Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,12,Mod(1,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(17.6718931529\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 16849 x^{9} - 2148 x^{8} + 97176782 x^{7} + 169360278 x^{6} - 226650696110 x^{5} - 940430954112 x^{4} + 180101325169073 x^{3} + \cdots - 51\!\cdots\!56 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-13.8911\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.8911 | 0.373244 | 0.186622 | − | 0.982432i | \(-0.440246\pi\) | ||||
0.186622 | + | 0.982432i | \(0.440246\pi\) | |||||||
\(3\) | −378.630 | −0.899597 | −0.449798 | − | 0.893130i | \(-0.648504\pi\) | ||||
−0.449798 | + | 0.893130i | \(0.648504\pi\) | |||||||
\(4\) | −1762.69 | −0.860689 | ||||||||
\(5\) | −6541.27 | −0.936110 | −0.468055 | − | 0.883699i | \(-0.655045\pi\) | ||||
−0.468055 | + | 0.883699i | \(0.655045\pi\) | |||||||
\(6\) | −6395.47 | −0.335769 | ||||||||
\(7\) | −3800.70 | −0.0854721 | −0.0427361 | − | 0.999086i | \(-0.513607\pi\) | ||||
−0.0427361 | + | 0.999086i | \(0.513607\pi\) | |||||||
\(8\) | −64366.7 | −0.694491 | ||||||||
\(9\) | −33786.5 | −0.190726 | ||||||||
\(10\) | −110489. | −0.349397 | ||||||||
\(11\) | 1.02487e6 | 1.91872 | 0.959359 | − | 0.282189i | \(-0.0910605\pi\) | ||||
0.959359 | + | 0.282189i | \(0.0910605\pi\) | |||||||
\(12\) | 667407. | 0.774273 | ||||||||
\(13\) | −1.69626e6 | −1.26708 | −0.633542 | − | 0.773709i | \(-0.718399\pi\) | ||||
−0.633542 | + | 0.773709i | \(0.718399\pi\) | |||||||
\(14\) | −64198.0 | −0.0319019 | ||||||||
\(15\) | 2.47672e6 | 0.842122 | ||||||||
\(16\) | 2.52277e6 | 0.601475 | ||||||||
\(17\) | 8.27076e6 | 1.41279 | 0.706393 | − | 0.707820i | \(-0.250321\pi\) | ||||
0.706393 | + | 0.707820i | \(0.250321\pi\) | |||||||
\(18\) | −570691. | −0.0711873 | ||||||||
\(19\) | −1.14578e7 | −1.06159 | −0.530795 | − | 0.847500i | \(-0.678107\pi\) | ||||
−0.530795 | + | 0.847500i | \(0.678107\pi\) | |||||||
\(20\) | 1.15302e7 | 0.805700 | ||||||||
\(21\) | 1.43906e6 | 0.0768904 | ||||||||
\(22\) | 1.73113e7 | 0.716150 | ||||||||
\(23\) | −6.43634e6 | −0.208514 | ||||||||
\(24\) | 2.43712e7 | 0.624761 | ||||||||
\(25\) | −6.03993e6 | −0.123698 | ||||||||
\(26\) | −2.86518e7 | −0.472931 | ||||||||
\(27\) | 7.98657e7 | 1.07117 | ||||||||
\(28\) | 6.69946e6 | 0.0735649 | ||||||||
\(29\) | 4.47832e7 | 0.405440 | 0.202720 | − | 0.979237i | \(-0.435022\pi\) | ||||
0.202720 | + | 0.979237i | \(0.435022\pi\) | |||||||
\(30\) | 4.18345e7 | 0.314317 | ||||||||
\(31\) | 2.61664e8 | 1.64155 | 0.820775 | − | 0.571252i | \(-0.193542\pi\) | ||||
0.820775 | + | 0.571252i | \(0.193542\pi\) | |||||||
\(32\) | 1.74435e8 | 0.918987 | ||||||||
\(33\) | −3.88048e8 | −1.72607 | ||||||||
\(34\) | 1.39702e8 | 0.527314 | ||||||||
\(35\) | 2.48614e7 | 0.0800113 | ||||||||
\(36\) | 5.95552e7 | 0.164156 | ||||||||
\(37\) | −1.68474e8 | −0.399414 | −0.199707 | − | 0.979856i | \(-0.563999\pi\) | ||||
−0.199707 | + | 0.979856i | \(0.563999\pi\) | |||||||
\(38\) | −1.93535e8 | −0.396232 | ||||||||
\(39\) | 6.42256e8 | 1.13986 | ||||||||
\(40\) | 4.21040e8 | 0.650120 | ||||||||
\(41\) | −1.43869e9 | −1.93935 | −0.969673 | − | 0.244408i | \(-0.921406\pi\) | ||||
−0.969673 | + | 0.244408i | \(0.921406\pi\) | |||||||
\(42\) | 2.43073e7 | 0.0286989 | ||||||||
\(43\) | −1.05453e9 | −1.09391 | −0.546955 | − | 0.837162i | \(-0.684213\pi\) | ||||
−0.546955 | + | 0.837162i | \(0.684213\pi\) | |||||||
\(44\) | −1.80654e9 | −1.65142 | ||||||||
\(45\) | 2.21007e8 | 0.178541 | ||||||||
\(46\) | −1.08717e8 | −0.0778267 | ||||||||
\(47\) | 2.31808e9 | 1.47432 | 0.737158 | − | 0.675721i | \(-0.236167\pi\) | ||||
0.737158 | + | 0.675721i | \(0.236167\pi\) | |||||||
\(48\) | −9.55195e8 | −0.541085 | ||||||||
\(49\) | −1.96288e9 | −0.992695 | ||||||||
\(50\) | −1.02021e8 | −0.0461694 | ||||||||
\(51\) | −3.13156e9 | −1.27094 | ||||||||
\(52\) | 2.98999e9 | 1.09056 | ||||||||
\(53\) | 1.59647e9 | 0.524378 | 0.262189 | − | 0.965017i | \(-0.415556\pi\) | ||||
0.262189 | + | 0.965017i | \(0.415556\pi\) | |||||||
\(54\) | 1.34902e9 | 0.399809 | ||||||||
\(55\) | −6.70398e9 | −1.79613 | ||||||||
\(56\) | 2.44639e8 | 0.0593596 | ||||||||
\(57\) | 4.33827e9 | 0.955003 | ||||||||
\(58\) | 7.56438e8 | 0.151328 | ||||||||
\(59\) | 4.93268e9 | 0.898250 | 0.449125 | − | 0.893469i | \(-0.351736\pi\) | ||||
0.449125 | + | 0.893469i | \(0.351736\pi\) | |||||||
\(60\) | −4.36569e9 | −0.724805 | ||||||||
\(61\) | −3.28664e8 | −0.0498239 | −0.0249119 | − | 0.999690i | \(-0.507931\pi\) | ||||
−0.0249119 | + | 0.999690i | \(0.507931\pi\) | |||||||
\(62\) | 4.41978e9 | 0.612698 | ||||||||
\(63\) | 1.28413e8 | 0.0163018 | ||||||||
\(64\) | −2.22023e9 | −0.258468 | ||||||||
\(65\) | 1.10957e10 | 1.18613 | ||||||||
\(66\) | −6.55455e9 | −0.644246 | ||||||||
\(67\) | 5.77514e9 | 0.522578 | 0.261289 | − | 0.965261i | \(-0.415853\pi\) | ||||
0.261289 | + | 0.965261i | \(0.415853\pi\) | |||||||
\(68\) | −1.45788e10 | −1.21597 | ||||||||
\(69\) | 2.43699e9 | 0.187579 | ||||||||
\(70\) | 4.19936e8 | 0.0298637 | ||||||||
\(71\) | 1.37955e10 | 0.907438 | 0.453719 | − | 0.891145i | \(-0.350097\pi\) | ||||
0.453719 | + | 0.891145i | \(0.350097\pi\) | |||||||
\(72\) | 2.17473e9 | 0.132457 | ||||||||
\(73\) | 2.90528e10 | 1.64026 | 0.820128 | − | 0.572180i | \(-0.193902\pi\) | ||||
0.820128 | + | 0.572180i | \(0.193902\pi\) | |||||||
\(74\) | −2.84571e9 | −0.149079 | ||||||||
\(75\) | 2.28690e9 | 0.111278 | ||||||||
\(76\) | 2.01966e10 | 0.913699 | ||||||||
\(77\) | −3.89524e9 | −0.163997 | ||||||||
\(78\) | 1.08484e10 | 0.425447 | ||||||||
\(79\) | −3.11198e8 | −0.0113786 | −0.00568929 | − | 0.999984i | \(-0.501811\pi\) | ||||
−0.00568929 | + | 0.999984i | \(0.501811\pi\) | |||||||
\(80\) | −1.65021e10 | −0.563047 | ||||||||
\(81\) | −2.42543e10 | −0.772898 | ||||||||
\(82\) | −2.43010e10 | −0.723849 | ||||||||
\(83\) | 4.34819e10 | 1.21165 | 0.605827 | − | 0.795596i | \(-0.292842\pi\) | ||||
0.605827 | + | 0.795596i | \(0.292842\pi\) | |||||||
\(84\) | −2.53662e9 | −0.0661787 | ||||||||
\(85\) | −5.41013e10 | −1.32252 | ||||||||
\(86\) | −1.78121e10 | −0.408295 | ||||||||
\(87\) | −1.69563e10 | −0.364732 | ||||||||
\(88\) | −6.59678e10 | −1.33253 | ||||||||
\(89\) | 6.88021e9 | 0.130604 | 0.0653020 | − | 0.997866i | \(-0.479199\pi\) | ||||
0.0653020 | + | 0.997866i | \(0.479199\pi\) | |||||||
\(90\) | 3.73305e9 | 0.0666392 | ||||||||
\(91\) | 6.44699e9 | 0.108300 | ||||||||
\(92\) | 1.13453e10 | 0.179466 | ||||||||
\(93\) | −9.90736e10 | −1.47673 | ||||||||
\(94\) | 3.91549e10 | 0.550279 | ||||||||
\(95\) | 7.49486e10 | 0.993765 | ||||||||
\(96\) | −6.60464e10 | −0.826718 | ||||||||
\(97\) | 8.92894e10 | 1.05574 | 0.527868 | − | 0.849326i | \(-0.322992\pi\) | ||||
0.527868 | + | 0.849326i | \(0.322992\pi\) | |||||||
\(98\) | −3.31552e10 | −0.370517 | ||||||||
\(99\) | −3.46270e10 | −0.365949 | ||||||||
\(100\) | 1.06465e10 | 0.106465 | ||||||||
\(101\) | 1.19965e11 | 1.13576 | 0.567882 | − | 0.823110i | \(-0.307763\pi\) | ||||
0.567882 | + | 0.823110i | \(0.307763\pi\) | |||||||
\(102\) | −5.28954e10 | −0.474370 | ||||||||
\(103\) | 6.01002e10 | 0.510824 | 0.255412 | − | 0.966832i | \(-0.417789\pi\) | ||||
0.255412 | + | 0.966832i | \(0.417789\pi\) | |||||||
\(104\) | 1.09183e11 | 0.879977 | ||||||||
\(105\) | −9.41327e9 | −0.0719779 | ||||||||
\(106\) | 2.69662e10 | 0.195721 | ||||||||
\(107\) | −2.39646e11 | −1.65181 | −0.825903 | − | 0.563812i | \(-0.809334\pi\) | ||||
−0.825903 | + | 0.563812i | \(0.809334\pi\) | |||||||
\(108\) | −1.40779e11 | −0.921947 | ||||||||
\(109\) | −1.12756e11 | −0.701928 | −0.350964 | − | 0.936389i | \(-0.614146\pi\) | ||||
−0.350964 | + | 0.936389i | \(0.614146\pi\) | |||||||
\(110\) | −1.13238e11 | −0.670395 | ||||||||
\(111\) | 6.37893e10 | 0.359312 | ||||||||
\(112\) | −9.58828e9 | −0.0514093 | ||||||||
\(113\) | 9.05850e10 | 0.462514 | 0.231257 | − | 0.972893i | \(-0.425716\pi\) | ||||
0.231257 | + | 0.972893i | \(0.425716\pi\) | |||||||
\(114\) | 7.32781e10 | 0.356449 | ||||||||
\(115\) | 4.21018e10 | 0.195192 | ||||||||
\(116\) | −7.89390e10 | −0.348958 | ||||||||
\(117\) | 5.73109e10 | 0.241666 | ||||||||
\(118\) | 8.33184e10 | 0.335266 | ||||||||
\(119\) | −3.14347e10 | −0.120754 | ||||||||
\(120\) | −1.59418e11 | −0.584846 | ||||||||
\(121\) | 7.65057e11 | 2.68148 | ||||||||
\(122\) | −5.55149e9 | −0.0185965 | ||||||||
\(123\) | 5.44730e11 | 1.74463 | ||||||||
\(124\) | −4.61232e11 | −1.41286 | ||||||||
\(125\) | 3.58907e11 | 1.05190 | ||||||||
\(126\) | 2.16903e9 | 0.00608453 | ||||||||
\(127\) | 4.75970e10 | 0.127838 | 0.0639189 | − | 0.997955i | \(-0.479640\pi\) | ||||
0.0639189 | + | 0.997955i | \(0.479640\pi\) | |||||||
\(128\) | −3.94746e11 | −1.01546 | ||||||||
\(129\) | 3.99275e11 | 0.984077 | ||||||||
\(130\) | 1.87419e11 | 0.442715 | ||||||||
\(131\) | −4.22725e10 | −0.0957340 | −0.0478670 | − | 0.998854i | \(-0.515242\pi\) | ||||
−0.0478670 | + | 0.998854i | \(0.515242\pi\) | |||||||
\(132\) | 6.84009e11 | 1.48561 | ||||||||
\(133\) | 4.35477e10 | 0.0907363 | ||||||||
\(134\) | 9.75483e10 | 0.195049 | ||||||||
\(135\) | −5.22423e11 | −1.00274 | ||||||||
\(136\) | −5.32362e11 | −0.981167 | ||||||||
\(137\) | −2.26639e11 | −0.401209 | −0.200605 | − | 0.979672i | \(-0.564291\pi\) | ||||
−0.200605 | + | 0.979672i | \(0.564291\pi\) | |||||||
\(138\) | 4.11634e10 | 0.0700127 | ||||||||
\(139\) | 1.60580e9 | 0.00262489 | 0.00131244 | − | 0.999999i | \(-0.499582\pi\) | ||||
0.00131244 | + | 0.999999i | \(0.499582\pi\) | |||||||
\(140\) | −4.38230e10 | −0.0688649 | ||||||||
\(141\) | −8.77695e11 | −1.32629 | ||||||||
\(142\) | 2.33021e11 | 0.338696 | ||||||||
\(143\) | −1.73846e12 | −2.43117 | ||||||||
\(144\) | −8.52356e10 | −0.114717 | ||||||||
\(145\) | −2.92939e11 | −0.379537 | ||||||||
\(146\) | 4.90733e11 | 0.612215 | ||||||||
\(147\) | 7.43205e11 | 0.893025 | ||||||||
\(148\) | 2.96968e11 | 0.343772 | ||||||||
\(149\) | 9.73616e11 | 1.08608 | 0.543042 | − | 0.839706i | \(-0.317273\pi\) | ||||
0.543042 | + | 0.839706i | \(0.317273\pi\) | |||||||
\(150\) | 3.86282e10 | 0.0415339 | ||||||||
\(151\) | −8.00653e11 | −0.829987 | −0.414993 | − | 0.909824i | \(-0.636216\pi\) | ||||
−0.414993 | + | 0.909824i | \(0.636216\pi\) | |||||||
\(152\) | 7.37502e11 | 0.737264 | ||||||||
\(153\) | −2.79440e11 | −0.269455 | ||||||||
\(154\) | −6.57949e10 | −0.0612108 | ||||||||
\(155\) | −1.71161e12 | −1.53667 | ||||||||
\(156\) | −1.13210e12 | −0.981068 | ||||||||
\(157\) | −7.49867e11 | −0.627388 | −0.313694 | − | 0.949524i | \(-0.601567\pi\) | ||||
−0.313694 | + | 0.949524i | \(0.601567\pi\) | |||||||
\(158\) | −5.25647e9 | −0.00424698 | ||||||||
\(159\) | −6.04472e11 | −0.471729 | ||||||||
\(160\) | −1.14103e12 | −0.860273 | ||||||||
\(161\) | 2.44626e10 | 0.0178222 | ||||||||
\(162\) | −4.09682e11 | −0.288479 | ||||||||
\(163\) | −4.12146e11 | −0.280556 | −0.140278 | − | 0.990112i | \(-0.544800\pi\) | ||||
−0.140278 | + | 0.990112i | \(0.544800\pi\) | |||||||
\(164\) | 2.53596e12 | 1.66917 | ||||||||
\(165\) | 2.53833e12 | 1.61579 | ||||||||
\(166\) | 7.34456e11 | 0.452242 | ||||||||
\(167\) | −4.65535e11 | −0.277340 | −0.138670 | − | 0.990339i | \(-0.544283\pi\) | ||||
−0.138670 | + | 0.990339i | \(0.544283\pi\) | |||||||
\(168\) | −9.26275e10 | −0.0533997 | ||||||||
\(169\) | 1.08515e12 | 0.605500 | ||||||||
\(170\) | −9.13830e11 | −0.493624 | ||||||||
\(171\) | 3.87120e11 | 0.202473 | ||||||||
\(172\) | 1.85881e12 | 0.941516 | ||||||||
\(173\) | −3.73536e11 | −0.183264 | −0.0916322 | − | 0.995793i | \(-0.529208\pi\) | ||||
−0.0916322 | + | 0.995793i | \(0.529208\pi\) | |||||||
\(174\) | −2.86410e11 | −0.136134 | ||||||||
\(175\) | 2.29560e10 | 0.0105727 | ||||||||
\(176\) | 2.58552e12 | 1.15406 | ||||||||
\(177\) | −1.86766e12 | −0.808063 | ||||||||
\(178\) | 1.16214e11 | 0.0487471 | ||||||||
\(179\) | 1.15011e12 | 0.467788 | 0.233894 | − | 0.972262i | \(-0.424853\pi\) | ||||
0.233894 | + | 0.972262i | \(0.424853\pi\) | |||||||
\(180\) | −3.89567e11 | −0.153668 | ||||||||
\(181\) | −9.40884e11 | −0.360001 | −0.180001 | − | 0.983666i | \(-0.557610\pi\) | ||||
−0.180001 | + | 0.983666i | \(0.557610\pi\) | |||||||
\(182\) | 1.08897e11 | 0.0404224 | ||||||||
\(183\) | 1.24442e11 | 0.0448214 | ||||||||
\(184\) | 4.14286e11 | 0.144811 | ||||||||
\(185\) | 1.10203e12 | 0.373896 | ||||||||
\(186\) | −1.67346e12 | −0.551181 | ||||||||
\(187\) | 8.47650e12 | 2.71074 | ||||||||
\(188\) | −4.08606e12 | −1.26893 | ||||||||
\(189\) | −3.03546e11 | −0.0915554 | ||||||||
\(190\) | 1.26596e12 | 0.370917 | ||||||||
\(191\) | −4.32339e12 | −1.23067 | −0.615334 | − | 0.788266i | \(-0.710979\pi\) | ||||
−0.615334 | + | 0.788266i | \(0.710979\pi\) | |||||||
\(192\) | 8.40643e11 | 0.232517 | ||||||||
\(193\) | 3.56015e12 | 0.956980 | 0.478490 | − | 0.878093i | \(-0.341184\pi\) | ||||
0.478490 | + | 0.878093i | \(0.341184\pi\) | |||||||
\(194\) | 1.50820e12 | 0.394047 | ||||||||
\(195\) | −4.20117e12 | −1.06704 | ||||||||
\(196\) | 3.45995e12 | 0.854401 | ||||||||
\(197\) | −2.01248e12 | −0.483246 | −0.241623 | − | 0.970370i | \(-0.577680\pi\) | ||||
−0.241623 | + | 0.970370i | \(0.577680\pi\) | |||||||
\(198\) | −5.84887e11 | −0.136588 | ||||||||
\(199\) | −6.26753e12 | −1.42365 | −0.711827 | − | 0.702355i | \(-0.752132\pi\) | ||||
−0.711827 | + | 0.702355i | \(0.752132\pi\) | |||||||
\(200\) | 3.88770e11 | 0.0859070 | ||||||||
\(201\) | −2.18664e12 | −0.470109 | ||||||||
\(202\) | 2.02634e12 | 0.423917 | ||||||||
\(203\) | −1.70208e11 | −0.0346538 | ||||||||
\(204\) | 5.51997e12 | 1.09388 | ||||||||
\(205\) | 9.41084e12 | 1.81544 | ||||||||
\(206\) | 1.01516e12 | 0.190662 | ||||||||
\(207\) | 2.17462e11 | 0.0397691 | ||||||||
\(208\) | −4.27928e12 | −0.762118 | ||||||||
\(209\) | −1.17428e13 | −2.03689 | ||||||||
\(210\) | −1.59000e11 | −0.0268653 | ||||||||
\(211\) | 9.34110e12 | 1.53760 | 0.768802 | − | 0.639487i | \(-0.220853\pi\) | ||||
0.768802 | + | 0.639487i | \(0.220853\pi\) | |||||||
\(212\) | −2.81409e12 | −0.451326 | ||||||||
\(213\) | −5.22339e12 | −0.816329 | ||||||||
\(214\) | −4.04788e12 | −0.616526 | ||||||||
\(215\) | 6.89795e12 | 1.02402 | ||||||||
\(216\) | −5.14069e12 | −0.743920 | ||||||||
\(217\) | −9.94505e11 | −0.140307 | ||||||||
\(218\) | −1.90457e12 | −0.261990 | ||||||||
\(219\) | −1.10002e13 | −1.47557 | ||||||||
\(220\) | 1.18170e13 | 1.54591 | ||||||||
\(221\) | −1.40294e13 | −1.79012 | ||||||||
\(222\) | 1.07747e12 | 0.134111 | ||||||||
\(223\) | 4.61925e12 | 0.560912 | 0.280456 | − | 0.959867i | \(-0.409514\pi\) | ||||
0.280456 | + | 0.959867i | \(0.409514\pi\) | |||||||
\(224\) | −6.62977e11 | −0.0785478 | ||||||||
\(225\) | 2.04068e11 | 0.0235924 | ||||||||
\(226\) | 1.53008e12 | 0.172630 | ||||||||
\(227\) | −1.58752e12 | −0.174814 | −0.0874071 | − | 0.996173i | \(-0.527858\pi\) | ||||
−0.0874071 | + | 0.996173i | \(0.527858\pi\) | |||||||
\(228\) | −7.64702e12 | −0.821960 | ||||||||
\(229\) | 4.60351e12 | 0.483052 | 0.241526 | − | 0.970394i | \(-0.422352\pi\) | ||||
0.241526 | + | 0.970394i | \(0.422352\pi\) | |||||||
\(230\) | 7.11146e11 | 0.0728544 | ||||||||
\(231\) | 1.47485e12 | 0.147531 | ||||||||
\(232\) | −2.88255e12 | −0.281574 | ||||||||
\(233\) | 5.72926e11 | 0.0546564 | 0.0273282 | − | 0.999627i | \(-0.491300\pi\) | ||||
0.0273282 | + | 0.999627i | \(0.491300\pi\) | |||||||
\(234\) | 9.68043e11 | 0.0902002 | ||||||||
\(235\) | −1.51632e13 | −1.38012 | ||||||||
\(236\) | −8.69480e12 | −0.773114 | ||||||||
\(237\) | 1.17829e11 | 0.0102361 | ||||||||
\(238\) | −5.30966e11 | −0.0450706 | ||||||||
\(239\) | −4.64149e12 | −0.385007 | −0.192504 | − | 0.981296i | \(-0.561661\pi\) | ||||
−0.192504 | + | 0.981296i | \(0.561661\pi\) | |||||||
\(240\) | 6.24819e12 | 0.506515 | ||||||||
\(241\) | 2.10084e13 | 1.66456 | 0.832279 | − | 0.554358i | \(-0.187036\pi\) | ||||
0.832279 | + | 0.554358i | \(0.187036\pi\) | |||||||
\(242\) | 1.29226e13 | 1.00085 | ||||||||
\(243\) | −4.96455e12 | −0.375877 | ||||||||
\(244\) | 5.79333e11 | 0.0428829 | ||||||||
\(245\) | 1.28397e13 | 0.929271 | ||||||||
\(246\) | 9.20108e12 | 0.651172 | ||||||||
\(247\) | 1.94355e13 | 1.34512 | ||||||||
\(248\) | −1.68424e13 | −1.14004 | ||||||||
\(249\) | −1.64635e13 | −1.09000 | ||||||||
\(250\) | 6.06232e12 | 0.392617 | ||||||||
\(251\) | −5.75426e12 | −0.364573 | −0.182286 | − | 0.983245i | \(-0.558350\pi\) | ||||
−0.182286 | + | 0.983245i | \(0.558350\pi\) | |||||||
\(252\) | −2.26352e11 | −0.0140307 | ||||||||
\(253\) | −6.59645e12 | −0.400080 | ||||||||
\(254\) | 8.03965e11 | 0.0477147 | ||||||||
\(255\) | 2.04844e13 | 1.18974 | ||||||||
\(256\) | −2.12066e12 | −0.120546 | ||||||||
\(257\) | 1.72946e13 | 0.962226 | 0.481113 | − | 0.876658i | \(-0.340233\pi\) | ||||
0.481113 | + | 0.876658i | \(0.340233\pi\) | |||||||
\(258\) | 6.74420e12 | 0.367301 | ||||||||
\(259\) | 6.40320e11 | 0.0341388 | ||||||||
\(260\) | −1.95583e13 | −1.02089 | ||||||||
\(261\) | −1.51307e12 | −0.0773279 | ||||||||
\(262\) | −7.14029e11 | −0.0357321 | ||||||||
\(263\) | 1.92961e13 | 0.945611 | 0.472805 | − | 0.881167i | \(-0.343241\pi\) | ||||
0.472805 | + | 0.881167i | \(0.343241\pi\) | |||||||
\(264\) | 2.49774e13 | 1.19874 | ||||||||
\(265\) | −1.04430e13 | −0.490876 | ||||||||
\(266\) | 7.35568e11 | 0.0338668 | ||||||||
\(267\) | −2.60505e12 | −0.117491 | ||||||||
\(268\) | −1.01798e13 | −0.449777 | ||||||||
\(269\) | −2.10306e13 | −0.910363 | −0.455182 | − | 0.890399i | \(-0.650426\pi\) | ||||
−0.455182 | + | 0.890399i | \(0.650426\pi\) | |||||||
\(270\) | −8.82429e12 | −0.374265 | ||||||||
\(271\) | 2.44065e13 | 1.01432 | 0.507160 | − | 0.861852i | \(-0.330695\pi\) | ||||
0.507160 | + | 0.861852i | \(0.330695\pi\) | |||||||
\(272\) | 2.08652e13 | 0.849755 | ||||||||
\(273\) | −2.44102e12 | −0.0974266 | ||||||||
\(274\) | −3.82817e12 | −0.149749 | ||||||||
\(275\) | −6.19017e12 | −0.237341 | ||||||||
\(276\) | −4.29566e12 | −0.161447 | ||||||||
\(277\) | 1.68895e13 | 0.622269 | 0.311134 | − | 0.950366i | \(-0.399291\pi\) | ||||
0.311134 | + | 0.950366i | \(0.399291\pi\) | |||||||
\(278\) | 2.71238e10 | 0.000979724 0 | ||||||||
\(279\) | −8.84071e12 | −0.313086 | ||||||||
\(280\) | −1.60025e12 | −0.0555671 | ||||||||
\(281\) | 1.46711e13 | 0.499549 | 0.249774 | − | 0.968304i | \(-0.419644\pi\) | ||||
0.249774 | + | 0.968304i | \(0.419644\pi\) | |||||||
\(282\) | −1.48252e13 | −0.495029 | ||||||||
\(283\) | 2.33741e13 | 0.765436 | 0.382718 | − | 0.923865i | \(-0.374988\pi\) | ||||
0.382718 | + | 0.923865i | \(0.374988\pi\) | |||||||
\(284\) | −2.43172e13 | −0.781022 | ||||||||
\(285\) | −2.83778e13 | −0.893988 | ||||||||
\(286\) | −2.93645e13 | −0.907421 | ||||||||
\(287\) | 5.46802e12 | 0.165760 | ||||||||
\(288\) | −5.89357e12 | −0.175275 | ||||||||
\(289\) | 3.41336e13 | 0.995966 | ||||||||
\(290\) | −4.94806e12 | −0.141660 | ||||||||
\(291\) | −3.38076e13 | −0.949737 | ||||||||
\(292\) | −5.12110e13 | −1.41175 | ||||||||
\(293\) | 3.92652e13 | 1.06227 | 0.531137 | − | 0.847286i | \(-0.321765\pi\) | ||||
0.531137 | + | 0.847286i | \(0.321765\pi\) | |||||||
\(294\) | 1.25535e13 | 0.333316 | ||||||||
\(295\) | −3.22660e13 | −0.840861 | ||||||||
\(296\) | 1.08441e13 | 0.277390 | ||||||||
\(297\) | 8.18524e13 | 2.05528 | ||||||||
\(298\) | 1.64454e13 | 0.405374 | ||||||||
\(299\) | 1.09177e13 | 0.264205 | ||||||||
\(300\) | −4.03109e12 | −0.0957758 | ||||||||
\(301\) | 4.00794e12 | 0.0934988 | ||||||||
\(302\) | −1.35239e13 | −0.309787 | ||||||||
\(303\) | −4.54224e13 | −1.02173 | ||||||||
\(304\) | −2.89054e13 | −0.638519 | ||||||||
\(305\) | 2.14988e12 | 0.0466407 | ||||||||
\(306\) | −4.72005e12 | −0.100572 | ||||||||
\(307\) | −4.58221e13 | −0.958989 | −0.479495 | − | 0.877545i | \(-0.659180\pi\) | ||||
−0.479495 | + | 0.877545i | \(0.659180\pi\) | |||||||
\(308\) | 6.86611e12 | 0.141150 | ||||||||
\(309\) | −2.27557e13 | −0.459535 | ||||||||
\(310\) | −2.89110e13 | −0.573553 | ||||||||
\(311\) | −5.88235e13 | −1.14649 | −0.573243 | − | 0.819386i | \(-0.694315\pi\) | ||||
−0.573243 | + | 0.819386i | \(0.694315\pi\) | |||||||
\(312\) | −4.13399e13 | −0.791625 | ||||||||
\(313\) | 3.23539e13 | 0.608741 | 0.304371 | − | 0.952554i | \(-0.401554\pi\) | ||||
0.304371 | + | 0.952554i | \(0.401554\pi\) | |||||||
\(314\) | −1.26661e13 | −0.234169 | ||||||||
\(315\) | −8.39981e11 | −0.0152602 | ||||||||
\(316\) | 5.48546e11 | 0.00979342 | ||||||||
\(317\) | −7.31260e13 | −1.28306 | −0.641528 | − | 0.767100i | \(-0.721699\pi\) | ||||
−0.641528 | + | 0.767100i | \(0.721699\pi\) | |||||||
\(318\) | −1.02102e13 | −0.176070 | ||||||||
\(319\) | 4.58972e13 | 0.777925 | ||||||||
\(320\) | 1.45231e13 | 0.241955 | ||||||||
\(321\) | 9.07370e13 | 1.48596 | ||||||||
\(322\) | 4.13200e11 | 0.00665201 | ||||||||
\(323\) | −9.47648e13 | −1.49980 | ||||||||
\(324\) | 4.27529e13 | 0.665224 | ||||||||
\(325\) | 1.02453e13 | 0.156735 | ||||||||
\(326\) | −6.96159e12 | −0.104716 | ||||||||
\(327\) | 4.26927e13 | 0.631452 | ||||||||
\(328\) | 9.26036e13 | 1.34686 | ||||||||
\(329\) | −8.81033e12 | −0.126013 | ||||||||
\(330\) | 4.28751e13 | 0.603085 | ||||||||
\(331\) | 2.93876e13 | 0.406547 | 0.203273 | − | 0.979122i | \(-0.434842\pi\) | ||||
0.203273 | + | 0.979122i | \(0.434842\pi\) | |||||||
\(332\) | −7.66451e13 | −1.04286 | ||||||||
\(333\) | 5.69216e12 | 0.0761787 | ||||||||
\(334\) | −7.86339e12 | −0.103515 | ||||||||
\(335\) | −3.77767e13 | −0.489190 | ||||||||
\(336\) | 3.63041e12 | 0.0462476 | ||||||||
\(337\) | 1.02524e13 | 0.128487 | 0.0642435 | − | 0.997934i | \(-0.479537\pi\) | ||||
0.0642435 | + | 0.997934i | \(0.479537\pi\) | |||||||
\(338\) | 1.83294e13 | 0.225999 | ||||||||
\(339\) | −3.42982e13 | −0.416076 | ||||||||
\(340\) | 9.53639e13 | 1.13828 | ||||||||
\(341\) | 2.68173e14 | 3.14967 | ||||||||
\(342\) | 6.53887e12 | 0.0755717 | ||||||||
\(343\) | 1.49756e13 | 0.170320 | ||||||||
\(344\) | 6.78765e13 | 0.759710 | ||||||||
\(345\) | −1.59410e13 | −0.175594 | ||||||||
\(346\) | −6.30942e12 | −0.0684023 | ||||||||
\(347\) | 1.20191e14 | 1.28251 | 0.641256 | − | 0.767327i | \(-0.278414\pi\) | ||||
0.641256 | + | 0.767327i | \(0.278414\pi\) | |||||||
\(348\) | 2.98887e13 | 0.313921 | ||||||||
\(349\) | −1.24212e14 | −1.28417 | −0.642085 | − | 0.766634i | \(-0.721930\pi\) | ||||
−0.642085 | + | 0.766634i | \(0.721930\pi\) | |||||||
\(350\) | 3.87751e11 | 0.00394620 | ||||||||
\(351\) | −1.35473e14 | −1.35727 | ||||||||
\(352\) | 1.78774e14 | 1.76328 | ||||||||
\(353\) | 6.01003e13 | 0.583601 | 0.291800 | − | 0.956479i | \(-0.405746\pi\) | ||||
0.291800 | + | 0.956479i | \(0.405746\pi\) | |||||||
\(354\) | −3.15468e13 | −0.301604 | ||||||||
\(355\) | −9.02402e13 | −0.849462 | ||||||||
\(356\) | −1.21277e13 | −0.112409 | ||||||||
\(357\) | 1.19021e13 | 0.108630 | ||||||||
\(358\) | 1.94267e13 | 0.174599 | ||||||||
\(359\) | 8.94457e13 | 0.791662 | 0.395831 | − | 0.918323i | \(-0.370457\pi\) | ||||
0.395831 | + | 0.918323i | \(0.370457\pi\) | |||||||
\(360\) | −1.42255e13 | −0.123995 | ||||||||
\(361\) | 1.47911e13 | 0.126973 | ||||||||
\(362\) | −1.58926e13 | −0.134368 | ||||||||
\(363\) | −2.89673e14 | −2.41225 | ||||||||
\(364\) | −1.13641e13 | −0.0932129 | ||||||||
\(365\) | −1.90042e14 | −1.53546 | ||||||||
\(366\) | 2.10196e12 | 0.0167293 | ||||||||
\(367\) | −1.97416e14 | −1.54782 | −0.773909 | − | 0.633297i | \(-0.781701\pi\) | ||||
−0.773909 | + | 0.633297i | \(0.781701\pi\) | |||||||
\(368\) | −1.62374e13 | −0.125416 | ||||||||
\(369\) | 4.86082e13 | 0.369884 | ||||||||
\(370\) | 1.86146e13 | 0.139554 | ||||||||
\(371\) | −6.06772e12 | −0.0448197 | ||||||||
\(372\) | 1.74636e14 | 1.27101 | ||||||||
\(373\) | −2.10543e13 | −0.150988 | −0.0754941 | − | 0.997146i | \(-0.524053\pi\) | ||||
−0.0754941 | + | 0.997146i | \(0.524053\pi\) | |||||||
\(374\) | 1.43177e14 | 1.01177 | ||||||||
\(375\) | −1.35893e14 | −0.946290 | ||||||||
\(376\) | −1.49207e14 | −1.02390 | ||||||||
\(377\) | −7.59642e13 | −0.513726 | ||||||||
\(378\) | −5.12722e12 | −0.0341725 | ||||||||
\(379\) | 9.20106e13 | 0.604397 | 0.302198 | − | 0.953245i | \(-0.402279\pi\) | ||||
0.302198 | + | 0.953245i | \(0.402279\pi\) | |||||||
\(380\) | −1.32111e14 | −0.855323 | ||||||||
\(381\) | −1.80216e13 | −0.115002 | ||||||||
\(382\) | −7.30268e13 | −0.459339 | ||||||||
\(383\) | 2.78887e14 | 1.72916 | 0.864580 | − | 0.502495i | \(-0.167585\pi\) | ||||
0.864580 | + | 0.502495i | \(0.167585\pi\) | |||||||
\(384\) | 1.49462e14 | 0.913504 | ||||||||
\(385\) | 2.54798e13 | 0.153519 | ||||||||
\(386\) | 6.01348e13 | 0.357187 | ||||||||
\(387\) | 3.56288e13 | 0.208637 | ||||||||
\(388\) | −1.57390e14 | −0.908660 | ||||||||
\(389\) | −7.22226e13 | −0.411103 | −0.205551 | − | 0.978646i | \(-0.565899\pi\) | ||||
−0.205551 | + | 0.978646i | \(0.565899\pi\) | |||||||
\(390\) | −7.09623e13 | −0.398265 | ||||||||
\(391\) | −5.32335e13 | −0.294586 | ||||||||
\(392\) | 1.26344e14 | 0.689417 | ||||||||
\(393\) | 1.60056e13 | 0.0861220 | ||||||||
\(394\) | −3.39930e13 | −0.180369 | ||||||||
\(395\) | 2.03563e12 | 0.0106516 | ||||||||
\(396\) | 6.10367e13 | 0.314969 | ||||||||
\(397\) | 2.26699e14 | 1.15372 | 0.576862 | − | 0.816842i | \(-0.304277\pi\) | ||||
0.576862 | + | 0.816842i | \(0.304277\pi\) | |||||||
\(398\) | −1.05865e14 | −0.531370 | ||||||||
\(399\) | −1.64885e13 | −0.0816261 | ||||||||
\(400\) | −1.52373e13 | −0.0744011 | ||||||||
\(401\) | 8.00200e12 | 0.0385394 | 0.0192697 | − | 0.999814i | \(-0.493866\pi\) | ||||
0.0192697 | + | 0.999814i | \(0.493866\pi\) | |||||||
\(402\) | −3.69347e13 | −0.175465 | ||||||||
\(403\) | −4.43851e14 | −2.07998 | ||||||||
\(404\) | −2.11462e14 | −0.977540 | ||||||||
\(405\) | 1.58654e14 | 0.723517 | ||||||||
\(406\) | −2.87499e12 | −0.0129343 | ||||||||
\(407\) | −1.72665e14 | −0.766364 | ||||||||
\(408\) | 2.01568e14 | 0.882655 | ||||||||
\(409\) | 2.38273e14 | 1.02943 | 0.514714 | − | 0.857362i | \(-0.327898\pi\) | ||||
0.514714 | + | 0.857362i | \(0.327898\pi\) | |||||||
\(410\) | 1.58959e14 | 0.677602 | ||||||||
\(411\) | 8.58121e13 | 0.360926 | ||||||||
\(412\) | −1.05938e14 | −0.439660 | ||||||||
\(413\) | −1.87477e13 | −0.0767753 | ||||||||
\(414\) | 3.67317e12 | 0.0148436 | ||||||||
\(415\) | −2.84427e14 | −1.13424 | ||||||||
\(416\) | −2.95888e14 | −1.16443 | ||||||||
\(417\) | −6.08005e11 | −0.00236134 | ||||||||
\(418\) | −1.98349e14 | −0.760257 | ||||||||
\(419\) | 2.34045e14 | 0.885366 | 0.442683 | − | 0.896678i | \(-0.354027\pi\) | ||||
0.442683 | + | 0.896678i | \(0.354027\pi\) | |||||||
\(420\) | 1.65927e13 | 0.0619506 | ||||||||
\(421\) | −4.46364e14 | −1.64489 | −0.822447 | − | 0.568842i | \(-0.807392\pi\) | ||||
−0.822447 | + | 0.568842i | \(0.807392\pi\) | |||||||
\(422\) | 1.57781e14 | 0.573901 | ||||||||
\(423\) | −7.83199e13 | −0.281190 | ||||||||
\(424\) | −1.02760e14 | −0.364176 | ||||||||
\(425\) | −4.99548e13 | −0.174759 | ||||||||
\(426\) | −8.82288e13 | −0.304690 | ||||||||
\(427\) | 1.24915e12 | 0.00425855 | ||||||||
\(428\) | 4.22421e14 | 1.42169 | ||||||||
\(429\) | 6.58232e14 | 2.18708 | ||||||||
\(430\) | 1.16514e14 | 0.382209 | ||||||||
\(431\) | −2.21713e14 | −0.718070 | −0.359035 | − | 0.933324i | \(-0.616894\pi\) | ||||
−0.359035 | + | 0.933324i | \(0.616894\pi\) | |||||||
\(432\) | 2.01483e14 | 0.644283 | ||||||||
\(433\) | 2.98167e14 | 0.941404 | 0.470702 | − | 0.882292i | \(-0.344001\pi\) | ||||
0.470702 | + | 0.882292i | \(0.344001\pi\) | |||||||
\(434\) | −1.67983e13 | −0.0523686 | ||||||||
\(435\) | 1.10916e14 | 0.341430 | ||||||||
\(436\) | 1.98753e14 | 0.604142 | ||||||||
\(437\) | 7.37464e13 | 0.221357 | ||||||||
\(438\) | −1.85806e14 | −0.550747 | ||||||||
\(439\) | 4.49628e14 | 1.31613 | 0.658064 | − | 0.752962i | \(-0.271375\pi\) | ||||
0.658064 | + | 0.752962i | \(0.271375\pi\) | |||||||
\(440\) | 4.31513e14 | 1.24740 | ||||||||
\(441\) | 6.63190e13 | 0.189333 | ||||||||
\(442\) | −2.36972e14 | −0.668151 | ||||||||
\(443\) | 3.08225e14 | 0.858316 | 0.429158 | − | 0.903230i | \(-0.358810\pi\) | ||||
0.429158 | + | 0.903230i | \(0.358810\pi\) | |||||||
\(444\) | −1.12441e14 | −0.309256 | ||||||||
\(445\) | −4.50053e13 | −0.122260 | ||||||||
\(446\) | 7.80242e13 | 0.209357 | ||||||||
\(447\) | −3.68640e14 | −0.977037 | ||||||||
\(448\) | 8.43841e12 | 0.0220918 | ||||||||
\(449\) | 1.43170e14 | 0.370253 | 0.185127 | − | 0.982715i | \(-0.440731\pi\) | ||||
0.185127 | + | 0.982715i | \(0.440731\pi\) | |||||||
\(450\) | 3.44694e12 | 0.00880571 | ||||||||
\(451\) | −1.47447e15 | −3.72106 | ||||||||
\(452\) | −1.59673e14 | −0.398081 | ||||||||
\(453\) | 3.03151e14 | 0.746653 | ||||||||
\(454\) | −2.68149e13 | −0.0652483 | ||||||||
\(455\) | −4.21715e13 | −0.101381 | ||||||||
\(456\) | −2.79240e14 | −0.663240 | ||||||||
\(457\) | 5.44489e14 | 1.27776 | 0.638881 | − | 0.769305i | \(-0.279398\pi\) | ||||
0.638881 | + | 0.769305i | \(0.279398\pi\) | |||||||
\(458\) | 7.77583e13 | 0.180296 | ||||||||
\(459\) | 6.60550e14 | 1.51334 | ||||||||
\(460\) | −7.42126e13 | −0.168000 | ||||||||
\(461\) | 8.11079e12 | 0.0181430 | 0.00907148 | − | 0.999959i | \(-0.497112\pi\) | ||||
0.00907148 | + | 0.999959i | \(0.497112\pi\) | |||||||
\(462\) | 2.49119e13 | 0.0550650 | ||||||||
\(463\) | 5.42140e14 | 1.18418 | 0.592088 | − | 0.805873i | \(-0.298304\pi\) | ||||
0.592088 | + | 0.805873i | \(0.298304\pi\) | |||||||
\(464\) | 1.12978e14 | 0.243862 | ||||||||
\(465\) | 6.48067e14 | 1.38238 | ||||||||
\(466\) | 9.67734e12 | 0.0204002 | ||||||||
\(467\) | −2.62493e14 | −0.546859 | −0.273430 | − | 0.961892i | \(-0.588158\pi\) | ||||
−0.273430 | + | 0.961892i | \(0.588158\pi\) | |||||||
\(468\) | −1.01021e14 | −0.207999 | ||||||||
\(469\) | −2.19496e13 | −0.0446658 | ||||||||
\(470\) | −2.56123e14 | −0.515122 | ||||||||
\(471\) | 2.83922e14 | 0.564396 | ||||||||
\(472\) | −3.17501e14 | −0.623826 | ||||||||
\(473\) | −1.08076e15 | −2.09890 | ||||||||
\(474\) | 1.99026e12 | 0.00382057 | ||||||||
\(475\) | 6.92044e13 | 0.131316 | ||||||||
\(476\) | 5.54097e13 | 0.103932 | ||||||||
\(477\) | −5.39393e13 | −0.100013 | ||||||||
\(478\) | −7.83998e13 | −0.143702 | ||||||||
\(479\) | −2.72054e14 | −0.492958 | −0.246479 | − | 0.969148i | \(-0.579274\pi\) | ||||
−0.246479 | + | 0.969148i | \(0.579274\pi\) | |||||||
\(480\) | 4.32027e14 | 0.773899 | ||||||||
\(481\) | 2.85777e14 | 0.506091 | ||||||||
\(482\) | 3.54854e14 | 0.621286 | ||||||||
\(483\) | −9.26227e12 | −0.0160328 | ||||||||
\(484\) | −1.34856e15 | −2.30792 | ||||||||
\(485\) | −5.84066e14 | −0.988285 | ||||||||
\(486\) | −8.38567e13 | −0.140294 | ||||||||
\(487\) | 1.73949e14 | 0.287748 | 0.143874 | − | 0.989596i | \(-0.454044\pi\) | ||||
0.143874 | + | 0.989596i | \(0.454044\pi\) | |||||||
\(488\) | 2.11550e13 | 0.0346022 | ||||||||
\(489\) | 1.56051e14 | 0.252387 | ||||||||
\(490\) | 2.16877e14 | 0.346845 | ||||||||
\(491\) | 2.26324e14 | 0.357916 | 0.178958 | − | 0.983857i | \(-0.442727\pi\) | ||||
0.178958 | + | 0.983857i | \(0.442727\pi\) | |||||||
\(492\) | −9.60190e14 | −1.50158 | ||||||||
\(493\) | 3.70392e14 | 0.572800 | ||||||||
\(494\) | 3.28286e14 | 0.502059 | ||||||||
\(495\) | 2.26504e14 | 0.342569 | ||||||||
\(496\) | 6.60117e14 | 0.987351 | ||||||||
\(497\) | −5.24327e13 | −0.0775607 | ||||||||
\(498\) | −2.78087e14 | −0.406836 | ||||||||
\(499\) | −3.66205e14 | −0.529873 | −0.264936 | − | 0.964266i | \(-0.585351\pi\) | ||||
−0.264936 | + | 0.964266i | \(0.585351\pi\) | |||||||
\(500\) | −6.32642e14 | −0.905363 | ||||||||
\(501\) | 1.76265e14 | 0.249494 | ||||||||
\(502\) | −9.71958e13 | −0.136075 | ||||||||
\(503\) | −6.01196e14 | −0.832515 | −0.416257 | − | 0.909247i | \(-0.636659\pi\) | ||||
−0.416257 | + | 0.909247i | \(0.636659\pi\) | |||||||
\(504\) | −8.26549e12 | −0.0113214 | ||||||||
\(505\) | −7.84725e14 | −1.06320 | ||||||||
\(506\) | −1.11421e14 | −0.149328 | ||||||||
\(507\) | −4.10871e14 | −0.544705 | ||||||||
\(508\) | −8.38988e13 | −0.110029 | ||||||||
\(509\) | −8.42096e14 | −1.09248 | −0.546241 | − | 0.837628i | \(-0.683942\pi\) | ||||
−0.546241 | + | 0.837628i | \(0.683942\pi\) | |||||||
\(510\) | 3.46003e14 | 0.444062 | ||||||||
\(511\) | −1.10421e14 | −0.140196 | ||||||||
\(512\) | 7.72619e14 | 0.970466 | ||||||||
\(513\) | −9.15086e14 | −1.13715 | ||||||||
\(514\) | 2.92124e14 | 0.359145 | ||||||||
\(515\) | −3.93131e14 | −0.478187 | ||||||||
\(516\) | −7.03799e14 | −0.846985 | ||||||||
\(517\) | 2.37574e15 | 2.82880 | ||||||||
\(518\) | 1.08157e13 | 0.0127421 | ||||||||
\(519\) | 1.41432e14 | 0.164864 | ||||||||
\(520\) | −7.14195e14 | −0.823756 | ||||||||
\(521\) | 6.79230e14 | 0.775192 | 0.387596 | − | 0.921829i | \(-0.373306\pi\) | ||||
0.387596 | + | 0.921829i | \(0.373306\pi\) | |||||||
\(522\) | −2.55574e13 | −0.0288622 | ||||||||
\(523\) | −3.67670e14 | −0.410864 | −0.205432 | − | 0.978671i | \(-0.565860\pi\) | ||||
−0.205432 | + | 0.978671i | \(0.565860\pi\) | |||||||
\(524\) | 7.45134e13 | 0.0823972 | ||||||||
\(525\) | −8.69181e12 | −0.00951117 | ||||||||
\(526\) | 3.25932e14 | 0.352943 | ||||||||
\(527\) | 2.16416e15 | 2.31916 | ||||||||
\(528\) | −9.78955e14 | −1.03819 | ||||||||
\(529\) | 4.14265e13 | 0.0434783 | ||||||||
\(530\) | −1.76393e14 | −0.183216 | ||||||||
\(531\) | −1.66658e14 | −0.171320 | ||||||||
\(532\) | −7.67612e13 | −0.0780958 | ||||||||
\(533\) | 2.44039e15 | 2.45731 | ||||||||
\(534\) | −4.40022e13 | −0.0438528 | ||||||||
\(535\) | 1.56759e15 | 1.54627 | ||||||||
\(536\) | −3.71727e14 | −0.362925 | ||||||||
\(537\) | −4.35468e14 | −0.420821 | ||||||||
\(538\) | −3.55230e14 | −0.339788 | ||||||||
\(539\) | −2.01171e15 | −1.90470 | ||||||||
\(540\) | 9.20870e14 | 0.863044 | ||||||||
\(541\) | −1.69417e15 | −1.57171 | −0.785855 | − | 0.618411i | \(-0.787777\pi\) | ||||
−0.785855 | + | 0.618411i | \(0.787777\pi\) | |||||||
\(542\) | 4.12253e14 | 0.378589 | ||||||||
\(543\) | 3.56247e14 | 0.323856 | ||||||||
\(544\) | 1.44271e15 | 1.29833 | ||||||||
\(545\) | 7.37565e14 | 0.657082 | ||||||||
\(546\) | −4.12315e13 | −0.0363639 | ||||||||
\(547\) | −5.60422e14 | −0.489311 | −0.244655 | − | 0.969610i | \(-0.578675\pi\) | ||||
−0.244655 | + | 0.969610i | \(0.578675\pi\) | |||||||
\(548\) | 3.99494e14 | 0.345316 | ||||||||
\(549\) | 1.11044e13 | 0.00950271 | ||||||||
\(550\) | −1.04559e14 | −0.0885861 | ||||||||
\(551\) | −5.13118e14 | −0.430411 | ||||||||
\(552\) | −1.56861e14 | −0.130272 | ||||||||
\(553\) | 1.18277e12 | 0.000972551 0 | ||||||||
\(554\) | 2.85282e14 | 0.232258 | ||||||||
\(555\) | −4.17263e14 | −0.336355 | ||||||||
\(556\) | −2.83054e12 | −0.00225921 | ||||||||
\(557\) | 6.65773e13 | 0.0526166 | 0.0263083 | − | 0.999654i | \(-0.491625\pi\) | ||||
0.0263083 | + | 0.999654i | \(0.491625\pi\) | |||||||
\(558\) | −1.49329e14 | −0.116858 | ||||||||
\(559\) | 1.78876e15 | 1.38607 | ||||||||
\(560\) | 6.27195e13 | 0.0481248 | ||||||||
\(561\) | −3.20945e15 | −2.43857 | ||||||||
\(562\) | 2.47811e14 | 0.186453 | ||||||||
\(563\) | 2.54438e15 | 1.89577 | 0.947887 | − | 0.318607i | \(-0.103215\pi\) | ||||
0.947887 | + | 0.318607i | \(0.103215\pi\) | |||||||
\(564\) | 1.54710e15 | 1.14152 | ||||||||
\(565\) | −5.92541e14 | −0.432964 | ||||||||
\(566\) | 3.94813e14 | 0.285694 | ||||||||
\(567\) | 9.21835e13 | 0.0660612 | ||||||||
\(568\) | −8.87972e14 | −0.630208 | ||||||||
\(569\) | −5.21696e13 | −0.0366691 | −0.0183346 | − | 0.999832i | \(-0.505836\pi\) | ||||
−0.0183346 | + | 0.999832i | \(0.505836\pi\) | |||||||
\(570\) | −4.79331e14 | −0.333675 | ||||||||
\(571\) | −2.79494e15 | −1.92696 | −0.963482 | − | 0.267773i | \(-0.913712\pi\) | ||||
−0.963482 | + | 0.267773i | \(0.913712\pi\) | |||||||
\(572\) | 3.06437e15 | 2.09249 | ||||||||
\(573\) | 1.63696e15 | 1.10711 | ||||||||
\(574\) | 9.23608e13 | 0.0618689 | ||||||||
\(575\) | 3.88751e13 | 0.0257928 | ||||||||
\(576\) | 7.50137e13 | 0.0492966 | ||||||||
\(577\) | 1.97977e15 | 1.28869 | 0.644344 | − | 0.764736i | \(-0.277130\pi\) | ||||
0.644344 | + | 0.764736i | \(0.277130\pi\) | |||||||
\(578\) | 5.76554e14 | 0.371738 | ||||||||
\(579\) | −1.34798e15 | −0.860896 | ||||||||
\(580\) | 5.16361e14 | 0.326663 | ||||||||
\(581\) | −1.65262e14 | −0.103563 | ||||||||
\(582\) | −5.71048e14 | −0.354483 | ||||||||
\(583\) | 1.63619e15 | 1.00613 | ||||||||
\(584\) | −1.87003e15 | −1.13914 | ||||||||
\(585\) | −3.74886e14 | −0.226226 | ||||||||
\(586\) | 6.63233e14 | 0.396487 | ||||||||
\(587\) | −1.11113e15 | −0.658047 | −0.329024 | − | 0.944322i | \(-0.606720\pi\) | ||||
−0.329024 | + | 0.944322i | \(0.606720\pi\) | |||||||
\(588\) | −1.31004e15 | −0.768616 | ||||||||
\(589\) | −2.99809e15 | −1.74265 | ||||||||
\(590\) | −5.45008e14 | −0.313846 | ||||||||
\(591\) | 7.61986e14 | 0.434726 | ||||||||
\(592\) | −4.25021e14 | −0.240238 | ||||||||
\(593\) | 1.47414e15 | 0.825537 | 0.412768 | − | 0.910836i | \(-0.364562\pi\) | ||||
0.412768 | + | 0.910836i | \(0.364562\pi\) | |||||||
\(594\) | 1.38258e15 | 0.767120 | ||||||||
\(595\) | 2.05623e14 | 0.113039 | ||||||||
\(596\) | −1.71618e15 | −0.934780 | ||||||||
\(597\) | 2.37307e15 | 1.28071 | ||||||||
\(598\) | 1.84413e14 | 0.0986129 | ||||||||
\(599\) | −3.73330e15 | −1.97809 | −0.989044 | − | 0.147624i | \(-0.952837\pi\) | ||||
−0.989044 | + | 0.147624i | \(0.952837\pi\) | |||||||
\(600\) | −1.47200e14 | −0.0772816 | ||||||||
\(601\) | −7.03077e13 | −0.0365757 | −0.0182879 | − | 0.999833i | \(-0.505822\pi\) | ||||
−0.0182879 | + | 0.999833i | \(0.505822\pi\) | |||||||
\(602\) | 6.76985e13 | 0.0348978 | ||||||||
\(603\) | −1.95122e14 | −0.0996691 | ||||||||
\(604\) | 1.41130e15 | 0.714360 | ||||||||
\(605\) | −5.00444e15 | −2.51016 | ||||||||
\(606\) | −7.67234e14 | −0.381354 | ||||||||
\(607\) | 2.40417e15 | 1.18420 | 0.592102 | − | 0.805863i | \(-0.298298\pi\) | ||||
0.592102 | + | 0.805863i | \(0.298298\pi\) | |||||||
\(608\) | −1.99865e15 | −0.975588 | ||||||||
\(609\) | 6.44457e13 | 0.0311745 | ||||||||
\(610\) | 3.63138e13 | 0.0174083 | ||||||||
\(611\) | −3.93208e15 | −1.86808 | ||||||||
\(612\) | 4.92567e14 | 0.231917 | ||||||||
\(613\) | 9.54801e14 | 0.445533 | 0.222767 | − | 0.974872i | \(-0.428491\pi\) | ||||
0.222767 | + | 0.974872i | \(0.428491\pi\) | |||||||
\(614\) | −7.73985e14 | −0.357937 | ||||||||
\(615\) | −3.56322e15 | −1.63316 | ||||||||
\(616\) | 2.50724e14 | 0.113894 | ||||||||
\(617\) | −8.16920e14 | −0.367800 | −0.183900 | − | 0.982945i | \(-0.558872\pi\) | ||||
−0.183900 | + | 0.982945i | \(0.558872\pi\) | |||||||
\(618\) | −3.84369e14 | −0.171519 | ||||||||
\(619\) | 3.03728e15 | 1.34334 | 0.671672 | − | 0.740849i | \(-0.265577\pi\) | ||||
0.671672 | + | 0.740849i | \(0.265577\pi\) | |||||||
\(620\) | 3.01704e15 | 1.32260 | ||||||||
\(621\) | −5.14043e14 | −0.223355 | ||||||||
\(622\) | −9.93592e14 | −0.427919 | ||||||||
\(623\) | −2.61496e13 | −0.0111630 | ||||||||
\(624\) | 1.62026e15 | 0.685599 | ||||||||
\(625\) | −2.05279e15 | −0.861001 | ||||||||
\(626\) | 5.46493e14 | 0.227209 | ||||||||
\(627\) | 4.44618e15 | 1.83238 | ||||||||
\(628\) | 1.32178e15 | 0.539986 | ||||||||
\(629\) | −1.39341e15 | −0.564287 | ||||||||
\(630\) | −1.41882e13 | −0.00569579 | ||||||||
\(631\) | −2.90418e15 | −1.15575 | −0.577873 | − | 0.816127i | \(-0.696117\pi\) | ||||
−0.577873 | + | 0.816127i | \(0.696117\pi\) | |||||||
\(632\) | 2.00308e13 | 0.00790232 | ||||||||
\(633\) | −3.53682e15 | −1.38322 | ||||||||
\(634\) | −1.23518e15 | −0.478893 | ||||||||
\(635\) | −3.11345e14 | −0.119670 | ||||||||
\(636\) | 1.06550e15 | 0.406012 | ||||||||
\(637\) | 3.32957e15 | 1.25783 | ||||||||
\(638\) | 7.75254e14 | 0.290356 | ||||||||
\(639\) | −4.66103e14 | −0.173072 | ||||||||
\(640\) | 2.58214e15 | 0.950582 | ||||||||
\(641\) | 1.07107e15 | 0.390931 | 0.195466 | − | 0.980711i | \(-0.437378\pi\) | ||||
0.195466 | + | 0.980711i | \(0.437378\pi\) | |||||||
\(642\) | 1.53265e15 | 0.554625 | ||||||||
\(643\) | −3.09817e14 | −0.111159 | −0.0555795 | − | 0.998454i | \(-0.517701\pi\) | ||||
−0.0555795 | + | 0.998454i | \(0.517701\pi\) | |||||||
\(644\) | −4.31200e13 | −0.0153393 | ||||||||
\(645\) | −2.61177e15 | −0.921205 | ||||||||
\(646\) | −1.60068e15 | −0.559791 | ||||||||
\(647\) | 1.64231e15 | 0.569485 | 0.284743 | − | 0.958604i | \(-0.408092\pi\) | ||||
0.284743 | + | 0.958604i | \(0.408092\pi\) | |||||||
\(648\) | 1.56117e15 | 0.536770 | ||||||||
\(649\) | 5.05538e15 | 1.72349 | ||||||||
\(650\) | 1.73055e14 | 0.0585005 | ||||||||
\(651\) | 3.76549e14 | 0.126219 | ||||||||
\(652\) | 7.26486e14 | 0.241471 | ||||||||
\(653\) | −2.52493e14 | −0.0832198 | −0.0416099 | − | 0.999134i | \(-0.513249\pi\) | ||||
−0.0416099 | + | 0.999134i | \(0.513249\pi\) | |||||||
\(654\) | 7.21125e14 | 0.235686 | ||||||||
\(655\) | 2.76516e14 | 0.0896176 | ||||||||
\(656\) | −3.62947e15 | −1.16647 | ||||||||
\(657\) | −9.81592e14 | −0.312839 | ||||||||
\(658\) | −1.48816e14 | −0.0470335 | ||||||||
\(659\) | 3.85339e15 | 1.20774 | 0.603869 | − | 0.797084i | \(-0.293625\pi\) | ||||
0.603869 | + | 0.797084i | \(0.293625\pi\) | |||||||
\(660\) | −4.47429e15 | −1.39070 | ||||||||
\(661\) | 5.10081e15 | 1.57228 | 0.786142 | − | 0.618045i | \(-0.212075\pi\) | ||||
0.786142 | + | 0.618045i | \(0.212075\pi\) | |||||||
\(662\) | 4.96389e14 | 0.151741 | ||||||||
\(663\) | 5.31195e15 | 1.61038 | ||||||||
\(664\) | −2.79879e15 | −0.841483 | ||||||||
\(665\) | −2.84857e14 | −0.0849392 | ||||||||
\(666\) | 9.61467e13 | 0.0284332 | ||||||||
\(667\) | −2.88240e14 | −0.0845401 | ||||||||
\(668\) | 8.20594e14 | 0.238703 | ||||||||
\(669\) | −1.74899e15 | −0.504595 | ||||||||
\(670\) | −6.38090e14 | −0.182587 | ||||||||
\(671\) | −3.36839e14 | −0.0955980 | ||||||||
\(672\) | 2.51023e14 | 0.0706613 | ||||||||
\(673\) | 2.75725e15 | 0.769827 | 0.384914 | − | 0.922953i | \(-0.374231\pi\) | ||||
0.384914 | + | 0.922953i | \(0.374231\pi\) | |||||||
\(674\) | 1.73174e14 | 0.0479570 | ||||||||
\(675\) | −4.82383e14 | −0.132502 | ||||||||
\(676\) | −1.91279e15 | −0.521147 | ||||||||
\(677\) | −1.16755e15 | −0.315528 | −0.157764 | − | 0.987477i | \(-0.550428\pi\) | ||||
−0.157764 | + | 0.987477i | \(0.550428\pi\) | |||||||
\(678\) | −5.79333e14 | −0.155298 | ||||||||
\(679\) | −3.39362e14 | −0.0902360 | ||||||||
\(680\) | 3.48232e15 | 0.918481 | ||||||||
\(681\) | 6.01082e14 | 0.157262 | ||||||||
\(682\) | 4.52973e15 | 1.17560 | ||||||||
\(683\) | 1.19784e15 | 0.308380 | 0.154190 | − | 0.988041i | \(-0.450723\pi\) | ||||
0.154190 | + | 0.988041i | \(0.450723\pi\) | |||||||
\(684\) | −6.82372e14 | −0.174266 | ||||||||
\(685\) | 1.48250e15 | 0.375576 | ||||||||
\(686\) | 2.52953e14 | 0.0635708 | ||||||||
\(687\) | −1.74303e15 | −0.434552 | ||||||||
\(688\) | −2.66033e15 | −0.657959 | ||||||||
\(689\) | −2.70804e15 | −0.664431 | ||||||||
\(690\) | −2.69261e14 | −0.0655396 | ||||||||
\(691\) | −4.05987e15 | −0.980354 | −0.490177 | − | 0.871623i | \(-0.663068\pi\) | ||||
−0.490177 | + | 0.871623i | \(0.663068\pi\) | |||||||
\(692\) | 6.58428e14 | 0.157734 | ||||||||
\(693\) | 1.31607e14 | 0.0312785 | ||||||||
\(694\) | 2.03016e15 | 0.478690 | ||||||||
\(695\) | −1.05040e13 | −0.00245719 | ||||||||
\(696\) | 1.09142e15 | 0.253303 | ||||||||
\(697\) | −1.18990e16 | −2.73988 | ||||||||
\(698\) | −2.09807e15 | −0.479308 | ||||||||
\(699\) | −2.16927e14 | −0.0491687 | ||||||||
\(700\) | −4.04643e13 | −0.00909982 | ||||||||
\(701\) | −2.71723e14 | −0.0606285 | −0.0303142 | − | 0.999540i | \(-0.509651\pi\) | ||||
−0.0303142 | + | 0.999540i | \(0.509651\pi\) | |||||||
\(702\) | −2.28829e15 | −0.506591 | ||||||||
\(703\) | 1.93034e15 | 0.424014 | ||||||||
\(704\) | −2.27545e15 | −0.495928 | ||||||||
\(705\) | 5.74124e15 | 1.24155 | ||||||||
\(706\) | 1.01516e15 | 0.217825 | ||||||||
\(707\) | −4.55952e14 | −0.0970761 | ||||||||
\(708\) | 3.29211e15 | 0.695491 | ||||||||
\(709\) | 7.65619e15 | 1.60494 | 0.802469 | − | 0.596694i | \(-0.203519\pi\) | ||||
0.802469 | + | 0.596694i | \(0.203519\pi\) | |||||||
\(710\) | −1.52426e15 | −0.317057 | ||||||||
\(711\) | 1.05143e13 | 0.00217019 | ||||||||
\(712\) | −4.42856e14 | −0.0907033 | ||||||||
\(713\) | −1.68416e15 | −0.342287 | ||||||||
\(714\) | 2.01040e14 | 0.0405454 | ||||||||
\(715\) | 1.13717e16 | 2.27585 | ||||||||
\(716\) | −2.02730e15 | −0.402620 | ||||||||
\(717\) | 1.75741e15 | 0.346351 | ||||||||
\(718\) | 1.51084e15 | 0.295483 | ||||||||
\(719\) | −7.64440e14 | −0.148366 | −0.0741830 | − | 0.997245i | \(-0.523635\pi\) | ||||
−0.0741830 | + | 0.997245i | \(0.523635\pi\) | |||||||
\(720\) | 5.57549e14 | 0.107388 | ||||||||
\(721\) | −2.28423e14 | −0.0436612 | ||||||||
\(722\) | 2.49838e14 | 0.0473919 | ||||||||
\(723\) | −7.95439e15 | −1.49743 | ||||||||
\(724\) | 1.65849e15 | 0.309849 | ||||||||
\(725\) | −2.70488e14 | −0.0501520 | ||||||||
\(726\) | −4.89290e15 | −0.900357 | ||||||||
\(727\) | 5.88535e15 | 1.07481 | 0.537406 | − | 0.843324i | \(-0.319404\pi\) | ||||
0.537406 | + | 0.843324i | \(0.319404\pi\) | |||||||
\(728\) | −4.14972e14 | −0.0752135 | ||||||||
\(729\) | 6.17631e15 | 1.11104 | ||||||||
\(730\) | −3.21001e15 | −0.573101 | ||||||||
\(731\) | −8.72175e15 | −1.54546 | ||||||||
\(732\) | −2.19353e14 | −0.0385773 | ||||||||
\(733\) | −8.92879e15 | −1.55855 | −0.779275 | − | 0.626682i | \(-0.784413\pi\) | ||||
−0.779275 | + | 0.626682i | \(0.784413\pi\) | |||||||
\(734\) | −3.33458e15 | −0.577714 | ||||||||
\(735\) | −4.86151e15 | −0.835969 | ||||||||
\(736\) | −1.12273e15 | −0.191622 | ||||||||
\(737\) | 5.91879e15 | 1.00268 | ||||||||
\(738\) | 8.21046e14 | 0.138057 | ||||||||
\(739\) | 8.63680e15 | 1.44148 | 0.720739 | − | 0.693206i | \(-0.243802\pi\) | ||||
0.720739 | + | 0.693206i | \(0.243802\pi\) | |||||||
\(740\) | −1.94255e15 | −0.321808 | ||||||||
\(741\) | −7.35885e15 | −1.21007 | ||||||||
\(742\) | −1.02490e14 | −0.0167287 | ||||||||
\(743\) | 6.31103e15 | 1.02250 | 0.511248 | − | 0.859433i | \(-0.329183\pi\) | ||||
0.511248 | + | 0.859433i | \(0.329183\pi\) | |||||||
\(744\) | 6.37705e15 | 1.02558 | ||||||||
\(745\) | −6.36868e15 | −1.01669 | ||||||||
\(746\) | −3.55631e14 | −0.0563554 | ||||||||
\(747\) | −1.46910e15 | −0.231094 | ||||||||
\(748\) | −1.49414e16 | −2.33310 | ||||||||
\(749\) | 9.10822e14 | 0.141183 | ||||||||
\(750\) | −2.29538e15 | −0.353197 | ||||||||
\(751\) | −6.31269e15 | −0.964261 | −0.482131 | − | 0.876099i | \(-0.660137\pi\) | ||||
−0.482131 | + | 0.876099i | \(0.660137\pi\) | |||||||
\(752\) | 5.84798e15 | 0.886763 | ||||||||
\(753\) | 2.17874e15 | 0.327968 | ||||||||
\(754\) | −1.28312e15 | −0.191745 | ||||||||
\(755\) | 5.23729e15 | 0.776959 | ||||||||
\(756\) | 5.35057e14 | 0.0788008 | ||||||||
\(757\) | −8.86188e15 | −1.29568 | −0.647841 | − | 0.761775i | \(-0.724328\pi\) | ||||
−0.647841 | + | 0.761775i | \(0.724328\pi\) | |||||||
\(758\) | 1.55416e15 | 0.225587 | ||||||||
\(759\) | 2.49761e15 | 0.359911 | ||||||||
\(760\) | −4.82420e15 | −0.690161 | ||||||||
\(761\) | 1.22632e15 | 0.174176 | 0.0870879 | − | 0.996201i | \(-0.472244\pi\) | ||||
0.0870879 | + | 0.996201i | \(0.472244\pi\) | |||||||
\(762\) | −3.04405e14 | −0.0429239 | ||||||||
\(763\) | 4.28551e14 | 0.0599953 | ||||||||
\(764\) | 7.62081e15 | 1.05922 | ||||||||
\(765\) | 1.82790e15 | 0.252240 | ||||||||
\(766\) | 4.71071e15 | 0.645398 | ||||||||
\(767\) | −8.36714e15 | −1.13816 | ||||||||
\(768\) | 8.02946e14 | 0.108442 | ||||||||
\(769\) | −8.27966e15 | −1.11024 | −0.555121 | − | 0.831770i | \(-0.687328\pi\) | ||||
−0.555121 | + | 0.831770i | \(0.687328\pi\) | |||||||
\(770\) | 4.30382e14 | 0.0573001 | ||||||||
\(771\) | −6.54823e15 | −0.865616 | ||||||||
\(772\) | −6.27544e15 | −0.823663 | ||||||||
\(773\) | −6.44373e15 | −0.839750 | −0.419875 | − | 0.907582i | \(-0.637926\pi\) | ||||
−0.419875 | + | 0.907582i | \(0.637926\pi\) | |||||||
\(774\) | 6.01810e14 | 0.0778725 | ||||||||
\(775\) | −1.58043e15 | −0.203056 | ||||||||
\(776\) | −5.74727e15 | −0.733199 | ||||||||
\(777\) | −2.42444e14 | −0.0307111 | ||||||||
\(778\) | −1.21992e15 | −0.153442 | ||||||||
\(779\) | 1.64842e16 | 2.05879 | ||||||||
\(780\) | 7.40536e15 | 0.918388 | ||||||||
\(781\) | 1.41387e16 | 1.74112 | ||||||||
\(782\) | −8.99171e14 | −0.109953 | ||||||||
\(783\) | 3.57665e15 | 0.434296 | ||||||||
\(784\) | −4.95189e15 | −0.597081 | ||||||||
\(785\) | 4.90508e15 | 0.587304 | ||||||||
\(786\) | 2.70353e14 | 0.0321445 | ||||||||
\(787\) | 2.25581e15 | 0.266343 | 0.133171 | − | 0.991093i | \(-0.457484\pi\) | ||||
0.133171 | + | 0.991093i | \(0.457484\pi\) | |||||||
\(788\) | 3.54739e15 | 0.415924 | ||||||||
\(789\) | −7.30607e15 | −0.850668 | ||||||||
\(790\) | 3.43840e13 | 0.00397564 | ||||||||
\(791\) | −3.44286e14 | −0.0395320 | ||||||||
\(792\) | 2.22882e15 | 0.254148 | ||||||||
\(793\) | 5.57501e14 | 0.0631310 | ||||||||
\(794\) | 3.82919e15 | 0.430620 | ||||||||
\(795\) | 3.95402e15 | 0.441590 | ||||||||
\(796\) | 1.10477e16 | 1.22532 | ||||||||
\(797\) | 6.89086e15 | 0.759019 | 0.379509 | − | 0.925188i | \(-0.376093\pi\) | ||||
0.379509 | + | 0.925188i | \(0.376093\pi\) | |||||||
\(798\) | −2.78508e14 | −0.0304664 | ||||||||
\(799\) | 1.91723e16 | 2.08289 | ||||||||
\(800\) | −1.05358e15 | −0.113677 | ||||||||
\(801\) | −2.32458e14 | −0.0249096 | ||||||||
\(802\) | 1.35163e14 | 0.0143846 | ||||||||
\(803\) | 2.97754e16 | 3.14719 | ||||||||
\(804\) | 3.85437e15 | 0.404618 | ||||||||
\(805\) | −1.60017e14 | −0.0166835 | ||||||||
\(806\) | −7.49712e15 | −0.776340 | ||||||||
\(807\) | 7.96282e15 | 0.818960 | ||||||||
\(808\) | −7.72177e15 | −0.788778 | ||||||||
\(809\) | −1.48659e16 | −1.50825 | −0.754127 | − | 0.656729i | \(-0.771940\pi\) | ||||
−0.754127 | + | 0.656729i | \(0.771940\pi\) | |||||||
\(810\) | 2.67984e15 | 0.270048 | ||||||||
\(811\) | −1.88038e15 | −0.188205 | −0.0941026 | − | 0.995563i | \(-0.529998\pi\) | ||||
−0.0941026 | + | 0.995563i | \(0.529998\pi\) | |||||||
\(812\) | 3.00024e14 | 0.0298262 | ||||||||
\(813\) | −9.24104e15 | −0.912479 | ||||||||
\(814\) | −2.91650e15 | −0.286040 | ||||||||
\(815\) | 2.69596e15 | 0.262631 | ||||||||
\(816\) | −7.90019e15 | −0.764437 | ||||||||
\(817\) | 1.20826e16 | 1.16128 | ||||||||
\(818\) | 4.02468e15 | 0.384228 | ||||||||
\(819\) | −2.17822e14 | −0.0206557 | ||||||||
\(820\) | −1.65884e16 | −1.56253 | ||||||||
\(821\) | −1.83324e16 | −1.71526 | −0.857632 | − | 0.514263i | \(-0.828065\pi\) | ||||
−0.857632 | + | 0.514263i | \(0.828065\pi\) | |||||||
\(822\) | 1.44946e15 | 0.134714 | ||||||||
\(823\) | 6.27295e15 | 0.579126 | 0.289563 | − | 0.957159i | \(-0.406490\pi\) | ||||
0.289563 | + | 0.957159i | \(0.406490\pi\) | |||||||
\(824\) | −3.86845e15 | −0.354762 | ||||||||
\(825\) | 2.34378e15 | 0.213511 | ||||||||
\(826\) | −3.16668e14 | −0.0286559 | ||||||||
\(827\) | 1.64096e14 | 0.0147509 | 0.00737545 | − | 0.999973i | \(-0.497652\pi\) | ||||
0.00737545 | + | 0.999973i | \(0.497652\pi\) | |||||||
\(828\) | −3.83318e14 | −0.0342288 | ||||||||
\(829\) | −7.03744e15 | −0.624259 | −0.312130 | − | 0.950040i | \(-0.601042\pi\) | ||||
−0.312130 | + | 0.950040i | \(0.601042\pi\) | |||||||
\(830\) | −4.80427e15 | −0.423349 | ||||||||
\(831\) | −6.39487e15 | −0.559791 | ||||||||
\(832\) | 3.76609e15 | 0.327501 | ||||||||
\(833\) | −1.62345e16 | −1.40247 | ||||||||
\(834\) | −1.02699e13 | −0.000881356 0 | ||||||||
\(835\) | 3.04519e15 | 0.259620 | ||||||||
\(836\) | 2.06990e16 | 1.75313 | ||||||||
\(837\) | 2.08980e16 | 1.75838 | ||||||||
\(838\) | 3.95328e15 | 0.330457 | ||||||||
\(839\) | 2.24738e16 | 1.86632 | 0.933160 | − | 0.359461i | \(-0.117039\pi\) | ||||
0.933160 | + | 0.359461i | \(0.117039\pi\) | |||||||
\(840\) | 6.05901e14 | 0.0499880 | ||||||||
\(841\) | −1.01950e16 | −0.835618 | ||||||||
\(842\) | −7.53958e15 | −0.613947 | ||||||||
\(843\) | −5.55491e15 | −0.449392 | ||||||||
\(844\) | −1.64655e16 | −1.32340 | ||||||||
\(845\) | −7.09827e15 | −0.566814 | ||||||||
\(846\) | −1.32291e15 | −0.104953 | ||||||||
\(847\) | −2.90775e15 | −0.229192 | ||||||||
\(848\) | 4.02753e15 | 0.315400 | ||||||||
\(849\) | −8.85012e15 | −0.688584 | ||||||||
\(850\) | −8.43792e14 | −0.0652276 | ||||||||
\(851\) | 1.08436e15 | 0.0832837 | ||||||||
\(852\) | 9.20723e15 | 0.702605 | ||||||||
\(853\) | −2.39348e16 | −1.81472 | −0.907360 | − | 0.420355i | \(-0.861906\pi\) | ||||
−0.907360 | + | 0.420355i | \(0.861906\pi\) | |||||||
\(854\) | 2.10995e13 | 0.00158948 | ||||||||
\(855\) | −2.53225e15 | −0.189537 | ||||||||
\(856\) | 1.54252e16 | 1.14716 | ||||||||
\(857\) | −8.96955e15 | −0.662790 | −0.331395 | − | 0.943492i | \(-0.607519\pi\) | ||||
−0.331395 | + | 0.943492i | \(0.607519\pi\) | |||||||
\(858\) | 1.11183e16 | 0.816313 | ||||||||
\(859\) | −1.70389e16 | −1.24303 | −0.621513 | − | 0.783404i | \(-0.713482\pi\) | ||||
−0.621513 | + | 0.783404i | \(0.713482\pi\) | |||||||
\(860\) | −1.21590e16 | −0.881363 | ||||||||
\(861\) | −2.07035e15 | −0.149117 | ||||||||
\(862\) | −3.74498e15 | −0.268015 | ||||||||
\(863\) | 1.39607e16 | 0.992767 | 0.496383 | − | 0.868103i | \(-0.334661\pi\) | ||||
0.496383 | + | 0.868103i | \(0.334661\pi\) | |||||||
\(864\) | 1.39314e16 | 0.984395 | ||||||||
\(865\) | 2.44340e15 | 0.171556 | ||||||||
\(866\) | 5.03637e15 | 0.351373 | ||||||||
\(867\) | −1.29240e16 | −0.895968 | ||||||||
\(868\) | 1.75301e15 | 0.120760 | ||||||||
\(869\) | −3.18939e14 | −0.0218323 | ||||||||
\(870\) | 1.87348e15 | 0.127437 | ||||||||
\(871\) | −9.79616e15 | −0.662149 | ||||||||
\(872\) | 7.25771e15 | 0.487483 | ||||||||
\(873\) | −3.01678e15 | −0.201356 | ||||||||
\(874\) | 1.24566e15 | 0.0826201 | ||||||||
\(875\) | −1.36410e15 | −0.0899085 | ||||||||
\(876\) | 1.93900e16 | 1.27001 | ||||||||
\(877\) | 2.17535e15 | 0.141589 | 0.0707947 | − | 0.997491i | \(-0.477446\pi\) | ||||
0.0707947 | + | 0.997491i | \(0.477446\pi\) | |||||||
\(878\) | 7.59471e15 | 0.491237 | ||||||||
\(879\) | −1.48670e16 | −0.955618 | ||||||||
\(880\) | −1.69126e16 | −1.08033 | ||||||||
\(881\) | −1.14121e15 | −0.0724431 | −0.0362215 | − | 0.999344i | \(-0.511532\pi\) | ||||
−0.0362215 | + | 0.999344i | \(0.511532\pi\) | |||||||
\(882\) | 1.12020e15 | 0.0706672 | ||||||||
\(883\) | −2.62009e16 | −1.64260 | −0.821302 | − | 0.570494i | \(-0.806752\pi\) | ||||
−0.821302 | + | 0.570494i | \(0.806752\pi\) | |||||||
\(884\) | 2.47295e16 | 1.54073 | ||||||||
\(885\) | 1.22169e16 | 0.756436 | ||||||||
\(886\) | 5.20625e15 | 0.320361 | ||||||||
\(887\) | −4.67640e15 | −0.285977 | −0.142989 | − | 0.989724i | \(-0.545671\pi\) | ||||
−0.142989 | + | 0.989724i | \(0.545671\pi\) | |||||||
\(888\) | −4.10591e15 | −0.249539 | ||||||||
\(889\) | −1.80902e14 | −0.0109266 | ||||||||
\(890\) | −7.60188e14 | −0.0456327 | ||||||||
\(891\) | −2.48577e16 | −1.48297 | ||||||||
\(892\) | −8.14232e15 | −0.482771 | ||||||||
\(893\) | −2.65601e16 | −1.56512 | ||||||||
\(894\) | −6.22673e15 | −0.364673 | ||||||||
\(895\) | −7.52321e15 | −0.437901 | ||||||||
\(896\) | 1.50031e15 | 0.0867934 | ||||||||
\(897\) | −4.13378e15 | −0.237678 | ||||||||
\(898\) | 2.41831e15 | 0.138195 | ||||||||
\(899\) | 1.17181e16 | 0.665550 | ||||||||
\(900\) | −3.59709e14 | −0.0203057 | ||||||||
\(901\) | 1.32041e16 | 0.740834 | ||||||||
\(902\) | −2.49055e16 | −1.38886 | ||||||||
\(903\) | −1.51753e15 | −0.0841112 | ||||||||
\(904\) | −5.83066e15 | −0.321212 | ||||||||
\(905\) | 6.15458e15 | 0.337001 | ||||||||
\(906\) | 5.12055e15 | 0.278684 | ||||||||
\(907\) | −9.99364e15 | −0.540610 | −0.270305 | − | 0.962775i | \(-0.587124\pi\) | ||||
−0.270305 | + | 0.962775i | \(0.587124\pi\) | |||||||
\(908\) | 2.79831e15 | 0.150461 | ||||||||
\(909\) | −4.05321e15 | −0.216620 | ||||||||
\(910\) | −7.12323e14 | −0.0378398 | ||||||||
\(911\) | 1.46086e16 | 0.771363 | 0.385682 | − | 0.922632i | \(-0.373966\pi\) | ||||
0.385682 | + | 0.922632i | \(0.373966\pi\) | |||||||
\(912\) | 1.09444e16 | 0.574410 | ||||||||
\(913\) | 4.45635e16 | 2.32482 | ||||||||
\(914\) | 9.19701e15 | 0.476917 | ||||||||
\(915\) | −8.14008e14 | −0.0419578 | ||||||||
\(916\) | −8.11456e15 | −0.415758 | ||||||||
\(917\) | 1.60665e14 | 0.00818259 | ||||||||
\(918\) | 1.11574e16 | 0.564844 | ||||||||
\(919\) | −9.65126e15 | −0.485678 | −0.242839 | − | 0.970067i | \(-0.578079\pi\) | ||||
−0.242839 | + | 0.970067i | \(0.578079\pi\) | |||||||
\(920\) | −2.70996e15 | −0.135559 | ||||||||
\(921\) | 1.73496e16 | 0.862704 | ||||||||
\(922\) | 1.37000e14 | 0.00677175 | ||||||||
\(923\) | −2.34009e16 | −1.14980 | ||||||||
\(924\) | −2.59971e15 | −0.126978 | ||||||||
\(925\) | 1.01757e15 | 0.0494067 | ||||||||
\(926\) | 9.15734e15 | 0.441986 | ||||||||
\(927\) | −2.03058e15 | −0.0974274 | ||||||||
\(928\) | 7.81178e15 | 0.372594 | ||||||||
\(929\) | 3.11901e16 | 1.47887 | 0.739437 | − | 0.673226i | \(-0.235092\pi\) | ||||
0.739437 | + | 0.673226i | \(0.235092\pi\) | |||||||
\(930\) | 1.09466e16 | 0.515966 | ||||||||
\(931\) | 2.24903e16 | 1.05383 | ||||||||
\(932\) | −1.00989e15 | −0.0470422 | ||||||||
\(933\) | 2.22723e16 | 1.03137 | ||||||||
\(934\) | −4.43380e15 | −0.204112 | ||||||||
\(935\) | −5.54471e16 | −2.53755 | ||||||||
\(936\) | −3.68891e15 | −0.167835 | ||||||||
\(937\) | 1.81848e16 | 0.822509 | 0.411255 | − | 0.911521i | \(-0.365091\pi\) | ||||
0.411255 | + | 0.911521i | \(0.365091\pi\) | |||||||
\(938\) | −3.70752e14 | −0.0166712 | ||||||||
\(939\) | −1.22502e16 | −0.547622 | ||||||||
\(940\) | 2.67280e16 | 1.18786 | ||||||||
\(941\) | −2.76588e16 | −1.22205 | −0.611027 | − | 0.791610i | \(-0.709243\pi\) | ||||
−0.611027 | + | 0.791610i | \(0.709243\pi\) | |||||||
\(942\) | 4.79575e15 | 0.210657 | ||||||||
\(943\) | 9.25988e15 | 0.404381 | ||||||||
\(944\) | 1.24440e16 | 0.540275 | ||||||||
\(945\) | 1.98557e15 | 0.0857060 | ||||||||
\(946\) | −1.82552e16 | −0.783403 | ||||||||
\(947\) | 3.44283e16 | 1.46890 | 0.734448 | − | 0.678665i | \(-0.237441\pi\) | ||||
0.734448 | + | 0.678665i | \(0.237441\pi\) | |||||||
\(948\) | −2.07696e14 | −0.00881012 | ||||||||
\(949\) | −4.92812e16 | −2.07834 | ||||||||
\(950\) | 1.16894e15 | 0.0490130 | ||||||||
\(951\) | 2.76877e16 | 1.15423 | ||||||||
\(952\) | 2.02335e15 | 0.0838624 | ||||||||
\(953\) | 3.73682e16 | 1.53990 | 0.769948 | − | 0.638106i | \(-0.220282\pi\) | ||||
0.769948 | + | 0.638106i | \(0.220282\pi\) | |||||||
\(954\) | −9.11094e14 | −0.0373291 | ||||||||
\(955\) | 2.82805e16 | 1.15204 | ||||||||
\(956\) | 8.18152e15 | 0.331372 | ||||||||
\(957\) | −1.73781e16 | −0.699819 | ||||||||
\(958\) | −4.59529e15 | −0.183993 | ||||||||
\(959\) | 8.61386e14 | 0.0342922 | ||||||||
\(960\) | −5.49887e15 | −0.217662 | ||||||||
\(961\) | 4.30594e16 | 1.69469 | ||||||||
\(962\) | 4.82708e15 | 0.188895 | ||||||||
\(963\) | 8.09680e15 | 0.315042 | ||||||||
\(964\) | −3.70313e16 | −1.43267 | ||||||||
\(965\) | −2.32879e16 | −0.895839 | ||||||||
\(966\) | −1.56450e14 | −0.00598413 | ||||||||
\(967\) | 1.55579e16 | 0.591706 | 0.295853 | − | 0.955233i | \(-0.404396\pi\) | ||||
0.295853 | + | 0.955233i | \(0.404396\pi\) | |||||||
\(968\) | −4.92442e16 | −1.86226 | ||||||||
\(969\) | 3.58808e16 | 1.34921 | ||||||||
\(970\) | −9.86551e15 | −0.368871 | ||||||||
\(971\) | −1.02839e16 | −0.382342 | −0.191171 | − | 0.981557i | \(-0.561229\pi\) | ||||
−0.191171 | + | 0.981557i | \(0.561229\pi\) | |||||||
\(972\) | 8.75098e15 | 0.323513 | ||||||||
\(973\) | −6.10318e12 | −0.000224355 0 | ||||||||
\(974\) | 2.93819e15 | 0.107400 | ||||||||
\(975\) | −3.87918e15 | −0.140999 | ||||||||
\(976\) | −8.29142e14 | −0.0299678 | ||||||||
\(977\) | −5.16632e16 | −1.85678 | −0.928391 | − | 0.371604i | \(-0.878808\pi\) | ||||
−0.928391 | + | 0.371604i | \(0.878808\pi\) | |||||||
\(978\) | 2.63587e15 | 0.0942019 | ||||||||
\(979\) | 7.05135e15 | 0.250592 | ||||||||
\(980\) | −2.26325e16 | −0.799814 | ||||||||
\(981\) | 3.80962e15 | 0.133876 | ||||||||
\(982\) | 3.82285e15 | 0.133590 | ||||||||
\(983\) | 1.75164e16 | 0.608694 | 0.304347 | − | 0.952561i | \(-0.401562\pi\) | ||||
0.304347 | + | 0.952561i | \(0.401562\pi\) | |||||||
\(984\) | −3.50625e16 | −1.21163 | ||||||||
\(985\) | 1.31642e16 | 0.452371 | ||||||||
\(986\) | 6.25632e15 | 0.213794 | ||||||||
\(987\) | 3.33585e15 | 0.113361 | ||||||||
\(988\) | −3.42587e16 | −1.15773 | ||||||||
\(989\) | 6.78730e15 | 0.228096 | ||||||||
\(990\) | 3.82590e15 | 0.127862 | ||||||||
\(991\) | −3.86595e16 | −1.28485 | −0.642423 | − | 0.766350i | \(-0.722071\pi\) | ||||
−0.642423 | + | 0.766350i | \(0.722071\pi\) | |||||||
\(992\) | 4.56434e16 | 1.50856 | ||||||||
\(993\) | −1.11270e16 | −0.365728 | ||||||||
\(994\) | −8.85645e14 | −0.0289491 | ||||||||
\(995\) | 4.09976e16 | 1.33270 | ||||||||
\(996\) | 2.90201e16 | 0.938151 | ||||||||
\(997\) | −3.63590e15 | −0.116893 | −0.0584465 | − | 0.998291i | \(-0.518615\pi\) | ||||
−0.0584465 | + | 0.998291i | \(0.518615\pi\) | |||||||
\(998\) | −6.18561e15 | −0.197772 | ||||||||
\(999\) | −1.34553e16 | −0.427842 |
(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 | 23.12.a.b.1.7 | ✓ | 11 | |
3.2 | odd | 2 | 207.12.a.d.1.5 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.12.a.b.1.7 | ✓ | 11 | 1.1 | even | 1 | trivial | |
207.12.a.d.1.5 | 11 | 3.2 | odd | 2 |