Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 1442 x^{8} + 59551 x^{7} + 2229058 x^{6} + 41253567 x^{5} + 582209889 x^{4} + \cdots + 63214027776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{9}\cdot 7^{6} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.5 | ||
Root | \(-7.84041 - 13.5800i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.73 |
Dual form | 252.9.z.c.145.5 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 951.520 | − | 549.361i | 1.52243 | − | 0.878977i | 0.522784 | − | 0.852465i | \(-0.324893\pi\) |
0.999649 | − | 0.0265117i | \(-0.00843992\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2332.69 | + | 568.626i | 0.971551 | + | 0.236829i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8373.68 | + | 14503.6i | −0.571934 | + | 0.990618i | 0.424434 | + | 0.905459i | \(0.360473\pi\) |
−0.996367 | + | 0.0851591i | \(0.972860\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 12172.5i | − | 0.426194i | −0.977031 | − | 0.213097i | \(-0.931645\pi\) | ||
0.977031 | − | 0.213097i | \(-0.0683551\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −92085.4 | − | 53165.5i | −1.10254 | − | 0.636553i | −0.165655 | − | 0.986184i | \(-0.552974\pi\) |
−0.936888 | + | 0.349631i | \(0.886307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −33869.3 | + | 19554.5i | −0.259892 | + | 0.150048i | −0.624285 | − | 0.781197i | \(-0.714610\pi\) |
0.364394 | + | 0.931245i | \(0.381276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −217614. | − | 376919.i | −0.777635 | − | 1.34690i | −0.933301 | − | 0.359094i | \(-0.883086\pi\) |
0.155666 | − | 0.987810i | \(-0.450248\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 408281. | − | 707164.i | 1.04520 | − | 1.81034i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −752691. | −1.06420 | −0.532102 | − | 0.846680i | \(-0.678598\pi\) | ||||
−0.532102 | + | 0.846680i | \(0.678598\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −611743. | − | 353190.i | −0.662403 | − | 0.382438i | 0.130789 | − | 0.991410i | \(-0.458249\pi\) |
−0.793192 | + | 0.608972i | \(0.791582\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.53199e6 | − | 740431.i | 1.68729 | − | 0.493415i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.25781e6 | − | 2.17859e6i | −0.671132 | − | 1.16244i | −0.977583 | − | 0.210549i | \(-0.932475\pi\) |
0.306451 | − | 0.951886i | \(-0.400858\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.11495e6i | − | 1.10234i | −0.834392 | − | 0.551171i | \(-0.814181\pi\) | ||
0.834392 | − | 0.551171i | \(-0.185819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65406e6 | 0.483812 | 0.241906 | − | 0.970300i | \(-0.422227\pi\) | ||||
0.241906 | + | 0.970300i | \(0.422227\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.50274e6 | + | 3.17701e6i | −1.12768 | + | 0.651069i | −0.943351 | − | 0.331795i | \(-0.892346\pi\) |
−0.184333 | + | 0.982864i | \(0.559012\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.11813e6 | + | 2.65286e6i | 0.887824 | + | 0.460183i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.79222e6 | + | 4.83627e6i | −0.353872 | + | 0.612924i | −0.986924 | − | 0.161185i | \(-0.948468\pi\) |
0.633052 | + | 0.774109i | \(0.281802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.84007e7i | 2.01087i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.66779e6 | − | 962898.i | −0.137636 | − | 0.0794643i | 0.429601 | − | 0.903019i | \(-0.358654\pi\) |
−0.567237 | + | 0.823555i | \(0.691988\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.54825e7 | − | 8.93885e6i | 1.11821 | − | 0.645598i | 0.177265 | − | 0.984163i | \(-0.443275\pi\) |
0.940943 | + | 0.338565i | \(0.109942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.68711e6 | − | 1.15824e7i | −0.374615 | − | 0.648852i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 509223. | − | 882001.i | 0.0252702 | − | 0.0437693i | −0.853114 | − | 0.521725i | \(-0.825289\pi\) |
0.878384 | + | 0.477956i | \(0.158622\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.80284e6 | −0.110297 | −0.0551486 | − | 0.998478i | \(-0.517563\pi\) | ||||
−0.0551486 | + | 0.998478i | \(0.517563\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.40868e7 | − | 8.13300e6i | −0.496044 | − | 0.286391i | 0.231035 | − | 0.972946i | \(-0.425789\pi\) |
−0.727078 | + | 0.686555i | \(0.759122\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.77804e7 | + | 2.90711e7i | −0.790270 | + | 0.826986i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.90749e7 | + | 5.03592e7i | 0.746466 | + | 1.29292i | 0.949507 | + | 0.313746i | \(0.101584\pi\) |
−0.203041 | + | 0.979170i | \(0.565083\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.45682e7i | − | 1.36053i | −0.732968 | − | 0.680263i | \(-0.761866\pi\) | ||
0.732968 | − | 0.680263i | \(-0.238134\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.16828e8 | −2.23806 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.07065e7 | − | 4.08224e7i | 1.12694 | − | 0.650637i | 0.183774 | − | 0.982969i | \(-0.441169\pi\) |
0.943163 | + | 0.332331i | \(0.107835\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.92162e6 | − | 2.83948e7i | 0.100935 | − | 0.414070i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.14849e7 | + | 3.72129e7i | −0.263778 | + | 0.456877i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.95327e7i | − | 1.12429i | −0.827038 | − | 0.562146i | \(-0.809976\pi\) | ||
0.827038 | − | 0.562146i | \(-0.190024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.72195e7 | − | 4.45827e7i | −0.742064 | − | 0.428431i | 0.0807553 | − | 0.996734i | \(-0.474267\pi\) |
−0.822819 | + | 0.568303i | \(0.807600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.19034e8 | − | 6.87243e7i | 1.05760 | − | 0.610606i | 0.132833 | − | 0.991138i | \(-0.457592\pi\) |
0.924768 | + | 0.380532i | \(0.124259\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.01907e7 | + | 3.49714e7i | 0.154034 | + | 0.266795i | 0.932707 | − | 0.360635i | \(-0.117440\pi\) |
−0.778673 | + | 0.627430i | \(0.784107\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.50017e7 | − | 6.06248e7i | 0.247961 | − | 0.429481i | −0.714999 | − | 0.699126i | \(-0.753573\pi\) |
0.962960 | + | 0.269644i | \(0.0869062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.09428e7 | 0.435105 | 0.217553 | − | 0.976049i | \(-0.430193\pi\) | ||||
0.217553 | + | 0.976049i | \(0.430193\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.14129e8 | − | 2.39097e8i | −2.36779 | − | 1.36705i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.84576e8 | − | 1.76381e8i | −0.920422 | − | 0.879558i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.30576e7 | − | 5.72574e7i | −0.154216 | − | 0.267110i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4.67987e8i | − | 1.91687i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.25545e8 | 1.25140 | 0.625701 | − | 0.780063i | \(-0.284813\pi\) | ||||
0.625701 | + | 0.780063i | \(0.284813\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.43722e7 | − | 1.40713e7i | 0.0827580 | − | 0.0477803i | −0.458050 | − | 0.888926i | \(-0.651452\pi\) |
0.540808 | + | 0.841146i | \(0.318119\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.01260e7 | + | 2.63556e7i | −0.288034 | + | 0.0842299i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.89204e8 | + | 3.27711e8i | −0.537092 | + | 0.930271i | 0.461967 | + | 0.886897i | \(0.347144\pi\) |
−0.999059 | + | 0.0433734i | \(0.986189\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.66055e8i | 0.980590i | 0.871557 | + | 0.490295i | \(0.163111\pi\) | ||||
−0.871557 | + | 0.490295i | \(0.836889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.76546e8 | + | 1.01929e8i | 0.422196 | + | 0.243755i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.16201e8 | + | 4.13499e8i | −1.62018 | + | 0.935410i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.03522e8 | − | 5.25716e8i | −0.615808 | − | 1.06661i | −0.990242 | − | 0.139358i | \(-0.955496\pi\) |
0.374434 | − | 0.927254i | \(-0.377837\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.16419e8 | − | 2.01644e8i | 0.223932 | − | 0.387862i | −0.732066 | − | 0.681233i | \(-0.761444\pi\) |
0.955999 | + | 0.293372i | \(0.0947773\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.76114e8 | −1.34462 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.35185e8 | − | 4.82194e8i | −1.37462 | − | 0.793640i | −0.383118 | − | 0.923699i | \(-0.625150\pi\) |
−0.991506 | + | 0.130060i | \(0.958483\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.93302e8 | − | 1.00298e9i | −0.436527 | − | 1.49275i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.96065e8 | + | 6.86005e8i | 0.561069 | + | 0.971800i | 0.997404 | + | 0.0720154i | \(0.0229431\pi\) |
−0.436335 | + | 0.899784i | \(0.643724\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.87494e8i | 0.369626i | 0.982774 | + | 0.184813i | \(0.0591679\pi\) | ||||
−0.982774 | + | 0.184813i | \(0.940832\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.67560e8 | 0.818359 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.55122e8 | + | 2.05030e8i | −0.396454 | + | 0.228893i | −0.684953 | − | 0.728587i | \(-0.740177\pi\) |
0.288499 | + | 0.957480i | \(0.406844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.35451e9 | − | 1.41744e9i | 1.44421 | − | 1.51130i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.85063e8 | − | 8.40154e8i | 0.472483 | − | 0.818364i | −0.527021 | − | 0.849852i | \(-0.676691\pi\) |
0.999504 | + | 0.0314879i | \(0.0100246\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.97202e8i | − | 0.276910i | −0.990369 | − | 0.138455i | \(-0.955786\pi\) | ||
0.990369 | − | 0.138455i | \(-0.0442136\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.39366e9 | − | 1.38198e9i | −2.04351 | − | 1.17982i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.54219e9 | − | 8.90383e8i | 1.26116 | − | 0.728132i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.42144e8 | − | 7.65816e8i | −0.332224 | − | 0.575428i | 0.650724 | − | 0.759314i | \(-0.274466\pi\) |
−0.982948 | + | 0.183886i | \(0.941132\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.15787e9 | + | 2.00549e9i | −0.834506 | + | 1.44541i | 0.0599252 | + | 0.998203i | \(0.480914\pi\) |
−0.894432 | + | 0.447205i | \(0.852420\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.93628e9 | 1.28559 | 0.642797 | − | 0.766036i | \(-0.277774\pi\) | ||||
0.642797 | + | 0.766036i | \(0.277774\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.76811e9 | − | 1.02082e9i | −1.12745 | − | 0.650933i | −0.184157 | − | 0.982897i | \(-0.558955\pi\) |
−0.943292 | + | 0.331964i | \(0.892289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.75580e9 | − | 4.28000e8i | −1.03393 | − | 0.252034i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.71123e9 | − | 2.96394e9i | −0.968933 | − | 1.67824i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.54971e8i | − | 0.343271i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.77399e8 | −0.341755 | −0.170877 | − | 0.985292i | \(-0.554660\pi\) | ||||
−0.170877 | + | 0.985292i | \(0.554660\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.57387e9 | − | 9.08674e8i | 0.736572 | − | 0.425260i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.22618e9 | − | 1.17174e9i | −0.552986 | − | 0.528435i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.47159e8 | + | 1.12091e9i | −0.271295 | + | 0.469897i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.59852e8i | − | 0.266826i | −0.991061 | − | 0.133413i | \(-0.957406\pi\) | ||
0.991061 | − | 0.133413i | \(-0.0425936\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.81748e9 | − | 1.04932e9i | −0.684488 | − | 0.395190i | 0.117056 | − | 0.993125i | \(-0.462654\pi\) |
−0.801544 | + | 0.597936i | \(0.795988\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.72622e9 | − | 9.96636e8i | 0.627705 | − | 0.362406i | −0.152158 | − | 0.988356i | \(-0.548622\pi\) |
0.779863 | + | 0.625951i | \(0.215289\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.79751e7 | + | 1.52377e8i | 0.0298494 | + | 0.0517007i | 0.880564 | − | 0.473927i | \(-0.157164\pi\) |
−0.850715 | + | 0.525628i | \(0.823831\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.49065e9 | + | 6.04598e9i | −1.14455 | + | 1.98242i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.35853e8 | −0.0722853 | −0.0361426 | − | 0.999347i | \(-0.511507\pi\) | ||||
−0.0361426 | + | 0.999347i | \(0.511507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.17101e9 | + | 6.76083e8i | 0.347130 | + | 0.200416i | 0.663421 | − | 0.748247i | \(-0.269104\pi\) |
−0.316290 | + | 0.948662i | \(0.602437\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.32738e9 | − | 2.87445e8i | 1.75614 | − | 0.0797793i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.38027e8 | + | 4.12275e8i | 0.0639498 | + | 0.110764i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.53179e9i | − | 0.385925i | −0.981206 | − | 0.192963i | \(-0.938190\pi\) | ||
0.981206 | − | 0.192963i | \(-0.0618096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.28893e9 | 1.77902 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.13579e9 | + | 3.54250e9i | −1.40649 | + | 0.812040i | −0.995048 | − | 0.0993948i | \(-0.968309\pi\) |
−0.411446 | + | 0.911434i | \(0.634976\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.69528e9 | − | 5.79721e9i | −0.376741 | − | 1.28831i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.07747e9 | + | 3.59828e9i | −0.434222 | + | 0.752094i | −0.997232 | − | 0.0743560i | \(-0.976310\pi\) |
0.563010 | + | 0.826450i | \(0.309643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.13574e9i | 1.24418i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.19738e9 | + | 1.26866e9i | 0.419659 | + | 0.242290i | 0.694931 | − | 0.719076i | \(-0.255435\pi\) |
−0.275272 | + | 0.961366i | \(0.588768\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.49814e9 | − | 8.64950e8i | 0.277763 | − | 0.160367i | −0.354647 | − | 0.935000i | \(-0.615399\pi\) |
0.632410 | + | 0.774634i | \(0.282066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.83764e9 | + | 1.18431e10i | 1.19557 | + | 2.07079i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.17823e9 | + | 8.96896e9i | −0.879554 | + | 1.52343i | −0.0277231 | + | 0.999616i | \(0.508826\pi\) |
−0.851831 | + | 0.523817i | \(0.824508\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.97916e9 | 1.11938 | 0.559690 | − | 0.828702i | \(-0.310920\pi\) | ||||
0.559690 | + | 0.828702i | \(0.310920\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.98236e9 | − | 2.29922e9i | −0.620861 | − | 0.358455i | 0.156343 | − | 0.987703i | \(-0.450030\pi\) |
−0.777204 | + | 0.629248i | \(0.783363\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.77125e9 | − | 7.26624e9i | 0.261066 | − | 1.07098i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.16527e9 | + | 3.75036e9i | 0.310400 | + | 0.537628i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.25131e10i | 1.69783i | 0.528531 | + | 0.848914i | \(0.322743\pi\) | ||||
−0.528531 | + | 0.848914i | \(0.677257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.11591e9 | −0.279389 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.58806e9 | + | 2.64892e9i | −0.574043 | + | 0.331424i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.85841e9 | + | 9.40541e8i | 0.470049 | + | 0.114581i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.82130e9 | − | 1.70110e10i | 1.13493 | − | 1.96576i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.27861e9i | − | 0.256517i | −0.991741 | − | 0.128258i | \(-0.959061\pi\) | ||
0.991741 | − | 0.128258i | \(-0.0409387\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.38801e9 | − | 3.11077e9i | −0.575953 | − | 0.332527i | 0.183570 | − | 0.983007i | \(-0.441234\pi\) |
−0.759523 | + | 0.650480i | \(0.774568\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.86903e9 | − | 5.69789e9i | 1.02825 | − | 0.593658i | 0.111765 | − | 0.993735i | \(-0.464350\pi\) |
0.916482 | + | 0.400076i | \(0.131016\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.63164e9 | + | 2.82609e9i | 0.161580 | + | 0.279865i | 0.935436 | − | 0.353497i | \(-0.115008\pi\) |
−0.773855 | + | 0.633362i | \(0.781674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.30279e9 | − | 1.09168e10i | 0.608654 | − | 1.05422i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.15849e9 | 0.382055 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.60798e9 | − | 4.96982e9i | −0.771557 | − | 0.445458i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.46427e10 | + | 4.28199e9i | −1.24980 | + | 0.365478i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.31434e9 | + | 9.20472e9i | 0.442729 | + | 0.766829i | 0.997891 | − | 0.0649134i | \(-0.0206771\pi\) |
−0.555162 | + | 0.831742i | \(0.687344\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.11899e9i | − | 0.0888478i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.04095e8 | −0.0235771 | −0.0117885 | − | 0.999931i | \(-0.503752\pi\) | ||||
−0.0117885 | + | 0.999931i | \(0.503752\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.02451e10 | − | 5.91500e9i | 0.757701 | − | 0.437459i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.04305e10 | + | 9.09862e9i | 0.753582 | + | 0.657354i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.60657e9 | + | 1.49070e10i | −0.593625 | + | 1.02819i | 0.400115 | + | 0.916465i | \(0.368970\pi\) |
−0.993739 | + | 0.111723i | \(0.964363\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.62412e10i | − | 1.09475i | −0.836886 | − | 0.547376i | \(-0.815627\pi\) | ||
0.836886 | − | 0.547376i | \(-0.184373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.21336e9 | + | 4.16464e9i | 0.464557 | + | 0.268212i | 0.713958 | − | 0.700188i | \(-0.246901\pi\) |
−0.249402 | + | 0.968400i | \(0.580234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.66696e9 | + | 1.53977e9i | −0.167920 | + | 0.0969486i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.18335e10 | + | 2.04963e10i | 0.712420 | + | 1.23395i | 0.963946 | + | 0.266098i | \(0.0857344\pi\) |
−0.251526 | + | 0.967851i | \(0.580932\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.72703e9 | + | 1.33836e10i | −0.454971 | + | 0.788033i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.78718e10 | −1.00692 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.71073e10 | + | 1.56504e10i | 1.49424 | + | 0.862702i | 0.999978 | − | 0.00660862i | \(-0.00210360\pi\) |
0.494266 | + | 0.869311i | \(0.335437\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.26342e9 | + | 9.69380e9i | −0.488963 | + | 0.511680i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.40622e9 | + | 5.89974e9i | 0.175969 | + | 0.304788i | 0.940496 | − | 0.339804i | \(-0.110361\pi\) |
−0.764527 | + | 0.644592i | \(0.777027\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.16215e9i | 0.453557i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.93276e9 | 0.190608 | 0.0953039 | − | 0.995448i | \(-0.469618\pi\) | ||||
0.0953039 | + | 0.995448i | \(0.469618\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.38753e10 | − | 1.37844e10i | 1.10957 | − | 0.640608i | 0.170849 | − | 0.985297i | \(-0.445349\pi\) |
0.938717 | + | 0.344689i | \(0.112016\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.04631e10 | + | 4.29232e10i | −0.476231 | + | 1.95366i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.53820e9 | + | 1.13245e10i | −0.285535 | + | 0.494562i | −0.972739 | − | 0.231903i | \(-0.925505\pi\) |
0.687204 | + | 0.726465i | \(0.258838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.62783e10i | 1.98002i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.53307e10 | + | 3.19452e10i | 2.27289 | + | 1.31225i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.20739e10 | − | 1.27443e10i | 0.888620 | − | 0.513045i | 0.0151293 | − | 0.999886i | \(-0.495184\pi\) |
0.873491 | + | 0.486840i | \(0.161851\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.61088e9 | + | 6.25423e9i | 0.139648 | + | 0.241878i | 0.927364 | − | 0.374162i | \(-0.122069\pi\) |
−0.787715 | + | 0.616040i | \(0.788736\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.29921e9 | + | 7.44646e9i | −0.162993 | + | 0.282312i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.21300e10 | 1.53537 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.57982e10 | − | 2.06681e10i | −1.27929 | − | 0.738596i | −0.302569 | − | 0.953127i | \(-0.597844\pi\) |
−0.976717 | + | 0.214531i | \(0.931178\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.34291e9 | − | 3.19449e9i | −0.114901 | − | 0.109800i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.54712e10 | − | 6.14380e10i | −1.19587 | − | 2.07131i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3.35673e10i | − | 1.08908i | −0.838735 | − | 0.544540i | \(-0.816704\pi\) | ||
0.838735 | − | 0.544540i | \(-0.183296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.07727e10 | −1.29790 | −0.648950 | − | 0.760831i | \(-0.724792\pi\) | ||||
−0.648950 | + | 0.760831i | \(0.724792\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.51936e10 | + | 4.34130e10i | −2.30476 | + | 1.33065i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.11989e10 | − | 1.20478e10i | 1.23929 | − | 0.362407i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.82732e10 | − | 4.89707e10i | 0.819344 | − | 1.41915i | −0.0868218 | − | 0.996224i | \(-0.527671\pi\) |
0.906166 | − | 0.422922i | \(-0.138996\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.51213e9i | 0.242151i | 0.992643 | + | 0.121076i | \(0.0386343\pi\) | ||||
−0.992643 | + | 0.121076i | \(0.961366\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.47409e10 | + | 8.51066e9i | 0.404202 | + | 0.233366i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.55373e10 | + | 8.97044e9i | −0.418328 | + | 0.241522i | −0.694362 | − | 0.719626i | \(-0.744313\pi\) |
0.276034 | + | 0.961148i | \(0.410980\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.16407e10 | − | 2.01623e10i | −0.302249 | − | 0.523511i | 0.674396 | − | 0.738370i | \(-0.264404\pi\) |
−0.976645 | + | 0.214859i | \(0.931071\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.48525e10 | − | 7.76867e10i | 1.14379 | − | 1.98110i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.92327e10 | −1.45739 | −0.728695 | − | 0.684838i | \(-0.759873\pi\) | ||||
−0.728695 | + | 0.684838i | \(0.759873\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.51782e10 | + | 2.60836e10i | 1.09200 | + | 0.630466i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.01292e9 | − | 3.08207e10i | −0.210291 | − | 0.719113i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.43452e10 | − | 5.94876e10i | −0.787411 | − | 1.36384i | −0.927548 | − | 0.373703i | \(-0.878088\pi\) |
0.140137 | − | 0.990132i | \(-0.455246\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.73123e10i | − | 0.604721i | −0.953194 | − | 0.302360i | \(-0.902225\pi\) | ||
0.953194 | − | 0.302360i | \(-0.0977746\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.67622e10 | −1.45280 | −0.726401 | − | 0.687271i | \(-0.758809\pi\) | ||||
−0.726401 | + | 0.687271i | \(0.758809\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.04633e10 | − | 6.04097e9i | 0.219988 | − | 0.127010i | −0.385956 | − | 0.922517i | \(-0.626129\pi\) |
0.605945 | + | 0.795507i | \(0.292795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.68939e9 | − | 1.76788e9i | 0.0349172 | − | 0.0365394i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.38506e10 | + | 2.39899e10i | −0.276709 | + | 0.479273i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.19349e10i | 0.627323i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.50748e10 | − | 2.02504e10i | −0.666274 | − | 0.384673i | 0.128390 | − | 0.991724i | \(-0.459019\pi\) |
−0.794663 | + | 0.607051i | \(0.792353\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.65190e10 | + | 1.53107e10i | −0.495423 | + | 0.286033i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.46793e10 | − | 9.47074e10i | −0.988226 | − | 1.71166i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.41202e10 | − | 7.64184e10i | 0.784370 | − | 1.35857i | −0.145004 | − | 0.989431i | \(-0.546319\pi\) |
0.929374 | − | 0.369138i | \(-0.120347\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.36572e10 | 0.407040 | 0.203520 | − | 0.979071i | \(-0.434762\pi\) | ||||
0.203520 | + | 0.979071i | \(0.434762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.93119e10 | + | 4.00172e10i | 1.17333 | + | 0.677422i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.53816e9 | − | 1.59377e9i | −0.107159 | − | 0.0261216i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.22878e10 | + | 2.12831e10i | 0.198186 | + | 0.343268i | 0.947940 | − | 0.318448i | \(-0.103162\pi\) |
−0.749754 | + | 0.661716i | \(0.769828\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.06519e10i | 0.947485i | 0.880663 | + | 0.473743i | \(0.157097\pi\) | ||||
−0.880663 | + | 0.473743i | \(0.842903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.79679e10 | −1.50632 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.13327e10 | + | 6.54296e9i | −0.168835 | + | 0.0974772i | −0.582037 | − | 0.813163i | \(-0.697744\pi\) |
0.413201 | + | 0.910640i | \(0.364411\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.82355e10 | − | 2.69819e10i | −0.414106 | − | 0.395721i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.55088e10 | − | 1.30785e11i | 1.07342 | − | 1.85921i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.06413e11i | − | 1.48947i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.34178e10 | − | 1.92938e10i | −0.453552 | − | 0.261859i | 0.255777 | − | 0.966736i | \(-0.417669\pi\) |
−0.709329 | + | 0.704877i | \(0.751002\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.72278e10 | + | 9.94646e9i | −0.230262 | + | 0.132942i | −0.610693 | − | 0.791867i | \(-0.709109\pi\) |
0.380431 | + | 0.924809i | \(0.375776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.75551e10 | + | 6.50473e10i | 0.486885 | + | 0.843309i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.55564e10 | + | 9.62266e10i | −0.709434 | + | 1.22877i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.79169e10 | −0.469812 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.84238e10 | + | 2.21840e10i | 0.469013 | + | 0.270785i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.13338e10 | + | 5.20173e10i | −0.963642 | + | 0.616300i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.36734e10 | + | 5.83241e10i | 0.393096 | + | 0.680862i | 0.992856 | − | 0.119318i | \(-0.0380707\pi\) |
−0.599760 | + | 0.800180i | \(0.704737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7.69143e10i | − | 0.871808i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.19574e10 | 0.915459 | 0.457730 | − | 0.889091i | \(-0.348663\pi\) | ||||
0.457730 | + | 0.889091i | \(0.348663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.54931e10 | − | 1.47185e10i | 0.276577 | − | 0.159682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.91873e10 | + | 1.34005e11i | 0.419030 | + | 1.43292i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.06558e8 | + | 1.05059e9i | −0.00630161 | + | 0.0109147i | −0.869159 | − | 0.494533i | \(-0.835339\pi\) |
0.862857 | + | 0.505447i | \(0.168673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.01341e10i | − | 0.206198i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.65134e10 | − | 1.53075e10i | −0.263895 | − | 0.152360i | 0.362215 | − | 0.932095i | \(-0.382021\pi\) |
−0.626110 | + | 0.779735i | \(0.715354\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.75035e10 | − | 3.89732e10i | 0.662419 | − | 0.382448i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.55965e10 | + | 2.70139e10i | 0.148791 | + | 0.257714i | 0.930781 | − | 0.365577i | \(-0.119128\pi\) |
−0.781990 | + | 0.623291i | \(0.785795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.85497e9 | + | 1.70693e10i | −0.0927066 | + | 0.160573i | −0.908649 | − | 0.417560i | \(-0.862885\pi\) |
0.815943 | + | 0.578133i | \(0.196219\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.55391e11 | −3.25114 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.34009e9 | − | 1.92840e9i | −0.0301339 | − | 0.0173978i | 0.484857 | − | 0.874593i | \(-0.338872\pi\) |
−0.514991 | + | 0.857195i | \(0.672205\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.67152e10 | − | 1.50618e11i | 0.322212 | − | 1.32182i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.67623e10 | − | 8.09947e10i | −0.404782 | − | 0.701104i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3.81949e10i | − | 0.321701i | −0.986979 | − | 0.160851i | \(-0.948576\pi\) | ||
0.986979 | − | 0.160851i | \(-0.0514238\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.76257e10 | 0.229537 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.00185e11 | + | 5.78419e10i | −0.810186 | + | 0.467761i | −0.847020 | − | 0.531561i | \(-0.821606\pi\) |
0.0368348 | + | 0.999321i | \(0.488272\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.72525e11 | − | 6.64316e10i | −2.17439 | − | 0.530038i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.59567e10 | − | 1.14240e11i | 0.512332 | − | 0.887385i | −0.487566 | − | 0.873086i | \(-0.662115\pi\) |
0.999898 | − | 0.0142987i | \(-0.00455158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 5.94719e10i | − | 0.455842i | −0.973680 | − | 0.227921i | \(-0.926807\pi\) | ||
0.973680 | − | 0.227921i | \(-0.0731927\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.29100e10 | − | 3.63211e10i | −0.469567 | − | 0.271105i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.36055e10 | − | 3.09492e10i | 0.394871 | − | 0.227979i | −0.289398 | − | 0.957209i | \(-0.593455\pi\) |
0.684268 | + | 0.729230i | \(0.260122\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.86722e10 | + | 6.69823e10i | 0.277482 | + | 0.480612i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.56037e9 | + | 1.30949e10i | −0.0535428 | + | 0.0927389i | −0.891555 | − | 0.452913i | \(-0.850385\pi\) |
0.838012 | + | 0.545652i | \(0.183718\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.79329e10 | 0.606752 | 0.303376 | − | 0.952871i | \(-0.401886\pi\) | ||||
0.303376 | + | 0.952871i | \(0.401886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.53923e10 | − | 3.19807e10i | −0.377300 | − | 0.217834i | 0.299343 | − | 0.954146i | \(-0.403233\pi\) |
−0.676643 | + | 0.736311i | \(0.736566\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.88149e11 | − | 5.50207e10i | 1.24897 | − | 0.365236i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.76086e10 | − | 1.69063e11i | −0.639688 | − | 1.10797i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.67489e11i | 1.70885i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.11045e11 | 0.700454 | 0.350227 | − | 0.936665i | \(-0.386104\pi\) | ||||
0.350227 | + | 0.936665i | \(0.386104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.09763e11 | − | 1.78842e11i | 1.90517 | − | 1.09995i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.22921e10 | − | 6.23006e10i | 0.196127 | − | 0.378385i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.52383e10 | + | 9.56756e10i | −0.327196 | + | 0.566721i | −0.981954 | − | 0.189118i | \(-0.939437\pi\) |
0.654758 | + | 0.755838i | \(0.272770\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.07943e11i | − | 0.631469i | −0.948848 | − | 0.315734i | \(-0.897749\pi\) | ||
0.948848 | − | 0.315734i | \(-0.102251\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.24745e11 | + | 7.20218e10i | 0.711881 | + | 0.411005i | 0.811757 | − | 0.583995i | \(-0.198511\pi\) |
−0.0998760 | + | 0.995000i | \(0.531845\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.79310e10 | − | 1.61260e10i | 0.157438 | − | 0.0908966i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.54870e11 | − | 2.68242e11i | −0.851754 | − | 1.47528i | −0.879624 | − | 0.475669i | \(-0.842206\pi\) |
0.0278708 | − | 0.999612i | \(-0.491127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.54604e10 | − | 2.67783e10i | 0.0839956 | − | 0.145485i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.36428e11 | 0.723374 | 0.361687 | − | 0.932300i | \(-0.382201\pi\) | ||||
0.361687 | + | 0.932300i | \(0.382201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.59491e11 | − | 9.20825e10i | −0.835472 | − | 0.482360i | 0.0202508 | − | 0.999795i | \(-0.493554\pi\) |
−0.855722 | + | 0.517435i | \(0.826887\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.12780e10 | + | 7.45895e10i | −0.364476 | + | 0.381409i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.63796e11 | + | 2.83704e11i | 0.827562 | + | 1.43338i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.99404e11i | 1.47696i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.79758e11 | −1.36371 | −0.681855 | − | 0.731488i | \(-0.738826\pi\) | ||||
−0.681855 | + | 0.731488i | \(0.738826\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.08685e11 | − | 1.20484e11i | 0.993427 | − | 0.573555i | 0.0871301 | − | 0.996197i | \(-0.472230\pi\) |
0.906297 | + | 0.422642i | \(0.138897\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.65969e10 | − | 2.32179e11i | 0.266265 | − | 1.09231i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.47119e10 | + | 7.74434e10i | −0.205466 | + | 0.355878i | −0.950281 | − | 0.311393i | \(-0.899204\pi\) |
0.744815 | + | 0.667271i | \(0.232538\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.15765e11i | 1.88837i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.88696e10 | + | 3.39884e10i | 0.261225 | + | 0.150818i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.31870e10 | − | 4.22545e10i | 0.321012 | − | 0.185337i | −0.330831 | − | 0.943690i | \(-0.607329\pi\) |
0.651844 | + | 0.758353i | \(0.273996\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.01096e11 | + | 3.48309e11i | 0.861916 | + | 1.49288i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.65608e11 | + | 2.86842e11i | −0.701699 | + | 1.21538i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.62284e10 | −0.150029 | −0.0750147 | − | 0.997182i | \(-0.523900\pi\) | ||||
−0.0750147 | + | 0.997182i | \(0.523900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.52024e10 | + | 4.91916e10i | 0.348843 | + | 0.201405i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.54779e11 | − | 1.47907e11i | −0.619488 | − | 0.591985i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.38422e11 | + | 4.12960e11i | 0.943544 | + | 1.63427i | 0.758641 | + | 0.651509i | \(0.225864\pi\) |
0.184903 | + | 0.982757i | \(0.440803\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.07437e11i | 1.18959i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.23983e11 | 0.857019 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.84901e10 | + | 2.22223e10i | −0.144024 | + | 0.0831520i | −0.570280 | − | 0.821450i | \(-0.693165\pi\) |
0.426257 | + | 0.904602i | \(0.359832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.16748e11 | − | 9.26269e10i | 1.17212 | − | 0.342765i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.07310e11 | + | 5.32276e11i | −1.11231 | + | 1.92657i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.67401e11i | 0.957249i | 0.878020 | + | 0.478624i | \(0.158864\pi\) | ||||
−0.878020 | + | 0.478624i | \(0.841136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.52315e11 | − | 8.79389e10i | −0.533424 | − | 0.307972i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.03305e11 | − | 1.17378e11i | 0.704257 | − | 0.406603i | −0.104674 | − | 0.994507i | \(-0.533380\pi\) |
0.808931 | + | 0.587903i | \(0.200047\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.52815e9 | + | 1.47712e10i | 0.0289058 | + | 0.0500663i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.82037e10 | − | 8.34913e10i | 0.161623 | − | 0.279939i | −0.773828 | − | 0.633396i | \(-0.781660\pi\) |
0.935451 | + | 0.353457i | \(0.114994\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.45547e11 | 1.79010 | 0.895049 | − | 0.445967i | \(-0.147140\pi\) | ||||
0.895049 | + | 0.445967i | \(0.147140\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.77615e11 | − | 3.33486e11i | −1.87505 | − | 1.08256i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.72132e10 | + | 9.30585e10i | 0.0864673 | + | 0.295685i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.58934e11 | + | 4.48487e11i | 0.814009 | + | 1.40990i | 0.910037 | + | 0.414526i | \(0.136053\pi\) |
−0.0960283 | + | 0.995379i | \(0.530614\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.55824e11i | − | 0.787324i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.93020e10 | 0.241491 | 0.120745 | − | 0.992684i | \(-0.461472\pi\) | ||||
0.120745 | + | 0.992684i | \(0.461472\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.52930e11 | − | 1.46029e11i | 0.754158 | − | 0.435413i | −0.0730362 | − | 0.997329i | \(-0.523269\pi\) |
0.827194 | + | 0.561916i | \(0.189936\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.16121e11 | − | 1.21516e11i | 0.342620 | − | 0.358539i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.17209e10 | + | 2.03012e10i | −0.0338672 | + | 0.0586598i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.74868e11i | 1.07195i | 0.844235 | + | 0.535973i | \(0.180055\pi\) | ||||
−0.844235 | + | 0.535973i | \(0.819945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.87493e10 | + | 4.54659e10i | 0.220561 | + | 0.127341i | 0.606210 | − | 0.795305i | \(-0.292689\pi\) |
−0.385649 | + | 0.922646i | \(0.626022\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.99526e11 | + | 2.88402e11i | −1.38469 | + | 0.799449i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.09113e10 | + | 1.05501e11i | 0.165405 | + | 0.286489i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.34701e10 | − | 4.06513e10i | 0.0630826 | − | 0.109262i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.05959e12 | −2.79036 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.02936e11 | + | 2.90370e11i | 1.31103 | + | 0.756925i | 0.982267 | − | 0.187487i | \(-0.0600342\pi\) |
0.328765 | + | 0.944412i | \(0.393367\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.65488e11 | + | 4.03399e10i | 0.422727 | + | 0.103046i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.08808e11 | − | 1.88462e11i | −0.275150 | − | 0.476574i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.24466e11i | 0.308473i | 0.988034 | + | 0.154237i | \(0.0492918\pi\) | ||||
−0.988034 | + | 0.154237i | \(0.950708\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.75629e11 | 1.65776 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.35916e11 | − | 1.36206e11i | 0.567408 | − | 0.327593i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.30079e11 | − | 7.93226e11i | −1.97668 | − | 1.88892i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.43040e11 | − | 2.47752e11i | 0.333936 | − | 0.578393i | −0.649344 | − | 0.760495i | \(-0.724957\pi\) |
0.983280 | + | 0.182101i | \(0.0582899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.88700e11i | − | 0.436203i | −0.975926 | − | 0.218101i | \(-0.930014\pi\) | ||
0.975926 | − | 0.218101i | \(-0.0699864\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.53728e11 | + | 4.35165e11i | 1.70838 | + | 0.986333i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.60218e10 | + | 3.23442e10i | −0.125739 | + | 0.0725953i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.55431e7 | − | 2.69215e7i | −3.42110e−5 | − | 5.92552e-5i | 0.866008 | − | 0.500030i | \(-0.166678\pi\) |
−0.866043 | + | 0.499970i | \(0.833344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.17131e11 | − | 7.22493e11i | 0.909229 | − | 1.57483i | 0.0940919 | − | 0.995564i | \(-0.470005\pi\) |
0.815137 | − | 0.579268i | \(-0.196661\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.64694e11 | 0.993447 | 0.496723 | − | 0.867909i | \(-0.334536\pi\) | ||||
0.496723 | + | 0.867909i | \(0.334536\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.04849e11 | − | 6.05349e10i | −0.221997 | − | 0.128170i | 0.384877 | − | 0.922968i | \(-0.374244\pi\) |
−0.606875 | + | 0.794797i | \(0.707577\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.30264e11 | − | 5.16398e11i | −0.685933 | − | 1.07252i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.57938e11 | + | 2.73556e11i | 0.324893 | + | 0.562731i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.96352e11i | 0.799895i | 0.916538 | + | 0.399947i | \(0.130972\pi\) | ||||
−0.916538 | + | 0.399947i | \(0.869028\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.62974e10 | 0.132529 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.35197e11 | − | 3.66731e11i | 1.24590 | − | 0.719318i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.45552e10 | − | 1.52362e11i | −0.0865695 | − | 0.296034i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.47435e11 | + | 9.48185e11i | −1.04379 | + | 1.80790i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.52086e11i | 1.60949i | 0.593624 | + | 0.804743i | \(0.297697\pi\) | ||||
−0.593624 | + | 0.804743i | \(0.702303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.09148e10 | + | 2.93957e10i | 0.0943889 | + | 0.0544955i | 0.546451 | − | 0.837491i | \(-0.315978\pi\) |
−0.452063 | + | 0.891986i | \(0.649312\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.19057e10 | + | 4.72883e10i | −0.150432 | + | 0.0868522i | −0.573327 | − | 0.819327i | \(-0.694347\pi\) |
0.422894 | + | 0.906179i | \(0.361014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.19265e10 | − | 1.07260e11i | −0.111643 | − | 0.193372i | 0.804790 | − | 0.593560i | \(-0.202278\pi\) |
−0.916433 | + | 0.400188i | \(0.868945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.25270e11 | + | 3.90180e11i | −0.402383 | + | 0.696947i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.73856e11 | −1.70772 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.07362e10 | − | 6.19854e9i | −0.0186542 | − | 0.0107700i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.66110e11 | − | 1.09167e12i | 0.453971 | − | 1.86234i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.14086e11 | − | 7.17218e11i | −0.699991 | − | 1.21242i | −0.968469 | − | 0.249134i | \(-0.919854\pi\) |
0.268478 | − | 0.963286i | \(-0.413479\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.49040e11i | 1.07738i | 0.842505 | + | 0.538689i | \(0.181080\pi\) | ||||
−0.842505 | + | 0.538689i | \(0.818920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.91705e11 | −0.644341 | −0.322171 | − | 0.946682i | \(-0.604413\pi\) | ||||
−0.322171 | + | 0.946682i | \(0.604413\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.35609e11 | + | 2.51499e11i | −0.703723 | + | 0.406295i | −0.808733 | − | 0.588176i | \(-0.799846\pi\) |
0.105009 | + | 0.994471i | \(0.466513\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.59398e11 | + | 1.85114e11i | 1.21580 | + | 0.296368i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.24249e11 | − | 2.15206e11i | 0.195384 | − | 0.338414i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.06590e12i | − | 1.66121i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.60453e11 | + | 2.65843e11i | 0.704931 | + | 0.406992i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.14245e11 | − | 2.96900e11i | 0.780317 | − | 0.450516i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.63271e11 | − | 2.82794e11i | −0.243397 | − | 0.421576i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.50039e11 | + | 4.33081e11i | −0.369470 | + | 0.639941i | −0.989483 | − | 0.144651i | \(-0.953794\pi\) |
0.620013 | + | 0.784592i | \(0.287127\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.21913e12 | −1.77002 | −0.885008 | − | 0.465576i | \(-0.845847\pi\) | ||||
−0.885008 | + | 0.465576i | \(0.845847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.36475e11 | + | 5.40674e11i | 1.34776 | + | 0.778130i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.48543e10 | − | 1.89654e10i | 0.0917194 | − | 0.0268216i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.75579e11 | + | 3.04112e11i | 0.246156 | + | 0.426355i | 0.962456 | − | 0.271438i | \(-0.0874990\pi\) |
−0.716300 | + | 0.697793i | \(0.754166\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.41176e10i | 0.0470080i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.05416e12 | −2.80587 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.75423e11 | − | 5.05426e11i | 1.17532 | − | 0.678570i | 0.220390 | − | 0.975412i | \(-0.429267\pi\) |
0.954927 | + | 0.296842i | \(0.0959335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.25223e11 | + | 1.02316e10i | −0.299788 | + | 0.0136190i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.78282e11 | − | 1.69443e12i | 1.28002 | − | 2.21706i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.93644e11i | − | 0.640406i | −0.947349 | − | 0.320203i | \(-0.896249\pi\) | ||
0.947349 | − | 0.320203i | \(-0.103751\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.43259e11 | − | 2.55916e11i | −0.565326 | − | 0.326391i | 0.189954 | − | 0.981793i | \(-0.439166\pi\) |
−0.755281 | + | 0.655402i | \(0.772499\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.17409e12 | + | 6.77858e11i | −1.48475 | + | 0.857220i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.79118e11 | − | 3.10242e11i | −0.222710 | − | 0.385745i | 0.732920 | − | 0.680315i | \(-0.238157\pi\) |
−0.955630 | + | 0.294570i | \(0.904824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.89992e10 | + | 1.71472e11i | −0.122058 | + | 0.211411i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.04177e11 | 0.611240 | 0.305620 | − | 0.952154i | \(-0.401136\pi\) | ||||
0.305620 | + | 0.952154i | \(0.401136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.41419e11 | − | 4.85793e11i | −1.01158 | − | 0.584034i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.27701e11 | + | 6.56864e11i | −0.742127 | + | 0.776607i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.76959e11 | − | 3.06503e11i | −0.207482 | − | 0.359369i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.54435e12i | 2.93405i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.60109e11 | −0.297475 | −0.148737 | − | 0.988877i | \(-0.547521\pi\) | ||||
−0.148737 | + | 0.988877i | \(0.547521\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.07503e11 | − | 2.93007e11i | 0.570902 | − | 0.329610i | −0.186607 | − | 0.982435i | \(-0.559749\pi\) |
0.757510 | + | 0.652824i | \(0.226416\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.08149e11 | + | 8.53895e11i | −0.232232 | + | 0.952694i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.83365e11 | − | 4.90803e11i | 0.311006 | − | 0.538678i | −0.667575 | − | 0.744543i | \(-0.732668\pi\) |
0.978580 | + | 0.205865i | \(0.0660009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.36734e12i | 1.48848i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.92810e11 | − | 3.42259e11i | −0.634894 | − | 0.366556i | 0.147751 | − | 0.989025i | \(-0.452797\pi\) |
−0.782645 | + | 0.622468i | \(0.786130\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.84241e12 | − | 1.06372e12i | 1.95723 | − | 1.13001i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.59947e11 | − | 6.23446e11i | −0.376230 | − | 0.651649i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.56595e11 | − | 1.65687e12i | 0.991822 | − | 1.71789i | 0.385381 | − | 0.922758i | \(-0.374070\pi\) |
0.606441 | − | 0.795128i | \(-0.292596\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.24319e12 | −2.28862 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.28100e12 | + | 7.39588e11i | 1.29649 | + | 0.748530i | 0.979796 | − | 0.199998i | \(-0.0640935\pi\) |
0.316695 | + | 0.948527i | \(0.397427\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.z.c.73.5 | 10 | ||
3.2 | odd | 2 | 28.9.h.a.17.1 | yes | 10 | ||
7.5 | odd | 6 | inner | 252.9.z.c.145.5 | 10 | ||
12.11 | even | 2 | 112.9.s.b.17.5 | 10 | |||
21.2 | odd | 6 | 196.9.h.a.117.5 | 10 | |||
21.5 | even | 6 | 28.9.h.a.5.1 | ✓ | 10 | ||
21.11 | odd | 6 | 196.9.b.a.97.10 | 10 | |||
21.17 | even | 6 | 196.9.b.a.97.1 | 10 | |||
21.20 | even | 2 | 196.9.h.a.129.5 | 10 | |||
84.47 | odd | 6 | 112.9.s.b.33.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.9.h.a.5.1 | ✓ | 10 | 21.5 | even | 6 | ||
28.9.h.a.17.1 | yes | 10 | 3.2 | odd | 2 | ||
112.9.s.b.17.5 | 10 | 12.11 | even | 2 | |||
112.9.s.b.33.5 | 10 | 84.47 | odd | 6 | |||
196.9.b.a.97.1 | 10 | 21.17 | even | 6 | |||
196.9.b.a.97.10 | 10 | 21.11 | odd | 6 | |||
196.9.h.a.117.5 | 10 | 21.2 | odd | 6 | |||
196.9.h.a.129.5 | 10 | 21.20 | even | 2 | |||
252.9.z.c.73.5 | 10 | 1.1 | even | 1 | trivial | ||
252.9.z.c.145.5 | 10 | 7.5 | odd | 6 | inner |