Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,9,Mod(101,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.101");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.g (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: | \(122.213583018\) |
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: | \( x^{16} - 7378 x^{14} + 23156928 x^{12} - 101588726286 x^{10} + \cdots + 34\!\cdots\!81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{38}\cdot 3^{20}\cdot 5^{18} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.2 | ||
Root | \(79.3447 - 16.2916i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.101 |
Dual form | 300.9.g.h.101.1 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −79.3447 | + | 16.2916i | −0.979564 | + | 0.201131i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3405.57 | −1.41839 | −0.709197 | − | 0.705010i | \(-0.750943\pi\) | ||||
−0.709197 | + | 0.705010i | \(0.750943\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6030.17 | − | 2585.30i | 0.919093 | − | 0.394041i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24573.8i | 1.67842i | 0.543805 | + | 0.839212i | \(0.316983\pi\) | ||||
−0.543805 | + | 0.839212i | \(0.683017\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −25174.6 | −0.881431 | −0.440715 | − | 0.897647i | \(-0.645275\pi\) | ||||
−0.440715 | + | 0.897647i | \(0.645275\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 127299.i | 1.52416i | 0.647485 | + | 0.762078i | \(0.275821\pi\) | ||||
−0.647485 | + | 0.762078i | \(0.724179\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 110754. | 0.849857 | 0.424929 | − | 0.905227i | \(-0.360299\pi\) | ||||
0.424929 | + | 0.905227i | \(0.360299\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 270214. | − | 55482.1i | 1.38941 | − | 0.285283i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 200166.i | − | 0.715286i | −0.933858 | − | 0.357643i | \(-0.883580\pi\) | ||
0.933858 | − | 0.357643i | \(-0.116420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −436343. | + | 303371.i | −0.821057 | + | 0.570846i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 185716.i | 0.262577i | 0.991344 | + | 0.131288i | \(0.0419114\pi\) | ||||
−0.991344 | + | 0.131288i | \(0.958089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 800734. | 0.867045 | 0.433522 | − | 0.901143i | \(-0.357270\pi\) | ||||
0.433522 | + | 0.901143i | \(0.357270\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −400346. | − | 1.94980e6i | −0.337582 | − | 1.64412i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 859139. | 0.458413 | 0.229206 | − | 0.973378i | \(-0.426387\pi\) | ||||
0.229206 | + | 0.973378i | \(0.426387\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.99747e6 | − | 410133.i | 0.863418 | − | 0.177283i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.07451e6i | 1.79580i | 0.440196 | + | 0.897902i | \(0.354909\pi\) | ||||
−0.440196 | + | 0.897902i | \(0.645091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.48899e6 | 1.31303 | 0.656515 | − | 0.754313i | \(-0.272030\pi\) | ||||
0.656515 | + | 0.754313i | \(0.272030\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.94005e6i | 1.42223i | 0.703073 | + | 0.711117i | \(0.251811\pi\) | ||||
−0.703073 | + | 0.711117i | \(0.748189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.83308e6 | 1.01184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.07390e6 | − | 1.01005e7i | −0.306555 | − | 1.49301i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.64060e6i | − | 0.461392i | −0.973026 | − | 0.230696i | \(-0.925900\pi\) | ||
0.973026 | − | 0.230696i | \(-0.0741002\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.78777e6 | + | 1.80436e6i | −0.832490 | + | 0.170932i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.92951e6i | 0.571866i | 0.958250 | + | 0.285933i | \(0.0923035\pi\) | ||||
−0.958250 | + | 0.285933i | \(0.907696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.58815e6 | −0.186926 | −0.0934629 | − | 0.995623i | \(-0.529794\pi\) | ||||
−0.0934629 | + | 0.995623i | \(0.529794\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.05361e7 | + | 8.80442e6i | −1.30364 | + | 0.558906i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.22264e6 | 0.308799 | 0.154399 | − | 0.988009i | \(-0.450656\pi\) | ||||
0.154399 | + | 0.988009i | \(0.450656\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.26103e6 | + | 1.58822e7i | 0.143866 | + | 0.700669i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.07705e7i | 1.21088i | 0.795890 | + | 0.605441i | \(0.207003\pi\) | ||||
−0.795890 | + | 0.605441i | \(0.792997\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.15853e7 | 0.407959 | 0.203979 | − | 0.978975i | \(-0.434612\pi\) | ||||
0.203979 | + | 0.978975i | \(0.434612\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 8.36877e7i | − | 2.38067i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00742e7 | 1.54234 | 0.771170 | − | 0.636630i | \(-0.219672\pi\) | ||||
0.771170 | + | 0.636630i | \(0.219672\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.96791e7 | − | 3.11796e7i | 0.689463 | − | 0.724320i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00247e7i | 0.843365i | 0.906744 | + | 0.421682i | \(0.138560\pi\) | ||||
−0.906744 | + | 0.421682i | \(0.861440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.02560e6 | − | 1.47356e7i | −0.0528123 | − | 0.257211i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.48778e7i | − | 0.715272i | −0.933861 | − | 0.357636i | \(-0.883583\pi\) | ||
0.933861 | − | 0.357636i | \(-0.116417\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.57336e7 | 1.25022 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.35340e7 | + | 1.30452e7i | −0.849326 | + | 0.174389i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.54198e7 | −0.738962 | −0.369481 | − | 0.929238i | \(-0.620465\pi\) | ||||
−0.369481 | + | 0.929238i | \(0.620465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.35307e7 | + | 1.48184e8i | 0.661367 | + | 1.54263i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 303020.i | − | 0.00291197i | −0.999999 | − | 0.00145598i | \(-0.999537\pi\) | ||
0.999999 | − | 0.00145598i | \(-0.000463454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.21296e7 | 0.818559 | 0.409280 | − | 0.912409i | \(-0.365780\pi\) | ||||
0.409280 | + | 0.912409i | \(0.365780\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.98998e8i | 1.51815i | 0.651005 | + | 0.759074i | \(0.274348\pi\) | ||||
−0.651005 | + | 0.759074i | \(0.725652\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.30400e8 | −1.63222 | −0.816108 | − | 0.577900i | \(-0.803872\pi\) | ||||
−0.816108 | + | 0.577900i | \(0.803872\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.81681e7 | + | 1.39967e7i | −0.449045 | + | 0.0922008i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.90409e7i | 0.178113i | 0.996027 | + | 0.0890566i | \(0.0283852\pi\) | ||||
−0.996027 | + | 0.0890566i | \(0.971615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.51807e8 | + | 6.50838e7i | −0.810117 | + | 0.347320i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.33525e8i | − | 2.16186i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.89512e8 | −1.81710 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.26719e7 | − | 4.02636e8i | −0.361191 | − | 1.75911i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.54560e8 | −1.36293 | −0.681467 | − | 0.731849i | \(-0.738658\pi\) | ||||
−0.681467 | + | 0.731849i | \(0.738658\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.56177e8 | + | 7.31327e7i | −1.28620 | + | 0.264091i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.81000e8i | 0.614603i | 0.951612 | + | 0.307301i | \(0.0994260\pi\) | ||||
−0.951612 | + | 0.307301i | \(0.900574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.77181e8 | −1.20543 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 4.06421e8i | − | 1.15370i | −0.816849 | − | 0.576851i | \(-0.804281\pi\) | ||
0.816849 | − | 0.576851i | \(-0.195719\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.47570e7 | −0.0395312 | −0.0197656 | − | 0.999805i | \(-0.506292\pi\) | ||||
−0.0197656 | + | 0.999805i | \(0.506292\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.13064e8 | − | 5.50656e8i | −0.286055 | − | 1.39317i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.18634e8i | − | 1.47941i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.62824e8 | + | 9.50301e7i | −0.991167 | + | 0.203513i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 7.35283e7i | − | 0.149180i | −0.997214 | − | 0.0745898i | \(-0.976235\pi\) | ||
0.997214 | − | 0.0745898i | \(-0.0237647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.16954e8 | 0.609661 | 0.304830 | − | 0.952407i | \(-0.401400\pi\) | ||||
0.304830 | + | 0.952407i | \(0.401400\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.29107e8 | + | 7.67635e8i | 0.600580 | + | 1.40084i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.14521e8 | −1.17602 | −0.588012 | − | 0.808852i | \(-0.700089\pi\) | ||||
−0.588012 | + | 0.808852i | \(0.700089\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.93112e7 | + | 2.88862e8i | 0.0928000 | + | 0.451963i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.81680e8i | 1.01456i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.11302e8 | −1.00764 | −0.503818 | − | 0.863810i | \(-0.668072\pi\) | ||||
−0.503818 | + | 0.863810i | \(0.668072\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.16724e8i | − | 0.278638i | −0.990248 | − | 0.139319i | \(-0.955509\pi\) | ||
0.990248 | − | 0.139319i | \(-0.0444913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.81973e8 | −0.223079 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.67867e8 | − | 2.86333e8i | 0.781098 | − | 0.334879i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.48836e9i | 1.66159i | 0.556581 | + | 0.830793i | \(0.312113\pi\) | ||||
−0.556581 | + | 0.830793i | \(0.687887\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.12893e8 | − | 5.49820e8i | −0.115020 | − | 0.560180i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.05726e8i | 0.492610i | 0.969192 | + | 0.246305i | \(0.0792165\pi\) | ||||
−0.969192 | + | 0.246305i | \(0.920784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.18187e8 | 0.389634 | 0.194817 | − | 0.980840i | \(-0.437589\pi\) | ||||
0.194817 | + | 0.980840i | \(0.437589\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.05356e8 | − | 4.21650e7i | 0.183106 | − | 0.0375965i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.12822e9 | −2.55818 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.48600e9 | − | 1.03315e9i | 1.16458 | − | 0.809685i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.58890e7i | − | 0.0495085i | −0.999694 | − | 0.0247542i | \(-0.992120\pi\) | ||
0.999694 | − | 0.0247542i | \(-0.00788032\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.16804e9 | −1.56257 | −0.781283 | − | 0.624176i | \(-0.785435\pi\) | ||||
−0.781283 | + | 0.624176i | \(0.785435\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.87186e9i | − | 1.24282i | −0.783484 | − | 0.621412i | \(-0.786559\pi\) | ||
0.783484 | − | 0.621412i | \(-0.213441\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.42274e8 | 0.600848 | 0.300424 | − | 0.953806i | \(-0.402872\pi\) | ||||
0.300424 | + | 0.953806i | \(0.402872\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.93734e8 | + | 1.01377e8i | −0.302488 | + | 0.0621089i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 6.32467e8i | − | 0.372438i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.17491e8 | − | 1.20704e9i | −0.281852 | − | 0.657415i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.72165e9i | 1.42642i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.71708e8 | −0.490237 | −0.245118 | − | 0.969493i | \(-0.578827\pi\) | ||||
−0.245118 | + | 0.969493i | \(0.578827\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.01301e8 | − | 2.44148e9i | −0.243545 | − | 1.18614i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.72695e9 | −1.22981 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.19233e8 | + | 1.88743e8i | −0.399622 | + | 0.0820530i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.20470e9i | − | 1.34344i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.54076e8 | −0.304927 | −0.152463 | − | 0.988309i | \(-0.548721\pi\) | ||||
−0.152463 | + | 0.988309i | \(0.548721\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.53094e9i | 1.32980i | 0.746931 | + | 0.664902i | \(0.231527\pi\) | ||||
−0.746931 | + | 0.664902i | \(0.768473\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.50568e9 | 0.911136 | 0.455568 | − | 0.890201i | \(-0.349436\pi\) | ||||
0.455568 | + | 0.890201i | \(0.349436\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.36341e9 | + | 6.64018e9i | 0.478825 | + | 2.33202i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.87132e9i | − | 1.31351i | −0.754102 | − | 0.656757i | \(-0.771928\pi\) | ||
0.754102 | − | 0.656757i | \(-0.228072\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.76657e9 | + | 9.78705e8i | −1.51082 | + | 0.310212i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.52584e9i | − | 0.467645i | −0.972279 | − | 0.233823i | \(-0.924876\pi\) | ||
0.972279 | − | 0.233823i | \(-0.0751235\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.57111e9 | −0.762171 | −0.381086 | − | 0.924540i | \(-0.624450\pi\) | ||||
−0.381086 | + | 0.924540i | \(0.624450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.84692e9 | + | 2.95746e9i | −0.529691 | + | 0.848191i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.78819e9 | −0.749091 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.52065e8 | − | 3.17575e9i | −0.169627 | − | 0.826130i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.56222e9i | − | 1.14943i | −0.818355 | − | 0.574714i | \(-0.805113\pi\) | ||
0.818355 | − | 0.574714i | \(-0.194887\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.91885e9 | 1.20055 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.22319e9i | 0.738844i | 0.929262 | + | 0.369422i | \(0.120444\pi\) | ||||
−0.929262 | + | 0.369422i | \(0.879556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.92585e9 | −0.650210 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.80131e8 | + | 1.11990e9i | 0.103466 | + | 0.241333i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 3.25948e7i | − | 0.00681280i | −0.999994 | − | 0.00340640i | \(-0.998916\pi\) | ||
0.999994 | − | 0.00340640i | \(-0.00108429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.31130e8 | + | 3.56081e9i | 0.143863 | + | 0.700655i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.55752e9i | 0.488438i | 0.969720 | + | 0.244219i | \(0.0785316\pi\) | ||||
−0.969720 | + | 0.244219i | \(0.921468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.24486e9 | 1.34324 | 0.671618 | − | 0.740897i | \(-0.265599\pi\) | ||||
0.671618 | + | 0.740897i | \(0.265599\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.80251e9 | + | 1.39674e9i | −1.22467 | + | 0.251457i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.29340e9 | 0.729259 | 0.364630 | − | 0.931153i | \(-0.381196\pi\) | ||||
0.364630 | + | 0.931153i | \(0.381196\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.82856e9 | − | 2.07014e9i | 0.796895 | − | 0.341651i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.81158e9i | 0.290557i | 0.989391 | + | 0.145279i | \(0.0464079\pi\) | ||||
−0.989391 | + | 0.145279i | \(0.953592\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.90902e9 | 0.453524 | 0.226762 | − | 0.973950i | \(-0.427186\pi\) | ||||
0.226762 | + | 0.973950i | \(0.427186\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.72816e10i | − | 2.54716i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.22930e9 | −1.32305 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.19072e9 | − | 1.06579e9i | 0.723861 | − | 0.148628i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.24005e9i | 0.168255i | 0.996455 | + | 0.0841276i | \(0.0268103\pi\) | ||||
−0.996455 | + | 0.0841276i | \(0.973190\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.45498e9 | − | 1.07226e10i | −0.958122 | − | 1.37808i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.03910e9i | 0.630476i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.52875e10 | −1.86240 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.93668e6 | + | 2.40431e7i | 0.000585686 | + | 0.00285246i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.66791e9 | 0.412919 | 0.206460 | − | 0.978455i | \(-0.433806\pi\) | ||||
0.206460 | + | 0.978455i | \(0.433806\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.31000e9 | + | 1.50094e9i | −0.801832 | + | 0.164637i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.25169e8i | − | 0.0133800i | −0.999978 | − | 0.00668998i | \(-0.997870\pi\) | ||
0.999978 | − | 0.00668998i | \(-0.00212950\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.49432e9 | −0.572449 | −0.286224 | − | 0.958163i | \(-0.592400\pi\) | ||||
−0.286224 | + | 0.958163i | \(0.592400\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.19225e10i | 1.18068i | 0.807155 | + | 0.590340i | \(0.201006\pi\) | ||||
−0.807155 | + | 0.590340i | \(0.798994\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.56374e9 | −0.440715 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.24200e9 | − | 1.57894e10i | −0.305346 | − | 1.48712i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.40989e10i | 1.29532i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.82811e10 | − | 3.75359e9i | 1.59886 | − | 0.328289i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.36348e10i | − | 2.01729i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.33201e10 | −1.10967 | −0.554837 | − | 0.831959i | \(-0.687220\pi\) | ||||
−0.554837 | + | 0.831959i | \(0.687220\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.18075e9 | − | 2.22113e9i | 0.421324 | − | 0.180633i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.00994e9 | 0.698558 | 0.349279 | − | 0.937019i | \(-0.386427\pi\) | ||||
0.349279 | + | 0.937019i | \(0.386427\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.73122e8 | − | 2.30424e9i | −0.0358240 | − | 0.174473i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.96771e10i | 1.45527i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.32530e8 | −0.0167998 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.53927e9i | 0.657956i | 0.944338 | + | 0.328978i | \(0.106704\pi\) | ||||
−0.944338 | + | 0.328978i | \(0.893296\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.23914e9 | −0.150931 | −0.0754657 | − | 0.997148i | \(-0.524044\pi\) | ||||
−0.0754657 | + | 0.997148i | \(0.524044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.09847e10 | − | 7.63723e9i | 0.723705 | − | 0.503162i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.38508e9i | − | 0.0892021i | −0.999005 | − | 0.0446011i | \(-0.985798\pi\) | ||
0.999005 | − | 0.0446011i | \(-0.0142017\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.06282e9 | + | 3.43980e10i | 0.434816 | + | 2.11768i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.18160e10i | 1.31340i | 0.754150 | + | 0.656702i | \(0.228049\pi\) | ||||
−0.754150 | + | 0.656702i | \(0.771951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.71705e9 | −0.277742 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.09058e10 | − | 6.34578e9i | 1.77997 | − | 0.365475i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.43071e8 | 0.0354482 | 0.0177241 | − | 0.999843i | \(-0.494358\pi\) | ||||
0.0177241 | + | 0.999843i | \(0.494358\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.31192e10 | + | 3.06002e10i | 0.707620 | + | 1.65051i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.23983e10i | 0.654435i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.52291e10 | 0.786752 | 0.393376 | − | 0.919378i | \(-0.371307\pi\) | ||||
0.393376 | + | 0.919378i | \(0.371307\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.67531e9i | − | 0.231443i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.15729e10 | 1.53023 | 0.765116 | − | 0.643892i | \(-0.222682\pi\) | ||||
0.765116 | + | 0.643892i | \(0.222682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.81325e10 | − | 5.77634e9i | 1.33508 | − | 0.274128i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.83628e10i | − | 0.853384i | −0.904397 | − | 0.426692i | \(-0.859679\pi\) | ||
0.904397 | − | 0.426692i | \(-0.140321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.70694e10 | − | 1.16054e10i | 1.20680 | − | 0.517388i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.15515e10i | − | 1.37791i | −0.724802 | − | 0.688957i | \(-0.758069\pi\) | ||
0.724802 | − | 0.688957i | \(-0.241931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.54810e10 | 1.09021 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.94878e9 | − | 1.43614e10i | −0.123615 | − | 0.602043i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.82543e10 | 1.94256 | 0.971280 | − | 0.237941i | \(-0.0764724\pi\) | ||||
0.971280 | + | 0.237941i | \(0.0764724\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.99273e10 | − | 6.14488e9i | 1.18080 | − | 0.242450i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.44335e9i | − | 0.171843i | −0.996302 | − | 0.0859217i | \(-0.972617\pi\) | ||
0.996302 | − | 0.0859217i | \(-0.0273835\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.01581e10 | −0.764240 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.11123e10i | 0.769410i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.06587e9 | −0.323979 | −0.161989 | − | 0.986793i | \(-0.551791\pi\) | ||||
−0.161989 | + | 0.986793i | \(0.551791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.62124e9 | + | 3.22474e10i | 0.232045 | + | 1.13013i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.35989e10i | − | 0.811132i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.17089e9 | − | 2.40416e8i | 0.0387234 | − | 0.00795094i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.48532e10i | − | 0.481906i | −0.970537 | − | 0.240953i | \(-0.922540\pi\) | ||
0.970537 | − | 0.240953i | \(-0.0774600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.82155e10 | −0.579846 | −0.289923 | − | 0.957050i | \(-0.593630\pi\) | ||||
−0.289923 | + | 0.957050i | \(0.593630\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.79421e10 | + | 4.18497e10i | 0.560419 | + | 1.30717i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.81410e9 | 0.265135 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00785e10 | + | 4.90854e10i | 0.297556 | + | 1.44918i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.12650e10i | − | 0.616249i | −0.951346 | − | 0.308125i | \(-0.900299\pi\) | ||
0.951346 | − | 0.308125i | \(-0.0997014\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.54370e9 | 0.129258 | 0.0646291 | − | 0.997909i | \(-0.479414\pi\) | ||||
0.0646291 | + | 0.997909i | \(0.479414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.21693e10i | − | 0.607892i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.38568e10 | −0.642324 | −0.321162 | − | 0.947024i | \(-0.604073\pi\) | ||||
−0.321162 | + | 0.947024i | \(0.604073\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.51745e10 | − | 1.50803e10i | 0.929979 | − | 0.398708i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.94183e10i | 1.02349i | 0.859138 | + | 0.511744i | \(0.171000\pi\) | ||||
−0.859138 | + | 0.511744i | \(0.829000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.19789e9 | + | 5.83408e9i | 0.0300046 | + | 0.146131i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.16040e10i | 0.531555i | 0.964034 | + | 0.265778i | \(0.0856287\pi\) | ||||
−0.964034 | + | 0.265778i | \(0.914371\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.24700e11 | −3.01412 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.51486e10 | + | 5.16368e9i | −0.597202 | + | 0.122622i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.37441e10 | 1.23216 | 0.616078 | − | 0.787685i | \(-0.288721\pi\) | ||||
0.616078 | + | 0.787685i | \(0.288721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.86189e10 | − | 5.55461e10i | −0.870059 | − | 1.25142i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.60037e10i | 0.354337i | 0.984181 | + | 0.177168i | \(0.0566937\pi\) | ||||
−0.984181 | + | 0.177168i | \(0.943306\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.87672e10 | 1.49643 | 0.748217 | − | 0.663454i | \(-0.230910\pi\) | ||||
0.748217 | + | 0.663454i | \(0.230910\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.62821e10i | 0.552577i | 0.961075 | + | 0.276289i | \(0.0891046\pi\) | ||||
−0.961075 | + | 0.276289i | \(0.910895\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.11916e10 | −0.437999 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.66935e10 | − | 1.16407e10i | 1.15199 | − | 0.236535i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.10311e11i | 2.20382i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.41206e9 | − | 2.19534e10i | −0.181807 | − | 0.424062i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.74718e10i | 1.09172i | 0.837875 | + | 0.545862i | \(0.183798\pi\) | ||||
−0.837875 | + | 0.545862i | \(0.816202\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.16284e10 | −0.404059 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.11057e10 | − | 5.40877e10i | −0.204059 | − | 0.993826i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.95448e10 | 1.41415 | 0.707076 | − | 0.707138i | \(-0.250014\pi\) | ||||
0.707076 | + | 0.707138i | \(0.250014\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.64381e10 | − | 1.15882e10i | 0.987044 | − | 0.202666i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.80767e10i | − | 1.51543i | −0.652587 | − | 0.757714i | \(-0.726316\pi\) | ||
0.652587 | − | 0.757714i | \(-0.273684\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.36414e10 | −0.400208 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.04791e11i | − | 1.71751i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.06941e11 | −1.72481 | −0.862404 | − | 0.506221i | \(-0.831042\pi\) | ||||
−0.862404 | + | 0.506221i | \(0.831042\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.53077e9 | + | 1.71959e10i | 0.0560427 | + | 0.272944i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 6.57043e10i | − | 1.02641i | −0.858265 | − | 0.513206i | \(-0.828458\pi\) | ||
0.858265 | − | 0.513206i | \(-0.171542\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.44386e10 | − | 2.96462e9i | 0.218521 | − | 0.0448681i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 8.25888e10i | − | 1.23041i | −0.788367 | − | 0.615205i | \(-0.789073\pi\) | ||
0.788367 | − | 0.615205i | \(-0.210927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.94545e10 | −0.578646 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.83269e10 | + | 3.35996e10i | −0.697781 | + | 0.485138i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.70543e11 | −2.38711 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.42477e10 | − | 1.18093e11i | −0.334196 | − | 1.62763i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.47463e10i | 1.15019i | 0.818086 | + | 0.575095i | \(0.195035\pi\) | ||||
−0.818086 | + | 0.575095i | \(0.804965\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.24977e11 | 1.67041 | 0.835207 | − | 0.549935i | \(-0.185348\pi\) | ||||
0.835207 | + | 0.549935i | \(0.185348\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.01933e11i | 1.32151i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.82444e10 | 0.488365 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.79149e10 | + | 4.17861e10i | 0.225339 | + | 0.525598i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.27749e11i | − | 1.58288i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.23908e9 | − | 4.01267e10i | −0.0990790 | − | 0.482543i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.43341e11i | 1.69830i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.07875e10 | 0.359406 | 0.179703 | − | 0.983721i | \(-0.442486\pi\) | ||||
0.179703 | + | 0.983721i | \(0.442486\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.31810e10 | + | 6.81294e9i | −0.381671 | + | 0.0783673i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.05128e10 | −0.452526 | −0.226263 | − | 0.974066i | \(-0.572651\pi\) | ||||
−0.226263 | + | 0.974066i | \(0.572651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.56070e10 | + | 6.69114e9i | −0.171802 | + | 0.0736564i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.05688e10i | 0.223153i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.04587e11 | −2.18765 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.74913e11i | 1.81719i | 0.417679 | + | 0.908595i | \(0.362844\pi\) | ||||
−0.417679 | + | 0.908595i | \(0.637156\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.13008e11 | −1.15735 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.48208e11 | − | 5.09637e10i | 2.50590 | − | 0.514528i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.26724e11i | − | 1.26132i | −0.776060 | − | 0.630659i | \(-0.782785\pi\) | ||
0.776060 | − | 0.630659i | \(-0.217215\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.01074e11 | + | 1.06184e11i | −0.977932 | + | 1.02737i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.40561e10i | 0.420298i | 0.977669 | + | 0.210149i | \(0.0673949\pi\) | ||||
−0.977669 | + | 0.210149i | \(0.932605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.97761e11 | −1.86036 | −0.930180 | − | 0.367105i | \(-0.880349\pi\) | ||||
−0.930180 | + | 0.367105i | \(0.880349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.07344e9 | + | 5.22794e9i | 0.00995767 | + | 0.0484967i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.70837e10 | −0.785658 | −0.392829 | − | 0.919612i | \(-0.628504\pi\) | ||||
−0.392829 | + | 0.919612i | \(0.628504\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.72023e11 | − | 3.53209e10i | 1.53063 | − | 0.314280i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.36307e11i | − | 1.19622i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.94634e10 | 0.774410 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.21607e11i | − | 1.02425i | −0.858910 | − | 0.512126i | \(-0.828858\pi\) | ||
0.858910 | − | 0.512126i | \(-0.171142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.86847e10 | 0.736865 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.04956e10 | + | 1.48523e11i | 0.249970 | + | 1.21743i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.34327e11i | 1.08629i | 0.839640 | + | 0.543144i | \(0.182766\pi\) | ||||
−0.839640 | + | 0.543144i | \(0.817234\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.47644e10 | + | 1.53511e10i | −0.588569 | + | 0.120849i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.21066e11i | − | 0.940406i | −0.882558 | − | 0.470203i | \(-0.844181\pi\) | ||
0.882558 | − | 0.470203i | \(-0.155819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.45545e11 | −1.11558 | −0.557789 | − | 0.829983i | \(-0.688350\pi\) | ||||
−0.557789 | + | 0.829983i | \(0.688350\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.75236e10 | − | 1.60874e10i | 0.283815 | − | 0.121679i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.20190e11 | −0.885346 | −0.442673 | − | 0.896683i | \(-0.645970\pi\) | ||||
−0.442673 | + | 0.896683i | \(0.645970\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.03039e10 | + | 5.01829e10i | 0.0749086 | + | 0.364827i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.74713e11i | − | 1.25360i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.50533e11 | −1.06608 | −0.533041 | − | 0.846089i | \(-0.678951\pi\) | ||||
−0.533041 | + | 0.846089i | \(0.678951\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.44657e11i | − | 1.68817i | −0.536206 | − | 0.844087i | \(-0.680143\pi\) | ||
0.536206 | − | 0.844087i | \(-0.319857\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.61556e10 | 0.314385 | 0.157192 | − | 0.987568i | \(-0.449756\pi\) | ||||
0.157192 | + | 0.987568i | \(0.449756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.07247e10 | + | 8.73413e10i | 0.408319 | + | 0.587291i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.52834e11i | 1.01454i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.43400e10 | − | 2.15949e11i | −0.286897 | − | 1.39727i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.09368e11i | 0.698692i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.75958e11 | −1.10992 | −0.554960 | − | 0.831877i | \(-0.687267\pi\) | ||||
−0.554960 | + | 0.831877i | \(0.687267\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.70999e10 | − | 1.58307e10i | 0.480218 | − | 0.0986016i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.46845e11 | −0.891871 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.95511e10 | + | 1.85551e11i | 0.477137 | + | 1.11291i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.37563e11i | 1.40717i | 0.710612 | + | 0.703584i | \(0.248418\pi\) | ||||
−0.710612 | + | 0.703584i | \(0.751582\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.28962e11 | −0.754427 | −0.377214 | − | 0.926126i | \(-0.623118\pi\) | ||||
−0.377214 | + | 0.926126i | \(0.623118\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.61483e11i | − | 0.921529i | −0.887523 | − | 0.460764i | \(-0.847575\pi\) | ||
0.887523 | − | 0.460764i | \(-0.152425\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.70284e11 | −0.959834 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.16369e11 | − | 4.44264e10i | 1.20468 | − | 0.247353i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.46894e11i | − | 0.807887i | −0.914784 | − | 0.403943i | \(-0.867639\pi\) | ||
0.914784 | − | 0.403943i | \(-0.132361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.98613e10 | − | 2.99515e10i | 0.374952 | − | 0.160752i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.59905e11i | − | 0.847855i | −0.905696 | − | 0.423927i | \(-0.860651\pi\) | ||
0.905696 | − | 0.423927i | \(-0.139349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.69483e10 | −0.141165 | −0.0705824 | − | 0.997506i | \(-0.522486\pi\) | ||||
−0.0705824 | + | 0.997506i | \(0.522486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.22096e10 | + | 2.54276e11i | 0.270207 | + | 1.31598i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.71740e10 | 0.187818 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.98320e10 | − | 1.22851e10i | 0.298696 | − | 0.0613302i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.36005e10i | − | 0.313741i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.57651e11 | −1.25595 | −0.627974 | − | 0.778234i | \(-0.716116\pi\) | ||||
−0.627974 | + | 0.778234i | \(0.716116\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.99005e11i | 0.947346i | 0.880701 | + | 0.473673i | \(0.157072\pi\) | ||||
−0.880701 | + | 0.473673i | \(0.842928\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.22792e11 | 1.04814 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.75247e10 | − | 2.80162e11i | −0.267464 | − | 1.30263i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.67991e11i | 1.69104i | 0.533943 | + | 0.845521i | \(0.320710\pi\) | ||||
−0.533943 | + | 0.845521i | \(0.679290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.98812e11 | + | 4.08215e10i | −0.892517 | + | 0.183257i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.16505e10i | 0.406685i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.29138e11 | 1.44366 | 0.721831 | − | 0.692069i | \(-0.243301\pi\) | ||||
0.721831 | + | 0.692069i | \(0.243301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.16358e11 | − | 5.04651e11i | −0.938080 | − | 2.18805i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.45981e11 | −2.73709 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.30699e10 | + | 3.07168e11i | 0.264188 | + | 1.28667i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.29137e11i | 0.534782i | 0.963588 | + | 0.267391i | \(0.0861616\pi\) | ||||
−0.963588 | + | 0.267391i | \(0.913838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.51533e10 | 0.389585 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.03196e9i | 0.00413032i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.17473e11 | −0.860639 | −0.430320 | − | 0.902677i | \(-0.641599\pi\) | ||||
−0.430320 | + | 0.902677i | \(0.641599\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.62258e11 | − | 1.55310e11i | 1.41755 | − | 0.607745i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.60280e11i | − | 0.620186i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.48583e10 | + | 1.21067e11i | 0.0940578 | + | 0.458089i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.91891e11i | − | 0.718022i | −0.933333 | − | 0.359011i | \(-0.883114\pi\) | ||
0.933333 | − | 0.359011i | \(-0.116886\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.13753e11 | −1.16104 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.04004e11 | − | 4.18875e10i | 0.746596 | − | 0.153296i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.64178e11 | 1.30370 | 0.651848 | − | 0.758349i | \(-0.273994\pi\) | ||||
0.651848 | + | 0.758349i | \(0.273994\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.83615e10 | − | 2.64748e11i | 0.348269 | − | 0.937395i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.71444e11i | 2.00126i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.73816e11 | −0.948511 | −0.474256 | − | 0.880387i | \(-0.657283\pi\) | ||||
−0.474256 | + | 0.880387i | \(0.657283\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.52914e11i | 0.518295i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.00973e10 | 0.302088 | 0.151044 | − | 0.988527i | \(-0.451736\pi\) | ||||
0.151044 | + | 0.988527i | \(0.451736\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.21228e11 | − | 4.54240e10i | 0.733783 | − | 0.150665i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.11015e11i | − | 0.692400i | −0.938161 | − | 0.346200i | \(-0.887472\pi\) | ||
0.938161 | − | 0.346200i | \(-0.112528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.03476e11 | + | 2.41356e11i | 0.332320 | + | 0.775131i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.77701e11i | − | 2.15333i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.45794e11 | −1.71581 | −0.857904 | − | 0.513809i | \(-0.828234\pi\) | ||||
−0.857904 | + | 0.513809i | \(0.828234\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.43258e10 | + | 3.61988e11i | 0.231185 | + | 1.12594i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.61963e11 | 0.493211 | 0.246605 | − | 0.969116i | \(-0.420685\pi\) | ||||
0.246605 | + | 0.969116i | \(0.420685\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.90285e11 | + | 8.01359e10i | −1.17602 | + | 0.241468i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.37983e10i | 0.190226i | 0.995466 | + | 0.0951131i | \(0.0303213\pi\) | ||||
−0.995466 | + | 0.0951131i | \(0.969679\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.84644e11 | 2.31513 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.74447e11i | − | 0.504061i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.24097e11 | −1.49867 | −0.749336 | − | 0.662190i | \(-0.769627\pi\) | ||||
−0.749336 | + | 0.662190i | \(0.769627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.25108e10 | − | 2.55743e11i | −0.148604 | − | 0.723746i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 6.47397e11i | − | 1.81323i | −0.421960 | − | 0.906614i | \(-0.638658\pi\) | ||
0.421960 | − | 0.906614i | \(-0.361342\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.32151e11 | − | 4.76668e10i | 0.636923 | − | 0.130777i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.62024e11i | 1.52618i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.56149e11 | −2.03237 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.63408e10 | − | 8.10358e10i | −0.149891 | − | 0.215591i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.64667e10 | −0.0950600 | −0.0475300 | − | 0.998870i | \(-0.515135\pi\) | ||||
−0.0475300 | + | 0.998870i | \(0.515135\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.31022e8 | + | 2.58623e9i | 0.00137026 | + | 0.00667358i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 9.89007e10i | − | 0.252635i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.51554e10 | 0.164762 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.73965e11i | 0.431150i | 0.976487 | + | 0.215575i | \(0.0691626\pi\) | ||||
−0.976487 | + | 0.215575i | \(0.930837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.83462e11 | −2.16771 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.16023e11 | − | 2.70621e11i | −0.281846 | − | 0.657401i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.84695e11i | 0.684727i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.16660e10 | − | 2.02926e11i | −0.0982400 | − | 0.478457i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.21348e11i | 0.516751i | 0.966045 | + | 0.258376i | \(0.0831872\pi\) | ||||
−0.966045 | + | 0.258376i | \(0.916813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.02335e11 | 1.16121 | 0.580604 | − | 0.814186i | \(-0.302817\pi\) | ||||
0.580604 | + | 0.814186i | \(0.302817\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.74841e11 | + | 1.18030e11i | −1.31579 | + | 0.270166i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.97175e11 | 1.11589 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.16988e11 | − | 2.21647e11i | 1.14907 | − | 0.492637i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 3.69491e11i | − | 0.813264i | −0.913592 | − | 0.406632i | \(-0.866703\pi\) | ||
0.913592 | − | 0.406632i | \(-0.133297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.33488e11 | 0.726910 | 0.363455 | − | 0.931612i | \(-0.381597\pi\) | ||||
0.363455 | + | 0.931612i | \(0.381597\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.18933e11i | 0.681832i | 0.940094 | + | 0.340916i | \(0.110737\pi\) | ||||
−0.940094 | + | 0.340916i | \(0.889263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.18645e11 | 1.09813 | 0.549063 | − | 0.835781i | \(-0.314985\pi\) | ||||
0.549063 | + | 0.835781i | \(0.314985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.40658e11 | + | 6.99462e10i | −0.714356 | + | 0.146676i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.42546e11i | 1.54221i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.49395e11 | + | 2.42920e11i | −0.711893 | + | 0.494949i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 9.44187e11i | − | 1.90551i | −0.303747 | − | 0.952753i | \(-0.598238\pi\) | ||
0.303747 | − | 0.952753i | \(-0.401762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.65756e11 | 0.931053 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.95135e10 | − | 1.43739e11i | −0.0584400 | − | 0.284620i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.32651e12 | 2.57737 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.30815e11 | + | 4.73925e10i | −0.444256 | + | 0.0912177i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.71971e11i | − | 0.327896i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.68425e11 | 0.318134 | 0.159067 | − | 0.987268i | \(-0.449151\pi\) | ||||
0.159067 | + | 0.987268i | \(0.449151\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 6.34379e11i | − | 1.17605i | −0.808843 | − | 0.588025i | \(-0.799906\pi\) | ||
0.808843 | − | 0.588025i | \(-0.200094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.11818e11 | 0.940033 | 0.470016 | − | 0.882658i | \(-0.344248\pi\) | ||||
0.470016 | + | 0.882658i | \(0.344248\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.81544e11 | + | 1.37120e12i | 0.512312 | + | 2.49511i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.33148e11i | 0.420329i | 0.977666 | + | 0.210164i | \(0.0673999\pi\) | ||||
−0.977666 | + | 0.210164i | \(0.932600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.32296e11 | − | 1.50360e11i | 1.29602 | − | 0.266107i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.47625e12i | 2.58870i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.56652e11 | −0.272185 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.94492e11 | + | 1.69130e11i | −0.679175 | + | 0.291181i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.06198e11 | −0.179522 | −0.0897611 | − | 0.995963i | \(-0.528610\pi\) | ||||
−0.0897611 | + | 0.995963i | \(0.528610\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.02024e10 | − | 9.83913e10i | −0.0338413 | − | 0.164817i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.10796e12i | − | 1.83916i | −0.392902 | − | 0.919580i | \(-0.628529\pi\) | ||
0.392902 | − | 0.919580i | \(-0.371471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.28093e11 | 0.704198 | 0.352099 | − | 0.935963i | \(-0.385468\pi\) | ||||
0.352099 | + | 0.935963i | \(0.385468\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.09034e11i | 0.660793i | 0.943842 | + | 0.330396i | \(0.107182\pi\) | ||||
−0.943842 | + | 0.330396i | \(0.892818\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.20748e12 | 1.93318 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.66202e11 | + | 7.29329e11i | 1.21572 | + | 1.15721i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.68640e11i | 1.20870i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.20949e10 | − | 3.99826e11i | −0.126808 | − | 0.617591i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.48709e11i | 0.227666i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.63445e11 | 0.703233 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.21299e12 | − | 2.49058e11i | 1.82434 | − | 0.374585i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.86396e11 | 1.01425 | 0.507126 | − | 0.861872i | \(-0.330708\pi\) | ||||
0.507126 | + | 0.861872i | \(0.330708\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.83399e8 | − | 1.82726e9i | −0.00114743 | − | 0.00267637i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.11887e11i | 0.888378i | 0.895933 | + | 0.444189i | \(0.146508\pi\) | ||||
−0.895933 | + | 0.444189i | \(0.853492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.83558e11 | −1.41552 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 6.16409e11i | − | 0.871749i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.23039e11 | −0.593087 | −0.296544 | − | 0.955019i | \(-0.595834\pi\) | ||||
−0.296544 | + | 0.955019i | \(0.595834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.91029e11 | + | 5.97561e10i | −0.404481 | + | 0.0830507i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 7.74634e11i | − | 1.06731i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.55557e11 | − | 2.38183e11i | 0.752332 | − | 0.322546i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.56450e11i | − | 0.210045i | −0.994470 | − | 0.105022i | \(-0.966509\pi\) | ||
0.994470 | − | 0.105022i | \(-0.0334914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.46039e11 | 0.859923 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.03920e9 | + | 9.93149e9i | 0.00269112 | + | 0.0131065i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.01239e12 | 1.31338 | 0.656691 | − | 0.754160i | \(-0.271956\pi\) | ||||
0.656691 | + | 0.754160i | \(0.271956\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.35945e11 | − | 8.95112e10i | 0.560751 | − | 0.115137i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.25449e12i | − | 1.59996i | −0.600026 | − | 0.799980i | \(-0.704843\pi\) | ||
0.600026 | − | 0.799980i | \(-0.295157\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.01575e12 | 1.28451 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.29119e12i | 1.60543i | 0.596365 | + | 0.802713i | \(0.296611\pi\) | ||||
−0.596365 | + | 0.802713i | \(0.703389\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.91655e11 | −0.359587 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.94237e11 | − | 9.45991e11i | −0.237471 | − | 1.15655i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.35954e12i | − | 1.64824i | −0.566418 | − | 0.824118i | \(-0.691671\pi\) | ||
0.566418 | − | 0.824118i | \(-0.308329\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.62108e11 | − | 7.43505e10i | 0.431709 | − | 0.0886413i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.38409e12i | 1.63641i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.11716e11 | −0.248233 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.14470e11 | + | 1.19999e12i | 0.598212 | + | 1.39532i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.18542e12 | −1.35571 | −0.677855 | − | 0.735195i | \(-0.737090\pi\) | ||||
−0.677855 | + | 0.735195i | \(0.737090\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.29694e11 | − | 1.11867e12i | −0.260528 | − | 1.26885i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.30844e11i | 0.259682i | 0.991535 | + | 0.129841i | \(0.0414467\pi\) | ||||
−0.991535 | + | 0.129841i | \(0.958553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.02561e10 | 0.0560709 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.05133e12i | 1.15388i | 0.816785 | + | 0.576942i | \(0.195754\pi\) | ||||
−0.816785 | + | 0.576942i | \(0.804246\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.10282e12 | 1.20053 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.38935e12 | + | 5.95655e11i | −1.50016 | + | 0.643160i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.65893e11i | − | 0.177669i | −0.996046 | − | 0.0888347i | \(-0.971686\pi\) | ||
0.996046 | − | 0.0888347i | \(-0.0283143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.85048e11 | + | 1.87530e12i | 0.405739 | + | 1.97607i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 8.98545e11i | − | 0.939193i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.77605e11 | −0.495192 | −0.247596 | − | 0.968863i | \(-0.579641\pi\) | ||||
−0.247596 | + | 0.968863i | \(0.579641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.05688e12 | − | 2.17006e11i | 1.08700 | − | 0.223190i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.99520e11 | 0.404350 | 0.202175 | − | 0.979349i | \(-0.435199\pi\) | ||||
0.202175 | + | 0.979349i | \(0.435199\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.74880e11 | + | 2.60638e11i | −0.376383 | + | 0.261683i |
(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 | 300.9.g.h.101.2 | 16 | ||
3.2 | odd | 2 | inner | 300.9.g.h.101.1 | 16 | ||
5.2 | odd | 4 | 60.9.b.a.29.10 | yes | 16 | ||
5.3 | odd | 4 | 60.9.b.a.29.7 | ✓ | 16 | ||
5.4 | even | 2 | inner | 300.9.g.h.101.15 | 16 | ||
15.2 | even | 4 | 60.9.b.a.29.8 | yes | 16 | ||
15.8 | even | 4 | 60.9.b.a.29.9 | yes | 16 | ||
15.14 | odd | 2 | inner | 300.9.g.h.101.16 | 16 | ||
20.3 | even | 4 | 240.9.c.d.209.10 | 16 | |||
20.7 | even | 4 | 240.9.c.d.209.7 | 16 | |||
60.23 | odd | 4 | 240.9.c.d.209.8 | 16 | |||
60.47 | odd | 4 | 240.9.c.d.209.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.9.b.a.29.7 | ✓ | 16 | 5.3 | odd | 4 | ||
60.9.b.a.29.8 | yes | 16 | 15.2 | even | 4 | ||
60.9.b.a.29.9 | yes | 16 | 15.8 | even | 4 | ||
60.9.b.a.29.10 | yes | 16 | 5.2 | odd | 4 | ||
240.9.c.d.209.7 | 16 | 20.7 | even | 4 | |||
240.9.c.d.209.8 | 16 | 60.23 | odd | 4 | |||
240.9.c.d.209.9 | 16 | 60.47 | odd | 4 | |||
240.9.c.d.209.10 | 16 | 20.3 | even | 4 | |||
300.9.g.h.101.1 | 16 | 3.2 | odd | 2 | inner | ||
300.9.g.h.101.2 | 16 | 1.1 | even | 1 | trivial | ||
300.9.g.h.101.15 | 16 | 5.4 | even | 2 | inner | ||
300.9.g.h.101.16 | 16 | 15.14 | odd | 2 | inner |