Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,11,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), 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: | \(112.458233723\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.3 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.98 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 59.8859i | − | 1.87143i | −0.352751 | − | 0.935717i | \(-0.614754\pi\) | ||
0.352751 | − | 0.935717i | \(-0.385246\pi\) | |||||||
\(3\) | 140.296 | 0.577350 | ||||||||
\(4\) | −2562.32 | −2.50227 | ||||||||
\(5\) | 3689.76 | 1.18072 | 0.590362 | − | 0.807138i | \(-0.298985\pi\) | ||||
0.590362 | + | 0.807138i | \(0.298985\pi\) | |||||||
\(6\) | − | 8401.76i | − | 1.08047i | ||||||
\(7\) | 4188.49 | 0.249211 | 0.124606 | − | 0.992206i | \(-0.460233\pi\) | ||||
0.124606 | + | 0.992206i | \(0.460233\pi\) | |||||||
\(8\) | 92123.7i | 2.81139i | ||||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | − | 220965.i | − | 2.20965i | ||||||
\(11\) | − | 108701.i | − | 0.674946i | −0.941335 | − | 0.337473i | \(-0.890428\pi\) | ||
0.941335 | − | 0.337473i | \(-0.109572\pi\) | |||||||
\(12\) | −359484. | −1.44468 | ||||||||
\(13\) | 582935.i | 1.57001i | 0.619487 | + | 0.785007i | \(0.287341\pi\) | ||||
−0.619487 | + | 0.785007i | \(0.712659\pi\) | |||||||
\(14\) | − | 250832.i | − | 0.466382i | ||||||
\(15\) | 517660. | 0.681692 | ||||||||
\(16\) | 2.89309e6 | 2.75907 | ||||||||
\(17\) | 733229. | 0.516410 | 0.258205 | − | 0.966090i | \(-0.416869\pi\) | ||||
0.258205 | + | 0.966090i | \(0.416869\pi\) | |||||||
\(18\) | − | 1.17873e6i | − | 0.623811i | ||||||
\(19\) | −2.47781e6 | −1.00069 | −0.500346 | − | 0.865825i | \(-0.666794\pi\) | ||||
−0.500346 | + | 0.865825i | \(0.666794\pi\) | |||||||
\(20\) | −9.45436e6 | −2.95449 | ||||||||
\(21\) | 587629. | 0.143882 | ||||||||
\(22\) | −6.50964e6 | −1.26312 | ||||||||
\(23\) | 273388.i | 0.0424757i | 0.999774 | + | 0.0212379i | \(0.00676073\pi\) | ||||
−0.999774 | + | 0.0212379i | \(0.993239\pi\) | |||||||
\(24\) | 1.29246e7i | 1.62316i | ||||||||
\(25\) | 3.84873e6 | 0.394110 | ||||||||
\(26\) | 3.49096e7 | 2.93818 | ||||||||
\(27\) | 2.76145e6 | 0.192450 | ||||||||
\(28\) | −1.07323e7 | −0.623593 | ||||||||
\(29\) | −7.13464e6 | −0.347842 | −0.173921 | − | 0.984760i | \(-0.555644\pi\) | ||||
−0.173921 | + | 0.984760i | \(0.555644\pi\) | |||||||
\(30\) | − | 3.10005e7i | − | 1.27574i | ||||||
\(31\) | 8.58497e6i | 0.299868i | 0.988696 | + | 0.149934i | \(0.0479061\pi\) | ||||
−0.988696 | + | 0.149934i | \(0.952094\pi\) | |||||||
\(32\) | − | 7.89208e7i | − | 2.35202i | ||||||
\(33\) | − | 1.52503e7i | − | 0.389680i | ||||||
\(34\) | − | 4.39101e7i | − | 0.966428i | ||||||
\(35\) | 1.54546e7 | 0.294250 | ||||||||
\(36\) | −5.04341e7 | −0.834089 | ||||||||
\(37\) | 1.12871e8i | 1.62770i | 0.581078 | + | 0.813848i | \(0.302631\pi\) | ||||
−0.581078 | + | 0.813848i | \(0.697369\pi\) | |||||||
\(38\) | 1.48386e8i | 1.87273i | ||||||||
\(39\) | 8.17835e7i | 0.906448i | ||||||||
\(40\) | 3.39915e8i | 3.31948i | ||||||||
\(41\) | 5.07042e7 | 0.437648 | 0.218824 | − | 0.975764i | \(-0.429778\pi\) | ||||
0.218824 | + | 0.975764i | \(0.429778\pi\) | |||||||
\(42\) | − | 3.51907e7i | − | 0.269266i | ||||||
\(43\) | 6.60375e7i | 0.449209i | 0.974450 | + | 0.224604i | \(0.0721090\pi\) | ||||
−0.974450 | + | 0.224604i | \(0.927891\pi\) | |||||||
\(44\) | 2.78526e8i | 1.68889i | ||||||||
\(45\) | 7.26256e7 | 0.393575 | ||||||||
\(46\) | 1.63721e7 | 0.0794906 | ||||||||
\(47\) | 4.56783e8i | 1.99169i | 0.0910858 | + | 0.995843i | \(0.470966\pi\) | ||||
−0.0910858 | + | 0.995843i | \(0.529034\pi\) | |||||||
\(48\) | 4.05890e8 | 1.59295 | ||||||||
\(49\) | −2.64932e8 | −0.937894 | ||||||||
\(50\) | − | 2.30485e8i | − | 0.737551i | ||||||
\(51\) | 1.02869e8 | 0.298150 | ||||||||
\(52\) | − | 1.49367e9i | − | 3.92859i | ||||||
\(53\) | 5.34760e8 | 1.27873 | 0.639366 | − | 0.768902i | \(-0.279197\pi\) | ||||
0.639366 | + | 0.768902i | \(0.279197\pi\) | |||||||
\(54\) | − | 1.65372e8i | − | 0.360158i | ||||||
\(55\) | − | 4.01080e8i | − | 0.796925i | ||||||
\(56\) | 3.85859e8i | 0.700630i | ||||||||
\(57\) | −3.47628e8 | −0.577750 | ||||||||
\(58\) | 4.27264e8i | 0.650963i | ||||||||
\(59\) | 3.64006e8 | + | 6.15318e8i | 0.509153 | + | 0.860676i | ||||
\(60\) | −1.32641e9 | −1.70577 | ||||||||
\(61\) | − | 5.64631e8i | − | 0.668522i | −0.942481 | − | 0.334261i | \(-0.891513\pi\) | ||
0.942481 | − | 0.334261i | \(-0.108487\pi\) | |||||||
\(62\) | 5.14118e8 | 0.561183 | ||||||||
\(63\) | 8.24421e7 | 0.0830704 | ||||||||
\(64\) | −1.76372e9 | −1.64259 | ||||||||
\(65\) | 2.15089e9i | 1.85375i | ||||||||
\(66\) | −9.13277e8 | −0.729261 | ||||||||
\(67\) | − | 3.92311e8i | − | 0.290574i | −0.989390 | − | 0.145287i | \(-0.953589\pi\) | ||
0.989390 | − | 0.145287i | \(-0.0464106\pi\) | |||||||
\(68\) | −1.87877e9 | −1.29220 | ||||||||
\(69\) | 3.83553e7i | 0.0245234i | ||||||||
\(70\) | − | 9.25510e8i | − | 0.550669i | ||||||
\(71\) | 2.57751e9 | 1.42860 | 0.714298 | − | 0.699842i | \(-0.246746\pi\) | ||||
0.714298 | + | 0.699842i | \(0.246746\pi\) | |||||||
\(72\) | 1.81327e9i | 0.937131i | ||||||||
\(73\) | − | 1.12186e9i | − | 0.541159i | −0.962698 | − | 0.270579i | \(-0.912785\pi\) | ||
0.962698 | − | 0.270579i | \(-0.0872152\pi\) | |||||||
\(74\) | 6.75937e9 | 3.04613 | ||||||||
\(75\) | 5.39962e8 | 0.227540 | ||||||||
\(76\) | 6.34895e9 | 2.50400 | ||||||||
\(77\) | − | 4.55292e8i | − | 0.168204i | ||||||
\(78\) | 4.89768e9 | 1.69636 | ||||||||
\(79\) | 2.65793e9 | 0.863791 | 0.431895 | − | 0.901924i | \(-0.357845\pi\) | ||||
0.431895 | + | 0.901924i | \(0.357845\pi\) | |||||||
\(80\) | 1.06748e10 | 3.25770 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | − | 3.03647e9i | − | 0.819029i | ||||||
\(83\) | − | 1.54998e8i | − | 0.0393492i | −0.999806 | − | 0.0196746i | \(-0.993737\pi\) | ||
0.999806 | − | 0.0196746i | \(-0.00626302\pi\) | |||||||
\(84\) | −1.50569e9 | −0.360031 | ||||||||
\(85\) | 2.70544e9 | 0.609738 | ||||||||
\(86\) | 3.95471e9 | 0.840665 | ||||||||
\(87\) | −1.00096e9 | −0.200827 | ||||||||
\(88\) | 1.00139e10 | 1.89754 | ||||||||
\(89\) | 7.28833e9i | 1.30520i | 0.757701 | + | 0.652602i | \(0.226322\pi\) | ||||
−0.757701 | + | 0.652602i | \(0.773678\pi\) | |||||||
\(90\) | − | 4.34925e9i | − | 0.736549i | ||||||
\(91\) | 2.44162e9i | 0.391265i | ||||||||
\(92\) | − | 7.00509e8i | − | 0.106286i | ||||||
\(93\) | 1.20444e9i | 0.173129i | ||||||||
\(94\) | 2.73549e10 | 3.72731 | ||||||||
\(95\) | −9.14255e9 | −1.18154 | ||||||||
\(96\) | − | 1.10723e10i | − | 1.35794i | ||||||
\(97\) | 3.03929e9i | 0.353927i | 0.984217 | + | 0.176963i | \(0.0566274\pi\) | ||||
−0.984217 | + | 0.176963i | \(0.943373\pi\) | |||||||
\(98\) | 1.58657e10i | 1.75521i | ||||||||
\(99\) | − | 2.13956e9i | − | 0.224982i | ||||||
\(100\) | −9.86168e9 | −0.986168 | ||||||||
\(101\) | − | 2.69242e9i | − | 0.256174i | −0.991763 | − | 0.128087i | \(-0.959116\pi\) | ||
0.991763 | − | 0.128087i | \(-0.0408837\pi\) | |||||||
\(102\) | − | 6.16041e9i | − | 0.557968i | ||||||
\(103\) | 4.44428e7i | 0.00383368i | 0.999998 | + | 0.00191684i | \(0.000610149\pi\) | ||||
−0.999998 | + | 0.00191684i | \(0.999390\pi\) | |||||||
\(104\) | −5.37021e10 | −4.41392 | ||||||||
\(105\) | 2.16821e9 | 0.169885 | ||||||||
\(106\) | − | 3.20246e10i | − | 2.39306i | ||||||
\(107\) | −9.08377e9 | −0.647660 | −0.323830 | − | 0.946115i | \(-0.604971\pi\) | ||||
−0.323830 | + | 0.946115i | \(0.604971\pi\) | |||||||
\(108\) | −7.07572e9 | −0.481561 | ||||||||
\(109\) | 5.38541e9i | 0.350015i | 0.984567 | + | 0.175007i | \(0.0559949\pi\) | ||||
−0.984567 | + | 0.175007i | \(0.944005\pi\) | |||||||
\(110\) | −2.40190e10 | −1.49139 | ||||||||
\(111\) | 1.58353e10i | 0.939751i | ||||||||
\(112\) | 1.21177e10 | 0.687591 | ||||||||
\(113\) | 3.54688e9i | 0.192510i | 0.995357 | + | 0.0962552i | \(0.0306865\pi\) | ||||
−0.995357 | + | 0.0962552i | \(0.969313\pi\) | |||||||
\(114\) | 2.08180e10i | 1.08122i | ||||||||
\(115\) | 1.00874e9i | 0.0501521i | ||||||||
\(116\) | 1.82812e10 | 0.870393 | ||||||||
\(117\) | 1.14739e10i | 0.523338i | ||||||||
\(118\) | 3.68489e10 | − | 2.17988e10i | 1.61070 | − | 0.952847i | ||||
\(119\) | 3.07112e9 | 0.128695 | ||||||||
\(120\) | 4.76887e10i | 1.91650i | ||||||||
\(121\) | 1.41216e10 | 0.544448 | ||||||||
\(122\) | −3.38134e10 | −1.25109 | ||||||||
\(123\) | 7.11360e9 | 0.252676 | ||||||||
\(124\) | − | 2.19974e10i | − | 0.750350i | ||||||
\(125\) | −2.18319e10 | −0.715389 | ||||||||
\(126\) | − | 4.93712e9i | − | 0.155461i | ||||||
\(127\) | −1.69243e10 | −0.512262 | −0.256131 | − | 0.966642i | \(-0.582448\pi\) | ||||
−0.256131 | + | 0.966642i | \(0.582448\pi\) | |||||||
\(128\) | 2.48068e10i | 0.721973i | ||||||||
\(129\) | 9.26480e9i | 0.259351i | ||||||||
\(130\) | 1.28808e11 | 3.46918 | ||||||||
\(131\) | − | 5.73326e9i | − | 0.148609i | −0.997236 | − | 0.0743045i | \(-0.976326\pi\) | ||
0.997236 | − | 0.0743045i | \(-0.0236737\pi\) | |||||||
\(132\) | 3.90761e10i | 0.975083i | ||||||||
\(133\) | −1.03783e10 | −0.249384 | ||||||||
\(134\) | −2.34939e10 | −0.543790 | ||||||||
\(135\) | 1.01891e10 | 0.227231 | ||||||||
\(136\) | 6.75478e10i | 1.45183i | ||||||||
\(137\) | 3.13369e10 | 0.649313 | 0.324656 | − | 0.945832i | \(-0.394751\pi\) | ||||
0.324656 | + | 0.945832i | \(0.394751\pi\) | |||||||
\(138\) | 2.29694e9 | 0.0458939 | ||||||||
\(139\) | −4.94543e10 | −0.953082 | −0.476541 | − | 0.879152i | \(-0.658110\pi\) | ||||
−0.476541 | + | 0.879152i | \(0.658110\pi\) | |||||||
\(140\) | −3.95995e10 | −0.736291 | ||||||||
\(141\) | 6.40849e10i | 1.14990i | ||||||||
\(142\) | − | 1.54357e11i | − | 2.67352i | ||||||
\(143\) | 6.33654e10 | 1.05967 | ||||||||
\(144\) | 5.69448e10 | 0.919690 | ||||||||
\(145\) | −2.63251e10 | −0.410706 | ||||||||
\(146\) | −6.71836e10 | −1.01274 | ||||||||
\(147\) | −3.71689e10 | −0.541493 | ||||||||
\(148\) | − | 2.89211e11i | − | 4.07293i | ||||||
\(149\) | 1.08170e11i | 1.47290i | 0.676490 | + | 0.736452i | \(0.263500\pi\) | ||||
−0.676490 | + | 0.736452i | \(0.736500\pi\) | |||||||
\(150\) | − | 3.23361e10i | − | 0.425825i | ||||||
\(151\) | − | 8.13371e10i | − | 1.03611i | −0.855349 | − | 0.518053i | \(-0.826657\pi\) | ||
0.855349 | − | 0.518053i | \(-0.173343\pi\) | |||||||
\(152\) | − | 2.28265e11i | − | 2.81334i | ||||||
\(153\) | 1.44321e10 | 0.172137 | ||||||||
\(154\) | −2.72656e10 | −0.314783 | ||||||||
\(155\) | 3.16765e10i | 0.354062i | ||||||||
\(156\) | − | 2.09556e11i | − | 2.26817i | ||||||
\(157\) | 7.35807e10i | 0.771375i | 0.922630 | + | 0.385687i | \(0.126036\pi\) | ||||
−0.922630 | + | 0.385687i | \(0.873964\pi\) | |||||||
\(158\) | − | 1.59173e11i | − | 1.61653i | ||||||
\(159\) | 7.50248e10 | 0.738276 | ||||||||
\(160\) | − | 2.91199e11i | − | 2.77709i | ||||||
\(161\) | 1.14509e9i | 0.0105854i | ||||||||
\(162\) | − | 2.32010e10i | − | 0.207937i | ||||||
\(163\) | −1.86149e11 | −1.61779 | −0.808894 | − | 0.587954i | \(-0.799934\pi\) | ||||
−0.808894 | + | 0.587954i | \(0.799934\pi\) | |||||||
\(164\) | −1.29920e11 | −1.09511 | ||||||||
\(165\) | − | 5.62699e10i | − | 0.460105i | ||||||
\(166\) | −9.28219e9 | −0.0736394 | ||||||||
\(167\) | 1.29426e11 | 0.996413 | 0.498206 | − | 0.867059i | \(-0.333992\pi\) | ||||
0.498206 | + | 0.867059i | \(0.333992\pi\) | |||||||
\(168\) | 5.41346e10i | 0.404509i | ||||||||
\(169\) | −2.01955e11 | −1.46494 | ||||||||
\(170\) | − | 1.62018e11i | − | 1.14109i | ||||||
\(171\) | −4.87708e10 | −0.333564 | ||||||||
\(172\) | − | 1.69209e11i | − | 1.12404i | ||||||
\(173\) | − | 2.96176e11i | − | 1.91126i | −0.294574 | − | 0.955629i | \(-0.595178\pi\) | ||
0.294574 | − | 0.955629i | \(-0.404822\pi\) | |||||||
\(174\) | 5.99435e10i | 0.375834i | ||||||||
\(175\) | 1.61204e10 | 0.0982167 | ||||||||
\(176\) | − | 3.14481e11i | − | 1.86222i | ||||||
\(177\) | 5.10686e10 | + | 8.63267e10i | 0.293960 | + | 0.496911i | ||||
\(178\) | 4.36468e11 | 2.44260 | ||||||||
\(179\) | 1.75062e11i | 0.952635i | 0.879273 | + | 0.476318i | \(0.158029\pi\) | ||||
−0.879273 | + | 0.476318i | \(0.841971\pi\) | |||||||
\(180\) | −1.86090e11 | −0.984829 | ||||||||
\(181\) | 1.31742e11 | 0.678158 | 0.339079 | − | 0.940758i | \(-0.389885\pi\) | ||||
0.339079 | + | 0.940758i | \(0.389885\pi\) | |||||||
\(182\) | 1.46219e11 | 0.732227 | ||||||||
\(183\) | − | 7.92156e10i | − | 0.385971i | ||||||
\(184\) | −2.51856e10 | −0.119416 | ||||||||
\(185\) | 4.16467e11i | 1.92186i | ||||||||
\(186\) | 7.21288e10 | 0.323999 | ||||||||
\(187\) | − | 7.97025e10i | − | 0.348549i | ||||||
\(188\) | − | 1.17042e12i | − | 4.98373i | ||||||
\(189\) | 1.15663e10 | 0.0479607 | ||||||||
\(190\) | 5.47510e11i | 2.21118i | ||||||||
\(191\) | − | 1.80546e11i | − | 0.710266i | −0.934816 | − | 0.355133i | \(-0.884436\pi\) | ||
0.934816 | − | 0.355133i | \(-0.115564\pi\) | |||||||
\(192\) | −2.47443e11 | −0.948349 | ||||||||
\(193\) | 3.40553e11 | 1.27174 | 0.635870 | − | 0.771796i | \(-0.280641\pi\) | ||||
0.635870 | + | 0.771796i | \(0.280641\pi\) | |||||||
\(194\) | 1.82011e11 | 0.662351 | ||||||||
\(195\) | 3.01762e11i | 1.07026i | ||||||||
\(196\) | 6.78840e11 | 2.34686 | ||||||||
\(197\) | 2.99654e10 | 0.100993 | 0.0504963 | − | 0.998724i | \(-0.483920\pi\) | ||||
0.0504963 | + | 0.998724i | \(0.483920\pi\) | |||||||
\(198\) | −1.28129e11 | −0.421039 | ||||||||
\(199\) | −3.92538e11 | −1.25781 | −0.628906 | − | 0.777481i | \(-0.716497\pi\) | ||||
−0.628906 | + | 0.777481i | \(0.716497\pi\) | |||||||
\(200\) | 3.54559e11i | 1.10800i | ||||||||
\(201\) | − | 5.50398e10i | − | 0.167763i | ||||||
\(202\) | −1.61238e11 | −0.479414 | ||||||||
\(203\) | −2.98834e10 | −0.0866861 | ||||||||
\(204\) | −2.63584e11 | −0.746050 | ||||||||
\(205\) | 1.87086e11 | 0.516741 | ||||||||
\(206\) | 2.66150e9 | 0.00717447 | ||||||||
\(207\) | 5.38110e9i | 0.0141586i | ||||||||
\(208\) | 1.68649e12i | 4.33177i | ||||||||
\(209\) | 2.69340e11i | 0.675413i | ||||||||
\(210\) | − | 1.29845e11i | − | 0.317929i | ||||||
\(211\) | − | 6.00627e11i | − | 1.43613i | −0.695978 | − | 0.718063i | \(-0.745029\pi\) | ||
0.695978 | − | 0.718063i | \(-0.254971\pi\) | |||||||
\(212\) | −1.37023e12 | −3.19973 | ||||||||
\(213\) | 3.61615e11 | 0.824800 | ||||||||
\(214\) | 5.43989e11i | 1.21205i | ||||||||
\(215\) | 2.43663e11i | 0.530392i | ||||||||
\(216\) | 2.54395e11i | 0.541053i | ||||||||
\(217\) | 3.59581e10i | 0.0747305i | ||||||||
\(218\) | 3.22510e11 | 0.655029 | ||||||||
\(219\) | − | 1.57393e11i | − | 0.312438i | ||||||
\(220\) | 1.02770e12i | 1.99412i | ||||||||
\(221\) | 4.27425e11i | 0.810771i | ||||||||
\(222\) | 9.48314e11 | 1.75868 | ||||||||
\(223\) | −5.76487e11 | −1.04536 | −0.522679 | − | 0.852529i | \(-0.675067\pi\) | ||||
−0.522679 | + | 0.852529i | \(0.675067\pi\) | |||||||
\(224\) | − | 3.30559e11i | − | 0.586151i | ||||||
\(225\) | 7.57546e10 | 0.131370 | ||||||||
\(226\) | 2.12408e11 | 0.360271 | ||||||||
\(227\) | − | 4.22740e9i | − | 0.00701366i | −0.999994 | − | 0.00350683i | \(-0.998884\pi\) | ||
0.999994 | − | 0.00350683i | \(-0.00111626\pi\) | |||||||
\(228\) | 8.90734e11 | 1.44568 | ||||||||
\(229\) | 8.05126e11i | 1.27846i | 0.769016 | + | 0.639229i | \(0.220746\pi\) | ||||
−0.769016 | + | 0.639229i | \(0.779254\pi\) | |||||||
\(230\) | 6.04092e10 | 0.0938564 | ||||||||
\(231\) | − | 6.38757e10i | − | 0.0971127i | ||||||
\(232\) | − | 6.57269e11i | − | 0.977920i | ||||||
\(233\) | − | 3.62083e11i | − | 0.527264i | −0.964623 | − | 0.263632i | \(-0.915080\pi\) | ||
0.964623 | − | 0.263632i | \(-0.0849205\pi\) | |||||||
\(234\) | 6.87125e11 | 0.979392 | ||||||||
\(235\) | 1.68542e12i | 2.35163i | ||||||||
\(236\) | −9.32700e11 | − | 1.57664e12i | −1.27404 | − | 2.15364i | ||||
\(237\) | 3.72898e11 | 0.498710 | ||||||||
\(238\) | − | 1.83917e11i | − | 0.240845i | ||||||
\(239\) | −1.53434e12 | −1.96758 | −0.983791 | − | 0.179319i | \(-0.942611\pi\) | ||||
−0.983791 | + | 0.179319i | \(0.942611\pi\) | |||||||
\(240\) | 1.49764e12 | 1.88083 | ||||||||
\(241\) | 6.63824e11 | 0.816522 | 0.408261 | − | 0.912865i | \(-0.366135\pi\) | ||||
0.408261 | + | 0.912865i | \(0.366135\pi\) | |||||||
\(242\) | − | 8.45684e11i | − | 1.01890i | ||||||
\(243\) | 5.43536e10 | 0.0641500 | ||||||||
\(244\) | 1.44677e12i | 1.67282i | ||||||||
\(245\) | −9.77536e11 | −1.10739 | ||||||||
\(246\) | − | 4.26004e11i | − | 0.472866i | ||||||
\(247\) | − | 1.44440e12i | − | 1.57110i | ||||||
\(248\) | −7.90879e11 | −0.843047 | ||||||||
\(249\) | − | 2.17456e10i | − | 0.0227182i | ||||||
\(250\) | 1.30743e12i | 1.33880i | ||||||||
\(251\) | 1.52621e12 | 1.53195 | 0.765977 | − | 0.642868i | \(-0.222256\pi\) | ||||
0.765977 | + | 0.642868i | \(0.222256\pi\) | |||||||
\(252\) | −2.11243e11 | −0.207864 | ||||||||
\(253\) | 2.97175e10 | 0.0286688 | ||||||||
\(254\) | 1.01353e12i | 0.958664i | ||||||||
\(255\) | 3.79563e11 | 0.352033 | ||||||||
\(256\) | −3.20468e11 | −0.291464 | ||||||||
\(257\) | 1.83131e12 | 1.63342 | 0.816709 | − | 0.577050i | \(-0.195796\pi\) | ||||
0.816709 | + | 0.577050i | \(0.195796\pi\) | |||||||
\(258\) | 5.54831e11 | 0.485358 | ||||||||
\(259\) | 4.72759e11i | 0.405640i | ||||||||
\(260\) | − | 5.51128e12i | − | 4.63858i | ||||||
\(261\) | −1.40431e11 | −0.115947 | ||||||||
\(262\) | −3.43341e11 | −0.278112 | ||||||||
\(263\) | 5.40085e11 | 0.429223 | 0.214612 | − | 0.976699i | \(-0.431151\pi\) | ||||
0.214612 | + | 0.976699i | \(0.431151\pi\) | |||||||
\(264\) | 1.40491e12 | 1.09554 | ||||||||
\(265\) | 1.97314e12 | 1.50983 | ||||||||
\(266\) | 6.21514e11i | 0.466706i | ||||||||
\(267\) | 1.02252e12i | 0.753559i | ||||||||
\(268\) | 1.00523e12i | 0.727094i | ||||||||
\(269\) | − | 1.39002e12i | − | 0.986868i | −0.869783 | − | 0.493434i | \(-0.835741\pi\) | ||
0.869783 | − | 0.493434i | \(-0.164259\pi\) | |||||||
\(270\) | − | 6.10183e11i | − | 0.425247i | ||||||
\(271\) | 5.54735e11 | 0.379524 | 0.189762 | − | 0.981830i | \(-0.439228\pi\) | ||||
0.189762 | + | 0.981830i | \(0.439228\pi\) | |||||||
\(272\) | 2.12130e12 | 1.42481 | ||||||||
\(273\) | 3.42550e11i | 0.225897i | ||||||||
\(274\) | − | 1.87664e12i | − | 1.21515i | ||||||
\(275\) | − | 4.18360e11i | − | 0.266003i | ||||||
\(276\) | − | 9.82787e10i | − | 0.0613640i | ||||||
\(277\) | −1.21573e12 | −0.745484 | −0.372742 | − | 0.927935i | \(-0.621582\pi\) | ||||
−0.372742 | + | 0.927935i | \(0.621582\pi\) | |||||||
\(278\) | 2.96162e12i | 1.78363i | ||||||||
\(279\) | 1.68978e11i | 0.0999560i | ||||||||
\(280\) | 1.42373e12i | 0.827251i | ||||||||
\(281\) | 2.31227e12 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(282\) | 3.83778e12 | 2.15196 | ||||||||
\(283\) | − | 2.17126e12i | − | 1.19613i | −0.801447 | − | 0.598065i | \(-0.795936\pi\) | ||
0.801447 | − | 0.598065i | \(-0.204064\pi\) | |||||||
\(284\) | −6.60441e12 | −3.57472 | ||||||||
\(285\) | −1.28266e12 | −0.682164 | ||||||||
\(286\) | − | 3.79470e12i | − | 1.98311i | ||||||
\(287\) | 2.12374e11 | 0.109067 | ||||||||
\(288\) | − | 1.55340e12i | − | 0.784008i | ||||||
\(289\) | −1.47837e12 | −0.733320 | ||||||||
\(290\) | 1.57650e12i | 0.768608i | ||||||||
\(291\) | 4.26401e11i | 0.204340i | ||||||||
\(292\) | 2.87457e12i | 1.35412i | ||||||||
\(293\) | 1.50545e12 | 0.697155 | 0.348578 | − | 0.937280i | \(-0.386665\pi\) | ||||
0.348578 | + | 0.937280i | \(0.386665\pi\) | |||||||
\(294\) | 2.22589e12i | 1.01337i | ||||||||
\(295\) | 1.34310e12 | + | 2.27038e12i | 0.601170 | + | 1.01622i | ||||
\(296\) | −1.03981e13 | −4.57609 | ||||||||
\(297\) | − | 3.00171e11i | − | 0.129893i | ||||||
\(298\) | 6.47784e12 | 2.75644 | ||||||||
\(299\) | −1.59368e11 | −0.0666875 | ||||||||
\(300\) | −1.38356e12 | −0.569365 | ||||||||
\(301\) | 2.76598e11i | 0.111948i | ||||||||
\(302\) | −4.87095e12 | −1.93900 | ||||||||
\(303\) | − | 3.77736e11i | − | 0.147902i | ||||||
\(304\) | −7.16855e12 | −2.76098 | ||||||||
\(305\) | − | 2.08336e12i | − | 0.789340i | ||||||
\(306\) | − | 8.64282e11i | − | 0.322143i | ||||||
\(307\) | 3.98881e12 | 1.46269 | 0.731344 | − | 0.682009i | \(-0.238894\pi\) | ||||
0.731344 | + | 0.682009i | \(0.238894\pi\) | |||||||
\(308\) | 1.16660e12i | 0.420891i | ||||||||
\(309\) | 6.23515e9i | 0.00221337i | ||||||||
\(310\) | 1.89698e12 | 0.662603 | ||||||||
\(311\) | −8.53242e11 | −0.293272 | −0.146636 | − | 0.989191i | \(-0.546845\pi\) | ||||
−0.146636 | + | 0.989191i | \(0.546845\pi\) | |||||||
\(312\) | −7.53420e12 | −2.54838 | ||||||||
\(313\) | 2.21559e12i | 0.737510i | 0.929527 | + | 0.368755i | \(0.120216\pi\) | ||||
−0.929527 | + | 0.368755i | \(0.879784\pi\) | |||||||
\(314\) | 4.40644e12 | 1.44358 | ||||||||
\(315\) | 3.04192e11 | 0.0980833 | ||||||||
\(316\) | −6.81048e12 | −2.16143 | ||||||||
\(317\) | 8.88746e11 | 0.277639 | 0.138820 | − | 0.990318i | \(-0.455669\pi\) | ||||
0.138820 | + | 0.990318i | \(0.455669\pi\) | |||||||
\(318\) | − | 4.49292e12i | − | 1.38164i | ||||||
\(319\) | 7.75540e11i | 0.234774i | ||||||||
\(320\) | −6.50770e12 | −1.93944 | ||||||||
\(321\) | −1.27442e12 | −0.373927 | ||||||||
\(322\) | 6.85745e10 | 0.0198099 | ||||||||
\(323\) | −1.81681e12 | −0.516768 | ||||||||
\(324\) | −9.92695e11 | −0.278030 | ||||||||
\(325\) | 2.24356e12i | 0.618758i | ||||||||
\(326\) | 1.11477e13i | 3.02758i | ||||||||
\(327\) | 7.55552e11i | 0.202081i | ||||||||
\(328\) | 4.67106e12i | 1.23040i | ||||||||
\(329\) | 1.91323e12i | 0.496351i | ||||||||
\(330\) | −3.36978e12 | −0.861056 | ||||||||
\(331\) | 2.15439e12 | 0.542232 | 0.271116 | − | 0.962547i | \(-0.412607\pi\) | ||||
0.271116 | + | 0.962547i | \(0.412607\pi\) | |||||||
\(332\) | 3.97154e11i | 0.0984621i | ||||||||
\(333\) | 2.22164e12i | 0.542565i | ||||||||
\(334\) | − | 7.75079e12i | − | 1.86472i | ||||||
\(335\) | − | 1.44754e12i | − | 0.343088i | ||||||
\(336\) | 1.70007e12 | 0.396981 | ||||||||
\(337\) | 6.35856e12i | 1.46288i | 0.681905 | + | 0.731441i | \(0.261152\pi\) | ||||
−0.681905 | + | 0.731441i | \(0.738848\pi\) | |||||||
\(338\) | 1.20942e13i | 2.74154i | ||||||||
\(339\) | 4.97614e11i | 0.111146i | ||||||||
\(340\) | −6.93221e12 | −1.52573 | ||||||||
\(341\) | 9.33192e11 | 0.202395 | ||||||||
\(342\) | 2.92068e12i | 0.624244i | ||||||||
\(343\) | −2.29281e12 | −0.482945 | ||||||||
\(344\) | −6.08362e12 | −1.26290 | ||||||||
\(345\) | 1.41522e11i | 0.0289554i | ||||||||
\(346\) | −1.77368e13 | −3.57679 | ||||||||
\(347\) | 2.39510e12i | 0.476076i | 0.971256 | + | 0.238038i | \(0.0765043\pi\) | ||||
−0.971256 | + | 0.238038i | \(0.923496\pi\) | |||||||
\(348\) | 2.56479e12 | 0.502522 | ||||||||
\(349\) | 5.67456e12i | 1.09599i | 0.836483 | + | 0.547993i | \(0.184608\pi\) | ||||
−0.836483 | + | 0.547993i | \(0.815392\pi\) | |||||||
\(350\) | − | 9.65384e11i | − | 0.183806i | ||||||
\(351\) | 1.60974e12i | 0.302149i | ||||||||
\(352\) | −8.57875e12 | −1.58749 | ||||||||
\(353\) | 6.15338e12i | 1.12264i | 0.827599 | + | 0.561320i | \(0.189706\pi\) | ||||
−0.827599 | + | 0.561320i | \(0.810294\pi\) | |||||||
\(354\) | 5.16975e12 | − | 3.05829e12i | 0.929937 | − | 0.550126i | ||||
\(355\) | 9.51041e12 | 1.68678 | ||||||||
\(356\) | − | 1.86750e13i | − | 3.26597i | ||||||
\(357\) | 4.30867e11 | 0.0743023 | ||||||||
\(358\) | 1.04837e13 | 1.78279 | ||||||||
\(359\) | −1.09396e11 | −0.0183454 | −0.00917271 | − | 0.999958i | \(-0.502920\pi\) | ||||
−0.00917271 | + | 0.999958i | \(0.502920\pi\) | |||||||
\(360\) | 6.69054e12i | 1.10649i | ||||||||
\(361\) | 8.49956e9 | 0.00138631 | ||||||||
\(362\) | − | 7.88948e12i | − | 1.26913i | ||||||
\(363\) | 1.98120e12 | 0.314337 | ||||||||
\(364\) | − | 6.25621e12i | − | 0.979049i | ||||||
\(365\) | − | 4.13940e12i | − | 0.638959i | ||||||
\(366\) | −4.74389e12 | −0.722320 | ||||||||
\(367\) | − | 3.95385e12i | − | 0.593868i | −0.954898 | − | 0.296934i | \(-0.904036\pi\) | ||
0.954898 | − | 0.296934i | \(-0.0959641\pi\) | |||||||
\(368\) | 7.90938e11i | 0.117193i | ||||||||
\(369\) | 9.98011e11 | 0.145883 | ||||||||
\(370\) | 2.49405e13 | 3.59664 | ||||||||
\(371\) | 2.23984e12 | 0.318674 | ||||||||
\(372\) | − | 3.08616e12i | − | 0.433215i | ||||||
\(373\) | 9.57607e12 | 1.32630 | 0.663152 | − | 0.748485i | \(-0.269218\pi\) | ||||
0.663152 | + | 0.748485i | \(0.269218\pi\) | |||||||
\(374\) | −4.77306e12 | −0.652287 | ||||||||
\(375\) | −3.06294e12 | −0.413030 | ||||||||
\(376\) | −4.20806e13 | −5.59941 | ||||||||
\(377\) | − | 4.15903e12i | − | 0.546117i | ||||||
\(378\) | − | 6.92659e11i | − | 0.0897553i | ||||||
\(379\) | 1.54106e13 | 1.97071 | 0.985356 | − | 0.170509i | \(-0.0545412\pi\) | ||||
0.985356 | + | 0.170509i | \(0.0545412\pi\) | |||||||
\(380\) | 2.34261e13 | 2.95653 | ||||||||
\(381\) | −2.37441e12 | −0.295754 | ||||||||
\(382\) | −1.08122e13 | −1.32922 | ||||||||
\(383\) | −3.03341e12 | −0.368076 | −0.184038 | − | 0.982919i | \(-0.558917\pi\) | ||||
−0.184038 | + | 0.982919i | \(0.558917\pi\) | |||||||
\(384\) | 3.48030e12i | 0.416831i | ||||||||
\(385\) | − | 1.67992e12i | − | 0.198603i | ||||||
\(386\) | − | 2.03943e13i | − | 2.37998i | ||||||
\(387\) | 1.29982e12i | 0.149736i | ||||||||
\(388\) | − | 7.78764e12i | − | 0.885619i | ||||||
\(389\) | −1.30546e13 | −1.46560 | −0.732799 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732799 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(390\) | 1.80713e13 | 2.00293 | ||||||||
\(391\) | 2.00456e11i | 0.0219349i | ||||||||
\(392\) | − | 2.44065e13i | − | 2.63679i | ||||||
\(393\) | − | 8.04354e11i | − | 0.0857994i | ||||||
\(394\) | − | 1.79451e12i | − | 0.189001i | ||||||
\(395\) | 9.80715e12 | 1.01990 | ||||||||
\(396\) | 5.48223e12i | 0.562965i | ||||||||
\(397\) | − | 1.07348e13i | − | 1.08853i | −0.838914 | − | 0.544264i | \(-0.816809\pi\) | ||
0.838914 | − | 0.544264i | \(-0.183191\pi\) | |||||||
\(398\) | 2.35075e13i | 2.35391i | ||||||||
\(399\) | −1.45604e12 | −0.143982 | ||||||||
\(400\) | 1.11347e13 | 1.08738 | ||||||||
\(401\) | 1.62822e13i | 1.57033i | 0.619286 | + | 0.785166i | \(0.287422\pi\) | ||||
−0.619286 | + | 0.785166i | \(0.712578\pi\) | |||||||
\(402\) | −3.29611e12 | −0.313957 | ||||||||
\(403\) | −5.00448e12 | −0.470797 | ||||||||
\(404\) | 6.89884e12i | 0.641016i | ||||||||
\(405\) | 1.42949e12 | 0.131192 | ||||||||
\(406\) | 1.78959e12i | 0.162227i | ||||||||
\(407\) | 1.22691e13 | 1.09861 | ||||||||
\(408\) | 9.47669e12i | 0.838216i | ||||||||
\(409\) | 6.46721e12i | 0.565068i | 0.959257 | + | 0.282534i | \(0.0911750\pi\) | ||||
−0.959257 | + | 0.282534i | \(0.908825\pi\) | |||||||
\(410\) | − | 1.12038e13i | − | 0.967047i | ||||||
\(411\) | 4.39645e12 | 0.374881 | ||||||||
\(412\) | − | 1.13877e11i | − | 0.00959288i | ||||||
\(413\) | 1.52464e12 | + | 2.57726e12i | 0.126887 | + | 0.214490i | ||||
\(414\) | 3.22252e11 | 0.0264969 | ||||||||
\(415\) | − | 5.71906e11i | − | 0.0464605i | ||||||
\(416\) | 4.60057e13 | 3.69271 | ||||||||
\(417\) | −6.93825e12 | −0.550262 | ||||||||
\(418\) | 1.61297e13 | 1.26399 | ||||||||
\(419\) | − | 6.56873e12i | − | 0.508641i | −0.967120 | − | 0.254320i | \(-0.918148\pi\) | ||
0.967120 | − | 0.254320i | \(-0.0818518\pi\) | |||||||
\(420\) | −5.55566e12 | −0.425098 | ||||||||
\(421\) | − | 5.80550e12i | − | 0.438964i | −0.975617 | − | 0.219482i | \(-0.929563\pi\) | ||
0.975617 | − | 0.219482i | \(-0.0704367\pi\) | |||||||
\(422\) | −3.59691e13 | −2.68762 | ||||||||
\(423\) | 8.99086e12i | 0.663895i | ||||||||
\(424\) | 4.92641e13i | 3.59502i | ||||||||
\(425\) | 2.82200e12 | 0.203523 | ||||||||
\(426\) | − | 2.16556e13i | − | 1.54356i | ||||||
\(427\) | − | 2.36495e12i | − | 0.166603i | ||||||
\(428\) | 2.32755e13 | 1.62062 | ||||||||
\(429\) | 8.88992e12 | 0.611803 | ||||||||
\(430\) | 1.45920e13 | 0.992593 | ||||||||
\(431\) | 1.22660e13i | 0.824737i | 0.911017 | + | 0.412369i | \(0.135298\pi\) | ||||
−0.911017 | + | 0.412369i | \(0.864702\pi\) | |||||||
\(432\) | 7.98913e12 | 0.530983 | ||||||||
\(433\) | −4.42984e12 | −0.291037 | −0.145518 | − | 0.989356i | \(-0.546485\pi\) | ||||
−0.145518 | + | 0.989356i | \(0.546485\pi\) | |||||||
\(434\) | 2.15338e12 | 0.139853 | ||||||||
\(435\) | −3.69331e12 | −0.237121 | ||||||||
\(436\) | − | 1.37991e13i | − | 0.875830i | ||||||
\(437\) | − | 6.77406e11i | − | 0.0425052i | ||||||
\(438\) | −9.42560e12 | −0.584707 | ||||||||
\(439\) | −9.48510e12 | −0.581727 | −0.290864 | − | 0.956765i | \(-0.593943\pi\) | ||||
−0.290864 | + | 0.956765i | \(0.593943\pi\) | |||||||
\(440\) | 3.69490e13 | 2.24047 | ||||||||
\(441\) | −5.21465e12 | −0.312631 | ||||||||
\(442\) | 2.55967e13 | 1.51731 | ||||||||
\(443\) | − | 1.92750e13i | − | 1.12973i | −0.825182 | − | 0.564867i | \(-0.808928\pi\) | ||
0.825182 | − | 0.564867i | \(-0.191072\pi\) | |||||||
\(444\) | − | 4.05752e13i | − | 2.35151i | ||||||
\(445\) | 2.68922e13i | 1.54109i | ||||||||
\(446\) | 3.45234e13i | 1.95632i | ||||||||
\(447\) | 1.51758e13i | 0.850382i | ||||||||
\(448\) | −7.38731e12 | −0.409352 | ||||||||
\(449\) | −1.18642e13 | −0.650139 | −0.325069 | − | 0.945690i | \(-0.605388\pi\) | ||||
−0.325069 | + | 0.945690i | \(0.605388\pi\) | |||||||
\(450\) | − | 4.53663e12i | − | 0.245850i | ||||||
\(451\) | − | 5.51158e12i | − | 0.295388i | ||||||
\(452\) | − | 9.08824e12i | − | 0.481712i | ||||||
\(453\) | − | 1.14113e13i | − | 0.598196i | ||||||
\(454\) | −2.53162e11 | −0.0131256 | ||||||||
\(455\) | 9.00900e12i | 0.461976i | ||||||||
\(456\) | − | 3.20248e13i | − | 1.62428i | ||||||
\(457\) | − | 1.68398e12i | − | 0.0844804i | −0.999107 | − | 0.0422402i | \(-0.986551\pi\) | ||
0.999107 | − | 0.0422402i | \(-0.0134495\pi\) | |||||||
\(458\) | 4.82157e13 | 2.39255 | ||||||||
\(459\) | 2.02477e12 | 0.0993832 | ||||||||
\(460\) | − | 2.58471e12i | − | 0.125494i | ||||||
\(461\) | −3.27427e13 | −1.57257 | −0.786286 | − | 0.617863i | \(-0.787999\pi\) | ||||
−0.786286 | + | 0.617863i | \(0.787999\pi\) | |||||||
\(462\) | −3.82525e12 | −0.181740 | ||||||||
\(463\) | 2.15339e13i | 1.01208i | 0.862509 | + | 0.506042i | \(0.168892\pi\) | ||||
−0.862509 | + | 0.506042i | \(0.831108\pi\) | |||||||
\(464\) | −2.06412e13 | −0.959720 | ||||||||
\(465\) | 4.44409e12i | 0.204418i | ||||||||
\(466\) | −2.16837e13 | −0.986740 | ||||||||
\(467\) | − | 6.68552e11i | − | 0.0300989i | −0.999887 | − | 0.0150495i | \(-0.995209\pi\) | ||
0.999887 | − | 0.0150495i | \(-0.00479057\pi\) | |||||||
\(468\) | − | 2.93998e13i | − | 1.30953i | ||||||
\(469\) | − | 1.64319e12i | − | 0.0724143i | ||||||
\(470\) | 1.00933e14 | 4.40093 | ||||||||
\(471\) | 1.03231e13i | 0.445353i | ||||||||
\(472\) | −5.66854e13 | + | 3.35336e13i | −2.41970 | + | 1.43143i | ||||
\(473\) | 7.17832e12 | 0.303192 | ||||||||
\(474\) | − | 2.23313e13i | − | 0.933303i | ||||||
\(475\) | −9.53645e12 | −0.394383 | ||||||||
\(476\) | −7.86921e12 | −0.322030 | ||||||||
\(477\) | 1.05257e13 | 0.426244 | ||||||||
\(478\) | 9.18855e13i | 3.68220i | ||||||||
\(479\) | 1.30537e13 | 0.517673 | 0.258836 | − | 0.965921i | \(-0.416661\pi\) | ||||
0.258836 | + | 0.965921i | \(0.416661\pi\) | |||||||
\(480\) | − | 4.08541e13i | − | 1.60335i | ||||||
\(481\) | −6.57964e13 | −2.55550 | ||||||||
\(482\) | − | 3.97537e13i | − | 1.52807i | ||||||
\(483\) | 1.60651e11i | 0.00611150i | ||||||||
\(484\) | −3.61840e13 | −1.36235 | ||||||||
\(485\) | 1.12143e13i | 0.417890i | ||||||||
\(486\) | − | 3.25501e12i | − | 0.120053i | ||||||
\(487\) | 2.60567e13 | 0.951206 | 0.475603 | − | 0.879660i | \(-0.342230\pi\) | ||||
0.475603 | + | 0.879660i | \(0.342230\pi\) | |||||||
\(488\) | 5.20159e13 | 1.87948 | ||||||||
\(489\) | −2.61159e13 | −0.934031 | ||||||||
\(490\) | 5.85406e13i | 2.07242i | ||||||||
\(491\) | 3.68761e13 | 1.29222 | 0.646112 | − | 0.763243i | \(-0.276394\pi\) | ||||
0.646112 | + | 0.763243i | \(0.276394\pi\) | |||||||
\(492\) | −1.82273e13 | −0.632262 | ||||||||
\(493\) | −5.23132e12 | −0.179629 | ||||||||
\(494\) | −8.64995e13 | −2.94021 | ||||||||
\(495\) | − | 7.89445e12i | − | 0.265642i | ||||||
\(496\) | 2.48371e13i | 0.827357i | ||||||||
\(497\) | 1.07959e13 | 0.356022 | ||||||||
\(498\) | −1.30226e12 | −0.0425157 | ||||||||
\(499\) | −6.15494e13 | −1.98939 | −0.994697 | − | 0.102849i | \(-0.967204\pi\) | ||||
−0.994697 | + | 0.102849i | \(0.967204\pi\) | |||||||
\(500\) | 5.59404e13 | 1.79009 | ||||||||
\(501\) | 1.81580e13 | 0.575279 | ||||||||
\(502\) | − | 9.13984e13i | − | 2.86695i | ||||||
\(503\) | − | 2.81370e13i | − | 0.873852i | −0.899497 | − | 0.436926i | \(-0.856067\pi\) | ||
0.899497 | − | 0.436926i | \(-0.143933\pi\) | |||||||
\(504\) | 7.59487e12i | 0.233543i | ||||||||
\(505\) | − | 9.93439e12i | − | 0.302471i | ||||||
\(506\) | − | 1.77966e12i | − | 0.0536518i | ||||||
\(507\) | −2.83335e13 | −0.845785 | ||||||||
\(508\) | 4.33654e13 | 1.28181 | ||||||||
\(509\) | − | 6.37637e13i | − | 1.86631i | −0.359469 | − | 0.933157i | \(-0.617042\pi\) | ||
0.359469 | − | 0.933157i | \(-0.382958\pi\) | |||||||
\(510\) | − | 2.27305e13i | − | 0.658806i | ||||||
\(511\) | − | 4.69891e12i | − | 0.134863i | ||||||
\(512\) | 4.45937e13i | 1.26743i | ||||||||
\(513\) | −6.84236e12 | −0.192583 | ||||||||
\(514\) | − | 1.09670e14i | − | 3.05683i | ||||||
\(515\) | 1.63983e11i | 0.00452651i | ||||||||
\(516\) | − | 2.37394e13i | − | 0.648965i | ||||||
\(517\) | 4.96527e13 | 1.34428 | ||||||||
\(518\) | 2.83116e13 | 0.759129 | ||||||||
\(519\) | − | 4.15523e13i | − | 1.10346i | ||||||
\(520\) | −1.98148e14 | −5.21163 | ||||||||
\(521\) | 7.61660e12 | 0.198414 | 0.0992070 | − | 0.995067i | \(-0.468369\pi\) | ||||
0.0992070 | + | 0.995067i | \(0.468369\pi\) | |||||||
\(522\) | 8.40984e12i | 0.216988i | ||||||||
\(523\) | 3.85918e13 | 0.986248 | 0.493124 | − | 0.869959i | \(-0.335855\pi\) | ||||
0.493124 | + | 0.869959i | \(0.335855\pi\) | |||||||
\(524\) | 1.46904e13i | 0.371859i | ||||||||
\(525\) | 2.26163e12 | 0.0567054 | ||||||||
\(526\) | − | 3.23434e13i | − | 0.803263i | ||||||
\(527\) | 6.29475e12i | 0.154855i | ||||||||
\(528\) | − | 4.41205e13i | − | 1.07515i | ||||||
\(529\) | 4.13518e13 | 0.998196 | ||||||||
\(530\) | − | 1.18163e14i | − | 2.82555i | ||||||
\(531\) | 7.16473e12 | + | 1.21113e13i | 0.169718 | + | 0.286892i | ||||
\(532\) | 2.65926e13 | 0.624025 | ||||||||
\(533\) | 2.95572e13i | 0.687113i | ||||||||
\(534\) | 6.12348e13 | 1.41024 | ||||||||
\(535\) | −3.35169e13 | −0.764708 | ||||||||
\(536\) | 3.61412e13 | 0.816918 | ||||||||
\(537\) | 2.45605e13i | 0.550004i | ||||||||
\(538\) | −8.32425e13 | −1.84686 | ||||||||
\(539\) | 2.87983e13i | 0.633027i | ||||||||
\(540\) | −2.61077e13 | −0.568591 | ||||||||
\(541\) | 4.17389e13i | 0.900646i | 0.892866 | + | 0.450323i | \(0.148691\pi\) | ||||
−0.892866 | + | 0.450323i | \(0.851309\pi\) | |||||||
\(542\) | − | 3.32208e13i | − | 0.710254i | ||||||
\(543\) | 1.84829e13 | 0.391535 | ||||||||
\(544\) | − | 5.78670e13i | − | 1.21461i | ||||||
\(545\) | 1.98709e13i | 0.413271i | ||||||||
\(546\) | 2.05139e13 | 0.422751 | ||||||||
\(547\) | −5.05567e13 | −1.03239 | −0.516193 | − | 0.856472i | \(-0.672651\pi\) | ||||
−0.516193 | + | 0.856472i | \(0.672651\pi\) | |||||||
\(548\) | −8.02953e13 | −1.62475 | ||||||||
\(549\) | − | 1.11136e13i | − | 0.222841i | ||||||
\(550\) | −2.50539e13 | −0.497807 | ||||||||
\(551\) | 1.76783e13 | 0.348083 | ||||||||
\(552\) | −3.53343e12 | −0.0689448 | ||||||||
\(553\) | 1.11327e13 | 0.215266 | ||||||||
\(554\) | 7.28051e13i | 1.39512i | ||||||||
\(555\) | 5.84287e13i | 1.10959i | ||||||||
\(556\) | 1.26718e14 | 2.38486 | ||||||||
\(557\) | −1.34896e12 | −0.0251607 | −0.0125803 | − | 0.999921i | \(-0.504005\pi\) | ||||
−0.0125803 | + | 0.999921i | \(0.504005\pi\) | |||||||
\(558\) | 1.01194e13 | 0.187061 | ||||||||
\(559\) | −3.84956e13 | −0.705264 | ||||||||
\(560\) | 4.47115e13 | 0.811855 | ||||||||
\(561\) | − | 1.11820e13i | − | 0.201235i | ||||||
\(562\) | − | 1.38472e14i | − | 2.46991i | ||||||
\(563\) | − | 8.53764e11i | − | 0.0150937i | −0.999972 | − | 0.00754685i | \(-0.997598\pi\) | ||
0.999972 | − | 0.00754685i | \(-0.00240226\pi\) | |||||||
\(564\) | − | 1.64206e14i | − | 2.87736i | ||||||
\(565\) | 1.30872e13i | 0.227302i | ||||||||
\(566\) | −1.30028e14 | −2.23848 | ||||||||
\(567\) | 1.62271e12 | 0.0276901 | ||||||||
\(568\) | 2.37450e14i | 4.01634i | ||||||||
\(569\) | 3.89773e13i | 0.653507i | 0.945110 | + | 0.326754i | \(0.105955\pi\) | ||||
−0.945110 | + | 0.326754i | \(0.894045\pi\) | |||||||
\(570\) | 7.68135e13i | 1.27662i | ||||||||
\(571\) | − | 2.89747e13i | − | 0.477351i | −0.971099 | − | 0.238676i | \(-0.923287\pi\) | ||
0.971099 | − | 0.238676i | \(-0.0767133\pi\) | |||||||
\(572\) | −1.62363e14 | −2.65159 | ||||||||
\(573\) | − | 2.53299e13i | − | 0.410072i | ||||||
\(574\) | − | 1.27182e13i | − | 0.204111i | ||||||
\(575\) | 1.05220e12i | 0.0167401i | ||||||||
\(576\) | −3.47152e13 | −0.547530 | ||||||||
\(577\) | 3.30742e13 | 0.517142 | 0.258571 | − | 0.965992i | \(-0.416748\pi\) | ||||
0.258571 | + | 0.965992i | \(0.416748\pi\) | |||||||
\(578\) | 8.85335e13i | 1.37236i | ||||||||
\(579\) | 4.77783e13 | 0.734240 | ||||||||
\(580\) | 6.74534e13 | 1.02769 | ||||||||
\(581\) | − | 6.49208e11i | − | 0.00980625i | ||||||
\(582\) | 2.55354e13 | 0.382408 | ||||||||
\(583\) | − | 5.81288e13i | − | 0.863075i | ||||||
\(584\) | 1.03350e14 | 1.52141 | ||||||||
\(585\) | 4.23360e13i | 0.617918i | ||||||||
\(586\) | − | 9.01555e13i | − | 1.30468i | ||||||
\(587\) | − | 3.07500e13i | − | 0.441219i | −0.975362 | − | 0.220609i | \(-0.929195\pi\) | ||
0.975362 | − | 0.220609i | \(-0.0708046\pi\) | |||||||
\(588\) | 9.52386e13 | 1.35496 | ||||||||
\(589\) | − | 2.12720e13i | − | 0.300076i | ||||||
\(590\) | 1.35964e14 | − | 8.04325e13i | 1.90179 | − | 1.12505i | ||||
\(591\) | 4.20403e12 | 0.0583081 | ||||||||
\(592\) | 3.26546e14i | 4.49092i | ||||||||
\(593\) | 6.88754e13 | 0.939271 | 0.469635 | − | 0.882860i | \(-0.344385\pi\) | ||||
0.469635 | + | 0.882860i | \(0.344385\pi\) | |||||||
\(594\) | −1.79760e13 | −0.243087 | ||||||||
\(595\) | 1.13317e13 | 0.151954 | ||||||||
\(596\) | − | 2.77166e14i | − | 3.68560i | ||||||
\(597\) | −5.50715e13 | −0.726198 | ||||||||
\(598\) | 9.54388e12i | 0.124801i | ||||||||
\(599\) | −9.66992e13 | −1.25398 | −0.626988 | − | 0.779029i | \(-0.715712\pi\) | ||||
−0.626988 | + | 0.779029i | \(0.715712\pi\) | |||||||
\(600\) | 4.97433e13i | 0.639703i | ||||||||
\(601\) | 9.80497e13i | 1.25047i | 0.780436 | + | 0.625236i | \(0.214997\pi\) | ||||
−0.780436 | + | 0.625236i | \(0.785003\pi\) | |||||||
\(602\) | 1.65643e13 | 0.209503 | ||||||||
\(603\) | − | 7.72187e12i | − | 0.0968580i | ||||||
\(604\) | 2.08412e14i | 2.59261i | ||||||||
\(605\) | 5.21053e13 | 0.642843 | ||||||||
\(606\) | −2.26211e13 | −0.276790 | ||||||||
\(607\) | −1.27930e14 | −1.55248 | −0.776242 | − | 0.630435i | \(-0.782877\pi\) | ||||
−0.776242 | + | 0.630435i | \(0.782877\pi\) | |||||||
\(608\) | 1.95551e14i | 2.35365i | ||||||||
\(609\) | −4.19252e12 | −0.0500483 | ||||||||
\(610\) | −1.24764e14 | −1.47720 | ||||||||
\(611\) | −2.66275e14 | −3.12697 | ||||||||
\(612\) | −3.69798e13 | −0.430732 | ||||||||
\(613\) | 1.02278e14i | 1.18162i | 0.806810 | + | 0.590811i | \(0.201192\pi\) | ||||
−0.806810 | + | 0.590811i | \(0.798808\pi\) | |||||||
\(614\) | − | 2.38873e14i | − | 2.73732i | ||||||
\(615\) | 2.62475e13 | 0.298341 | ||||||||
\(616\) | 4.19432e13 | 0.472888 | ||||||||
\(617\) | −1.44309e14 | −1.61387 | −0.806936 | − | 0.590639i | \(-0.798876\pi\) | ||||
−0.806936 | + | 0.590639i | \(0.798876\pi\) | |||||||
\(618\) | 3.73398e11 | 0.00414218 | ||||||||
\(619\) | −6.82218e13 | −0.750706 | −0.375353 | − | 0.926882i | \(-0.622479\pi\) | ||||
−0.375353 | + | 0.926882i | \(0.622479\pi\) | |||||||
\(620\) | − | 8.11653e13i | − | 0.885956i | ||||||
\(621\) | 7.54948e11i | 0.00817446i | ||||||||
\(622\) | 5.10971e13i | 0.548839i | ||||||||
\(623\) | 3.05271e13i | 0.325271i | ||||||||
\(624\) | 2.36607e14i | 2.50095i | ||||||||
\(625\) | −1.18140e14 | −1.23879 | ||||||||
\(626\) | 1.32683e14 | 1.38020 | ||||||||
\(627\) | 3.77874e13i | 0.389950i | ||||||||
\(628\) | − | 1.88537e14i | − | 1.93019i | ||||||
\(629\) | 8.27602e13i | 0.840559i | ||||||||
\(630\) | − | 1.82168e13i | − | 0.183556i | ||||||
\(631\) | −5.13267e13 | −0.513093 | −0.256547 | − | 0.966532i | \(-0.582585\pi\) | ||||
−0.256547 | + | 0.966532i | \(0.582585\pi\) | |||||||
\(632\) | 2.44859e14i | 2.42845i | ||||||||
\(633\) | − | 8.42656e13i | − | 0.829148i | ||||||
\(634\) | − | 5.32233e13i | − | 0.519584i | ||||||
\(635\) | −6.24466e13 | −0.604840 | ||||||||
\(636\) | −1.92237e14 | −1.84736 | ||||||||
\(637\) | − | 1.54438e14i | − | 1.47251i | ||||||
\(638\) | 4.64439e13 | 0.439365 | ||||||||
\(639\) | 5.07332e13 | 0.476198 | ||||||||
\(640\) | 9.15312e13i | 0.852451i | ||||||||
\(641\) | −1.34940e14 | −1.24696 | −0.623478 | − | 0.781841i | \(-0.714281\pi\) | ||||
−0.623478 | + | 0.781841i | \(0.714281\pi\) | |||||||
\(642\) | 7.63196e13i | 0.699779i | ||||||||
\(643\) | 1.94621e14 | 1.77066 | 0.885328 | − | 0.464966i | \(-0.153934\pi\) | ||||
0.885328 | + | 0.464966i | \(0.153934\pi\) | |||||||
\(644\) | − | 2.93408e12i | − | 0.0264876i | ||||||
\(645\) | 3.41849e13i | 0.306222i | ||||||||
\(646\) | 1.08801e14i | 0.967098i | ||||||||
\(647\) | 4.61702e13 | 0.407230 | 0.203615 | − | 0.979051i | \(-0.434731\pi\) | ||||
0.203615 | + | 0.979051i | \(0.434731\pi\) | |||||||
\(648\) | 3.56906e13i | 0.312377i | ||||||||
\(649\) | 6.68855e13 | − | 3.95677e13i | 0.580910 | − | 0.343651i | ||||
\(650\) | 1.34358e14 | 1.15797 | ||||||||
\(651\) | 5.04478e12i | 0.0431457i | ||||||||
\(652\) | 4.76972e14 | 4.04814 | ||||||||
\(653\) | −1.65374e14 | −1.39284 | −0.696420 | − | 0.717635i | \(-0.745225\pi\) | ||||
−0.696420 | + | 0.717635i | \(0.745225\pi\) | |||||||
\(654\) | 4.52469e13 | 0.378181 | ||||||||
\(655\) | − | 2.11544e13i | − | 0.175466i | ||||||
\(656\) | 1.46692e14 | 1.20750 | ||||||||
\(657\) | − | 2.20816e13i | − | 0.180386i | ||||||
\(658\) | 1.14576e14 | 0.928887 | ||||||||
\(659\) | − | 1.51824e14i | − | 1.22156i | −0.791801 | − | 0.610779i | \(-0.790856\pi\) | ||
0.791801 | − | 0.610779i | \(-0.209144\pi\) | |||||||
\(660\) | 1.44182e14i | 1.15130i | ||||||||
\(661\) | −1.09780e13 | −0.0869994 | −0.0434997 | − | 0.999053i | \(-0.513851\pi\) | ||||
−0.0434997 | + | 0.999053i | \(0.513851\pi\) | |||||||
\(662\) | − | 1.29018e14i | − | 1.01475i | ||||||
\(663\) | 5.99660e13i | 0.468099i | ||||||||
\(664\) | 1.42790e13 | 0.110626 | ||||||||
\(665\) | −3.82935e13 | −0.294454 | ||||||||
\(666\) | 1.33045e14 | 1.01538 | ||||||||
\(667\) | − | 1.95053e12i | − | 0.0147748i | ||||||
\(668\) | −3.31631e14 | −2.49329 | ||||||||
\(669\) | −8.08789e13 | −0.603538 | ||||||||
\(670\) | −8.66870e13 | −0.642067 | ||||||||
\(671\) | −6.13758e13 | −0.451216 | ||||||||
\(672\) | − | 4.63762e13i | − | 0.338414i | ||||||
\(673\) | − | 1.83915e13i | − | 0.133211i | −0.997779 | − | 0.0666057i | \(-0.978783\pi\) | ||
0.997779 | − | 0.0666057i | \(-0.0212170\pi\) | |||||||
\(674\) | 3.80788e14 | 2.73769 | ||||||||
\(675\) | 1.06281e13 | 0.0758465 | ||||||||
\(676\) | 5.17473e14 | 3.66567 | ||||||||
\(677\) | −8.09994e13 | −0.569559 | −0.284779 | − | 0.958593i | \(-0.591920\pi\) | ||||
−0.284779 | + | 0.958593i | \(0.591920\pi\) | |||||||
\(678\) | 2.98000e13 | 0.208002 | ||||||||
\(679\) | 1.27301e13i | 0.0882026i | ||||||||
\(680\) | 2.49235e14i | 1.71421i | ||||||||
\(681\) | − | 5.93088e11i | − | 0.00404934i | ||||||
\(682\) | − | 5.58850e13i | − | 0.378768i | ||||||
\(683\) | 2.28666e14i | 1.53850i | 0.638947 | + | 0.769251i | \(0.279370\pi\) | ||||
−0.638947 | + | 0.769251i | \(0.720630\pi\) | |||||||
\(684\) | 1.24966e14 | 0.834667 | ||||||||
\(685\) | 1.15626e14 | 0.766659 | ||||||||
\(686\) | 1.37307e14i | 0.903800i | ||||||||
\(687\) | 1.12956e14i | 0.738118i | ||||||||
\(688\) | 1.91053e14i | 1.23940i | ||||||||
\(689\) | 3.11730e14i | 2.00763i | ||||||||
\(690\) | 8.47518e12 | 0.0541880 | ||||||||
\(691\) | 1.24377e14i | 0.789497i | 0.918789 | + | 0.394749i | \(0.129168\pi\) | ||||
−0.918789 | + | 0.394749i | \(0.870832\pi\) | |||||||
\(692\) | 7.58897e14i | 4.78247i | ||||||||
\(693\) | − | 8.96151e12i | − | 0.0560680i | ||||||
\(694\) | 1.43433e14 | 0.890946 | ||||||||
\(695\) | −1.82475e14 | −1.12533 | ||||||||
\(696\) | − | 9.22123e13i | − | 0.564602i | ||||||
\(697\) | 3.71778e13 | 0.226006 | ||||||||
\(698\) | 3.39826e14 | 2.05107 | ||||||||
\(699\) | − | 5.07988e13i | − | 0.304416i | ||||||
\(700\) | −4.13056e13 | −0.245764 | ||||||||
\(701\) | − | 2.12939e14i | − | 1.25796i | −0.777423 | − | 0.628978i | \(-0.783473\pi\) | ||
0.777423 | − | 0.628978i | \(-0.216527\pi\) | |||||||
\(702\) | 9.64010e13 | 0.565452 | ||||||||
\(703\) | − | 2.79673e14i | − | 1.62882i | ||||||
\(704\) | 1.91717e14i | 1.10866i | ||||||||
\(705\) | 2.36458e14i | 1.35772i | ||||||||
\(706\) | 3.68501e14 | 2.10095 | ||||||||
\(707\) | − | 1.12772e13i | − | 0.0638415i | ||||||
\(708\) | −1.30854e14 | − | 2.21197e14i | −0.735565 | − | 1.24340i | ||||
\(709\) | −1.03181e14 | −0.575930 | −0.287965 | − | 0.957641i | \(-0.592979\pi\) | ||||
−0.287965 | + | 0.957641i | \(0.592979\pi\) | |||||||
\(710\) | − | 5.69540e14i | − | 3.15669i | ||||||
\(711\) | 5.23161e13 | 0.287930 | ||||||||
\(712\) | −6.71428e14 | −3.66944 | ||||||||
\(713\) | −2.34703e12 | −0.0127371 | ||||||||
\(714\) | − | 2.58028e13i | − | 0.139052i | ||||||
\(715\) | 2.33803e14 | 1.25118 | ||||||||
\(716\) | − | 4.48565e14i | − | 2.38375i | ||||||
\(717\) | −2.15262e14 | −1.13598 | ||||||||
\(718\) | 6.55126e12i | 0.0343323i | ||||||||
\(719\) | − | 2.82697e14i | − | 1.47122i | −0.677408 | − | 0.735608i | \(-0.736897\pi\) | ||
0.677408 | − | 0.735608i | \(-0.263103\pi\) | |||||||
\(720\) | 2.10113e14 | 1.08590 | ||||||||
\(721\) | 1.86148e11i | 0.000955395i | ||||||||
\(722\) | − | 5.09004e11i | − | 0.00259439i | ||||||
\(723\) | 9.31319e13 | 0.471419 | ||||||||
\(724\) | −3.37565e14 | −1.69693 | ||||||||
\(725\) | −2.74593e13 | −0.137088 | ||||||||
\(726\) | − | 1.18646e14i | − | 0.588262i | ||||||
\(727\) | −3.94443e14 | −1.94228 | −0.971140 | − | 0.238510i | \(-0.923341\pi\) | ||||
−0.971140 | + | 0.238510i | \(0.923341\pi\) | |||||||
\(728\) | −2.24931e14 | −1.10000 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | −2.47892e14 | −1.19577 | ||||||||
\(731\) | 4.84206e13i | 0.231976i | ||||||||
\(732\) | 2.02976e14i | 0.965803i | ||||||||
\(733\) | −1.37662e14 | −0.650572 | −0.325286 | − | 0.945616i | \(-0.605461\pi\) | ||||
−0.325286 | + | 0.945616i | \(0.605461\pi\) | |||||||
\(734\) | −2.36780e14 | −1.11138 | ||||||||
\(735\) | −1.37144e14 | −0.639354 | ||||||||
\(736\) | 2.15760e13 | 0.0999039 | ||||||||
\(737\) | −4.26445e13 | −0.196122 | ||||||||
\(738\) | − | 5.97668e13i | − | 0.273010i | ||||||
\(739\) | 1.66109e14i | 0.753654i | 0.926284 | + | 0.376827i | \(0.122985\pi\) | ||||
−0.926284 | + | 0.376827i | \(0.877015\pi\) | |||||||
\(740\) | − | 1.06712e15i | − | 4.80901i | ||||||
\(741\) | − | 2.02644e14i | − | 0.907076i | ||||||
\(742\) | − | 1.34135e14i | − | 0.596378i | ||||||
\(743\) | 2.91675e14 | 1.28812 | 0.644058 | − | 0.764976i | \(-0.277249\pi\) | ||||
0.644058 | + | 0.764976i | \(0.277249\pi\) | |||||||
\(744\) | −1.10957e14 | −0.486733 | ||||||||
\(745\) | 3.99121e14i | 1.73909i | ||||||||
\(746\) | − | 5.73471e14i | − | 2.48209i | ||||||
\(747\) | − | 3.05082e12i | − | 0.0131164i | ||||||
\(748\) | 2.04223e14i | 0.872162i | ||||||||
\(749\) | −3.80473e13 | −0.161404 | ||||||||
\(750\) | 1.83427e14i | 0.772958i | ||||||||
\(751\) | − | 2.42985e13i | − | 0.101714i | −0.998706 | − | 0.0508569i | \(-0.983805\pi\) | ||
0.998706 | − | 0.0508569i | \(-0.0161952\pi\) | |||||||
\(752\) | 1.32152e15i | 5.49520i | ||||||||
\(753\) | 2.14121e14 | 0.884474 | ||||||||
\(754\) | −2.49067e14 | −1.02202 | ||||||||
\(755\) | − | 3.00115e14i | − | 1.22336i | ||||||
\(756\) | −2.96366e13 | −0.120010 | ||||||||
\(757\) | 3.15140e14 | 1.26772 | 0.633861 | − | 0.773447i | \(-0.281469\pi\) | ||||
0.633861 | + | 0.773447i | \(0.281469\pi\) | |||||||
\(758\) | − | 9.22877e14i | − | 3.68806i | ||||||
\(759\) | 4.16925e12 | 0.0165520 | ||||||||
\(760\) | − | 8.42245e14i | − | 3.32178i | ||||||
\(761\) | −2.69468e14 | −1.05581 | −0.527903 | − | 0.849305i | \(-0.677022\pi\) | ||||
−0.527903 | + | 0.849305i | \(0.677022\pi\) | |||||||
\(762\) | 1.42194e14i | 0.553485i | ||||||||
\(763\) | 2.25568e13i | 0.0872276i | ||||||||
\(764\) | 4.62617e14i | 1.77727i | ||||||||
\(765\) | 5.32512e13 | 0.203246 | ||||||||
\(766\) | 1.81658e14i | 0.688829i | ||||||||
\(767\) | −3.58690e14 | + | 2.12192e14i | −1.35127 | + | 0.799377i | ||||
\(768\) | −4.49604e13 | −0.168277 | ||||||||
\(769\) | 4.26168e14i | 1.58471i | 0.610063 | + | 0.792353i | \(0.291144\pi\) | ||||
−0.610063 | + | 0.792353i | \(0.708856\pi\) | |||||||
\(770\) | −1.00604e14 | −0.371672 | ||||||||
\(771\) | 2.56926e14 | 0.943054 | ||||||||
\(772\) | −8.72607e14 | −3.18223 | ||||||||
\(773\) | − | 4.02297e14i | − | 1.45764i | −0.684707 | − | 0.728818i | \(-0.740070\pi\) | ||
0.684707 | − | 0.728818i | \(-0.259930\pi\) | |||||||
\(774\) | 7.78406e13 | 0.280222 | ||||||||
\(775\) | 3.30412e13i | 0.118181i | ||||||||
\(776\) | −2.79991e14 | −0.995027 | ||||||||
\(777\) | 6.63262e13i | 0.234196i | ||||||||
\(778\) | 7.81785e14i | 2.74277i | ||||||||
\(779\) | −1.25636e14 | −0.437951 | ||||||||
\(780\) | − | 7.73210e14i | − | 2.67809i | ||||||
\(781\) | − | 2.80177e14i | − | 0.964224i | ||||||
\(782\) | 1.20045e13 | 0.0410498 | ||||||||
\(783\) | −1.97019e13 | −0.0669422 | ||||||||
\(784\) | −7.66472e14 | −2.58771 | ||||||||
\(785\) | 2.71495e14i | 0.910781i | ||||||||
\(786\) | −4.81695e13 | −0.160568 | ||||||||
\(787\) | −4.45257e13 | −0.147481 | −0.0737407 | − | 0.997277i | \(-0.523494\pi\) | ||||
−0.0737407 | + | 0.997277i | \(0.523494\pi\) | |||||||
\(788\) | −7.67810e13 | −0.252710 | ||||||||
\(789\) | 7.57718e13 | 0.247812 | ||||||||
\(790\) | − | 5.87310e14i | − | 1.90867i | ||||||
\(791\) | 1.48561e13i | 0.0479758i | ||||||||
\(792\) | 1.97104e14 | 0.632512 | ||||||||
\(793\) | 3.29143e14 | 1.04959 | ||||||||
\(794\) | −6.42861e14 | −2.03711 | ||||||||
\(795\) | 2.76824e14 | 0.871701 | ||||||||
\(796\) | 1.00581e15 | 3.14738 | ||||||||
\(797\) | 3.77346e14i | 1.17341i | 0.809802 | + | 0.586703i | \(0.199575\pi\) | ||||
−0.809802 | + | 0.586703i | \(0.800425\pi\) | |||||||
\(798\) | 8.71961e13i | 0.269453i | ||||||||
\(799\) | 3.34927e14i | 1.02853i | ||||||||
\(800\) | − | 3.03745e14i | − | 0.926956i | ||||||
\(801\) | 1.43456e14i | 0.435068i | ||||||||
\(802\) | 9.75074e14 | 2.93877 | ||||||||
\(803\) | −1.21947e14 | −0.365253 | ||||||||
\(804\) | 1.41030e14i | 0.419788i | ||||||||
\(805\) | 4.22510e12i | 0.0124985i | ||||||||
\(806\) | 2.99698e14i | 0.881065i | ||||||||
\(807\) | − | 1.95014e14i | − | 0.569768i | ||||||
\(808\) | 2.48036e14 | 0.720207 | ||||||||
\(809\) | − | 1.55441e14i | − | 0.448564i | −0.974524 | − | 0.224282i | \(-0.927996\pi\) | ||
0.974524 | − | 0.224282i | \(-0.0720036\pi\) | |||||||
\(810\) | − | 8.56063e13i | − | 0.245516i | ||||||
\(811\) | 3.61757e14i | 1.03113i | 0.856851 | + | 0.515563i | \(0.172417\pi\) | ||||
−0.856851 | + | 0.515563i | \(0.827583\pi\) | |||||||
\(812\) | 7.65708e13 | 0.216912 | ||||||||
\(813\) | 7.78271e13 | 0.219118 | ||||||||
\(814\) | − | 7.34749e14i | − | 2.05597i | ||||||
\(815\) | −6.86844e14 | −1.91016 | ||||||||
\(816\) | 2.97610e14 | 0.822616 | ||||||||
\(817\) | − | 1.63629e14i | − | 0.449520i | ||||||
\(818\) | 3.87295e14 | 1.05749 | ||||||||
\(819\) | 4.80584e13i | 0.130422i | ||||||||
\(820\) | −4.79376e14 | −1.29302 | ||||||||
\(821\) | 4.29545e14i | 1.15158i | 0.817599 | + | 0.575788i | \(0.195305\pi\) | ||||
−0.817599 | + | 0.575788i | \(0.804695\pi\) | |||||||
\(822\) | − | 2.63285e14i | − | 0.701565i | ||||||
\(823\) | 1.59700e14i | 0.422967i | 0.977382 | + | 0.211484i | \(0.0678295\pi\) | ||||
−0.977382 | + | 0.211484i | \(0.932171\pi\) | |||||||
\(824\) | −4.09424e12 | −0.0107780 | ||||||||
\(825\) | − | 5.86943e13i | − | 0.153577i | ||||||
\(826\) | 1.54341e14 | − | 9.13042e13i | 0.401404 | − | 0.237460i | ||||
\(827\) | 6.59003e14 | 1.70357 | 0.851784 | − | 0.523893i | \(-0.175521\pi\) | ||||
0.851784 | + | 0.523893i | \(0.175521\pi\) | |||||||
\(828\) | − | 1.37881e13i | − | 0.0354285i | ||||||
\(829\) | 1.37351e14 | 0.350800 | 0.175400 | − | 0.984497i | \(-0.443878\pi\) | ||||
0.175400 | + | 0.984497i | \(0.443878\pi\) | |||||||
\(830\) | −3.42491e13 | −0.0869478 | ||||||||
\(831\) | −1.70562e14 | −0.430405 | ||||||||
\(832\) | − | 1.02813e15i | − | 2.57889i | ||||||
\(833\) | −1.94256e14 | −0.484338 | ||||||||
\(834\) | 4.15503e14i | 1.02978i | ||||||||
\(835\) | 4.77551e14 | 1.17649 | ||||||||
\(836\) | − | 6.90136e14i | − | 1.69006i | ||||||
\(837\) | 2.37069e13i | 0.0577096i | ||||||||
\(838\) | −3.93374e14 | −0.951888 | ||||||||
\(839\) | 3.04420e14i | 0.732257i | 0.930564 | + | 0.366128i | \(0.119317\pi\) | ||||
−0.930564 | + | 0.366128i | \(0.880683\pi\) | |||||||
\(840\) | 1.99744e14i | 0.477614i | ||||||||
\(841\) | −3.69804e14 | −0.879006 | ||||||||
\(842\) | −3.47667e14 | −0.821492 | ||||||||
\(843\) | 3.24402e14 | 0.761983 | ||||||||
\(844\) | 1.53900e15i | 3.59357i | ||||||||
\(845\) | −7.45165e14 | −1.72969 | ||||||||
\(846\) | 5.38426e14 | 1.24244 | ||||||||
\(847\) | 5.91482e13 | 0.135683 | ||||||||
\(848\) | 1.54711e15 | 3.52811 | ||||||||
\(849\) | − | 3.04619e14i | − | 0.690587i | ||||||
\(850\) | − | 1.68998e14i | − | 0.380879i | ||||||
\(851\) | −3.08576e13 | −0.0691376 | ||||||||
\(852\) | −9.26574e14 | −2.06387 | ||||||||
\(853\) | 3.25749e14 | 0.721338 | 0.360669 | − | 0.932694i | \(-0.382548\pi\) | ||||
0.360669 | + | 0.932694i | \(0.382548\pi\) | |||||||
\(854\) | −1.41627e14 | −0.311787 | ||||||||
\(855\) | −1.79953e14 | −0.393848 | ||||||||
\(856\) | − | 8.36830e14i | − | 1.82083i | ||||||
\(857\) | − | 6.18698e14i | − | 1.33837i | −0.743098 | − | 0.669183i | \(-0.766644\pi\) | ||
0.743098 | − | 0.669183i | \(-0.233356\pi\) | |||||||
\(858\) | − | 5.32381e14i | − | 1.14495i | ||||||
\(859\) | 4.26341e14i | 0.911573i | 0.890089 | + | 0.455786i | \(0.150642\pi\) | ||||
−0.890089 | + | 0.455786i | \(0.849358\pi\) | |||||||
\(860\) | − | 6.24342e14i | − | 1.32718i | ||||||
\(861\) | 2.97953e13 | 0.0629697 | ||||||||
\(862\) | 7.34559e14 | 1.54344 | ||||||||
\(863\) | 1.07136e14i | 0.223810i | 0.993719 | + | 0.111905i | \(0.0356952\pi\) | ||||
−0.993719 | + | 0.111905i | \(0.964305\pi\) | |||||||
\(864\) | − | 2.17936e14i | − | 0.452647i | ||||||
\(865\) | − | 1.09282e15i | − | 2.25667i | ||||||
\(866\) | 2.65285e14i | 0.544656i | ||||||||
\(867\) | −2.07409e14 | −0.423383 | ||||||||
\(868\) | − | 9.21361e13i | − | 0.186996i | ||||||
\(869\) | − | 2.88919e14i | − | 0.583012i | ||||||
\(870\) | 2.21177e14i | 0.443756i | ||||||||
\(871\) | 2.28692e14 | 0.456205 | ||||||||
\(872\) | −4.96124e14 | −0.984028 | ||||||||
\(873\) | 5.98224e13i | 0.117976i | ||||||||
\(874\) | −4.05671e13 | −0.0795456 | ||||||||
\(875\) | −9.14429e13 | −0.178283 | ||||||||
\(876\) | 4.03290e14i | 0.781803i | ||||||||
\(877\) | −1.66758e14 | −0.321432 | −0.160716 | − | 0.987001i | \(-0.551380\pi\) | ||||
−0.160716 | + | 0.987001i | \(0.551380\pi\) | |||||||
\(878\) | 5.68024e14i | 1.08866i | ||||||||
\(879\) | 2.11209e14 | 0.402503 | ||||||||
\(880\) | − | 1.16036e15i | − | 2.19877i | ||||||
\(881\) | − | 1.46706e14i | − | 0.276419i | −0.990403 | − | 0.138209i | \(-0.955865\pi\) | ||
0.990403 | − | 0.138209i | \(-0.0441347\pi\) | |||||||
\(882\) | 3.12284e14i | 0.585069i | ||||||||
\(883\) | −9.41163e14 | −1.75332 | −0.876661 | − | 0.481109i | \(-0.840234\pi\) | ||||
−0.876661 | + | 0.481109i | \(0.840234\pi\) | |||||||
\(884\) | − | 1.09520e15i | − | 2.02877i | ||||||
\(885\) | 1.88431e14 | + | 3.18525e14i | 0.347085 | + | 0.586716i | ||||
\(886\) | −1.15430e15 | −2.11422 | ||||||||
\(887\) | − | 3.31171e14i | − | 0.603163i | −0.953440 | − | 0.301581i | \(-0.902486\pi\) | ||
0.953440 | − | 0.301581i | \(-0.0975145\pi\) | |||||||
\(888\) | −1.45881e15 | −2.64201 | ||||||||
\(889\) | −7.08873e13 | −0.127661 | ||||||||
\(890\) | 1.61046e15 | 2.88404 | ||||||||
\(891\) | − | 4.21129e13i | − | 0.0749940i | ||||||
\(892\) | 1.47714e15 | 2.61577 | ||||||||
\(893\) | − | 1.13182e15i | − | 1.99307i | ||||||
\(894\) | 9.08816e14 | 1.59143 | ||||||||
\(895\) | 6.45937e14i | 1.12480i | ||||||||
\(896\) | 1.03903e14i | 0.179924i | ||||||||
\(897\) | −2.23587e13 | −0.0385020 | ||||||||
\(898\) | 7.10497e14i | 1.21669i | ||||||||
\(899\) | − | 6.12507e13i | − | 0.104307i | ||||||
\(900\) | −1.94108e14 | −0.328723 | ||||||||
\(901\) | 3.92102e14 | 0.660351 | ||||||||
\(902\) | −3.30066e14 | −0.552800 | ||||||||
\(903\) | 3.88056e13i | 0.0646331i | ||||||||
\(904\) | −3.26752e14 | −0.541222 | ||||||||
\(905\) | 4.86096e14 | 0.800718 | ||||||||
\(906\) | −6.83375e14 | −1.11948 | ||||||||
\(907\) | 7.74383e14 | 1.26159 | 0.630797 | − | 0.775948i | \(-0.282728\pi\) | ||||
0.630797 | + | 0.775948i | \(0.282728\pi\) | |||||||
\(908\) | 1.08320e13i | 0.0175500i | ||||||||
\(909\) | − | 5.29949e13i | − | 0.0853915i | ||||||
\(910\) | 5.39512e14 | 0.864558 | ||||||||
\(911\) | 9.32031e14 | 1.48538 | 0.742692 | − | 0.669634i | \(-0.233549\pi\) | ||||
0.742692 | + | 0.669634i | \(0.233549\pi\) | |||||||
\(912\) | −1.00572e15 | −1.59405 | ||||||||
\(913\) | −1.68484e13 | −0.0265585 | ||||||||
\(914\) | −1.00847e14 | −0.158100 | ||||||||
\(915\) | − | 2.92287e14i | − | 0.455726i | ||||||
\(916\) | − | 2.06299e15i | − | 3.19904i | ||||||
\(917\) | − | 2.40137e13i | − | 0.0370350i | ||||||
\(918\) | − | 1.21255e14i | − | 0.185989i | ||||||
\(919\) | 4.86822e14i | 0.742664i | 0.928500 | + | 0.371332i | \(0.121099\pi\) | ||||
−0.928500 | + | 0.371332i | \(0.878901\pi\) | |||||||
\(920\) | −9.29287e13 | −0.140997 | ||||||||
\(921\) | 5.59614e14 | 0.844483 | ||||||||
\(922\) | 1.96083e15i | 2.94296i | ||||||||
\(923\) | 1.50252e15i | 2.24291i | ||||||||
\(924\) | 1.63670e14i | 0.243002i | ||||||||
\(925\) | 4.34410e14i | 0.641492i | ||||||||
\(926\) | 1.28957e15 | 1.89405 | ||||||||
\(927\) | 8.74768e11i | 0.00127789i | ||||||||
\(928\) | 5.63072e14i | 0.818133i | ||||||||
\(929\) | 9.38539e14i | 1.35636i | 0.734898 | + | 0.678178i | \(0.237230\pi\) | ||||
−0.734898 | + | 0.678178i | \(0.762770\pi\) | |||||||
\(930\) | 2.66138e14 | 0.382554 | ||||||||
\(931\) | 6.56452e14 | 0.938544 | ||||||||
\(932\) | 9.27772e14i | 1.31936i | ||||||||
\(933\) | −1.19706e14 | −0.169320 | ||||||||
\(934\) | −4.00368e13 | −0.0563281 | ||||||||
\(935\) | − | 2.94083e14i | − | 0.411540i | ||||||
\(936\) | −1.05702e15 | −1.47131 | ||||||||
\(937\) | − | 7.79446e14i | − | 1.07916i | −0.841933 | − | 0.539582i | \(-0.818582\pi\) | ||
0.841933 | − | 0.539582i | \(-0.181418\pi\) | |||||||
\(938\) | −9.84041e13 | −0.135519 | ||||||||
\(939\) | 3.10839e14i | 0.425802i | ||||||||
\(940\) | − | 4.31859e15i | − | 5.88441i | ||||||
\(941\) | 5.05583e14i | 0.685242i | 0.939474 | + | 0.342621i | \(0.111315\pi\) | ||||
−0.939474 | + | 0.342621i | \(0.888685\pi\) | |||||||
\(942\) | 6.18207e14 | 0.833450 | ||||||||
\(943\) | 1.38619e13i | 0.0185894i | ||||||||
\(944\) | 1.05310e15 | + | 1.78017e15i | 1.40479 | + | 2.37466i | ||||
\(945\) | 4.26769e13 | 0.0566284 | ||||||||
\(946\) | − | 4.29880e14i | − | 0.567403i | ||||||
\(947\) | −6.47854e14 | −0.850604 | −0.425302 | − | 0.905051i | \(-0.639832\pi\) | ||||
−0.425302 | + | 0.905051i | \(0.639832\pi\) | |||||||
\(948\) | −9.55483e14 | −1.24790 | ||||||||
\(949\) | 6.53972e14 | 0.849626 | ||||||||
\(950\) | 5.71099e14i | 0.738062i | ||||||||
\(951\) | 1.24688e14 | 0.160295 | ||||||||
\(952\) | 2.82923e14i | 0.361813i | ||||||||
\(953\) | 9.29642e14 | 1.18264 | 0.591318 | − | 0.806438i | \(-0.298608\pi\) | ||||
0.591318 | + | 0.806438i | \(0.298608\pi\) | |||||||
\(954\) | − | 6.30340e14i | − | 0.797688i | ||||||
\(955\) | − | 6.66172e14i | − | 0.838629i | ||||||
\(956\) | 3.93148e15 | 4.92341 | ||||||||
\(957\) | 1.08805e14i | 0.135547i | ||||||||
\(958\) | − | 7.81731e14i | − | 0.968790i | ||||||
\(959\) | 1.31255e14 | 0.161816 | ||||||||
\(960\) | −9.13004e14 | −1.11974 | ||||||||
\(961\) | 7.45927e14 | 0.910079 | ||||||||
\(962\) | 3.94028e15i | 4.78246i | ||||||||
\(963\) | −1.78796e14 | −0.215887 | ||||||||
\(964\) | −1.70093e15 | −2.04315 | ||||||||
\(965\) | 1.25656e15 | 1.50158 | ||||||||
\(966\) | 9.62073e12 | 0.0114373 | ||||||||
\(967\) | 3.68363e14i | 0.435656i | 0.975987 | + | 0.217828i | \(0.0698971\pi\) | ||||
−0.975987 | + | 0.217828i | \(0.930103\pi\) | |||||||
\(968\) | 1.30093e15i | 1.53066i | ||||||||
\(969\) | −2.54891e14 | −0.298356 | ||||||||
\(970\) | 6.71576e14 | 0.782054 | ||||||||
\(971\) | 3.97937e14 | 0.461018 | 0.230509 | − | 0.973070i | \(-0.425961\pi\) | ||||
0.230509 | + | 0.973070i | \(0.425961\pi\) | |||||||
\(972\) | −1.39271e14 | −0.160520 | ||||||||
\(973\) | −2.07139e14 | −0.237519 | ||||||||
\(974\) | − | 1.56043e15i | − | 1.78012i | ||||||
\(975\) | 3.14763e14i | 0.357240i | ||||||||
\(976\) | − | 1.63353e15i | − | 1.84450i | ||||||
\(977\) | 9.78481e13i | 0.109921i | 0.998489 | + | 0.0549603i | \(0.0175032\pi\) | ||||
−0.998489 | + | 0.0549603i | \(0.982497\pi\) | |||||||
\(978\) | 1.56398e15i | 1.74798i | ||||||||
\(979\) | 7.92247e14 | 0.880941 | ||||||||
\(980\) | 2.50476e15 | 2.77099 | ||||||||
\(981\) | 1.06001e14i | 0.116672i | ||||||||
\(982\) | − | 2.20836e15i | − | 2.41831i | ||||||
\(983\) | − | 5.70380e13i | − | 0.0621436i | −0.999517 | − | 0.0310718i | \(-0.990108\pi\) | ||
0.999517 | − | 0.0310718i | \(-0.00989206\pi\) | |||||||
\(984\) | 6.55331e14i | 0.710371i | ||||||||
\(985\) | 1.10565e14 | 0.119244 | ||||||||
\(986\) | 3.13283e14i | 0.336164i | ||||||||
\(987\) | 2.68419e14i | 0.286568i | ||||||||
\(988\) | 3.70103e15i | 3.93131i | ||||||||
\(989\) | −1.80539e13 | −0.0190805 | ||||||||
\(990\) | −4.72766e14 | −0.497131 | ||||||||
\(991\) | − | 5.44837e14i | − | 0.570031i | −0.958523 | − | 0.285016i | \(-0.908001\pi\) | ||
0.958523 | − | 0.285016i | \(-0.0919988\pi\) | |||||||
\(992\) | 6.77533e14 | 0.705297 | ||||||||
\(993\) | 3.02253e14 | 0.313058 | ||||||||
\(994\) | − | 6.46522e14i | − | 0.666272i | ||||||
\(995\) | −1.44837e15 | −1.48513 | ||||||||
\(996\) | 5.57192e13i | 0.0568471i | ||||||||
\(997\) | −4.59934e14 | −0.466896 | −0.233448 | − | 0.972369i | \(-0.575001\pi\) | ||||
−0.233448 | + | 0.972369i | \(0.575001\pi\) | |||||||
\(998\) | 3.68594e15i | 3.72302i | ||||||||
\(999\) | 3.11687e14i | 0.313250i |
(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 | 177.11.c.a.58.3 | ✓ | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.98 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.3 | ✓ | 100 | 1.1 | even | 1 | trivial | |
177.11.c.a.58.98 | yes | 100 | 59.58 | odd | 2 | inner |