Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not 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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.289 |
Dual form | 336.4.q.e.193.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | − | 2.59808i | 0.134164 | − | 0.232379i | −0.791114 | − | 0.611669i | \(-0.790498\pi\) |
0.925278 | + | 0.379290i | \(0.123832\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.50000 | − | 18.1865i | 0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.50000 | − | 12.9904i | −0.205576 | − | 0.356068i | 0.744740 | − | 0.667355i | \(-0.232573\pi\) |
−0.950316 | + | 0.311287i | \(0.899240\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −64.0000 | −1.36542 | −0.682708 | − | 0.730691i | \(-0.739198\pi\) | ||||
−0.682708 | + | 0.730691i | \(0.739198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.00000 | 0.154919 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −42.0000 | − | 72.7461i | −0.599206 | − | 1.03785i | −0.992939 | − | 0.118630i | \(-0.962150\pi\) |
0.393733 | − | 0.919225i | \(-0.371183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.00000 | + | 13.8564i | −0.0965961 | + | 0.167309i | −0.910274 | − | 0.414007i | \(-0.864129\pi\) |
0.813678 | + | 0.581317i | \(0.197462\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 52.5000 | − | 18.1865i | 0.545545 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −42.0000 | + | 72.7461i | −0.380765 | + | 0.659505i | −0.991172 | − | 0.132583i | \(-0.957673\pi\) |
0.610406 | + | 0.792088i | \(0.291006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 58.0000 | + | 100.459i | 0.464000 | + | 0.803672i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −297.000 | −1.90178 | −0.950888 | − | 0.309535i | \(-0.899827\pi\) | ||||
−0.950888 | + | 0.309535i | \(0.899827\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −126.500 | − | 219.104i | −0.732906 | − | 1.26943i | −0.955636 | − | 0.294550i | \(-0.904830\pi\) |
0.222731 | − | 0.974880i | \(-0.428503\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 22.5000 | − | 38.9711i | 0.118689 | − | 0.205576i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −42.0000 | − | 36.3731i | −0.202837 | − | 0.175662i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 158.000 | − | 273.664i | 0.702028 | − | 1.21595i | −0.265725 | − | 0.964049i | \(-0.585611\pi\) |
0.967753 | − | 0.251900i | \(-0.0810553\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −96.0000 | − | 166.277i | −0.394162 | − | 0.682708i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 360.000 | 1.37128 | 0.685641 | − | 0.727940i | \(-0.259522\pi\) | ||||
0.685641 | + | 0.727940i | \(0.259522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −26.0000 | −0.0922084 | −0.0461042 | − | 0.998937i | \(-0.514681\pi\) | ||||
−0.0461042 | + | 0.998937i | \(0.514681\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.5000 | + | 23.3827i | 0.0447214 | + | 0.0774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −15.0000 | + | 25.9808i | −0.0465527 | + | 0.0806316i | −0.888363 | − | 0.459142i | \(-0.848157\pi\) |
0.841810 | + | 0.539774i | \(0.181490\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −318.500 | − | 127.306i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 126.000 | − | 218.238i | 0.345952 | − | 0.599206i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −181.500 | − | 314.367i | −0.470395 | − | 0.814748i | 0.529032 | − | 0.848602i | \(-0.322555\pi\) |
−0.999427 | + | 0.0338538i | \(0.989222\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −45.0000 | −0.110324 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −48.0000 | −0.111540 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.50000 | − | 12.9904i | −0.0165494 | − | 0.0286645i | 0.857632 | − | 0.514264i | \(-0.171935\pi\) |
−0.874182 | + | 0.485599i | \(0.838601\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 59.0000 | − | 102.191i | 0.123839 | − | 0.214495i | −0.797440 | − | 0.603399i | \(-0.793813\pi\) |
0.921279 | + | 0.388903i | \(0.127146\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 126.000 | + | 109.119i | 0.251976 | + | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −96.0000 | + | 166.277i | −0.183190 | + | 0.317294i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −185.000 | − | 320.429i | −0.337334 | − | 0.584279i | 0.646597 | − | 0.762832i | \(-0.276192\pi\) |
−0.983930 | + | 0.178553i | \(0.942858\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −252.000 | −0.439670 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 342.000 | 0.571661 | 0.285831 | − | 0.958280i | \(-0.407731\pi\) | ||||
0.285831 | + | 0.958280i | \(0.407731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −181.000 | − | 313.501i | −0.290198 | − | 0.502638i | 0.683658 | − | 0.729802i | \(-0.260388\pi\) |
−0.973856 | + | 0.227165i | \(0.927054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −174.000 | + | 301.377i | −0.267891 | + | 0.464000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −262.500 | + | 90.9327i | −0.388502 | + | 0.134581i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 233.500 | − | 404.434i | 0.332542 | − | 0.575979i | −0.650468 | − | 0.759534i | \(-0.725427\pi\) |
0.983010 | + | 0.183555i | \(0.0587604\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −477.000 | −0.630814 | −0.315407 | − | 0.948957i | \(-0.602141\pi\) | ||||
−0.315407 | + | 0.948957i | \(0.602141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −252.000 | −0.321568 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −445.500 | − | 771.629i | −0.548996 | − | 0.950888i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −453.000 | + | 784.619i | −0.539527 | + | 0.934488i | 0.459402 | + | 0.888228i | \(0.348064\pi\) |
−0.998929 | + | 0.0462600i | \(0.985270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −224.000 | + | 1163.94i | −0.258039 | + | 1.34081i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 379.500 | − | 657.313i | 0.423143 | − | 0.732906i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24.0000 | + | 41.5692i | 0.0259195 | + | 0.0448938i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 503.000 | 0.526515 | 0.263257 | − | 0.964726i | \(-0.415203\pi\) | ||||
0.263257 | + | 0.964726i | \(0.415203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 135.000 | 0.137051 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 543.000 | + | 940.504i | 0.534956 | + | 0.926570i | 0.999165 | + | 0.0408451i | \(0.0130050\pi\) |
−0.464210 | + | 0.885725i | \(0.653662\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 868.000 | − | 1503.42i | 0.830355 | − | 1.43822i | −0.0674017 | − | 0.997726i | \(-0.521471\pi\) |
0.897757 | − | 0.440491i | \(-0.145196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 31.5000 | − | 163.679i | 0.0292770 | − | 0.152128i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −676.500 | + | 1171.73i | −0.611212 | + | 1.05865i | 0.379824 | + | 0.925059i | \(0.375985\pi\) |
−0.991036 | + | 0.133592i | \(0.957349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 185.000 | + | 320.429i | 0.162567 | + | 0.281574i | 0.935789 | − | 0.352562i | \(-0.114689\pi\) |
−0.773222 | + | 0.634136i | \(0.781356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 948.000 | 0.810632 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −648.000 | −0.539458 | −0.269729 | − | 0.962936i | \(-0.586934\pi\) | ||||
−0.269729 | + | 0.962936i | \(0.586934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 126.000 | + | 218.238i | 0.102170 | + | 0.176964i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 288.000 | − | 498.831i | 0.227569 | − | 0.394162i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1470.00 | + | 509.223i | −1.13239 | + | 0.392272i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 553.000 | − | 957.824i | 0.415477 | − | 0.719627i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 540.000 | + | 935.307i | 0.395855 | + | 0.685641i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 723.000 | 0.517337 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −377.000 | −0.263412 | −0.131706 | − | 0.991289i | \(-0.542046\pi\) | ||||
−0.131706 | + | 0.991289i | \(0.542046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −39.0000 | − | 67.5500i | −0.0266183 | − | 0.0461042i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −325.500 | + | 563.783i | −0.217092 | + | 0.376015i | −0.953918 | − | 0.300068i | \(-0.902991\pi\) |
0.736826 | + | 0.676083i | \(0.236324\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 224.000 | + | 193.990i | 0.146040 | + | 0.126474i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −40.5000 | + | 70.1481i | −0.0258199 | + | 0.0447214i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 885.000 | + | 1532.86i | 0.551903 | + | 0.955923i | 0.998137 | + | 0.0610074i | \(0.0194313\pi\) |
−0.446235 | + | 0.894916i | \(0.647235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1558.00 | 0.950704 | 0.475352 | − | 0.879796i | \(-0.342321\pi\) | ||||
0.475352 | + | 0.879796i | \(0.342321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −90.0000 | −0.0537544 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 480.000 | + | 831.384i | 0.280697 | + | 0.486181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −445.500 | + | 771.629i | −0.255150 | + | 0.441933i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | − | 1018.45i | −0.0824786 | − | 0.571429i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1227.00 | + | 2125.23i | −0.674629 | + | 1.16849i | 0.301948 | + | 0.953324i | \(0.402363\pi\) |
−0.976577 | + | 0.215168i | \(0.930970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 629.500 | + | 1090.33i | 0.339258 | + | 0.587612i | 0.984293 | − | 0.176540i | \(-0.0564906\pi\) |
−0.645035 | + | 0.764153i | \(0.723157\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 756.000 | 0.399470 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −759.000 | −0.393318 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 98.0000 | + | 169.741i | 0.0498169 | + | 0.0862854i | 0.889859 | − | 0.456236i | \(-0.150803\pi\) |
−0.840042 | + | 0.542522i | \(0.817470\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 544.500 | − | 943.102i | 0.271583 | − | 0.470395i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1176.00 | + | 1018.45i | 0.575663 | + | 0.498539i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −626.000 | + | 1084.26i | −0.300810 | + | 0.521019i | −0.976320 | − | 0.216332i | \(-0.930590\pi\) |
0.675509 | + | 0.737351i | \(0.263924\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −67.5000 | − | 116.913i | −0.0318477 | − | 0.0551618i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2646.00 | 1.22607 | 0.613035 | − | 0.790056i | \(-0.289949\pi\) | ||||
0.613035 | + | 0.790056i | \(0.289949\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1899.00 | 0.864360 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −72.0000 | − | 124.708i | −0.0321987 | − | 0.0557698i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 393.000 | − | 680.696i | 0.172712 | − | 0.299147i | −0.766655 | − | 0.642059i | \(-0.778080\pi\) |
0.939367 | + | 0.342913i | \(0.111414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2030.00 | − | 703.213i | 0.876878 | − | 0.303759i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.5000 | − | 38.9711i | 0.00955482 | − | 0.0165494i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1446.00 | + | 2504.55i | 0.603794 | + | 1.04580i | 0.992241 | + | 0.124331i | \(0.0396784\pi\) |
−0.388447 | + | 0.921471i | \(0.626988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1352.00 | 0.555212 | 0.277606 | − | 0.960695i | \(-0.410459\pi\) | ||||
0.277606 | + | 0.960695i | \(0.410459\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 354.000 | 0.142997 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −474.000 | − | 820.992i | −0.188374 | − | 0.326273i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −630.000 | + | 1091.19i | −0.246365 | + | 0.426716i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −94.5000 | + | 491.036i | −0.0363696 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1956.00 | − | 3387.89i | 0.741001 | − | 1.28345i | −0.211039 | − | 0.977478i | \(-0.567685\pi\) |
0.952040 | − | 0.305974i | \(-0.0989820\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −746.500 | − | 1292.98i | −0.278416 | − | 0.482230i | 0.692575 | − | 0.721345i | \(-0.256476\pi\) |
−0.970991 | + | 0.239115i | \(0.923143\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −576.000 | −0.211529 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4086.00 | −1.47774 | −0.738872 | − | 0.673846i | \(-0.764641\pi\) | ||||
−0.738872 | + | 0.673846i | \(0.764641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1778.00 | − | 3079.59i | −0.633362 | − | 1.09702i | −0.986860 | − | 0.161580i | \(-0.948341\pi\) |
0.353497 | − | 0.935436i | \(-0.384992\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 555.000 | − | 961.288i | 0.194760 | − | 0.337334i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1039.50 | + | 5401.40i | −0.359402 | + | 1.86751i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 540.000 | − | 935.307i | 0.183977 | − | 0.318657i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −378.000 | − | 654.715i | −0.126922 | − | 0.219835i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 240.000 | 0.0794313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1250.00 | −0.407837 | −0.203918 | − | 0.978988i | \(-0.565368\pi\) | ||||
−0.203918 | + | 0.978988i | \(0.565368\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 513.000 | + | 888.542i | 0.165024 | + | 0.285831i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −39.0000 | + | 67.5500i | −0.0123711 | + | 0.0214273i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4427.50 | + | 1533.73i | −1.38506 | + | 0.479799i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 543.000 | − | 940.504i | 0.167546 | − | 0.290198i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2688.00 | + | 4655.75i | 0.818165 | + | 1.41710i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −425.000 | −0.127624 | −0.0638119 | − | 0.997962i | \(-0.520326\pi\) | ||||
−0.0638119 | + | 0.997962i | \(0.520326\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1044.00 | −0.309333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1927.50 | + | 3338.53i | 0.563580 | + | 0.976149i | 0.997180 | + | 0.0750439i | \(0.0239097\pi\) |
−0.433600 | + | 0.901105i | \(0.642757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1094.00 | − | 1894.86i | 0.315692 | − | 0.546795i | −0.663892 | − | 0.747828i | \(-0.731097\pi\) |
0.979584 | + | 0.201033i | \(0.0644299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −630.000 | − | 545.596i | −0.179441 | − | 0.155401i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −426.000 | + | 737.854i | −0.119778 | + | 0.207461i | −0.919679 | − | 0.392670i | \(-0.871551\pi\) |
0.799902 | + | 0.600131i | \(0.204885\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 45.0000 | + | 77.9423i | 0.0124914 | + | 0.0216357i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1401.00 | 0.383986 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5508.00 | −1.49072 | −0.745362 | − | 0.666660i | \(-0.767723\pi\) | ||||
−0.745362 | + | 0.666660i | \(0.767723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −395.500 | − | 685.026i | −0.105711 | − | 0.183097i | 0.808317 | − | 0.588747i | \(-0.200379\pi\) |
−0.914029 | + | 0.405650i | \(0.867045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −808.500 | + | 636.529i | −0.210829 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 512.000 | − | 886.810i | 0.131894 | − | 0.228447i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −715.500 | − | 1239.28i | −0.182100 | − | 0.315407i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5265.00 | −1.32400 | −0.662000 | − | 0.749504i | \(-0.730292\pi\) | ||||
−0.662000 | + | 0.749504i | \(0.730292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1260.00 | 0.313105 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −378.000 | − | 654.715i | −0.0928285 | − | 0.160784i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3435.00 | − | 5949.59i | 0.833733 | − | 1.44407i | −0.0613246 | − | 0.998118i | \(-0.519532\pi\) |
0.895058 | − | 0.445950i | \(-0.147134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4424.00 | − | 3831.30i | −1.06137 | − | 0.919171i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1336.50 | − | 2314.89i | 0.316963 | − | 0.548996i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −111.000 | − | 192.258i | −0.0260249 | − | 0.0450765i | 0.852720 | − | 0.522369i | \(-0.174952\pi\) |
−0.878745 | + | 0.477292i | \(0.841618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1089.00 | −0.252441 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2718.00 | −0.622992 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3925.50 | − | 6799.17i | −0.889747 | − | 1.54109i | −0.840174 | − | 0.542317i | \(-0.817547\pi\) |
−0.0495729 | − | 0.998771i | \(-0.515786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2591.50 | − | 4488.61i | 0.580895 | − | 1.00614i | −0.414479 | − | 0.910059i | \(-0.636036\pi\) |
0.995374 | − | 0.0960800i | \(-0.0306305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3360.00 | + | 1163.94i | −0.744895 | + | 0.258039i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 870.000 | − | 1506.88i | 0.190774 | − | 0.330431i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2480.00 | + | 4295.49i | 0.537938 | + | 0.931736i | 0.999015 | + | 0.0443755i | \(0.0141298\pi\) |
−0.461077 | + | 0.887360i | \(0.652537\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2277.00 | 0.488604 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −774.000 | −0.164317 | −0.0821583 | − | 0.996619i | \(-0.526181\pi\) | ||||
−0.0821583 | + | 0.996619i | \(0.526181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1849.00 | + | 3202.56i | 0.388380 | + | 0.672695i | 0.992232 | − | 0.124402i | \(-0.0397013\pi\) |
−0.603852 | + | 0.797097i | \(0.706368\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −72.0000 | + | 124.708i | −0.0149646 | + | 0.0259195i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1260.00 | − | 6547.15i | 0.259148 | − | 1.34657i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1071.50 | + | 1855.89i | −0.218095 | + | 0.377751i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 754.500 | + | 1306.83i | 0.151992 | + | 0.263257i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6273.00 | −1.25076 | −0.625380 | − | 0.780321i | \(-0.715056\pi\) | ||||
−0.625380 | + | 0.780321i | \(0.715056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −45.0000 | −0.00888136 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 202.500 | + | 350.740i | 0.0395631 | + | 0.0685253i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2688.00 | − | 4655.75i | 0.519903 | − | 0.900499i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −91.0000 | + | 472.850i | −0.0174258 | + | 0.0905469i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1629.00 | + | 2821.51i | −0.308857 | + | 0.534956i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −177.000 | − | 306.573i | −0.0332295 | − | 0.0575551i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1684.00 | 0.313065 | 0.156533 | − | 0.987673i | \(-0.449968\pi\) | ||||
0.156533 | + | 0.987673i | \(0.449968\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5208.00 | 0.958812 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −660.000 | − | 1143.15i | −0.120338 | − | 0.208432i | 0.799563 | − | 0.600582i | \(-0.205065\pi\) |
−0.919901 | + | 0.392151i | \(0.871731\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4251.50 | − | 7363.81i | 0.767760 | − | 1.32980i | −0.171014 | − | 0.985269i | \(-0.554704\pi\) |
0.938775 | − | 0.344531i | \(-0.111962\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 472.500 | − | 163.679i | 0.0845154 | − | 0.0292770i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1288.50 | − | 2231.75i | 0.228295 | − | 0.395418i | −0.729008 | − | 0.684505i | \(-0.760018\pi\) |
0.957303 | + | 0.289087i | \(0.0933517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2227.50 | + | 3858.14i | 0.390959 | + | 0.677162i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4059.00 | −0.705767 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1344.00 | 0.231524 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3712.00 | − | 6429.37i | −0.633553 | − | 1.09735i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −555.000 | + | 961.288i | −0.0938580 | + | 0.162567i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 420.000 | + | 363.731i | 0.0703810 | + | 0.0609517i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −242.000 | + | 419.156i | −0.0401859 | + | 0.0696040i | −0.885419 | − | 0.464794i | \(-0.846128\pi\) |
0.845233 | + | 0.534398i | \(0.179462\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1422.00 | + | 2462.98i | 0.234009 | + | 0.405316i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1110.00 | −0.181032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8359.00 | −1.35117 | −0.675584 | − | 0.737283i | \(-0.736109\pi\) | ||||
−0.675584 | + | 0.737283i | \(0.736109\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −972.000 | − | 1683.55i | −0.155728 | − | 0.269729i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1897.50 | + | 3286.57i | −0.301335 | + | 0.521928i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3430.00 | + | 5346.84i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −378.000 | + | 654.715i | −0.0589879 | + | 0.102170i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −930.000 | − | 1610.81i | −0.143876 | − | 0.249201i | 0.785077 | − | 0.619398i | \(-0.212623\pi\) |
−0.928953 | + | 0.370197i | \(0.879290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1918.00 | −0.294178 | −0.147089 | − | 0.989123i | \(-0.546990\pi\) | ||||
−0.147089 | + | 0.989123i | \(0.546990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1728.00 | 0.262774 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1524.00 | + | 2639.65i | 0.229786 | + | 0.398000i | 0.957744 | − | 0.287620i | \(-0.0928642\pi\) |
−0.727959 | + | 0.685621i | \(0.759531\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 513.000 | − | 888.542i | 0.0766964 | − | 0.132842i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3528.00 | − | 3055.34i | −0.523030 | − | 0.452957i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0000 | + | 25.9808i | −0.00220521 | + | 0.00381953i | −0.867126 | − | 0.498089i | \(-0.834035\pi\) |
0.864921 | + | 0.501909i | \(0.167369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3301.50 | + | 5718.37i | 0.481338 | + | 0.833703i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3318.00 | 0.479752 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1086.00 | −0.155737 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5655.50 | − | 9795.61i | −0.804400 | − | 1.39326i | −0.916696 | − | 0.399586i | \(-0.869154\pi\) |
0.112296 | − | 0.993675i | \(-0.464180\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1620.00 | + | 2805.92i | −0.228547 | + | 0.395855i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6352.50 | + | 2200.57i | −0.888963 | + | 0.307946i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −604.000 | + | 1046.16i | −0.0838443 | + | 0.145223i | −0.904898 | − | 0.425628i | \(-0.860053\pi\) |
0.821054 | + | 0.570851i | \(0.193387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1084.50 | + | 1878.41i | 0.149342 | + | 0.258668i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19008.0 | 2.59672 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7640.00 | −1.03546 | −0.517731 | − | 0.855543i | \(-0.673223\pi\) | ||||
−0.517731 | + | 0.855543i | \(0.673223\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −565.500 | − | 979.475i | −0.0760405 | − | 0.131706i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6375.00 | − | 11041.8i | 0.850515 | − | 1.47314i | −0.0302291 | − | 0.999543i | \(-0.509624\pi\) |
0.880744 | − | 0.473592i | \(-0.157043\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −157.500 | + | 818.394i | −0.0208492 | + | 0.108336i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 117.000 | − | 202.650i | 0.0153681 | − | 0.0266183i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1563.00 | − | 2707.20i | −0.203720 | − | 0.352854i | 0.746004 | − | 0.665942i | \(-0.231970\pi\) |
−0.949724 | + | 0.313087i | \(0.898637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7056.00 | 0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1953.00 | −0.250676 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −700.500 | − | 1213.30i | −0.0892303 | − | 0.154551i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2966.00 | − | 5137.26i | 0.374960 | − | 0.649450i | −0.615361 | − | 0.788246i | \(-0.710990\pi\) |
0.990321 | + | 0.138795i | \(0.0443230\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −168.000 | + | 872.954i | −0.0210790 | + | 0.109530i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −804.000 | + | 1392.57i | −0.100124 | + | 0.173420i | −0.911736 | − | 0.410777i | \(-0.865257\pi\) |
0.811611 | + | 0.584198i | \(0.198591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8096.00 | + | 14022.7i | 1.00072 | + | 1.73330i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −243.000 | −0.0298142 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4740.00 | −0.577280 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2232.50 | + | 3866.80i | 0.269902 | + | 0.467484i | 0.968836 | − | 0.247702i | \(-0.0796753\pi\) |
−0.698934 | + | 0.715186i | \(0.746342\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2655.00 | + | 4598.59i | −0.318641 | + | 0.551903i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −262.500 | + | 90.9327i | −0.0312755 | + | 0.0108342i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −715.500 | + | 1239.28i | −0.0846326 | + | 0.146588i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2337.00 | + | 4047.80i | 0.274445 | + | 0.475352i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1584.00 | 0.184686 | 0.0923430 | − | 0.995727i | \(-0.470564\pi\) | ||||
0.0923430 | + | 0.995727i | \(0.470564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1330.00 | −0.153967 | −0.0769837 | − | 0.997032i | \(-0.524529\pi\) | ||||
−0.0769837 | + | 0.997032i | \(0.524529\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −135.000 | − | 233.827i | −0.0155176 | − | 0.0268772i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4872.00 | − | 8438.55i | 0.556063 | − | 0.963129i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1652.00 | − | 1430.67i | −0.187227 | − | 0.162143i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1440.00 | + | 2494.15i | −0.162060 | + | 0.280697i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4794.00 | + | 8303.45i | 0.535775 | + | 0.927989i | 0.999125 | + | 0.0418139i | \(0.0133137\pi\) |
−0.463351 | + | 0.886175i | \(0.653353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 494.000 | 0.0548271 | 0.0274135 | − | 0.999624i | \(-0.491273\pi\) | ||||
0.0274135 | + | 0.999624i | \(0.491273\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2673.00 | −0.294622 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −672.000 | − | 1163.94i | −0.0735609 | − | 0.127411i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8004.50 | + | 13864.2i | −0.870237 | + | 1.50729i | −0.00848508 | + | 0.999964i | \(0.502701\pi\) |
−0.861752 | + | 0.507330i | \(0.830632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2425.50 | − | 1909.59i | 0.261905 | − | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3886.50 | − | 6731.62i | 0.416824 | − | 0.721961i | −0.578794 | − | 0.815474i | \(-0.696476\pi\) |
0.995618 | + | 0.0935130i | \(0.0298097\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1359.00 | + | 2353.86i | 0.144770 | + | 0.250749i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7362.00 | −0.778995 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 864.000 | 0.0908122 | 0.0454061 | − | 0.998969i | \(-0.485542\pi\) | ||||
0.0454061 | + | 0.998969i | \(0.485542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2700.00 | − | 4676.54i | −0.281903 | − | 0.488269i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1888.50 | + | 3270.98i | −0.195871 | + | 0.339258i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2688.00 | + | 2327.88i | 0.276957 | + | 0.239852i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1259.50 | + | 2181.52i | −0.128921 | + | 0.223298i | −0.923259 | − | 0.384179i | \(-0.874485\pi\) |
0.794338 | + | 0.607476i | \(0.207818\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1134.00 | + | 1964.15i | 0.115317 | + | 0.199735i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −342.000 | −0.0345521 | −0.0172761 | − | 0.999851i | \(-0.505499\pi\) | ||||
−0.0172761 | + | 0.999851i | \(0.505499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4336.00 | 0.435229 | 0.217614 | − | 0.976035i | \(-0.430172\pi\) | ||||
0.217614 | + | 0.976035i | \(0.430172\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1138.50 | − | 1971.94i | −0.113541 | − | 0.196659i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9318.00 | − | 16139.2i | 0.923310 | − | 1.59922i | 0.129052 | − | 0.991638i | \(-0.458806\pi\) |
0.794257 | − | 0.607581i | \(-0.207860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6475.00 | + | 2243.01i | −0.637500 | + | 0.220837i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −294.000 | + | 509.223i | −0.0287618 | + | 0.0498169i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 195.000 | + | 337.750i | 0.0189558 | + | 0.0328325i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1856.00 | −0.179282 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3267.00 | 0.313597 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7539.00 | + | 13057.9i | 0.719135 | + | 1.24558i | 0.961343 | + | 0.275354i | \(0.0887951\pi\) |
−0.242208 | + | 0.970224i | \(0.577872\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10112.0 | + | 17514.5i | −0.958560 | + | 1.66028i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −882.000 | + | 4583.01i | −0.0830898 | + | 0.431747i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 754.500 | − | 1306.83i | 0.0706393 | − | 0.122351i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3110.50 | + | 5387.54i | 0.289425 | + | 0.501300i | 0.973673 | − | 0.227950i | \(-0.0732024\pi\) |
−0.684247 | + | 0.729250i | \(0.739869\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3756.00 | −0.347346 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7371.00 | 0.677492 | 0.338746 | − | 0.940878i | \(-0.389997\pi\) | ||||
0.338746 | + | 0.940878i | \(0.389997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12474.0 | + | 21605.6i | 1.13956 | + | 1.97377i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 202.500 | − | 350.740i | 0.0183873 | − | 0.0318477i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1197.00 | − | 6219.79i | 0.108034 | − | 0.561360i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2137.00 | − | 3701.39i | 0.191714 | − | 0.332058i | −0.754104 | − | 0.656755i | \(-0.771929\pi\) |
0.945818 | + | 0.324696i | \(0.105262\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3969.00 | + | 6874.51i | 0.353936 | + | 0.613035i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2520.00 | 0.223382 | 0.111691 | − | 0.993743i | \(-0.464373\pi\) | ||||
0.111691 | + | 0.993743i | \(0.464373\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3258.00 | 0.287087 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2848.50 | + | 4933.75i | 0.249519 | + | 0.432180i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7138.50 | − | 12364.2i | 0.621628 | − | 1.07669i | −0.367555 | − | 0.930002i | \(-0.619805\pi\) |
0.989183 | − | 0.146689i | \(-0.0468616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6335.00 | + | 2194.51i | −0.548423 | + | 0.189979i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 216.000 | − | 374.123i | 0.0185899 | − | 0.0321987i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2604.00 | − | 4510.26i | −0.222808 | − | 0.385914i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 450.000 | 0.0382804 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2358.00 | 0.199431 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3153.00 | + | 5461.16i | 0.265135 | + | 0.459228i | 0.967599 | − | 0.252492i | \(-0.0812501\pi\) |
−0.702464 | + | 0.711719i | \(0.747917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4036.00 | − | 6990.56i | 0.337442 | − | 0.584466i | −0.646509 | − | 0.762906i | \(-0.723772\pi\) |
0.983951 | + | 0.178440i | \(0.0571051\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4872.00 | + | 4219.28i | 0.405012 | + | 0.350751i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10626.0 | + | 18404.8i | −0.878322 | + | 1.52130i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2555.50 | + | 4426.26i | 0.210035 | + | 0.363792i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 135.000 | 0.0110330 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23040.0 | −1.87237 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2029.50 | + | 3515.20i | 0.164005 | + | 0.284066i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4338.00 | + | 7513.64i | −0.348601 | + | 0.603794i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 735.000 | + | 5092.23i | 0.0587360 | + | 0.406935i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11429.0 | − | 19795.6i | 0.908264 | − | 1.57316i | 0.0917903 | − | 0.995778i | \(-0.470741\pi\) |
0.816474 | − | 0.577382i | \(-0.195926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2028.00 | + | 3512.60i | 0.160276 | + | 0.277606i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1110.00 | 0.0872425 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24724.0 | 1.93258 | 0.966291 | − | 0.257454i | \(-0.0828835\pi\) | ||||
0.966291 | + | 0.257454i | \(0.0828835\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 531.000 | + | 919.719i | 0.0412796 | + | 0.0714985i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2376.00 | − | 4115.35i | 0.183704 | − | 0.318185i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6538.00 | − | 5662.07i | −0.502756 | − | 0.435399i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1422.00 | − | 2462.98i | 0.108758 | − | 0.188374i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4921.50 | + | 8524.29i | 0.374382 | + | 0.648448i | 0.990234 | − | 0.139413i | \(-0.0445216\pi\) |
−0.615853 | + | 0.787861i | \(0.711188\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1664.00 | 0.125903 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3780.00 | −0.284477 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6685.50 | − | 11579.6i | −0.500462 | − | 0.866826i | −1.00000 | 0.000533812i | \(-0.999830\pi\) | |
0.499538 | − | 0.866292i | \(-0.333503\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −972.000 | + | 1683.55i | −0.0723758 | + | 0.125359i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1417.50 | + | 491.036i | −0.104990 | + | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2616.00 | − | 4531.04i | 0.192739 | − | 0.333834i | −0.753418 | − | 0.657542i | \(-0.771596\pi\) |
0.946157 | + | 0.323708i | \(0.104930\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7199.00 | − | 12469.0i | −0.527616 | − | 0.913858i | −0.999482 | − | 0.0321874i | \(-0.989753\pi\) |
0.471866 | − | 0.881670i | \(-0.343581\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11736.0 | 0.855634 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9744.00 | −0.706701 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9935.50 | − | 17208.8i | −0.716846 | − | 1.24161i | −0.962243 | − | 0.272191i | \(-0.912252\pi\) |
0.245397 | − | 0.969423i | \(-0.421082\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2239.50 | − | 3878.93i | 0.160743 | − | 0.278416i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1669.50 | + | 8674.98i | −0.119213 | + | 0.619447i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2722.50 | + | 4715.51i | −0.193404 | + | 0.334985i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −864.000 | − | 1496.49i | −0.0610633 | − | 0.105765i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16137.0 | 1.13466 | 0.567330 | − | 0.823491i | \(-0.307976\pi\) | ||||
0.567330 | + | 0.823491i | \(0.307976\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4048.00 | 0.283183 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6129.00 | − | 10615.7i | −0.426588 | − | 0.738872i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10662.0 | − | 18467.1i | 0.738340 | − | 1.27884i | −0.214902 | − | 0.976636i | \(-0.568943\pi\) |
0.953242 | − | 0.302207i | \(-0.0977235\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −882.000 | + | 4583.01i | −0.0607705 | + | 0.315773i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5334.00 | − | 9238.76i | 0.365672 | − | 0.633362i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4323.00 | − | 7487.66i | −0.294880 | − | 0.510747i | 0.680077 | − | 0.733141i | \(-0.261946\pi\) |
−0.974957 | + | 0.222394i | \(0.928613\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11195.0 | 0.759823 | 0.379911 | − | 0.925023i | \(-0.375954\pi\) | ||||
0.379911 | + | 0.925023i | \(0.375954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3330.00 | 0.224889 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1659.00 | − | 2873.47i | −0.111484 | − | 0.193096i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4485.50 | + | 7769.11i | −0.299935 | + | 0.519503i | −0.976121 | − | 0.217228i | \(-0.930298\pi\) |
0.676185 | + | 0.736731i | \(0.263632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15592.5 | + | 5401.40i | −1.03750 | + | 0.359402i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 960.000 | − | 1662.77i | 0.0635637 | − | 0.110096i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6386.00 | + | 11060.9i | 0.420764 | + | 0.728784i | 0.996014 | − | 0.0891932i | \(-0.0284288\pi\) |
−0.575251 | + | 0.817977i | \(0.695096\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3240.00 | 0.212438 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12762.0 | 0.832705 | 0.416352 | − | 0.909203i | \(-0.363308\pi\) | ||||
0.416352 | + | 0.909203i | \(0.363308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6421.00 | + | 11121.5i | 0.416933 | + | 0.722150i | 0.995629 | − | 0.0933936i | \(-0.0297715\pi\) |
−0.578696 | + | 0.815543i | \(0.696438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1134.00 | − | 1964.15i | 0.0732783 | − | 0.126922i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12684.0 | + | 10984.7i | 0.815688 | + | 0.706407i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6165.50 | + | 10679.0i | −0.394592 | + | 0.683453i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 360.000 | + | 623.538i | 0.0229298 | + | 0.0397157i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26544.0 | −1.68264 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21365.0 | −1.34790 | −0.673952 | − | 0.738775i | \(-0.735404\pi\) | ||||
−0.673952 | + | 0.738775i | \(0.735404\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1875.00 | − | 3247.60i | −0.117732 | − | 0.203918i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −565.500 | + | 979.475i | −0.0353404 | + | 0.0612114i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20384.0 | + | 8147.57i | 1.26789 | + | 0.506779i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1539.00 | + | 2665.63i | −0.0952768 | + | 0.165024i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4137.00 | − | 7165.49i | −0.254917 | − | 0.441529i | 0.709956 | − | 0.704246i | \(-0.248715\pi\) |
−0.964873 | + | 0.262717i | \(0.915381\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27998.0 | −1.71716 | −0.858580 | − | 0.512680i | \(-0.828653\pi\) | ||||
−0.858580 | + | 0.512680i | \(0.828653\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −234.000 | −0.0142849 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8733.00 | − | 15126.0i | −0.530649 | − | 0.919110i | −0.999360 | − | 0.0357592i | \(-0.988615\pi\) |
0.468712 | − | 0.883351i | \(-0.344718\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −112.500 | + | 194.856i | −0.00680433 | + | 0.0117854i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10626.0 | − | 9202.39i | −0.639732 | − | 0.554024i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1078.50 | + | 1868.02i | −0.0646324 | + | 0.111947i | −0.896531 | − | 0.442981i | \(-0.853921\pi\) |
0.831898 | + | 0.554928i | \(0.187254\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 976.500 | + | 1691.35i | 0.0582519 | + | 0.100895i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3258.00 | 0.193465 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19944.0 | −1.17892 | −0.589460 | − | 0.807798i | \(-0.700659\pi\) | ||||
−0.589460 | + | 0.807798i | \(0.700659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13753.0 | − | 23820.9i | −0.809273 | − | 1.40170i | −0.913368 | − | 0.407135i | \(-0.866528\pi\) |
0.104095 | − | 0.994567i | \(-0.466806\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8064.00 | + | 13967.3i | −0.472368 | + | 0.818165i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 840.000 | − | 290.985i | 0.0489832 | − | 0.0169683i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12474.0 | − | 21605.6i | 0.724131 | − | 1.25423i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −637.500 | − | 1104.18i | −0.0368418 | − | 0.0638119i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1770.00 | −0.101833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19123.0 | −1.09530 | −0.547650 | − | 0.836707i | \(-0.684478\pi\) | ||||
−0.547650 | + | 0.836707i | \(0.684478\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1566.00 | − | 2712.39i | −0.0892968 | − | 0.154667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6928.50 | + | 12000.5i | −0.393329 | + | 0.681266i | −0.992886 | − | 0.119066i | \(-0.962010\pi\) |
0.599557 | + | 0.800332i | \(0.295343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1760.50 | − | 9147.83i | 0.0995019 | − | 0.517027i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5782.50 | + | 10015.6i | −0.325383 | + | 0.563580i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11122.5 | − | 19264.7i | −0.623120 | − | 1.07927i | −0.988901 | − | 0.148574i | \(-0.952532\pi\) |
0.365782 | − | 0.930701i | \(-0.380802\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5310.00 | 0.296182 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6564.00 | 0.364530 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11616.0 | + | 20119.5i | 0.642285 | + | 1.11247i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −320.000 | + | 554.256i | −0.0176170 | + | 0.0305136i | −0.874700 | − | 0.484666i | \(-0.838941\pi\) |
0.857082 | + | 0.515179i | \(0.172275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 472.500 | − | 2455.18i | 0.0259001 | − | 0.134581i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2337.00 | − | 4047.80i | 0.127550 | − | 0.220924i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15120.0 | − | 26188.6i | −0.821680 | − | 1.42319i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2556.00 | −0.138307 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15561.0 | −0.838418 | −0.419209 | − | 0.907890i | \(-0.637693\pi\) | ||||
−0.419209 | + | 0.907890i | \(0.637693\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2528.00 | + | 4378.62i | 0.135626 | + | 0.234912i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −135.000 | + | 233.827i | −0.00721191 | + | 0.0124914i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19005.0 | − | 6583.53i | 1.01097 | − | 0.350211i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2767.00 | + | 4792.58i | −0.146568 | + | 0.253864i | −0.929957 | − | 0.367668i | \(-0.880156\pi\) |
0.783389 | + | 0.621532i | \(0.213489\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2101.50 | + | 3639.90i | 0.110847 | + | 0.191993i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21252.0 | 1.11626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2880.00 | 0.150638 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8262.00 | − | 14310.2i | −0.430335 | − | 0.745362i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10923.0 | + | 18919.2i | −0.566564 | + | 0.981317i | 0.430339 | + | 0.902667i | \(0.358394\pi\) |
−0.996902 | + | 0.0786494i | \(0.974939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24304.0 | − | 21047.9i | −1.25538 | − | 1.08719i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1186.50 | − | 2055.08i | 0.0610324 | − | 0.105711i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17226.0 | − | 29836.3i | −0.882424 | − | 1.52840i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11089.0 | 0.565706 | 0.282853 | − | 0.959163i | \(-0.408719\pi\) | ||||
0.282853 | + | 0.959163i | \(0.408719\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1092.00 | + | 1891.40i | 0.0552518 | + | 0.0956990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5881.00 | + | 10186.2i | −0.296343 | + | 0.513282i | −0.975296 | − | 0.220900i | \(-0.929101\pi\) |
0.678953 | + | 0.734182i | \(0.262434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2866.50 | − | 1145.75i | −0.143854 | − | 0.0574989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2775.00 | + | 4806.44i | −0.138695 | + | 0.240227i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11363.0 | − | 19681.3i | −0.565622 | − | 0.979686i | −0.996992 | − | 0.0775108i | \(-0.975303\pi\) |
0.431369 | − | 0.902175i | \(-0.358031\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3072.00 | 0.152298 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6678.00 | −0.329734 | −0.164867 | − | 0.986316i | \(-0.552719\pi\) | ||||
−0.164867 | + | 0.986316i | \(0.552719\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3681.00 | + | 6375.68i | 0.181022 | + | 0.313539i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2146.50 | − | 3717.85i | 0.105136 | − | 0.182100i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18942.0 | + | 16404.3i | 0.924066 | + | 0.800265i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9993.50 | + | 17309.2i | −0.485577 | + | 0.841043i | −0.999863 | − | 0.0165754i | \(-0.994724\pi\) |
0.514286 | + | 0.857619i | \(0.328057\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7897.50 | − | 13678.9i | −0.382206 | − | 0.662000i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3777.00 | 0.182065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 314.000 | 0.0150760 | 0.00753799 | − | 0.999972i | \(-0.497601\pi\) | ||||
0.00753799 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1890.00 | + | 3273.58i | 0.0903856 | + | 0.156552i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5748.00 | − | 9955.83i | 0.273804 | − | 0.474242i | −0.696029 | − | 0.718014i | \(-0.745051\pi\) |
0.969833 | + | 0.243772i | \(0.0783847\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6475.00 | − | 2243.01i | 0.307222 | − | 0.106425i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1134.00 | − | 1964.15i | 0.0535946 | − | 0.0928285i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 480.000 | + | 831.384i | 0.0225969 | + | 0.0391389i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2765.00 | 0.129660 | 0.0648299 | − | 0.997896i | \(-0.479350\pi\) | ||||
0.0648299 | + | 0.997896i | \(0.479350\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20610.0 | 0.962712 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7023.00 | + | 12164.2i | 0.326778 | + | 0.565997i | 0.981871 | − | 0.189552i | \(-0.0607036\pi\) |
−0.655092 | + | 0.755549i | \(0.727370\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14674.0 | − | 25416.1i | 0.680136 | − | 1.17803i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3318.00 | − | 17240.8i | 0.153195 | − | 0.796025i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2880.00 | + | 4988.31i | −0.132460 | + | 0.229428i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2565.00 | − | 4442.71i | −0.117520 | − | 0.203550i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8019.00 | 0.365997 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 588.000 | 0.0267345 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9257.00 | − | 16033.6i | −0.419284 | − | 0.726221i | 0.576584 | − | 0.817038i | \(-0.304385\pi\) |
−0.995868 | + | 0.0908171i | \(0.971052\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 333.000 | − | 576.773i | 0.0150255 | − | 0.0260249i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2268.00 | + | 11784.9i | −0.101948 | + | 0.529737i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3776.00 | + | 6540.22i | −0.169092 | + | 0.292875i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1633.50 | − | 2829.30i | −0.0728733 | − | 0.126220i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27495.0 | −1.22199 | −0.610993 | − | 0.791636i | \(-0.709230\pi\) | ||||
−0.610993 | + | 0.791636i | \(0.709230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2520.00 | 0.111578 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4077.00 | − | 7061.57i | −0.179842 | − | 0.311496i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2715.00 | + | 4702.52i | −0.119315 | + | 0.206660i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4410.00 | − | 1527.67i | 0.193083 | − | 0.0668860i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11776.5 | − | 20397.5i | 0.513696 | − | 0.889747i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3972.00 | + | 6879.71i | 0.172618 | + | 0.298983i | 0.939334 | − | 0.343003i | \(-0.111444\pi\) |
−0.766716 | + | 0.641986i | \(0.778111\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28942.0 | 1.25313 | 0.626567 | − | 0.779368i | \(-0.284460\pi\) | ||||
0.626567 | + | 0.779368i | \(0.284460\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15549.0 | 0.670759 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1878.00 | + | 3252.79i | 0.0807159 | + | 0.139804i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 208.000 | − | 360.267i | 0.00890698 | − | 0.0154273i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8064.00 | − | 6983.63i | −0.344052 | − | 0.297958i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4093.50 | + | 7090.15i | −0.174012 | + | 0.301398i | −0.939819 | − | 0.341673i | \(-0.889007\pi\) |
0.765807 | + | 0.643071i | \(0.222340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −140.000 | − | 242.487i | −0.00592964 | − | 0.0102704i | 0.863045 | − | 0.505126i | \(-0.168554\pi\) |
−0.868975 | + | 0.494856i | \(0.835221\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5220.00 | 0.220287 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25317.0 | −1.06452 | −0.532260 | − | 0.846581i | \(-0.678657\pi\) | ||||
−0.532260 | + | 0.846581i | \(0.678657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7660.00 | − | 13267.5i | −0.320920 | − | 0.555850i | 0.659758 | − | 0.751478i | \(-0.270659\pi\) |
−0.980678 | + | 0.195628i | \(0.937325\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7440.00 | + | 12886.5i | −0.310579 | + | 0.537938i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4116.00 | + | 28516.5i | 0.171202 | + | 1.18612i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3969.00 | − | 6874.51i | 0.164495 | − | 0.284913i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3415.50 | + | 5915.82i | 0.141048 | + | 0.244302i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34092.0 | −1.40284 | −0.701422 | − | 0.712746i | \(-0.747451\pi\) | ||||
−0.701422 | + | 0.712746i | \(0.747451\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63820.0 | 2.61675 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1161.00 | − | 2010.91i | −0.0474341 | − | 0.0821583i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2848.50 | − | 4933.75i | 0.115966 | − | 0.200859i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15484.0 | − | 13409.5i | −0.628142 | − | 0.543987i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5547.00 | + | 9607.69i | −0.224232 | + | 0.388380i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13272.0 | + | 22987.8i | 0.534616 | + | 0.925982i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7378.00 | −0.296152 | −0.148076 | − | 0.988976i | \(-0.547308\pi\) | ||||
−0.148076 | + | 0.988976i | \(0.547308\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −432.000 | −0.0172796 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7797.00 | + | 13504.8i | 0.310782 | + | 0.538291i | 0.978532 | − | 0.206095i | \(-0.0660757\pi\) |
−0.667750 | + | 0.744386i | \(0.732742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15269.0 | + | 26446.7i | −0.606486 | + | 1.05046i | 0.385329 | + | 0.922779i | \(0.374088\pi\) |
−0.991815 | + | 0.127685i | \(0.959245\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18900.0 | − | 6547.15i | 0.748096 | − | 0.259148i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −411.000 | + | 711.873i | −0.0162116 | + | 0.0280793i | −0.874017 | − | 0.485895i | \(-0.838494\pi\) |
0.857806 | + | 0.513974i | \(0.171827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1179.00 | − | 2042.09i | −0.0463436 | − | 0.0802694i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6429.00 | −0.251834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7005.00 | −0.273450 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11840.0 | + | 20507.5i | 0.460601 | + | 0.797784i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2263.50 | + | 3920.50i | −0.0877524 | + | 0.151992i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2530.50 | − | 13148.9i | 0.0977674 | − | 0.508015i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20912.0 | − | 36220.6i | 0.805186 | − | 1.39462i | −0.110980 | − | 0.993823i | \(-0.535399\pi\) |
0.916165 | − | 0.400800i | \(-0.131268\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9409.50 | − | 16297.7i | −0.361063 | − | 0.625380i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46098.0 | −1.76286 | −0.881431 | − | 0.472313i | \(-0.843419\pi\) | ||||
−0.881431 | + | 0.472313i | \(0.843419\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21008.0 | −0.800652 | −0.400326 | − | 0.916373i | \(-0.631103\pi\) | ||||
−0.400326 | + | 0.916373i | \(0.631103\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −67.5000 | − | 116.913i | −0.00256383 | − | 0.00444068i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12018.0 | − | 20815.8i | 0.454932 | − | 0.787966i | −0.543752 | − | 0.839246i | \(-0.682997\pi\) |
0.998684 | + | 0.0512801i | \(0.0163301\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1319.50 | + | 6856.32i | −0.0497802 | + | 0.258666i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −607.500 | + | 1052.22i | −0.0228418 | + | 0.0395631i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −240.000 | − | 415.692i | −0.00899361 | − | 0.0155774i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8676.00 | 0.324030 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16128.0 | 0.600332 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37570.5 | + | 65074.0i | 1.39382 | + | 2.41417i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15246.0 | + | 26406.8i | −0.563727 | + | 0.976404i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1365.00 | + | 472.850i | −0.0503038 | + | 0.0174258i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2028.00 | − | 3512.60i | 0.0744895 | − | 0.129020i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6646.00 | + | 11511.2i | 0.243304 | + | 0.421415i | 0.961653 | − | 0.274268i | \(-0.0884354\pi\) |
−0.718349 | + | 0.695683i | \(0.755102\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9774.00 | −0.356637 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9306.00 | 0.338443 | 0.169221 | − | 0.985578i | \(-0.445875\pi\) | ||||
0.169221 | + | 0.985578i | \(0.445875\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3577.50 | + | 6196.41i | 0.129680 | + | 0.224613i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 531.000 | − | 919.719i | 0.0191850 | − | 0.0332295i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9114.00 | + | 7892.96i | 0.328212 | + | 0.284240i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8248.00 | − | 14286.0i | 0.296057 | − | 0.512786i | −0.679173 | − | 0.733978i | \(-0.737661\pi\) |
0.975230 | + | 0.221192i | \(0.0709948\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2526.00 | + | 4375.16i | 0.0903741 | + | 0.156533i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21888.0 | −0.780555 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36656.0 | 1.30296 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7812.00 | + | 13530.8i | 0.276785 | + | 0.479406i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7077.00 | + | 12257.7i | −0.249934 | + | 0.432899i | −0.963507 | − | 0.267682i | \(-0.913742\pi\) |
0.713573 | + | 0.700581i | \(0.247076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4312.00 | − | 3394.82i | 0.151794 | − | 0.119507i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1980.00 | − | 3429.46i | 0.0694773 | − | 0.120338i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1890.00 | + | 3273.58i | 0.0661065 | + | 0.114500i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3781.00 | −0.131825 | −0.0659124 | − | 0.997825i | \(-0.520996\pi\) | ||||
−0.0659124 | + | 0.997825i | \(0.520996\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25509.0 | 0.886533 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12931.5 | + | 22398.0i | 0.447986 | + | 0.775935i | 0.998255 | − | 0.0590530i | \(-0.0188081\pi\) |
−0.550269 | + | 0.834988i | \(0.685475\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15120.0 | + | 26188.6i | −0.522137 | + | 0.904367i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1134.00 | + | 982.073i | 0.0390360 | + | 0.0338062i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21192.0 | + | 36705.6i | −0.727188 | + | 1.25953i | 0.230878 | + | 0.972983i | \(0.425840\pi\) |
−0.958067 | + | 0.286545i | \(0.907493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11584.0 | + | 20064.1i | 0.396241 | + | 0.686309i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7731.00 | 0.263612 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10530.0 | 0.357923 | 0.178961 | − | 0.983856i | \(-0.442726\pi\) | ||||
0.178961 | + | 0.983856i | \(0.442726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5868.00 | − | 10163.7i | −0.198831 | − | 0.344386i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6682.50 | + | 11574.4i | −0.225721 | + | 0.390959i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30975.0 | − | 10730.1i | 1.04300 | − | 0.361305i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17109.0 | + | 29633.7i | −0.574301 | + | 0.994718i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6088.50 | − | 10545.6i | −0.203737 | − | 0.352884i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4479.00 | −0.149414 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38341.0 | 1.27504 | 0.637520 | − | 0.770434i | \(-0.279960\pi\) | ||||
0.637520 | + | 0.770434i | \(0.279960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2016.00 | + | 3491.81i | 0.0668351 | + | 0.115762i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 961.500 | − | 1665.37i | 0.0317776 | − | 0.0550403i | −0.849699 | − | 0.527268i | \(-0.823217\pi\) |
0.881477 | + | 0.472227i | \(0.156550\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5453.00 | − | 28334.6i | 0.179666 | − | 0.933573i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11136.0 | − | 19288.1i | 0.365782 | − | 0.633553i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28545.0 | − | 49441.4i | −0.934734 | − | 1.61901i | −0.775107 | − | 0.631830i | \(-0.782304\pi\) |
−0.159627 | − | 0.987177i | \(-0.551029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13590.0 | 0.443655 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3330.00 | −0.108378 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2742.00 | + | 4749.28i | 0.0889687 | + | 0.154098i | 0.907075 | − | 0.420968i | \(-0.138310\pi\) |
−0.818107 | + | 0.575066i | \(0.804976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6129.00 | + | 10615.7i | −0.198260 | + | 0.343397i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −315.000 | + | 1636.79i | −0.0101586 | + | 0.0527858i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1092.00 | − | 1891.40i | 0.0351098 | − | 0.0608119i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11232.5 | − | 19455.3i | −0.360053 | − | 0.623629i | 0.627917 | − | 0.778281i | \(-0.283908\pi\) |
−0.987969 | + | 0.154651i | \(0.950575\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1452.00 | −0.0464026 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10668.0 | −0.339898 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14683.0 | − | 25431.7i | −0.466415 | − | 0.807854i | 0.532850 | − | 0.846210i | \(-0.321121\pi\) |
−0.999264 | + | 0.0383563i | \(0.987788\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4266.00 | + | 7388.93i | −0.135105 | + | 0.234009i |
(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 | 336.4.q.e.289.1 | 2 | ||
4.3 | odd | 2 | 21.4.e.a.16.1 | yes | 2 | ||
7.2 | even | 3 | 2352.4.a.i.1.1 | 1 | |||
7.4 | even | 3 | inner | 336.4.q.e.193.1 | 2 | ||
7.5 | odd | 6 | 2352.4.a.bd.1.1 | 1 | |||
12.11 | even | 2 | 63.4.e.a.37.1 | 2 | |||
28.3 | even | 6 | 147.4.e.h.67.1 | 2 | |||
28.11 | odd | 6 | 21.4.e.a.4.1 | ✓ | 2 | ||
28.19 | even | 6 | 147.4.a.a.1.1 | 1 | |||
28.23 | odd | 6 | 147.4.a.b.1.1 | 1 | |||
28.27 | even | 2 | 147.4.e.h.79.1 | 2 | |||
84.11 | even | 6 | 63.4.e.a.46.1 | 2 | |||
84.23 | even | 6 | 441.4.a.l.1.1 | 1 | |||
84.47 | odd | 6 | 441.4.a.k.1.1 | 1 | |||
84.59 | odd | 6 | 441.4.e.c.361.1 | 2 | |||
84.83 | odd | 2 | 441.4.e.c.226.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.a.4.1 | ✓ | 2 | 28.11 | odd | 6 | ||
21.4.e.a.16.1 | yes | 2 | 4.3 | odd | 2 | ||
63.4.e.a.37.1 | 2 | 12.11 | even | 2 | |||
63.4.e.a.46.1 | 2 | 84.11 | even | 6 | |||
147.4.a.a.1.1 | 1 | 28.19 | even | 6 | |||
147.4.a.b.1.1 | 1 | 28.23 | odd | 6 | |||
147.4.e.h.67.1 | 2 | 28.3 | even | 6 | |||
147.4.e.h.79.1 | 2 | 28.27 | even | 2 | |||
336.4.q.e.193.1 | 2 | 7.4 | even | 3 | inner | ||
336.4.q.e.289.1 | 2 | 1.1 | even | 1 | trivial | ||
441.4.a.k.1.1 | 1 | 84.47 | odd | 6 | |||
441.4.a.l.1.1 | 1 | 84.23 | even | 6 | |||
441.4.e.c.226.1 | 2 | 84.83 | odd | 2 | |||
441.4.e.c.361.1 | 2 | 84.59 | odd | 6 | |||
2352.4.a.i.1.1 | 1 | 7.2 | even | 3 | |||
2352.4.a.bd.1.1 | 1 | 7.5 | odd | 6 |