Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,8,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, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(78.7210264220\) |
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: | \( x^{16} + 89566 x^{14} - 207320 x^{13} + 5161603375 x^{12} - 17143558340 x^{11} + 178819626045814 x^{10} + \cdots + 34\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{13}\cdot 7^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.5 | ||
Root | \(67.3630 + 116.676i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.109 |
Dual form | 252.8.k.e.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 | ||||||||
\(5\) | 117.526 | + | 203.561i | 0.420474 | + | 0.728282i | 0.995986 | − | 0.0895111i | \(-0.0285304\pi\) |
−0.575512 | + | 0.817793i | \(0.695197\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 881.619 | − | 215.154i | 0.971489 | − | 0.237086i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3934.09 | + | 6814.05i | −0.891189 | + | 1.54359i | −0.0527383 | + | 0.998608i | \(0.516795\pi\) |
−0.838451 | + | 0.544977i | \(0.816538\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5762.92 | −0.727514 | −0.363757 | − | 0.931494i | \(-0.618506\pi\) | ||||
−0.363757 | + | 0.931494i | \(0.618506\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3577.84 | + | 6196.99i | −0.176624 | + | 0.305921i | −0.940722 | − | 0.339179i | \(-0.889851\pi\) |
0.764098 | + | 0.645100i | \(0.223184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19965.0 | − | 34580.3i | −0.667776 | − | 1.15662i | −0.978525 | − | 0.206130i | \(-0.933913\pi\) |
0.310749 | − | 0.950492i | \(-0.399420\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −28266.6 | − | 48959.2i | −0.484425 | − | 0.839048i | 0.515415 | − | 0.856940i | \(-0.327638\pi\) |
−0.999840 | + | 0.0178925i | \(0.994304\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11437.7 | − | 19810.8i | 0.146403 | − | 0.253578i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −130038. | −0.990096 | −0.495048 | − | 0.868866i | \(-0.664850\pi\) | ||||
−0.495048 | + | 0.868866i | \(0.664850\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −25781.5 | + | 44654.8i | −0.155432 | + | 0.269217i | −0.933216 | − | 0.359315i | \(-0.883010\pi\) |
0.777784 | + | 0.628532i | \(0.216344\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 147410. | + | 154177.i | 0.581151 | + | 0.607830i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 139818. | + | 242173.i | 0.453794 | + | 0.785994i | 0.998618 | − | 0.0525566i | \(-0.0167370\pi\) |
−0.544824 | + | 0.838550i | \(0.683404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −345556. | −0.783024 | −0.391512 | − | 0.920173i | \(-0.628048\pi\) | ||||
−0.391512 | + | 0.920173i | \(0.628048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −111709. | −0.214264 | −0.107132 | − | 0.994245i | \(-0.534167\pi\) | ||||
−0.107132 | + | 0.994245i | \(0.534167\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 425409. | + | 736830.i | 0.597674 | + | 1.03520i | 0.993164 | + | 0.116731i | \(0.0372417\pi\) |
−0.395489 | + | 0.918471i | \(0.629425\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 730961. | − | 379368.i | 0.887580 | − | 0.460653i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 599912. | − | 1.03908e6i | 0.553506 | − | 0.958700i | −0.444512 | − | 0.895773i | \(-0.646623\pi\) |
0.998018 | − | 0.0629273i | \(-0.0200436\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.84943e6 | −1.49889 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 856228. | − | 1.48303e6i | 0.542759 | − | 0.940086i | −0.455985 | − | 0.889987i | \(-0.650713\pi\) |
0.998744 | − | 0.0500990i | \(-0.0159537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.22726e6 | − | 2.12568e6i | −0.692282 | − | 1.19907i | −0.971088 | − | 0.238721i | \(-0.923272\pi\) |
0.278806 | − | 0.960347i | \(-0.410061\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −677294. | − | 1.17311e6i | −0.305901 | − | 0.529835i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −313531. | + | 543052.i | −0.127356 | + | 0.220587i | −0.922651 | − | 0.385635i | \(-0.873982\pi\) |
0.795296 | + | 0.606222i | \(0.207316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.97409e6 | 0.986165 | 0.493082 | − | 0.869983i | \(-0.335870\pi\) | ||||
0.493082 | + | 0.869983i | \(0.335870\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 476382. | − | 825118.i | 0.143326 | − | 0.248248i | −0.785421 | − | 0.618962i | \(-0.787554\pi\) |
0.928747 | + | 0.370714i | \(0.120887\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00230e6 | + | 6.85383e6i | −0.499818 | + | 1.71086i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.95297e6 | − | 5.11469e6i | −0.673852 | − | 1.16715i | −0.976803 | − | 0.214139i | \(-0.931305\pi\) |
0.302952 | − | 0.953006i | \(-0.402028\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.78669e6 | −1.87872 | −0.939361 | − | 0.342930i | \(-0.888581\pi\) | ||||
−0.939361 | + | 0.342930i | \(0.888581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.68196e6 | −0.297063 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.59171e6 | + | 4.48897e6i | 0.389692 | + | 0.674966i | 0.992408 | − | 0.122989i | \(-0.0392481\pi\) |
−0.602716 | + | 0.797956i | \(0.705915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.08070e6 | + | 1.23992e6i | −0.706771 | + | 0.172483i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.69281e6 | − | 8.12818e6i | 0.561565 | − | 0.972659i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.87158e6 | −0.541962 | −0.270981 | − | 0.962585i | \(-0.587348\pi\) | ||||
−0.270981 | + | 0.962585i | \(0.587348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.03637e6 | + | 3.52710e6i | −0.196667 | + | 0.340638i | −0.947446 | − | 0.319916i | \(-0.896345\pi\) |
0.750778 | + | 0.660554i | \(0.229679\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.15804e6 | − | 1.23981e7i | −0.645452 | − | 1.11795i | −0.984197 | − | 0.177077i | \(-0.943336\pi\) |
0.338745 | − | 0.940878i | \(-0.389997\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.47668e6 | − | 1.64141e7i | −0.747847 | − | 1.29531i | −0.948853 | − | 0.315720i | \(-0.897754\pi\) |
0.201005 | − | 0.979590i | \(-0.435579\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.83878e6 | + | 4.91690e6i | −0.209961 | + | 0.363663i | −0.951702 | − | 0.307023i | \(-0.900667\pi\) |
0.741741 | + | 0.670686i | \(0.234000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.34292e6 | 0.413537 | 0.206769 | − | 0.978390i | \(-0.433705\pi\) | ||||
0.206769 | + | 0.978390i | \(0.433705\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.64412e6 | − | 1.15080e7i | 0.407376 | − | 0.705596i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.82098e6 | + | 6.23317e6i | −0.0990583 | + | 0.339074i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.12106e7 | − | 3.67378e7i | −1.08844 | − | 1.88523i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.37404e7 | 1.08718 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.12014e7 | −1.78484 | −0.892420 | − | 0.451205i | \(-0.850994\pi\) | ||||
−0.892420 | + | 0.451205i | \(0.850994\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.09350e7 | + | 1.89400e7i | 0.424982 | + | 0.736091i | 0.996419 | − | 0.0845554i | \(-0.0269470\pi\) |
−0.571436 | + | 0.820646i | \(0.693614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50416e7 | − | 2.61911e7i | −0.922956 | − | 0.965324i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.87470e7 | + | 3.24708e7i | −0.622889 | + | 1.07888i | 0.366056 | + | 0.930593i | \(0.380708\pi\) |
−0.988945 | + | 0.148283i | \(0.952625\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.15043e7 | −0.994989 | −0.497494 | − | 0.867467i | \(-0.665746\pi\) | ||||
−0.497494 | + | 0.867467i | \(0.665746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.26719e7 | − | 3.92688e7i | 0.648352 | − | 1.12298i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.52829e7 | − | 2.64707e7i | −0.416310 | − | 0.721070i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.28779e6 | − | 1.43549e7i | −0.205252 | − | 0.355506i | 0.744961 | − | 0.667108i | \(-0.232468\pi\) |
−0.950213 | + | 0.311601i | \(0.899135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.11762e7 | − | 5.39987e7i | 0.736891 | − | 1.27633i | −0.216997 | − | 0.976172i | \(-0.569626\pi\) |
0.953888 | − | 0.300161i | \(-0.0970405\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.21200e7 | −0.261421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.99021e7 | + | 3.44715e7i | −0.410441 | + | 0.710905i | −0.994938 | − | 0.100491i | \(-0.967959\pi\) |
0.584497 | + | 0.811396i | \(0.301292\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.54541e7 | − | 3.70817e7i | −0.669540 | − | 0.700275i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.67496e7 | + | 2.90111e7i | 0.302933 | + | 0.524695i | 0.976799 | − | 0.214158i | \(-0.0687008\pi\) |
−0.673866 | + | 0.738854i | \(0.735367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.31239e7 | 1.38108 | 0.690539 | − | 0.723295i | \(-0.257373\pi\) | ||||
0.690539 | + | 0.723295i | \(0.257373\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.95372e7 | −0.470724 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.73005e7 | − | 6.46063e7i | −0.547713 | − | 0.948666i | −0.998431 | − | 0.0560000i | \(-0.982165\pi\) |
0.450718 | − | 0.892666i | \(-0.351168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.82137e6 | − | 1.99264e7i | 0.0821093 | − | 0.281058i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.29744e7 | + | 1.26395e8i | −0.951010 | + | 1.64720i | −0.207765 | + | 0.978179i | \(0.566619\pi\) |
−0.743245 | + | 0.669019i | \(0.766714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.25291e7 | −1.03450 | −0.517252 | − | 0.855833i | \(-0.673045\pi\) | ||||
−0.517252 | + | 0.855833i | \(0.673045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.28646e7 | + | 5.69232e7i | −0.381617 | + | 0.660980i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.81511e7 | − | 4.87591e7i | −0.314810 | − | 0.545268i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.07989e6 | + | 1.22627e7i | 0.0735207 | + | 0.127342i | 0.900442 | − | 0.434976i | \(-0.143243\pi\) |
−0.826921 | + | 0.562318i | \(0.809910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.70040e6 | + | 9.87338e6i | −0.0570761 | + | 0.0988588i | −0.893152 | − | 0.449756i | \(-0.851511\pi\) |
0.836076 | + | 0.548614i | \(0.184844\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.08549e7 | −0.567106 | −0.283553 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283553 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.04759e7 | − | 7.01063e7i | 0.364092 | − | 0.630625i | −0.624538 | − | 0.780994i | \(-0.714713\pi\) |
0.988630 | + | 0.150369i | \(0.0480461\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.14644e8 | + | 2.79782e7i | −0.961867 | + | 0.234738i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.06119e7 | − | 7.03418e7i | −0.329241 | − | 0.570263i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.14176e8 | 2.38046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.64186e6 | 0.0413460 | 0.0206730 | − | 0.999786i | \(-0.493419\pi\) | ||||
0.0206730 | + | 0.999786i | \(0.493419\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.31288e7 | − | 2.27397e7i | −0.0900926 | − | 0.156045i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.31218e7 | + | 4.49155e7i | −0.0871732 | + | 0.298392i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.06188e7 | − | 3.57128e7i | 0.128496 | − | 0.222562i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.69180e8 | 1.02160 | 0.510801 | − | 0.859699i | \(-0.329349\pi\) | ||||
0.510801 | + | 0.859699i | \(0.329349\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.58940e7 | − | 1.31452e8i | 0.430643 | − | 0.745895i | −0.566286 | − | 0.824209i | \(-0.691620\pi\) |
0.996929 | + | 0.0783137i | \(0.0249536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.01394e8 | + | 1.75620e8i | 0.557942 | + | 0.966384i | 0.997668 | + | 0.0682522i | \(0.0217423\pi\) |
−0.439726 | + | 0.898132i | \(0.644924\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.53553e8 | − | 2.65962e8i | −0.795266 | − | 1.37744i | −0.922670 | − | 0.385591i | \(-0.873998\pi\) |
0.127403 | − | 0.991851i | \(-0.459336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.99934e7 | + | 1.73194e8i | −0.502613 | + | 0.870551i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.38306e8 | 1.12913 | 0.564564 | − | 0.825389i | \(-0.309044\pi\) | ||||
0.564564 | + | 0.825389i | \(0.309044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −695427. | + | 1.20451e6i | −0.00320031 | + | 0.00554309i | −0.867621 | − | 0.497226i | \(-0.834352\pi\) |
0.864421 | + | 0.502769i | \(0.167685\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.63131e8 | + | 1.04210e8i | 0.708690 | + | 0.452717i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.15056e8 | + | 1.99284e8i | 0.485816 | + | 0.841458i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.96244e8 | −1.58163 | −0.790815 | − | 0.612055i | \(-0.790343\pi\) | ||||
−0.790815 | + | 0.612055i | \(0.790343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.44814e8 | 1.72686 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.72046e8 | + | 2.97993e8i | 0.632237 | + | 1.09507i | 0.987093 | + | 0.160146i | \(0.0511964\pi\) |
−0.354857 | + | 0.934921i | \(0.615470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.75371e8 | + | 1.83421e8i | 0.627203 | + | 0.655996i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.01986e6 | + | 1.56229e7i | −0.0305742 | + | 0.0529560i | −0.880908 | − | 0.473288i | \(-0.843067\pi\) |
0.850333 | + | 0.526244i | \(0.176400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.82021e8 | 0.930939 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.13538e7 | + | 3.69859e7i | −0.0668871 | + | 0.115852i | −0.897530 | − | 0.440954i | \(-0.854640\pi\) |
0.830642 | + | 0.556806i | \(0.187973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.46844e7 | + | 1.29357e8i | 0.227949 | + | 0.394819i | 0.957200 | − | 0.289427i | \(-0.0934648\pi\) |
−0.729251 | + | 0.684246i | \(0.760131\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.99943e7 | + | 1.55875e8i | 0.260946 | + | 0.451972i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.80069e8 | + | 3.11889e8i | −0.509050 | + | 0.881701i | 0.490895 | + | 0.871219i | \(0.336670\pi\) |
−0.999945 | + | 0.0104821i | \(0.996663\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.84959e8 | −0.497282 | −0.248641 | − | 0.968596i | \(-0.579984\pi\) | ||||
−0.248641 | + | 0.968596i | \(0.579984\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.14592e7 | − | 3.71684e7i | 0.0562809 | − | 0.0974813i | −0.836512 | − | 0.547948i | \(-0.815409\pi\) |
0.892793 | + | 0.450467i | \(0.148742\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.04649e8 | + | 7.43478e7i | −0.760699 | + | 0.185644i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.79568e8 | + | 3.11020e8i | 0.437608 | + | 0.757959i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.88345e8 | −1.36646 | −0.683228 | − | 0.730205i | \(-0.739424\pi\) | ||||
−0.683228 | + | 0.730205i | \(0.739424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.02516e8 | 0.912865 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.62898e8 | + | 2.82148e8i | 0.352425 | + | 0.610419i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.84850e7 | + | 2.40347e7i | −0.208155 | + | 0.0507991i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.88471e8 | − | 4.99646e8i | 0.582173 | − | 1.00835i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.17824e7 | −0.0824155 | −0.0412077 | − | 0.999151i | \(-0.513121\pi\) | ||||
−0.0412077 | + | 0.999151i | \(0.513121\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.03292e8 | − | 3.52113e8i | 0.383230 | − | 0.663774i | −0.608292 | − | 0.793714i | \(-0.708145\pi\) |
0.991522 | + | 0.129939i | \(0.0414782\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.29934e8 | + | 3.98258e8i | 0.423837 | + | 0.734107i | 0.996311 | − | 0.0858160i | \(-0.0273497\pi\) |
−0.572474 | + | 0.819923i | \(0.694016\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.06886e8 | − | 5.31543e8i | −0.541091 | − | 0.937197i | −0.998842 | − | 0.0481166i | \(-0.984678\pi\) |
0.457751 | − | 0.889081i | \(-0.348655\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.11581e8 | − | 8.86085e8i | 0.882363 | − | 1.52830i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.85725e8 | 0.471780 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.59149e7 | + | 1.14168e8i | −0.106510 | + | 0.184481i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.33581e8 | + | 5.58075e8i | 0.826066 | + | 0.863987i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.71651e8 | + | 9.90129e8i | 0.866429 | + | 1.50070i | 0.865621 | + | 0.500700i | \(0.166924\pi\) |
0.000808163 | 1.00000i | \(0.499743\pi\) | ||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.47392e8 | −0.214199 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.58803e8 | −1.22233 | −0.611166 | − | 0.791503i | \(-0.709299\pi\) | ||||
−0.611166 | + | 0.791503i | \(0.709299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.02853e8 | − | 3.51352e8i | −0.277039 | − | 0.479846i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.62806e8 | − | 4.91727e8i | 0.753060 | − | 0.657952i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.59150e8 | − | 4.48860e8i | 0.332964 | − | 0.576711i | −0.650128 | − | 0.759825i | \(-0.725285\pi\) |
0.983092 | + | 0.183114i | \(0.0586179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.10903e8 | −0.517428 | −0.258714 | − | 0.965954i | \(-0.583299\pi\) | ||||
−0.258714 | + | 0.965954i | \(0.583299\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.77472e8 | + | 1.34662e9i | −0.940749 | + | 1.62942i | −0.176701 | + | 0.984265i | \(0.556542\pi\) |
−0.764048 | + | 0.645160i | \(0.776791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.49533e8 | + | 6.05409e8i | 0.414657 | + | 0.718206i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.73553e8 | + | 1.51304e9i | 0.996457 | + | 1.72591i | 0.571062 | + | 0.820907i | \(0.306531\pi\) |
0.425395 | + | 0.905008i | \(0.360135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50263e8 | + | 6.06673e8i | −0.391849 | + | 0.678703i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.23949e8 | 0.241060 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.44227e8 | − | 2.49808e8i | 0.152305 | − | 0.263800i | −0.779769 | − | 0.626067i | \(-0.784664\pi\) |
0.932074 | + | 0.362267i | \(0.117997\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.05332e8 | − | 1.04514e9i | 0.310430 | − | 1.06259i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.04946e7 | − | 1.56741e8i | −0.0902904 | − | 0.156388i | 0.817343 | − | 0.576152i | \(-0.195446\pi\) |
−0.907633 | + | 0.419764i | \(0.862113\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.49399e8 | 0.720308 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.42653e9 | 1.34599 | 0.672997 | − | 0.739645i | \(-0.265007\pi\) | ||||
0.672997 | + | 0.739645i | \(0.265007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.99160e8 | − | 1.55739e9i | −0.817789 | − | 1.41645i | −0.907308 | − | 0.420467i | \(-0.861866\pi\) |
0.0895186 | − | 0.995985i | \(-0.471467\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.63049e9 | + | 3.97913e8i | −1.45615 | + | 0.355366i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.57575e8 | + | 2.72928e8i | −0.135726 | + | 0.235085i | −0.925875 | − | 0.377831i | \(-0.876670\pi\) |
0.790148 | + | 0.612916i | \(0.210003\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.04533e8 | 0.342244 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.94102e8 | − | 1.20222e9i | 0.566674 | − | 0.981509i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.25550e8 | − | 1.42989e9i | −0.662181 | − | 1.14693i | −0.980041 | − | 0.198793i | \(-0.936298\pi\) |
0.317861 | − | 0.948137i | \(-0.397036\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.17565e8 | + | 8.96449e8i | 0.400830 | + | 0.694257i | 0.993826 | − | 0.110948i | \(-0.0353886\pi\) |
−0.592997 | + | 0.805205i | \(0.702055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.48577e8 | − | 2.57342e8i | 0.113079 | − | 0.195859i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.20023e9 | −1.61766 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.39925e8 | − | 7.61973e8i | 0.317941 | − | 0.550691i | −0.662117 | − | 0.749401i | \(-0.730342\pi\) |
0.980058 | + | 0.198710i | \(0.0636751\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.35787e8 | − | 1.49169e9i | 0.304403 | − | 1.04196i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.15019e9 | − | 1.99219e9i | −0.789954 | − | 1.36824i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.88360e8 | −0.125095 | −0.0625473 | − | 0.998042i | \(-0.519922\pi\) | ||||
−0.0625473 | + | 0.998042i | \(0.519922\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.55915e9 | −1.67151 | −0.835753 | − | 0.549106i | \(-0.814968\pi\) | ||||
−0.835753 | + | 0.549106i | \(0.814968\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.18448e7 | + | 1.41759e8i | 0.0517166 | + | 0.0895757i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.53933e9 | − | 1.60999e9i | −0.956827 | − | 1.00075i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.09832e9 | + | 1.90235e9i | −0.660785 | + | 1.14451i | 0.319625 | + | 0.947544i | \(0.396443\pi\) |
−0.980410 | + | 0.196969i | \(0.936890\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.66829e9 | −1.57952 | −0.789761 | − | 0.613414i | \(-0.789796\pi\) | ||||
−0.789761 | + | 0.613414i | \(0.789796\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.12868e9 | + | 1.95494e9i | −0.646974 | + | 1.12059i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.10653e8 | − | 7.11272e8i | −0.231659 | − | 0.401245i | 0.726637 | − | 0.687021i | \(-0.241082\pi\) |
−0.958296 | + | 0.285776i | \(0.907749\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.27229e8 | + | 1.08639e9i | 0.342778 | + | 0.593709i | 0.984948 | − | 0.172854i | \(-0.0552987\pi\) |
−0.642169 | + | 0.766563i | \(0.721965\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.09187e8 | + | 1.05514e9i | −0.327711 | + | 0.567612i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.34122e7 | −0.0434878 | −0.0217439 | − | 0.999764i | \(-0.506922\pi\) | ||||
−0.0217439 | + | 0.999764i | \(0.506922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.35945e9 | − | 2.35464e9i | 0.697823 | − | 1.20866i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.49513e8 | − | 8.88511e8i | −0.422796 | − | 0.442204i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.00176e8 | − | 3.46714e8i | −0.0981080 | − | 0.169928i | 0.812794 | − | 0.582552i | \(-0.197946\pi\) |
−0.910901 | + | 0.412624i | \(0.864612\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.55230e7 | 0.0216410 | 0.0108205 | − | 0.999941i | \(-0.496556\pi\) | ||||
0.0108205 | + | 0.999941i | \(0.496556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.41715e9 | 0.663565 | 0.331782 | − | 0.943356i | \(-0.392350\pi\) | ||||
0.331782 | + | 0.943356i | \(0.392350\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.76416e8 | + | 1.34479e9i | 0.352765 | + | 0.611007i | 0.986733 | − | 0.162352i | \(-0.0519082\pi\) |
−0.633968 | + | 0.773359i | \(0.718575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.59575e8 | + | 5.46222e8i | −0.0714267 | + | 0.244492i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.39475e8 | − | 7.61192e8i | 0.190950 | − | 0.330735i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.13416e8 | −0.391058 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.98584e8 | − | 1.03678e9i | 0.248857 | − | 0.431034i | −0.714352 | − | 0.699787i | \(-0.753278\pi\) |
0.963209 | + | 0.268753i | \(0.0866116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.05763e8 | − | 1.39562e9i | −0.330141 | − | 0.571821i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.72538e8 | − | 9.91664e8i | −0.227881 | − | 0.394701i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.14788e8 | + | 1.41125e9i | −0.319664 | + | 0.553674i | −0.980418 | − | 0.196929i | \(-0.936903\pi\) |
0.660754 | + | 0.750602i | \(0.270237\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.66094e9 | 0.633240 | 0.316620 | − | 0.948553i | \(-0.397452\pi\) | ||||
0.316620 | + | 0.948553i | \(0.397452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.65255e8 | − | 8.05845e8i | 0.174875 | − | 0.302892i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.62201e9 | − | 6.39887e8i | 0.958048 | − | 0.233806i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.21787e8 | + | 7.30556e8i | 0.151964 | + | 0.263210i | 0.931949 | − | 0.362588i | \(-0.118107\pi\) |
−0.779985 | + | 0.625798i | \(0.784774\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.39033e7 | 0.00837472 | 0.00418736 | − | 0.999991i | \(-0.498667\pi\) | ||||
0.00418736 | + | 0.999991i | \(0.498667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.57307e8 | −0.330774 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.04440e9 | − | 3.54101e9i | −0.687153 | − | 1.19018i | −0.972755 | − | 0.231836i | \(-0.925527\pi\) |
0.285601 | − | 0.958348i | \(-0.407807\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.42460e8 | − | 8.29935e8i | 0.0803836 | − | 0.275151i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.68251e9 | − | 2.91420e9i | 0.542791 | − | 0.940142i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.69440e9 | −2.13056 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.40519e7 | − | 1.28262e8i | 0.0229406 | − | 0.0397342i | −0.854327 | − | 0.519736i | \(-0.826030\pi\) |
0.877268 | + | 0.480001i | \(0.159364\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.06974e8 | − | 1.39772e9i | −0.246663 | − | 0.427232i | 0.715935 | − | 0.698167i | \(-0.246001\pi\) |
−0.962598 | + | 0.270934i | \(0.912667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.84484e8 | − | 3.19535e8i | −0.0549061 | − | 0.0951002i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.04411e8 | − | 1.80846e8i | 0.0306657 | − | 0.0531145i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.99141e9 | 0.569661 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.22751e9 | − | 3.85817e9i | 0.628901 | − | 1.08929i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.90638e8 | + | 6.47326e9i | −0.0799450 | + | 1.78058i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.89435e9 | + | 3.28111e9i | 0.514362 | + | 0.890902i | 0.999861 | + | 0.0166643i | \(0.00530466\pi\) |
−0.485499 | + | 0.874237i | \(0.661362\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.33452e9 | −0.353132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.21090e9 | 0.577582 | 0.288791 | − | 0.957392i | \(-0.406747\pi\) | ||||
0.288791 | + | 0.957392i | \(0.406747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.59620e9 | + | 4.49676e9i | 0.661162 | + | 1.14517i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.70384e9 | − | 3.87387e9i | −0.931353 | − | 0.974107i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.70947e7 | + | 1.68173e8i | −0.0238069 | + | 0.0412347i | −0.877683 | − | 0.479241i | \(-0.840912\pi\) |
0.853877 | + | 0.520476i | \(0.174245\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.43772e8 | 0.155880 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.43470e9 | + | 2.48497e9i | −0.338830 | + | 0.586871i | −0.984213 | − | 0.176989i | \(-0.943364\pi\) |
0.645383 | + | 0.763859i | \(0.276698\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.45458e8 | + | 1.29117e9i | 0.173882 | + | 0.301172i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.75350e9 | − | 4.76921e9i | −0.626604 | − | 1.08531i | −0.988228 | − | 0.152986i | \(-0.951111\pi\) |
0.361625 | − | 0.932324i | \(-0.382222\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.55175e9 | − | 4.41975e9i | 0.573603 | − | 0.993509i | −0.422589 | − | 0.906321i | \(-0.638879\pi\) |
0.996192 | − | 0.0871876i | \(-0.0277880\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.29322e9 | −0.283685 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.72918e9 | + | 2.99503e9i | −0.374736 | + | 0.649062i | −0.990287 | − | 0.139035i | \(-0.955600\pi\) |
0.615552 | + | 0.788097i | \(0.288933\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.62813e9 | + | 2.10564e9i | −1.82516 | + | 0.445419i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.72022e9 | + | 8.17566e9i | 0.986557 | + | 1.70877i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.14732e9 | −0.846318 | −0.423159 | − | 0.906055i | \(-0.639079\pi\) | ||||
−0.423159 | + | 0.906055i | \(0.639079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.05890e9 | 0.415176 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.97134e9 | + | 6.87856e9i | 0.782069 | + | 1.35458i | 0.930734 | + | 0.365696i | \(0.119169\pi\) |
−0.148665 | + | 0.988888i | \(0.547498\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.48284e9 | + | 3.61879e8i | −0.288593 | + | 0.0704295i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.80065e9 | − | 3.11882e9i | 0.342323 | − | 0.592921i | −0.642541 | − | 0.766252i | \(-0.722120\pi\) |
0.984864 | + | 0.173331i | \(0.0554530\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.09831e8 | −0.133381 | −0.0666906 | − | 0.997774i | \(-0.521244\pi\) | ||||
−0.0666906 | + | 0.997774i | \(0.521244\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.98559e9 | − | 8.63529e9i | 0.915319 | − | 1.58538i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.94285e9 | + | 6.82922e9i | 0.715566 | + | 1.23940i | 0.962741 | + | 0.270426i | \(0.0871646\pi\) |
−0.247174 | + | 0.968971i | \(0.579502\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.45160e9 | − | 4.24630e9i | −0.434816 | − | 0.753123i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.08263e9 | + | 8.80338e9i | −0.891204 | + | 1.54361i | −0.0527708 | + | 0.998607i | \(0.516805\pi\) |
−0.838433 | + | 0.545004i | \(0.816528\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.64250e9 | 0.967105 | 0.483552 | − | 0.875315i | \(-0.339346\pi\) | ||||
0.483552 | + | 0.875315i | \(0.339346\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.82276e9 | − | 1.00853e10i | 0.986760 | − | 1.70912i | 0.352922 | − | 0.935653i | \(-0.385188\pi\) |
0.633838 | − | 0.773466i | \(-0.281479\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.25072e9 | + | 3.39995e9i | 0.538607 | + | 0.563332i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.89654e9 | + | 3.28490e9i | 0.310729 | + | 0.538199i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.00099e9 | −0.320603 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.07600e10 | 1.70494 | 0.852469 | − | 0.522777i | \(-0.175104\pi\) | ||||
0.852469 | + | 0.522777i | \(0.175104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.84224e9 | − | 8.38701e9i | −0.750479 | − | 1.29987i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.21247e9 | + | 2.18627e9i | −0.645727 | + | 0.335131i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.13595e9 | + | 8.89572e9i | −0.770225 | + | 1.33407i | 0.167215 | + | 0.985921i | \(0.446523\pi\) |
−0.937439 | + | 0.348148i | \(0.886811\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.16555e10 | 1.72899 | 0.864497 | − | 0.502638i | \(-0.167637\pi\) | ||||
0.864497 | + | 0.502638i | \(0.167637\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.47741e9 | − | 2.55895e9i | 0.214455 | − | 0.371447i | −0.738649 | − | 0.674090i | \(-0.764536\pi\) |
0.953104 | + | 0.302644i | \(0.0978692\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.73695e9 | + | 1.16687e10i | 0.967402 | + | 1.67559i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.44343e9 | + | 4.23214e9i | 0.343403 | + | 0.594791i | 0.985062 | − | 0.172199i | \(-0.0550871\pi\) |
−0.641660 | + | 0.766990i | \(0.721754\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.57030e9 | + | 4.45190e9i | −0.357388 | + | 0.619014i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.12839e10 | −1.53589 | −0.767947 | − | 0.640513i | \(-0.778722\pi\) | ||||
−0.767947 | + | 0.640513i | \(0.778722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.19740e9 | − | 5.53807e9i | 0.430618 | − | 0.745853i | −0.566308 | − | 0.824193i | \(-0.691629\pi\) |
0.996927 | + | 0.0783406i | \(0.0249622\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.38846e9 | − | 8.17563e9i | 0.314950 | − | 1.07807i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.67573e9 | + | 6.36656e9i | 0.479627 | + | 0.830738i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.93127e10 | 2.46782 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.86561e8 | 0.0362380 | 0.0181190 | − | 0.999836i | \(-0.494232\pi\) | ||||
0.0181190 | + | 0.999836i | \(0.494232\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.77078e9 | + | 1.17273e10i | 0.838646 | + | 1.45258i | 0.891027 | + | 0.453950i | \(0.149985\pi\) |
−0.0523818 | + | 0.998627i | \(0.516681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.29488e9 | + | 1.04814e9i | −0.526510 | + | 0.128492i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.56295e9 | + | 2.70711e9i | −0.187704 | + | 0.325112i | −0.944484 | − | 0.328557i | \(-0.893438\pi\) |
0.756781 | + | 0.653669i | \(0.226771\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.81307e9 | −1.04763 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.45725e9 | + | 5.98813e9i | −0.402683 | + | 0.697467i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.72246e9 | + | 6.44749e9i | 0.429197 | + | 0.743392i | 0.996802 | − | 0.0799095i | \(-0.0254631\pi\) |
−0.567605 | + | 0.823301i | \(0.692130\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.70258e9 | − | 6.41305e9i | −0.418367 | − | 0.724633i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.23634e9 | − | 2.14141e9i | 0.138301 | − | 0.239544i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.02247e9 | 0.879620 | 0.439810 | − | 0.898091i | \(-0.355046\pi\) | ||||
0.439810 | + | 0.898091i | \(0.355046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.58294e9 | − | 9.66993e9i | 0.606065 | − | 1.04974i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.03643e9 | + | 3.54769e9i | −0.110300 | + | 0.377553i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.07598e9 | + | 1.57201e10i | 0.956383 | + | 1.65650i | 0.731172 | + | 0.682193i | \(0.238974\pi\) |
0.225211 | + | 0.974310i | \(0.427693\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.91502e9 | 0.301181 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.06581e10 | 1.09046 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.98920e9 | − | 1.21056e10i | −0.701255 | − | 1.21461i | −0.968026 | − | 0.250850i | \(-0.919290\pi\) |
0.266771 | − | 0.963760i | \(-0.414043\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.97816e9 | − | 9.39030e9i | −0.892100 | − | 0.933053i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.48734e9 | + | 2.57615e9i | −0.144953 | + | 0.251066i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.81996e9 | −0.658281 | −0.329140 | − | 0.944281i | \(-0.606759\pi\) | ||||
−0.329140 | + | 0.944281i | \(0.606759\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.99678e8 | − | 6.92262e8i | 0.0378442 | − | 0.0655480i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.74796e9 | − | 9.95576e9i | −0.539076 | − | 0.933706i | −0.998954 | − | 0.0457245i | \(-0.985440\pi\) |
0.459879 | − | 0.887982i | \(-0.347893\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.46692e9 | − | 4.27283e9i | −0.226996 | − | 0.393169i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.74312e8 | + | 1.16794e9i | −0.0614618 | + | 0.106455i | −0.895119 | − | 0.445827i | \(-0.852910\pi\) |
0.833657 | + | 0.552282i | \(0.186243\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.00361e9 | 0.179206 | 0.0896029 | − | 0.995978i | \(-0.471440\pi\) | ||||
0.0896029 | + | 0.995978i | \(0.471440\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.94806e9 | − | 3.37414e9i | 0.172606 | − | 0.298962i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.18864e10 | − | 1.24320e10i | −1.03363 | − | 1.08107i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.69709e9 | + | 6.40354e9i | 0.318508 | + | 0.551671i | 0.980177 | − | 0.198125i | \(-0.0634850\pi\) |
−0.661669 | + | 0.749796i | \(0.730152\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.46561e10 | 1.23937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.79000e10 | 1.49975 | 0.749874 | − | 0.661581i | \(-0.230114\pi\) | ||||
0.749874 | + | 0.661581i | \(0.230114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.51905e9 | − | 1.12913e10i | −0.536214 | − | 0.928749i | −0.999104 | − | 0.0423334i | \(-0.986521\pi\) |
0.462890 | − | 0.886416i | \(-0.346812\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.44483e9 | + | 4.94561e9i | −0.117755 | + | 0.403073i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.93437e9 | + | 8.54658e9i | −0.394865 | + | 0.683926i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.72914e10 | −1.37116 | −0.685580 | − | 0.727997i | \(-0.740451\pi\) | ||||
−0.685580 | + | 0.727997i | \(0.740451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.33950e9 | + | 9.24829e9i | −0.415789 | + | 0.720167i | −0.995511 | − | 0.0946470i | \(-0.969828\pi\) |
0.579722 | + | 0.814814i | \(0.303161\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.89764e8 | + | 1.02150e9i | 0.0455116 | + | 0.0788284i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.89902e9 | + | 1.19494e10i | 0.522885 | + | 0.905663i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.17003e10 | + | 2.02656e10i | −0.878860 | + | 1.52223i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.35608e9 | −0.690319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.13691e10 | − | 1.96918e10i | 0.831407 | − | 1.44004i | −0.0655160 | − | 0.997852i | \(-0.520869\pi\) |
0.896923 | − | 0.442187i | \(-0.145797\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.59204e9 | − | 1.36470e9i | 0.401747 | − | 0.0980440i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.07262e9 | + | 1.22501e10i | 0.503645 | + | 0.872338i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.15349e10 | −0.807067 | −0.403534 | − | 0.914965i | \(-0.632218\pi\) | ||||
−0.403534 | + | 0.914965i | \(0.632218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.08818e9 | −0.422254 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.74826e9 | + | 6.49218e9i | 0.255462 | + | 0.442472i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.38160e9 | − | 1.15751e10i | 0.228474 | − | 0.782061i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.85450e8 | + | 1.18723e9i | −0.0455152 | + | 0.0788346i | −0.887885 | − | 0.460065i | \(-0.847826\pi\) |
0.842370 | + | 0.538899i | \(0.181160\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.38277e10 | −1.56859 | −0.784293 | − | 0.620390i | \(-0.786974\pi\) | ||||
−0.784293 | + | 0.620390i | \(0.786974\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.93702e9 | + | 6.81912e9i | −0.254751 | + | 0.441242i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.23027e9 | + | 3.86294e9i | 0.143081 | + | 0.247823i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.09835e10 | + | 1.90240e10i | 0.692691 | + | 1.19978i | 0.970953 | + | 0.239271i | \(0.0769083\pi\) |
−0.278262 | + | 0.960505i | \(0.589758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.92559e8 | + | 8.53137e8i | −0.0308006 | + | 0.0533481i | −0.881015 | − | 0.473089i | \(-0.843139\pi\) |
0.850214 | + | 0.526437i | \(0.176472\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.53940e10 | −0.946415 | −0.473208 | − | 0.880951i | \(-0.656904\pi\) | ||||
−0.473208 | + | 0.880951i | \(0.656904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.18113e10 | − | 2.04578e10i | 0.720040 | − | 1.24715i | −0.240944 | − | 0.970539i | \(-0.577457\pi\) |
0.960983 | − | 0.276606i | \(-0.0892097\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.64319e8 | + | 5.88707e9i | −0.0158442 | + | 0.352892i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.76923e9 | + | 1.69208e10i | 0.580708 | + | 1.00582i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.00471e10 | −0.587319 | −0.293660 | − | 0.955910i | \(-0.594873\pi\) | ||||
−0.293660 | + | 0.955910i | \(0.594873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.39991e8 | −0.0197098 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.47140e9 | − | 6.01263e9i | −0.197927 | − | 0.342820i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.66039e10 | − | 2.78252e10i | −1.50437 | − | 1.57342i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.90438e9 | − | 1.36908e10i | 0.439658 | − | 0.761509i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.86048e10 | −1.02637 | −0.513185 | − | 0.858278i | \(-0.671534\pi\) | ||||
−0.513185 | + | 0.858278i | \(0.671534\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.41716e10 | − | 2.45459e10i | 0.769105 | − | 1.33213i | −0.168944 | − | 0.985626i | \(-0.554036\pi\) |
0.938049 | − | 0.346503i | \(-0.112631\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.72295e10 | − | 2.98424e10i | −0.927463 | − | 1.60641i | −0.787551 | − | 0.616250i | \(-0.788651\pi\) |
−0.139913 | − | 0.990164i | \(-0.544682\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.59668e9 | − | 4.49758e9i | −0.137525 | − | 0.238199i | 0.789034 | − | 0.614349i | \(-0.210581\pi\) |
−0.926559 | + | 0.376149i | \(0.877248\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.76755e9 | − | 1.51858e10i | 0.460598 | − | 0.797779i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.64690e10 | 2.40212 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.80686e9 | − | 3.12957e9i | 0.0926531 | − | 0.160480i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.09300e10 | − | 5.10784e9i | 1.05619 | − | 0.257756i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.25283e10 | − | 2.16997e10i | −0.627184 | − | 1.08632i | −0.988114 | − | 0.153722i | \(-0.950874\pi\) |
0.360930 | − | 0.932593i | \(-0.382459\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.93660e10 | −1.44687 | −0.723434 | − | 0.690394i | \(-0.757437\pi\) | ||||
−0.723434 | + | 0.690394i | \(0.757437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.74989e10 | −0.855360 | −0.427680 | − | 0.903930i | \(-0.640669\pi\) | ||||
−0.427680 | + | 0.903930i | \(0.640669\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.08503e9 | + | 5.34343e9i | 0.148432 | + | 0.257091i | 0.930648 | − | 0.365916i | \(-0.119244\pi\) |
−0.782216 | + | 0.623007i | \(0.785911\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.63240e10 | + | 8.86465e9i | −1.73395 | + | 0.423161i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.69866e10 | − | 2.94216e10i | 0.798225 | − | 1.38257i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.43056e10 | −1.59950 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.35257e9 | − | 5.80682e9i | 0.153893 | − | 0.266551i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.29277e9 | + | 7.43530e9i | 0.195525 | + | 0.338658i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.69932e9 | − | 1.67997e10i | −0.434982 | − | 0.753411i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.53133e10 | + | 2.65234e10i | −0.681464 | + | 1.18033i | 0.293069 | + | 0.956091i | \(0.405323\pi\) |
−0.974534 | + | 0.224240i | \(0.928010\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.76610e10 | −1.21214 | −0.606071 | − | 0.795411i | \(-0.707255\pi\) | ||||
−0.606071 | + | 0.795411i | \(0.707255\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.85017e10 | − | 6.66869e10i | 1.67430 | − | 2.89997i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.37156e10 | + | 1.43452e10i | 0.587382 | + | 0.614347i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.88796e8 | + | 1.01982e9i | 0.0250242 | + | 0.0433432i | 0.878266 | − | 0.478172i | \(-0.158700\pi\) |
−0.853242 | + | 0.521515i | \(0.825367\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.71394e10 | −0.717448 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.39683e9 | 0.265747 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.36178e10 | + | 4.09073e10i | 0.966463 | + | 1.67396i | 0.705633 | + | 0.708578i | \(0.250663\pi\) |
0.260830 | + | 0.965385i | \(0.416004\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.77122e10 | − | 1.77028e10i | −1.12551 | − | 0.718982i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.61697e9 | − | 1.14609e10i | 0.264739 | − | 0.458542i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.50207e10 | 0.596489 | 0.298245 | − | 0.954489i | \(-0.403599\pi\) | ||||
0.298245 | + | 0.954489i | \(0.403599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.66955e10 | + | 2.89175e10i | −0.653185 | + | 1.13135i | 0.329161 | + | 0.944274i | \(0.393234\pi\) |
−0.982346 | + | 0.187075i | \(0.940099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.76770e9 | + | 1.69182e10i | 0.379316 | + | 0.656995i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.60668e9 | + | 1.14431e10i | 0.252789 | + | 0.437843i | 0.964293 | − | 0.264839i | \(-0.0853188\pi\) |
−0.711504 | + | 0.702682i | \(0.751985\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.74535e9 | + | 4.75509e9i | −0.104272 | + | 0.180604i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.62784e10 | −0.983499 | −0.491750 | − | 0.870737i | \(-0.663642\pi\) | ||||
−0.491750 | + | 0.870737i | \(0.663642\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.66414e9 | + | 2.88238e9i | −0.0618271 | + | 0.107088i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.54152e9 | + | 3.26604e10i | −0.349343 | + | 1.19579i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.24269e10 | + | 2.15241e10i | 0.451682 | + | 0.782335i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.67978e9 | −0.0959961 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.66478e10 | 1.65897 | 0.829486 | − | 0.558528i | \(-0.188634\pi\) | ||||
0.829486 | + | 0.558528i | \(0.188634\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.09381e9 | − | 7.09069e9i | −0.143503 | − | 0.248554i | 0.785310 | − | 0.619102i | \(-0.212503\pi\) |
−0.928813 | + | 0.370548i | \(0.879170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.77748e10 | + | 6.77828e9i | −0.966620 | + | 0.235898i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.36224e9 | − | 1.10197e10i | 0.218262 | − | 0.378042i | −0.736014 | − | 0.676966i | \(-0.763294\pi\) |
0.954277 | + | 0.298924i | \(0.0966278\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.07841e10 | −1.38916 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.99730e9 | + | 8.65558e9i | −0.167802 | + | 0.290642i | −0.937647 | − | 0.347589i | \(-0.887000\pi\) |
0.769844 | + | 0.638232i | \(0.220334\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.15204e9 | − | 1.23877e10i | −0.238453 | − | 0.413013i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.15764e9 | + | 5.46920e9i | 0.103795 | + | 0.179778i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.83437e8 | − | 1.18375e9i | 0.0223070 | − | 0.0386368i | −0.854656 | − | 0.519194i | \(-0.826232\pi\) |
0.876963 | + | 0.480557i | \(0.159566\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.90279e10 | 0.612364 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.10973e9 | − | 1.23144e10i | 0.227206 | − | 0.393533i | −0.729773 | − | 0.683690i | \(-0.760374\pi\) |
0.956979 | + | 0.290157i | \(0.0937075\pi\) | |||||||
\(998\) | 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 | 252.8.k.e.109.5 | yes | 16 | |
3.2 | odd | 2 | inner | 252.8.k.e.109.4 | yes | 16 | |
7.2 | even | 3 | inner | 252.8.k.e.37.5 | yes | 16 | |
21.2 | odd | 6 | inner | 252.8.k.e.37.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.8.k.e.37.4 | ✓ | 16 | 21.2 | odd | 6 | inner | |
252.8.k.e.37.5 | yes | 16 | 7.2 | even | 3 | inner | |
252.8.k.e.109.4 | yes | 16 | 3.2 | odd | 2 | inner | |
252.8.k.e.109.5 | yes | 16 | 1.1 | even | 1 | trivial |