Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,10,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(2.57517918082\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | −114.000 | −0.812567 | −0.406284 | − | 0.913747i | \(-0.633175\pi\) | ||||
−0.406284 | + | 0.913747i | \(0.633175\pi\) | |||||||
\(4\) | −448.000 | −0.875000 | ||||||||
\(5\) | −625.000 | −0.447214 | ||||||||
\(6\) | 912.000 | 0.287286 | ||||||||
\(7\) | 4242.00 | 0.667774 | 0.333887 | − | 0.942613i | \(-0.391640\pi\) | ||||
0.333887 | + | 0.942613i | \(0.391640\pi\) | |||||||
\(8\) | 7680.00 | 0.662913 | ||||||||
\(9\) | −6687.00 | −0.339735 | ||||||||
\(10\) | 5000.00 | 0.158114 | ||||||||
\(11\) | −46208.0 | −0.951590 | −0.475795 | − | 0.879556i | \(-0.657840\pi\) | ||||
−0.475795 | + | 0.879556i | \(0.657840\pi\) | |||||||
\(12\) | 51072.0 | 0.710996 | ||||||||
\(13\) | −115934. | −1.12581 | −0.562906 | − | 0.826521i | \(-0.690317\pi\) | ||||
−0.562906 | + | 0.826521i | \(0.690317\pi\) | |||||||
\(14\) | −33936.0 | −0.236094 | ||||||||
\(15\) | 71250.0 | 0.363391 | ||||||||
\(16\) | 167936. | 0.640625 | ||||||||
\(17\) | 494842. | 1.43697 | 0.718483 | − | 0.695545i | \(-0.244837\pi\) | ||||
0.718483 | + | 0.695545i | \(0.244837\pi\) | |||||||
\(18\) | 53496.0 | 0.120114 | ||||||||
\(19\) | −1.00874e6 | −1.77578 | −0.887888 | − | 0.460060i | \(-0.847828\pi\) | ||||
−0.887888 | + | 0.460060i | \(0.847828\pi\) | |||||||
\(20\) | 280000. | 0.391312 | ||||||||
\(21\) | −483588. | −0.542611 | ||||||||
\(22\) | 369664. | 0.336438 | ||||||||
\(23\) | −532554. | −0.396815 | −0.198408 | − | 0.980120i | \(-0.563577\pi\) | ||||
−0.198408 | + | 0.980120i | \(0.563577\pi\) | |||||||
\(24\) | −875520. | −0.538661 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | 927472. | 0.398035 | ||||||||
\(27\) | 3.00618e6 | 1.08862 | ||||||||
\(28\) | −1.90042e6 | −0.584302 | ||||||||
\(29\) | 4.19639e6 | 1.10175 | 0.550877 | − | 0.834586i | \(-0.314293\pi\) | ||||
0.550877 | + | 0.834586i | \(0.314293\pi\) | |||||||
\(30\) | −570000. | −0.128478 | ||||||||
\(31\) | −3.36503e6 | −0.654427 | −0.327213 | − | 0.944950i | \(-0.606110\pi\) | ||||
−0.327213 | + | 0.944950i | \(0.606110\pi\) | |||||||
\(32\) | −5.27565e6 | −0.889408 | ||||||||
\(33\) | 5.26771e6 | 0.773231 | ||||||||
\(34\) | −3.95874e6 | −0.508044 | ||||||||
\(35\) | −2.65125e6 | −0.298638 | ||||||||
\(36\) | 2.99578e6 | 0.297268 | ||||||||
\(37\) | −1.49314e7 | −1.30976 | −0.654880 | − | 0.755733i | \(-0.727281\pi\) | ||||
−0.654880 | + | 0.755733i | \(0.727281\pi\) | |||||||
\(38\) | 8.06992e6 | 0.627831 | ||||||||
\(39\) | 1.32165e7 | 0.914797 | ||||||||
\(40\) | −4.80000e6 | −0.296464 | ||||||||
\(41\) | 1.10563e7 | 0.611056 | 0.305528 | − | 0.952183i | \(-0.401167\pi\) | ||||
0.305528 | + | 0.952183i | \(0.401167\pi\) | |||||||
\(42\) | 3.86870e6 | 0.191842 | ||||||||
\(43\) | −6.39679e6 | −0.285335 | −0.142667 | − | 0.989771i | \(-0.545568\pi\) | ||||
−0.142667 | + | 0.989771i | \(0.545568\pi\) | |||||||
\(44\) | 2.07012e7 | 0.832642 | ||||||||
\(45\) | 4.17937e6 | 0.151934 | ||||||||
\(46\) | 4.26043e6 | 0.140295 | ||||||||
\(47\) | −3.55592e7 | −1.06295 | −0.531473 | − | 0.847075i | \(-0.678361\pi\) | ||||
−0.531473 | + | 0.847075i | \(0.678361\pi\) | |||||||
\(48\) | −1.91447e7 | −0.520551 | ||||||||
\(49\) | −2.23590e7 | −0.554078 | ||||||||
\(50\) | −3.12500e6 | −0.0707107 | ||||||||
\(51\) | −5.64120e7 | −1.16763 | ||||||||
\(52\) | 5.19384e7 | 0.985085 | ||||||||
\(53\) | 3.97386e7 | 0.691785 | 0.345892 | − | 0.938274i | \(-0.387576\pi\) | ||||
0.345892 | + | 0.938274i | \(0.387576\pi\) | |||||||
\(54\) | −2.40494e7 | −0.384887 | ||||||||
\(55\) | 2.88800e7 | 0.425564 | ||||||||
\(56\) | 3.25786e7 | 0.442676 | ||||||||
\(57\) | 1.14996e8 | 1.44294 | ||||||||
\(58\) | −3.35711e7 | −0.389529 | ||||||||
\(59\) | −8.51856e7 | −0.915234 | −0.457617 | − | 0.889149i | \(-0.651297\pi\) | ||||
−0.457617 | + | 0.889149i | \(0.651297\pi\) | |||||||
\(60\) | −3.19200e7 | −0.317967 | ||||||||
\(61\) | 4.57486e7 | 0.423052 | 0.211526 | − | 0.977372i | \(-0.432157\pi\) | ||||
0.211526 | + | 0.977372i | \(0.432157\pi\) | |||||||
\(62\) | 2.69202e7 | 0.231375 | ||||||||
\(63\) | −2.83663e7 | −0.226866 | ||||||||
\(64\) | −4.37780e7 | −0.326172 | ||||||||
\(65\) | 7.24588e7 | 0.503478 | ||||||||
\(66\) | −4.21417e7 | −0.273378 | ||||||||
\(67\) | −4.52862e7 | −0.274555 | −0.137277 | − | 0.990533i | \(-0.543835\pi\) | ||||
−0.137277 | + | 0.990533i | \(0.543835\pi\) | |||||||
\(68\) | −2.21689e8 | −1.25735 | ||||||||
\(69\) | 6.07112e7 | 0.322439 | ||||||||
\(70\) | 2.12100e7 | 0.105584 | ||||||||
\(71\) | −1.89967e8 | −0.887190 | −0.443595 | − | 0.896227i | \(-0.646297\pi\) | ||||
−0.443595 | + | 0.896227i | \(0.646297\pi\) | |||||||
\(72\) | −5.13562e7 | −0.225214 | ||||||||
\(73\) | 4.12171e8 | 1.69873 | 0.849365 | − | 0.527805i | \(-0.176985\pi\) | ||||
0.849365 | + | 0.527805i | \(0.176985\pi\) | |||||||
\(74\) | 1.19451e8 | 0.463070 | ||||||||
\(75\) | −4.45312e7 | −0.162513 | ||||||||
\(76\) | 4.51916e8 | 1.55380 | ||||||||
\(77\) | −1.96014e8 | −0.635447 | ||||||||
\(78\) | −1.05732e8 | −0.323430 | ||||||||
\(79\) | 9.50408e7 | 0.274529 | 0.137265 | − | 0.990534i | \(-0.456169\pi\) | ||||
0.137265 | + | 0.990534i | \(0.456169\pi\) | |||||||
\(80\) | −1.04960e8 | −0.286496 | ||||||||
\(81\) | −2.11084e8 | −0.544845 | ||||||||
\(82\) | −8.84501e7 | −0.216041 | ||||||||
\(83\) | 2.61706e8 | 0.605289 | 0.302645 | − | 0.953104i | \(-0.402131\pi\) | ||||
0.302645 | + | 0.953104i | \(0.402131\pi\) | |||||||
\(84\) | 2.16647e8 | 0.474785 | ||||||||
\(85\) | −3.09276e8 | −0.642631 | ||||||||
\(86\) | 5.11744e7 | 0.100881 | ||||||||
\(87\) | −4.78388e8 | −0.895249 | ||||||||
\(88\) | −3.54877e8 | −0.630821 | ||||||||
\(89\) | −1.99386e7 | −0.0336853 | −0.0168426 | − | 0.999858i | \(-0.505361\pi\) | ||||
−0.0168426 | + | 0.999858i | \(0.505361\pi\) | |||||||
\(90\) | −3.34350e7 | −0.0537168 | ||||||||
\(91\) | −4.91792e8 | −0.751788 | ||||||||
\(92\) | 2.38584e8 | 0.347213 | ||||||||
\(93\) | 3.83613e8 | 0.531766 | ||||||||
\(94\) | 2.84473e8 | 0.375808 | ||||||||
\(95\) | 6.30462e8 | 0.794151 | ||||||||
\(96\) | 6.01424e8 | 0.722703 | ||||||||
\(97\) | −1.95034e7 | −0.0223685 | −0.0111842 | − | 0.999937i | \(-0.503560\pi\) | ||||
−0.0111842 | + | 0.999937i | \(0.503560\pi\) | |||||||
\(98\) | 1.78872e8 | 0.195896 | ||||||||
\(99\) | 3.08993e8 | 0.323288 | ||||||||
\(100\) | −1.75000e8 | −0.175000 | ||||||||
\(101\) | −2.16672e8 | −0.207184 | −0.103592 | − | 0.994620i | \(-0.533034\pi\) | ||||
−0.103592 | + | 0.994620i | \(0.533034\pi\) | |||||||
\(102\) | 4.51296e8 | 0.412820 | ||||||||
\(103\) | −7.48234e8 | −0.655043 | −0.327522 | − | 0.944844i | \(-0.606213\pi\) | ||||
−0.327522 | + | 0.944844i | \(0.606213\pi\) | |||||||
\(104\) | −8.90373e8 | −0.746315 | ||||||||
\(105\) | 3.02242e8 | 0.242663 | ||||||||
\(106\) | −3.17909e8 | −0.244583 | ||||||||
\(107\) | 1.05711e9 | 0.779637 | 0.389819 | − | 0.920892i | \(-0.372538\pi\) | ||||
0.389819 | + | 0.920892i | \(0.372538\pi\) | |||||||
\(108\) | −1.34677e9 | −0.952546 | ||||||||
\(109\) | −2.49659e9 | −1.69406 | −0.847029 | − | 0.531547i | \(-0.821611\pi\) | ||||
−0.847029 | + | 0.531547i | \(0.821611\pi\) | |||||||
\(110\) | −2.31040e8 | −0.150460 | ||||||||
\(111\) | 1.70217e9 | 1.06427 | ||||||||
\(112\) | 7.12385e8 | 0.427793 | ||||||||
\(113\) | 1.11566e9 | 0.643695 | 0.321848 | − | 0.946791i | \(-0.395696\pi\) | ||||
0.321848 | + | 0.946791i | \(0.395696\pi\) | |||||||
\(114\) | −9.19971e8 | −0.510155 | ||||||||
\(115\) | 3.32846e8 | 0.177461 | ||||||||
\(116\) | −1.87998e9 | −0.964035 | ||||||||
\(117\) | 7.75251e8 | 0.382477 | ||||||||
\(118\) | 6.81485e8 | 0.323584 | ||||||||
\(119\) | 2.09912e9 | 0.959568 | ||||||||
\(120\) | 5.47200e8 | 0.240896 | ||||||||
\(121\) | −2.22768e8 | −0.0944756 | ||||||||
\(122\) | −3.65989e8 | −0.149572 | ||||||||
\(123\) | −1.26041e9 | −0.496524 | ||||||||
\(124\) | 1.50753e9 | 0.572623 | ||||||||
\(125\) | −2.44141e8 | −0.0894427 | ||||||||
\(126\) | 2.26930e8 | 0.0802093 | ||||||||
\(127\) | 3.12054e8 | 0.106442 | 0.0532210 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532210 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(128\) | 3.05136e9 | 1.00473 | ||||||||
\(129\) | 7.29235e8 | 0.231853 | ||||||||
\(130\) | −5.79670e8 | −0.178006 | ||||||||
\(131\) | −2.81701e9 | −0.835733 | −0.417867 | − | 0.908508i | \(-0.637222\pi\) | ||||
−0.417867 | + | 0.908508i | \(0.637222\pi\) | |||||||
\(132\) | −2.35993e9 | −0.676577 | ||||||||
\(133\) | −4.27908e9 | −1.18582 | ||||||||
\(134\) | 3.62289e8 | 0.0970697 | ||||||||
\(135\) | −1.87886e9 | −0.486848 | ||||||||
\(136\) | 3.80039e9 | 0.952583 | ||||||||
\(137\) | −7.15311e9 | −1.73481 | −0.867406 | − | 0.497600i | \(-0.834215\pi\) | ||||
−0.867406 | + | 0.497600i | \(0.834215\pi\) | |||||||
\(138\) | −4.85689e8 | −0.113999 | ||||||||
\(139\) | 2.52323e9 | 0.573310 | 0.286655 | − | 0.958034i | \(-0.407457\pi\) | ||||
0.286655 | + | 0.958034i | \(0.407457\pi\) | |||||||
\(140\) | 1.18776e9 | 0.261308 | ||||||||
\(141\) | 4.05374e9 | 0.863715 | ||||||||
\(142\) | 1.51974e9 | 0.313669 | ||||||||
\(143\) | 5.35708e9 | 1.07131 | ||||||||
\(144\) | −1.12299e9 | −0.217643 | ||||||||
\(145\) | −2.62274e9 | −0.492720 | ||||||||
\(146\) | −3.29737e9 | −0.600592 | ||||||||
\(147\) | 2.54893e9 | 0.450225 | ||||||||
\(148\) | 6.68925e9 | 1.14604 | ||||||||
\(149\) | 1.46531e9 | 0.243551 | 0.121775 | − | 0.992558i | \(-0.461141\pi\) | ||||
0.121775 | + | 0.992558i | \(0.461141\pi\) | |||||||
\(150\) | 3.56250e8 | 0.0574572 | ||||||||
\(151\) | 3.65515e9 | 0.572149 | 0.286075 | − | 0.958207i | \(-0.407650\pi\) | ||||
0.286075 | + | 0.958207i | \(0.407650\pi\) | |||||||
\(152\) | −7.74712e9 | −1.17718 | ||||||||
\(153\) | −3.30901e9 | −0.488187 | ||||||||
\(154\) | 1.56811e9 | 0.224665 | ||||||||
\(155\) | 2.10314e9 | 0.292669 | ||||||||
\(156\) | −5.92098e9 | −0.800448 | ||||||||
\(157\) | 5.55191e9 | 0.729279 | 0.364639 | − | 0.931149i | \(-0.381192\pi\) | ||||
0.364639 | + | 0.931149i | \(0.381192\pi\) | |||||||
\(158\) | −7.60327e8 | −0.0970607 | ||||||||
\(159\) | −4.53020e9 | −0.562122 | ||||||||
\(160\) | 3.29728e9 | 0.397755 | ||||||||
\(161\) | −2.25909e9 | −0.264983 | ||||||||
\(162\) | 1.68867e9 | 0.192632 | ||||||||
\(163\) | −1.67637e10 | −1.86006 | −0.930029 | − | 0.367485i | \(-0.880219\pi\) | ||||
−0.930029 | + | 0.367485i | \(0.880219\pi\) | |||||||
\(164\) | −4.95321e9 | −0.534674 | ||||||||
\(165\) | −3.29232e9 | −0.345799 | ||||||||
\(166\) | −2.09365e9 | −0.214002 | ||||||||
\(167\) | 1.39549e10 | 1.38836 | 0.694182 | − | 0.719799i | \(-0.255766\pi\) | ||||
0.694182 | + | 0.719799i | \(0.255766\pi\) | |||||||
\(168\) | −3.71396e9 | −0.359704 | ||||||||
\(169\) | 2.83619e9 | 0.267452 | ||||||||
\(170\) | 2.47421e9 | 0.227204 | ||||||||
\(171\) | 6.74544e9 | 0.603293 | ||||||||
\(172\) | 2.86576e9 | 0.249668 | ||||||||
\(173\) | 1.57000e10 | 1.33258 | 0.666289 | − | 0.745694i | \(-0.267882\pi\) | ||||
0.666289 | + | 0.745694i | \(0.267882\pi\) | |||||||
\(174\) | 3.82711e9 | 0.316518 | ||||||||
\(175\) | 1.65703e9 | 0.133555 | ||||||||
\(176\) | −7.75999e9 | −0.609613 | ||||||||
\(177\) | 9.71116e9 | 0.743689 | ||||||||
\(178\) | 1.59509e8 | 0.0119095 | ||||||||
\(179\) | −2.51902e10 | −1.83397 | −0.916985 | − | 0.398921i | \(-0.869385\pi\) | ||||
−0.916985 | + | 0.398921i | \(0.869385\pi\) | |||||||
\(180\) | −1.87236e9 | −0.132942 | ||||||||
\(181\) | 1.04482e10 | 0.723579 | 0.361789 | − | 0.932260i | \(-0.382166\pi\) | ||||
0.361789 | + | 0.932260i | \(0.382166\pi\) | |||||||
\(182\) | 3.93434e9 | 0.265797 | ||||||||
\(183\) | −5.21535e9 | −0.343758 | ||||||||
\(184\) | −4.09001e9 | −0.263054 | ||||||||
\(185\) | 9.33210e9 | 0.585742 | ||||||||
\(186\) | −3.06891e9 | −0.188008 | ||||||||
\(187\) | −2.28657e10 | −1.36740 | ||||||||
\(188\) | 1.59305e10 | 0.930078 | ||||||||
\(189\) | 1.27522e10 | 0.726955 | ||||||||
\(190\) | −5.04370e9 | −0.280775 | ||||||||
\(191\) | −9.68625e9 | −0.526630 | −0.263315 | − | 0.964710i | \(-0.584816\pi\) | ||||
−0.263315 | + | 0.964710i | \(0.584816\pi\) | |||||||
\(192\) | 4.99070e9 | 0.265037 | ||||||||
\(193\) | −2.04431e10 | −1.06057 | −0.530285 | − | 0.847820i | \(-0.677915\pi\) | ||||
−0.530285 | + | 0.847820i | \(0.677915\pi\) | |||||||
\(194\) | 1.56027e8 | 0.00790845 | ||||||||
\(195\) | −8.26030e9 | −0.409110 | ||||||||
\(196\) | 1.00169e10 | 0.484818 | ||||||||
\(197\) | −2.52431e10 | −1.19411 | −0.597056 | − | 0.802200i | \(-0.703663\pi\) | ||||
−0.597056 | + | 0.802200i | \(0.703663\pi\) | |||||||
\(198\) | −2.47194e9 | −0.114300 | ||||||||
\(199\) | 8.06736e9 | 0.364664 | 0.182332 | − | 0.983237i | \(-0.441635\pi\) | ||||
0.182332 | + | 0.983237i | \(0.441635\pi\) | |||||||
\(200\) | 3.00000e9 | 0.132583 | ||||||||
\(201\) | 5.16262e9 | 0.223094 | ||||||||
\(202\) | 1.73338e9 | 0.0732506 | ||||||||
\(203\) | 1.78011e10 | 0.735723 | ||||||||
\(204\) | 2.52726e10 | 1.02168 | ||||||||
\(205\) | −6.91016e9 | −0.273273 | ||||||||
\(206\) | 5.98587e9 | 0.231593 | ||||||||
\(207\) | 3.56119e9 | 0.134812 | ||||||||
\(208\) | −1.94695e10 | −0.721223 | ||||||||
\(209\) | 4.66119e10 | 1.68981 | ||||||||
\(210\) | −2.41794e9 | −0.0857944 | ||||||||
\(211\) | −8.04589e9 | −0.279449 | −0.139725 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139725 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(212\) | −1.78029e10 | −0.605312 | ||||||||
\(213\) | 2.16563e10 | 0.720901 | ||||||||
\(214\) | −8.45687e9 | −0.275643 | ||||||||
\(215\) | 3.99800e9 | 0.127605 | ||||||||
\(216\) | 2.30875e10 | 0.721663 | ||||||||
\(217\) | −1.42744e10 | −0.437009 | ||||||||
\(218\) | 1.99727e10 | 0.598940 | ||||||||
\(219\) | −4.69875e10 | −1.38033 | ||||||||
\(220\) | −1.29382e10 | −0.372369 | ||||||||
\(221\) | −5.73690e10 | −1.61775 | ||||||||
\(222\) | −1.36174e10 | −0.376275 | ||||||||
\(223\) | 3.18618e10 | 0.862777 | 0.431388 | − | 0.902166i | \(-0.358024\pi\) | ||||
0.431388 | + | 0.902166i | \(0.358024\pi\) | |||||||
\(224\) | −2.23793e10 | −0.593923 | ||||||||
\(225\) | −2.61211e9 | −0.0679470 | ||||||||
\(226\) | −8.92531e9 | −0.227581 | ||||||||
\(227\) | 3.02621e10 | 0.756454 | 0.378227 | − | 0.925713i | \(-0.376534\pi\) | ||||
0.378227 | + | 0.925713i | \(0.376534\pi\) | |||||||
\(228\) | −5.15184e10 | −1.26257 | ||||||||
\(229\) | 2.06101e10 | 0.495245 | 0.247623 | − | 0.968857i | \(-0.420351\pi\) | ||||
0.247623 | + | 0.968857i | \(0.420351\pi\) | |||||||
\(230\) | −2.66277e9 | −0.0627420 | ||||||||
\(231\) | 2.23456e10 | 0.516344 | ||||||||
\(232\) | 3.22283e10 | 0.730367 | ||||||||
\(233\) | 3.61735e9 | 0.0804061 | 0.0402031 | − | 0.999192i | \(-0.487200\pi\) | ||||
0.0402031 | + | 0.999192i | \(0.487200\pi\) | |||||||
\(234\) | −6.20201e9 | −0.135226 | ||||||||
\(235\) | 2.22245e10 | 0.475364 | ||||||||
\(236\) | 3.81632e10 | 0.800830 | ||||||||
\(237\) | −1.08347e10 | −0.223073 | ||||||||
\(238\) | −1.67930e10 | −0.339259 | ||||||||
\(239\) | 2.21916e9 | 0.0439945 | 0.0219973 | − | 0.999758i | \(-0.492997\pi\) | ||||
0.0219973 | + | 0.999758i | \(0.492997\pi\) | |||||||
\(240\) | 1.19654e10 | 0.232797 | ||||||||
\(241\) | 2.57977e10 | 0.492611 | 0.246306 | − | 0.969192i | \(-0.420783\pi\) | ||||
0.246306 | + | 0.969192i | \(0.420783\pi\) | |||||||
\(242\) | 1.78215e9 | 0.0334022 | ||||||||
\(243\) | −3.51070e10 | −0.645901 | ||||||||
\(244\) | −2.04954e10 | −0.370171 | ||||||||
\(245\) | 1.39744e10 | 0.247791 | ||||||||
\(246\) | 1.00833e10 | 0.175548 | ||||||||
\(247\) | 1.16947e11 | 1.99919 | ||||||||
\(248\) | −2.58434e10 | −0.433828 | ||||||||
\(249\) | −2.98345e10 | −0.491838 | ||||||||
\(250\) | 1.95312e9 | 0.0316228 | ||||||||
\(251\) | −8.91848e10 | −1.41827 | −0.709135 | − | 0.705072i | \(-0.750914\pi\) | ||||
−0.709135 | + | 0.705072i | \(0.750914\pi\) | |||||||
\(252\) | 1.27081e10 | 0.198508 | ||||||||
\(253\) | 2.46083e10 | 0.377606 | ||||||||
\(254\) | −2.49643e9 | −0.0376329 | ||||||||
\(255\) | 3.52575e10 | 0.522180 | ||||||||
\(256\) | −1.99649e9 | −0.0290527 | ||||||||
\(257\) | −1.10058e11 | −1.57371 | −0.786853 | − | 0.617141i | \(-0.788291\pi\) | ||||
−0.786853 | + | 0.617141i | \(0.788291\pi\) | |||||||
\(258\) | −5.83388e9 | −0.0819726 | ||||||||
\(259\) | −6.33388e10 | −0.874623 | ||||||||
\(260\) | −3.24615e10 | −0.440543 | ||||||||
\(261\) | −2.80613e10 | −0.374304 | ||||||||
\(262\) | 2.25361e10 | 0.295476 | ||||||||
\(263\) | 2.06374e10 | 0.265983 | 0.132992 | − | 0.991117i | \(-0.457542\pi\) | ||||
0.132992 | + | 0.991117i | \(0.457542\pi\) | |||||||
\(264\) | 4.04560e10 | 0.512585 | ||||||||
\(265\) | −2.48366e10 | −0.309376 | ||||||||
\(266\) | 3.42326e10 | 0.419249 | ||||||||
\(267\) | 2.27300e9 | 0.0273716 | ||||||||
\(268\) | 2.02882e10 | 0.240235 | ||||||||
\(269\) | −2.64890e10 | −0.308446 | −0.154223 | − | 0.988036i | \(-0.549287\pi\) | ||||
−0.154223 | + | 0.988036i | \(0.549287\pi\) | |||||||
\(270\) | 1.50309e10 | 0.172127 | ||||||||
\(271\) | 3.44004e10 | 0.387438 | 0.193719 | − | 0.981057i | \(-0.437945\pi\) | ||||
0.193719 | + | 0.981057i | \(0.437945\pi\) | |||||||
\(272\) | 8.31018e10 | 0.920556 | ||||||||
\(273\) | 5.60643e10 | 0.610878 | ||||||||
\(274\) | 5.72249e10 | 0.613349 | ||||||||
\(275\) | −1.80500e10 | −0.190318 | ||||||||
\(276\) | −2.71986e10 | −0.282134 | ||||||||
\(277\) | −1.06023e11 | −1.08203 | −0.541017 | − | 0.841012i | \(-0.681960\pi\) | ||||
−0.541017 | + | 0.841012i | \(0.681960\pi\) | |||||||
\(278\) | −2.01858e10 | −0.202696 | ||||||||
\(279\) | 2.25019e10 | 0.222332 | ||||||||
\(280\) | −2.03616e10 | −0.197971 | ||||||||
\(281\) | 1.00299e11 | 0.959662 | 0.479831 | − | 0.877361i | \(-0.340698\pi\) | ||||
0.479831 | + | 0.877361i | \(0.340698\pi\) | |||||||
\(282\) | −3.24300e10 | −0.305369 | ||||||||
\(283\) | −2.49296e9 | −0.0231035 | −0.0115517 | − | 0.999933i | \(-0.503677\pi\) | ||||
−0.0115517 | + | 0.999933i | \(0.503677\pi\) | |||||||
\(284\) | 8.51054e10 | 0.776291 | ||||||||
\(285\) | −7.18727e10 | −0.645301 | ||||||||
\(286\) | −4.28566e10 | −0.378766 | ||||||||
\(287\) | 4.69007e10 | 0.408047 | ||||||||
\(288\) | 3.52783e10 | 0.302163 | ||||||||
\(289\) | 1.26281e11 | 1.06487 | ||||||||
\(290\) | 2.09820e10 | 0.174203 | ||||||||
\(291\) | 2.22338e9 | 0.0181759 | ||||||||
\(292\) | −1.84653e11 | −1.48639 | ||||||||
\(293\) | −8.47068e10 | −0.671451 | −0.335725 | − | 0.941960i | \(-0.608981\pi\) | ||||
−0.335725 | + | 0.941960i | \(0.608981\pi\) | |||||||
\(294\) | −2.03914e10 | −0.159179 | ||||||||
\(295\) | 5.32410e10 | 0.409305 | ||||||||
\(296\) | −1.14673e11 | −0.868256 | ||||||||
\(297\) | −1.38910e11 | −1.03592 | ||||||||
\(298\) | −1.17224e10 | −0.0861083 | ||||||||
\(299\) | 6.17411e10 | 0.446739 | ||||||||
\(300\) | 1.99500e10 | 0.142199 | ||||||||
\(301\) | −2.71352e10 | −0.190539 | ||||||||
\(302\) | −2.92412e10 | −0.202285 | ||||||||
\(303\) | 2.47006e10 | 0.168351 | ||||||||
\(304\) | −1.69404e11 | −1.13761 | ||||||||
\(305\) | −2.85929e10 | −0.189195 | ||||||||
\(306\) | 2.64721e10 | 0.172600 | ||||||||
\(307\) | 6.35507e9 | 0.0408317 | 0.0204159 | − | 0.999792i | \(-0.493501\pi\) | ||||
0.0204159 | + | 0.999792i | \(0.493501\pi\) | |||||||
\(308\) | 8.78144e10 | 0.556016 | ||||||||
\(309\) | 8.52987e10 | 0.532267 | ||||||||
\(310\) | −1.68251e10 | −0.103474 | ||||||||
\(311\) | 2.71253e11 | 1.64419 | 0.822096 | − | 0.569350i | \(-0.192805\pi\) | ||||
0.822096 | + | 0.569350i | \(0.192805\pi\) | |||||||
\(312\) | 1.01503e11 | 0.606431 | ||||||||
\(313\) | 1.63499e11 | 0.962865 | 0.481432 | − | 0.876483i | \(-0.340117\pi\) | ||||
0.481432 | + | 0.876483i | \(0.340117\pi\) | |||||||
\(314\) | −4.44153e10 | −0.257839 | ||||||||
\(315\) | 1.77289e10 | 0.101458 | ||||||||
\(316\) | −4.25783e10 | −0.240213 | ||||||||
\(317\) | 2.53606e11 | 1.41056 | 0.705282 | − | 0.708927i | \(-0.250820\pi\) | ||||
0.705282 | + | 0.708927i | \(0.250820\pi\) | |||||||
\(318\) | 3.62416e10 | 0.198740 | ||||||||
\(319\) | −1.93907e11 | −1.04842 | ||||||||
\(320\) | 2.73613e10 | 0.145868 | ||||||||
\(321\) | −1.20510e11 | −0.633508 | ||||||||
\(322\) | 1.80728e10 | 0.0936856 | ||||||||
\(323\) | −4.99167e11 | −2.55173 | ||||||||
\(324\) | 9.45658e10 | 0.476740 | ||||||||
\(325\) | −4.52867e10 | −0.225162 | ||||||||
\(326\) | 1.34110e11 | 0.657630 | ||||||||
\(327\) | 2.84611e11 | 1.37654 | ||||||||
\(328\) | 8.49121e10 | 0.405077 | ||||||||
\(329\) | −1.50842e11 | −0.709808 | ||||||||
\(330\) | 2.63386e10 | 0.122259 | ||||||||
\(331\) | −2.40064e11 | −1.09926 | −0.549631 | − | 0.835408i | \(-0.685232\pi\) | ||||
−0.549631 | + | 0.835408i | \(0.685232\pi\) | |||||||
\(332\) | −1.17244e11 | −0.529628 | ||||||||
\(333\) | 9.98460e10 | 0.444971 | ||||||||
\(334\) | −1.11639e11 | −0.490861 | ||||||||
\(335\) | 2.83038e10 | 0.122785 | ||||||||
\(336\) | −8.12118e10 | −0.347610 | ||||||||
\(337\) | −5.13812e10 | −0.217005 | −0.108502 | − | 0.994096i | \(-0.534606\pi\) | ||||
−0.108502 | + | 0.994096i | \(0.534606\pi\) | |||||||
\(338\) | −2.26895e10 | −0.0945585 | ||||||||
\(339\) | −1.27186e11 | −0.523046 | ||||||||
\(340\) | 1.38556e11 | 0.562302 | ||||||||
\(341\) | 1.55491e11 | 0.622746 | ||||||||
\(342\) | −5.39636e10 | −0.213296 | ||||||||
\(343\) | −2.66027e11 | −1.03777 | ||||||||
\(344\) | −4.91274e10 | −0.189152 | ||||||||
\(345\) | −3.79445e10 | −0.144199 | ||||||||
\(346\) | −1.25600e11 | −0.471137 | ||||||||
\(347\) | 2.76560e11 | 1.02401 | 0.512007 | − | 0.858981i | \(-0.328902\pi\) | ||||
0.512007 | + | 0.858981i | \(0.328902\pi\) | |||||||
\(348\) | 2.14318e11 | 0.783343 | ||||||||
\(349\) | 4.66592e11 | 1.68354 | 0.841770 | − | 0.539837i | \(-0.181514\pi\) | ||||
0.841770 | + | 0.539837i | \(0.181514\pi\) | |||||||
\(350\) | −1.32562e10 | −0.0472188 | ||||||||
\(351\) | −3.48518e11 | −1.22559 | ||||||||
\(352\) | 2.43777e11 | 0.846352 | ||||||||
\(353\) | −1.00998e11 | −0.346198 | −0.173099 | − | 0.984904i | \(-0.555378\pi\) | ||||
−0.173099 | + | 0.984904i | \(0.555378\pi\) | |||||||
\(354\) | −7.76893e10 | −0.262934 | ||||||||
\(355\) | 1.18730e11 | 0.396763 | ||||||||
\(356\) | 8.93251e9 | 0.0294746 | ||||||||
\(357\) | −2.39300e11 | −0.779714 | ||||||||
\(358\) | 2.01521e11 | 0.648406 | ||||||||
\(359\) | −1.66447e11 | −0.528874 | −0.264437 | − | 0.964403i | \(-0.585186\pi\) | ||||
−0.264437 | + | 0.964403i | \(0.585186\pi\) | |||||||
\(360\) | 3.20976e10 | 0.100719 | ||||||||
\(361\) | 6.94869e11 | 2.15338 | ||||||||
\(362\) | −8.35852e10 | −0.255824 | ||||||||
\(363\) | 2.53956e10 | 0.0767677 | ||||||||
\(364\) | 2.20323e11 | 0.657814 | ||||||||
\(365\) | −2.57607e11 | −0.759695 | ||||||||
\(366\) | 4.17228e10 | 0.121537 | ||||||||
\(367\) | −2.97381e11 | −0.855688 | −0.427844 | − | 0.903853i | \(-0.640727\pi\) | ||||
−0.427844 | + | 0.903853i | \(0.640727\pi\) | |||||||
\(368\) | −8.94350e10 | −0.254210 | ||||||||
\(369\) | −7.39332e10 | −0.207597 | ||||||||
\(370\) | −7.46568e10 | −0.207091 | ||||||||
\(371\) | 1.68571e11 | 0.461956 | ||||||||
\(372\) | −1.71859e11 | −0.465295 | ||||||||
\(373\) | 1.95714e11 | 0.523517 | 0.261759 | − | 0.965133i | \(-0.415698\pi\) | ||||
0.261759 | + | 0.965133i | \(0.415698\pi\) | |||||||
\(374\) | 1.82925e11 | 0.483450 | ||||||||
\(375\) | 2.78320e10 | 0.0726782 | ||||||||
\(376\) | −2.73094e11 | −0.704640 | ||||||||
\(377\) | −4.86504e11 | −1.24037 | ||||||||
\(378\) | −1.02018e11 | −0.257017 | ||||||||
\(379\) | −1.67009e11 | −0.415781 | −0.207890 | − | 0.978152i | \(-0.566660\pi\) | ||||
−0.207890 | + | 0.978152i | \(0.566660\pi\) | |||||||
\(380\) | −2.82447e11 | −0.694882 | ||||||||
\(381\) | −3.55741e10 | −0.0864912 | ||||||||
\(382\) | 7.74900e10 | 0.186192 | ||||||||
\(383\) | 7.20782e10 | 0.171163 | 0.0855814 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855814 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(384\) | −3.47855e11 | −0.816408 | ||||||||
\(385\) | 1.22509e11 | 0.284181 | ||||||||
\(386\) | 1.63545e11 | 0.374968 | ||||||||
\(387\) | 4.27754e10 | 0.0969381 | ||||||||
\(388\) | 8.73750e9 | 0.0195724 | ||||||||
\(389\) | 7.92249e11 | 1.75424 | 0.877119 | − | 0.480272i | \(-0.159462\pi\) | ||||
0.877119 | + | 0.480272i | \(0.159462\pi\) | |||||||
\(390\) | 6.60824e10 | 0.144642 | ||||||||
\(391\) | −2.63530e11 | −0.570210 | ||||||||
\(392\) | −1.71717e11 | −0.367305 | ||||||||
\(393\) | 3.21139e11 | 0.679089 | ||||||||
\(394\) | 2.01945e11 | 0.422182 | ||||||||
\(395\) | −5.94005e10 | −0.122773 | ||||||||
\(396\) | −1.38429e11 | −0.282877 | ||||||||
\(397\) | −1.47288e11 | −0.297584 | −0.148792 | − | 0.988869i | \(-0.547538\pi\) | ||||
−0.148792 | + | 0.988869i | \(0.547538\pi\) | |||||||
\(398\) | −6.45389e10 | −0.128928 | ||||||||
\(399\) | 4.87815e11 | 0.963555 | ||||||||
\(400\) | 6.56000e10 | 0.128125 | ||||||||
\(401\) | −3.22101e11 | −0.622075 | −0.311037 | − | 0.950398i | \(-0.600676\pi\) | ||||
−0.311037 | + | 0.950398i | \(0.600676\pi\) | |||||||
\(402\) | −4.13010e10 | −0.0788757 | ||||||||
\(403\) | 3.90121e11 | 0.736761 | ||||||||
\(404\) | 9.70690e10 | 0.181286 | ||||||||
\(405\) | 1.31928e11 | 0.243662 | ||||||||
\(406\) | −1.42409e11 | −0.260117 | ||||||||
\(407\) | 6.89948e11 | 1.24635 | ||||||||
\(408\) | −4.33244e11 | −0.774037 | ||||||||
\(409\) | −3.96423e11 | −0.700493 | −0.350247 | − | 0.936658i | \(-0.613902\pi\) | ||||
−0.350247 | + | 0.936658i | \(0.613902\pi\) | |||||||
\(410\) | 5.52813e10 | 0.0966164 | ||||||||
\(411\) | 8.15455e11 | 1.40965 | ||||||||
\(412\) | 3.35209e11 | 0.573163 | ||||||||
\(413\) | −3.61357e11 | −0.611170 | ||||||||
\(414\) | −2.84895e10 | −0.0476632 | ||||||||
\(415\) | −1.63566e11 | −0.270693 | ||||||||
\(416\) | 6.11627e11 | 1.00131 | ||||||||
\(417\) | −2.87648e11 | −0.465853 | ||||||||
\(418\) | −3.72895e11 | −0.597438 | ||||||||
\(419\) | −1.23162e12 | −1.95215 | −0.976074 | − | 0.217441i | \(-0.930229\pi\) | ||||
−0.976074 | + | 0.217441i | \(0.930229\pi\) | |||||||
\(420\) | −1.35405e11 | −0.212330 | ||||||||
\(421\) | −1.17500e12 | −1.82293 | −0.911465 | − | 0.411379i | \(-0.865047\pi\) | ||||
−0.911465 | + | 0.411379i | \(0.865047\pi\) | |||||||
\(422\) | 6.43671e10 | 0.0988002 | ||||||||
\(423\) | 2.37784e11 | 0.361120 | ||||||||
\(424\) | 3.05192e11 | 0.458593 | ||||||||
\(425\) | 1.93298e11 | 0.287393 | ||||||||
\(426\) | −1.73250e11 | −0.254877 | ||||||||
\(427\) | 1.94066e11 | 0.282503 | ||||||||
\(428\) | −4.73585e11 | −0.682183 | ||||||||
\(429\) | −6.10707e11 | −0.870513 | ||||||||
\(430\) | −3.19840e10 | −0.0451153 | ||||||||
\(431\) | −2.32327e11 | −0.324304 | −0.162152 | − | 0.986766i | \(-0.551843\pi\) | ||||
−0.162152 | + | 0.986766i | \(0.551843\pi\) | |||||||
\(432\) | 5.04846e11 | 0.697400 | ||||||||
\(433\) | −1.51554e11 | −0.207191 | −0.103596 | − | 0.994620i | \(-0.533035\pi\) | ||||
−0.103596 | + | 0.994620i | \(0.533035\pi\) | |||||||
\(434\) | 1.14196e11 | 0.154506 | ||||||||
\(435\) | 2.98993e11 | 0.400368 | ||||||||
\(436\) | 1.11847e12 | 1.48230 | ||||||||
\(437\) | 5.37209e11 | 0.704655 | ||||||||
\(438\) | 3.75900e11 | 0.488021 | ||||||||
\(439\) | −5.21385e11 | −0.669990 | −0.334995 | − | 0.942220i | \(-0.608735\pi\) | ||||
−0.334995 | + | 0.942220i | \(0.608735\pi\) | |||||||
\(440\) | 2.21798e11 | 0.282112 | ||||||||
\(441\) | 1.49515e11 | 0.188240 | ||||||||
\(442\) | 4.58952e11 | 0.571962 | ||||||||
\(443\) | 1.10169e12 | 1.35908 | 0.679539 | − | 0.733639i | \(-0.262180\pi\) | ||||
0.679539 | + | 0.733639i | \(0.262180\pi\) | |||||||
\(444\) | −7.62574e11 | −0.931234 | ||||||||
\(445\) | 1.24616e10 | 0.0150645 | ||||||||
\(446\) | −2.54894e11 | −0.305038 | ||||||||
\(447\) | −1.67045e11 | −0.197901 | ||||||||
\(448\) | −1.85706e11 | −0.217809 | ||||||||
\(449\) | 5.85672e11 | 0.680058 | 0.340029 | − | 0.940415i | \(-0.389563\pi\) | ||||
0.340029 | + | 0.940415i | \(0.389563\pi\) | |||||||
\(450\) | 2.08969e10 | 0.0240229 | ||||||||
\(451\) | −5.10888e11 | −0.581475 | ||||||||
\(452\) | −4.99817e11 | −0.563233 | ||||||||
\(453\) | −4.16687e11 | −0.464909 | ||||||||
\(454\) | −2.42097e11 | −0.267447 | ||||||||
\(455\) | 3.07370e11 | 0.336210 | ||||||||
\(456\) | 8.83172e11 | 0.956541 | ||||||||
\(457\) | −5.70804e11 | −0.612159 | −0.306079 | − | 0.952006i | \(-0.599017\pi\) | ||||
−0.306079 | + | 0.952006i | \(0.599017\pi\) | |||||||
\(458\) | −1.64881e11 | −0.175096 | ||||||||
\(459\) | 1.48758e12 | 1.56432 | ||||||||
\(460\) | −1.49115e11 | −0.155279 | ||||||||
\(461\) | −7.60279e11 | −0.784005 | −0.392002 | − | 0.919964i | \(-0.628218\pi\) | ||||
−0.392002 | + | 0.919964i | \(0.628218\pi\) | |||||||
\(462\) | −1.78765e11 | −0.182555 | ||||||||
\(463\) | −7.14289e11 | −0.722370 | −0.361185 | − | 0.932494i | \(-0.617628\pi\) | ||||
−0.361185 | + | 0.932494i | \(0.617628\pi\) | |||||||
\(464\) | 7.04725e11 | 0.705812 | ||||||||
\(465\) | −2.39758e11 | −0.237813 | ||||||||
\(466\) | −2.89388e10 | −0.0284279 | ||||||||
\(467\) | 7.82521e11 | 0.761325 | 0.380662 | − | 0.924714i | \(-0.375696\pi\) | ||||
0.380662 | + | 0.924714i | \(0.375696\pi\) | |||||||
\(468\) | −3.47312e11 | −0.334668 | ||||||||
\(469\) | −1.92104e11 | −0.183340 | ||||||||
\(470\) | −1.77796e11 | −0.168066 | ||||||||
\(471\) | −6.32917e11 | −0.592588 | ||||||||
\(472\) | −6.54226e11 | −0.606720 | ||||||||
\(473\) | 2.95583e11 | 0.271522 | ||||||||
\(474\) | 8.66772e10 | 0.0788683 | ||||||||
\(475\) | −3.94039e11 | −0.355155 | ||||||||
\(476\) | −9.40406e11 | −0.839622 | ||||||||
\(477\) | −2.65732e11 | −0.235023 | ||||||||
\(478\) | −1.77533e10 | −0.0155544 | ||||||||
\(479\) | −6.95738e11 | −0.603860 | −0.301930 | − | 0.953330i | \(-0.597631\pi\) | ||||
−0.301930 | + | 0.953330i | \(0.597631\pi\) | |||||||
\(480\) | −3.75890e11 | −0.323203 | ||||||||
\(481\) | 1.73105e12 | 1.47454 | ||||||||
\(482\) | −2.06382e11 | −0.174164 | ||||||||
\(483\) | 2.57537e11 | 0.215316 | ||||||||
\(484\) | 9.98003e10 | 0.0826661 | ||||||||
\(485\) | 1.21896e10 | 0.0100035 | ||||||||
\(486\) | 2.80856e11 | 0.228360 | ||||||||
\(487\) | −1.65196e12 | −1.33082 | −0.665408 | − | 0.746480i | \(-0.731742\pi\) | ||||
−0.665408 | + | 0.746480i | \(0.731742\pi\) | |||||||
\(488\) | 3.51350e11 | 0.280447 | ||||||||
\(489\) | 1.91107e12 | 1.51142 | ||||||||
\(490\) | −1.11795e11 | −0.0876074 | ||||||||
\(491\) | 1.19989e12 | 0.931694 | 0.465847 | − | 0.884865i | \(-0.345750\pi\) | ||||
0.465847 | + | 0.884865i | \(0.345750\pi\) | |||||||
\(492\) | 5.64665e11 | 0.434458 | ||||||||
\(493\) | 2.07655e12 | 1.58318 | ||||||||
\(494\) | −9.35578e11 | −0.706820 | ||||||||
\(495\) | −1.93121e11 | −0.144579 | ||||||||
\(496\) | −5.65109e11 | −0.419242 | ||||||||
\(497\) | −8.05842e11 | −0.592442 | ||||||||
\(498\) | 2.38676e11 | 0.173891 | ||||||||
\(499\) | 1.43146e12 | 1.03354 | 0.516768 | − | 0.856125i | \(-0.327135\pi\) | ||||
0.516768 | + | 0.856125i | \(0.327135\pi\) | |||||||
\(500\) | 1.09375e11 | 0.0782624 | ||||||||
\(501\) | −1.59086e12 | −1.12814 | ||||||||
\(502\) | 7.13478e11 | 0.501434 | ||||||||
\(503\) | 1.41833e12 | 0.987919 | 0.493959 | − | 0.869485i | \(-0.335549\pi\) | ||||
0.493959 | + | 0.869485i | \(0.335549\pi\) | |||||||
\(504\) | −2.17853e11 | −0.150392 | ||||||||
\(505\) | 1.35420e11 | 0.0926555 | ||||||||
\(506\) | −1.96866e11 | −0.133504 | ||||||||
\(507\) | −3.23326e11 | −0.217323 | ||||||||
\(508\) | −1.39800e11 | −0.0931367 | ||||||||
\(509\) | −1.16463e12 | −0.769059 | −0.384529 | − | 0.923113i | \(-0.625636\pi\) | ||||
−0.384529 | + | 0.923113i | \(0.625636\pi\) | |||||||
\(510\) | −2.82060e11 | −0.184619 | ||||||||
\(511\) | 1.74843e12 | 1.13437 | ||||||||
\(512\) | −1.54632e12 | −0.994455 | ||||||||
\(513\) | −3.03245e12 | −1.93315 | ||||||||
\(514\) | 8.80466e11 | 0.556389 | ||||||||
\(515\) | 4.67646e11 | 0.292944 | ||||||||
\(516\) | −3.26697e11 | −0.202872 | ||||||||
\(517\) | 1.64312e12 | 1.01149 | ||||||||
\(518\) | 5.06711e11 | 0.309226 | ||||||||
\(519\) | −1.78980e12 | −1.08281 | ||||||||
\(520\) | 5.56483e11 | 0.333762 | ||||||||
\(521\) | −8.36946e11 | −0.497654 | −0.248827 | − | 0.968548i | \(-0.580045\pi\) | ||||
−0.248827 | + | 0.968548i | \(0.580045\pi\) | |||||||
\(522\) | 2.24490e11 | 0.132337 | ||||||||
\(523\) | −2.60288e12 | −1.52124 | −0.760618 | − | 0.649199i | \(-0.775104\pi\) | ||||
−0.760618 | + | 0.649199i | \(0.775104\pi\) | |||||||
\(524\) | 1.26202e12 | 0.731267 | ||||||||
\(525\) | −1.88902e11 | −0.108522 | ||||||||
\(526\) | −1.65099e11 | −0.0940394 | ||||||||
\(527\) | −1.66516e12 | −0.940389 | ||||||||
\(528\) | 8.84638e11 | 0.495351 | ||||||||
\(529\) | −1.51754e12 | −0.842538 | ||||||||
\(530\) | 1.98693e11 | 0.109381 | ||||||||
\(531\) | 5.69636e11 | 0.310937 | ||||||||
\(532\) | 1.91703e12 | 1.03759 | ||||||||
\(533\) | −1.28180e12 | −0.687934 | ||||||||
\(534\) | −1.81840e10 | −0.00967731 | ||||||||
\(535\) | −6.60693e11 | −0.348664 | ||||||||
\(536\) | −3.47798e11 | −0.182006 | ||||||||
\(537\) | 2.87168e12 | 1.49022 | ||||||||
\(538\) | 2.11912e11 | 0.109052 | ||||||||
\(539\) | 1.03317e12 | 0.527255 | ||||||||
\(540\) | 8.41730e11 | 0.425992 | ||||||||
\(541\) | 3.07406e12 | 1.54286 | 0.771428 | − | 0.636317i | \(-0.219543\pi\) | ||||
0.771428 | + | 0.636317i | \(0.219543\pi\) | |||||||
\(542\) | −2.75203e11 | −0.136980 | ||||||||
\(543\) | −1.19109e12 | −0.587956 | ||||||||
\(544\) | −2.61061e12 | −1.27805 | ||||||||
\(545\) | 1.56037e12 | 0.757606 | ||||||||
\(546\) | −4.48514e11 | −0.215978 | ||||||||
\(547\) | 1.32972e12 | 0.635062 | 0.317531 | − | 0.948248i | \(-0.397146\pi\) | ||||
0.317531 | + | 0.948248i | \(0.397146\pi\) | |||||||
\(548\) | 3.20460e12 | 1.51796 | ||||||||
\(549\) | −3.05921e11 | −0.143726 | ||||||||
\(550\) | 1.44400e11 | 0.0672876 | ||||||||
\(551\) | −4.23307e12 | −1.95647 | ||||||||
\(552\) | 4.66262e11 | 0.213749 | ||||||||
\(553\) | 4.03163e11 | 0.183323 | ||||||||
\(554\) | 8.48183e11 | 0.382557 | ||||||||
\(555\) | −1.06386e12 | −0.475955 | ||||||||
\(556\) | −1.13041e12 | −0.501647 | ||||||||
\(557\) | 2.49418e12 | 1.09794 | 0.548971 | − | 0.835841i | \(-0.315020\pi\) | ||||
0.548971 | + | 0.835841i | \(0.315020\pi\) | |||||||
\(558\) | −1.80016e11 | −0.0786061 | ||||||||
\(559\) | 7.41606e11 | 0.321233 | ||||||||
\(560\) | −4.45240e11 | −0.191315 | ||||||||
\(561\) | 2.60669e12 | 1.11111 | ||||||||
\(562\) | −8.02392e11 | −0.339292 | ||||||||
\(563\) | 1.06689e12 | 0.447541 | 0.223770 | − | 0.974642i | \(-0.428163\pi\) | ||||
0.223770 | + | 0.974642i | \(0.428163\pi\) | |||||||
\(564\) | −1.81608e12 | −0.755750 | ||||||||
\(565\) | −6.97290e11 | −0.287869 | ||||||||
\(566\) | 1.99437e10 | 0.00816831 | ||||||||
\(567\) | −8.95420e11 | −0.363834 | ||||||||
\(568\) | −1.45895e12 | −0.588129 | ||||||||
\(569\) | −4.57278e12 | −1.82884 | −0.914420 | − | 0.404768i | \(-0.867352\pi\) | ||||
−0.914420 | + | 0.404768i | \(0.867352\pi\) | |||||||
\(570\) | 5.74982e11 | 0.228148 | ||||||||
\(571\) | −2.32305e12 | −0.914525 | −0.457263 | − | 0.889332i | \(-0.651170\pi\) | ||||
−0.457263 | + | 0.889332i | \(0.651170\pi\) | |||||||
\(572\) | −2.39997e12 | −0.937398 | ||||||||
\(573\) | 1.10423e12 | 0.427922 | ||||||||
\(574\) | −3.75205e11 | −0.144266 | ||||||||
\(575\) | −2.08029e11 | −0.0793631 | ||||||||
\(576\) | 2.92744e11 | 0.110812 | ||||||||
\(577\) | 1.01144e12 | 0.379881 | 0.189940 | − | 0.981796i | \(-0.439171\pi\) | ||||
0.189940 | + | 0.981796i | \(0.439171\pi\) | |||||||
\(578\) | −1.01025e12 | −0.376489 | ||||||||
\(579\) | 2.33051e12 | 0.861784 | ||||||||
\(580\) | 1.17499e12 | 0.431130 | ||||||||
\(581\) | 1.11016e12 | 0.404196 | ||||||||
\(582\) | −1.77871e10 | −0.00642615 | ||||||||
\(583\) | −1.83624e12 | −0.658296 | ||||||||
\(584\) | 3.16547e12 | 1.12611 | ||||||||
\(585\) | −4.84532e11 | −0.171049 | ||||||||
\(586\) | 6.77654e11 | 0.237394 | ||||||||
\(587\) | −1.10143e12 | −0.382899 | −0.191449 | − | 0.981502i | \(-0.561319\pi\) | ||||
−0.191449 | + | 0.981502i | \(0.561319\pi\) | |||||||
\(588\) | −1.14192e12 | −0.393947 | ||||||||
\(589\) | 3.39444e12 | 1.16211 | ||||||||
\(590\) | −4.25928e11 | −0.144711 | ||||||||
\(591\) | 2.87772e12 | 0.970296 | ||||||||
\(592\) | −2.50751e12 | −0.839065 | ||||||||
\(593\) | 9.84366e11 | 0.326897 | 0.163448 | − | 0.986552i | \(-0.447738\pi\) | ||||
0.163448 | + | 0.986552i | \(0.447738\pi\) | |||||||
\(594\) | 1.11128e12 | 0.366255 | ||||||||
\(595\) | −1.31195e12 | −0.429132 | ||||||||
\(596\) | −6.56457e11 | −0.213107 | ||||||||
\(597\) | −9.19679e11 | −0.296314 | ||||||||
\(598\) | −4.93929e11 | −0.157946 | ||||||||
\(599\) | 4.51397e12 | 1.43264 | 0.716321 | − | 0.697771i | \(-0.245825\pi\) | ||||
0.716321 | + | 0.697771i | \(0.245825\pi\) | |||||||
\(600\) | −3.42000e11 | −0.107732 | ||||||||
\(601\) | −1.44212e12 | −0.450885 | −0.225443 | − | 0.974256i | \(-0.572383\pi\) | ||||
−0.225443 | + | 0.974256i | \(0.572383\pi\) | |||||||
\(602\) | 2.17082e11 | 0.0673657 | ||||||||
\(603\) | 3.02829e11 | 0.0932758 | ||||||||
\(604\) | −1.63751e12 | −0.500630 | ||||||||
\(605\) | 1.39230e11 | 0.0422508 | ||||||||
\(606\) | −1.97605e11 | −0.0595211 | ||||||||
\(607\) | −4.12105e12 | −1.23214 | −0.616069 | − | 0.787692i | \(-0.711276\pi\) | ||||
−0.616069 | + | 0.787692i | \(0.711276\pi\) | |||||||
\(608\) | 5.32176e12 | 1.57939 | ||||||||
\(609\) | −2.02932e12 | −0.597824 | ||||||||
\(610\) | 2.28743e11 | 0.0668904 | ||||||||
\(611\) | 4.12252e12 | 1.19668 | ||||||||
\(612\) | 1.48244e12 | 0.427164 | ||||||||
\(613\) | 1.38470e12 | 0.396080 | 0.198040 | − | 0.980194i | \(-0.436542\pi\) | ||||
0.198040 | + | 0.980194i | \(0.436542\pi\) | |||||||
\(614\) | −5.08406e10 | −0.0144362 | ||||||||
\(615\) | 7.87759e11 | 0.222052 | ||||||||
\(616\) | −1.50539e12 | −0.421246 | ||||||||
\(617\) | 6.22714e11 | 0.172984 | 0.0864918 | − | 0.996253i | \(-0.472434\pi\) | ||||
0.0864918 | + | 0.996253i | \(0.472434\pi\) | |||||||
\(618\) | −6.82390e11 | −0.188185 | ||||||||
\(619\) | 1.89438e12 | 0.518631 | 0.259315 | − | 0.965793i | \(-0.416503\pi\) | ||||
0.259315 | + | 0.965793i | \(0.416503\pi\) | |||||||
\(620\) | −9.42208e11 | −0.256085 | ||||||||
\(621\) | −1.60095e12 | −0.431983 | ||||||||
\(622\) | −2.17002e12 | −0.581309 | ||||||||
\(623\) | −8.45797e10 | −0.0224942 | ||||||||
\(624\) | 2.21952e12 | 0.586042 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | −1.30799e12 | −0.340424 | ||||||||
\(627\) | −5.31375e12 | −1.37308 | ||||||||
\(628\) | −2.48725e12 | −0.638119 | ||||||||
\(629\) | −7.38866e12 | −1.88208 | ||||||||
\(630\) | −1.41831e11 | −0.0358707 | ||||||||
\(631\) | −1.10160e12 | −0.276624 | −0.138312 | − | 0.990389i | \(-0.544168\pi\) | ||||
−0.138312 | + | 0.990389i | \(0.544168\pi\) | |||||||
\(632\) | 7.29914e11 | 0.181989 | ||||||||
\(633\) | 9.17231e11 | 0.227071 | ||||||||
\(634\) | −2.02885e12 | −0.498710 | ||||||||
\(635\) | −1.95034e11 | −0.0476023 | ||||||||
\(636\) | 2.02953e12 | 0.491856 | ||||||||
\(637\) | 2.59217e12 | 0.623787 | ||||||||
\(638\) | 1.55125e12 | 0.370672 | ||||||||
\(639\) | 1.27031e12 | 0.301409 | ||||||||
\(640\) | −1.90710e12 | −0.449328 | ||||||||
\(641\) | −4.85252e12 | −1.13529 | −0.567644 | − | 0.823274i | \(-0.692145\pi\) | ||||
−0.567644 | + | 0.823274i | \(0.692145\pi\) | |||||||
\(642\) | 9.64083e11 | 0.223979 | ||||||||
\(643\) | 1.57487e12 | 0.363325 | 0.181662 | − | 0.983361i | \(-0.441852\pi\) | ||||
0.181662 | + | 0.983361i | \(0.441852\pi\) | |||||||
\(644\) | 1.01207e12 | 0.231860 | ||||||||
\(645\) | −4.55772e11 | −0.103688 | ||||||||
\(646\) | 3.99334e12 | 0.902172 | ||||||||
\(647\) | 6.93025e12 | 1.55482 | 0.777410 | − | 0.628995i | \(-0.216533\pi\) | ||||
0.777410 | + | 0.628995i | \(0.216533\pi\) | |||||||
\(648\) | −1.62113e12 | −0.361185 | ||||||||
\(649\) | 3.93626e12 | 0.870928 | ||||||||
\(650\) | 3.62294e11 | 0.0796069 | ||||||||
\(651\) | 1.62729e12 | 0.355099 | ||||||||
\(652\) | 7.51015e12 | 1.62755 | ||||||||
\(653\) | −8.15499e12 | −1.75515 | −0.877575 | − | 0.479440i | \(-0.840840\pi\) | ||||
−0.877575 | + | 0.479440i | \(0.840840\pi\) | |||||||
\(654\) | −2.27689e12 | −0.486679 | ||||||||
\(655\) | 1.76063e12 | 0.373751 | ||||||||
\(656\) | 1.85674e12 | 0.391458 | ||||||||
\(657\) | −2.75619e12 | −0.577118 | ||||||||
\(658\) | 1.20674e12 | 0.250955 | ||||||||
\(659\) | −2.92553e12 | −0.604255 | −0.302127 | − | 0.953268i | \(-0.597697\pi\) | ||||
−0.302127 | + | 0.953268i | \(0.597697\pi\) | |||||||
\(660\) | 1.47496e12 | 0.302575 | ||||||||
\(661\) | −1.62921e12 | −0.331947 | −0.165974 | − | 0.986130i | \(-0.553077\pi\) | ||||
−0.165974 | + | 0.986130i | \(0.553077\pi\) | |||||||
\(662\) | 1.92051e12 | 0.388648 | ||||||||
\(663\) | 6.54007e12 | 1.31453 | ||||||||
\(664\) | 2.00990e12 | 0.401254 | ||||||||
\(665\) | 2.67442e12 | 0.530313 | ||||||||
\(666\) | −7.98768e11 | −0.157321 | ||||||||
\(667\) | −2.23480e12 | −0.437193 | ||||||||
\(668\) | −6.25181e12 | −1.21482 | ||||||||
\(669\) | −3.63225e12 | −0.701064 | ||||||||
\(670\) | −2.26431e11 | −0.0434109 | ||||||||
\(671\) | −2.11395e12 | −0.402572 | ||||||||
\(672\) | 2.55124e12 | 0.482603 | ||||||||
\(673\) | −2.87521e12 | −0.540258 | −0.270129 | − | 0.962824i | \(-0.587066\pi\) | ||||
−0.270129 | + | 0.962824i | \(0.587066\pi\) | |||||||
\(674\) | 4.11049e11 | 0.0767228 | ||||||||
\(675\) | 1.17429e12 | 0.217725 | ||||||||
\(676\) | −1.27061e12 | −0.234020 | ||||||||
\(677\) | 3.19620e12 | 0.584769 | 0.292385 | − | 0.956301i | \(-0.405551\pi\) | ||||
0.292385 | + | 0.956301i | \(0.405551\pi\) | |||||||
\(678\) | 1.01749e12 | 0.184925 | ||||||||
\(679\) | −8.27332e10 | −0.0149371 | ||||||||
\(680\) | −2.37524e12 | −0.426008 | ||||||||
\(681\) | −3.44988e12 | −0.614670 | ||||||||
\(682\) | −1.24393e12 | −0.220174 | ||||||||
\(683\) | −5.47901e11 | −0.0963406 | −0.0481703 | − | 0.998839i | \(-0.515339\pi\) | ||||
−0.0481703 | + | 0.998839i | \(0.515339\pi\) | |||||||
\(684\) | −3.02196e12 | −0.527881 | ||||||||
\(685\) | 4.47070e12 | 0.775832 | ||||||||
\(686\) | 2.12822e12 | 0.366908 | ||||||||
\(687\) | −2.34955e12 | −0.402420 | ||||||||
\(688\) | −1.07425e12 | −0.182792 | ||||||||
\(689\) | −4.60705e12 | −0.778819 | ||||||||
\(690\) | 3.03556e11 | 0.0509821 | ||||||||
\(691\) | 5.90996e11 | 0.0986128 | 0.0493064 | − | 0.998784i | \(-0.484299\pi\) | ||||
0.0493064 | + | 0.998784i | \(0.484299\pi\) | |||||||
\(692\) | −7.03361e12 | −1.16601 | ||||||||
\(693\) | 1.31075e12 | 0.215884 | ||||||||
\(694\) | −2.21248e12 | −0.362044 | ||||||||
\(695\) | −1.57702e12 | −0.256392 | ||||||||
\(696\) | −3.67402e12 | −0.593472 | ||||||||
\(697\) | 5.47110e12 | 0.878066 | ||||||||
\(698\) | −3.73274e12 | −0.595221 | ||||||||
\(699\) | −4.12378e11 | −0.0653354 | ||||||||
\(700\) | −7.42350e11 | −0.116860 | ||||||||
\(701\) | 7.12738e12 | 1.11481 | 0.557403 | − | 0.830242i | \(-0.311798\pi\) | ||||
0.557403 | + | 0.830242i | \(0.311798\pi\) | |||||||
\(702\) | 2.78815e12 | 0.433310 | ||||||||
\(703\) | 1.50619e13 | 2.32584 | ||||||||
\(704\) | 2.02290e12 | 0.310382 | ||||||||
\(705\) | −2.53359e12 | −0.386265 | ||||||||
\(706\) | 8.07981e11 | 0.122400 | ||||||||
\(707\) | −9.19122e11 | −0.138352 | ||||||||
\(708\) | −4.35060e12 | −0.650728 | ||||||||
\(709\) | 9.09269e11 | 0.135140 | 0.0675701 | − | 0.997715i | \(-0.478475\pi\) | ||||
0.0675701 | + | 0.997715i | \(0.478475\pi\) | |||||||
\(710\) | −9.49837e11 | −0.140277 | ||||||||
\(711\) | −6.35538e11 | −0.0932671 | ||||||||
\(712\) | −1.53129e11 | −0.0223304 | ||||||||
\(713\) | 1.79206e12 | 0.259687 | ||||||||
\(714\) | 1.91440e12 | 0.275670 | ||||||||
\(715\) | −3.34817e12 | −0.479105 | ||||||||
\(716\) | 1.12852e13 | 1.60472 | ||||||||
\(717\) | −2.52985e11 | −0.0357485 | ||||||||
\(718\) | 1.33158e12 | 0.186985 | ||||||||
\(719\) | 1.08017e13 | 1.50734 | 0.753669 | − | 0.657254i | \(-0.228282\pi\) | ||||
0.753669 | + | 0.657254i | \(0.228282\pi\) | |||||||
\(720\) | 7.01868e11 | 0.0973327 | ||||||||
\(721\) | −3.17401e12 | −0.437421 | ||||||||
\(722\) | −5.55895e12 | −0.761334 | ||||||||
\(723\) | −2.94094e12 | −0.400280 | ||||||||
\(724\) | −4.68077e12 | −0.633132 | ||||||||
\(725\) | 1.63921e12 | 0.220351 | ||||||||
\(726\) | −2.03165e11 | −0.0271415 | ||||||||
\(727\) | −9.77691e12 | −1.29807 | −0.649033 | − | 0.760760i | \(-0.724826\pi\) | ||||
−0.649033 | + | 0.760760i | \(0.724826\pi\) | |||||||
\(728\) | −3.77696e12 | −0.498370 | ||||||||
\(729\) | 8.15697e12 | 1.06968 | ||||||||
\(730\) | 2.06085e12 | 0.268593 | ||||||||
\(731\) | −3.16540e12 | −0.410016 | ||||||||
\(732\) | 2.33647e12 | 0.300788 | ||||||||
\(733\) | 3.52295e11 | 0.0450753 | 0.0225377 | − | 0.999746i | \(-0.492825\pi\) | ||||
0.0225377 | + | 0.999746i | \(0.492825\pi\) | |||||||
\(734\) | 2.37905e12 | 0.302531 | ||||||||
\(735\) | −1.59308e12 | −0.201347 | ||||||||
\(736\) | 2.80957e12 | 0.352931 | ||||||||
\(737\) | 2.09258e12 | 0.261264 | ||||||||
\(738\) | 5.91466e11 | 0.0733966 | ||||||||
\(739\) | −2.72124e12 | −0.335635 | −0.167818 | − | 0.985818i | \(-0.553672\pi\) | ||||
−0.167818 | + | 0.985818i | \(0.553672\pi\) | |||||||
\(740\) | −4.18078e12 | −0.512524 | ||||||||
\(741\) | −1.33320e13 | −1.62447 | ||||||||
\(742\) | −1.34857e12 | −0.163326 | ||||||||
\(743\) | −5.85311e12 | −0.704590 | −0.352295 | − | 0.935889i | \(-0.614599\pi\) | ||||
−0.352295 | + | 0.935889i | \(0.614599\pi\) | |||||||
\(744\) | 2.94615e12 | 0.352514 | ||||||||
\(745\) | −9.15816e11 | −0.108919 | ||||||||
\(746\) | −1.56571e12 | −0.185091 | ||||||||
\(747\) | −1.75003e12 | −0.205638 | ||||||||
\(748\) | 1.02438e13 | 1.19648 | ||||||||
\(749\) | 4.48426e12 | 0.520622 | ||||||||
\(750\) | −2.22656e11 | −0.0256956 | ||||||||
\(751\) | −5.13723e12 | −0.589317 | −0.294659 | − | 0.955603i | \(-0.595206\pi\) | ||||
−0.294659 | + | 0.955603i | \(0.595206\pi\) | |||||||
\(752\) | −5.97166e12 | −0.680950 | ||||||||
\(753\) | 1.01671e13 | 1.15244 | ||||||||
\(754\) | 3.89203e12 | 0.438536 | ||||||||
\(755\) | −2.28447e12 | −0.255873 | ||||||||
\(756\) | −5.71299e12 | −0.636086 | ||||||||
\(757\) | −1.45713e13 | −1.61275 | −0.806373 | − | 0.591407i | \(-0.798573\pi\) | ||||
−0.806373 | + | 0.591407i | \(0.798573\pi\) | |||||||
\(758\) | 1.33607e12 | 0.147001 | ||||||||
\(759\) | −2.80534e12 | −0.306830 | ||||||||
\(760\) | 4.84195e12 | 0.526453 | ||||||||
\(761\) | 1.03936e13 | 1.12340 | 0.561700 | − | 0.827341i | \(-0.310148\pi\) | ||||
0.561700 | + | 0.827341i | \(0.310148\pi\) | |||||||
\(762\) | 2.84593e11 | 0.0305793 | ||||||||
\(763\) | −1.05905e13 | −1.13125 | ||||||||
\(764\) | 4.33944e12 | 0.460801 | ||||||||
\(765\) | 2.06813e12 | 0.218324 | ||||||||
\(766\) | −5.76626e11 | −0.0605152 | ||||||||
\(767\) | 9.87591e12 | 1.03038 | ||||||||
\(768\) | 2.27600e11 | 0.0236073 | ||||||||
\(769\) | −3.91664e12 | −0.403873 | −0.201936 | − | 0.979399i | \(-0.564723\pi\) | ||||
−0.201936 | + | 0.979399i | \(0.564723\pi\) | |||||||
\(770\) | −9.80072e11 | −0.100473 | ||||||||
\(771\) | 1.25466e13 | 1.27874 | ||||||||
\(772\) | 9.15851e12 | 0.927998 | ||||||||
\(773\) | −6.36894e12 | −0.641592 | −0.320796 | − | 0.947148i | \(-0.603950\pi\) | ||||
−0.320796 | + | 0.947148i | \(0.603950\pi\) | |||||||
\(774\) | −3.42203e11 | −0.0342728 | ||||||||
\(775\) | −1.31446e12 | −0.130885 | ||||||||
\(776\) | −1.49786e11 | −0.0148284 | ||||||||
\(777\) | 7.22063e12 | 0.710690 | ||||||||
\(778\) | −6.33800e12 | −0.620217 | ||||||||
\(779\) | −1.11529e13 | −1.08510 | ||||||||
\(780\) | 3.70061e12 | 0.357971 | ||||||||
\(781\) | 8.77802e12 | 0.844242 | ||||||||
\(782\) | 2.10824e12 | 0.201600 | ||||||||
\(783\) | 1.26151e13 | 1.19940 | ||||||||
\(784\) | −3.75489e12 | −0.354956 | ||||||||
\(785\) | −3.46994e12 | −0.326143 | ||||||||
\(786\) | −2.56911e12 | −0.240094 | ||||||||
\(787\) | 6.55343e11 | 0.0608951 | 0.0304475 | − | 0.999536i | \(-0.490307\pi\) | ||||
0.0304475 | + | 0.999536i | \(0.490307\pi\) | |||||||
\(788\) | 1.13089e13 | 1.04485 | ||||||||
\(789\) | −2.35267e12 | −0.216129 | ||||||||
\(790\) | 4.75204e11 | 0.0434069 | ||||||||
\(791\) | 4.73265e12 | 0.429843 | ||||||||
\(792\) | 2.37307e12 | 0.214312 | ||||||||
\(793\) | −5.30382e12 | −0.476277 | ||||||||
\(794\) | 1.17830e12 | 0.105212 | ||||||||
\(795\) | 2.83137e12 | 0.251388 | ||||||||
\(796\) | −3.61418e12 | −0.319081 | ||||||||
\(797\) | 3.83799e12 | 0.336931 | 0.168466 | − | 0.985708i | \(-0.446119\pi\) | ||||
0.168466 | + | 0.985708i | \(0.446119\pi\) | |||||||
\(798\) | −3.90252e12 | −0.340668 | ||||||||
\(799\) | −1.75962e13 | −1.52742 | ||||||||
\(800\) | −2.06080e12 | −0.177882 | ||||||||
\(801\) | 1.33330e11 | 0.0114441 | ||||||||
\(802\) | 2.57681e12 | 0.219937 | ||||||||
\(803\) | −1.90456e13 | −1.61650 | ||||||||
\(804\) | −2.31285e12 | −0.195207 | ||||||||
\(805\) | 1.41193e12 | 0.118504 | ||||||||
\(806\) | −3.12097e12 | −0.260484 | ||||||||
\(807\) | 3.01974e12 | 0.250633 | ||||||||
\(808\) | −1.66404e12 | −0.137345 | ||||||||
\(809\) | 2.67581e12 | 0.219627 | 0.109814 | − | 0.993952i | \(-0.464975\pi\) | ||||
0.109814 | + | 0.993952i | \(0.464975\pi\) | |||||||
\(810\) | −1.05542e12 | −0.0861476 | ||||||||
\(811\) | −2.32586e13 | −1.88795 | −0.943973 | − | 0.330023i | \(-0.892943\pi\) | ||||
−0.943973 | + | 0.330023i | \(0.892943\pi\) | |||||||
\(812\) | −7.97489e12 | −0.643758 | ||||||||
\(813\) | −3.92165e12 | −0.314819 | ||||||||
\(814\) | −5.51959e12 | −0.440653 | ||||||||
\(815\) | 1.04773e13 | 0.831843 | ||||||||
\(816\) | −9.47360e12 | −0.748014 | ||||||||
\(817\) | 6.45270e12 | 0.506690 | ||||||||
\(818\) | 3.17138e12 | 0.247662 | ||||||||
\(819\) | 3.28861e12 | 0.255408 | ||||||||
\(820\) | 3.09575e12 | 0.239113 | ||||||||
\(821\) | 1.65740e13 | 1.27316 | 0.636580 | − | 0.771211i | \(-0.280349\pi\) | ||||
0.636580 | + | 0.771211i | \(0.280349\pi\) | |||||||
\(822\) | −6.52364e12 | −0.498387 | ||||||||
\(823\) | 1.37332e13 | 1.04345 | 0.521726 | − | 0.853113i | \(-0.325288\pi\) | ||||
0.521726 | + | 0.853113i | \(0.325288\pi\) | |||||||
\(824\) | −5.74644e12 | −0.434236 | ||||||||
\(825\) | 2.05770e12 | 0.154646 | ||||||||
\(826\) | 2.89086e12 | 0.216081 | ||||||||
\(827\) | 1.80036e13 | 1.33840 | 0.669198 | − | 0.743085i | \(-0.266638\pi\) | ||||
0.669198 | + | 0.743085i | \(0.266638\pi\) | |||||||
\(828\) | −1.59541e12 | −0.117960 | ||||||||
\(829\) | 2.11116e13 | 1.55248 | 0.776240 | − | 0.630438i | \(-0.217125\pi\) | ||||
0.776240 | + | 0.630438i | \(0.217125\pi\) | |||||||
\(830\) | 1.30853e12 | 0.0957046 | ||||||||
\(831\) | 1.20866e13 | 0.879225 | ||||||||
\(832\) | 5.07536e12 | 0.367208 | ||||||||
\(833\) | −1.10642e13 | −0.796191 | ||||||||
\(834\) | 2.30118e12 | 0.164704 | ||||||||
\(835\) | −8.72183e12 | −0.620896 | ||||||||
\(836\) | −2.08821e13 | −1.47858 | ||||||||
\(837\) | −1.01159e13 | −0.712425 | ||||||||
\(838\) | 9.85294e12 | 0.690188 | ||||||||
\(839\) | −3.47988e12 | −0.242458 | −0.121229 | − | 0.992625i | \(-0.538683\pi\) | ||||
−0.121229 | + | 0.992625i | \(0.538683\pi\) | |||||||
\(840\) | 2.32122e12 | 0.160864 | ||||||||
\(841\) | 3.10254e12 | 0.213863 | ||||||||
\(842\) | 9.40003e12 | 0.644503 | ||||||||
\(843\) | −1.14341e13 | −0.779789 | ||||||||
\(844\) | 3.60456e12 | 0.244518 | ||||||||
\(845\) | −1.77262e12 | −0.119608 | ||||||||
\(846\) | −1.90227e12 | −0.127675 | ||||||||
\(847\) | −9.44984e11 | −0.0630883 | ||||||||
\(848\) | 6.67354e12 | 0.443175 | ||||||||
\(849\) | 2.84198e11 | 0.0187731 | ||||||||
\(850\) | −1.54638e12 | −0.101609 | ||||||||
\(851\) | 7.95175e12 | 0.519733 | ||||||||
\(852\) | −9.70202e12 | −0.630789 | ||||||||
\(853\) | 1.12686e13 | 0.728784 | 0.364392 | − | 0.931246i | \(-0.381277\pi\) | ||||
0.364392 | + | 0.931246i | \(0.381277\pi\) | |||||||
\(854\) | −1.55253e12 | −0.0998800 | ||||||||
\(855\) | −4.21590e12 | −0.269801 | ||||||||
\(856\) | 8.11860e12 | 0.516832 | ||||||||
\(857\) | 3.75227e12 | 0.237618 | 0.118809 | − | 0.992917i | \(-0.462092\pi\) | ||||
0.118809 | + | 0.992917i | \(0.462092\pi\) | |||||||
\(858\) | 4.88566e12 | 0.307773 | ||||||||
\(859\) | 1.57014e13 | 0.983944 | 0.491972 | − | 0.870611i | \(-0.336276\pi\) | ||||
0.491972 | + | 0.870611i | \(0.336276\pi\) | |||||||
\(860\) | −1.79110e12 | −0.111655 | ||||||||
\(861\) | −5.34668e12 | −0.331566 | ||||||||
\(862\) | 1.85862e12 | 0.114659 | ||||||||
\(863\) | −1.39316e13 | −0.854975 | −0.427487 | − | 0.904021i | \(-0.640601\pi\) | ||||
−0.427487 | + | 0.904021i | \(0.640601\pi\) | |||||||
\(864\) | −1.58595e13 | −0.968231 | ||||||||
\(865\) | −9.81251e12 | −0.595947 | ||||||||
\(866\) | 1.21243e12 | 0.0732531 | ||||||||
\(867\) | −1.43960e13 | −0.865279 | ||||||||
\(868\) | 6.39495e12 | 0.382383 | ||||||||
\(869\) | −4.39165e12 | −0.261239 | ||||||||
\(870\) | −2.39194e12 | −0.141551 | ||||||||
\(871\) | 5.25021e12 | 0.309097 | ||||||||
\(872\) | −1.91738e13 | −1.12301 | ||||||||
\(873\) | 1.30419e11 | 0.00759935 | ||||||||
\(874\) | −4.29767e12 | −0.249133 | ||||||||
\(875\) | −1.03564e12 | −0.0597275 | ||||||||
\(876\) | 2.10504e13 | 1.20779 | ||||||||
\(877\) | −1.59832e13 | −0.912357 | −0.456179 | − | 0.889888i | \(-0.650782\pi\) | ||||
−0.456179 | + | 0.889888i | \(0.650782\pi\) | |||||||
\(878\) | 4.17108e12 | 0.236877 | ||||||||
\(879\) | 9.65658e12 | 0.545599 | ||||||||
\(880\) | 4.84999e12 | 0.272627 | ||||||||
\(881\) | −3.16227e13 | −1.76851 | −0.884255 | − | 0.467005i | \(-0.845333\pi\) | ||||
−0.884255 | + | 0.467005i | \(0.845333\pi\) | |||||||
\(882\) | −1.19612e12 | −0.0665527 | ||||||||
\(883\) | −1.48526e13 | −0.822202 | −0.411101 | − | 0.911590i | \(-0.634856\pi\) | ||||
−0.411101 | + | 0.911590i | \(0.634856\pi\) | |||||||
\(884\) | 2.57013e13 | 1.41553 | ||||||||
\(885\) | −6.06948e12 | −0.332588 | ||||||||
\(886\) | −8.81356e12 | −0.480507 | ||||||||
\(887\) | −9.39325e12 | −0.509518 | −0.254759 | − | 0.967005i | \(-0.581996\pi\) | ||||
−0.254759 | + | 0.967005i | \(0.581996\pi\) | |||||||
\(888\) | 1.30727e13 | 0.705516 | ||||||||
\(889\) | 1.32373e12 | 0.0710792 | ||||||||
\(890\) | −9.96932e10 | −0.00532611 | ||||||||
\(891\) | 9.75378e12 | 0.518470 | ||||||||
\(892\) | −1.42741e13 | −0.754930 | ||||||||
\(893\) | 3.58699e13 | 1.88755 | ||||||||
\(894\) | 1.33636e12 | 0.0699687 | ||||||||
\(895\) | 1.57438e13 | 0.820176 | ||||||||
\(896\) | 1.29439e13 | 0.670930 | ||||||||
\(897\) | −7.03849e12 | −0.363006 | ||||||||
\(898\) | −4.68538e12 | −0.240437 | ||||||||
\(899\) | −1.41210e13 | −0.721018 | ||||||||
\(900\) | 1.17022e12 | 0.0594536 | ||||||||
\(901\) | 1.96643e13 | 0.994071 | ||||||||
\(902\) | 4.08710e12 | 0.205582 | ||||||||
\(903\) | 3.09341e12 | 0.154826 | ||||||||
\(904\) | 8.56830e12 | 0.426714 | ||||||||
\(905\) | −6.53010e12 | −0.323594 | ||||||||
\(906\) | 3.33350e12 | 0.164370 | ||||||||
\(907\) | 2.64429e13 | 1.29741 | 0.648704 | − | 0.761041i | \(-0.275311\pi\) | ||||
0.648704 | + | 0.761041i | \(0.275311\pi\) | |||||||
\(908\) | −1.35574e13 | −0.661898 | ||||||||
\(909\) | 1.44888e12 | 0.0703876 | ||||||||
\(910\) | −2.45896e12 | −0.118868 | ||||||||
\(911\) | −3.41645e13 | −1.64339 | −0.821697 | − | 0.569924i | \(-0.806972\pi\) | ||||
−0.821697 | + | 0.569924i | \(0.806972\pi\) | |||||||
\(912\) | 1.93120e13 | 0.924381 | ||||||||
\(913\) | −1.20929e13 | −0.575987 | ||||||||
\(914\) | 4.56643e12 | 0.216431 | ||||||||
\(915\) | 3.25959e12 | 0.153733 | ||||||||
\(916\) | −9.23333e12 | −0.433340 | ||||||||
\(917\) | −1.19498e13 | −0.558081 | ||||||||
\(918\) | −1.19007e13 | −0.553069 | ||||||||
\(919\) | 3.14366e13 | 1.45384 | 0.726920 | − | 0.686723i | \(-0.240951\pi\) | ||||
0.726920 | + | 0.686723i | \(0.240951\pi\) | |||||||
\(920\) | 2.55626e12 | 0.117641 | ||||||||
\(921\) | −7.24478e11 | −0.0331785 | ||||||||
\(922\) | 6.08223e12 | 0.277188 | ||||||||
\(923\) | 2.20237e13 | 0.998809 | ||||||||
\(924\) | −1.00108e13 | −0.451801 | ||||||||
\(925\) | −5.83256e12 | −0.261952 | ||||||||
\(926\) | 5.71431e12 | 0.255396 | ||||||||
\(927\) | 5.00344e12 | 0.222541 | ||||||||
\(928\) | −2.21387e13 | −0.979909 | ||||||||
\(929\) | −8.77007e12 | −0.386307 | −0.193153 | − | 0.981169i | \(-0.561872\pi\) | ||||
−0.193153 | + | 0.981169i | \(0.561872\pi\) | |||||||
\(930\) | 1.91807e12 | 0.0840795 | ||||||||
\(931\) | 2.25545e13 | 0.983918 | ||||||||
\(932\) | −1.62057e12 | −0.0703553 | ||||||||
\(933\) | −3.09228e13 | −1.33602 | ||||||||
\(934\) | −6.26017e12 | −0.269169 | ||||||||
\(935\) | 1.42910e13 | 0.611521 | ||||||||
\(936\) | 5.95393e12 | 0.253549 | ||||||||
\(937\) | −1.66294e13 | −0.704770 | −0.352385 | − | 0.935855i | \(-0.614629\pi\) | ||||
−0.352385 | + | 0.935855i | \(0.614629\pi\) | |||||||
\(938\) | 1.53683e12 | 0.0648206 | ||||||||
\(939\) | −1.86389e13 | −0.782392 | ||||||||
\(940\) | −9.95656e12 | −0.415943 | ||||||||
\(941\) | −7.56052e12 | −0.314339 | −0.157169 | − | 0.987572i | \(-0.550237\pi\) | ||||
−0.157169 | + | 0.987572i | \(0.550237\pi\) | |||||||
\(942\) | 5.06334e12 | 0.209512 | ||||||||
\(943\) | −5.88806e12 | −0.242476 | ||||||||
\(944\) | −1.43057e13 | −0.586322 | ||||||||
\(945\) | −7.97013e12 | −0.325104 | ||||||||
\(946\) | −2.36466e12 | −0.0959974 | ||||||||
\(947\) | 3.40925e13 | 1.37747 | 0.688737 | − | 0.725011i | \(-0.258165\pi\) | ||||
0.688737 | + | 0.725011i | \(0.258165\pi\) | |||||||
\(948\) | 4.85393e12 | 0.195189 | ||||||||
\(949\) | −4.77846e13 | −1.91245 | ||||||||
\(950\) | 3.15231e12 | 0.125566 | ||||||||
\(951\) | −2.89111e13 | −1.14618 | ||||||||
\(952\) | 1.61212e13 | 0.636110 | ||||||||
\(953\) | 3.45885e13 | 1.35836 | 0.679178 | − | 0.733973i | \(-0.262336\pi\) | ||||
0.679178 | + | 0.733973i | \(0.262336\pi\) | |||||||
\(954\) | 2.12586e12 | 0.0830933 | ||||||||
\(955\) | 6.05391e12 | 0.235516 | ||||||||
\(956\) | −9.94185e11 | −0.0384952 | ||||||||
\(957\) | 2.21054e13 | 0.851911 | ||||||||
\(958\) | 5.56591e12 | 0.213497 | ||||||||
\(959\) | −3.03435e13 | −1.15846 | ||||||||
\(960\) | −3.11919e12 | −0.118528 | ||||||||
\(961\) | −1.51162e13 | −0.571726 | ||||||||
\(962\) | −1.38484e13 | −0.521329 | ||||||||
\(963\) | −7.06889e12 | −0.264870 | ||||||||
\(964\) | −1.15574e13 | −0.431035 | ||||||||
\(965\) | 1.27769e13 | 0.474301 | ||||||||
\(966\) | −2.06029e12 | −0.0761258 | ||||||||
\(967\) | 4.59891e13 | 1.69136 | 0.845680 | − | 0.533691i | \(-0.179195\pi\) | ||||
0.845680 | + | 0.533691i | \(0.179195\pi\) | |||||||
\(968\) | −1.71086e12 | −0.0626290 | ||||||||
\(969\) | 5.69050e13 | 2.07345 | ||||||||
\(970\) | −9.75168e10 | −0.00353677 | ||||||||
\(971\) | 2.72663e13 | 0.984327 | 0.492164 | − | 0.870503i | \(-0.336206\pi\) | ||||
0.492164 | + | 0.870503i | \(0.336206\pi\) | |||||||
\(972\) | 1.57279e13 | 0.565163 | ||||||||
\(973\) | 1.07035e13 | 0.382842 | ||||||||
\(974\) | 1.32156e13 | 0.470515 | ||||||||
\(975\) | 5.16269e12 | 0.182959 | ||||||||
\(976\) | 7.68284e12 | 0.271018 | ||||||||
\(977\) | −4.92228e13 | −1.72839 | −0.864193 | − | 0.503160i | \(-0.832171\pi\) | ||||
−0.864193 | + | 0.503160i | \(0.832171\pi\) | |||||||
\(978\) | −1.52885e13 | −0.534368 | ||||||||
\(979\) | 9.21324e11 | 0.0320546 | ||||||||
\(980\) | −6.26053e12 | −0.216817 | ||||||||
\(981\) | 1.66947e13 | 0.575530 | ||||||||
\(982\) | −9.59909e12 | −0.329404 | ||||||||
\(983\) | 3.98337e13 | 1.36069 | 0.680346 | − | 0.732891i | \(-0.261830\pi\) | ||||
0.680346 | + | 0.732891i | \(0.261830\pi\) | |||||||
\(984\) | −9.67998e12 | −0.329152 | ||||||||
\(985\) | 1.57770e13 | 0.534023 | ||||||||
\(986\) | −1.66124e13 | −0.559740 | ||||||||
\(987\) | 1.71960e13 | 0.576766 | ||||||||
\(988\) | −5.23924e13 | −1.74929 | ||||||||
\(989\) | 3.40664e12 | 0.113225 | ||||||||
\(990\) | 1.54496e12 | 0.0511164 | ||||||||
\(991\) | −2.56388e13 | −0.844434 | −0.422217 | − | 0.906495i | \(-0.638748\pi\) | ||||
−0.422217 | + | 0.906495i | \(0.638748\pi\) | |||||||
\(992\) | 1.77527e13 | 0.582052 | ||||||||
\(993\) | 2.73673e13 | 0.893224 | ||||||||
\(994\) | 6.44674e12 | 0.209460 | ||||||||
\(995\) | −5.04210e12 | −0.163083 | ||||||||
\(996\) | 1.33659e13 | 0.430358 | ||||||||
\(997\) | −4.97241e13 | −1.59382 | −0.796909 | − | 0.604099i | \(-0.793533\pi\) | ||||
−0.796909 | + | 0.604099i | \(0.793533\pi\) | |||||||
\(998\) | −1.14517e13 | −0.365410 | ||||||||
\(999\) | −4.48863e13 | −1.42584 |
(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 | 5.10.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 45.10.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 80.10.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 25.10.b.a.24.1 | 2 | |||
5.3 | odd | 4 | 25.10.b.a.24.2 | 2 | |||
5.4 | even | 2 | 25.10.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 245.10.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 320.10.a.c.1.1 | 1 | |||
8.5 | even | 2 | 320.10.a.h.1.1 | 1 | |||
15.2 | even | 4 | 225.10.b.d.199.2 | 2 | |||
15.8 | even | 4 | 225.10.b.d.199.1 | 2 | |||
15.14 | odd | 2 | 225.10.a.b.1.1 | 1 | |||
20.3 | even | 4 | 400.10.c.e.49.2 | 2 | |||
20.7 | even | 4 | 400.10.c.e.49.1 | 2 | |||
20.19 | odd | 2 | 400.10.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.10.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
25.10.a.a.1.1 | 1 | 5.4 | even | 2 | |||
25.10.b.a.24.1 | 2 | 5.2 | odd | 4 | |||
25.10.b.a.24.2 | 2 | 5.3 | odd | 4 | |||
45.10.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
80.10.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
225.10.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
225.10.b.d.199.1 | 2 | 15.8 | even | 4 | |||
225.10.b.d.199.2 | 2 | 15.2 | even | 4 | |||
245.10.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
320.10.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
320.10.a.h.1.1 | 1 | 8.5 | even | 2 | |||
400.10.a.c.1.1 | 1 | 20.19 | odd | 2 | |||
400.10.c.e.49.1 | 2 | 20.7 | even | 4 | |||
400.10.c.e.49.2 | 2 | 20.3 | even | 4 |