Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,6,Mod(31,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.31");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(35.9259756381\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.11 | ||
Character | \(\chi\) | \(=\) | 224.31 |
Dual form | 224.6.p.a.159.11 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −8.16376 | + | 14.1401i | −0.523706 | + | 0.907085i | 0.475913 | + | 0.879492i | \(0.342118\pi\) |
−0.999619 | + | 0.0275929i | \(0.991216\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 19.2452 | − | 11.1112i | 0.344268 | − | 0.198763i | −0.317890 | − | 0.948128i | \(-0.602974\pi\) |
0.662158 | + | 0.749364i | \(0.269641\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 103.004 | − | 78.7217i | 0.794530 | − | 0.607224i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.7941 | − | 20.4280i | −0.0485354 | − | 0.0840658i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −230.097 | − | 132.846i | −0.573362 | − | 0.331031i | 0.185129 | − | 0.982714i | \(-0.440730\pi\) |
−0.758491 | + | 0.651684i | \(0.774063\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 31.5899i | − | 0.0518430i | −0.999664 | − | 0.0259215i | \(-0.991748\pi\) | ||
0.999664 | − | 0.0259215i | \(-0.00825199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 362.837i | 0.416374i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 110.876 | + | 64.0143i | 0.0930498 | + | 0.0537223i | 0.545803 | − | 0.837914i | \(-0.316225\pi\) |
−0.452753 | + | 0.891636i | \(0.649558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1375.26 | − | 2382.02i | −0.873979 | − | 1.51378i | −0.857847 | − | 0.513905i | \(-0.828198\pi\) |
−0.0161318 | − | 0.999870i | \(-0.505135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 272.226 | + | 2099.15i | 0.134704 | + | 1.03871i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2222.74 | + | 1283.30i | −0.876130 | + | 0.505834i | −0.869381 | − | 0.494143i | \(-0.835482\pi\) |
−0.00674965 | + | 0.999977i | \(0.502148\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1315.58 | + | 2278.66i | −0.420986 | + | 0.729170i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3582.45 | −0.945738 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1603.73 | 0.354108 | 0.177054 | − | 0.984201i | \(-0.443343\pi\) | ||||
0.177054 | + | 0.984201i | \(0.443343\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −349.938 | + | 606.110i | −0.0654014 | + | 0.113278i | −0.896872 | − | 0.442290i | \(-0.854166\pi\) |
0.831471 | + | 0.555569i | \(0.187499\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3756.91 | − | 2169.05i | 0.600546 | − | 0.346725i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1107.64 | − | 2659.51i | 0.152838 | − | 0.366971i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2421.84 | − | 4194.76i | −0.290832 | − | 0.503735i | 0.683175 | − | 0.730255i | \(-0.260599\pi\) |
−0.974007 | + | 0.226519i | \(0.927265\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 446.683 | + | 257.893i | 0.0470260 | + | 0.0271505i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5910.34i | − | 0.549101i | −0.961573 | − | 0.274551i | \(-0.911471\pi\) | ||
0.961573 | − | 0.274551i | \(-0.0885291\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 15217.5i | − | 1.25508i | −0.778585 | − | 0.627540i | \(-0.784062\pi\) | ||
0.778585 | − | 0.627540i | \(-0.215938\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −453.959 | − | 262.093i | −0.0334184 | − | 0.0192941i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −49.5838 | − | 85.8817i | −0.00327413 | − | 0.00567095i | 0.864384 | − | 0.502833i | \(-0.167709\pi\) |
−0.867658 | + | 0.497162i | \(0.834376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4412.79 | − | 16217.4i | 0.262557 | − | 0.964916i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1810.33 | + | 1045.20i | −0.0974614 | + | 0.0562694i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17857.4 | − | 30929.9i | 0.873228 | − | 1.51248i | 0.0145896 | − | 0.999894i | \(-0.495356\pi\) |
0.858638 | − | 0.512582i | \(-0.171311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5904.34 | −0.263187 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 44909.2 | 1.83083 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3443.80 | − | 5964.84i | 0.128798 | − | 0.223084i | −0.794413 | − | 0.607378i | \(-0.792222\pi\) |
0.923211 | + | 0.384293i | \(0.125555\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3111.85 | + | 1796.62i | −0.107076 | + | 0.0618205i | −0.552582 | − | 0.833459i | \(-0.686357\pi\) |
0.445505 | + | 0.895279i | \(0.353024\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2822.97 | − | 1175.72i | −0.0896097 | − | 0.0373209i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −351.002 | − | 607.953i | −0.0103045 | − | 0.0178479i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −42290.4 | − | 24416.4i | −1.15095 | − | 0.664499i | −0.201829 | − | 0.979421i | \(-0.564689\pi\) |
−0.949118 | + | 0.314921i | \(0.898022\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 41906.2i | − | 1.05963i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 31698.2i | − | 0.746257i | −0.927780 | − | 0.373128i | \(-0.878285\pi\) | ||
0.927780 | − | 0.373128i | \(-0.121715\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 27063.6 | + | 15625.2i | 0.594399 | + | 0.343176i | 0.766835 | − | 0.641844i | \(-0.221831\pi\) |
−0.172436 | + | 0.985021i | \(0.555164\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −21480.2 | − | 37204.8i | −0.440946 | − | 0.763741i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −34158.9 | + | 4429.84i | −0.656563 | + | 0.0851455i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −20637.0 | + | 11914.8i | −0.372031 | + | 0.214792i | −0.674345 | − | 0.738416i | \(-0.735574\pi\) |
0.302314 | + | 0.953208i | \(0.402241\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 32112.3 | − | 55620.1i | 0.543824 | − | 0.941931i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18288.6 | 0.291398 | 0.145699 | − | 0.989329i | \(-0.453457\pi\) | ||||
0.145699 | + | 0.989329i | \(0.453457\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2845.11 | 0.0427121 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13092.5 | + | 22676.8i | −0.185449 | + | 0.321206i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 60686.8 | − | 35037.5i | 0.812118 | − | 0.468876i | −0.0355730 | − | 0.999367i | \(-0.511326\pi\) |
0.847691 | + | 0.530491i | \(0.177992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2486.81 | − | 3253.90i | −0.0314803 | − | 0.0411908i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5713.62 | − | 9896.28i | −0.0685021 | − | 0.118649i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −52934.2 | − | 30561.6i | −0.601766 | − | 0.347430i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 122256.i | 1.31929i | 0.751579 | + | 0.659644i | \(0.229293\pi\) | ||||
−0.751579 | + | 0.659644i | \(0.770707\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6267.22i | 0.0642668i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −91505.7 | − | 52830.9i | −0.892575 | − | 0.515329i | −0.0177913 | − | 0.999842i | \(-0.505663\pi\) |
−0.874784 | + | 0.484513i | \(0.838997\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −90044.5 | − | 155962.i | −0.836304 | − | 1.44852i | −0.892964 | − | 0.450127i | \(-0.851379\pi\) |
0.0566605 | − | 0.998394i | \(-0.481955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 28563.1 | + | 37373.8i | 0.252832 | + | 0.330822i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −130537. | + | 75365.5i | −1.10223 | + | 0.636375i | −0.936807 | − | 0.349847i | \(-0.886234\pi\) |
−0.165427 | + | 0.986222i | \(0.552900\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −39532.1 | + | 68471.7i | −0.318701 | + | 0.552007i | −0.980217 | − | 0.197924i | \(-0.936580\pi\) |
0.661516 | + | 0.749931i | \(0.269913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 79085.5 | 0.609241 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 100179. | 0.738040 | 0.369020 | − | 0.929421i | \(-0.379693\pi\) | ||||
0.369020 | + | 0.929421i | \(0.379693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −28518.0 | + | 49394.6i | −0.201082 | + | 0.348285i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −645.318 | + | 372.575i | −0.00435822 | + | 0.00251622i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16460.0 | − | 2134.60i | 0.106552 | − | 0.0138181i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −45229.2 | − | 78339.2i | −0.280837 | − | 0.486425i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 83572.5 | + | 48250.6i | 0.498082 | + | 0.287568i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 127916.i | 0.732233i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 133657.i | − | 0.735329i | −0.929959 | − | 0.367664i | \(-0.880158\pi\) | ||
0.929959 | − | 0.367664i | \(-0.119842\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 215176. | + | 124232.i | 1.13846 | + | 0.657292i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 64841.1 | + | 112308.i | 0.330120 | + | 0.571785i | 0.982535 | − | 0.186077i | \(-0.0595773\pi\) |
−0.652415 | + | 0.757862i | \(0.726244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −329174. | − | 137096.i | −1.61360 | − | 0.672039i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −68944.9 | + | 39805.4i | −0.325588 | + | 0.187978i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 23507.7 | − | 40716.5i | 0.107006 | − | 0.185340i | −0.807550 | − | 0.589799i | \(-0.799207\pi\) |
0.914556 | + | 0.404459i | \(0.132540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 323808. | 1.42151 | 0.710756 | − | 0.703439i | \(-0.248353\pi\) | ||||
0.710756 | + | 0.703439i | \(0.248353\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1619.16 | 0.00685871 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4196.61 | + | 7268.73i | −0.0171616 | + | 0.0297248i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30864.0 | − | 17819.4i | 0.121908 | − | 0.0703837i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 193289. | + | 194792.i | 0.737759 | + | 0.743494i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −88736.6 | − | 153696.i | −0.327444 | − | 0.567150i | 0.654560 | − | 0.756010i | \(-0.272854\pi\) |
−0.982004 | + | 0.188860i | \(0.939521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 132002. | + | 76211.4i | 0.471128 | + | 0.272006i | 0.716712 | − | 0.697370i | \(-0.245646\pi\) |
−0.245584 | + | 0.969375i | \(0.578980\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 3019.97i | − | 0.0104297i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15552.9i | 0.0519976i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −269397. | − | 155536.i | −0.872254 | − | 0.503596i | −0.00415732 | − | 0.999991i | \(-0.501323\pi\) |
−0.868097 | + | 0.496395i | \(0.834657\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 291567. | + | 505008.i | 0.914629 | + | 1.58418i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −127928. | + | 307163.i | −0.388957 | + | 0.933908i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 152716. | − | 88170.5i | 0.450210 | − | 0.259929i | −0.257709 | − | 0.966223i | \(-0.582968\pi\) |
0.707919 | + | 0.706294i | \(0.249634\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 48201.6 | − | 83487.6i | 0.137832 | − | 0.238733i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 469993. | 1.30407 | 0.652035 | − | 0.758189i | \(-0.273916\pi\) | ||||
0.652035 | + | 0.758189i | \(0.273916\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 370295. | 0.997312 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −32439.9 | + | 56187.6i | −0.0848378 | + | 0.146943i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −674698. | + | 389537.i | −1.71393 | + | 0.989540i | −0.784839 | + | 0.619700i | \(0.787254\pi\) |
−0.929095 | + | 0.369841i | \(0.879412\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 43868.9 | + | 338276.i | 0.108283 | + | 0.834981i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 56228.8 | + | 97391.1i | 0.134904 | + | 0.233661i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −535593. | − | 309225.i | −1.24940 | − | 0.721343i | −0.278412 | − | 0.960462i | \(-0.589808\pi\) |
−0.970990 | + | 0.239119i | \(0.923141\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 178785.i | 0.405635i | 0.979217 | + | 0.202818i | \(0.0650098\pi\) | ||||
−0.979217 | + | 0.202818i | \(0.934990\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 58668.9i | − | 0.129503i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −93217.6 | − | 53819.2i | −0.200248 | − | 0.115613i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17008.1 | − | 29459.0i | −0.0355675 | − | 0.0616047i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −369008. | + | 282017.i | −0.751418 | + | 0.574275i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9396.44 | − | 5425.04i | 0.0186372 | − | 0.0107602i | −0.490652 | − | 0.871355i | \(-0.663242\pi\) |
0.509290 | + | 0.860595i | \(0.329908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −473563. | + | 820235.i | −0.915133 | + | 1.58506i | −0.108427 | + | 0.994104i | \(0.534581\pi\) |
−0.806706 | + | 0.590953i | \(0.798752\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11462.0 | 0.0215861 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −81454.8 | −0.149538 | −0.0747689 | − | 0.997201i | \(-0.523822\pi\) | ||||
−0.0747689 | + | 0.997201i | \(0.523822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −491764. | + | 851761.i | −0.880287 | + | 1.52470i | −0.0292649 | + | 0.999572i | \(0.509317\pi\) |
−0.851022 | + | 0.525130i | \(0.824017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 690498. | − | 398659.i | 1.20551 | − | 0.696004i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 165191. | − | 126248.i | 0.281350 | − | 0.215023i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −65671.0 | − | 113745.i | −0.109141 | − | 0.189038i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 52430.4 | + | 30270.7i | 0.0850467 | + | 0.0491017i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 730793.i | 1.15725i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 427608.i | − | 0.661210i | −0.943769 | − | 0.330605i | \(-0.892747\pi\) | ||
0.943769 | − | 0.330605i | \(-0.107253\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 448214. | + | 258776.i | 0.676918 | + | 0.390819i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −169084. | − | 292863.i | −0.249464 | − | 0.432084i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11668.9 | + | 89979.7i | 0.0168221 | + | 0.129716i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −441881. | + | 255120.i | −0.622580 | + | 0.359447i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2022.21 | − | 3502.56i | 0.00278513 | − | 0.00482398i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 60238.8 | 0.0811174 | 0.0405587 | − | 0.999177i | \(-0.487086\pi\) | ||||
0.0405587 | + | 0.999177i | \(0.487086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 62064.5 | 0.0817310 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27615.1 | − | 47830.8i | 0.0355699 | − | 0.0616088i | −0.847692 | − | 0.530488i | \(-0.822009\pi\) |
0.883262 | + | 0.468879i | \(0.155342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3063.24 | + | 1768.56i | −0.00386004 | + | 0.00222859i | −0.501929 | − | 0.864909i | \(-0.667376\pi\) |
0.498069 | + | 0.867138i | \(0.334043\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 216227. | − | 519172.i | 0.266612 | − | 0.640150i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −599259. | − | 1.03795e6i | −0.723143 | − | 1.25252i | −0.959734 | − | 0.280912i | \(-0.909363\pi\) |
0.236590 | − | 0.971610i | \(-0.423970\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1908.50 | − | 1101.87i | −0.00225435 | − | 0.00130155i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 389078.i | − | 0.449952i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 531464.i | − | 0.601837i | −0.953650 | − | 0.300918i | \(-0.902707\pi\) | ||
0.953650 | − | 0.300918i | \(-0.0972932\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −487249. | − | 281313.i | −0.540391 | − | 0.311995i | 0.204846 | − | 0.978794i | \(-0.434331\pi\) |
−0.745237 | + | 0.666799i | \(0.767664\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 89046.0 | + | 154232.i | 0.0967384 | + | 0.167556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −95269.3 | − | 361137.i | −0.101400 | − | 0.384377i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −75247.8 | + | 43444.3i | −0.0784786 | + | 0.0453096i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −149304. | + | 258602.i | −0.152607 | + | 0.264323i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.06837e6 | 1.07037 | 0.535187 | − | 0.844734i | \(-0.320241\pi\) | ||||
0.535187 | + | 0.844734i | \(0.320241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 681926. | 0.669786 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23226.8 | + | 40229.9i | −0.0223686 | + | 0.0387435i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.16285e6 | − | 671372.i | 1.09822 | − | 0.634060i | 0.162470 | − | 0.986714i | \(-0.448054\pi\) |
0.935754 | + | 0.352654i | \(0.114721\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −579679. | − | 241427.i | −0.536955 | − | 0.223633i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18914.6 | − | 32761.0i | −0.0171868 | − | 0.0297684i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.39724e6 | − | 806697.i | −1.24561 | − | 0.719153i | −0.275378 | − | 0.961336i | \(-0.588803\pi\) |
−0.970231 | + | 0.242183i | \(0.922136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 793667.i | − | 0.694263i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.14415e6i | 0.982213i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.89088e6 | + | 1.09170e6i | 1.59325 | + | 0.919864i | 0.992744 | + | 0.120245i | \(0.0383679\pi\) |
0.600507 | + | 0.799619i | \(0.294965\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 203437. | + | 352363.i | 0.168270 | + | 0.291452i | 0.937812 | − | 0.347144i | \(-0.112849\pi\) |
−0.769542 | + | 0.638597i | \(0.779515\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 66312.0 | − | 8599.58i | 0.0538500 | − | 0.00698346i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 605422. | − | 349541.i | 0.482755 | − | 0.278719i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 254717. | − | 441182.i | 0.199461 | − | 0.345477i | −0.748893 | − | 0.662691i | \(-0.769414\pi\) |
0.948354 | + | 0.317215i | \(0.102748\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16508.8 | 0.0126971 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.11878e6 | −0.845240 | −0.422620 | − | 0.906307i | \(-0.638889\pi\) | ||||
−0.422620 | + | 0.906307i | \(0.638889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −134959. | + | 233755.i | −0.100169 | + | 0.173498i | −0.911754 | − | 0.410736i | \(-0.865272\pi\) |
0.811585 | + | 0.584234i | \(0.198605\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 864285. | − | 498995.i | 0.630296 | − | 0.363902i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −465272. | − | 608790.i | −0.333428 | − | 0.436278i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −701733. | − | 1.21544e6i | −0.494228 | − | 0.856028i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.72870e6 | − | 998066.i | −1.19671 | − | 0.690918i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.92194e6i | − | 1.30789i | −0.756542 | − | 0.653945i | \(-0.773113\pi\) | ||
0.756542 | − | 0.653945i | \(-0.226887\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 153059.i | − | 0.102401i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 824311. | + | 475916.i | 0.542250 | + | 0.313068i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 40539.3 | + | 70216.1i | 0.0262239 | + | 0.0454212i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.19794e6 | − | 1.56747e6i | −0.762115 | − | 0.997199i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.49406e6 | − | 862597.i | 0.934894 | − | 0.539761i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −39925.3 | + | 69152.7i | −0.0245753 | + | 0.0425657i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −940708. | −0.569651 | −0.284825 | − | 0.958579i | \(-0.591936\pi\) | ||||
−0.284825 | + | 0.958579i | \(0.591936\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.94041e6 | 1.75191 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 365640. | − | 633306.i | 0.214364 | − | 0.371290i | −0.738712 | − | 0.674022i | \(-0.764565\pi\) |
0.953076 | + | 0.302732i | \(0.0978987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 271139. | − | 156542.i | 0.156434 | − | 0.0903171i | −0.419740 | − | 0.907645i | \(-0.637879\pi\) |
0.576173 | + | 0.817327i | \(0.304545\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −67392.2 | + | 8739.66i | −0.0382678 | + | 0.00496270i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.65827e6 | + | 2.87221e6i | 0.926846 | + | 1.60534i | 0.788565 | + | 0.614951i | \(0.210824\pi\) |
0.138281 | + | 0.990393i | \(0.455842\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −369013. | − | 213050.i | −0.203032 | − | 0.117221i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2.46107e6i | − | 1.33309i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 352145.i | − | 0.187809i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 71982.5 | + | 41559.1i | 0.0378023 | + | 0.0218252i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −645462. | − | 1.11797e6i | −0.333812 | − | 0.578179i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11868.1 | − | 4942.87i | −0.00604493 | − | 0.00251761i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 908606. | − | 524584.i | 0.455833 | − | 0.263175i | −0.254458 | − | 0.967084i | \(-0.581897\pi\) |
0.710290 | + | 0.703909i | \(0.248564\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −57127.0 | + | 98946.8i | −0.0282313 | + | 0.0488980i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.08518e6 | −0.528312 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.90507e6 | −1.39342 | −0.696710 | − | 0.717353i | \(-0.745353\pi\) | ||||
−0.696710 | + | 0.717353i | \(0.745353\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −817837. | + | 1.41653e6i | −0.386516 | + | 0.669465i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 161039. | − | 92976.0i | 0.0749973 | − | 0.0432997i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −822120. | − | 2.01784e6i | −0.377311 | − | 0.926086i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −465628. | − | 806492.i | −0.210616 | − | 0.364798i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −391122. | − | 225815.i | −0.174377 | − | 0.100677i | 0.410271 | − | 0.911964i | \(-0.365434\pi\) |
−0.584648 | + | 0.811287i | \(0.698767\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.27258e6i | − | 0.559269i | −0.960107 | − | 0.279634i | \(-0.909787\pi\) | ||
0.960107 | − | 0.279634i | \(-0.0902132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 113169.i | 0.0490299i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.73409e6 | + | 1.00118e6i | 0.740686 | + | 0.427636i | 0.822319 | − | 0.569027i | \(-0.192680\pi\) |
−0.0816324 | + | 0.996663i | \(0.526013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −352205. | − | 610037.i | −0.148328 | − | 0.256912i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −104193. | + | 250172.i | −0.0432679 | + | 0.103889i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.09761e6 | + | 633703.i | −0.449480 | + | 0.259507i | −0.707610 | − | 0.706603i | \(-0.750227\pi\) |
0.258131 | + | 0.966110i | \(0.416893\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.54463e6 | + | 4.40743e6i | −1.02768 | + | 1.77999i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.47696e6 | 0.588305 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 694457. | 0.272843 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.18287e6 | + | 3.78084e6i | −0.845985 | + | 1.46529i | 0.0387779 | + | 0.999248i | \(0.487654\pi\) |
−0.884763 | + | 0.466041i | \(0.845680\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −120736. | + | 69707.1i | −0.0461607 | + | 0.0266509i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −595464. | − | 4.59167e6i | −0.224606 | − | 1.73195i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.74926e6 | + | 3.02980e6i | 0.651001 | + | 1.12757i | 0.982880 | + | 0.184245i | \(0.0589840\pi\) |
−0.331879 | + | 0.943322i | \(0.607683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.80874e6 | − | 1.04427e6i | −0.664198 | − | 0.383475i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 50661.7i | − | 0.0183580i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.42455e6i | 1.58224i | 0.611663 | + | 0.791118i | \(0.290501\pi\) | ||||
−0.611663 | + | 0.791118i | \(0.709499\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.88991e6 | + | 1.09114e6i | 0.667006 | + | 0.385096i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.38842e6 | + | 4.13686e6i | 0.831980 | + | 1.44103i | 0.896466 | + | 0.443113i | \(0.146126\pi\) |
−0.0644852 | + | 0.997919i | \(0.520541\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −608172. | + | 464799.i | −0.209110 | + | 0.159814i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −310862. | + | 179476.i | −0.105509 | + | 0.0609158i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.27234e6 | + | 2.20375e6i | −0.426312 | + | 0.738395i | −0.996542 | − | 0.0830906i | \(-0.973521\pi\) |
0.570230 | + | 0.821485i | \(0.306854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −328598. | −0.108698 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.11739e6 | −0.691544 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −264775. | + | 458604.i | −0.0853856 | + | 0.147892i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −988211. | + | 570544.i | −0.314683 | + | 0.181682i | −0.649020 | − | 0.760771i | \(-0.724821\pi\) |
0.334337 | + | 0.942454i | \(0.391488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.62584e6 | − | 3.53533e6i | 1.45465 | − | 1.11173i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.23541e6 | − | 3.87184e6i | −0.694217 | − | 1.20242i | −0.970444 | − | 0.241327i | \(-0.922417\pi\) |
0.276227 | − | 0.961093i | \(-0.410916\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19147.0 | + | 11054.5i | 0.00587269 | + | 0.00339060i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.42722e6i | − | 0.432369i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.28693e6i | 0.385097i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −497871. | − | 287446.i | −0.147167 | − | 0.0849666i | 0.424609 | − | 0.905377i | \(-0.360412\pi\) |
−0.571775 | + | 0.820410i | \(0.693745\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 383823. | + | 664801.i | 0.112080 | + | 0.194127i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −114836. | − | 885507.i | −0.0331285 | − | 0.255456i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 351968. | − | 203209.i | 0.100319 | − | 0.0579192i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.64349e6 | + | 4.57866e6i | −0.744454 | + | 1.28943i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.06791e6 | 0.575434 | 0.287717 | − | 0.957715i | \(-0.407104\pi\) | ||||
0.287717 | + | 0.957715i | \(0.407104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.36685e6 | −1.20078 | −0.600390 | − | 0.799708i | \(-0.704988\pi\) | ||||
−0.600390 | + | 0.799708i | \(0.704988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1169.59 | + | 2025.80i | −0.000317822 | + | 0.000550484i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −291733. | + | 168432.i | −0.0783454 | + | 0.0452327i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −179100. | + | 430030.i | −0.0475364 | + | 0.114138i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −68520.2 | − | 118680.i | −0.0179753 | − | 0.0311341i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.19547e6 | + | 2.99961e6i | 1.34720 | + | 0.777806i | 0.987852 | − | 0.155398i | \(-0.0496659\pi\) |
0.359348 | + | 0.933204i | \(0.382999\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.69706e6i | − | 1.46026i | −0.683307 | − | 0.730131i | \(-0.739459\pi\) | ||
0.683307 | − | 0.730131i | \(-0.260541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 581892.i | 0.147441i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.11368e6 | + | 3.52974e6i | 1.53144 | + | 0.884176i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.73386e6 | + | 4.73519e6i | 0.677042 | + | 1.17267i | 0.975867 | + | 0.218364i | \(0.0700718\pi\) |
−0.298825 | + | 0.954308i | \(0.596595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −383333. | + | 101125.i | −0.0938598 | + | 0.0247606i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.51411e6 | − | 3.18357e6i | 1.33495 | − | 0.770735i | 0.348898 | − | 0.937161i | \(-0.386556\pi\) |
0.986054 | + | 0.166426i | \(0.0532225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 778618. | − | 1.34861e6i | 0.186391 | − | 0.322838i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.89770e6 | 0.685938 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.50171e6 | 1.05381 | 0.526904 | − | 0.849925i | \(-0.323353\pi\) | ||||
0.526904 | + | 0.849925i | \(0.323353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −785167. | + | 1.35995e6i | −0.181769 | + | 0.314834i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.15527e6 | + | 1.24434e6i | −0.493464 | + | 0.284902i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −84013.8 | − | 34990.4i | −0.0190249 | − | 0.00792355i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 718680. | + | 1.24479e6i | 0.160970 | + | 0.278808i | 0.935217 | − | 0.354075i | \(-0.115204\pi\) |
−0.774247 | + | 0.632884i | \(0.781871\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −397208. | − | 229328.i | −0.0880008 | − | 0.0508073i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.30635e6i | − | 1.38206i | −0.722828 | − | 0.691028i | \(-0.757158\pi\) | ||
0.722828 | − | 0.691028i | \(-0.242842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.12301e6i | 1.97782i | 0.148531 | + | 0.988908i | \(0.452545\pi\) | ||||
−0.148531 | + | 0.988908i | \(0.547455\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −219919. | − | 126970.i | −0.0471662 | − | 0.0272314i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −664462. | − | 1.15088e6i | −0.140987 | − | 0.244196i | 0.786882 | − | 0.617104i | \(-0.211694\pi\) |
−0.927868 | + | 0.372908i | \(0.878361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.27820e6 | + | 814179.i | −1.31796 | + | 0.170918i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.39858e6 | − | 2.53952e6i | 0.913609 | − | 0.527472i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.02159e6 | + | 3.50149e6i | −0.415470 | + | 0.719615i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.23707e6 | 1.47173 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −842447. | −0.169530 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.00910e6 | + | 3.47987e6i | −0.400095 | + | 0.692985i | −0.993737 | − | 0.111744i | \(-0.964356\pi\) |
0.593642 | + | 0.804729i | \(0.297690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −132512. | + | 76505.8i | −0.0261151 | + | 0.0150776i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.29892e6 | − | 4.31652e6i | −0.643435 | − | 0.841910i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.35841e6 | + | 2.35283e6i | 0.262226 | + | 0.454188i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.43986e6 | − | 4.29540e6i | −1.42148 | − | 0.820695i | −0.425059 | − | 0.905166i | \(-0.639747\pi\) |
−0.996426 | + | 0.0844709i | \(0.973080\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.87921e6i | 0.544505i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.57232e6i | 0.294332i | 0.989112 | + | 0.147166i | \(0.0470151\pi\) | ||||
−0.989112 | + | 0.147166i | \(0.952985\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 177815. | + | 102662.i | 0.0329497 | + | 0.0190235i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 69636.4 | + | 120614.i | 0.0127739 | + | 0.0221250i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.49533e6 | − | 3.26505e6i | −0.453145 | − | 0.592924i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.25743e6 | + | 725978.i | −0.226065 | + | 0.130518i | −0.608755 | − | 0.793358i | \(-0.708331\pi\) |
0.382691 | + | 0.923877i | \(0.374998\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.83692e6 | + | 6.64573e6i | −0.682948 | + | 1.18290i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.59897e6 | −0.634247 | −0.317123 | − | 0.948384i | \(-0.602717\pi\) | ||||
−0.317123 | + | 0.948384i | \(0.602717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.34806e6 | −0.409714 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.02300e6 | + | 5.23599e6i | −0.522298 | + | 0.904647i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.76938e6 | + | 1.02155e6i | −0.302711 | + | 0.174770i | −0.643660 | − | 0.765312i | \(-0.722585\pi\) |
0.340949 | + | 0.940082i | \(0.389252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.01770e6 | − | 521030.i | 0.680653 | − | 0.0882695i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.92680e6 | + | 8.53347e6i | 0.826555 | + | 1.43164i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.46584e6 | − | 2.00101e6i | −0.575825 | − | 0.332453i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26348.1i | 0.00433534i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.27204e7i | − | 2.07291i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.36726e6 | + | 3.67614e6i | 1.02768 | + | 0.593332i | 0.916320 | − | 0.400448i | \(-0.131145\pi\) |
0.111362 | + | 0.993780i | \(0.464479\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.56417e6 | + | 7.90537e6i | 0.729638 | + | 1.26377i | 0.957036 | + | 0.289968i | \(0.0936445\pi\) |
−0.227399 | + | 0.973802i | \(0.573022\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.14138e6 | − | 2.14130e6i | −0.814107 | − | 0.339062i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −77599.5 | + | 44802.1i | −0.0121712 | + | 0.00702703i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 75537.1 | − | 130834.i | 0.0117360 | − | 0.0203274i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −162466. | −0.0250050 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −186707. | −0.0284670 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.67480e6 | + | 2.90085e6i | −0.252976 | + | 0.438167i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.74491e6 | − | 5.04887e6i | 1.30864 | − | 0.755542i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.16979e6 | + | 3.14534e6i | −0.469957 | + | 0.466332i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.66666e6 | − | 9.81493e6i | −0.832403 | − | 1.44176i | −0.896128 | − | 0.443797i | \(-0.853631\pi\) |
0.0637246 | − | 0.997968i | \(-0.479702\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.52804e6 | − | 1.45956e6i | −0.367946 | − | 0.212433i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.75700e6i | 0.253385i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.79610e6i | 1.39986i | 0.714211 | + | 0.699930i | \(0.246786\pi\) | ||||
−0.714211 | + | 0.699930i | \(0.753214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 73402.9 | + | 42379.2i | 0.0103940 | + | 0.00600097i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.20555e6 | − | 3.82012e6i | −0.309483 | − | 0.536040i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.18775e6 | + | 2.85186e6i | −0.165163 | + | 0.396565i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.52201e6 | − | 878735.i | 0.209742 | − | 0.121095i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.23228e6 | + | 5.59847e6i | −0.441439 | + | 0.764595i | −0.997797 | − | 0.0663481i | \(-0.978865\pi\) |
0.556357 | + | 0.830943i | \(0.312199\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −480718. | −0.0650670 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 555402. | 0.0745076 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 627220. | − | 1.08638e6i | 0.0833967 | − | 0.144447i | −0.821310 | − | 0.570482i | \(-0.806756\pi\) |
0.904707 | + | 0.426035i | \(0.140090\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.92796e6 | − | 1.11311e6i | 0.254084 | − | 0.146695i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.07080e6 | − | 8.25704e6i | −0.139879 | − | 1.07862i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.77361e6 | − | 4.80403e6i | −0.359140 | − | 0.622050i | 0.628677 | − | 0.777667i | \(-0.283597\pi\) |
−0.987817 | + | 0.155617i | \(0.950263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.57019e6 | − | 3.21595e6i | −0.714956 | − | 0.412780i | 0.0979373 | − | 0.995193i | \(-0.468776\pi\) |
−0.812893 | + | 0.582412i | \(0.802109\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 177155.i | 0.0225407i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.75314e6i | − | 0.851797i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.92482e6 | + | 5.73010e6i | 1.24103 | + | 0.716510i | 0.969304 | − | 0.245864i | \(-0.0790715\pi\) |
0.271728 | + | 0.962374i | \(0.412405\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.73211e6 | − | 1.33924e7i | −0.958521 | − | 1.66021i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.88381e6 | − | 1.43971e6i | 0.231524 | − | 0.176944i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.21784e6 | + | 4.74457e6i | −1.00135 | + | 0.578130i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8279.51 | + | 14340.5i | −0.00100026 | + | 0.00173251i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.54952e7 | 1.85610 | 0.928052 | − | 0.372451i | \(-0.121483\pi\) | ||||
0.928052 | + | 0.372451i | \(0.121483\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.92502e6 | 0.228638 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 664978. | − | 1.15178e6i | 0.0783138 | − | 0.135644i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.54037e6 | − | 4.35344e6i | 0.880554 | − | 0.508388i | 0.00971325 | − | 0.999953i | \(-0.496908\pi\) |
0.870841 | + | 0.491564i | \(0.163575\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 293058. | − | 223971.i | 0.0339361 | − | 0.0259358i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.02929e6 | − | 1.39071e7i | −0.922023 | − | 1.59699i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.92434e6 | − | 5.72982e6i | −1.13015 | − | 0.652490i | −0.186175 | − | 0.982517i | \(-0.559609\pi\) |
−0.943972 | + | 0.330026i | \(0.892942\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 9.83228e6i | − | 1.11037i | −0.831727 | − | 0.555185i | \(-0.812647\pi\) | ||
0.831727 | − | 0.555185i | \(-0.187353\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.15188e6i | 0.129007i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.74089e6 | − | 1.00510e6i | −0.193367 | − | 0.111640i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.70187e6 | + | 1.16080e7i | 0.738286 | + | 1.27875i | 0.953267 | + | 0.302130i | \(0.0976977\pi\) |
−0.214981 | + | 0.976618i | \(0.568969\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 436576. | + | 3.36647e6i | 0.0476998 | + | 0.367817i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2712.99 | + | 1566.35i | −0.000293999 | + | 0.000169740i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −838947. | + | 1.45310e6i | −0.0901744 | + | 0.156187i | −0.907584 | − | 0.419870i | \(-0.862076\pi\) |
0.817410 | + | 0.576056i | \(0.195409\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.14449e6 | 0.228631 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.48745e7 | 1.57300 | 0.786499 | − | 0.617592i | \(-0.211891\pi\) | ||||
0.786499 | + | 0.617592i | \(0.211891\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.56661e6 | + | 6.17755e6i | −0.374136 | + | 0.648022i | −0.990197 | − | 0.139676i | \(-0.955394\pi\) |
0.616061 | + | 0.787698i | \(0.288727\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.96285e6 | − | 4.59735e6i | 0.828590 | − | 0.478387i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.49279e6 | − | 8.38638e6i | 0.360539 | − | 0.865674i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.68990e6 | − | 4.65904e6i | −0.275445 | − | 0.477085i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.03335e7 | − | 5.96603e6i | −1.04973 | − | 0.606061i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 620131.i | − | 0.0624967i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.49875e6i | − | 0.949715i | −0.880063 | − | 0.474857i | \(-0.842500\pi\) | ||
0.880063 | − | 0.474857i | \(-0.157500\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.04639e6 | + | 3.49089e6i | 0.599773 | + | 0.346279i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.48509e6 | − | 2.57225e6i | −0.146156 | − | 0.253150i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −512305. | − | 139400.i | −0.0500241 | − | 0.0136117i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −647530. | + | 373852.i | −0.0627347 | + | 0.0362199i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.67359e6 | − | 1.32910e7i | 0.737655 | − | 1.27766i | −0.215894 | − | 0.976417i | \(-0.569266\pi\) |
0.953549 | − | 0.301239i | \(-0.0974002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −988668. | −0.0943025 | −0.0471512 | − | 0.998888i | \(-0.515014\pi\) | ||||
−0.0471512 | + | 0.998888i | \(0.515014\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.52146e6 | 0.522582 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.51747e6 | + | 9.55655e6i | −0.518179 | + | 0.897512i | 0.481598 | + | 0.876392i | \(0.340056\pi\) |
−0.999777 | + | 0.0211198i | \(0.993277\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.58482e6 | + | 914994.i | −0.147695 | + | 0.0852720i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.36758e6 | − | 569574.i | −0.126474 | − | 0.0526742i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.55762e6 | + | 4.42993e6i | 0.234722 | + | 0.406550i | 0.959192 | − | 0.282756i | \(-0.0912488\pi\) |
−0.724470 | + | 0.689306i | \(0.757915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.49576e6 | + | 1.44093e6i | 0.227300 | + | 0.131232i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 737139.i | − | 0.0666248i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.13694e7i | − | 1.01982i | −0.860227 | − | 0.509911i | \(-0.829678\pi\) | ||
0.860227 | − | 0.509911i | \(-0.170322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.41836e7 | − | 8.18893e6i | −1.26265 | − | 0.728993i | −0.289066 | − | 0.957309i | \(-0.593345\pi\) |
−0.973587 | + | 0.228316i | \(0.926678\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33017.6 | + | 57188.2i | 0.00291717 | + | 0.00505269i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.85832e6 | + | 1.01909e6i | −0.689089 | + | 0.0893635i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.56467e6 | + | 2.05806e6i | −0.310245 | + | 0.179120i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −491775. | + | 851779.i | −0.0424816 | + | 0.0735803i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 954701. | 0.0818580 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.53588e6 | 0.811564 | 0.405782 | − | 0.913970i | \(-0.366999\pi\) | ||||
0.405782 | + | 0.913970i | \(0.366999\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.71301e6 | − | 8.16317e6i | 0.398143 | − | 0.689604i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.06224e7 | − | 6.13284e6i | 0.890740 | − | 0.514269i | 0.0165554 | − | 0.999863i | \(-0.494730\pi\) |
0.874184 | + | 0.485594i | \(0.161397\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.62416e6 | + | 1.25929e7i | 0.801103 | + | 1.04821i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 450887. | + | 780959.i | 0.0372563 | + | 0.0645298i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.91586e6 | − | 1.68347e6i | −0.239175 | − | 0.138088i | 0.375623 | − | 0.926773i | \(-0.377429\pi\) |
−0.614797 | + | 0.788685i | \(0.710762\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.04480e6i | − | 0.0850756i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 57752.4i | − | 0.00466851i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −977071. | − | 564112.i | −0.0784112 | − | 0.0452707i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.65246e6 | − | 4.59420e6i | −0.211327 | − | 0.366028i | 0.740803 | − | 0.671722i | \(-0.234445\pi\) |
−0.952130 | + | 0.305694i | \(0.901112\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 493366. | + | 645551.i | 0.0390244 | + | 0.0510620i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.23174e6 | − | 3.59789e6i | 0.489381 | − | 0.282544i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 378346. | − | 655315.i | 0.0294990 | − | 0.0510938i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.95688e7 | 1.51486 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.03260e6 | 0.233088 | 0.116544 | − | 0.993186i | \(-0.462818\pi\) | ||||
0.116544 | + | 0.993186i | \(0.462818\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.66133e6 | + | 1.15378e7i | −0.508362 | + | 0.880508i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31161.1 | − | 17990.8i | 0.00236124 | − | 0.00136326i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.35844e7 | + | 1.76168e6i | −1.02210 | + | 0.132549i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.72319e6 | − | 1.33770e7i | −0.577007 | − | 0.999406i | −0.995820 | − | 0.0913332i | \(-0.970887\pi\) |
0.418813 | − | 0.908072i | \(-0.362446\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 486790. | + | 281049.i | 0.0361134 | + | 0.0208501i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.79630e6i | − | 0.132329i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 186517.i | 0.0136444i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.51492e6 | + | 4.33874e6i | 0.545917 | + | 0.315185i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.99286e6 | + | 1.55761e7i | 0.648748 | + | 1.12366i | 0.983422 | + | 0.181330i | \(0.0580402\pi\) |
−0.334675 | + | 0.942334i | \(0.608626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.15525e7 | − | 8.97627e6i | −1.54405 | − | 0.643070i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.95557e6 | − | 4.59315e6i | 0.566012 | − | 0.326787i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.10984e6 | + | 3.65435e6i | −0.149075 | + | 0.258205i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.55969e7 | −1.09447 | −0.547234 | − | 0.836980i | \(-0.684319\pi\) | ||||
−0.547234 | + | 0.836980i | \(0.684319\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.26988e7 | 0.884998 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 974136. | − | 1.68725e6i | 0.0674258 | − | 0.116785i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.11442e7 | + | 6.43409e6i | −0.766104 | + | 0.442310i | −0.831483 | − | 0.555550i | \(-0.812508\pi\) |
0.0653790 | + | 0.997861i | \(0.479174\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.88426e6 | + | 1.60113e6i | 0.401766 | + | 0.109322i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.48726e6 | + | 1.12363e7i | 0.439939 | + | 0.761997i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.72415e7 | − | 9.95440e6i | −1.16135 | − | 0.670508i | −0.209726 | − | 0.977760i | \(-0.567257\pi\) |
−0.951628 | + | 0.307252i | \(0.900591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.41868e6i | − | 0.0949157i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.89554e7i | − | 1.92423i | −0.272640 | − | 0.962116i | \(-0.587897\pi\) | ||
0.272640 | − | 0.962116i | \(-0.412103\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.41550e6 | − | 1.97194e6i | −0.225457 | − | 0.130168i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −215698. | − | 373600.i | −0.0141431 | − | 0.0244966i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.51297e6 | + | 1.80391e7i | −0.489336 | + | 1.17492i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 56095.8 | − | 32386.9i | 0.00362936 | − | 0.00209541i | −0.498184 | − | 0.867071i | \(-0.666000\pi\) |
0.501814 | + | 0.864976i | \(0.332666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.72188e6 | + | 1.51067e7i | −0.560561 | + | 0.970920i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.38720e6 | 0.216259 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.28686e7 | −0.816190 | −0.408095 | − | 0.912940i | \(-0.633807\pi\) | ||||
−0.408095 | + | 0.912940i | \(0.633807\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.56709e6 | + | 9.64248e6i | −0.350771 | + | 0.607553i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.58510e7 | + | 9.15160e6i | −0.992193 | + | 0.572843i | −0.905929 | − | 0.423429i | \(-0.860826\pi\) |
−0.0862641 | + | 0.996272i | \(0.527493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.31822e6 | + | 1.01649e7i | 0.0819742 | + | 0.632110i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33555.5 | − | 58119.8i | −0.00207305 | − | 0.00359063i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −188429. | − | 108789.i | −0.0115654 | − | 0.00667726i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.68118e7i | 1.02518i | 0.858634 | + | 0.512589i | \(0.171314\pi\) | ||||
−0.858634 | + | 0.512589i | \(0.828686\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.19237e7i | 1.32824i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.16919e7 | + | 1.25238e7i | 1.30571 | + | 0.753854i | 0.981378 | − | 0.192088i | \(-0.0615259\pi\) |
0.324336 | + | 0.945942i | \(0.394859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −920744. | − | 1.59478e6i | −0.0550662 | − | 0.0953774i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.14615e6 | − | 6.22574e6i | 0.484061 | − | 0.369946i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.40785e7 | + | 8.12825e6i | −0.831216 | + | 0.479903i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.21099e6 | + | 7.29365e6i | −0.247034 | + | 0.427875i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.74528e6 | −0.334894 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.91278e6 | −0.400386 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.99502e6 | − | 3.45547e6i | 0.114818 | − | 0.198870i | −0.802889 | − | 0.596128i | \(-0.796705\pi\) |
0.917707 | + | 0.397258i | \(0.130038\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.28135e7 | − | 1.31714e7i | 1.30467 | − | 0.753249i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.03189e7 | − | 7.88625e6i | 0.586395 | − | 0.448156i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 56755.2 | + | 98302.9i | 0.00320496 | + | 0.00555115i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.12225e7 | + | 6.47931e6i | 0.629755 | + | 0.363589i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.69992e7i | 1.50558i | 0.658259 | + | 0.752792i | \(0.271293\pi\) | ||||
−0.658259 | + | 0.752792i | \(0.728707\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12696.3i | − | 0.000703575i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.43149e6 | − | 826473.i | −0.0788330 | − | 0.0455142i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.15149e6 | − | 7.19060e6i | −0.227204 | − | 0.393528i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 950949. | + | 7.33284e6i | 0.0517211 | + | 0.398825i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.08735e7 | + | 1.78248e7i | −1.66879 | + | 0.963476i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.61028e6 | − | 1.49134e7i | 0.462536 | − | 0.801136i | −0.536550 | − | 0.843868i | \(-0.680273\pi\) |
0.999087 | + | 0.0427321i | \(0.0136062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.90148e7 | 1.01517 | 0.507587 | − | 0.861601i | \(-0.330538\pi\) | ||||
0.507587 | + | 0.861601i | \(0.330538\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.64325e6 | −0.352496 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.95936e6 | − | 3.39371e6i | 0.103329 | − | 0.178970i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.62483e7 | + | 2.09280e7i | −1.89991 | + | 1.09691i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −37140.9 | + | 89177.3i | −0.00193483 | + | 0.00464563i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.54355e6 | − | 2.67352e6i | −0.0799216 | − | 0.138428i | 0.823294 | − | 0.567615i | \(-0.192134\pi\) |
−0.903216 | + | 0.429186i | \(0.858800\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.03659e7 | + | 1.17582e7i | 1.04810 | + | 0.605122i | 0.922117 | − | 0.386910i | \(-0.126458\pi\) |
0.125984 | + | 0.992032i | \(0.459791\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.14143e7i | 0.583866i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.15389e7i | 1.09512i | 0.836767 | + | 0.547559i | \(0.184443\pi\) | ||||
−0.836767 | + | 0.547559i | \(0.815557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.14533e7 | − | 6.61258e6i | −0.578823 | − | 0.334183i | 0.181843 | − | 0.983328i | \(-0.441794\pi\) |
−0.760665 | + | 0.649144i | \(0.775127\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.15889e6 | + | 7.20342e6i | 0.208918 | + | 0.361856i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.52742e6 | − | 1.51563e6i | 0.0762684 | − | 0.0756801i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.04510e6 | − | 5.22219e6i | 0.448949 | − | 0.259201i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.25364e6 | − | 2.17136e6i | 0.0618526 | − | 0.107132i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.67107e7 | 0.819575 | 0.409788 | − | 0.912181i | \(-0.365603\pi\) | ||||
0.409788 | + | 0.912181i | \(0.365603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.79392e7 | −0.874607 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.13348e6 | − | 1.58196e7i | 0.442657 | − | 0.766704i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.12639e6 | − | 4.11442e6i | 0.343343 | − | 0.198229i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.08258e7 | − | 4.50876e6i | −0.518503 | − | 0.215948i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.20354e6 | − | 3.81664e6i | −0.104918 | − | 0.181724i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.07662e7 | + | 6.21590e6i | 0.509613 | + | 0.294225i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 484559.i | 0.0228020i | 0.999935 | + | 0.0114010i | \(0.00362914\pi\) | ||||
−0.999935 | + | 0.0114010i | \(0.996371\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.44179e6i | 0.0674506i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.82629e7 | − | 1.63176e7i | −1.31451 | − | 0.758935i | −0.331674 | − | 0.943394i | \(-0.607613\pi\) |
−0.982840 | + | 0.184459i | \(0.940947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.10980e6 | − | 8.85044e6i | −0.236277 | − | 0.409243i | 0.723366 | − | 0.690465i | \(-0.242594\pi\) |
−0.959643 | + | 0.281221i | \(0.909261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.24067e7 | − | 1.60894e6i | 0.570359 | − | 0.0739662i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.91512e7 | − | 1.68305e7i | 1.33239 | − | 0.769253i | 0.346721 | − | 0.937968i | \(-0.387295\pi\) |
0.985665 | + | 0.168715i | \(0.0539617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.65645e6 | + | 1.49934e7i | −0.393369 | + | 0.681334i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.29151e7 | 1.03532 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.33135e6 | 0.284411 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −771312. | + | 1.33595e6i | −0.0344496 | + | 0.0596685i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.49744e6 | − | 1.44190e6i | 0.110907 | − | 0.0640322i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00697e7 | + | 1.31759e7i | 0.444630 | + | 0.581781i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.88346e6 | + | 6.72635e6i | 0.170498 | + | 0.295311i | 0.938594 | − | 0.345023i | \(-0.112129\pi\) |
−0.768096 | + | 0.640335i | \(0.778796\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.71764e7 | + | 1.56903e7i | 1.18637 | + | 0.684950i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.44116e7i | − | 1.49370i | −0.664990 | − | 0.746852i | \(-0.731564\pi\) | ||
0.664990 | − | 0.746852i | \(-0.268436\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.33214e7i | 1.86982i | 0.354880 | + | 0.934912i | \(0.384522\pi\) | ||||
−0.354880 | + | 0.934912i | \(0.615478\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.16427e6 | + | 1.24954e6i | 0.0928865 | + | 0.0536280i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40392.9 | − | 69962.6i | −0.00172384 | − | 0.00298577i | 0.865162 | − | 0.501492i | \(-0.167215\pi\) |
−0.866886 | + | 0.498506i | \(0.833882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.05217e7 | − | 1.37672e7i | −0.446510 | − | 0.584241i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.47779e7 | + | 8.53200e6i | −0.623616 | + | 0.360045i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −136381. | + | 236219.i | −0.00572303 | + | 0.00991258i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.37434e7 | −0.573506 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.32381e6 | −0.0549345 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −561206. | + | 972037.i | −0.0231592 | + | 0.0401129i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.95991e6 | − | 2.28625e6i | 0.162507 | − | 0.0938237i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.19438e7 | − | 4.14258e6i | 1.30367 | − | 0.169064i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.98652e6 | + | 3.44076e6i | 0.0806254 | + | 0.139647i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.05859e6 | + | 5.22998e6i | 0.365630 | + | 0.211097i | 0.671548 | − | 0.740961i | \(-0.265630\pi\) |
−0.305917 | + | 0.952058i | \(0.598963\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.49237e6i | 0.100047i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.12503e7i | − | 0.449127i | −0.974459 | − | 0.224563i | \(-0.927904\pi\) | ||
0.974459 | − | 0.224563i | \(-0.0720956\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.20816e6 | − | 2.42958e6i | −0.167076 | − | 0.0964616i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −651882. | − | 1.12909e6i | −0.0257405 | − | 0.0445838i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.55200e7 | + | 6.46383e6i | 0.609493 | + | 0.253844i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.64723e6 | + | 2.68308e6i | −0.181512 | + | 0.104796i | −0.588003 | − | 0.808859i | \(-0.700086\pi\) |
0.406491 | + | 0.913655i | \(0.366752\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.67972e6 | − | 1.33017e7i | 0.298329 | − | 0.516722i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.00134e6 | −0.0386882 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.27445e7 | 0.489745 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.12399e6 | + | 3.67886e6i | −0.0811807 | + | 0.140609i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.14406e7 | + | 1.23787e7i | −0.815074 | + | 0.470583i | −0.848715 | − | 0.528851i | \(-0.822623\pi\) |
0.0336410 | + | 0.999434i | \(0.489290\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.46988e7 | + | 1.17917e7i | −1.69014 | + | 0.445864i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.96999e6 | + | 1.03403e7i | 0.224527 | + | 0.388893i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −654649. | − | 377962.i | −0.0244895 | − | 0.0141390i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.46850e6i | 0.0546419i | 0.999627 | + | 0.0273210i | \(0.00869762\pi\) | ||||
−0.999627 | + | 0.0273210i | \(0.991302\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.11189e6i | 0.189198i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.16498e6 | + | 2.98200e6i | 0.190149 | + | 0.109783i | 0.592052 | − | 0.805899i | \(-0.298318\pi\) |
−0.401903 | + | 0.915682i | \(0.631651\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.58472e6 | + | 1.31371e7i | 0.277754 | + | 0.481084i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.96808e6 | + | 9.52758e6i | −0.144544 | + | 0.347059i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.13119e7 | − | 2.38514e7i | 1.49692 | − | 0.864250i | 0.496931 | − | 0.867790i | \(-0.334460\pi\) |
0.999994 | + | 0.00353991i | \(0.00112679\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 493597. | − | 854935.i | 0.0177913 | − | 0.0308154i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.41510e7 | −1.94158 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.82889e7 | −1.72232 | −0.861162 | − | 0.508330i | \(-0.830263\pi\) | ||||
−0.861162 | + | 0.508330i | \(0.830263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 120557. | − | 208812.i | 0.00427746 | − | 0.00740877i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.02507e6 | − | 3.47858e6i | 0.212658 | − | 0.122778i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −783878. | − | 6.04455e6i | −0.0275234 | − | 0.212235i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.40697e7 | + | 2.43694e7i | 0.491445 | + | 0.851208i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.07913e6 | + | 1.77774e6i | 0.106995 | + | 0.0617735i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.10474e7i | 0.727580i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.23912e7i | − | 1.80174i | −0.434089 | − | 0.900870i | \(-0.642930\pi\) | ||
0.434089 | − | 0.900870i | \(-0.357070\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.97935e6 | + | 2.87483e6i | 0.170358 | + | 0.0983565i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.39434e7 | − | 2.41507e7i | −0.474592 | − | 0.822017i | 0.524985 | − | 0.851112i | \(-0.324071\pi\) |
−0.999577 | + | 0.0290944i | \(0.990738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.33536e7 | − | 2.54907e7i | 1.12943 | − | 0.863176i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.17530e6 | + | 678558.i | −0.0395946 | + | 0.0228599i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.87737e7 | − | 4.98375e7i | 0.964405 | − | 1.67040i | 0.253201 | − | 0.967414i | \(-0.418517\pi\) |
0.711204 | − | 0.702985i | \(-0.248150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.86184e7 | −0.620850 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.86499e6 | 0.0618732 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.32884e6 | − | 9.22981e6i | 0.175893 | − | 0.304656i | −0.764577 | − | 0.644532i | \(-0.777052\pi\) |
0.940470 | + | 0.339877i | \(0.110385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.56761e6 | + | 905061.i | −0.0514811 | + | 0.0297226i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 166781. | − | 127463.i | 0.00544946 | − | 0.00416478i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.95285e7 | + | 3.38244e7i | 0.634862 | + | 1.09961i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.15687e6 | − | 2.97732e6i | −0.166802 | − | 0.0963034i | 0.414275 | − | 0.910152i | \(-0.364035\pi\) |
−0.581077 | + | 0.813848i | \(0.697369\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.71303e7i | 0.551306i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.18564e7i | 0.699875i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.30824e7 | − | 1.91001e7i | −1.05404 | − | 0.608552i | −0.130265 | − | 0.991479i | \(-0.541583\pi\) |
−0.923779 | + | 0.382927i | \(0.874916\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.67614e6 | + | 1.50275e7i | 0.275051 | + | 0.476402i |
(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 | 224.6.p.a.31.11 | ✓ | 80 | |
4.3 | odd | 2 | inner | 224.6.p.a.31.30 | yes | 80 | |
7.5 | odd | 6 | inner | 224.6.p.a.159.30 | yes | 80 | |
28.19 | even | 6 | inner | 224.6.p.a.159.11 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.p.a.31.11 | ✓ | 80 | 1.1 | even | 1 | trivial | |
224.6.p.a.31.30 | yes | 80 | 4.3 | odd | 2 | inner | |
224.6.p.a.159.11 | yes | 80 | 28.19 | even | 6 | inner | |
224.6.p.a.159.30 | yes | 80 | 7.5 | odd | 6 | inner |