Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(289,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.289");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 39122x^{12} + 391243971x^{8} + 75462898750x^{4} + 18538406640625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{42}\cdot 5^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(0.526271 + 11.8760i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.289 |
Dual form | 320.6.f.c.289.1 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −24.8046 | −1.59121 | −0.795607 | − | 0.605813i | \(-0.792848\pi\) | ||||
−0.795607 | + | 0.605813i | \(0.792848\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −53.4447 | + | 16.3911i | −0.956047 | + | 0.293212i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 100.281i | − | 0.773526i | −0.922179 | − | 0.386763i | \(-0.873593\pi\) | ||
0.922179 | − | 0.386763i | \(-0.126407\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 372.267 | 1.53196 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.36667i | − | 0.0133728i | −0.999978 | − | 0.00668641i | \(-0.997872\pi\) | ||
0.999978 | − | 0.00668641i | \(-0.00212837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −506.854 | −0.831811 | −0.415906 | − | 0.909408i | \(-0.636535\pi\) | ||||
−0.415906 | + | 0.909408i | \(0.636535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1325.67 | − | 406.573i | 1.52128 | − | 0.466563i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1454.37i | 1.22055i | 0.792191 | + | 0.610273i | \(0.208940\pi\) | ||||
−0.792191 | + | 0.610273i | \(0.791060\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 722.433i | 0.459107i | 0.973296 | + | 0.229553i | \(0.0737266\pi\) | ||||
−0.973296 | + | 0.229553i | \(0.926273\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2487.43i | 1.23084i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3086.22i | 1.21649i | 0.793750 | + | 0.608244i | \(0.208126\pi\) | ||||
−0.793750 | + | 0.608244i | \(0.791874\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2587.67 | − | 1752.03i | 0.828053 | − | 0.560649i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3206.40 | −0.846465 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7298.39i | 1.61151i | 0.592251 | + | 0.805753i | \(0.298239\pi\) | ||||
−0.592251 | + | 0.805753i | \(0.701761\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8609.68 | 1.60910 | 0.804549 | − | 0.593886i | \(-0.202407\pi\) | ||||
0.804549 | + | 0.593886i | \(0.202407\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 133.118i | 0.0212790i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1643.72 | + | 5359.50i | 0.226807 | + | 0.739527i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5276.52 | −0.633641 | −0.316821 | − | 0.948485i | \(-0.602615\pi\) | ||||
−0.316821 | + | 0.948485i | \(0.602615\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12572.3 | 1.32359 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18175.5 | −1.68860 | −0.844301 | − | 0.535869i | \(-0.819984\pi\) | ||||
−0.844301 | + | 0.535869i | \(0.819984\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8340.95 | 0.687930 | 0.343965 | − | 0.938982i | \(-0.388230\pi\) | ||||
0.343965 | + | 0.938982i | \(0.388230\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −19895.7 | + | 6101.84i | −1.46463 | + | 0.449190i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 22120.2i | − | 1.46064i | −0.683103 | − | 0.730322i | \(-0.739370\pi\) | ||
0.683103 | − | 0.730322i | \(-0.260630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6750.67 | 0.401658 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 36075.1i | − | 1.94215i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13363.7 | −0.653489 | −0.326745 | − | 0.945113i | \(-0.605952\pi\) | ||||
−0.326745 | + | 0.945113i | \(0.605952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 87.9654 | + | 286.820i | 0.00392108 | + | 0.0127851i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 17919.6i | − | 0.730537i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10958.8i | 0.409859i | 0.978777 | + | 0.204929i | \(0.0656965\pi\) | ||||
−0.978777 | + | 0.204929i | \(0.934304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10982.0i | − | 0.377883i | −0.981988 | − | 0.188941i | \(-0.939494\pi\) | ||
0.981988 | − | 0.188941i | \(-0.0605056\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 37331.4i | − | 1.18501i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 27088.7 | − | 8307.88i | 0.795251 | − | 0.243897i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13007.5 | 0.354003 | 0.177002 | − | 0.984211i | \(-0.443360\pi\) | ||||
0.177002 | + | 0.984211i | \(0.443360\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 76552.4i | − | 1.93569i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −36009.0 | −0.847744 | −0.423872 | − | 0.905722i | \(-0.639329\pi\) | ||||
−0.423872 | + | 0.905722i | \(0.639329\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 64286.0i | 1.41192i | 0.708253 | + | 0.705959i | \(0.249484\pi\) | ||||
−0.708253 | + | 0.705959i | \(0.750516\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −64186.0 | + | 43458.3i | −1.31761 | + | 0.892113i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −538.177 | −0.0103442 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −48638.8 | −0.876830 | −0.438415 | − | 0.898773i | \(-0.644460\pi\) | ||||
−0.438415 | + | 0.898773i | \(0.644460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10927.3 | −0.185055 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 49784.4 | 0.793228 | 0.396614 | − | 0.917985i | \(-0.370185\pi\) | ||||
0.396614 | + | 0.917985i | \(0.370185\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23838.7 | − | 77728.6i | −0.357879 | − | 1.16690i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 181033.i | − | 2.56425i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7764.40 | 0.103904 | 0.0519521 | − | 0.998650i | \(-0.483456\pi\) | ||||
0.0519521 | + | 0.998650i | \(0.483456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 50828.0i | 0.643427i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −213559. | −2.56042 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11841.4 | − | 38610.2i | −0.134616 | − | 0.438928i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 36848.8i | − | 0.397644i | −0.980036 | − | 0.198822i | \(-0.936288\pi\) | ||
0.980036 | − | 0.198822i | \(-0.0637116\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1997.83i | − | 0.0204867i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 174557.i | − | 1.70268i | −0.524611 | − | 0.851342i | \(-0.675789\pi\) | ||
0.524611 | − | 0.851342i | \(-0.324211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 172505.i | − | 1.60217i | −0.598551 | − | 0.801085i | \(-0.704257\pi\) | ||
0.598551 | − | 0.801085i | \(-0.295743\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −40771.7 | − | 132940.i | −0.360899 | − | 1.17675i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −155176. | −1.31028 | −0.655140 | − | 0.755507i | \(-0.727391\pi\) | ||||
−0.655140 | + | 0.755507i | \(0.727391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 111055.i | 0.895306i | 0.894207 | + | 0.447653i | \(0.147740\pi\) | ||||
−0.894207 | + | 0.447653i | \(0.852260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 130882. | 1.00826 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 199647.i | 1.47084i | 0.677609 | + | 0.735422i | \(0.263016\pi\) | ||||
−0.677609 | + | 0.735422i | \(0.736984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −50586.4 | − | 164942.i | −0.356689 | − | 1.16302i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −188685. | −1.27430 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 145847. | 0.944123 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 161022. | 0.999821 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 450836. | 2.68693 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −109579. | + | 136051.i | −0.627269 | + | 0.778803i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 93300.5i | 0.513304i | 0.966504 | + | 0.256652i | \(0.0826194\pi\) | ||||
−0.966504 | + | 0.256652i | \(0.917381\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −206894. | −1.09464 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 174939.i | 0.890655i | 0.895368 | + | 0.445328i | \(0.146913\pi\) | ||||
−0.895368 | + | 0.445328i | \(0.853087\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 72446.5 | 0.355131 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 171365. | − | 52556.3i | 0.809260 | − | 0.248194i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 127441.i | − | 0.580106i | −0.957011 | − | 0.290053i | \(-0.906327\pi\) | ||
0.957011 | − | 0.290053i | \(-0.0936730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 393660.i | − | 1.72816i | −0.503352 | − | 0.864082i | \(-0.667900\pi\) | ||
0.503352 | − | 0.864082i | \(-0.332100\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 548682.i | 2.32420i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2720.12i | 0.0111237i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −119628. | − | 390060.i | −0.472513 | − | 1.54068i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −167447. | −0.639124 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 167112.i | − | 0.616656i | −0.951280 | − | 0.308328i | \(-0.900231\pi\) | ||
0.951280 | − | 0.308328i | \(-0.0997694\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 184305. | 0.657803 | 0.328901 | − | 0.944364i | \(-0.393322\pi\) | ||||
0.328901 | + | 0.944364i | \(0.393322\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 541415.i | 1.86983i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −460141. | + | 141122.i | −1.53837 | + | 0.471807i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −403676. | −1.30702 | −0.653512 | − | 0.756916i | \(-0.726705\pi\) | ||||
−0.653512 | + | 0.756916i | \(0.726705\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 331482. | 1.03984 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 309490. | 0.940984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 357436. | 1.05373 | 0.526864 | − | 0.849949i | \(-0.323368\pi\) | ||||
0.526864 | + | 0.849949i | \(0.323368\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2181.94 | − | 7114.45i | −0.00623927 | − | 0.0203438i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 38221.8i | − | 0.106052i | −0.998593 | − | 0.0530262i | \(-0.983113\pi\) | ||
0.998593 | − | 0.0530262i | \(-0.0168867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −114392. | −0.308090 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 268938.i | 0.703334i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 134258. | 0.341056 | 0.170528 | − | 0.985353i | \(-0.445453\pi\) | ||||
0.170528 | + | 0.985353i | \(0.445453\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −175696. | − | 259494.i | −0.433677 | − | 0.640520i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 271829.i | − | 0.652173i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 566014.i | 1.32037i | 0.751105 | + | 0.660183i | \(0.229521\pi\) | ||||
−0.751105 | + | 0.660183i | \(0.770479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 572156.i | − | 1.29813i | −0.760733 | − | 0.649065i | \(-0.775160\pi\) | ||
0.760733 | − | 0.649065i | \(-0.224840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 272404.i | 0.601292i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 282002. | − | 86487.8i | 0.605791 | − | 0.185791i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7805.15 | 0.0163221 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 321542.i | 0.654762i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −685564. | −1.35977 | −0.679883 | − | 0.733320i | \(-0.737970\pi\) | ||||
−0.679883 | + | 0.733320i | \(0.737970\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 931503.i | 1.80008i | 0.435810 | + | 0.900039i | \(0.356462\pi\) | ||||
−0.435810 | + | 0.900039i | \(0.643538\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −671923. | + | 206073.i | −1.26541 | + | 0.388093i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 692118. | 1.27062 | 0.635308 | − | 0.772259i | \(-0.280873\pi\) | ||||
0.635308 | + | 0.772259i | \(0.280873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −969167. | −1.73487 | −0.867433 | − | 0.497554i | \(-0.834232\pi\) | ||||
−0.867433 | + | 0.497554i | \(0.834232\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −322646. | −0.563295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 731892. | 1.24654 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 971385. | − | 297916.i | 1.61438 | − | 0.495119i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.14890e6i | 1.86361i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3877.06 | 0.00613956 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 800177.i | − | 1.23731i | −0.785661 | − | 0.618657i | \(-0.787677\pi\) | ||
0.785661 | − | 0.618657i | \(-0.212323\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 893187. | 1.34894 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −445779. | + | 136717.i | −0.657694 | + | 0.201709i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 863389.i | − | 1.24468i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1.59459e6i | − | 2.24666i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 737156.i | − | 1.01526i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 619923.i | 0.834787i | 0.908726 | + | 0.417394i | \(0.137056\pi\) | ||||
−0.908726 | + | 0.417394i | \(0.862944\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 963302. | − | 652222.i | 1.26855 | − | 0.858893i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −547541. | −0.705264 | −0.352632 | − | 0.935762i | \(-0.614713\pi\) | ||||
−0.352632 | + | 0.935762i | \(0.614713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 368527.i | − | 0.464387i | −0.972670 | − | 0.232194i | \(-0.925410\pi\) | ||
0.972670 | − | 0.232194i | \(-0.0745903\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13349.2 | 0.0164599 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 347048.i | 0.418794i | 0.977831 | + | 0.209397i | \(0.0671500\pi\) | ||||
−0.977831 | + | 0.209397i | \(0.932850\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 362573. | + | 1.18221e6i | 0.428278 | + | 1.39644i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.20646e6 | 1.39522 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.17224e6 | −1.32746 | −0.663731 | − | 0.747971i | \(-0.731028\pi\) | ||||
−0.663731 | + | 0.747971i | \(0.731028\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.10163e6 | −1.22178 | −0.610889 | − | 0.791716i | \(-0.709188\pi\) | ||||
−0.610889 | + | 0.791716i | \(0.709188\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.05020e6 | 1.14093 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −360787. | + | 110651.i | −0.384004 | + | 0.117771i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 366168.i | − | 0.381890i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.23488e6 | −1.26220 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 97443.4i | − | 0.0976265i | −0.998808 | − | 0.0488133i | \(-0.984456\pi\) | ||
0.998808 | − | 0.0488133i | \(-0.0155439\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16562.7 | 0.0162679 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 591310. | + | 1.92802e6i | 0.569462 | + | 1.85679i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.35298e6i | 1.27779i | 0.769296 | + | 0.638893i | \(0.220607\pi\) | ||||
−0.769296 | + | 0.638893i | \(0.779393\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 529136.i | 0.490138i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.71695e6i | 2.46877i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 892943.i | − | 0.796039i | −0.917377 | − | 0.398019i | \(-0.869698\pi\) | ||
0.917377 | − | 0.398019i | \(-0.130302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 714221. | − | 219046.i | 0.624766 | − | 0.191611i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −192593. | −0.165334 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 395573.i | − | 0.333308i | −0.986015 | − | 0.166654i | \(-0.946704\pi\) | ||
0.986015 | − | 0.166654i | \(-0.0532963\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −548411. | −0.453610 | −0.226805 | − | 0.973940i | \(-0.572828\pi\) | ||||
−0.226805 | + | 0.973940i | \(0.572828\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.26077e6i | − | 1.02383i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9402.56 | − | 13887.2i | −0.00749747 | − | 0.0110734i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 84078.7 | 0.0658395 | 0.0329198 | − | 0.999458i | \(-0.489519\pi\) | ||||
0.0329198 | + | 0.999458i | \(0.489519\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.20509e6 | 2.46508 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 869957. | 0.657252 | 0.328626 | − | 0.944460i | \(-0.393414\pi\) | ||||
0.328626 | + | 0.944460i | \(0.393414\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.80499e6 | −1.33970 | −0.669852 | − | 0.742495i | \(-0.733642\pi\) | ||||
−0.669852 | + | 0.742495i | \(0.733642\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 293722. | + | 957710.i | 0.214202 | + | 0.698428i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.82267e6i | 1.30618i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −695348. | −0.489731 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 914020.i | 0.632737i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 734707. | 0.499972 | 0.249986 | − | 0.968250i | \(-0.419574\pi\) | ||||
0.249986 | + | 0.968250i | \(0.419574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −179627. | − | 585691.i | −0.120176 | − | 0.391844i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17207.7i | 0.0113196i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.56427e6i | − | 1.01189i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 836441.i | − | 0.532132i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.32981e6i | 2.70933i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 180007. | + | 586930.i | 0.110800 | + | 0.361274i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 568071. | 0.343999 | 0.171999 | − | 0.985097i | \(-0.444977\pi\) | ||||
0.171999 | + | 0.985097i | \(0.444977\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.27891e6i | 2.54939i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.69667e6 | 0.994712 | 0.497356 | − | 0.867547i | \(-0.334304\pi\) | ||||
0.497356 | + | 0.867547i | \(0.334304\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 349961.i | 0.201910i | 0.994891 | + | 0.100955i | \(0.0321899\pi\) | ||||
−0.994891 | + | 0.100955i | \(0.967810\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 611901. | + | 1.99516e6i | 0.347460 | + | 1.13293i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.16674e6 | 1.21104 | 0.605520 | − | 0.795830i | \(-0.292965\pi\) | ||||
0.605520 | + | 0.795830i | \(0.292965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39168.1 | 0.0215504 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.84907e6 | 2.08494 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.05069e6 | −0.560361 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.31157e6 | + | 888024.i | −0.688784 | + | 0.466354i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.75467e6i | − | 1.42462i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.21824e6 | −1.12985 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.09909e6i | 1.55476i | 0.629031 | + | 0.777380i | \(0.283452\pi\) | ||||
−0.629031 | + | 0.777380i | \(0.716548\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.96427e6 | −0.970714 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −695182. | + | 213207.i | −0.338444 | + | 0.103798i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 913351.i | 0.438089i | 0.975715 | + | 0.219045i | \(0.0702941\pi\) | ||||
−0.975715 | + | 0.219045i | \(0.929706\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 4.95216e6i | − | 2.34043i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 46205.3i | − | 0.0215182i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.36239e6i | − | 1.08422i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.25478e6 | + | 4.09132e6i | 0.567568 | + | 1.85061i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.81927e6 | 0.811100 | 0.405550 | − | 0.914073i | \(-0.367080\pi\) | ||||
0.405550 | + | 0.914073i | \(0.367080\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.66132e6i | − | 1.60907i | −0.593908 | − | 0.804533i | \(-0.702416\pi\) | ||
0.593908 | − | 0.804533i | \(-0.297584\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.62518e6 | 0.704099 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.00606e6i | − | 1.71112i | −0.517703 | − | 0.855560i | \(-0.673213\pi\) | ||
0.517703 | − | 0.855560i | \(-0.326787\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.92449e6 | − | 590225.i | 0.810483 | − | 0.248569i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.61766e6 | −1.50230 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.37100e6 | −1.38046 | −0.690228 | − | 0.723592i | \(-0.742490\pi\) | ||||
−0.690228 | + | 0.723592i | \(0.742490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.95419e6 | 0.789221 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.99409e6 | −1.59093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.05372e6 | − | 3.43574e6i | −0.413991 | − | 1.34986i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.30503e6i | − | 1.28089i | −0.768005 | − | 0.640444i | \(-0.778751\pi\) | ||
0.768005 | − | 0.640444i | \(-0.221249\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.76614e6 | −2.58687 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.34013e6i | 0.505491i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −582132. | −0.216646 | −0.108323 | − | 0.994116i | \(-0.534548\pi\) | ||||
−0.108323 | + | 0.994116i | \(0.534548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.71807e6 | − | 3.37469e6i | 0.998119 | − | 1.23924i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.69922e6i | − | 1.34047i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.24404e6i | − | 0.802478i | −0.915973 | − | 0.401239i | \(-0.868580\pi\) | ||
0.915973 | − | 0.401239i | \(-0.131420\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 2.31428e6i | − | 0.816776i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 2.03163e6i | − | 0.707696i | −0.935303 | − | 0.353848i | \(-0.884873\pi\) | ||
0.935303 | − | 0.353848i | \(-0.115127\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28762.7 | − | 8821.28i | 0.00988957 | − | 0.00303305i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.10506e6 | 1.05388 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.29458e6i | − | 1.10389i | −0.833881 | − | 0.551945i | \(-0.813886\pi\) | ||
0.833881 | − | 0.551945i | \(-0.186114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.48852e6 | −1.48478 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.33930e6i | − | 1.41722i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.59949e6 | − | 797242.i | 0.838291 | − | 0.257097i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.66575e6 | −0.848875 | −0.424438 | − | 0.905457i | \(-0.639528\pi\) | ||||
−0.424438 | + | 0.905457i | \(0.639528\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.79700e6 | −0.565089 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.41349e6 | −0.438965 | −0.219483 | − | 0.975616i | \(-0.570437\pi\) | ||||
−0.219483 | + | 0.975616i | \(0.570437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.36385e6 | −1.33847 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 584008. | − | 179111.i | 0.176922 | − | 0.0542605i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28317.4i | 0.00847358i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.65117e6 | −0.488072 | −0.244036 | − | 0.969766i | \(-0.578472\pi\) | ||||
−0.244036 | + | 0.969766i | \(0.578472\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.16112e6i | 0.923073i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.09897e6 | 0.317036 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.66071e6 | + | 816019.i | −0.758364 | + | 0.232584i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.76458e6i | 2.74988i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.58123e6i | − | 1.27482i | −0.770527 | − | 0.637408i | \(-0.780007\pi\) | ||
0.770527 | − | 0.637408i | \(-0.219993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.54620e6i | − | 0.975120i | −0.873089 | − | 0.487560i | \(-0.837887\pi\) | ||
0.873089 | − | 0.487560i | \(-0.162113\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 8.23461e6i | − | 2.23765i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.54811e6 | + | 3.76344e6i | 0.684298 | + | 1.01068i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.10129e6 | −0.292302 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 67471.4i | − | 0.0177001i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.24667e6 | −0.841871 | −0.420935 | − | 0.907091i | \(-0.638298\pi\) | ||||
−0.420935 | + | 0.907091i | \(0.638298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.93639e6i | − | 1.26529i | −0.774443 | − | 0.632644i | \(-0.781970\pi\) | ||
0.774443 | − | 0.632644i | \(-0.218030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.96733e6 | + | 9.67527e6i | 0.751870 | + | 2.45155i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.22959e6 | −0.558498 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.91592e6 | 1.46508 | 0.732539 | − | 0.680725i | \(-0.238335\pi\) | ||||
0.732539 | + | 0.680725i | \(0.238335\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.51305e6 | 0.615325 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −723323. | −0.175115 | −0.0875574 | − | 0.996159i | \(-0.527906\pi\) | ||||
−0.0875574 | + | 0.996159i | \(0.527906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −414966. | + | 127267.i | −0.0993373 | + | 0.0304660i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.14515e6i | 0.981231i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.61902e6 | −0.378999 | −0.189499 | − | 0.981881i | \(-0.560686\pi\) | ||||
−0.189499 | + | 0.981881i | \(0.560686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 97542.1i | 0.0225814i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.57162e6 | −1.04670 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −833125. | − | 2.71649e6i | −0.188661 | − | 0.615147i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 419909.i | − | 0.0940512i | −0.998894 | − | 0.0470256i | \(-0.985026\pi\) | ||
0.998894 | − | 0.0470256i | \(-0.0149742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 4.66331e6i | − | 1.03315i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.17942e6i | 0.696780i | 0.937350 | + | 0.348390i | \(0.113272\pi\) | ||||
−0.937350 | + | 0.348390i | \(0.886728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 620530.i | − | 0.134527i | −0.997735 | − | 0.0672636i | \(-0.978573\pi\) | ||
0.997735 | − | 0.0672636i | \(-0.0214269\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.14136e7 | − | 3.50046e6i | 2.44788 | − | 0.750746i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.96565e6 | −0.417075 | −0.208538 | − | 0.978014i | \(-0.566870\pi\) | ||||
−0.208538 | + | 0.978014i | \(0.566870\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.30441e6i | − | 0.273831i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.00130e7 | 2.07975 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 44763.1i | − | 0.00919957i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.26572e6 | + | 1.86942e6i | 0.257398 | + | 0.380165i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.97487e6 | −1.00112 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.57977e6 | 0.912022 | 0.456011 | − | 0.889974i | \(-0.349278\pi\) | ||||
0.456011 | + | 0.889974i | \(0.349278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.67443e6 | 0.527070 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.67677e6 | −1.49731 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 603991. | + | 1.96937e6i | 0.116594 | + | 0.380167i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.22794e6i | − | 1.76312i | −0.472070 | − | 0.881561i | \(-0.656493\pi\) | ||
0.472070 | − | 0.881561i | \(-0.343507\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.86603e6 | −1.67671 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.77438e6i | − | 1.26814i | −0.773277 | − | 0.634068i | \(-0.781384\pi\) | ||
0.773277 | − | 0.634068i | \(-0.218616\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.06146e7 | −1.96692 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 32746.6 | + | 106774.i | 0.00600694 | + | 0.0195862i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.61102e6i | 0.655752i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.54380e6i | − | 0.637115i | −0.947903 | − | 0.318558i | \(-0.896802\pi\) | ||
0.947903 | − | 0.318558i | \(-0.103198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 948077.i | 0.168752i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 582992.i | − | 0.102741i | −0.998680 | − | 0.0513704i | \(-0.983641\pi\) | ||
0.998680 | − | 0.0513704i | \(-0.0163589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.86118e6 | + | 9.32915e6i | 0.499248 | + | 1.62785i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.83744e6 | 0.490237 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.00694e7i | 1.72270i | 0.508013 | + | 0.861349i | \(0.330380\pi\) | ||||
−0.508013 | + | 0.861349i | \(0.669620\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.44668e6 | 1.09215 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2.31641e6i | − | 0.388618i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.82754e6 | + | 9.21947e6i | 0.469775 | + | 1.53175i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −118712. | −0.0195329 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.33022e6 | −0.542693 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.76200e6 | −1.09139 | −0.545696 | − | 0.837983i | \(-0.683735\pi\) | ||||
−0.545696 | + | 0.837983i | \(0.683735\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.39905e6 | 1.02297 | 0.511483 | − | 0.859293i | \(-0.329096\pi\) | ||||
0.511483 | + | 0.859293i | \(0.329096\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.35806e6 | + | 6.43665e6i | 0.690072 | + | 1.01921i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.25217e7i | 1.96398i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.08843e6 | −0.479842 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.07961e6i | 0.627888i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.21235e6 | 1.40460 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.29332e6 | − | 2.54349e6i | 1.25269 | − | 0.384190i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.40397e7i | − | 2.10098i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 36228.6i | − | 0.00537130i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.42388e6i | 1.38432i | 0.721744 | + | 0.692160i | \(0.243341\pi\) | ||||
−0.721744 | + | 0.692160i | \(0.756659\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.41921e7i | 2.06560i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.82031e6 | − | 5.93529e6i | −0.262514 | − | 0.855955i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.39418e6 | 0.199228 | 0.0996138 | − | 0.995026i | \(-0.468239\pi\) | ||||
0.0996138 | + | 0.995026i | \(0.468239\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 4.08824e6i | − | 0.578902i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.27260e6 | −0.739854 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.87756e6i | 0.678250i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.99494e6 | + | 2.14529e6i | −0.963943 | + | 0.295634i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.27617e6 | 0.174289 | 0.0871445 | − | 0.996196i | \(-0.472226\pi\) | ||||
0.0871445 | + | 0.996196i | \(0.472226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.22765e6 | −0.572228 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −193603. | −0.0259720 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.87381e6 | 0.249146 | 0.124573 | − | 0.992210i | \(-0.460244\pi\) | ||||
0.124573 | + | 0.992210i | \(0.460244\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.27243e6 | − | 1.06701e7i | −0.431269 | − | 1.40620i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.09581e6i | 0.143145i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.96458e6 | −0.901808 | −0.450904 | − | 0.892572i | \(-0.648898\pi\) | ||||
−0.450904 | + | 0.892572i | \(0.648898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 344717.i | − | 0.0442458i | −0.999755 | − | 0.0221229i | \(-0.992957\pi\) | ||
0.999755 | − | 0.0221229i | \(-0.00704251\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.70051e7 | 2.16368 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.40715e6 | + | 7.98612e6i | 0.682023 | + | 1.00732i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.35769e6i | 0.669944i | 0.942228 | + | 0.334972i | \(0.108727\pi\) | ||||
−0.942228 | + | 0.334972i | \(0.891273\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 2.31055e7i | − | 2.86431i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.99245e6i | − | 0.613583i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 71718.8i | 0.00873900i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00842e7 | − | 3.09275e6i | 1.21829 | − | 0.373641i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.33004e6 | 0.159320 | 0.0796599 | − | 0.996822i | \(-0.474617\pi\) | ||||
0.0796599 | + | 0.996822i | \(0.474617\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.21992e6i | 0.738748i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.71677e7 | −2.02182 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.87875e6i | 0.569734i | 0.958567 | + | 0.284867i | \(0.0919494\pi\) | ||||
−0.958567 | + | 0.284867i | \(0.908051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.79472e6 | + | 2.39058e6i | −0.902627 | + | 0.276828i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.40398e7 | 2.76054 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.71017e6 | 0.308624 | 0.154312 | − | 0.988022i | \(-0.450684\pi\) | ||||
0.154312 | + | 0.988022i | \(0.450684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.02295e7 | 1.15523 | 0.577615 | − | 0.816309i | \(-0.303983\pi\) | ||||
0.577615 | + | 0.816309i | \(0.303983\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.84226e6 | 0.542319 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.60578e6 | + | 2.63932e6i | −0.955876 | + | 0.293160i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.63212e6i | − | 0.730602i | −0.930890 | − | 0.365301i | \(-0.880966\pi\) | ||
0.930890 | − | 0.365301i | \(-0.119034\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.81543e7 | −1.98351 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.12117e7i | 1.21498i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.17868e6 | −0.771602 | −0.385801 | − | 0.922582i | \(-0.626075\pi\) | ||||
−0.385801 | + | 0.922582i | \(0.626075\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.40948e7 | + | 7.38968e6i | −2.56883 | + | 0.787840i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.22481e7i | − | 1.29526i | −0.761956 | − | 0.647629i | \(-0.775761\pi\) | ||
0.761956 | − | 0.647629i | \(-0.224239\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.10012e6i | − | 0.220302i | −0.993915 | − | 0.110151i | \(-0.964867\pi\) | ||
0.993915 | − | 0.110151i | \(-0.0351334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 9.89568e6i | − | 1.02971i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 778624.i | − | 0.0803725i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.62641e6 | − | 9.06734e6i | 0.371345 | − | 0.928495i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −96168.9 | −0.00976935 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7.67404e6i | − | 0.773388i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.94323e6 | 0.594223 | 0.297111 | − | 0.954843i | \(-0.403977\pi\) | ||||
0.297111 | + | 0.954843i | \(0.403977\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.98481e7i | 1.96883i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.52929e6 | − | 4.98641e6i | −0.150507 | − | 0.490743i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.42160e6 | −0.334104 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.34049e7 | −1.29871 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.73665e7 | 1.66943 | 0.834713 | − | 0.550686i | \(-0.185634\pi\) | ||||
0.834713 | + | 0.550686i | \(0.185634\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.88563e7 | 1.79858 | 0.899290 | − | 0.437353i | \(-0.144084\pi\) | ||||
0.899290 | + | 0.437353i | \(0.144084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.10574e7 | − | 3.39121e6i | 1.04653 | − | 0.320963i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.16987e6i | 0.203785i | 0.994795 | + | 0.101893i | \(0.0324898\pi\) | ||||
−0.994795 | + | 0.101893i | \(0.967510\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 58812.5 | 0.00548097 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.14160e7i | 1.98055i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.97704e7 | 1.81440 | 0.907198 | − | 0.420703i | \(-0.138217\pi\) | ||||
0.907198 | + | 0.420703i | \(0.138217\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.86744e6 | − | 9.34958e6i | −0.261151 | − | 0.851509i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.39315e7i | 2.16300i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.61872e6i | − | 0.324595i | −0.986742 | − | 0.162297i | \(-0.948110\pi\) | ||
0.986742 | − | 0.162297i | \(-0.0518904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.75269e6i | − | 0.334071i | −0.985951 | − | 0.167036i | \(-0.946580\pi\) | ||
0.985951 | − | 0.167036i | \(-0.0534195\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.82848e7i | 1.61550i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.87188e6 | + | 1.18748e6i | −0.339522 | + | 0.104129i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.25245e7 | −1.96038 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.53769e7i | − | 1.32833i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −58936.8 | −0.00505336 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.93077e6i | − | 0.164321i | −0.996619 | − | 0.0821606i | \(-0.973818\pi\) | ||
0.996619 | − | 0.0821606i | \(-0.0261820\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.29710e6 | + | 5.61771e6i | −0.700918 | + | 0.474570i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.53721e6 | 0.632032 | 0.316016 | − | 0.948754i | \(-0.397655\pi\) | ||||
0.316016 | + | 0.948754i | \(0.397655\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.69525e6 | −0.307588 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.35815e7 | 1.12223 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.28279e6 | 0.187247 | 0.0936234 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936234 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.08889e6 | + | 6.81104e6i | 0.170094 | + | 0.554609i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.14114e6i | 0.738939i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.77347e6 | 0.543580 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 4.89825e6i | − | 0.390252i | −0.980778 | − | 0.195126i | \(-0.937488\pi\) | ||
0.980778 | − | 0.195126i | \(-0.0625116\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −200345. | −0.0158470 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.45251e6 | + | 2.10391e7i | 0.506718 | + | 1.65221i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.64340e7i | − | 2.06102i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 8.60838e6i | − | 0.666390i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.36266e7i | 1.04735i | 0.851917 | + | 0.523676i | \(0.175440\pi\) | ||||
−0.851917 | + | 0.523676i | \(0.824560\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.81194e6i | − | 0.290909i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.99347e6 | − | 2.93241e7i | −0.681483 | − | 2.22204i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.75048e7 | −1.31707 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.03111e7i | 0.770350i | 0.922843 | + | 0.385175i | \(0.125859\pi\) | ||||
−0.922843 | + | 0.385175i | \(0.874141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.81066e7 | −1.34327 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.65714e7i | 1.95745i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −44585.6 | − | 145376.i | −0.00326159 | − | 0.0106348i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.90769e7 | 2.11228 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.38661e6 | 0.677153 | 0.338576 | − | 0.940939i | \(-0.390055\pi\) | ||||
0.338576 | + | 0.940939i | \(0.390055\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.72990e7 | −1.23932 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.73254e7 | 1.94411 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.27870e7 | + | 1.88858e7i | 0.903490 | + | 1.33441i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.62442e6i | 0.324505i | 0.986749 | + | 0.162252i | \(0.0518759\pi\) | ||||
−0.986749 | + | 0.162252i | \(0.948124\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.33945e7 | −1.63040 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.21309e7i | 0.839650i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.68859e7 | −1.84827 | −0.924134 | − | 0.382068i | \(-0.875212\pi\) | ||||
−0.924134 | + | 0.382068i | \(0.875212\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.94917e6 | − | 2.74464e6i | 0.611033 | − | 0.187399i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 69807.0i | − | 0.00473403i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 686127.i | 0.0462161i | 0.999733 | + | 0.0231081i | \(0.00735618\pi\) | ||||
−0.999733 | + | 0.0231081i | \(0.992644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.08265e6i | 0.607669i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.09400e7i | 0.727017i | 0.931591 | + | 0.363508i | \(0.118421\pi\) | ||||
−0.931591 | + | 0.363508i | \(0.881579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.73915e6 | + | 8.93126e6i | 0.180811 | + | 0.589552i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.85331e7 | 1.21520 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.55612e7i | 1.01354i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.37534e7 | 1.53683 | 0.768416 | − | 0.639951i | \(-0.221045\pi\) | ||||
0.768416 | + | 0.639951i | \(0.221045\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.41704e6i | 0.155345i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.85014e6 | + | 3.02096e6i | −0.628891 | + | 0.192876i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.95506e7 | −1.87424 | −0.937122 | − | 0.349003i | \(-0.886520\pi\) | ||||
−0.937122 | + | 0.349003i | \(0.886520\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −410832. | −0.0258857 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.38225e6 | 0.149116 | 0.0745582 | − | 0.997217i | \(-0.476245\pi\) | ||||
0.0745582 | + | 0.997217i | \(0.476245\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.11367e7 | 0.692542 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.87437e6 | − | 2.89358e7i | −0.548256 | − | 1.78764i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.55453e6i | − | 0.340925i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.58003e7 | −0.963495 | −0.481747 | − | 0.876310i | \(-0.659998\pi\) | ||||
−0.481747 | + | 0.876310i | \(0.659998\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 3.35600e7i | − | 2.03323i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.84834e6 | −0.532615 | −0.266307 | − | 0.963888i | \(-0.585804\pi\) | ||||
−0.266307 | + | 0.963888i | \(0.585804\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.22790e7 | − | 1.50844e7i | 1.33242 | − | 0.902140i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.31250e7i | − | 0.779914i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.31306e7i | − | 0.775249i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 193248.i | 0.0113367i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.34016e7i | − | 1.36408i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.15743e7 | − | 6.61667e6i | 1.24958 | − | 0.383235i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.30753e6 | 0.305461 | 0.152730 | − | 0.988268i | \(-0.451193\pi\) | ||||
0.152730 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.21491e7i | 1.26667i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00209e7 | 1.13774 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.56628e6i | 0.314327i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.77159e7 | + | 5.43334e6i | −0.994137 | + | 0.304894i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.99099e7 | −1.11026 | −0.555128 | − | 0.831765i | \(-0.687331\pi\) | ||||
−0.555128 | + | 0.831765i | \(0.687331\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.21710e7 | 1.78278 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.89043e6 | 0.159177 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 345002. | 0.0188813 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.65406e7 | + | 5.07287e6i | −0.899626 | + | 0.275908i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.81202e6i | 0.530365i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.14513e7 | 1.15234 | 0.576172 | − | 0.817329i | \(-0.304546\pi\) | ||||
0.576172 | + | 0.817329i | \(0.304546\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.07036e6i | 0.110534i | 0.998472 | + | 0.0552668i | \(0.0176009\pi\) | ||||
−0.998472 | + | 0.0552668i | \(0.982399\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.36031e7 | 0.721791 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.91030e7 | + | 5.85875e6i | −1.00741 | + | 0.308966i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.02578e6i | 0.315833i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.89216e7i | 0.985706i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.97968e7i | 1.02503i | 0.858677 | + | 0.512517i | \(0.171287\pi\) | ||||
−0.858677 | + | 0.512517i | \(0.828713\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.89602e7i | − | 1.49040i | −0.666842 | − | 0.745199i | \(-0.732355\pi\) | ||
0.666842 | − | 0.745199i | \(-0.267645\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 233227. | + | 344465.i | 0.0119301 | + | 0.0176202i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.81070e6 | −0.0920624 | −0.0460312 | − | 0.998940i | \(-0.514657\pi\) | ||||
−0.0460312 | + | 0.998940i | \(0.514657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.35089e7i | − | 0.682706i | −0.939935 | − | 0.341353i | \(-0.889115\pi\) | ||
0.939935 | − | 0.341353i | \(-0.110885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.08554e6 | −0.104765 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.81800e6i | 0.490242i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 626496. | + | 2.04275e6i | 0.0310959 | + | 0.101391i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.76061e7 | −1.36204 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.09747e7 | −0.538252 | −0.269126 | − | 0.963105i | \(-0.586735\pi\) | ||||
−0.269126 | + | 0.963105i | \(0.586735\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.27554e7 | −1.59695 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.15789e7 | −1.04583 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.11363e6 | − | 1.87500e6i | 0.294549 | − | 0.0903357i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.61475e7i | − | 0.773387i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.47720e7 | 2.13176 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.62845e7i | − | 0.770817i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.28394e6 | −0.0604186 | −0.0302093 | − | 0.999544i | \(-0.509617\pi\) | ||||
−0.0302093 | + | 0.999544i | \(0.509617\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.40817e6 | − | 1.43733e7i | −0.206226 | − | 0.672421i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.48910e7i | − | 0.692582i | −0.938127 | − | 0.346291i | \(-0.887441\pi\) | ||
0.938127 | − | 0.346291i | \(-0.112559\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.77820e6i | − | 0.0822239i | −0.999155 | − | 0.0411120i | \(-0.986910\pi\) | ||
0.999155 | − | 0.0411120i | \(-0.0130900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 4.52104e7i | − | 2.07841i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 601133.i | − | 0.0274754i | −0.999906 | − | 0.0137377i | \(-0.995627\pi\) | ||
0.999906 | − | 0.0137377i | \(-0.00437298\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.17539e6 | + | 2.20064e6i | −0.326066 | + | 0.100002i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.72478e7 | 0.779267 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 261029.i | 0.0117257i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.59292e6 | −0.294464 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.37176e7i | − | 0.609175i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.36434e7 | + | 1.09888e7i | 0.602424 | + | 0.485209i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.57080e7 | −1.12868 | −0.564338 | − | 0.825544i | \(-0.690868\pi\) | ||||
−0.564338 | + | 0.825544i | \(0.690868\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.82241e7 | −0.795562 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.82816e7 | −0.793551 | −0.396775 | − | 0.917916i | \(-0.629871\pi\) | ||||
−0.396775 | + | 0.917916i | \(0.629871\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.27706e6 | −0.357252 | −0.178626 | − | 0.983917i | \(-0.557165\pi\) | ||||
−0.178626 | + | 0.983917i | \(0.557165\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.45557e6 | + | 1.45278e7i | 0.191225 | + | 0.623508i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.11992e7i | 0.477947i | 0.971026 | + | 0.238973i | \(0.0768109\pi\) | ||||
−0.971026 | + | 0.238973i | \(0.923189\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.35629e6 | 0.397054 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 58643.4i | 0.00247471i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.59804e7 | 0.670591 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.27756e6 | − | 3.02504e7i | −0.387147 | − | 1.26233i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.88009e7i | 1.61013i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.28368e7i | 2.59307i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.94359e7i | − | 0.797613i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.07476e7i | 0.846735i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.37824e6 | + | 3.05787e7i | 0.380627 | + | 1.24107i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.21915e7 | −0.895712 | −0.447856 | − | 0.894106i | \(-0.647812\pi\) | ||||
−0.447856 | + | 0.894106i | \(0.647812\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 6.49818e7i | − | 2.60845i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.01968e6 | 0.0806281 | 0.0403140 | − | 0.999187i | \(-0.487164\pi\) | ||||
0.0403140 | + | 0.999187i | \(0.487164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 267177.i | − | 0.0106077i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.46499e6 | − | 1.45585e7i | −0.176306 | − | 0.574864i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.75432e7 | 0.688945 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.22871e6 | 0.0479909 | 0.0239955 | − | 0.999712i | \(-0.492361\pi\) | ||||
0.0239955 | + | 0.999712i | \(0.492361\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.40908e7 | −0.547375 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.82513e7 | 0.705163 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.36539e7 | + | 9.24462e6i | −0.524689 | + | 0.355251i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 6.42178e7i | − | 2.45446i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.87347e7 | −1.09236 | −0.546182 | − | 0.837666i | \(-0.683919\pi\) | ||||
−0.546182 | + | 0.837666i | \(0.683919\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.87691e6i | 0.184404i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.20852e7 | −1.58280 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −417144. | + | 127935.i | −0.0156047 | + | 0.00478585i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.96219e7i | − | 0.730117i | −0.930985 | − | 0.365059i | \(-0.881049\pi\) | ||
0.930985 | − | 0.365059i | \(-0.118951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 8.68063e6i | − | 0.321283i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.28766e7i | − | 0.474054i | −0.971503 | − | 0.237027i | \(-0.923827\pi\) | ||
0.971503 | − | 0.237027i | \(-0.0761731\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.60937e7i | − | 2.05416i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.27042e6 | − | 1.71847e7i | −0.191984 | − | 0.625984i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.29327e7 | −1.19331 | −0.596654 | − | 0.802498i | \(-0.703504\pi\) | ||||
−0.596654 | + | 0.802498i | \(0.703504\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.25836e7i | − | 1.17445i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.37451e7 | −1.92702 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.23485e7i | − | 1.15378i | −0.816823 | − | 0.576889i | \(-0.804267\pi\) | ||
0.816823 | − | 0.576889i | \(-0.195733\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.66397e7 | − | 1.12371e7i | 1.30000 | − | 0.398700i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −971547. | −0.0342913 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.27799e7 | −0.448727 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.54974e7 | 1.58920 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.77667e7 | −2.00730 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.52683e7 | − | 4.97839e7i | −0.527804 | − | 1.72096i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.94417e6i | − | 0.204421i | −0.994763 | − | 0.102210i | \(-0.967409\pi\) | ||
0.994763 | − | 0.102210i | \(-0.0325915\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.60619e7 | 0.891654 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.42360e7i | − | 0.484551i | −0.970208 | − | 0.242275i | \(-0.922106\pi\) | ||
0.970208 | − | 0.242275i | \(-0.0778938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.94768e7 | −1.33678 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.25329e7 | − | 2.20270e7i | 1.09600 | − | 0.742070i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.01878e7i | 0.341464i | 0.985318 | + | 0.170732i | \(0.0546132\pi\) | ||||
−0.985318 | + | 0.170732i | \(0.945387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 41669.0i | − | 0.00138949i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.13420e7i | 1.37157i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.72803e7i | 0.570384i | 0.958470 | + | 0.285192i | \(0.0920574\pi\) | ||||
−0.958470 | + | 0.285192i | \(0.907943\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.69900e7 | + | 1.13445e7i | −1.21477 | + | 0.372560i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.50225e7 | 1.79783 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.57420e7i | 0.836858i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.41374e6 | 0.239802 | 0.119901 | − | 0.992786i | \(-0.461742\pi\) | ||||
0.119901 | + | 0.992786i | \(0.461742\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 7.68715e7i | − | 2.47396i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.17968e7 | − | 1.58857e7i | 1.65861 | − | 0.508684i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.79839e7 | −0.891601 | −0.445800 | − | 0.895132i | \(-0.647081\pi\) | ||||
−0.445800 | + | 0.895132i | \(0.647081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.69187e7 | 0.536355 |
(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 | 320.6.f.c.289.2 | yes | 16 | |
4.3 | odd | 2 | inner | 320.6.f.c.289.14 | yes | 16 | |
5.4 | even | 2 | inner | 320.6.f.c.289.16 | yes | 16 | |
8.3 | odd | 2 | inner | 320.6.f.c.289.3 | yes | 16 | |
8.5 | even | 2 | inner | 320.6.f.c.289.15 | yes | 16 | |
20.19 | odd | 2 | inner | 320.6.f.c.289.4 | yes | 16 | |
40.19 | odd | 2 | inner | 320.6.f.c.289.13 | yes | 16 | |
40.29 | even | 2 | inner | 320.6.f.c.289.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.f.c.289.1 | ✓ | 16 | 40.29 | even | 2 | inner | |
320.6.f.c.289.2 | yes | 16 | 1.1 | even | 1 | trivial | |
320.6.f.c.289.3 | yes | 16 | 8.3 | odd | 2 | inner | |
320.6.f.c.289.4 | yes | 16 | 20.19 | odd | 2 | inner | |
320.6.f.c.289.13 | yes | 16 | 40.19 | odd | 2 | inner | |
320.6.f.c.289.14 | yes | 16 | 4.3 | odd | 2 | inner | |
320.6.f.c.289.15 | yes | 16 | 8.5 | even | 2 | inner | |
320.6.f.c.289.16 | yes | 16 | 5.4 | even | 2 | inner |