Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(55,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.55");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 38x^{14} + 1016x^{12} + 13512x^{10} + 130640x^{8} + 569472x^{6} + 1783808x^{4} + 352256x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.15 | ||
Root | \(0.222504 - 0.385387i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.55 |
Dual form | 108.5.d.b.55.16 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.98139 | − | 0.385387i | 0.995348 | − | 0.0963469i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.7030 | − | 3.06876i | 0.981435 | − | 0.191797i | ||||
\(5\) | −22.8093 | −0.912371 | −0.456186 | − | 0.889885i | \(-0.650785\pi\) | ||||
−0.456186 | + | 0.889885i | \(0.650785\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 82.1204i | − | 1.67593i | −0.545726 | − | 0.837964i | \(-0.683746\pi\) | ||
0.545726 | − | 0.837964i | \(-0.316254\pi\) | |||||||
\(8\) | 61.3369 | − | 18.2696i | 0.958390 | − | 0.285463i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −90.8127 | + | 8.79041i | −0.908127 | + | 0.0879041i | ||||
\(11\) | − | 107.306i | − | 0.886825i | −0.896318 | − | 0.443413i | \(-0.853768\pi\) | ||
0.896318 | − | 0.443413i | \(-0.146232\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 57.1351 | 0.338077 | 0.169039 | − | 0.985609i | \(-0.445934\pi\) | ||||
0.169039 | + | 0.985609i | \(0.445934\pi\) | |||||||
\(14\) | −31.6482 | − | 326.954i | −0.161470 | − | 1.66813i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 237.165 | − | 96.3771i | 0.926428 | − | 0.376473i | ||||
\(17\) | 291.903 | 1.01005 | 0.505023 | − | 0.863106i | \(-0.331484\pi\) | ||||
0.505023 | + | 0.863106i | \(0.331484\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 304.924i | − | 0.844664i | −0.906441 | − | 0.422332i | \(-0.861212\pi\) | ||
0.906441 | − | 0.422332i | \(-0.138788\pi\) | |||||||
\(20\) | −358.173 | + | 69.9961i | −0.895433 | + | 0.174990i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −41.3543 | − | 427.227i | −0.0854428 | − | 0.882699i | ||||
\(23\) | 982.813i | 1.85787i | 0.370243 | + | 0.928935i | \(0.379274\pi\) | ||||
−0.370243 | + | 0.928935i | \(0.620726\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −104.737 | −0.167579 | ||||||||
\(26\) | 227.477 | − | 22.0191i | 0.336505 | − | 0.0325727i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −252.008 | − | 1289.53i | −0.321438 | − | 1.64481i | ||||
\(29\) | −1049.98 | −1.24849 | −0.624244 | − | 0.781230i | \(-0.714593\pi\) | ||||
−0.624244 | + | 0.781230i | \(0.714593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 783.041i | − | 0.814819i | −0.913246 | − | 0.407409i | \(-0.866432\pi\) | ||
0.913246 | − | 0.407409i | \(-0.133568\pi\) | |||||||
\(32\) | 907.106 | − | 475.115i | 0.885846 | − | 0.463980i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1162.18 | − | 112.496i | 1.00535 | − | 0.0973148i | ||||
\(35\) | 1873.11i | 1.52907i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1404.40 | 1.02586 | 0.512930 | − | 0.858431i | \(-0.328560\pi\) | ||||
0.512930 | + | 0.858431i | \(0.328560\pi\) | |||||||
\(38\) | −117.514 | − | 1214.02i | −0.0813808 | − | 0.840735i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1399.05 | + | 416.717i | −0.874407 | + | 0.260448i | ||||
\(41\) | −363.412 | −0.216188 | −0.108094 | − | 0.994141i | \(-0.534475\pi\) | ||||
−0.108094 | + | 0.994141i | \(0.534475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.7059i | 0.0349951i | 0.999847 | + | 0.0174975i | \(0.00556992\pi\) | ||||
−0.999847 | + | 0.0174975i | \(0.994430\pi\) | |||||||
\(44\) | −329.295 | − | 1685.02i | −0.170091 | − | 0.870361i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 378.764 | + | 3912.96i | 0.179000 | + | 1.84923i | ||||
\(47\) | 3495.66i | 1.58246i | 0.611518 | + | 0.791230i | \(0.290559\pi\) | ||||
−0.611518 | + | 0.791230i | \(0.709441\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4342.77 | −1.80873 | ||||||||
\(50\) | −416.998 | + | 40.3642i | −0.166799 | + | 0.0161457i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 897.189 | − | 175.334i | 0.331801 | − | 0.0648423i | ||||
\(53\) | 3268.87 | 1.16371 | 0.581856 | − | 0.813292i | \(-0.302327\pi\) | ||||
0.581856 | + | 0.813292i | \(0.302327\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2447.57i | 0.809114i | ||||||||
\(56\) | −1500.31 | − | 5037.02i | −0.478415 | − | 1.60619i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4180.37 | + | 404.648i | −1.24268 | + | 0.120288i | ||||
\(59\) | − | 867.469i | − | 0.249201i | −0.992207 | − | 0.124601i | \(-0.960235\pi\) | ||
0.992207 | − | 0.124601i | \(-0.0397650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6034.94 | 1.62186 | 0.810929 | − | 0.585144i | \(-0.198962\pi\) | ||||
0.810929 | + | 0.585144i | \(0.198962\pi\) | |||||||
\(62\) | −301.774 | − | 3117.59i | −0.0785052 | − | 0.811028i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3428.44 | − | 2241.21i | 0.837022 | − | 0.547170i | ||||
\(65\) | −1303.21 | −0.308452 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3421.54i | 0.762205i | 0.924533 | + | 0.381103i | \(0.124456\pi\) | ||||
−0.924533 | + | 0.381103i | \(0.875544\pi\) | |||||||
\(68\) | 4583.74 | − | 895.780i | 0.991294 | − | 0.193724i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 721.872 | + | 7457.58i | 0.147321 | + | 1.52195i | ||||
\(71\) | 3188.67i | 0.632547i | 0.948668 | + | 0.316273i | \(0.102432\pi\) | ||||
−0.948668 | + | 0.316273i | \(0.897568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4267.98 | −0.800896 | −0.400448 | − | 0.916319i | \(-0.631146\pi\) | ||||
−0.400448 | + | 0.916319i | \(0.631146\pi\) | |||||||
\(74\) | 5591.47 | − | 541.239i | 1.02109 | − | 0.0988383i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −935.737 | − | 4788.20i | −0.162004 | − | 0.828983i | ||||
\(77\) | −8812.00 | −1.48625 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7530.43i | 1.20661i | 0.797512 | + | 0.603303i | \(0.206149\pi\) | ||||
−0.797512 | + | 0.603303i | \(0.793851\pi\) | |||||||
\(80\) | −5409.57 | + | 2198.29i | −0.845246 | + | 0.343483i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1446.89 | + | 140.055i | −0.215182 | + | 0.0208290i | ||||
\(83\) | − | 586.258i | − | 0.0851006i | −0.999094 | − | 0.0425503i | \(-0.986452\pi\) | ||
0.999094 | − | 0.0425503i | \(-0.0135483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6658.11 | −0.921537 | ||||||||
\(86\) | 24.9368 | + | 257.619i | 0.00337167 | + | 0.0348323i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1960.44 | − | 6581.81i | −0.253156 | − | 0.849924i | ||||
\(89\) | 5789.27 | 0.730876 | 0.365438 | − | 0.930836i | \(-0.380919\pi\) | ||||
0.365438 | + | 0.930836i | \(0.380919\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4691.96i | − | 0.566593i | ||||||
\(92\) | 3016.01 | + | 15433.1i | 0.356334 | + | 1.82338i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1347.18 | + | 13917.6i | 0.152465 | + | 1.57510i | ||||
\(95\) | 6955.09i | 0.770647i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10837.8 | 1.15185 | 0.575927 | − | 0.817501i | \(-0.304641\pi\) | ||||
0.575927 | + | 0.817501i | \(0.304641\pi\) | |||||||
\(98\) | −17290.3 | + | 1673.65i | −1.80032 | + | 0.174266i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1644.68 | + | 321.411i | −0.164468 | + | 0.0321411i | ||||
\(101\) | 11502.9 | 1.12763 | 0.563813 | − | 0.825903i | \(-0.309334\pi\) | ||||
0.563813 | + | 0.825903i | \(0.309334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13839.0i | − | 1.30446i | −0.758020 | − | 0.652231i | \(-0.773833\pi\) | ||
0.758020 | − | 0.652231i | \(-0.226167\pi\) | |||||||
\(104\) | 3504.49 | − | 1043.84i | 0.324010 | − | 0.0965086i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13014.6 | − | 1259.78i | 1.15830 | − | 0.112120i | ||||
\(107\) | − | 14731.9i | − | 1.28674i | −0.765555 | − | 0.643371i | \(-0.777535\pi\) | ||
0.765555 | − | 0.643371i | \(-0.222465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3545.18 | 0.298391 | 0.149195 | − | 0.988808i | \(-0.452332\pi\) | ||||
0.149195 | + | 0.988808i | \(0.452332\pi\) | |||||||
\(110\) | 943.262 | + | 9744.73i | 0.0779556 | + | 0.805350i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7914.53 | − | 19476.1i | −0.630941 | − | 1.55263i | ||||
\(113\) | −12472.0 | −0.976742 | −0.488371 | − | 0.872636i | \(-0.662409\pi\) | ||||
−0.488371 | + | 0.872636i | \(0.662409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 22417.3i | − | 1.69507i | ||||||
\(116\) | −16487.8 | + | 3222.13i | −1.22531 | + | 0.239456i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −334.312 | − | 3453.73i | −0.0240098 | − | 0.248042i | ||||
\(119\) | − | 23971.2i | − | 1.69276i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3126.46 | 0.213541 | ||||||||
\(122\) | 24027.4 | − | 2325.79i | 1.61431 | − | 0.156261i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2402.96 | − | 12296.1i | −0.156280 | − | 0.799691i | ||||
\(125\) | 16644.8 | 1.06527 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1002.07i | 0.0621284i | 0.999517 | + | 0.0310642i | \(0.00988964\pi\) | ||||
−0.999517 | + | 0.0310642i | \(0.990110\pi\) | |||||||
\(128\) | 12786.2 | − | 10244.4i | 0.780410 | − | 0.625269i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5188.59 | + | 502.241i | −0.307017 | + | 0.0297184i | ||||
\(131\) | − | 33549.8i | − | 1.95500i | −0.210933 | − | 0.977501i | \(-0.567650\pi\) | ||
0.210933 | − | 0.977501i | \(-0.432350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25040.5 | −1.41560 | ||||||||
\(134\) | 1318.62 | + | 13622.5i | 0.0734361 | + | 0.758659i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17904.5 | − | 5332.97i | 0.968018 | − | 0.288331i | ||||
\(137\) | −19700.7 | −1.04964 | −0.524821 | − | 0.851213i | \(-0.675868\pi\) | ||||
−0.524821 | + | 0.851213i | \(0.675868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12634.4i | 0.653922i | 0.945038 | + | 0.326961i | \(0.106025\pi\) | ||||
−0.945038 | + | 0.326961i | \(0.893975\pi\) | |||||||
\(140\) | 5748.11 | + | 29413.3i | 0.293271 | + | 1.50068i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1228.87 | + | 12695.3i | 0.0609439 | + | 0.629604i | ||||
\(143\) | − | 6130.93i | − | 0.299816i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23949.2 | 1.13908 | ||||||||
\(146\) | −16992.5 | + | 1644.82i | −0.797171 | + | 0.0771639i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 22053.2 | − | 4309.76i | 1.00681 | − | 0.196757i | ||||
\(149\) | −24054.7 | −1.08350 | −0.541749 | − | 0.840541i | \(-0.682238\pi\) | ||||
−0.541749 | + | 0.840541i | \(0.682238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 29000.6i | 1.27190i | 0.771730 | + | 0.635951i | \(0.219392\pi\) | ||||
−0.771730 | + | 0.635951i | \(0.780608\pi\) | |||||||
\(152\) | −5570.85 | − | 18703.1i | −0.241121 | − | 0.809518i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −35084.0 | + | 3396.04i | −1.47934 | + | 0.143196i | ||||
\(155\) | 17860.6i | 0.743417i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11143.2 | 0.452074 | 0.226037 | − | 0.974119i | \(-0.427423\pi\) | ||||
0.226037 | + | 0.974119i | \(0.427423\pi\) | |||||||
\(158\) | 2902.13 | + | 29981.6i | 0.116253 | + | 1.20099i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −20690.4 | + | 10837.0i | −0.808220 | + | 0.423322i | ||||
\(161\) | 80709.0 | 3.11365 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3212.14i | − | 0.120898i | −0.998171 | − | 0.0604490i | \(-0.980747\pi\) | ||
0.998171 | − | 0.0604490i | \(-0.0192533\pi\) | |||||||
\(164\) | −5706.65 | + | 1115.22i | −0.212175 | + | 0.0414643i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −225.937 | − | 2334.12i | −0.00819918 | − | 0.0847047i | ||||
\(167\) | − | 22589.6i | − | 0.809983i | −0.914320 | − | 0.404992i | \(-0.867274\pi\) | ||
0.914320 | − | 0.404992i | \(-0.132726\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −25296.6 | −0.885704 | ||||||||
\(170\) | −26508.5 | + | 2565.95i | −0.917250 | + | 0.0887872i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 198.567 | + | 1016.07i | 0.00671196 | + | 0.0343454i | ||||
\(173\) | −20741.2 | −0.693013 | −0.346506 | − | 0.938048i | \(-0.612632\pi\) | ||||
−0.346506 | + | 0.938048i | \(0.612632\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8601.02i | 0.280850i | ||||||||
\(176\) | −10341.8 | − | 25449.2i | −0.333866 | − | 0.821579i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 23049.3 | − | 2231.11i | 0.727476 | − | 0.0704176i | ||||
\(179\) | 37551.2i | 1.17197i | 0.810321 | + | 0.585986i | \(0.199293\pi\) | ||||
−0.810321 | + | 0.585986i | \(0.800707\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −38019.3 | −1.16050 | −0.580252 | − | 0.814437i | \(-0.697046\pi\) | ||||
−0.580252 | + | 0.814437i | \(0.697046\pi\) | |||||||
\(182\) | −1808.22 | − | 18680.5i | −0.0545895 | − | 0.563957i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17955.6 | + | 60282.7i | 0.530353 | + | 1.78056i | ||||
\(185\) | −32033.4 | −0.935964 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 31322.9i | − | 0.895734i | ||||||
\(188\) | 10727.3 | + | 54892.1i | 0.303512 | + | 1.55308i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2680.41 | + | 27690.9i | 0.0742495 | + | 0.767062i | ||||
\(191\) | 7313.44i | 0.200473i | 0.994964 | + | 0.100236i | \(0.0319599\pi\) | ||||
−0.994964 | + | 0.100236i | \(0.968040\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 60987.7 | 1.63730 | 0.818649 | − | 0.574294i | \(-0.194724\pi\) | ||||
0.818649 | + | 0.574294i | \(0.194724\pi\) | |||||||
\(194\) | 43149.5 | − | 4176.75i | 1.14650 | − | 0.110978i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −68194.3 | + | 13326.9i | −1.77515 | + | 0.346910i | ||||
\(197\) | −13891.0 | −0.357934 | −0.178967 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178967 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 43065.2i | 1.08748i | 0.839255 | + | 0.543738i | \(0.182992\pi\) | ||||
−0.839255 | + | 0.543738i | \(0.817008\pi\) | |||||||
\(200\) | −6424.23 | + | 1913.50i | −0.160606 | + | 0.0478375i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 45797.6 | − | 4433.08i | 1.12238 | − | 0.108643i | ||||
\(203\) | 86224.6i | 2.09237i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8289.17 | 0.197244 | ||||||||
\(206\) | −5333.39 | − | 55098.6i | −0.125681 | − | 1.29839i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13550.5 | − | 5506.51i | 0.313204 | − | 0.127277i | ||||
\(209\) | −32720.1 | −0.749070 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23061.3i | 0.517987i | 0.965879 | + | 0.258993i | \(0.0833908\pi\) | ||||
−0.965879 | + | 0.258993i | \(0.916609\pi\) | |||||||
\(212\) | 51330.9 | − | 10031.4i | 1.14211 | − | 0.223197i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5677.49 | − | 58653.5i | −0.123973 | − | 1.28076i | ||||
\(215\) | − | 1475.89i | − | 0.0319285i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −64303.6 | −1.36558 | ||||||||
\(218\) | 14114.8 | − | 1366.27i | 0.297003 | − | 0.0287490i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7510.99 | + | 38434.1i | 0.155186 | + | 0.794092i | ||||
\(221\) | 16677.9 | 0.341474 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 59739.3i | 1.20130i | 0.799514 | + | 0.600648i | \(0.205091\pi\) | ||||
−0.799514 | + | 0.600648i | \(0.794909\pi\) | |||||||
\(224\) | −39016.7 | − | 74491.9i | −0.777597 | − | 1.48461i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −49656.0 | + | 4806.56i | −0.972198 | + | 0.0941060i | ||||
\(227\) | − | 33998.0i | − | 0.659784i | −0.944019 | − | 0.329892i | \(-0.892988\pi\) | ||
0.944019 | − | 0.329892i | \(-0.107012\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14052.1 | 0.267959 | 0.133980 | − | 0.990984i | \(-0.457224\pi\) | ||||
0.133980 | + | 0.990984i | \(0.457224\pi\) | |||||||
\(230\) | −8639.33 | − | 89251.9i | −0.163314 | − | 1.68718i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −64402.4 | + | 19182.7i | −1.19654 | + | 0.356397i | ||||
\(233\) | 9622.25 | 0.177241 | 0.0886206 | − | 0.996065i | \(-0.471754\pi\) | ||||
0.0886206 | + | 0.996065i | \(0.471754\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 79733.4i | − | 1.44379i | ||||||
\(236\) | −2662.05 | − | 13621.8i | −0.0477961 | − | 0.244575i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9238.21 | − | 95438.9i | −0.163092 | − | 1.68489i | ||||
\(239\) | 28426.1i | 0.497647i | 0.968549 | + | 0.248824i | \(0.0800439\pi\) | ||||
−0.968549 | + | 0.248824i | \(0.919956\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9489.78 | −0.163389 | −0.0816943 | − | 0.996657i | \(-0.526033\pi\) | ||||
−0.0816943 | + | 0.996657i | \(0.526033\pi\) | |||||||
\(242\) | 12447.6 | − | 1204.90i | 0.212548 | − | 0.0205740i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 94766.3 | − | 18519.7i | 1.59175 | − | 0.311068i | ||||
\(245\) | 99055.4 | 1.65024 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 17421.8i | − | 0.285562i | ||||||
\(248\) | −14305.9 | − | 48029.3i | −0.232601 | − | 0.780914i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 66269.3 | − | 6414.68i | 1.06031 | − | 0.102635i | ||||
\(251\) | 29529.8i | 0.468720i | 0.972150 | + | 0.234360i | \(0.0752994\pi\) | ||||
−0.972150 | + | 0.234360i | \(0.924701\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 105462. | 1.64761 | ||||||||
\(254\) | 386.185 | + | 3989.63i | 0.00598588 | + | 0.0618394i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 46958.9 | − | 45714.6i | 0.716536 | − | 0.697550i | ||||
\(257\) | −14174.7 | −0.214609 | −0.107304 | − | 0.994226i | \(-0.534222\pi\) | ||||
−0.107304 | + | 0.994226i | \(0.534222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 115330.i | − | 1.71927i | ||||||
\(260\) | −20464.2 | + | 3999.23i | −0.302726 | + | 0.0591603i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12929.7 | − | 133575.i | −0.188358 | − | 1.94591i | ||||
\(263\) | 106157.i | 1.53475i | 0.641197 | + | 0.767377i | \(0.278438\pi\) | ||||
−0.641197 | + | 0.767377i | \(0.721562\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −74560.5 | −1.06174 | ||||||||
\(266\) | −99695.9 | + | 9650.29i | −1.40901 | + | 0.136388i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10499.9 | + | 53728.3i | 0.146189 | + | 0.748055i | ||||
\(269\) | −57391.1 | −0.793122 | −0.396561 | − | 0.918008i | \(-0.629796\pi\) | ||||
−0.396561 | + | 0.918008i | \(0.629796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22027.2i | 0.299930i | 0.988691 | + | 0.149965i | \(0.0479161\pi\) | ||||
−0.988691 | + | 0.149965i | \(0.952084\pi\) | |||||||
\(272\) | 69229.4 | − | 28132.8i | 0.935735 | − | 0.380255i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −78436.3 | + | 7592.41i | −1.04476 | + | 0.101130i | ||||
\(275\) | 11238.9i | 0.148613i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30261.0 | 0.394388 | 0.197194 | − | 0.980364i | \(-0.436817\pi\) | ||||
0.197194 | + | 0.980364i | \(0.436817\pi\) | |||||||
\(278\) | 4869.15 | + | 50302.6i | 0.0630034 | + | 0.650880i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 34221.0 | + | 114891.i | 0.436492 | + | 1.46544i | ||||
\(281\) | −30448.5 | −0.385615 | −0.192807 | − | 0.981237i | \(-0.561759\pi\) | ||||
−0.192807 | + | 0.981237i | \(0.561759\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 102769.i | − | 1.28318i | −0.767046 | − | 0.641592i | \(-0.778274\pi\) | ||
0.767046 | − | 0.641592i | \(-0.221726\pi\) | |||||||
\(284\) | 9785.25 | + | 50071.5i | 0.121321 | + | 0.620803i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2362.78 | − | 24409.6i | −0.0288863 | − | 0.298421i | ||||
\(287\) | 29843.6i | 0.362316i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1686.57 | 0.0201934 | ||||||||
\(290\) | 95351.3 | − | 9229.73i | 1.13378 | − | 0.109747i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −67019.8 | + | 13097.4i | −0.786027 | + | 0.153610i | ||||
\(293\) | −40053.4 | −0.466557 | −0.233278 | − | 0.972410i | \(-0.574945\pi\) | ||||
−0.233278 | + | 0.972410i | \(0.574945\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19786.4i | 0.227364i | ||||||||
\(296\) | 86141.7 | − | 25657.9i | 0.983173 | − | 0.292845i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −95771.3 | + | 9270.39i | −1.07846 | + | 0.104392i | ||||
\(299\) | 56153.1i | 0.628104i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5313.68 | 0.0586492 | ||||||||
\(302\) | 11176.5 | + | 115463.i | 0.122544 | + | 1.26598i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −29387.7 | − | 72317.4i | −0.317993 | − | 0.782520i | ||||
\(305\) | −137653. | −1.47974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17196.5i | − | 0.182458i | −0.995830 | − | 0.0912291i | \(-0.970920\pi\) | ||
0.995830 | − | 0.0912291i | \(-0.0290796\pi\) | |||||||
\(308\) | −138374. | + | 27041.9i | −1.45866 | + | 0.285060i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6883.25 | + | 71110.0i | 0.0716259 | + | 0.739958i | ||||
\(311\) | − | 135448.i | − | 1.40039i | −0.713949 | − | 0.700197i | \(-0.753095\pi\) | ||
0.713949 | − | 0.700197i | \(-0.246905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29263.8 | −0.298705 | −0.149352 | − | 0.988784i | \(-0.547719\pi\) | ||||
−0.149352 | + | 0.988784i | \(0.547719\pi\) | |||||||
\(314\) | 44365.3 | − | 4294.44i | 0.449971 | − | 0.0435559i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23109.0 | + | 118250.i | 0.231424 | + | 1.18420i | ||||
\(317\) | 58389.3 | 0.581051 | 0.290526 | − | 0.956867i | \(-0.406170\pi\) | ||||
0.290526 | + | 0.956867i | \(0.406170\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 112669.i | 1.10719i | ||||||||
\(320\) | −78200.3 | + | 51120.3i | −0.763674 | + | 0.499222i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 321334. | − | 31104.2i | 3.09917 | − | 0.299991i | ||||
\(323\) | − | 89008.3i | − | 0.853150i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5984.14 | −0.0566546 | ||||||||
\(326\) | −1237.92 | − | 12788.8i | −0.0116481 | − | 0.120336i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −22290.6 | + | 6639.41i | −0.207193 | + | 0.0617137i | ||||
\(329\) | 287065. | 2.65209 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 92155.6i | 0.841135i | 0.907261 | + | 0.420568i | \(0.138169\pi\) | ||||
−0.907261 | + | 0.420568i | \(0.861831\pi\) | |||||||
\(332\) | −1799.08 | − | 9205.98i | −0.0163221 | − | 0.0835207i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8705.76 | − | 89938.1i | −0.0780393 | − | 0.806215i | ||||
\(335\) | − | 78042.8i | − | 0.695414i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −44787.4 | −0.394363 | −0.197182 | − | 0.980367i | \(-0.563179\pi\) | ||||
−0.197182 | + | 0.980367i | \(0.563179\pi\) | |||||||
\(338\) | −100716. | + | 9748.98i | −0.881583 | + | 0.0853348i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −104552. | + | 20432.1i | −0.904428 | + | 0.176748i | ||||
\(341\) | −84024.8 | −0.722602 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 159459.i | 1.35538i | ||||||||
\(344\) | 1182.15 | + | 3968.86i | 0.00998980 | + | 0.0335389i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −82578.8 | + | 7993.39i | −0.689789 | + | 0.0667696i | ||||
\(347\) | − | 105966.i | − | 0.880049i | −0.897986 | − | 0.440024i | \(-0.854970\pi\) | ||
0.897986 | − | 0.440024i | \(-0.145030\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 66799.1 | 0.548428 | 0.274214 | − | 0.961669i | \(-0.411582\pi\) | ||||
0.274214 | + | 0.961669i | \(0.411582\pi\) | |||||||
\(350\) | 3314.73 | + | 34244.0i | 0.0270590 | + | 0.279543i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −50982.7 | − | 97337.8i | −0.411469 | − | 0.785590i | ||||
\(353\) | 37451.3 | 0.300551 | 0.150275 | − | 0.988644i | \(-0.451984\pi\) | ||||
0.150275 | + | 0.988644i | \(0.451984\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 72731.2i | − | 0.577118i | ||||||
\(356\) | 90908.6 | − | 17765.8i | 0.717307 | − | 0.140180i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14471.7 | + | 149506.i | 0.112916 | + | 1.16652i | ||||
\(359\) | − | 117783.i | − | 0.913893i | −0.889494 | − | 0.456947i | \(-0.848943\pi\) | ||
0.889494 | − | 0.456947i | \(-0.151057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37342.4 | 0.286542 | ||||||||
\(362\) | −151370. | + | 14652.2i | −1.15511 | + | 0.111811i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14398.5 | − | 73677.6i | −0.108671 | − | 0.556074i | ||||
\(365\) | 97349.5 | 0.730715 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 119975.i | 0.890753i | 0.895343 | + | 0.445376i | \(0.146930\pi\) | ||||
−0.895343 | + | 0.445376i | \(0.853070\pi\) | |||||||
\(368\) | 94720.6 | + | 233089.i | 0.699438 | + | 1.72118i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −127537. | + | 12345.3i | −0.931610 | + | 0.0901772i | ||||
\(371\) | − | 268441.i | − | 1.95030i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −261060. | −1.87638 | −0.938192 | − | 0.346114i | \(-0.887501\pi\) | ||||
−0.938192 | + | 0.346114i | \(0.887501\pi\) | |||||||
\(374\) | −12071.5 | − | 124709.i | −0.0863012 | − | 0.891567i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 63864.4 | + | 214413.i | 0.451734 | + | 1.51661i | ||||
\(377\) | −59990.6 | −0.422085 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 138313.i | − | 0.962907i | −0.876472 | − | 0.481454i | \(-0.840109\pi\) | ||
0.876472 | − | 0.481454i | \(-0.159891\pi\) | |||||||
\(380\) | 21343.5 | + | 109216.i | 0.147808 | + | 0.756340i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2818.51 | + | 29117.7i | 0.0193149 | + | 0.199540i | ||||
\(383\) | 182153.i | 1.24176i | 0.783905 | + | 0.620880i | \(0.213225\pi\) | ||||
−0.783905 | + | 0.620880i | \(0.786775\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 200995. | 1.35602 | ||||||||
\(386\) | 242816. | − | 23503.9i | 1.62968 | − | 0.157748i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 170185. | − | 33258.6i | 1.13047 | − | 0.220922i | ||||
\(389\) | −143024. | −0.945171 | −0.472586 | − | 0.881285i | \(-0.656679\pi\) | ||||
−0.472586 | + | 0.881285i | \(0.656679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 286886.i | 1.87653i | ||||||||
\(392\) | −266372. | + | 79340.8i | −1.73347 | + | 0.516326i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −55305.7 | + | 5353.43i | −0.356268 | + | 0.0344858i | ||||
\(395\) | − | 171764.i | − | 1.10087i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −55426.8 | −0.351673 | −0.175837 | − | 0.984419i | \(-0.556263\pi\) | ||||
−0.175837 | + | 0.984419i | \(0.556263\pi\) | |||||||
\(398\) | 16596.8 | + | 171459.i | 0.104775 | + | 1.08242i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −24839.9 | + | 10094.2i | −0.155250 | + | 0.0630889i | ||||
\(401\) | −70455.5 | −0.438154 | −0.219077 | − | 0.975708i | \(-0.570305\pi\) | ||||
−0.219077 | + | 0.975708i | \(0.570305\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 44739.1i | − | 0.275472i | ||||||
\(404\) | 180630. | − | 35299.6i | 1.10669 | − | 0.216275i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 33229.9 | + | 343294.i | 0.201594 | + | 2.08264i | ||||
\(407\) | − | 150700.i | − | 0.909758i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 157877. | 0.943785 | 0.471892 | − | 0.881656i | \(-0.343571\pi\) | ||||
0.471892 | + | 0.881656i | \(0.343571\pi\) | |||||||
\(410\) | 33002.4 | − | 3194.54i | 0.196326 | − | 0.0190038i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −42468.6 | − | 217314.i | −0.250192 | − | 1.28024i | ||||
\(413\) | −71237.0 | −0.417643 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13372.1i | 0.0776434i | ||||||||
\(416\) | 51827.6 | − | 27145.8i | 0.299484 | − | 0.156861i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −130272. | + | 12609.9i | −0.745585 | + | 0.0721705i | ||||
\(419\) | − | 22310.6i | − | 0.127082i | −0.997979 | − | 0.0635409i | \(-0.979761\pi\) | ||
0.997979 | − | 0.0635409i | \(-0.0202393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −106342. | −0.599985 | −0.299992 | − | 0.953942i | \(-0.596984\pi\) | ||||
−0.299992 | + | 0.953942i | \(0.596984\pi\) | |||||||
\(422\) | 8887.53 | + | 91816.0i | 0.0499064 | + | 0.515577i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 200502. | − | 59721.0i | 1.11529 | − | 0.332197i | ||||
\(425\) | −30573.0 | −0.169262 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 495592.i | − | 2.71812i | ||||||
\(428\) | −45208.6 | − | 231334.i | −0.246793 | − | 1.26285i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −568.791 | − | 5876.12i | −0.00307621 | − | 0.0317800i | ||||
\(431\) | 270251.i | 1.45483i | 0.686197 | + | 0.727416i | \(0.259279\pi\) | ||||
−0.686197 | + | 0.727416i | \(0.740721\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −115964. | −0.618513 | −0.309256 | − | 0.950979i | \(-0.600080\pi\) | ||||
−0.309256 | + | 0.950979i | \(0.600080\pi\) | |||||||
\(434\) | −256018. | + | 24781.8i | −1.35922 | + | 0.131569i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 55669.8 | − | 10879.3i | 0.292851 | − | 0.0572306i | ||||
\(437\) | 299683. | 1.56928 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 285409.i | − | 1.48095i | −0.672087 | − | 0.740473i | \(-0.734602\pi\) | ||
0.672087 | − | 0.740473i | \(-0.265398\pi\) | |||||||
\(440\) | 44716.2 | + | 150126.i | 0.230972 | + | 0.775446i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 66401.3 | − | 6427.46i | 0.339885 | − | 0.0328999i | ||||
\(443\) | 269606.i | 1.37380i | 0.726753 | + | 0.686899i | \(0.241028\pi\) | ||||
−0.726753 | + | 0.686899i | \(0.758972\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −132049. | −0.666830 | ||||||||
\(446\) | 23022.8 | + | 237845.i | 0.115741 | + | 1.19571i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −184049. | − | 281545.i | −0.917017 | − | 1.40279i | ||||
\(449\) | 12218.4 | 0.0606070 | 0.0303035 | − | 0.999541i | \(-0.490353\pi\) | ||||
0.0303035 | + | 0.999541i | \(0.490353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38996.3i | 0.191721i | ||||||||
\(452\) | −195848. | + | 38273.6i | −0.958608 | + | 0.187336i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13102.4 | − | 135359.i | −0.0635681 | − | 0.656715i | ||||
\(455\) | 107020.i | 0.516943i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 296484. | 1.41961 | 0.709805 | − | 0.704398i | \(-0.248783\pi\) | ||||
0.709805 | + | 0.704398i | \(0.248783\pi\) | |||||||
\(458\) | 55946.8 | − | 5415.49i | 0.266713 | − | 0.0258171i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −68793.1 | − | 352017.i | −0.325109 | − | 1.66360i | ||||
\(461\) | 38233.3 | 0.179904 | 0.0899519 | − | 0.995946i | \(-0.471329\pi\) | ||||
0.0899519 | + | 0.995946i | \(0.471329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 210426.i | 0.981607i | 0.871270 | + | 0.490804i | \(0.163297\pi\) | ||||
−0.871270 | + | 0.490804i | \(0.836703\pi\) | |||||||
\(464\) | −249018. | + | 101194.i | −1.15663 | + | 0.470022i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 38309.9 | − | 3708.29i | 0.176417 | − | 0.0170766i | ||||
\(467\) | 58599.8i | 0.268697i | 0.990934 | + | 0.134348i | \(0.0428941\pi\) | ||||
−0.990934 | + | 0.134348i | \(0.957106\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 280978. | 1.27740 | ||||||||
\(470\) | −30728.2 | − | 317450.i | −0.139105 | − | 1.43707i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15848.4 | − | 53207.9i | −0.0711378 | − | 0.238832i | ||||
\(473\) | 6943.32 | 0.0310345 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31936.7i | 0.141548i | ||||||||
\(476\) | −73561.9 | − | 376419.i | −0.324668 | − | 1.66134i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10955.1 | + | 113175.i | 0.0479467 | + | 0.495332i | ||||
\(479\) | 123721.i | 0.539227i | 0.962969 | + | 0.269614i | \(0.0868960\pi\) | ||||
−0.962969 | + | 0.269614i | \(0.913104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 80240.6 | 0.346820 | ||||||||
\(482\) | −37782.5 | + | 3657.24i | −0.162629 | + | 0.0157420i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 49094.6 | − | 9594.33i | 0.209577 | − | 0.0409566i | ||||
\(485\) | −247202. | −1.05092 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 39541.5i | − | 0.166723i | −0.996519 | − | 0.0833614i | \(-0.973434\pi\) | ||
0.996519 | − | 0.0833614i | \(-0.0265656\pi\) | |||||||
\(488\) | 370164. | − | 110256.i | 1.55437 | − | 0.462981i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 394378. | − | 38174.7i | 1.64256 | − | 0.158995i | ||||
\(491\) | − | 97311.7i | − | 0.403647i | −0.979422 | − | 0.201824i | \(-0.935313\pi\) | ||
0.979422 | − | 0.201824i | \(-0.0646868\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −306492. | −1.26103 | ||||||||
\(494\) | −6714.16 | − | 69363.2i | −0.0275130 | − | 0.284233i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −75467.2 | − | 185710.i | −0.306757 | − | 0.754870i | ||||
\(497\) | 261855. | 1.06010 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 217620.i | − | 0.873974i | −0.899468 | − | 0.436987i | \(-0.856046\pi\) | ||
0.899468 | − | 0.436987i | \(-0.143954\pi\) | |||||||
\(500\) | 261372. | − | 51078.7i | 1.04549 | − | 0.204315i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11380.4 | + | 117570.i | 0.0451597 | + | 0.466539i | ||||
\(503\) | − | 190305.i | − | 0.752169i | −0.926585 | − | 0.376084i | \(-0.877270\pi\) | ||
0.926585 | − | 0.376084i | \(-0.122730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −262373. | −1.02881 | ||||||||
\(506\) | 419884. | − | 40643.6i | 1.63994 | − | 0.158742i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3075.11 | + | 15735.4i | 0.0119161 | + | 0.0609750i | ||||
\(509\) | −100460. | −0.387755 | −0.193878 | − | 0.981026i | \(-0.562106\pi\) | ||||
−0.193878 | + | 0.981026i | \(0.562106\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 350488.i | 1.34224i | ||||||||
\(512\) | 169344. | − | 200105.i | 0.645996 | − | 0.763341i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −56435.1 | + | 5462.75i | −0.213611 | + | 0.0206769i | ||||
\(515\) | 315658.i | 1.19015i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 375104. | 1.40337 | ||||||||
\(518\) | −44446.7 | − | 459174.i | −0.165646 | − | 1.71127i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −79934.9 | + | 23809.2i | −0.295617 | + | 0.0880517i | ||||
\(521\) | −417246. | −1.53715 | −0.768575 | − | 0.639759i | \(-0.779034\pi\) | ||||
−0.768575 | + | 0.639759i | \(0.779034\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 246542.i | − | 0.901339i | −0.892691 | − | 0.450669i | \(-0.851185\pi\) | ||
0.892691 | − | 0.450669i | \(-0.148815\pi\) | |||||||
\(524\) | −102956. | − | 526831.i | −0.374964 | − | 1.91871i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40911.7 | + | 422654.i | 0.147869 | + | 1.52761i | ||||
\(527\) | − | 228572.i | − | 0.823004i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −686081. | −2.45168 | ||||||||
\(530\) | −296855. | + | 28734.7i | −1.05680 | + | 0.102295i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −393209. | + | 76843.1i | −1.38931 | + | 0.271507i | ||||
\(533\) | −20763.6 | −0.0730883 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 336024.i | 1.17399i | ||||||||
\(536\) | 62510.3 | + | 209867.i | 0.217581 | + | 0.730490i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −228496. | + | 22117.8i | −0.789432 | + | 0.0764148i | ||||
\(539\) | 466004.i | 1.60403i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 65384.7 | 0.223399 | 0.111700 | − | 0.993742i | \(-0.464371\pi\) | ||||
0.111700 | + | 0.993742i | \(0.464371\pi\) | |||||||
\(542\) | 8489.00 | + | 87698.8i | 0.0288973 | + | 0.298535i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 264787. | − | 138688.i | 0.894745 | − | 0.468641i | ||||
\(545\) | −80863.1 | −0.272243 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 238533.i | − | 0.797213i | −0.917122 | − | 0.398607i | \(-0.869494\pi\) | ||
0.917122 | − | 0.398607i | \(-0.130506\pi\) | |||||||
\(548\) | −309360. | + | 60456.7i | −1.03016 | + | 0.201318i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4331.32 | + | 44746.3i | 0.0143184 | + | 0.147922i | ||||
\(551\) | 320163.i | 1.05455i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 618402. | 2.02218 | ||||||||
\(554\) | 120481. | − | 11662.2i | 0.392554 | − | 0.0379981i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 38772.0 | + | 198398.i | 0.125421 | + | 0.641782i | ||||
\(557\) | 412118. | 1.32835 | 0.664173 | − | 0.747579i | \(-0.268784\pi\) | ||||
0.664173 | + | 0.747579i | \(0.268784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3696.98i | 0.0118310i | ||||||||
\(560\) | 180525. | + | 444237.i | 0.575653 | + | 1.41657i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −121227. | + | 11734.5i | −0.383821 | + | 0.0371528i | ||||
\(563\) | 451490.i | 1.42440i | 0.701978 | + | 0.712199i | \(0.252301\pi\) | ||||
−0.701978 | + | 0.712199i | \(0.747699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 284478. | 0.891151 | ||||||||
\(566\) | −39605.8 | − | 409163.i | −0.123631 | − | 1.27721i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 58255.8 | + | 195583.i | 0.180569 | + | 0.606226i | ||||
\(569\) | 125491. | 0.387603 | 0.193801 | − | 0.981041i | \(-0.437918\pi\) | ||||
0.193801 | + | 0.981041i | \(0.437918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 295508.i | 0.906352i | 0.891421 | + | 0.453176i | \(0.149709\pi\) | ||||
−0.891421 | + | 0.453176i | \(0.850291\pi\) | |||||||
\(572\) | −18814.3 | − | 96273.7i | −0.0575038 | − | 0.294249i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11501.3 | + | 118819.i | 0.0349080 | + | 0.360630i | ||||
\(575\) | − | 102937.i | − | 0.311339i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −169123. | −0.507986 | −0.253993 | − | 0.967206i | \(-0.581744\pi\) | ||||
−0.253993 | + | 0.967206i | \(0.581744\pi\) | |||||||
\(578\) | 6714.89 | − | 649.983i | 0.0200994 | − | 0.00194557i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 376074. | − | 73494.4i | 1.11794 | − | 0.218473i | ||||
\(581\) | −48143.8 | −0.142622 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 350769.i | − | 1.03201i | ||||||
\(584\) | −261785. | + | 77974.4i | −0.767571 | + | 0.228626i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −159468. | + | 15436.1i | −0.464386 | + | 0.0449513i | ||||
\(587\) | − | 287012.i | − | 0.832959i | −0.909145 | − | 0.416480i | \(-0.863264\pi\) | ||
0.909145 | − | 0.416480i | \(-0.136736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −238768. | −0.688248 | ||||||||
\(590\) | 7625.41 | + | 78777.2i | 0.0219058 | + | 0.226306i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 333075. | − | 135352.i | 0.950384 | − | 0.386208i | ||||
\(593\) | 275747. | 0.784155 | 0.392078 | − | 0.919932i | \(-0.371756\pi\) | ||||
0.392078 | + | 0.919932i | \(0.371756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 546767.i | 1.54443i | ||||||||
\(596\) | −377730. | + | 73818.1i | −1.06338 | + | 0.207812i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21640.7 | + | 223567.i | 0.0605158 | + | 0.625182i | ||||
\(599\) | 498296.i | 1.38878i | 0.719598 | + | 0.694391i | \(0.244326\pi\) | ||||
−0.719598 | + | 0.694391i | \(0.755674\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −382620. | −1.05930 | −0.529650 | − | 0.848216i | \(-0.677677\pi\) | ||||
−0.529650 | + | 0.848216i | \(0.677677\pi\) | |||||||
\(602\) | 21155.8 | − | 2047.82i | 0.0583764 | − | 0.00565067i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 88995.9 | + | 455395.i | 0.243947 | + | 1.24829i | ||||
\(605\) | −71312.2 | −0.194829 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 11197.4i | − | 0.0303907i | −0.999885 | − | 0.0151954i | \(-0.995163\pi\) | ||
0.999885 | − | 0.0151954i | \(-0.00483702\pi\) | |||||||
\(608\) | −144874. | − | 276598.i | −0.391907 | − | 0.748242i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −548049. | + | 53049.6i | −1.47285 | + | 0.142568i | ||||
\(611\) | 199725.i | 0.534994i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 289927. | 0.771558 | 0.385779 | − | 0.922591i | \(-0.373933\pi\) | ||||
0.385779 | + | 0.922591i | \(0.373933\pi\) | |||||||
\(614\) | −6627.32 | − | 68466.0i | −0.0175793 | − | 0.181609i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −540501. | + | 160992.i | −1.42441 | + | 0.424271i | ||||
\(617\) | −477462. | −1.25420 | −0.627102 | − | 0.778937i | \(-0.715759\pi\) | ||||
−0.627102 | + | 0.778937i | \(0.715759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 254686.i | 0.664698i | 0.943156 | + | 0.332349i | \(0.107841\pi\) | ||||
−0.943156 | + | 0.332349i | \(0.892159\pi\) | |||||||
\(620\) | 54809.8 | + | 280464.i | 0.142585 | + | 0.729615i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −52199.8 | − | 539270.i | −0.134924 | − | 1.39388i | ||||
\(623\) | − | 475417.i | − | 1.22489i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −314195. | −0.804339 | ||||||||
\(626\) | −116511. | + | 11277.9i | −0.297315 | + | 0.0287793i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 174981. | − | 34195.7i | 0.443681 | − | 0.0867065i | ||||
\(629\) | 409949. | 1.03617 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 522734.i | 1.31287i | 0.754383 | + | 0.656435i | \(0.227936\pi\) | ||||
−0.754383 | + | 0.656435i | \(0.772064\pi\) | |||||||
\(632\) | 137578. | + | 461893.i | 0.344441 | + | 1.15640i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 232471. | − | 22502.5i | 0.578348 | − | 0.0559825i | ||||
\(635\) | − | 22856.5i | − | 0.0566842i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −248124. | −0.611492 | ||||||||
\(638\) | 43421.1 | + | 448578.i | 0.106674 | + | 1.10204i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −291645. | + | 233667.i | −0.712023 | + | 0.570477i | ||||
\(641\) | −399966. | −0.973434 | −0.486717 | − | 0.873560i | \(-0.661806\pi\) | ||||
−0.486717 | + | 0.873560i | \(0.661806\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 95576.4i | 0.231169i | 0.993298 | + | 0.115584i | \(0.0368740\pi\) | ||||
−0.993298 | + | 0.115584i | \(0.963126\pi\) | |||||||
\(644\) | 1.26737e6 | − | 247676.i | 3.05585 | − | 0.597190i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −34302.7 | − | 354377.i | −0.0821983 | − | 0.849181i | ||||
\(647\) | − | 310762.i | − | 0.742367i | −0.928560 | − | 0.371184i | \(-0.878952\pi\) | ||
0.928560 | − | 0.371184i | \(-0.121048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −93084.5 | −0.220998 | ||||||||
\(650\) | −23825.2 | + | 2306.21i | −0.0563910 | + | 0.00545849i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9857.28 | − | 50440.1i | −0.0231879 | − | 0.118654i | ||||
\(653\) | −648837. | −1.52163 | −0.760815 | − | 0.648969i | \(-0.775201\pi\) | ||||
−0.760815 | + | 0.648969i | \(0.775201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 765246.i | 1.78369i | ||||||||
\(656\) | −86188.8 | + | 35024.6i | −0.200283 | + | 0.0813890i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.14292e6 | − | 110631.i | 2.63975 | − | 0.255520i | ||||
\(659\) | − | 149570.i | − | 0.344408i | −0.985061 | − | 0.172204i | \(-0.944911\pi\) | ||
0.985061 | − | 0.172204i | \(-0.0550889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 170849. | 0.391029 | 0.195515 | − | 0.980701i | \(-0.437362\pi\) | ||||
0.195515 | + | 0.980701i | \(0.437362\pi\) | |||||||
\(662\) | 35515.6 | + | 366907.i | 0.0810407 | + | 0.837222i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10710.7 | − | 35959.3i | −0.0242931 | − | 0.0815596i | ||||
\(665\) | 571155. | 1.29155 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.03193e6i | − | 2.31953i | ||||||
\(668\) | −69322.0 | − | 354724.i | −0.155353 | − | 0.794945i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −30076.7 | − | 310719.i | −0.0670010 | − | 0.692179i | ||||
\(671\) | − | 647584.i | − | 1.43830i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 782980. | 1.72870 | 0.864351 | − | 0.502888i | \(-0.167729\pi\) | ||||
0.864351 | + | 0.502888i | \(0.167729\pi\) | |||||||
\(674\) | −178316. | + | 17260.5i | −0.392528 | + | 0.0379956i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −397231. | + | 77629.0i | −0.869260 | + | 0.169876i | ||||
\(677\) | −458234. | −0.999792 | −0.499896 | − | 0.866085i | \(-0.666628\pi\) | ||||
−0.499896 | + | 0.866085i | \(0.666628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 890005.i | − | 1.93042i | ||||||
\(680\) | −408388. | + | 121641.i | −0.883192 | + | 0.263065i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −334536. | + | 32382.1i | −0.719240 | + | 0.0696204i | ||||
\(683\) | − | 444767.i | − | 0.953434i | −0.879057 | − | 0.476717i | \(-0.841827\pi\) | ||
0.879057 | − | 0.476717i | \(-0.158173\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 449360. | 0.957663 | ||||||||
\(686\) | 61453.4 | + | 634868.i | 0.130586 | + | 1.34907i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6236.16 | + | 15346.0i | 0.0131747 | + | 0.0324204i | ||||
\(689\) | 186767. | 0.393425 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 373248.i | − | 0.781702i | −0.920454 | − | 0.390851i | \(-0.872181\pi\) | ||
0.920454 | − | 0.390851i | \(-0.127819\pi\) | |||||||
\(692\) | −325698. | + | 63649.6i | −0.680147 | + | 0.132918i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −40837.9 | − | 421891.i | −0.0847899 | − | 0.875955i | ||||
\(695\) | − | 288182.i | − | 0.596620i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −106081. | −0.218360 | ||||||||
\(698\) | 265953. | − | 25743.5i | 0.545877 | − | 0.0528393i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 26394.4 | + | 135061.i | 0.0538662 | + | 0.275636i | ||||
\(701\) | 699890. | 1.42427 | 0.712137 | − | 0.702041i | \(-0.247727\pi\) | ||||
0.712137 | + | 0.702041i | \(0.247727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 428235.i | − | 0.866507i | ||||||
\(704\) | −240495. | − | 367892.i | −0.485244 | − | 0.742292i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 149108. | − | 14433.3i | 0.299153 | − | 0.0289571i | ||||
\(707\) | − | 944624.i | − | 1.88982i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 305897. | 0.608531 | 0.304265 | − | 0.952587i | \(-0.401589\pi\) | ||||
0.304265 | + | 0.952587i | \(0.401589\pi\) | |||||||
\(710\) | −28029.7 | − | 289571.i | −0.0556035 | − | 0.574433i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 355096. | − | 105768.i | 0.700464 | − | 0.208638i | ||||
\(713\) | 769583. | 1.51383 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 139842.i | 0.273543i | ||||||||
\(716\) | 115235. | + | 589664.i | 0.224781 | + | 1.15021i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −45392.3 | − | 468942.i | −0.0880507 | − | 0.909641i | ||||
\(719\) | 265534.i | 0.513644i | 0.966459 | + | 0.256822i | \(0.0826755\pi\) | ||||
−0.966459 | + | 0.256822i | \(0.917325\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.13647e6 | −2.18618 | ||||||||
\(722\) | 148675. | − | 14391.3i | 0.285209 | − | 0.0276074i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −597015. | + | 116672.i | −1.13896 | + | 0.222582i | ||||
\(725\) | 109971. | 0.209220 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 901047.i | − | 1.70482i | −0.522874 | − | 0.852410i | \(-0.675140\pi\) | ||
0.522874 | − | 0.852410i | \(-0.324860\pi\) | |||||||
\(728\) | −85720.4 | − | 287790.i | −0.161741 | − | 0.543017i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 387586. | − | 37517.3i | 0.727315 | − | 0.0704021i | ||||
\(731\) | 18887.9i | 0.0353466i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −887881. | −1.65252 | −0.826261 | − | 0.563288i | \(-0.809536\pi\) | ||||
−0.826261 | + | 0.563288i | \(0.809536\pi\) | |||||||
\(734\) | 46236.7 | + | 477666.i | 0.0858212 | + | 0.886609i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 466950. | + | 891516.i | 0.862014 | + | 1.64579i | ||||
\(737\) | 367151. | 0.675943 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 401381.i | 0.734966i | 0.930030 | + | 0.367483i | \(0.119780\pi\) | ||||
−0.930030 | + | 0.367483i | \(0.880220\pi\) | |||||||
\(740\) | −503019. | + | 98302.6i | −0.918588 | + | 0.179515i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −103454. | − | 1.06877e6i | −0.187905 | − | 1.94122i | ||||
\(743\) | − | 314050.i | − | 0.568880i | −0.958694 | − | 0.284440i | \(-0.908192\pi\) | ||
0.958694 | − | 0.284440i | \(-0.0918077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 548671. | 0.988552 | ||||||||
\(746\) | −1.03938e6 | + | 100609.i | −1.86766 | + | 0.180784i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −96122.5 | − | 491863.i | −0.171799 | − | 0.879105i | ||||
\(749\) | −1.20979e6 | −2.15648 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 331743.i | − | 0.588195i | −0.955775 | − | 0.294098i | \(-0.904981\pi\) | ||
0.955775 | − | 0.294098i | \(-0.0950191\pi\) | |||||||
\(752\) | 336901. | + | 829049.i | 0.595754 | + | 1.46604i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −238846. | + | 23119.6i | −0.420122 | + | 0.0406666i | ||||
\(755\) | − | 661483.i | − | 1.16045i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 300610. | 0.524581 | 0.262290 | − | 0.964989i | \(-0.415522\pi\) | ||||
0.262290 | + | 0.964989i | \(0.415522\pi\) | |||||||
\(758\) | −53304.1 | − | 550678.i | −0.0927731 | − | 0.958428i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 127067. | + | 426604.i | 0.219991 | + | 0.738581i | ||||
\(761\) | −78374.5 | −0.135334 | −0.0676668 | − | 0.997708i | \(-0.521555\pi\) | ||||
−0.0676668 | + | 0.997708i | \(0.521555\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 291132.i | − | 0.500081i | ||||||
\(764\) | 22443.2 | + | 114843.i | 0.0384501 | + | 0.196751i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 70199.3 | + | 725221.i | 0.119640 | + | 1.23598i | ||||
\(767\) | − | 49562.9i | − | 0.0842493i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 987499. | 1.66988 | 0.834938 | − | 0.550345i | \(-0.185504\pi\) | ||||
0.834938 | + | 0.550345i | \(0.185504\pi\) | |||||||
\(770\) | 800242. | − | 77461.1i | 1.34971 | − | 0.130648i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 957687. | − | 187156.i | 1.60690 | − | 0.314029i | ||||
\(773\) | 622600. | 1.04196 | 0.520979 | − | 0.853569i | \(-0.325567\pi\) | ||||
0.520979 | + | 0.853569i | \(0.325567\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 82013.1i | 0.136546i | ||||||||
\(776\) | 664757. | − | 198003.i | 1.10393 | − | 0.328812i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −569436. | + | 55119.8i | −0.940774 | + | 0.0910643i | ||||
\(779\) | 110813.i | 0.182606i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 342163. | 0.560958 | ||||||||
\(782\) | 110562. | + | 1.14221e6i | 0.180798 | + | 1.86780i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.02995e6 | + | 418543.i | −1.67566 | + | 0.680939i | ||||
\(785\) | −254168. | −0.412459 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.09638e6i | 1.77016i | 0.465437 | + | 0.885081i | \(0.345897\pi\) | ||||
−0.465437 | + | 0.885081i | \(0.654103\pi\) | |||||||
\(788\) | −218130. | + | 42628.2i | −0.351288 | + | 0.0686507i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −66195.5 | − | 683858.i | −0.106066 | − | 1.09575i | ||||
\(791\) | 1.02421e6i | 1.63695i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 344807. | 0.548314 | ||||||||
\(794\) | −220676. | + | 21360.8i | −0.350037 | + | 0.0338826i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 132156. | + | 676250.i | 0.208575 | + | 1.06729i | ||||
\(797\) | −666106. | −1.04864 | −0.524321 | − | 0.851521i | \(-0.675681\pi\) | ||||
−0.524321 | + | 0.851521i | \(0.675681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.02039e6i | 1.59836i | ||||||||
\(800\) | −95007.3 | + | 49762.0i | −0.148449 | + | 0.0777532i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −280511. | + | 27152.7i | −0.436115 | + | 0.0422147i | ||||
\(803\) | 457979.i | 0.710255i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.84092e6 | −2.84081 | ||||||||
\(806\) | −17241.9 | − | 178124.i | −0.0265408 | − | 0.274190i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 705553. | − | 210154.i | 1.08070 | − | 0.321895i | ||||
\(809\) | −1.18960e6 | −1.81762 | −0.908812 | − | 0.417206i | \(-0.863009\pi\) | ||||
−0.908812 | + | 0.417206i | \(0.863009\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 189071.i | 0.287464i | 0.989617 | + | 0.143732i | \(0.0459104\pi\) | ||||
−0.989617 | + | 0.143732i | \(0.954090\pi\) | |||||||
\(812\) | 264602. | + | 1.35398e6i | 0.401312 | + | 2.05353i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −58078.1 | − | 599997.i | −0.0876523 | − | 0.905525i | ||||
\(815\) | 73266.6i | 0.110304i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19730.4 | 0.0295591 | ||||||||
\(818\) | 628571. | − | 60843.9i | 0.939394 | − | 0.0909307i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 130164. | − | 25437.5i | 0.193582 | − | 0.0378308i | ||||
\(821\) | 1.32025e6 | 1.95870 | 0.979352 | − | 0.202164i | \(-0.0647973\pi\) | ||||
0.979352 | + | 0.202164i | \(0.0647973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 498753.i | − | 0.736353i | −0.929756 | − | 0.368176i | \(-0.879982\pi\) | ||
0.929756 | − | 0.368176i | \(-0.120018\pi\) | |||||||
\(824\) | −252834. | − | 848844.i | −0.372376 | − | 1.25018i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −283622. | + | 27453.8i | −0.415700 | + | 0.0402386i | ||||
\(827\) | − | 160812.i | − | 0.235130i | −0.993065 | − | 0.117565i | \(-0.962491\pi\) | ||
0.993065 | − | 0.117565i | \(-0.0375088\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 70245.8 | 0.102214 | 0.0511071 | − | 0.998693i | \(-0.483725\pi\) | ||||
0.0511071 | + | 0.998693i | \(0.483725\pi\) | |||||||
\(830\) | 5153.45 | + | 53239.7i | 0.00748069 | + | 0.0772821i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 195884. | − | 128052.i | 0.282978 | − | 0.184986i | ||||
\(833\) | −1.26767e6 | −1.82690 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 515253.i | 0.739005i | ||||||||
\(836\) | −513802. | + | 100410.i | −0.735163 | + | 0.143670i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8598.23 | − | 88827.2i | −0.0122439 | − | 0.126491i | ||||
\(839\) | 568844.i | 0.808108i | 0.914735 | + | 0.404054i | \(0.132399\pi\) | ||||
−0.914735 | + | 0.404054i | \(0.867601\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 395172. | 0.558720 | ||||||||
\(842\) | −423389. | + | 40982.8i | −0.597193 | + | 0.0578066i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 70769.5 | + | 362130.i | 0.0993484 | + | 0.508370i | ||||
\(845\) | 576997. | 0.808091 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 256746.i | − | 0.357879i | ||||||
\(848\) | 775263. | − | 315044.i | 1.07810 | − | 0.438106i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −121723. | + | 11782.4i | −0.168475 | + | 0.0163079i | ||||
\(851\) | 1.38026e6i | 1.90591i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −959646. | −1.31890 | −0.659452 | − | 0.751747i | \(-0.729212\pi\) | ||||
−0.659452 | + | 0.751747i | \(0.729212\pi\) | |||||||
\(854\) | −190995. | − | 1.97314e6i | −0.261882 | − | 2.70547i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −269147. | − | 903610.i | −0.367317 | − | 1.23320i | ||||
\(857\) | −171138. | −0.233016 | −0.116508 | − | 0.993190i | \(-0.537170\pi\) | ||||
−0.116508 | + | 0.993190i | \(0.537170\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 75902.7i | 0.102866i | 0.998676 | + | 0.0514329i | \(0.0163788\pi\) | ||||
−0.998676 | + | 0.0514329i | \(0.983621\pi\) | |||||||
\(860\) | −4529.16 | − | 23175.9i | −0.00612380 | − | 0.0313357i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 104151. | + | 1.07597e6i | 0.140168 | + | 1.44806i | ||||
\(863\) | − | 727039.i | − | 0.976194i | −0.872790 | − | 0.488097i | \(-0.837691\pi\) | ||
0.872790 | − | 0.488097i | \(-0.162309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 473091. | 0.632285 | ||||||||
\(866\) | −461700. | + | 44691.2i | −0.615635 | + | 0.0595918i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.00976e6 | + | 197332.i | −1.34022 | + | 0.261914i | ||||
\(869\) | 808059. | 1.07005 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 195490.i | 0.257684i | ||||||||
\(872\) | 217451. | − | 64769.2i | 0.285975 | − | 0.0851796i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.19316e6 | − | 115494.i | 1.56198 | − | 0.151195i | ||||
\(875\) | − | 1.36688e6i | − | 1.78531i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5985.62 | 0.00778233 | 0.00389117 | − | 0.999992i | \(-0.498761\pi\) | ||||
0.00389117 | + | 0.999992i | \(0.498761\pi\) | |||||||
\(878\) | −109993. | − | 1.13633e6i | −0.142684 | − | 1.47406i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 235890. | + | 580479.i | 0.304609 | + | 0.749585i | ||||
\(881\) | 1.04403e6 | 1.34512 | 0.672559 | − | 0.740043i | \(-0.265195\pi\) | ||||
0.672559 | + | 0.740043i | \(0.265195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.43819e6i | 1.84457i | 0.386512 | + | 0.922284i | \(0.373680\pi\) | ||||
−0.386512 | + | 0.922284i | \(0.626320\pi\) | |||||||
\(884\) | 261893. | − | 51180.5i | 0.335134 | − | 0.0654937i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 103903. | + | 1.07341e6i | 0.132361 | + | 1.36741i | ||||
\(887\) | 29669.6i | 0.0377106i | 0.999822 | + | 0.0188553i | \(0.00600219\pi\) | ||||
−0.999822 | + | 0.0188553i | \(0.993998\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 82290.4 | 0.104123 | ||||||||
\(890\) | −525739. | + | 50890.0i | −0.663728 | + | 0.0642470i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 183325. | + | 938083.i | 0.230405 | + | 1.17899i | ||||
\(893\) | 1.06591e6 | 1.33665 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 856515.i | − | 1.06927i | ||||||
\(896\) | −841275. | − | 1.05001e6i | −1.04790 | − | 1.30791i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 48646.4 | − | 4708.83i | 0.0603251 | − | 0.00583930i | ||||
\(899\) | 822175.i | 1.01729i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 954194. | 1.17540 | ||||||||
\(902\) | 15028.7 | + | 155259.i | 0.0184717 | + | 0.190829i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −764996. | + | 227859.i | −0.936100 | + | 0.278824i | ||||
\(905\) | 867193. | 1.05881 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 110783.i | 0.134666i | 0.997731 | + | 0.0673331i | \(0.0214490\pi\) | ||||
−0.997731 | + | 0.0673331i | \(0.978551\pi\) | |||||||
\(908\) | −104332. | − | 533869.i | −0.126545 | − | 0.647535i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41244.2 | + | 426089.i | 0.0498059 | + | 0.514538i | ||||
\(911\) | 951442.i | 1.14642i | 0.819407 | + | 0.573212i | \(0.194303\pi\) | ||||
−0.819407 | + | 0.573212i | \(0.805697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −62908.9 | −0.0754694 | ||||||||
\(914\) | 1.18042e6 | − | 114261.i | 1.41301 | − | 0.136775i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 220659. | − | 43122.4i | 0.262985 | − | 0.0513939i | ||||
\(917\) | −2.75512e6 | −3.27644 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 930589.i | − | 1.10186i | −0.834551 | − | 0.550931i | \(-0.814273\pi\) | ||
0.834551 | − | 0.550931i | \(-0.185727\pi\) | |||||||
\(920\) | −409555. | − | 1.37501e6i | −0.483879 | − | 1.62453i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 152222. | − | 14734.6i | 0.179067 | − | 0.0173332i | ||||
\(923\) | 182185.i | 0.213850i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −147092. | −0.171912 | ||||||||
\(926\) | 81095.6 | + | 837789.i | 0.0945748 | + | 0.977041i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −952441. | + | 498861.i | −1.10597 | + | 0.579273i | ||||
\(929\) | 188066. | 0.217911 | 0.108955 | − | 0.994047i | \(-0.465249\pi\) | ||||
0.108955 | + | 0.994047i | \(0.465249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.32421e6i | 1.52777i | ||||||||
\(932\) | 151098. | − | 29528.3i | 0.173951 | − | 0.0339944i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22583.6 | + | 233309.i | 0.0258881 | + | 0.267447i | ||||
\(935\) | 714454.i | 0.817242i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.37071e6 | −1.56123 | −0.780613 | − | 0.625014i | \(-0.785093\pi\) | ||||
−0.780613 | + | 0.625014i | \(0.785093\pi\) | |||||||
\(938\) | 1.11868e6 | − | 108286.i | 1.27146 | − | 0.123074i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −244682. | − | 1.25205e6i | −0.276915 | − | 1.41699i | ||||
\(941\) | −256232. | −0.289370 | −0.144685 | − | 0.989478i | \(-0.546217\pi\) | ||||
−0.144685 | + | 0.989478i | \(0.546217\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 357166.i | − | 0.401649i | ||||||
\(944\) | −83604.2 | − | 205734.i | −0.0938175 | − | 0.230867i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27644.1 | − | 2675.87i | 0.0308901 | − | 0.00299008i | ||||
\(947\) | − | 397.662i | − | 0.000443419i | −1.00000 | 0.000221709i | \(-0.999929\pi\) | |||
1.00000 | 0.000221709i | \(-7.05723e-5\pi\) | ||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −243851. | −0.270765 | ||||||||
\(950\) | 12308.0 | + | 127153.i | 0.0136377 | + | 0.140889i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −437946. | − | 1.47032e6i | −0.483222 | − | 1.62233i | ||||
\(953\) | −709501. | −0.781209 | −0.390605 | − | 0.920559i | \(-0.627734\pi\) | ||||
−0.390605 | + | 0.920559i | \(0.627734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 166814.i | − | 0.182905i | ||||||
\(956\) | 87232.8 | + | 446374.i | 0.0954474 | + | 0.488408i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 47680.5 | + | 492581.i | 0.0519529 | + | 0.536719i | ||||
\(959\) | 1.61783e6i | 1.75912i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 310368. | 0.336071 | ||||||||
\(962\) | 319469. | − | 30923.7i | 0.345206 | − | 0.0334150i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −149018. | + | 29121.8i | −0.160355 | + | 0.0313375i | ||||
\(965\) | −1.39109e6 | −1.49382 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 506695.i | − | 0.541868i | −0.962598 | − | 0.270934i | \(-0.912667\pi\) | ||
0.962598 | − | 0.270934i | \(-0.0873326\pi\) | |||||||
\(968\) | 191767. | − | 57119.2i | 0.204656 | − | 0.0609581i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −984209. | + | 95268.7i | −1.04603 | + | 0.101253i | ||||
\(971\) | − | 27400.1i | − | 0.0290612i | −0.999894 | − | 0.0145306i | \(-0.995375\pi\) | ||
0.999894 | − | 0.0145306i | \(-0.00462540\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.03755e6 | 1.09593 | ||||||||
\(974\) | −15238.8 | − | 157430.i | −0.0160632 | − | 0.165947i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.43128e6 | − | 581629.i | 1.50253 | − | 0.610586i | ||||
\(977\) | 1.08148e6 | 1.13300 | 0.566500 | − | 0.824062i | \(-0.308297\pi\) | ||||
0.566500 | + | 0.824062i | \(0.308297\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 621222.i | − | 0.648159i | ||||||
\(980\) | 1.55546e6 | − | 303977.i | 1.61960 | − | 0.316511i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −37502.7 | − | 387436.i | −0.0388902 | − | 0.401770i | ||||
\(983\) | 1.10339e6i | 1.14188i | 0.820992 | + | 0.570940i | \(0.193421\pi\) | ||||
−0.820992 | + | 0.570940i | \(0.806579\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 316845. | 0.326568 | ||||||||
\(986\) | −1.22026e6 | + | 118118.i | −1.25516 | + | 0.121496i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −53463.4 | − | 273574.i | −0.0547700 | − | 0.280260i | ||||
\(989\) | −63593.8 | −0.0650163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 52573.8i | − | 0.0535331i | −0.999642 | − | 0.0267666i | \(-0.991479\pi\) | ||
0.999642 | − | 0.0267666i | \(-0.00852108\pi\) | |||||||
\(992\) | −372035. | − | 710301.i | −0.378059 | − | 0.721804i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.04255e6 | − | 100916.i | 1.05517 | − | 0.102138i | ||||
\(995\) | − | 982285.i | − | 0.992182i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −87335.5 | −0.0878619 | −0.0439309 | − | 0.999035i | \(-0.513988\pi\) | ||||
−0.0439309 | + | 0.999035i | \(0.513988\pi\) | |||||||
\(998\) | −83868.2 | − | 866432.i | −0.0842047 | − | 0.869908i | ||||
\(999\) | 0 | 0 |
(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 | 108.5.d.b.55.15 | yes | 16 | |
3.2 | odd | 2 | inner | 108.5.d.b.55.2 | yes | 16 | |
4.3 | odd | 2 | inner | 108.5.d.b.55.16 | yes | 16 | |
12.11 | even | 2 | inner | 108.5.d.b.55.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.d.b.55.1 | ✓ | 16 | 12.11 | even | 2 | inner | |
108.5.d.b.55.2 | yes | 16 | 3.2 | odd | 2 | inner | |
108.5.d.b.55.15 | yes | 16 | 1.1 | even | 1 | trivial | |
108.5.d.b.55.16 | yes | 16 | 4.3 | odd | 2 | inner |