Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(1,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.a (trivial) |
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: | yes |
Analytic conductor: | \(8.75560921479\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-35.0613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −42.0613 | −1.85887 | −0.929433 | − | 0.368992i | \(-0.879703\pi\) | ||||
−0.929433 | + | 0.368992i | \(0.879703\pi\) | |||||||
\(3\) | −256.773 | −1.83022 | −0.915112 | − | 0.403199i | \(-0.867898\pi\) | ||||
−0.915112 | + | 0.403199i | \(0.867898\pi\) | |||||||
\(4\) | 1257.15 | 2.45538 | ||||||||
\(5\) | 1407.25 | 1.00694 | 0.503472 | − | 0.864012i | \(-0.332056\pi\) | ||||
0.503472 | + | 0.864012i | \(0.332056\pi\) | |||||||
\(6\) | 10800.2 | 3.40214 | ||||||||
\(7\) | −5138.64 | −0.808923 | −0.404461 | − | 0.914555i | \(-0.632541\pi\) | ||||
−0.404461 | + | 0.914555i | \(0.632541\pi\) | |||||||
\(8\) | −31342.2 | −2.70536 | ||||||||
\(9\) | 46249.6 | 2.34972 | ||||||||
\(10\) | −59190.7 | −1.87177 | ||||||||
\(11\) | 26560.4 | 0.546975 | 0.273487 | − | 0.961876i | \(-0.411823\pi\) | ||||
0.273487 | + | 0.961876i | \(0.411823\pi\) | |||||||
\(12\) | −322804. | −4.49390 | ||||||||
\(13\) | 71402.0 | 0.693371 | 0.346685 | − | 0.937981i | \(-0.387307\pi\) | ||||
0.346685 | + | 0.937981i | \(0.387307\pi\) | |||||||
\(14\) | 216138. | 1.50368 | ||||||||
\(15\) | −361344. | −1.84293 | ||||||||
\(16\) | 674631. | 2.57351 | ||||||||
\(17\) | −83521.0 | −0.242536 | ||||||||
\(18\) | −1.94532e6 | −4.36782 | ||||||||
\(19\) | −548715. | −0.965951 | −0.482976 | − | 0.875634i | \(-0.660444\pi\) | ||||
−0.482976 | + | 0.875634i | \(0.660444\pi\) | |||||||
\(20\) | 1.76913e6 | 2.47243 | ||||||||
\(21\) | 1.31947e6 | 1.48051 | ||||||||
\(22\) | −1.11716e6 | −1.01675 | ||||||||
\(23\) | 1.15988e6 | 0.864247 | 0.432124 | − | 0.901814i | \(-0.357764\pi\) | ||||
0.432124 | + | 0.901814i | \(0.357764\pi\) | |||||||
\(24\) | 8.04785e6 | 4.95141 | ||||||||
\(25\) | 27218.8 | 0.0139360 | ||||||||
\(26\) | −3.00326e6 | −1.28888 | ||||||||
\(27\) | −6.82160e6 | −2.47030 | ||||||||
\(28\) | −6.46007e6 | −1.98621 | ||||||||
\(29\) | 1.44199e6 | 0.378592 | 0.189296 | − | 0.981920i | \(-0.439380\pi\) | ||||
0.189296 | + | 0.981920i | \(0.439380\pi\) | |||||||
\(30\) | 1.51986e7 | 3.42577 | ||||||||
\(31\) | −6.05781e6 | −1.17812 | −0.589058 | − | 0.808091i | \(-0.700501\pi\) | ||||
−0.589058 | + | 0.808091i | \(0.700501\pi\) | |||||||
\(32\) | −1.23287e7 | −2.07846 | ||||||||
\(33\) | −6.82000e6 | −1.00109 | ||||||||
\(34\) | 3.51300e6 | 0.450841 | ||||||||
\(35\) | −7.23134e6 | −0.814540 | ||||||||
\(36\) | 5.81429e7 | 5.76947 | ||||||||
\(37\) | −9.50334e6 | −0.833621 | −0.416810 | − | 0.908993i | \(-0.636852\pi\) | ||||
−0.416810 | + | 0.908993i | \(0.636852\pi\) | |||||||
\(38\) | 2.30797e7 | 1.79557 | ||||||||
\(39\) | −1.83341e7 | −1.26902 | ||||||||
\(40\) | −4.41062e7 | −2.72414 | ||||||||
\(41\) | 1.75776e7 | 0.971476 | 0.485738 | − | 0.874104i | \(-0.338551\pi\) | ||||
0.485738 | + | 0.874104i | \(0.338551\pi\) | |||||||
\(42\) | −5.54985e7 | −2.75207 | ||||||||
\(43\) | −2.06503e7 | −0.921125 | −0.460562 | − | 0.887627i | \(-0.652352\pi\) | ||||
−0.460562 | + | 0.887627i | \(0.652352\pi\) | |||||||
\(44\) | 3.33905e7 | 1.34303 | ||||||||
\(45\) | 6.50846e7 | 2.36604 | ||||||||
\(46\) | −4.87861e7 | −1.60652 | ||||||||
\(47\) | 3.15997e7 | 0.944587 | 0.472294 | − | 0.881441i | \(-0.343426\pi\) | ||||
0.472294 | + | 0.881441i | \(0.343426\pi\) | |||||||
\(48\) | −1.73227e8 | −4.71011 | ||||||||
\(49\) | −1.39480e7 | −0.345644 | ||||||||
\(50\) | −1.14486e6 | −0.0259052 | ||||||||
\(51\) | 2.14460e7 | 0.443895 | ||||||||
\(52\) | 8.97634e7 | 1.70249 | ||||||||
\(53\) | −1.02011e8 | −1.77585 | −0.887924 | − | 0.459990i | \(-0.847853\pi\) | ||||
−0.887924 | + | 0.459990i | \(0.847853\pi\) | |||||||
\(54\) | 2.86925e8 | 4.59195 | ||||||||
\(55\) | 3.73770e7 | 0.550773 | ||||||||
\(56\) | 1.61056e8 | 2.18842 | ||||||||
\(57\) | 1.40895e8 | 1.76791 | ||||||||
\(58\) | −6.06520e7 | −0.703751 | ||||||||
\(59\) | −5.95270e7 | −0.639558 | −0.319779 | − | 0.947492i | \(-0.603609\pi\) | ||||
−0.319779 | + | 0.947492i | \(0.603609\pi\) | |||||||
\(60\) | −4.54265e8 | −4.52510 | ||||||||
\(61\) | 5.34058e7 | 0.493860 | 0.246930 | − | 0.969033i | \(-0.420578\pi\) | ||||
0.246930 | + | 0.969033i | \(0.420578\pi\) | |||||||
\(62\) | 2.54799e8 | 2.18996 | ||||||||
\(63\) | −2.37660e8 | −1.90074 | ||||||||
\(64\) | 1.73149e8 | 1.29006 | ||||||||
\(65\) | 1.00480e8 | 0.698185 | ||||||||
\(66\) | 2.86858e8 | 1.86089 | ||||||||
\(67\) | −6.45107e7 | −0.391107 | −0.195553 | − | 0.980693i | \(-0.562650\pi\) | ||||
−0.195553 | + | 0.980693i | \(0.562650\pi\) | |||||||
\(68\) | −1.04999e8 | −0.595517 | ||||||||
\(69\) | −2.97827e8 | −1.58177 | ||||||||
\(70\) | 3.04160e8 | 1.51412 | ||||||||
\(71\) | −2.71132e8 | −1.26625 | −0.633123 | − | 0.774051i | \(-0.718227\pi\) | ||||
−0.633123 | + | 0.774051i | \(0.718227\pi\) | |||||||
\(72\) | −1.44956e9 | −6.35684 | ||||||||
\(73\) | 2.75443e8 | 1.13522 | 0.567609 | − | 0.823298i | \(-0.307868\pi\) | ||||
0.567609 | + | 0.823298i | \(0.307868\pi\) | |||||||
\(74\) | 3.99723e8 | 1.54959 | ||||||||
\(75\) | −6.98908e6 | −0.0255061 | ||||||||
\(76\) | −6.89819e8 | −2.37178 | ||||||||
\(77\) | −1.36484e8 | −0.442460 | ||||||||
\(78\) | 7.71158e8 | 2.35895 | ||||||||
\(79\) | −4.33372e8 | −1.25181 | −0.625906 | − | 0.779898i | \(-0.715271\pi\) | ||||
−0.625906 | + | 0.779898i | \(0.715271\pi\) | |||||||
\(80\) | 9.49373e8 | 2.59138 | ||||||||
\(81\) | 8.41275e8 | 2.17148 | ||||||||
\(82\) | −7.39337e8 | −1.80584 | ||||||||
\(83\) | 1.23703e8 | 0.286106 | 0.143053 | − | 0.989715i | \(-0.454308\pi\) | ||||
0.143053 | + | 0.989715i | \(0.454308\pi\) | |||||||
\(84\) | 1.65877e9 | 3.63522 | ||||||||
\(85\) | −1.17535e8 | −0.244220 | ||||||||
\(86\) | 8.68579e8 | 1.71225 | ||||||||
\(87\) | −3.70264e8 | −0.692908 | ||||||||
\(88\) | −8.32461e8 | −1.47976 | ||||||||
\(89\) | −8.87168e8 | −1.49882 | −0.749412 | − | 0.662104i | \(-0.769664\pi\) | ||||
−0.749412 | + | 0.662104i | \(0.769664\pi\) | |||||||
\(90\) | −2.73755e9 | −4.39815 | ||||||||
\(91\) | −3.66909e8 | −0.560883 | ||||||||
\(92\) | 1.45815e9 | 2.12206 | ||||||||
\(93\) | 1.55548e9 | 2.15622 | ||||||||
\(94\) | −1.32912e9 | −1.75586 | ||||||||
\(95\) | −7.72177e8 | −0.972659 | ||||||||
\(96\) | 3.16568e9 | 3.80405 | ||||||||
\(97\) | −4.41697e8 | −0.506585 | −0.253292 | − | 0.967390i | \(-0.581513\pi\) | ||||
−0.253292 | + | 0.967390i | \(0.581513\pi\) | |||||||
\(98\) | 5.86670e8 | 0.642506 | ||||||||
\(99\) | 1.22841e9 | 1.28524 | ||||||||
\(100\) | 3.42183e7 | 0.0342183 | ||||||||
\(101\) | −1.14036e9 | −1.09042 | −0.545212 | − | 0.838298i | \(-0.683551\pi\) | ||||
−0.545212 | + | 0.838298i | \(0.683551\pi\) | |||||||
\(102\) | −9.02046e8 | −0.825141 | ||||||||
\(103\) | 8.49153e8 | 0.743393 | 0.371696 | − | 0.928354i | \(-0.378776\pi\) | ||||
0.371696 | + | 0.928354i | \(0.378776\pi\) | |||||||
\(104\) | −2.23790e9 | −1.87582 | ||||||||
\(105\) | 1.85682e9 | 1.49079 | ||||||||
\(106\) | 4.29072e9 | 3.30106 | ||||||||
\(107\) | 2.23234e9 | 1.64639 | 0.823196 | − | 0.567758i | \(-0.192189\pi\) | ||||
0.823196 | + | 0.567758i | \(0.192189\pi\) | |||||||
\(108\) | −8.57581e9 | −6.06552 | ||||||||
\(109\) | 1.34014e9 | 0.909352 | 0.454676 | − | 0.890657i | \(-0.349755\pi\) | ||||
0.454676 | + | 0.890657i | \(0.349755\pi\) | |||||||
\(110\) | −1.57213e9 | −1.02381 | ||||||||
\(111\) | 2.44021e9 | 1.52571 | ||||||||
\(112\) | −3.46669e9 | −2.08177 | ||||||||
\(113\) | −2.00028e9 | −1.15408 | −0.577042 | − | 0.816715i | \(-0.695793\pi\) | ||||
−0.577042 | + | 0.816715i | \(0.695793\pi\) | |||||||
\(114\) | −5.92624e9 | −3.28630 | ||||||||
\(115\) | 1.63224e9 | 0.870248 | ||||||||
\(116\) | 1.81280e9 | 0.929586 | ||||||||
\(117\) | 3.30232e9 | 1.62923 | ||||||||
\(118\) | 2.50379e9 | 1.18885 | ||||||||
\(119\) | 4.29184e8 | 0.196193 | ||||||||
\(120\) | 1.13253e10 | 4.98579 | ||||||||
\(121\) | −1.65249e9 | −0.700819 | ||||||||
\(122\) | −2.24632e9 | −0.918020 | ||||||||
\(123\) | −4.51346e9 | −1.77802 | ||||||||
\(124\) | −7.61560e9 | −2.89272 | ||||||||
\(125\) | −2.71023e9 | −0.992911 | ||||||||
\(126\) | 9.99630e9 | 3.53323 | ||||||||
\(127\) | −3.35970e9 | −1.14600 | −0.572999 | − | 0.819556i | \(-0.694220\pi\) | ||||
−0.572999 | + | 0.819556i | \(0.694220\pi\) | |||||||
\(128\) | −9.70602e8 | −0.319592 | ||||||||
\(129\) | 5.30245e9 | 1.68587 | ||||||||
\(130\) | −4.22633e9 | −1.29783 | ||||||||
\(131\) | −2.27481e8 | −0.0674876 | −0.0337438 | − | 0.999431i | \(-0.510743\pi\) | ||||
−0.0337438 | + | 0.999431i | \(0.510743\pi\) | |||||||
\(132\) | −8.57380e9 | −2.45805 | ||||||||
\(133\) | 2.81965e9 | 0.781380 | ||||||||
\(134\) | 2.71341e9 | 0.727014 | ||||||||
\(135\) | −9.59967e9 | −2.48745 | ||||||||
\(136\) | 2.61773e9 | 0.656145 | ||||||||
\(137\) | −3.72862e9 | −0.904285 | −0.452142 | − | 0.891946i | \(-0.649340\pi\) | ||||
−0.452142 | + | 0.891946i | \(0.649340\pi\) | |||||||
\(138\) | 1.25270e10 | 2.94029 | ||||||||
\(139\) | −8.72554e8 | −0.198256 | −0.0991279 | − | 0.995075i | \(-0.531605\pi\) | ||||
−0.0991279 | + | 0.995075i | \(0.531605\pi\) | |||||||
\(140\) | −9.09091e9 | −2.00001 | ||||||||
\(141\) | −8.11395e9 | −1.72881 | ||||||||
\(142\) | 1.14042e10 | 2.35378 | ||||||||
\(143\) | 1.89647e9 | 0.379256 | ||||||||
\(144\) | 3.12014e10 | 6.04705 | ||||||||
\(145\) | 2.02923e9 | 0.381220 | ||||||||
\(146\) | −1.15855e10 | −2.11022 | ||||||||
\(147\) | 3.58147e9 | 0.632606 | ||||||||
\(148\) | −1.19472e10 | −2.04686 | ||||||||
\(149\) | 5.86193e9 | 0.974323 | 0.487161 | − | 0.873312i | \(-0.338032\pi\) | ||||
0.487161 | + | 0.873312i | \(0.338032\pi\) | |||||||
\(150\) | 2.93970e8 | 0.0474124 | ||||||||
\(151\) | 1.01489e10 | 1.58864 | 0.794318 | − | 0.607502i | \(-0.207828\pi\) | ||||
0.794318 | + | 0.607502i | \(0.207828\pi\) | |||||||
\(152\) | 1.71979e10 | 2.61324 | ||||||||
\(153\) | −3.86281e9 | −0.569892 | ||||||||
\(154\) | 5.74071e9 | 0.822474 | ||||||||
\(155\) | −8.52483e9 | −1.18630 | ||||||||
\(156\) | −2.30489e10 | −3.11594 | ||||||||
\(157\) | −5.31929e9 | −0.698723 | −0.349362 | − | 0.936988i | \(-0.613601\pi\) | ||||
−0.349362 | + | 0.936988i | \(0.613601\pi\) | |||||||
\(158\) | 1.82282e10 | 2.32695 | ||||||||
\(159\) | 2.61937e10 | 3.25020 | ||||||||
\(160\) | −1.73495e10 | −2.09289 | ||||||||
\(161\) | −5.96021e9 | −0.699109 | ||||||||
\(162\) | −3.53851e10 | −4.03648 | ||||||||
\(163\) | −1.08994e10 | −1.20937 | −0.604685 | − | 0.796465i | \(-0.706701\pi\) | ||||
−0.604685 | + | 0.796465i | \(0.706701\pi\) | |||||||
\(164\) | 2.20978e10 | 2.38534 | ||||||||
\(165\) | −9.59743e9 | −1.00804 | ||||||||
\(166\) | −5.20309e9 | −0.531833 | ||||||||
\(167\) | −5.90585e9 | −0.587569 | −0.293784 | − | 0.955872i | \(-0.594915\pi\) | ||||
−0.293784 | + | 0.955872i | \(0.594915\pi\) | |||||||
\(168\) | −4.13550e10 | −4.00531 | ||||||||
\(169\) | −5.50625e9 | −0.519237 | ||||||||
\(170\) | 4.94366e9 | 0.453972 | ||||||||
\(171\) | −2.53778e10 | −2.26972 | ||||||||
\(172\) | −2.59606e10 | −2.26171 | ||||||||
\(173\) | 1.33412e10 | 1.13237 | 0.566183 | − | 0.824280i | \(-0.308420\pi\) | ||||
0.566183 | + | 0.824280i | \(0.308420\pi\) | |||||||
\(174\) | 1.55738e10 | 1.28802 | ||||||||
\(175\) | −1.39868e8 | −0.0112732 | ||||||||
\(176\) | 1.79185e10 | 1.40765 | ||||||||
\(177\) | 1.52850e10 | 1.17054 | ||||||||
\(178\) | 3.73154e10 | 2.78611 | ||||||||
\(179\) | 1.62530e10 | 1.18330 | 0.591651 | − | 0.806194i | \(-0.298476\pi\) | ||||
0.591651 | + | 0.806194i | \(0.298476\pi\) | |||||||
\(180\) | 8.18214e10 | 5.80953 | ||||||||
\(181\) | −4.03320e9 | −0.279316 | −0.139658 | − | 0.990200i | \(-0.544600\pi\) | ||||
−0.139658 | + | 0.990200i | \(0.544600\pi\) | |||||||
\(182\) | 1.54327e10 | 1.04261 | ||||||||
\(183\) | −1.37132e10 | −0.903875 | ||||||||
\(184\) | −3.63532e10 | −2.33810 | ||||||||
\(185\) | −1.33735e10 | −0.839409 | ||||||||
\(186\) | −6.54257e10 | −4.00812 | ||||||||
\(187\) | −2.21835e9 | −0.132661 | ||||||||
\(188\) | 3.97257e10 | 2.31932 | ||||||||
\(189\) | 3.50537e10 | 1.99828 | ||||||||
\(190\) | 3.24788e10 | 1.80804 | ||||||||
\(191\) | −1.09015e10 | −0.592700 | −0.296350 | − | 0.955079i | \(-0.595769\pi\) | ||||
−0.296350 | + | 0.955079i | \(0.595769\pi\) | |||||||
\(192\) | −4.44601e10 | −2.36110 | ||||||||
\(193\) | 1.29615e10 | 0.672428 | 0.336214 | − | 0.941786i | \(-0.390853\pi\) | ||||
0.336214 | + | 0.941786i | \(0.390853\pi\) | |||||||
\(194\) | 1.85784e10 | 0.941673 | ||||||||
\(195\) | −2.58007e10 | −1.27784 | ||||||||
\(196\) | −1.75348e10 | −0.848687 | ||||||||
\(197\) | 7.15882e9 | 0.338644 | 0.169322 | − | 0.985561i | \(-0.445842\pi\) | ||||
0.169322 | + | 0.985561i | \(0.445842\pi\) | |||||||
\(198\) | −5.16684e10 | −2.38909 | ||||||||
\(199\) | 3.03762e9 | 0.137307 | 0.0686537 | − | 0.997641i | \(-0.478130\pi\) | ||||
0.0686537 | + | 0.997641i | \(0.478130\pi\) | |||||||
\(200\) | −8.53098e8 | −0.0377020 | ||||||||
\(201\) | 1.65646e10 | 0.715813 | ||||||||
\(202\) | 4.79650e10 | 2.02695 | ||||||||
\(203\) | −7.40986e9 | −0.306251 | ||||||||
\(204\) | 2.69609e10 | 1.08993 | ||||||||
\(205\) | 2.47360e10 | 0.978222 | ||||||||
\(206\) | −3.57165e10 | −1.38187 | ||||||||
\(207\) | 5.36440e10 | 2.03074 | ||||||||
\(208\) | 4.81700e10 | 1.78440 | ||||||||
\(209\) | −1.45741e10 | −0.528351 | ||||||||
\(210\) | −7.81001e10 | −2.77118 | ||||||||
\(211\) | −3.30011e10 | −1.14619 | −0.573097 | − | 0.819488i | \(-0.694258\pi\) | ||||
−0.573097 | + | 0.819488i | \(0.694258\pi\) | |||||||
\(212\) | −1.28244e11 | −4.36038 | ||||||||
\(213\) | 6.96195e10 | 2.31752 | ||||||||
\(214\) | −9.38951e10 | −3.06042 | ||||||||
\(215\) | −2.90601e10 | −0.927521 | ||||||||
\(216\) | 2.13804e11 | 6.68304 | ||||||||
\(217\) | 3.11289e10 | 0.953004 | ||||||||
\(218\) | −5.63682e10 | −1.69036 | ||||||||
\(219\) | −7.07266e10 | −2.07771 | ||||||||
\(220\) | 4.69887e10 | 1.35236 | ||||||||
\(221\) | −5.96357e9 | −0.168167 | ||||||||
\(222\) | −1.02638e11 | −2.83610 | ||||||||
\(223\) | −3.03057e10 | −0.820640 | −0.410320 | − | 0.911942i | \(-0.634583\pi\) | ||||
−0.410320 | + | 0.911942i | \(0.634583\pi\) | |||||||
\(224\) | 6.33526e10 | 1.68131 | ||||||||
\(225\) | 1.25886e9 | 0.0327459 | ||||||||
\(226\) | 8.41343e10 | 2.14529 | ||||||||
\(227\) | −4.49193e10 | −1.12284 | −0.561418 | − | 0.827532i | \(-0.689744\pi\) | ||||
−0.561418 | + | 0.827532i | \(0.689744\pi\) | |||||||
\(228\) | 1.77127e11 | 4.34089 | ||||||||
\(229\) | 4.68022e10 | 1.12462 | 0.562311 | − | 0.826926i | \(-0.309913\pi\) | ||||
0.562311 | + | 0.826926i | \(0.309913\pi\) | |||||||
\(230\) | −6.86541e10 | −1.61767 | ||||||||
\(231\) | 3.50455e10 | 0.809802 | ||||||||
\(232\) | −4.51951e10 | −1.02423 | ||||||||
\(233\) | −2.08143e10 | −0.462658 | −0.231329 | − | 0.972876i | \(-0.574307\pi\) | ||||
−0.231329 | + | 0.972876i | \(0.574307\pi\) | |||||||
\(234\) | −1.38900e11 | −3.02852 | ||||||||
\(235\) | 4.44685e10 | 0.951146 | ||||||||
\(236\) | −7.48347e10 | −1.57036 | ||||||||
\(237\) | 1.11279e11 | 2.29110 | ||||||||
\(238\) | −1.80521e10 | −0.364696 | ||||||||
\(239\) | 1.23779e9 | 0.0245390 | 0.0122695 | − | 0.999925i | \(-0.496094\pi\) | ||||
0.0122695 | + | 0.999925i | \(0.496094\pi\) | |||||||
\(240\) | −2.43774e11 | −4.74282 | ||||||||
\(241\) | −3.29491e10 | −0.629167 | −0.314584 | − | 0.949230i | \(-0.601865\pi\) | ||||
−0.314584 | + | 0.949230i | \(0.601865\pi\) | |||||||
\(242\) | 6.95061e10 | 1.30273 | ||||||||
\(243\) | −8.17474e10 | −1.50399 | ||||||||
\(244\) | 6.71394e10 | 1.21262 | ||||||||
\(245\) | −1.96283e10 | −0.348044 | ||||||||
\(246\) | 1.89842e11 | 3.30510 | ||||||||
\(247\) | −3.91793e10 | −0.669762 | ||||||||
\(248\) | 1.89865e11 | 3.18722 | ||||||||
\(249\) | −3.17635e10 | −0.523638 | ||||||||
\(250\) | 1.13996e11 | 1.84569 | ||||||||
\(251\) | −3.15140e10 | −0.501154 | −0.250577 | − | 0.968097i | \(-0.580620\pi\) | ||||
−0.250577 | + | 0.968097i | \(0.580620\pi\) | |||||||
\(252\) | −2.98776e11 | −4.66705 | ||||||||
\(253\) | 3.08069e10 | 0.472721 | ||||||||
\(254\) | 1.41313e11 | 2.13026 | ||||||||
\(255\) | 3.01798e10 | 0.446977 | ||||||||
\(256\) | −4.78276e10 | −0.695983 | ||||||||
\(257\) | −7.36840e10 | −1.05360 | −0.526798 | − | 0.849991i | \(-0.676607\pi\) | ||||
−0.526798 | + | 0.849991i | \(0.676607\pi\) | |||||||
\(258\) | −2.23028e11 | −3.13380 | ||||||||
\(259\) | 4.88342e10 | 0.674335 | ||||||||
\(260\) | 1.26319e11 | 1.71431 | ||||||||
\(261\) | 6.66914e10 | 0.889585 | ||||||||
\(262\) | 9.56814e9 | 0.125450 | ||||||||
\(263\) | −5.81832e10 | −0.749888 | −0.374944 | − | 0.927047i | \(-0.622338\pi\) | ||||
−0.374944 | + | 0.927047i | \(0.622338\pi\) | |||||||
\(264\) | 2.13754e11 | 2.70830 | ||||||||
\(265\) | −1.43555e11 | −1.78818 | ||||||||
\(266\) | −1.18598e11 | −1.45248 | ||||||||
\(267\) | 2.27801e11 | 2.74318 | ||||||||
\(268\) | −8.10999e10 | −0.960315 | ||||||||
\(269\) | 1.32703e11 | 1.54523 | 0.772617 | − | 0.634872i | \(-0.218947\pi\) | ||||
0.772617 | + | 0.634872i | \(0.218947\pi\) | |||||||
\(270\) | 4.03775e11 | 4.62384 | ||||||||
\(271\) | −1.25505e11 | −1.41351 | −0.706757 | − | 0.707456i | \(-0.749843\pi\) | ||||
−0.706757 | + | 0.707456i | \(0.749843\pi\) | |||||||
\(272\) | −5.63459e10 | −0.624169 | ||||||||
\(273\) | 9.42126e10 | 1.02654 | ||||||||
\(274\) | 1.56831e11 | 1.68094 | ||||||||
\(275\) | 7.22943e8 | 0.00762267 | ||||||||
\(276\) | −3.74414e11 | −3.88384 | ||||||||
\(277\) | −1.08560e11 | −1.10792 | −0.553961 | − | 0.832542i | \(-0.686884\pi\) | ||||
−0.553961 | + | 0.832542i | \(0.686884\pi\) | |||||||
\(278\) | 3.67008e10 | 0.368531 | ||||||||
\(279\) | −2.80171e11 | −2.76825 | ||||||||
\(280\) | 2.26646e11 | 2.20362 | ||||||||
\(281\) | −1.21647e11 | −1.16392 | −0.581961 | − | 0.813216i | \(-0.697714\pi\) | ||||
−0.581961 | + | 0.813216i | \(0.697714\pi\) | |||||||
\(282\) | 3.41284e11 | 3.21362 | ||||||||
\(283\) | 1.97694e11 | 1.83212 | 0.916060 | − | 0.401041i | \(-0.131352\pi\) | ||||
0.916060 | + | 0.401041i | \(0.131352\pi\) | |||||||
\(284\) | −3.40855e11 | −3.10912 | ||||||||
\(285\) | 1.98275e11 | 1.78018 | ||||||||
\(286\) | −7.97678e10 | −0.704986 | ||||||||
\(287\) | −9.03249e10 | −0.785849 | ||||||||
\(288\) | −5.70196e11 | −4.88380 | ||||||||
\(289\) | 6.97576e9 | 0.0588235 | ||||||||
\(290\) | −8.53523e10 | −0.708637 | ||||||||
\(291\) | 1.13416e11 | 0.927164 | ||||||||
\(292\) | 3.46275e11 | 2.78739 | ||||||||
\(293\) | −5.29206e10 | −0.419489 | −0.209745 | − | 0.977756i | \(-0.567263\pi\) | ||||
−0.209745 | + | 0.977756i | \(0.567263\pi\) | |||||||
\(294\) | −1.50641e11 | −1.17593 | ||||||||
\(295\) | −8.37692e10 | −0.643999 | ||||||||
\(296\) | 2.97856e11 | 2.25524 | ||||||||
\(297\) | −1.81184e11 | −1.35119 | ||||||||
\(298\) | −2.46561e11 | −1.81113 | ||||||||
\(299\) | 8.28178e10 | 0.599244 | ||||||||
\(300\) | −8.78635e9 | −0.0626272 | ||||||||
\(301\) | 1.06115e11 | 0.745119 | ||||||||
\(302\) | −4.26878e11 | −2.95306 | ||||||||
\(303\) | 2.92814e11 | 1.99572 | ||||||||
\(304\) | −3.70180e11 | −2.48589 | ||||||||
\(305\) | 7.51551e10 | 0.497290 | ||||||||
\(306\) | 1.62475e11 | 1.05935 | ||||||||
\(307\) | 6.66906e10 | 0.428491 | 0.214246 | − | 0.976780i | \(-0.431271\pi\) | ||||
0.214246 | + | 0.976780i | \(0.431271\pi\) | |||||||
\(308\) | −1.71582e11 | −1.08641 | ||||||||
\(309\) | −2.18040e11 | −1.36058 | ||||||||
\(310\) | 3.58566e11 | 2.20516 | ||||||||
\(311\) | 2.16895e11 | 1.31470 | 0.657352 | − | 0.753584i | \(-0.271676\pi\) | ||||
0.657352 | + | 0.753584i | \(0.271676\pi\) | |||||||
\(312\) | 5.74633e11 | 3.43316 | ||||||||
\(313\) | 2.03438e11 | 1.19807 | 0.599034 | − | 0.800723i | \(-0.295551\pi\) | ||||
0.599034 | + | 0.800723i | \(0.295551\pi\) | |||||||
\(314\) | 2.23736e11 | 1.29883 | ||||||||
\(315\) | −3.34446e11 | −1.91394 | ||||||||
\(316\) | −5.44816e11 | −3.07368 | ||||||||
\(317\) | 2.27635e11 | 1.26611 | 0.633056 | − | 0.774106i | \(-0.281800\pi\) | ||||
0.633056 | + | 0.774106i | \(0.281800\pi\) | |||||||
\(318\) | −1.10174e12 | −6.04169 | ||||||||
\(319\) | 3.82998e10 | 0.207080 | ||||||||
\(320\) | 2.43664e11 | 1.29902 | ||||||||
\(321\) | −5.73205e11 | −3.01327 | ||||||||
\(322\) | 2.50694e11 | 1.29955 | ||||||||
\(323\) | 4.58292e10 | 0.234278 | ||||||||
\(324\) | 1.05761e12 | 5.33180 | ||||||||
\(325\) | 1.94348e9 | 0.00966285 | ||||||||
\(326\) | 4.58444e11 | 2.24806 | ||||||||
\(327\) | −3.44113e11 | −1.66432 | ||||||||
\(328\) | −5.50921e11 | −2.62819 | ||||||||
\(329\) | −1.62379e11 | −0.764098 | ||||||||
\(330\) | 4.03680e11 | 1.87381 | ||||||||
\(331\) | 1.97602e11 | 0.904828 | 0.452414 | − | 0.891808i | \(-0.350563\pi\) | ||||
0.452414 | + | 0.891808i | \(0.350563\pi\) | |||||||
\(332\) | 1.55513e11 | 0.702499 | ||||||||
\(333\) | −4.39526e11 | −1.95878 | ||||||||
\(334\) | 2.48408e11 | 1.09221 | ||||||||
\(335\) | −9.07825e10 | −0.393822 | ||||||||
\(336\) | 8.90153e11 | 3.81011 | ||||||||
\(337\) | 4.61396e9 | 0.0194867 | 0.00974337 | − | 0.999953i | \(-0.496899\pi\) | ||||
0.00974337 | + | 0.999953i | \(0.496899\pi\) | |||||||
\(338\) | 2.31600e11 | 0.965192 | ||||||||
\(339\) | 5.13618e11 | 2.11223 | ||||||||
\(340\) | −1.47759e11 | −0.599653 | ||||||||
\(341\) | −1.60898e11 | −0.644399 | ||||||||
\(342\) | 1.06743e12 | 4.21910 | ||||||||
\(343\) | 2.79036e11 | 1.08852 | ||||||||
\(344\) | 6.47226e11 | 2.49197 | ||||||||
\(345\) | −4.19115e11 | −1.59275 | ||||||||
\(346\) | −5.61148e11 | −2.10492 | ||||||||
\(347\) | −3.34855e11 | −1.23987 | −0.619933 | − | 0.784655i | \(-0.712840\pi\) | ||||
−0.619933 | + | 0.784655i | \(0.712840\pi\) | |||||||
\(348\) | −4.65480e11 | −1.70135 | ||||||||
\(349\) | −1.38047e11 | −0.498095 | −0.249048 | − | 0.968491i | \(-0.580118\pi\) | ||||
−0.249048 | + | 0.968491i | \(0.580118\pi\) | |||||||
\(350\) | 5.88303e9 | 0.0209553 | ||||||||
\(351\) | −4.87076e11 | −1.71283 | ||||||||
\(352\) | −3.27454e11 | −1.13686 | ||||||||
\(353\) | 3.22524e11 | 1.10554 | 0.552771 | − | 0.833333i | \(-0.313570\pi\) | ||||
0.552771 | + | 0.833333i | \(0.313570\pi\) | |||||||
\(354\) | −6.42906e11 | −2.17587 | ||||||||
\(355\) | −3.81550e11 | −1.27504 | ||||||||
\(356\) | −1.11531e12 | −3.68018 | ||||||||
\(357\) | −1.10203e11 | −0.359077 | ||||||||
\(358\) | −6.83624e11 | −2.19960 | ||||||||
\(359\) | 1.09669e11 | 0.348465 | 0.174232 | − | 0.984705i | \(-0.444256\pi\) | ||||
0.174232 | + | 0.984705i | \(0.444256\pi\) | |||||||
\(360\) | −2.03990e12 | −6.40098 | ||||||||
\(361\) | −2.16000e10 | −0.0669378 | ||||||||
\(362\) | 1.69642e11 | 0.519212 | ||||||||
\(363\) | 4.24316e11 | 1.28266 | ||||||||
\(364\) | −4.61262e11 | −1.37718 | ||||||||
\(365\) | 3.87617e11 | 1.14310 | ||||||||
\(366\) | 5.76795e11 | 1.68018 | ||||||||
\(367\) | 1.91239e11 | 0.550273 | 0.275137 | − | 0.961405i | \(-0.411277\pi\) | ||||
0.275137 | + | 0.961405i | \(0.411277\pi\) | |||||||
\(368\) | 7.82492e11 | 2.22415 | ||||||||
\(369\) | 8.12957e11 | 2.28270 | ||||||||
\(370\) | 5.62509e11 | 1.56035 | ||||||||
\(371\) | 5.24198e11 | 1.43652 | ||||||||
\(372\) | 1.95548e12 | 5.29433 | ||||||||
\(373\) | 1.18077e11 | 0.315846 | 0.157923 | − | 0.987451i | \(-0.449520\pi\) | ||||
0.157923 | + | 0.987451i | \(0.449520\pi\) | |||||||
\(374\) | 9.33067e10 | 0.246599 | ||||||||
\(375\) | 6.95914e11 | 1.81725 | ||||||||
\(376\) | −9.90403e11 | −2.55545 | ||||||||
\(377\) | 1.02961e11 | 0.262504 | ||||||||
\(378\) | −1.47441e12 | −3.71453 | ||||||||
\(379\) | −1.76959e11 | −0.440551 | −0.220276 | − | 0.975438i | \(-0.570696\pi\) | ||||
−0.220276 | + | 0.975438i | \(0.570696\pi\) | |||||||
\(380\) | −9.70746e11 | −2.38825 | ||||||||
\(381\) | 8.62682e11 | 2.09743 | ||||||||
\(382\) | 4.58530e11 | 1.10175 | ||||||||
\(383\) | 1.29043e11 | 0.306436 | 0.153218 | − | 0.988192i | \(-0.451036\pi\) | ||||
0.153218 | + | 0.988192i | \(0.451036\pi\) | |||||||
\(384\) | 2.49225e11 | 0.584926 | ||||||||
\(385\) | −1.92067e11 | −0.445533 | ||||||||
\(386\) | −5.45176e11 | −1.24995 | ||||||||
\(387\) | −9.55069e11 | −2.16439 | ||||||||
\(388\) | −5.55282e11 | −1.24386 | ||||||||
\(389\) | 6.86269e10 | 0.151957 | 0.0759785 | − | 0.997109i | \(-0.475792\pi\) | ||||
0.0759785 | + | 0.997109i | \(0.475792\pi\) | |||||||
\(390\) | 1.08521e12 | 2.37533 | ||||||||
\(391\) | −9.68744e10 | −0.209611 | ||||||||
\(392\) | 4.37160e11 | 0.935090 | ||||||||
\(393\) | 5.84110e10 | 0.123517 | ||||||||
\(394\) | −3.01110e11 | −0.629494 | ||||||||
\(395\) | −6.09862e11 | −1.26051 | ||||||||
\(396\) | 1.54430e12 | 3.15575 | ||||||||
\(397\) | 7.83412e11 | 1.58283 | 0.791413 | − | 0.611282i | \(-0.209346\pi\) | ||||
0.791413 | + | 0.611282i | \(0.209346\pi\) | |||||||
\(398\) | −1.27766e11 | −0.255236 | ||||||||
\(399\) | −7.24011e11 | −1.43010 | ||||||||
\(400\) | 1.83627e10 | 0.0358646 | ||||||||
\(401\) | 1.06747e11 | 0.206161 | 0.103080 | − | 0.994673i | \(-0.467130\pi\) | ||||
0.103080 | + | 0.994673i | \(0.467130\pi\) | |||||||
\(402\) | −6.96730e11 | −1.33060 | ||||||||
\(403\) | −4.32540e11 | −0.816871 | ||||||||
\(404\) | −1.43361e12 | −2.67741 | ||||||||
\(405\) | 1.18388e12 | 2.18656 | ||||||||
\(406\) | 3.11669e11 | 0.569280 | ||||||||
\(407\) | −2.52412e11 | −0.455969 | ||||||||
\(408\) | −6.72164e11 | −1.20089 | ||||||||
\(409\) | −1.08641e12 | −1.91973 | −0.959863 | − | 0.280469i | \(-0.909510\pi\) | ||||
−0.959863 | + | 0.280469i | \(0.909510\pi\) | |||||||
\(410\) | −1.04043e12 | −1.81838 | ||||||||
\(411\) | 9.57410e11 | 1.65504 | ||||||||
\(412\) | 1.06752e12 | 1.82531 | ||||||||
\(413\) | 3.05888e11 | 0.517353 | ||||||||
\(414\) | −2.25634e12 | −3.77488 | ||||||||
\(415\) | 1.74080e11 | 0.288093 | ||||||||
\(416\) | −8.80292e11 | −1.44114 | ||||||||
\(417\) | 2.24049e11 | 0.362853 | ||||||||
\(418\) | 6.13005e11 | 0.982134 | ||||||||
\(419\) | 6.48628e11 | 1.02809 | 0.514047 | − | 0.857762i | \(-0.328146\pi\) | ||||
0.514047 | + | 0.857762i | \(0.328146\pi\) | |||||||
\(420\) | 2.33430e12 | 3.66046 | ||||||||
\(421\) | −8.74376e11 | −1.35653 | −0.678264 | − | 0.734818i | \(-0.737267\pi\) | ||||
−0.678264 | + | 0.734818i | \(0.737267\pi\) | |||||||
\(422\) | 1.38807e12 | 2.13062 | ||||||||
\(423\) | 1.46147e12 | 2.21952 | ||||||||
\(424\) | 3.19725e12 | 4.80430 | ||||||||
\(425\) | −2.27334e9 | −0.00337999 | ||||||||
\(426\) | −2.92829e12 | −4.30795 | ||||||||
\(427\) | −2.74433e11 | −0.399495 | ||||||||
\(428\) | 2.80640e12 | 4.04252 | ||||||||
\(429\) | −4.86962e11 | −0.694124 | ||||||||
\(430\) | 1.22231e12 | 1.72414 | ||||||||
\(431\) | 2.93756e10 | 0.0410052 | 0.0205026 | − | 0.999790i | \(-0.493473\pi\) | ||||
0.0205026 | + | 0.999790i | \(0.493473\pi\) | |||||||
\(432\) | −4.60206e12 | −6.35734 | ||||||||
\(433\) | −1.33717e12 | −1.82806 | −0.914029 | − | 0.405648i | \(-0.867046\pi\) | ||||
−0.914029 | + | 0.405648i | \(0.867046\pi\) | |||||||
\(434\) | −1.30932e12 | −1.77151 | ||||||||
\(435\) | −5.21053e11 | −0.697719 | ||||||||
\(436\) | 1.68477e12 | 2.23280 | ||||||||
\(437\) | −6.36443e11 | −0.834821 | ||||||||
\(438\) | 2.97485e12 | 3.86218 | ||||||||
\(439\) | 7.90604e11 | 1.01594 | 0.507971 | − | 0.861374i | \(-0.330396\pi\) | ||||
0.507971 | + | 0.861374i | \(0.330396\pi\) | |||||||
\(440\) | −1.17148e12 | −1.49004 | ||||||||
\(441\) | −6.45089e11 | −0.812168 | ||||||||
\(442\) | 2.50836e11 | 0.312600 | ||||||||
\(443\) | 1.18811e12 | 1.46569 | 0.732843 | − | 0.680398i | \(-0.238193\pi\) | ||||
0.732843 | + | 0.680398i | \(0.238193\pi\) | |||||||
\(444\) | 3.06772e12 | 3.74621 | ||||||||
\(445\) | −1.24846e12 | −1.50923 | ||||||||
\(446\) | 1.27470e12 | 1.52546 | ||||||||
\(447\) | −1.50519e12 | −1.78323 | ||||||||
\(448\) | −8.89751e11 | −1.04356 | ||||||||
\(449\) | 6.04411e11 | 0.701817 | 0.350909 | − | 0.936410i | \(-0.385873\pi\) | ||||
0.350909 | + | 0.936410i | \(0.385873\pi\) | |||||||
\(450\) | −5.29493e10 | −0.0608701 | ||||||||
\(451\) | 4.66868e11 | 0.531373 | ||||||||
\(452\) | −2.51466e12 | −2.83371 | ||||||||
\(453\) | −2.60598e12 | −2.90756 | ||||||||
\(454\) | 1.88936e12 | 2.08720 | ||||||||
\(455\) | −5.16332e11 | −0.564778 | ||||||||
\(456\) | −4.41597e12 | −4.78282 | ||||||||
\(457\) | −9.65513e11 | −1.03546 | −0.517732 | − | 0.855543i | \(-0.673224\pi\) | ||||
−0.517732 | + | 0.855543i | \(0.673224\pi\) | |||||||
\(458\) | −1.96856e12 | −2.09052 | ||||||||
\(459\) | 5.69747e11 | 0.599135 | ||||||||
\(460\) | 2.05198e12 | 2.13679 | ||||||||
\(461\) | 5.15082e10 | 0.0531156 | 0.0265578 | − | 0.999647i | \(-0.491545\pi\) | ||||
0.0265578 | + | 0.999647i | \(0.491545\pi\) | |||||||
\(462\) | −1.47406e12 | −1.50531 | ||||||||
\(463\) | −7.66043e11 | −0.774709 | −0.387355 | − | 0.921931i | \(-0.626611\pi\) | ||||
−0.387355 | + | 0.921931i | \(0.626611\pi\) | |||||||
\(464\) | 9.72811e11 | 0.974310 | ||||||||
\(465\) | 2.18895e12 | 2.17119 | ||||||||
\(466\) | 8.75477e11 | 0.860019 | ||||||||
\(467\) | −1.55842e12 | −1.51621 | −0.758104 | − | 0.652133i | \(-0.773874\pi\) | ||||
−0.758104 | + | 0.652133i | \(0.773874\pi\) | |||||||
\(468\) | 4.15152e12 | 4.00038 | ||||||||
\(469\) | 3.31497e11 | 0.316375 | ||||||||
\(470\) | −1.87041e12 | −1.76805 | ||||||||
\(471\) | 1.36585e12 | 1.27882 | ||||||||
\(472\) | 1.86571e12 | 1.73023 | ||||||||
\(473\) | −5.48480e11 | −0.503832 | ||||||||
\(474\) | −4.68052e12 | −4.25885 | ||||||||
\(475\) | −1.49354e10 | −0.0134615 | ||||||||
\(476\) | 5.39551e11 | 0.481728 | ||||||||
\(477\) | −4.71797e12 | −4.17275 | ||||||||
\(478\) | −5.20632e10 | −0.0456147 | ||||||||
\(479\) | 1.36399e12 | 1.18386 | 0.591931 | − | 0.805989i | \(-0.298366\pi\) | ||||
0.591931 | + | 0.805989i | \(0.298366\pi\) | |||||||
\(480\) | 4.45489e12 | 3.83046 | ||||||||
\(481\) | −6.78558e11 | −0.578008 | ||||||||
\(482\) | 1.38588e12 | 1.16954 | ||||||||
\(483\) | 1.53042e12 | 1.27953 | ||||||||
\(484\) | −2.07744e12 | −1.72078 | ||||||||
\(485\) | −6.21577e11 | −0.510102 | ||||||||
\(486\) | 3.43841e12 | 2.79572 | ||||||||
\(487\) | −9.00584e11 | −0.725511 | −0.362755 | − | 0.931884i | \(-0.618164\pi\) | ||||
−0.362755 | + | 0.931884i | \(0.618164\pi\) | |||||||
\(488\) | −1.67386e12 | −1.33607 | ||||||||
\(489\) | 2.79868e12 | 2.21342 | ||||||||
\(490\) | 8.25590e11 | 0.646967 | ||||||||
\(491\) | 2.39477e12 | 1.85950 | 0.929751 | − | 0.368189i | \(-0.120022\pi\) | ||||
0.929751 | + | 0.368189i | \(0.120022\pi\) | |||||||
\(492\) | −5.67412e12 | −4.36572 | ||||||||
\(493\) | −1.20436e11 | −0.0918219 | ||||||||
\(494\) | 1.64793e12 | 1.24500 | ||||||||
\(495\) | 1.72867e12 | 1.29416 | ||||||||
\(496\) | −4.08679e12 | −3.03190 | ||||||||
\(497\) | 1.39325e12 | 1.02430 | ||||||||
\(498\) | 1.33602e12 | 0.973373 | ||||||||
\(499\) | −1.19891e12 | −0.865637 | −0.432819 | − | 0.901481i | \(-0.642481\pi\) | ||||
−0.432819 | + | 0.901481i | \(0.642481\pi\) | |||||||
\(500\) | −3.40717e12 | −2.43797 | ||||||||
\(501\) | 1.51647e12 | 1.07538 | ||||||||
\(502\) | 1.32552e12 | 0.931579 | ||||||||
\(503\) | −3.61742e11 | −0.251967 | −0.125983 | − | 0.992032i | \(-0.540209\pi\) | ||||
−0.125983 | + | 0.992032i | \(0.540209\pi\) | |||||||
\(504\) | 7.44879e12 | 5.14219 | ||||||||
\(505\) | −1.60477e12 | −1.09800 | ||||||||
\(506\) | −1.29578e12 | −0.878725 | ||||||||
\(507\) | 1.41386e12 | 0.950321 | ||||||||
\(508\) | −4.22366e12 | −2.81386 | ||||||||
\(509\) | 1.61404e12 | 1.06582 | 0.532910 | − | 0.846172i | \(-0.321098\pi\) | ||||
0.532910 | + | 0.846172i | \(0.321098\pi\) | |||||||
\(510\) | −1.26940e12 | −0.830870 | ||||||||
\(511\) | −1.41541e12 | −0.918304 | ||||||||
\(512\) | 2.50864e12 | 1.61333 | ||||||||
\(513\) | 3.74311e12 | 2.38619 | ||||||||
\(514\) | 3.09924e12 | 1.95849 | ||||||||
\(515\) | 1.19497e12 | 0.748555 | ||||||||
\(516\) | 6.66600e12 | 4.13944 | ||||||||
\(517\) | 8.39299e11 | 0.516665 | ||||||||
\(518\) | −2.05403e12 | −1.25350 | ||||||||
\(519\) | −3.42566e12 | −2.07248 | ||||||||
\(520\) | −3.14927e12 | −1.88884 | ||||||||
\(521\) | −2.86199e12 | −1.70176 | −0.850881 | − | 0.525358i | \(-0.823931\pi\) | ||||
−0.850881 | + | 0.525358i | \(0.823931\pi\) | |||||||
\(522\) | −2.80513e12 | −1.65362 | ||||||||
\(523\) | 1.01799e12 | 0.594957 | 0.297479 | − | 0.954728i | \(-0.403854\pi\) | ||||
0.297479 | + | 0.954728i | \(0.403854\pi\) | |||||||
\(524\) | −2.85979e11 | −0.165708 | ||||||||
\(525\) | 3.59143e10 | 0.0206325 | ||||||||
\(526\) | 2.44726e12 | 1.39394 | ||||||||
\(527\) | 5.05954e11 | 0.285735 | ||||||||
\(528\) | −4.60099e12 | −2.57631 | ||||||||
\(529\) | −4.55830e11 | −0.253077 | ||||||||
\(530\) | 6.03810e12 | 3.32399 | ||||||||
\(531\) | −2.75310e12 | −1.50278 | ||||||||
\(532\) | 3.54473e12 | 1.91859 | ||||||||
\(533\) | 1.25508e12 | 0.673593 | ||||||||
\(534\) | −9.58161e12 | −5.09921 | ||||||||
\(535\) | 3.14145e12 | 1.65782 | ||||||||
\(536\) | 2.02191e12 | 1.05808 | ||||||||
\(537\) | −4.17335e12 | −2.16571 | ||||||||
\(538\) | −5.58165e12 | −2.87238 | ||||||||
\(539\) | −3.70464e11 | −0.189058 | ||||||||
\(540\) | −1.20683e13 | −6.10764 | ||||||||
\(541\) | −1.10637e12 | −0.555283 | −0.277642 | − | 0.960685i | \(-0.589553\pi\) | ||||
−0.277642 | + | 0.960685i | \(0.589553\pi\) | |||||||
\(542\) | 5.27892e12 | 2.62753 | ||||||||
\(543\) | 1.03562e12 | 0.511212 | ||||||||
\(544\) | 1.02970e12 | 0.504100 | ||||||||
\(545\) | 1.88591e12 | 0.915666 | ||||||||
\(546\) | −3.96271e12 | −1.90820 | ||||||||
\(547\) | −1.37273e12 | −0.655605 | −0.327803 | − | 0.944746i | \(-0.606308\pi\) | ||||
−0.327803 | + | 0.944746i | \(0.606308\pi\) | |||||||
\(548\) | −4.68745e12 | −2.22036 | ||||||||
\(549\) | 2.47000e12 | 1.16044 | ||||||||
\(550\) | −3.04079e10 | −0.0141695 | ||||||||
\(551\) | −7.91240e11 | −0.365701 | ||||||||
\(552\) | 9.33454e12 | 4.27924 | ||||||||
\(553\) | 2.22695e12 | 1.01262 | ||||||||
\(554\) | 4.56616e12 | 2.05948 | ||||||||
\(555\) | 3.43397e12 | 1.53631 | ||||||||
\(556\) | −1.09694e12 | −0.486793 | ||||||||
\(557\) | −2.29710e12 | −1.01119 | −0.505594 | − | 0.862771i | \(-0.668727\pi\) | ||||
−0.505594 | + | 0.862771i | \(0.668727\pi\) | |||||||
\(558\) | 1.17844e13 | 5.14580 | ||||||||
\(559\) | −1.47447e12 | −0.638681 | ||||||||
\(560\) | −4.87849e12 | −2.09623 | ||||||||
\(561\) | 5.69613e11 | 0.242799 | ||||||||
\(562\) | 5.11665e12 | 2.16358 | ||||||||
\(563\) | −1.84812e11 | −0.0775250 | −0.0387625 | − | 0.999248i | \(-0.512342\pi\) | ||||
−0.0387625 | + | 0.999248i | \(0.512342\pi\) | |||||||
\(564\) | −1.02005e13 | −4.24488 | ||||||||
\(565\) | −2.81488e12 | −1.16210 | ||||||||
\(566\) | −8.31526e12 | −3.40566 | ||||||||
\(567\) | −4.32301e12 | −1.75656 | ||||||||
\(568\) | 8.49788e12 | 3.42565 | ||||||||
\(569\) | −2.10912e11 | −0.0843523 | −0.0421761 | − | 0.999110i | \(-0.513429\pi\) | ||||
−0.0421761 | + | 0.999110i | \(0.513429\pi\) | |||||||
\(570\) | −8.33969e12 | −3.30912 | ||||||||
\(571\) | 2.37391e12 | 0.934548 | 0.467274 | − | 0.884112i | \(-0.345236\pi\) | ||||
0.467274 | + | 0.884112i | \(0.345236\pi\) | |||||||
\(572\) | 2.38415e12 | 0.931219 | ||||||||
\(573\) | 2.79921e12 | 1.08477 | ||||||||
\(574\) | 3.79919e12 | 1.46079 | ||||||||
\(575\) | 3.15706e10 | 0.0120442 | ||||||||
\(576\) | 8.00808e12 | 3.03129 | ||||||||
\(577\) | 1.71792e12 | 0.645225 | 0.322613 | − | 0.946531i | \(-0.395439\pi\) | ||||
0.322613 | + | 0.946531i | \(0.395439\pi\) | |||||||
\(578\) | −2.93410e11 | −0.109345 | ||||||||
\(579\) | −3.32816e12 | −1.23070 | ||||||||
\(580\) | 2.55106e12 | 0.936041 | ||||||||
\(581\) | −6.35663e11 | −0.231438 | ||||||||
\(582\) | −4.77043e12 | −1.72347 | ||||||||
\(583\) | −2.70945e12 | −0.971344 | ||||||||
\(584\) | −8.63301e12 | −3.07117 | ||||||||
\(585\) | 4.64717e12 | 1.64054 | ||||||||
\(586\) | 2.22591e12 | 0.779774 | ||||||||
\(587\) | 2.32455e12 | 0.808103 | 0.404052 | − | 0.914736i | \(-0.367602\pi\) | ||||
0.404052 | + | 0.914736i | \(0.367602\pi\) | |||||||
\(588\) | 4.50246e12 | 1.55329 | ||||||||
\(589\) | 3.32401e12 | 1.13800 | ||||||||
\(590\) | 3.52344e12 | 1.19711 | ||||||||
\(591\) | −1.83820e12 | −0.619795 | ||||||||
\(592\) | −6.41125e12 | −2.14533 | ||||||||
\(593\) | 2.36534e12 | 0.785503 | 0.392751 | − | 0.919645i | \(-0.371523\pi\) | ||||
0.392751 | + | 0.919645i | \(0.371523\pi\) | |||||||
\(594\) | 7.62085e12 | 2.51168 | ||||||||
\(595\) | 6.03968e11 | 0.197555 | ||||||||
\(596\) | 7.36936e12 | 2.39233 | ||||||||
\(597\) | −7.79979e11 | −0.251303 | ||||||||
\(598\) | −3.48343e12 | −1.11391 | ||||||||
\(599\) | 1.14807e12 | 0.364375 | 0.182188 | − | 0.983264i | \(-0.441682\pi\) | ||||
0.182188 | + | 0.983264i | \(0.441682\pi\) | |||||||
\(600\) | 2.19053e11 | 0.0690031 | ||||||||
\(601\) | −3.38041e12 | −1.05690 | −0.528451 | − | 0.848964i | \(-0.677227\pi\) | ||||
−0.528451 | + | 0.848964i | \(0.677227\pi\) | |||||||
\(602\) | −4.46332e12 | −1.38508 | ||||||||
\(603\) | −2.98359e12 | −0.918992 | ||||||||
\(604\) | 1.27588e13 | 3.90071 | ||||||||
\(605\) | −2.32547e12 | −0.705685 | ||||||||
\(606\) | −1.23161e13 | −3.70978 | ||||||||
\(607\) | 2.57549e12 | 0.770036 | 0.385018 | − | 0.922909i | \(-0.374195\pi\) | ||||
0.385018 | + | 0.922909i | \(0.374195\pi\) | |||||||
\(608\) | 6.76492e12 | 2.00769 | ||||||||
\(609\) | 1.90266e12 | 0.560509 | ||||||||
\(610\) | −3.16112e12 | −0.924395 | ||||||||
\(611\) | 2.25628e12 | 0.654949 | ||||||||
\(612\) | −4.85615e12 | −1.39930 | ||||||||
\(613\) | −1.91477e12 | −0.547701 | −0.273851 | − | 0.961772i | \(-0.588297\pi\) | ||||
−0.273851 | + | 0.961772i | \(0.588297\pi\) | |||||||
\(614\) | −2.80509e12 | −0.796507 | ||||||||
\(615\) | −6.35155e12 | −1.79037 | ||||||||
\(616\) | 4.27772e12 | 1.19701 | ||||||||
\(617\) | 5.24069e12 | 1.45581 | 0.727907 | − | 0.685676i | \(-0.240493\pi\) | ||||
0.727907 | + | 0.685676i | \(0.240493\pi\) | |||||||
\(618\) | 9.17105e12 | 2.52913 | ||||||||
\(619\) | −5.64576e10 | −0.0154566 | −0.00772831 | − | 0.999970i | \(-0.502460\pi\) | ||||
−0.00772831 | + | 0.999970i | \(0.502460\pi\) | |||||||
\(620\) | −1.07170e13 | −2.91281 | ||||||||
\(621\) | −7.91224e12 | −2.13495 | ||||||||
\(622\) | −9.12290e12 | −2.44386 | ||||||||
\(623\) | 4.55884e12 | 1.21243 | ||||||||
\(624\) | −1.23688e13 | −3.26585 | ||||||||
\(625\) | −3.86712e12 | −1.01374 | ||||||||
\(626\) | −8.55685e12 | −2.22705 | ||||||||
\(627\) | 3.74223e12 | 0.967001 | ||||||||
\(628\) | −6.68717e12 | −1.71563 | ||||||||
\(629\) | 7.93728e11 | 0.202183 | ||||||||
\(630\) | 1.40673e13 | 3.55776 | ||||||||
\(631\) | 3.44629e12 | 0.865405 | 0.432703 | − | 0.901537i | \(-0.357560\pi\) | ||||
0.432703 | + | 0.901537i | \(0.357560\pi\) | |||||||
\(632\) | 1.35828e13 | 3.38660 | ||||||||
\(633\) | 8.47382e12 | 2.09779 | ||||||||
\(634\) | −9.57462e12 | −2.35353 | ||||||||
\(635\) | −4.72793e12 | −1.15396 | ||||||||
\(636\) | 3.29296e13 | 7.98048 | ||||||||
\(637\) | −9.95914e11 | −0.239659 | ||||||||
\(638\) | −1.61094e12 | −0.384934 | ||||||||
\(639\) | −1.25398e13 | −2.97533 | ||||||||
\(640\) | −1.36588e12 | −0.321811 | ||||||||
\(641\) | −5.50971e12 | −1.28904 | −0.644522 | − | 0.764586i | \(-0.722943\pi\) | ||||
−0.644522 | + | 0.764586i | \(0.722943\pi\) | |||||||
\(642\) | 2.41098e13 | 5.60126 | ||||||||
\(643\) | 5.98753e11 | 0.138133 | 0.0690667 | − | 0.997612i | \(-0.477998\pi\) | ||||
0.0690667 | + | 0.997612i | \(0.477998\pi\) | |||||||
\(644\) | −7.49291e12 | −1.71658 | ||||||||
\(645\) | 7.46186e12 | 1.69757 | ||||||||
\(646\) | −1.92764e12 | −0.435491 | ||||||||
\(647\) | −2.84687e12 | −0.638701 | −0.319351 | − | 0.947637i | \(-0.603465\pi\) | ||||
−0.319351 | + | 0.947637i | \(0.603465\pi\) | |||||||
\(648\) | −2.63674e13 | −5.87462 | ||||||||
\(649\) | −1.58106e12 | −0.349822 | ||||||||
\(650\) | −8.17454e10 | −0.0179619 | ||||||||
\(651\) | −7.99307e12 | −1.74421 | ||||||||
\(652\) | −1.37023e13 | −2.96946 | ||||||||
\(653\) | −1.82215e12 | −0.392170 | −0.196085 | − | 0.980587i | \(-0.562823\pi\) | ||||
−0.196085 | + | 0.980587i | \(0.562823\pi\) | |||||||
\(654\) | 1.44739e13 | 3.09374 | ||||||||
\(655\) | −3.20122e11 | −0.0679562 | ||||||||
\(656\) | 1.18584e13 | 2.50011 | ||||||||
\(657\) | 1.27392e13 | 2.66745 | ||||||||
\(658\) | 6.82989e12 | 1.42036 | ||||||||
\(659\) | −3.55378e12 | −0.734017 | −0.367008 | − | 0.930218i | \(-0.619618\pi\) | ||||
−0.367008 | + | 0.930218i | \(0.619618\pi\) | |||||||
\(660\) | −1.20655e13 | −2.47512 | ||||||||
\(661\) | 4.80541e12 | 0.979093 | 0.489546 | − | 0.871977i | \(-0.337162\pi\) | ||||
0.489546 | + | 0.871977i | \(0.337162\pi\) | |||||||
\(662\) | −8.31141e12 | −1.68195 | ||||||||
\(663\) | 1.53129e12 | 0.307784 | ||||||||
\(664\) | −3.87711e12 | −0.774019 | ||||||||
\(665\) | 3.96794e12 | 0.786806 | ||||||||
\(666\) | 1.84870e13 | 3.64110 | ||||||||
\(667\) | 1.67253e12 | 0.327197 | ||||||||
\(668\) | −7.42457e12 | −1.44270 | ||||||||
\(669\) | 7.78170e12 | 1.50196 | ||||||||
\(670\) | 3.81843e12 | 0.732063 | ||||||||
\(671\) | 1.41848e12 | 0.270129 | ||||||||
\(672\) | −1.62673e13 | −3.07718 | ||||||||
\(673\) | 5.10315e12 | 0.958894 | 0.479447 | − | 0.877571i | \(-0.340837\pi\) | ||||
0.479447 | + | 0.877571i | \(0.340837\pi\) | |||||||
\(674\) | −1.94069e11 | −0.0362232 | ||||||||
\(675\) | −1.85676e11 | −0.0344262 | ||||||||
\(676\) | −6.92221e12 | −1.27492 | ||||||||
\(677\) | 2.66255e12 | 0.487134 | 0.243567 | − | 0.969884i | \(-0.421682\pi\) | ||||
0.243567 | + | 0.969884i | \(0.421682\pi\) | |||||||
\(678\) | −2.16035e13 | −3.92636 | ||||||||
\(679\) | 2.26972e12 | 0.409788 | ||||||||
\(680\) | 3.68380e12 | 0.660702 | ||||||||
\(681\) | 1.15341e13 | 2.05504 | ||||||||
\(682\) | 6.76757e12 | 1.19785 | ||||||||
\(683\) | −3.15981e12 | −0.555607 | −0.277804 | − | 0.960638i | \(-0.589606\pi\) | ||||
−0.277804 | + | 0.960638i | \(0.589606\pi\) | |||||||
\(684\) | −3.19039e13 | −5.57302 | ||||||||
\(685\) | −5.24708e12 | −0.910564 | ||||||||
\(686\) | −1.17366e13 | −2.02342 | ||||||||
\(687\) | −1.20176e13 | −2.05831 | ||||||||
\(688\) | −1.39313e13 | −2.37053 | ||||||||
\(689\) | −7.28380e12 | −1.23132 | ||||||||
\(690\) | 1.76286e13 | 2.96071 | ||||||||
\(691\) | −7.41599e12 | −1.23742 | −0.618711 | − | 0.785619i | \(-0.712345\pi\) | ||||
−0.618711 | + | 0.785619i | \(0.712345\pi\) | |||||||
\(692\) | 1.67719e13 | 2.78039 | ||||||||
\(693\) | −6.31234e12 | −1.03966 | ||||||||
\(694\) | 1.40845e13 | 2.30474 | ||||||||
\(695\) | −1.22790e12 | −0.199632 | ||||||||
\(696\) | 1.16049e13 | 1.87456 | ||||||||
\(697\) | −1.46810e12 | −0.235618 | ||||||||
\(698\) | 5.80644e12 | 0.925892 | ||||||||
\(699\) | 5.34456e12 | 0.846768 | ||||||||
\(700\) | −1.75836e11 | −0.0276800 | ||||||||
\(701\) | −9.39002e12 | −1.46871 | −0.734354 | − | 0.678767i | \(-0.762515\pi\) | ||||
−0.734354 | + | 0.678767i | \(0.762515\pi\) | |||||||
\(702\) | 2.04871e13 | 3.18392 | ||||||||
\(703\) | 5.21462e12 | 0.805237 | ||||||||
\(704\) | 4.59891e12 | 0.705631 | ||||||||
\(705\) | −1.14183e13 | −1.74081 | ||||||||
\(706\) | −1.35658e13 | −2.05505 | ||||||||
\(707\) | 5.85989e12 | 0.882069 | ||||||||
\(708\) | 1.92156e13 | 2.87411 | ||||||||
\(709\) | 4.58730e11 | 0.0681788 | 0.0340894 | − | 0.999419i | \(-0.489147\pi\) | ||||
0.0340894 | + | 0.999419i | \(0.489147\pi\) | |||||||
\(710\) | 1.60485e13 | 2.37013 | ||||||||
\(711\) | −2.00433e13 | −2.94141 | ||||||||
\(712\) | 2.78058e13 | 4.05485 | ||||||||
\(713\) | −7.02633e12 | −1.01818 | ||||||||
\(714\) | 4.63529e12 | 0.667475 | ||||||||
\(715\) | 2.66880e12 | 0.381890 | ||||||||
\(716\) | 2.04326e13 | 2.90546 | ||||||||
\(717\) | −3.17832e11 | −0.0449119 | ||||||||
\(718\) | −4.61282e12 | −0.647749 | ||||||||
\(719\) | 4.10035e12 | 0.572191 | 0.286096 | − | 0.958201i | \(-0.407643\pi\) | ||||
0.286096 | + | 0.958201i | \(0.407643\pi\) | |||||||
\(720\) | 4.39081e13 | 6.08904 | ||||||||
\(721\) | −4.36349e12 | −0.601347 | ||||||||
\(722\) | 9.08525e11 | 0.124428 | ||||||||
\(723\) | 8.46044e12 | 1.15152 | ||||||||
\(724\) | −5.07036e12 | −0.685828 | ||||||||
\(725\) | 3.92493e10 | 0.00527607 | ||||||||
\(726\) | −1.78473e13 | −2.38428 | ||||||||
\(727\) | 3.64967e12 | 0.484561 | 0.242280 | − | 0.970206i | \(-0.422105\pi\) | ||||
0.242280 | + | 0.970206i | \(0.422105\pi\) | |||||||
\(728\) | 1.14997e13 | 1.51739 | ||||||||
\(729\) | 4.43176e12 | 0.581169 | ||||||||
\(730\) | −1.63037e13 | −2.12487 | ||||||||
\(731\) | 1.72473e12 | 0.223406 | ||||||||
\(732\) | −1.72396e13 | −2.21936 | ||||||||
\(733\) | −2.77480e11 | −0.0355029 | −0.0177514 | − | 0.999842i | \(-0.505651\pi\) | ||||
−0.0177514 | + | 0.999842i | \(0.505651\pi\) | |||||||
\(734\) | −8.04375e12 | −1.02288 | ||||||||
\(735\) | 5.04001e12 | 0.636999 | ||||||||
\(736\) | −1.42998e13 | −1.79630 | ||||||||
\(737\) | −1.71343e12 | −0.213925 | ||||||||
\(738\) | −3.41940e13 | −4.24323 | ||||||||
\(739\) | 1.15877e13 | 1.42922 | 0.714608 | − | 0.699525i | \(-0.246605\pi\) | ||||
0.714608 | + | 0.699525i | \(0.246605\pi\) | |||||||
\(740\) | −1.68126e13 | −2.06107 | ||||||||
\(741\) | 1.00602e13 | 1.22582 | ||||||||
\(742\) | −2.20485e13 | −2.67031 | ||||||||
\(743\) | 4.79681e12 | 0.577434 | 0.288717 | − | 0.957414i | \(-0.406771\pi\) | ||||
0.288717 | + | 0.957414i | \(0.406771\pi\) | |||||||
\(744\) | −4.87523e13 | −5.83333 | ||||||||
\(745\) | 8.24919e12 | 0.981088 | ||||||||
\(746\) | −4.96648e12 | −0.587116 | ||||||||
\(747\) | 5.72119e12 | 0.672270 | ||||||||
\(748\) | −2.78881e12 | −0.325733 | ||||||||
\(749\) | −1.14712e13 | −1.33180 | ||||||||
\(750\) | −2.92711e13 | −3.37802 | ||||||||
\(751\) | −2.32776e12 | −0.267029 | −0.133515 | − | 0.991047i | \(-0.542626\pi\) | ||||
−0.133515 | + | 0.991047i | \(0.542626\pi\) | |||||||
\(752\) | 2.13181e13 | 2.43091 | ||||||||
\(753\) | 8.09196e12 | 0.917225 | ||||||||
\(754\) | −4.33067e12 | −0.487960 | ||||||||
\(755\) | 1.42821e13 | 1.59967 | ||||||||
\(756\) | 4.40680e13 | 4.90654 | ||||||||
\(757\) | −6.01494e12 | −0.665732 | −0.332866 | − | 0.942974i | \(-0.608016\pi\) | ||||
−0.332866 | + | 0.942974i | \(0.608016\pi\) | |||||||
\(758\) | 7.44314e12 | 0.818926 | ||||||||
\(759\) | −7.91039e12 | −0.865187 | ||||||||
\(760\) | 2.42017e13 | 2.63139 | ||||||||
\(761\) | −1.12427e13 | −1.21518 | −0.607589 | − | 0.794252i | \(-0.707863\pi\) | ||||
−0.607589 | + | 0.794252i | \(0.707863\pi\) | |||||||
\(762\) | −3.62855e13 | −3.89885 | ||||||||
\(763\) | −6.88651e12 | −0.735595 | ||||||||
\(764\) | −1.37048e13 | −1.45530 | ||||||||
\(765\) | −5.43593e12 | −0.573849 | ||||||||
\(766\) | −5.42772e12 | −0.569623 | ||||||||
\(767\) | −4.25035e12 | −0.443451 | ||||||||
\(768\) | 1.22809e13 | 1.27381 | ||||||||
\(769\) | 1.35036e13 | 1.39246 | 0.696230 | − | 0.717819i | \(-0.254860\pi\) | ||||
0.696230 | + | 0.717819i | \(0.254860\pi\) | |||||||
\(770\) | 8.07860e12 | 0.828185 | ||||||||
\(771\) | 1.89201e13 | 1.92832 | ||||||||
\(772\) | 1.62946e13 | 1.65107 | ||||||||
\(773\) | 2.43055e12 | 0.244848 | 0.122424 | − | 0.992478i | \(-0.460933\pi\) | ||||
0.122424 | + | 0.992478i | \(0.460933\pi\) | |||||||
\(774\) | 4.01715e13 | 4.02331 | ||||||||
\(775\) | −1.64886e11 | −0.0164183 | ||||||||
\(776\) | 1.38438e13 | 1.37049 | ||||||||
\(777\) | −1.25393e13 | −1.23418 | ||||||||
\(778\) | −2.88654e12 | −0.282468 | ||||||||
\(779\) | −9.64508e12 | −0.938399 | ||||||||
\(780\) | −3.24354e13 | −3.13757 | ||||||||
\(781\) | −7.20137e12 | −0.692605 | ||||||||
\(782\) | 4.07466e12 | 0.389638 | ||||||||
\(783\) | −9.83667e12 | −0.935234 | ||||||||
\(784\) | −9.40974e12 | −0.889519 | ||||||||
\(785\) | −7.48555e12 | −0.703575 | ||||||||
\(786\) | −2.45684e12 | −0.229602 | ||||||||
\(787\) | −3.78714e12 | −0.351905 | −0.175953 | − | 0.984399i | \(-0.556301\pi\) | ||||
−0.175953 | + | 0.984399i | \(0.556301\pi\) | |||||||
\(788\) | 8.99975e12 | 0.831501 | ||||||||
\(789\) | 1.49399e13 | 1.37246 | ||||||||
\(790\) | 2.56516e13 | 2.34311 | ||||||||
\(791\) | 1.02787e13 | 0.933565 | ||||||||
\(792\) | −3.85010e13 | −3.47703 | ||||||||
\(793\) | 3.81328e12 | 0.342428 | ||||||||
\(794\) | −3.29514e13 | −2.94226 | ||||||||
\(795\) | 3.68611e13 | 3.27277 | ||||||||
\(796\) | 3.81875e12 | 0.337142 | ||||||||
\(797\) | 2.23878e12 | 0.196539 | 0.0982694 | − | 0.995160i | \(-0.468669\pi\) | ||||
0.0982694 | + | 0.995160i | \(0.468669\pi\) | |||||||
\(798\) | 3.04528e13 | 2.65837 | ||||||||
\(799\) | −2.63924e12 | −0.229096 | ||||||||
\(800\) | −3.35572e11 | −0.0289655 | ||||||||
\(801\) | −4.10311e13 | −3.52182 | ||||||||
\(802\) | −4.48992e12 | −0.383225 | ||||||||
\(803\) | 7.31588e12 | 0.620936 | ||||||||
\(804\) | 2.08243e13 | 1.75759 | ||||||||
\(805\) | −8.38749e12 | −0.703964 | ||||||||
\(806\) | 1.81932e13 | 1.51845 | ||||||||
\(807\) | −3.40745e13 | −2.82813 | ||||||||
\(808\) | 3.57414e13 | 2.94999 | ||||||||
\(809\) | −6.77107e12 | −0.555762 | −0.277881 | − | 0.960615i | \(-0.589632\pi\) | ||||
−0.277881 | + | 0.960615i | \(0.589632\pi\) | |||||||
\(810\) | −4.97956e13 | −4.06451 | ||||||||
\(811\) | 1.26099e13 | 1.02357 | 0.511785 | − | 0.859113i | \(-0.328984\pi\) | ||||
0.511785 | + | 0.859113i | \(0.328984\pi\) | |||||||
\(812\) | −9.31534e12 | −0.751964 | ||||||||
\(813\) | 3.22264e13 | 2.58705 | ||||||||
\(814\) | 1.06168e13 | 0.847586 | ||||||||
\(815\) | −1.53382e13 | −1.21777 | ||||||||
\(816\) | 1.44681e13 | 1.14237 | ||||||||
\(817\) | 1.13311e13 | 0.889762 | ||||||||
\(818\) | 4.56959e13 | 3.56851 | ||||||||
\(819\) | −1.69694e13 | −1.31792 | ||||||||
\(820\) | 3.10970e13 | 2.40191 | ||||||||
\(821\) | 1.40858e13 | 1.08203 | 0.541013 | − | 0.841014i | \(-0.318041\pi\) | ||||
0.541013 | + | 0.841014i | \(0.318041\pi\) | |||||||
\(822\) | −4.02699e13 | −3.07650 | ||||||||
\(823\) | −1.62081e13 | −1.23150 | −0.615748 | − | 0.787943i | \(-0.711146\pi\) | ||||
−0.615748 | + | 0.787943i | \(0.711146\pi\) | |||||||
\(824\) | −2.66143e13 | −2.01114 | ||||||||
\(825\) | −1.85633e11 | −0.0139512 | ||||||||
\(826\) | −1.28661e13 | −0.961690 | ||||||||
\(827\) | 8.84797e12 | 0.657762 | 0.328881 | − | 0.944371i | \(-0.393329\pi\) | ||||
0.328881 | + | 0.944371i | \(0.393329\pi\) | |||||||
\(828\) | 6.74388e13 | 4.98624 | ||||||||
\(829\) | 9.64554e12 | 0.709302 | 0.354651 | − | 0.934999i | \(-0.384600\pi\) | ||||
0.354651 | + | 0.934999i | \(0.384600\pi\) | |||||||
\(830\) | −7.32203e12 | −0.535526 | ||||||||
\(831\) | 2.78752e13 | 2.02775 | ||||||||
\(832\) | 1.23632e13 | 0.894491 | ||||||||
\(833\) | 1.16495e12 | 0.0838310 | ||||||||
\(834\) | −9.42379e12 | −0.674494 | ||||||||
\(835\) | −8.31099e12 | −0.591649 | ||||||||
\(836\) | −1.83219e13 | −1.29730 | ||||||||
\(837\) | 4.13239e13 | 2.91030 | ||||||||
\(838\) | −2.72822e13 | −1.91109 | ||||||||
\(839\) | 1.77288e13 | 1.23524 | 0.617618 | − | 0.786478i | \(-0.288098\pi\) | ||||
0.617618 | + | 0.786478i | \(0.288098\pi\) | |||||||
\(840\) | −5.81967e13 | −4.03312 | ||||||||
\(841\) | −1.24278e13 | −0.856668 | ||||||||
\(842\) | 3.67774e13 | 2.52160 | ||||||||
\(843\) | 3.12358e13 | 2.13024 | ||||||||
\(844\) | −4.14876e13 | −2.81434 | ||||||||
\(845\) | −7.74865e12 | −0.522843 | ||||||||
\(846\) | −6.14714e13 | −4.12579 | ||||||||
\(847\) | 8.49157e12 | 0.566908 | ||||||||
\(848\) | −6.88198e13 | −4.57017 | ||||||||
\(849\) | −5.07625e13 | −3.35319 | ||||||||
\(850\) | 9.56199e10 | 0.00628294 | ||||||||
\(851\) | −1.10227e13 | −0.720454 | ||||||||
\(852\) | 8.75225e13 | 5.69039 | ||||||||
\(853\) | 1.82317e13 | 1.17911 | 0.589557 | − | 0.807727i | \(-0.299303\pi\) | ||||
0.589557 | + | 0.807727i | \(0.299303\pi\) | |||||||
\(854\) | 1.15430e13 | 0.742607 | ||||||||
\(855\) | −3.57129e13 | −2.28548 | ||||||||
\(856\) | −6.99664e13 | −4.45408 | ||||||||
\(857\) | −4.46174e12 | −0.282547 | −0.141273 | − | 0.989971i | \(-0.545120\pi\) | ||||
−0.141273 | + | 0.989971i | \(0.545120\pi\) | |||||||
\(858\) | 2.04823e13 | 1.29028 | ||||||||
\(859\) | 2.49571e13 | 1.56395 | 0.781977 | − | 0.623307i | \(-0.214211\pi\) | ||||
0.781977 | + | 0.623307i | \(0.214211\pi\) | |||||||
\(860\) | −3.65330e13 | −2.27742 | ||||||||
\(861\) | 2.31930e13 | 1.43828 | ||||||||
\(862\) | −1.23558e12 | −0.0762231 | ||||||||
\(863\) | −4.92247e12 | −0.302089 | −0.151044 | − | 0.988527i | \(-0.548264\pi\) | ||||
−0.151044 | + | 0.988527i | \(0.548264\pi\) | |||||||
\(864\) | 8.41013e13 | 5.13441 | ||||||||
\(865\) | 1.87743e13 | 1.14023 | ||||||||
\(866\) | 5.62430e13 | 3.39812 | ||||||||
\(867\) | −1.79119e12 | −0.107660 | ||||||||
\(868\) | 3.91338e13 | 2.33999 | ||||||||
\(869\) | −1.15105e13 | −0.684710 | ||||||||
\(870\) | 2.19162e13 | 1.29697 | ||||||||
\(871\) | −4.60619e12 | −0.271182 | ||||||||
\(872\) | −4.20030e13 | −2.46012 | ||||||||
\(873\) | −2.04283e13 | −1.19033 | ||||||||
\(874\) | 2.67696e13 | 1.55182 | ||||||||
\(875\) | 1.39269e13 | 0.803188 | ||||||||
\(876\) | −8.89143e13 | −5.10156 | ||||||||
\(877\) | −1.68831e13 | −0.963725 | −0.481863 | − | 0.876247i | \(-0.660040\pi\) | ||||
−0.481863 | + | 0.876247i | \(0.660040\pi\) | |||||||
\(878\) | −3.32539e13 | −1.88850 | ||||||||
\(879\) | 1.35886e13 | 0.767760 | ||||||||
\(880\) | 2.52157e13 | 1.41742 | ||||||||
\(881\) | −1.26880e13 | −0.709583 | −0.354792 | − | 0.934945i | \(-0.615448\pi\) | ||||
−0.354792 | + | 0.934945i | \(0.615448\pi\) | |||||||
\(882\) | 2.71333e13 | 1.50971 | ||||||||
\(883\) | −2.65648e13 | −1.47056 | −0.735281 | − | 0.677762i | \(-0.762950\pi\) | ||||
−0.735281 | + | 0.677762i | \(0.762950\pi\) | |||||||
\(884\) | −7.49713e12 | −0.412914 | ||||||||
\(885\) | 2.15097e13 | 1.17866 | ||||||||
\(886\) | −4.99736e13 | −2.72451 | ||||||||
\(887\) | −5.71289e11 | −0.0309885 | −0.0154942 | − | 0.999880i | \(-0.504932\pi\) | ||||
−0.0154942 | + | 0.999880i | \(0.504932\pi\) | |||||||
\(888\) | −7.64814e13 | −4.12760 | ||||||||
\(889\) | 1.72643e13 | 0.927023 | ||||||||
\(890\) | 5.25120e13 | 2.80546 | ||||||||
\(891\) | 2.23446e13 | 1.18774 | ||||||||
\(892\) | −3.80990e13 | −2.01498 | ||||||||
\(893\) | −1.73392e13 | −0.912425 | ||||||||
\(894\) | 6.33103e13 | 3.31478 | ||||||||
\(895\) | 2.28720e13 | 1.19152 | ||||||||
\(896\) | 4.98757e12 | 0.258525 | ||||||||
\(897\) | −2.12654e13 | −1.09675 | ||||||||
\(898\) | −2.54223e13 | −1.30458 | ||||||||
\(899\) | −8.73529e12 | −0.446025 | ||||||||
\(900\) | 1.58258e12 | 0.0804035 | ||||||||
\(901\) | 8.52007e12 | 0.430706 | ||||||||
\(902\) | −1.96371e13 | −0.987751 | ||||||||
\(903\) | −2.72474e13 | −1.36374 | ||||||||
\(904\) | 6.26931e13 | 3.12221 | ||||||||
\(905\) | −5.67571e12 | −0.281256 | ||||||||
\(906\) | 1.09611e14 | 5.40477 | ||||||||
\(907\) | 3.29210e12 | 0.161525 | 0.0807625 | − | 0.996733i | \(-0.474264\pi\) | ||||
0.0807625 | + | 0.996733i | \(0.474264\pi\) | |||||||
\(908\) | −5.64705e13 | −2.75699 | ||||||||
\(909\) | −5.27411e13 | −2.56219 | ||||||||
\(910\) | 2.17176e13 | 1.04985 | ||||||||
\(911\) | −1.27945e13 | −0.615445 | −0.307723 | − | 0.951476i | \(-0.599567\pi\) | ||||
−0.307723 | + | 0.951476i | \(0.599567\pi\) | |||||||
\(912\) | 9.50524e13 | 4.54974 | ||||||||
\(913\) | 3.28559e12 | 0.156493 | ||||||||
\(914\) | 4.06107e13 | 1.92479 | ||||||||
\(915\) | −1.92978e13 | −0.910152 | ||||||||
\(916\) | 5.88376e13 | 2.76137 | ||||||||
\(917\) | 1.16894e12 | 0.0545922 | ||||||||
\(918\) | −2.39643e13 | −1.11371 | ||||||||
\(919\) | −3.16626e13 | −1.46429 | −0.732146 | − | 0.681148i | \(-0.761481\pi\) | ||||
−0.732146 | + | 0.681148i | \(0.761481\pi\) | |||||||
\(920\) | −5.11579e13 | −2.35433 | ||||||||
\(921\) | −1.71244e13 | −0.784235 | ||||||||
\(922\) | −2.16650e12 | −0.0987348 | ||||||||
\(923\) | −1.93594e13 | −0.877979 | ||||||||
\(924\) | 4.40577e13 | 1.98837 | ||||||||
\(925\) | −2.58670e11 | −0.0116174 | ||||||||
\(926\) | 3.22208e13 | 1.44008 | ||||||||
\(927\) | 3.92730e13 | 1.74677 | ||||||||
\(928\) | −1.77778e13 | −0.786887 | ||||||||
\(929\) | −1.31826e13 | −0.580673 | −0.290336 | − | 0.956925i | \(-0.593767\pi\) | ||||
−0.290336 | + | 0.956925i | \(0.593767\pi\) | |||||||
\(930\) | −9.20701e13 | −4.03595 | ||||||||
\(931\) | 7.65346e12 | 0.333875 | ||||||||
\(932\) | −2.61668e13 | −1.13600 | ||||||||
\(933\) | −5.56929e13 | −2.40620 | ||||||||
\(934\) | 6.55493e13 | 2.81843 | ||||||||
\(935\) | −3.12177e12 | −0.133582 | ||||||||
\(936\) | −1.03502e14 | −4.40765 | ||||||||
\(937\) | −2.06204e13 | −0.873916 | −0.436958 | − | 0.899482i | \(-0.643944\pi\) | ||||
−0.436958 | + | 0.899482i | \(0.643944\pi\) | |||||||
\(938\) | −1.39432e13 | −0.588099 | ||||||||
\(939\) | −5.22374e13 | −2.19273 | ||||||||
\(940\) | 5.59038e13 | 2.33543 | ||||||||
\(941\) | 2.43975e13 | 1.01436 | 0.507180 | − | 0.861840i | \(-0.330688\pi\) | ||||
0.507180 | + | 0.861840i | \(0.330688\pi\) | |||||||
\(942\) | −5.74495e13 | −2.37715 | ||||||||
\(943\) | 2.03879e13 | 0.839596 | ||||||||
\(944\) | −4.01588e13 | −1.64591 | ||||||||
\(945\) | 4.93293e13 | 2.01216 | ||||||||
\(946\) | 2.30698e13 | 0.936556 | ||||||||
\(947\) | −4.10278e13 | −1.65769 | −0.828845 | − | 0.559478i | \(-0.811002\pi\) | ||||
−0.828845 | + | 0.559478i | \(0.811002\pi\) | |||||||
\(948\) | 1.39894e14 | 5.62552 | ||||||||
\(949\) | 1.96672e13 | 0.787128 | ||||||||
\(950\) | 6.28202e11 | 0.0250232 | ||||||||
\(951\) | −5.84506e13 | −2.31727 | ||||||||
\(952\) | −1.34516e13 | −0.530771 | ||||||||
\(953\) | 4.09880e13 | 1.60968 | 0.804839 | − | 0.593494i | \(-0.202252\pi\) | ||||
0.804839 | + | 0.593494i | \(0.202252\pi\) | |||||||
\(954\) | 1.98444e14 | 7.75659 | ||||||||
\(955\) | −1.53410e13 | −0.596815 | ||||||||
\(956\) | 1.55610e12 | 0.0602527 | ||||||||
\(957\) | −9.83437e12 | −0.379003 | ||||||||
\(958\) | −5.73711e13 | −2.20064 | ||||||||
\(959\) | 1.91600e13 | 0.731496 | ||||||||
\(960\) | −6.25663e13 | −2.37750 | ||||||||
\(961\) | 1.02574e13 | 0.387956 | ||||||||
\(962\) | 2.85410e13 | 1.07444 | ||||||||
\(963\) | 1.03245e14 | 3.86856 | ||||||||
\(964\) | −4.14221e13 | −1.54485 | ||||||||
\(965\) | 1.82400e13 | 0.677098 | ||||||||
\(966\) | −6.43716e13 | −2.37847 | ||||||||
\(967\) | −4.45707e12 | −0.163919 | −0.0819597 | − | 0.996636i | \(-0.526118\pi\) | ||||
−0.0819597 | + | 0.996636i | \(0.526118\pi\) | |||||||
\(968\) | 5.17928e13 | 1.89596 | ||||||||
\(969\) | −1.17677e13 | −0.428781 | ||||||||
\(970\) | 2.61444e13 | 0.948211 | ||||||||
\(971\) | 3.69975e13 | 1.33563 | 0.667815 | − | 0.744327i | \(-0.267230\pi\) | ||||
0.667815 | + | 0.744327i | \(0.267230\pi\) | |||||||
\(972\) | −1.02769e14 | −3.69288 | ||||||||
\(973\) | 4.48374e12 | 0.160374 | ||||||||
\(974\) | 3.78797e13 | 1.34863 | ||||||||
\(975\) | −4.99034e11 | −0.0176852 | ||||||||
\(976\) | 3.60292e13 | 1.27096 | ||||||||
\(977\) | 4.72608e13 | 1.65949 | 0.829746 | − | 0.558141i | \(-0.188485\pi\) | ||||
0.829746 | + | 0.558141i | \(0.188485\pi\) | |||||||
\(978\) | −1.17716e14 | −4.11445 | ||||||||
\(979\) | −2.35635e13 | −0.819819 | ||||||||
\(980\) | −2.46758e13 | −0.854581 | ||||||||
\(981\) | 6.19811e13 | 2.13673 | ||||||||
\(982\) | −1.00727e14 | −3.45656 | ||||||||
\(983\) | −1.37629e13 | −0.470130 | −0.235065 | − | 0.971980i | \(-0.575530\pi\) | ||||
−0.235065 | + | 0.971980i | \(0.575530\pi\) | |||||||
\(984\) | 1.41462e14 | 4.81018 | ||||||||
\(985\) | 1.00742e13 | 0.340996 | ||||||||
\(986\) | 5.06571e12 | 0.170685 | ||||||||
\(987\) | 4.16947e13 | 1.39847 | ||||||||
\(988\) | −4.92545e13 | −1.64452 | ||||||||
\(989\) | −2.39519e13 | −0.796080 | ||||||||
\(990\) | −7.27102e13 | −2.40568 | ||||||||
\(991\) | −3.34745e13 | −1.10251 | −0.551255 | − | 0.834337i | \(-0.685851\pi\) | ||||
−0.551255 | + | 0.834337i | \(0.685851\pi\) | |||||||
\(992\) | 7.46847e13 | 2.44866 | ||||||||
\(993\) | −5.07390e13 | −1.65604 | ||||||||
\(994\) | −5.86020e13 | −1.90403 | ||||||||
\(995\) | 4.27468e12 | 0.138261 | ||||||||
\(996\) | −3.99317e13 | −1.28573 | ||||||||
\(997\) | −4.78709e13 | −1.53442 | −0.767209 | − | 0.641398i | \(-0.778355\pi\) | ||||
−0.767209 | + | 0.641398i | \(0.778355\pi\) | |||||||
\(998\) | 5.04279e13 | 1.60910 | ||||||||
\(999\) | 6.48280e13 | 2.05929 |
(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 | 17.10.a.a.1.1 | ✓ | 5 | |
3.2 | odd | 2 | 153.10.a.c.1.5 | 5 | |||
4.3 | odd | 2 | 272.10.a.f.1.5 | 5 | |||
17.16 | even | 2 | 289.10.a.a.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.a.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
153.10.a.c.1.5 | 5 | 3.2 | odd | 2 | |||
272.10.a.f.1.5 | 5 | 4.3 | odd | 2 | |||
289.10.a.a.1.1 | 5 | 17.16 | even | 2 |