Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(239,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.239");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.h (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: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 444940 x^{16} + 56262171366 x^{12} + \cdots + 77\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{35}\cdot 3^{14}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.14 | ||
Root | \(7.46608 + 7.46608i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.6.h.a.239.13 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 7.46608 | + | 13.6842i | 0.478949 | + | 0.877842i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 31.0107i | − | 0.554736i | −0.960764 | − | 0.277368i | \(-0.910538\pi\) | ||
0.960764 | − | 0.277368i | \(-0.0894621\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −131.515 | + | 204.335i | −0.541215 | + | 0.840884i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −273.251 | −0.680894 | −0.340447 | − | 0.940264i | \(-0.610578\pi\) | ||||
−0.340447 | + | 0.940264i | \(0.610578\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 431.702 | 0.708478 | 0.354239 | − | 0.935155i | \(-0.384740\pi\) | ||||
0.354239 | + | 0.935155i | \(0.384740\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 424.356 | − | 231.528i | 0.486970 | − | 0.265690i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 648.939i | − | 0.544605i | −0.962212 | − | 0.272303i | \(-0.912215\pi\) | ||
0.962212 | − | 0.272303i | \(-0.0877852\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2309.56i | 1.46773i | 0.679296 | + | 0.733864i | \(0.262285\pi\) | ||||
−0.679296 | + | 0.733864i | \(0.737715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −670.526 | + | 365.838i | −0.331793 | + | 0.181026i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3727.31 | −1.46918 | −0.734592 | − | 0.678509i | \(-0.762627\pi\) | ||||
−0.734592 | + | 0.678509i | \(0.762627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2163.34 | 0.692268 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3778.07 | − | 274.100i | −0.997379 | − | 0.0723602i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7005.12i | − | 1.54675i | −0.633948 | − | 0.773376i | \(-0.718567\pi\) | ||
0.633948 | − | 0.773376i | \(-0.281433\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1725.19i | − | 0.322429i | −0.986919 | − | 0.161214i | \(-0.948459\pi\) | ||
0.986919 | − | 0.161214i | \(-0.0515410\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2040.11 | − | 3739.22i | −0.326114 | − | 0.597718i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1519.52 | 0.209670 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12257.2 | −1.47193 | −0.735967 | − | 0.677018i | \(-0.763272\pi\) | ||||
−0.735967 | + | 0.677018i | \(0.763272\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3223.13 | + | 5907.51i | 0.339325 | + | 0.621932i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16640.7i | 1.54601i | 0.634401 | + | 0.773004i | \(0.281247\pi\) | ||||
−0.634401 | + | 0.773004i | \(0.718753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9182.45i | 0.757334i | 0.925533 | + | 0.378667i | \(0.123617\pi\) | ||||
−0.925533 | + | 0.378667i | \(0.876383\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6336.56 | + | 4078.37i | 0.466469 | + | 0.300231i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −23236.3 | −1.53434 | −0.767171 | − | 0.641443i | \(-0.778336\pi\) | ||||
−0.767171 | + | 0.641443i | \(0.778336\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2401.00 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8880.22 | − | 4845.04i | 0.478078 | − | 0.260838i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 19112.1i | − | 0.934584i | −0.884103 | − | 0.467292i | \(-0.845230\pi\) | ||
0.884103 | − | 0.467292i | \(-0.154770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8473.68i | 0.377716i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −31604.5 | + | 17243.4i | −1.28843 | + | 0.702968i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10334.1 | −0.386495 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7055.07 | −0.242760 | −0.121380 | − | 0.992606i | \(-0.538732\pi\) | ||||
−0.121380 | + | 0.992606i | \(0.538732\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10012.4 | − | 6444.24i | −0.317824 | − | 0.204560i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 13387.4i | − | 0.393018i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 46154.6i | − | 1.25611i | −0.778168 | − | 0.628056i | \(-0.783851\pi\) | ||
0.778168 | − | 0.628056i | \(-0.216149\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −27828.4 | − | 51005.3i | −0.703665 | − | 1.28971i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 75909.3 | 1.78710 | 0.893551 | − | 0.448962i | \(-0.148206\pi\) | ||||
0.893551 | + | 0.448962i | \(0.148206\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −51116.5 | −1.12267 | −0.561337 | − | 0.827587i | \(-0.689713\pi\) | ||||
−0.561337 | + | 0.827587i | \(0.689713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16151.7 | + | 29603.6i | 0.331562 | + | 0.607703i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 13389.3i | − | 0.257354i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10609.7i | 0.191264i | 0.995417 | + | 0.0956320i | \(0.0304872\pi\) | ||||
−0.995417 | + | 0.0956320i | \(0.969513\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −24456.5 | − | 53746.3i | −0.414173 | − | 0.910198i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −67540.1 | −1.07613 | −0.538067 | − | 0.842902i | \(-0.680845\pi\) | ||||
−0.538067 | + | 0.842902i | \(0.680845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20124.0 | −0.302112 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 95859.5 | − | 52300.8i | 1.35780 | − | 0.740816i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 73333.0i | − | 0.981351i | −0.871342 | − | 0.490675i | \(-0.836750\pi\) | ||
0.871342 | − | 0.490675i | \(-0.163250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21153.4i | 0.267779i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23607.9 | − | 12880.4i | 0.283042 | − | 0.154427i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 71621.1 | 0.814201 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −134051. | −1.44657 | −0.723285 | − | 0.690549i | \(-0.757369\pi\) | ||||
−0.723285 | + | 0.690549i | \(0.757369\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 35936.6 | − | 55834.6i | 0.368510 | − | 0.572553i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 34452.8i | 0.336063i | 0.985782 | + | 0.168032i | \(0.0537411\pi\) | ||||
−0.985782 | + | 0.168032i | \(0.946259\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 41975.0i | − | 0.389850i | −0.980818 | − | 0.194925i | \(-0.937554\pi\) | ||
0.980818 | − | 0.194925i | \(-0.0624464\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11344.9 | + | 20793.5i | 0.100422 | + | 0.184058i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −716.196 | −0.00604745 | −0.00302373 | − | 0.999995i | \(-0.500962\pi\) | ||||
−0.00302373 | + | 0.999995i | \(0.500962\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −176002. | −1.41890 | −0.709450 | − | 0.704755i | \(-0.751057\pi\) | ||||
−0.709450 | + | 0.704755i | \(0.751057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −91513.5 | − | 167731.i | −0.704982 | − | 1.29213i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 119037.i | − | 0.876973i | −0.898738 | − | 0.438487i | \(-0.855515\pi\) | ||
0.898738 | − | 0.438487i | \(-0.144485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115586.i | 0.815009i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −56775.4 | + | 88211.9i | −0.383439 | + | 0.595748i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 31798.0 | 0.205841 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −86385.1 | −0.536384 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −227715. | + | 124241.i | −1.35715 | + | 0.740460i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 163995.i | − | 0.938762i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 119105.i | 0.655272i | 0.944804 | + | 0.327636i | \(0.106252\pi\) | ||||
−0.944804 | + | 0.327636i | \(0.893748\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −125655. | + | 68556.9i | −0.664820 | + | 0.362725i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19611.7 | −0.0998477 | −0.0499238 | − | 0.998753i | \(-0.515898\pi\) | ||||
−0.0499238 | + | 0.998753i | \(0.515898\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −113169. | −0.554749 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8500.02 | + | 117160.i | −0.0401408 | + | 0.553281i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 111921.i | − | 0.509462i | −0.967012 | − | 0.254731i | \(-0.918013\pi\) | ||
0.967012 | − | 0.254731i | \(-0.0819869\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 151822.i | 0.666495i | 0.942839 | + | 0.333247i | \(0.108144\pi\) | ||||
−0.942839 | + | 0.333247i | \(0.891856\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −173484. | − | 317970.i | −0.734872 | − | 1.34691i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −117963. | −0.482398 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −217233. | −0.858038 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17926.1 | − | 32855.8i | −0.0684214 | − | 0.125406i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 224095.i | 0.826926i | 0.910521 | + | 0.413463i | \(0.135681\pi\) | ||||
−0.910521 | + | 0.413463i | \(0.864319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 75904.1i | − | 0.270909i | −0.990784 | − | 0.135454i | \(-0.956751\pi\) | ||
0.990784 | − | 0.135454i | \(-0.0432494\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 132601. | + | 85345.4i | 0.457950 | + | 0.294748i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −53499.4 | −0.178863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 539676. | 1.74737 | 0.873684 | − | 0.486494i | \(-0.161725\pi\) | ||||
0.873684 | + | 0.486494i | \(0.161725\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 261534. | − | 142692.i | 0.820418 | − | 0.447619i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 182638.i | − | 0.555300i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 278911.i | 0.822236i | 0.911582 | + | 0.411118i | \(0.134862\pi\) | ||||
−0.911582 | + | 0.411118i | \(0.865138\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −115956. | + | 63265.2i | −0.331575 | + | 0.180907i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −140515. | −0.389880 | −0.194940 | − | 0.980815i | \(-0.562451\pi\) | ||||
−0.194940 | + | 0.980815i | \(0.562451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −184926. | −0.498060 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −471924. | − | 303743.i | −1.23419 | − | 0.794356i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 383778.i | 0.974910i | 0.873148 | + | 0.487455i | \(0.162075\pi\) | ||||
−0.873148 | + | 0.487455i | \(0.837925\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 106004.i | 0.261653i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −77155.4 | − | 141414.i | −0.185111 | − | 0.339281i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −216235. | −0.504421 | −0.252210 | − | 0.967672i | \(-0.581157\pi\) | ||||
−0.252210 | + | 0.967672i | \(0.581157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17131.1 | 0.0388677 | 0.0194339 | − | 0.999811i | \(-0.493814\pi\) | ||||
0.0194339 | + | 0.999811i | \(0.493814\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −52673.7 | − | 96543.0i | −0.116270 | − | 0.213105i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 380105.i | 0.816534i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 177323.i | 0.370818i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13430.9 | − | 185125.i | 0.0273496 | − | 0.376974i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 563825. | 1.11831 | 0.559153 | − | 0.829064i | \(-0.311126\pi\) | ||||
0.559153 | + | 0.829064i | \(0.311126\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 111313. | 0.215106 | 0.107553 | − | 0.994199i | \(-0.465699\pi\) | ||||
0.107553 | + | 0.994199i | \(0.465699\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 183196. | − | 99951.3i | 0.345008 | − | 0.188236i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 175093.i | − | 0.321442i | −0.987000 | − | 0.160721i | \(-0.948618\pi\) | ||
0.987000 | − | 0.160721i | \(-0.0513820\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25023.4i | 0.0447934i | 0.999749 | + | 0.0223967i | \(0.00712968\pi\) | ||||
−0.999749 | + | 0.0223967i | \(0.992870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 631590. | − | 344594.i | 1.10267 | − | 0.601614i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 343251. | 0.584617 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 516039. | 0.857626 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 490198. | − | 761620.i | 0.795145 | − | 1.23541i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 631089.i | − | 0.999367i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 543279.i | 0.840073i | 0.907507 | + | 0.420037i | \(0.137983\pi\) | ||||
−0.907507 | + | 0.420037i | \(0.862017\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 566745. | + | 1.03876e6i | 0.855932 | + | 1.56879i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 284754. | 0.420120 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 84534.5 | 0.121867 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −381640. | − | 699489.i | −0.537705 | − | 0.985532i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 280149.i | − | 0.385841i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 93393.8i | − | 0.125764i | −0.998021 | − | 0.0628819i | \(-0.979971\pi\) | ||
0.998021 | − | 0.0628819i | \(-0.0200292\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −284512. | + | 442046.i | −0.374666 | + | 0.582118i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 968469. | 1.24744 | 0.623722 | − | 0.781646i | \(-0.285620\pi\) | ||||
0.623722 | + | 0.781646i | \(0.285620\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 698135. | 0.879733 | 0.439867 | − | 0.898063i | \(-0.355026\pi\) | ||||
0.439867 | + | 0.898063i | \(0.355026\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 183222. | − | 99965.5i | 0.225916 | − | 0.123259i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.39409e6i | 1.68228i | 0.540814 | + | 0.841142i | \(0.318116\pi\) | ||||
−0.540814 | + | 0.841142i | \(0.681884\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 720572.i | 0.851154i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −145185. | + | 79212.5i | −0.167900 | + | 0.0916058i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.42313e6 | −1.61157 | −0.805783 | − | 0.592210i | \(-0.798255\pi\) | ||||
−0.805783 | + | 0.592210i | \(0.798255\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 846607. | 0.938943 | 0.469471 | − | 0.882948i | \(-0.344445\pi\) | ||||
0.469471 | + | 0.882948i | \(0.344445\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 552881. | − | 735942.i | 0.600643 | − | 0.799518i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 74456.6i | 0.0792479i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 997044.i | 1.03985i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −504260. | − | 924233.i | −0.515414 | − | 0.944677i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −96135.7 | −0.0963164 | −0.0481582 | − | 0.998840i | \(-0.515335\pi\) | ||||
−0.0481582 | + | 0.998840i | \(0.515335\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.01849e6 | 1.00036 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −150248. | − | 275382.i | −0.144696 | − | 0.265207i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 695936.i | 0.657259i | 0.944459 | + | 0.328630i | \(0.106587\pi\) | ||||
−0.944459 | + | 0.328630i | \(0.893413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 600604.i | − | 0.556338i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.43139e6 | + | 921279.i | 1.30064 | + | 0.837125i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 303934. | 0.270950 | 0.135475 | − | 0.990781i | \(-0.456744\pi\) | ||||
0.135475 | + | 0.990781i | \(0.456744\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −592679. | −0.518447 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.00350e6 | − | 547510.i | 0.861471 | − | 0.470017i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.20360e6i | 1.85675i | 0.371648 | + | 0.928374i | \(0.378793\pi\) | ||||
−0.371648 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.28050e6i | 1.05915i | 0.848263 | + | 0.529575i | \(0.177648\pi\) | ||||
−0.848263 | + | 0.529575i | \(0.822352\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −289468. | + | 157933.i | −0.235068 | + | 0.128253i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −591134. | −0.471361 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 749476. | 0.586892 | 0.293446 | − | 0.955976i | \(-0.405198\pi\) | ||||
0.293446 | + | 0.955976i | \(0.405198\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 352517. | + | 226889.i | 0.271125 | + | 0.174503i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.94049e6i | − | 1.46604i | −0.680208 | − | 0.733019i | \(-0.738111\pi\) | ||
0.680208 | − | 0.733019i | \(-0.261889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 577899.i | − | 0.428930i | −0.976732 | − | 0.214465i | \(-0.931199\pi\) | ||
0.976732 | − | 0.214465i | \(-0.0688007\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 534729. | + | 980078.i | 0.389961 | + | 0.714740i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −815394. | −0.584336 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 998735. | 0.703405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00083e6 | − | 1.83438e6i | −0.692834 | − | 1.26986i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 914960.i | 0.622634i | 0.950306 | + | 0.311317i | \(0.100770\pi\) | ||||
−0.950306 | + | 0.311317i | \(0.899230\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 320468.i | 0.214402i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.03236e6 | + | 74898.0i | 0.679109 | + | 0.0492696i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.60909e6 | −1.04088 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −449940. | −0.286245 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −471460. | + | 257228.i | −0.295011 | + | 0.160957i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 218782.i | 0.134667i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.55889e6i | 1.54955i | 0.632237 | + | 0.774775i | \(0.282137\pi\) | ||||
−0.632237 | + | 0.774775i | \(0.717863\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 574395. | − | 313389.i | 0.342227 | − | 0.186719i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 160879. | 0.0943189 | 0.0471595 | − | 0.998887i | \(-0.484983\pi\) | ||||
0.0471595 | + | 0.998887i | \(0.484983\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25303.8 | 0.0145991 | 0.00729954 | − | 0.999973i | \(-0.497676\pi\) | ||||
0.00729954 | + | 0.999973i | \(0.497676\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −199840. | + | 310491.i | −0.113477 | + | 0.176309i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.07422e6i | − | 1.15933i | −0.814856 | − | 0.579663i | \(-0.803184\pi\) | ||
0.814856 | − | 0.579663i | \(-0.196816\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.91415e6i | 1.05317i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5347.18 | − | 9800.57i | −0.00289642 | − | 0.00530871i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.49877e6 | 0.799333 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 933918. | 0.490457 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.31405e6 | − | 2.40845e6i | −0.679582 | − | 1.24557i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.13858e6i | − | 0.579926i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.79890e6i | 1.90585i | 0.303211 | + | 0.952924i | \(0.401941\pi\) | ||||
−0.303211 | + | 0.952924i | \(0.598059\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.61201e6 | − | 2.50458e6i | 0.796632 | − | 1.23773i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.43129e6 | −0.696810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.26997e6 | −1.56845 | −0.784223 | − | 0.620479i | \(-0.786938\pi\) | ||||
−0.784223 | + | 0.620479i | \(0.786938\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.62893e6 | − | 888741.i | 0.769844 | − | 0.420026i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 471410.i | 0.219540i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 117649.i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.58171e6 | + | 862978.i | −0.715450 | + | 0.390348i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.21278e6 | 0.986542 | 0.493271 | − | 0.869876i | \(-0.335801\pi\) | ||||
0.493271 | + | 0.869876i | \(0.335801\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.11399e6 | 1.36853 | 0.684264 | − | 0.729234i | \(-0.260124\pi\) | ||||
0.684264 | + | 0.729234i | \(0.260124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.63100e6 | − | 118330.i | −0.706620 | − | 0.0512656i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.19521e6i | 0.510513i | 0.966873 | + | 0.255256i | \(0.0821599\pi\) | ||||
−0.966873 | + | 0.255256i | \(0.917840\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.35400e6i | − | 0.991369i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 237407. | + | 435131.i | 0.0985877 | + | 0.180696i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.53735e6 | −1.85809 | −0.929045 | − | 0.369968i | \(-0.879369\pi\) | ||||
−0.929045 | + | 0.369968i | \(0.879369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.85798e6 | −1.15423 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −644959. | − | 1.18211e6i | −0.256901 | − | 0.470860i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.58516e6i | 0.622788i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.10438e6i | 0.428008i | 0.976833 | + | 0.214004i | \(0.0686506\pi\) | ||||
−0.976833 | + | 0.214004i | \(0.931349\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.40028e6 | − | 2.18850e6i | −1.30001 | − | 0.836723i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 936492. | 0.353240 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −665317. | −0.247603 | −0.123802 | − | 0.992307i | \(-0.539509\pi\) | ||||
−0.123802 | + | 0.992307i | \(0.539509\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.24414e6 | − | 1.22440e6i | 0.824085 | − | 0.449619i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.02413e6i | − | 1.09584i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.17286e6i | 0.419420i | 0.977764 | + | 0.209710i | \(0.0672521\pi\) | ||||
−0.977764 | + | 0.209710i | \(0.932748\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.62986e6 | + | 889250.i | −0.575226 | + | 0.313842i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.41559e6 | 1.18979 | 0.594893 | − | 0.803805i | \(-0.297195\pi\) | ||||
0.594893 | + | 0.803805i | \(0.297195\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −415210. | −0.142763 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.87629e6 | − | 1.20763e6i | −0.636830 | − | 0.409880i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.49028e6i | 1.16946i | 0.811227 | + | 0.584731i | \(0.198800\pi\) | ||||
−0.811227 | + | 0.584731i | \(0.801200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.41880e6i | 0.800126i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −146423. | − | 268371.i | −0.0478220 | − | 0.0876505i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 329012. | 0.106101 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.87522e6 | 0.597139 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −844926. | − | 1.54862e6i | −0.265697 | − | 0.486982i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 921836.i | 0.286281i | 0.989702 | + | 0.143141i | \(0.0457201\pi\) | ||||
−0.989702 | + | 0.143141i | \(0.954280\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 744770.i | − | 0.228433i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.66671e6 | + | 758413.i | −0.504919 | + | 0.229757i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.34930e6 | 1.00223 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.95540e6 | −0.578000 | −0.289000 | − | 0.957329i | \(-0.593323\pi\) | ||||
−0.289000 | + | 0.957329i | \(0.593323\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.53156e6 | − | 835615.i | 0.447227 | − | 0.244007i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 506372.i | − | 0.146081i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.09446e6i | 0.596970i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.07756e6 | + | 1.13351e6i | −0.585077 | + | 0.319217i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.10515e6 | 1.69887 | 0.849437 | − | 0.527690i | \(-0.176942\pi\) | ||||
0.849437 | + | 0.527690i | \(0.176942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.22827e6 | −0.337746 | −0.168873 | − | 0.985638i | \(-0.554013\pi\) | ||||
−0.168873 | + | 0.985638i | \(0.554013\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.05592e6 | − | 4.74798e6i | 0.830408 | − | 1.29020i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.40388e6i | − | 0.377013i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 345698.i | − | 0.0917546i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −880721. | − | 1.61423e6i | −0.231044 | − | 0.423469i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14052.6 | 0.00364387 | 0.00182193 | − | 0.999998i | \(-0.499420\pi\) | ||||
0.00182193 | + | 0.999998i | \(0.499420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.42099e6 | −1.64582 | −0.822909 | − | 0.568172i | \(-0.807651\pi\) | ||||
−0.822909 | + | 0.568172i | \(0.807651\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.62188e6 | − | 2.97267e6i | −0.410957 | − | 0.753222i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 8.60846e6i | − | 2.15636i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.88754e6i | − | 0.467450i | −0.972303 | − | 0.233725i | \(-0.924908\pi\) | ||
0.972303 | − | 0.233725i | \(-0.0750916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 315768. | − | 490608.i | 0.0773164 | − | 0.120126i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.58093e6 | −0.624836 | −0.312418 | − | 0.949945i | \(-0.601139\pi\) | ||||
−0.312418 | + | 0.949945i | \(0.601139\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.27410e6 | −0.544390 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.06656e6 | + | 1.67311e6i | −0.725911 | + | 0.396056i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.08339e6i | − | 1.18998i | −0.803735 | − | 0.594988i | \(-0.797157\pi\) | ||
0.803735 | − | 0.594988i | \(-0.202843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.54708e6i | − | 1.05267i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.03869e6 | − | 566706.i | 0.237815 | − | 0.129752i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 655981. | 0.148547 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.34884e6 | −0.974055 | −0.487027 | − | 0.873387i | \(-0.661919\pi\) | ||||
−0.487027 | + | 0.873387i | \(0.661919\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −177874. | + | 2.45174e6i | −0.0394077 | + | 0.543178i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.77026e6i | − | 0.826265i | −0.910671 | − | 0.413133i | \(-0.864435\pi\) | ||
0.910671 | − | 0.413133i | \(-0.135565\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.26552e6i | 0.707946i | 0.935256 | + | 0.353973i | \(0.115170\pi\) | ||||
−0.935256 | + | 0.353973i | \(0.884830\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −399431. | − | 732097.i | −0.0856662 | − | 0.157013i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.02593e6 | −0.217683 | −0.108842 | − | 0.994059i | \(-0.534714\pi\) | ||||
−0.108842 | + | 0.994059i | \(0.534714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.26158e6 | 0.474766 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.02927e6 | + | 7.38504e6i | 0.836901 | + | 1.53391i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.50911e6i | − | 0.515664i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.99637e6i | 1.01606i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.90527e6 | + | 2.51353e6i | 0.785877 | + | 0.505811i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 776699. | 0.154673 | 0.0773364 | − | 0.997005i | \(-0.475358\pi\) | ||||
0.0773364 | + | 0.997005i | \(0.475358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.29148e6 | −1.04283 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.49926e6 | − | 1.36359e6i | 0.487466 | − | 0.265960i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.15700e6i | 0.802464i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.66548e6i | − | 1.84672i | −0.383935 | − | 0.923360i | \(-0.625431\pi\) | ||
0.383935 | − | 0.923360i | \(-0.374569\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.81667e6 | + | 2.08237e6i | −0.721793 | + | 0.393809i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.98460e6 | −1.49469 | −0.747343 | − | 0.664439i | \(-0.768671\pi\) | ||||
−0.747343 | + | 0.664439i | \(0.768671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.54590e6 | −0.842369 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.73147e6 | − | 1.11442e6i | −0.317616 | − | 0.204426i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.71956e6i | 0.675461i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.05004e7i | 1.88779i | 0.330244 | + | 0.943896i | \(0.392869\pi\) | ||||
−0.330244 | + | 0.943896i | \(0.607131\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.04910e6 | − | 1.92283e6i | −0.186733 | − | 0.342253i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.98180e6 | −1.05417 | −0.527086 | − | 0.849812i | \(-0.676715\pi\) | ||||
−0.527086 | + | 0.849812i | \(0.676715\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.06840e6 | 0.186426 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.38067e6 | − | 2.53057e6i | −0.238545 | − | 0.437218i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.18196e6i | 1.05762i | 0.848739 | + | 0.528812i | \(0.177362\pi\) | ||||
−0.848739 | + | 0.528812i | \(0.822638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.50471e6i | − | 0.424331i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 633051. | − | 8.72568e6i | 0.106205 | − | 1.46388i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.30167e6 | −0.216264 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.34933e6 | 1.04472 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.25169e6 | + | 2.86532e6i | −0.855817 | + | 0.466933i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.27286e6i | − | 1.33525i | −0.744500 | − | 0.667623i | \(-0.767312\pi\) | ||
0.744500 | − | 0.667623i | \(-0.232688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.75488e6i | − | 0.280539i | −0.990113 | − | 0.140269i | \(-0.955203\pi\) | ||
0.990113 | − | 0.140269i | \(-0.0447969\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.45058e6 | + | 791432.i | −0.229690 | + | 0.125319i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.11955e6 | −0.175596 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.45653e6 | 1.15850 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.35909e6 | − | 2.11162e6i | 0.209177 | − | 0.324997i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.18383e6i | 1.09531i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22209.7i | 0.00335474i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.61443e6 | − | 2.95900e6i | −0.241592 | − | 0.442802i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 656075. | 0.0972705 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −597706. | −0.0877999 | −0.0439000 | − | 0.999036i | \(-0.513978\pi\) | ||||
−0.0439000 | + | 0.999036i | \(0.513978\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 127902. | + | 234426.i | 0.0186157 | + | 0.0341198i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.45795e6i | 0.787115i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.85127e6i | 1.40775i | 0.710326 | + | 0.703873i | \(0.248547\pi\) | ||||
−0.710326 | + | 0.703873i | \(0.751453\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 927849. | − | 1.44160e6i | 0.131385 | − | 0.204133i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.61788e7 | 2.27021 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −519873. | −0.0722910 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.20144e6 | + | 2.83789e6i | −0.716788 | + | 0.391078i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.17315e6i | 0.979652i | 0.871820 | + | 0.489826i | \(0.162940\pi\) | ||||
−0.871820 | + | 0.489826i | \(0.837060\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.96409e6i | 0.536554i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.42653e6 | + | 1.32391e6i | −0.325520 | + | 0.177603i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −527120. | −0.0700872 | −0.0350436 | − | 0.999386i | \(-0.511157\pi\) | ||||
−0.0350436 | + | 0.999386i | \(0.511157\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.69142e6 | −0.486488 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.63357e6 | − | 1.19837e6i | 0.344023 | − | 0.156543i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.75497e6i | − | 0.874667i | −0.899299 | − | 0.437334i | \(-0.855923\pi\) | ||
0.899299 | − | 0.437334i | \(-0.144077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 6.26648e6i | − | 0.804329i | −0.915568 | − | 0.402164i | \(-0.868258\pi\) | ||
0.915568 | − | 0.402164i | \(-0.131742\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.20956e6 | + | 7.71550e6i | 0.535612 | + | 0.981697i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.06344e6 | −1.01707 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.10962e7 | −1.38750 | −0.693751 | − | 0.720215i | \(-0.744043\pi\) | ||||
−0.693751 | + | 0.720215i | \(0.744043\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 831070. | + | 1.52323e6i | 0.103025 | + | 0.188829i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 3.30947e6i | − | 0.406741i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.22239e6i | 0.636353i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.73551e6 | + | 1.76064e6i | 0.330482 | + | 0.212707i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.48039e7 | −1.77329 | −0.886645 | − | 0.462450i | \(-0.846970\pi\) | ||||
−0.886645 | + | 0.462450i | \(0.846970\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.98444e6 | 0.473238 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.39601e6 | − | 1.30726e6i | 0.282176 | − | 0.153955i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.45962e7i | − | 1.70452i | −0.523116 | − | 0.852262i | \(-0.675230\pi\) | ||
0.523116 | − | 0.852262i | \(-0.324770\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 986078.i | − | 0.114188i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −342426. | + | 186827.i | −0.0393215 | + | 0.0214538i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.89256e6 | −0.443270 | −0.221635 | − | 0.975130i | \(-0.571139\pi\) | ||||
−0.221635 | + | 0.975130i | \(0.571139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.15955e7 | 1.30949 | 0.654746 | − | 0.755849i | \(-0.272776\pi\) | ||||
0.654746 | + | 0.755849i | \(0.272776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.43101e6 | + | 6.07004e6i | 1.05625 | + | 0.679827i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.67886e6i | 0.297551i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.63844e7i | − | 1.80492i | −0.430775 | − | 0.902459i | \(-0.641760\pi\) | ||
0.430775 | − | 0.902459i | \(-0.358240\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.56274e6 | + | 4.69712e6i | 0.280002 | + | 0.513202i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.00312e7 | −1.08705 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.08825e6 | 0.976853 | 0.488426 | − | 0.872605i | \(-0.337571\pi\) | ||||
0.488426 | + | 0.872605i | \(0.337571\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.85279e6 | + | 7.06159e6i | 0.410760 | + | 0.752861i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.26021e7i | 1.33270i | 0.745641 | + | 0.666348i | \(0.232143\pi\) | ||||
−0.745641 | + | 0.666348i | \(0.767857\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.79908e7i | − | 1.88723i | −0.331047 | − | 0.943614i | \(-0.607402\pi\) | ||
0.331047 | − | 0.943614i | \(-0.392598\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.40820e7 | + | 1.02166e6i | 1.46533 | + | 0.106310i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.59332e6 | 0.370916 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.67484e6 | 0.171504 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.63596e6 | − | 4.71177e6i | 0.877287 | − | 0.478646i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.95420e6i | 0.801623i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.52790e7i | − | 1.52764i | −0.645428 | − | 0.763821i | \(-0.723321\pi\) | ||
0.645428 | − | 0.763821i | \(-0.276679\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.43435e6 | + | 4.05617e6i | −0.737452 | + | 0.402353i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.69353e6 | 0.363503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.03652e6 | −0.101211 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.98323e6 | + | 1.55109e7i | −0.967206 | + | 1.50275i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.52864e7i | 1.46947i | 0.678354 | + | 0.734736i | \(0.262694\pi\) | ||||
−0.678354 | + | 0.734736i | \(0.737306\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.31579e6i | 0.220888i | 0.993882 | + | 0.110444i | \(0.0352272\pi\) | ||||
−0.993882 | + | 0.110444i | \(0.964773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.12600e6 | + | 3.89663e6i | 0.201216 | + | 0.368799i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.83598e7 | 1.72428 | 0.862140 | − | 0.506671i | \(-0.169124\pi\) | ||||
0.862140 | + | 0.506671i | \(0.169124\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.82380e6 | 0.263162 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 631142. | + | 1.15679e6i | 0.0583679 | + | 0.106980i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 9.96514e6i | − | 0.914535i | −0.889329 | − | 0.457267i | \(-0.848828\pi\) | ||
0.889329 | − | 0.457267i | \(-0.151172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 608173.i | 0.0553891i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.72260e6 | − | 1.04449e7i | 0.607608 | − | 0.944040i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.49253e7 | 1.33878 | 0.669390 | − | 0.742911i | \(-0.266556\pi\) | ||||
0.669390 | + | 0.742911i | \(0.266556\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.95642e7 | 1.74164 | 0.870822 | − | 0.491598i | \(-0.163587\pi\) | ||||
0.870822 | + | 0.491598i | \(0.163587\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.83361e6 | − | 2.09161e6i | 0.338707 | − | 0.184798i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.50943e6i | 0.307739i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.61103e7i | 2.27246i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.27802e6 | − | 697286.i | 0.110401 | − | 0.0602345i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.92780e6 | 0.165294 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.47877e6 | 0.636491 | 0.318246 | − | 0.948008i | \(-0.396906\pi\) | ||||
0.318246 | + | 0.948008i | \(0.396906\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.17323e6 | − | 592971.i | −0.690454 | − | 0.0500927i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.33357e6i | 0.447245i | 0.974676 | + | 0.223623i | \(0.0717884\pi\) | ||||
−0.974676 | + | 0.223623i | \(0.928212\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.56848e6i | − | 0.546752i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.23067e6 | + | 1.32527e7i | 0.597463 | + | 1.09506i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.72244e6 | 0.797487 | 0.398743 | − | 0.917063i | \(-0.369446\pi\) | ||||
0.398743 | + | 0.917063i | \(0.369446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.47076e6 | −0.282617 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.21234e6 | + | 9.55343e6i | 0.421348 | + | 0.772267i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 8.25073e6i | − | 0.662132i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.54033e7i | − | 1.22721i | −0.789612 | − | 0.613606i | \(-0.789718\pi\) | ||
0.789612 | − | 0.613606i | \(-0.210282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.73590e6 | + | 1.76089e6i | 0.216405 | + | 0.139284i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.70809e6 | 0.369728 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.07988e7 | 0.841965 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.90770e7 | + | 1.04084e7i | −1.47678 | + | 0.805729i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 47107.8i | − | 0.00362075i | −0.999998 | − | 0.00181037i | \(-0.999424\pi\) | ||
0.999998 | − | 0.00181037i | \(-0.000576260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.83088e7i | − | 2.16040i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.86046e6 | + | 5.37985e6i | −0.747179 | + | 0.407660i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.68819e6 | −0.127020 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.79314e6 | −0.133967 | −0.0669836 | − | 0.997754i | \(-0.521338\pi\) | ||||
−0.0669836 | + | 0.997754i | \(0.521338\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.16792e6 | − | 1.39533e6i | −0.160831 | − | 0.103515i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.43034e6i | 0.473707i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.65811e6i | 0.267603i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.06252e7 | − | 1.94743e7i | −0.771859 | − | 1.41470i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.45978e7 | −1.05309 | −0.526544 | − | 0.850148i | \(-0.676513\pi\) | ||||
−0.526544 | + | 0.850148i | \(0.676513\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.05678e6 | 0.147350 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.32084e6 | + | 1.15851e7i | 0.449706 | + | 0.824244i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.51544e7i | − | 1.07077i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.77708e7i | − | 1.24701i | −0.781818 | − | 0.623507i | \(-0.785707\pi\) | ||
0.781818 | − | 0.623507i | \(-0.214293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.41986e7 | + | 2.07114e6i | 0.989528 | + | 0.144341i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.95885e6 | 0.412448 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.27593e7 | 0.877138 | 0.438569 | − | 0.898697i | \(-0.355485\pi\) | ||||
0.438569 | + | 0.898697i | \(0.355485\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.01888e6 | + | 555899.i | −0.0695672 | + | 0.0379558i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.26118e7i | 0.855279i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 9.57582e6i | − | 0.645008i | −0.946568 | − | 0.322504i | \(-0.895475\pi\) | ||
0.946568 | − | 0.322504i | \(-0.104525\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.36438e7 | + | 7.44401e6i | −0.912827 | + | 0.498037i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.65898e6 | 0.641888 | 0.320944 | − | 0.947098i | \(-0.396000\pi\) | ||||
0.320944 | + | 0.947098i | \(0.396000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.94934e6 | 0.458725 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.88255e6 | − | 1.38008e7i | 0.582420 | − | 0.904905i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 35093.6i | − | 0.00228572i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.44433e7i | 0.934475i | 0.884132 | + | 0.467238i | \(0.154751\pi\) | ||||
−0.884132 | + | 0.467238i | \(0.845249\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −717757. | − | 1.31554e6i | −0.0461307 | − | 0.0845507i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.35384e6 | −0.150283 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.70339e7 | 1.08037 | 0.540187 | − | 0.841545i | \(-0.318354\pi\) | ||||
0.540187 | + | 0.841545i | \(0.318354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.60414e6 | + | 1.39372e7i | 0.479121 | + | 0.878157i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.06579e7i | 0.667128i | 0.942727 | + | 0.333564i | \(0.108251\pi\) | ||||
−0.942727 | + | 0.333564i | \(0.891749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.62411e6i | − | 0.536294i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.64662e6 | − | 4.11204e6i | 0.163507 | − | 0.254041i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.46126e6 | −0.273823 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.31211e6 | −0.0800118 | −0.0400059 | − | 0.999199i | \(-0.512738\pi\) | ||||
−0.0400059 | + | 0.999199i | \(0.512738\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.52334e6 | + | 5.19592e6i | −0.576970 | + | 0.314794i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 3.80328e6i | − | 0.228934i | −0.993427 | − | 0.114467i | \(-0.963484\pi\) | ||
0.993427 | − | 0.114467i | \(-0.0365160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.73218e6i | − | 0.223207i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.21880e6 | − | 4.48416e6i | 0.488378 | − | 0.266458i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.84327e7 | −2.26912 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.07423e7 | −1.21683 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.92010e6 | + | 2.64658e7i | −0.111923 | + | 1.54270i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.67357e7i | − | 0.969327i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7.73357e6i | − | 0.445085i | −0.974923 | − | 0.222543i | \(-0.928564\pi\) | ||
0.974923 | − | 0.222543i | \(-0.0714357\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.26919e6 | + | 4.15909e6i | 0.129771 | + | 0.237852i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.83282e6 | 0.331465 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.04569e6 | −0.171990 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.42499e6 | − | 8.11034e6i | −0.248310 | − | 0.455115i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.37650e6i | − | 0.188287i | −0.995559 | − | 0.0941437i | \(-0.969989\pi\) | ||
0.995559 | − | 0.0941437i | \(-0.0300113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.50789e7i | 0.835610i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.49845e7 | + | 9.64440e6i | 0.825203 | + | 0.531122i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.39676e7 | 0.764422 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.66374e6 | −0.308044 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.01546e7 | + | 1.64523e7i | −1.62993 | + | 0.889288i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.08570e7i | 1.65761i | 0.559537 | + | 0.828805i | \(0.310979\pi\) | ||||
−0.559537 | + | 0.828805i | \(0.689021\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.39558e7i | 1.27897i | 0.768805 | + | 0.639483i | \(0.220852\pi\) | ||||
−0.768805 | + | 0.639483i | \(0.779148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.75227e7 | + | 9.56034e6i | −0.929766 | + | 0.507279i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.64921e6 | 0.456123 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.12074e7 | −1.11156 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.32238e6 | − | 2.78200e6i | −0.225171 | − | 0.144926i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.08818e6i | − | 0.0563435i | −0.999603 | − | 0.0281718i | \(-0.991031\pi\) | ||
0.999603 | − | 0.0281718i | \(-0.00896854\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.75123e7i | − | 0.901248i | −0.892714 | − | 0.450624i | \(-0.851202\pi\) | ||
0.892714 | − | 0.450624i | \(-0.148798\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.41345e6 | − | 8.08920e6i | −0.225758 | − | 0.413781i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.23971e7 | −1.13875 | −0.569375 | − | 0.822078i | \(-0.692815\pi\) | ||||
−0.569375 | + | 0.822078i | \(0.692815\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.84316e7 | −0.931486 | −0.465743 | − | 0.884920i | \(-0.654213\pi\) | ||||
−0.465743 | + | 0.884920i | \(0.654213\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.59565e6 | + | 1.02560e7i | 0.281092 | + | 0.515199i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.55810e6i | 0.0778008i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.35746e6i | 0.216280i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −472876. | + | 6.51789e6i | −0.0233310 | + | 0.321583i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.98579e7 | −1.46438 | −0.732192 | − | 0.681098i | \(-0.761503\pi\) | ||||
−0.732192 | + | 0.681098i | \(0.761503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.85605e7 | −1.39244 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.65540e7 | − | 1.44878e7i | 1.28695 | − | 0.702158i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.73468e6i | 0.276291i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.23287e6i | − | 0.202734i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.90810e6 | − | 4.31464e6i | 0.376533 | − | 0.205436i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.56866e7 | 2.16254 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.57574e7 | 0.741501 | 0.370750 | − | 0.928733i | \(-0.379101\pi\) | ||||
0.370750 | + | 0.928733i | \(0.379101\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.41926e6 | + | 1.46347e7i | −0.440658 | + | 0.684649i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.87916e7i | 0.874001i | 0.899461 | + | 0.437000i | \(0.143959\pi\) | ||||
−0.899461 | + | 0.437000i | \(0.856041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 978284.i | − | 0.0452358i | −0.999744 | − | 0.0226179i | \(-0.992800\pi\) | ||
0.999744 | − | 0.0226179i | \(-0.00720011\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.08780e6 | − | 1.11580e7i | −0.279868 | − | 0.512955i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.09831e6 | −0.233023 | −0.116512 | − | 0.993189i | \(-0.537171\pi\) | ||||
−0.116512 | + | 0.993189i | \(0.537171\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.19012e7 | 0.540817 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.45664e6 | + | 1.36669e7i | 0.336895 | + | 0.617479i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.89909e6i | − | 0.130231i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.99251e7i | − | 0.889927i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.76297e7 | − | 2.73912e7i | 0.782906 | − | 1.21640i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.03575e6 | 0.354819 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.76613e7 | −1.65347 | −0.826734 | − | 0.562592i | \(-0.809804\pi\) | ||||
−0.826734 | + | 0.562592i | \(0.809804\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.25205e7 | + | 6.83117e6i | −0.546575 | + | 0.298210i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.15933e7i | − | 1.37137i | −0.727898 | − | 0.685686i | \(-0.759502\pi\) | ||
0.727898 | − | 0.685686i | \(-0.240498\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.57917e7i | − | 1.54483i | −0.635119 | − | 0.772415i | \(-0.719049\pi\) | ||
0.635119 | − | 0.772415i | \(-0.280951\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.38535e6 | + | 2.39264e6i | −0.188211 | + | 0.102688i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.24956e7 | −0.960039 | −0.480019 | − | 0.877258i | \(-0.659370\pi\) | ||||
−0.480019 | + | 0.877258i | \(0.659370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.83616e6 | −0.247670 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.68275e6 | + | 1.46862e7i | 0.282008 | + | 0.619748i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.36656e7i | − | 2.25200i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.70558e6i | 0.279820i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.20136e7 | − | 2.20191e7i | −0.498531 | − | 0.913732i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.20852e7 | −0.498717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.24026e7 | −0.508980 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.35929e6 | − | 6.15707e6i | −0.137097 | − | 0.251278i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 531247.i | − | 0.0215613i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.85191e6i | − | 0.0747485i | −0.999301 | − | 0.0373743i | \(-0.988101\pi\) | ||
0.999301 | − | 0.0373743i | \(-0.0118994\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.03991e6 | − | 4.53107e6i | −0.282590 | − | 0.181883i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.53681e7 | −1.01272 | −0.506362 | − | 0.862321i | \(-0.669010\pi\) | ||||
−0.506362 | + | 0.862321i | \(0.669010\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.84554e7 | 0.732733 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.99386e6 | + | 1.63345e6i | −0.118217 | + | 0.0644989i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 960976.i | − | 0.0377389i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.36040e7i | 0.921929i | 0.887419 | + | 0.460964i | \(0.152496\pi\) | ||||
−0.887419 | + | 0.460964i | \(0.847504\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.50164e7 | + | 1.91049e7i | −1.36026 | + | 0.742156i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.27702e7 | 1.26612 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.65165e7 | −1.01897 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.57696e6 | + | 5.52035e6i | 0.327819 | + | 0.210993i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.77392e7i | − | 1.43467i | −0.696726 | − | 0.717337i | \(-0.745361\pi\) | ||
0.696726 | − | 0.717337i | \(-0.254639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5.54526e6i | − | 0.209675i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.20114e6 | + | 2.20150e6i | 0.0451740 | + | 0.0827972i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.49891e6 | 0.205706 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.25373e7 | 0.838595 | 0.419297 | − | 0.907849i | \(-0.362276\pi\) | ||||
0.419297 | + | 0.907849i | \(0.362276\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 188921. | + | 346263.i | 0.00699223 | + | 0.0128157i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.35680e7i | 0.867657i | 0.900996 | + | 0.433828i | \(0.142838\pi\) | ||||
−0.900996 | + | 0.433828i | \(0.857162\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.20251e7i | − | 2.27137i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.74086e6 | − | 416501.i | −0.209121 | − | 0.0151718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.44399e7 | 0.523228 | 0.261614 | − | 0.965173i | \(-0.415745\pi\) | ||||
0.261614 | + | 0.965173i | \(0.415745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.20671e7 | −0.795390 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.83840e7 | − | 1.54863e7i | 1.01771 | − | 0.555259i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.00105e6i | − | 0.107039i | −0.998567 | − | 0.0535193i | \(-0.982956\pi\) | ||
0.998567 | − | 0.0535193i | \(-0.0170439\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.74846e7i | − | 0.620365i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.61937e7 | + | 1.42912e7i | −0.924520 | + | 0.504417i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.48415e6 | 0.192559 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.56529e7 | 0.896040 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 94190.6 | − | 146344.i | 0.00327297 | − | 0.00508521i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 3.45188e6i | − | 0.119327i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.14615e7i | 1.08196i | 0.841034 | + | 0.540982i | \(0.181947\pi\) | ||||
−0.841034 | + | 0.540982i | \(0.818053\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.11899e7 | + | 2.05094e7i | 0.382840 | + | 0.701688i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.01639e7 | 1.02669 | 0.513345 | − | 0.858182i | \(-0.328406\pi\) | ||||
0.513345 | + | 0.858182i | \(0.328406\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.43926e6 | −0.251911 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.97271e6 | + | 1.27799e7i | 0.234904 | + | 0.430544i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.28234e7i | − | 1.43531i | −0.696401 | − | 0.717653i | \(-0.745216\pi\) | ||
0.696401 | − | 0.717653i | \(-0.254784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.00383e7i | 0.668196i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.31470e7 | − | 3.59634e7i | 0.767930 | − | 1.19313i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.59677e6 | −0.250752 | −0.125376 | − | 0.992109i | \(-0.540014\pi\) | ||||
−0.125376 | + | 0.992109i | \(0.540014\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.42975e6 | −0.178315 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.55805e7 | − | 8.50072e6i | 0.509084 | − | 0.277755i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.42259e7i | − | 1.11266i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.05487e7i | − | 1.31157i | −0.754947 | − | 0.655786i | \(-0.772337\pi\) | ||
0.754947 | − | 0.655786i | \(-0.227663\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.19850e7 | + | 2.83629e7i | −1.67303 | + | 0.912805i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 775993. | 0.0248485 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.62460e7 | −1.15484 | −0.577421 | − | 0.816447i | \(-0.695941\pi\) | ||||
−0.577421 | + | 0.816447i | \(0.695941\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.63086e7 | + | 3.35971e6i | 1.46807 | + | 0.106509i |
(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 | 336.6.h.a.239.14 | yes | 20 | |
3.2 | odd | 2 | inner | 336.6.h.a.239.8 | yes | 20 | |
4.3 | odd | 2 | inner | 336.6.h.a.239.7 | ✓ | 20 | |
12.11 | even | 2 | inner | 336.6.h.a.239.13 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.6.h.a.239.7 | ✓ | 20 | 4.3 | odd | 2 | inner | |
336.6.h.a.239.8 | yes | 20 | 3.2 | odd | 2 | inner | |
336.6.h.a.239.13 | yes | 20 | 12.11 | even | 2 | inner | |
336.6.h.a.239.14 | yes | 20 | 1.1 | even | 1 | trivial |