Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,12,Mod(33,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.33");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.e (of order \(4\), degree \(2\), not 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: | \(98.3479271116\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 33.14 | ||
Character | \(\chi\) | \(=\) | 128.33 |
Dual form | 128.12.e.b.97.14 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 179.701 | + | 179.701i | 0.426956 | + | 0.426956i | 0.887590 | − | 0.460634i | \(-0.152378\pi\) |
−0.460634 | + | 0.887590i | \(0.652378\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2961.29 | + | 2961.29i | −0.423785 | + | 0.423785i | −0.886505 | − | 0.462719i | \(-0.846874\pi\) |
0.462719 | + | 0.886505i | \(0.346874\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5179.04i | 0.116469i | 0.998303 | + | 0.0582345i | \(0.0185471\pi\) | ||||
−0.998303 | + | 0.0582345i | \(0.981453\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 112562.i | − | 0.635416i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −694803. | + | 694803.i | −1.30077 | + | 1.30077i | −0.372903 | + | 0.927870i | \(0.621638\pi\) |
−0.927870 | + | 0.372903i | \(0.878362\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −524615. | − | 524615.i | −0.391879 | − | 0.391879i | 0.483478 | − | 0.875357i | \(-0.339373\pi\) |
−0.875357 | + | 0.483478i | \(0.839373\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.06429e6 | −0.361876 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.82572e6 | 0.311864 | 0.155932 | − | 0.987768i | \(-0.450162\pi\) | ||||
0.155932 | + | 0.987768i | \(0.450162\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 601185. | + | 601185.i | 0.0557011 | + | 0.0557011i | 0.734409 | − | 0.678708i | \(-0.237460\pi\) |
−0.678708 | + | 0.734409i | \(0.737460\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −930679. | + | 930679.i | −0.0497272 | + | 0.0497272i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.32829e7i | − | 0.754284i | −0.926156 | − | 0.377142i | \(-0.876907\pi\) | ||
0.926156 | − | 0.377142i | \(-0.123093\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.12896e7i | 0.640812i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.20610e7 | − | 5.20610e7i | 0.698252 | − | 0.698252i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −189495. | − | 189495.i | −0.00171557 | − | 0.00171557i | 0.706248 | − | 0.707964i | \(-0.250386\pi\) |
−0.707964 | + | 0.706248i | \(0.750386\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.48770e8 | −1.56066 | −0.780330 | − | 0.625367i | \(-0.784949\pi\) | ||||
−0.780330 | + | 0.625367i | \(0.784949\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.49713e8 | −1.11075 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.53366e7 | − | 1.53366e7i | −0.0493578 | − | 0.0493578i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.30934e8 | − | 4.30934e8i | 1.02165 | − | 1.02165i | 0.0218884 | − | 0.999760i | \(-0.493032\pi\) |
0.999760 | − | 0.0218884i | \(-0.00696786\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.88548e8i | − | 0.334630i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.02672e8i | 0.138401i | 0.997603 | + | 0.0692007i | \(0.0220449\pi\) | ||||
−0.997603 | + | 0.0692007i | \(0.977955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.91645e7 | − | 6.91645e7i | 0.0717475 | − | 0.0717475i | −0.670322 | − | 0.742070i | \(-0.733844\pi\) |
0.742070 | + | 0.670322i | \(0.233844\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.33329e8 | + | 3.33329e8i | 0.269280 | + | 0.269280i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.50575e8 | 0.159367 | 0.0796836 | − | 0.996820i | \(-0.474609\pi\) | ||||
0.0796836 | + | 0.996820i | \(0.474609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.95050e9 | 0.986435 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.28084e8 | + | 3.28084e8i | 0.133152 | + | 0.133152i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.76937e9 | − | 1.76937e9i | 0.581169 | − | 0.581169i | −0.354056 | − | 0.935224i | \(-0.615198\pi\) |
0.935224 | + | 0.354056i | \(0.115198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.11502e9i | − | 1.10250i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.16067e8i | 0.0475639i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.82611e9 | + | 3.82611e9i | −0.696742 | + | 0.696742i | −0.963706 | − | 0.266964i | \(-0.913979\pi\) |
0.266964 | + | 0.963706i | \(0.413979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.80093e9 | − | 7.80093e9i | −1.18258 | − | 1.18258i | −0.979072 | − | 0.203512i | \(-0.934764\pi\) |
−0.203512 | − | 0.979072i | \(-0.565236\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.82964e8 | 0.0740063 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.10707e9 | 0.332145 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.53658e9 | + | 6.53658e9i | 0.591479 | + | 0.591479i | 0.938031 | − | 0.346552i | \(-0.112648\pi\) |
−0.346552 | + | 0.938031i | \(0.612648\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.18397e9 | − | 4.18397e9i | 0.322046 | − | 0.322046i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.53408e10i | − | 1.00908i | −0.863388 | − | 0.504541i | \(-0.831662\pi\) | ||
0.863388 | − | 0.504541i | \(-0.168338\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.49847e10i | 1.41058i | 0.708917 | + | 0.705291i | \(0.249184\pi\) | ||||
−0.708917 | + | 0.705291i | \(0.750816\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.62278e9 | + | 5.62278e9i | −0.273599 | + | 0.273599i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.59841e9 | − | 3.59841e9i | −0.151500 | − | 0.151500i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.46282e10 | 0.900499 | 0.450249 | − | 0.892903i | \(-0.351335\pi\) | ||||
0.450249 | + | 0.892903i | \(0.351335\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.22922e9 | −0.0391706 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.00793e10 | + | 2.00793e10i | 0.559524 | + | 0.559524i | 0.929172 | − | 0.369648i | \(-0.120522\pi\) |
−0.369648 | + | 0.929172i | \(0.620522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.40649e9 | + | 5.40649e9i | −0.132163 | + | 0.132163i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 6.81047e7i | − | 0.00146495i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.72435e10i | − | 0.706978i | −0.935439 | − | 0.353489i | \(-0.884995\pi\) | ||
0.935439 | − | 0.353489i | \(-0.115005\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.71700e9 | − | 2.71700e9i | 0.0456417 | − | 0.0456417i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.47042e10 | − | 4.47042e10i | −0.666334 | − | 0.666334i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.56057e9 | −0.0472106 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.06041e11 | −1.25381 | −0.626904 | − | 0.779097i | \(-0.715678\pi\) | ||||
−0.626904 | + | 0.779097i | \(0.715678\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.82084e10 | + | 7.82084e10i | 0.826533 | + | 0.826533i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.45309e11 | − | 1.45309e11i | 1.37571 | − | 1.37571i | 0.523973 | − | 0.851735i | \(-0.324449\pi\) |
0.851735 | − | 0.523973i | \(-0.175551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.17356e10i | 0.779710i | 0.920876 | + | 0.389855i | \(0.127475\pi\) | ||||
−0.920876 | + | 0.389855i | \(0.872525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 5.51202e9i | − | 0.0421473i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.50629e11 | − | 1.50629e11i | 1.03824 | − | 1.03824i | 0.0390029 | − | 0.999239i | \(-0.487582\pi\) |
0.999239 | − | 0.0390029i | \(-0.0124182\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.29906e10 | + | 7.29906e10i | 0.454382 | + | 0.454382i | 0.896806 | − | 0.442424i | \(-0.145881\pi\) |
−0.442424 | + | 0.896806i | \(0.645881\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.54879e11 | 0.872399 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.01998e11 | 1.54196 | 0.770979 | − | 0.636861i | \(-0.219767\pi\) | ||||
0.770979 | + | 0.636861i | \(0.219767\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.89475e10 | + | 6.89475e10i | 0.319654 | + | 0.319654i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.90517e10 | + | 5.90517e10i | −0.249006 | + | 0.249006i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.45549e9i | 0.0363225i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 6.80189e11i | − | 2.38402i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.84502e10 | + | 1.84502e10i | −0.0590913 | + | 0.0590913i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.37252e11 | − | 2.37252e11i | −0.695352 | − | 0.695352i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.26018e11 | 1.14421 | 0.572107 | − | 0.820179i | \(-0.306126\pi\) | ||||
0.572107 | + | 0.820179i | \(0.306126\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.48578e10 | 0.0612661 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.65762e11 | − | 3.65762e11i | −0.828336 | − | 0.828336i | 0.158951 | − | 0.987287i | \(-0.449189\pi\) |
−0.987287 | + | 0.158951i | \(0.949189\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.11356e9 | + | 3.11356e9i | −0.00648744 | + | 0.00648744i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.08335e11i | 0.591817i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 9.23893e11i | − | 1.63553i | −0.575552 | − | 0.817765i | \(-0.695213\pi\) | ||
0.575552 | − | 0.817765i | \(-0.304787\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.31354e11 | − | 4.31354e11i | 0.705103 | − | 0.705103i | −0.260398 | − | 0.965501i | \(-0.583854\pi\) |
0.965501 | + | 0.260398i | \(0.0838538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.50285e10 | + | 4.50285e10i | 0.0680428 | + | 0.0680428i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.29007e11 | 1.01949 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.12230e9 | 0.00145406 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.50508e11 | + | 3.50508e11i | 0.421165 | + | 0.421165i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.92517e11 | − | 6.92517e11i | 0.772513 | − | 0.772513i | −0.206032 | − | 0.978545i | \(-0.566055\pi\) |
0.978545 | + | 0.206032i | \(0.0660551\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.06664e11i | 0.110572i | 0.998471 | + | 0.0552862i | \(0.0176071\pi\) | ||||
−0.998471 | + | 0.0552862i | \(0.982393\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.05507e11i | − | 0.198164i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.36680e11 | − | 7.36680e11i | 0.661385 | − | 0.661385i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.38255e11 | + | 2.38255e11i | 0.199339 | + | 0.199339i | 0.799717 | − | 0.600377i | \(-0.204983\pi\) |
−0.600377 | + | 0.799717i | \(0.704983\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.35916e11 | 0.496267 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.20583e11 | 0.0878506 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.01643e12 | + | 2.01643e12i | 1.37262 | + | 1.37262i | 0.856539 | + | 0.516082i | \(0.172610\pi\) |
0.516082 | + | 0.856539i | \(0.327390\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.39474e11 | − | 7.39474e11i | 0.470718 | − | 0.470718i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.58210e12i | 0.942525i | 0.881993 | + | 0.471263i | \(0.156202\pi\) | ||||
−0.881993 | + | 0.471263i | \(0.843798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.24172e12i | − | 0.692862i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.76707e10 | − | 6.76707e10i | 0.0353934 | − | 0.0353934i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.50263e12 | − | 2.50263e12i | −1.22784 | − | 1.22784i | −0.964778 | − | 0.263066i | \(-0.915266\pi\) |
−0.263066 | − | 0.964778i | \(-0.584734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.62050e11 | −0.0746347 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.37511e12 | −0.594957 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.34310e12 | + | 1.34310e12i | 0.546283 | + | 0.546283i | 0.925364 | − | 0.379081i | \(-0.123760\pi\) |
−0.379081 | + | 0.925364i | \(0.623760\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.48029e12 | − | 1.48029e12i | 0.566390 | − | 0.566390i | −0.364725 | − | 0.931115i | \(-0.618837\pi\) |
0.931115 | + | 0.364725i | \(0.118837\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.80367e12i | − | 1.00982i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.55224e12i | 0.865920i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.26852e12 | + | 1.26852e12i | −0.405665 | + | 0.405665i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.69626e11 | + | 2.69626e11i | 0.0813246 | + | 0.0813246i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.79477e12 | 1.08020 | 0.540098 | − | 0.841602i | \(-0.318387\pi\) | ||||
0.540098 | + | 0.841602i | \(0.318387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.92445e12 | 0.517299 | 0.258650 | − | 0.965971i | \(-0.416723\pi\) | ||||
0.258650 | + | 0.965971i | \(0.416723\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.58344e11 | + | 5.58344e11i | 0.141811 | + | 0.141811i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.87881e12 | + | 1.87881e12i | −0.451147 | + | 0.451147i | −0.895735 | − | 0.444588i | \(-0.853350\pi\) |
0.444588 | + | 0.895735i | \(0.353350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.42680e12i | − | 0.778390i | −0.921155 | − | 0.389195i | \(-0.872753\pi\) | ||
0.921155 | − | 0.389195i | \(-0.127247\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.34926e12i | 0.505071i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.81400e8 | − | 9.81400e8i | 0.000199810 | − | 0.000199810i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.04041e11 | − | 3.04041e11i | −0.0586525 | − | 0.0586525i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.62078e12 | −0.479284 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.35410e11 | −0.144909 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.45545e12 | − | 4.45545e12i | −0.733395 | − | 0.733395i | 0.237896 | − | 0.971291i | \(-0.423542\pi\) |
−0.971291 | + | 0.237896i | \(0.923542\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.75675e12 | − | 2.75675e12i | 0.430834 | − | 0.430834i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.09632e11i | 0.0608111i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.28839e12i | − | 0.181769i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.48978e12 | + | 4.48978e12i | −0.602257 | + | 0.602257i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.57801e11 | − | 9.57801e11i | −0.122213 | − | 0.122213i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.95131e12 | −0.722663 | −0.361332 | − | 0.932437i | \(-0.617678\pi\) | ||||
−0.361332 | + | 0.932437i | \(0.617678\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.52203e12 | 0.407183 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.36916e12 | − | 1.36916e12i | −0.150769 | − | 0.150769i | 0.627692 | − | 0.778462i | \(-0.284000\pi\) |
−0.778462 | + | 0.627692i | \(0.784000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.82685e12 | + | 5.82685e12i | −0.611419 | + | 0.611419i | −0.943316 | − | 0.331897i | \(-0.892311\pi\) |
0.331897 | + | 0.943316i | \(0.392311\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.29328e12i | − | 0.129368i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.78470e12i | 0.265657i | 0.991139 | + | 0.132828i | \(0.0424059\pi\) | ||||
−0.991139 | + | 0.132828i | \(0.957594\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.42024e11 | + | 7.42024e11i | −0.0675375 | + | 0.0675375i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.42571e12 | + | 4.42571e12i | 0.384474 | + | 0.384474i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.89713e12 | −0.655059 | −0.327530 | − | 0.944841i | \(-0.606216\pi\) | ||||
−0.327530 | + | 0.944841i | \(0.606216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.72861e12 | 0.533128 | 0.266564 | − | 0.963817i | \(-0.414112\pi\) | ||||
0.266564 | + | 0.963817i | \(0.414112\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.44334e12 | − | 9.44334e12i | −0.714976 | − | 0.714976i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.77601e12 | + | 5.77601e12i | −0.418037 | + | 0.418037i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.30781e11i | − | 0.0436562i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.21653e12i | 0.477784i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.58474e12 | − | 5.58474e12i | 0.353832 | − | 0.353832i | −0.507701 | − | 0.861533i | \(-0.669505\pi\) |
0.861533 | + | 0.507701i | \(0.169505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.61770e13 | + | 1.61770e13i | 0.981152 | + | 0.981152i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.94310e12 | −0.112856 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.56783e13 | −1.42868 | −0.714340 | − | 0.699799i | \(-0.753273\pi\) | ||||
−0.714340 | + | 0.699799i | \(0.753273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.23183e12 | + | 2.23183e12i | 0.118990 | + | 0.118990i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.13299e10 | + | 2.13299e10i | −0.00109010 | + | 0.00109010i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.11569e13i | 1.03680i | 0.855138 | + | 0.518401i | \(0.173473\pi\) | ||||
−0.855138 | + | 0.518401i | \(0.826527\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.04793e13i | 0.492582i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.69270e12 | − | 6.69270e12i | 0.301849 | − | 0.301849i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.13645e13 | + | 1.13645e13i | 0.491940 | + | 0.491940i | 0.908917 | − | 0.416977i | \(-0.136911\pi\) |
−0.416977 | + | 0.908917i | \(0.636911\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.20682e13 | −1.74833 | −0.874163 | − | 0.485633i | \(-0.838589\pi\) | ||||
−0.874163 | + | 0.485633i | \(0.838589\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.76495e11 | 0.0389741 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.17401e13 | − | 2.17401e13i | −0.833551 | − | 0.833551i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.99399e13 | + | 2.99399e13i | −1.10309 | + | 1.10309i | −0.109056 | + | 0.994036i | \(0.534783\pi\) |
−0.994036 | + | 0.109056i | \(0.965217\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.80021e13i | 0.991670i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.93200e13i | − | 0.657844i | −0.944357 | − | 0.328922i | \(-0.893315\pi\) | ||
0.944357 | − | 0.328922i | \(-0.106685\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.01259e13 | + | 2.01259e13i | −0.659068 | + | 0.659068i | −0.955160 | − | 0.296092i | \(-0.904317\pi\) |
0.296092 | + | 0.955160i | \(0.404317\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.39837e11 | − | 6.39837e11i | −0.0201569 | − | 0.0201569i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.31742e11 | −0.0161195 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.09386e13 | −0.902741 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.90557e13 | − | 1.90557e13i | −0.535321 | − | 0.535321i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.16215e13 | + | 1.16215e13i | −0.314406 | + | 0.314406i | −0.846614 | − | 0.532207i | \(-0.821363\pi\) |
0.532207 | + | 0.846614i | \(0.321363\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.26605e13i | − | 0.590538i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.23442e13i | 1.81653i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.22146e13 | + | 1.22146e13i | −0.295588 | + | 0.295588i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.58206e11 | + | 3.58206e11i | 0.00835635 | + | 0.00835635i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.22245e13 | 1.17473 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.62016e13 | 1.00232 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.57889e13 | + | 2.57889e13i | 0.539723 | + | 0.539723i | 0.923448 | − | 0.383724i | \(-0.125359\pi\) |
−0.383724 | + | 0.923448i | \(0.625359\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.64850e13 | + | 1.64850e13i | −0.332902 | + | 0.332902i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.96609e13i | − | 1.74752i | −0.486361 | − | 0.873758i | \(-0.661676\pi\) | ||
0.486361 | − | 0.873758i | \(-0.338324\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.96628e13i | − | 0.558108i | −0.960275 | − | 0.279054i | \(-0.909979\pi\) | ||
0.960275 | − | 0.279054i | \(-0.0900209\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.72633e12 | + | 1.72633e12i | −0.0313628 | + | 0.0313628i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.58883e13 | − | 2.58883e13i | −0.454233 | − | 0.454233i | 0.442524 | − | 0.896757i | \(-0.354083\pi\) |
−0.896757 | + | 0.442524i | \(0.854083\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.63323e11 | 0.00446313 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.41365e13 | 0.886568 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.09760e12 | + | 1.09760e12i | 0.0173712 | + | 0.0173712i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.64150e13 | − | 1.64150e13i | 0.251121 | − | 0.251121i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.62330e13i | 0.388003i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.29774e12i | 0.0185613i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.92511e13 | + | 2.92511e13i | −0.404658 | + | 0.404658i | −0.879871 | − | 0.475213i | \(-0.842371\pi\) |
0.475213 | + | 0.879871i | \(0.342371\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.85069e13 | − | 4.85069e13i | −0.649173 | − | 0.649173i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.87134e13 | −0.501320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.74548e13 | −0.218751 | −0.109376 | − | 0.994000i | \(-0.534885\pi\) | ||||
−0.109376 | + | 0.994000i | \(0.534885\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.42693e13 | + | 5.42693e13i | 0.658349 | + | 0.658349i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.72846e14 | − | 1.72846e14i | 2.03007 | − | 2.03007i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.03424e13i | 0.231358i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.47799e13i | 0.272957i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.65389e13 | − | 1.65389e13i | 0.176480 | − | 0.176480i | −0.613340 | − | 0.789819i | \(-0.710174\pi\) |
0.789819 | + | 0.613340i | \(0.210174\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.01630e13 | + | 4.01630e13i | 0.415228 | + | 0.415228i | 0.883555 | − | 0.468327i | \(-0.155143\pi\) |
−0.468327 | + | 0.883555i | \(0.655143\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.46239e13 | −0.547260 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.14061e13 | −0.596281 | −0.298140 | − | 0.954522i | \(-0.596366\pi\) | ||||
−0.298140 | + | 0.954522i | \(0.596366\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.54285e13 | + | 4.54285e13i | 0.427634 | + | 0.427634i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.69916e12 | + | 1.69916e12i | −0.0155081 | + | 0.0155081i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.12990e13i | − | 0.188512i | −0.995548 | − | 0.0942560i | \(-0.969953\pi\) | ||
0.995548 | − | 0.0942560i | \(-0.0300472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.15767e14i | − | 0.993795i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.22231e14 | − | 1.22231e14i | 1.01787 | − | 1.01787i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.39870e13 | − | 7.39870e13i | −0.597784 | − | 0.597784i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.60814e14 | 1.26084 | 0.630420 | − | 0.776254i | \(-0.282883\pi\) | ||||
0.630420 | + | 0.776254i | \(0.282883\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.15570e13 | 0.0879425 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.16366e12 | + | 9.16366e12i | 0.0676881 | + | 0.0676881i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.26476e13 | − | 5.26476e13i | 0.377555 | − | 0.377555i | −0.492665 | − | 0.870219i | \(-0.663977\pi\) |
0.870219 | + | 0.492665i | \(0.163977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 8.52688e13i | − | 0.593770i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.98823e11i | 0.00134459i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.01266e13 | − | 1.01266e13i | 0.0665196 | − | 0.0665196i | −0.673064 | − | 0.739584i | \(-0.735022\pi\) |
0.739584 | + | 0.673064i | \(0.235022\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.65558e13 | + | 7.65558e13i | 0.488529 | + | 0.488529i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.19772e14 | 1.36263 | 0.681315 | − | 0.731990i | \(-0.261408\pi\) | ||||
0.681315 | + | 0.731990i | \(0.261408\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.13119e13 | 0.128407 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.78530e12 | − | 7.78530e12i | −0.0455895 | − | 0.0455895i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.11456e14 | + | 1.11456e14i | −0.634428 | + | 0.634428i | −0.949175 | − | 0.314748i | \(-0.898080\pi\) |
0.314748 | + | 0.949175i | \(0.398080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.25082e13i | − | 0.235234i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.31456e14i | − | 0.707327i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.29312e13 | + | 7.29312e13i | −0.381618 | + | 0.381618i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.72989e14 | − | 1.72989e14i | −0.880379 | − | 0.880379i | 0.113194 | − | 0.993573i | \(-0.463892\pi\) |
−0.993573 | + | 0.113194i | \(0.963892\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.11902e12 | −0.00553971 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.99669e13 | −0.336976 | −0.168488 | − | 0.985704i | \(-0.553888\pi\) | ||||
−0.168488 | + | 0.985704i | \(0.553888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.30508e14 | + | 1.30508e14i | 0.611590 | + | 0.611590i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.64006e12 | − | 3.64006e12i | 0.0165999 | − | 0.0165999i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.98829e14i | 2.65787i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.35300e14i | − | 1.44862i | −0.689472 | − | 0.724312i | \(-0.742157\pi\) | ||
0.689472 | − | 0.724312i | \(-0.257843\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.66025e14 | − | 1.66025e14i | 0.698300 | − | 0.698300i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.98156e13 | − | 1.98156e13i | −0.0811488 | − | 0.0811488i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.18921e14 | −0.474236 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.55030e14 | 0.602097 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.19319e13 | − | 2.19319e13i | −0.0829657 | − | 0.0829657i | 0.664406 | − | 0.747372i | \(-0.268685\pi\) |
−0.747372 | + | 0.664406i | \(0.768685\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.94928e13 | + | 2.94928e13i | −0.108684 | + | 0.108684i | −0.759357 | − | 0.650674i | \(-0.774487\pi\) |
0.650674 | + | 0.759357i | \(0.274487\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.82052e13i | − | 0.101265i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.71262e13i | 0.199846i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.04013e13 | − | 4.04013e13i | 0.137734 | − | 0.137734i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.31003e14 | + | 1.31003e14i | 0.435278 | + | 0.435278i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.93229e14 | 1.59744 | 0.798718 | − | 0.601705i | \(-0.205512\pi\) | ||||
0.798718 | + | 0.601705i | \(0.205512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.29557e14 | 0.724781 | 0.362391 | − | 0.932026i | \(-0.381961\pi\) | ||||
0.362391 | + | 0.932026i | \(0.381961\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.01678e11 | + | 2.01678e11i | 0.000620822 | + | 0.000620822i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.39974e13 | − | 1.39974e13i | 0.0420144 | − | 0.0420144i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.66738e14i | − | 0.488067i | −0.969767 | − | 0.244033i | \(-0.921529\pi\) | ||
0.969767 | − | 0.244033i | \(-0.0784707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.19553e14i | − | 0.626797i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.92405e13 | + | 4.92405e13i | −0.137120 | + | 0.137120i | −0.772335 | − | 0.635215i | \(-0.780911\pi\) |
0.635215 | + | 0.772335i | \(0.280911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.10289e14 | + | 1.10289e14i | 0.299607 | + | 0.299607i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.48892e14 | 0.659659 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.21793e14 | −1.09080 | −0.545399 | − | 0.838177i | \(-0.683622\pi\) | ||||
−0.545399 | + | 0.838177i | \(0.683622\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.13367e13 | − | 7.13367e13i | −0.180029 | − | 0.180029i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.91677e13 | + | 1.91677e13i | −0.0472096 | + | 0.0472096i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.60917e13i | 0.0386846i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.74966e13i | 0.158396i | 0.996859 | + | 0.0791978i | \(0.0252359\pi\) | ||||
−0.996859 | + | 0.0791978i | \(0.974764\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.50489e13 | − | 9.50489e13i | 0.217760 | − | 0.217760i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.27861e14 | + | 1.27861e14i | 0.286011 | + | 0.286011i | 0.835501 | − | 0.549489i | \(-0.185178\pi\) |
−0.549489 | + | 0.835501i | \(0.685178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.04481e14 | −1.53877 | −0.769385 | − | 0.638785i | \(-0.779437\pi\) | ||||
−0.769385 | + | 0.638785i | \(0.779437\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.64764e14 | 0.564765 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.44528e14 | − | 3.44528e14i | −0.717764 | − | 0.717764i | 0.250383 | − | 0.968147i | \(-0.419443\pi\) |
−0.968147 | + | 0.250383i | \(0.919443\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.38532e13 | + | 3.38532e13i | −0.0688889 | + | 0.0688889i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.56292e13i | 0.170219i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.61113e13i | 0.186654i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.88109e13 | + | 1.88109e13i | −0.0356939 | + | 0.0356939i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.99164e14 | − | 1.99164e14i | −0.369284 | − | 0.369284i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.93135e14 | −1.25595 | −0.627975 | − | 0.778234i | \(-0.716116\pi\) | ||||
−0.627975 | + | 0.778234i | \(0.716116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.52149e14 | −0.800726 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.16689e13 | + | 2.16689e13i | 0.0375084 | + | 0.0375084i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.14019e14 | − | 3.14019e14i | 0.531345 | − | 0.531345i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.22683e14i | − | 0.368365i | −0.982892 | − | 0.184182i | \(-0.941036\pi\) | ||
0.982892 | − | 0.184182i | \(-0.0589637\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.24708e14i | 1.17210i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.87841e14 | + | 5.87841e14i | −0.929634 | + | 0.929634i | −0.997682 | − | 0.0680481i | \(-0.978323\pi\) |
0.0680481 | + | 0.997682i | \(0.478323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.45964e11 | − | 3.45964e11i | −0.000535024 | − | 0.000535024i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.63196e14 | −0.700545 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.94506e13 | 0.117527 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.60683e13 | + | 9.60683e13i | 0.139004 | + | 0.139004i | 0.773185 | − | 0.634181i | \(-0.218663\pi\) |
−0.634181 | + | 0.773185i | \(0.718663\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.84305e14 | + | 2.84305e14i | −0.402417 | + | 0.402417i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 9.12018e14i | − | 1.26293i | −0.775404 | − | 0.631466i | \(-0.782454\pi\) | ||
0.775404 | − | 0.631466i | \(-0.217546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.60607e14i | 1.16601i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.23138e14 | − | 2.23138e14i | 0.295822 | − | 0.295822i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.32018e14 | + | 4.32018e14i | 0.560472 | + | 0.560472i | 0.929441 | − | 0.368970i | \(-0.120289\pi\) |
−0.368970 | + | 0.929441i | \(0.620289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.29397e14 | −0.164289 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.25966e13 | 0.0777867 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.71656e14 | − | 2.71656e14i | −0.330430 | − | 0.330430i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.74100e14 | + | 1.74100e14i | −0.207301 | + | 0.207301i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.99450e14i | − | 1.04847i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.04084e15i | 1.18789i | 0.804504 | + | 0.593947i | \(0.202431\pi\) | ||||
−0.804504 | + | 0.593947i | \(0.797569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.46703e12 | − | 2.46703e12i | 0.00275686 | − | 0.00275686i | −0.705727 | − | 0.708484i | \(-0.749379\pi\) |
0.708484 | + | 0.705727i | \(0.249379\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.91206e13 | − | 2.91206e13i | −0.0318658 | − | 0.0318658i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.54185e14 | −0.486714 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.10715e14 | 0.431056 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.30676e14 | + | 4.30676e14i | 0.442721 | + | 0.442721i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.38632e13 | − | 5.38632e13i | 0.0542366 | − | 0.0542366i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.92114e14i | 0.879983i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.82714e14i | 0.466478i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.35522e15 | + | 1.35522e15i | −1.28313 | + | 1.28313i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.03487e15 | − | 1.03487e15i | −0.960065 | − | 0.960065i | 0.0391680 | − | 0.999233i | \(-0.487529\pi\) |
−0.999233 | + | 0.0391680i | \(0.987529\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.32020e14 | 0.483648 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.32293e14 | −0.385121 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.79056e14 | − | 5.79056e14i | −0.505580 | − | 0.505580i | 0.407586 | − | 0.913167i | \(-0.366371\pi\) |
−0.913167 | + | 0.407586i | \(0.866371\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.78089e14 | + | 8.78089e14i | −0.751434 | + | 0.751434i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.27843e11i | − | 0.000191118i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.27550e14i | 0.104880i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.58641e14 | + | 4.58641e14i | −0.369710 | + | 0.369710i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.19074e14 | + | 7.19074e14i | 0.568290 | + | 0.568290i | 0.931649 | − | 0.363359i | \(-0.118370\pi\) |
−0.363359 | + | 0.931649i | \(0.618370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.25694e13 | −0.0562327 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.55907e14 | −0.346402 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.57706e14 | − | 5.57706e14i | −0.415536 | − | 0.415536i | 0.468126 | − | 0.883662i | \(-0.344929\pi\) |
−0.883662 | + | 0.468126i | \(0.844929\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.94303e14 | + | 8.94303e14i | −0.653459 | + | 0.653459i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 6.36616e12i | − | 0.00456216i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.80466e15i | − | 1.26846i | −0.773143 | − | 0.634231i | \(-0.781317\pi\) | ||
0.773143 | − | 0.634231i | \(-0.218683\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.82563e14 | + | 1.82563e14i | −0.125868 | + | 0.125868i | −0.767235 | − | 0.641367i | \(-0.778368\pi\) |
0.641367 | + | 0.767235i | \(0.278368\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.81924e14 | + | 6.81924e14i | 0.461196 | + | 0.461196i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.28515e14 | 0.483354 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.15369e15 | 1.40190 | 0.700950 | − | 0.713211i | \(-0.252760\pi\) | ||||
0.700950 | + | 0.713211i | \(0.252760\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.45826e14 | + | 3.45826e14i | 0.220864 | + | 0.220864i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.03991e14 | + | 1.03991e14i | −0.0651671 | + | 0.0651671i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.45873e15i | 1.51194i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 3.49739e14i | − | 0.211051i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.54304e15 | − | 1.54304e15i | 0.913833 | − | 0.913833i | −0.0827383 | − | 0.996571i | \(-0.526367\pi\) |
0.996571 | + | 0.0827383i | \(0.0263666\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.49557e14 | − | 1.49557e14i | −0.0869305 | − | 0.0869305i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.75247e14 | −0.385240 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.91327e15 | −1.63147 | −0.815737 | − | 0.578424i | \(-0.803668\pi\) | ||||
−0.815737 | + | 0.578424i | \(0.803668\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.80004e13 | − | 2.80004e13i | −0.0153929 | − | 0.0153929i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.15800e14 | − | 6.15800e14i | 0.332339 | − | 0.332339i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.31209e15i | − | 0.695210i | −0.937641 | − | 0.347605i | \(-0.886995\pi\) | ||
0.937641 | − | 0.347605i | \(-0.113005\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.98203e15i | 1.55132i | 0.631148 | + | 0.775662i | \(0.282584\pi\) | ||||
−0.631148 | + | 0.775662i | \(0.717416\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.35772e14 | − | 7.35772e14i | 0.375836 | − | 0.375836i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.01424e15 | + | 2.01424e15i | 1.01031 | + | 1.01031i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.61957e14 | −0.424569 | −0.212284 | − | 0.977208i | \(-0.568090\pi\) | ||||
−0.212284 | + | 0.977208i | \(0.568090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.52717e11 | 0.000170621 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.31455e14 | − | 1.31455e14i | −0.0624526 | − | 0.0624526i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.86904e14 | − | 8.86904e14i | 0.413851 | − | 0.413851i | −0.469227 | − | 0.883078i | \(-0.655467\pi\) |
0.883078 | + | 0.469227i | \(0.155467\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1.09273e14i | − | 0.0500841i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.31474e15i | − | 1.49239i | −0.665730 | − | 0.746193i | \(-0.731880\pi\) | ||
0.665730 | − | 0.746193i | \(-0.268120\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.60524e15 | − | 2.60524e15i | 1.15226 | − | 1.15226i | 0.166156 | − | 0.986099i | \(-0.446864\pi\) |
0.986099 | − | 0.166156i | \(-0.0531356\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.21213e15 | − | 1.21213e15i | −0.526680 | − | 0.526680i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.92886e14 | 0.0823409 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.22671e14 | −0.0514520 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.50124e14 | − | 1.50124e14i | −0.0618698 | − | 0.0618698i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.86766e14 | − | 7.86766e14i | 0.318616 | − | 0.318616i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.45185e15i | 0.975737i | 0.872917 | + | 0.487868i | \(0.162225\pi\) | ||||
−0.872917 | + | 0.487868i | \(0.837775\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.60130e15i | − | 0.626255i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.26156e15 | + | 1.26156e15i | −0.484901 | + | 0.484901i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.02326e15 | − | 1.02326e15i | −0.386563 | − | 0.386563i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.72679e15 | −0.641188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.41404e14 | −0.197607 | −0.0988035 | − | 0.995107i | \(-0.531502\pi\) | ||||
−0.0988035 | + | 0.995107i | \(0.531502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.59814e14 | − | 6.59814e14i | −0.236734 | − | 0.236734i | 0.578762 | − | 0.815496i | \(-0.303536\pi\) |
−0.815496 | + | 0.578762i | \(0.803536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.36113e13 | + | 7.36113e13i | −0.0259637 | + | 0.0259637i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.35482e15i | − | 0.469795i | −0.972020 | − | 0.234898i | \(-0.924524\pi\) | ||
0.972020 | − | 0.234898i | \(-0.0754755\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.31679e15i | − | 1.81261i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.31525e14 | − | 2.31525e14i | 0.0776072 | − | 0.0776072i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.93736e14 | − | 9.93736e14i | −0.327528 | − | 0.327528i | 0.524118 | − | 0.851646i | \(-0.324395\pi\) |
−0.851646 | + | 0.524118i | \(0.824395\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.16625e15 | 0.702073 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.81233e15 | 0.896308 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.25994e15 | + | 1.25994e15i | 0.394894 | + | 0.394894i | 0.876428 | − | 0.481534i | \(-0.159920\pi\) |
−0.481534 | + | 0.876428i | \(0.659920\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.61831e14 | − | 7.61831e14i | 0.234828 | − | 0.234828i | −0.579876 | − | 0.814705i | \(-0.696899\pi\) |
0.814705 | + | 0.579876i | \(0.196899\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.44235e14i | − | 0.104359i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.84403e13i | − | 0.00549857i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.41199e12 | + | 4.41199e12i | −0.00129402 | + | 0.00129402i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.06946e15 | − | 1.06946e15i | −0.308546 | − | 0.308546i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.08402e16 | 3.07655 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.75717e15 | 1.32821 | 0.664103 | − | 0.747641i | \(-0.268814\pi\) | ||||
0.664103 | + | 0.747641i | \(0.268814\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.62897e15 | + | 1.62897e15i | 0.447448 | + | 0.447448i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.85656e15 | − | 1.85656e15i | 0.501733 | − | 0.501733i | −0.410243 | − | 0.911976i | \(-0.634556\pi\) |
0.911976 | + | 0.410243i | \(0.134556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.49193e14i | − | 0.146030i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.92080e14i | − | 0.128744i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.05012e14 | − | 4.05012e14i | 0.104269 | − | 0.104269i | −0.653048 | − | 0.757317i | \(-0.726510\pi\) |
0.757317 | + | 0.653048i | \(0.226510\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.73592e15 | + | 2.73592e15i | 0.693114 | + | 0.693114i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.09418e15 | −0.522098 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.85648e15 | −0.455496 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.79390e15 | + | 2.79390e15i | 0.674656 | + | 0.674656i | 0.958786 | − | 0.284130i | \(-0.0917047\pi\) |
−0.284130 | + | 0.958786i | \(0.591705\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.05045e14 | + | 4.05045e14i | −0.0962654 | + | 0.0962654i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.55473e15i | 0.597625i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.87450e14i | 0.0431624i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.00413e14 | + | 5.00413e14i | −0.113424 | + | 0.113424i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.76553e15 | − | 3.76553e15i | −0.840189 | − | 0.840189i | 0.148694 | − | 0.988883i | \(-0.452493\pi\) |
−0.988883 | + | 0.148694i | \(0.952493\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.18143e14 | 0.113814 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.66685e14 | −0.0576711 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.52564e14 | + | 7.52564e14i | 0.160227 | + | 0.160227i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.41294e15 | − | 3.41294e15i | 0.715442 | − | 0.715442i | −0.252226 | − | 0.967668i | \(-0.581163\pi\) |
0.967668 | + | 0.252226i | \(0.0811628\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2.77220e15i | − | 0.572192i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.79209e15i | 1.17718i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.15880e15 | + | 2.15880e15i | −0.432046 | + | 0.432046i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.41912e15 | − | 1.41912e15i | −0.279682 | − | 0.279682i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.05222e15 | 0.786474 | 0.393237 | − | 0.919437i | \(-0.371355\pi\) | ||||
0.393237 | + | 0.919437i | \(0.371355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.75102e14 | −0.0908120 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.20914e15 | + | 1.20914e15i | 0.227623 | + | 0.227623i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.92922e12 | − | 5.92922e12i | 0.00109936 | − | 0.00109936i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.88621e15i | − | 0.709720i | −0.934920 | − | 0.354860i | \(-0.884529\pi\) | ||
0.934920 | − | 0.354860i | \(-0.115471\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 3.17620e15i | − | 0.571356i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.26275e14 | − | 1.26275e14i | 0.0223755 | − | 0.0223755i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.83093e15 | − | 5.83093e15i | −1.01781 | − | 1.01781i | −0.999839 | − | 0.0179691i | \(-0.994280\pi\) |
−0.0179691 | − | 0.999839i | \(-0.505720\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.07591e15 | −0.356967 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.08327e15 | −1.53876 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.69206e15 | + | 3.69206e15i | 0.616203 | + | 0.616203i | 0.944555 | − | 0.328352i | \(-0.106493\pi\) |
−0.328352 | + | 0.944555i | \(0.606493\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.13352e14 | − | 1.13352e14i | 0.0186393 | − | 0.0186393i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.42369e15i | − | 0.230663i | −0.993327 | − | 0.115331i | \(-0.963207\pi\) | ||
0.993327 | − | 0.115331i | \(-0.0367930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.10149e15i | 0.654759i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.26017e15 | − | 2.26017e15i | 0.355531 | − | 0.355531i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.80115e14 | + | 7.80115e14i | 0.120923 | + | 0.120923i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.14591e16 | −1.75037 | −0.875185 | − | 0.483788i | \(-0.839261\pi\) | ||||
−0.875185 | + | 0.483788i | \(0.839261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.00716e15 | 0.302142 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.15865e14 | − | 3.15865e14i | −0.0468590 | − | 0.0468590i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.28545e15 | + | 5.28545e15i | −0.772778 | + | 0.772778i | −0.978591 | − | 0.205813i | \(-0.934016\pi\) |
0.205813 | + | 0.978591i | \(0.434016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.81406e15i | 0.837818i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.00264e15i | 0.142407i | 0.997462 | + | 0.0712034i | \(0.0226839\pi\) | ||||
−0.997462 | + | 0.0712034i | \(0.977316\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.78021e14 | + | 3.78021e14i | −0.0529214 | + | 0.0529214i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.08566e14 | + | 6.08566e14i | 0.0839789 | + | 0.0839789i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.01447e15 | 0.546077 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.50821e15 | 0.872703 | 0.436352 | − | 0.899776i | \(-0.356270\pi\) | ||||
0.436352 | + | 0.899776i | \(0.356270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.61442e15 | − | 4.61442e15i | −0.609984 | − | 0.609984i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.27938e15 | − | 4.27938e15i | 0.557691 | − | 0.557691i | −0.370958 | − | 0.928650i | \(-0.620971\pi\) |
0.928650 | + | 0.370958i | \(0.120971\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.78392e15i | − | 1.00009i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.02123e14i | 0.101607i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.17248e13 | + | 6.17248e13i | −0.00770910 | + | 0.00770910i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.06588e16 | + | 1.06588e16i | 1.31259 | + | 1.31259i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.97306e13 | −0.00239580 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.41108e15 | −0.168954 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.86881e15 | + | 5.86881e15i | 0.692929 | + | 0.692929i | 0.962875 | − | 0.269946i | \(-0.0870059\pi\) |
−0.269946 | + | 0.962875i | \(0.587006\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.80192e15 | + | 3.80192e15i | −0.442669 | + | 0.442669i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.56406e15i | 0.179590i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.18496e15i | 0.926860i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.88313e15 | + | 1.88313e15i | −0.210311 | + | 0.210311i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.58799e15 | + | 6.58799e15i | 0.725658 | + | 0.725658i | 0.969752 | − | 0.244093i | \(-0.0784903\pi\) |
−0.244093 | + | 0.969752i | \(0.578490\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.57479e14 | 0.0497009 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.19221e15 | −0.449225 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.73594e16 | − | 1.73594e16i | −1.83485 | − | 1.83485i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.57082e14 | + | 3.57082e14i | −0.0372298 | + | 0.0372298i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.08441e15i | 0.420074i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4.37501e15i | − | 0.443877i | −0.975061 | − | 0.221938i | \(-0.928762\pi\) | ||
0.975061 | − | 0.221938i | \(-0.0712384\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.70532e14 | − | 4.70532e14i | 0.0470949 | − | 0.0470949i | −0.683167 | − | 0.730262i | \(-0.739398\pi\) |
0.730262 | + | 0.683167i | \(0.239398\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.55969e15 | − | 7.55969e15i | −0.746459 | − | 0.746459i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.19424e16 | −1.16339 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.31613e13 | 0.00799282 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.05831e14 | − | 3.05831e14i | −0.0290015 | − | 0.0290015i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.92788e15 | − | 5.92788e15i | 0.554641 | − | 0.554641i | −0.373136 | − | 0.927777i | \(-0.621717\pi\) |
0.927777 | + | 0.373136i | \(0.121717\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.89761e16i | 1.75189i | 0.482408 | + | 0.875947i | \(0.339762\pi\) | ||||
−0.482408 | + | 0.875947i | \(0.660238\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 7.81344e15i | − | 0.711780i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.01913e14 | + | 4.01913e14i | −0.0361286 | + | 0.0361286i | −0.724940 | − | 0.688812i | \(-0.758133\pi\) |
0.688812 | + | 0.724940i | \(0.258133\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.59288e15 | + | 5.59288e15i | 0.496119 | + | 0.496119i | 0.910228 | − | 0.414109i | \(-0.135907\pi\) |
−0.414109 | + | 0.910228i | \(0.635907\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.07605e16 | −0.941944 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.56108e15 | 0.307634 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.68505e15 | − | 4.68505e15i | −0.399428 | − | 0.399428i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.29512e16 | + | 1.29512e16i | −1.08973 | + | 1.08973i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.32289e16i | − | 1.09858i | −0.835631 | − | 0.549291i | \(-0.814898\pi\) | ||
0.835631 | − | 0.549291i | \(-0.185102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 1.22004e16i | − | 0.999994i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.47182e15 | − | 3.47182e15i | 0.280871 | − | 0.280871i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.67709e15 | + | 3.67709e15i | 0.293625 | + | 0.293625i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.52273e15 | 0.277665 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.23329e15 | −0.562787 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.00334e16 | − | 1.00334e16i | −0.770613 | − | 0.770613i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.41615e15 | + | 8.41615e15i | −0.638107 | + | 0.638107i | −0.950088 | − | 0.311981i | \(-0.899007\pi\) |
0.311981 | + | 0.950088i | \(0.399007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00785e14i | 0.0299984i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.65720e16i | 1.22456i | 0.790641 | + | 0.612280i | \(0.209748\pi\) | ||||
−0.790641 | + | 0.612280i | \(0.790252\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.37657e16 | + | 1.37657e16i | −1.00424 | + | 1.00424i | −0.00424510 | + | 0.999991i | \(0.501351\pi\) |
−0.999991 | + | 0.00424510i | \(0.998649\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.55545e13 | − | 9.55545e13i | −0.00688231 | − | 0.00688231i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.13724e15 | 0.578652 | 0.289326 | − | 0.957231i | \(-0.406569\pi\) | ||||
0.289326 | + | 0.957231i | \(0.406569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.48220e16 | 1.04068 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.55970e15 | − | 5.55970e15i | −0.385431 | − | 0.385431i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.71117e16 | + | 1.71117e16i | −1.17134 | + | 1.17134i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.85837e15i | − | 0.463576i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.19362e16i | 0.796690i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.22874e15 | − | 1.22874e15i | 0.0809869 | − | 0.0809869i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.99391e15 | + | 8.99391e15i | 0.585397 | + | 0.585397i | 0.936381 | − | 0.350984i | \(-0.114153\pi\) |
−0.350984 | + | 0.936381i | \(0.614153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.17680e15 | −0.268476 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.35360e16 | 0.859255 | 0.429628 | − | 0.903006i | \(-0.358645\pi\) | ||||
0.429628 | + | 0.903006i | \(0.358645\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.86996e15 | + | 5.86996e15i | 0.368003 | + | 0.368003i | 0.866749 | − | 0.498745i | \(-0.166206\pi\) |
−0.498745 | + | 0.866749i | \(0.666206\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.07211e15 | − | 4.07211e15i | 0.252134 | − | 0.252134i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.36497e15i | − | 0.0834723i | −0.999129 | − | 0.0417362i | \(-0.986711\pi\) | ||
0.999129 | − | 0.0417362i | \(-0.0132889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.20636e15i | 0.133265i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.54062e14 | − | 8.54062e14i | 0.0509521 | − | 0.0509521i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.50642e14 | + | 1.50642e14i | 0.00887692 | + | 0.00887692i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.95463e15 | −0.463013 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.38994e15 | −0.252406 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.71406e13 | + | 4.71406e13i | 0.00267742 | + | 0.00267742i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.23038e15 | − | 3.23038e15i | 0.181246 | − | 0.181246i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.28740e14i | 0.00713560i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.76715e15i | 0.480056i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.23091e15 | − | 4.23091e15i | 0.228873 | − | 0.228873i | −0.583349 | − | 0.812222i | \(-0.698258\pi\) |
0.812222 | + | 0.583349i | \(0.198258\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.63563e16 | − | 1.63563e16i | −0.874148 | − | 0.874148i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.76552e16 | −0.932229 | −0.466114 | − | 0.884724i | \(-0.654346\pi\) | ||||
−0.466114 | + | 0.884724i | \(0.654346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.79023e16 | −1.45563 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.30247e15 | + | 8.30247e15i | 0.427949 | + | 0.427949i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.89430e15 | − | 1.89430e15i | 0.0964754 | − | 0.0964754i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.51316e16i | 0.761464i | 0.924685 | + | 0.380732i | \(0.124328\pi\) | ||||
−0.924685 | + | 0.380732i | \(0.875672\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.26856e15i | 0.460876i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.04800e15 | + | 8.04800e15i | −0.395438 | + | 0.395438i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.34838e16 | + | 1.34838e16i | 0.654685 | + | 0.654685i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.03260e16 | 0.495441 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.73662e16 | −1.77171 | −0.885856 | − | 0.463961i | \(-0.846428\pi\) | ||||
−0.885856 | + | 0.463961i | \(0.846428\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.17261e15 | + | 1.17261e15i | 0.0549455 | + | 0.0549455i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.61122e16 | − | 1.61122e16i | 0.746113 | − | 0.746113i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 7.51289e15i | − | 0.343829i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.60131e15i | 0.0724284i | 0.999344 | + | 0.0362142i | \(0.0115299\pi\) | ||||
−0.999344 | + | 0.0362142i | \(0.988470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.33044e15 | − | 5.33044e15i | 0.238288 | − | 0.238288i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.89984e16 | − | 1.89984e16i | −0.839411 | − | 0.839411i | 0.149370 | − | 0.988781i | \(-0.452275\pi\) |
−0.988781 | + | 0.149370i | \(0.952275\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.39050e15 | 0.104394 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.59688e15 | −0.0689284 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.90069e16 | + | 2.90069e16i | 1.23759 | + | 1.23759i | 0.960984 | + | 0.276603i | \(0.0892088\pi\) |
0.276603 | + | 0.960984i | \(0.410791\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.31073e16 | − | 1.31073e16i | 0.552778 | − | 0.552778i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 9.30432e15i | − | 0.387875i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 9.02554e15i | − | 0.371931i | −0.982556 | − | 0.185965i | \(-0.940459\pi\) | ||
0.982556 | − | 0.185965i | \(-0.0595412\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.12374e16 | + | 1.12374e16i | −0.457771 | + | 0.457771i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.73193e13 | + | 4.73193e13i | 0.00190556 | + | 0.00190556i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.78488e15 | 0.190489 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.64780e16 | 1.43566 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.69552e16 | − | 1.69552e16i | −0.659716 | − | 0.659716i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.69886e15 | + | 5.69886e15i | −0.219224 | + | 0.219224i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.17299e16i | − | 0.446118i | −0.974805 | − | 0.223059i | \(-0.928396\pi\) | ||
0.974805 | − | 0.223059i | \(-0.0716042\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.94479e14i | 0.0148335i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.94649e16 | − | 2.94649e16i | 1.09547 | − | 1.09547i | 0.100534 | − | 0.994934i | \(-0.467945\pi\) |
0.994934 | − | 0.100534i | \(-0.0320552\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.23400e15 | + | 2.23400e15i | 0.0821227 | + | 0.0821227i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.89959e15 | 0.214435 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.36971e16 | 0.851677 | 0.425838 | − | 0.904799i | \(-0.359979\pi\) | ||||
0.425838 | + | 0.904799i | \(0.359979\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.58769e16 | + | 2.58769e16i | 0.919618 | + | 0.919618i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.21598e15 | − | 8.21598e15i | 0.288722 | − | 0.288722i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.60613e16i | 0.905634i | 0.891604 | + | 0.452817i | \(0.149581\pi\) | ||||
−0.891604 | + | 0.452817i | \(0.850419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1.11274e16i | − | 0.382379i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.33204e14 | + | 2.33204e14i | −0.00792487 | + | 0.00792487i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.61035e15 | − | 1.61035e15i | −0.0541179 | − | 0.0541179i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.19445e16 | 1.39402 | 0.697011 | − | 0.717060i | \(-0.254513\pi\) | ||||
0.697011 | + | 0.717060i | \(0.254513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.05129e16 | −0.345542 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.01478e16 | + | 1.01478e16i | 0.329870 | + | 0.329870i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.65082e16 | − | 2.65082e16i | 0.852231 | − | 0.852231i | −0.138177 | − | 0.990408i | \(-0.544124\pi\) |
0.990408 | + | 0.138177i | \(0.0441242\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 4.48698e16i | − | 1.42674i |
(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 | 128.12.e.b.33.14 | 42 | ||
4.3 | odd | 2 | 128.12.e.a.33.8 | 42 | |||
8.3 | odd | 2 | 64.12.e.a.17.14 | 42 | |||
8.5 | even | 2 | 16.12.e.a.13.20 | yes | 42 | ||
16.3 | odd | 4 | 64.12.e.a.49.14 | 42 | |||
16.5 | even | 4 | inner | 128.12.e.b.97.14 | 42 | ||
16.11 | odd | 4 | 128.12.e.a.97.8 | 42 | |||
16.13 | even | 4 | 16.12.e.a.5.20 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.12.e.a.5.20 | ✓ | 42 | 16.13 | even | 4 | ||
16.12.e.a.13.20 | yes | 42 | 8.5 | even | 2 | ||
64.12.e.a.17.14 | 42 | 8.3 | odd | 2 | |||
64.12.e.a.49.14 | 42 | 16.3 | odd | 4 | |||
128.12.e.a.33.8 | 42 | 4.3 | odd | 2 | |||
128.12.e.a.97.8 | 42 | 16.11 | odd | 4 | |||
128.12.e.b.33.14 | 42 | 1.1 | even | 1 | trivial | ||
128.12.e.b.97.14 | 42 | 16.5 | even | 4 | inner |