.428182i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −726266. | − | 1.25793e6i | −0.944270 | − | 1.63552i | −0.757206 | − | 0.653177i | \(-0.773436\pi\) |
−0.187065 | − | 0.982348i | \(-0.559897\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 230517. | − | 399268.i | 0.298350 | − | 0.516757i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 880963.i | − | 1.13503i | −0.823364 | − | 0.567513i | \(-0.807906\pi\) | ||
0.823364 | − | 0.567513i | \(-0.192094\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −324767. | −0.416534 | −0.208267 | − | 0.978072i | \(-0.566782\pi\) | ||||
−0.208267 | + | 0.978072i | \(0.566782\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −102569. | − | 59218.1i | −0.130957 | − | 0.0756081i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −394415. | + | 227716.i | −0.501310 | + | 0.289431i | −0.729254 | − | 0.684243i | \(-0.760133\pi\) |
0.227945 | + | 0.973674i | \(0.426800\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −523547. | − | 498964.i | −0.662448 | − | 0.631344i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4928.78 | + | 8536.90i | 0.00620846 | + | 0.0107534i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16300.5 | − | 28233.4i | 0.0204409 | − | 0.0354046i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 386013.i | − | 0.481899i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 145375. | 0.180678 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 386543. | + | 223171.i | 0.478276 | + | 0.276133i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −87295.5 | + | 50400.1i | −0.107533 | + | 0.0620843i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 139055. | + | 473163.i | 0.170534 | + | 0.580277i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −85259.4 | − | 147674.i | −0.104099 | − | 0.180304i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 375844. | − | 650981.i | 0.456871 | − | 0.791323i | −0.541923 | − | 0.840428i | \(-0.682304\pi\) |
0.998794 | + | 0.0491051i | \(0.0156369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 391922.i | − | 0.474320i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −938776. | −1.13116 | −0.565581 | − | 0.824692i | \(-0.691348\pi\) | ||||
−0.565581 | + | 0.824692i | \(0.691348\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −117477. | − | 67825.1i | −0.140932 | − | 0.0813671i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −121782. | + | 70310.7i | −0.145459 | + | 0.0839806i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 719494. | + | 174367.i | 0.855634 | + | 0.207360i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −703984. | − | 1.21934e6i | −0.833551 | − | 1.44375i | −0.895205 | − | 0.445655i | \(-0.852971\pi\) |
0.0616544 | − | 0.998098i | \(-0.480362\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −437682. | + | 758088.i | −0.515988 | + | 0.893718i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 172774.i | 0.202803i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.29152e6 | −1.50945 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −63574.1 | − | 36704.5i | −0.0739810 | − | 0.0427130i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 857278. | − | 494950.i | 0.993323 | − | 0.573495i | 0.0870569 | − | 0.996203i | \(-0.472254\pi\) |
0.906266 | + | 0.422708i | \(0.138920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 54841.4 | + | 85246.1i | 0.0632716 | + | 0.0983501i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 131184. | + | 227218.i | 0.150702 | + | 0.261024i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7154.47 | + | 12391.9i | −0.00818378 | + | 0.0141747i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 88009.0i | − | 0.100242i | −0.998743 | − | 0.0501208i | \(-0.984039\pi\) | ||
0.998743 | − | 0.0501208i | \(-0.0159606\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 441767. | 0.501028 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −933046. | − | 538694.i | −1.05372 | − | 0.608364i | −0.130029 | − | 0.991510i | \(-0.541507\pi\) |
−0.923688 | + | 0.383147i | \(0.874840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −332911. | + | 192206.i | −0.374373 | + | 0.216145i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12578.8 | − | 51904.1i | 0.0140856 | − | 0.0581217i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 270050. | + | 467740.i | 0.301123 | + | 0.521561i | 0.976391 | − | 0.216012i | \(-0.0693051\pi\) |
−0.675267 | + | 0.737573i | \(0.735972\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53330.6 | − | 92371.3i | 0.0592167 | − | 0.102566i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 320228.i | − | 0.354077i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 675288. | 0.743538 | 0.371769 | − | 0.928325i | \(-0.378751\pi\) | ||||
0.371769 | + | 0.928325i | \(0.378751\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −411395. | − | 237519.i | −0.451079 | − | 0.260431i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30479.7 | + | 17597.5i | −0.0332803 | + | 0.0192144i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −584389. | + | 171743.i | −0.635426 | + | 0.186741i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −64758.5 | − | 112165.i | −0.0701213 | − | 0.121454i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 211681. | − | 366643.i | 0.228260 | − | 0.395358i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 116470.i | − | 0.125072i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.01409e6 | 1.08449 | 0.542244 | − | 0.840221i | \(-0.317575\pi\) | ||||
0.542244 | + | 0.840221i | \(0.317575\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25876.9 | − | 14940.0i | −0.0275591 | − | 0.0159112i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 66792.2 | − | 38562.5i | 0.0708414 | − | 0.0409003i | −0.464161 | − | 0.885751i | \(-0.653644\pi\) |
0.535002 | + | 0.844851i | \(0.320311\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 156667. | − | 164385.i | 0.165482 | − | 0.173635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 110890. | + | 192067.i | 0.116649 | + | 0.202042i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 436977. | − | 756866.i | 0.457793 | − | 0.792921i | −0.541051 | − | 0.840990i | \(-0.681973\pi\) |
0.998844 | + | 0.0480689i | \(0.0153067\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 30553.6i | − | 0.0318784i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −425711. | −0.442361 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −269678. | − | 155698.i | −0.279086 | − | 0.161130i | 0.353924 | − | 0.935274i | \(-0.384847\pi\) |
−0.633010 | + | 0.774144i | \(0.718181\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −470690. | + | 271753.i | −0.485134 | + | 0.280092i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 142331. | + | 135648.i | 0.146105 | + | 0.139245i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 358456. | + | 620864.i | 0.366474 | + | 0.634752i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −137603. | + | 238335.i | −0.140113 | + | 0.242683i | −0.927539 | − | 0.373726i | \(-0.878080\pi\) |
0.787426 | + | 0.616409i | \(0.211413\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 612799.i | 0.621470i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −187728. | −0.189619 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 389290. | + | 224757.i | 0.391637 | + | 0.226112i | 0.682869 | − | 0.730541i | \(-0.260732\pi\) |
−0.291232 | + | 0.956652i | \(0.594065\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 277908. | − | 160450.i | 0.278465 | − | 0.160772i |
(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 | 168.5.z.a.73.3 | ✓ | 16 | |
3.2 | odd | 2 | 504.5.by.a.73.6 | 16 | |||
4.3 | odd | 2 | 336.5.bh.i.241.3 | 16 | |||
7.3 | odd | 6 | 1176.5.f.b.97.6 | 16 | |||
7.4 | even | 3 | 1176.5.f.b.97.11 | 16 | |||
7.5 | odd | 6 | inner | 168.5.z.a.145.3 | yes | 16 | |
21.5 | even | 6 | 504.5.by.a.145.6 | 16 | |||
28.19 | even | 6 | 336.5.bh.i.145.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.5.z.a.73.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
168.5.z.a.145.3 | yes | 16 | 7.5 | odd | 6 | inner | |
336.5.bh.i.145.3 | 16 | 28.19 | even | 6 | |||
336.5.bh.i.241.3 | 16 | 4.3 | odd | 2 | |||
504.5.by.a.73.6 | 16 | 3.2 | odd | 2 | |||
504.5.by.a.145.6 | 16 | 21.5 | even | 6 | |||
1176.5.f.b.97.6 | 16 | 7.3 | odd | 6 | |||
1176.5.f.b.97.11 | 16 | 7.4 | even | 3 |