Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,12,Mod(41,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.41");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.f (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: | \(64.5408271670\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.10 | ||
Character | \(\chi\) | \(=\) | 84.41 |
Dual form | 84.12.f.b.41.9 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −240.448 | + | 345.444i | −0.571287 | + | 0.820751i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 113.306 | 0.0162150 | 0.00810752 | − | 0.999967i | \(-0.497419\pi\) | ||||
0.00810752 | + | 0.999967i | \(0.497419\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 44008.9 | − | 6367.04i | 0.989696 | − | 0.143185i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −61516.6 | − | 166123.i | −0.347263 | − | 0.937768i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 471963.i | 0.883585i | 0.897117 | + | 0.441793i | \(0.145657\pi\) | ||||
−0.897117 | + | 0.441793i | \(0.854343\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.52458e6i | − | 1.13884i | −0.822048 | − | 0.569419i | \(-0.807168\pi\) | ||
0.822048 | − | 0.569419i | \(-0.192832\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −27244.2 | + | 39141.0i | −0.00926344 | + | 0.0133085i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.63168e6 | −0.278718 | −0.139359 | − | 0.990242i | \(-0.544504\pi\) | ||||
−0.139359 | + | 0.990242i | \(0.544504\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.97596e6i | − | 0.275729i | −0.990451 | − | 0.137864i | \(-0.955976\pi\) | ||
0.990451 | − | 0.137864i | \(-0.0440238\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.38240e6 | + | 1.67336e7i | −0.447881 | + | 0.894093i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.79258e7i | 0.904697i | 0.891841 | + | 0.452348i | \(0.149414\pi\) | ||||
−0.891841 | + | 0.452348i | \(0.850586\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88153e7 | −0.999737 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.21777e7 | + | 1.86933e7i | 0.968060 | + | 0.250718i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.72679e8i | 1.56333i | 0.623702 | + | 0.781663i | \(0.285628\pi\) | ||||
−0.623702 | + | 0.781663i | \(0.714372\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.77394e7i | − | 0.424964i | −0.977165 | − | 0.212482i | \(-0.931845\pi\) | ||
0.977165 | − | 0.212482i | \(-0.0681546\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.63037e8 | − | 1.13483e8i | −0.725203 | − | 0.504780i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.98648e6 | − | 721424.i | 0.0160480 | − | 0.00232175i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.11171e8 | −0.500640 | −0.250320 | − | 0.968163i | \(-0.580536\pi\) | ||||
−0.250320 | + | 0.968163i | \(0.580536\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.26658e8 | + | 3.66582e8i | 0.934702 | + | 0.650603i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.13330e9 | −1.52769 | −0.763845 | − | 0.645400i | \(-0.776691\pi\) | ||||
−0.763845 | + | 0.645400i | \(0.776691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.22129e9 | −1.26690 | −0.633451 | − | 0.773782i | \(-0.718362\pi\) | ||||
−0.633451 | + | 0.773782i | \(0.718362\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.97021e6 | − | 1.88227e7i | −0.00563089 | − | 0.0152059i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.73123e9 | 1.73708 | 0.868540 | − | 0.495618i | \(-0.165058\pi\) | ||||
0.868540 | + | 0.495618i | \(0.165058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.89625e9 | − | 5.60413e8i | 0.958996 | − | 0.283420i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.92333e8 | − | 5.63654e8i | 0.159228 | − | 0.228758i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.10043e9i | − | 1.34683i | −0.739266 | − | 0.673413i | \(-0.764827\pi\) | ||
0.739266 | − | 0.673413i | \(-0.235173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.34763e7i | 0.0143274i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.02803e9 | + | 7.15563e8i | 0.226305 | + | 0.157520i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.33617e9 | −1.70013 | −0.850066 | − | 0.526676i | \(-0.823438\pi\) | ||||
−0.850066 | + | 0.526676i | \(0.823438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.27679e9i | − | 1.40632i | −0.711033 | − | 0.703159i | \(-0.751772\pi\) | ||
0.711033 | − | 0.703159i | \(-0.248228\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.76499e9 | − | 6.91921e9i | −0.477959 | − | 0.878382i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.72744e8i | − | 0.0184663i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.31784e9 | 0.843148 | 0.421574 | − | 0.906794i | \(-0.361478\pi\) | ||||
0.421574 | + | 0.906794i | \(0.361478\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.64682e9 | − | 6.71471e9i | −0.742531 | − | 0.516841i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.13341e9i | − | 0.0745535i | −0.999305 | − | 0.0372767i | \(-0.988132\pi\) | ||
0.999305 | − | 0.0372767i | \(-0.0118683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.18753e10i | − | 0.670456i | −0.942137 | − | 0.335228i | \(-0.891187\pi\) | ||
0.942137 | − | 0.335228i | \(-0.108813\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.17375e10 | − | 1.68630e10i | 0.571136 | − | 0.820535i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00501e9 | + | 2.07706e10i | 0.126516 | + | 0.874481i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.57625e9 | 0.0941974 | 0.0470987 | − | 0.998890i | \(-0.485002\pi\) | ||||
0.0470987 | + | 0.998890i | \(0.485002\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.38125e10 | + | 2.04386e10i | −0.758817 | + | 0.651304i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.83358e10 | −1.06826 | −0.534128 | − | 0.845404i | \(-0.679360\pi\) | ||||
−0.534128 | + | 0.845404i | \(0.679360\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.84879e8 | −0.00451943 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.96508e10 | − | 4.15202e10i | −1.28310 | − | 0.893107i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.88289e10 | −0.926898 | −0.463449 | − | 0.886124i | \(-0.653388\pi\) | ||||
−0.463449 | + | 0.886124i | \(0.653388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.70706e9 | − | 6.70952e10i | −0.163065 | − | 1.12710i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.34002e10 | + | 1.62878e10i | 0.348789 | + | 0.242776i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 3.37194e8i | − | 0.00447096i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.23963e11i | − | 1.46570i | −0.680388 | − | 0.732852i | \(-0.738189\pi\) | ||
0.680388 | − | 0.732852i | \(-0.261811\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.84038e10 | − | 2.90336e10i | 0.828598 | − | 0.306836i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.69904e10 | −0.634227 | −0.317114 | − | 0.948388i | \(-0.602714\pi\) | ||||
−0.317114 | + | 0.948388i | \(0.602714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.17600e11i | − | 0.999542i | −0.866158 | − | 0.499771i | \(-0.833417\pi\) | ||
0.866158 | − | 0.499771i | \(-0.166583\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.49777e8 | + | 1.89602e9i | −0.00726241 | + | 0.0144978i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.80768e11i | − | 1.24598i | −0.782229 | − | 0.622991i | \(-0.785917\pi\) | ||
0.782229 | − | 0.622991i | \(-0.214083\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.05519e10 | −0.190192 | −0.0950962 | − | 0.995468i | \(-0.530316\pi\) | ||||
−0.0950962 | + | 0.995468i | \(0.530316\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.07757e10 | − | 7.29480e10i | 0.286009 | − | 0.410901i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.95662e10i | 0.0999021i | 0.998752 | + | 0.0499510i | \(0.0159065\pi\) | ||||
−0.998752 | + | 0.0499510i | \(0.984093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.16417e9i | 0.0146697i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.53267e11 | + | 9.37870e10i | −1.06797 | + | 0.395476i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.18084e10 | + | 1.03889e10i | −0.275846 | + | 0.0399083i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.25624e10 | 0.219277 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.72501e11 | − | 3.91494e11i | 0.872749 | − | 1.25385i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.10636e10 | −0.0324258 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.23978e11 | −0.332985 | −0.166492 | − | 0.986043i | \(-0.553244\pi\) | ||||
−0.166492 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.93657e11 | − | 4.21889e11i | 0.723765 | − | 1.03981i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.22104e11 | −0.502995 | −0.251497 | − | 0.967858i | \(-0.580923\pi\) | ||||
−0.251497 | + | 0.967858i | \(0.580923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.89480e10 | − | 1.30969e11i | −0.0394803 | − | 0.272888i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.17817e9 | + | 2.11806e9i | 0.0156971 | + | 0.00406540i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.28893e11i | 0.759252i | 0.925140 | + | 0.379626i | \(0.123947\pi\) | ||||
−0.925140 | + | 0.379626i | \(0.876053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.91079e11i | 0.475806i | 0.971289 | + | 0.237903i | \(0.0764600\pi\) | ||||
−0.971289 | + | 0.237903i | \(0.923540\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.56719e11 | + | 9.43488e11i | −0.992371 | + | 1.42571i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.19546e11 | 1.00626 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.95655e10i | 0.0253494i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.62357e11 | + | 7.89798e11i | −0.315245 | + | 0.949010i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3.55911e11i | − | 0.397024i | −0.980098 | − | 0.198512i | \(-0.936389\pi\) | ||
0.980098 | − | 0.198512i | \(-0.0636109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.84819e11 | −0.191591 | −0.0957954 | − | 0.995401i | \(-0.530539\pi\) | ||||
−0.0957954 | + | 0.995401i | \(0.530539\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.00375e11 | + | 2.71059e11i | 0.0967885 | + | 0.261373i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 7.67528e9i | − | 0.00689081i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.75361e12i | 1.46719i | 0.679589 | + | 0.733593i | \(0.262158\pi\) | ||||
−0.679589 | + | 0.733593i | \(0.737842\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.41647e12 | + | 9.85939e11i | 1.10541 | + | 0.769424i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.77805e11 | + | 1.22899e12i | 0.129539 | + | 0.895375i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.54989e11 | −0.173576 | −0.0867880 | − | 0.996227i | \(-0.527660\pi\) | ||||
−0.0867880 | + | 0.996227i | \(0.527660\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.84731e10 | − | 1.28583e10i | −0.0117592 | − | 0.00818504i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.69349e11 | 0.398760 | 0.199380 | − | 0.979922i | \(-0.436107\pi\) | ||||
0.199380 | + | 0.979922i | \(0.436107\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.32184e11 | −0.296951 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.94375e11 | + | 1.83071e11i | −0.258570 | + | 0.0957504i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.24751e12 | 1.10268 | 0.551338 | − | 0.834282i | \(-0.314118\pi\) | ||||
0.551338 | + | 0.834282i | \(0.314118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.14831e12 | + | 3.10809e11i | −0.989436 | + | 0.143148i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.24486e12 | − | 3.22513e12i | 0.971263 | − | 1.39538i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.24133e12i | − | 0.504890i | −0.967611 | − | 0.252445i | \(-0.918765\pi\) | ||
0.967611 | − | 0.252445i | \(-0.0812347\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.74804e12i | 1.43407i | 0.697035 | + | 0.717037i | \(0.254502\pi\) | ||||
−0.697035 | + | 0.717037i | \(0.745498\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.20461e12 | + | 2.23058e12i | 1.15424 | + | 0.803411i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.39270e10 | −0.00811791 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.70091e11i | − | 0.246271i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.29549e12 | + | 3.63114e11i | 0.993984 | + | 0.109523i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.80965e12i | − | 1.36908i | −0.728973 | − | 0.684542i | \(-0.760002\pi\) | ||
0.728973 | − | 0.684542i | \(-0.239998\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.81562e12 | −0.756849 | −0.378425 | − | 0.925632i | \(-0.623534\pi\) | ||||
−0.378425 | + | 0.925632i | \(0.623534\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.96735e10 | + | 4.15360e10i | 0.0151562 | + | 0.0105496i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.63844e10i | − | 0.00633554i | −0.999995 | − | 0.00316777i | \(-0.998992\pi\) | ||
0.999995 | − | 0.00316777i | \(-0.00100833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.49140e12i | 0.338767i | 0.985550 | + | 0.169383i | \(0.0541776\pi\) | ||||
−0.985550 | + | 0.169383i | \(0.945822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.24045e12 | + | 3.21879e12i | −0.481679 | + | 0.692014i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.09945e12 | + | 7.59940e12i | 0.223845 | + | 1.54722i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.28410e11 | −0.0247716 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.63912e12 | − | 1.71790e12i | 0.848396 | − | 0.314168i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.40454e12 | 0.243630 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.03449e13 | −1.70283 | −0.851416 | − | 0.524491i | \(-0.824256\pi\) | ||||
−0.851416 | + | 0.524491i | \(0.824256\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.91532e11 | + | 2.72527e11i | 0.0611898 | + | 0.0425914i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.38380e11 | −0.0205429 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.31299e11 | − | 2.98114e12i | −0.0608485 | − | 0.420585i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.10227e12 | + | 2.85540e12i | 0.550277 | + | 0.383023i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.48762e12i | 0.317415i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.16788e13i | − | 1.41815i | −0.705133 | − | 0.709075i | \(-0.749113\pi\) | ||
0.705133 | − | 0.709075i | \(-0.250887\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00295e12 | + | 8.10933e12i | 0.347172 | + | 0.937521i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.14378e13 | −1.25950 | −0.629751 | − | 0.776797i | \(-0.716843\pi\) | ||||
−0.629751 | + | 0.776797i | \(0.716843\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.18535e12i | 0.124380i | 0.998064 | + | 0.0621901i | \(0.0198085\pi\) | ||||
−0.998064 | + | 0.0621901i | \(0.980192\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.89764e12 | − | 3.95619e12i | −0.790007 | − | 0.395741i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.79976e13i | − | 1.71694i | −0.512860 | − | 0.858472i | \(-0.671414\pi\) | ||
0.512860 | − | 0.858472i | \(-0.328586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.09465e11 | 0.0281669 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.19453e11 | + | 8.89950e11i | −0.0538137 | + | 0.0773125i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.99328e13i | 1.65341i | 0.562639 | + | 0.826703i | \(0.309786\pi\) | ||||
−0.562639 | + | 0.826703i | \(0.690214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.50138e13i | − | 1.18959i | −0.803879 | − | 0.594793i | \(-0.797234\pi\) | ||
0.803879 | − | 0.594793i | \(-0.202766\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.33475e12 | − | 1.31403e13i | −0.101056 | − | 0.994881i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.14857e11 | − | 6.34982e10i | 0.0155502 | − | 0.00459566i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.53709e12 | −0.314010 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.21776e12 | − | 1.32429e13i | 0.610280 | − | 0.876771i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.21675e12 | −0.457231 | −0.228616 | − | 0.973517i | \(-0.573420\pi\) | ||||
−0.228616 | + | 0.973517i | \(0.573420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31800e13 | −0.799377 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.44538e10 | − | 6.38654e10i | 0.00258189 | − | 0.00370932i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.35142e13 | −1.30827 | −0.654136 | − | 0.756377i | \(-0.726968\pi\) | ||||
−0.654136 | + | 0.756377i | \(0.726968\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.29344e12 | + | 1.34454e12i | −0.495482 | + | 0.0716843i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.86858e13 | − | 1.06226e13i | 1.46604 | − | 0.542885i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.15132e13i | − | 0.564209i | −0.959384 | − | 0.282105i | \(-0.908967\pi\) | ||
0.959384 | − | 0.282105i | \(-0.0910325\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.64603e11i | − | 0.0218389i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.17408e13 | − | 1.68677e13i | 0.529525 | − | 0.760752i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.61870e13 | 1.13357 | 0.566784 | − | 0.823866i | \(-0.308187\pi\) | ||||
0.566784 | + | 0.823866i | \(0.308187\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.74929e13i | − | 0.726993i | −0.931596 | − | 0.363497i | \(-0.881583\pi\) | ||
0.931596 | − | 0.363497i | \(-0.118417\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.55117e13 | + | 1.27796e13i | 1.01823 | + | 0.510063i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.30390e13i | − | 0.883353i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.77920e13 | −1.02395 | −0.511977 | − | 0.858999i | \(-0.671087\pi\) | ||||
−0.511977 | + | 0.858999i | \(0.671087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.12530e13 | + | 4.16710e12i | −0.398517 | + | 0.147574i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.10085e12i | − | 0.139633i | −0.997560 | − | 0.0698166i | \(-0.977759\pi\) | ||
0.997560 | − | 0.0698166i | \(-0.0222414\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5.14769e13i | − | 1.68573i | −0.538129 | − | 0.842863i | \(-0.680869\pi\) | ||
0.538129 | − | 0.842863i | \(-0.319131\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.16482e11 | + | 8.10777e10i | 0.00366954 | + | 0.00255420i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.98755e13 | + | 7.21579e12i | −1.51195 | + | 0.218743i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.16095e13 | −0.922316 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.28222e13 | + | 2.98065e13i | 1.20298 | + | 0.837337i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.12690e12 | 0.246917 | 0.123459 | − | 0.992350i | \(-0.460601\pi\) | ||||
0.123459 | + | 0.992350i | \(0.460601\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.05784e12 | −0.0275677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.82255e12 | + | 3.40652e13i | −0.221531 | + | 0.855364i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.25752e13 | 1.03030 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.37478e13 | + | 7.77602e12i | −1.25385 | + | 0.181402i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.61077e13 | − | 2.31414e13i | 0.362325 | − | 0.520542i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.05112e12i | − | 0.0228035i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.90280e11i | − | 0.00816799i | −0.999992 | − | 0.00408399i | \(-0.998700\pi\) | ||
0.999992 | − | 0.00408399i | \(-0.00129998\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.06241e13 | + | 2.82766e13i | 0.820375 | + | 0.571025i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.11599e13 | −0.412412 | −0.206206 | − | 0.978509i | \(-0.566112\pi\) | ||||
−0.206206 | + | 0.978509i | \(0.566112\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.94527e13i | 1.30676i | 0.757031 | + | 0.653379i | \(0.226649\pi\) | ||||
−0.757031 | + | 0.653379i | \(0.773351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.26596e11 | − | 7.83989e11i | −0.00775013 | − | 0.0142430i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.00483e14i | 1.76306i | 0.472126 | + | 0.881531i | \(0.343487\pi\) | ||||
−0.472126 | + | 0.881531i | \(0.656513\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.14979e13 | −1.38133 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.24454e13 | + | 4.34654e13i | 1.02264 | + | 0.711813i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.85580e12i | 0.0768506i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.44228e13i | 1.13854i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.34615e12 | − | 1.05540e13i | 0.108654 | − | 0.156100i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.20199e14 | − | 1.73898e13i | 1.71918 | − | 0.248724i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.85084e12 | −0.0394384 | −0.0197192 | − | 0.999806i | \(-0.506277\pi\) | ||||
−0.0197192 | + | 0.999806i | \(0.506277\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.29906e13 | + | 3.50804e13i | 0.173854 | + | 0.469484i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.05577e12 | 0.0136717 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.58892e13 | −1.07640 | −0.538200 | − | 0.842817i | \(-0.680896\pi\) | ||||
−0.538200 | + | 0.842817i | \(0.680896\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.75903e12 | − | 4.70465e12i | −0.0819947 | − | 0.0570727i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.19705e13 | 0.375492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.98837e13 | − | 3.67367e13i | 0.908533 | − | 0.417813i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.09304e12 | − | 7.60818e11i | −0.0120402 | − | 0.00838061i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 4.52064e13i | − | 0.482379i | −0.970478 | − | 0.241189i | \(-0.922462\pi\) | ||
0.970478 | − | 0.241189i | \(-0.0775375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.57965e14i | 1.63313i | 0.577255 | + | 0.816564i | \(0.304124\pi\) | ||||
−0.577255 | + | 0.816564i | \(0.695876\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.84994e13 | − | 1.10041e14i | 0.285527 | − | 1.10246i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.92063e13 | −0.574920 | −0.287460 | − | 0.957793i | \(-0.592811\pi\) | ||||
−0.287460 | + | 0.957793i | \(0.592811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.28423e11i | − | 0.00120889i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.36774e13 | − | 2.73038e13i | 0.124832 | − | 0.249200i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.18285e13i | 0.281706i | 0.990031 | + | 0.140853i | \(0.0449845\pi\) | ||||
−0.990031 | + | 0.140853i | \(0.955015\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.07634e14 | 0.923974 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.50430e13 | + | 2.16118e13i | −0.125270 | + | 0.179972i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.34555e12i | − | 0.0108715i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.52552e12i | − | 0.0198010i | −0.999951 | − | 0.00990052i | \(-0.996849\pi\) | ||
0.999951 | − | 0.00990052i | \(-0.00315149\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.97170e13 | + | 1.88268e14i | 0.530510 | + | 1.43262i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.61076e13 | − | 1.80455e14i | −0.192846 | − | 1.33295i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.93885e14 | −1.39042 | −0.695208 | − | 0.718809i | \(-0.744688\pi\) | ||||
−0.695208 | + | 0.718809i | \(0.744688\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.66022e12 | − | 3.82186e12i | 0.0185244 | − | 0.0266135i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.63262e14 | 1.78037 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.46192e13 | −0.0960304 | −0.0480152 | − | 0.998847i | \(-0.515290\pi\) | ||||
−0.0480152 | + | 0.998847i | \(0.515290\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.98103e13 | − | 4.28275e13i | 0.190230 | − | 0.273297i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.79797e13 | −0.235482 | −0.117741 | − | 0.993044i | \(-0.537565\pi\) | ||||
−0.117741 | + | 0.993044i | \(0.537565\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.40486e11 | + | 2.35344e12i | 0.00205147 | + | 0.0141797i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.51298e13 | + | 2.02885e14i | 0.439949 | + | 1.18806i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.11062e13i | 0.290905i | 0.989365 | + | 0.145452i | \(0.0464637\pi\) | ||||
−0.989365 | + | 0.145452i | \(0.953536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.55659e13i | − | 0.252155i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.34043e13 | − | 7.67244e13i | 0.287354 | − | 0.412833i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.91905e11 | 0.00152741 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8.08783e13i | − | 0.411608i | −0.978593 | − | 0.205804i | \(-0.934019\pi\) | ||
0.978593 | − | 0.205804i | \(-0.0659810\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.97985e13 | + | 2.49457e13i | 0.246527 | + | 0.123494i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.30846e13i | 0.448316i | 0.974553 | + | 0.224158i | \(0.0719631\pi\) | ||||
−0.974553 | + | 0.224158i | \(0.928037\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.03274e14 | −0.483965 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.69810e12 | + | 2.31582e12i | −0.0123043 | + | 0.0105609i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.96652e13i | − | 0.442358i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.22974e13i | − | 0.269148i | −0.990904 | − | 0.134574i | \(-0.957033\pi\) | ||
0.990904 | − | 0.134574i | \(-0.0429666\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.48159e14 | − | 1.03126e14i | −0.623157 | − | 0.433751i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.10875e14 | + | 5.94437e13i | −1.68261 | + | 0.243434i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.34368e12 | −0.0173218 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.00552e14 | − | 6.99894e13i | −0.390518 | − | 0.271822i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.19690e14 | −1.20935 | −0.604674 | − | 0.796473i | \(-0.706697\pi\) | ||||
−0.604674 | + | 0.796473i | \(0.706697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.62841e14 | 0.968595 | 0.484298 | − | 0.874903i | \(-0.339075\pi\) | ||||
0.484298 | + | 0.874903i | \(0.339075\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.68016e14 | − | 4.53719e14i | −0.603224 | − | 1.62898i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.96508e13 | 0.278645 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.90656e13 | − | 4.08262e14i | −0.201364 | − | 1.39183i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.73013e14 | + | 2.48563e14i | −0.574863 | + | 0.825888i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.43722e14i | 1.43710i | 0.695478 | + | 0.718548i | \(0.255193\pi\) | ||||
−0.695478 | + | 0.718548i | \(0.744807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.37507e14i | 1.06561i | 0.846237 | + | 0.532807i | \(0.178863\pi\) | ||||
−0.846237 | + | 0.532807i | \(0.821137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.75880e12 | − | 4.70449e12i | −0.0208055 | − | 0.0144818i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.31062e13 | 0.249451 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.82690e14i | − | 0.827477i | −0.910396 | − | 0.413738i | \(-0.864223\pi\) | ||
0.910396 | − | 0.413738i | \(-0.135777\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.09748e14 | − | 2.80535e14i | −0.598806 | − | 0.800894i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.15455e14i | 0.599979i | 0.953943 | + | 0.299989i | \(0.0969831\pi\) | ||||
−0.953943 | + | 0.299989i | \(0.903017\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.53261e12 | −0.0150297 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.22947e14 | + | 8.55780e13i | 0.325858 | + | 0.226815i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.16411e14i | − | 1.33549i | −0.744390 | − | 0.667746i | \(-0.767259\pi\) | ||
0.744390 | − | 0.667746i | \(-0.232741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.34878e14i | − | 1.34984i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.44394e13 | − | 6.38448e13i | 0.109453 | − | 0.157248i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.09987e12 | − | 7.60229e12i | −0.00264410 | − | 0.0182760i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.55705e14 | 1.30408 | 0.652042 | − | 0.758183i | \(-0.273913\pi\) | ||||
0.652042 | + | 0.758183i | \(0.273913\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.17771e14 | − | 3.05014e13i | −0.269816 | − | 0.0698796i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.68184e14 | 0.823588 | 0.411794 | − | 0.911277i | \(-0.364902\pi\) | ||||
0.411794 | + | 0.911277i | \(0.364902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.82936e14 | 1.05486 | 0.527429 | − | 0.849599i | \(-0.323156\pi\) | ||||
0.527429 | + | 0.849599i | \(0.323156\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.65138e12 | + | 1.84551e12i | 0.00565563 | + | 0.00393663i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.21669e14 | −0.878473 | −0.439237 | − | 0.898371i | \(-0.644751\pi\) | ||||
−0.439237 | + | 0.898371i | \(0.644751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.10068e14 | − | 5.93270e13i | 0.834460 | − | 0.120726i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.05775e14 | − | 4.21652e14i | −1.20419 | − | 0.838184i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.76405e14i | − | 1.11942i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.45272e14i | 0.275656i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.81174e14 | + | 2.52244e14i | −1.26301 | + | 0.467703i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.10387e14 | −1.64961 | −0.824804 | − | 0.565419i | \(-0.808715\pi\) | ||||
−0.824804 | + | 0.565419i | \(0.808715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.21948e14i | 0.570148i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.67299e14 | − | 2.34086e14i | −0.808884 | − | 0.405196i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.40457e13i | − | 0.0237665i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.22998e14 | 1.19599 | 0.597996 | − | 0.801499i | \(-0.295964\pi\) | ||||
0.597996 | + | 0.801499i | \(0.295964\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.13116e13 | − | 8.80846e13i | 0.0991617 | − | 0.142463i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.25939e14i | − | 0.515452i | −0.966218 | − | 0.257726i | \(-0.917027\pi\) | ||
0.966218 | − | 0.257726i | \(-0.0829731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.81756e14i | − | 0.435727i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.88363e12 | − | 3.28968e12i | 0.0134358 | − | 0.00497537i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.21649e12 | − | 4.98804e13i | −0.0106750 | − | 0.0737853i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.89680e14 | 0.419145 | 0.209573 | − | 0.977793i | \(-0.432793\pi\) | ||||
0.209573 | + | 0.977793i | \(0.432793\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.60943e14 | + | 2.31223e14i | −0.227806 | + | 0.327283i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.11093e15 | 1.53838 | 0.769190 | − | 0.639020i | \(-0.220660\pi\) | ||||
0.769190 | + | 0.639020i | \(0.220660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.59042e12 | −0.0102840 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.27962e14 | − | 1.83840e14i | 0.169644 | − | 0.243723i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.51657e14 | 1.10488 | 0.552442 | − | 0.833551i | \(-0.313696\pi\) | ||||
0.552442 | + | 0.833551i | \(0.313696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.56107e13 | − | 5.22621e14i | −0.0959994 | − | 0.663548i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.56305e13 | − | 2.14798e14i | 0.0691301 | − | 0.266922i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1.33248e13i | − | 0.0162076i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.28904e15i | 1.53486i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.40409e14 | + | 7.76389e14i | −0.629944 | + | 0.905022i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.11623e14 | −0.583905 | −0.291953 | − | 0.956433i | \(-0.594305\pi\) | ||||
−0.291953 | + | 0.956433i | \(0.594305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.57592e15i | 1.76107i | 0.473985 | + | 0.880533i | \(0.342815\pi\) | ||||
−0.473985 | + | 0.880533i | \(0.657185\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.09189e14 | − | 8.16855e14i | 0.447763 | − | 0.893858i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.10529e14i | 0.118445i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.72957e14 | 0.181523 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.74329e14 | + | 1.55095e15i | 0.590393 | + | 1.59433i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.72781e15i | 1.73979i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.04822e13i | − | 0.0202037i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.28812e14 | + | 2.98476e14i | 0.414389 | + | 0.288437i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.64494e14 | + | 8.94959e14i | 0.250425 | + | 0.847355i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.87278e14 | −0.359284 | −0.179642 | − | 0.983732i | \(-0.557494\pi\) | ||||
−0.179642 | + | 0.983732i | \(0.557494\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.29474e15 | − | 9.01207e14i | −1.17702 | − | 0.819267i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.46172e12 | −0.00308398 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.47364e13 | −0.0739843 | −0.0369922 | − | 0.999316i | \(-0.511778\pi\) | ||||
−0.0369922 | + | 0.999316i | \(0.511778\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.54109e15 | + | 5.70677e14i | −1.31880 | + | 0.488362i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.13884e14 | 0.431054 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.13378e14 | − | 1.64031e13i | 0.0932267 | − | 0.0134877i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.75320e12 | − | 8.26545e12i | 0.00463765 | − | 0.00666278i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.79014e14i | 0.773722i | 0.922138 | + | 0.386861i | \(0.126441\pi\) | ||||
−0.922138 | + | 0.386861i | \(0.873559\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.86196e15i | 1.44280i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.66024e14 | + | 1.85167e14i | 0.202127 | + | 0.140691i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.69442e14 | 0.424281 | 0.212140 | − | 0.977239i | \(-0.431957\pi\) | ||||
0.212140 | + | 0.977239i | \(0.431957\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.21697e12i | 0.00161992i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.17829e14 | + | 1.05110e15i | −0.657741 | + | 0.753244i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.99429e15i | − | 1.40175i | −0.713282 | − | 0.700877i | \(-0.752792\pi\) | ||
0.713282 | − | 0.700877i | \(-0.247208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.48496e15 | 1.02380 | 0.511900 | − | 0.859045i | \(-0.328942\pi\) | ||||
0.511900 | + | 0.859045i | \(0.328942\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.66147e15 | + | 1.15647e15i | 1.12368 | + | 0.782140i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.36321e15i | − | 0.904459i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.20019e15i | − | 1.43217i | −0.698014 | − | 0.716084i | \(-0.745933\pi\) | ||
0.698014 | − | 0.716084i | \(-0.254067\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.77011e14 | − | 9.72642e14i | 0.432378 | − | 0.621185i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.68712e15 | + | 2.44085e14i | −1.05725 | + | 0.152958i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.93525e15 | 1.19004 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.86967e13 | + | 1.06266e13i | −0.0173171 | + | 0.00641267i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.65537e15 | 1.57259 | 0.786294 | − | 0.617852i | \(-0.211997\pi\) | ||||
0.786294 | + | 0.617852i | \(0.211997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.01590e14 | −0.117175 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.11436e12 | + | 6.34408e12i | 0.00519990 | + | 0.00361941i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.13671e14 | 0.343664 | 0.171832 | − | 0.985126i | \(-0.445031\pi\) | ||||
0.171832 | + | 0.985126i | \(0.445031\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.13633e12 | + | 1.17713e12i | −0.00447286 | + | 0.000647115i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.15194e14 | − | 3.58603e14i | −0.278043 | − | 0.193533i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.89153e12i | − | 0.00418133i | −0.999998 | − | 0.00209066i | \(-0.999335\pi\) | ||
0.999998 | − | 0.00209066i | \(-0.000665479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.97556e15i | 1.54796i | 0.633212 | + | 0.773979i | \(0.281736\pi\) | ||||
−0.633212 | + | 0.773979i | \(0.718264\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.73202e14 | − | 1.54790e15i | −0.292794 | − | 0.790677i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.08870e12 | 0.00355559 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.34064e15i | 1.15292i | 0.817127 | + | 0.576458i | \(0.195565\pi\) | ||||
−0.817127 | + | 0.576458i | \(0.804435\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.88953e15 | − | 1.44746e15i | −1.39776 | − | 0.700183i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.16398e15i | − | 1.97825i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.49622e15 | −0.698174 | −0.349087 | − | 0.937090i | \(-0.613508\pi\) | ||||
−0.349087 | + | 0.937090i | \(0.613508\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.08760e13 | − | 4.43586e13i | 0.0141517 | − | 0.0203313i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.75120e15i | 1.68889i | 0.535640 | + | 0.844447i | \(0.320071\pi\) | ||||
−0.535640 | + | 0.844447i | \(0.679929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.64285e15i | − | 0.726605i | −0.931671 | − | 0.363302i | \(-0.881649\pi\) | ||
0.931671 | − | 0.363302i | \(-0.118351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.22026e14 | + | 2.01562e15i | −0.226824 | + | 0.875801i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.14891e15 | + | 3.10895e14i | −0.917347 | + | 0.132718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.38231e15 | 0.999211 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.37720e14 | + | 4.85192e14i | −0.139183 | + | 0.199959i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.44564e14 | 0.139537 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.10544e15 | 0.837879 | 0.418939 | − | 0.908014i | \(-0.362402\pi\) | ||||
0.418939 | + | 0.908014i | \(0.362402\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.48740e15 | − | 3.57358e15i | 0.972805 | − | 1.39760i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.40475e13 | −0.00539936 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.54395e14 | − | 2.89098e15i | −0.322769 | − | 1.09214i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.88286e14 | + | 6.97238e13i | −0.0699138 | + | 0.0258897i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5.36092e15i | − | 1.95668i | −0.207004 | − | 0.978340i | \(-0.566371\pi\) | ||
0.207004 | − | 0.978340i | \(-0.433629\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.60720e15i | 0.935437i | 0.883878 | + | 0.467718i | \(0.154924\pi\) | ||||
−0.883878 | + | 0.467718i | \(0.845076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.32732e13 | − | 4.78026e13i | 0.0117359 | − | 0.0168606i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.92537e15 | −1.36115 | −0.680577 | − | 0.732677i | \(-0.738271\pi\) | ||||
−0.680577 | + | 0.732677i | \(0.738271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.40633e15i | − | 1.50221i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.13352e15 | + | 5.67819e14i | 0.379957 | + | 0.190333i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.35551e15i | 1.43554i | 0.696279 | + | 0.717772i | \(0.254838\pi\) | ||||
−0.696279 | + | 0.717772i | \(0.745162\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.51657e13 | −0.00815608 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.97276e15 | + | 7.30531e14i | −0.628732 | + | 0.232825i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.33227e15i | 1.04441i | 0.852821 | + | 0.522204i | \(0.174890\pi\) | ||||
−0.852821 | + | 0.522204i | \(0.825110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 5.98355e15i | − | 1.84438i | −0.386735 | − | 0.922191i | \(-0.626397\pi\) | ||
0.386735 | − | 0.922191i | \(-0.373603\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.59335e14 | − | 5.98143e14i | −0.260518 | − | 0.181335i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.14693e12 | − | 1.48396e13i | −0.000640175 | − | 0.00442489i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.82219e15 | −1.41434 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.03438e15 | + | 2.80815e15i | 1.16395 | + | 0.810170i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.37830e15 | 1.24260 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.22800e15 | −1.45966 | −0.729832 | − | 0.683627i | \(-0.760402\pi\) | ||||
−0.729832 | + | 0.683627i | \(0.760402\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.52338e15 | − | 9.12519e14i | −0.967806 | − | 0.250652i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.82002e15 | −1.30260 | −0.651301 | − | 0.758820i | \(-0.725776\pi\) | ||||
−0.651301 | + | 0.758820i | \(0.725776\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.89274e14 | − | 5.45546e15i | −0.209867 | − | 1.45060i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.75019e15 | − | 3.95111e15i | 0.719537 | − | 1.03374i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.65834e15i | 1.19927i | 0.800273 | + | 0.599636i | \(0.204688\pi\) | ||||
−0.800273 | + | 0.599636i | \(0.795312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.85962e13i | 0.0123113i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.09472e14 | − | 2.85015e14i | −0.102085 | − | 0.0710567i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.25143e15 | −1.53382 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.84813e15i | 0.446277i | 0.974787 | + | 0.223138i | \(0.0716302\pi\) | ||||
−0.974787 | + | 0.223138i | \(0.928370\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.26561e15 | − | 1.77694e15i | 0.776125 | − | 0.422318i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.29811e13i | 0.00771522i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.84919e15 | 0.425795 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.21716e15 | + | 4.32748e15i | 1.40918 | + | 0.980868i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.40698e15i | − | 0.760188i | −0.924948 | − | 0.380094i | \(-0.875892\pi\) | ||
0.924948 | − | 0.380094i | \(-0.124108\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.28438e14i | 0.138041i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.44102e13 | + | 1.06903e14i | −0.0160913 | + | 0.0231180i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.94818e15 | + | 4.26530e14i | −0.627692 | + | 0.0908119i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.55797e15 | −0.955471 | −0.477735 | − | 0.878504i | \(-0.658542\pi\) | ||||
−0.477735 | + | 0.878504i | \(0.658542\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.58482e14 | − | 4.27973e14i | −0.0327113 | − | 0.0883352i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.89168e15 | 0.384463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.15289e13 | 0.0163166 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.88567e15 | − | 4.79280e15i | −1.35703 | − | 0.944569i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.27426e15 | 1.41182 | 0.705911 | − | 0.708301i | \(-0.250538\pi\) | ||||
0.705911 | + | 0.708301i | \(0.250538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.48761e14 | − | 5.17543e15i | −0.143120 | − | 0.989243i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.18642e15 | + | 3.61003e15i | 0.976354 | + | 0.679595i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 8.42935e15i | − | 1.56291i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.59525e15i | 1.02183i | 0.859630 | + | 0.510917i | \(0.170694\pi\) | ||||
−0.859630 | + | 0.510917i | \(0.829306\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.86018e15 | + | 2.69848e15i | 0.874281 | + | 0.485420i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.99276e15 | 0.353109 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.99585e14i | − | 0.0872042i | −0.999049 | − | 0.0436021i | \(-0.986117\pi\) | ||
0.999049 | − | 0.0436021i | \(-0.0138834\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.97267e13 | + | 8.94890e13i | −0.00511171 | + | 0.0153882i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.39768e15i | 0.744993i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.66339e15 | −1.61282 | −0.806409 | − | 0.591358i | \(-0.798592\pi\) | ||||
−0.806409 | + | 0.591358i | \(0.798592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.09093e15 | − | 1.56731e15i | 0.179390 | − | 0.257724i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.79574e15i | − | 1.42506i | −0.701640 | − | 0.712531i | \(-0.747549\pi\) | ||
0.701640 | − | 0.712531i | \(-0.252451\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 4.03269e13i | − | 0.00643776i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.35829e15 | + | 6.36845e15i | 0.370966 | + | 1.00178i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.15096e15 | − | 7.95543e15i | −0.178406 | − | 1.23314i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.90400e15 | 0.443586 | 0.221793 | − | 0.975094i | \(-0.428809\pi\) | ||||
0.221793 | + | 0.975094i | \(0.428809\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.73525e15 | − | 2.49299e15i | 0.261210 | − | 0.375273i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.09412e13 | −0.00310665 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.79420e15 | 0.408536 | 0.204268 | − | 0.978915i | \(-0.434519\pi\) | ||||
0.204268 | + | 0.978915i | \(0.434519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.16910e15 | − | 4.55295e15i | 0.456673 | − | 0.656089i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.29618e15 | 0.184099 | 0.0920494 | − | 0.995754i | \(-0.470658\pi\) | ||||
0.0920494 | + | 0.995754i | \(0.470658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.34456e15 | + | 1.94525e14i | −0.188233 | + | 0.0272327i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.13731e13 | + | 3.07126e13i | 0.00156943 | + | 0.00423817i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.42337e16i | 1.93617i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.10991e16i | 1.48831i | 0.668008 | + | 0.744154i | \(0.267147\pi\) | ||||
−0.668008 | + | 0.744154i | \(0.732853\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.65394e15 | − | 8.12285e15i | 0.747398 | − | 1.07377i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.39635e15 | −0.572935 | −0.286467 | − | 0.958090i | \(-0.592481\pi\) | ||||
−0.286467 | + | 0.958090i | \(0.592481\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.30672e15i | 0.424852i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.77012e15 | − | 3.53366e15i | 0.224227 | − | 0.447619i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.37267e15i | 0.421228i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.34930e14 | 0.0658743 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.22793e15 | + | 1.24635e16i | −0.391954 | + | 1.51339i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.98695e14i | 0.0237905i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.03107e15i | − | 0.357878i | −0.983860 | − | 0.178939i | \(-0.942734\pi\) | ||
0.983860 | − | 0.178939i | \(-0.0572664\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.97718e15 | + | 2.76833e15i | 0.463075 | + | 0.322325i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.24579e14 | + | 8.61087e14i | 0.0143045 | + | 0.0988727i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.41432e16 | −1.60157 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.60495e14 | + | 1.11713e14i | 0.0179243 | + | 0.0124762i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.76272e16 | 1.94162 | 0.970808 | − | 0.239859i | \(-0.0771012\pi\) | ||||
0.970808 | + | 0.239859i | \(0.0771012\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.45648e15 | −0.484156 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00379e15 | + | 8.11159e15i | 0.321878 | + | 0.869215i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.60472e15 | 0.592405 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.01464e13 | + | 1.39252e14i | 0.00210048 | + | 0.0145185i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.29661e15 | + | 9.04615e15i | −0.647593 | + | 0.930377i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.57791e15i | 0.768834i | 0.923159 | + | 0.384417i | \(0.125598\pi\) | ||||
−0.923159 | + | 0.384417i | \(0.874402\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.26576e16i | 1.26689i | 0.773789 | + | 0.633443i | \(0.218359\pi\) | ||||
−0.773789 | + | 0.633443i | \(0.781641\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.04282e15 | + | 4.20613e15i | 0.596680 | + | 0.415322i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.88918e13 | −0.00281454 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.63452e15i | 0.349322i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.05489e16 | + | 5.74003e15i | −1.00033 | + | 0.544318i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.09052e16i | 1.02034i | 0.860072 | + | 0.510172i | \(0.170418\pi\) | ||||
−0.860072 | + | 0.510172i | \(0.829582\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.29130e15 | −0.211535 | −0.105767 | − | 0.994391i | \(-0.533730\pi\) | ||||
−0.105767 | + | 0.994391i | \(0.533730\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.95870e15 | + | 5.53968e15i | 0.725012 | + | 0.504648i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 4.99940e15i | − | 0.449404i | −0.974427 | − | 0.224702i | \(-0.927859\pi\) | ||
0.974427 | − | 0.224702i | \(-0.0721409\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.13328e15i | − | 0.189233i | −0.995514 | − | 0.0946167i | \(-0.969837\pi\) | ||
0.995514 | − | 0.0946167i | \(-0.0301625\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.68252e15 | − | 9.60058e15i | 0.584972 | − | 0.840411i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.09406e15 | + | 9.14413e14i | −0.267289 | + | 0.0789941i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.58413e13 | 0.00646592 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.26627e15 | − | 4.88927e15i | 0.106546 | − | 0.411390i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.56897e15 | −0.213338 | −0.106669 | − | 0.994295i | \(-0.534018\pi\) | ||||
−0.106669 | + | 0.994295i | \(0.534018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.76174e16 | −1.44399 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.41661e15 | + | 9.86040e14i | 0.114604 | + | 0.0797706i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.02997e13 | −0.00481507 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.75331e15 | − | 3.98337e14i | 0.217018 | − | 0.0313973i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.77824e16 | + | 1.23775e16i | 1.38356 | + | 0.963032i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 5.89714e15i | − | 0.452928i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.63407e15i | − | 0.199714i | −0.995002 | − | 0.0998569i | \(-0.968162\pi\) | ||
0.995002 | − | 0.0998569i | \(-0.0318385\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.60157e13 | + | 2.07431e13i | −0.00419272 | + | 0.00155260i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.18512e15 | 0.383146 | 0.191573 | − | 0.981478i | \(-0.438641\pi\) | ||||
0.191573 | + | 0.981478i | \(0.438641\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.64925e15i | 0.703933i | 0.936013 | + | 0.351966i | \(0.114487\pi\) | ||||
−0.936013 | + | 0.351966i | \(0.885513\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.49981e15 | − | 1.89642e16i | 0.684223 | − | 1.36590i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.04845e16i | − | 0.745569i | −0.927918 | − | 0.372785i | \(-0.878403\pi\) | ||
0.927918 | − | 0.372785i | \(-0.121597\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.54656e14 | 0.0178799 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.60044e15 | − | 1.09193e16i | 0.526907 | − | 0.756992i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.21589e15i | 0.0832314i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.42058e16i | − | 0.960208i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.05930e16 | + | 7.62576e15i | −1.37449 | + | 0.508985i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.86897e14 | + | 7.04423e13i | −0.0320917 | + | 0.00464290i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.66548e16 | −1.08403 | −0.542014 | − | 0.840369i | \(-0.682338\pi\) | ||||
−0.542014 | + | 0.840369i | \(0.682338\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.19455e15 | + | 3.15284e15i | −0.141061 | + | 0.202658i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.96162e15 | −0.314960 | −0.157480 | − | 0.987522i | \(-0.550337\pi\) | ||||
−0.157480 | + | 0.987522i | \(0.550337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00877e16 | 1.25935 | 0.629674 | − | 0.776860i | \(-0.283189\pi\) | ||||
0.629674 | + | 0.776860i | \(0.283189\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.54357e14 | − | 3.65427e14i | 0.0157491 | − | 0.0226262i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.27546e16 | −0.779989 | −0.389994 | − | 0.920817i | \(-0.627523\pi\) | ||||
−0.389994 | + | 0.920817i | \(0.627523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.45614e15 | + | 7.89373e14i | −0.329554 | + | 0.0476785i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.64627e15 | − | 1.12386e16i | −0.575483 | − | 0.670479i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 8.12803e15i | − | 0.478963i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.40651e14i | − | 0.00818681i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.02371e16 | + | 1.47074e16i | −0.588598 | + | 0.845622i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.16971e16 | 0.664356 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.69057e15i | 0.375385i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.02374e16 | − | 2.04366e16i | 0.567421 | − | 1.13273i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.24675e14i | 0.0232536i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.31435e16 | 1.25195 | 0.625977 | − | 0.779842i | \(-0.284700\pi\) | ||||
0.625977 | + | 0.779842i | \(0.284700\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.12102e15 | + | 1.11286e16i | 0.220244 | + | 0.594758i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.91442e16i | − | 1.53887i | −0.638727 | − | 0.769433i | \(-0.720539\pi\) | ||
0.638727 | − | 0.769433i | \(-0.279461\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.80931e16i | − | 0.943895i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.63102e14 | + | 2.52739e14i | 0.0187160 | + | 0.0130273i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.77454e15 | + | 1.41414e15i | −0.497812 | + | 0.0720214i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.19996e16 | 1.10708 | 0.553540 | − | 0.832822i | \(-0.313276\pi\) | ||||
0.553540 | + | 0.832822i | \(0.313276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.34820e14 | + | 9.38419e13i | 0.00670388 | + | 0.00466626i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.72798e15 | −0.0849043 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.03084e16 | 0.500509 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.95360e16 | + | 7.23433e15i | −0.937338 | + | 0.347104i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.34636e14 | −0.0111252 | −0.00556261 | − | 0.999985i | \(-0.501771\pi\) | ||||
−0.00556261 | + | 0.999985i | \(0.501771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.66777e15 | − | 5.64316e15i | −0.0781470 | − | 0.264423i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.08785e15 | − | 7.30957e15i | 0.235605 | − | 0.338487i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 8.72561e13i | − | 0.00399330i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.41493e16i | − | 1.09229i | −0.837691 | − | 0.546144i | \(-0.816095\pi\) | ||
0.837691 | − | 0.546144i | \(-0.183905\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.39920e16 | − | 1.66997e16i | −1.07252 | − | 0.746533i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.95434e16 | −0.863488 | −0.431744 | − | 0.901996i | \(-0.642102\pi\) | ||||
−0.431744 | + | 0.901996i | \(0.642102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.16485e16i | − | 1.38210i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.73399e14 | + | 4.11431e13i | 0.0161175 | + | 0.00177591i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.04855e16i | 0.447367i | 0.974662 | + | 0.223684i | \(0.0718082\pi\) | ||||
−0.974662 | + | 0.223684i | \(0.928192\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.81049e16 | −0.763541 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.47114e16 | − | 2.41610e16i | −1.44703 | − | 1.00721i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.69378e16i | 1.93425i | 0.254306 | + | 0.967124i | \(0.418153\pi\) | ||||
−0.254306 | + | 0.967124i | \(0.581847\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.44963e14i | − | 0.0221998i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.95960e16 | − | 2.81530e16i | 0.789136 | − | 1.13373i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.73078e15 | + | 1.88751e16i | 0.108714 | + | 0.751429i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.08199e16 | 0.819406 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.00297e16 | + | 1.11203e16i | −1.16844 | + | 0.432683i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.19027e14 | −0.0122724 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.43829e16 | 1.30767 | 0.653834 | − | 0.756638i | \(-0.273160\pi\) | ||||
0.653834 | + | 0.756638i | \(0.273160\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.67741e15 | − | 1.16757e15i | −0.0630752 | − | 0.0439037i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.39816e16 | −0.891603 | −0.445802 | − | 0.895132i | \(-0.647081\pi\) | ||||
−0.445802 | + | 0.895132i | \(0.647081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.85331e15 | + | 1.28101e16i | 0.0681284 | + | 0.470903i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.57089e16 | − | 1.78948e16i | −0.934456 | − | 0.650432i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.52938e15i | − | 0.162786i | −0.996682 | − | 0.0813932i | \(-0.974063\pi\) | ||
0.996682 | − | 0.0813932i | \(-0.0259370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.30455e16i | − | 0.818993i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.87945e15 | + | 5.07537e15i | 0.0660468 | + | 0.178356i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.58087e16 | −1.93935 | −0.969677 | − | 0.244389i | \(-0.921413\pi\) | ||||
−0.969677 | + | 0.244389i | \(0.921413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.98952e12i | − | 0.000102731i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.28943e16 | + | 4.57033e16i | −0.778005 | + | 1.55311i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.41056e16i | − | 1.14616i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.93480e16 | 1.30773 | 0.653864 | − | 0.756612i | \(-0.273147\pi\) | ||||
0.653864 | + | 0.756612i | \(0.273147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.85478e14 | − | 9.84806e14i | 0.0225306 | − | 0.0323691i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.68984e14i | 0.00549312i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.97785e16i | 1.60036i | 0.599758 | + | 0.800181i | \(0.295263\pi\) | ||||
−0.599758 | + | 0.800181i | \(0.704737\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.52419e16 | − | 3.94749e15i | −0.484650 | − | 0.125519i |
(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 | 84.12.f.b.41.10 | yes | 28 | |
3.2 | odd | 2 | inner | 84.12.f.b.41.20 | yes | 28 | |
7.6 | odd | 2 | inner | 84.12.f.b.41.19 | yes | 28 | |
21.20 | even | 2 | inner | 84.12.f.b.41.9 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.f.b.41.9 | ✓ | 28 | 21.20 | even | 2 | inner | |
84.12.f.b.41.10 | yes | 28 | 1.1 | even | 1 | trivial | |
84.12.f.b.41.19 | yes | 28 | 7.6 | odd | 2 | inner | |
84.12.f.b.41.20 | yes | 28 | 3.2 | odd | 2 | inner |