Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(47,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.47");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.n (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: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + \cdots + 57\!\cdots\!24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{65}\cdot 3^{4}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 63.2 | ||
Root | \(3.75557 - 3.81117i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.63 |
Dual form | 80.6.n.d.47.2 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −17.2921 | + | 17.2921i | −1.10929 | + | 1.10929i | −0.116048 | + | 0.993244i | \(0.537023\pi\) |
−0.993244 | + | 0.116048i | \(0.962977\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 46.1930 | − | 31.4834i | 0.826326 | − | 0.563192i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 154.079 | + | 154.079i | 1.18849 | + | 1.18849i | 0.977484 | + | 0.211011i | \(0.0676755\pi\) |
0.211011 | + | 0.977484i | \(0.432324\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 355.037i | − | 1.46106i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 127.489i | − | 0.317682i | −0.987304 | − | 0.158841i | \(-0.949224\pi\) | ||
0.987304 | − | 0.158841i | \(-0.0507757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 335.067 | + | 335.067i | 0.549887 | + | 0.549887i | 0.926408 | − | 0.376521i | \(-0.122880\pi\) |
−0.376521 | + | 0.926408i | \(0.622880\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −254.362 | + | 1343.19i | −0.291893 | + | 1.54138i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1155.01 | + | 1155.01i | −0.969310 | + | 0.969310i | −0.999543 | − | 0.0302331i | \(-0.990375\pi\) |
0.0302331 | + | 0.999543i | \(0.490375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.2166 | 0.0179317 | 0.00896584 | − | 0.999960i | \(-0.497146\pi\) | ||||
0.00896584 | + | 0.999960i | \(0.497146\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5328.70 | −2.63677 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2783.04 | + | 2783.04i | −1.09698 | + | 1.09698i | −0.102219 | + | 0.994762i | \(0.532594\pi\) |
−0.994762 | + | 0.102219i | \(0.967406\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1142.60 | − | 2908.63i | 0.365631 | − | 0.930760i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1937.35 | + | 1937.35i | 0.511446 | + | 0.511446i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3388.31i | 0.748149i | 0.927399 | + | 0.374074i | \(0.122040\pi\) | ||||
−0.927399 | + | 0.374074i | \(0.877960\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5384.41i | 1.00631i | 0.864195 | + | 0.503157i | \(0.167828\pi\) | ||||
−0.864195 | + | 0.503157i | \(0.832172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2204.56 | + | 2204.56i | 0.352402 | + | 0.352402i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11968.3 | + | 2266.45i | 1.65143 | + | 0.312734i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11534.0 | − | 11534.0i | 1.38508 | − | 1.38508i | 0.549757 | − | 0.835324i | \(-0.314720\pi\) |
0.835324 | − | 0.549757i | \(-0.185280\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11588.1 | −1.21997 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11147.8 | −1.03569 | −0.517844 | − | 0.855475i | \(-0.673265\pi\) | ||||
−0.517844 | + | 0.855475i | \(0.673265\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1437.07 | + | 1437.07i | −0.118524 | + | 0.118524i | −0.763881 | − | 0.645357i | \(-0.776709\pi\) |
0.645357 | + | 0.763881i | \(0.276709\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11177.7 | − | 16400.2i | −0.822855 | − | 1.20731i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −219.040 | − | 219.040i | −0.0144637 | − | 0.0144637i | 0.699838 | − | 0.714302i | \(-0.253256\pi\) |
−0.714302 | + | 0.699838i | \(0.753256\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 30673.4i | 1.82504i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 39945.1i | − | 2.15049i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 22745.6 | + | 22745.6i | 1.11226 | + | 1.11226i | 0.992844 | + | 0.119421i | \(0.0381037\pi\) |
0.119421 | + | 0.992844i | \(0.461896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4013.79 | − | 5889.12i | −0.178916 | − | 0.262509i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −487.926 | + | 487.926i | −0.0198915 | + | 0.0198915i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −22196.6 | −0.830149 | −0.415074 | − | 0.909787i | \(-0.636244\pi\) | ||||
−0.415074 | + | 0.909787i | \(0.636244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1431.25 | −0.0492484 | −0.0246242 | − | 0.999697i | \(-0.507839\pi\) | ||||
−0.0246242 | + | 0.999697i | \(0.507839\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 54703.5 | − | 54703.5i | 1.73646 | − | 1.73646i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 26026.8 | + | 4928.73i | 0.764078 | + | 0.144694i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −28948.2 | − | 28948.2i | −0.787835 | − | 0.787835i | 0.193304 | − | 0.981139i | \(-0.438080\pi\) |
−0.981139 | + | 0.193304i | \(0.938080\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 96249.3i | − | 2.43374i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 24188.3i | 0.569456i | 0.958608 | + | 0.284728i | \(0.0919032\pi\) | ||||
−0.958608 | + | 0.284728i | \(0.908097\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28574.8 | + | 28574.8i | 0.627591 | + | 0.627591i | 0.947461 | − | 0.319871i | \(-0.103639\pi\) |
−0.319871 | + | 0.947461i | \(0.603639\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 30538.4 | + | 70054.3i | 0.626894 | + | 1.43808i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19643.4 | − | 19643.4i | 0.377563 | − | 0.377563i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23417.0 | 0.422147 | 0.211073 | − | 0.977470i | \(-0.432304\pi\) | ||||
0.211073 | + | 0.977470i | \(0.432304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 19271.9 | 0.326371 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −18919.5 | + | 18919.5i | −0.301450 | + | 0.301450i | −0.841581 | − | 0.540131i | \(-0.818375\pi\) |
0.540131 | + | 0.841581i | \(0.318375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16989.8 | + | 89716.9i | −0.255059 | + | 1.34687i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −58591.1 | − | 58591.1i | −0.829915 | − | 0.829915i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8179.53i | − | 0.109459i | −0.998501 | − | 0.0547297i | \(-0.982570\pi\) | ||
0.998501 | − | 0.0547297i | \(-0.0174297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 103253.i | 1.30708i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −93107.9 | − | 93107.9i | −1.11630 | − | 1.11630i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1303.41 | − | 888.354i | 0.0148174 | − | 0.0100990i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −76747.2 | + | 76747.2i | −0.828196 | + | 0.828196i | −0.987267 | − | 0.159071i | \(-0.949150\pi\) |
0.159071 | + | 0.987267i | \(0.449150\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −45263.4 | −0.464151 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1379.60 | −0.0134570 | −0.00672851 | − | 0.999977i | \(-0.502142\pi\) | ||||
−0.00672851 | + | 0.999977i | \(0.502142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 127370. | − | 127370.i | 1.18297 | − | 1.18297i | 0.203994 | − | 0.978972i | \(-0.434608\pi\) |
0.978972 | − | 0.203994i | \(-0.0653924\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −246149. | + | 167765.i | −2.17884 | + | 1.48501i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17327.3 | − | 17327.3i | −0.146309 | − | 0.146309i | 0.630158 | − | 0.776467i | \(-0.282990\pi\) |
−0.776467 | + | 0.630158i | \(0.782990\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 105777.i | − | 0.852759i | −0.904544 | − | 0.426379i | \(-0.859789\pi\) | ||
0.904544 | − | 0.426379i | \(-0.140211\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 398895.i | 3.07292i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 63449.7 | + | 63449.7i | 0.467449 | + | 0.467449i | 0.901087 | − | 0.433638i | \(-0.142770\pi\) |
−0.433638 | + | 0.901087i | \(0.642770\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −40937.6 | + | 216176.i | −0.288654 | + | 1.52428i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 118961. | − | 118961.i | 0.803416 | − | 0.803416i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −355924. | −2.30404 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 144797. | 0.899078 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 192769. | − | 192769.i | 1.14888 | − | 1.14888i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −38793.3 | − | 170331.i | −0.222066 | − | 0.975032i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 150685. | + | 150685.i | 0.829009 | + | 0.829009i | 0.987380 | − | 0.158370i | \(-0.0506240\pi\) |
−0.158370 | + | 0.987380i | \(0.550624\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 49700.1i | − | 0.262956i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 218406.i | − | 1.11195i | −0.831199 | − | 0.555976i | \(-0.812345\pi\) | ||
0.831199 | − | 0.555976i | \(-0.187655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4347.58 | + | 4347.58i | 0.0213117 | + | 0.0213117i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 150487. | + | 28497.9i | 0.710663 | + | 0.134579i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 48858.6 | − | 48858.6i | 0.222403 | − | 0.222403i | −0.587107 | − | 0.809509i | \(-0.699733\pi\) |
0.809509 | + | 0.587107i | \(0.199733\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 356608. | 1.56550 | 0.782752 | − | 0.622334i | \(-0.213815\pi\) | ||||
0.782752 | + | 0.622334i | \(0.213815\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7575.36 | 0.0320889 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 42717.5 | − | 42717.5i | 0.174689 | − | 0.174689i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 106675. | + | 156516.i | 0.421351 | + | 0.618215i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −530409. | − | 530409.i | −2.02450 | − | 2.02450i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 39079.0i | − | 0.144204i | −0.997397 | − | 0.0721022i | \(-0.977029\pi\) | ||
0.997397 | − | 0.0721022i | \(-0.0229708\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 355671.i | − | 1.26942i | −0.772750 | − | 0.634711i | \(-0.781119\pi\) | ||
0.772750 | − | 0.634711i | \(-0.218881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 410070. | + | 410070.i | 1.41622 | + | 1.41622i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 169519. | + | 248722.i | 0.566748 | + | 0.831544i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −37305.0 | + | 37305.0i | −0.120786 | + | 0.120786i | −0.764916 | − | 0.644130i | \(-0.777220\pi\) |
0.644130 | + | 0.764916i | \(0.277220\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −786641. | −2.46765 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −857612. | −2.60751 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 180954. | − | 180954.i | 0.533458 | − | 0.533458i | −0.388142 | − | 0.921600i | \(-0.626883\pi\) |
0.921600 | + | 0.388142i | \(0.126883\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 171243. | + | 32428.4i | 0.489668 | + | 0.0927291i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −174882. | − | 174882.i | −0.485236 | − | 0.485236i | 0.421563 | − | 0.906799i | \(-0.361482\pi\) |
−0.906799 | + | 0.421563i | \(0.861482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 146753.i | − | 0.395249i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 10017.9i | − | 0.0261992i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 376164. | + | 376164.i | 0.955568 | + | 0.955568i | 0.999054 | − | 0.0434856i | \(-0.0138463\pi\) |
−0.0434856 | + | 0.999054i | \(0.513846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 624206. | − | 272107.i | 1.54075 | − | 0.671653i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 383826. | − | 383826.i | 0.920877 | − | 0.920877i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 384984. | 0.898070 | 0.449035 | − | 0.893514i | \(-0.351768\pi\) | ||||
0.449035 | + | 0.893514i | \(0.351768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −332337. | −0.754020 | −0.377010 | − | 0.926209i | \(-0.623048\pi\) | ||||
−0.377010 | + | 0.926209i | \(0.623048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24749.5 | − | 24749.5i | 0.0546308 | − | 0.0546308i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 169661. | − | 895919.i | 0.364463 | − | 1.92460i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 147251. | + | 147251.i | 0.307932 | + | 0.307932i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 597010.i | 1.21570i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 164553.i | − | 0.326378i | −0.986595 | − | 0.163189i | \(-0.947822\pi\) | ||
0.986595 | − | 0.163189i | \(-0.0521781\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −58078.0 | − | 58078.0i | −0.112232 | − | 0.112232i | 0.648760 | − | 0.760993i | \(-0.275288\pi\) |
−0.760993 | + | 0.648760i | \(0.775288\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −535288. | + | 364831.i | −1.00809 | + | 0.687077i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 386719. | − | 386719.i | 0.709954 | − | 0.709954i | −0.256571 | − | 0.966525i | \(-0.582593\pi\) |
0.966525 | + | 0.256571i | \(0.0825929\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14055.2 | 0.0251596 | 0.0125798 | − | 0.999921i | \(-0.495996\pi\) | ||||
0.0125798 | + | 0.999921i | \(0.495996\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00115e6 | 1.74788 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −522066. | + | 522066.i | −0.889171 | + | 0.889171i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −514950. | + | 350970.i | −0.855816 | + | 0.583291i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 988080. | + | 988080.i | 1.60275 | + | 1.60275i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3597.32i | − | 0.00569657i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 438963.i | 0.678768i | 0.940648 | + | 0.339384i | \(0.110219\pi\) | ||||
−0.940648 | + | 0.339384i | \(0.889781\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −418268. | − | 418268.i | −0.631692 | − | 0.631692i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21138.9 | + | 111627.i | −0.0311878 | + | 0.164691i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −829622. | + | 829622.i | −1.19600 | + | 1.19600i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −988240. | −1.39236 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −774010. | −1.06602 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 413890. | − | 413890.i | 0.557343 | − | 0.557343i | −0.371207 | − | 0.928550i | \(-0.621056\pi\) |
0.928550 | + | 0.371207i | \(0.121056\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.03267e6 | − | 405663.i | −1.35989 | − | 0.534207i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −165742. | − | 165742.i | −0.213485 | − | 0.213485i | 0.592261 | − | 0.805746i | \(-0.298235\pi\) |
−0.805746 | + | 0.592261i | \(0.798235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 590717.i | 0.744373i | 0.928158 | + | 0.372187i | \(0.121392\pi\) | ||||
−0.928158 | + | 0.372187i | \(0.878608\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 679352.i | 0.837655i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −849795. | − | 849795.i | −1.02547 | − | 1.02547i | −0.999667 | − | 0.0258063i | \(-0.991785\pi\) |
−0.0258063 | − | 0.999667i | \(-0.508215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17014.3 | − | 3222.02i | −0.0200976 | − | 0.00380591i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −404930. | + | 404930.i | −0.468284 | + | 0.468284i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 72025.5 | 0.0815627 | 0.0407814 | − | 0.999168i | \(-0.487015\pi\) | ||||
0.0407814 | + | 0.999168i | \(0.487015\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 358847. | 0.397985 | 0.198992 | − | 0.980001i | \(-0.436233\pi\) | ||||
0.198992 | + | 0.980001i | \(0.436233\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −804029. | + | 804029.i | −0.873486 | + | 0.873486i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 965703. | + | 1.41690e6i | 1.02785 | + | 1.50808i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9454.46 | + | 9454.46i | 0.00986040 | + | 0.00986040i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 654318.i | − | 0.668791i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 209249.i | − | 0.209642i | −0.994491 | − | 0.104821i | \(-0.966573\pi\) | ||
0.994491 | − | 0.104821i | \(-0.0334270\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 354807. | + | 354807.i | 0.348491 | + | 0.348491i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.25761e6 | − | 1.84519e6i | −1.21114 | − | 1.77701i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −228218. | + | 228218.i | −0.215535 | + | 0.215535i | −0.806614 | − | 0.591079i | \(-0.798702\pi\) |
0.591079 | + | 0.806614i | \(0.298702\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.55428e6 | 3.29232 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.20297e6 | 1.09309 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −945242. | + | 945242.i | −0.842663 | + | 0.842663i | −0.989204 | − | 0.146542i | \(-0.953186\pi\) |
0.146542 | + | 0.989204i | \(0.453186\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.76680e6 | + | 334581.i | 1.54551 | + | 0.292675i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 141442. | + | 141442.i | 0.121422 | + | 0.121422i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.56559e6i | − | 1.31916i | −0.751635 | − | 0.659579i | \(-0.770735\pi\) | ||
0.751635 | − | 0.659579i | \(-0.229265\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 990821.i | 0.819543i | 0.912188 | + | 0.409772i | \(0.134392\pi\) | ||||
−0.912188 | + | 0.409772i | \(0.865608\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.78547e6 | − | 1.78547e6i | −1.44993 | − | 1.44993i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −370819. | − | 145669.i | −0.295685 | − | 0.116154i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −174283. | + | 174283.i | −0.136476 | + | 0.136476i | −0.772044 | − | 0.635569i | \(-0.780766\pi\) |
0.635569 | + | 0.772044i | \(0.280766\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.91166e6 | 1.47028 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.17766e6 | 1.64522 | 0.822609 | − | 0.568607i | \(-0.192517\pi\) | ||||
0.822609 | + | 0.568607i | \(0.192517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 502126. | − | 502126.i | 0.372689 | − | 0.372689i | −0.495767 | − | 0.868456i | \(-0.665113\pi\) |
0.868456 | + | 0.495767i | \(0.165113\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7177.24 | + | 37900.3i | −0.00523414 | + | 0.0276396i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.71763e6 | − | 1.71763e6i | −1.23091 | − | 1.23091i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.24823e6i | − | 0.879123i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 2.65425e6i | − | 1.83742i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 45772.5 | + | 45772.5i | 0.0311484 | + | 0.0311484i | 0.722509 | − | 0.691361i | \(-0.242989\pi\) |
−0.691361 | + | 0.722509i | \(0.742989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.02533e6 | + | 698823.i | −0.685974 | + | 0.467533i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 246992. | − | 246992.i | 0.162477 | − | 0.162477i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.86501e6 | −1.20643 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −442844. | −0.281731 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 23856.2 | − | 23856.2i | 0.0149277 | − | 0.0149277i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −66114.0 | + | 45060.7i | −0.0406953 | + | 0.0277363i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.39565e6 | + | 1.39565e6i | 0.845144 | + | 0.845144i | 0.989523 | − | 0.144379i | \(-0.0461183\pi\) |
−0.144379 | + | 0.989523i | \(0.546118\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.40498e6i | 2.62451i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.84115e6i | − | 1.07942i | −0.841852 | − | 0.539709i | \(-0.818534\pi\) | ||
0.841852 | − | 0.539709i | \(-0.181466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.22340e6 | + | 2.22340e6i | 1.28279 | + | 1.28279i | 0.939073 | + | 0.343718i | \(0.111686\pi\) |
0.343718 | + | 0.939073i | \(0.388314\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 804672. | − | 4.24918e6i | 0.456922 | − | 2.41284i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.35501e6 | + | 1.35501e6i | −0.757344 | + | 0.757344i | −0.975838 | − | 0.218495i | \(-0.929885\pi\) |
0.218495 | + | 0.975838i | \(0.429885\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 431973. | 0.237673 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 599254. | 0.324600 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32590.4 | + | 32590.4i | −0.0173814 | + | 0.0173814i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.35743e6 | − | 591738.i | 0.712868 | − | 0.310757i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.82912e6 | + | 1.82912e6i | 0.945958 | + | 0.945958i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 67498.9i | − | 0.0343801i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.40493e6i | − | 1.20652i | −0.797546 | − | 0.603258i | \(-0.793869\pi\) | ||
0.797546 | − | 0.603258i | \(-0.206131\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.09499e6 | − | 4.09499e6i | −2.02368 | − | 2.02368i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.24859e6 | − | 425819.i | −1.09471 | − | 0.207307i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.72476e6 | + | 1.72476e6i | −0.827284 | + | 0.827284i | −0.987140 | − | 0.159856i | \(-0.948897\pi\) |
0.159856 | + | 0.987140i | \(0.448897\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.19436e6 | −1.03707 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 686454. | 0.319687 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.13652e6 | + | 2.13652e6i | −0.980554 | + | 0.980554i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.03025e6 | − | 4.44605e6i | −1.37066 | − | 2.01107i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.06948e6 | + | 2.06948e6i | 0.922653 | + | 0.922653i | 0.997216 | − | 0.0745635i | \(-0.0237563\pi\) |
−0.0745635 | + | 0.997216i | \(0.523756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.88338e6i | 0.827702i | 0.910345 | + | 0.413851i | \(0.135817\pi\) | ||||
−0.910345 | + | 0.413851i | \(0.864183\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.29829e6i | 0.562475i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.77943e6 | + | 1.77943e6i | 0.760054 | + | 0.760054i | 0.976332 | − | 0.216278i | \(-0.0693916\pi\) |
−0.216278 | + | 0.976332i | \(0.569392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 761530. | + | 1.11733e6i | 0.320713 | + | 0.470556i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.15469e6 | − | 6.15469e6i | 2.55585 | − | 2.55585i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.50238e6 | 1.84377 | 0.921884 | − | 0.387466i | \(-0.126650\pi\) | ||||
0.921884 | + | 0.387466i | \(0.126650\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47530e6 | −0.999678 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.50386e6 | + | 2.50386e6i | −0.997340 | + | 0.997340i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.21959e6 | + | 420327.i | 0.872049 | + | 0.165141i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −604369. | − | 604369.i | −0.234227 | − | 0.234227i | 0.580227 | − | 0.814455i | \(-0.302964\pi\) |
−0.814455 | + | 0.580227i | \(0.802964\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.95787e6i | 1.51320i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.00922e6i | 2.64384i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 87601.5 | + | 87601.5i | 0.0326016 | + | 0.0326016i | 0.723220 | − | 0.690618i | \(-0.242661\pi\) |
−0.690618 | + | 0.723220i | \(0.742661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.61621e6 | + | 2.27457e6i | 1.32793 | + | 0.835258i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.13531e6 | + | 1.13531e6i | −0.411397 | + | 0.411397i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.48550e6 | −0.888824 | −0.444412 | − | 0.895823i | \(-0.646587\pi\) | ||||
−0.444412 | + | 0.895823i | \(0.646587\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.21132e6 | −1.83923 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −601337. | + | 601337.i | −0.209470 | + | 0.209470i | −0.804042 | − | 0.594572i | \(-0.797321\pi\) |
0.594572 | + | 0.804042i | \(0.297321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 288948. | − | 1.52583e6i | 0.0993499 | − | 0.524630i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 510213. | + | 510213.i | 0.173171 | + | 0.173171i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.73874e6i | − | 1.25271i | −0.779537 | − | 0.626356i | \(-0.784546\pi\) | ||
0.779537 | − | 0.626356i | \(-0.215454\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.42886e6i | − | 2.12663i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.77670e6 | + | 3.77670e6i | 1.23348 | + | 1.23348i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.08170e6 | − | 737246.i | 0.348831 | − | 0.237750i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −209001. | + | 209001.i | −0.0665538 | + | 0.0665538i | −0.739600 | − | 0.673046i | \(-0.764985\pi\) |
0.673046 | + | 0.739600i | \(0.264985\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −150358. | −0.0472818 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.88404e6 | −1.20621 | −0.603104 | − | 0.797662i | \(-0.706070\pi\) | ||||
−0.603104 | + | 0.797662i | \(0.706070\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.80414e6 | + | 1.80414e6i | −0.553359 | + | 0.553359i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 890227. | − | 606743.i | 0.269689 | − | 0.183809i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.47046e6 | − | 1.47046e6i | −0.440015 | − | 0.440015i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.17358e6i | − | 0.346899i | −0.984843 | − | 0.173450i | \(-0.944509\pi\) | ||
0.984843 | − | 0.173450i | \(-0.0554913\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.68974e6i | 0.493419i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.42002e6 | − | 3.42002e6i | −0.986627 | − | 0.986627i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −278300. | + | 1.46960e6i | −0.0793219 | + | 0.418870i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.16652e6 | + | 6.16652e6i | −1.73660 | + | 1.73660i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.60340e6 | 0.446177 | 0.223089 | − | 0.974798i | \(-0.428386\pi\) | ||||
0.223089 | + | 0.974798i | \(0.428386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.71020e6 | −1.02022 | −0.510108 | − | 0.860111i | \(-0.670394\pi\) | ||||
−0.510108 | + | 0.860111i | \(0.670394\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −77767.4 | + | 77767.4i | −0.0211323 | + | 0.0211323i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.03978e6 | + | 4.67919e6i | 0.547786 | + | 1.25660i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −220526. | − | 220526.i | −0.0585315 | − | 0.0585315i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.47735e6i | 0.387562i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.29101e6i | − | 0.594065i | −0.954867 | − | 0.297033i | \(-0.904003\pi\) | ||
0.954867 | − | 0.297033i | \(-0.0959971\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −972567. | − | 972567.i | −0.249287 | − | 0.249287i | 0.571391 | − | 0.820678i | \(-0.306404\pi\) |
−0.820678 | + | 0.571391i | \(0.806404\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.55115e6 | − | 861857.i | −1.15318 | − | 0.218380i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −78527.9 | + | 78527.9i | −0.0196707 | + | 0.0196707i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.49284e6 | −0.865002 | −0.432501 | − | 0.901633i | \(-0.642369\pi\) | ||||
−0.432501 | + | 0.901633i | \(0.642369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.08902e7 | 2.66648 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.91464e6 | − | 4.91464e6i | 1.18982 | − | 1.18982i | 0.212707 | − | 0.977116i | \(-0.431772\pi\) |
0.977116 | − | 0.212707i | \(-0.0682281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −257519. | − | 377837.i | −0.0616466 | − | 0.0904492i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 675761. | + | 675761.i | 0.159965 | + | 0.159965i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.79845e6i | − | 0.889182i | −0.895734 | − | 0.444591i | \(-0.853349\pi\) | ||
0.895734 | − | 0.444591i | \(-0.146651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.42122e6i | 0.329019i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.15031e6 | + | 6.15031e6i | 1.40816 | + | 1.40816i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.25076e6 | + | 4.76959e6i | 0.736134 | + | 1.08007i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.14446e6 | − | 4.14446e6i | 0.928276 | − | 0.928276i | −0.0693189 | − | 0.997595i | \(-0.522083\pi\) |
0.997595 | + | 0.0693189i | \(0.0220826\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.47532e6 | −0.991499 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.33612e6 | 0.292815 | 0.146407 | − | 0.989224i | \(-0.453229\pi\) | ||||
0.146407 | + | 0.989224i | \(0.453229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.66263e6 | − | 3.66263e6i | 0.794036 | − | 0.794036i | −0.188112 | − | 0.982148i | \(-0.560237\pi\) |
0.982148 | + | 0.188112i | \(0.0602367\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.23229e6 | − | 1.36959e6i | −1.55111 | − | 0.293736i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.58287e6 | − | 4.58287e6i | −0.972401 | − | 0.972401i | 0.0272279 | − | 0.999629i | \(-0.491332\pi\) |
−0.999629 | + | 0.0272279i | \(0.991332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 8.92061e6i | − | 1.87267i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.29017e6i | − | 0.267975i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 183211. | + | 183211.i | 0.0376530 | + | 0.0376530i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32240.2 | − | 82071.6i | 0.00655637 | − | 0.0166901i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.07553e6 | − | 8.07553e6i | 1.62508 | − | 1.62508i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.00075e6 | 1.39414 | 0.697069 | − | 0.717004i | \(-0.254487\pi\) | ||||
0.697069 | + | 0.717004i | \(0.254487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.72932e6 | 1.52328 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.48300e7 | − | 1.48300e7i | 2.89249 | − | 2.89249i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.12893e6 | + | 5.96145e6i | −0.217927 | + | 1.15079i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.98892e6 | − | 3.98892e6i | −0.762137 | − | 0.762137i | 0.214571 | − | 0.976708i | \(-0.431165\pi\) |
−0.976708 | + | 0.214571i | \(0.931165\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.25818e6i | 1.18352i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.30379e6i | 0.431260i | 0.976475 | + | 0.215630i | \(0.0691805\pi\) | ||||
−0.976475 | + | 0.215630i | \(0.930819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.91352e6 | − | 3.91352e6i | −0.725188 | − | 0.725188i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.09085e6 | + | 1.42504e6i | −0.383540 | + | 0.261406i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.72690e6 | + | 3.72690e6i | −0.676795 | + | 0.676795i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.47982e6 | −0.445829 | −0.222914 | − | 0.974838i | \(-0.571557\pi\) | ||||
−0.222914 | + | 0.974838i | \(0.571557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.04816e6 | 1.07654 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.08077e6 | + | 4.08077e6i | −0.719154 | + | 0.719154i | −0.968432 | − | 0.249278i | \(-0.919807\pi\) |
0.249278 | + | 0.968432i | \(0.419807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −63727.8 | + | 43434.3i | −0.0111199 | + | 0.00757887i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.53768e6 | + | 2.53768e6i | 0.438446 | + | 0.438446i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.80205e6i | 0.479382i | 0.970849 | + | 0.239691i | \(0.0770461\pi\) | ||||
−0.970849 | + | 0.239691i | \(0.922954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.80554e6i | 1.49178i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 54665.6 | + | 54665.6i | 0.00917109 | + | 0.00917109i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.87357e6 | − | 9.89361e6i | 0.311280 | − | 1.64375i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27925.3 | + | 27925.3i | −0.00459485 | + | 0.00459485i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.30094e7 | −2.12001 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 144765. | 0.0233652 | 0.0116826 | − | 0.999932i | \(-0.496281\pi\) | ||||
0.0116826 | + | 0.999932i | \(0.496281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.79906e6 | + | 3.79906e6i | −0.607327 | + | 0.607327i | −0.942247 | − | 0.334920i | \(-0.891291\pi\) |
0.334920 | + | 0.942247i | \(0.391291\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.08855e6 | + | 1.54992e7i | −0.964085 | + | 2.45420i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.21903e6 | − | 6.21903e6i | −0.975430 | − | 0.975430i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9.05423e6i | − | 1.40674i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.88060e6i | 1.21289i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.73526e6 | − | 3.73526e6i | −0.569511 | − | 0.569511i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.34593e6 | − | 254880.i | −0.203300 | − | 0.0384991i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.65720e6 | + | 6.65720e6i | −0.996221 | + | 0.996221i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.91053e6 | 0.579781 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.17321e7 | −1.72339 | −0.861695 | − | 0.507426i | \(-0.830597\pi\) | ||||
−0.861695 | + | 0.507426i | \(0.830597\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.74683e6 | − | 5.74683e6i | 0.836428 | − | 0.836428i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.33023e6 | − | 4.88618e6i | −0.480267 | − | 0.704657i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.24186e6 | − | 5.24186e6i | −0.749060 | − | 0.749060i | 0.225243 | − | 0.974303i | \(-0.427683\pi\) |
−0.974303 | + | 0.225243i | \(0.927683\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 508148.i | 0.0719547i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 95606.6i | 0.0134156i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.60806e6 | + | 3.60806e6i | 0.501719 | + | 0.501719i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.25586e7 | + | 1.84262e7i | 1.73064 | + | 2.53923i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.61782e6 | − | 7.61782e6i | 1.04038 | − | 1.04038i | 0.0412325 | − | 0.999150i | \(-0.486872\pi\) |
0.999150 | − | 0.0412325i | \(-0.0131284\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −963030. | −0.130350 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.09258e6 | −0.683173 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −86277.5 | + | 86277.5i | −0.0114717 | + | 0.0114717i | −0.712819 | − | 0.701348i | \(-0.752582\pi\) |
0.701348 | + | 0.712819i | \(0.252582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.92855e6 | + | 933326.i | 0.649528 | + | 0.123002i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.96938e6 | + | 2.96938e6i | 0.387890 | + | 0.387890i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5.02097e6i | − | 0.650140i | −0.945690 | − | 0.325070i | \(-0.894612\pi\) | ||
0.945690 | − | 0.325070i | \(-0.105388\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 8.08321e6i | − | 1.03751i | −0.854922 | − | 0.518756i | \(-0.826395\pi\) | ||
0.854922 | − | 0.518756i | \(-0.173605\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.84547e6 | + | 2.84547e6i | 0.362049 | + | 0.362049i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.91492e6 | + | 1.12747e7i | 0.619936 | + | 1.42212i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.25025e6 | + | 3.25025e6i | −0.406422 | + | 0.406422i | −0.880489 | − | 0.474067i | \(-0.842786\pi\) |
0.474067 | + | 0.880489i | \(0.342786\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.00859e6 | 0.248997 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.83018e6 | −0.716542 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.89982e6 | − | 2.89982e6i | 0.353346 | − | 0.353346i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.74988e6 | − | 9.24047e6i | 0.211407 | − | 1.11636i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.79350e6 | + | 3.79350e6i | 0.454407 | + | 0.454407i | 0.896814 | − | 0.442407i | \(-0.145875\pi\) |
−0.442407 | + | 0.896814i | \(0.645875\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 151930.i | 0.0180449i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.33744e7i | 1.57509i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.01322e7 | + | 1.01322e7i | 1.18323 | + | 1.18323i | 0.978904 | + | 0.204321i | \(0.0654987\pi\) |
0.204321 | + | 0.978904i | \(0.434501\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.64412e7 | + | 1.12057e7i | −1.90389 | + | 1.29762i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −243044. | + | 243044.i | −0.0279093 | + | 0.0279093i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.84016e6 | −0.209550 | −0.104775 | − | 0.994496i | \(-0.533412\pi\) | ||||
−0.104775 | + | 0.994496i | \(0.533412\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.07660e6 | 0.234513 | 0.117257 | − | 0.993102i | \(-0.462590\pi\) | ||||
0.117257 | + | 0.993102i | \(0.462590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.02777e7 | + | 1.02777e7i | −1.15107 | + | 1.15107i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.68864e6 | − | 4.55871e6i | 0.742932 | − | 0.506353i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.47671e6 | + | 7.47671e6i | 0.823643 | + | 0.823643i | 0.986628 | − | 0.162986i | \(-0.0521125\pi\) |
−0.162986 | + | 0.986628i | \(0.552112\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1.80553e7i | − | 1.97270i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 146786.i | − | 0.0159068i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 421185. | + | 421185.i | 0.0452712 | + | 0.0452712i | 0.729380 | − | 0.684109i | \(-0.239809\pi\) |
−0.684109 | + | 0.729380i | \(0.739809\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.83557e6 | − | 1.49736e7i | 0.302310 | − | 1.59639i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.79146e6 | − | 4.79146e6i | 0.506705 | − | 0.506705i | −0.406808 | − | 0.913514i | \(-0.633358\pi\) |
0.913514 | + | 0.406808i | \(0.133358\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.81805e6 | −0.925009 | −0.462505 | − | 0.886617i | \(-0.653049\pi\) | ||||
−0.462505 | + | 0.886617i | \(0.653049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.07835e7 | −1.12209 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.26029e6 | − | 1.26029e6i | 0.130092 | − | 0.130092i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.15458e6 | − | 6.64676e6i | −0.732629 | − | 0.680629i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 62205.4 | + | 62205.4i | 0.00631915 | + | 0.00631915i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.66437e7i | 2.68515i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.57807e6i | − | 0.457730i | −0.973458 | − | 0.228865i | \(-0.926499\pi\) | ||
0.973458 | − | 0.228865i | \(-0.0735014\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.59061e6 | − | 7.59061e6i | −0.752952 | − | 0.752952i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.17046e7 | + | 2.21652e6i | 1.15192 | + | 0.218141i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.02777e7 | + | 1.02777e7i | −1.00356 | + | 1.00356i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.58774e6 | 0.832007 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.62758e7 | −1.56458 | −0.782288 | − | 0.622917i | \(-0.785947\pi\) | ||||
−0.782288 | + | 0.622917i | \(0.785947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.99416e6 | + | 2.99416e6i | −0.285593 | + | 0.285593i | −0.835335 | − | 0.549742i | \(-0.814726\pi\) |
0.549742 | + | 0.835335i | \(0.314726\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.56473e6 | − | 2.29580e6i | −0.148094 | − | 0.217287i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.92387e6 | + | 4.92387e6i | 0.462430 | + | 0.462430i | 0.899451 | − | 0.437021i | \(-0.143967\pi\) |
−0.437021 | + | 0.899451i | \(0.643967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.82983e6i | 0.263723i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 2.86919e7i | − | 2.65342i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.05307e7 | + | 1.05307e7i | 0.966441 | + | 0.966441i | 0.999455 | − | 0.0330138i | \(-0.0105105\pi\) |
−0.0330138 | + | 0.999455i | \(0.510511\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.87615e6 | − | 1.00888e7i | −0.626241 | − | 0.918835i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.01451e7 | − | 1.01451e7i | 0.916945 | − | 0.916945i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.29023e7 | −1.15732 | −0.578659 | − | 0.815570i | \(-0.696424\pi\) | ||||
−0.578659 | + | 0.815570i | \(0.696424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.60437e6 | 0.587933 | 0.293967 | − | 0.955816i | \(-0.405025\pi\) | ||||
0.293967 | + | 0.955816i | \(0.405025\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.33843e7 | − | 1.33843e7i | 1.18253 | − | 1.18253i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 337704. | + | 63951.5i | 0.0296130 | + | 0.00560785i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.42978e6 | − | 9.42978e6i | −0.820705 | − | 0.820705i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.43141e7i | 1.23651i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 182470.i | 0.0156453i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.01077e7 | + | 1.01077e7i | 0.860230 | + | 0.860230i | 0.991365 | − | 0.131135i | \(-0.0418621\pi\) |
−0.131135 | + | 0.991365i | \(0.541862\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.84865e6 | − | 3.42143e6i | 0.663034 | − | 0.289033i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.24850e6 | − | 5.24850e6i | 0.440112 | − | 0.440112i | −0.451938 | − | 0.892050i | \(-0.649267\pi\) |
0.892050 | + | 0.451938i | \(0.149267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.36502e7 | −1.96861 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.73207e6 | 0.473635 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.03798e7 | + | 1.03798e7i | −0.851407 | + | 0.851407i | −0.990306 | − | 0.138900i | \(-0.955643\pi\) |
0.138900 | + | 0.990306i | \(0.455643\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 718695. | − | 3.79516e6i | 0.0585218 | − | 0.309032i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.02148e7 | − | 1.02148e7i | −0.825727 | − | 0.825727i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.52426e7i | 1.22324i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.06155e6i | 0.482935i | 0.970409 | + | 0.241468i | \(0.0776288\pi\) | ||||
−0.970409 | + | 0.241468i | \(0.922371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.97412e6 | − | 6.97412e6i | −0.551641 | − | 0.551641i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.64728e7 | − | 1.12272e7i | 1.29362 | − | 0.881679i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.28758e7 | − | 1.28758e7i | 1.00390 | − | 1.00390i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.93896e7 | 2.27510 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.87503e6 | 0.220977 | 0.110489 | − | 0.993877i | \(-0.464758\pi\) | ||||
0.110489 | + | 0.993877i | \(0.464758\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 325450. | − | 325450.i | 0.0248368 | − | 0.0248368i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 349929. | − | 238498.i | 0.0265159 | − | 0.0180722i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −212566. | − | 212566.i | −0.0159936 | − | 0.0159936i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 528547.i | 0.0394883i | 0.999805 | + | 0.0197441i | \(0.00628516\pi\) | ||||
−0.999805 | + | 0.0197441i | \(0.993715\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.31390e6i | − | 0.616780i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.49850e7 | − | 1.49850e7i | −1.10391 | − | 1.10391i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 628360. | − | 3.31814e6i | 0.0459667 | − | 0.242733i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.24548e6 | + | 1.24548e6i | −0.0904769 | + | 0.0904769i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.66055e7 | 1.19793 | 0.598963 | − | 0.800777i | \(-0.295580\pi\) | ||||
0.598963 | + | 0.800777i | \(0.295580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.92498e7 | 2.81190 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.20523e6 | + | 6.20523e6i | −0.441481 | + | 0.441481i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.85532e6 | + | 3.87147e6i | 0.696347 | + | 0.273546i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.54075e7 | + | 1.54075e7i | 1.08118 | + | 1.08118i | 0.996400 | + | 0.0847783i | \(0.0270182\pi\) |
0.0847783 | + | 0.996400i | \(0.472982\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 2.31237e7i | − | 1.61153i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.31966e6i | − | 0.229773i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.69113e7 | − | 1.69113e7i | −1.16256 | − | 1.16256i | −0.983913 | − | 0.178650i | \(-0.942827\pi\) |
−0.178650 | − | 0.983913i | \(-0.557173\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.12003e7 | − | 7.80215e6i | −2.81308 | − | 0.532716i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.69059e6 | + | 3.69059e6i | −0.250281 | + | 0.250281i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.76180e7 | 1.86029 | 0.930147 | − | 0.367187i | \(-0.119679\pi\) | ||||
0.930147 | + | 0.367187i | \(0.119679\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −326976. | −0.0218761 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.71922e7 | + | 1.71922e7i | −1.14251 | + | 1.14251i | −0.154521 | + | 0.987990i | \(0.549383\pi\) |
−0.987990 | + | 0.154521i | \(0.950617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.23034e6 | − | 1.80518e6i | −0.0812147 | − | 0.119160i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.71712e6 | + | 6.71712e6i | 0.440435 | + | 0.440435i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 5.33954e6i | − | 0.347776i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.11896e7i | 0.723961i | 0.932186 | + | 0.361981i | \(0.117899\pi\) | ||||
−0.932186 | + | 0.361981i | \(0.882101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.61836e6 | + | 3.61836e6i | 0.232554 | + | 0.232554i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.11977e7 | − | 1.64295e7i | −0.714928 | − | 1.04896i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.17247e6 | + | 1.17247e6i | −0.0743637 | + | 0.0743637i | −0.743310 | − | 0.668947i | \(-0.766745\pi\) |
0.668947 | + | 0.743310i | \(0.266745\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.22708e7 | −0.773156 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.79138e6 | −0.612890 | −0.306445 | − | 0.951888i | \(-0.599140\pi\) | ||||
−0.306445 | + | 0.951888i | \(0.599140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.62980e7 | − | 1.62980e7i | 1.01350 | − | 1.01350i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.18528e7 | + | 6.03200e6i | 1.96786 | + | 0.372656i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.43734e6 | − | 7.43734e6i | −0.456488 | − | 0.456488i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.10059e7i | 0.671138i | 0.942016 | + | 0.335569i | \(0.108929\pi\) | ||||
−0.942016 | + | 0.335569i | \(0.891071\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 7.89277e6i | − | 0.478182i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.90959e6 | + | 8.90959e6i | 0.536302 | + | 0.536302i | 0.922441 | − | 0.386139i | \(-0.126191\pi\) |
−0.386139 | + | 0.922441i | \(0.626191\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.56612e7 | + | 6.15220e6i | 0.936637 | + | 0.367939i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.14612e7 | + | 6.14612e7i | −3.65215 | + | 3.65215i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −314553. | −0.0185716 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.08375e6 | 0.180906 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.56435e6 | + | 6.56435e6i | −0.382638 | + | 0.382638i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −548745. | + | 2.89772e6i | −0.0317831 | + | 0.167835i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.88094e6 | + | 4.88094e6i | 0.280910 | + | 0.280910i | 0.833472 | − | 0.552562i | \(-0.186350\pi\) |
−0.552562 | + | 0.833472i | \(0.686350\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 3.26905e7i | − | 1.86952i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.95525e7i | 1.11112i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −479566. | − | 479566.i | −0.0270811 | − | 0.0270811i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.63373e7 | + | 2.47661e7i | −2.03909 | + | 1.38976i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.86412e6 | − | 7.86412e6i | 0.438535 | − | 0.438535i | −0.452984 | − | 0.891519i | \(-0.649640\pi\) |
0.891519 | + | 0.452984i | \(0.149640\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 505987. | 0.0280396 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.90403e6 | −0.159926 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.64299e6 | − | 3.64299e6i | 0.199374 | − | 0.199374i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.96157e7 | + | 2.70005e7i | −2.15466 | + | 1.46853i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.70724e7 | + | 2.70724e7i | 1.46333 | + | 1.46333i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.59398e6i | 0.193065i | 0.995330 | + | 0.0965327i | \(0.0307752\pi\) | ||||
−0.995330 | + | 0.0965327i | \(0.969225\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.96828e7i | − | 1.05084i | −0.850844 | − | 0.525418i | \(-0.823909\pi\) | ||
0.850844 | − | 0.525418i | \(-0.176091\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.71334e7 | − | 1.71334e7i | −0.909113 | − | 0.909113i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.66178e6 | − | 1.40559e7i | 0.140371 | − | 0.741249i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40549.3 | + | 40549.3i | −0.00212534 | + | 0.00212534i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.66587e7 | 1.90971 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.87305e6 | −0.355870 | −0.177935 | − | 0.984042i | \(-0.556942\pi\) | ||||
−0.177935 | + | 0.984042i | \(0.556942\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.46199e7 | + | 2.46199e7i | −1.26703 | + | 1.26703i | −0.319415 | + | 0.947615i | \(0.603486\pi\) |
−0.947615 | + | 0.319415i | \(0.896514\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.93117e6 | − | 3.89333e6i | 0.456850 | − | 0.199153i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.64914e7 | − | 2.64914e7i | −1.34692 | − | 1.34692i | −0.888988 | − | 0.457931i | \(-0.848591\pi\) |
−0.457931 | − | 0.888988i | \(-0.651409\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.71839e6i | − | 0.238456i | −0.992867 | − | 0.119228i | \(-0.961958\pi\) | ||
0.992867 | − | 0.119228i | \(-0.0380419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 6.02745e6i | − | 0.302782i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.54280e7 | − | 3.54280e7i | −1.76903 | − | 1.76903i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.35842e7 | − | 2.57246e6i | −0.674245 | − | 0.127683i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.04315e7 | + | 1.04315e7i | −0.514675 | + | 0.514675i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.18851e6 | 0.107336 | 0.0536678 | − | 0.998559i | \(-0.482909\pi\) | ||||
0.0536678 | + | 0.998559i | \(0.482909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.03051e6 | 0.440273 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.76564e7 | + | 3.76564e7i | −1.82503 | + | 1.82503i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.62028e6 | − | 6.77897e6i | −0.222601 | − | 0.326605i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.23102e7 | + | 2.23102e7i | 1.06855 | + | 1.06855i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.73657e7i | 0.826842i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.41990e7i | 3.03882i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.82806e7 | − | 1.82806e7i | −0.860238 | − | 0.860238i | 0.131127 | − | 0.991366i | \(-0.458140\pi\) |
−0.991366 | + | 0.131127i | \(0.958140\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −315398. | − | 462759.i | −0.0147552 | − | 0.0216491i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.39122e7 | − | 2.39122e7i | 1.11216 | − | 1.11216i | 0.119303 | − | 0.992858i | \(-0.461934\pi\) |
0.992858 | − | 0.119303i | \(-0.0380660\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.15768e7 | 0.535309 | 0.267654 | − | 0.963515i | \(-0.413751\pi\) | ||||
0.267654 | + | 0.963515i | \(0.413751\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.94032e7 | 2.73088 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.08022e6 | + | 3.08022e6i | −0.140784 | + | 0.140784i | −0.773987 | − | 0.633202i | \(-0.781740\pi\) |
0.633202 | + | 0.773987i | \(0.281740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.92191e7 | + | 5.53325e6i | 1.32778 | + | 0.251443i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.15846e7 | + | 2.15846e7i | 0.975204 | + | 0.975204i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.98542e6i | − | 0.134108i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.93992e7i | − | 0.866440i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.72481e7 | + | 2.72481e7i | 1.21004 | + | 1.21004i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.02671e7 | − | 3.22216e7i | 0.894895 | − | 1.42274i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.24010e7 | + | 1.24010e7i | −0.544449 | + | 0.544449i | −0.924830 | − | 0.380381i | \(-0.875793\pi\) |
0.380381 | + | 0.924830i | \(0.375793\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.58301e6 | −0.0691053 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.61119e6 | 0.373786 | 0.186893 | − | 0.982380i | \(-0.440158\pi\) | ||||
0.186893 | + | 0.982380i | \(0.440158\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.44433e7 | − | 2.44433e7i | 1.05502 | − | 1.05502i | 0.0566197 | − | 0.998396i | \(-0.481968\pi\) |
0.998396 | − | 0.0566197i | \(-0.0180323\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.64596e6 | − | 2.98143e7i | 0.242315 | − | 1.27958i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.94644e7 | − | 1.94644e7i | −0.830678 | − | 0.830678i | 0.156932 | − | 0.987609i | \(-0.449840\pi\) |
−0.987609 | + | 0.156932i | \(0.949840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.64345e7i | 1.97055i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2.45696e6i | − | 0.103682i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6180.58 | − | 6180.58i | −0.000259359 | − | 0.000259359i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.77836e7 | − | 1.21206e7i | 0.742099 | − | 0.505785i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.22500e7 | − | 3.22500e7i | 1.33828 | − | 1.33828i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.82440e7 | −0.752873 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.25427e7 | −2.15626 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.65772e6 | − | 7.65772e6i | 0.312522 | − | 0.312522i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.53517e7 | + | 1.04631e7i | −0.623066 | + | 0.424658i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.02098e7 | + | 2.02098e7i | 0.815724 | + | 0.815724i | 0.985485 | − | 0.169761i | \(-0.0542997\pi\) |
−0.169761 | + | 0.985485i | \(0.554300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 489807.i | 0.0196614i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.45272e7i | − | 0.979155i | −0.871960 | − | 0.489577i | \(-0.837151\pi\) | ||
0.871960 | − | 0.489577i | \(-0.162849\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.41204e6 | + | 2.41204e6i | 0.0957650 | + | 0.0957650i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 364057. | − | 1.92245e6i | 0.0143753 | − | 0.0759105i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.36516e7 | − | 3.36516e7i | 1.32155 | − | 1.32155i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.34572e7 | 0.525613 | 0.262806 | − | 0.964849i | \(-0.415352\pi\) | ||||
0.262806 | + | 0.964849i | \(0.415352\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.82676e7 | −1.87502 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.10471e6 | + | 8.10471e6i | −0.313136 | + | 0.313136i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.03694e7 | − | 4.67268e7i | −0.782751 | − | 1.79561i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.52208e7 | − | 4.52208e7i | −1.72838 | − | 1.72838i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.09539e7i | 0.416417i | 0.978084 | + | 0.208209i | \(0.0667633\pi\) | ||||
−0.978084 | + | 0.208209i | \(0.933237\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 865500.i | 0.0327260i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.18375e7 | + | 3.18375e7i | 1.19739 | + | 1.19739i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.14379e7 | + | 2.16602e6i | 0.427877 | + | 0.0810276i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.46236e7 | + | 2.46236e7i | −0.916224 | + | 0.916224i | −0.996752 | − | 0.0805282i | \(-0.974339\pi\) |
0.0805282 | + | 0.996752i | \(0.474339\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.68946e7 | −2.84598 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.79774e7 | 1.02999 | 0.514995 | − | 0.857193i | \(-0.327794\pi\) | ||||
0.514995 | + | 0.857193i | \(0.327794\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.10247e7 | − | 3.10247e7i | 1.13613 | − | 1.13613i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.87959e7 | + | 2.75777e7i | 0.684673 | + | 1.00457i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.34277e7 | − | 1.34277e7i | −0.486550 | − | 0.486550i | 0.420666 | − | 0.907216i | \(-0.361796\pi\) |
−0.907216 | + | 0.420666i | \(0.861796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.91490e7i | 0.690208i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.68619e7i | − | 1.68023i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.47107e7 | − | 2.47107e7i | −0.881359 | − | 0.881359i | 0.112313 | − | 0.993673i | \(-0.464174\pi\) |
−0.993673 | + | 0.112313i | \(0.964174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.18067e6 | − | 7.60119e6i | −0.183814 | − | 0.269695i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.46974e6 | + | 7.46974e6i | −0.263649 | + | 0.263649i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.50561e7 | 0.528648 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −362678. | −0.0126681 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.15184e6 | + | 6.15184e6i | −0.213766 | + | 0.213766i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.51129e6 | − | 854309.i | −0.155949 | − | 0.0295323i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.49726e7 | + | 2.49726e7i | 0.858811 | + | 0.858811i | 0.991198 | − | 0.132387i | \(-0.0422641\pi\) |
−0.132387 | + | 0.991198i | \(0.542264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.12712e6i | − | 0.0385620i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.77496e7i | − | 0.604143i | −0.953285 | − | 0.302071i | \(-0.902322\pi\) | ||
0.953285 | − | 0.302071i | \(-0.0976781\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.49457e7 | + | 5.49457e7i | 1.86059 | + | 1.86059i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.32405e7 | + | 3.37053e7i | −0.446058 | + | 1.13550i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.06328e7 | + | 2.06328e7i | −0.691548 | + | 0.691548i | −0.962572 | − | 0.271024i | \(-0.912638\pi\) |
0.271024 | + | 0.962572i | \(0.412638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.04280e6 | −0.0347733 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.75548e7 | −1.24593 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.82547e7 | + | 1.82547e7i | −0.602546 | + | 0.602546i | −0.940987 | − | 0.338442i | \(-0.890100\pi\) |
0.338442 | + | 0.940987i | \(0.390100\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.68852e6 | − | 3.00390e7i | 0.186814 | − | 0.986494i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.16720e6 | + | 1.16720e6i | 0.0381375 | + | 0.0381375i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 7.99884e6i | − | 0.260038i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.83326e7i | − | 1.23989i | −0.784644 | − | 0.619947i | \(-0.787154\pi\) | ||
0.784644 | − | 0.619947i | \(-0.212846\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.15865e7 | + | 4.15865e7i | 1.33838 | + | 1.33838i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 649252. | − | 442504.i | 0.0207900 | − | 0.0141697i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.22874e7 | − | 1.22874e7i | 0.391491 | − | 0.391491i | −0.483727 | − | 0.875219i | \(-0.660717\pi\) |
0.875219 | + | 0.483727i | \(0.160717\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.46909e7 | 1.41679 |
(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 | 80.6.n.d.63.2 | yes | 20 | |
4.3 | odd | 2 | inner | 80.6.n.d.63.9 | yes | 20 | |
5.2 | odd | 4 | inner | 80.6.n.d.47.9 | yes | 20 | |
5.3 | odd | 4 | 400.6.n.g.207.2 | 20 | |||
5.4 | even | 2 | 400.6.n.g.143.9 | 20 | |||
20.3 | even | 4 | 400.6.n.g.207.9 | 20 | |||
20.7 | even | 4 | inner | 80.6.n.d.47.2 | ✓ | 20 | |
20.19 | odd | 2 | 400.6.n.g.143.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.n.d.47.2 | ✓ | 20 | 20.7 | even | 4 | inner | |
80.6.n.d.47.9 | yes | 20 | 5.2 | odd | 4 | inner | |
80.6.n.d.63.2 | yes | 20 | 1.1 | even | 1 | trivial | |
80.6.n.d.63.9 | yes | 20 | 4.3 | odd | 2 | inner | |
400.6.n.g.143.2 | 20 | 20.19 | odd | 2 | |||
400.6.n.g.143.9 | 20 | 5.4 | even | 2 | |||
400.6.n.g.207.2 | 20 | 5.3 | odd | 4 | |||
400.6.n.g.207.9 | 20 | 20.3 | even | 4 |