Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,60,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 60, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 60);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 60 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(22.0458005510\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots - 23\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{13}\cdot 5^{3}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.35709e7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.55640e8 | −0.863536 | −0.431768 | − | 0.901985i | \(-0.642110\pi\) | ||||
−0.431768 | + | 0.901985i | \(0.642110\pi\) | |||||||
\(3\) | 1.58783e14 | 1.33576 | 0.667878 | − | 0.744271i | \(-0.267203\pi\) | ||||
0.667878 | + | 0.744271i | \(0.267203\pi\) | |||||||
\(4\) | −1.46597e17 | −0.254306 | ||||||||
\(5\) | 7.23713e20 | 1.73761 | 0.868803 | − | 0.495159i | \(-0.164890\pi\) | ||||
0.868803 | + | 0.495159i | \(0.164890\pi\) | |||||||
\(6\) | −1.04104e23 | −1.15347 | ||||||||
\(7\) | 1.08717e25 | 1.27617 | 0.638083 | − | 0.769968i | \(-0.279728\pi\) | ||||
0.638083 | + | 0.769968i | \(0.279728\pi\) | |||||||
\(8\) | 4.74066e26 | 1.08314 | ||||||||
\(9\) | 1.10817e28 | 0.784243 | ||||||||
\(10\) | −4.74495e29 | −1.50048 | ||||||||
\(11\) | −2.58746e30 | −0.491802 | −0.245901 | − | 0.969295i | \(-0.579084\pi\) | ||||
−0.245901 | + | 0.969295i | \(0.579084\pi\) | |||||||
\(12\) | −2.32772e31 | −0.339691 | ||||||||
\(13\) | −5.56960e32 | −0.766469 | −0.383235 | − | 0.923651i | \(-0.625190\pi\) | ||||
−0.383235 | + | 0.923651i | \(0.625190\pi\) | |||||||
\(14\) | −7.12795e33 | −1.10201 | ||||||||
\(15\) | 1.14913e35 | 2.32102 | ||||||||
\(16\) | −2.26309e35 | −0.681022 | ||||||||
\(17\) | 1.35524e35 | 0.0681984 | 0.0340992 | − | 0.999418i | \(-0.489144\pi\) | ||||
0.0340992 | + | 0.999418i | \(0.489144\pi\) | |||||||
\(18\) | −7.26557e36 | −0.677222 | ||||||||
\(19\) | 4.79817e37 | 0.907496 | 0.453748 | − | 0.891130i | \(-0.350087\pi\) | ||||
0.453748 | + | 0.891130i | \(0.350087\pi\) | |||||||
\(20\) | −1.06094e38 | −0.441883 | ||||||||
\(21\) | 1.72625e39 | 1.70465 | ||||||||
\(22\) | 1.69644e39 | 0.424688 | ||||||||
\(23\) | −3.11625e39 | −0.210214 | −0.105107 | − | 0.994461i | \(-0.533518\pi\) | ||||
−0.105107 | + | 0.994461i | \(0.533518\pi\) | |||||||
\(24\) | 7.52736e40 | 1.44681 | ||||||||
\(25\) | 3.50288e41 | 2.01927 | ||||||||
\(26\) | 3.65165e41 | 0.661874 | ||||||||
\(27\) | −4.84086e41 | −0.288198 | ||||||||
\(28\) | −1.59377e42 | −0.324537 | ||||||||
\(29\) | 1.44322e43 | 1.04374 | 0.521869 | − | 0.853026i | \(-0.325235\pi\) | ||||
0.521869 | + | 0.853026i | \(0.325235\pi\) | |||||||
\(30\) | −7.53417e43 | −2.00428 | ||||||||
\(31\) | −1.86617e43 | −0.188704 | −0.0943518 | − | 0.995539i | \(-0.530078\pi\) | ||||
−0.0943518 | + | 0.995539i | \(0.530078\pi\) | |||||||
\(32\) | −1.24903e44 | −0.495051 | ||||||||
\(33\) | −4.10845e44 | −0.656927 | ||||||||
\(34\) | −8.88552e43 | −0.0588918 | ||||||||
\(35\) | 7.86802e45 | 2.21747 | ||||||||
\(36\) | −1.62454e45 | −0.199438 | ||||||||
\(37\) | 1.60698e46 | 0.879141 | 0.439571 | − | 0.898208i | \(-0.355131\pi\) | ||||
0.439571 | + | 0.898208i | \(0.355131\pi\) | |||||||
\(38\) | −3.14587e46 | −0.783655 | ||||||||
\(39\) | −8.84357e46 | −1.02382 | ||||||||
\(40\) | 3.43087e47 | 1.88207 | ||||||||
\(41\) | −6.72686e47 | −1.78110 | −0.890550 | − | 0.454885i | \(-0.849681\pi\) | ||||
−0.890550 | + | 0.454885i | \(0.849681\pi\) | |||||||
\(42\) | −1.13180e48 | −1.47202 | ||||||||
\(43\) | 1.54440e48 | 1.00332 | 0.501660 | − | 0.865065i | \(-0.332723\pi\) | ||||
0.501660 | + | 0.865065i | \(0.332723\pi\) | |||||||
\(44\) | 3.79316e47 | 0.125068 | ||||||||
\(45\) | 8.01994e48 | 1.36270 | ||||||||
\(46\) | 2.04314e48 | 0.181527 | ||||||||
\(47\) | 4.96944e48 | 0.234110 | 0.117055 | − | 0.993125i | \(-0.462655\pi\) | ||||
0.117055 | + | 0.993125i | \(0.462655\pi\) | |||||||
\(48\) | −3.59339e49 | −0.909680 | ||||||||
\(49\) | 4.56203e49 | 0.628599 | ||||||||
\(50\) | −2.29663e50 | −1.74371 | ||||||||
\(51\) | 2.15190e49 | 0.0910964 | ||||||||
\(52\) | 8.16489e49 | 0.194918 | ||||||||
\(53\) | 3.89245e50 | 0.529768 | 0.264884 | − | 0.964280i | \(-0.414666\pi\) | ||||
0.264884 | + | 0.964280i | \(0.414666\pi\) | |||||||
\(54\) | 3.17386e50 | 0.248870 | ||||||||
\(55\) | −1.87258e51 | −0.854557 | ||||||||
\(56\) | 5.15392e51 | 1.38226 | ||||||||
\(57\) | 7.61868e51 | 1.21219 | ||||||||
\(58\) | −9.46232e51 | −0.901305 | ||||||||
\(59\) | −2.34464e52 | −1.34878 | −0.674390 | − | 0.738375i | \(-0.735593\pi\) | ||||
−0.674390 | + | 0.738375i | \(0.735593\pi\) | |||||||
\(60\) | −1.68460e52 | −0.590248 | ||||||||
\(61\) | −7.62724e51 | −0.164111 | −0.0820554 | − | 0.996628i | \(-0.526148\pi\) | ||||
−0.0820554 | + | 0.996628i | \(0.526148\pi\) | |||||||
\(62\) | 1.22353e52 | 0.162952 | ||||||||
\(63\) | 1.20477e53 | 1.00082 | ||||||||
\(64\) | 2.12350e53 | 1.10852 | ||||||||
\(65\) | −4.03079e53 | −1.33182 | ||||||||
\(66\) | 2.69366e53 | 0.567280 | ||||||||
\(67\) | 2.92761e53 | 0.395646 | 0.197823 | − | 0.980238i | \(-0.436613\pi\) | ||||
0.197823 | + | 0.980238i | \(0.436613\pi\) | |||||||
\(68\) | −1.98675e52 | −0.0173433 | ||||||||
\(69\) | −4.94807e53 | −0.280794 | ||||||||
\(70\) | −5.15859e54 | −1.91487 | ||||||||
\(71\) | 2.90747e54 | 0.710223 | 0.355111 | − | 0.934824i | \(-0.384443\pi\) | ||||
0.355111 | + | 0.934824i | \(0.384443\pi\) | |||||||
\(72\) | 5.25343e54 | 0.849444 | ||||||||
\(73\) | −6.77367e54 | −0.729121 | −0.364561 | − | 0.931180i | \(-0.618781\pi\) | ||||
−0.364561 | + | 0.931180i | \(0.618781\pi\) | |||||||
\(74\) | −1.05360e55 | −0.759170 | ||||||||
\(75\) | 5.56197e55 | 2.69725 | ||||||||
\(76\) | −7.03400e54 | −0.230782 | ||||||||
\(77\) | −2.81302e55 | −0.627620 | ||||||||
\(78\) | 5.79820e55 | 0.884101 | ||||||||
\(79\) | −1.07018e56 | −1.12062 | −0.560308 | − | 0.828284i | \(-0.689317\pi\) | ||||
−0.560308 | + | 0.828284i | \(0.689317\pi\) | |||||||
\(80\) | −1.63782e56 | −1.18335 | ||||||||
\(81\) | −2.33453e56 | −1.16921 | ||||||||
\(82\) | 4.41039e56 | 1.53804 | ||||||||
\(83\) | 5.08183e56 | 1.23941 | 0.619707 | − | 0.784834i | \(-0.287252\pi\) | ||||
0.619707 | + | 0.784834i | \(0.287252\pi\) | |||||||
\(84\) | −2.53064e56 | −0.433502 | ||||||||
\(85\) | 9.80807e55 | 0.118502 | ||||||||
\(86\) | −1.01257e57 | −0.866403 | ||||||||
\(87\) | 2.29159e57 | 1.39418 | ||||||||
\(88\) | −1.22663e57 | −0.532689 | ||||||||
\(89\) | 3.31938e57 | 1.03289 | 0.516443 | − | 0.856322i | \(-0.327256\pi\) | ||||
0.516443 | + | 0.856322i | \(0.327256\pi\) | |||||||
\(90\) | −5.25819e57 | −1.17674 | ||||||||
\(91\) | −6.05512e57 | −0.978142 | ||||||||
\(92\) | 4.56834e56 | 0.0534586 | ||||||||
\(93\) | −2.96315e57 | −0.252062 | ||||||||
\(94\) | −3.25816e57 | −0.202163 | ||||||||
\(95\) | 3.47250e58 | 1.57687 | ||||||||
\(96\) | −1.98325e58 | −0.661267 | ||||||||
\(97\) | 7.26288e58 | 1.78379 | 0.891893 | − | 0.452246i | \(-0.149377\pi\) | ||||
0.891893 | + | 0.452246i | \(0.149377\pi\) | |||||||
\(98\) | −2.99105e58 | −0.542817 | ||||||||
\(99\) | −2.86734e58 | −0.385692 | ||||||||
\(100\) | −5.13513e58 | −0.513513 | ||||||||
\(101\) | 2.72416e58 | 0.203120 | 0.101560 | − | 0.994829i | \(-0.467617\pi\) | ||||
0.101560 | + | 0.994829i | \(0.467617\pi\) | |||||||
\(102\) | −1.41087e58 | −0.0786650 | ||||||||
\(103\) | −4.07754e59 | −1.70490 | −0.852452 | − | 0.522805i | \(-0.824886\pi\) | ||||
−0.852452 | + | 0.522805i | \(0.824886\pi\) | |||||||
\(104\) | −2.64035e59 | −0.830192 | ||||||||
\(105\) | 1.24931e60 | 2.96200 | ||||||||
\(106\) | −2.55205e59 | −0.457473 | ||||||||
\(107\) | 4.45535e59 | 0.605425 | 0.302713 | − | 0.953082i | \(-0.402108\pi\) | ||||
0.302713 | + | 0.953082i | \(0.402108\pi\) | |||||||
\(108\) | 7.09658e58 | 0.0732906 | ||||||||
\(109\) | −1.92062e60 | −1.51133 | −0.755664 | − | 0.654959i | \(-0.772686\pi\) | ||||
−0.755664 | + | 0.654959i | \(0.772686\pi\) | |||||||
\(110\) | 1.22774e60 | 0.737941 | ||||||||
\(111\) | 2.55161e60 | 1.17432 | ||||||||
\(112\) | −2.46037e60 | −0.869097 | ||||||||
\(113\) | 1.02620e60 | 0.278881 | 0.139440 | − | 0.990230i | \(-0.455470\pi\) | ||||
0.139440 | + | 0.990230i | \(0.455470\pi\) | |||||||
\(114\) | −4.99511e60 | −1.04677 | ||||||||
\(115\) | −2.25527e60 | −0.365268 | ||||||||
\(116\) | −2.11572e60 | −0.265429 | ||||||||
\(117\) | −6.17204e60 | −0.601098 | ||||||||
\(118\) | 1.53724e61 | 1.16472 | ||||||||
\(119\) | 1.47339e60 | 0.0870325 | ||||||||
\(120\) | 5.44764e61 | 2.51398 | ||||||||
\(121\) | −2.09852e61 | −0.758131 | ||||||||
\(122\) | 5.00072e60 | 0.141716 | ||||||||
\(123\) | −1.06811e62 | −2.37912 | ||||||||
\(124\) | 2.73575e60 | 0.0479885 | ||||||||
\(125\) | 1.27964e62 | 1.77109 | ||||||||
\(126\) | −7.89895e61 | −0.864247 | ||||||||
\(127\) | −1.57917e62 | −1.36842 | −0.684212 | − | 0.729284i | \(-0.739853\pi\) | ||||
−0.684212 | + | 0.729284i | \(0.739853\pi\) | |||||||
\(128\) | −6.72229e61 | −0.462193 | ||||||||
\(129\) | 2.45224e62 | 1.34019 | ||||||||
\(130\) | 2.64274e62 | 1.15007 | ||||||||
\(131\) | −2.72028e62 | −0.944300 | −0.472150 | − | 0.881518i | \(-0.656522\pi\) | ||||
−0.472150 | + | 0.881518i | \(0.656522\pi\) | |||||||
\(132\) | 6.02289e61 | 0.167060 | ||||||||
\(133\) | 5.21645e62 | 1.15811 | ||||||||
\(134\) | −1.91946e62 | −0.341654 | ||||||||
\(135\) | −3.50339e62 | −0.500775 | ||||||||
\(136\) | 6.42475e61 | 0.0738683 | ||||||||
\(137\) | −4.95801e62 | −0.459251 | −0.229626 | − | 0.973279i | \(-0.573750\pi\) | ||||
−0.229626 | + | 0.973279i | \(0.573750\pi\) | |||||||
\(138\) | 3.24415e62 | 0.242476 | ||||||||
\(139\) | −5.52437e62 | −0.333692 | −0.166846 | − | 0.985983i | \(-0.553358\pi\) | ||||
−0.166846 | + | 0.985983i | \(0.553358\pi\) | |||||||
\(140\) | −1.15343e63 | −0.563916 | ||||||||
\(141\) | 7.89062e62 | 0.312714 | ||||||||
\(142\) | −1.90626e63 | −0.613303 | ||||||||
\(143\) | 1.44111e63 | 0.376951 | ||||||||
\(144\) | −2.50787e63 | −0.534087 | ||||||||
\(145\) | 1.04448e64 | 1.81361 | ||||||||
\(146\) | 4.44109e63 | 0.629622 | ||||||||
\(147\) | 7.24372e63 | 0.839654 | ||||||||
\(148\) | −2.35579e63 | −0.223571 | ||||||||
\(149\) | −1.36260e64 | −1.06016 | −0.530081 | − | 0.847947i | \(-0.677838\pi\) | ||||
−0.530081 | + | 0.847947i | \(0.677838\pi\) | |||||||
\(150\) | −3.64665e64 | −2.32917 | ||||||||
\(151\) | −1.02852e63 | −0.0540000 | −0.0270000 | − | 0.999635i | \(-0.508595\pi\) | ||||
−0.0270000 | + | 0.999635i | \(0.508595\pi\) | |||||||
\(152\) | 2.27465e64 | 0.982943 | ||||||||
\(153\) | 1.50184e63 | 0.0534842 | ||||||||
\(154\) | 1.84433e64 | 0.541973 | ||||||||
\(155\) | −1.35057e64 | −0.327892 | ||||||||
\(156\) | 1.29645e64 | 0.260363 | ||||||||
\(157\) | −2.81384e64 | −0.468015 | −0.234007 | − | 0.972235i | \(-0.575184\pi\) | ||||
−0.234007 | + | 0.972235i | \(0.575184\pi\) | |||||||
\(158\) | 7.01651e64 | 0.967692 | ||||||||
\(159\) | 6.18056e64 | 0.707640 | ||||||||
\(160\) | −9.03942e64 | −0.860203 | ||||||||
\(161\) | −3.38790e64 | −0.268267 | ||||||||
\(162\) | 1.53061e65 | 1.00965 | ||||||||
\(163\) | −1.02410e65 | −0.563387 | −0.281693 | − | 0.959504i | \(-0.590896\pi\) | ||||
−0.281693 | + | 0.959504i | \(0.590896\pi\) | |||||||
\(164\) | 9.86140e64 | 0.452945 | ||||||||
\(165\) | −2.97334e65 | −1.14148 | ||||||||
\(166\) | −3.33185e65 | −1.07028 | ||||||||
\(167\) | −1.89739e65 | −0.510529 | −0.255264 | − | 0.966871i | \(-0.582162\pi\) | ||||
−0.255264 | + | 0.966871i | \(0.582162\pi\) | |||||||
\(168\) | 8.18355e65 | 1.84637 | ||||||||
\(169\) | −2.17825e65 | −0.412525 | ||||||||
\(170\) | −6.43056e64 | −0.102331 | ||||||||
\(171\) | 5.31717e65 | 0.711697 | ||||||||
\(172\) | −2.26405e65 | −0.255150 | ||||||||
\(173\) | 7.44337e65 | 0.706984 | 0.353492 | − | 0.935438i | \(-0.384994\pi\) | ||||
0.353492 | + | 0.935438i | \(0.384994\pi\) | |||||||
\(174\) | −1.50246e66 | −1.20392 | ||||||||
\(175\) | 3.80824e66 | 2.57692 | ||||||||
\(176\) | 5.85565e65 | 0.334928 | ||||||||
\(177\) | −3.72288e66 | −1.80164 | ||||||||
\(178\) | −2.17632e66 | −0.891934 | ||||||||
\(179\) | −3.24427e66 | −1.12707 | −0.563537 | − | 0.826091i | \(-0.690560\pi\) | ||||
−0.563537 | + | 0.826091i | \(0.690560\pi\) | |||||||
\(180\) | −1.17570e66 | −0.346544 | ||||||||
\(181\) | 2.66375e66 | 0.666770 | 0.333385 | − | 0.942791i | \(-0.391809\pi\) | ||||
0.333385 | + | 0.942791i | \(0.391809\pi\) | |||||||
\(182\) | 3.96998e66 | 0.844660 | ||||||||
\(183\) | −1.21108e66 | −0.219212 | ||||||||
\(184\) | −1.47731e66 | −0.227690 | ||||||||
\(185\) | 1.16299e67 | 1.52760 | ||||||||
\(186\) | 1.94276e66 | 0.217664 | ||||||||
\(187\) | −3.50664e65 | −0.0335401 | ||||||||
\(188\) | −7.28507e65 | −0.0595356 | ||||||||
\(189\) | −5.26286e66 | −0.367789 | ||||||||
\(190\) | −2.27671e67 | −1.36168 | ||||||||
\(191\) | −5.19175e66 | −0.265968 | −0.132984 | − | 0.991118i | \(-0.542456\pi\) | ||||
−0.132984 | + | 0.991118i | \(0.542456\pi\) | |||||||
\(192\) | 3.37175e67 | 1.48071 | ||||||||
\(193\) | 4.45977e67 | 1.68024 | 0.840121 | − | 0.542399i | \(-0.182484\pi\) | ||||
0.840121 | + | 0.542399i | \(0.182484\pi\) | |||||||
\(194\) | −4.76183e67 | −1.54036 | ||||||||
\(195\) | −6.40020e67 | −1.77899 | ||||||||
\(196\) | −6.68782e66 | −0.159856 | ||||||||
\(197\) | 2.05470e67 | 0.422663 | 0.211331 | − | 0.977414i | \(-0.432220\pi\) | ||||
0.211331 | + | 0.977414i | \(0.432220\pi\) | |||||||
\(198\) | 1.87994e67 | 0.333059 | ||||||||
\(199\) | −8.18192e67 | −1.24936 | −0.624682 | − | 0.780879i | \(-0.714772\pi\) | ||||
−0.624682 | + | 0.780879i | \(0.714772\pi\) | |||||||
\(200\) | 1.66059e68 | 2.18715 | ||||||||
\(201\) | 4.64855e67 | 0.528486 | ||||||||
\(202\) | −1.78607e67 | −0.175401 | ||||||||
\(203\) | 1.56903e68 | 1.33198 | ||||||||
\(204\) | −3.15463e66 | −0.0231664 | ||||||||
\(205\) | −4.86831e68 | −3.09485 | ||||||||
\(206\) | 2.67340e68 | 1.47225 | ||||||||
\(207\) | −3.45332e67 | −0.164859 | ||||||||
\(208\) | 1.26045e68 | 0.521983 | ||||||||
\(209\) | −1.24151e68 | −0.446308 | ||||||||
\(210\) | −8.19096e68 | −2.55779 | ||||||||
\(211\) | 4.28352e68 | 1.16270 | 0.581351 | − | 0.813653i | \(-0.302524\pi\) | ||||
0.581351 | + | 0.813653i | \(0.302524\pi\) | |||||||
\(212\) | −5.70624e67 | −0.134723 | ||||||||
\(213\) | 4.61658e68 | 0.948684 | ||||||||
\(214\) | −2.92111e68 | −0.522806 | ||||||||
\(215\) | 1.11770e69 | 1.74337 | ||||||||
\(216\) | −2.29489e68 | −0.312159 | ||||||||
\(217\) | −2.02885e68 | −0.240817 | ||||||||
\(218\) | 1.25923e69 | 1.30509 | ||||||||
\(219\) | −1.07554e69 | −0.973928 | ||||||||
\(220\) | 2.74515e68 | 0.217319 | ||||||||
\(221\) | −7.54816e67 | −0.0522720 | ||||||||
\(222\) | −1.67293e69 | −1.01407 | ||||||||
\(223\) | −1.66903e69 | −0.886076 | −0.443038 | − | 0.896503i | \(-0.646099\pi\) | ||||
−0.443038 | + | 0.896503i | \(0.646099\pi\) | |||||||
\(224\) | −1.35792e69 | −0.631767 | ||||||||
\(225\) | 3.88177e69 | 1.58360 | ||||||||
\(226\) | −6.72818e68 | −0.240823 | ||||||||
\(227\) | 3.77482e69 | 1.18613 | 0.593066 | − | 0.805154i | \(-0.297917\pi\) | ||||
0.593066 | + | 0.805154i | \(0.297917\pi\) | |||||||
\(228\) | −1.11688e69 | −0.308268 | ||||||||
\(229\) | −6.77671e69 | −1.64389 | −0.821944 | − | 0.569569i | \(-0.807110\pi\) | ||||
−0.821944 | + | 0.569569i | \(0.807110\pi\) | |||||||
\(230\) | 1.47864e69 | 0.315422 | ||||||||
\(231\) | −4.46660e69 | −0.838348 | ||||||||
\(232\) | 6.84181e69 | 1.13051 | ||||||||
\(233\) | 8.16171e69 | 1.18791 | 0.593953 | − | 0.804500i | \(-0.297567\pi\) | ||||
0.593953 | + | 0.804500i | \(0.297567\pi\) | |||||||
\(234\) | 4.04663e69 | 0.519070 | ||||||||
\(235\) | 3.59644e69 | 0.406791 | ||||||||
\(236\) | 3.43718e69 | 0.343003 | ||||||||
\(237\) | −1.69926e70 | −1.49687 | ||||||||
\(238\) | −9.66011e68 | −0.0751557 | ||||||||
\(239\) | 5.21276e69 | 0.358368 | 0.179184 | − | 0.983816i | \(-0.442654\pi\) | ||||
0.179184 | + | 0.983816i | \(0.442654\pi\) | |||||||
\(240\) | −2.60059e70 | −1.58066 | ||||||||
\(241\) | −9.20131e69 | −0.494706 | −0.247353 | − | 0.968925i | \(-0.579561\pi\) | ||||
−0.247353 | + | 0.968925i | \(0.579561\pi\) | |||||||
\(242\) | 1.37587e70 | 0.654673 | ||||||||
\(243\) | −3.02280e70 | −1.27357 | ||||||||
\(244\) | 1.11813e69 | 0.0417344 | ||||||||
\(245\) | 3.30160e70 | 1.09226 | ||||||||
\(246\) | 7.00296e70 | 2.05445 | ||||||||
\(247\) | −2.67239e70 | −0.695568 | ||||||||
\(248\) | −8.84685e69 | −0.204392 | ||||||||
\(249\) | 8.06908e70 | 1.65555 | ||||||||
\(250\) | −8.38980e70 | −1.52940 | ||||||||
\(251\) | −2.03203e70 | −0.329272 | −0.164636 | − | 0.986354i | \(-0.552645\pi\) | ||||
−0.164636 | + | 0.986354i | \(0.552645\pi\) | |||||||
\(252\) | −1.76616e70 | −0.254516 | ||||||||
\(253\) | 8.06318e69 | 0.103383 | ||||||||
\(254\) | 1.03537e71 | 1.18168 | ||||||||
\(255\) | 1.55736e70 | 0.158290 | ||||||||
\(256\) | −7.83372e70 | −0.709397 | ||||||||
\(257\) | −2.26975e71 | −1.83211 | −0.916055 | − | 0.401053i | \(-0.868644\pi\) | ||||
−0.916055 | + | 0.401053i | \(0.868644\pi\) | |||||||
\(258\) | −1.60779e71 | −1.15730 | ||||||||
\(259\) | 1.74706e71 | 1.12193 | ||||||||
\(260\) | 5.90903e70 | 0.338690 | ||||||||
\(261\) | 1.59933e71 | 0.818545 | ||||||||
\(262\) | 1.78352e71 | 0.815437 | ||||||||
\(263\) | −9.72811e70 | −0.397497 | −0.198749 | − | 0.980051i | \(-0.563688\pi\) | ||||
−0.198749 | + | 0.980051i | \(0.563688\pi\) | |||||||
\(264\) | −1.94768e71 | −0.711543 | ||||||||
\(265\) | 2.81702e71 | 0.920527 | ||||||||
\(266\) | −3.42011e71 | −1.00007 | ||||||||
\(267\) | 5.27062e71 | 1.37968 | ||||||||
\(268\) | −4.29180e70 | −0.100615 | ||||||||
\(269\) | −3.85798e71 | −0.810340 | −0.405170 | − | 0.914241i | \(-0.632788\pi\) | ||||
−0.405170 | + | 0.914241i | \(0.632788\pi\) | |||||||
\(270\) | 2.29696e71 | 0.432437 | ||||||||
\(271\) | 4.86572e71 | 0.821398 | 0.410699 | − | 0.911771i | \(-0.365285\pi\) | ||||
0.410699 | + | 0.911771i | \(0.365285\pi\) | |||||||
\(272\) | −3.06703e70 | −0.0464447 | ||||||||
\(273\) | −9.61450e71 | −1.30656 | ||||||||
\(274\) | 3.25067e71 | 0.396580 | ||||||||
\(275\) | −9.06357e71 | −0.993081 | ||||||||
\(276\) | 7.25375e70 | 0.0714076 | ||||||||
\(277\) | −1.75710e72 | −1.55469 | −0.777344 | − | 0.629076i | \(-0.783433\pi\) | ||||
−0.777344 | + | 0.629076i | \(0.783433\pi\) | |||||||
\(278\) | 3.62199e71 | 0.288155 | ||||||||
\(279\) | −2.06802e71 | −0.147990 | ||||||||
\(280\) | 3.72996e72 | 2.40183 | ||||||||
\(281\) | 3.44814e71 | 0.199870 | 0.0999351 | − | 0.994994i | \(-0.468136\pi\) | ||||
0.0999351 | + | 0.994994i | \(0.468136\pi\) | |||||||
\(282\) | −5.17340e71 | −0.270040 | ||||||||
\(283\) | 1.33526e72 | 0.627863 | 0.313932 | − | 0.949446i | \(-0.398354\pi\) | ||||
0.313932 | + | 0.949446i | \(0.398354\pi\) | |||||||
\(284\) | −4.26228e71 | −0.180614 | ||||||||
\(285\) | 5.51374e72 | 2.10631 | ||||||||
\(286\) | −9.44850e71 | −0.325511 | ||||||||
\(287\) | −7.31327e72 | −2.27298 | ||||||||
\(288\) | −1.38414e72 | −0.388240 | ||||||||
\(289\) | −3.93063e72 | −0.995349 | ||||||||
\(290\) | −6.84800e72 | −1.56611 | ||||||||
\(291\) | 1.15322e73 | 2.38270 | ||||||||
\(292\) | 9.93003e71 | 0.185420 | ||||||||
\(293\) | 7.74487e72 | 1.30743 | 0.653716 | − | 0.756740i | \(-0.273209\pi\) | ||||
0.653716 | + | 0.756740i | \(0.273209\pi\) | |||||||
\(294\) | −4.74927e72 | −0.725071 | ||||||||
\(295\) | −1.69684e73 | −2.34365 | ||||||||
\(296\) | 7.61812e72 | 0.952232 | ||||||||
\(297\) | 1.25255e72 | 0.141736 | ||||||||
\(298\) | 8.93372e72 | 0.915488 | ||||||||
\(299\) | 1.73562e72 | 0.161122 | ||||||||
\(300\) | −8.15371e72 | −0.685928 | ||||||||
\(301\) | 1.67903e73 | 1.28040 | ||||||||
\(302\) | 6.74340e71 | 0.0466310 | ||||||||
\(303\) | 4.32551e72 | 0.271318 | ||||||||
\(304\) | −1.08587e73 | −0.618025 | ||||||||
\(305\) | −5.51993e72 | −0.285160 | ||||||||
\(306\) | −9.84663e71 | −0.0461855 | ||||||||
\(307\) | 1.91212e73 | 0.814577 | 0.407288 | − | 0.913300i | \(-0.366474\pi\) | ||||
0.407288 | + | 0.913300i | \(0.366474\pi\) | |||||||
\(308\) | 4.12382e72 | 0.159608 | ||||||||
\(309\) | −6.47444e73 | −2.27734 | ||||||||
\(310\) | 8.85486e72 | 0.283147 | ||||||||
\(311\) | 1.53350e73 | 0.445914 | 0.222957 | − | 0.974828i | \(-0.428429\pi\) | ||||
0.222957 | + | 0.974828i | \(0.428429\pi\) | |||||||
\(312\) | −4.19243e73 | −1.10893 | ||||||||
\(313\) | −9.46132e72 | −0.227716 | −0.113858 | − | 0.993497i | \(-0.536321\pi\) | ||||
−0.113858 | + | 0.993497i | \(0.536321\pi\) | |||||||
\(314\) | 1.84486e73 | 0.404147 | ||||||||
\(315\) | 8.71907e73 | 1.73904 | ||||||||
\(316\) | 1.56885e73 | 0.284979 | ||||||||
\(317\) | −5.08207e73 | −0.840993 | −0.420496 | − | 0.907294i | \(-0.638144\pi\) | ||||
−0.420496 | + | 0.907294i | \(0.638144\pi\) | |||||||
\(318\) | −4.05222e73 | −0.611072 | ||||||||
\(319\) | −3.73428e73 | −0.513312 | ||||||||
\(320\) | 1.53680e74 | 1.92616 | ||||||||
\(321\) | 7.07434e73 | 0.808700 | ||||||||
\(322\) | 2.22124e73 | 0.231658 | ||||||||
\(323\) | 6.50269e72 | 0.0618898 | ||||||||
\(324\) | 3.42236e73 | 0.297336 | ||||||||
\(325\) | −1.95096e74 | −1.54771 | ||||||||
\(326\) | 6.71438e73 | 0.486505 | ||||||||
\(327\) | −3.04961e74 | −2.01876 | ||||||||
\(328\) | −3.18897e74 | −1.92918 | ||||||||
\(329\) | 5.40264e73 | 0.298763 | ||||||||
\(330\) | 1.94944e74 | 0.985708 | ||||||||
\(331\) | 2.90945e74 | 1.34551 | 0.672753 | − | 0.739867i | \(-0.265112\pi\) | ||||
0.672753 | + | 0.739867i | \(0.265112\pi\) | |||||||
\(332\) | −7.44983e73 | −0.315190 | ||||||||
\(333\) | 1.78080e74 | 0.689461 | ||||||||
\(334\) | 1.24400e74 | 0.440860 | ||||||||
\(335\) | 2.11875e74 | 0.687476 | ||||||||
\(336\) | −3.90665e74 | −1.16090 | ||||||||
\(337\) | −4.42174e73 | −0.120368 | −0.0601840 | − | 0.998187i | \(-0.519169\pi\) | ||||
−0.0601840 | + | 0.998187i | \(0.519169\pi\) | |||||||
\(338\) | 1.42815e74 | 0.356230 | ||||||||
\(339\) | 1.62943e74 | 0.372517 | ||||||||
\(340\) | −1.43784e73 | −0.0301358 | ||||||||
\(341\) | 4.82864e73 | 0.0928048 | ||||||||
\(342\) | −3.48615e74 | −0.614576 | ||||||||
\(343\) | −2.93040e74 | −0.473970 | ||||||||
\(344\) | 7.32146e74 | 1.08673 | ||||||||
\(345\) | −3.58098e74 | −0.487909 | ||||||||
\(346\) | −4.88017e74 | −0.610506 | ||||||||
\(347\) | 1.08045e75 | 1.24133 | 0.620663 | − | 0.784078i | \(-0.286864\pi\) | ||||
0.620663 | + | 0.784078i | \(0.286864\pi\) | |||||||
\(348\) | −3.35941e74 | −0.354548 | ||||||||
\(349\) | −3.17015e74 | −0.307419 | −0.153709 | − | 0.988116i | \(-0.549122\pi\) | ||||
−0.153709 | + | 0.988116i | \(0.549122\pi\) | |||||||
\(350\) | −2.49683e75 | −2.22527 | ||||||||
\(351\) | 2.69616e74 | 0.220895 | ||||||||
\(352\) | 3.23183e74 | 0.243467 | ||||||||
\(353\) | −6.44178e74 | −0.446326 | −0.223163 | − | 0.974781i | \(-0.571638\pi\) | ||||
−0.223163 | + | 0.974781i | \(0.571638\pi\) | |||||||
\(354\) | 2.44087e75 | 1.55578 | ||||||||
\(355\) | 2.10418e75 | 1.23409 | ||||||||
\(356\) | −4.86613e74 | −0.262669 | ||||||||
\(357\) | 2.33949e74 | 0.116254 | ||||||||
\(358\) | 2.12707e75 | 0.973268 | ||||||||
\(359\) | −3.30229e75 | −1.39164 | −0.695822 | − | 0.718214i | \(-0.744960\pi\) | ||||
−0.695822 | + | 0.718214i | \(0.744960\pi\) | |||||||
\(360\) | 3.80198e75 | 1.47600 | ||||||||
\(361\) | −4.93274e74 | −0.176452 | ||||||||
\(362\) | −1.74646e75 | −0.575779 | ||||||||
\(363\) | −3.33209e75 | −1.01268 | ||||||||
\(364\) | 8.87665e74 | 0.248747 | ||||||||
\(365\) | −4.90219e75 | −1.26693 | ||||||||
\(366\) | 7.94029e74 | 0.189297 | ||||||||
\(367\) | 5.43152e75 | 1.19474 | 0.597368 | − | 0.801967i | \(-0.296213\pi\) | ||||
0.597368 | + | 0.801967i | \(0.296213\pi\) | |||||||
\(368\) | 7.05233e74 | 0.143160 | ||||||||
\(369\) | −7.45448e75 | −1.39682 | ||||||||
\(370\) | −7.62502e75 | −1.31914 | ||||||||
\(371\) | 4.23178e75 | 0.676071 | ||||||||
\(372\) | 4.34391e74 | 0.0641009 | ||||||||
\(373\) | 5.16798e75 | 0.704547 | 0.352274 | − | 0.935897i | \(-0.385409\pi\) | ||||
0.352274 | + | 0.935897i | \(0.385409\pi\) | |||||||
\(374\) | 2.29910e74 | 0.0289631 | ||||||||
\(375\) | 2.03184e76 | 2.36574 | ||||||||
\(376\) | 2.35584e75 | 0.253574 | ||||||||
\(377\) | −8.03815e75 | −0.799993 | ||||||||
\(378\) | 3.45054e75 | 0.317599 | ||||||||
\(379\) | 1.10163e75 | 0.0937950 | 0.0468975 | − | 0.998900i | \(-0.485067\pi\) | ||||
0.0468975 | + | 0.998900i | \(0.485067\pi\) | |||||||
\(380\) | −5.09059e75 | −0.401007 | ||||||||
\(381\) | −2.50746e76 | −1.82788 | ||||||||
\(382\) | 3.40392e75 | 0.229673 | ||||||||
\(383\) | 3.09321e76 | 1.93217 | 0.966084 | − | 0.258228i | \(-0.0831384\pi\) | ||||
0.966084 | + | 0.258228i | \(0.0831384\pi\) | |||||||
\(384\) | −1.06739e76 | −0.617377 | ||||||||
\(385\) | −2.03582e76 | −1.09056 | ||||||||
\(386\) | −2.92400e76 | −1.45095 | ||||||||
\(387\) | 1.71145e76 | 0.786847 | ||||||||
\(388\) | −1.06472e76 | −0.453628 | ||||||||
\(389\) | 1.22185e76 | 0.482507 | 0.241254 | − | 0.970462i | \(-0.422441\pi\) | ||||
0.241254 | + | 0.970462i | \(0.422441\pi\) | |||||||
\(390\) | 4.19623e76 | 1.53622 | ||||||||
\(391\) | −4.22328e74 | −0.0143362 | ||||||||
\(392\) | 2.16270e76 | 0.680859 | ||||||||
\(393\) | −4.31934e76 | −1.26135 | ||||||||
\(394\) | −1.34714e76 | −0.364984 | ||||||||
\(395\) | −7.74501e76 | −1.94719 | ||||||||
\(396\) | 4.20345e75 | 0.0980838 | ||||||||
\(397\) | 8.16439e76 | 1.76850 | 0.884248 | − | 0.467018i | \(-0.154672\pi\) | ||||
0.884248 | + | 0.467018i | \(0.154672\pi\) | |||||||
\(398\) | 5.36439e76 | 1.07887 | ||||||||
\(399\) | 8.28284e76 | 1.54696 | ||||||||
\(400\) | −7.92731e76 | −1.37517 | ||||||||
\(401\) | 8.81919e76 | 1.42125 | 0.710623 | − | 0.703573i | \(-0.248413\pi\) | ||||
0.710623 | + | 0.703573i | \(0.248413\pi\) | |||||||
\(402\) | −3.04777e76 | −0.456367 | ||||||||
\(403\) | 1.03938e76 | 0.144636 | ||||||||
\(404\) | −3.99355e75 | −0.0516546 | ||||||||
\(405\) | −1.68953e77 | −2.03162 | ||||||||
\(406\) | −1.02872e77 | −1.15021 | ||||||||
\(407\) | −4.15799e76 | −0.432363 | ||||||||
\(408\) | 1.02014e76 | 0.0986700 | ||||||||
\(409\) | −9.51763e76 | −0.856428 | −0.428214 | − | 0.903677i | \(-0.640857\pi\) | ||||
−0.428214 | + | 0.903677i | \(0.640857\pi\) | |||||||
\(410\) | 3.19186e77 | 2.67251 | ||||||||
\(411\) | −7.87248e76 | −0.613448 | ||||||||
\(412\) | 5.97757e76 | 0.433568 | ||||||||
\(413\) | −2.54903e77 | −1.72127 | ||||||||
\(414\) | 2.26413e76 | 0.142361 | ||||||||
\(415\) | 3.67778e77 | 2.15361 | ||||||||
\(416\) | 6.95661e76 | 0.379441 | ||||||||
\(417\) | −8.77176e76 | −0.445731 | ||||||||
\(418\) | 8.13983e76 | 0.385403 | ||||||||
\(419\) | 3.31477e77 | 1.46265 | 0.731324 | − | 0.682030i | \(-0.238903\pi\) | ||||
0.731324 | + | 0.682030i | \(0.238903\pi\) | |||||||
\(420\) | −1.83145e77 | −0.753255 | ||||||||
\(421\) | −2.10408e77 | −0.806752 | −0.403376 | − | 0.915034i | \(-0.632163\pi\) | ||||
−0.403376 | + | 0.915034i | \(0.632163\pi\) | |||||||
\(422\) | −2.80844e77 | −1.00403 | ||||||||
\(423\) | 5.50696e76 | 0.183599 | ||||||||
\(424\) | 1.84528e77 | 0.573811 | ||||||||
\(425\) | 4.74725e76 | 0.137711 | ||||||||
\(426\) | −3.02681e77 | −0.819223 | ||||||||
\(427\) | −8.29214e76 | −0.209433 | ||||||||
\(428\) | −6.53143e76 | −0.153963 | ||||||||
\(429\) | 2.28824e77 | 0.503514 | ||||||||
\(430\) | −7.32808e77 | −1.50547 | ||||||||
\(431\) | 4.43348e77 | 0.850482 | 0.425241 | − | 0.905080i | \(-0.360189\pi\) | ||||
0.425241 | + | 0.905080i | \(0.360189\pi\) | |||||||
\(432\) | 1.09553e77 | 0.196270 | ||||||||
\(433\) | −1.00421e78 | −1.68047 | −0.840236 | − | 0.542220i | \(-0.817584\pi\) | ||||
−0.840236 | + | 0.542220i | \(0.817584\pi\) | |||||||
\(434\) | 1.33019e77 | 0.207954 | ||||||||
\(435\) | 1.65845e78 | 2.42253 | ||||||||
\(436\) | 2.81557e77 | 0.384340 | ||||||||
\(437\) | −1.49523e77 | −0.190768 | ||||||||
\(438\) | 7.05169e77 | 0.841022 | ||||||||
\(439\) | −5.00093e77 | −0.557631 | −0.278816 | − | 0.960345i | \(-0.589942\pi\) | ||||
−0.278816 | + | 0.960345i | \(0.589942\pi\) | |||||||
\(440\) | −8.87726e77 | −0.925603 | ||||||||
\(441\) | 5.05548e77 | 0.492974 | ||||||||
\(442\) | 4.94887e76 | 0.0451387 | ||||||||
\(443\) | −1.24372e78 | −1.06124 | −0.530618 | − | 0.847611i | \(-0.678040\pi\) | ||||
−0.530618 | + | 0.847611i | \(0.678040\pi\) | |||||||
\(444\) | −3.74059e77 | −0.298636 | ||||||||
\(445\) | 2.40228e78 | 1.79475 | ||||||||
\(446\) | 1.09428e78 | 0.765158 | ||||||||
\(447\) | −2.16357e78 | −1.41612 | ||||||||
\(448\) | 2.30861e78 | 1.41465 | ||||||||
\(449\) | −2.77078e78 | −1.58977 | −0.794886 | − | 0.606759i | \(-0.792469\pi\) | ||||
−0.794886 | + | 0.606759i | \(0.792469\pi\) | |||||||
\(450\) | −2.54504e78 | −1.36749 | ||||||||
\(451\) | 1.74055e78 | 0.875948 | ||||||||
\(452\) | −1.50439e77 | −0.0709211 | ||||||||
\(453\) | −1.63312e77 | −0.0721309 | ||||||||
\(454\) | −2.47492e78 | −1.02427 | ||||||||
\(455\) | −4.38217e78 | −1.69962 | ||||||||
\(456\) | 3.61175e78 | 1.31297 | ||||||||
\(457\) | 1.86231e78 | 0.634636 | 0.317318 | − | 0.948319i | \(-0.397218\pi\) | ||||
0.317318 | + | 0.948319i | \(0.397218\pi\) | |||||||
\(458\) | 4.44308e78 | 1.41956 | ||||||||
\(459\) | −6.56055e76 | −0.0196547 | ||||||||
\(460\) | 3.30617e77 | 0.0928899 | ||||||||
\(461\) | 3.95029e78 | 1.04100 | 0.520501 | − | 0.853861i | \(-0.325745\pi\) | ||||
0.520501 | + | 0.853861i | \(0.325745\pi\) | |||||||
\(462\) | 2.92848e78 | 0.723943 | ||||||||
\(463\) | 3.19378e78 | 0.740739 | 0.370370 | − | 0.928884i | \(-0.379231\pi\) | ||||
0.370370 | + | 0.928884i | \(0.379231\pi\) | |||||||
\(464\) | −3.26613e78 | −0.710809 | ||||||||
\(465\) | −2.14447e78 | −0.437984 | ||||||||
\(466\) | −5.35114e78 | −1.02580 | ||||||||
\(467\) | −5.82978e78 | −1.04907 | −0.524535 | − | 0.851389i | \(-0.675761\pi\) | ||||
−0.524535 | + | 0.851389i | \(0.675761\pi\) | |||||||
\(468\) | 9.04805e77 | 0.152863 | ||||||||
\(469\) | 3.18282e78 | 0.504910 | ||||||||
\(470\) | −2.35797e78 | −0.351279 | ||||||||
\(471\) | −4.46790e78 | −0.625153 | ||||||||
\(472\) | −1.11151e79 | −1.46091 | ||||||||
\(473\) | −3.99607e78 | −0.493435 | ||||||||
\(474\) | 1.11410e79 | 1.29260 | ||||||||
\(475\) | 1.68074e79 | 1.83248 | ||||||||
\(476\) | −2.15995e77 | −0.0221329 | ||||||||
\(477\) | 4.31349e78 | 0.415467 | ||||||||
\(478\) | −3.41769e78 | −0.309464 | ||||||||
\(479\) | 2.24826e78 | 0.191403 | 0.0957017 | − | 0.995410i | \(-0.469491\pi\) | ||||
0.0957017 | + | 0.995410i | \(0.469491\pi\) | |||||||
\(480\) | −1.43531e79 | −1.14902 | ||||||||
\(481\) | −8.95021e78 | −0.673835 | ||||||||
\(482\) | 6.03274e78 | 0.427196 | ||||||||
\(483\) | −5.37942e78 | −0.358340 | ||||||||
\(484\) | 3.07637e78 | 0.192797 | ||||||||
\(485\) | 5.25624e79 | 3.09952 | ||||||||
\(486\) | 1.98187e79 | 1.09978 | ||||||||
\(487\) | −3.09514e79 | −1.61650 | −0.808251 | − | 0.588838i | \(-0.799586\pi\) | ||||
−0.808251 | + | 0.588838i | \(0.799586\pi\) | |||||||
\(488\) | −3.61581e78 | −0.177755 | ||||||||
\(489\) | −1.62609e79 | −0.752547 | ||||||||
\(490\) | −2.16466e79 | −0.943202 | ||||||||
\(491\) | −2.38917e79 | −0.980262 | −0.490131 | − | 0.871649i | \(-0.663051\pi\) | ||||
−0.490131 | + | 0.871649i | \(0.663051\pi\) | |||||||
\(492\) | 1.56582e79 | 0.605023 | ||||||||
\(493\) | 1.95592e78 | 0.0711813 | ||||||||
\(494\) | 1.75212e79 | 0.600647 | ||||||||
\(495\) | −2.07513e79 | −0.670181 | ||||||||
\(496\) | 4.22329e78 | 0.128511 | ||||||||
\(497\) | 3.16093e79 | 0.906362 | ||||||||
\(498\) | −5.29041e79 | −1.42963 | ||||||||
\(499\) | 1.08643e79 | 0.276717 | 0.138358 | − | 0.990382i | \(-0.455817\pi\) | ||||
0.138358 | + | 0.990382i | \(0.455817\pi\) | |||||||
\(500\) | −1.87591e79 | −0.450399 | ||||||||
\(501\) | −3.01273e79 | −0.681941 | ||||||||
\(502\) | 1.33228e79 | 0.284338 | ||||||||
\(503\) | 5.40902e79 | 1.08859 | 0.544293 | − | 0.838895i | \(-0.316798\pi\) | ||||
0.544293 | + | 0.838895i | \(0.316798\pi\) | |||||||
\(504\) | 5.71140e79 | 1.08403 | ||||||||
\(505\) | 1.97151e79 | 0.352942 | ||||||||
\(506\) | −5.28654e78 | −0.0892752 | ||||||||
\(507\) | −3.45869e79 | −0.551032 | ||||||||
\(508\) | 2.31503e79 | 0.347998 | ||||||||
\(509\) | 4.74617e79 | 0.673238 | 0.336619 | − | 0.941641i | \(-0.390717\pi\) | ||||
0.336619 | + | 0.941641i | \(0.390717\pi\) | |||||||
\(510\) | −1.02106e79 | −0.136689 | ||||||||
\(511\) | −7.36416e79 | −0.930480 | ||||||||
\(512\) | 9.01123e79 | 1.07478 | ||||||||
\(513\) | −2.32273e79 | −0.261539 | ||||||||
\(514\) | 1.48814e80 | 1.58209 | ||||||||
\(515\) | −2.95097e80 | −2.96245 | ||||||||
\(516\) | −3.59492e79 | −0.340819 | ||||||||
\(517\) | −1.28582e79 | −0.115136 | ||||||||
\(518\) | −1.14544e80 | −0.968827 | ||||||||
\(519\) | 1.18188e80 | 0.944358 | ||||||||
\(520\) | −1.91086e80 | −1.44255 | ||||||||
\(521\) | 1.73445e79 | 0.123723 | 0.0618613 | − | 0.998085i | \(-0.480296\pi\) | ||||
0.0618613 | + | 0.998085i | \(0.480296\pi\) | |||||||
\(522\) | −1.04858e80 | −0.706843 | ||||||||
\(523\) | 1.18403e80 | 0.754335 | 0.377167 | − | 0.926145i | \(-0.376898\pi\) | ||||
0.377167 | + | 0.926145i | \(0.376898\pi\) | |||||||
\(524\) | 3.98786e79 | 0.240141 | ||||||||
\(525\) | 6.04684e80 | 3.44214 | ||||||||
\(526\) | 6.37814e79 | 0.343253 | ||||||||
\(527\) | −2.52911e78 | −0.0128693 | ||||||||
\(528\) | 9.29778e79 | 0.447382 | ||||||||
\(529\) | −2.10046e80 | −0.955810 | ||||||||
\(530\) | −1.84695e80 | −0.794908 | ||||||||
\(531\) | −2.59825e80 | −1.05777 | ||||||||
\(532\) | −7.64718e79 | −0.294516 | ||||||||
\(533\) | 3.74659e80 | 1.36516 | ||||||||
\(534\) | −3.45563e80 | −1.19141 | ||||||||
\(535\) | 3.22440e80 | 1.05199 | ||||||||
\(536\) | 1.38788e80 | 0.428539 | ||||||||
\(537\) | −5.15135e80 | −1.50549 | ||||||||
\(538\) | 2.52944e80 | 0.699758 | ||||||||
\(539\) | −1.18041e80 | −0.309146 | ||||||||
\(540\) | 5.13588e79 | 0.127350 | ||||||||
\(541\) | 7.98203e79 | 0.187411 | 0.0937053 | − | 0.995600i | \(-0.470129\pi\) | ||||
0.0937053 | + | 0.995600i | \(0.470129\pi\) | |||||||
\(542\) | −3.19016e80 | −0.709306 | ||||||||
\(543\) | 4.22959e80 | 0.890641 | ||||||||
\(544\) | −1.69275e79 | −0.0337617 | ||||||||
\(545\) | −1.38997e81 | −2.62609 | ||||||||
\(546\) | 6.30365e80 | 1.12826 | ||||||||
\(547\) | −1.05852e79 | −0.0179504 | −0.00897518 | − | 0.999960i | \(-0.502857\pi\) | ||||
−0.00897518 | + | 0.999960i | \(0.502857\pi\) | |||||||
\(548\) | 7.26831e79 | 0.116790 | ||||||||
\(549\) | −8.45225e79 | −0.128703 | ||||||||
\(550\) | 5.94243e80 | 0.857561 | ||||||||
\(551\) | 6.92482e80 | 0.947188 | ||||||||
\(552\) | −2.34571e80 | −0.304139 | ||||||||
\(553\) | −1.16347e81 | −1.43009 | ||||||||
\(554\) | 1.15202e81 | 1.34253 | ||||||||
\(555\) | 1.84663e81 | 2.04050 | ||||||||
\(556\) | 8.09858e79 | 0.0848599 | ||||||||
\(557\) | −4.29933e80 | −0.427241 | −0.213620 | − | 0.976917i | \(-0.568526\pi\) | ||||
−0.213620 | + | 0.976917i | \(0.568526\pi\) | |||||||
\(558\) | 1.35588e80 | 0.127794 | ||||||||
\(559\) | −8.60167e80 | −0.769014 | ||||||||
\(560\) | −1.78060e81 | −1.51015 | ||||||||
\(561\) | −5.56796e79 | −0.0448014 | ||||||||
\(562\) | −2.26074e80 | −0.172595 | ||||||||
\(563\) | −1.67492e78 | −0.00121338 | −0.000606690 | − | 1.00000i | \(-0.500193\pi\) | ||||
−0.000606690 | 1.00000i | \(0.500193\pi\) | ||||||||
\(564\) | −1.15674e80 | −0.0795251 | ||||||||
\(565\) | 7.42675e80 | 0.484585 | ||||||||
\(566\) | −8.75447e80 | −0.542182 | ||||||||
\(567\) | −2.53804e81 | −1.49210 | ||||||||
\(568\) | 1.37833e81 | 0.769269 | ||||||||
\(569\) | 3.30406e81 | 1.75080 | 0.875399 | − | 0.483401i | \(-0.160599\pi\) | ||||
0.875399 | + | 0.483401i | \(0.160599\pi\) | |||||||
\(570\) | −3.61502e81 | −1.81888 | ||||||||
\(571\) | 5.82486e80 | 0.278305 | 0.139152 | − | 0.990271i | \(-0.455562\pi\) | ||||
0.139152 | + | 0.990271i | \(0.455562\pi\) | |||||||
\(572\) | −2.11263e80 | −0.0958609 | ||||||||
\(573\) | −8.24361e80 | −0.355268 | ||||||||
\(574\) | 4.79487e81 | 1.96280 | ||||||||
\(575\) | −1.09158e81 | −0.424478 | ||||||||
\(576\) | 2.35319e81 | 0.869347 | ||||||||
\(577\) | −4.10666e81 | −1.44146 | −0.720730 | − | 0.693216i | \(-0.756193\pi\) | ||||
−0.720730 | + | 0.693216i | \(0.756193\pi\) | |||||||
\(578\) | 2.57707e81 | 0.859519 | ||||||||
\(579\) | 7.08136e81 | 2.24439 | ||||||||
\(580\) | −1.53118e81 | −0.461211 | ||||||||
\(581\) | 5.52483e81 | 1.58170 | ||||||||
\(582\) | −7.56098e81 | −2.05755 | ||||||||
\(583\) | −1.00716e81 | −0.260541 | ||||||||
\(584\) | −3.21117e81 | −0.789739 | ||||||||
\(585\) | −4.46678e81 | −1.04447 | ||||||||
\(586\) | −5.07784e81 | −1.12901 | ||||||||
\(587\) | −4.15508e80 | −0.0878528 | −0.0439264 | − | 0.999035i | \(-0.513987\pi\) | ||||
−0.0439264 | + | 0.999035i | \(0.513987\pi\) | |||||||
\(588\) | −1.06191e81 | −0.213529 | ||||||||
\(589\) | −8.95418e80 | −0.171248 | ||||||||
\(590\) | 1.11252e82 | 2.02382 | ||||||||
\(591\) | 3.26251e81 | 0.564574 | ||||||||
\(592\) | −3.63672e81 | −0.598715 | ||||||||
\(593\) | −5.04161e80 | −0.0789689 | −0.0394845 | − | 0.999220i | \(-0.512572\pi\) | ||||
−0.0394845 | + | 0.999220i | \(0.512572\pi\) | |||||||
\(594\) | −8.21225e80 | −0.122394 | ||||||||
\(595\) | 1.06631e81 | 0.151228 | ||||||||
\(596\) | 1.99753e81 | 0.269606 | ||||||||
\(597\) | −1.29915e82 | −1.66885 | ||||||||
\(598\) | −1.13794e81 | −0.139135 | ||||||||
\(599\) | 1.04485e82 | 1.21608 | 0.608041 | − | 0.793906i | \(-0.291956\pi\) | ||||
0.608041 | + | 0.793906i | \(0.291956\pi\) | |||||||
\(600\) | 2.63674e82 | 2.92150 | ||||||||
\(601\) | −1.04932e82 | −1.10690 | −0.553452 | − | 0.832881i | \(-0.686690\pi\) | ||||
−0.553452 | + | 0.832881i | \(0.686690\pi\) | |||||||
\(602\) | −1.10084e82 | −1.10567 | ||||||||
\(603\) | 3.24428e81 | 0.310283 | ||||||||
\(604\) | 1.50779e80 | 0.0137325 | ||||||||
\(605\) | −1.51872e82 | −1.31733 | ||||||||
\(606\) | −2.83597e81 | −0.234293 | ||||||||
\(607\) | 1.83220e82 | 1.44180 | 0.720902 | − | 0.693037i | \(-0.243728\pi\) | ||||
0.720902 | + | 0.693037i | \(0.243728\pi\) | |||||||
\(608\) | −5.99308e81 | −0.449257 | ||||||||
\(609\) | 2.49136e82 | 1.77920 | ||||||||
\(610\) | 3.61908e81 | 0.246246 | ||||||||
\(611\) | −2.76778e81 | −0.179438 | ||||||||
\(612\) | −2.20165e80 | −0.0136013 | ||||||||
\(613\) | 7.20904e81 | 0.424418 | 0.212209 | − | 0.977224i | \(-0.431934\pi\) | ||||
0.212209 | + | 0.977224i | \(0.431934\pi\) | |||||||
\(614\) | −1.25366e82 | −0.703416 | ||||||||
\(615\) | −7.73005e82 | −4.13396 | ||||||||
\(616\) | −1.33356e82 | −0.679800 | ||||||||
\(617\) | −1.07578e82 | −0.522772 | −0.261386 | − | 0.965234i | \(-0.584180\pi\) | ||||
−0.261386 | + | 0.965234i | \(0.584180\pi\) | |||||||
\(618\) | 4.24490e82 | 1.96656 | ||||||||
\(619\) | 1.25527e82 | 0.554449 | 0.277224 | − | 0.960805i | \(-0.410585\pi\) | ||||
0.277224 | + | 0.960805i | \(0.410585\pi\) | |||||||
\(620\) | 1.97990e81 | 0.0833850 | ||||||||
\(621\) | 1.50853e81 | 0.0605832 | ||||||||
\(622\) | −1.00542e82 | −0.385063 | ||||||||
\(623\) | 3.60875e82 | 1.31813 | ||||||||
\(624\) | 2.00138e82 | 0.697241 | ||||||||
\(625\) | 3.18436e82 | 1.05819 | ||||||||
\(626\) | 6.20321e81 | 0.196641 | ||||||||
\(627\) | −1.97131e82 | −0.596158 | ||||||||
\(628\) | 4.12502e81 | 0.119019 | ||||||||
\(629\) | 2.17785e81 | 0.0599561 | ||||||||
\(630\) | −5.71657e82 | −1.50172 | ||||||||
\(631\) | 5.54665e82 | 1.39048 | 0.695239 | − | 0.718778i | \(-0.255298\pi\) | ||||
0.695239 | + | 0.718778i | \(0.255298\pi\) | |||||||
\(632\) | −5.07335e82 | −1.21378 | ||||||||
\(633\) | 6.80150e82 | 1.55308 | ||||||||
\(634\) | 3.33200e82 | 0.726227 | ||||||||
\(635\) | −1.14287e83 | −2.37778 | ||||||||
\(636\) | −9.06054e81 | −0.179957 | ||||||||
\(637\) | −2.54086e82 | −0.481802 | ||||||||
\(638\) | 2.44834e82 | 0.443264 | ||||||||
\(639\) | 3.22196e82 | 0.556987 | ||||||||
\(640\) | −4.86501e82 | −0.803108 | ||||||||
\(641\) | −2.80336e82 | −0.441944 | −0.220972 | − | 0.975280i | \(-0.570923\pi\) | ||||
−0.220972 | + | 0.975280i | \(0.570923\pi\) | |||||||
\(642\) | −4.63822e82 | −0.698342 | ||||||||
\(643\) | −3.52192e82 | −0.506473 | −0.253236 | − | 0.967404i | \(-0.581495\pi\) | ||||
−0.253236 | + | 0.967404i | \(0.581495\pi\) | |||||||
\(644\) | 4.96658e81 | 0.0682220 | ||||||||
\(645\) | 1.77472e83 | 2.32872 | ||||||||
\(646\) | −4.26342e81 | −0.0534440 | ||||||||
\(647\) | −1.31942e82 | −0.158018 | −0.0790088 | − | 0.996874i | \(-0.525176\pi\) | ||||
−0.0790088 | + | 0.996874i | \(0.525176\pi\) | |||||||
\(648\) | −1.10672e83 | −1.26641 | ||||||||
\(649\) | 6.06666e82 | 0.663332 | ||||||||
\(650\) | 1.27913e83 | 1.33650 | ||||||||
\(651\) | −3.22147e82 | −0.321673 | ||||||||
\(652\) | 1.50130e82 | 0.143273 | ||||||||
\(653\) | −1.65618e82 | −0.151066 | −0.0755332 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755332 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(654\) | 1.99945e83 | 1.74328 | ||||||||
\(655\) | −1.96870e83 | −1.64082 | ||||||||
\(656\) | 1.52235e83 | 1.21297 | ||||||||
\(657\) | −7.50635e82 | −0.571809 | ||||||||
\(658\) | −3.54219e82 | −0.257993 | ||||||||
\(659\) | −9.65525e81 | −0.0672425 | −0.0336212 | − | 0.999435i | \(-0.510704\pi\) | ||||
−0.0336212 | + | 0.999435i | \(0.510704\pi\) | |||||||
\(660\) | 4.35884e82 | 0.290285 | ||||||||
\(661\) | −2.85133e83 | −1.81595 | −0.907976 | − | 0.419022i | \(-0.862373\pi\) | ||||
−0.907976 | + | 0.419022i | \(0.862373\pi\) | |||||||
\(662\) | −1.90755e83 | −1.16189 | ||||||||
\(663\) | −1.19852e82 | −0.0698226 | ||||||||
\(664\) | 2.40912e83 | 1.34246 | ||||||||
\(665\) | 3.77521e83 | 2.01235 | ||||||||
\(666\) | −1.16756e83 | −0.595374 | ||||||||
\(667\) | −4.49743e82 | −0.219408 | ||||||||
\(668\) | 2.78152e82 | 0.129831 | ||||||||
\(669\) | −2.65014e83 | −1.18358 | ||||||||
\(670\) | −1.38914e83 | −0.593660 | ||||||||
\(671\) | 1.97352e82 | 0.0807100 | ||||||||
\(672\) | −2.15614e83 | −0.843886 | ||||||||
\(673\) | 2.49097e83 | 0.933091 | 0.466546 | − | 0.884497i | \(-0.345498\pi\) | ||||
0.466546 | + | 0.884497i | \(0.345498\pi\) | |||||||
\(674\) | 2.89907e82 | 0.103942 | ||||||||
\(675\) | −1.69569e83 | −0.581951 | ||||||||
\(676\) | 3.19326e82 | 0.104908 | ||||||||
\(677\) | −1.42903e82 | −0.0449445 | −0.0224722 | − | 0.999747i | \(-0.507154\pi\) | ||||
−0.0224722 | + | 0.999747i | \(0.507154\pi\) | |||||||
\(678\) | −1.06832e83 | −0.321681 | ||||||||
\(679\) | 7.89602e83 | 2.27641 | ||||||||
\(680\) | 4.64967e82 | 0.128354 | ||||||||
\(681\) | 5.99377e83 | 1.58438 | ||||||||
\(682\) | −3.16584e82 | −0.0801402 | ||||||||
\(683\) | 2.48288e83 | 0.601928 | 0.300964 | − | 0.953635i | \(-0.402692\pi\) | ||||
0.300964 | + | 0.953635i | \(0.402692\pi\) | |||||||
\(684\) | −7.79484e82 | −0.180989 | ||||||||
\(685\) | −3.58817e83 | −0.797998 | ||||||||
\(686\) | 1.92129e83 | 0.409290 | ||||||||
\(687\) | −1.07603e84 | −2.19583 | ||||||||
\(688\) | −3.49510e83 | −0.683284 | ||||||||
\(689\) | −2.16794e83 | −0.406051 | ||||||||
\(690\) | 2.34783e83 | 0.421327 | ||||||||
\(691\) | 5.53022e82 | 0.0950912 | 0.0475456 | − | 0.998869i | \(-0.484860\pi\) | ||||
0.0475456 | + | 0.998869i | \(0.484860\pi\) | |||||||
\(692\) | −1.09118e83 | −0.179790 | ||||||||
\(693\) | −3.11730e83 | −0.492207 | ||||||||
\(694\) | −7.08387e83 | −1.07193 | ||||||||
\(695\) | −3.99805e83 | −0.579825 | ||||||||
\(696\) | 1.08636e84 | 1.51009 | ||||||||
\(697\) | −9.11653e82 | −0.121468 | ||||||||
\(698\) | 2.07848e83 | 0.265467 | ||||||||
\(699\) | 1.29594e84 | 1.58675 | ||||||||
\(700\) | −5.58278e83 | −0.655328 | ||||||||
\(701\) | 3.90202e83 | 0.439145 | 0.219572 | − | 0.975596i | \(-0.429534\pi\) | ||||
0.219572 | + | 0.975596i | \(0.429534\pi\) | |||||||
\(702\) | −1.76771e83 | −0.190751 | ||||||||
\(703\) | 7.71055e83 | 0.797817 | ||||||||
\(704\) | −5.49447e83 | −0.545170 | ||||||||
\(705\) | 5.71054e83 | 0.543373 | ||||||||
\(706\) | 4.22349e83 | 0.385418 | ||||||||
\(707\) | 2.96164e83 | 0.259215 | ||||||||
\(708\) | 5.45765e83 | 0.458168 | ||||||||
\(709\) | −1.40891e84 | −1.13454 | −0.567270 | − | 0.823532i | \(-0.692001\pi\) | ||||
−0.567270 | + | 0.823532i | \(0.692001\pi\) | |||||||
\(710\) | −1.37958e84 | −1.06568 | ||||||||
\(711\) | −1.18593e84 | −0.878835 | ||||||||
\(712\) | 1.57361e84 | 1.11876 | ||||||||
\(713\) | 5.81543e82 | 0.0396681 | ||||||||
\(714\) | −1.53386e83 | −0.100390 | ||||||||
\(715\) | 1.04295e84 | 0.654992 | ||||||||
\(716\) | 4.75601e83 | 0.286622 | ||||||||
\(717\) | 8.27698e83 | 0.478693 | ||||||||
\(718\) | 2.16511e84 | 1.20173 | ||||||||
\(719\) | −3.73873e84 | −1.99169 | −0.995845 | − | 0.0910630i | \(-0.970974\pi\) | ||||
−0.995845 | + | 0.0910630i | \(0.970974\pi\) | |||||||
\(720\) | −1.81498e84 | −0.928033 | ||||||||
\(721\) | −4.43300e84 | −2.17574 | ||||||||
\(722\) | 3.23410e83 | 0.152372 | ||||||||
\(723\) | −1.46101e84 | −0.660806 | ||||||||
\(724\) | −3.90499e83 | −0.169564 | ||||||||
\(725\) | 5.05542e84 | 2.10759 | ||||||||
\(726\) | 2.18465e84 | 0.874484 | ||||||||
\(727\) | 4.53192e84 | 1.74188 | 0.870938 | − | 0.491392i | \(-0.163512\pi\) | ||||
0.870938 | + | 0.491392i | \(0.163512\pi\) | |||||||
\(728\) | −2.87052e84 | −1.05946 | ||||||||
\(729\) | −1.50092e84 | −0.531979 | ||||||||
\(730\) | 3.21407e84 | 1.09404 | ||||||||
\(731\) | 2.09304e83 | 0.0684249 | ||||||||
\(732\) | 1.77541e83 | 0.0557469 | ||||||||
\(733\) | −5.45127e84 | −1.64411 | −0.822054 | − | 0.569409i | \(-0.807172\pi\) | ||||
−0.822054 | + | 0.569409i | \(0.807172\pi\) | |||||||
\(734\) | −3.56112e84 | −1.03170 | ||||||||
\(735\) | 5.24237e84 | 1.45899 | ||||||||
\(736\) | 3.89230e83 | 0.104066 | ||||||||
\(737\) | −7.57508e83 | −0.194579 | ||||||||
\(738\) | 4.88745e84 | 1.20620 | ||||||||
\(739\) | 7.25178e84 | 1.71963 | 0.859813 | − | 0.510609i | \(-0.170580\pi\) | ||||
0.859813 | + | 0.510609i | \(0.170580\pi\) | |||||||
\(740\) | −1.70491e84 | −0.388478 | ||||||||
\(741\) | −4.24330e84 | −0.929108 | ||||||||
\(742\) | −2.77452e84 | −0.583812 | ||||||||
\(743\) | 1.87471e84 | 0.379108 | 0.189554 | − | 0.981870i | \(-0.439296\pi\) | ||||
0.189554 | + | 0.981870i | \(0.439296\pi\) | |||||||
\(744\) | −1.40473e84 | −0.273018 | ||||||||
\(745\) | −9.86128e84 | −1.84214 | ||||||||
\(746\) | −3.38833e84 | −0.608402 | ||||||||
\(747\) | 5.63151e84 | 0.972001 | ||||||||
\(748\) | 5.14065e82 | 0.00852945 | ||||||||
\(749\) | 4.84375e84 | 0.772623 | ||||||||
\(750\) | −1.33216e85 | −2.04291 | ||||||||
\(751\) | 5.00370e83 | 0.0737756 | 0.0368878 | − | 0.999319i | \(-0.488256\pi\) | ||||
0.0368878 | + | 0.999319i | \(0.488256\pi\) | |||||||
\(752\) | −1.12463e84 | −0.159434 | ||||||||
\(753\) | −3.22652e84 | −0.439827 | ||||||||
\(754\) | 5.27013e84 | 0.690823 | ||||||||
\(755\) | −7.44355e83 | −0.0938307 | ||||||||
\(756\) | 7.71522e83 | 0.0935309 | ||||||||
\(757\) | 1.39411e85 | 1.62543 | 0.812714 | − | 0.582663i | \(-0.197989\pi\) | ||||
0.812714 | + | 0.582663i | \(0.197989\pi\) | |||||||
\(758\) | −7.22273e83 | −0.0809953 | ||||||||
\(759\) | 1.28030e84 | 0.138095 | ||||||||
\(760\) | 1.64619e85 | 1.70797 | ||||||||
\(761\) | 4.02373e84 | 0.401588 | 0.200794 | − | 0.979633i | \(-0.435648\pi\) | ||||
0.200794 | + | 0.979633i | \(0.435648\pi\) | |||||||
\(762\) | 1.64399e85 | 1.57844 | ||||||||
\(763\) | −2.08804e85 | −1.92870 | ||||||||
\(764\) | 7.61097e83 | 0.0676372 | ||||||||
\(765\) | 1.08690e84 | 0.0929343 | ||||||||
\(766\) | −2.02803e85 | −1.66850 | ||||||||
\(767\) | 1.30587e85 | 1.03380 | ||||||||
\(768\) | −1.24386e85 | −0.947581 | ||||||||
\(769\) | −1.19509e85 | −0.876143 | −0.438072 | − | 0.898940i | \(-0.644338\pi\) | ||||
−0.438072 | + | 0.898940i | \(0.644338\pi\) | |||||||
\(770\) | 1.33477e85 | 0.941734 | ||||||||
\(771\) | −3.60398e85 | −2.44725 | ||||||||
\(772\) | −6.53791e84 | −0.427296 | ||||||||
\(773\) | 2.46928e85 | 1.55337 | 0.776685 | − | 0.629889i | \(-0.216900\pi\) | ||||
0.776685 | + | 0.629889i | \(0.216900\pi\) | |||||||
\(774\) | −1.12209e85 | −0.679471 | ||||||||
\(775\) | −6.53695e84 | −0.381044 | ||||||||
\(776\) | 3.44308e85 | 1.93209 | ||||||||
\(777\) | 2.77404e85 | 1.49862 | ||||||||
\(778\) | −8.01092e84 | −0.416662 | ||||||||
\(779\) | −3.22766e85 | −1.61634 | ||||||||
\(780\) | 9.38254e84 | 0.452407 | ||||||||
\(781\) | −7.52298e84 | −0.349289 | ||||||||
\(782\) | 2.76895e83 | 0.0123799 | ||||||||
\(783\) | −6.98643e84 | −0.300804 | ||||||||
\(784\) | −1.03243e85 | −0.428090 | ||||||||
\(785\) | −2.03641e85 | −0.813225 | ||||||||
\(786\) | 2.83193e85 | 1.08922 | ||||||||
\(787\) | 2.95880e85 | 1.09613 | 0.548064 | − | 0.836437i | \(-0.315365\pi\) | ||||
0.548064 | + | 0.836437i | \(0.315365\pi\) | |||||||
\(788\) | −3.01213e84 | −0.107486 | ||||||||
\(789\) | −1.54466e85 | −0.530959 | ||||||||
\(790\) | 5.07794e85 | 1.68147 | ||||||||
\(791\) | 1.11566e85 | 0.355898 | ||||||||
\(792\) | −1.35931e85 | −0.417758 | ||||||||
\(793\) | 4.24806e84 | 0.125786 | ||||||||
\(794\) | −5.35290e85 | −1.52716 | ||||||||
\(795\) | 4.47295e85 | 1.22960 | ||||||||
\(796\) | 1.19945e85 | 0.317721 | ||||||||
\(797\) | 2.78567e85 | 0.711065 | 0.355532 | − | 0.934664i | \(-0.384300\pi\) | ||||
0.355532 | + | 0.934664i | \(0.384300\pi\) | |||||||
\(798\) | −5.43056e85 | −1.33585 | ||||||||
\(799\) | 6.73480e83 | 0.0159659 | ||||||||
\(800\) | −4.37521e85 | −0.999642 | ||||||||
\(801\) | 3.67843e85 | 0.810034 | ||||||||
\(802\) | −5.78221e85 | −1.22730 | ||||||||
\(803\) | 1.75266e85 | 0.358583 | ||||||||
\(804\) | −6.81465e84 | −0.134397 | ||||||||
\(805\) | −2.45187e85 | −0.466143 | ||||||||
\(806\) | −6.81458e84 | −0.124898 | ||||||||
\(807\) | −6.12581e85 | −1.08242 | ||||||||
\(808\) | 1.29143e85 | 0.220007 | ||||||||
\(809\) | −3.79734e85 | −0.623732 | −0.311866 | − | 0.950126i | \(-0.600954\pi\) | ||||
−0.311866 | + | 0.950126i | \(0.600954\pi\) | |||||||
\(810\) | 1.10772e86 | 1.75437 | ||||||||
\(811\) | 1.37244e85 | 0.209594 | 0.104797 | − | 0.994494i | \(-0.466581\pi\) | ||||
0.104797 | + | 0.994494i | \(0.466581\pi\) | |||||||
\(812\) | −2.30016e85 | −0.338731 | ||||||||
\(813\) | 7.72594e85 | 1.09719 | ||||||||
\(814\) | 2.72615e85 | 0.373361 | ||||||||
\(815\) | −7.41152e85 | −0.978944 | ||||||||
\(816\) | −4.86993e84 | −0.0620387 | ||||||||
\(817\) | 7.41028e85 | 0.910509 | ||||||||
\(818\) | 6.24013e85 | 0.739557 | ||||||||
\(819\) | −6.71008e85 | −0.767101 | ||||||||
\(820\) | 7.13682e85 | 0.787039 | ||||||||
\(821\) | 5.67502e85 | 0.603732 | 0.301866 | − | 0.953350i | \(-0.402390\pi\) | ||||
0.301866 | + | 0.953350i | \(0.402390\pi\) | |||||||
\(822\) | 5.16151e85 | 0.529734 | ||||||||
\(823\) | −3.36239e85 | −0.332930 | −0.166465 | − | 0.986047i | \(-0.553235\pi\) | ||||
−0.166465 | + | 0.986047i | \(0.553235\pi\) | |||||||
\(824\) | −1.93302e86 | −1.84665 | ||||||||
\(825\) | −1.43914e86 | −1.32651 | ||||||||
\(826\) | 1.67124e86 | 1.48638 | ||||||||
\(827\) | 1.72236e86 | 1.47812 | 0.739061 | − | 0.673638i | \(-0.235269\pi\) | ||||
0.739061 | + | 0.673638i | \(0.235269\pi\) | |||||||
\(828\) | 5.06248e84 | 0.0419245 | ||||||||
\(829\) | 1.06995e86 | 0.855080 | 0.427540 | − | 0.903996i | \(-0.359380\pi\) | ||||
0.427540 | + | 0.903996i | \(0.359380\pi\) | |||||||
\(830\) | −2.41130e86 | −1.85972 | ||||||||
\(831\) | −2.78998e86 | −2.07668 | ||||||||
\(832\) | −1.18270e86 | −0.849644 | ||||||||
\(833\) | 6.18266e84 | 0.0428694 | ||||||||
\(834\) | 5.75111e85 | 0.384905 | ||||||||
\(835\) | −1.37316e86 | −0.887097 | ||||||||
\(836\) | 1.82002e85 | 0.113499 | ||||||||
\(837\) | 9.03385e84 | 0.0543841 | ||||||||
\(838\) | −2.17330e86 | −1.26305 | ||||||||
\(839\) | 2.77617e86 | 1.55764 | 0.778822 | − | 0.627245i | \(-0.215817\pi\) | ||||
0.778822 | + | 0.627245i | \(0.215817\pi\) | |||||||
\(840\) | 5.92254e86 | 3.20826 | ||||||||
\(841\) | 1.70911e85 | 0.0893898 | ||||||||
\(842\) | 1.37952e86 | 0.696659 | ||||||||
\(843\) | 5.47506e85 | 0.266978 | ||||||||
\(844\) | −6.27953e85 | −0.295682 | ||||||||
\(845\) | −1.57643e86 | −0.716805 | ||||||||
\(846\) | −3.61058e85 | −0.158545 | ||||||||
\(847\) | −2.28146e86 | −0.967501 | ||||||||
\(848\) | −8.80895e85 | −0.360784 | ||||||||
\(849\) | 2.12016e86 | 0.838672 | ||||||||
\(850\) | −3.11249e85 | −0.118918 | ||||||||
\(851\) | −5.00774e85 | −0.184807 | ||||||||
\(852\) | −6.76778e85 | −0.241256 | ||||||||
\(853\) | −2.60122e86 | −0.895737 | −0.447869 | − | 0.894099i | \(-0.647817\pi\) | ||||
−0.447869 | + | 0.894099i | \(0.647817\pi\) | |||||||
\(854\) | 5.43665e85 | 0.180853 | ||||||||
\(855\) | 3.84810e86 | 1.23665 | ||||||||
\(856\) | 2.11213e86 | 0.655759 | ||||||||
\(857\) | 1.69052e86 | 0.507091 | 0.253545 | − | 0.967323i | \(-0.418403\pi\) | ||||
0.253545 | + | 0.967323i | \(0.418403\pi\) | |||||||
\(858\) | −1.50026e86 | −0.434803 | ||||||||
\(859\) | 3.14436e86 | 0.880509 | 0.440254 | − | 0.897873i | \(-0.354888\pi\) | ||||
0.440254 | + | 0.897873i | \(0.354888\pi\) | |||||||
\(860\) | −1.63852e86 | −0.443351 | ||||||||
\(861\) | −1.16122e87 | −3.03615 | ||||||||
\(862\) | −2.90676e86 | −0.734422 | ||||||||
\(863\) | 1.46329e86 | 0.357282 | 0.178641 | − | 0.983914i | \(-0.442830\pi\) | ||||
0.178641 | + | 0.983914i | \(0.442830\pi\) | |||||||
\(864\) | 6.04640e85 | 0.142673 | ||||||||
\(865\) | 5.38686e86 | 1.22846 | ||||||||
\(866\) | 6.58400e86 | 1.45115 | ||||||||
\(867\) | −6.24117e86 | −1.32954 | ||||||||
\(868\) | 2.97424e85 | 0.0612412 | ||||||||
\(869\) | 2.76905e86 | 0.551121 | ||||||||
\(870\) | −1.08735e87 | −2.09194 | ||||||||
\(871\) | −1.63056e86 | −0.303250 | ||||||||
\(872\) | −9.10498e86 | −1.63698 | ||||||||
\(873\) | 8.04848e86 | 1.39892 | ||||||||
\(874\) | 9.80331e85 | 0.164735 | ||||||||
\(875\) | 1.39119e87 | 2.26021 | ||||||||
\(876\) | 1.57672e86 | 0.247676 | ||||||||
\(877\) | 5.57754e86 | 0.847139 | 0.423570 | − | 0.905864i | \(-0.360777\pi\) | ||||
0.423570 | + | 0.905864i | \(0.360777\pi\) | |||||||
\(878\) | 3.27881e86 | 0.481535 | ||||||||
\(879\) | 1.22975e87 | 1.74641 | ||||||||
\(880\) | 4.23781e86 | 0.581972 | ||||||||
\(881\) | −8.88813e86 | −1.18038 | −0.590189 | − | 0.807265i | \(-0.700947\pi\) | ||||
−0.590189 | + | 0.807265i | \(0.700947\pi\) | |||||||
\(882\) | −3.31457e86 | −0.425701 | ||||||||
\(883\) | −1.03961e87 | −1.29131 | −0.645654 | − | 0.763630i | \(-0.723415\pi\) | ||||
−0.645654 | + | 0.763630i | \(0.723415\pi\) | |||||||
\(884\) | 1.10654e85 | 0.0132931 | ||||||||
\(885\) | −2.69430e87 | −3.13054 | ||||||||
\(886\) | 8.15431e86 | 0.916415 | ||||||||
\(887\) | 1.24157e87 | 1.34967 | 0.674833 | − | 0.737971i | \(-0.264216\pi\) | ||||
0.674833 | + | 0.737971i | \(0.264216\pi\) | |||||||
\(888\) | 1.20963e87 | 1.27195 | ||||||||
\(889\) | −1.71684e87 | −1.74633 | ||||||||
\(890\) | −1.57503e87 | −1.54983 | ||||||||
\(891\) | 6.04050e86 | 0.575017 | ||||||||
\(892\) | 2.44676e86 | 0.225334 | ||||||||
\(893\) | 2.38442e86 | 0.212454 | ||||||||
\(894\) | 1.41852e87 | 1.22287 | ||||||||
\(895\) | −2.34792e87 | −1.95841 | ||||||||
\(896\) | −7.30830e86 | −0.589834 | ||||||||
\(897\) | 2.75588e86 | 0.215220 | ||||||||
\(898\) | 1.81663e87 | 1.37282 | ||||||||
\(899\) | −2.69329e86 | −0.196957 | ||||||||
\(900\) | −5.69058e86 | −0.402719 | ||||||||
\(901\) | 5.27523e85 | 0.0361293 | ||||||||
\(902\) | −1.14117e87 | −0.756413 | ||||||||
\(903\) | 2.66601e87 | 1.71031 | ||||||||
\(904\) | 4.86487e86 | 0.302066 | ||||||||
\(905\) | 1.92779e87 | 1.15858 | ||||||||
\(906\) | 1.07074e86 | 0.0622876 | ||||||||
\(907\) | −1.22203e87 | −0.688122 | −0.344061 | − | 0.938947i | \(-0.611803\pi\) | ||||
−0.344061 | + | 0.938947i | \(0.611803\pi\) | |||||||
\(908\) | −5.53378e86 | −0.301640 | ||||||||
\(909\) | 3.01882e86 | 0.159295 | ||||||||
\(910\) | 2.87312e87 | 1.46769 | ||||||||
\(911\) | 1.00822e87 | 0.498611 | 0.249306 | − | 0.968425i | \(-0.419798\pi\) | ||||
0.249306 | + | 0.968425i | \(0.419798\pi\) | |||||||
\(912\) | −1.72417e87 | −0.825530 | ||||||||
\(913\) | −1.31490e87 | −0.609546 | ||||||||
\(914\) | −1.22101e87 | −0.548031 | ||||||||
\(915\) | −8.76471e86 | −0.380904 | ||||||||
\(916\) | 9.93448e86 | 0.418051 | ||||||||
\(917\) | −2.95742e87 | −1.20508 | ||||||||
\(918\) | 4.30135e85 | 0.0169725 | ||||||||
\(919\) | −3.55829e86 | −0.135967 | −0.0679835 | − | 0.997686i | \(-0.521657\pi\) | ||||
−0.0679835 | + | 0.997686i | \(0.521657\pi\) | |||||||
\(920\) | −1.06914e87 | −0.395636 | ||||||||
\(921\) | 3.03612e87 | 1.08808 | ||||||||
\(922\) | −2.58996e87 | −0.898942 | ||||||||
\(923\) | −1.61935e87 | −0.544364 | ||||||||
\(924\) | 6.54793e86 | 0.213197 | ||||||||
\(925\) | 5.62904e87 | 1.77522 | ||||||||
\(926\) | −2.09397e87 | −0.639655 | ||||||||
\(927\) | −4.51859e87 | −1.33706 | ||||||||
\(928\) | −1.80263e87 | −0.516704 | ||||||||
\(929\) | 3.60367e87 | 1.00065 | 0.500324 | − | 0.865838i | \(-0.333214\pi\) | ||||
0.500324 | + | 0.865838i | \(0.333214\pi\) | |||||||
\(930\) | 1.40600e87 | 0.378215 | ||||||||
\(931\) | 2.18894e87 | 0.570451 | ||||||||
\(932\) | −1.19649e87 | −0.302091 | ||||||||
\(933\) | 2.43493e87 | 0.595633 | ||||||||
\(934\) | 3.82224e87 | 0.905909 | ||||||||
\(935\) | −2.53780e86 | −0.0582794 | ||||||||
\(936\) | −2.92595e87 | −0.651073 | ||||||||
\(937\) | −4.13844e87 | −0.892316 | −0.446158 | − | 0.894954i | \(-0.647208\pi\) | ||||
−0.446158 | + | 0.894954i | \(0.647208\pi\) | |||||||
\(938\) | −2.08678e87 | −0.436007 | ||||||||
\(939\) | −1.50230e87 | −0.304173 | ||||||||
\(940\) | −5.27230e86 | −0.103449 | ||||||||
\(941\) | 6.38918e87 | 1.21493 | 0.607465 | − | 0.794346i | \(-0.292186\pi\) | ||||
0.607465 | + | 0.794346i | \(0.292186\pi\) | |||||||
\(942\) | 2.92933e87 | 0.539842 | ||||||||
\(943\) | 2.09626e87 | 0.374412 | ||||||||
\(944\) | 5.30611e87 | 0.918549 | ||||||||
\(945\) | −3.80880e87 | −0.639072 | ||||||||
\(946\) | 2.61998e87 | 0.426098 | ||||||||
\(947\) | 3.09168e87 | 0.487383 | 0.243692 | − | 0.969853i | \(-0.421641\pi\) | ||||
0.243692 | + | 0.969853i | \(0.421641\pi\) | |||||||
\(948\) | 2.49107e87 | 0.380663 | ||||||||
\(949\) | 3.77266e87 | 0.558849 | ||||||||
\(950\) | −1.10196e88 | −1.58241 | ||||||||
\(951\) | −8.06946e87 | −1.12336 | ||||||||
\(952\) | 6.98482e86 | 0.0942682 | ||||||||
\(953\) | −1.26538e88 | −1.65569 | −0.827845 | − | 0.560957i | \(-0.810433\pi\) | ||||
−0.827845 | + | 0.560957i | \(0.810433\pi\) | |||||||
\(954\) | −2.82809e87 | −0.358770 | ||||||||
\(955\) | −3.75733e87 | −0.462147 | ||||||||
\(956\) | −7.64177e86 | −0.0911352 | ||||||||
\(957\) | −5.92940e87 | −0.685660 | ||||||||
\(958\) | −1.47405e87 | −0.165284 | ||||||||
\(959\) | −5.39022e87 | −0.586081 | ||||||||
\(960\) | 2.44018e88 | 2.57288 | ||||||||
\(961\) | −9.43177e87 | −0.964391 | ||||||||
\(962\) | 5.86811e87 | 0.581880 | ||||||||
\(963\) | 4.93727e87 | 0.474801 | ||||||||
\(964\) | 1.34889e87 | 0.125807 | ||||||||
\(965\) | 3.22759e88 | 2.91960 | ||||||||
\(966\) | 3.52696e87 | 0.309439 | ||||||||
\(967\) | 2.19059e87 | 0.186415 | 0.0932073 | − | 0.995647i | \(-0.470288\pi\) | ||||
0.0932073 | + | 0.995647i | \(0.470288\pi\) | |||||||
\(968\) | −9.94835e87 | −0.821161 | ||||||||
\(969\) | 1.03252e87 | 0.0826696 | ||||||||
\(970\) | −3.44620e88 | −2.67654 | ||||||||
\(971\) | 2.13221e88 | 1.60643 | 0.803217 | − | 0.595686i | \(-0.203120\pi\) | ||||
0.803217 | + | 0.595686i | \(0.203120\pi\) | |||||||
\(972\) | 4.43135e87 | 0.323878 | ||||||||
\(973\) | −6.00595e87 | −0.425846 | ||||||||
\(974\) | 2.02930e88 | 1.39591 | ||||||||
\(975\) | −3.09779e88 | −2.06736 | ||||||||
\(976\) | 1.72611e87 | 0.111763 | ||||||||
\(977\) | 6.88952e87 | 0.432812 | 0.216406 | − | 0.976303i | \(-0.430566\pi\) | ||||
0.216406 | + | 0.976303i | \(0.430566\pi\) | |||||||
\(978\) | 1.06613e88 | 0.649851 | ||||||||
\(979\) | −8.58878e87 | −0.507975 | ||||||||
\(980\) | −4.84006e87 | −0.277767 | ||||||||
\(981\) | −2.12836e88 | −1.18525 | ||||||||
\(982\) | 1.56643e88 | 0.846491 | ||||||||
\(983\) | 4.93080e87 | 0.258576 | 0.129288 | − | 0.991607i | \(-0.458731\pi\) | ||||
0.129288 | + | 0.991607i | \(0.458731\pi\) | |||||||
\(984\) | −5.06355e88 | −2.57691 | ||||||||
\(985\) | 1.48701e88 | 0.734421 | ||||||||
\(986\) | −1.28238e87 | −0.0614676 | ||||||||
\(987\) | 8.57848e87 | 0.399075 | ||||||||
\(988\) | 3.91765e87 | 0.176887 | ||||||||
\(989\) | −4.81272e87 | −0.210912 | ||||||||
\(990\) | 1.36054e88 | 0.578725 | ||||||||
\(991\) | 4.59414e87 | 0.189684 | 0.0948421 | − | 0.995492i | \(-0.469765\pi\) | ||||
0.0948421 | + | 0.995492i | \(0.469765\pi\) | |||||||
\(992\) | 2.33090e87 | 0.0934179 | ||||||||
\(993\) | 4.61972e88 | 1.79727 | ||||||||
\(994\) | −2.07243e88 | −0.782676 | ||||||||
\(995\) | −5.92136e88 | −2.17090 | ||||||||
\(996\) | −1.18291e88 | −0.421017 | ||||||||
\(997\) | 3.03646e88 | 1.04921 | 0.524603 | − | 0.851347i | \(-0.324214\pi\) | ||||
0.524603 | + | 0.851347i | \(0.324214\pi\) | |||||||
\(998\) | −7.12306e87 | −0.238955 | ||||||||
\(999\) | −7.77915e87 | −0.253367 |
(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 | 1.60.a.a.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 9.60.a.c.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.60.a.a.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.60.a.c.1.4 | 5 | 3.2 | odd | 2 |