Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,56,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, 56, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 56);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 56 \) |
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: | \(19.1581467685\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 149272663100531x^{2} + 190291401428579434725x + 325546600176957146615614350 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{9}\cdot 5^{2}\cdot 7\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-972934.\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.88052e7 | 0.151756 | 0.0758780 | − | 0.997117i | \(-0.475824\pi\) | ||||
0.0758780 | + | 0.997117i | \(0.475824\pi\) | |||||||
\(3\) | 1.23937e13 | 0.938355 | 0.469177 | − | 0.883104i | \(-0.344550\pi\) | ||||
0.469177 | + | 0.883104i | \(0.344550\pi\) | |||||||
\(4\) | −3.51991e16 | −0.976970 | ||||||||
\(5\) | −1.26520e19 | −0.759426 | −0.379713 | − | 0.925104i | \(-0.623977\pi\) | ||||
−0.379713 | + | 0.925104i | \(0.623977\pi\) | |||||||
\(6\) | 3.57004e20 | 0.142401 | ||||||||
\(7\) | 2.79909e23 | 1.60998 | 0.804990 | − | 0.593288i | \(-0.202171\pi\) | ||||
0.804990 | + | 0.593288i | \(0.202171\pi\) | |||||||
\(8\) | −2.05173e24 | −0.300017 | ||||||||
\(9\) | −2.08450e25 | −0.119490 | ||||||||
\(10\) | −3.64445e26 | −0.115247 | ||||||||
\(11\) | 4.43027e28 | 1.01890 | 0.509449 | − | 0.860501i | \(-0.329849\pi\) | ||||
0.509449 | + | 0.860501i | \(0.329849\pi\) | |||||||
\(12\) | −4.36247e29 | −0.916745 | ||||||||
\(13\) | 1.55064e30 | 0.360636 | 0.180318 | − | 0.983608i | \(-0.442287\pi\) | ||||
0.180318 | + | 0.983608i | \(0.442287\pi\) | |||||||
\(14\) | 8.06283e30 | 0.244324 | ||||||||
\(15\) | −1.56806e32 | −0.712611 | ||||||||
\(16\) | 1.20908e33 | 0.931441 | ||||||||
\(17\) | 8.73107e32 | 0.126976 | 0.0634881 | − | 0.997983i | \(-0.479778\pi\) | ||||
0.0634881 | + | 0.997983i | \(0.479778\pi\) | |||||||
\(18\) | −6.00444e32 | −0.0181334 | ||||||||
\(19\) | 1.64892e35 | 1.12584 | 0.562918 | − | 0.826513i | \(-0.309679\pi\) | ||||
0.562918 | + | 0.826513i | \(0.309679\pi\) | |||||||
\(20\) | 4.45340e35 | 0.741936 | ||||||||
\(21\) | 3.46911e36 | 1.51073 | ||||||||
\(22\) | 1.27615e36 | 0.154624 | ||||||||
\(23\) | 5.17737e37 | 1.84754 | 0.923770 | − | 0.382948i | \(-0.125091\pi\) | ||||
0.923770 | + | 0.382948i | \(0.125091\pi\) | |||||||
\(24\) | −2.54286e37 | −0.281523 | ||||||||
\(25\) | −1.17482e38 | −0.423272 | ||||||||
\(26\) | 4.46665e37 | 0.0547287 | ||||||||
\(27\) | −2.42042e39 | −1.05048 | ||||||||
\(28\) | −9.85253e39 | −1.57290 | ||||||||
\(29\) | 1.58882e40 | 0.966338 | 0.483169 | − | 0.875527i | \(-0.339486\pi\) | ||||
0.483169 | + | 0.875527i | \(0.339486\pi\) | |||||||
\(30\) | −4.51682e39 | −0.108143 | ||||||||
\(31\) | 5.89422e40 | 0.572770 | 0.286385 | − | 0.958115i | \(-0.407546\pi\) | ||||
0.286385 | + | 0.958115i | \(0.407546\pi\) | |||||||
\(32\) | 1.08749e41 | 0.441369 | ||||||||
\(33\) | 5.49075e41 | 0.956089 | ||||||||
\(34\) | 2.51500e40 | 0.0192694 | ||||||||
\(35\) | −3.54142e42 | −1.22266 | ||||||||
\(36\) | 7.33724e41 | 0.116738 | ||||||||
\(37\) | −1.50183e43 | −1.12479 | −0.562396 | − | 0.826868i | \(-0.690120\pi\) | ||||
−0.562396 | + | 0.826868i | \(0.690120\pi\) | |||||||
\(38\) | 4.74974e42 | 0.170853 | ||||||||
\(39\) | 1.92182e43 | 0.338404 | ||||||||
\(40\) | 2.59586e43 | 0.227841 | ||||||||
\(41\) | 2.49038e44 | 1.10843 | 0.554217 | − | 0.832372i | \(-0.313018\pi\) | ||||
0.554217 | + | 0.832372i | \(0.313018\pi\) | |||||||
\(42\) | 9.99285e43 | 0.229263 | ||||||||
\(43\) | −2.64200e44 | −0.317359 | −0.158680 | − | 0.987330i | \(-0.550724\pi\) | ||||
−0.158680 | + | 0.987330i | \(0.550724\pi\) | |||||||
\(44\) | −1.55941e45 | −0.995434 | ||||||||
\(45\) | 2.63732e44 | 0.0907440 | ||||||||
\(46\) | 1.49135e45 | 0.280375 | ||||||||
\(47\) | −1.75786e46 | −1.82934 | −0.914669 | − | 0.404204i | \(-0.867549\pi\) | ||||
−0.914669 | + | 0.404204i | \(0.867549\pi\) | |||||||
\(48\) | 1.49850e46 | 0.874022 | ||||||||
\(49\) | 4.81222e46 | 1.59204 | ||||||||
\(50\) | −3.38408e45 | −0.0642341 | ||||||||
\(51\) | 1.08210e46 | 0.119149 | ||||||||
\(52\) | −5.45811e46 | −0.352330 | ||||||||
\(53\) | −7.37942e46 | −0.282121 | −0.141061 | − | 0.990001i | \(-0.545051\pi\) | ||||
−0.141061 | + | 0.990001i | \(0.545051\pi\) | |||||||
\(54\) | −6.97207e46 | −0.159417 | ||||||||
\(55\) | −5.60519e47 | −0.773778 | ||||||||
\(56\) | −5.74298e47 | −0.483022 | ||||||||
\(57\) | 2.04362e48 | 1.05643 | ||||||||
\(58\) | 4.57662e47 | 0.146648 | ||||||||
\(59\) | 2.54720e48 | 0.510073 | 0.255036 | − | 0.966931i | \(-0.417913\pi\) | ||||
0.255036 | + | 0.966931i | \(0.417913\pi\) | |||||||
\(60\) | 5.51942e48 | 0.696200 | ||||||||
\(61\) | −1.07207e49 | −0.858325 | −0.429162 | − | 0.903227i | \(-0.641191\pi\) | ||||
−0.429162 | + | 0.903227i | \(0.641191\pi\) | |||||||
\(62\) | 1.69784e48 | 0.0869213 | ||||||||
\(63\) | −5.83470e48 | −0.192377 | ||||||||
\(64\) | −4.04291e49 | −0.864460 | ||||||||
\(65\) | −1.96188e49 | −0.273876 | ||||||||
\(66\) | 1.58162e49 | 0.145092 | ||||||||
\(67\) | 1.06094e50 | 0.643627 | 0.321814 | − | 0.946803i | \(-0.395708\pi\) | ||||
0.321814 | + | 0.946803i | \(0.395708\pi\) | |||||||
\(68\) | −3.07325e49 | −0.124052 | ||||||||
\(69\) | 6.41669e50 | 1.73365 | ||||||||
\(70\) | −1.02011e50 | −0.185546 | ||||||||
\(71\) | −1.17879e51 | −1.45156 | −0.725778 | − | 0.687929i | \(-0.758520\pi\) | ||||
−0.725778 | + | 0.687929i | \(0.758520\pi\) | |||||||
\(72\) | 4.27683e49 | 0.0358491 | ||||||||
\(73\) | 2.92361e50 | 0.167703 | 0.0838516 | − | 0.996478i | \(-0.473278\pi\) | ||||
0.0838516 | + | 0.996478i | \(0.473278\pi\) | |||||||
\(74\) | −4.32604e50 | −0.170694 | ||||||||
\(75\) | −1.45603e51 | −0.397180 | ||||||||
\(76\) | −5.80404e51 | −1.09991 | ||||||||
\(77\) | 1.24007e52 | 1.64041 | ||||||||
\(78\) | 5.53584e50 | 0.0513549 | ||||||||
\(79\) | 2.26793e52 | 1.48212 | 0.741062 | − | 0.671436i | \(-0.234322\pi\) | ||||
0.741062 | + | 0.671436i | \(0.234322\pi\) | |||||||
\(80\) | −1.52973e52 | −0.707360 | ||||||||
\(81\) | −2.63616e52 | −0.866232 | ||||||||
\(82\) | 7.17360e51 | 0.168212 | ||||||||
\(83\) | 3.10804e52 | 0.522203 | 0.261101 | − | 0.965311i | \(-0.415914\pi\) | ||||
0.261101 | + | 0.965311i | \(0.415914\pi\) | |||||||
\(84\) | −1.22109e53 | −1.47594 | ||||||||
\(85\) | −1.10466e52 | −0.0964290 | ||||||||
\(86\) | −7.61035e51 | −0.0481612 | ||||||||
\(87\) | 1.96914e53 | 0.906768 | ||||||||
\(88\) | −9.08973e52 | −0.305687 | ||||||||
\(89\) | 4.89902e53 | 1.20749 | 0.603745 | − | 0.797177i | \(-0.293674\pi\) | ||||
0.603745 | + | 0.797177i | \(0.293674\pi\) | |||||||
\(90\) | 7.59684e51 | 0.0137710 | ||||||||
\(91\) | 4.34038e53 | 0.580616 | ||||||||
\(92\) | −1.82239e54 | −1.80499 | ||||||||
\(93\) | 7.30513e53 | 0.537461 | ||||||||
\(94\) | −5.06356e53 | −0.277613 | ||||||||
\(95\) | −2.08622e54 | −0.854989 | ||||||||
\(96\) | 1.34781e54 | 0.414161 | ||||||||
\(97\) | 4.57966e53 | 0.105830 | 0.0529152 | − | 0.998599i | \(-0.483149\pi\) | ||||
0.0529152 | + | 0.998599i | \(0.483149\pi\) | |||||||
\(98\) | 1.38617e54 | 0.241601 | ||||||||
\(99\) | −9.23488e53 | −0.121749 | ||||||||
\(100\) | 4.13524e54 | 0.413524 | ||||||||
\(101\) | 1.50130e55 | 1.14191 | 0.570953 | − | 0.820983i | \(-0.306574\pi\) | ||||
0.570953 | + | 0.820983i | \(0.306574\pi\) | |||||||
\(102\) | 3.11702e53 | 0.0180815 | ||||||||
\(103\) | −1.70225e55 | −0.755090 | −0.377545 | − | 0.925991i | \(-0.623232\pi\) | ||||
−0.377545 | + | 0.925991i | \(0.623232\pi\) | |||||||
\(104\) | −3.18150e54 | −0.108197 | ||||||||
\(105\) | −4.38913e55 | −1.14729 | ||||||||
\(106\) | −2.12566e54 | −0.0428136 | ||||||||
\(107\) | −2.90724e55 | −0.452300 | −0.226150 | − | 0.974092i | \(-0.572614\pi\) | ||||
−0.226150 | + | 0.974092i | \(0.572614\pi\) | |||||||
\(108\) | 8.51965e55 | 1.02629 | ||||||||
\(109\) | 5.37285e55 | 0.502315 | 0.251157 | − | 0.967946i | \(-0.419189\pi\) | ||||
0.251157 | + | 0.967946i | \(0.419189\pi\) | |||||||
\(110\) | −1.61459e55 | −0.117426 | ||||||||
\(111\) | −1.86132e56 | −1.05545 | ||||||||
\(112\) | 3.38432e56 | 1.49960 | ||||||||
\(113\) | 2.45020e56 | 0.850247 | 0.425123 | − | 0.905135i | \(-0.360231\pi\) | ||||
0.425123 | + | 0.905135i | \(0.360231\pi\) | |||||||
\(114\) | 5.88670e55 | 0.160320 | ||||||||
\(115\) | −6.55043e56 | −1.40307 | ||||||||
\(116\) | −5.59249e56 | −0.944083 | ||||||||
\(117\) | −3.23231e55 | −0.0430925 | ||||||||
\(118\) | 7.33725e55 | 0.0774066 | ||||||||
\(119\) | 2.44390e56 | 0.204429 | ||||||||
\(120\) | 3.21724e56 | 0.213796 | ||||||||
\(121\) | 7.21357e55 | 0.0381551 | ||||||||
\(122\) | −3.08811e56 | −0.130256 | ||||||||
\(123\) | 3.08651e57 | 1.04010 | ||||||||
\(124\) | −2.07471e57 | −0.559579 | ||||||||
\(125\) | 4.99803e57 | 1.08087 | ||||||||
\(126\) | −1.68070e56 | −0.0291944 | ||||||||
\(127\) | −5.35925e57 | −0.749035 | −0.374517 | − | 0.927220i | \(-0.622192\pi\) | ||||
−0.374517 | + | 0.927220i | \(0.622192\pi\) | |||||||
\(128\) | −5.08267e57 | −0.572556 | ||||||||
\(129\) | −3.27443e57 | −0.297796 | ||||||||
\(130\) | −5.65122e56 | −0.0415624 | ||||||||
\(131\) | −5.72408e57 | −0.340993 | −0.170496 | − | 0.985358i | \(-0.554537\pi\) | ||||
−0.170496 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(132\) | −1.93269e58 | −0.934070 | ||||||||
\(133\) | 4.61547e58 | 1.81257 | ||||||||
\(134\) | 3.05606e57 | 0.0976744 | ||||||||
\(135\) | 3.06233e58 | 0.797761 | ||||||||
\(136\) | −1.79138e57 | −0.0380950 | ||||||||
\(137\) | −3.04892e58 | −0.530067 | −0.265033 | − | 0.964239i | \(-0.585383\pi\) | ||||
−0.265033 | + | 0.964239i | \(0.585383\pi\) | |||||||
\(138\) | 1.84834e58 | 0.263092 | ||||||||
\(139\) | −5.38797e58 | −0.628809 | −0.314404 | − | 0.949289i | \(-0.601805\pi\) | ||||
−0.314404 | + | 0.949289i | \(0.601805\pi\) | |||||||
\(140\) | 1.24655e59 | 1.19450 | ||||||||
\(141\) | −2.17865e59 | −1.71657 | ||||||||
\(142\) | −3.39554e58 | −0.220282 | ||||||||
\(143\) | 6.86975e58 | 0.367451 | ||||||||
\(144\) | −2.52032e58 | −0.111298 | ||||||||
\(145\) | −2.01018e59 | −0.733862 | ||||||||
\(146\) | 8.42153e57 | 0.0254500 | ||||||||
\(147\) | 5.96413e59 | 1.49390 | ||||||||
\(148\) | 5.28629e59 | 1.09889 | ||||||||
\(149\) | −2.75514e59 | −0.475907 | −0.237953 | − | 0.971277i | \(-0.576477\pi\) | ||||
−0.237953 | + | 0.971277i | \(0.576477\pi\) | |||||||
\(150\) | −4.19414e58 | −0.0602744 | ||||||||
\(151\) | −3.94876e59 | −0.472709 | −0.236355 | − | 0.971667i | \(-0.575953\pi\) | ||||
−0.236355 | + | 0.971667i | \(0.575953\pi\) | |||||||
\(152\) | −3.38314e59 | −0.337770 | ||||||||
\(153\) | −1.81999e58 | −0.0151724 | ||||||||
\(154\) | 3.57205e59 | 0.248942 | ||||||||
\(155\) | −7.45739e59 | −0.434976 | ||||||||
\(156\) | −6.76462e59 | −0.330611 | ||||||||
\(157\) | −1.28546e60 | −0.527009 | −0.263505 | − | 0.964658i | \(-0.584878\pi\) | ||||
−0.263505 | + | 0.964658i | \(0.584878\pi\) | |||||||
\(158\) | 6.53282e59 | 0.224921 | ||||||||
\(159\) | −9.14584e59 | −0.264730 | ||||||||
\(160\) | −1.37590e60 | −0.335187 | ||||||||
\(161\) | 1.44919e61 | 2.97450 | ||||||||
\(162\) | −7.59352e59 | −0.131456 | ||||||||
\(163\) | 8.10357e59 | 0.118445 | 0.0592226 | − | 0.998245i | \(-0.481138\pi\) | ||||
0.0592226 | + | 0.998245i | \(0.481138\pi\) | |||||||
\(164\) | −8.76591e60 | −1.08291 | ||||||||
\(165\) | −6.94692e60 | −0.726079 | ||||||||
\(166\) | 8.95277e59 | 0.0792474 | ||||||||
\(167\) | 8.63145e60 | 0.647710 | 0.323855 | − | 0.946107i | \(-0.395021\pi\) | ||||
0.323855 | + | 0.946107i | \(0.395021\pi\) | |||||||
\(168\) | −7.11769e60 | −0.453246 | ||||||||
\(169\) | −1.60833e61 | −0.869942 | ||||||||
\(170\) | −3.18199e59 | −0.0146337 | ||||||||
\(171\) | −3.43717e60 | −0.134526 | ||||||||
\(172\) | 9.29961e60 | 0.310050 | ||||||||
\(173\) | 2.85400e61 | 0.811307 | 0.405654 | − | 0.914027i | \(-0.367044\pi\) | ||||
0.405654 | + | 0.914027i | \(0.367044\pi\) | |||||||
\(174\) | 5.67214e60 | 0.137608 | ||||||||
\(175\) | −3.28842e61 | −0.681460 | ||||||||
\(176\) | 5.35654e61 | 0.949044 | ||||||||
\(177\) | 3.15692e61 | 0.478629 | ||||||||
\(178\) | 1.41117e61 | 0.183244 | ||||||||
\(179\) | −4.09139e61 | −0.455421 | −0.227710 | − | 0.973729i | \(-0.573124\pi\) | ||||
−0.227710 | + | 0.973729i | \(0.573124\pi\) | |||||||
\(180\) | −9.28310e60 | −0.0886542 | ||||||||
\(181\) | −1.09499e62 | −0.897946 | −0.448973 | − | 0.893545i | \(-0.648210\pi\) | ||||
−0.448973 | + | 0.893545i | \(0.648210\pi\) | |||||||
\(182\) | 1.25025e61 | 0.0881121 | ||||||||
\(183\) | −1.32869e62 | −0.805413 | ||||||||
\(184\) | −1.06226e62 | −0.554294 | ||||||||
\(185\) | 1.90012e62 | 0.854197 | ||||||||
\(186\) | 2.10426e61 | 0.0815630 | ||||||||
\(187\) | 3.86810e61 | 0.129376 | ||||||||
\(188\) | 6.18751e62 | 1.78721 | ||||||||
\(189\) | −6.77497e62 | −1.69125 | ||||||||
\(190\) | −6.00940e61 | −0.129750 | ||||||||
\(191\) | 9.82615e62 | 1.83639 | 0.918197 | − | 0.396125i | \(-0.129645\pi\) | ||||
0.918197 | + | 0.396125i | \(0.129645\pi\) | |||||||
\(192\) | −5.01067e62 | −0.811170 | ||||||||
\(193\) | 3.58891e62 | 0.503659 | 0.251830 | − | 0.967772i | \(-0.418968\pi\) | ||||
0.251830 | + | 0.967772i | \(0.418968\pi\) | |||||||
\(194\) | 1.31918e61 | 0.0160604 | ||||||||
\(195\) | −2.43149e62 | −0.256993 | ||||||||
\(196\) | −1.69386e63 | −1.55537 | ||||||||
\(197\) | −1.12979e62 | −0.0901937 | −0.0450968 | − | 0.998983i | \(-0.514360\pi\) | ||||
−0.0450968 | + | 0.998983i | \(0.514360\pi\) | |||||||
\(198\) | −2.66013e61 | −0.0184761 | ||||||||
\(199\) | −6.41270e62 | −0.387776 | −0.193888 | − | 0.981024i | \(-0.562110\pi\) | ||||
−0.193888 | + | 0.981024i | \(0.562110\pi\) | |||||||
\(200\) | 2.41041e62 | 0.126989 | ||||||||
\(201\) | 1.31490e63 | 0.603951 | ||||||||
\(202\) | 4.32453e62 | 0.173291 | ||||||||
\(203\) | 4.44724e63 | 1.55579 | ||||||||
\(204\) | −3.80890e62 | −0.116405 | ||||||||
\(205\) | −3.15084e63 | −0.841774 | ||||||||
\(206\) | −4.90335e62 | −0.114589 | ||||||||
\(207\) | −1.07922e63 | −0.220763 | ||||||||
\(208\) | 1.87485e63 | 0.335911 | ||||||||
\(209\) | 7.30515e63 | 1.14711 | ||||||||
\(210\) | −1.26430e63 | −0.174108 | ||||||||
\(211\) | −1.25121e64 | −1.51204 | −0.756019 | − | 0.654550i | \(-0.772858\pi\) | ||||
−0.756019 | + | 0.654550i | \(0.772858\pi\) | |||||||
\(212\) | 2.59749e63 | 0.275624 | ||||||||
\(213\) | −1.46096e64 | −1.36207 | ||||||||
\(214\) | −8.37436e62 | −0.0686393 | ||||||||
\(215\) | 3.34267e63 | 0.241011 | ||||||||
\(216\) | 4.96606e63 | 0.315162 | ||||||||
\(217\) | 1.64985e64 | 0.922148 | ||||||||
\(218\) | 1.54766e63 | 0.0762293 | ||||||||
\(219\) | 3.62344e63 | 0.157365 | ||||||||
\(220\) | 1.97297e64 | 0.755958 | ||||||||
\(221\) | 1.35387e63 | 0.0457921 | ||||||||
\(222\) | −5.36158e63 | −0.160172 | ||||||||
\(223\) | −3.80868e64 | −1.00552 | −0.502760 | − | 0.864426i | \(-0.667682\pi\) | ||||
−0.502760 | + | 0.864426i | \(0.667682\pi\) | |||||||
\(224\) | 3.04399e64 | 0.710595 | ||||||||
\(225\) | 2.44890e63 | 0.0505769 | ||||||||
\(226\) | 7.05786e63 | 0.129030 | ||||||||
\(227\) | −8.04148e64 | −1.30204 | −0.651021 | − | 0.759060i | \(-0.725659\pi\) | ||||
−0.651021 | + | 0.759060i | \(0.725659\pi\) | |||||||
\(228\) | −7.19336e64 | −1.03210 | ||||||||
\(229\) | 3.89160e64 | 0.495054 | 0.247527 | − | 0.968881i | \(-0.420382\pi\) | ||||
0.247527 | + | 0.968881i | \(0.420382\pi\) | |||||||
\(230\) | −1.88686e64 | −0.212924 | ||||||||
\(231\) | 1.53691e65 | 1.53928 | ||||||||
\(232\) | −3.25983e64 | −0.289918 | ||||||||
\(233\) | −9.97362e64 | −0.788070 | −0.394035 | − | 0.919095i | \(-0.628921\pi\) | ||||
−0.394035 | + | 0.919095i | \(0.628921\pi\) | |||||||
\(234\) | −9.31072e62 | −0.00653954 | ||||||||
\(235\) | 2.22405e65 | 1.38925 | ||||||||
\(236\) | −8.96589e64 | −0.498326 | ||||||||
\(237\) | 2.81081e65 | 1.39076 | ||||||||
\(238\) | 7.03972e63 | 0.0310234 | ||||||||
\(239\) | −4.18204e62 | −0.00164227 | −0.000821137 | − | 1.00000i | \(-0.500261\pi\) | ||||
−0.000821137 | 1.00000i | \(0.500261\pi\) | ||||||||
\(240\) | −1.89591e65 | −0.663755 | ||||||||
\(241\) | −5.42301e65 | −1.69345 | −0.846724 | − | 0.532033i | \(-0.821428\pi\) | ||||
−0.846724 | + | 0.532033i | \(0.821428\pi\) | |||||||
\(242\) | 2.07788e63 | 0.00579026 | ||||||||
\(243\) | 9.55220e64 | 0.237646 | ||||||||
\(244\) | 3.77358e65 | 0.838558 | ||||||||
\(245\) | −6.08844e65 | −1.20903 | ||||||||
\(246\) | 8.89076e64 | 0.157842 | ||||||||
\(247\) | 2.55688e65 | 0.406017 | ||||||||
\(248\) | −1.20934e65 | −0.171841 | ||||||||
\(249\) | 3.85202e65 | 0.490011 | ||||||||
\(250\) | 1.43969e65 | 0.164029 | ||||||||
\(251\) | −7.66365e65 | −0.782363 | −0.391181 | − | 0.920314i | \(-0.627933\pi\) | ||||
−0.391181 | + | 0.920314i | \(0.627933\pi\) | |||||||
\(252\) | 2.05376e65 | 0.187947 | ||||||||
\(253\) | 2.29371e66 | 1.88246 | ||||||||
\(254\) | −1.54374e65 | −0.113671 | ||||||||
\(255\) | −1.36908e65 | −0.0904846 | ||||||||
\(256\) | 1.31021e66 | 0.777571 | ||||||||
\(257\) | −2.62578e66 | −1.39990 | −0.699952 | − | 0.714190i | \(-0.746795\pi\) | ||||
−0.699952 | + | 0.714190i | \(0.746795\pi\) | |||||||
\(258\) | −9.43205e64 | −0.0451923 | ||||||||
\(259\) | −4.20375e66 | −1.81089 | ||||||||
\(260\) | 6.90562e65 | 0.267569 | ||||||||
\(261\) | −3.31189e65 | −0.115468 | ||||||||
\(262\) | −1.64883e65 | −0.0517477 | ||||||||
\(263\) | 3.10641e66 | 0.877962 | 0.438981 | − | 0.898496i | \(-0.355339\pi\) | ||||
0.438981 | + | 0.898496i | \(0.355339\pi\) | |||||||
\(264\) | −1.12655e66 | −0.286843 | ||||||||
\(265\) | 9.33647e65 | 0.214250 | ||||||||
\(266\) | 1.32950e66 | 0.275069 | ||||||||
\(267\) | 6.07170e66 | 1.13305 | ||||||||
\(268\) | −3.73441e66 | −0.628805 | ||||||||
\(269\) | −2.44880e66 | −0.372192 | −0.186096 | − | 0.982532i | \(-0.559583\pi\) | ||||
−0.186096 | + | 0.982532i | \(0.559583\pi\) | |||||||
\(270\) | 8.82109e65 | 0.121065 | ||||||||
\(271\) | 4.59005e66 | 0.569065 | 0.284533 | − | 0.958666i | \(-0.408162\pi\) | ||||
0.284533 | + | 0.958666i | \(0.408162\pi\) | |||||||
\(272\) | 1.05566e66 | 0.118271 | ||||||||
\(273\) | 5.37934e66 | 0.544824 | ||||||||
\(274\) | −8.78248e65 | −0.0804408 | ||||||||
\(275\) | −5.20475e66 | −0.431272 | ||||||||
\(276\) | −2.25861e67 | −1.69372 | ||||||||
\(277\) | −3.77433e66 | −0.256240 | −0.128120 | − | 0.991759i | \(-0.540894\pi\) | ||||
−0.128120 | + | 0.991759i | \(0.540894\pi\) | |||||||
\(278\) | −1.55202e66 | −0.0954255 | ||||||||
\(279\) | −1.22865e66 | −0.0684404 | ||||||||
\(280\) | 7.26604e66 | 0.366819 | ||||||||
\(281\) | 2.01573e67 | 0.922591 | 0.461295 | − | 0.887247i | \(-0.347385\pi\) | ||||
0.461295 | + | 0.887247i | \(0.347385\pi\) | |||||||
\(282\) | −6.27563e66 | −0.260500 | ||||||||
\(283\) | −1.57152e67 | −0.591824 | −0.295912 | − | 0.955215i | \(-0.595624\pi\) | ||||
−0.295912 | + | 0.955215i | \(0.595624\pi\) | |||||||
\(284\) | 4.14925e67 | 1.41813 | ||||||||
\(285\) | −2.58560e67 | −0.802283 | ||||||||
\(286\) | 1.97885e66 | 0.0557630 | ||||||||
\(287\) | 6.97080e67 | 1.78456 | ||||||||
\(288\) | −2.26688e66 | −0.0527393 | ||||||||
\(289\) | −4.65191e67 | −0.983877 | ||||||||
\(290\) | −5.79036e66 | −0.111368 | ||||||||
\(291\) | 5.67590e66 | 0.0993064 | ||||||||
\(292\) | −1.02908e67 | −0.163841 | ||||||||
\(293\) | −5.33382e67 | −0.772999 | −0.386500 | − | 0.922290i | \(-0.626316\pi\) | ||||
−0.386500 | + | 0.922290i | \(0.626316\pi\) | |||||||
\(294\) | 1.71798e67 | 0.226708 | ||||||||
\(295\) | −3.22272e67 | −0.387363 | ||||||||
\(296\) | 3.08135e67 | 0.337457 | ||||||||
\(297\) | −1.07231e68 | −1.07033 | ||||||||
\(298\) | −7.93625e66 | −0.0722218 | ||||||||
\(299\) | 8.02824e67 | 0.666289 | ||||||||
\(300\) | 5.12510e67 | 0.388033 | ||||||||
\(301\) | −7.39521e67 | −0.510942 | ||||||||
\(302\) | −1.13745e67 | −0.0717365 | ||||||||
\(303\) | 1.86067e68 | 1.07151 | ||||||||
\(304\) | 1.99367e68 | 1.04865 | ||||||||
\(305\) | 1.35638e68 | 0.651834 | ||||||||
\(306\) | −5.24252e65 | −0.00230251 | ||||||||
\(307\) | −2.80514e67 | −0.112629 | −0.0563144 | − | 0.998413i | \(-0.517935\pi\) | ||||
−0.0563144 | + | 0.998413i | \(0.517935\pi\) | |||||||
\(308\) | −4.36493e68 | −1.60263 | ||||||||
\(309\) | −2.10971e68 | −0.708542 | ||||||||
\(310\) | −2.14812e67 | −0.0660103 | ||||||||
\(311\) | −7.41937e67 | −0.208668 | −0.104334 | − | 0.994542i | \(-0.533271\pi\) | ||||
−0.104334 | + | 0.994542i | \(0.533271\pi\) | |||||||
\(312\) | −3.94306e67 | −0.101527 | ||||||||
\(313\) | 4.59840e68 | 1.08427 | 0.542135 | − | 0.840291i | \(-0.317616\pi\) | ||||
0.542135 | + | 0.840291i | \(0.317616\pi\) | |||||||
\(314\) | −3.70279e67 | −0.0799768 | ||||||||
\(315\) | 7.38208e67 | 0.146096 | ||||||||
\(316\) | −7.98290e68 | −1.44799 | ||||||||
\(317\) | −3.97467e67 | −0.0660955 | −0.0330477 | − | 0.999454i | \(-0.510521\pi\) | ||||
−0.0330477 | + | 0.999454i | \(0.510521\pi\) | |||||||
\(318\) | −2.63448e67 | −0.0401744 | ||||||||
\(319\) | 7.03889e68 | 0.984601 | ||||||||
\(320\) | 5.11511e68 | 0.656494 | ||||||||
\(321\) | −3.60315e68 | −0.424418 | ||||||||
\(322\) | 4.17443e68 | 0.451399 | ||||||||
\(323\) | 1.43968e68 | 0.142954 | ||||||||
\(324\) | 9.27904e68 | 0.846283 | ||||||||
\(325\) | −1.82172e68 | −0.152647 | ||||||||
\(326\) | 2.33425e67 | 0.0179748 | ||||||||
\(327\) | 6.65895e68 | 0.471349 | ||||||||
\(328\) | −5.10960e68 | −0.332549 | ||||||||
\(329\) | −4.92041e69 | −2.94520 | ||||||||
\(330\) | −2.00107e68 | −0.110187 | ||||||||
\(331\) | 2.81395e69 | 1.42576 | 0.712879 | − | 0.701287i | \(-0.247391\pi\) | ||||
0.712879 | + | 0.701287i | \(0.247391\pi\) | |||||||
\(332\) | −1.09400e69 | −0.510176 | ||||||||
\(333\) | 3.13056e68 | 0.134402 | ||||||||
\(334\) | 2.48631e68 | 0.0982939 | ||||||||
\(335\) | −1.34231e69 | −0.488787 | ||||||||
\(336\) | 4.19443e69 | 1.40716 | ||||||||
\(337\) | −3.53381e69 | −1.09250 | −0.546249 | − | 0.837623i | \(-0.683945\pi\) | ||||
−0.546249 | + | 0.837623i | \(0.683945\pi\) | |||||||
\(338\) | −4.63282e68 | −0.132019 | ||||||||
\(339\) | 3.03671e69 | 0.797833 | ||||||||
\(340\) | 3.88829e68 | 0.0942082 | ||||||||
\(341\) | 2.61130e69 | 0.583594 | ||||||||
\(342\) | −9.90083e67 | −0.0204152 | ||||||||
\(343\) | 5.00907e69 | 0.953167 | ||||||||
\(344\) | 5.42069e68 | 0.0952132 | ||||||||
\(345\) | −8.11842e69 | −1.31658 | ||||||||
\(346\) | 8.22099e68 | 0.123121 | ||||||||
\(347\) | 7.81225e69 | 1.08073 | 0.540363 | − | 0.841432i | \(-0.318287\pi\) | ||||
0.540363 | + | 0.841432i | \(0.318287\pi\) | |||||||
\(348\) | −6.93117e69 | −0.885885 | ||||||||
\(349\) | −1.46742e70 | −1.73323 | −0.866614 | − | 0.498978i | \(-0.833709\pi\) | ||||
−0.866614 | + | 0.498978i | \(0.833709\pi\) | |||||||
\(350\) | −9.47235e68 | −0.103416 | ||||||||
\(351\) | −3.75320e69 | −0.378840 | ||||||||
\(352\) | 4.81788e69 | 0.449710 | ||||||||
\(353\) | 3.73450e69 | 0.322425 | 0.161212 | − | 0.986920i | \(-0.448460\pi\) | ||||
0.161212 | + | 0.986920i | \(0.448460\pi\) | |||||||
\(354\) | 9.09358e68 | 0.0726349 | ||||||||
\(355\) | 1.49142e70 | 1.10235 | ||||||||
\(356\) | −1.72441e70 | −1.17968 | ||||||||
\(357\) | 3.02891e69 | 0.191827 | ||||||||
\(358\) | −1.17853e69 | −0.0691129 | ||||||||
\(359\) | 2.97159e70 | 1.61396 | 0.806979 | − | 0.590580i | \(-0.201101\pi\) | ||||
0.806979 | + | 0.590580i | \(0.201101\pi\) | |||||||
\(360\) | −5.41107e68 | −0.0272248 | ||||||||
\(361\) | 5.73832e69 | 0.267508 | ||||||||
\(362\) | −3.15415e69 | −0.136269 | ||||||||
\(363\) | 8.94029e68 | 0.0358030 | ||||||||
\(364\) | −1.52777e70 | −0.567245 | ||||||||
\(365\) | −3.69897e69 | −0.127358 | ||||||||
\(366\) | −3.82732e69 | −0.122226 | ||||||||
\(367\) | −5.08197e70 | −1.50562 | −0.752811 | − | 0.658237i | \(-0.771302\pi\) | ||||
−0.752811 | + | 0.658237i | \(0.771302\pi\) | |||||||
\(368\) | 6.25985e70 | 1.72087 | ||||||||
\(369\) | −5.19120e69 | −0.132447 | ||||||||
\(370\) | 5.47333e69 | 0.129630 | ||||||||
\(371\) | −2.06556e70 | −0.454210 | ||||||||
\(372\) | −2.57134e70 | −0.525083 | ||||||||
\(373\) | −8.75772e70 | −1.66111 | −0.830554 | − | 0.556938i | \(-0.811976\pi\) | ||||
−0.830554 | + | 0.556938i | \(0.811976\pi\) | |||||||
\(374\) | 1.11421e69 | 0.0196336 | ||||||||
\(375\) | 6.19442e70 | 1.01424 | ||||||||
\(376\) | 3.60666e70 | 0.548833 | ||||||||
\(377\) | 2.46368e70 | 0.348496 | ||||||||
\(378\) | −1.95154e70 | −0.256658 | ||||||||
\(379\) | 1.26223e71 | 1.54369 | 0.771847 | − | 0.635808i | \(-0.219333\pi\) | ||||
0.771847 | + | 0.635808i | \(0.219333\pi\) | |||||||
\(380\) | 7.34329e70 | 0.835299 | ||||||||
\(381\) | −6.64211e70 | −0.702860 | ||||||||
\(382\) | 2.83044e70 | 0.278684 | ||||||||
\(383\) | −5.28430e69 | −0.0484196 | −0.0242098 | − | 0.999707i | \(-0.507707\pi\) | ||||
−0.0242098 | + | 0.999707i | \(0.507707\pi\) | |||||||
\(384\) | −6.29932e70 | −0.537261 | ||||||||
\(385\) | −1.56894e71 | −1.24577 | ||||||||
\(386\) | 1.03379e70 | 0.0764334 | ||||||||
\(387\) | 5.50725e69 | 0.0379213 | ||||||||
\(388\) | −1.61200e70 | −0.103393 | ||||||||
\(389\) | 2.99174e70 | 0.178776 | 0.0893882 | − | 0.995997i | \(-0.471509\pi\) | ||||
0.0893882 | + | 0.995997i | \(0.471509\pi\) | |||||||
\(390\) | −7.00397e69 | −0.0390002 | ||||||||
\(391\) | 4.52040e70 | 0.234594 | ||||||||
\(392\) | −9.87338e70 | −0.477638 | ||||||||
\(393\) | −7.09426e70 | −0.319972 | ||||||||
\(394\) | −3.25438e69 | −0.0136874 | ||||||||
\(395\) | −2.86939e71 | −1.12556 | ||||||||
\(396\) | 3.25059e70 | 0.118945 | ||||||||
\(397\) | 4.68857e71 | 1.60067 | 0.800335 | − | 0.599553i | \(-0.204655\pi\) | ||||
0.800335 | + | 0.599553i | \(0.204655\pi\) | |||||||
\(398\) | −1.84719e70 | −0.0588474 | ||||||||
\(399\) | 5.72028e71 | 1.70084 | ||||||||
\(400\) | −1.42045e71 | −0.394253 | ||||||||
\(401\) | 1.15088e70 | 0.0298236 | 0.0149118 | − | 0.999889i | \(-0.495253\pi\) | ||||
0.0149118 | + | 0.999889i | \(0.495253\pi\) | |||||||
\(402\) | 3.78760e70 | 0.0916532 | ||||||||
\(403\) | 9.13981e70 | 0.206561 | ||||||||
\(404\) | −5.28445e71 | −1.11561 | ||||||||
\(405\) | 3.33528e71 | 0.657839 | ||||||||
\(406\) | 1.28104e71 | 0.236100 | ||||||||
\(407\) | −6.65350e71 | −1.14605 | ||||||||
\(408\) | −2.22019e70 | −0.0357467 | ||||||||
\(409\) | −5.99712e71 | −0.902717 | −0.451358 | − | 0.892343i | \(-0.649060\pi\) | ||||
−0.451358 | + | 0.892343i | \(0.649060\pi\) | |||||||
\(410\) | −9.07607e70 | −0.127744 | ||||||||
\(411\) | −3.77875e71 | −0.497391 | ||||||||
\(412\) | 5.99174e71 | 0.737700 | ||||||||
\(413\) | 7.12983e71 | 0.821207 | ||||||||
\(414\) | −3.10872e70 | −0.0335021 | ||||||||
\(415\) | −3.93230e71 | −0.396574 | ||||||||
\(416\) | 1.68631e71 | 0.159173 | ||||||||
\(417\) | −6.67770e71 | −0.590046 | ||||||||
\(418\) | 2.10426e71 | 0.174081 | ||||||||
\(419\) | −6.48026e71 | −0.502004 | −0.251002 | − | 0.967987i | \(-0.580760\pi\) | ||||
−0.251002 | + | 0.967987i | \(0.580760\pi\) | |||||||
\(420\) | 1.54493e72 | 1.12087 | ||||||||
\(421\) | 1.99937e72 | 1.35874 | 0.679369 | − | 0.733797i | \(-0.262254\pi\) | ||||
0.679369 | + | 0.733797i | \(0.262254\pi\) | |||||||
\(422\) | −3.60413e71 | −0.229461 | ||||||||
\(423\) | 3.66426e71 | 0.218588 | ||||||||
\(424\) | 1.51406e71 | 0.0846412 | ||||||||
\(425\) | −1.02574e71 | −0.0537455 | ||||||||
\(426\) | −4.20834e71 | −0.206703 | ||||||||
\(427\) | −3.00081e72 | −1.38189 | ||||||||
\(428\) | 1.02332e72 | 0.441884 | ||||||||
\(429\) | 8.51417e71 | 0.344800 | ||||||||
\(430\) | 9.62864e70 | 0.0365749 | ||||||||
\(431\) | −3.24265e72 | −1.15551 | −0.577756 | − | 0.816209i | \(-0.696072\pi\) | ||||
−0.577756 | + | 0.816209i | \(0.696072\pi\) | |||||||
\(432\) | −2.92648e72 | −0.978459 | ||||||||
\(433\) | 1.58622e72 | 0.497675 | 0.248838 | − | 0.968545i | \(-0.419951\pi\) | ||||
0.248838 | + | 0.968545i | \(0.419951\pi\) | |||||||
\(434\) | 4.75241e71 | 0.139942 | ||||||||
\(435\) | −2.49136e72 | −0.688623 | ||||||||
\(436\) | −1.89119e72 | −0.490746 | ||||||||
\(437\) | 8.53707e72 | 2.08003 | ||||||||
\(438\) | 1.04374e71 | 0.0238811 | ||||||||
\(439\) | 1.49705e72 | 0.321708 | 0.160854 | − | 0.986978i | \(-0.448575\pi\) | ||||
0.160854 | + | 0.986978i | \(0.448575\pi\) | |||||||
\(440\) | 1.15004e72 | 0.232147 | ||||||||
\(441\) | −1.00311e72 | −0.190233 | ||||||||
\(442\) | 3.89986e70 | 0.00694923 | ||||||||
\(443\) | 3.40583e72 | 0.570322 | 0.285161 | − | 0.958480i | \(-0.407953\pi\) | ||||
0.285161 | + | 0.958480i | \(0.407953\pi\) | |||||||
\(444\) | 6.55168e72 | 1.03115 | ||||||||
\(445\) | −6.19825e72 | −0.917000 | ||||||||
\(446\) | −1.09710e72 | −0.152594 | ||||||||
\(447\) | −3.41465e72 | −0.446570 | ||||||||
\(448\) | −1.13165e73 | −1.39176 | ||||||||
\(449\) | 8.20452e72 | 0.949027 | 0.474514 | − | 0.880248i | \(-0.342624\pi\) | ||||
0.474514 | + | 0.880248i | \(0.342624\pi\) | |||||||
\(450\) | 7.05411e70 | 0.00767535 | ||||||||
\(451\) | 1.10331e73 | 1.12938 | ||||||||
\(452\) | −8.62449e72 | −0.830666 | ||||||||
\(453\) | −4.89398e72 | −0.443569 | ||||||||
\(454\) | −2.31636e72 | −0.197593 | ||||||||
\(455\) | −5.49146e72 | −0.440935 | ||||||||
\(456\) | −4.19297e72 | −0.316948 | ||||||||
\(457\) | −1.34921e73 | −0.960247 | −0.480124 | − | 0.877201i | \(-0.659408\pi\) | ||||
−0.480124 | + | 0.877201i | \(0.659408\pi\) | |||||||
\(458\) | 1.12098e72 | 0.0751275 | ||||||||
\(459\) | −2.11329e72 | −0.133386 | ||||||||
\(460\) | 2.30569e73 | 1.37076 | ||||||||
\(461\) | 3.22702e73 | 1.80728 | 0.903641 | − | 0.428290i | \(-0.140884\pi\) | ||||
0.903641 | + | 0.428290i | \(0.140884\pi\) | |||||||
\(462\) | 4.42710e72 | 0.233596 | ||||||||
\(463\) | −7.30279e72 | −0.363088 | −0.181544 | − | 0.983383i | \(-0.558109\pi\) | ||||
−0.181544 | + | 0.983383i | \(0.558109\pi\) | |||||||
\(464\) | 1.92101e73 | 0.900087 | ||||||||
\(465\) | −9.24248e72 | −0.408162 | ||||||||
\(466\) | −2.87292e72 | −0.119594 | ||||||||
\(467\) | −4.40634e73 | −1.72927 | −0.864636 | − | 0.502398i | \(-0.832451\pi\) | ||||
−0.864636 | + | 0.502398i | \(0.832451\pi\) | |||||||
\(468\) | 1.13774e72 | 0.0421000 | ||||||||
\(469\) | 2.96967e73 | 1.03623 | ||||||||
\(470\) | 6.40644e72 | 0.210827 | ||||||||
\(471\) | −1.59316e73 | −0.494522 | ||||||||
\(472\) | −5.22617e72 | −0.153031 | ||||||||
\(473\) | −1.17048e73 | −0.323357 | ||||||||
\(474\) | 8.09659e72 | 0.211056 | ||||||||
\(475\) | −1.93718e73 | −0.476535 | ||||||||
\(476\) | −8.60231e72 | −0.199721 | ||||||||
\(477\) | 1.53824e72 | 0.0337107 | ||||||||
\(478\) | −1.20464e70 | −0.000249225 0 | ||||||||
\(479\) | −3.18111e73 | −0.621373 | −0.310687 | − | 0.950512i | \(-0.600559\pi\) | ||||
−0.310687 | + | 0.950512i | \(0.600559\pi\) | |||||||
\(480\) | −1.70525e73 | −0.314524 | ||||||||
\(481\) | −2.32879e73 | −0.405640 | ||||||||
\(482\) | −1.56211e73 | −0.256991 | ||||||||
\(483\) | 1.79609e74 | 2.79114 | ||||||||
\(484\) | −2.53911e72 | −0.0372764 | ||||||||
\(485\) | −5.79420e72 | −0.0803703 | ||||||||
\(486\) | 2.75153e72 | 0.0360643 | ||||||||
\(487\) | 6.34796e73 | 0.786299 | 0.393149 | − | 0.919475i | \(-0.371386\pi\) | ||||
0.393149 | + | 0.919475i | \(0.371386\pi\) | |||||||
\(488\) | 2.19960e73 | 0.257512 | ||||||||
\(489\) | 1.00433e73 | 0.111144 | ||||||||
\(490\) | −1.75379e73 | −0.183478 | ||||||||
\(491\) | −6.91619e73 | −0.684110 | −0.342055 | − | 0.939680i | \(-0.611123\pi\) | ||||
−0.342055 | + | 0.939680i | \(0.611123\pi\) | |||||||
\(492\) | −1.08642e74 | −1.01615 | ||||||||
\(493\) | 1.38721e73 | 0.122702 | ||||||||
\(494\) | 7.36514e72 | 0.0616155 | ||||||||
\(495\) | 1.16840e73 | 0.0924590 | ||||||||
\(496\) | 7.12658e73 | 0.533501 | ||||||||
\(497\) | −3.29955e74 | −2.33698 | ||||||||
\(498\) | 1.10958e73 | 0.0743622 | ||||||||
\(499\) | 1.91941e74 | 1.21732 | 0.608659 | − | 0.793432i | \(-0.291708\pi\) | ||||
0.608659 | + | 0.793432i | \(0.291708\pi\) | |||||||
\(500\) | −1.75926e74 | −1.05598 | ||||||||
\(501\) | 1.06976e74 | 0.607782 | ||||||||
\(502\) | −2.20753e73 | −0.118728 | ||||||||
\(503\) | 2.48789e74 | 1.26681 | 0.633406 | − | 0.773820i | \(-0.281656\pi\) | ||||
0.633406 | + | 0.773820i | \(0.281656\pi\) | |||||||
\(504\) | 1.19712e73 | 0.0577164 | ||||||||
\(505\) | −1.89945e74 | −0.867194 | ||||||||
\(506\) | 6.60709e73 | 0.285674 | ||||||||
\(507\) | −1.99332e74 | −0.816314 | ||||||||
\(508\) | 1.88641e74 | 0.731785 | ||||||||
\(509\) | 3.43699e74 | 1.26311 | 0.631553 | − | 0.775333i | \(-0.282418\pi\) | ||||
0.631553 | + | 0.775333i | \(0.282418\pi\) | |||||||
\(510\) | −3.94367e72 | −0.0137316 | ||||||||
\(511\) | 8.18345e73 | 0.269999 | ||||||||
\(512\) | 2.20863e74 | 0.690557 | ||||||||
\(513\) | −3.99108e74 | −1.18267 | ||||||||
\(514\) | −7.56362e73 | −0.212444 | ||||||||
\(515\) | 2.15369e74 | 0.573435 | ||||||||
\(516\) | 1.15257e74 | 0.290937 | ||||||||
\(517\) | −7.78780e74 | −1.86391 | ||||||||
\(518\) | −1.21090e74 | −0.274814 | ||||||||
\(519\) | 3.53716e74 | 0.761294 | ||||||||
\(520\) | 4.02524e73 | 0.0821675 | ||||||||
\(521\) | −3.30970e74 | −0.640842 | −0.320421 | − | 0.947275i | \(-0.603824\pi\) | ||||
−0.320421 | + | 0.947275i | \(0.603824\pi\) | |||||||
\(522\) | −9.53996e72 | −0.0175230 | ||||||||
\(523\) | −5.36017e74 | −0.934076 | −0.467038 | − | 0.884237i | \(-0.654679\pi\) | ||||
−0.467038 | + | 0.884237i | \(0.654679\pi\) | |||||||
\(524\) | 2.01482e74 | 0.333140 | ||||||||
\(525\) | −4.07557e74 | −0.639451 | ||||||||
\(526\) | 8.94808e73 | 0.133236 | ||||||||
\(527\) | 5.14629e73 | 0.0727281 | ||||||||
\(528\) | 6.63875e74 | 0.890540 | ||||||||
\(529\) | 1.89523e75 | 2.41340 | ||||||||
\(530\) | 2.68939e73 | 0.0325138 | ||||||||
\(531\) | −5.30963e73 | −0.0609487 | ||||||||
\(532\) | −1.62460e75 | −1.77083 | ||||||||
\(533\) | 3.86169e74 | 0.399741 | ||||||||
\(534\) | 1.74897e74 | 0.171948 | ||||||||
\(535\) | 3.67825e74 | 0.343489 | ||||||||
\(536\) | −2.17677e74 | −0.193099 | ||||||||
\(537\) | −5.07076e74 | −0.427346 | ||||||||
\(538\) | −7.05383e73 | −0.0564823 | ||||||||
\(539\) | 2.13194e75 | 1.62212 | ||||||||
\(540\) | −1.07791e75 | −0.779389 | ||||||||
\(541\) | −9.01034e74 | −0.619179 | −0.309590 | − | 0.950870i | \(-0.600192\pi\) | ||||
−0.309590 | + | 0.950870i | \(0.600192\pi\) | |||||||
\(542\) | 1.32217e74 | 0.0863591 | ||||||||
\(543\) | −1.35710e75 | −0.842592 | ||||||||
\(544\) | 9.49497e73 | 0.0560433 | ||||||||
\(545\) | −6.79775e74 | −0.381471 | ||||||||
\(546\) | 1.54953e74 | 0.0826804 | ||||||||
\(547\) | −3.28535e75 | −1.66698 | −0.833491 | − | 0.552534i | \(-0.813661\pi\) | ||||
−0.833491 | + | 0.552534i | \(0.813661\pi\) | |||||||
\(548\) | 1.07319e75 | 0.517859 | ||||||||
\(549\) | 2.23472e74 | 0.102561 | ||||||||
\(550\) | −1.49924e74 | −0.0654481 | ||||||||
\(551\) | 2.61983e75 | 1.08794 | ||||||||
\(552\) | −1.31653e75 | −0.520124 | ||||||||
\(553\) | 6.34814e75 | 2.38619 | ||||||||
\(554\) | −1.08720e74 | −0.0388859 | ||||||||
\(555\) | 2.35495e75 | 0.801540 | ||||||||
\(556\) | 1.89652e75 | 0.614327 | ||||||||
\(557\) | −5.67764e75 | −1.75045 | −0.875226 | − | 0.483715i | \(-0.839287\pi\) | ||||
−0.875226 | + | 0.483715i | \(0.839287\pi\) | |||||||
\(558\) | −3.53915e73 | −0.0103862 | ||||||||
\(559\) | −4.09680e74 | −0.114451 | ||||||||
\(560\) | −4.28185e75 | −1.13884 | ||||||||
\(561\) | 4.79401e74 | 0.121400 | ||||||||
\(562\) | 5.80636e74 | 0.140009 | ||||||||
\(563\) | 1.20573e74 | 0.0276866 | 0.0138433 | − | 0.999904i | \(-0.495593\pi\) | ||||
0.0138433 | + | 0.999904i | \(0.495593\pi\) | |||||||
\(564\) | 7.66863e75 | 1.67704 | ||||||||
\(565\) | −3.10001e75 | −0.645700 | ||||||||
\(566\) | −4.52679e74 | −0.0898129 | ||||||||
\(567\) | −7.37885e75 | −1.39462 | ||||||||
\(568\) | 2.41857e75 | 0.435492 | ||||||||
\(569\) | −3.59495e75 | −0.616745 | −0.308372 | − | 0.951266i | \(-0.599784\pi\) | ||||
−0.308372 | + | 0.951266i | \(0.599784\pi\) | |||||||
\(570\) | −7.44788e74 | −0.121751 | ||||||||
\(571\) | −5.41913e75 | −0.844183 | −0.422092 | − | 0.906553i | \(-0.638704\pi\) | ||||
−0.422092 | + | 0.906553i | \(0.638704\pi\) | |||||||
\(572\) | −2.41809e75 | −0.358989 | ||||||||
\(573\) | 1.21782e76 | 1.72319 | ||||||||
\(574\) | 2.00795e75 | 0.270817 | ||||||||
\(575\) | −6.08246e75 | −0.782012 | ||||||||
\(576\) | 8.42744e74 | 0.103295 | ||||||||
\(577\) | 4.19846e75 | 0.490631 | 0.245316 | − | 0.969443i | \(-0.421108\pi\) | ||||
0.245316 | + | 0.969443i | \(0.421108\pi\) | |||||||
\(578\) | −1.33999e75 | −0.149309 | ||||||||
\(579\) | 4.44800e75 | 0.472611 | ||||||||
\(580\) | 7.07564e75 | 0.716961 | ||||||||
\(581\) | 8.69968e75 | 0.840736 | ||||||||
\(582\) | 1.63495e74 | 0.0150704 | ||||||||
\(583\) | −3.26928e75 | −0.287453 | ||||||||
\(584\) | −5.99847e74 | −0.0503138 | ||||||||
\(585\) | 4.08953e74 | 0.0327255 | ||||||||
\(586\) | −1.53642e75 | −0.117307 | ||||||||
\(587\) | −4.18417e75 | −0.304833 | −0.152417 | − | 0.988316i | \(-0.548706\pi\) | ||||
−0.152417 | + | 0.988316i | \(0.548706\pi\) | |||||||
\(588\) | −2.09932e76 | −1.45949 | ||||||||
\(589\) | 9.71910e75 | 0.644845 | ||||||||
\(590\) | −9.28312e74 | −0.0587846 | ||||||||
\(591\) | −1.40023e75 | −0.0846337 | ||||||||
\(592\) | −1.81583e76 | −1.04768 | ||||||||
\(593\) | 4.80739e75 | 0.264792 | 0.132396 | − | 0.991197i | \(-0.457733\pi\) | ||||
0.132396 | + | 0.991197i | \(0.457733\pi\) | |||||||
\(594\) | −3.08881e75 | −0.162429 | ||||||||
\(595\) | −3.09204e75 | −0.155249 | ||||||||
\(596\) | 9.69785e75 | 0.464947 | ||||||||
\(597\) | −7.94772e75 | −0.363872 | ||||||||
\(598\) | 2.31255e75 | 0.101113 | ||||||||
\(599\) | 3.85877e75 | 0.161143 | 0.0805714 | − | 0.996749i | \(-0.474325\pi\) | ||||
0.0805714 | + | 0.996749i | \(0.474325\pi\) | |||||||
\(600\) | 2.98739e75 | 0.119161 | ||||||||
\(601\) | 2.69061e76 | 1.02519 | 0.512593 | − | 0.858632i | \(-0.328685\pi\) | ||||
0.512593 | + | 0.858632i | \(0.328685\pi\) | |||||||
\(602\) | −2.13020e75 | −0.0775386 | ||||||||
\(603\) | −2.21153e75 | −0.0769072 | ||||||||
\(604\) | 1.38992e76 | 0.461823 | ||||||||
\(605\) | −9.12663e74 | −0.0289760 | ||||||||
\(606\) | 5.35971e75 | 0.162609 | ||||||||
\(607\) | −2.83247e76 | −0.821252 | −0.410626 | − | 0.911804i | \(-0.634690\pi\) | ||||
−0.410626 | + | 0.911804i | \(0.634690\pi\) | |||||||
\(608\) | 1.79319e76 | 0.496909 | ||||||||
\(609\) | 5.51179e76 | 1.45988 | ||||||||
\(610\) | 3.90709e75 | 0.0989198 | ||||||||
\(611\) | −2.72581e76 | −0.659724 | ||||||||
\(612\) | 6.40619e74 | 0.0148230 | ||||||||
\(613\) | −5.22770e76 | −1.15651 | −0.578253 | − | 0.815858i | \(-0.696265\pi\) | ||||
−0.578253 | + | 0.815858i | \(0.696265\pi\) | |||||||
\(614\) | −8.08026e74 | −0.0170921 | ||||||||
\(615\) | −3.90507e76 | −0.789883 | ||||||||
\(616\) | −2.54429e76 | −0.492150 | ||||||||
\(617\) | 3.43035e76 | 0.634595 | 0.317297 | − | 0.948326i | \(-0.397225\pi\) | ||||
0.317297 | + | 0.948326i | \(0.397225\pi\) | |||||||
\(618\) | −6.07708e75 | −0.107526 | ||||||||
\(619\) | −1.83217e76 | −0.310080 | −0.155040 | − | 0.987908i | \(-0.549551\pi\) | ||||
−0.155040 | + | 0.987908i | \(0.549551\pi\) | |||||||
\(620\) | 2.62493e76 | 0.424959 | ||||||||
\(621\) | −1.25314e77 | −1.94080 | ||||||||
\(622\) | −2.13716e75 | −0.0316667 | ||||||||
\(623\) | 1.37128e77 | 1.94404 | ||||||||
\(624\) | 2.32363e76 | 0.315203 | ||||||||
\(625\) | −3.06276e76 | −0.397568 | ||||||||
\(626\) | 1.32458e76 | 0.164545 | ||||||||
\(627\) | 9.05380e76 | 1.07640 | ||||||||
\(628\) | 4.52470e76 | 0.514872 | ||||||||
\(629\) | −1.31126e76 | −0.142822 | ||||||||
\(630\) | 2.12642e75 | 0.0221710 | ||||||||
\(631\) | 3.00198e76 | 0.299640 | 0.149820 | − | 0.988713i | \(-0.452131\pi\) | ||||
0.149820 | + | 0.988713i | \(0.452131\pi\) | |||||||
\(632\) | −4.65319e76 | −0.444663 | ||||||||
\(633\) | −1.55071e77 | −1.41883 | ||||||||
\(634\) | −1.14491e75 | −0.0100304 | ||||||||
\(635\) | 6.78055e76 | 0.568836 | ||||||||
\(636\) | 3.21925e76 | 0.258633 | ||||||||
\(637\) | 7.46201e76 | 0.574145 | ||||||||
\(638\) | 2.02757e76 | 0.149419 | ||||||||
\(639\) | 2.45720e76 | 0.173447 | ||||||||
\(640\) | 6.43062e76 | 0.434814 | ||||||||
\(641\) | −7.84590e76 | −0.508214 | −0.254107 | − | 0.967176i | \(-0.581782\pi\) | ||||
−0.254107 | + | 0.967176i | \(0.581782\pi\) | |||||||
\(642\) | −1.03789e76 | −0.0644080 | ||||||||
\(643\) | −1.61526e77 | −0.960374 | −0.480187 | − | 0.877166i | \(-0.659431\pi\) | ||||
−0.480187 | + | 0.877166i | \(0.659431\pi\) | |||||||
\(644\) | −5.10102e77 | −2.90600 | ||||||||
\(645\) | 4.14282e76 | 0.226154 | ||||||||
\(646\) | 4.14704e75 | 0.0216942 | ||||||||
\(647\) | 1.73743e77 | 0.871044 | 0.435522 | − | 0.900178i | \(-0.356564\pi\) | ||||
0.435522 | + | 0.900178i | \(0.356564\pi\) | |||||||
\(648\) | 5.40870e76 | 0.259884 | ||||||||
\(649\) | 1.12848e77 | 0.519713 | ||||||||
\(650\) | −5.24749e75 | −0.0231651 | ||||||||
\(651\) | 2.04477e77 | 0.865302 | ||||||||
\(652\) | −2.85238e76 | −0.115717 | ||||||||
\(653\) | 1.79111e77 | 0.696641 | 0.348320 | − | 0.937376i | \(-0.386752\pi\) | ||||
0.348320 | + | 0.937376i | \(0.386752\pi\) | |||||||
\(654\) | 1.91813e76 | 0.0715301 | ||||||||
\(655\) | 7.24213e76 | 0.258959 | ||||||||
\(656\) | 3.01107e77 | 1.03244 | ||||||||
\(657\) | −6.09427e75 | −0.0200389 | ||||||||
\(658\) | −1.41734e77 | −0.446952 | ||||||||
\(659\) | −5.64076e77 | −1.70604 | −0.853018 | − | 0.521881i | \(-0.825231\pi\) | ||||
−0.853018 | + | 0.521881i | \(0.825231\pi\) | |||||||
\(660\) | 2.44525e77 | 0.709357 | ||||||||
\(661\) | 5.54552e76 | 0.154313 | 0.0771565 | − | 0.997019i | \(-0.475416\pi\) | ||||
0.0771565 | + | 0.997019i | \(0.475416\pi\) | |||||||
\(662\) | 8.10563e76 | 0.216368 | ||||||||
\(663\) | 1.67795e76 | 0.0429693 | ||||||||
\(664\) | −6.37687e76 | −0.156670 | ||||||||
\(665\) | −5.83951e77 | −1.37652 | ||||||||
\(666\) | 9.01763e75 | 0.0203963 | ||||||||
\(667\) | 8.22590e77 | 1.78535 | ||||||||
\(668\) | −3.03819e77 | −0.632793 | ||||||||
\(669\) | −4.72037e77 | −0.943535 | ||||||||
\(670\) | −3.86654e76 | −0.0741764 | ||||||||
\(671\) | −4.74955e77 | −0.874546 | ||||||||
\(672\) | 3.77263e77 | 0.666791 | ||||||||
\(673\) | −7.57599e77 | −1.28536 | −0.642680 | − | 0.766135i | \(-0.722178\pi\) | ||||
−0.642680 | + | 0.766135i | \(0.722178\pi\) | |||||||
\(674\) | −1.01792e77 | −0.165793 | ||||||||
\(675\) | 2.84355e77 | 0.444639 | ||||||||
\(676\) | 5.66116e77 | 0.849907 | ||||||||
\(677\) | 9.51246e77 | 1.37121 | 0.685606 | − | 0.727973i | \(-0.259537\pi\) | ||||
0.685606 | + | 0.727973i | \(0.259537\pi\) | |||||||
\(678\) | 8.74732e76 | 0.121076 | ||||||||
\(679\) | 1.28189e77 | 0.170385 | ||||||||
\(680\) | 2.26646e76 | 0.0289304 | ||||||||
\(681\) | −9.96638e77 | −1.22178 | ||||||||
\(682\) | 7.52190e76 | 0.0885640 | ||||||||
\(683\) | 9.13435e77 | 1.03302 | 0.516510 | − | 0.856281i | \(-0.327231\pi\) | ||||
0.516510 | + | 0.856281i | \(0.327231\pi\) | |||||||
\(684\) | 1.20985e77 | 0.131428 | ||||||||
\(685\) | 3.85751e77 | 0.402546 | ||||||||
\(686\) | 1.44287e77 | 0.144649 | ||||||||
\(687\) | 4.82314e77 | 0.464537 | ||||||||
\(688\) | −3.19439e77 | −0.295601 | ||||||||
\(689\) | −1.14428e77 | −0.101743 | ||||||||
\(690\) | −2.33853e77 | −0.199799 | ||||||||
\(691\) | −1.64704e78 | −1.35225 | −0.676127 | − | 0.736785i | \(-0.736343\pi\) | ||||
−0.676127 | + | 0.736785i | \(0.736343\pi\) | |||||||
\(692\) | −1.00458e78 | −0.792623 | ||||||||
\(693\) | −2.58493e77 | −0.196013 | ||||||||
\(694\) | 2.25034e77 | 0.164007 | ||||||||
\(695\) | 6.81689e77 | 0.477534 | ||||||||
\(696\) | −4.04014e77 | −0.272046 | ||||||||
\(697\) | 2.17437e77 | 0.140745 | ||||||||
\(698\) | −4.22694e77 | −0.263028 | ||||||||
\(699\) | −1.23610e78 | −0.739489 | ||||||||
\(700\) | 1.15749e78 | 0.665766 | ||||||||
\(701\) | 2.19900e78 | 1.21613 | 0.608066 | − | 0.793886i | \(-0.291946\pi\) | ||||
0.608066 | + | 0.793886i | \(0.291946\pi\) | |||||||
\(702\) | −1.08112e77 | −0.0574913 | ||||||||
\(703\) | −2.47639e78 | −1.26633 | ||||||||
\(704\) | −1.79112e78 | −0.880798 | ||||||||
\(705\) | 2.75643e78 | 1.30361 | ||||||||
\(706\) | 1.07573e77 | 0.0489299 | ||||||||
\(707\) | 4.20228e78 | 1.83845 | ||||||||
\(708\) | −1.11121e78 | −0.467607 | ||||||||
\(709\) | −5.02468e77 | −0.203393 | −0.101697 | − | 0.994815i | \(-0.532427\pi\) | ||||
−0.101697 | + | 0.994815i | \(0.532427\pi\) | |||||||
\(710\) | 4.29605e77 | 0.167288 | ||||||||
\(711\) | −4.72750e77 | −0.177099 | ||||||||
\(712\) | −1.00515e78 | −0.362268 | ||||||||
\(713\) | 3.05166e78 | 1.05821 | ||||||||
\(714\) | 8.72482e76 | 0.0291109 | ||||||||
\(715\) | −8.69163e77 | −0.279052 | ||||||||
\(716\) | 1.44013e78 | 0.444933 | ||||||||
\(717\) | −5.18310e75 | −0.00154104 | ||||||||
\(718\) | 8.55974e77 | 0.244928 | ||||||||
\(719\) | −5.31416e78 | −1.46349 | −0.731745 | − | 0.681578i | \(-0.761294\pi\) | ||||
−0.731745 | + | 0.681578i | \(0.761294\pi\) | |||||||
\(720\) | 3.18872e77 | 0.0845227 | ||||||||
\(721\) | −4.76474e78 | −1.21568 | ||||||||
\(722\) | 1.65293e77 | 0.0405959 | ||||||||
\(723\) | −6.72113e78 | −1.58905 | ||||||||
\(724\) | 3.85427e78 | 0.877267 | ||||||||
\(725\) | −1.86657e78 | −0.409024 | ||||||||
\(726\) | 2.57527e76 | 0.00543332 | ||||||||
\(727\) | 3.83847e78 | 0.779761 | 0.389880 | − | 0.920865i | \(-0.372516\pi\) | ||||
0.389880 | + | 0.920865i | \(0.372516\pi\) | |||||||
\(728\) | −8.90530e77 | −0.174195 | ||||||||
\(729\) | 5.78264e78 | 1.08923 | ||||||||
\(730\) | −1.06550e77 | −0.0193274 | ||||||||
\(731\) | −2.30675e77 | −0.0402970 | ||||||||
\(732\) | 4.67686e78 | 0.786865 | ||||||||
\(733\) | 4.93828e78 | 0.800233 | 0.400116 | − | 0.916464i | \(-0.368970\pi\) | ||||
0.400116 | + | 0.916464i | \(0.368970\pi\) | |||||||
\(734\) | −1.46387e78 | −0.228487 | ||||||||
\(735\) | −7.54584e78 | −1.13450 | ||||||||
\(736\) | 5.63035e78 | 0.815447 | ||||||||
\(737\) | 4.70026e78 | 0.655791 | ||||||||
\(738\) | −1.49534e77 | −0.0200997 | ||||||||
\(739\) | −7.07383e78 | −0.916078 | −0.458039 | − | 0.888932i | \(-0.651448\pi\) | ||||
−0.458039 | + | 0.888932i | \(0.651448\pi\) | |||||||
\(740\) | −6.68824e78 | −0.834525 | ||||||||
\(741\) | 3.16892e78 | 0.380988 | ||||||||
\(742\) | −5.94990e77 | −0.0689291 | ||||||||
\(743\) | 9.59859e78 | 1.07156 | 0.535778 | − | 0.844359i | \(-0.320018\pi\) | ||||
0.535778 | + | 0.844359i | \(0.320018\pi\) | |||||||
\(744\) | −1.49882e78 | −0.161248 | ||||||||
\(745\) | 3.48582e78 | 0.361416 | ||||||||
\(746\) | −2.52268e78 | −0.252083 | ||||||||
\(747\) | −6.47870e77 | −0.0623981 | ||||||||
\(748\) | −1.36153e78 | −0.126396 | ||||||||
\(749\) | −8.13762e78 | −0.728195 | ||||||||
\(750\) | 1.78431e78 | 0.153917 | ||||||||
\(751\) | −6.76425e78 | −0.562499 | −0.281249 | − | 0.959635i | \(-0.590749\pi\) | ||||
−0.281249 | + | 0.959635i | \(0.590749\pi\) | |||||||
\(752\) | −2.12540e79 | −1.70392 | ||||||||
\(753\) | −9.49811e78 | −0.734134 | ||||||||
\(754\) | 7.09669e77 | 0.0528864 | ||||||||
\(755\) | 4.99598e78 | 0.358988 | ||||||||
\(756\) | 2.38473e79 | 1.65230 | ||||||||
\(757\) | −6.22716e78 | −0.416057 | −0.208029 | − | 0.978123i | \(-0.566705\pi\) | ||||
−0.208029 | + | 0.978123i | \(0.566705\pi\) | |||||||
\(758\) | 3.63589e78 | 0.234265 | ||||||||
\(759\) | 2.84276e79 | 1.76641 | ||||||||
\(760\) | 4.28036e78 | 0.256512 | ||||||||
\(761\) | −6.20793e77 | −0.0358814 | −0.0179407 | − | 0.999839i | \(-0.505711\pi\) | ||||
−0.0179407 | + | 0.999839i | \(0.505711\pi\) | |||||||
\(762\) | −1.91327e78 | −0.106663 | ||||||||
\(763\) | 1.50391e79 | 0.808717 | ||||||||
\(764\) | −3.45871e79 | −1.79410 | ||||||||
\(765\) | 2.30266e77 | 0.0115223 | ||||||||
\(766\) | −1.52215e77 | −0.00734797 | ||||||||
\(767\) | 3.94978e78 | 0.183950 | ||||||||
\(768\) | 1.62383e79 | 0.729638 | ||||||||
\(769\) | 2.93043e79 | 1.27045 | 0.635224 | − | 0.772328i | \(-0.280908\pi\) | ||||
0.635224 | + | 0.772328i | \(0.280908\pi\) | |||||||
\(770\) | −4.51937e78 | −0.189053 | ||||||||
\(771\) | −3.25432e79 | −1.31361 | ||||||||
\(772\) | −1.26326e79 | −0.492060 | ||||||||
\(773\) | 9.72409e78 | 0.365521 | 0.182761 | − | 0.983157i | \(-0.441497\pi\) | ||||
0.182761 | + | 0.983157i | \(0.441497\pi\) | |||||||
\(774\) | 1.58638e77 | 0.00575479 | ||||||||
\(775\) | −6.92463e78 | −0.242437 | ||||||||
\(776\) | −9.39623e77 | −0.0317509 | ||||||||
\(777\) | −5.21001e79 | −1.69926 | ||||||||
\(778\) | 8.61777e77 | 0.0271304 | ||||||||
\(779\) | 4.10644e79 | 1.24792 | ||||||||
\(780\) | 8.55863e78 | 0.251074 | ||||||||
\(781\) | −5.22238e79 | −1.47899 | ||||||||
\(782\) | 1.30211e78 | 0.0356010 | ||||||||
\(783\) | −3.84561e79 | −1.01512 | ||||||||
\(784\) | 5.81835e79 | 1.48289 | ||||||||
\(785\) | 1.62637e79 | 0.400224 | ||||||||
\(786\) | −2.04352e78 | −0.0485577 | ||||||||
\(787\) | −1.67187e79 | −0.383617 | −0.191808 | − | 0.981432i | \(-0.561435\pi\) | ||||
−0.191808 | + | 0.981432i | \(0.561435\pi\) | |||||||
\(788\) | 3.97675e78 | 0.0881165 | ||||||||
\(789\) | 3.85000e79 | 0.823840 | ||||||||
\(790\) | −8.26535e78 | −0.170811 | ||||||||
\(791\) | 6.85834e79 | 1.36888 | ||||||||
\(792\) | 1.89475e78 | 0.0365266 | ||||||||
\(793\) | −1.66239e79 | −0.309543 | ||||||||
\(794\) | 1.35055e79 | 0.242911 | ||||||||
\(795\) | 1.15714e79 | 0.201043 | ||||||||
\(796\) | 2.25721e79 | 0.378846 | ||||||||
\(797\) | −4.63054e79 | −0.750806 | −0.375403 | − | 0.926862i | \(-0.622496\pi\) | ||||
−0.375403 | + | 0.926862i | \(0.622496\pi\) | |||||||
\(798\) | 1.64774e79 | 0.258112 | ||||||||
\(799\) | −1.53480e79 | −0.232282 | ||||||||
\(800\) | −1.27760e79 | −0.186819 | ||||||||
\(801\) | −1.02120e79 | −0.144283 | ||||||||
\(802\) | 3.31513e77 | 0.00452591 | ||||||||
\(803\) | 1.29524e79 | 0.170873 | ||||||||
\(804\) | −4.62833e79 | −0.590042 | ||||||||
\(805\) | −1.83352e80 | −2.25891 | ||||||||
\(806\) | 2.63274e78 | 0.0313469 | ||||||||
\(807\) | −3.03498e79 | −0.349248 | ||||||||
\(808\) | −3.08027e79 | −0.342592 | ||||||||
\(809\) | 1.81292e80 | 1.94892 | 0.974459 | − | 0.224565i | \(-0.0720962\pi\) | ||||
0.974459 | + | 0.224565i | \(0.0720962\pi\) | |||||||
\(810\) | 9.60735e78 | 0.0998310 | ||||||||
\(811\) | 1.57811e80 | 1.58512 | 0.792562 | − | 0.609791i | \(-0.208747\pi\) | ||||
0.792562 | + | 0.609791i | \(0.208747\pi\) | |||||||
\(812\) | −1.56539e80 | −1.51996 | ||||||||
\(813\) | 5.68878e79 | 0.533985 | ||||||||
\(814\) | −1.91655e79 | −0.173920 | ||||||||
\(815\) | −1.02527e79 | −0.0899504 | ||||||||
\(816\) | 1.30835e79 | 0.110980 | ||||||||
\(817\) | −4.35645e79 | −0.357295 | ||||||||
\(818\) | −1.72748e79 | −0.136993 | ||||||||
\(819\) | −9.04751e78 | −0.0693780 | ||||||||
\(820\) | 1.10907e80 | 0.822388 | ||||||||
\(821\) | 5.17464e79 | 0.371059 | 0.185530 | − | 0.982639i | \(-0.440600\pi\) | ||||
0.185530 | + | 0.982639i | \(0.440600\pi\) | |||||||
\(822\) | −1.08848e79 | −0.0754820 | ||||||||
\(823\) | 1.22160e80 | 0.819279 | 0.409640 | − | 0.912247i | \(-0.365654\pi\) | ||||
0.409640 | + | 0.912247i | \(0.365654\pi\) | |||||||
\(824\) | 3.49255e79 | 0.226540 | ||||||||
\(825\) | −6.45062e79 | −0.404686 | ||||||||
\(826\) | 2.05376e79 | 0.124623 | ||||||||
\(827\) | 5.64616e79 | 0.331400 | 0.165700 | − | 0.986176i | \(-0.447012\pi\) | ||||
0.165700 | + | 0.986176i | \(0.447012\pi\) | |||||||
\(828\) | 3.79876e79 | 0.215679 | ||||||||
\(829\) | −1.62760e80 | −0.893921 | −0.446961 | − | 0.894554i | \(-0.647494\pi\) | ||||
−0.446961 | + | 0.894554i | \(0.647494\pi\) | |||||||
\(830\) | −1.13271e79 | −0.0601826 | ||||||||
\(831\) | −4.67780e79 | −0.240444 | ||||||||
\(832\) | −6.26910e79 | −0.311755 | ||||||||
\(833\) | 4.20158e79 | 0.202151 | ||||||||
\(834\) | −1.92353e79 | −0.0895430 | ||||||||
\(835\) | −1.09205e80 | −0.491888 | ||||||||
\(836\) | −2.57134e80 | −1.12070 | ||||||||
\(837\) | −1.42665e80 | −0.601682 | ||||||||
\(838\) | −1.86665e79 | −0.0761821 | ||||||||
\(839\) | −7.61754e79 | −0.300858 | −0.150429 | − | 0.988621i | \(-0.548065\pi\) | ||||
−0.150429 | + | 0.988621i | \(0.548065\pi\) | |||||||
\(840\) | 9.00533e79 | 0.344207 | ||||||||
\(841\) | −1.78931e79 | −0.0661906 | ||||||||
\(842\) | 5.75923e79 | 0.206197 | ||||||||
\(843\) | 2.49824e80 | 0.865717 | ||||||||
\(844\) | 4.40414e80 | 1.47722 | ||||||||
\(845\) | 2.03486e80 | 0.660656 | ||||||||
\(846\) | 1.05550e79 | 0.0331721 | ||||||||
\(847\) | 2.01914e79 | 0.0614289 | ||||||||
\(848\) | −8.92230e79 | −0.262779 | ||||||||
\(849\) | −1.94770e80 | −0.555341 | ||||||||
\(850\) | −2.95467e78 | −0.00815620 | ||||||||
\(851\) | −7.77552e80 | −2.07810 | ||||||||
\(852\) | 5.14246e80 | 1.33071 | ||||||||
\(853\) | 6.55715e80 | 1.64292 | 0.821461 | − | 0.570265i | \(-0.193160\pi\) | ||||
0.821461 | + | 0.570265i | \(0.193160\pi\) | |||||||
\(854\) | −8.64390e79 | −0.209710 | ||||||||
\(855\) | 4.34872e79 | 0.102163 | ||||||||
\(856\) | 5.96488e79 | 0.135698 | ||||||||
\(857\) | −2.43562e80 | −0.536584 | −0.268292 | − | 0.963338i | \(-0.586459\pi\) | ||||
−0.268292 | + | 0.963338i | \(0.586459\pi\) | |||||||
\(858\) | 2.45252e79 | 0.0523254 | ||||||||
\(859\) | −2.70552e80 | −0.559035 | −0.279517 | − | 0.960141i | \(-0.590174\pi\) | ||||
−0.279517 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(860\) | −1.17659e80 | −0.235460 | ||||||||
\(861\) | 8.63942e80 | 1.67455 | ||||||||
\(862\) | −9.34051e79 | −0.175356 | ||||||||
\(863\) | −9.09815e80 | −1.65446 | −0.827230 | − | 0.561863i | \(-0.810085\pi\) | ||||
−0.827230 | + | 0.561863i | \(0.810085\pi\) | |||||||
\(864\) | −2.63219e80 | −0.463649 | ||||||||
\(865\) | −3.61089e80 | −0.616128 | ||||||||
\(866\) | 4.56914e79 | 0.0755252 | ||||||||
\(867\) | −5.76545e80 | −0.923226 | ||||||||
\(868\) | −5.80730e80 | −0.900911 | ||||||||
\(869\) | 1.00475e81 | 1.51013 | ||||||||
\(870\) | −7.17641e79 | −0.104503 | ||||||||
\(871\) | 1.64514e80 | 0.232115 | ||||||||
\(872\) | −1.10236e80 | −0.150703 | ||||||||
\(873\) | −9.54629e78 | −0.0126457 | ||||||||
\(874\) | 2.45912e80 | 0.315657 | ||||||||
\(875\) | 1.39899e81 | 1.74018 | ||||||||
\(876\) | −1.27542e80 | −0.153741 | ||||||||
\(877\) | 1.05076e81 | 1.22749 | 0.613743 | − | 0.789506i | \(-0.289663\pi\) | ||||
0.613743 | + | 0.789506i | \(0.289663\pi\) | |||||||
\(878\) | 4.31228e79 | 0.0488211 | ||||||||
\(879\) | −6.61059e80 | −0.725348 | ||||||||
\(880\) | −6.77712e80 | −0.720729 | ||||||||
\(881\) | 6.98981e80 | 0.720490 | 0.360245 | − | 0.932858i | \(-0.382693\pi\) | ||||
0.360245 | + | 0.932858i | \(0.382693\pi\) | |||||||
\(882\) | −2.88947e79 | −0.0288690 | ||||||||
\(883\) | −7.95621e80 | −0.770525 | −0.385263 | − | 0.922807i | \(-0.625889\pi\) | ||||
−0.385263 | + | 0.922807i | \(0.625889\pi\) | |||||||
\(884\) | −4.76551e79 | −0.0447375 | ||||||||
\(885\) | −3.99415e80 | −0.363484 | ||||||||
\(886\) | 9.81055e79 | 0.0865498 | ||||||||
\(887\) | 2.23142e81 | 1.90846 | 0.954228 | − | 0.299079i | \(-0.0966794\pi\) | ||||
0.954228 | + | 0.299079i | \(0.0966794\pi\) | |||||||
\(888\) | 3.81894e80 | 0.316655 | ||||||||
\(889\) | −1.50010e81 | −1.20593 | ||||||||
\(890\) | −1.78542e80 | −0.139160 | ||||||||
\(891\) | −1.16789e81 | −0.882603 | ||||||||
\(892\) | 1.34062e81 | 0.982364 | ||||||||
\(893\) | −2.89857e81 | −2.05954 | ||||||||
\(894\) | −9.83596e79 | −0.0677696 | ||||||||
\(895\) | 5.17645e80 | 0.345858 | ||||||||
\(896\) | −1.42269e81 | −0.921804 | ||||||||
\(897\) | 9.94997e80 | 0.625215 | ||||||||
\(898\) | 2.36333e80 | 0.144021 | ||||||||
\(899\) | 9.36484e80 | 0.553489 | ||||||||
\(900\) | −8.61991e79 | −0.0494121 | ||||||||
\(901\) | −6.44302e79 | −0.0358227 | ||||||||
\(902\) | 3.17810e80 | 0.171391 | ||||||||
\(903\) | −9.16541e80 | −0.479445 | ||||||||
\(904\) | −5.02716e80 | −0.255089 | ||||||||
\(905\) | 1.38539e81 | 0.681924 | ||||||||
\(906\) | −1.40972e80 | −0.0673143 | ||||||||
\(907\) | −1.64651e81 | −0.762716 | −0.381358 | − | 0.924427i | \(-0.624543\pi\) | ||||
−0.381358 | + | 0.924427i | \(0.624543\pi\) | |||||||
\(908\) | 2.83053e81 | 1.27206 | ||||||||
\(909\) | −3.12946e80 | −0.136447 | ||||||||
\(910\) | −1.58183e80 | −0.0669146 | ||||||||
\(911\) | 1.86319e81 | 0.764718 | 0.382359 | − | 0.924014i | \(-0.375112\pi\) | ||||
0.382359 | + | 0.924014i | \(0.375112\pi\) | |||||||
\(912\) | 2.47090e81 | 0.984006 | ||||||||
\(913\) | 1.37694e81 | 0.532072 | ||||||||
\(914\) | −3.88642e80 | −0.145723 | ||||||||
\(915\) | 1.68106e81 | 0.611652 | ||||||||
\(916\) | −1.36981e81 | −0.483653 | ||||||||
\(917\) | −1.60222e81 | −0.548992 | ||||||||
\(918\) | −6.08737e79 | −0.0202421 | ||||||||
\(919\) | −5.59344e81 | −1.80510 | −0.902552 | − | 0.430580i | \(-0.858309\pi\) | ||||
−0.902552 | + | 0.430580i | \(0.858309\pi\) | |||||||
\(920\) | 1.34397e81 | 0.420945 | ||||||||
\(921\) | −3.47661e80 | −0.105686 | ||||||||
\(922\) | 9.29550e80 | 0.274266 | ||||||||
\(923\) | −1.82789e81 | −0.523483 | ||||||||
\(924\) | −5.40978e81 | −1.50383 | ||||||||
\(925\) | 1.76437e81 | 0.476094 | ||||||||
\(926\) | −2.10358e80 | −0.0551008 | ||||||||
\(927\) | 3.54833e80 | 0.0902258 | ||||||||
\(928\) | 1.72783e81 | 0.426512 | ||||||||
\(929\) | −5.85958e81 | −1.40422 | −0.702109 | − | 0.712070i | \(-0.747758\pi\) | ||||
−0.702109 | + | 0.712070i | \(0.747758\pi\) | |||||||
\(930\) | −2.66232e80 | −0.0619410 | ||||||||
\(931\) | 7.93496e81 | 1.79237 | ||||||||
\(932\) | 3.51062e81 | 0.769921 | ||||||||
\(933\) | −9.19536e80 | −0.195805 | ||||||||
\(934\) | −1.26925e81 | −0.262428 | ||||||||
\(935\) | −4.89393e80 | −0.0982514 | ||||||||
\(936\) | 6.63183e79 | 0.0129285 | ||||||||
\(937\) | 2.38829e81 | 0.452115 | 0.226057 | − | 0.974114i | \(-0.427416\pi\) | ||||
0.226057 | + | 0.974114i | \(0.427416\pi\) | |||||||
\(938\) | 8.55419e80 | 0.157254 | ||||||||
\(939\) | 5.69913e81 | 1.01743 | ||||||||
\(940\) | −7.82846e81 | −1.35725 | ||||||||
\(941\) | −8.27740e81 | −1.39373 | −0.696866 | − | 0.717201i | \(-0.745423\pi\) | ||||
−0.696866 | + | 0.717201i | \(0.745423\pi\) | |||||||
\(942\) | −4.58914e80 | −0.0750467 | ||||||||
\(943\) | 1.28936e82 | 2.04788 | ||||||||
\(944\) | 3.07976e81 | 0.475103 | ||||||||
\(945\) | 8.57172e81 | 1.28438 | ||||||||
\(946\) | −3.37159e80 | −0.0490714 | ||||||||
\(947\) | 6.70100e80 | 0.0947360 | 0.0473680 | − | 0.998878i | \(-0.484917\pi\) | ||||
0.0473680 | + | 0.998878i | \(0.484917\pi\) | |||||||
\(948\) | −9.89378e81 | −1.35873 | ||||||||
\(949\) | 4.53347e80 | 0.0604797 | ||||||||
\(950\) | −5.58008e80 | −0.0723171 | ||||||||
\(951\) | −4.92610e80 | −0.0620210 | ||||||||
\(952\) | −5.01424e80 | −0.0613322 | ||||||||
\(953\) | −1.01290e82 | −1.20368 | −0.601839 | − | 0.798617i | \(-0.705565\pi\) | ||||
−0.601839 | + | 0.798617i | \(0.705565\pi\) | |||||||
\(954\) | 4.43093e79 | 0.00511581 | ||||||||
\(955\) | −1.24321e82 | −1.39460 | ||||||||
\(956\) | 1.47204e79 | 0.00160445 | ||||||||
\(957\) | 8.72380e81 | 0.923905 | ||||||||
\(958\) | −9.16326e80 | −0.0942972 | ||||||||
\(959\) | −8.53420e81 | −0.853397 | ||||||||
\(960\) | 6.33952e81 | 0.616024 | ||||||||
\(961\) | −7.11575e81 | −0.671935 | ||||||||
\(962\) | −6.70813e80 | −0.0615584 | ||||||||
\(963\) | 6.06014e80 | 0.0540455 | ||||||||
\(964\) | 1.90885e82 | 1.65445 | ||||||||
\(965\) | −4.54071e81 | −0.382492 | ||||||||
\(966\) | 5.17367e81 | 0.423572 | ||||||||
\(967\) | 5.45472e81 | 0.434055 | 0.217027 | − | 0.976166i | \(-0.430364\pi\) | ||||
0.217027 | + | 0.976166i | \(0.430364\pi\) | |||||||
\(968\) | −1.48003e80 | −0.0114472 | ||||||||
\(969\) | 1.78430e81 | 0.134142 | ||||||||
\(970\) | −1.66903e80 | −0.0121967 | ||||||||
\(971\) | 1.71965e82 | 1.22155 | 0.610776 | − | 0.791803i | \(-0.290858\pi\) | ||||
0.610776 | + | 0.791803i | \(0.290858\pi\) | |||||||
\(972\) | −3.36229e81 | −0.232173 | ||||||||
\(973\) | −1.50814e82 | −1.01237 | ||||||||
\(974\) | 1.82854e81 | 0.119326 | ||||||||
\(975\) | −2.25778e81 | −0.143237 | ||||||||
\(976\) | −1.29621e82 | −0.799479 | ||||||||
\(977\) | −2.16132e81 | −0.129604 | −0.0648020 | − | 0.997898i | \(-0.520642\pi\) | ||||
−0.0648020 | + | 0.997898i | \(0.520642\pi\) | |||||||
\(978\) | 2.89300e80 | 0.0168667 | ||||||||
\(979\) | 2.17040e82 | 1.23031 | ||||||||
\(980\) | 2.14307e82 | 1.18119 | ||||||||
\(981\) | −1.11997e81 | −0.0600217 | ||||||||
\(982\) | −1.99222e81 | −0.103818 | ||||||||
\(983\) | −3.94403e81 | −0.199856 | −0.0999282 | − | 0.994995i | \(-0.531861\pi\) | ||||
−0.0999282 | + | 0.994995i | \(0.531861\pi\) | |||||||
\(984\) | −6.33269e81 | −0.312049 | ||||||||
\(985\) | 1.42941e81 | 0.0684954 | ||||||||
\(986\) | 3.99588e80 | 0.0186208 | ||||||||
\(987\) | −6.09822e82 | −2.76364 | ||||||||
\(988\) | −8.99997e81 | −0.396666 | ||||||||
\(989\) | −1.36786e82 | −0.586334 | ||||||||
\(990\) | 3.36560e80 | 0.0140312 | ||||||||
\(991\) | 4.34814e81 | 0.176310 | 0.0881551 | − | 0.996107i | \(-0.471903\pi\) | ||||
0.0881551 | + | 0.996107i | \(0.471903\pi\) | |||||||
\(992\) | 6.40992e81 | 0.252803 | ||||||||
\(993\) | 3.48753e82 | 1.33787 | ||||||||
\(994\) | −9.50442e81 | −0.354650 | ||||||||
\(995\) | 8.11337e81 | 0.294487 | ||||||||
\(996\) | −1.35587e82 | −0.478726 | ||||||||
\(997\) | 3.26514e81 | 0.112146 | 0.0560732 | − | 0.998427i | \(-0.482142\pi\) | ||||
0.0560732 | + | 0.998427i | \(0.482142\pi\) | |||||||
\(998\) | 5.52891e81 | 0.184735 | ||||||||
\(999\) | 3.63505e82 | 1.18157 |
(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 | 1.56.a.a.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 9.56.a.a.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.56.a.a.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.56.a.a.1.3 | 4 | 3.2 | odd | 2 |