Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,12,Mod(37,252)]
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, 2]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), 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: | \(193.622481501\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{42}\cdot 3^{15}\cdot 7^{9} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.5 | ||
Root | \(2396.04 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.109 |
Dual form | 252.12.k.d.37.5 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 1332.77 | + | 2308.42i | 0.190730 | + | 0.330355i | 0.945492 | − | 0.325644i | \(-0.105581\pi\) |
−0.754762 | + | 0.655999i | \(0.772248\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 43648.5 | + | 8493.30i | 0.981590 | + | 0.191002i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −262991. | + | 455515.i | −0.492359 | + | 0.852791i | −0.999961 | − | 0.00880080i | \(-0.997199\pi\) |
0.507602 | + | 0.861591i | \(0.330532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.10180e6 | −0.823024 | −0.411512 | − | 0.911404i | \(-0.634999\pi\) | ||||
−0.411512 | + | 0.911404i | \(0.634999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 222021. | − | 384552.i | 0.0379250 | − | 0.0656880i | −0.846440 | − | 0.532484i | \(-0.821259\pi\) |
0.884365 | + | 0.466796i | \(0.154592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.58519e6 | − | 2.74562e6i | −0.146871 | − | 0.254388i | 0.783199 | − | 0.621772i | \(-0.213587\pi\) |
−0.930069 | + | 0.367384i | \(0.880253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.38816e7 | − | 4.13641e7i | −0.773677 | − | 1.34005i | −0.935535 | − | 0.353234i | \(-0.885082\pi\) |
0.161857 | − | 0.986814i | \(-0.448252\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.08615e7 | − | 3.61332e7i | 0.427244 | − | 0.740008i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.65232e8 | 1.49591 | 0.747954 | − | 0.663750i | \(-0.231036\pi\) | ||||
0.747954 | + | 0.663750i | \(0.231036\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.05562e7 | + | 1.39527e8i | −0.505370 | + | 0.875327i | 0.494611 | + | 0.869115i | \(0.335311\pi\) |
−0.999981 | + | 0.00621203i | \(0.998023\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.85672e7 | + | 1.12079e8i | 0.124121 | + | 0.360703i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.73311e8 | − | 3.00184e8i | −0.410882 | − | 0.711669i | 0.584104 | − | 0.811679i | \(-0.301446\pi\) |
−0.994986 | + | 0.100010i | \(0.968113\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.07369e9 | 1.44734 | 0.723668 | − | 0.690148i | \(-0.242455\pi\) | ||||
0.723668 | + | 0.690148i | \(0.242455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.10803e9 | 1.14941 | 0.574706 | − | 0.818360i | \(-0.305117\pi\) | ||||
0.574706 | + | 0.818360i | \(0.305117\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.49033e7 | + | 7.77748e7i | 0.0285588 | + | 0.0494653i | 0.879952 | − | 0.475063i | \(-0.157575\pi\) |
−0.851393 | + | 0.524529i | \(0.824242\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.83305e9 | + | 7.41439e8i | 0.927037 | + | 0.374970i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.97953e8 | + | 3.42864e8i | −0.0650196 | + | 0.112617i | −0.896703 | − | 0.442633i | \(-0.854044\pi\) |
0.831683 | + | 0.555251i | \(0.187378\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.40203e9 | −0.375631 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.65401e9 | + | 6.32894e9i | −0.665402 | + | 1.15251i | 0.313774 | + | 0.949498i | \(0.398407\pi\) |
−0.979176 | + | 0.203012i | \(0.934927\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.05057e9 | − | 1.04799e10i | −0.917238 | − | 1.58870i | −0.803591 | − | 0.595182i | \(-0.797080\pi\) |
−0.113647 | − | 0.993521i | \(-0.536253\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.46844e9 | − | 2.54341e9i | −0.156976 | − | 0.271890i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.63592e9 | − | 1.49578e10i | 0.781442 | − | 1.35350i | −0.149659 | − | 0.988738i | \(-0.547818\pi\) |
0.931101 | − | 0.364760i | \(-0.118849\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.31065e10 | 0.862113 | 0.431056 | − | 0.902325i | \(-0.358141\pi\) | ||||
0.431056 | + | 0.902325i | \(0.358141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.39348e9 | + | 1.28059e10i | −0.417420 | + | 0.722993i | −0.995679 | − | 0.0928606i | \(-0.970399\pi\) |
0.578259 | + | 0.815853i | \(0.303732\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.53480e10 | + | 1.76489e10i | −0.646179 | + | 0.743049i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.45406e10 | − | 2.51850e10i | −0.531658 | − | 0.920859i | −0.999317 | − | 0.0369500i | \(-0.988236\pi\) |
0.467659 | − | 0.883909i | \(-0.345098\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.43778e9 | −0.0679305 | −0.0339652 | − | 0.999423i | \(-0.510814\pi\) | ||||
−0.0339652 | + | 0.999423i | \(0.510814\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18361e9 | 0.0289338 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.46315e10 | + | 7.73040e10i | 0.847220 | + | 1.46743i | 0.883679 | + | 0.468094i | \(0.155059\pi\) |
−0.0364584 | + | 0.999335i | \(0.511608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.80917e10 | − | 9.35787e9i | −0.807872 | − | 0.157199i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.22537e9 | − | 7.31856e9i | 0.0560254 | − | 0.0970389i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.63296e10 | 0.784265 | 0.392132 | − | 0.919909i | \(-0.371738\pi\) | ||||
0.392132 | + | 0.919909i | \(0.371738\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.40959e10 | + | 2.44149e10i | −0.133452 | + | 0.231146i | −0.925005 | − | 0.379954i | \(-0.875940\pi\) |
0.791553 | + | 0.611101i | \(0.209273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.47509e10 | − | 1.29472e11i | −0.635348 | − | 1.10045i | −0.986441 | − | 0.164114i | \(-0.947523\pi\) |
0.351093 | − | 0.936340i | \(-0.385810\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.31786e11 | + | 2.28259e11i | 0.908358 | + | 1.57332i | 0.816345 | + | 0.577564i | \(0.195997\pi\) |
0.0920128 | + | 0.995758i | \(0.470670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.35713e10 | − | 4.08266e10i | 0.146736 | − | 0.254155i | −0.783283 | − | 0.621665i | \(-0.786456\pi\) |
0.930019 | + | 0.367511i | \(0.119790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.07560e10 | −0.361270 | −0.180635 | − | 0.983550i | \(-0.557815\pi\) | ||||
−0.180635 | + | 0.983550i | \(0.557815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.36572e10 | − | 1.10258e11i | 0.295128 | − | 0.511176i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.29570e10 | − | 1.48994e10i | 0.0497733 | − | 0.0572350i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.32686e9 | + | 7.49434e9i | 0.0151654 | + | 0.0262672i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.41368e11 | 0.707414 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.35541e10 | −0.251271 | −0.125635 | − | 0.992076i | \(-0.540097\pi\) | ||||
−0.125635 | + | 0.992076i | \(0.540097\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.03929e10 | − | 5.26420e10i | −0.0688303 | − | 0.119218i | 0.829556 | − | 0.558423i | \(-0.188593\pi\) |
−0.898387 | + | 0.439205i | \(0.855260\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.58716e10 | − | 1.33306e11i | −0.0955784 | − | 0.277757i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.72230e11 | + | 2.98311e11i | −0.304891 | + | 0.528087i | −0.977237 | − | 0.212150i | \(-0.931954\pi\) |
0.672346 | + | 0.740237i | \(0.265287\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.54339e11 | 0.579211 | 0.289606 | − | 0.957146i | \(-0.406476\pi\) | ||||
0.289606 | + | 0.957146i | \(0.406476\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.89763e11 | − | 5.01884e11i | 0.405223 | − | 0.701867i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.20216e11 | + | 3.81425e11i | 0.285315 | + | 0.494180i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.87394e11 | − | 3.24576e11i | −0.209041 | − | 0.362069i | 0.742372 | − | 0.669988i | \(-0.233701\pi\) |
−0.951413 | + | 0.307919i | \(0.900368\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.29692e11 | + | 3.97838e11i | −0.238107 | + | 0.412413i | −0.960171 | − | 0.279413i | \(-0.909860\pi\) |
0.722064 | + | 0.691826i | \(0.243194\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.29451e11 | −0.385558 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.37048e11 | + | 1.10340e12i | −0.532996 | + | 0.923176i | 0.466261 | + | 0.884647i | \(0.345601\pi\) |
−0.999257 | + | 0.0385292i | \(0.987733\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.91077e11 | − | 2.00831e12i | −0.503482 | − | 1.46315i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.84049e11 | + | 1.53122e12i | 0.601790 | + | 1.04233i | 0.992550 | + | 0.121838i | \(0.0388787\pi\) |
−0.390761 | + | 0.920492i | \(0.627788\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.36833e12 | 0.815174 | 0.407587 | − | 0.913166i | \(-0.366370\pi\) | ||||
0.407587 | + | 0.913166i | \(0.366370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.78208e11 | −0.322632 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.14381e12 | + | 1.98114e12i | 0.561179 | + | 0.971990i | 0.997394 | + | 0.0721478i | \(0.0229853\pi\) |
−0.436215 | + | 0.899842i | \(0.643681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.21746e12 | − | 1.39998e12i | 0.560721 | − | 0.644780i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.28321e12 | − | 2.22258e12i | 0.521922 | − | 0.903995i | −0.477753 | − | 0.878494i | \(-0.658549\pi\) |
0.999675 | − | 0.0255010i | \(-0.00811811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.37998e12 | 1.67587 | 0.837934 | − | 0.545771i | \(-0.183763\pi\) | ||||
0.837934 | + | 0.545771i | \(0.183763\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.61968e11 | − | 8.00152e11i | 0.156735 | − | 0.271474i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.16779e11 | + | 2.02268e11i | 0.0373454 | + | 0.0646842i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.48818e10 | + | 1.47020e11i | 0.0241619 | + | 0.0418496i | 0.877854 | − | 0.478929i | \(-0.158975\pi\) |
−0.853692 | + | 0.520779i | \(0.825642\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.61580e11 | + | 2.79865e11i | −0.0434333 | + | 0.0752286i | −0.886925 | − | 0.461914i | \(-0.847163\pi\) |
0.843492 | + | 0.537142i | \(0.180496\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.26787e11 | −0.198531 | −0.0992657 | − | 0.995061i | \(-0.531649\pi\) | ||||
−0.0992657 | + | 0.995061i | \(0.531649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.12706e12 | + | 3.68418e12i | −0.483157 | + | 0.836853i | −0.999813 | − | 0.0193401i | \(-0.993843\pi\) |
0.516656 | + | 0.856193i | \(0.327177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.21213e12 | + | 1.40336e12i | 1.46837 | + | 0.285721i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.43099e12 | + | 2.47854e12i | 0.276051 | + | 0.478134i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.66756e12 | 0.289253 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.58675e12 | 1.08422 | 0.542110 | − | 0.840307i | \(-0.317626\pi\) | ||||
0.542110 | + | 0.840307i | \(0.317626\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.47675e12 | + | 2.55780e12i | 0.219228 | + | 0.379713i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.70120e12 | + | 5.40597e12i | −0.663255 | + | 0.762685i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.44622e11 | + | 4.23698e11i | −0.0312132 | + | 0.0540628i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.33282e11 | −0.0890419 | −0.0445209 | − | 0.999008i | \(-0.514176\pi\) | ||||
−0.0445209 | + | 0.999008i | \(0.514176\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.85905e11 | + | 1.01482e12i | −0.0645186 | + | 0.111749i | −0.896480 | − | 0.443084i | \(-0.853885\pi\) |
0.831962 | + | 0.554833i | \(0.187218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.12391e12 | − | 1.23390e13i | −0.747521 | − | 1.29474i | −0.949008 | − | 0.315253i | \(-0.897911\pi\) |
0.201487 | − | 0.979491i | \(-0.435423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.16183e12 | + | 1.24047e13i | 0.683229 | + | 1.18339i | 0.973990 | + | 0.226592i | \(0.0727584\pi\) |
−0.290760 | + | 0.956796i | \(0.593908\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.19692e11 | + | 2.07312e11i | −0.0108941 | + | 0.0188691i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.00149e13 | 0.830728 | 0.415364 | − | 0.909655i | \(-0.363654\pi\) | ||||
0.415364 | + | 0.909655i | \(0.363654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.58907e12 | − | 1.14126e13i | 0.522072 | − | 0.904255i | −0.477598 | − | 0.878578i | \(-0.658493\pi\) |
0.999670 | − | 0.0256770i | \(-0.00817415\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.31483e11 | + | 5.21963e12i | 0.0529408 | + | 0.377769i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.74655e12 | + | 3.02511e12i | 0.120878 | + | 0.209367i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.25032e13 | 1.42574 | 0.712868 | − | 0.701298i | \(-0.247396\pi\) | ||||
0.712868 | + | 0.701298i | \(0.247396\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.51226e13 | 1.52371 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.53000e12 | + | 1.13103e13i | 0.363313 | + | 0.629276i | 0.988504 | − | 0.151195i | \(-0.0483123\pi\) |
−0.625191 | + | 0.780472i | \(0.714979\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.01523e12 | − | 1.45746e13i | −0.267388 | − | 0.777046i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.14385e13 | + | 1.98121e13i | −0.560547 | + | 0.970897i | 0.436901 | + | 0.899509i | \(0.356076\pi\) |
−0.997449 | + | 0.0713872i | \(0.977257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.05530e12 | −0.0496048 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.89726e12 | − | 1.19464e13i | 0.298565 | − | 0.517130i | −0.677243 | − | 0.735760i | \(-0.736825\pi\) |
0.975808 | + | 0.218630i | \(0.0701586\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.69926e11 | − | 9.87141e11i | −0.0236858 | − | 0.0410250i | 0.853940 | − | 0.520372i | \(-0.174207\pi\) |
−0.877625 | + | 0.479347i | \(0.840873\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.09728e13 | + | 1.90054e13i | 0.420715 | + | 0.728699i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.28587e13 | − | 3.95924e13i | 0.842195 | − | 1.45873i | −0.0458392 | − | 0.998949i | \(-0.514596\pi\) |
0.888035 | − | 0.459777i | \(-0.152070\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.91820e13 | 1.33414 | 0.667072 | − | 0.744994i | \(-0.267548\pi\) | ||||
0.667072 | + | 0.744994i | \(0.267548\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.93169e12 | + | 3.34578e12i | −0.0632574 | + | 0.109565i | −0.895920 | − | 0.444216i | \(-0.853482\pi\) |
0.832662 | + | 0.553781i | \(0.186816\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.68651e13 | + | 9.11921e12i | 1.42069 | + | 0.276444i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.70374e13 | + | 2.95096e13i | 0.497123 | + | 0.861043i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.78633e12 | 0.264757 | 0.132379 | − | 0.991199i | \(-0.457739\pi\) | ||||
0.132379 | + | 0.991199i | \(0.457739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.94798e13 | −0.507649 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.63126e13 | + | 4.55748e13i | 0.636755 | + | 1.10289i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.83639e13 | + | 9.41084e12i | 1.12825 | + | 0.219539i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.61280e13 | − | 2.79346e13i | 0.349890 | − | 0.606028i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.68832e12 | 0.202762 | 0.101381 | − | 0.994848i | \(-0.467674\pi\) | ||||
0.101381 | + | 0.994848i | \(0.467674\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.64052e13 | − | 2.84146e13i | 0.319741 | − | 0.553808i | −0.660693 | − | 0.750656i | \(-0.729737\pi\) |
0.980434 | + | 0.196849i | \(0.0630707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.65288e13 | + | 8.05902e13i | 0.875443 | + | 1.51631i | 0.856290 | + | 0.516496i | \(0.172764\pi\) |
0.0191533 | + | 0.999817i | \(0.493903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.88239e13 | − | 3.26039e13i | −0.330281 | − | 0.572063i | 0.652286 | − | 0.757973i | \(-0.273810\pi\) |
−0.982567 | + | 0.185910i | \(0.940477\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.34546e13 | + | 7.52656e13i | −0.736524 | + | 1.27570i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.40778e12 | −0.0222803 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.29851e13 | + | 3.98114e13i | −0.351632 | + | 0.609044i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.29940e12 | + | 3.77613e12i | 0.0185851 | + | 0.0540094i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00419e13 | − | 8.66751e13i | −0.692276 | − | 1.19906i | −0.971090 | − | 0.238713i | \(-0.923275\pi\) |
0.278814 | − | 0.960345i | \(-0.410059\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.60387e13 | 0.596179 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.73473e13 | 1.09467 | 0.547337 | − | 0.836912i | \(-0.315642\pi\) | ||||
0.547337 | + | 0.836912i | \(0.315642\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.23712e13 | − | 7.33890e13i | −0.497647 | − | 0.861950i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.37128e13 | + | 4.79314e13i | 0.838350 | + | 0.545133i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.55238e13 | − | 6.15290e13i | 0.379059 | − | 0.656550i | −0.611866 | − | 0.790961i | \(-0.709581\pi\) |
0.990926 | + | 0.134411i | \(0.0429142\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.50390e13 | −0.775796 | −0.387898 | − | 0.921702i | \(-0.626799\pi\) | ||||
−0.387898 | + | 0.921702i | \(0.626799\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.79326e12 | − | 1.17663e13i | 0.0659655 | − | 0.114256i | −0.831156 | − | 0.556039i | \(-0.812321\pi\) |
0.897122 | + | 0.441783i | \(0.145654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.74679e13 | + | 3.02552e13i | 0.164431 | + | 0.284803i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.02740e13 | + | 1.21718e14i | 0.621978 | + | 1.07730i | 0.989117 | + | 0.147131i | \(0.0470040\pi\) |
−0.367139 | + | 0.930166i | \(0.619663\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.32195e13 | − | 9.21789e13i | 0.456858 | − | 0.791301i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.94152e13 | −0.318459 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.75641e13 | + | 3.04219e13i | −0.137709 | + | 0.238519i | −0.926629 | − | 0.375977i | \(-0.877307\pi\) |
0.788920 | + | 0.614496i | \(0.210641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.15524e13 | + | 1.32842e13i | −0.0853326 | + | 0.0981251i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.94455e13 | + | 1.54924e14i | 0.641446 | + | 1.11102i | 0.985110 | + | 0.171924i | \(0.0549985\pi\) |
−0.343664 | + | 0.939093i | \(0.611668\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.82052e14 | −1.23117 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.33296e13 | −0.218935 | −0.109467 | − | 0.993990i | \(-0.534915\pi\) | ||||
−0.109467 | + | 0.993990i | \(0.534915\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.37824e13 | − | 2.38718e13i | −0.0854539 | − | 0.148010i | 0.820131 | − | 0.572176i | \(-0.193901\pi\) |
−0.905585 | + | 0.424166i | \(0.860567\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.11964e13 | − | 1.19078e13i | −0.368716 | − | 0.0717462i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.16390e14 | − | 2.01594e14i | 0.662513 | − | 1.14751i | −0.317440 | − | 0.948278i | \(-0.602823\pi\) |
0.979953 | − | 0.199228i | \(-0.0638436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.12089e13 | −0.117367 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.87584e13 | − | 6.71316e13i | 0.202807 | − | 0.351272i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.15857e13 | + | 1.23990e14i | 0.364316 | + | 0.631014i | 0.988666 | − | 0.150131i | \(-0.0479694\pi\) |
−0.624350 | + | 0.781145i | \(0.714636\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.44586e14 | + | 2.50431e14i | 0.696359 | + | 1.20613i | 0.969721 | + | 0.244217i | \(0.0785310\pi\) |
−0.273362 | + | 0.961911i | \(0.588136\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.87564e13 | − | 1.53731e14i | 0.415932 | − | 0.720415i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.82318e14 | 0.809206 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.66276e13 | − | 8.07613e13i | 0.201449 | − | 0.348919i | −0.747547 | − | 0.664209i | \(-0.768768\pi\) |
0.948995 | + | 0.315290i | \(0.102102\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.13246e14 | + | 2.45214e14i | −0.873283 | + | 1.00420i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.24900e12 | − | 5.62742e12i | −0.0129564 | − | 0.0224412i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.50519e14 | 1.70426 | 0.852130 | − | 0.523330i | \(-0.175311\pi\) | ||||
0.852130 | + | 0.523330i | \(0.175311\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.82722e14 | 0.673347 | 0.336673 | − | 0.941621i | \(-0.390698\pi\) | ||||
0.336673 | + | 0.941621i | \(0.390698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.26341e12 | − | 1.60447e13i | −0.0324065 | − | 0.0561296i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.75089e14 | − | 5.08821e14i | −0.596907 | − | 1.73465i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.13121e13 | + | 1.23516e14i | −0.230961 | + | 0.400036i | −0.958091 | − | 0.286463i | \(-0.907520\pi\) |
0.727130 | + | 0.686500i | \(0.240854\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.67830e14 | −0.529892 | −0.264946 | − | 0.964263i | \(-0.585354\pi\) | ||||
−0.264946 | + | 0.964263i | \(0.585354\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.57135e13 | + | 1.31140e14i | −0.227261 | + | 0.393628i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.55296e14 | − | 4.42186e14i | −0.747291 | − | 1.29435i | −0.949117 | − | 0.314925i | \(-0.898021\pi\) |
0.201826 | − | 0.979421i | \(-0.435313\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.38404e14 | − | 2.39723e14i | −0.385415 | − | 0.667559i | 0.606411 | − | 0.795151i | \(-0.292609\pi\) |
−0.991827 | + | 0.127592i | \(0.959275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.18967e14 | + | 2.06057e14i | −0.323181 | + | 0.559766i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.18277e14 | −1.85754 | −0.928768 | − | 0.370661i | \(-0.879131\pi\) | ||||
−0.928768 | + | 0.370661i | \(0.879131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.82372e14 | + | 4.89083e14i | −0.712609 | + | 1.23428i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.24932e13 | − | 1.23488e14i | −0.102154 | − | 0.296867i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.69134e14 | − | 4.66153e14i | −0.631581 | − | 1.09393i | −0.987229 | − | 0.159310i | \(-0.949073\pi\) |
0.355648 | − | 0.934620i | \(-0.384260\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.08940e14 | −0.691065 | −0.345532 | − | 0.938407i | \(-0.612302\pi\) | ||||
−0.345532 | + | 0.938407i | \(0.612302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.55334e14 | −0.776142 | −0.388071 | − | 0.921630i | \(-0.626858\pi\) | ||||
−0.388071 | + | 0.921630i | \(0.626858\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.09007e14 | − | 1.88806e14i | −0.227097 | − | 0.393344i | 0.729849 | − | 0.683608i | \(-0.239590\pi\) |
−0.956947 | + | 0.290264i | \(0.906257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.03986e14 | − | 5.79540e14i | 1.02558 | − | 1.17932i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.91403e14 | + | 5.04724e14i | −0.565923 | + | 0.980207i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.32278e14 | −0.250999 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.15790e14 | + | 5.46965e14i | −0.572207 | + | 0.991092i | 0.424132 | + | 0.905601i | \(0.360579\pi\) |
−0.996339 | + | 0.0854915i | \(0.972754\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.90954e14 | + | 3.30741e14i | 0.338166 | + | 0.585721i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.84020e13 | + | 1.53117e14i | 0.149583 | + | 0.259085i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.36327e14 | + | 2.36125e14i | −0.225513 | + | 0.390600i | −0.956473 | − | 0.291820i | \(-0.905739\pi\) |
0.730960 | + | 0.682420i | \(0.239072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.03331e15 | −1.63411 | −0.817055 | − | 0.576560i | \(-0.804395\pi\) | ||||
−0.817055 | + | 0.576560i | \(0.804395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.66850e13 | − | 6.35403e13i | 0.0567324 | − | 0.0982633i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.72077e14 | + | 1.11317e14i | 0.846241 | + | 0.164665i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.89945e14 | − | 3.28995e14i | −0.274837 | − | 0.476031i | 0.695257 | − | 0.718761i | \(-0.255291\pi\) |
−0.970094 | + | 0.242730i | \(0.921957\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.88084e14 | −0.398928 | −0.199464 | − | 0.979905i | \(-0.563920\pi\) | ||||
−0.199464 | + | 0.979905i | \(0.563920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.51465e13 | −0.101814 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.02577e14 | − | 1.21690e15i | −0.911478 | − | 1.57873i | −0.811977 | − | 0.583690i | \(-0.801608\pi\) |
−0.0995016 | − | 0.995037i | \(-0.531725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.31478e14 | + | 4.96162e14i | −0.547828 | + | 0.629954i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.99251e14 | − | 3.45113e14i | 0.242360 | − | 0.419780i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.72368e13 | −0.0562448 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.31749e14 | − | 1.44063e15i | 0.949259 | − | 1.64417i | 0.202269 | − | 0.979330i | \(-0.435168\pi\) |
0.746990 | − | 0.664835i | \(-0.231498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.23224e13 | + | 9.06250e13i | 0.0584693 | + | 0.101272i | 0.893778 | − | 0.448509i | \(-0.148045\pi\) |
−0.835309 | + | 0.549781i | \(0.814711\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.57704e13 | + | 6.19561e13i | 0.0383323 | + | 0.0663936i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.64255e14 | + | 1.15052e15i | −0.697154 | + | 1.20751i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.18299e15 | −1.19119 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.51279e14 | + | 6.08434e14i | −0.346503 | + | 0.600161i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.19814e14 | + | 6.39991e14i | −0.776206 | + | 0.605948i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.40174e13 | + | 1.62843e14i | 0.0872215 | + | 0.151072i | 0.906336 | − | 0.422558i | \(-0.138868\pi\) |
−0.819114 | + | 0.573630i | \(0.805535\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.25660e14 | 0.111948 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.21322e15 | 1.93238 | 0.966192 | − | 0.257824i | \(-0.0830056\pi\) | ||||
0.966192 | + | 0.257824i | \(0.0830056\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.61923e14 | − | 4.53665e14i | −0.219705 | − | 0.380541i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.20770e14 | − | 1.22279e15i | −0.345985 | − | 1.00545i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.08922e14 | − | 7.08274e14i | 0.323174 | − | 0.559755i | −0.657967 | − | 0.753047i | \(-0.728583\pi\) |
0.981141 | + | 0.193292i | \(0.0619166\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.22082e15 | −0.945993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.06151e15 | − | 1.83858e15i | 0.790909 | − | 1.36989i | −0.134495 | − | 0.990914i | \(-0.542941\pi\) |
0.925405 | − | 0.378981i | \(-0.123725\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.43014e13 | − | 1.63335e14i | −0.0689051 | − | 0.119347i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.39692e14 | − | 7.61570e14i | −0.309052 | − | 0.535294i | 0.669103 | − | 0.743169i | \(-0.266678\pi\) |
−0.978155 | + | 0.207876i | \(0.933345\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.97661e14 | − | 6.88769e14i | 0.274166 | − | 0.474870i | −0.695758 | − | 0.718276i | \(-0.744931\pi\) |
0.969924 | + | 0.243406i | \(0.0782648\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.99282e15 | −1.32220 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.87379e14 | + | 1.53699e15i | −0.577620 | + | 1.00047i | 0.418132 | + | 0.908386i | \(0.362685\pi\) |
−0.995752 | + | 0.0920805i | \(0.970648\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.06405e14 | − | 2.07048e13i | −0.0666799 | − | 0.0129748i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.04120e14 | − | 1.80341e14i | −0.0640260 | − | 0.110896i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.91619e15 | −1.13482 | −0.567412 | − | 0.823434i | \(-0.692055\pi\) | ||||
−0.567412 | + | 0.823434i | \(0.692055\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.10786e14 | 0.296896 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.37770e14 | − | 4.11829e14i | −0.133154 | − | 0.230630i | 0.791736 | − | 0.610863i | \(-0.209177\pi\) |
−0.924891 | + | 0.380233i | \(0.875844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.16629e13 | + | 1.00528e13i | 0.0284011 | + | 0.00552640i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.06635e15 | + | 1.84697e15i | −0.565006 | + | 0.978618i | 0.432044 | + | 0.901853i | \(0.357793\pi\) |
−0.997049 | + | 0.0767657i | \(0.975541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.19165e12 | 0.00166037 | 0.000830187 | − | 1.00000i | \(-0.499736\pi\) | ||||
0.000830187 | 1.00000i | \(0.499736\pi\) | ||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.15334e13 | + | 1.99765e13i | −0.00578500 | + | 0.0100199i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.33721e14 | + | 1.09764e15i | 0.312148 | + | 0.540656i | 0.978827 | − | 0.204689i | \(-0.0656183\pi\) |
−0.666679 | + | 0.745345i | \(0.732285\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.94743e13 | − | 8.56919e13i | −0.0235046 | − | 0.0407111i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.75304e14 | − | 9.96455e14i | 0.268451 | − | 0.464970i | −0.700011 | − | 0.714132i | \(-0.746822\pi\) |
0.968462 | + | 0.249162i | \(0.0801550\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.65065e14 | 0.0743169 | 0.0371584 | − | 0.999309i | \(-0.488169\pi\) | ||||
0.0371584 | + | 0.999309i | \(0.488169\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.48618e15 | + | 2.57414e15i | −0.657313 | + | 1.13850i | 0.323995 | + | 0.946059i | \(0.394974\pi\) |
−0.981308 | + | 0.192441i | \(0.938360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.29153e15 | + | 3.75327e15i | 0.551342 | + | 1.60223i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.96942e14 | − | 1.20714e15i | −0.292319 | − | 0.506310i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.53915e14 | −0.0623309 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.28671e15 | 1.70594 | 0.852968 | − | 0.521964i | \(-0.174800\pi\) | ||||
0.852968 | + | 0.521964i | \(0.174800\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.24686e14 | − | 2.15962e14i | −0.0479250 | − | 0.0830085i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.01965e15 | − | 8.16914e14i | −0.762973 | − | 0.308610i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.32146e15 | − | 2.28884e15i | 0.482321 | − | 0.835404i | −0.517473 | − | 0.855699i | \(-0.673127\pi\) |
0.999794 | + | 0.0202954i | \(0.00646067\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.07428e15 | −0.744228 | −0.372114 | − | 0.928187i | \(-0.621367\pi\) | ||||
−0.372114 | + | 0.928187i | \(0.621367\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.01990e15 | − | 1.76651e15i | 0.353657 | − | 0.612552i | −0.633230 | − | 0.773964i | \(-0.718271\pi\) |
0.986887 | + | 0.161412i | \(0.0516047\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.92195e15 | − | 3.32891e15i | −0.655233 | − | 1.13490i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.93480e15 | + | 5.08322e15i | 0.967289 | + | 1.67539i | 0.703336 | + | 0.710858i | \(0.251693\pi\) |
0.263953 | + | 0.964536i | \(0.414974\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.10133e13 | − | 1.40319e14i | 0.0262561 | − | 0.0454768i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.41751e15 | −1.38455 | −0.692274 | − | 0.721634i | \(-0.743391\pi\) | ||||
−0.692274 | + | 0.721634i | \(0.743391\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.04436e13 | + | 8.73709e13i | −0.0155488 | + | 0.0269314i | −0.873695 | − | 0.486474i | \(-0.838283\pi\) |
0.858146 | + | 0.513405i | \(0.171616\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.46590e14 | − | 2.83557e14i | 0.0735286 | − | 0.0845514i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.94600e15 | − | 6.83467e15i | −1.15735 | − | 2.00459i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.36499e15 | 1.80644 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.37415e15 | 0.662866 | 0.331433 | − | 0.943479i | \(-0.392468\pi\) | ||||
0.331433 | + | 0.943479i | \(0.392468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.65318e15 | + | 2.86340e15i | 0.446769 | + | 0.773827i | 0.998174 | − | 0.0604114i | \(-0.0192412\pi\) |
−0.551405 | + | 0.834238i | \(0.685908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.89519e15 | + | 5.63357e14i | 0.769826 | + | 0.149796i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.56905e15 | + | 2.71767e15i | −0.403946 | + | 0.699654i | −0.994198 | − | 0.107564i | \(-0.965695\pi\) |
0.590253 | + | 0.807219i | \(0.299028\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.18170e14 | −0.232608 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.18103e14 | − | 3.77766e14i | 0.0535127 | − | 0.0926867i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.74263e15 | + | 6.48243e15i | 0.903749 | + | 1.56534i | 0.822588 | + | 0.568638i | \(0.192529\pi\) |
0.0811608 | + | 0.996701i | \(0.474137\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.72251e14 | + | 8.17963e14i | 0.110473 | + | 0.191345i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.38383e14 | − | 4.12892e14i | 0.0548903 | − | 0.0950727i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.02232e15 | 0.897487 | 0.448743 | − | 0.893661i | \(-0.351872\pi\) | ||||
0.448743 | + | 0.893661i | \(0.351872\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.49461e14 | + | 9.51695e14i | −0.120693 | + | 0.209047i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.22630e14 | + | 9.45952e14i | −0.175145 | + | 0.201401i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.43811e14 | − | 1.11511e15i | −0.134960 | − | 0.233757i | 0.790622 | − | 0.612304i | \(-0.209757\pi\) |
−0.925582 | + | 0.378547i | \(0.876424\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.69524e15 | 1.56397 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.54475e15 | 0.309153 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.68896e14 | + | 1.67818e15i | 0.188048 | + | 0.325708i | 0.944599 | − | 0.328226i | \(-0.106451\pi\) |
−0.756552 | + | 0.653934i | \(0.773117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.16312e15 | − | 6.28615e15i | −0.413462 | − | 1.20155i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.44699e15 | − | 5.97036e15i | 0.639118 | − | 1.10698i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.16531e15 | 1.49119 | 0.745596 | − | 0.666398i | \(-0.232165\pi\) | ||||
0.745596 | + | 0.666398i | \(0.232165\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.46007e14 | − | 4.26096e14i | 0.0435914 | − | 0.0755026i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.09691e15 | + | 7.09605e15i | 0.715129 | + | 1.23864i | 0.962910 | + | 0.269824i | \(0.0869655\pi\) |
−0.247781 | + | 0.968816i | \(0.579701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.54234e15 | + | 7.86757e15i | 0.769500 | + | 1.33281i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.53817e14 | + | 4.39624e14i | −0.0423620 | + | 0.0733731i | −0.886429 | − | 0.462865i | \(-0.846822\pi\) |
0.844067 | + | 0.536238i | \(0.180155\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.56283e15 | −1.22531 | −0.612655 | − | 0.790350i | \(-0.709899\pi\) | ||||
−0.612655 | + | 0.790350i | \(0.709899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.99506e14 | − | 8.65169e14i | 0.0797409 | − | 0.138115i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.81357e15 | + | 1.10825e16i | 0.591128 | + | 1.71785i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.98511e15 | − | 3.43832e15i | −0.303226 | − | 0.525202i | 0.673639 | − | 0.739061i | \(-0.264730\pi\) |
−0.976865 | + | 0.213858i | \(0.931397\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.22450e15 | −0.181657 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.28767e15 | 0.773103 | 0.386551 | − | 0.922268i | \(-0.373666\pi\) | ||||
0.386551 | + | 0.922268i | \(0.373666\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.14612e14 | − | 1.23774e15i | −0.101497 | − | 0.175798i | 0.810804 | − | 0.585317i | \(-0.199030\pi\) |
−0.912302 | + | 0.409519i | \(0.865697\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.37560e15 | − | 1.58182e15i | 0.192579 | − | 0.221449i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.02597e15 | − | 6.97319e15i | 0.547642 | − | 0.948543i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.17246e15 | −0.693589 | −0.346795 | − | 0.937941i | \(-0.612730\pi\) | ||||
−0.346795 | + | 0.937941i | \(0.612730\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.71899e15 | − | 1.16376e16i | 0.875622 | − | 1.51662i | 0.0195238 | − | 0.999809i | \(-0.493785\pi\) |
0.856098 | − | 0.516813i | \(-0.172882\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.36105e15 | + | 5.82151e15i | 0.431833 | + | 0.747956i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.70201e15 | − | 2.94796e15i | −0.212571 | − | 0.368185i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.44688e15 | + | 5.97018e15i | −0.424469 | + | 0.735202i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.39615e15 | −0.406634 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.09229e14 | + | 7.08805e14i | −0.0483176 | + | 0.0836885i | −0.889173 | − | 0.457572i | \(-0.848719\pi\) |
0.840855 | + | 0.541260i | \(0.182053\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.08839e15 | − | 6.00952e14i | −0.354619 | − | 0.0690031i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.66649e15 | + | 1.15467e16i | 0.754909 | + | 1.30754i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.45305e15 | 0.600646 | 0.300323 | − | 0.953838i | \(-0.402906\pi\) | ||||
0.300323 | + | 0.953838i | \(0.402906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.98780e13 | 0.00433237 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.88884e15 | − | 6.73568e15i | −0.411041 | − | 0.711944i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.71499e15 | − | 4.27192e15i | 0.387330 | − | 0.445395i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.18150e15 | − | 2.04641e15i | 0.119871 | − | 0.207623i | −0.799845 | − | 0.600206i | \(-0.795085\pi\) |
0.919717 | + | 0.392583i | \(0.128418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.42723e15 | −0.142849 | −0.0714247 | − | 0.997446i | \(-0.522755\pi\) | ||||
−0.0714247 | + | 0.997446i | \(0.522755\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.35647e15 | + | 4.08152e15i | −0.229559 | + | 0.397608i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.75644e15 | − | 3.04224e15i | −0.168815 | − | 0.292396i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.71415e15 | − | 1.16293e16i | −0.628209 | − | 1.08809i | −0.987911 | − | 0.155022i | \(-0.950455\pi\) |
0.359702 | − | 0.933067i | \(-0.382878\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.39480e15 | + | 9.34408e15i | −0.498054 | + | 0.862655i | −0.999997 | − | 0.00224537i | \(-0.999285\pi\) |
0.501943 | + | 0.864901i | \(0.332619\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.09410e16 | 0.983505 | 0.491753 | − | 0.870735i | \(-0.336356\pi\) | ||||
0.491753 | + | 0.870735i | \(0.336356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.00194e15 | + | 1.73541e15i | −0.0888773 | + | 0.153940i | −0.907037 | − | 0.421051i | \(-0.861661\pi\) |
0.818160 | + | 0.574991i | \(0.194995\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.92099e14 | − | 5.40290e14i | 0.0597890 | − | 0.0466745i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.82367e15 | + | 3.15869e15i | 0.155478 | + | 0.269297i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.04104e16 | 1.69497 | 0.847483 | − | 0.530822i | \(-0.178117\pi\) | ||||
0.847483 | + | 0.530822i | \(0.178117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.51011e16 | 1.23774 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.70618e14 | − | 1.33475e15i | −0.0615357 | − | 0.106583i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.25209e14 | + | 3.63866e14i | 0.00986911 | + | 0.0286802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.27790e15 | + | 1.43377e16i | −0.635781 | + | 1.10120i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.92536e15 | 0.676715 | 0.338358 | − | 0.941018i | \(-0.390129\pi\) | ||||
0.338358 | + | 0.941018i | \(0.390129\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.45345e15 | − | 5.98155e15i | 0.255187 | − | 0.441997i | −0.709759 | − | 0.704444i | \(-0.751196\pi\) |
0.964946 | + | 0.262447i | \(0.0845296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.64574e14 | + | 1.67069e15i | 0.0703677 | + | 0.121880i | 0.899062 | − | 0.437820i | \(-0.144249\pi\) |
−0.828695 | + | 0.559701i | \(0.810916\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.08319e16 | + | 1.87614e16i | 0.770273 | + | 1.33415i | 0.937413 | + | 0.348219i | \(0.113213\pi\) |
−0.167140 | + | 0.985933i | \(0.553453\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.04888e15 | + | 5.28081e15i | −0.214068 | + | 0.370776i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.52962e16 | 1.04707 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.51501e15 | + | 1.64805e16i | −0.643146 | + | 1.11396i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.05353e16 | + | 2.05001e15i | 0.694391 | + | 0.135117i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.84189e15 | − | 1.70467e16i | −0.640591 | − | 1.10954i | −0.985301 | − | 0.170827i | \(-0.945356\pi\) |
0.344710 | − | 0.938709i | \(-0.387977\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.36545e16 | −0.866780 | −0.433390 | − | 0.901206i | \(-0.642683\pi\) | ||||
−0.433390 | + | 0.901206i | \(0.642683\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.49342e15 | 0.0936266 | 0.0468133 | − | 0.998904i | \(-0.485093\pi\) | ||||
0.0468133 | + | 0.998904i | \(0.485093\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.38670e15 | − | 1.62582e16i | −0.574028 | − | 0.994246i | −0.996146 | − | 0.0877050i | \(-0.972047\pi\) |
0.422118 | − | 0.906541i | \(-0.361287\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.08350e15 | − | 7.94583e14i | −0.246645 | − | 0.0479932i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.42360e14 | − | 2.46575e14i | 0.00838891 | − | 0.0145300i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.84088e15 | 0.398185 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.33105e16 | + | 2.30544e16i | −0.755988 | + | 1.30941i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.78995e13 | + | 1.52246e14i | 0.00493174 | + | 0.00854202i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.83750e15 | + | 1.01109e16i | 0.319639 | + | 0.553631i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.19397e16 | − | 2.06802e16i | 0.645882 | − | 1.11870i | −0.338215 | − | 0.941069i | \(-0.609823\pi\) |
0.984097 | − | 0.177632i | \(-0.0568437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.54913e16 | −1.34599 | −0.672995 | − | 0.739647i | \(-0.734992\pi\) | ||||
−0.672995 | + | 0.739647i | \(0.734992\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.41115e14 | − | 1.11044e15i | 0.0334462 | − | 0.0579305i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.79499e14 | − | 2.55588e15i | −0.0447924 | − | 0.130169i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.65752e15 | − | 9.79911e15i | −0.284702 | − | 0.493119i | 0.687835 | − | 0.725867i | \(-0.258561\pi\) |
−0.972537 | + | 0.232749i | \(0.925228\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.44406e16 | −0.709539 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.44621e16 | −0.702188 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.74021e15 | − | 4.74619e15i | −0.129927 | − | 0.225039i | 0.793721 | − | 0.608281i | \(-0.208141\pi\) |
−0.923648 | + | 0.383242i | \(0.874807\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.70020e14 | − | 6.20820e15i | −0.0407668 | − | 0.290899i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.11280e14 | + | 5.39153e14i | −0.0142458 | + | 0.0246745i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.11059e16 | 0.502328 | 0.251164 | − | 0.967945i | \(-0.419187\pi\) | ||||
0.251164 | + | 0.967945i | \(0.419187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.49099e15 | − | 9.51067e15i | 0.242609 | − | 0.420212i | −0.718847 | − | 0.695168i | \(-0.755330\pi\) |
0.961457 | + | 0.274956i | \(0.0886634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.56415e16 | − | 4.44124e16i | −1.11977 | − | 1.93950i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.51676e14 | + | 4.35915e14i | 0.0107378 | + | 0.0185985i | 0.871344 | − | 0.490672i | \(-0.163249\pi\) |
−0.860607 | + | 0.509270i | \(0.829915\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.14610e15 | − | 1.41095e16i | 0.343547 | − | 0.595040i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.91219e16 | −0.787989 | −0.393995 | − | 0.919113i | \(-0.628907\pi\) | ||||
−0.393995 | + | 0.919113i | \(0.628907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.26256e14 | + | 3.91886e14i | −0.00921681 | + | 0.0159640i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.00512e16 | + | 1.15580e16i | −0.400144 | + | 0.460130i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.74359e14 | − | 4.75204e14i | −0.0107979 | − | 0.0187026i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.61396e14 | −0.0331362 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.64208e16 | −1.76550 | −0.882749 | − | 0.469845i | \(-0.844310\pi\) | ||||
−0.882749 | + | 0.469845i | \(0.844310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.39295e16 | + | 2.41265e16i | 0.517879 | + | 0.896993i | 0.999784 | + | 0.0207694i | \(0.00661157\pi\) |
−0.481905 | + | 0.876223i | \(0.660055\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.54663e16 | + | 3.00950e15i | 0.568548 | + | 0.110630i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.76702e15 | − | 8.25672e15i | 0.171327 | − | 0.296748i | −0.767557 | − | 0.640981i | \(-0.778528\pi\) |
0.938884 | + | 0.344233i | \(0.111861\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.69508e16 | −1.66855 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.88383e16 | + | 3.26290e16i | −0.654634 | + | 1.13386i | 0.327352 | + | 0.944903i | \(0.393844\pi\) |
−0.981985 | + | 0.188957i | \(0.939489\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.10192e15 | − | 1.90857e15i | −0.0378660 | − | 0.0655858i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.64615e16 | − | 4.58327e16i | −0.889273 | − | 1.54027i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.07442e16 | + | 3.59301e16i | −0.689434 | + | 1.19413i | 0.282588 | + | 0.959242i | \(0.408807\pi\) |
−0.972021 | + | 0.234893i | \(0.924526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.13395e16 | −0.368611 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.88055e16 | − | 3.25721e16i | 0.604591 | − | 1.04718i | −0.387525 | − | 0.921859i | \(-0.626670\pi\) |
0.992116 | − | 0.125323i | \(-0.0399969\pi\) | |||||||
\(998\) | 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 | 252.12.k.d.109.5 | 16 | ||
3.2 | odd | 2 | 84.12.i.b.25.4 | ✓ | 16 | ||
7.2 | even | 3 | inner | 252.12.k.d.37.5 | 16 | ||
21.2 | odd | 6 | 84.12.i.b.37.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.i.b.25.4 | ✓ | 16 | 3.2 | odd | 2 | ||
84.12.i.b.37.4 | yes | 16 | 21.2 | odd | 6 | ||
252.12.k.d.37.5 | 16 | 7.2 | even | 3 | inner | ||
252.12.k.d.109.5 | 16 | 1.1 | even | 1 | trivial |