Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,6,Mod(557,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.557");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.j (of order \(4\), 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: | \(144.345437832\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 16112194x^{12} + 72373894590801x^{8} + 60780662400876311824x^{4} + 14178241191207403341807616 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{49}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 557.3 | ||
Root | \(-19.1476 - 19.1476i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.557 |
Dual form | 900.6.j.a.593.4 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −53.1577 | − | 53.1577i | −0.410035 | − | 0.410035i | 0.471716 | − | 0.881751i | \(-0.343635\pi\) |
−0.881751 | + | 0.471716i | \(0.843635\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 540.614i | − | 1.34712i | −0.739133 | − | 0.673559i | \(-0.764765\pi\) | ||
0.739133 | − | 0.673559i | \(-0.235235\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −744.598 | + | 744.598i | −1.22198 | + | 1.22198i | −0.255050 | + | 0.966928i | \(0.582092\pi\) |
−0.966928 | + | 0.255050i | \(0.917908\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1654.43 | + | 1654.43i | −1.38844 | + | 1.38844i | −0.559830 | + | 0.828608i | \(0.689133\pi\) |
−0.828608 | + | 0.559830i | \(0.810867\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2265.63i | 1.43981i | 0.694072 | + | 0.719905i | \(0.255815\pi\) | ||||
−0.694072 | + | 0.719905i | \(0.744185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1279.10 | − | 1279.10i | −0.504180 | − | 0.504180i | 0.408554 | − | 0.912734i | \(-0.366033\pi\) |
−0.912734 | + | 0.408554i | \(0.866033\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4554.02 | 1.00554 | 0.502770 | − | 0.864420i | \(-0.332314\pi\) | ||||
0.502770 | + | 0.864420i | \(0.332314\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4435.26 | 0.828925 | 0.414462 | − | 0.910066i | \(-0.363970\pi\) | ||||
0.414462 | + | 0.910066i | \(0.363970\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7124.30 | + | 7124.30i | 0.855535 | + | 0.855535i | 0.990808 | − | 0.135273i | \(-0.0431912\pi\) |
−0.135273 | + | 0.990808i | \(0.543191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1360.60i | 0.126407i | 0.998001 | + | 0.0632033i | \(0.0201317\pi\) | ||||
−0.998001 | + | 0.0632033i | \(0.979868\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10634.7 | − | 10634.7i | 0.877107 | − | 0.877107i | −0.116128 | − | 0.993234i | \(-0.537048\pi\) |
0.993234 | + | 0.116128i | \(0.0370482\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4365.75 | − | 4365.75i | 0.288280 | − | 0.288280i | −0.548120 | − | 0.836400i | \(-0.684656\pi\) |
0.836400 | + | 0.548120i | \(0.184656\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 11155.5i | − | 0.663743i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 23315.1 | + | 23315.1i | 1.14011 | + | 1.14011i | 0.988429 | + | 0.151686i | \(0.0484701\pi\) |
0.151686 | + | 0.988429i | \(0.451530\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25023.2 | −0.935863 | −0.467931 | − | 0.883765i | \(-0.655001\pi\) | ||||
−0.467931 | + | 0.883765i | \(0.655001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40116.1 | −1.38037 | −0.690183 | − | 0.723635i | \(-0.742470\pi\) | ||||
−0.690183 | + | 0.723635i | \(0.742470\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −34777.6 | − | 34777.6i | −0.946483 | − | 0.946483i | 0.0521561 | − | 0.998639i | \(-0.483391\pi\) |
−0.998639 | + | 0.0521561i | \(0.983391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10245.3i | − | 0.241202i | −0.992701 | − | 0.120601i | \(-0.961518\pi\) | ||
0.992701 | − | 0.120601i | \(-0.0384821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −27434.8 | + | 27434.8i | −0.602553 | + | 0.602553i | −0.940989 | − | 0.338437i | \(-0.890102\pi\) |
0.338437 | + | 0.940989i | \(0.390102\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −28737.8 | + | 28737.8i | −0.552365 | + | 0.552365i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 45219.6i | − | 0.815190i | −0.913163 | − | 0.407595i | \(-0.866368\pi\) | ||
0.913163 | − | 0.407595i | \(-0.133632\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −70849.2 | − | 70849.2i | −1.12886 | − | 1.12886i | −0.990363 | − | 0.138496i | \(-0.955773\pi\) |
−0.138496 | − | 0.990363i | \(-0.544227\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 107473. | 1.43821 | 0.719107 | − | 0.694900i | \(-0.244551\pi\) | ||||
0.719107 | + | 0.694900i | \(0.244551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 79162.2 | 1.00211 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 85951.2 | + | 85951.2i | 0.927519 | + | 0.927519i | 0.997545 | − | 0.0700263i | \(-0.0223083\pi\) |
−0.0700263 | + | 0.997545i | \(0.522308\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15317.0i | − | 0.149407i | −0.997206 | − | 0.0747035i | \(-0.976199\pi\) | ||
0.997206 | − | 0.0747035i | \(-0.0238010\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18040.8 | + | 18040.8i | −0.167557 | + | 0.167557i | −0.785905 | − | 0.618348i | \(-0.787802\pi\) |
0.618348 | + | 0.785905i | \(0.287802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 126626. | − | 126626.i | 1.06921 | − | 1.06921i | 0.0717877 | − | 0.997420i | \(-0.477130\pi\) |
0.997420 | − | 0.0717877i | \(-0.0228704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 116529.i | 0.939434i | 0.882817 | + | 0.469717i | \(0.155644\pi\) | ||||
−0.882817 | + | 0.469717i | \(0.844356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −36520.8 | − | 36520.8i | −0.269057 | − | 0.269057i | 0.559663 | − | 0.828720i | \(-0.310930\pi\) |
−0.828720 | + | 0.559663i | \(0.810930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 175891. | 1.13862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −131213. | −0.814728 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −122586. | − | 122586.i | −0.674423 | − | 0.674423i | 0.284310 | − | 0.958733i | \(-0.408236\pi\) |
−0.958733 | + | 0.284310i | \(0.908236\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 339658.i | − | 1.72927i | −0.502399 | − | 0.864636i | \(-0.667549\pi\) | ||
0.502399 | − | 0.864636i | \(-0.332451\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 120436. | − | 120436.i | 0.590372 | − | 0.590372i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −105088. | + | 105088.i | −0.478357 | + | 0.478357i | −0.904606 | − | 0.426249i | \(-0.859835\pi\) |
0.426249 | + | 0.904606i | \(0.359835\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 356120.i | − | 1.56336i | −0.623679 | − | 0.781681i | \(-0.714363\pi\) | ||
0.623679 | − | 0.781681i | \(-0.285637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 402540. | + | 402540.i | 1.64615 | + | 1.64615i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 59416.0 | 0.219249 | 0.109625 | − | 0.993973i | \(-0.465035\pi\) | ||||
0.109625 | + | 0.993973i | \(0.465035\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −247958. | −0.884986 | −0.442493 | − | 0.896772i | \(-0.645906\pi\) | ||||
−0.442493 | + | 0.896772i | \(0.645906\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −187130. | − | 187130.i | −0.605891 | − | 0.605891i | 0.335978 | − | 0.941870i | \(-0.390933\pi\) |
−0.941870 | + | 0.335978i | \(0.890933\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 135988.i | 0.413463i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −56297.1 | + | 56297.1i | −0.165965 | + | 0.165965i | −0.785203 | − | 0.619238i | \(-0.787442\pi\) |
0.619238 | + | 0.785203i | \(0.287442\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −189578. | + | 189578.i | −0.526013 | + | 0.526013i | −0.919381 | − | 0.393368i | \(-0.871310\pi\) |
0.393368 | + | 0.919381i | \(0.371310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 737559.i | − | 1.98646i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −408674. | − | 408674.i | −1.03815 | − | 1.03815i | −0.999243 | − | 0.0389119i | \(-0.987611\pi\) |
−0.0389119 | − | 0.999243i | \(-0.512389\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 753137. | 1.75688 | 0.878439 | − | 0.477855i | \(-0.158585\pi\) | ||||
0.878439 | + | 0.477855i | \(0.158585\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −220257. | −0.499727 | −0.249863 | − | 0.968281i | \(-0.580386\pi\) | ||||
−0.249863 | + | 0.968281i | \(0.580386\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 894409. | + | 894409.i | 1.87039 | + | 1.87039i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 159911.i | − | 0.317173i | −0.987345 | − | 0.158586i | \(-0.949306\pi\) | ||
0.987345 | − | 0.158586i | \(-0.0506936\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −188370. | + | 188370.i | −0.364013 | + | 0.364013i | −0.865288 | − | 0.501275i | \(-0.832865\pi\) |
0.501275 | + | 0.865288i | \(0.332865\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 125767. | − | 125767.i | 0.230887 | − | 0.230887i | −0.582176 | − | 0.813063i | \(-0.697798\pi\) |
0.813063 | + | 0.582176i | \(0.197798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 204329.i | − | 0.365760i | −0.983135 | − | 0.182880i | \(-0.941458\pi\) | ||
0.983135 | − | 0.182880i | \(-0.0585420\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −242081. | − | 242081.i | −0.412307 | − | 0.412307i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.22483e6 | 1.93959 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −472424. | −0.730510 | −0.365255 | − | 0.930908i | \(-0.619018\pi\) | ||||
−0.365255 | + | 0.930908i | \(0.619018\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −235768. | − | 235768.i | −0.339888 | − | 0.339888i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.46377e6i | − | 3.39328i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 436887. | − | 436887.i | 0.588311 | − | 0.588311i | −0.348863 | − | 0.937174i | \(-0.613432\pi\) |
0.937174 | + | 0.348863i | \(0.113432\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −122133. | + | 122133.i | −0.157314 | + | 0.157314i | −0.781375 | − | 0.624061i | \(-0.785481\pi\) |
0.624061 | + | 0.781375i | \(0.285481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 274403.i | − | 0.345781i | −0.984941 | − | 0.172890i | \(-0.944689\pi\) | ||
0.984941 | − | 0.172890i | \(-0.0553106\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 208701. | + | 208701.i | 0.251846 | + | 0.251846i | 0.821727 | − | 0.569881i | \(-0.193011\pi\) |
−0.569881 | + | 0.821727i | \(0.693011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.37069e6 | 1.55219 | 0.776096 | − | 0.630615i | \(-0.217197\pi\) | ||||
0.776096 | + | 0.630615i | \(0.217197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26377.0 | −0.0292539 | −0.0146269 | − | 0.999893i | \(-0.504656\pi\) | ||||
−0.0146269 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.68698e6 | − | 1.68698e6i | −1.75942 | − | 1.75942i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 239275.i | 0.239724i | 0.992791 | + | 0.119862i | \(0.0382453\pi\) | ||||
−0.992791 | + | 0.119862i | \(0.961755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −691501. | + | 691501.i | −0.679190 | + | 0.679190i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 785914. | − | 785914.i | 0.742237 | − | 0.742237i | −0.230771 | − | 0.973008i | \(-0.574125\pi\) |
0.973008 | + | 0.230771i | \(0.0741250\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 757422.i | − | 0.701598i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 910319. | + | 910319.i | 0.811530 | + | 0.811530i | 0.984863 | − | 0.173334i | \(-0.0554539\pi\) |
−0.173334 | + | 0.984863i | \(0.555454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.23439e6 | 1.88269 | 0.941345 | − | 0.337446i | \(-0.109563\pi\) | ||||
0.941345 | + | 0.337446i | \(0.109563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.42257e6 | −1.17666 | −0.588331 | − | 0.808620i | \(-0.700215\pi\) | ||||
−0.588331 | + | 0.808620i | \(0.700215\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 444169. | + | 444169.i | 0.347816 | + | 0.347816i | 0.859295 | − | 0.511480i | \(-0.170902\pi\) |
−0.511480 | + | 0.859295i | \(0.670902\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 372453.i | − | 0.281388i | −0.990053 | − | 0.140694i | \(-0.955067\pi\) | ||
0.990053 | − | 0.140694i | \(-0.0449334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 634765. | − | 634765.i | 0.471137 | − | 0.471137i | −0.431146 | − | 0.902282i | \(-0.641891\pi\) |
0.902282 | + | 0.431146i | \(0.141891\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 72326.2 | − | 72326.2i | 0.0518311 | − | 0.0518311i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 4.05443e6i | − | 2.85552i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 95284.8 | + | 95284.8i | 0.0648418 | + | 0.0648418i | 0.738784 | − | 0.673942i | \(-0.235400\pi\) |
−0.673942 | + | 0.738784i | \(0.735400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.90483e6 | 1.23219 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.13063e6 | −0.719288 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.54273e6 | + | 1.54273e6i | 0.934210 | + | 0.934210i | 0.997966 | − | 0.0637554i | \(-0.0203078\pi\) |
−0.0637554 | + | 0.997966i | \(0.520308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.64625e6i | − | 0.965152i | −0.875854 | − | 0.482576i | \(-0.839701\pi\) | ||
0.875854 | − | 0.482576i | \(-0.160299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 93309.7 | − | 93309.7i | 0.0538351 | − | 0.0538351i | −0.679677 | − | 0.733512i | \(-0.737880\pi\) |
0.733512 | + | 0.679677i | \(0.237880\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −317919. | + | 317919.i | −0.177692 | + | 0.177692i | −0.790349 | − | 0.612657i | \(-0.790101\pi\) |
0.612657 | + | 0.790349i | \(0.290101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.46197e6i | − | 1.35458i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.74833e6 | − | 3.74833e6i | −1.99909 | − | 1.99909i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −464146. | −0.236410 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.34869e6 | −0.676614 | −0.338307 | − | 0.941036i | \(-0.609854\pi\) | ||||
−0.338307 | + | 0.941036i | \(0.609854\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.46174e6 | + | 1.46174e6i | 0.701124 | + | 0.701124i | 0.964652 | − | 0.263528i | \(-0.0848861\pi\) |
−0.263528 | + | 0.964652i | \(0.584886\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.39777e6i | − | 1.11666i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.48642e6 | + | 1.48642e6i | −0.682193 | + | 0.682193i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −852331. | + | 852331.i | −0.380001 | + | 0.380001i | −0.871102 | − | 0.491101i | \(-0.836594\pi\) |
0.491101 | + | 0.871102i | \(0.336594\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.98238e6i | 0.871211i | 0.900138 | + | 0.435605i | \(0.143466\pi\) | ||||
−0.900138 | + | 0.435605i | \(0.856534\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.88845e6 | + | 1.88845e6i | 0.806621 | + | 0.806621i | 0.984121 | − | 0.177500i | \(-0.0568010\pi\) |
−0.177500 | + | 0.984121i | \(0.556801\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.13908e6 | 1.69499 | 0.847497 | − | 0.530800i | \(-0.178109\pi\) | ||||
0.847497 | + | 0.530800i | \(0.178109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.65699e6 | −1.07305 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.29291e6 | − | 2.29291e6i | −0.888633 | − | 0.888633i | 0.105759 | − | 0.994392i | \(-0.466273\pi\) |
−0.994392 | + | 0.105759i | \(0.966273\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.47876e6i | − | 0.934973i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.52699e6 | − | 2.52699e6i | 0.940442 | − | 0.940442i | −0.0578815 | − | 0.998323i | \(-0.518435\pi\) |
0.998323 | + | 0.0578815i | \(0.0184345\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.39091e6 | + | 3.39091e6i | −1.22875 | + | 1.22875i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.34056e6i | − | 0.479389i | −0.970848 | − | 0.239694i | \(-0.922953\pi\) | ||
0.970848 | − | 0.239694i | \(-0.0770473\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.29180e6 | + | 3.29180e6i | 1.14666 | + | 1.14666i | 0.987204 | + | 0.159459i | \(0.0509751\pi\) |
0.159459 | + | 0.987204i | \(0.449025\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.37280e6 | 1.46516 | 0.732581 | − | 0.680680i | \(-0.238315\pi\) | ||||
0.732581 | + | 0.680680i | \(0.238315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.23237e6 | 1.40004 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.75223e6 | − | 1.75223e6i | −0.557974 | − | 0.557974i | 0.370756 | − | 0.928730i | \(-0.379098\pi\) |
−0.928730 | + | 0.370756i | \(0.879098\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.43495e6i | 0.445632i | 0.974860 | + | 0.222816i | \(0.0715250\pi\) | ||||
−0.974860 | + | 0.222816i | \(0.928475\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.30249e6 | + | 3.30249e6i | −1.01293 | + | 1.01293i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.85150e6 | − | 3.85150e6i | 1.15251 | − | 1.15251i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.23589e6i | 0.365318i | 0.983176 | + | 0.182659i | \(0.0584704\pi\) | ||||
−0.983176 | + | 0.182659i | \(0.941530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.33017e6 | + | 1.33017e6i | 0.383736 | + | 0.383736i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.18784e6 | 0.887077 | 0.443539 | − | 0.896255i | \(-0.353723\pi\) | ||||
0.443539 | + | 0.896255i | \(0.353723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 234906. | 0.0645936 | 0.0322968 | − | 0.999478i | \(-0.489718\pi\) | ||||
0.0322968 | + | 0.999478i | \(0.489718\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.13248e6 | + | 2.13248e6i | 0.565998 | + | 0.565998i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 199673.i | − | 0.0517758i | −0.999665 | − | 0.0258879i | \(-0.991759\pi\) | ||
0.999665 | − | 0.0258879i | \(-0.00824129\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.83325e6 | − | 3.83325e6i | 0.982533 | − | 0.982533i | −0.0173172 | − | 0.999850i | \(-0.505513\pi\) |
0.999850 | + | 0.0173172i | \(0.00551250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.89797e6 | − | 2.89797e6i | 0.725923 | − | 0.725923i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.69942e6i | − | 1.16381i | −0.813256 | − | 0.581906i | \(-0.802307\pi\) | ||
0.813256 | − | 0.581906i | \(-0.197693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.79107e6 | − | 1.79107e6i | −0.433615 | − | 0.433615i | 0.456241 | − | 0.889856i | \(-0.349195\pi\) |
−0.889856 | + | 0.456241i | \(0.849195\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.25095e6 | −1.22920 | −0.614599 | − | 0.788839i | \(-0.710682\pi\) | ||||
−0.614599 | + | 0.788839i | \(0.710682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 735558. | 0.170285 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.58768e6 | − | 1.58768e6i | −0.355609 | − | 0.355609i | 0.506582 | − | 0.862192i | \(-0.330909\pi\) |
−0.862192 | + | 0.506582i | \(0.830909\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.78398e6i | − | 0.390965i | −0.980707 | − | 0.195483i | \(-0.937373\pi\) | ||
0.980707 | − | 0.195483i | \(-0.0626273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.23125e6 | − | 3.23125e6i | 0.700517 | − | 0.700517i | −0.264004 | − | 0.964521i | \(-0.585043\pi\) |
0.964521 | + | 0.264004i | \(0.0850433\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −79429.9 | + | 79429.9i | −0.0168536 | + | 0.0168536i | −0.715483 | − | 0.698630i | \(-0.753793\pi\) |
0.698630 | + | 0.715483i | \(0.253793\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.69739e6i | 0.776182i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.74925e6 | − | 5.74925e6i | −1.18157 | − | 1.18157i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.52977e6 | −1.69863 | −0.849314 | − | 0.527888i | \(-0.822984\pi\) | ||||
−0.849314 | + | 0.527888i | \(0.822984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.06095e7 | −2.09089 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.16662e6 | + | 5.16662e6i | 0.987152 | + | 0.987152i | 0.999919 | − | 0.0127666i | \(-0.00406384\pi\) |
−0.0127666 | + | 0.999919i | \(0.504064\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.30691e6i | 1.36782i | 0.729565 | + | 0.683912i | \(0.239723\pi\) | ||||
−0.729565 | + | 0.683912i | \(0.760277\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.53430e6 | + | 7.53430e6i | −1.39613 | + | 1.39613i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −544618. | + | 544618.i | −0.0989011 | + | 0.0989011i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.40509e6i | − | 0.252611i | −0.991991 | − | 0.126306i | \(-0.959688\pi\) | ||
0.991991 | − | 0.126306i | \(-0.0403120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −906766. | − | 906766.i | −0.159799 | − | 0.159799i | 0.622678 | − | 0.782478i | \(-0.286045\pi\) |
−0.782478 | + | 0.622678i | \(0.786045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.11833e6 | 0.191327 | 0.0956636 | − | 0.995414i | \(-0.469503\pi\) | ||||
0.0956636 | + | 0.995414i | \(0.469503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.91674e6 | 0.494135 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.36019e6 | − | 2.36019e6i | −0.388347 | − | 0.388347i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4.88692e6i | − | 0.788753i | −0.918949 | − | 0.394376i | \(-0.870961\pi\) | ||
0.918949 | − | 0.394376i | \(-0.129039\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.85618e6 | + | 3.85618e6i | −0.616458 | + | 0.616458i | −0.944621 | − | 0.328163i | \(-0.893570\pi\) |
0.328163 | + | 0.944621i | \(0.393570\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.33784e6 | + | 7.33784e6i | −1.15091 | + | 1.15091i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 3.16414e6i | − | 0.491605i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.01310e6 | − | 1.01310e6i | −0.154466 | − | 0.154466i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.03084e6 | −0.894140 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.22094e6 | 1.35451 | 0.677255 | − | 0.735749i | \(-0.263169\pi\) | ||||
0.677255 | + | 0.735749i | \(0.263169\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.90650e6 | − | 8.90650e6i | −1.27274 | − | 1.27274i | −0.944646 | − | 0.328090i | \(-0.893595\pi\) |
−0.328090 | − | 0.944646i | \(-0.606405\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.03177e7i | 1.44779i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.40377e6 | + | 2.40377e6i | −0.334256 | + | 0.334256i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.10687e6 | − | 7.10687e6i | 0.970600 | − | 0.970600i | −0.0289800 | − | 0.999580i | \(-0.509226\pi\) |
0.999580 | + | 0.0289800i | \(0.00922592\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.58371e7i | 2.14361i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.50929e6 | + | 6.50929e6i | 0.865491 | + | 0.865491i | 0.991969 | − | 0.126479i | \(-0.0403675\pi\) |
−0.126479 | + | 0.991969i | \(0.540367\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.05713e6 | −1.04328 | −0.521639 | − | 0.853167i | \(-0.674679\pi\) | ||||
−0.521639 | + | 0.853167i | \(0.674679\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.28050e7 | 1.64358 | 0.821789 | − | 0.569793i | \(-0.192976\pi\) | ||||
0.821789 | + | 0.569793i | \(0.192976\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.23483e6 | + | 3.23483e6i | 0.404494 | + | 0.404494i | 0.879813 | − | 0.475320i | \(-0.157668\pi\) |
−0.475320 | + | 0.879813i | \(0.657668\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.53236e6i | 0.925743i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.26045e7 | − | 1.26045e7i | 1.53587 | − | 1.53587i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.88015e6 | + | 5.88015e6i | −0.704358 | + | 0.704358i | −0.965343 | − | 0.260985i | \(-0.915953\pi\) |
0.260985 | + | 0.965343i | \(0.415953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.00487e7i | 1.19349i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.07735e7 | + | 1.07735e7i | 1.25811 | + | 1.25811i | 0.951993 | + | 0.306119i | \(0.0990307\pi\) |
0.306119 | + | 0.951993i | \(0.400969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.78362e6 | 0.772493 | 0.386246 | − | 0.922396i | \(-0.373771\pi\) | ||||
0.386246 | + | 0.922396i | \(0.373771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.04350e6 | 0.343706 | 0.171853 | − | 0.985123i | \(-0.445025\pi\) | ||||
0.171853 | + | 0.985123i | \(0.445025\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.66065e6 | + | 5.66065e6i | 0.623583 | + | 0.623583i | 0.946446 | − | 0.322863i | \(-0.104645\pi\) |
−0.322863 | + | 0.946446i | \(0.604645\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.50146e6i | 0.704543i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.52027e6 | − | 4.52027e6i | 0.485862 | − | 0.485862i | −0.421135 | − | 0.906998i | \(-0.638368\pi\) |
0.906998 | + | 0.421135i | \(0.138368\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.01198e6 | − | 4.01198e6i | 0.424274 | − | 0.424274i | −0.462398 | − | 0.886672i | \(-0.653011\pi\) |
0.886672 | + | 0.462398i | \(0.153011\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.13209e7i | 1.18755i | 0.804630 | + | 0.593776i | \(0.202364\pi\) | ||||
−0.804630 | + | 0.593776i | \(0.797636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.71300e6 | − | 5.71300e6i | −0.589718 | − | 0.589718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.35733e7 | −2.37571 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.30746e6 | −0.530657 | −0.265328 | − | 0.964158i | \(-0.585480\pi\) | ||||
−0.265328 | + | 0.964158i | \(0.585480\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.30638e6 | + | 8.30638e6i | 0.811079 | + | 0.811079i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.46710e7i | − | 1.41031i | −0.709052 | − | 0.705156i | \(-0.750877\pi\) | ||
0.709052 | − | 0.705156i | \(-0.249123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.54761e6 | − | 4.54761e6i | 0.433766 | − | 0.433766i | −0.456141 | − | 0.889907i | \(-0.650769\pi\) |
0.889907 | + | 0.456141i | \(0.150769\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.16861e6 | − | 9.16861e6i | 0.861078 | − | 0.861078i | −0.130385 | − | 0.991463i | \(-0.541621\pi\) |
0.991463 | + | 0.130385i | \(0.0416214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.35279e7i | 1.26072i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.15310e6 | − | 9.15310e6i | −0.840011 | − | 0.840011i | 0.148849 | − | 0.988860i | \(-0.452443\pi\) |
−0.988860 | + | 0.148849i | \(0.952443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.19398e6 | −0.824689 | −0.412344 | − | 0.911028i | \(-0.635290\pi\) | ||||
−0.412344 | + | 0.911028i | \(0.635290\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.89018e6 | 0.346311 | 0.173155 | − | 0.984895i | \(-0.444604\pi\) | ||||
0.173155 | + | 0.984895i | \(0.444604\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.82505e6 | − | 5.82505e6i | −0.506973 | − | 0.506973i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.16873e7i | 1.85952i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.60598e6 | + | 6.60598e6i | −0.562211 | + | 0.562211i | −0.929935 | − | 0.367724i | \(-0.880137\pi\) |
0.367724 | + | 0.929935i | \(0.380137\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.23121e7 | + | 1.23121e7i | −1.03243 | + | 1.03243i | −0.0329739 | + | 0.999456i | \(0.510498\pi\) |
−0.999456 | + | 0.0329739i | \(0.989502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 9.13793e6i | − | 0.760630i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.79590e6 | + | 7.79590e6i | 0.639462 | + | 0.639462i | 0.950423 | − | 0.310961i | \(-0.100651\pi\) |
−0.310961 | + | 0.950423i | \(0.600651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.47208e7 | −2.78639 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.97218e6 | 0.635158 | 0.317579 | − | 0.948232i | \(-0.397130\pi\) | ||||
0.317579 | + | 0.948232i | \(0.397130\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.25101e6 | − | 2.25101e6i | −0.175508 | − | 0.175508i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.97246e6i | 0.459048i | 0.973303 | + | 0.229524i | \(0.0737170\pi\) | ||||
−0.973303 | + | 0.229524i | \(0.926283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.61410e7 | + | 1.61410e7i | −1.23181 | + | 1.23181i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −814217. | + | 814217.i | −0.0612621 | + | 0.0612621i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.80745e6i | 0.433881i | 0.976185 | + | 0.216940i | \(0.0696077\pi\) | ||||
−0.976185 | + | 0.216940i | \(0.930392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.67315e6 | − | 5.67315e6i | −0.417927 | − | 0.417927i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.90921e6 | −0.137731 | −0.0688654 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688654 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.91801e6 | 0.137408 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.90786e6 | + | 4.90786e6i | 0.344394 | + | 0.344394i | 0.858016 | − | 0.513622i | \(-0.171697\pi\) |
−0.513622 | + | 0.858016i | \(0.671697\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.51886e7i | 2.43561i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.12824e7 | + | 1.12824e7i | −0.775604 | + | 0.775604i | −0.979080 | − | 0.203476i | \(-0.934776\pi\) |
0.203476 | + | 0.979080i | \(0.434776\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.88013e7 | + | 1.88013e7i | −1.27502 | + | 1.27502i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 9.09279e6i | − | 0.612472i | −0.951956 | − | 0.306236i | \(-0.900930\pi\) | ||
0.951956 | − | 0.306236i | \(-0.0990697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.09450e6 | − | 9.09450e6i | −0.604375 | − | 0.604375i | 0.337095 | − | 0.941471i | \(-0.390556\pi\) |
−0.941471 | + | 0.337095i | \(0.890556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.34622e7 | −0.876825 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.22164e7 | 0.790394 | 0.395197 | − | 0.918596i | \(-0.370676\pi\) | ||||
0.395197 | + | 0.918596i | \(0.370676\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.78724e7 | − | 1.78724e7i | −1.13356 | − | 1.13356i | −0.989581 | − | 0.143978i | \(-0.954010\pi\) |
−0.143978 | − | 0.989581i | \(-0.545990\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32938.4i | 0.00206177i | 0.999999 | + | 0.00103089i | \(0.000328141\pi\) | ||||
−0.999999 | + | 0.00103089i | \(0.999672\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.19438e6 | − | 6.19438e6i | 0.385200 | − | 0.385200i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.86322e7 | − | 1.86322e7i | 1.14360 | − | 1.14360i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.64362e7i | 1.61207i | 0.591870 | + | 0.806033i | \(0.298390\pi\) | ||||
−0.591870 | + | 0.806033i | \(0.701610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.30090e6 | − | 5.30090e6i | −0.319081 | − | 0.319081i | 0.529333 | − | 0.848414i | \(-0.322442\pi\) |
−0.848414 | + | 0.529333i | \(0.822442\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.08261e6 | −0.182002 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.53877e6 | −0.324927 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.11065e7 | − | 1.11065e7i | −0.639208 | − | 0.639208i | 0.311152 | − | 0.950360i | \(-0.399285\pi\) |
−0.950360 | + | 0.311152i | \(0.899285\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.88272e6i | 0.220645i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.98704e7 | − | 2.98704e7i | 1.68678 | − | 1.68678i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.51828e7 | − | 1.51828e7i | 0.846656 | − | 0.846656i | −0.143058 | − | 0.989714i | \(-0.545694\pi\) |
0.989714 | + | 0.143058i | \(0.0456936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.44457e7i | 0.800517i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.48317e7 | + | 1.48317e7i | 0.811710 | + | 0.811710i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.98692e6 | 0.321612 | 0.160806 | − | 0.986986i | \(-0.448591\pi\) | ||||
0.160806 | + | 0.986986i | \(0.448591\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.69659e6 | 0.517686 | 0.258843 | − | 0.965919i | \(-0.416659\pi\) | ||||
0.258843 | + | 0.965919i | \(0.416659\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.40942e7 | + | 2.40942e7i | 1.26287 | + | 1.26287i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.39957e7i | − | 1.24244i | −0.783636 | − | 0.621220i | \(-0.786637\pi\) | ||
0.783636 | − | 0.621220i | \(-0.213363\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.70610e7 | + | 1.70610e7i | −0.878022 | + | 0.878022i | −0.993330 | − | 0.115307i | \(-0.963215\pi\) |
0.115307 | + | 0.993330i | \(0.463215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.07936e7 | − | 2.07936e7i | 1.05722 | − | 1.05722i | 0.0589625 | − | 0.998260i | \(-0.481221\pi\) |
0.998260 | − | 0.0589625i | \(-0.0187792\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.04142e7i | 0.526305i | 0.964754 | + | 0.263153i | \(0.0847623\pi\) | ||||
−0.964754 | + | 0.263153i | \(0.915238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.84560e7 | + | 1.84560e7i | 0.921565 | + | 0.921565i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.26427e6 | −0.356277 | −0.178138 | − | 0.984005i | \(-0.557007\pi\) | ||||
−0.178138 | + | 0.984005i | \(0.557007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 227913. | 0.0111117 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.97496e6 | + | 6.97496e6i | 0.334067 | + | 0.334067i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.82254e7i | − | 0.862687i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.52834e7 | − | 2.52834e7i | 1.18977 | − | 1.18977i | 0.212636 | − | 0.977131i | \(-0.431795\pi\) |
0.977131 | − | 0.212636i | \(-0.0682049\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −875598. | + | 875598.i | −0.0407242 | + | 0.0407242i | −0.727176 | − | 0.686451i | \(-0.759167\pi\) |
0.686451 | + | 0.727176i | \(0.259167\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.76413e7i | 0.815731i | 0.913042 | + | 0.407865i | \(0.133727\pi\) | ||||
−0.913042 | + | 0.407865i | \(0.866273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.90490e7 | − | 1.90490e7i | −0.870652 | − | 0.870652i | 0.121891 | − | 0.992543i | \(-0.461104\pi\) |
−0.992543 | + | 0.121891i | \(0.961104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.44463e7 | −1.09816 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.17907e7 | 2.31316 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.20695e6 | − | 2.20695e6i | −0.0968932 | − | 0.0968932i | 0.656999 | − | 0.753892i | \(-0.271826\pi\) |
−0.753892 | + | 0.656999i | \(0.771826\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.42358e6i | 0.322236i | 0.986935 | + | 0.161118i | \(0.0515099\pi\) | ||||
−0.986935 | + | 0.161118i | \(0.948490\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.14031e6 | + | 1.14031e6i | −0.0492179 | + | 0.0492179i | −0.731287 | − | 0.682069i | \(-0.761080\pi\) |
0.682069 | + | 0.731287i | \(0.261080\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.00968e7 | + | 3.00968e7i | −1.28443 | + | 1.28443i | −0.346316 | + | 0.938118i | \(0.612568\pi\) |
−0.938118 | + | 0.346316i | \(0.887432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.30328e7i | 0.553074i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.89118e6 | + | 9.89118e6i | 0.415068 | + | 0.415068i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.01983e7 | 0.833518 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.71466e7 | −3.16595 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 943761. | + | 943761.i | 0.0380929 | + | 0.0380929i | 0.725897 | − | 0.687804i | \(-0.241425\pi\) |
−0.687804 | + | 0.725897i | \(0.741425\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.29726e7i | 1.71552i | 0.514050 | + | 0.857760i | \(0.328145\pi\) | ||||
−0.514050 | + | 0.857760i | \(0.671855\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.83021e7 | + | 3.83021e7i | −1.52071 | + | 1.52071i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.80554e7 | + | 1.80554e7i | −0.709062 | + | 0.709062i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.52785e7i | − | 1.37791i | −0.724804 | − | 0.688955i | \(-0.758070\pi\) | ||
0.724804 | − | 0.688955i | \(-0.241930\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.62865e6 | + | 7.62865e6i | 0.294743 | + | 0.294743i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.75506e7 | 1.42751 | 0.713753 | − | 0.700398i | \(-0.246994\pi\) | ||||
0.713753 | + | 0.700398i | \(0.246994\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.52743e7 | 0.955664 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.80918e7 | − | 1.80918e7i | −0.673182 | − | 0.673182i | 0.285266 | − | 0.958448i | \(-0.407918\pi\) |
−0.958448 | + | 0.285266i | \(0.907918\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.68014e7i | − | 1.35485i | −0.735594 | − | 0.677423i | \(-0.763097\pi\) | ||
0.735594 | − | 0.677423i | \(-0.236903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.74034e6 | − | 1.74034e6i | 0.0637317 | − | 0.0637317i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.46623e7 | + | 1.46623e7i | −0.531284 | + | 0.531284i | −0.920954 | − | 0.389671i | \(-0.872589\pi\) |
0.389671 | + | 0.920954i | \(0.372589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.08558e7i | − | 1.47261i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.80395e7 | − | 2.80395e7i | −1.00009 | − | 1.00009i | −1.00000 | 8.73085e-5i | \(-0.999972\pi\) | |
−8.73085e−5 | − | 1.00000i | \(-0.500028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.11725e7 | 0.392286 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.95759e6 | −0.312884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.44518e6 | − | 2.44518e6i | −0.0840901 | − | 0.0840901i | 0.663811 | − | 0.747901i | \(-0.268938\pi\) |
−0.747901 | + | 0.663811i | \(0.768938\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.90773e7i | 1.67045i | 0.549910 | + | 0.835224i | \(0.314662\pi\) | ||||
−0.549910 | + | 0.835224i | \(0.685338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.89305e7 | + | 1.89305e7i | −0.641033 | + | 0.641033i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.26540e7 | − | 1.26540e7i | 0.424121 | − | 0.424121i | −0.462499 | − | 0.886620i | \(-0.653047\pi\) |
0.886620 | + | 0.462499i | \(0.153047\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5.81013e7i | − | 1.93744i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.28130e6 | − | 3.28130e6i | −0.108308 | − | 0.108308i | 0.650876 | − | 0.759184i | \(-0.274402\pi\) |
−0.759184 | + | 0.650876i | \(0.774402\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.72056e7 | −0.884439 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.02332e6 | −0.259520 | −0.129760 | − | 0.991545i | \(-0.541421\pi\) | ||||
−0.129760 | + | 0.991545i | \(0.541421\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.28213e7 | + | 1.28213e7i | 0.408501 | + | 0.408501i | 0.881216 | − | 0.472714i | \(-0.156726\pi\) |
−0.472714 | + | 0.881216i | \(0.656726\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 900.6.j.a.557.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 900.6.j.a.557.4 | yes | 16 | |
5.2 | odd | 4 | inner | 900.6.j.a.593.5 | yes | 16 | |
5.3 | odd | 4 | inner | 900.6.j.a.593.3 | yes | 16 | |
5.4 | even | 2 | inner | 900.6.j.a.557.5 | yes | 16 | |
15.2 | even | 4 | inner | 900.6.j.a.593.6 | yes | 16 | |
15.8 | even | 4 | inner | 900.6.j.a.593.4 | yes | 16 | |
15.14 | odd | 2 | inner | 900.6.j.a.557.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.6.j.a.557.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
900.6.j.a.557.4 | yes | 16 | 3.2 | odd | 2 | inner | |
900.6.j.a.557.5 | yes | 16 | 5.4 | even | 2 | inner | |
900.6.j.a.557.6 | yes | 16 | 15.14 | odd | 2 | inner | |
900.6.j.a.593.3 | yes | 16 | 5.3 | odd | 4 | inner | |
900.6.j.a.593.4 | yes | 16 | 15.8 | even | 4 | inner | |
900.6.j.a.593.5 | yes | 16 | 5.2 | odd | 4 | inner | |
900.6.j.a.593.6 | yes | 16 | 15.2 | even | 4 | inner |