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 | 58.17 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.84 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 46.8090i | − | 1.46278i | −0.681959 | − | 0.731390i | \(-0.738872\pi\) | ||
0.681959 | − | 0.731390i | \(-0.261128\pi\) | |||||||
\(3\) | 140.296 | 0.577350 | ||||||||
\(4\) | −1167.08 | −1.13973 | ||||||||
\(5\) | −1767.61 | −0.565635 | −0.282817 | − | 0.959174i | \(-0.591269\pi\) | ||||
−0.282817 | + | 0.959174i | \(0.591269\pi\) | |||||||
\(6\) | − | 6567.12i | − | 0.844537i | ||||||
\(7\) | 23434.9 | 1.39436 | 0.697178 | − | 0.716898i | \(-0.254439\pi\) | ||||
0.697178 | + | 0.716898i | \(0.254439\pi\) | |||||||
\(8\) | 6697.50i | 0.204391i | ||||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | 82740.0i | 0.827400i | ||||||||
\(11\) | 94929.5i | 0.589437i | 0.955584 | + | 0.294719i | \(0.0952259\pi\) | ||||
−0.955584 | + | 0.294719i | \(0.904774\pi\) | |||||||
\(12\) | −163737. | −0.658022 | ||||||||
\(13\) | 313428.i | 0.844152i | 0.906561 | + | 0.422076i | \(0.138698\pi\) | ||||
−0.906561 | + | 0.422076i | \(0.861302\pi\) | |||||||
\(14\) | − | 1.09697e6i | − | 2.03964i | ||||||
\(15\) | −247989. | −0.326570 | ||||||||
\(16\) | −881588. | −0.840748 | ||||||||
\(17\) | −1.98271e6 | −1.39642 | −0.698208 | − | 0.715895i | \(-0.746019\pi\) | ||||
−0.698208 | + | 0.715895i | \(0.746019\pi\) | |||||||
\(18\) | − | 921341.i | − | 0.487594i | ||||||
\(19\) | 4.75901e6 | 1.92198 | 0.960989 | − | 0.276587i | \(-0.0892035\pi\) | ||||
0.960989 | + | 0.276587i | \(0.0892035\pi\) | |||||||
\(20\) | 2.06294e6 | 0.644670 | ||||||||
\(21\) | 3.28783e6 | 0.805032 | ||||||||
\(22\) | 4.44355e6 | 0.862218 | ||||||||
\(23\) | − | 3.91113e6i | − | 0.607663i | −0.952726 | − | 0.303831i | \(-0.901734\pi\) | ||
0.952726 | − | 0.303831i | \(-0.0982659\pi\) | |||||||
\(24\) | 939633.i | 0.118005i | ||||||||
\(25\) | −6.64118e6 | −0.680057 | ||||||||
\(26\) | 1.46712e7 | 1.23481 | ||||||||
\(27\) | 2.76145e6 | 0.192450 | ||||||||
\(28\) | −2.73505e7 | −1.58919 | ||||||||
\(29\) | −311027. | −0.0151638 | −0.00758190 | − | 0.999971i | \(-0.502413\pi\) | ||||
−0.00758190 | + | 0.999971i | \(0.502413\pi\) | |||||||
\(30\) | 1.16081e7i | 0.477700i | ||||||||
\(31\) | 2.23439e7i | 0.780460i | 0.920717 | + | 0.390230i | \(0.127605\pi\) | ||||
−0.920717 | + | 0.390230i | \(0.872395\pi\) | |||||||
\(32\) | 4.81245e7i | 1.43422i | ||||||||
\(33\) | 1.33182e7i | 0.340312i | ||||||||
\(34\) | 9.28087e7i | 2.04265i | ||||||||
\(35\) | −4.14238e7 | −0.788696 | ||||||||
\(36\) | −2.29717e7 | −0.379909 | ||||||||
\(37\) | 7.51676e7i | 1.08398i | 0.840384 | + | 0.541991i | \(0.182329\pi\) | ||||
−0.840384 | + | 0.541991i | \(0.817671\pi\) | |||||||
\(38\) | − | 2.22764e8i | − | 2.81143i | ||||||
\(39\) | 4.39727e7i | 0.487371i | ||||||||
\(40\) | − | 1.18386e7i | − | 0.115611i | ||||||
\(41\) | −3.58676e7 | −0.309587 | −0.154794 | − | 0.987947i | \(-0.549471\pi\) | ||||
−0.154794 | + | 0.987947i | \(0.549471\pi\) | |||||||
\(42\) | − | 1.53900e8i | − | 1.17758i | ||||||
\(43\) | 9.01042e7i | 0.612919i | 0.951884 | + | 0.306459i | \(0.0991444\pi\) | ||||
−0.951884 | + | 0.306459i | \(0.900856\pi\) | |||||||
\(44\) | − | 1.10790e8i | − | 0.671798i | ||||||
\(45\) | −3.47919e7 | −0.188545 | ||||||||
\(46\) | −1.83076e8 | −0.888877 | ||||||||
\(47\) | 3.59705e8i | 1.56840i | 0.620508 | + | 0.784200i | \(0.286926\pi\) | ||||
−0.620508 | + | 0.784200i | \(0.713074\pi\) | |||||||
\(48\) | −1.23683e8 | −0.485406 | ||||||||
\(49\) | 2.66721e8 | 0.944227 | ||||||||
\(50\) | 3.10867e8i | 0.994775i | ||||||||
\(51\) | −2.78167e8 | −0.806221 | ||||||||
\(52\) | − | 3.65796e8i | − | 0.962103i | ||||||
\(53\) | −5.69545e8 | −1.36191 | −0.680956 | − | 0.732324i | \(-0.738435\pi\) | ||||
−0.680956 | + | 0.732324i | \(0.738435\pi\) | |||||||
\(54\) | − | 1.29261e8i | − | 0.281512i | ||||||
\(55\) | − | 1.67798e8i | − | 0.333406i | ||||||
\(56\) | 1.56955e8i | 0.284994i | ||||||||
\(57\) | 6.67670e8 | 1.10965 | ||||||||
\(58\) | 1.45589e7i | 0.0221813i | ||||||||
\(59\) | 6.58825e8 | + | 2.77609e8i | 0.921531 | + | 0.388306i | ||||
\(60\) | 2.89423e8 | 0.372200 | ||||||||
\(61\) | 1.36499e9i | 1.61614i | 0.589086 | + | 0.808070i | \(0.299488\pi\) | ||||
−0.589086 | + | 0.808070i | \(0.700512\pi\) | |||||||
\(62\) | 1.04590e9 | 1.14164 | ||||||||
\(63\) | 4.61270e8 | 0.464785 | ||||||||
\(64\) | 1.34991e9 | 1.25720 | ||||||||
\(65\) | − | 5.54018e8i | − | 0.477482i | ||||||
\(66\) | 6.23413e8 | 0.497802 | ||||||||
\(67\) | − | 2.32778e8i | − | 0.172413i | −0.996277 | − | 0.0862063i | \(-0.972526\pi\) | ||
0.996277 | − | 0.0862063i | \(-0.0274744\pi\) | |||||||
\(68\) | 2.31398e9 | 1.59153 | ||||||||
\(69\) | − | 5.48716e8i | − | 0.350834i | ||||||
\(70\) | 1.93901e9i | 1.15369i | ||||||||
\(71\) | 1.05078e9 | 0.582397 | 0.291198 | − | 0.956663i | \(-0.405946\pi\) | ||||
0.291198 | + | 0.956663i | \(0.405946\pi\) | |||||||
\(72\) | 1.31827e8i | 0.0681305i | ||||||||
\(73\) | − | 8.01361e8i | − | 0.386557i | −0.981144 | − | 0.193279i | \(-0.938088\pi\) | ||
0.981144 | − | 0.193279i | \(-0.0619121\pi\) | |||||||
\(74\) | 3.51852e9 | 1.58563 | ||||||||
\(75\) | −9.31732e8 | −0.392631 | ||||||||
\(76\) | −5.55415e9 | −2.19053 | ||||||||
\(77\) | 2.22467e9i | 0.821885i | ||||||||
\(78\) | 2.05832e9 | 0.712917 | ||||||||
\(79\) | 5.31912e8 | 0.172864 | 0.0864319 | − | 0.996258i | \(-0.472454\pi\) | ||||
0.0864319 | + | 0.996258i | \(0.472454\pi\) | |||||||
\(80\) | 1.55830e9 | 0.475557 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | 1.67893e9i | 0.452858i | ||||||||
\(83\) | 4.89302e9i | 1.24218i | 0.783737 | + | 0.621092i | \(0.213311\pi\) | ||||
−0.783737 | + | 0.621092i | \(0.786689\pi\) | |||||||
\(84\) | −3.83717e9 | −0.917517 | ||||||||
\(85\) | 3.50466e9 | 0.789862 | ||||||||
\(86\) | 4.21769e9 | 0.896566 | ||||||||
\(87\) | −4.36359e7 | −0.00875483 | ||||||||
\(88\) | −6.35790e8 | −0.120476 | ||||||||
\(89\) | 1.74792e9i | 0.313020i | 0.987676 | + | 0.156510i | \(0.0500243\pi\) | ||||
−0.987676 | + | 0.156510i | \(0.949976\pi\) | |||||||
\(90\) | 1.62857e9i | 0.275800i | ||||||||
\(91\) | 7.34516e9i | 1.17705i | ||||||||
\(92\) | 4.56460e9i | 0.692570i | ||||||||
\(93\) | 3.13477e9i | 0.450599i | ||||||||
\(94\) | 1.68374e10 | 2.29423 | ||||||||
\(95\) | −8.41206e9 | −1.08714 | ||||||||
\(96\) | 6.75168e9i | 0.828048i | ||||||||
\(97\) | − | 3.83740e9i | − | 0.446867i | −0.974719 | − | 0.223433i | \(-0.928273\pi\) | ||
0.974719 | − | 0.223433i | \(-0.0717265\pi\) | |||||||
\(98\) | − | 1.24849e10i | − | 1.38120i | ||||||
\(99\) | 1.86850e9i | 0.196479i | ||||||||
\(100\) | 7.75080e9 | 0.775080 | ||||||||
\(101\) | − | 3.98484e9i | − | 0.379144i | −0.981867 | − | 0.189572i | \(-0.939290\pi\) | ||
0.981867 | − | 0.189572i | \(-0.0607100\pi\) | |||||||
\(102\) | 1.30207e10i | 1.17932i | ||||||||
\(103\) | − | 2.06401e10i | − | 1.78043i | −0.455538 | − | 0.890216i | \(-0.650553\pi\) | ||
0.455538 | − | 0.890216i | \(-0.349447\pi\) | |||||||
\(104\) | −2.09918e9 | −0.172537 | ||||||||
\(105\) | −5.81160e9 | −0.455354 | ||||||||
\(106\) | 2.66598e10i | 1.99218i | ||||||||
\(107\) | −1.07525e10 | −0.766638 | −0.383319 | − | 0.923616i | \(-0.625219\pi\) | ||||
−0.383319 | + | 0.923616i | \(0.625219\pi\) | |||||||
\(108\) | −3.22284e9 | −0.219341 | ||||||||
\(109\) | 2.23699e10i | 1.45389i | 0.686696 | + | 0.726944i | \(0.259060\pi\) | ||||
−0.686696 | + | 0.726944i | \(0.740940\pi\) | |||||||
\(110\) | −7.85446e9 | −0.487700 | ||||||||
\(111\) | 1.05457e10i | 0.625837i | ||||||||
\(112\) | −2.06600e10 | −1.17230 | ||||||||
\(113\) | − | 6.77175e9i | − | 0.367544i | −0.982969 | − | 0.183772i | \(-0.941169\pi\) | ||
0.982969 | − | 0.183772i | \(-0.0588308\pi\) | |||||||
\(114\) | − | 3.12530e10i | − | 1.62318i | ||||||
\(115\) | 6.91334e9i | 0.343715i | ||||||||
\(116\) | 3.62994e8 | 0.0172826 | ||||||||
\(117\) | 6.16920e9i | 0.281384i | ||||||||
\(118\) | 1.29946e10 | − | 3.08389e10i | 0.568006 | − | 1.34800i | ||||
\(119\) | −4.64647e10 | −1.94710 | ||||||||
\(120\) | − | 1.66090e9i | − | 0.0667480i | ||||||
\(121\) | 1.69258e10 | 0.652564 | ||||||||
\(122\) | 6.38936e10 | 2.36406 | ||||||||
\(123\) | −5.03209e9 | −0.178740 | ||||||||
\(124\) | − | 2.60772e10i | − | 0.889513i | ||||||
\(125\) | 2.90008e10 | 0.950299 | ||||||||
\(126\) | − | 2.15916e10i | − | 0.679879i | ||||||
\(127\) | 3.98283e10 | 1.20552 | 0.602758 | − | 0.797924i | \(-0.294068\pi\) | ||||
0.602758 | + | 0.797924i | \(0.294068\pi\) | |||||||
\(128\) | − | 1.39086e10i | − | 0.404792i | ||||||
\(129\) | 1.26413e10i | 0.353869i | ||||||||
\(130\) | −2.59330e10 | −0.698451 | ||||||||
\(131\) | 3.06971e10i | 0.795684i | 0.917454 | + | 0.397842i | \(0.130241\pi\) | ||||
−0.917454 | + | 0.397842i | \(0.869759\pi\) | |||||||
\(132\) | − | 1.55435e10i | − | 0.387863i | ||||||
\(133\) | 1.11527e11 | 2.67992 | ||||||||
\(134\) | −1.08961e10 | −0.252202 | ||||||||
\(135\) | −4.88116e9 | −0.108857 | ||||||||
\(136\) | − | 1.32792e10i | − | 0.285415i | ||||||
\(137\) | 1.42474e10 | 0.295211 | 0.147606 | − | 0.989046i | \(-0.452843\pi\) | ||||
0.147606 | + | 0.989046i | \(0.452843\pi\) | |||||||
\(138\) | −2.56848e10 | −0.513194 | ||||||||
\(139\) | 5.30355e9 | 0.102210 | 0.0511049 | − | 0.998693i | \(-0.483726\pi\) | ||||
0.0511049 | + | 0.998693i | \(0.483726\pi\) | |||||||
\(140\) | 4.83450e10 | 0.898899 | ||||||||
\(141\) | 5.04652e10i | 0.905516i | ||||||||
\(142\) | − | 4.91858e10i | − | 0.851919i | ||||||
\(143\) | −2.97535e10 | −0.497575 | ||||||||
\(144\) | −1.73523e10 | −0.280249 | ||||||||
\(145\) | 5.49774e8 | 0.00857718 | ||||||||
\(146\) | −3.75109e10 | −0.565449 | ||||||||
\(147\) | 3.74199e10 | 0.545150 | ||||||||
\(148\) | − | 8.77267e10i | − | 1.23544i | ||||||
\(149\) | − | 1.39088e11i | − | 1.89391i | −0.321367 | − | 0.946955i | \(-0.604142\pi\) | ||
0.321367 | − | 0.946955i | \(-0.395858\pi\) | |||||||
\(150\) | 4.36134e10i | 0.574333i | ||||||||
\(151\) | − | 2.16390e10i | − | 0.275646i | −0.990457 | − | 0.137823i | \(-0.955989\pi\) | ||
0.990457 | − | 0.137823i | \(-0.0440106\pi\) | |||||||
\(152\) | 3.18734e10i | 0.392836i | ||||||||
\(153\) | −3.90257e10 | −0.465472 | ||||||||
\(154\) | 1.04134e11 | 1.20224 | ||||||||
\(155\) | − | 3.94953e10i | − | 0.441456i | ||||||
\(156\) | − | 5.13197e10i | − | 0.555471i | ||||||
\(157\) | 1.78422e10i | 0.187047i | 0.995617 | + | 0.0935233i | \(0.0298130\pi\) | ||||
−0.995617 | + | 0.0935233i | \(0.970187\pi\) | |||||||
\(158\) | − | 2.48982e10i | − | 0.252862i | ||||||
\(159\) | −7.99050e10 | −0.786300 | ||||||||
\(160\) | − | 8.50653e10i | − | 0.811246i | ||||||
\(161\) | − | 9.16570e10i | − | 0.847298i | ||||||
\(162\) | − | 1.81348e10i | − | 0.162531i | ||||||
\(163\) | 1.59769e11 | 1.38853 | 0.694265 | − | 0.719720i | \(-0.255730\pi\) | ||||
0.694265 | + | 0.719720i | \(0.255730\pi\) | |||||||
\(164\) | 4.18604e10 | 0.352845 | ||||||||
\(165\) | − | 2.35414e10i | − | 0.192492i | ||||||
\(166\) | 2.29037e11 | 1.81704 | ||||||||
\(167\) | −9.17186e10 | −0.706115 | −0.353057 | − | 0.935602i | \(-0.614858\pi\) | ||||
−0.353057 | + | 0.935602i | \(0.614858\pi\) | |||||||
\(168\) | 2.20202e10i | 0.164542i | ||||||||
\(169\) | 3.96216e10 | 0.287408 | ||||||||
\(170\) | − | 1.64049e11i | − | 1.15539i | ||||||
\(171\) | 9.36715e10 | 0.640659 | ||||||||
\(172\) | − | 1.05159e11i | − | 0.698561i | ||||||
\(173\) | − | 1.28145e11i | − | 0.826934i | −0.910519 | − | 0.413467i | \(-0.864318\pi\) | ||
0.910519 | − | 0.413467i | \(-0.135682\pi\) | |||||||
\(174\) | 2.04255e9i | 0.0128064i | ||||||||
\(175\) | −1.55636e11 | −0.948241 | ||||||||
\(176\) | − | 8.36887e10i | − | 0.495568i | ||||||
\(177\) | 9.24305e10 | + | 3.89475e10i | 0.532046 | + | 0.224188i | ||||
\(178\) | 8.18184e10 | 0.457879 | ||||||||
\(179\) | 6.15213e10i | 0.334781i | 0.985891 | + | 0.167390i | \(0.0535340\pi\) | ||||
−0.985891 | + | 0.167390i | \(0.946466\pi\) | |||||||
\(180\) | 4.06049e10 | 0.214890 | ||||||||
\(181\) | −1.23559e11 | −0.636037 | −0.318018 | − | 0.948085i | \(-0.603017\pi\) | ||||
−0.318018 | + | 0.948085i | \(0.603017\pi\) | |||||||
\(182\) | 3.43819e11 | 1.72176 | ||||||||
\(183\) | 1.91502e11i | 0.933079i | ||||||||
\(184\) | 2.61948e10 | 0.124201 | ||||||||
\(185\) | − | 1.32867e11i | − | 0.613138i | ||||||
\(186\) | 1.46735e11 | 0.659128 | ||||||||
\(187\) | − | 1.88218e11i | − | 0.823099i | ||||||
\(188\) | − | 4.19805e11i | − | 1.78755i | ||||||
\(189\) | 6.47144e10 | 0.268344 | ||||||||
\(190\) | 3.93760e11i | 1.59024i | ||||||||
\(191\) | − | 2.99961e11i | − | 1.18004i | −0.807387 | − | 0.590022i | \(-0.799119\pi\) | ||
0.807387 | − | 0.590022i | \(-0.200881\pi\) | |||||||
\(192\) | 1.89387e11 | 0.725847 | ||||||||
\(193\) | 3.30759e11 | 1.23517 | 0.617583 | − | 0.786506i | \(-0.288112\pi\) | ||||
0.617583 | + | 0.786506i | \(0.288112\pi\) | |||||||
\(194\) | −1.79625e11 | −0.653668 | ||||||||
\(195\) | − | 7.77265e10i | − | 0.275674i | ||||||
\(196\) | −3.11285e11 | −1.07616 | ||||||||
\(197\) | −7.32865e10 | −0.246998 | −0.123499 | − | 0.992345i | \(-0.539411\pi\) | ||||
−0.123499 | + | 0.992345i | \(0.539411\pi\) | |||||||
\(198\) | 8.74624e10 | 0.287406 | ||||||||
\(199\) | −1.66376e11 | −0.533119 | −0.266559 | − | 0.963818i | \(-0.585887\pi\) | ||||
−0.266559 | + | 0.963818i | \(0.585887\pi\) | |||||||
\(200\) | − | 4.44793e10i | − | 0.138998i | ||||||
\(201\) | − | 3.26579e10i | − | 0.0995424i | ||||||
\(202\) | −1.86526e11 | −0.554604 | ||||||||
\(203\) | −7.28890e9 | −0.0211437 | ||||||||
\(204\) | 3.24643e11 | 0.918873 | ||||||||
\(205\) | 6.33999e10 | 0.175113 | ||||||||
\(206\) | −9.66142e11 | −2.60438 | ||||||||
\(207\) | − | 7.69827e10i | − | 0.202554i | ||||||
\(208\) | − | 2.76314e11i | − | 0.709719i | ||||||
\(209\) | 4.51770e11i | 1.13289i | ||||||||
\(210\) | 2.72035e11i | 0.666083i | ||||||||
\(211\) | 7.07742e11i | 1.69224i | 0.532990 | + | 0.846121i | \(0.321068\pi\) | ||||
−0.532990 | + | 0.846121i | \(0.678932\pi\) | |||||||
\(212\) | 6.64706e11 | 1.55221 | ||||||||
\(213\) | 1.47420e11 | 0.336247 | ||||||||
\(214\) | 5.03313e11i | 1.12142i | ||||||||
\(215\) | − | 1.59269e11i | − | 0.346688i | ||||||
\(216\) | 1.84948e10i | 0.0393351i | ||||||||
\(217\) | 5.23628e11i | 1.08824i | ||||||||
\(218\) | 1.04711e12 | 2.12672 | ||||||||
\(219\) | − | 1.12428e11i | − | 0.223179i | ||||||
\(220\) | 1.95834e11i | 0.379993i | ||||||||
\(221\) | − | 6.21436e11i | − | 1.17879i | ||||||
\(222\) | 4.93634e11 | 0.915463 | ||||||||
\(223\) | −4.68814e11 | −0.850112 | −0.425056 | − | 0.905167i | \(-0.639746\pi\) | ||||
−0.425056 | + | 0.905167i | \(0.639746\pi\) | |||||||
\(224\) | 1.12779e12i | 1.99981i | ||||||||
\(225\) | −1.30718e11 | −0.226686 | ||||||||
\(226\) | −3.16979e11 | −0.537636 | ||||||||
\(227\) | 5.84135e10i | 0.0969134i | 0.998825 | + | 0.0484567i | \(0.0154303\pi\) | ||||
−0.998825 | + | 0.0484567i | \(0.984570\pi\) | |||||||
\(228\) | −7.79225e11 | −1.26470 | ||||||||
\(229\) | 3.60838e11i | 0.572975i | 0.958084 | + | 0.286487i | \(0.0924876\pi\) | ||||
−0.958084 | + | 0.286487i | \(0.907512\pi\) | |||||||
\(230\) | 3.23607e11 | 0.502780 | ||||||||
\(231\) | 3.12112e11i | 0.474516i | ||||||||
\(232\) | − | 2.08310e9i | − | 0.00309935i | ||||||
\(233\) | 7.99418e11i | 1.16411i | 0.813149 | + | 0.582056i | \(0.197751\pi\) | ||||
−0.813149 | + | 0.582056i | \(0.802249\pi\) | |||||||
\(234\) | 2.88774e11 | 0.411603 | ||||||||
\(235\) | − | 6.35817e11i | − | 0.887142i | ||||||
\(236\) | −7.68902e11 | − | 3.23993e11i | −1.05029 | − | 0.442563i | ||||
\(237\) | 7.46251e10 | 0.0998029 | ||||||||
\(238\) | 2.17497e12i | 2.84818i | ||||||||
\(239\) | 1.02266e12 | 1.31142 | 0.655711 | − | 0.755012i | \(-0.272369\pi\) | ||||
0.655711 | + | 0.755012i | \(0.272369\pi\) | |||||||
\(240\) | 2.18624e11 | 0.274563 | ||||||||
\(241\) | −1.27239e12 | −1.56508 | −0.782538 | − | 0.622603i | \(-0.786075\pi\) | ||||
−0.782538 | + | 0.622603i | \(0.786075\pi\) | |||||||
\(242\) | − | 7.92281e11i | − | 0.954558i | ||||||
\(243\) | 5.43536e10 | 0.0641500 | ||||||||
\(244\) | − | 1.59305e12i | − | 1.84196i | ||||||
\(245\) | −4.71458e11 | −0.534088 | ||||||||
\(246\) | 2.35547e11i | 0.261458i | ||||||||
\(247\) | 1.49160e12i | 1.62244i | ||||||||
\(248\) | −1.49648e11 | −0.159519 | ||||||||
\(249\) | 6.86471e11i | 0.717176i | ||||||||
\(250\) | − | 1.35750e12i | − | 1.39008i | ||||||
\(251\) | −9.11290e10 | −0.0914720 | −0.0457360 | − | 0.998954i | \(-0.514563\pi\) | ||||
−0.0457360 | + | 0.998954i | \(0.514563\pi\) | |||||||
\(252\) | −5.38339e11 | −0.529729 | ||||||||
\(253\) | 3.71281e11 | 0.358179 | ||||||||
\(254\) | − | 1.86432e12i | − | 1.76341i | ||||||
\(255\) | 4.91690e11 | 0.456027 | ||||||||
\(256\) | 7.31265e11 | 0.665082 | ||||||||
\(257\) | −2.55145e11 | −0.227573 | −0.113787 | − | 0.993505i | \(-0.536298\pi\) | ||||
−0.113787 | + | 0.993505i | \(0.536298\pi\) | |||||||
\(258\) | 5.91725e11 | 0.517633 | ||||||||
\(259\) | 1.76155e12i | 1.51146i | ||||||||
\(260\) | 6.46584e11i | 0.544199i | ||||||||
\(261\) | −6.12195e9 | −0.00505460 | ||||||||
\(262\) | 1.43690e12 | 1.16391 | ||||||||
\(263\) | −7.33648e11 | −0.583055 | −0.291527 | − | 0.956563i | \(-0.594163\pi\) | ||||
−0.291527 | + | 0.956563i | \(0.594163\pi\) | |||||||
\(264\) | −8.91989e10 | −0.0695568 | ||||||||
\(265\) | 1.00673e12 | 0.770345 | ||||||||
\(266\) | − | 5.22047e12i | − | 3.92014i | ||||||
\(267\) | 2.45226e11i | 0.180722i | ||||||||
\(268\) | 2.71671e11i | 0.196503i | ||||||||
\(269\) | 1.39603e12i | 0.991138i | 0.868569 | + | 0.495569i | \(0.165040\pi\) | ||||
−0.868569 | + | 0.495569i | \(0.834960\pi\) | |||||||
\(270\) | 2.28482e11i | 0.159233i | ||||||||
\(271\) | −9.96160e10 | −0.0681527 | −0.0340763 | − | 0.999419i | \(-0.510849\pi\) | ||||
−0.0340763 | + | 0.999419i | \(0.510849\pi\) | |||||||
\(272\) | 1.74793e12 | 1.17403 | ||||||||
\(273\) | 1.03050e12i | 0.679569i | ||||||||
\(274\) | − | 6.66907e11i | − | 0.431830i | ||||||
\(275\) | − | 6.30444e11i | − | 0.400851i | ||||||
\(276\) | 6.40396e11i | 0.399856i | ||||||||
\(277\) | 3.71966e11 | 0.228089 | 0.114045 | − | 0.993476i | \(-0.463619\pi\) | ||||
0.114045 | + | 0.993476i | \(0.463619\pi\) | |||||||
\(278\) | − | 2.48254e11i | − | 0.149510i | ||||||
\(279\) | 4.39795e11i | 0.260153i | ||||||||
\(280\) | − | 2.77436e11i | − | 0.161203i | ||||||
\(281\) | −6.97032e11 | −0.397852 | −0.198926 | − | 0.980015i | \(-0.563745\pi\) | ||||
−0.198926 | + | 0.980015i | \(0.563745\pi\) | |||||||
\(282\) | 2.36222e12 | 1.32457 | ||||||||
\(283\) | 3.25531e12i | 1.79333i | 0.442709 | + | 0.896665i | \(0.354017\pi\) | ||||
−0.442709 | + | 0.896665i | \(0.645983\pi\) | |||||||
\(284\) | −1.22634e12 | −0.663774 | ||||||||
\(285\) | −1.18018e12 | −0.627659 | ||||||||
\(286\) | 1.39273e12i | 0.727843i | ||||||||
\(287\) | −8.40555e11 | −0.431675 | ||||||||
\(288\) | 9.47234e11i | 0.478074i | ||||||||
\(289\) | 1.91515e12 | 0.949977 | ||||||||
\(290\) | − | 2.57344e10i | − | 0.0125465i | ||||||
\(291\) | − | 5.38372e11i | − | 0.257999i | ||||||
\(292\) | 9.35254e11i | 0.440570i | ||||||||
\(293\) | −3.61416e12 | −1.67367 | −0.836834 | − | 0.547457i | \(-0.815596\pi\) | ||||
−0.836834 | + | 0.547457i | \(0.815596\pi\) | |||||||
\(294\) | − | 1.75159e12i | − | 0.797435i | ||||||
\(295\) | −1.16454e12 | − | 4.90705e11i | −0.521250 | − | 0.219639i | ||||
\(296\) | −5.03435e11 | −0.221557 | ||||||||
\(297\) | 2.62143e11i | 0.113437i | ||||||||
\(298\) | −6.51058e12 | −2.77037 | ||||||||
\(299\) | 1.22585e12 | 0.512960 | ||||||||
\(300\) | 1.08741e12 | 0.447493 | ||||||||
\(301\) | 2.11159e12i | 0.854627i | ||||||||
\(302\) | −1.01290e12 | −0.403210 | ||||||||
\(303\) | − | 5.59057e11i | − | 0.218899i | ||||||
\(304\) | −4.19548e12 | −1.61590 | ||||||||
\(305\) | − | 2.41276e12i | − | 0.914145i | ||||||
\(306\) | 1.82675e12i | 0.680883i | ||||||||
\(307\) | 5.03330e12 | 1.84570 | 0.922849 | − | 0.385162i | \(-0.125855\pi\) | ||||
0.922849 | + | 0.385162i | \(0.125855\pi\) | |||||||
\(308\) | − | 2.59637e12i | − | 0.936725i | ||||||
\(309\) | − | 2.89573e12i | − | 1.02793i | ||||||
\(310\) | −1.84874e12 | −0.645753 | ||||||||
\(311\) | 1.10745e12 | 0.380648 | 0.190324 | − | 0.981721i | \(-0.439046\pi\) | ||||
0.190324 | + | 0.981721i | \(0.439046\pi\) | |||||||
\(312\) | −2.94507e11 | −0.0996145 | ||||||||
\(313\) | − | 5.97747e12i | − | 1.98974i | −0.101170 | − | 0.994869i | \(-0.532259\pi\) | ||
0.101170 | − | 0.994869i | \(-0.467741\pi\) | |||||||
\(314\) | 8.35175e11 | 0.273608 | ||||||||
\(315\) | −8.15345e11 | −0.262899 | ||||||||
\(316\) | −6.20784e11 | −0.197018 | ||||||||
\(317\) | 4.52422e12 | 1.41334 | 0.706671 | − | 0.707542i | \(-0.250196\pi\) | ||||
0.706671 | + | 0.707542i | \(0.250196\pi\) | |||||||
\(318\) | 3.74027e12i | 1.15018i | ||||||||
\(319\) | − | 2.95256e10i | − | 0.00893811i | ||||||
\(320\) | −2.38612e12 | −0.711119 | ||||||||
\(321\) | −1.50853e12 | −0.442619 | ||||||||
\(322\) | −4.29037e12 | −1.23941 | ||||||||
\(323\) | −9.43573e12 | −2.68388 | ||||||||
\(324\) | −4.52151e11 | −0.126636 | ||||||||
\(325\) | − | 2.08153e12i | − | 0.574071i | ||||||
\(326\) | − | 7.47864e12i | − | 2.03111i | ||||||
\(327\) | 3.13841e12i | 0.839403i | ||||||||
\(328\) | − | 2.40223e11i | − | 0.0632770i | ||||||
\(329\) | 8.42965e12i | 2.18691i | ||||||||
\(330\) | −1.10195e12 | −0.281574 | ||||||||
\(331\) | −3.81915e12 | −0.961228 | −0.480614 | − | 0.876932i | \(-0.659586\pi\) | ||||
−0.480614 | + | 0.876932i | \(0.659586\pi\) | |||||||
\(332\) | − | 5.71055e12i | − | 1.41575i | ||||||
\(333\) | 1.47952e12i | 0.361327i | ||||||||
\(334\) | 4.29326e12i | 1.03289i | ||||||||
\(335\) | 4.11461e11i | 0.0975226i | ||||||||
\(336\) | −2.89851e12 | −0.676829 | ||||||||
\(337\) | 1.65690e11i | 0.0381196i | 0.999818 | + | 0.0190598i | \(0.00606728\pi\) | ||||
−0.999818 | + | 0.0190598i | \(0.993933\pi\) | |||||||
\(338\) | − | 1.85465e12i | − | 0.420415i | ||||||
\(339\) | − | 9.50051e11i | − | 0.212201i | ||||||
\(340\) | −4.09022e12 | −0.900227 | ||||||||
\(341\) | −2.12110e12 | −0.460033 | ||||||||
\(342\) | − | 4.38467e12i | − | 0.937144i | ||||||
\(343\) | −3.69204e11 | −0.0777670 | ||||||||
\(344\) | −6.03473e11 | −0.125275 | ||||||||
\(345\) | 9.69915e11i | 0.198444i | ||||||||
\(346\) | −5.99833e12 | −1.20962 | ||||||||
\(347\) | 5.16211e12i | 1.02608i | 0.858366 | + | 0.513038i | \(0.171480\pi\) | ||||
−0.858366 | + | 0.513038i | \(0.828520\pi\) | |||||||
\(348\) | 5.09267e10 | 0.00997812 | ||||||||
\(349\) | 1.91896e12i | 0.370628i | 0.982679 | + | 0.185314i | \(0.0593302\pi\) | ||||
−0.982679 | + | 0.185314i | \(0.940670\pi\) | |||||||
\(350\) | 7.28515e12i | 1.38707i | ||||||||
\(351\) | 8.65514e11i | 0.162457i | ||||||||
\(352\) | −4.56843e12 | −0.845384 | ||||||||
\(353\) | − | 1.14718e12i | − | 0.209295i | −0.994509 | − | 0.104647i | \(-0.966629\pi\) | ||
0.994509 | − | 0.104647i | \(-0.0333714\pi\) | |||||||
\(354\) | 1.82309e12 | − | 4.32658e12i | 0.327939 | − | 0.778267i | ||||
\(355\) | −1.85736e12 | −0.329424 | ||||||||
\(356\) | − | 2.03997e12i | − | 0.356757i | ||||||
\(357\) | −6.51882e12 | −1.12416 | ||||||||
\(358\) | 2.87975e12 | 0.489711 | ||||||||
\(359\) | 9.15431e12 | 1.53516 | 0.767579 | − | 0.640954i | \(-0.221461\pi\) | ||||
0.767579 | + | 0.640954i | \(0.221461\pi\) | |||||||
\(360\) | − | 2.33018e11i | − | 0.0385370i | ||||||
\(361\) | 1.65171e13 | 2.69400 | ||||||||
\(362\) | 5.78368e12i | 0.930383i | ||||||||
\(363\) | 2.37463e12 | 0.376758 | ||||||||
\(364\) | − | 8.57240e12i | − | 1.34151i | ||||||
\(365\) | 1.41649e12i | 0.218650i | ||||||||
\(366\) | 8.96403e12 | 1.36489 | ||||||||
\(367\) | − | 7.00729e12i | − | 1.05249i | −0.850331 | − | 0.526247i | \(-0.823599\pi\) | ||
0.850331 | − | 0.526247i | \(-0.176401\pi\) | |||||||
\(368\) | 3.44800e12i | 0.510891i | ||||||||
\(369\) | −7.05982e11 | −0.103196 | ||||||||
\(370\) | −6.21937e12 | −0.896887 | ||||||||
\(371\) | −1.33473e13 | −1.89899 | ||||||||
\(372\) | − | 3.65853e12i | − | 0.513560i | ||||||
\(373\) | 1.19357e13 | 1.65312 | 0.826558 | − | 0.562851i | \(-0.190296\pi\) | ||||
0.826558 | + | 0.562851i | \(0.190296\pi\) | |||||||
\(374\) | −8.81028e12 | −1.20401 | ||||||||
\(375\) | 4.06870e12 | 0.548655 | ||||||||
\(376\) | −2.40912e12 | −0.320567 | ||||||||
\(377\) | − | 9.74845e10i | − | 0.0128006i | ||||||
\(378\) | − | 3.02921e12i | − | 0.392528i | ||||||
\(379\) | −1.25306e13 | −1.60242 | −0.801211 | − | 0.598382i | \(-0.795810\pi\) | ||||
−0.801211 | + | 0.598382i | \(0.795810\pi\) | |||||||
\(380\) | 9.81756e12 | 1.23904 | ||||||||
\(381\) | 5.58776e12 | 0.696005 | ||||||||
\(382\) | −1.40409e13 | −1.72615 | ||||||||
\(383\) | 2.41110e12 | 0.292564 | 0.146282 | − | 0.989243i | \(-0.453269\pi\) | ||||
0.146282 | + | 0.989243i | \(0.453269\pi\) | |||||||
\(384\) | − | 1.95132e12i | − | 0.233707i | ||||||
\(385\) | − | 3.93234e12i | − | 0.464887i | ||||||
\(386\) | − | 1.54825e13i | − | 1.80678i | ||||||
\(387\) | 1.77352e12i | 0.204306i | ||||||||
\(388\) | 4.47856e12i | 0.509307i | ||||||||
\(389\) | 1.42297e12 | 0.159753 | 0.0798764 | − | 0.996805i | \(-0.474547\pi\) | ||||
0.0798764 | + | 0.996805i | \(0.474547\pi\) | |||||||
\(390\) | −3.63830e12 | −0.403251 | ||||||||
\(391\) | 7.75463e12i | 0.848550i | ||||||||
\(392\) | 1.78636e12i | 0.192992i | ||||||||
\(393\) | 4.30668e12i | 0.459388i | ||||||||
\(394\) | 3.43047e12i | 0.361303i | ||||||||
\(395\) | −9.40212e11 | −0.0977778 | ||||||||
\(396\) | − | 2.18069e12i | − | 0.223933i | ||||||
\(397\) | 1.22123e13i | 1.23835i | 0.785252 | + | 0.619176i | \(0.212533\pi\) | ||||
−0.785252 | + | 0.619176i | \(0.787467\pi\) | |||||||
\(398\) | 7.78787e12i | 0.779836i | ||||||||
\(399\) | 1.56468e13 | 1.54725 | ||||||||
\(400\) | 5.85479e12 | 0.571757 | ||||||||
\(401\) | − | 1.38555e13i | − | 1.33629i | −0.744031 | − | 0.668145i | \(-0.767089\pi\) | ||
0.744031 | − | 0.668145i | \(-0.232911\pi\) | |||||||
\(402\) | −1.52868e12 | −0.145609 | ||||||||
\(403\) | −7.00320e12 | −0.658827 | ||||||||
\(404\) | 4.65063e12i | 0.432121i | ||||||||
\(405\) | −6.84808e11 | −0.0628483 | ||||||||
\(406\) | 3.41186e11i | 0.0309287i | ||||||||
\(407\) | −7.13562e12 | −0.638939 | ||||||||
\(408\) | − | 1.86302e12i | − | 0.164785i | ||||||
\(409\) | 1.09414e13i | 0.956000i | 0.878360 | + | 0.478000i | \(0.158638\pi\) | ||||
−0.878360 | + | 0.478000i | \(0.841362\pi\) | |||||||
\(410\) | − | 2.96769e12i | − | 0.256152i | ||||||
\(411\) | 1.99886e12 | 0.170440 | ||||||||
\(412\) | 2.40887e13i | 2.02921i | ||||||||
\(413\) | 1.54395e13 | + | 6.50575e12i | 1.28494 | + | 0.541436i | ||||
\(414\) | −3.60348e12 | −0.296292 | ||||||||
\(415\) | − | 8.64894e12i | − | 0.702623i | ||||||
\(416\) | −1.50835e13 | −1.21070 | ||||||||
\(417\) | 7.44067e11 | 0.0590108 | ||||||||
\(418\) | 2.11469e13 | 1.65716 | ||||||||
\(419\) | 8.31526e12i | 0.643881i | 0.946760 | + | 0.321941i | \(0.104335\pi\) | ||||
−0.946760 | + | 0.321941i | \(0.895665\pi\) | |||||||
\(420\) | 6.78261e12 | 0.518980 | ||||||||
\(421\) | − | 6.87852e11i | − | 0.0520097i | −0.999662 | − | 0.0260049i | \(-0.991721\pi\) | ||
0.999662 | − | 0.0260049i | \(-0.00827853\pi\) | |||||||
\(422\) | 3.31287e13 | 2.47538 | ||||||||
\(423\) | 7.08007e12i | 0.522800i | ||||||||
\(424\) | − | 3.81453e12i | − | 0.278363i | ||||||
\(425\) | 1.31675e13 | 0.949642 | ||||||||
\(426\) | − | 6.90058e12i | − | 0.491855i | ||||||
\(427\) | 3.19884e13i | 2.25347i | ||||||||
\(428\) | 1.25490e13 | 0.873759 | ||||||||
\(429\) | −4.17430e12 | −0.287275 | ||||||||
\(430\) | −7.45523e12 | −0.507129 | ||||||||
\(431\) | 1.96055e13i | 1.31823i | 0.752042 | + | 0.659115i | \(0.229069\pi\) | ||||
−0.752042 | + | 0.659115i | \(0.770931\pi\) | |||||||
\(432\) | −2.43446e12 | −0.161802 | ||||||||
\(433\) | −2.62642e12 | −0.172554 | −0.0862770 | − | 0.996271i | \(-0.527497\pi\) | ||||
−0.0862770 | + | 0.996271i | \(0.527497\pi\) | |||||||
\(434\) | 2.45105e13 | 1.59186 | ||||||||
\(435\) | 7.71312e10 | 0.00495204 | ||||||||
\(436\) | − | 2.61075e13i | − | 1.65704i | ||||||
\(437\) | − | 1.86131e13i | − | 1.16791i | ||||||
\(438\) | −5.26263e12 | −0.326462 | ||||||||
\(439\) | 3.30354e12 | 0.202608 | 0.101304 | − | 0.994855i | \(-0.467698\pi\) | ||||
0.101304 | + | 0.994855i | \(0.467698\pi\) | |||||||
\(440\) | 1.12383e12 | 0.0681454 | ||||||||
\(441\) | 5.24987e12 | 0.314742 | ||||||||
\(442\) | −2.90888e13 | −1.72431 | ||||||||
\(443\) | 2.95988e13i | 1.73482i | 0.497592 | + | 0.867411i | \(0.334218\pi\) | ||||
−0.497592 | + | 0.867411i | \(0.665782\pi\) | |||||||
\(444\) | − | 1.23077e13i | − | 0.713284i | ||||||
\(445\) | − | 3.08964e12i | − | 0.177055i | ||||||
\(446\) | 2.19447e13i | 1.24353i | ||||||||
\(447\) | − | 1.95135e13i | − | 1.09345i | ||||||
\(448\) | 3.16351e13 | 1.75299 | ||||||||
\(449\) | 2.67342e13 | 1.46499 | 0.732497 | − | 0.680770i | \(-0.238355\pi\) | ||||
0.732497 | + | 0.680770i | \(0.238355\pi\) | |||||||
\(450\) | 6.11880e12i | 0.331592i | ||||||||
\(451\) | − | 3.40489e12i | − | 0.182482i | ||||||
\(452\) | 7.90319e12i | 0.418900i | ||||||||
\(453\) | − | 3.03587e12i | − | 0.159145i | ||||||
\(454\) | 2.73428e12 | 0.141763 | ||||||||
\(455\) | − | 1.29834e13i | − | 0.665779i | ||||||
\(456\) | 4.47172e12i | 0.226804i | ||||||||
\(457\) | − | 3.62683e13i | − | 1.81947i | −0.415186 | − | 0.909737i | \(-0.636283\pi\) | ||
0.415186 | − | 0.909737i | \(-0.363717\pi\) | |||||||
\(458\) | 1.68905e13 | 0.838136 | ||||||||
\(459\) | −5.47515e12 | −0.268740 | ||||||||
\(460\) | − | 8.06843e12i | − | 0.391742i | ||||||
\(461\) | 6.27032e12 | 0.301152 | 0.150576 | − | 0.988598i | \(-0.451887\pi\) | ||||
0.150576 | + | 0.988598i | \(0.451887\pi\) | |||||||
\(462\) | 1.46096e13 | 0.694112 | ||||||||
\(463\) | 8.72483e12i | 0.410064i | 0.978755 | + | 0.205032i | \(0.0657299\pi\) | ||||
−0.978755 | + | 0.205032i | \(0.934270\pi\) | |||||||
\(464\) | 2.74198e11 | 0.0127489 | ||||||||
\(465\) | − | 5.54104e12i | − | 0.254875i | ||||||
\(466\) | 3.74200e13 | 1.70284 | ||||||||
\(467\) | − | 1.01511e13i | − | 0.457012i | −0.973543 | − | 0.228506i | \(-0.926616\pi\) | ||
0.973543 | − | 0.228506i | \(-0.0733840\pi\) | |||||||
\(468\) | − | 7.19995e12i | − | 0.320701i | ||||||
\(469\) | − | 5.45515e12i | − | 0.240404i | ||||||
\(470\) | −2.97620e13 | −1.29769 | ||||||||
\(471\) | 2.50319e12i | 0.107991i | ||||||||
\(472\) | −1.85929e12 | + | 4.41248e12i | −0.0793664 | + | 0.188353i | ||||
\(473\) | −8.55355e12 | −0.361277 | ||||||||
\(474\) | − | 3.49313e12i | − | 0.145990i | ||||||
\(475\) | −3.16054e13 | −1.30705 | ||||||||
\(476\) | 5.42281e13 | 2.21916 | ||||||||
\(477\) | −1.12104e13 | −0.453971 | ||||||||
\(478\) | − | 4.78698e13i | − | 1.91832i | ||||||
\(479\) | −3.02354e13 | −1.19905 | −0.599525 | − | 0.800356i | \(-0.704644\pi\) | ||||
−0.599525 | + | 0.800356i | \(0.704644\pi\) | |||||||
\(480\) | − | 1.19343e13i | − | 0.468373i | ||||||
\(481\) | −2.35596e13 | −0.915045 | ||||||||
\(482\) | 5.95593e13i | 2.28936i | ||||||||
\(483\) | − | 1.28591e13i | − | 0.489188i | ||||||
\(484\) | −1.97538e13 | −0.743745 | ||||||||
\(485\) | 6.78302e12i | 0.252764i | ||||||||
\(486\) | − | 2.54424e12i | − | 0.0938374i | ||||||
\(487\) | −3.69676e13 | −1.34951 | −0.674755 | − | 0.738042i | \(-0.735751\pi\) | ||||
−0.674755 | + | 0.738042i | \(0.735751\pi\) | |||||||
\(488\) | −9.14199e12 | −0.330325 | ||||||||
\(489\) | 2.24150e13 | 0.801668 | ||||||||
\(490\) | 2.20685e13i | 0.781254i | ||||||||
\(491\) | −8.28368e12 | −0.290279 | −0.145140 | − | 0.989411i | \(-0.546363\pi\) | ||||
−0.145140 | + | 0.989411i | \(0.546363\pi\) | |||||||
\(492\) | 5.87285e12 | 0.203715 | ||||||||
\(493\) | 6.16677e11 | 0.0211750 | ||||||||
\(494\) | 6.98205e13 | 2.37328 | ||||||||
\(495\) | − | 3.30277e12i | − | 0.111135i | ||||||
\(496\) | − | 1.96981e13i | − | 0.656171i | ||||||
\(497\) | 2.46249e13 | 0.812068 | ||||||||
\(498\) | 3.21330e13 | 1.04907 | ||||||||
\(499\) | −4.89323e13 | −1.58159 | −0.790793 | − | 0.612083i | \(-0.790332\pi\) | ||||
−0.790793 | + | 0.612083i | \(0.790332\pi\) | |||||||
\(500\) | −3.38463e13 | −1.08308 | ||||||||
\(501\) | −1.28678e13 | −0.407675 | ||||||||
\(502\) | 4.26566e12i | 0.133803i | ||||||||
\(503\) | 2.94499e13i | 0.914626i | 0.889306 | + | 0.457313i | \(0.151188\pi\) | ||||
−0.889306 | + | 0.457313i | \(0.848812\pi\) | |||||||
\(504\) | 3.08935e12i | 0.0949981i | ||||||||
\(505\) | 7.04364e12i | 0.214457i | ||||||||
\(506\) | − | 1.73793e13i | − | 0.523937i | ||||||
\(507\) | 5.55876e12 | 0.165935 | ||||||||
\(508\) | −4.64829e13 | −1.37396 | ||||||||
\(509\) | 1.45727e13i | 0.426532i | 0.976994 | + | 0.213266i | \(0.0684100\pi\) | ||||
−0.976994 | + | 0.213266i | \(0.931590\pi\) | |||||||
\(510\) | − | 2.30155e13i | − | 0.667067i | ||||||
\(511\) | − | 1.87798e13i | − | 0.538998i | ||||||
\(512\) | − | 4.84721e13i | − | 1.37766i | ||||||
\(513\) | 1.31418e13 | 0.369885 | ||||||||
\(514\) | 1.19431e13i | 0.332890i | ||||||||
\(515\) | 3.64836e13i | 1.00708i | ||||||||
\(516\) | − | 1.47534e13i | − | 0.403314i | ||||||
\(517\) | −3.41466e13 | −0.924473 | ||||||||
\(518\) | 8.24562e13 | 2.21093 | ||||||||
\(519\) | − | 1.79782e13i | − | 0.477430i | ||||||
\(520\) | 3.71053e12 | 0.0975932 | ||||||||
\(521\) | 3.17829e13 | 0.827952 | 0.413976 | − | 0.910288i | \(-0.364140\pi\) | ||||
0.413976 | + | 0.910288i | \(0.364140\pi\) | |||||||
\(522\) | 2.86562e11i | 0.00739378i | ||||||||
\(523\) | −2.72361e13 | −0.696044 | −0.348022 | − | 0.937486i | \(-0.613147\pi\) | ||||
−0.348022 | + | 0.937486i | \(0.613147\pi\) | |||||||
\(524\) | − | 3.58260e13i | − | 0.906863i | ||||||
\(525\) | −2.18351e13 | −0.547467 | ||||||||
\(526\) | 3.43413e13i | 0.852881i | ||||||||
\(527\) | − | 4.43015e13i | − | 1.08985i | ||||||
\(528\) | − | 1.17412e13i | − | 0.286116i | ||||||
\(529\) | 2.61296e13 | 0.630746 | ||||||||
\(530\) | − | 4.71242e13i | − | 1.12685i | ||||||
\(531\) | 1.29676e13 | + | 5.46418e12i | 0.307177 | + | 0.129435i | ||||
\(532\) | −1.30161e14 | −3.05438 | ||||||||
\(533\) | − | 1.12419e13i | − | 0.261339i | ||||||
\(534\) | 1.14788e13 | 0.264357 | ||||||||
\(535\) | 1.90062e13 | 0.433637 | ||||||||
\(536\) | 1.55903e12 | 0.0352396 | ||||||||
\(537\) | 8.63120e12i | 0.193286i | ||||||||
\(538\) | 6.53469e13 | 1.44982 | ||||||||
\(539\) | 2.53197e13i | 0.556563i | ||||||||
\(540\) | 5.69671e12 | 0.124067 | ||||||||
\(541\) | 6.37938e13i | 1.37655i | 0.725450 | + | 0.688275i | \(0.241632\pi\) | ||||
−0.725450 | + | 0.688275i | \(0.758368\pi\) | |||||||
\(542\) | 4.66293e12i | 0.0996924i | ||||||||
\(543\) | −1.73349e13 | −0.367216 | ||||||||
\(544\) | − | 9.54169e13i | − | 2.00277i | ||||||
\(545\) | − | 3.95412e13i | − | 0.822370i | ||||||
\(546\) | 4.82365e13 | 0.994060 | ||||||||
\(547\) | −3.69130e13 | −0.753776 | −0.376888 | − | 0.926259i | \(-0.623006\pi\) | ||||
−0.376888 | + | 0.926259i | \(0.623006\pi\) | |||||||
\(548\) | −1.66279e13 | −0.336461 | ||||||||
\(549\) | 2.68670e13i | 0.538713i | ||||||||
\(550\) | −2.95104e13 | −0.586357 | ||||||||
\(551\) | −1.48018e12 | −0.0291445 | ||||||||
\(552\) | 3.67502e12 | 0.0717075 | ||||||||
\(553\) | 1.24653e13 | 0.241034 | ||||||||
\(554\) | − | 1.74114e13i | − | 0.333644i | ||||||
\(555\) | − | 1.86407e13i | − | 0.353995i | ||||||
\(556\) | −6.18967e12 | −0.116491 | ||||||||
\(557\) | −6.25309e13 | −1.16632 | −0.583161 | − | 0.812356i | \(-0.698184\pi\) | ||||
−0.583161 | + | 0.812356i | \(0.698184\pi\) | |||||||
\(558\) | 2.05864e13 | 0.380548 | ||||||||
\(559\) | −2.82412e13 | −0.517396 | ||||||||
\(560\) | 3.65187e13 | 0.663095 | ||||||||
\(561\) | − | 2.64062e13i | − | 0.475217i | ||||||
\(562\) | 3.26274e13i | 0.581970i | ||||||||
\(563\) | − | 7.84435e13i | − | 1.38680i | −0.720551 | − | 0.693402i | \(-0.756111\pi\) | ||
0.720551 | − | 0.693402i | \(-0.243889\pi\) | |||||||
\(564\) | − | 5.88970e13i | − | 1.03204i | ||||||
\(565\) | 1.19698e13i | 0.207896i | ||||||||
\(566\) | 1.52378e14 | 2.62325 | ||||||||
\(567\) | 9.07917e12 | 0.154928 | ||||||||
\(568\) | 7.03758e12i | 0.119037i | ||||||||
\(569\) | − | 7.06371e13i | − | 1.18433i | −0.805818 | − | 0.592163i | \(-0.798274\pi\) | ||
0.805818 | − | 0.592163i | \(-0.201726\pi\) | |||||||
\(570\) | 5.52430e13i | 0.918128i | ||||||||
\(571\) | − | 2.77152e13i | − | 0.456601i | −0.973591 | − | 0.228300i | \(-0.926683\pi\) | ||
0.973591 | − | 0.228300i | \(-0.0733169\pi\) | |||||||
\(572\) | 3.47248e13 | 0.567100 | ||||||||
\(573\) | − | 4.20834e13i | − | 0.681299i | ||||||
\(574\) | 3.93455e13i | 0.631445i | ||||||||
\(575\) | 2.59745e13i | 0.413245i | ||||||||
\(576\) | 2.65703e13 | 0.419068 | ||||||||
\(577\) | 1.24044e13 | 0.193952 | 0.0969762 | − | 0.995287i | \(-0.469083\pi\) | ||||
0.0969762 | + | 0.995287i | \(0.469083\pi\) | |||||||
\(578\) | − | 8.96461e13i | − | 1.38961i | ||||||
\(579\) | 4.64042e13 | 0.713123 | ||||||||
\(580\) | −6.41632e11 | −0.00977565 | ||||||||
\(581\) | 1.14667e14i | 1.73205i | ||||||||
\(582\) | −2.52007e13 | −0.377396 | ||||||||
\(583\) | − | 5.40666e13i | − | 0.802762i | ||||||
\(584\) | 5.36711e12 | 0.0790090 | ||||||||
\(585\) | − | 1.09047e13i | − | 0.159161i | ||||||
\(586\) | 1.69175e14i | 2.44821i | ||||||||
\(587\) | − | 7.69311e13i | − | 1.10385i | −0.833893 | − | 0.551926i | \(-0.813893\pi\) | ||
0.833893 | − | 0.551926i | \(-0.186107\pi\) | |||||||
\(588\) | −4.36721e13 | −0.621323 | ||||||||
\(589\) | 1.06335e14i | 1.50003i | ||||||||
\(590\) | −2.29694e13 | + | 5.45111e13i | −0.321284 | + | 0.762474i | ||||
\(591\) | −1.02818e13 | −0.142604 | ||||||||
\(592\) | − | 6.62669e13i | − | 0.911356i | ||||||
\(593\) | −1.05383e14 | −1.43713 | −0.718567 | − | 0.695458i | \(-0.755202\pi\) | ||||
−0.718567 | + | 0.695458i | \(0.755202\pi\) | |||||||
\(594\) | 1.22706e13 | 0.165934 | ||||||||
\(595\) | 8.21314e13 | 1.10135 | ||||||||
\(596\) | 1.62327e14i | 2.15854i | ||||||||
\(597\) | −2.33418e13 | −0.307796 | ||||||||
\(598\) | − | 5.73810e13i | − | 0.750347i | ||||||
\(599\) | 3.76129e13 | 0.487756 | 0.243878 | − | 0.969806i | \(-0.421580\pi\) | ||||
0.243878 | + | 0.969806i | \(0.421580\pi\) | |||||||
\(600\) | − | 6.24027e12i | − | 0.0802504i | ||||||
\(601\) | − | 8.72793e13i | − | 1.11311i | −0.830810 | − | 0.556556i | \(-0.812123\pi\) | ||
0.830810 | − | 0.556556i | \(-0.187877\pi\) | |||||||
\(602\) | 9.88412e13 | 1.25013 | ||||||||
\(603\) | − | 4.58178e12i | − | 0.0574708i | ||||||
\(604\) | 2.52545e13i | 0.314162i | ||||||||
\(605\) | −2.99182e13 | −0.369113 | ||||||||
\(606\) | −2.61689e13 | −0.320201 | ||||||||
\(607\) | −7.53303e13 | −0.914169 | −0.457084 | − | 0.889423i | \(-0.651106\pi\) | ||||
−0.457084 | + | 0.889423i | \(0.651106\pi\) | |||||||
\(608\) | 2.29025e14i | 2.75654i | ||||||||
\(609\) | −1.02260e12 | −0.0122073 | ||||||||
\(610\) | −1.12939e14 | −1.33719 | ||||||||
\(611\) | −1.12741e14 | −1.32397 | ||||||||
\(612\) | 4.55462e13 | 0.530511 | ||||||||
\(613\) | 1.41627e13i | 0.163622i | 0.996648 | + | 0.0818112i | \(0.0260705\pi\) | ||||
−0.996648 | + | 0.0818112i | \(0.973930\pi\) | |||||||
\(614\) | − | 2.35603e14i | − | 2.69985i | ||||||
\(615\) | 8.89476e12 | 0.101102 | ||||||||
\(616\) | −1.48997e13 | −0.167986 | ||||||||
\(617\) | −1.12007e14 | −1.25262 | −0.626310 | − | 0.779574i | \(-0.715435\pi\) | ||||
−0.626310 | + | 0.779574i | \(0.715435\pi\) | |||||||
\(618\) | −1.35546e14 | −1.50364 | ||||||||
\(619\) | −4.68024e13 | −0.515009 | −0.257504 | − | 0.966277i | \(-0.582900\pi\) | ||||
−0.257504 | + | 0.966277i | \(0.582900\pi\) | |||||||
\(620\) | 4.60943e13i | 0.503139i | ||||||||
\(621\) | − | 1.08004e13i | − | 0.116945i | ||||||
\(622\) | − | 5.18388e13i | − | 0.556805i | ||||||
\(623\) | 4.09624e13i | 0.436461i | ||||||||
\(624\) | − | 3.87658e13i | − | 0.409756i | ||||||
\(625\) | 1.35932e13 | 0.142535 | ||||||||
\(626\) | −2.79799e14 | −2.91055 | ||||||||
\(627\) | 6.33816e13i | 0.654072i | ||||||||
\(628\) | − | 2.08233e13i | − | 0.213182i | ||||||
\(629\) | − | 1.49036e14i | − | 1.51369i | ||||||
\(630\) | 3.81655e13i | 0.384563i | ||||||||
\(631\) | 1.21461e14 | 1.21420 | 0.607099 | − | 0.794626i | \(-0.292333\pi\) | ||||
0.607099 | + | 0.794626i | \(0.292333\pi\) | |||||||
\(632\) | 3.56248e12i | 0.0353319i | ||||||||
\(633\) | 9.92934e13i | 0.977017i | ||||||||
\(634\) | − | 2.11774e14i | − | 2.06741i | ||||||
\(635\) | −7.04009e13 | −0.681882 | ||||||||
\(636\) | 9.32556e13 | 0.896168 | ||||||||
\(637\) | 8.35977e13i | 0.797071i | ||||||||
\(638\) | −1.38207e12 | −0.0130745 | ||||||||
\(639\) | 2.06824e13 | 0.194132 | ||||||||
\(640\) | 2.45849e13i | 0.228965i | ||||||||
\(641\) | 1.69559e14 | 1.56686 | 0.783431 | − | 0.621478i | \(-0.213468\pi\) | ||||
0.783431 | + | 0.621478i | \(0.213468\pi\) | |||||||
\(642\) | 7.06129e13i | 0.647454i | ||||||||
\(643\) | −1.18664e14 | −1.07960 | −0.539801 | − | 0.841792i | \(-0.681501\pi\) | ||||
−0.539801 | + | 0.841792i | \(0.681501\pi\) | |||||||
\(644\) | 1.06971e14i | 0.965689i | ||||||||
\(645\) | − | 2.23448e13i | − | 0.200161i | ||||||
\(646\) | 4.41677e14i | 3.92593i | ||||||||
\(647\) | 9.89076e13 | 0.872385 | 0.436192 | − | 0.899853i | \(-0.356327\pi\) | ||||
0.436192 | + | 0.899853i | \(0.356327\pi\) | |||||||
\(648\) | 2.59475e12i | 0.0227102i | ||||||||
\(649\) | −2.63533e13 | + | 6.25419e13i | −0.228882 | + | 0.543184i | ||||
\(650\) | −9.74343e13 | −0.839741 | ||||||||
\(651\) | 7.34630e13i | 0.628295i | ||||||||
\(652\) | −1.86464e14 | −1.58255 | ||||||||
\(653\) | −1.28969e14 | −1.08622 | −0.543110 | − | 0.839661i | \(-0.682753\pi\) | ||||
−0.543110 | + | 0.839661i | \(0.682753\pi\) | |||||||
\(654\) | 1.46906e14 | 1.22786 | ||||||||
\(655\) | − | 5.42604e13i | − | 0.450067i | ||||||
\(656\) | 3.16205e13 | 0.260285 | ||||||||
\(657\) | − | 1.57732e13i | − | 0.128852i | ||||||
\(658\) | 3.94584e14 | 3.19897 | ||||||||
\(659\) | 7.29197e13i | 0.586702i | 0.956005 | + | 0.293351i | \(0.0947705\pi\) | ||||
−0.956005 | + | 0.293351i | \(0.905229\pi\) | |||||||
\(660\) | 2.74748e13i | 0.219389i | ||||||||
\(661\) | −1.40088e14 | −1.11018 | −0.555092 | − | 0.831789i | \(-0.687317\pi\) | ||||
−0.555092 | + | 0.831789i | \(0.687317\pi\) | |||||||
\(662\) | 1.78770e14i | 1.40607i | ||||||||
\(663\) | − | 8.71851e13i | − | 0.680573i | ||||||
\(664\) | −3.27710e13 | −0.253892 | ||||||||
\(665\) | −1.97136e14 | −1.51586 | ||||||||
\(666\) | 6.92550e13 | 0.528543 | ||||||||
\(667\) | 1.21647e12i | 0.00921448i | ||||||||
\(668\) | 1.07043e14 | 0.804779 | ||||||||
\(669\) | −6.57727e13 | −0.490812 | ||||||||
\(670\) | 1.92601e13 | 0.142654 | ||||||||
\(671\) | −1.29577e14 | −0.952613 | ||||||||
\(672\) | 1.58225e14i | 1.15459i | ||||||||
\(673\) | 2.59237e14i | 1.87768i | 0.344351 | + | 0.938841i | \(0.388099\pi\) | ||||
−0.344351 | + | 0.938841i | \(0.611901\pi\) | |||||||
\(674\) | 7.75580e12 | 0.0557606 | ||||||||
\(675\) | −1.83393e13 | −0.130877 | ||||||||
\(676\) | −4.62416e13 | −0.327567 | ||||||||
\(677\) | 4.40432e13 | 0.309696 | 0.154848 | − | 0.987938i | \(-0.450511\pi\) | ||||
0.154848 | + | 0.987938i | \(0.450511\pi\) | |||||||
\(678\) | −4.44709e13 | −0.310404 | ||||||||
\(679\) | − | 8.99292e13i | − | 0.623091i | ||||||
\(680\) | 2.34724e13i | 0.161441i | ||||||||
\(681\) | 8.19518e12i | 0.0559530i | ||||||||
\(682\) | 9.92864e13i | 0.672927i | ||||||||
\(683\) | 1.45348e14i | 0.977923i | 0.872305 | + | 0.488962i | \(0.162624\pi\) | ||||
−0.872305 | + | 0.488962i | \(0.837376\pi\) | |||||||
\(684\) | −1.09322e14 | −0.730177 | ||||||||
\(685\) | −2.51839e13 | −0.166982 | ||||||||
\(686\) | 1.72821e13i | 0.113756i | ||||||||
\(687\) | 5.06242e13i | 0.330807i | ||||||||
\(688\) | − | 7.94348e13i | − | 0.515310i | ||||||
\(689\) | − | 1.78511e14i | − | 1.14966i | ||||||
\(690\) | 4.54007e13 | 0.290280 | ||||||||
\(691\) | 2.12932e13i | 0.135161i | 0.997714 | + | 0.0675803i | \(0.0215279\pi\) | ||||
−0.997714 | + | 0.0675803i | \(0.978472\pi\) | |||||||
\(692\) | 1.49556e14i | 0.942480i | ||||||||
\(693\) | 4.37881e13i | 0.273962i | ||||||||
\(694\) | 2.41633e14 | 1.50093 | ||||||||
\(695\) | −9.37460e12 | −0.0578134 | ||||||||
\(696\) | − | 2.92251e11i | − | 0.00178941i | ||||||
\(697\) | 7.11151e13 | 0.432312 | ||||||||
\(698\) | 8.98245e13 | 0.542148 | ||||||||
\(699\) | 1.12155e14i | 0.672100i | ||||||||
\(700\) | 1.81639e14 | 1.08074 | ||||||||
\(701\) | − | 2.46761e14i | − | 1.45776i | −0.684642 | − | 0.728880i | \(-0.740041\pi\) | ||
0.684642 | − | 0.728880i | \(-0.259959\pi\) | |||||||
\(702\) | 4.05138e13 | 0.237639 | ||||||||
\(703\) | 3.57723e14i | 2.08339i | ||||||||
\(704\) | 1.28146e14i | 0.741043i | ||||||||
\(705\) | − | 8.92027e13i | − | 0.512192i | ||||||
\(706\) | −5.36984e13 | −0.306153 | ||||||||
\(707\) | − | 9.33844e13i | − | 0.528661i | ||||||
\(708\) | −1.07874e14 | − | 4.54549e13i | −0.606388 | − | 0.255514i | ||||
\(709\) | −5.55549e13 | −0.310092 | −0.155046 | − | 0.987907i | \(-0.549553\pi\) | ||||
−0.155046 | + | 0.987907i | \(0.549553\pi\) | |||||||
\(710\) | 8.69413e13i | 0.481875i | ||||||||
\(711\) | 1.04696e13 | 0.0576213 | ||||||||
\(712\) | −1.17067e13 | −0.0639785 | ||||||||
\(713\) | 8.73899e13 | 0.474257 | ||||||||
\(714\) | 3.05139e14i | 1.64440i | ||||||||
\(715\) | 5.25926e13 | 0.281446 | ||||||||
\(716\) | − | 7.18004e13i | − | 0.381559i | ||||||
\(717\) | 1.43475e14 | 0.757150 | ||||||||
\(718\) | − | 4.28504e14i | − | 2.24560i | ||||||
\(719\) | − | 2.35164e14i | − | 1.22385i | −0.790917 | − | 0.611923i | \(-0.790396\pi\) | ||
0.790917 | − | 0.611923i | \(-0.209604\pi\) | |||||||
\(720\) | 3.06721e13 | 0.158519 | ||||||||
\(721\) | − | 4.83699e14i | − | 2.48256i | ||||||
\(722\) | − | 7.73148e14i | − | 3.94073i | ||||||
\(723\) | −1.78511e14 | −0.903597 | ||||||||
\(724\) | 1.44204e14 | 0.724909 | ||||||||
\(725\) | 2.06559e12 | 0.0103123 | ||||||||
\(726\) | − | 1.11154e14i | − | 0.551114i | ||||||
\(727\) | −2.62595e14 | −1.29305 | −0.646524 | − | 0.762894i | \(-0.723778\pi\) | ||||
−0.646524 | + | 0.762894i | \(0.723778\pi\) | |||||||
\(728\) | −4.91942e13 | −0.240578 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | 6.63046e13 | 0.319838 | ||||||||
\(731\) | − | 1.78651e14i | − | 0.855889i | ||||||
\(732\) | − | 2.23499e14i | − | 1.06346i | ||||||
\(733\) | 1.07122e14 | 0.506242 | 0.253121 | − | 0.967435i | \(-0.418543\pi\) | ||||
0.253121 | + | 0.967435i | \(0.418543\pi\) | |||||||
\(734\) | −3.28004e14 | −1.53957 | ||||||||
\(735\) | −6.61438e13 | −0.308356 | ||||||||
\(736\) | 1.88221e14 | 0.871523 | ||||||||
\(737\) | 2.20975e13 | 0.101626 | ||||||||
\(738\) | 3.30463e13i | 0.150953i | ||||||||
\(739\) | − | 1.38816e14i | − | 0.629821i | −0.949121 | − | 0.314911i | \(-0.898025\pi\) | ||
0.949121 | − | 0.314911i | \(-0.101975\pi\) | |||||||
\(740\) | 1.55067e14i | 0.698811i | ||||||||
\(741\) | 2.09266e14i | 0.936717i | ||||||||
\(742\) | 6.24772e14i | 2.77780i | ||||||||
\(743\) | 4.74890e13 | 0.209725 | 0.104862 | − | 0.994487i | \(-0.466560\pi\) | ||||
0.104862 | + | 0.994487i | \(0.466560\pi\) | |||||||
\(744\) | −2.09951e13 | −0.0920986 | ||||||||
\(745\) | 2.45854e14i | 1.07126i | ||||||||
\(746\) | − | 5.58698e14i | − | 2.41815i | ||||||
\(747\) | 9.63092e13i | 0.414062i | ||||||||
\(748\) | 2.19665e14i | 0.938110i | ||||||||
\(749\) | −2.51984e14 | −1.06897 | ||||||||
\(750\) | − | 1.90452e14i | − | 0.802563i | ||||||
\(751\) | 2.08342e13i | 0.0872120i | 0.999049 | + | 0.0436060i | \(0.0138846\pi\) | ||||
−0.999049 | + | 0.0436060i | \(0.986115\pi\) | |||||||
\(752\) | − | 3.17111e14i | − | 1.31863i | ||||||
\(753\) | −1.27850e13 | −0.0528114 | ||||||||
\(754\) | −4.56315e12 | −0.0187244 | ||||||||
\(755\) | 3.82493e13i | 0.155915i | ||||||||
\(756\) | −7.55269e13 | −0.305839 | ||||||||
\(757\) | −2.46077e13 | −0.0989902 | −0.0494951 | − | 0.998774i | \(-0.515761\pi\) | ||||
−0.0494951 | + | 0.998774i | \(0.515761\pi\) | |||||||
\(758\) | 5.86546e14i | 2.34399i | ||||||||
\(759\) | 5.20893e13 | 0.206795 | ||||||||
\(760\) | − | 5.63398e13i | − | 0.222202i | ||||||
\(761\) | 1.25845e14 | 0.493074 | 0.246537 | − | 0.969133i | \(-0.420707\pi\) | ||||
0.246537 | + | 0.969133i | \(0.420707\pi\) | |||||||
\(762\) | − | 2.61557e14i | − | 1.01810i | ||||||
\(763\) | 5.24237e14i | 2.02724i | ||||||||
\(764\) | 3.50079e14i | 1.34493i | ||||||||
\(765\) | 6.89822e13 | 0.263287 | ||||||||
\(766\) | − | 1.12861e14i | − | 0.427957i | ||||||
\(767\) | −8.70104e13 | + | 2.06494e14i | −0.327789 | + | 0.777912i | ||||
\(768\) | 1.02594e14 | 0.383985 | ||||||||
\(769\) | − | 4.86302e14i | − | 1.80832i | −0.427198 | − | 0.904158i | \(-0.640499\pi\) | ||
0.427198 | − | 0.904158i | \(-0.359501\pi\) | |||||||
\(770\) | −1.84069e14 | −0.680028 | ||||||||
\(771\) | −3.57958e13 | −0.131389 | ||||||||
\(772\) | −3.86023e14 | −1.40775 | ||||||||
\(773\) | − | 5.16389e14i | − | 1.87102i | −0.353294 | − | 0.935512i | \(-0.614938\pi\) | ||
0.353294 | − | 0.935512i | \(-0.385062\pi\) | |||||||
\(774\) | 8.30168e13 | 0.298855 | ||||||||
\(775\) | − | 1.48390e14i | − | 0.530758i | ||||||
\(776\) | 2.57010e13 | 0.0913358 | ||||||||
\(777\) | 2.47138e14i | 0.872639i | ||||||||
\(778\) | − | 6.66079e13i | − | 0.233683i | ||||||
\(779\) | −1.70694e14 | −0.595020 | ||||||||
\(780\) | 9.07132e13i | 0.314194i | ||||||||
\(781\) | 9.97497e13i | 0.343286i | ||||||||
\(782\) | 3.62986e14 | 1.24124 | ||||||||
\(783\) | −8.58885e11 | −0.00291828 | ||||||||
\(784\) | −2.35138e14 | −0.793857 | ||||||||
\(785\) | − | 3.15380e13i | − | 0.105800i | ||||||
\(786\) | 2.01591e14 | 0.671984 | ||||||||
\(787\) | −3.53830e14 | −1.17198 | −0.585990 | − | 0.810318i | \(-0.699294\pi\) | ||||
−0.585990 | + | 0.810318i | \(0.699294\pi\) | |||||||
\(788\) | 8.55313e13 | 0.281510 | ||||||||
\(789\) | −1.02928e14 | −0.336627 | ||||||||
\(790\) | 4.40104e13i | 0.143027i | ||||||||
\(791\) | − | 1.58696e14i | − | 0.512487i | ||||||
\(792\) | −1.25143e13 | −0.0401586 | ||||||||
\(793\) | −4.27824e14 | −1.36427 | ||||||||
\(794\) | 5.71645e14 | 1.81144 | ||||||||
\(795\) | 1.41241e14 | 0.444759 | ||||||||
\(796\) | 1.94174e14 | 0.607610 | ||||||||
\(797\) | − | 6.12913e13i | − | 0.190593i | −0.995449 | − | 0.0952966i | \(-0.969620\pi\) | ||
0.995449 | − | 0.0952966i | \(-0.0303800\pi\) | |||||||
\(798\) | − | 7.32411e14i | − | 2.26329i | ||||||
\(799\) | − | 7.13190e14i | − | 2.19014i | ||||||
\(800\) | − | 3.19604e14i | − | 0.975353i | ||||||
\(801\) | 3.44043e13i | 0.104340i | ||||||||
\(802\) | −6.48562e14 | −1.95470 | ||||||||
\(803\) | 7.60728e13 | 0.227851 | ||||||||
\(804\) | 3.81144e13i | 0.113451i | ||||||||
\(805\) | 1.62014e14i | 0.479261i | ||||||||
\(806\) | 3.27813e14i | 0.963720i | ||||||||
\(807\) | 1.95858e14i | 0.572234i | ||||||||
\(808\) | 2.66884e13 | 0.0774937 | ||||||||
\(809\) | 8.68518e13i | 0.250632i | 0.992117 | + | 0.125316i | \(0.0399944\pi\) | ||||
−0.992117 | + | 0.125316i | \(0.960006\pi\) | |||||||
\(810\) | 3.20552e13i | 0.0919333i | ||||||||
\(811\) | 4.87840e13i | 0.139051i | 0.997580 | + | 0.0695253i | \(0.0221485\pi\) | ||||
−0.997580 | + | 0.0695253i | \(0.977852\pi\) | |||||||
\(812\) | 8.50674e12 | 0.0240981 | ||||||||
\(813\) | −1.39757e13 | −0.0393480 | ||||||||
\(814\) | 3.34011e14i | 0.934628i | ||||||||
\(815\) | −2.82410e14 | −0.785401 | ||||||||
\(816\) | 2.45228e14 | 0.677829 | ||||||||
\(817\) | 4.28807e14i | 1.17802i | ||||||||
\(818\) | 5.12158e14 | 1.39842 | ||||||||
\(819\) | 1.44575e14i | 0.392349i | ||||||||
\(820\) | −7.39929e13 | −0.199582 | ||||||||
\(821\) | − | 3.20044e14i | − | 0.858014i | −0.903301 | − | 0.429007i | \(-0.858864\pi\) | ||
0.903301 | − | 0.429007i | \(-0.141136\pi\) | |||||||
\(822\) | − | 9.35644e13i | − | 0.249317i | ||||||
\(823\) | − | 7.44070e13i | − | 0.197067i | −0.995134 | − | 0.0985337i | \(-0.968585\pi\) | ||
0.995134 | − | 0.0985337i | \(-0.0314152\pi\) | |||||||
\(824\) | 1.38237e14 | 0.363905 | ||||||||
\(825\) | − | 8.84488e13i | − | 0.231431i | ||||||
\(826\) | 3.04528e14 | − | 7.22708e14i | 0.792003 | − | 1.87959i | ||||
\(827\) | −5.49597e14 | −1.42075 | −0.710373 | − | 0.703825i | \(-0.751474\pi\) | ||||
−0.710373 | + | 0.703825i | \(0.751474\pi\) | |||||||
\(828\) | 8.98451e13i | 0.230857i | ||||||||
\(829\) | 4.80400e14 | 1.22696 | 0.613479 | − | 0.789711i | \(-0.289769\pi\) | ||||
0.613479 | + | 0.789711i | \(0.289769\pi\) | |||||||
\(830\) | −4.04848e14 | −1.02778 | ||||||||
\(831\) | 5.21854e13 | 0.131687 | ||||||||
\(832\) | 4.23100e14i | 1.06127i | ||||||||
\(833\) | −5.28830e14 | −1.31853 | ||||||||
\(834\) | − | 3.48290e13i | − | 0.0863199i | ||||||
\(835\) | 1.62123e14 | 0.399403 | ||||||||
\(836\) | − | 5.27252e14i | − | 1.29118i | ||||||
\(837\) | 6.17016e13i | 0.150200i | ||||||||
\(838\) | 3.89229e14 | 0.941858 | ||||||||
\(839\) | − | 5.38116e14i | − | 1.29439i | −0.762323 | − | 0.647197i | \(-0.775941\pi\) | ||
0.762323 | − | 0.647197i | \(-0.224059\pi\) | |||||||
\(840\) | − | 3.89232e13i | − | 0.0930704i | ||||||
\(841\) | −4.20610e14 | −0.999770 | ||||||||
\(842\) | −3.21976e13 | −0.0760788 | ||||||||
\(843\) | −9.77909e13 | −0.229700 | ||||||||
\(844\) | − | 8.25992e14i | − | 1.92870i | ||||||
\(845\) | −7.00355e13 | −0.162568 | ||||||||
\(846\) | 3.31411e14 | 0.764742 | ||||||||
\(847\) | 3.96655e14 | 0.909906 | ||||||||
\(848\) | 5.02104e14 | 1.14502 | ||||||||
\(849\) | 4.56708e14i | 1.03538i | ||||||||
\(850\) | − | 6.16359e14i | − | 1.38912i | ||||||
\(851\) | 2.93990e14 | 0.658695 | ||||||||
\(852\) | −1.72051e14 | −0.383230 | ||||||||
\(853\) | 2.66754e14 | 0.590698 | 0.295349 | − | 0.955389i | \(-0.404564\pi\) | ||||
0.295349 | + | 0.955389i | \(0.404564\pi\) | |||||||
\(854\) | 1.49734e15 | 3.29634 | ||||||||
\(855\) | −1.65575e14 | −0.362379 | ||||||||
\(856\) | − | 7.20148e13i | − | 0.156694i | ||||||
\(857\) | − | 6.07947e14i | − | 1.31511i | −0.753407 | − | 0.657555i | \(-0.771591\pi\) | ||
0.753407 | − | 0.657555i | \(-0.228409\pi\) | |||||||
\(858\) | 1.95395e14i | 0.420220i | ||||||||
\(859\) | 6.97204e14i | 1.49071i | 0.666666 | + | 0.745357i | \(0.267721\pi\) | ||||
−0.666666 | + | 0.745357i | \(0.732279\pi\) | |||||||
\(860\) | 1.85880e14i | 0.395130i | ||||||||
\(861\) | −1.17927e14 | −0.249227 | ||||||||
\(862\) | 9.17713e14 | 1.92828 | ||||||||
\(863\) | 3.15027e14i | 0.658102i | 0.944312 | + | 0.329051i | \(0.106729\pi\) | ||||
−0.944312 | + | 0.329051i | \(0.893271\pi\) | |||||||
\(864\) | 1.32893e14i | 0.276016i | ||||||||
\(865\) | 2.26510e14i | 0.467743i | ||||||||
\(866\) | 1.22940e14i | 0.252409i | ||||||||
\(867\) | 2.68688e14 | 0.548469 | ||||||||
\(868\) | − | 6.11117e14i | − | 1.24030i | ||||||
\(869\) | 5.04941e13i | 0.101892i | ||||||||
\(870\) | − | 3.61043e12i | − | 0.00724375i | ||||||
\(871\) | 7.29592e13 | 0.145542 | ||||||||
\(872\) | −1.49822e14 | −0.297162 | ||||||||
\(873\) | − | 7.55315e13i | − | 0.148956i | ||||||
\(874\) | −8.71259e14 | −1.70840 | ||||||||
\(875\) | 6.79632e14 | 1.32505 | ||||||||
\(876\) | 1.31212e14i | 0.254363i | ||||||||
\(877\) | −1.50156e14 | −0.289431 | −0.144716 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144716 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(878\) | − | 1.54636e14i | − | 0.296372i | ||||||
\(879\) | −5.07052e14 | −0.966292 | ||||||||
\(880\) | 1.47929e14i | 0.280311i | ||||||||
\(881\) | 4.08782e14i | 0.770215i | 0.922872 | + | 0.385107i | \(0.125836\pi\) | ||||
−0.922872 | + | 0.385107i | \(0.874164\pi\) | |||||||
\(882\) | − | 2.45741e14i | − | 0.460399i | ||||||
\(883\) | 7.57877e14 | 1.41187 | 0.705936 | − | 0.708276i | \(-0.250527\pi\) | ||||
0.705936 | + | 0.708276i | \(0.250527\pi\) | |||||||
\(884\) | 7.25267e14i | 1.34350i | ||||||||
\(885\) | −1.63381e14 | − | 6.88440e13i | −0.300944 | − | 0.126809i | ||||
\(886\) | 1.38549e15 | 2.53767 | ||||||||
\(887\) | 4.73147e14i | 0.861743i | 0.902413 | + | 0.430872i | \(0.141794\pi\) | ||||
−0.902413 | + | 0.430872i | \(0.858206\pi\) | |||||||
\(888\) | −7.06299e13 | −0.127916 | ||||||||
\(889\) | 9.33374e14 | 1.68092 | ||||||||
\(890\) | −1.44623e14 | −0.258992 | ||||||||
\(891\) | 3.67776e13i | 0.0654930i | ||||||||
\(892\) | 5.47144e14 | 0.968896 | ||||||||
\(893\) | 1.71184e15i | 3.01443i | ||||||||
\(894\) | −9.13409e14 | −1.59948 | ||||||||
\(895\) | − | 1.08746e14i | − | 0.189364i | ||||||
\(896\) | − | 3.25946e14i | − | 0.564424i | ||||||
\(897\) | 1.71983e14 | 0.296157 | ||||||||
\(898\) | − | 1.25140e15i | − | 2.14297i | ||||||
\(899\) | − | 6.94957e12i | − | 0.0118348i | ||||||
\(900\) | 1.52559e14 | 0.258360 | ||||||||
\(901\) | 1.12924e15 | 1.90179 | ||||||||
\(902\) | −1.59380e14 | −0.266932 | ||||||||
\(903\) | 2.96247e14i | 0.493419i | ||||||||
\(904\) | 4.53538e13 | 0.0751228 | ||||||||
\(905\) | 2.18404e14 | 0.359765 | ||||||||
\(906\) | −1.42106e14 | −0.232794 | ||||||||
\(907\) | −2.82055e14 | −0.459513 | −0.229756 | − | 0.973248i | \(-0.573793\pi\) | ||||
−0.229756 | + | 0.973248i | \(0.573793\pi\) | |||||||
\(908\) | − | 6.81733e13i | − | 0.110455i | ||||||
\(909\) | − | 7.84336e13i | − | 0.126381i | ||||||
\(910\) | −6.07738e14 | −0.973889 | ||||||||
\(911\) | 5.76841e14 | 0.919314 | 0.459657 | − | 0.888096i | \(-0.347972\pi\) | ||||
0.459657 | + | 0.888096i | \(0.347972\pi\) | |||||||
\(912\) | −5.88610e14 | −0.932940 | ||||||||
\(913\) | −4.64491e14 | −0.732190 | ||||||||
\(914\) | −1.69768e15 | −2.66149 | ||||||||
\(915\) | − | 3.38501e14i | − | 0.527782i | ||||||
\(916\) | − | 4.21128e14i | − | 0.653035i | ||||||
\(917\) | 7.19384e14i | 1.10947i | ||||||||
\(918\) | 2.56286e14i | 0.393108i | ||||||||
\(919\) | 1.81901e14i | 0.277496i | 0.990328 | + | 0.138748i | \(0.0443079\pi\) | ||||
−0.990328 | + | 0.138748i | \(0.955692\pi\) | |||||||
\(920\) | −4.63021e13 | −0.0702525 | ||||||||
\(921\) | 7.06152e14 | 1.06561 | ||||||||
\(922\) | − | 2.93507e14i | − | 0.440519i | ||||||
\(923\) | 3.29343e14i | 0.491631i | ||||||||
\(924\) | − | 3.64260e14i | − | 0.540819i | ||||||
\(925\) | − | 4.99202e14i | − | 0.737169i | ||||||
\(926\) | 4.08400e14 | 0.599834 | ||||||||
\(927\) | − | 4.06259e14i | − | 0.593478i | ||||||
\(928\) | − | 1.49680e13i | − | 0.0217483i | ||||||
\(929\) | 2.71549e14i | 0.392436i | 0.980560 | + | 0.196218i | \(0.0628661\pi\) | ||||
−0.980560 | + | 0.196218i | \(0.937134\pi\) | |||||||
\(930\) | −2.59370e14 | −0.372826 | ||||||||
\(931\) | 1.26933e15 | 1.81478 | ||||||||
\(932\) | − | 9.32986e14i | − | 1.32677i | ||||||
\(933\) | 1.55372e14 | 0.219767 | ||||||||
\(934\) | −4.75161e14 | −0.668508 | ||||||||
\(935\) | 3.32695e14i | 0.465574i | ||||||||
\(936\) | −4.13182e13 | −0.0575125 | ||||||||
\(937\) | 3.79809e12i | 0.00525856i | 0.999997 | + | 0.00262928i | \(0.000836927\pi\) | ||||
−0.999997 | + | 0.00262928i | \(0.999163\pi\) | |||||||
\(938\) | −2.55350e14 | −0.351659 | ||||||||
\(939\) | − | 8.38616e14i | − | 1.14878i | ||||||
\(940\) | 7.42051e14i | 1.01110i | ||||||||
\(941\) | − | 5.88769e14i | − | 0.797988i | −0.916953 | − | 0.398994i | \(-0.869359\pi\) | ||
0.916953 | − | 0.398994i | \(-0.130641\pi\) | |||||||
\(942\) | 1.17172e14 | 0.157968 | ||||||||
\(943\) | 1.40283e14i | 0.188125i | ||||||||
\(944\) | −5.80812e14 | − | 2.44737e14i | −0.774775 | − | 0.326467i | ||||
\(945\) | −1.14390e14 | −0.151785 | ||||||||
\(946\) | 4.00383e14i | 0.528469i | ||||||||
\(947\) | 3.10228e14 | 0.407315 | 0.203658 | − | 0.979042i | \(-0.434717\pi\) | ||||
0.203658 | + | 0.979042i | \(0.434717\pi\) | |||||||
\(948\) | −8.70936e13 | −0.113748 | ||||||||
\(949\) | 2.51169e14 | 0.326313 | ||||||||
\(950\) | 1.47942e15i | 1.91193i | ||||||||
\(951\) | 6.34730e14 | 0.815994 | ||||||||
\(952\) | − | 3.11197e14i | − | 0.397971i | ||||||
\(953\) | −4.33173e14 | −0.551057 | −0.275529 | − | 0.961293i | \(-0.588853\pi\) | ||||
−0.275529 | + | 0.961293i | \(0.588853\pi\) | |||||||
\(954\) | 5.24746e14i | 0.664059i | ||||||||
\(955\) | 5.30214e14i | 0.667474i | ||||||||
\(956\) | −1.19353e15 | −1.49466 | ||||||||
\(957\) | − | 4.14233e12i | − | 0.00516042i | ||||||
\(958\) | 1.41529e15i | 1.75395i | ||||||||
\(959\) | 3.33887e14 | 0.411630 | ||||||||
\(960\) | −3.34763e14 | −0.410564 | ||||||||
\(961\) | 3.20377e14 | 0.390881 | ||||||||
\(962\) | 1.10280e15i | 1.33851i | ||||||||
\(963\) | −2.11641e14 | −0.255546 | ||||||||
\(964\) | 1.48498e15 | 1.78376 | ||||||||
\(965\) | −5.84653e14 | −0.698653 | ||||||||
\(966\) | −6.01922e14 | −0.715574 | ||||||||
\(967\) | 4.55402e14i | 0.538595i | 0.963057 | + | 0.269297i | \(0.0867915\pi\) | ||||
−0.963057 | + | 0.269297i | \(0.913209\pi\) | |||||||
\(968\) | 1.13361e14i | 0.133378i | ||||||||
\(969\) | −1.32380e15 | −1.54954 | ||||||||
\(970\) | 3.17506e14 | 0.369738 | ||||||||
\(971\) | 2.88128e14 | 0.333802 | 0.166901 | − | 0.985974i | \(-0.446624\pi\) | ||||
0.166901 | + | 0.985974i | \(0.446624\pi\) | |||||||
\(972\) | −6.34351e13 | −0.0731136 | ||||||||
\(973\) | 1.24288e14 | 0.142517 | ||||||||
\(974\) | 1.73041e15i | 1.97404i | ||||||||
\(975\) | − | 2.92031e14i | − | 0.331440i | ||||||
\(976\) | − | 1.20336e15i | − | 1.35877i | ||||||
\(977\) | 8.29144e14i | 0.931444i | 0.884931 | + | 0.465722i | \(0.154205\pi\) | ||||
−0.884931 | + | 0.465722i | \(0.845795\pi\) | |||||||
\(978\) | − | 1.04922e15i | − | 1.17266i | ||||||
\(979\) | −1.65929e14 | −0.184505 | ||||||||
\(980\) | 5.50230e14 | 0.608715 | ||||||||
\(981\) | 4.40306e14i | 0.484630i | ||||||||
\(982\) | 3.87751e14i | 0.424615i | ||||||||
\(983\) | 6.86977e13i | 0.0748471i | 0.999299 | + | 0.0374235i | \(0.0119151\pi\) | ||||
−0.999299 | + | 0.0374235i | \(0.988085\pi\) | |||||||
\(984\) | − | 3.37024e13i | − | 0.0365330i | ||||||
\(985\) | 1.29542e14 | 0.139710 | ||||||||
\(986\) | − | 2.88660e13i | − | 0.0309744i | ||||||
\(987\) | 1.18265e15i | 1.26261i | ||||||||
\(988\) | − | 1.74082e15i | − | 1.84914i | ||||||
\(989\) | 3.52409e14 | 0.372448 | ||||||||
\(990\) | −1.54599e14 | −0.162567 | ||||||||
\(991\) | 4.35728e14i | 0.455876i | 0.973676 | + | 0.227938i | \(0.0731984\pi\) | ||||
−0.973676 | + | 0.227938i | \(0.926802\pi\) | |||||||
\(992\) | −1.07529e15 | −1.11935 | ||||||||
\(993\) | −5.35812e14 | −0.554965 | ||||||||
\(994\) | − | 1.15267e15i | − | 1.18788i | ||||||
\(995\) | 2.94087e14 | 0.301551 | ||||||||
\(996\) | − | 8.01168e14i | − | 0.817385i | ||||||
\(997\) | 8.47152e14 | 0.859974 | 0.429987 | − | 0.902835i | \(-0.358518\pi\) | ||||
0.429987 | + | 0.902835i | \(0.358518\pi\) | |||||||
\(998\) | 2.29047e15i | 2.31351i | ||||||||
\(999\) | 2.07571e14i | 0.208612i |
(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.58.17 | ✓ | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.84 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.17 | ✓ | 100 | 1.1 | even | 1 | trivial | |
177.11.c.a.58.84 | yes | 100 | 59.58 | odd | 2 | inner |