Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,12,Mod(1,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.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: | \(209.757688293\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 26640 x^{14} - 38138 x^{13} + 279954048 x^{12} + 940095168 x^{11} - 1473489774048 x^{10} - 6951601887328 x^{9} + \cdots + 45\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{12}\cdot 5\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(78.0478\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 74.0478 | 1.63624 | 0.818120 | − | 0.575047i | \(-0.195016\pi\) | ||||
0.818120 | + | 0.575047i | \(0.195016\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 3435.08 | 1.67728 | ||||||||
\(5\) | −7551.16 | −1.08063 | −0.540317 | − | 0.841462i | \(-0.681696\pi\) | ||||
−0.540317 | + | 0.841462i | \(0.681696\pi\) | |||||||
\(6\) | −17993.6 | −0.944684 | ||||||||
\(7\) | 16807.0 | 0.377964 | ||||||||
\(8\) | 102710. | 1.10820 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −559147. | −1.76818 | ||||||||
\(11\) | 26767.7 | 0.0501130 | 0.0250565 | − | 0.999686i | \(-0.492023\pi\) | ||||
0.0250565 | + | 0.999686i | \(0.492023\pi\) | |||||||
\(12\) | −834724. | −0.968380 | ||||||||
\(13\) | −371293. | −0.277350 | ||||||||
\(14\) | 1.24452e6 | 0.618441 | ||||||||
\(15\) | 1.83493e6 | 0.623904 | ||||||||
\(16\) | 570411. | 0.135997 | ||||||||
\(17\) | 4.90051e6 | 0.837091 | 0.418545 | − | 0.908196i | \(-0.362540\pi\) | ||||
0.418545 | + | 0.908196i | \(0.362540\pi\) | |||||||
\(18\) | 4.37245e6 | 0.545414 | ||||||||
\(19\) | 7.70090e6 | 0.713505 | 0.356752 | − | 0.934199i | \(-0.383884\pi\) | ||||
0.356752 | + | 0.934199i | \(0.383884\pi\) | |||||||
\(20\) | −2.59388e7 | −1.81253 | ||||||||
\(21\) | −4.08410e6 | −0.218218 | ||||||||
\(22\) | 1.98209e6 | 0.0819970 | ||||||||
\(23\) | −4.21892e6 | −0.136678 | −0.0683390 | − | 0.997662i | \(-0.521770\pi\) | ||||
−0.0683390 | + | 0.997662i | \(0.521770\pi\) | |||||||
\(24\) | −2.49585e7 | −0.639819 | ||||||||
\(25\) | 8.19188e6 | 0.167770 | ||||||||
\(26\) | −2.74934e7 | −0.453812 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 5.77333e7 | 0.633954 | ||||||||
\(29\) | 3.93732e7 | 0.356461 | 0.178230 | − | 0.983989i | \(-0.442963\pi\) | ||||
0.178230 | + | 0.983989i | \(0.442963\pi\) | |||||||
\(30\) | 1.35873e8 | 1.02086 | ||||||||
\(31\) | 1.64135e8 | 1.02970 | 0.514852 | − | 0.857279i | \(-0.327847\pi\) | ||||
0.514852 | + | 0.857279i | \(0.327847\pi\) | |||||||
\(32\) | −1.68112e8 | −0.885676 | ||||||||
\(33\) | −6.50454e6 | −0.0289328 | ||||||||
\(34\) | 3.62872e8 | 1.36968 | ||||||||
\(35\) | −1.26912e8 | −0.408441 | ||||||||
\(36\) | 2.02838e8 | 0.559095 | ||||||||
\(37\) | −5.78538e7 | −0.137158 | −0.0685792 | − | 0.997646i | \(-0.521847\pi\) | ||||
−0.0685792 | + | 0.997646i | \(0.521847\pi\) | |||||||
\(38\) | 5.70235e8 | 1.16747 | ||||||||
\(39\) | 9.02242e7 | 0.160128 | ||||||||
\(40\) | −7.75579e8 | −1.19756 | ||||||||
\(41\) | 8.05799e7 | 0.108621 | 0.0543107 | − | 0.998524i | \(-0.482704\pi\) | ||||
0.0543107 | + | 0.998524i | \(0.482704\pi\) | |||||||
\(42\) | −3.02419e8 | −0.357057 | ||||||||
\(43\) | 4.19612e8 | 0.435283 | 0.217641 | − | 0.976029i | \(-0.430164\pi\) | ||||
0.217641 | + | 0.976029i | \(0.430164\pi\) | |||||||
\(44\) | 9.19489e7 | 0.0840537 | ||||||||
\(45\) | −4.45888e8 | −0.360211 | ||||||||
\(46\) | −3.12402e8 | −0.223638 | ||||||||
\(47\) | −2.32137e9 | −1.47641 | −0.738205 | − | 0.674576i | \(-0.764326\pi\) | ||||
−0.738205 | + | 0.674576i | \(0.764326\pi\) | |||||||
\(48\) | −1.38610e8 | −0.0785177 | ||||||||
\(49\) | 2.82475e8 | 0.142857 | ||||||||
\(50\) | 6.06590e8 | 0.274511 | ||||||||
\(51\) | −1.19082e9 | −0.483294 | ||||||||
\(52\) | −1.27542e9 | −0.465195 | ||||||||
\(53\) | −5.68055e9 | −1.86584 | −0.932918 | − | 0.360090i | \(-0.882746\pi\) | ||||
−0.932918 | + | 0.360090i | \(0.882746\pi\) | |||||||
\(54\) | −1.06250e9 | −0.314895 | ||||||||
\(55\) | −2.02127e8 | −0.0541538 | ||||||||
\(56\) | 1.72625e9 | 0.418860 | ||||||||
\(57\) | −1.87132e9 | −0.411942 | ||||||||
\(58\) | 2.91550e9 | 0.583255 | ||||||||
\(59\) | 7.14205e9 | 1.30058 | 0.650290 | − | 0.759686i | \(-0.274648\pi\) | ||||
0.650290 | + | 0.759686i | \(0.274648\pi\) | |||||||
\(60\) | 6.30313e9 | 1.04646 | ||||||||
\(61\) | −5.20435e9 | −0.788955 | −0.394477 | − | 0.918906i | \(-0.629074\pi\) | ||||
−0.394477 | + | 0.918906i | \(0.629074\pi\) | |||||||
\(62\) | 1.21539e10 | 1.68484 | ||||||||
\(63\) | 9.92437e8 | 0.125988 | ||||||||
\(64\) | −1.36166e10 | −1.58518 | ||||||||
\(65\) | 2.80369e9 | 0.299714 | ||||||||
\(66\) | −4.81647e8 | −0.0473410 | ||||||||
\(67\) | 9.22856e8 | 0.0835069 | 0.0417535 | − | 0.999128i | \(-0.486706\pi\) | ||||
0.0417535 | + | 0.999128i | \(0.486706\pi\) | |||||||
\(68\) | 1.68336e10 | 1.40404 | ||||||||
\(69\) | 1.02520e9 | 0.0789110 | ||||||||
\(70\) | −9.39758e9 | −0.668308 | ||||||||
\(71\) | 9.37905e9 | 0.616933 | 0.308467 | − | 0.951235i | \(-0.400184\pi\) | ||||
0.308467 | + | 0.951235i | \(0.400184\pi\) | |||||||
\(72\) | 6.06492e9 | 0.369400 | ||||||||
\(73\) | −6.60345e8 | −0.0372817 | −0.0186408 | − | 0.999826i | \(-0.505934\pi\) | ||||
−0.0186408 | + | 0.999826i | \(0.505934\pi\) | |||||||
\(74\) | −4.28395e9 | −0.224424 | ||||||||
\(75\) | −1.99063e9 | −0.0968618 | ||||||||
\(76\) | 2.64532e10 | 1.19675 | ||||||||
\(77\) | 4.49884e8 | 0.0189409 | ||||||||
\(78\) | 6.68090e9 | 0.262008 | ||||||||
\(79\) | −2.52311e10 | −0.922543 | −0.461272 | − | 0.887259i | \(-0.652607\pi\) | ||||
−0.461272 | + | 0.887259i | \(0.652607\pi\) | |||||||
\(80\) | −4.30726e9 | −0.146962 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 5.96676e9 | 0.177731 | ||||||||
\(83\) | −4.44273e10 | −1.23800 | −0.618999 | − | 0.785392i | \(-0.712462\pi\) | ||||
−0.618999 | + | 0.785392i | \(0.712462\pi\) | |||||||
\(84\) | −1.40292e10 | −0.366013 | ||||||||
\(85\) | −3.70045e10 | −0.904588 | ||||||||
\(86\) | 3.10713e10 | 0.712227 | ||||||||
\(87\) | −9.56768e9 | −0.205803 | ||||||||
\(88\) | 2.74931e9 | 0.0555352 | ||||||||
\(89\) | −3.34083e10 | −0.634175 | −0.317087 | − | 0.948396i | \(-0.602705\pi\) | ||||
−0.317087 | + | 0.948396i | \(0.602705\pi\) | |||||||
\(90\) | −3.30171e10 | −0.589392 | ||||||||
\(91\) | −6.24032e9 | −0.104828 | ||||||||
\(92\) | −1.44923e10 | −0.229248 | ||||||||
\(93\) | −3.98849e10 | −0.594500 | ||||||||
\(94\) | −1.71893e11 | −2.41576 | ||||||||
\(95\) | −5.81507e10 | −0.771037 | ||||||||
\(96\) | 4.08513e10 | 0.511345 | ||||||||
\(97\) | −7.25700e10 | −0.858050 | −0.429025 | − | 0.903293i | \(-0.641143\pi\) | ||||
−0.429025 | + | 0.903293i | \(0.641143\pi\) | |||||||
\(98\) | 2.09167e10 | 0.233749 | ||||||||
\(99\) | 1.58060e9 | 0.0167043 | ||||||||
\(100\) | 2.81397e10 | 0.281397 | ||||||||
\(101\) | 9.43401e10 | 0.893159 | 0.446580 | − | 0.894744i | \(-0.352642\pi\) | ||||
0.446580 | + | 0.894744i | \(0.352642\pi\) | |||||||
\(102\) | −8.81779e10 | −0.790786 | ||||||||
\(103\) | 6.03518e10 | 0.512963 | 0.256481 | − | 0.966549i | \(-0.417437\pi\) | ||||
0.256481 | + | 0.966549i | \(0.417437\pi\) | |||||||
\(104\) | −3.81355e10 | −0.307359 | ||||||||
\(105\) | 3.08397e10 | 0.235814 | ||||||||
\(106\) | −4.20632e11 | −3.05296 | ||||||||
\(107\) | −6.07139e9 | −0.0418483 | −0.0209241 | − | 0.999781i | \(-0.506661\pi\) | ||||
−0.0209241 | + | 0.999781i | \(0.506661\pi\) | |||||||
\(108\) | −4.92896e10 | −0.322793 | ||||||||
\(109\) | −1.82295e11 | −1.13482 | −0.567412 | − | 0.823434i | \(-0.692055\pi\) | ||||
−0.567412 | + | 0.823434i | \(0.692055\pi\) | |||||||
\(110\) | −1.49670e10 | −0.0886087 | ||||||||
\(111\) | 1.40585e10 | 0.0791885 | ||||||||
\(112\) | 9.58690e9 | 0.0514019 | ||||||||
\(113\) | −3.05548e11 | −1.56008 | −0.780042 | − | 0.625727i | \(-0.784802\pi\) | ||||
−0.780042 | + | 0.625727i | \(0.784802\pi\) | |||||||
\(114\) | −1.38567e11 | −0.674037 | ||||||||
\(115\) | 3.18578e10 | 0.147699 | ||||||||
\(116\) | 1.35250e11 | 0.597885 | ||||||||
\(117\) | −2.19245e10 | −0.0924500 | ||||||||
\(118\) | 5.28853e11 | 2.12806 | ||||||||
\(119\) | 8.23629e10 | 0.316390 | ||||||||
\(120\) | 1.88466e11 | 0.691410 | ||||||||
\(121\) | −2.84595e11 | −0.997489 | ||||||||
\(122\) | −3.85370e11 | −1.29092 | ||||||||
\(123\) | −1.95809e10 | −0.0627126 | ||||||||
\(124\) | 5.63817e11 | 1.72711 | ||||||||
\(125\) | 3.06851e11 | 0.899336 | ||||||||
\(126\) | 7.34877e10 | 0.206147 | ||||||||
\(127\) | −8.29857e10 | −0.222886 | −0.111443 | − | 0.993771i | \(-0.535547\pi\) | ||||
−0.111443 | + | 0.993771i | \(0.535547\pi\) | |||||||
\(128\) | −6.63982e11 | −1.70805 | ||||||||
\(129\) | −1.01966e11 | −0.251310 | ||||||||
\(130\) | 2.07607e11 | 0.490404 | ||||||||
\(131\) | −3.54952e11 | −0.803854 | −0.401927 | − | 0.915672i | \(-0.631659\pi\) | ||||
−0.401927 | + | 0.915672i | \(0.631659\pi\) | |||||||
\(132\) | −2.23436e10 | −0.0485284 | ||||||||
\(133\) | 1.29429e11 | 0.269679 | ||||||||
\(134\) | 6.83354e10 | 0.136637 | ||||||||
\(135\) | 1.08351e11 | 0.207968 | ||||||||
\(136\) | 5.03332e11 | 0.927663 | ||||||||
\(137\) | −1.81410e11 | −0.321142 | −0.160571 | − | 0.987024i | \(-0.551334\pi\) | ||||
−0.160571 | + | 0.987024i | \(0.551334\pi\) | |||||||
\(138\) | 7.59137e10 | 0.129117 | ||||||||
\(139\) | −1.56877e11 | −0.256436 | −0.128218 | − | 0.991746i | \(-0.540926\pi\) | ||||
−0.128218 | + | 0.991746i | \(0.540926\pi\) | |||||||
\(140\) | −4.35954e11 | −0.685072 | ||||||||
\(141\) | 5.64094e11 | 0.852406 | ||||||||
\(142\) | 6.94498e11 | 1.00945 | ||||||||
\(143\) | −9.93864e9 | −0.0138988 | ||||||||
\(144\) | 3.36822e10 | 0.0453322 | ||||||||
\(145\) | −2.97313e11 | −0.385203 | ||||||||
\(146\) | −4.88971e10 | −0.0610018 | ||||||||
\(147\) | −6.86415e10 | −0.0824786 | ||||||||
\(148\) | −1.98732e11 | −0.230054 | ||||||||
\(149\) | 8.00500e11 | 0.892970 | 0.446485 | − | 0.894791i | \(-0.352676\pi\) | ||||
0.446485 | + | 0.894791i | \(0.352676\pi\) | |||||||
\(150\) | −1.47401e11 | −0.158489 | ||||||||
\(151\) | 1.03859e11 | 0.107664 | 0.0538319 | − | 0.998550i | \(-0.482856\pi\) | ||||
0.0538319 | + | 0.998550i | \(0.482856\pi\) | |||||||
\(152\) | 7.90960e11 | 0.790705 | ||||||||
\(153\) | 2.89370e11 | 0.279030 | ||||||||
\(154\) | 3.33129e10 | 0.0309919 | ||||||||
\(155\) | −1.23941e12 | −1.11273 | ||||||||
\(156\) | 3.09927e11 | 0.268580 | ||||||||
\(157\) | 5.90129e11 | 0.493741 | 0.246870 | − | 0.969049i | \(-0.420598\pi\) | ||||
0.246870 | + | 0.969049i | \(0.420598\pi\) | |||||||
\(158\) | −1.86831e12 | −1.50950 | ||||||||
\(159\) | 1.38037e12 | 1.07724 | ||||||||
\(160\) | 1.26944e12 | 0.957091 | ||||||||
\(161\) | −7.09074e10 | −0.0516594 | ||||||||
\(162\) | 2.58189e11 | 0.181805 | ||||||||
\(163\) | −2.44174e12 | −1.66214 | −0.831069 | − | 0.556169i | \(-0.812271\pi\) | ||||
−0.831069 | + | 0.556169i | \(0.812271\pi\) | |||||||
\(164\) | 2.76798e11 | 0.182189 | ||||||||
\(165\) | 4.91168e10 | 0.0312657 | ||||||||
\(166\) | −3.28974e12 | −2.02566 | ||||||||
\(167\) | −1.06031e12 | −0.631675 | −0.315838 | − | 0.948813i | \(-0.602285\pi\) | ||||
−0.315838 | + | 0.948813i | \(0.602285\pi\) | |||||||
\(168\) | −4.19478e11 | −0.241829 | ||||||||
\(169\) | 1.37858e11 | 0.0769231 | ||||||||
\(170\) | −2.74011e12 | −1.48012 | ||||||||
\(171\) | 4.54731e11 | 0.237835 | ||||||||
\(172\) | 1.44140e12 | 0.730092 | ||||||||
\(173\) | −2.75822e12 | −1.35324 | −0.676620 | − | 0.736332i | \(-0.736556\pi\) | ||||
−0.676620 | + | 0.736332i | \(0.736556\pi\) | |||||||
\(174\) | −7.08466e11 | −0.336743 | ||||||||
\(175\) | 1.37681e11 | 0.0634110 | ||||||||
\(176\) | 1.52686e10 | 0.00681520 | ||||||||
\(177\) | −1.73552e12 | −0.750890 | ||||||||
\(178\) | −2.47381e12 | −1.03766 | ||||||||
\(179\) | −3.22952e12 | −1.31355 | −0.656774 | − | 0.754088i | \(-0.728079\pi\) | ||||
−0.656774 | + | 0.754088i | \(0.728079\pi\) | |||||||
\(180\) | −1.53166e12 | −0.604176 | ||||||||
\(181\) | −3.90867e10 | −0.0149554 | −0.00747768 | − | 0.999972i | \(-0.502380\pi\) | ||||
−0.00747768 | + | 0.999972i | \(0.502380\pi\) | |||||||
\(182\) | −4.62082e11 | −0.171525 | ||||||||
\(183\) | 1.26466e12 | 0.455503 | ||||||||
\(184\) | −4.33325e11 | −0.151466 | ||||||||
\(185\) | 4.36864e11 | 0.148218 | ||||||||
\(186\) | −2.95339e12 | −0.972746 | ||||||||
\(187\) | 1.31175e11 | 0.0419491 | ||||||||
\(188\) | −7.97410e12 | −2.47636 | ||||||||
\(189\) | −2.41162e11 | −0.0727393 | ||||||||
\(190\) | −4.30593e12 | −1.26160 | ||||||||
\(191\) | −2.64705e12 | −0.753493 | −0.376747 | − | 0.926316i | \(-0.622957\pi\) | ||||
−0.376747 | + | 0.926316i | \(0.622957\pi\) | |||||||
\(192\) | 3.30882e12 | 0.915201 | ||||||||
\(193\) | −1.33531e12 | −0.358935 | −0.179467 | − | 0.983764i | \(-0.557437\pi\) | ||||
−0.179467 | + | 0.983764i | \(0.557437\pi\) | |||||||
\(194\) | −5.37365e12 | −1.40398 | ||||||||
\(195\) | −6.81297e11 | −0.173040 | ||||||||
\(196\) | 9.70324e11 | 0.239612 | ||||||||
\(197\) | −7.91698e12 | −1.90106 | −0.950529 | − | 0.310636i | \(-0.899458\pi\) | ||||
−0.950529 | + | 0.310636i | \(0.899458\pi\) | |||||||
\(198\) | 1.17040e11 | 0.0273323 | ||||||||
\(199\) | 4.02527e12 | 0.914331 | 0.457165 | − | 0.889382i | \(-0.348865\pi\) | ||||
0.457165 | + | 0.889382i | \(0.348865\pi\) | |||||||
\(200\) | 8.41387e11 | 0.185922 | ||||||||
\(201\) | −2.24254e11 | −0.0482127 | ||||||||
\(202\) | 6.98568e12 | 1.46142 | ||||||||
\(203\) | 6.61745e11 | 0.134729 | ||||||||
\(204\) | −4.09057e12 | −0.810622 | ||||||||
\(205\) | −6.08471e11 | −0.117380 | ||||||||
\(206\) | 4.46892e12 | 0.839330 | ||||||||
\(207\) | −2.49123e11 | −0.0455593 | ||||||||
\(208\) | −2.11790e11 | −0.0377187 | ||||||||
\(209\) | 2.06135e11 | 0.0357559 | ||||||||
\(210\) | 2.28361e12 | 0.385848 | ||||||||
\(211\) | 6.06937e12 | 0.999056 | 0.499528 | − | 0.866298i | \(-0.333507\pi\) | ||||
0.499528 | + | 0.866298i | \(0.333507\pi\) | |||||||
\(212\) | −1.95131e13 | −3.12953 | ||||||||
\(213\) | −2.27911e12 | −0.356186 | ||||||||
\(214\) | −4.49573e11 | −0.0684739 | ||||||||
\(215\) | −3.16856e12 | −0.470381 | ||||||||
\(216\) | −1.47378e12 | −0.213273 | ||||||||
\(217\) | 2.75862e12 | 0.389192 | ||||||||
\(218\) | −1.34985e13 | −1.85685 | ||||||||
\(219\) | 1.60464e11 | 0.0215246 | ||||||||
\(220\) | −6.94321e11 | −0.0908313 | ||||||||
\(221\) | −1.81953e12 | −0.232167 | ||||||||
\(222\) | 1.04100e12 | 0.129571 | ||||||||
\(223\) | −3.68640e12 | −0.447636 | −0.223818 | − | 0.974631i | \(-0.571852\pi\) | ||||
−0.223818 | + | 0.974631i | \(0.571852\pi\) | |||||||
\(224\) | −2.82546e12 | −0.334754 | ||||||||
\(225\) | 4.83722e11 | 0.0559232 | ||||||||
\(226\) | −2.26252e13 | −2.55267 | ||||||||
\(227\) | 8.41053e12 | 0.926149 | 0.463075 | − | 0.886319i | \(-0.346746\pi\) | ||||
0.463075 | + | 0.886319i | \(0.346746\pi\) | |||||||
\(228\) | −6.42813e12 | −0.690944 | ||||||||
\(229\) | 2.57053e12 | 0.269729 | 0.134865 | − | 0.990864i | \(-0.456940\pi\) | ||||
0.134865 | + | 0.990864i | \(0.456940\pi\) | |||||||
\(230\) | 2.35900e12 | 0.241671 | ||||||||
\(231\) | −1.09322e11 | −0.0109356 | ||||||||
\(232\) | 4.04402e12 | 0.395029 | ||||||||
\(233\) | −1.07349e12 | −0.102409 | −0.0512047 | − | 0.998688i | \(-0.516306\pi\) | ||||
−0.0512047 | + | 0.998688i | \(0.516306\pi\) | |||||||
\(234\) | −1.62346e12 | −0.151271 | ||||||||
\(235\) | 1.75291e13 | 1.59546 | ||||||||
\(236\) | 2.45335e13 | 2.18144 | ||||||||
\(237\) | 6.13115e12 | 0.532631 | ||||||||
\(238\) | 6.09879e12 | 0.517691 | ||||||||
\(239\) | −1.27872e12 | −0.106069 | −0.0530343 | − | 0.998593i | \(-0.516889\pi\) | ||||
−0.0530343 | + | 0.998593i | \(0.516889\pi\) | |||||||
\(240\) | 1.04667e12 | 0.0848488 | ||||||||
\(241\) | 7.22056e12 | 0.572107 | 0.286053 | − | 0.958214i | \(-0.407657\pi\) | ||||
0.286053 | + | 0.958214i | \(0.407657\pi\) | |||||||
\(242\) | −2.10736e13 | −1.63213 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | −1.78773e13 | −1.32330 | ||||||||
\(245\) | −2.13302e12 | −0.154376 | ||||||||
\(246\) | −1.44992e12 | −0.102613 | ||||||||
\(247\) | −2.85929e12 | −0.197891 | ||||||||
\(248\) | 1.68583e13 | 1.14112 | ||||||||
\(249\) | 1.07958e13 | 0.714759 | ||||||||
\(250\) | 2.27216e13 | 1.47153 | ||||||||
\(251\) | 2.42498e13 | 1.53639 | 0.768197 | − | 0.640214i | \(-0.221154\pi\) | ||||
0.768197 | + | 0.640214i | \(0.221154\pi\) | |||||||
\(252\) | 3.40910e12 | 0.211318 | ||||||||
\(253\) | −1.12931e11 | −0.00684934 | ||||||||
\(254\) | −6.14491e12 | −0.364695 | ||||||||
\(255\) | 8.99211e12 | 0.522264 | ||||||||
\(256\) | −2.12797e13 | −1.20961 | ||||||||
\(257\) | 4.89674e12 | 0.272442 | 0.136221 | − | 0.990678i | \(-0.456504\pi\) | ||||
0.136221 | + | 0.990678i | \(0.456504\pi\) | |||||||
\(258\) | −7.55033e12 | −0.411204 | ||||||||
\(259\) | −9.72349e11 | −0.0518410 | ||||||||
\(260\) | 9.63090e12 | 0.502705 | ||||||||
\(261\) | 2.32495e12 | 0.118820 | ||||||||
\(262\) | −2.62834e13 | −1.31530 | ||||||||
\(263\) | −8.13628e12 | −0.398721 | −0.199361 | − | 0.979926i | \(-0.563886\pi\) | ||||
−0.199361 | + | 0.979926i | \(0.563886\pi\) | |||||||
\(264\) | −6.68081e11 | −0.0320633 | ||||||||
\(265\) | 4.28948e13 | 2.01628 | ||||||||
\(266\) | 9.58394e12 | 0.441260 | ||||||||
\(267\) | 8.11821e12 | 0.366141 | ||||||||
\(268\) | 3.17008e12 | 0.140065 | ||||||||
\(269\) | 4.93951e11 | 0.0213819 | 0.0106910 | − | 0.999943i | \(-0.496597\pi\) | ||||
0.0106910 | + | 0.999943i | \(0.496597\pi\) | |||||||
\(270\) | 8.02314e12 | 0.340286 | ||||||||
\(271\) | 8.89977e12 | 0.369869 | 0.184934 | − | 0.982751i | \(-0.440793\pi\) | ||||
0.184934 | + | 0.982751i | \(0.440793\pi\) | |||||||
\(272\) | 2.79531e12 | 0.113841 | ||||||||
\(273\) | 1.51640e12 | 0.0605228 | ||||||||
\(274\) | −1.34330e13 | −0.525466 | ||||||||
\(275\) | 2.19277e11 | 0.00840744 | ||||||||
\(276\) | 3.52163e12 | 0.132356 | ||||||||
\(277\) | −1.30989e11 | −0.00482608 | −0.00241304 | − | 0.999997i | \(-0.500768\pi\) | ||||
−0.00241304 | + | 0.999997i | \(0.500768\pi\) | |||||||
\(278\) | −1.16164e13 | −0.419591 | ||||||||
\(279\) | 9.69203e12 | 0.343235 | ||||||||
\(280\) | −1.30352e13 | −0.452634 | ||||||||
\(281\) | −7.91457e12 | −0.269490 | −0.134745 | − | 0.990880i | \(-0.543022\pi\) | ||||
−0.134745 | + | 0.990880i | \(0.543022\pi\) | |||||||
\(282\) | 4.17699e13 | 1.39474 | ||||||||
\(283\) | −4.12306e12 | −0.135019 | −0.0675094 | − | 0.997719i | \(-0.521505\pi\) | ||||
−0.0675094 | + | 0.997719i | \(0.521505\pi\) | |||||||
\(284\) | 3.22178e13 | 1.03477 | ||||||||
\(285\) | 1.41306e13 | 0.445159 | ||||||||
\(286\) | −7.35935e11 | −0.0227419 | ||||||||
\(287\) | 1.35431e12 | 0.0410550 | ||||||||
\(288\) | −9.92687e12 | −0.295225 | ||||||||
\(289\) | −1.02569e13 | −0.299279 | ||||||||
\(290\) | −2.20154e13 | −0.630285 | ||||||||
\(291\) | 1.76345e13 | 0.495395 | ||||||||
\(292\) | −2.26834e12 | −0.0625319 | ||||||||
\(293\) | 7.85049e11 | 0.0212385 | 0.0106193 | − | 0.999944i | \(-0.496620\pi\) | ||||
0.0106193 | + | 0.999944i | \(0.496620\pi\) | |||||||
\(294\) | −5.08275e12 | −0.134955 | ||||||||
\(295\) | −5.39307e13 | −1.40545 | ||||||||
\(296\) | −5.94217e12 | −0.151999 | ||||||||
\(297\) | −3.84087e11 | −0.00964425 | ||||||||
\(298\) | 5.92753e13 | 1.46111 | ||||||||
\(299\) | 1.56646e12 | 0.0379076 | ||||||||
\(300\) | −6.83795e12 | −0.162465 | ||||||||
\(301\) | 7.05242e12 | 0.164521 | ||||||||
\(302\) | 7.69051e12 | 0.176164 | ||||||||
\(303\) | −2.29246e13 | −0.515666 | ||||||||
\(304\) | 4.39268e12 | 0.0970342 | ||||||||
\(305\) | 3.92989e13 | 0.852571 | ||||||||
\(306\) | 2.14272e13 | 0.456561 | ||||||||
\(307\) | 3.69209e13 | 0.772700 | 0.386350 | − | 0.922352i | \(-0.373736\pi\) | ||||
0.386350 | + | 0.922352i | \(0.373736\pi\) | |||||||
\(308\) | 1.54539e12 | 0.0317693 | ||||||||
\(309\) | −1.46655e13 | −0.296159 | ||||||||
\(310\) | −9.17757e13 | −1.82070 | ||||||||
\(311\) | −8.09125e12 | −0.157701 | −0.0788503 | − | 0.996886i | \(-0.525125\pi\) | ||||
−0.0788503 | + | 0.996886i | \(0.525125\pi\) | |||||||
\(312\) | 9.26693e12 | 0.177454 | ||||||||
\(313\) | −3.29887e13 | −0.620686 | −0.310343 | − | 0.950625i | \(-0.600444\pi\) | ||||
−0.310343 | + | 0.950625i | \(0.600444\pi\) | |||||||
\(314\) | 4.36978e13 | 0.807879 | ||||||||
\(315\) | −7.49405e12 | −0.136147 | ||||||||
\(316\) | −8.66707e13 | −1.54737 | ||||||||
\(317\) | 9.24380e13 | 1.62190 | 0.810951 | − | 0.585114i | \(-0.198950\pi\) | ||||
0.810951 | + | 0.585114i | \(0.198950\pi\) | |||||||
\(318\) | 1.02214e14 | 1.76262 | ||||||||
\(319\) | 1.05393e12 | 0.0178633 | ||||||||
\(320\) | 1.02821e14 | 1.71299 | ||||||||
\(321\) | 1.47535e12 | 0.0241611 | ||||||||
\(322\) | −5.25054e12 | −0.0845272 | ||||||||
\(323\) | 3.77384e13 | 0.597268 | ||||||||
\(324\) | 1.19774e13 | 0.186365 | ||||||||
\(325\) | −3.04159e12 | −0.0465309 | ||||||||
\(326\) | −1.80805e14 | −2.71966 | ||||||||
\(327\) | 4.42976e13 | 0.655191 | ||||||||
\(328\) | 8.27636e12 | 0.120374 | ||||||||
\(329\) | −3.90153e13 | −0.558031 | ||||||||
\(330\) | 3.63699e12 | 0.0511582 | ||||||||
\(331\) | 8.77559e13 | 1.21401 | 0.607005 | − | 0.794698i | \(-0.292371\pi\) | ||||
0.607005 | + | 0.794698i | \(0.292371\pi\) | |||||||
\(332\) | −1.52611e14 | −2.07647 | ||||||||
\(333\) | −3.41621e12 | −0.0457195 | ||||||||
\(334\) | −7.85139e13 | −1.03357 | ||||||||
\(335\) | −6.96863e12 | −0.0902404 | ||||||||
\(336\) | −2.32962e12 | −0.0296769 | ||||||||
\(337\) | 1.55668e13 | 0.195090 | 0.0975448 | − | 0.995231i | \(-0.468901\pi\) | ||||
0.0975448 | + | 0.995231i | \(0.468901\pi\) | |||||||
\(338\) | 1.02081e13 | 0.125865 | ||||||||
\(339\) | 7.42482e13 | 0.900715 | ||||||||
\(340\) | −1.27113e14 | −1.51725 | ||||||||
\(341\) | 4.39352e12 | 0.0516016 | ||||||||
\(342\) | 3.36718e13 | 0.389155 | ||||||||
\(343\) | 4.74756e12 | 0.0539949 | ||||||||
\(344\) | 4.30983e13 | 0.482380 | ||||||||
\(345\) | −7.74143e12 | −0.0852739 | ||||||||
\(346\) | −2.04240e14 | −2.21423 | ||||||||
\(347\) | −1.33313e14 | −1.42253 | −0.711264 | − | 0.702925i | \(-0.751877\pi\) | ||||
−0.711264 | + | 0.702925i | \(0.751877\pi\) | |||||||
\(348\) | −3.28657e13 | −0.345189 | ||||||||
\(349\) | −8.67103e12 | −0.0896459 | −0.0448230 | − | 0.998995i | \(-0.514272\pi\) | ||||
−0.0448230 | + | 0.998995i | \(0.514272\pi\) | |||||||
\(350\) | 1.01950e13 | 0.103756 | ||||||||
\(351\) | 5.32765e12 | 0.0533761 | ||||||||
\(352\) | −4.49997e12 | −0.0443839 | ||||||||
\(353\) | −8.26111e13 | −0.802190 | −0.401095 | − | 0.916036i | \(-0.631370\pi\) | ||||
−0.401095 | + | 0.916036i | \(0.631370\pi\) | |||||||
\(354\) | −1.28511e14 | −1.22864 | ||||||||
\(355\) | −7.08227e13 | −0.666679 | ||||||||
\(356\) | −1.14760e14 | −1.06369 | ||||||||
\(357\) | −2.00142e13 | −0.182668 | ||||||||
\(358\) | −2.39139e14 | −2.14928 | ||||||||
\(359\) | −1.08444e14 | −0.959810 | −0.479905 | − | 0.877321i | \(-0.659329\pi\) | ||||
−0.479905 | + | 0.877321i | \(0.659329\pi\) | |||||||
\(360\) | −4.57972e13 | −0.399186 | ||||||||
\(361\) | −5.71863e13 | −0.490911 | ||||||||
\(362\) | −2.89428e12 | −0.0244706 | ||||||||
\(363\) | 6.91566e13 | 0.575900 | ||||||||
\(364\) | −2.14360e13 | −0.175827 | ||||||||
\(365\) | 4.98637e12 | 0.0402878 | ||||||||
\(366\) | 9.36450e13 | 0.745313 | ||||||||
\(367\) | −6.54309e13 | −0.513003 | −0.256501 | − | 0.966544i | \(-0.582570\pi\) | ||||
−0.256501 | + | 0.966544i | \(0.582570\pi\) | |||||||
\(368\) | −2.40652e12 | −0.0185877 | ||||||||
\(369\) | 4.75816e12 | 0.0362071 | ||||||||
\(370\) | 3.23488e13 | 0.242520 | ||||||||
\(371\) | −9.54730e13 | −0.705219 | ||||||||
\(372\) | −1.37008e14 | −0.997146 | ||||||||
\(373\) | −1.56255e14 | −1.12056 | −0.560279 | − | 0.828304i | \(-0.689306\pi\) | ||||
−0.560279 | + | 0.828304i | \(0.689306\pi\) | |||||||
\(374\) | 9.71324e12 | 0.0686389 | ||||||||
\(375\) | −7.45647e13 | −0.519232 | ||||||||
\(376\) | −2.38428e14 | −1.63616 | ||||||||
\(377\) | −1.46190e13 | −0.0988644 | ||||||||
\(378\) | −1.78575e13 | −0.119019 | ||||||||
\(379\) | 1.97868e14 | 1.29975 | 0.649875 | − | 0.760041i | \(-0.274821\pi\) | ||||
0.649875 | + | 0.760041i | \(0.274821\pi\) | |||||||
\(380\) | −1.99752e14 | −1.29325 | ||||||||
\(381\) | 2.01655e13 | 0.128683 | ||||||||
\(382\) | −1.96009e14 | −1.23290 | ||||||||
\(383\) | 1.37771e14 | 0.854207 | 0.427103 | − | 0.904203i | \(-0.359534\pi\) | ||||
0.427103 | + | 0.904203i | \(0.359534\pi\) | |||||||
\(384\) | 1.61348e14 | 0.986145 | ||||||||
\(385\) | −3.39715e12 | −0.0204682 | ||||||||
\(386\) | −9.88765e13 | −0.587304 | ||||||||
\(387\) | 2.47777e13 | 0.145094 | ||||||||
\(388\) | −2.49283e14 | −1.43919 | ||||||||
\(389\) | −1.98544e14 | −1.13014 | −0.565072 | − | 0.825042i | \(-0.691152\pi\) | ||||
−0.565072 | + | 0.825042i | \(0.691152\pi\) | |||||||
\(390\) | −5.04486e13 | −0.283135 | ||||||||
\(391\) | −2.06749e13 | −0.114412 | ||||||||
\(392\) | 2.90130e13 | 0.158314 | ||||||||
\(393\) | 8.62533e13 | 0.464105 | ||||||||
\(394\) | −5.86235e14 | −3.11059 | ||||||||
\(395\) | 1.90524e14 | 0.996932 | ||||||||
\(396\) | 5.42949e12 | 0.0280179 | ||||||||
\(397\) | −3.35455e14 | −1.70721 | −0.853605 | − | 0.520922i | \(-0.825588\pi\) | ||||
−0.853605 | + | 0.520922i | \(0.825588\pi\) | |||||||
\(398\) | 2.98062e14 | 1.49606 | ||||||||
\(399\) | −3.14513e13 | −0.155700 | ||||||||
\(400\) | 4.67274e12 | 0.0228161 | ||||||||
\(401\) | 3.09515e14 | 1.49069 | 0.745346 | − | 0.666678i | \(-0.232284\pi\) | ||||
0.745346 | + | 0.666678i | \(0.232284\pi\) | |||||||
\(402\) | −1.66055e13 | −0.0788877 | ||||||||
\(403\) | −6.09423e13 | −0.285589 | ||||||||
\(404\) | 3.24066e14 | 1.49808 | ||||||||
\(405\) | −2.63293e13 | −0.120070 | ||||||||
\(406\) | 4.90008e13 | 0.220450 | ||||||||
\(407\) | −1.54861e12 | −0.00687343 | ||||||||
\(408\) | −1.22310e14 | −0.535586 | ||||||||
\(409\) | 6.06851e12 | 0.0262183 | 0.0131091 | − | 0.999914i | \(-0.495827\pi\) | ||||
0.0131091 | + | 0.999914i | \(0.495827\pi\) | |||||||
\(410\) | −4.50560e13 | −0.192062 | ||||||||
\(411\) | 4.40826e13 | 0.185412 | ||||||||
\(412\) | 2.07313e14 | 0.860384 | ||||||||
\(413\) | 1.20036e14 | 0.491573 | ||||||||
\(414\) | −1.84470e13 | −0.0745460 | ||||||||
\(415\) | 3.35477e14 | 1.33782 | ||||||||
\(416\) | 6.24189e13 | 0.245642 | ||||||||
\(417\) | 3.81212e13 | 0.148053 | ||||||||
\(418\) | 1.52639e13 | 0.0585052 | ||||||||
\(419\) | −2.80816e13 | −0.106229 | −0.0531147 | − | 0.998588i | \(-0.516915\pi\) | ||||
−0.0531147 | + | 0.998588i | \(0.516915\pi\) | |||||||
\(420\) | 1.05937e14 | 0.395526 | ||||||||
\(421\) | 2.30457e14 | 0.849254 | 0.424627 | − | 0.905368i | \(-0.360405\pi\) | ||||
0.424627 | + | 0.905368i | \(0.360405\pi\) | |||||||
\(422\) | 4.49423e14 | 1.63470 | ||||||||
\(423\) | −1.37075e14 | −0.492137 | ||||||||
\(424\) | −5.83449e14 | −2.06772 | ||||||||
\(425\) | 4.01444e13 | 0.140438 | ||||||||
\(426\) | −1.68763e14 | −0.582807 | ||||||||
\(427\) | −8.74695e13 | −0.298197 | ||||||||
\(428\) | −2.08557e13 | −0.0701914 | ||||||||
\(429\) | 2.41509e12 | 0.00802450 | ||||||||
\(430\) | −2.34625e14 | −0.769657 | ||||||||
\(431\) | 2.21137e14 | 0.716202 | 0.358101 | − | 0.933683i | \(-0.383424\pi\) | ||||
0.358101 | + | 0.933683i | \(0.383424\pi\) | |||||||
\(432\) | −8.18477e12 | −0.0261726 | ||||||||
\(433\) | −2.61484e14 | −0.825586 | −0.412793 | − | 0.910825i | \(-0.635447\pi\) | ||||
−0.412793 | + | 0.910825i | \(0.635447\pi\) | |||||||
\(434\) | 2.04270e14 | 0.636812 | ||||||||
\(435\) | 7.22471e13 | 0.222397 | ||||||||
\(436\) | −6.26197e14 | −1.90342 | ||||||||
\(437\) | −3.24895e13 | −0.0975204 | ||||||||
\(438\) | 1.18820e13 | 0.0352194 | ||||||||
\(439\) | 5.90911e14 | 1.72969 | 0.864843 | − | 0.502042i | \(-0.167418\pi\) | ||||
0.864843 | + | 0.502042i | \(0.167418\pi\) | |||||||
\(440\) | −2.07604e13 | −0.0600132 | ||||||||
\(441\) | 1.66799e13 | 0.0476190 | ||||||||
\(442\) | −1.34732e14 | −0.379881 | ||||||||
\(443\) | −2.36657e14 | −0.659021 | −0.329511 | − | 0.944152i | \(-0.606884\pi\) | ||||
−0.329511 | + | 0.944152i | \(0.606884\pi\) | |||||||
\(444\) | 4.82920e13 | 0.132822 | ||||||||
\(445\) | 2.52271e14 | 0.685311 | ||||||||
\(446\) | −2.72969e14 | −0.732440 | ||||||||
\(447\) | −1.94521e14 | −0.515556 | ||||||||
\(448\) | −2.28853e14 | −0.599140 | ||||||||
\(449\) | 6.05587e14 | 1.56611 | 0.783054 | − | 0.621954i | \(-0.213661\pi\) | ||||
0.783054 | + | 0.621954i | \(0.213661\pi\) | |||||||
\(450\) | 3.58186e13 | 0.0915038 | ||||||||
\(451\) | 2.15693e12 | 0.00544334 | ||||||||
\(452\) | −1.04958e15 | −2.61670 | ||||||||
\(453\) | −2.52377e13 | −0.0621597 | ||||||||
\(454\) | 6.22781e14 | 1.51540 | ||||||||
\(455\) | 4.71217e13 | 0.113281 | ||||||||
\(456\) | −1.92203e14 | −0.456514 | ||||||||
\(457\) | −2.20199e14 | −0.516746 | −0.258373 | − | 0.966045i | \(-0.583186\pi\) | ||||
−0.258373 | + | 0.966045i | \(0.583186\pi\) | |||||||
\(458\) | 1.90342e14 | 0.441342 | ||||||||
\(459\) | −7.03170e13 | −0.161098 | ||||||||
\(460\) | 1.09434e14 | 0.247733 | ||||||||
\(461\) | 1.02556e14 | 0.229406 | 0.114703 | − | 0.993400i | \(-0.463408\pi\) | ||||
0.114703 | + | 0.993400i | \(0.463408\pi\) | |||||||
\(462\) | −8.09504e12 | −0.0178932 | ||||||||
\(463\) | 4.97674e14 | 1.08705 | 0.543525 | − | 0.839393i | \(-0.317089\pi\) | ||||
0.543525 | + | 0.839393i | \(0.317089\pi\) | |||||||
\(464\) | 2.24589e13 | 0.0484774 | ||||||||
\(465\) | 3.01177e14 | 0.642437 | ||||||||
\(466\) | −7.94894e13 | −0.167566 | ||||||||
\(467\) | 8.45430e14 | 1.76131 | 0.880653 | − | 0.473763i | \(-0.157105\pi\) | ||||
0.880653 | + | 0.473763i | \(0.157105\pi\) | |||||||
\(468\) | −7.53123e13 | −0.155065 | ||||||||
\(469\) | 1.55104e13 | 0.0315626 | ||||||||
\(470\) | 1.29799e15 | 2.61055 | ||||||||
\(471\) | −1.43401e14 | −0.285061 | ||||||||
\(472\) | 7.33560e14 | 1.44130 | ||||||||
\(473\) | 1.12320e13 | 0.0218133 | ||||||||
\(474\) | 4.53998e14 | 0.871512 | ||||||||
\(475\) | 6.30848e13 | 0.119704 | ||||||||
\(476\) | 2.82923e14 | 0.530677 | ||||||||
\(477\) | −3.35431e14 | −0.621945 | ||||||||
\(478\) | −9.46864e13 | −0.173554 | ||||||||
\(479\) | −7.91708e14 | −1.43456 | −0.717281 | − | 0.696784i | \(-0.754614\pi\) | ||||
−0.717281 | + | 0.696784i | \(0.754614\pi\) | |||||||
\(480\) | −3.08475e14 | −0.552577 | ||||||||
\(481\) | 2.14807e13 | 0.0380409 | ||||||||
\(482\) | 5.34667e14 | 0.936105 | ||||||||
\(483\) | 1.72305e13 | 0.0298256 | ||||||||
\(484\) | −9.77606e14 | −1.67307 | ||||||||
\(485\) | 5.47987e14 | 0.927238 | ||||||||
\(486\) | −6.27399e13 | −0.104965 | ||||||||
\(487\) | −7.26034e14 | −1.20101 | −0.600506 | − | 0.799620i | \(-0.705034\pi\) | ||||
−0.600506 | + | 0.799620i | \(0.705034\pi\) | |||||||
\(488\) | −5.34538e14 | −0.874319 | ||||||||
\(489\) | 5.93342e14 | 0.959636 | ||||||||
\(490\) | −1.57945e14 | −0.252597 | ||||||||
\(491\) | 2.64224e14 | 0.417853 | 0.208926 | − | 0.977931i | \(-0.433003\pi\) | ||||
0.208926 | + | 0.977931i | \(0.433003\pi\) | |||||||
\(492\) | −6.72619e13 | −0.105187 | ||||||||
\(493\) | 1.92949e14 | 0.298390 | ||||||||
\(494\) | −2.11724e14 | −0.323797 | ||||||||
\(495\) | −1.19354e13 | −0.0180513 | ||||||||
\(496\) | 9.36246e13 | 0.140036 | ||||||||
\(497\) | 1.57634e14 | 0.233179 | ||||||||
\(498\) | 7.99407e14 | 1.16952 | ||||||||
\(499\) | −3.62474e14 | −0.524474 | −0.262237 | − | 0.965003i | \(-0.584460\pi\) | ||||
−0.262237 | + | 0.965003i | \(0.584460\pi\) | |||||||
\(500\) | 1.05406e15 | 1.50844 | ||||||||
\(501\) | 2.57656e14 | 0.364698 | ||||||||
\(502\) | 1.79564e15 | 2.51391 | ||||||||
\(503\) | −1.20660e15 | −1.67086 | −0.835431 | − | 0.549595i | \(-0.814782\pi\) | ||||
−0.835431 | + | 0.549595i | \(0.814782\pi\) | |||||||
\(504\) | 1.01933e14 | 0.139620 | ||||||||
\(505\) | −7.12377e14 | −0.965178 | ||||||||
\(506\) | −8.36227e12 | −0.0112072 | ||||||||
\(507\) | −3.34996e13 | −0.0444116 | ||||||||
\(508\) | −2.85062e14 | −0.373843 | ||||||||
\(509\) | 3.83919e14 | 0.498072 | 0.249036 | − | 0.968494i | \(-0.419886\pi\) | ||||
0.249036 | + | 0.968494i | \(0.419886\pi\) | |||||||
\(510\) | 6.65846e14 | 0.854550 | ||||||||
\(511\) | −1.10984e13 | −0.0140912 | ||||||||
\(512\) | −2.15879e14 | −0.271160 | ||||||||
\(513\) | −1.10500e14 | −0.137314 | ||||||||
\(514\) | 3.62593e14 | 0.445781 | ||||||||
\(515\) | −4.55726e14 | −0.554325 | ||||||||
\(516\) | −3.50260e14 | −0.421519 | ||||||||
\(517\) | −6.21378e13 | −0.0739874 | ||||||||
\(518\) | −7.20003e13 | −0.0848244 | ||||||||
\(519\) | 6.70247e14 | 0.781294 | ||||||||
\(520\) | 2.87967e14 | 0.332143 | ||||||||
\(521\) | −2.07500e14 | −0.236815 | −0.118408 | − | 0.992965i | \(-0.537779\pi\) | ||||
−0.118408 | + | 0.992965i | \(0.537779\pi\) | |||||||
\(522\) | 1.72157e14 | 0.194418 | ||||||||
\(523\) | 7.56464e14 | 0.845335 | 0.422668 | − | 0.906285i | \(-0.361094\pi\) | ||||
0.422668 | + | 0.906285i | \(0.361094\pi\) | |||||||
\(524\) | −1.21929e15 | −1.34829 | ||||||||
\(525\) | −3.34564e13 | −0.0366103 | ||||||||
\(526\) | −6.02473e14 | −0.652404 | ||||||||
\(527\) | 8.04347e14 | 0.861956 | ||||||||
\(528\) | −3.71026e12 | −0.00393476 | ||||||||
\(529\) | −9.35010e14 | −0.981319 | ||||||||
\(530\) | 3.17626e15 | 3.29913 | ||||||||
\(531\) | 4.21731e14 | 0.433526 | ||||||||
\(532\) | 4.44599e14 | 0.452329 | ||||||||
\(533\) | −2.99187e13 | −0.0301262 | ||||||||
\(534\) | 6.01136e14 | 0.599095 | ||||||||
\(535\) | 4.58461e13 | 0.0452227 | ||||||||
\(536\) | 9.47865e13 | 0.0925423 | ||||||||
\(537\) | 7.84772e14 | 0.758377 | ||||||||
\(538\) | 3.65760e13 | 0.0349859 | ||||||||
\(539\) | 7.56120e12 | 0.00715900 | ||||||||
\(540\) | 3.72194e14 | 0.348821 | ||||||||
\(541\) | 3.73843e14 | 0.346820 | 0.173410 | − | 0.984850i | \(-0.444521\pi\) | ||||
0.173410 | + | 0.984850i | \(0.444521\pi\) | |||||||
\(542\) | 6.59008e14 | 0.605194 | ||||||||
\(543\) | 9.49807e12 | 0.00863448 | ||||||||
\(544\) | −8.23837e14 | −0.741391 | ||||||||
\(545\) | 1.37654e15 | 1.22633 | ||||||||
\(546\) | 1.12286e14 | 0.0990298 | ||||||||
\(547\) | 1.25122e14 | 0.109246 | 0.0546229 | − | 0.998507i | \(-0.482604\pi\) | ||||
0.0546229 | + | 0.998507i | \(0.482604\pi\) | |||||||
\(548\) | −6.23157e14 | −0.538647 | ||||||||
\(549\) | −3.07312e14 | −0.262985 | ||||||||
\(550\) | 1.62370e13 | 0.0137566 | ||||||||
\(551\) | 3.03209e14 | 0.254336 | ||||||||
\(552\) | 1.05298e14 | 0.0874491 | ||||||||
\(553\) | −4.24059e14 | −0.348689 | ||||||||
\(554\) | −9.69941e12 | −0.00789663 | ||||||||
\(555\) | −1.06158e14 | −0.0855738 | ||||||||
\(556\) | −5.38886e14 | −0.430116 | ||||||||
\(557\) | −1.67532e15 | −1.32402 | −0.662009 | − | 0.749496i | \(-0.730296\pi\) | ||||
−0.662009 | + | 0.749496i | \(0.730296\pi\) | |||||||
\(558\) | 7.17673e14 | 0.561615 | ||||||||
\(559\) | −1.55799e14 | −0.120726 | ||||||||
\(560\) | −7.23922e13 | −0.0555466 | ||||||||
\(561\) | −3.18756e13 | −0.0242193 | ||||||||
\(562\) | −5.86056e14 | −0.440950 | ||||||||
\(563\) | 3.81298e14 | 0.284098 | 0.142049 | − | 0.989860i | \(-0.454631\pi\) | ||||
0.142049 | + | 0.989860i | \(0.454631\pi\) | |||||||
\(564\) | 1.93771e15 | 1.42973 | ||||||||
\(565\) | 2.30724e15 | 1.68588 | ||||||||
\(566\) | −3.05304e14 | −0.220923 | ||||||||
\(567\) | 5.86024e13 | 0.0419961 | ||||||||
\(568\) | 9.63322e14 | 0.683684 | ||||||||
\(569\) | −2.07246e15 | −1.45669 | −0.728346 | − | 0.685210i | \(-0.759711\pi\) | ||||
−0.728346 | + | 0.685210i | \(0.759711\pi\) | |||||||
\(570\) | 1.04634e15 | 0.728387 | ||||||||
\(571\) | 5.18865e14 | 0.357730 | 0.178865 | − | 0.983874i | \(-0.442757\pi\) | ||||
0.178865 | + | 0.983874i | \(0.442757\pi\) | |||||||
\(572\) | −3.41400e13 | −0.0233123 | ||||||||
\(573\) | 6.43234e14 | 0.435029 | ||||||||
\(574\) | 1.00283e14 | 0.0671759 | ||||||||
\(575\) | −3.45609e13 | −0.0229304 | ||||||||
\(576\) | −8.04044e14 | −0.528392 | ||||||||
\(577\) | −3.40748e14 | −0.221802 | −0.110901 | − | 0.993831i | \(-0.535374\pi\) | ||||
−0.110901 | + | 0.993831i | \(0.535374\pi\) | |||||||
\(578\) | −7.59499e14 | −0.489693 | ||||||||
\(579\) | 3.24479e14 | 0.207231 | ||||||||
\(580\) | −1.02129e15 | −0.646095 | ||||||||
\(581\) | −7.46689e14 | −0.467919 | ||||||||
\(582\) | 1.30580e15 | 0.810586 | ||||||||
\(583\) | −1.52055e14 | −0.0935026 | ||||||||
\(584\) | −6.78241e13 | −0.0413155 | ||||||||
\(585\) | 1.65555e14 | 0.0999046 | ||||||||
\(586\) | 5.81311e13 | 0.0347514 | ||||||||
\(587\) | −1.68276e15 | −0.996579 | −0.498289 | − | 0.867011i | \(-0.666038\pi\) | ||||
−0.498289 | + | 0.867011i | \(0.666038\pi\) | |||||||
\(588\) | −2.35789e14 | −0.138340 | ||||||||
\(589\) | 1.26399e15 | 0.734699 | ||||||||
\(590\) | −3.99345e15 | −2.29965 | ||||||||
\(591\) | 1.92383e15 | 1.09758 | ||||||||
\(592\) | −3.30005e13 | −0.0186531 | ||||||||
\(593\) | −1.14269e15 | −0.639924 | −0.319962 | − | 0.947430i | \(-0.603670\pi\) | ||||
−0.319962 | + | 0.947430i | \(0.603670\pi\) | |||||||
\(594\) | −2.84408e13 | −0.0157803 | ||||||||
\(595\) | −6.21935e14 | −0.341902 | ||||||||
\(596\) | 2.74978e15 | 1.49776 | ||||||||
\(597\) | −9.78141e14 | −0.527889 | ||||||||
\(598\) | 1.15993e14 | 0.0620260 | ||||||||
\(599\) | 6.29717e14 | 0.333655 | 0.166828 | − | 0.985986i | \(-0.446648\pi\) | ||||
0.166828 | + | 0.985986i | \(0.446648\pi\) | |||||||
\(600\) | −2.04457e14 | −0.107342 | ||||||||
\(601\) | 1.27665e14 | 0.0664142 | 0.0332071 | − | 0.999448i | \(-0.489428\pi\) | ||||
0.0332071 | + | 0.999448i | \(0.489428\pi\) | |||||||
\(602\) | 5.22216e14 | 0.269197 | ||||||||
\(603\) | 5.44937e13 | 0.0278356 | ||||||||
\(604\) | 3.56763e14 | 0.180583 | ||||||||
\(605\) | 2.14902e15 | 1.07792 | ||||||||
\(606\) | −1.69752e15 | −0.843753 | ||||||||
\(607\) | 2.44083e15 | 1.20226 | 0.601131 | − | 0.799150i | \(-0.294717\pi\) | ||||
0.601131 | + | 0.799150i | \(0.294717\pi\) | |||||||
\(608\) | −1.29462e15 | −0.631934 | ||||||||
\(609\) | −1.60804e14 | −0.0777861 | ||||||||
\(610\) | 2.90999e15 | 1.39501 | ||||||||
\(611\) | 8.61910e14 | 0.409483 | ||||||||
\(612\) | 9.94009e14 | 0.468013 | ||||||||
\(613\) | −4.98053e14 | −0.232404 | −0.116202 | − | 0.993226i | \(-0.537072\pi\) | ||||
−0.116202 | + | 0.993226i | \(0.537072\pi\) | |||||||
\(614\) | 2.73391e15 | 1.26432 | ||||||||
\(615\) | 1.47859e14 | 0.0677693 | ||||||||
\(616\) | 4.62076e13 | 0.0209903 | ||||||||
\(617\) | 3.55669e15 | 1.60132 | 0.800660 | − | 0.599119i | \(-0.204482\pi\) | ||||
0.800660 | + | 0.599119i | \(0.204482\pi\) | |||||||
\(618\) | −1.08595e15 | −0.484587 | ||||||||
\(619\) | 3.46294e15 | 1.53161 | 0.765803 | − | 0.643076i | \(-0.222342\pi\) | ||||
0.765803 | + | 0.643076i | \(0.222342\pi\) | |||||||
\(620\) | −4.25748e15 | −1.86637 | ||||||||
\(621\) | 6.05369e13 | 0.0263037 | ||||||||
\(622\) | −5.99139e14 | −0.258036 | ||||||||
\(623\) | −5.61493e14 | −0.239696 | ||||||||
\(624\) | 5.14649e13 | 0.0217769 | ||||||||
\(625\) | −2.71707e15 | −1.13962 | ||||||||
\(626\) | −2.44274e15 | −1.01559 | ||||||||
\(627\) | −5.00908e13 | −0.0206437 | ||||||||
\(628\) | 2.02714e15 | 0.828143 | ||||||||
\(629\) | −2.83513e14 | −0.114814 | ||||||||
\(630\) | −5.54918e14 | −0.222769 | ||||||||
\(631\) | −9.75899e14 | −0.388368 | −0.194184 | − | 0.980965i | \(-0.562206\pi\) | ||||
−0.194184 | + | 0.980965i | \(0.562206\pi\) | |||||||
\(632\) | −2.59148e15 | −1.02236 | ||||||||
\(633\) | −1.47486e15 | −0.576806 | ||||||||
\(634\) | 6.84483e15 | 2.65382 | ||||||||
\(635\) | 6.26638e14 | 0.240858 | ||||||||
\(636\) | 4.74169e15 | 1.80684 | ||||||||
\(637\) | −1.04881e14 | −0.0396214 | ||||||||
\(638\) | 7.80410e13 | 0.0292287 | ||||||||
\(639\) | 5.53824e14 | 0.205644 | ||||||||
\(640\) | 5.01383e15 | 1.84578 | ||||||||
\(641\) | 8.49728e14 | 0.310142 | 0.155071 | − | 0.987903i | \(-0.450439\pi\) | ||||
0.155071 | + | 0.987903i | \(0.450439\pi\) | |||||||
\(642\) | 1.09246e14 | 0.0395334 | ||||||||
\(643\) | −2.73146e15 | −0.980019 | −0.490009 | − | 0.871717i | \(-0.663007\pi\) | ||||
−0.490009 | + | 0.871717i | \(0.663007\pi\) | |||||||
\(644\) | −2.43572e14 | −0.0866475 | ||||||||
\(645\) | 7.69959e14 | 0.271575 | ||||||||
\(646\) | 2.79444e15 | 0.977274 | ||||||||
\(647\) | 3.19400e15 | 1.10755 | 0.553773 | − | 0.832668i | \(-0.313188\pi\) | ||||
0.553773 | + | 0.832668i | \(0.313188\pi\) | |||||||
\(648\) | 3.58128e14 | 0.123133 | ||||||||
\(649\) | 1.91176e14 | 0.0651759 | ||||||||
\(650\) | −2.25223e14 | −0.0761358 | ||||||||
\(651\) | −6.70345e14 | −0.224700 | ||||||||
\(652\) | −8.38755e15 | −2.78788 | ||||||||
\(653\) | 6.96891e14 | 0.229690 | 0.114845 | − | 0.993383i | \(-0.463363\pi\) | ||||
0.114845 | + | 0.993383i | \(0.463363\pi\) | |||||||
\(654\) | 3.28014e15 | 1.07205 | ||||||||
\(655\) | 2.68030e15 | 0.868672 | ||||||||
\(656\) | 4.59636e13 | 0.0147721 | ||||||||
\(657\) | −3.89927e13 | −0.0124272 | ||||||||
\(658\) | −2.88900e15 | −0.913072 | ||||||||
\(659\) | 1.50402e15 | 0.471393 | 0.235697 | − | 0.971827i | \(-0.424263\pi\) | ||||
0.235697 | + | 0.971827i | \(0.424263\pi\) | |||||||
\(660\) | 1.68720e14 | 0.0524415 | ||||||||
\(661\) | 4.38530e15 | 1.35173 | 0.675867 | − | 0.737024i | \(-0.263770\pi\) | ||||
0.675867 | + | 0.737024i | \(0.263770\pi\) | |||||||
\(662\) | 6.49813e15 | 1.98641 | ||||||||
\(663\) | 4.42145e14 | 0.134042 | ||||||||
\(664\) | −4.56312e15 | −1.37195 | ||||||||
\(665\) | −9.77340e14 | −0.291425 | ||||||||
\(666\) | −2.52963e14 | −0.0748081 | ||||||||
\(667\) | −1.66112e14 | −0.0487203 | ||||||||
\(668\) | −3.64226e15 | −1.05950 | ||||||||
\(669\) | 8.95794e14 | 0.258443 | ||||||||
\(670\) | −5.16012e14 | −0.147655 | ||||||||
\(671\) | −1.39308e14 | −0.0395369 | ||||||||
\(672\) | 6.86588e14 | 0.193270 | ||||||||
\(673\) | 6.14083e15 | 1.71453 | 0.857263 | − | 0.514879i | \(-0.172163\pi\) | ||||
0.857263 | + | 0.514879i | \(0.172163\pi\) | |||||||
\(674\) | 1.15268e15 | 0.319213 | ||||||||
\(675\) | −1.17544e14 | −0.0322873 | ||||||||
\(676\) | 4.73554e14 | 0.129022 | ||||||||
\(677\) | −1.92471e15 | −0.520149 | −0.260074 | − | 0.965589i | \(-0.583747\pi\) | ||||
−0.260074 | + | 0.965589i | \(0.583747\pi\) | |||||||
\(678\) | 5.49791e15 | 1.47379 | ||||||||
\(679\) | −1.21968e15 | −0.324312 | ||||||||
\(680\) | −3.80074e15 | −1.00246 | ||||||||
\(681\) | −2.04376e15 | −0.534713 | ||||||||
\(682\) | 3.25330e14 | 0.0844327 | ||||||||
\(683\) | −2.11279e15 | −0.543930 | −0.271965 | − | 0.962307i | \(-0.587673\pi\) | ||||
−0.271965 | + | 0.962307i | \(0.587673\pi\) | |||||||
\(684\) | 1.56203e15 | 0.398917 | ||||||||
\(685\) | 1.36985e15 | 0.347037 | ||||||||
\(686\) | 3.51546e14 | 0.0883487 | ||||||||
\(687\) | −6.24639e14 | −0.155728 | ||||||||
\(688\) | 2.39351e14 | 0.0591969 | ||||||||
\(689\) | 2.10915e15 | 0.517490 | ||||||||
\(690\) | −5.73236e14 | −0.139529 | ||||||||
\(691\) | 3.89904e15 | 0.941518 | 0.470759 | − | 0.882262i | \(-0.343980\pi\) | ||||
0.470759 | + | 0.882262i | \(0.343980\pi\) | |||||||
\(692\) | −9.47469e15 | −2.26977 | ||||||||
\(693\) | 2.65652e13 | 0.00631365 | ||||||||
\(694\) | −9.87155e15 | −2.32760 | ||||||||
\(695\) | 1.18461e15 | 0.277114 | ||||||||
\(696\) | −9.82696e14 | −0.228070 | ||||||||
\(697\) | 3.94883e14 | 0.0909259 | ||||||||
\(698\) | −6.42070e14 | −0.146682 | ||||||||
\(699\) | 2.60858e14 | 0.0591261 | ||||||||
\(700\) | 4.72944e14 | 0.106358 | ||||||||
\(701\) | 1.40144e15 | 0.312699 | 0.156349 | − | 0.987702i | \(-0.450027\pi\) | ||||
0.156349 | + | 0.987702i | \(0.450027\pi\) | |||||||
\(702\) | 3.94501e14 | 0.0873361 | ||||||||
\(703\) | −4.45527e14 | −0.0978632 | ||||||||
\(704\) | −3.64483e14 | −0.0794379 | ||||||||
\(705\) | −4.25956e15 | −0.921139 | ||||||||
\(706\) | −6.11717e15 | −1.31258 | ||||||||
\(707\) | 1.58557e15 | 0.337582 | ||||||||
\(708\) | −5.96164e15 | −1.25945 | ||||||||
\(709\) | −1.28974e15 | −0.270364 | −0.135182 | − | 0.990821i | \(-0.543162\pi\) | ||||
−0.135182 | + | 0.990821i | \(0.543162\pi\) | |||||||
\(710\) | −5.24427e15 | −1.09085 | ||||||||
\(711\) | −1.48987e15 | −0.307514 | ||||||||
\(712\) | −3.43136e15 | −0.702792 | ||||||||
\(713\) | −6.92474e14 | −0.140738 | ||||||||
\(714\) | −1.48201e15 | −0.298889 | ||||||||
\(715\) | 7.50483e13 | 0.0150196 | ||||||||
\(716\) | −1.10936e16 | −2.20319 | ||||||||
\(717\) | 3.10729e14 | 0.0612388 | ||||||||
\(718\) | −8.03002e15 | −1.57048 | ||||||||
\(719\) | −8.30132e14 | −0.161116 | −0.0805579 | − | 0.996750i | \(-0.525670\pi\) | ||||
−0.0805579 | + | 0.996750i | \(0.525670\pi\) | |||||||
\(720\) | −2.54340e14 | −0.0489875 | ||||||||
\(721\) | 1.01433e15 | 0.193882 | ||||||||
\(722\) | −4.23452e15 | −0.803248 | ||||||||
\(723\) | −1.75460e15 | −0.330306 | ||||||||
\(724\) | −1.34266e14 | −0.0250844 | ||||||||
\(725\) | 3.22540e14 | 0.0598033 | ||||||||
\(726\) | 5.12090e15 | 0.942312 | ||||||||
\(727\) | 7.61457e15 | 1.39061 | 0.695306 | − | 0.718714i | \(-0.255269\pi\) | ||||
0.695306 | + | 0.718714i | \(0.255269\pi\) | |||||||
\(728\) | −6.40943e14 | −0.116171 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 3.69230e14 | 0.0659206 | ||||||||
\(731\) | 2.05631e15 | 0.364371 | ||||||||
\(732\) | 4.34419e15 | 0.764008 | ||||||||
\(733\) | −6.17483e15 | −1.07784 | −0.538918 | − | 0.842358i | \(-0.681167\pi\) | ||||
−0.538918 | + | 0.842358i | \(0.681167\pi\) | |||||||
\(734\) | −4.84501e15 | −0.839396 | ||||||||
\(735\) | 5.18323e14 | 0.0891292 | ||||||||
\(736\) | 7.09253e14 | 0.121052 | ||||||||
\(737\) | 2.47027e13 | 0.00418478 | ||||||||
\(738\) | 3.52331e14 | 0.0592436 | ||||||||
\(739\) | 1.02585e16 | 1.71214 | 0.856071 | − | 0.516859i | \(-0.172899\pi\) | ||||
0.856071 | + | 0.516859i | \(0.172899\pi\) | |||||||
\(740\) | 1.50066e15 | 0.248604 | ||||||||
\(741\) | 6.94808e14 | 0.114252 | ||||||||
\(742\) | −7.06957e15 | −1.15391 | ||||||||
\(743\) | −6.76264e15 | −1.09567 | −0.547833 | − | 0.836588i | \(-0.684547\pi\) | ||||
−0.547833 | + | 0.836588i | \(0.684547\pi\) | |||||||
\(744\) | −4.09658e15 | −0.658825 | ||||||||
\(745\) | −6.04470e15 | −0.964974 | ||||||||
\(746\) | −1.15703e16 | −1.83350 | ||||||||
\(747\) | −2.62339e15 | −0.412666 | ||||||||
\(748\) | 4.50597e14 | 0.0703606 | ||||||||
\(749\) | −1.02042e14 | −0.0158172 | ||||||||
\(750\) | −5.52135e15 | −0.849589 | ||||||||
\(751\) | 5.71122e15 | 0.872387 | 0.436193 | − | 0.899853i | \(-0.356326\pi\) | ||||
0.436193 | + | 0.899853i | \(0.356326\pi\) | |||||||
\(752\) | −1.32414e15 | −0.200787 | ||||||||
\(753\) | −5.89270e15 | −0.887037 | ||||||||
\(754\) | −1.08250e15 | −0.161766 | ||||||||
\(755\) | −7.84254e14 | −0.116345 | ||||||||
\(756\) | −8.28410e14 | −0.122004 | ||||||||
\(757\) | 9.93012e15 | 1.45187 | 0.725934 | − | 0.687765i | \(-0.241408\pi\) | ||||
0.725934 | + | 0.687765i | \(0.241408\pi\) | |||||||
\(758\) | 1.46517e16 | 2.12671 | ||||||||
\(759\) | 2.74421e13 | 0.00395447 | ||||||||
\(760\) | −5.97266e15 | −0.854463 | ||||||||
\(761\) | −9.02345e15 | −1.28161 | −0.640807 | − | 0.767702i | \(-0.721400\pi\) | ||||
−0.640807 | + | 0.767702i | \(0.721400\pi\) | |||||||
\(762\) | 1.49321e15 | 0.210557 | ||||||||
\(763\) | −3.06383e15 | −0.428923 | ||||||||
\(764\) | −9.09283e15 | −1.26382 | ||||||||
\(765\) | −2.18508e15 | −0.301529 | ||||||||
\(766\) | 1.02016e16 | 1.39769 | ||||||||
\(767\) | −2.65179e15 | −0.360716 | ||||||||
\(768\) | 5.17096e15 | 0.698369 | ||||||||
\(769\) | −2.66286e15 | −0.357070 | −0.178535 | − | 0.983934i | \(-0.557136\pi\) | ||||
−0.178535 | + | 0.983934i | \(0.557136\pi\) | |||||||
\(770\) | −2.51551e14 | −0.0334909 | ||||||||
\(771\) | −1.18991e15 | −0.157295 | ||||||||
\(772\) | −4.58688e15 | −0.602035 | ||||||||
\(773\) | 5.60938e15 | 0.731018 | 0.365509 | − | 0.930808i | \(-0.380895\pi\) | ||||
0.365509 | + | 0.930808i | \(0.380895\pi\) | |||||||
\(774\) | 1.83473e15 | 0.237409 | ||||||||
\(775\) | 1.34458e15 | 0.172753 | ||||||||
\(776\) | −7.45366e15 | −0.950890 | ||||||||
\(777\) | 2.36281e14 | 0.0299304 | ||||||||
\(778\) | −1.47017e16 | −1.84919 | ||||||||
\(779\) | 6.20538e14 | 0.0775019 | ||||||||
\(780\) | −2.34031e15 | −0.290237 | ||||||||
\(781\) | 2.51055e14 | 0.0309164 | ||||||||
\(782\) | −1.53093e15 | −0.187205 | ||||||||
\(783\) | −5.64962e14 | −0.0686009 | ||||||||
\(784\) | 1.61127e14 | 0.0194281 | ||||||||
\(785\) | −4.45616e15 | −0.533553 | ||||||||
\(786\) | 6.38687e15 | 0.759388 | ||||||||
\(787\) | −9.15425e15 | −1.08084 | −0.540420 | − | 0.841395i | \(-0.681735\pi\) | ||||
−0.540420 | + | 0.841395i | \(0.681735\pi\) | |||||||
\(788\) | −2.71954e16 | −3.18861 | ||||||||
\(789\) | 1.97712e15 | 0.230202 | ||||||||
\(790\) | 1.41079e16 | 1.63122 | ||||||||
\(791\) | −5.13535e15 | −0.589657 | ||||||||
\(792\) | 1.62344e14 | 0.0185117 | ||||||||
\(793\) | 1.93234e15 | 0.218817 | ||||||||
\(794\) | −2.48397e16 | −2.79340 | ||||||||
\(795\) | −1.04234e16 | −1.16410 | ||||||||
\(796\) | 1.38271e16 | 1.53359 | ||||||||
\(797\) | 3.59302e14 | 0.0395767 | 0.0197883 | − | 0.999804i | \(-0.493701\pi\) | ||||
0.0197883 | + | 0.999804i | \(0.493701\pi\) | |||||||
\(798\) | −2.32890e15 | −0.254762 | ||||||||
\(799\) | −1.13759e16 | −1.23589 | ||||||||
\(800\) | −1.37716e15 | −0.148589 | ||||||||
\(801\) | −1.97272e15 | −0.211392 | ||||||||
\(802\) | 2.29189e16 | 2.43913 | ||||||||
\(803\) | −1.76759e13 | −0.00186830 | ||||||||
\(804\) | −7.70330e14 | −0.0808664 | ||||||||
\(805\) | 5.35433e14 | 0.0558249 | ||||||||
\(806\) | −4.51264e15 | −0.467292 | ||||||||
\(807\) | −1.20030e14 | −0.0123448 | ||||||||
\(808\) | 9.68967e15 | 0.989798 | ||||||||
\(809\) | 2.58777e14 | 0.0262548 | 0.0131274 | − | 0.999914i | \(-0.495821\pi\) | ||||
0.0131274 | + | 0.999914i | \(0.495821\pi\) | |||||||
\(810\) | −1.94962e15 | −0.196464 | ||||||||
\(811\) | 2.69714e15 | 0.269953 | 0.134977 | − | 0.990849i | \(-0.456904\pi\) | ||||
0.134977 | + | 0.990849i | \(0.456904\pi\) | |||||||
\(812\) | 2.27314e15 | 0.225979 | ||||||||
\(813\) | −2.16264e15 | −0.213544 | ||||||||
\(814\) | −1.14671e14 | −0.0112466 | ||||||||
\(815\) | 1.84379e16 | 1.79616 | ||||||||
\(816\) | −6.79259e14 | −0.0657264 | ||||||||
\(817\) | 3.23139e15 | 0.310576 | ||||||||
\(818\) | 4.49360e14 | 0.0428994 | ||||||||
\(819\) | −3.68485e14 | −0.0349428 | ||||||||
\(820\) | −2.09015e15 | −0.196879 | ||||||||
\(821\) | −8.55122e15 | −0.800093 | −0.400047 | − | 0.916495i | \(-0.631006\pi\) | ||||
−0.400047 | + | 0.916495i | \(0.631006\pi\) | |||||||
\(822\) | 3.26422e15 | 0.303378 | ||||||||
\(823\) | 3.60803e15 | 0.333097 | 0.166549 | − | 0.986033i | \(-0.446738\pi\) | ||||
0.166549 | + | 0.986033i | \(0.446738\pi\) | |||||||
\(824\) | 6.19873e15 | 0.568464 | ||||||||
\(825\) | −5.32844e13 | −0.00485404 | ||||||||
\(826\) | 8.88843e15 | 0.804331 | ||||||||
\(827\) | −5.08928e14 | −0.0457484 | −0.0228742 | − | 0.999738i | \(-0.507282\pi\) | ||||
−0.0228742 | + | 0.999738i | \(0.507282\pi\) | |||||||
\(828\) | −8.55757e14 | −0.0764159 | ||||||||
\(829\) | −5.41270e15 | −0.480136 | −0.240068 | − | 0.970756i | \(-0.577170\pi\) | ||||
−0.240068 | + | 0.970756i | \(0.577170\pi\) | |||||||
\(830\) | 2.48414e16 | 2.18900 | ||||||||
\(831\) | 3.18302e13 | 0.00278634 | ||||||||
\(832\) | 5.05573e15 | 0.439649 | ||||||||
\(833\) | 1.38427e15 | 0.119584 | ||||||||
\(834\) | 2.82279e15 | 0.242251 | ||||||||
\(835\) | 8.00660e15 | 0.682610 | ||||||||
\(836\) | 7.08090e14 | 0.0599727 | ||||||||
\(837\) | −2.35516e15 | −0.198167 | ||||||||
\(838\) | −2.07938e15 | −0.173817 | ||||||||
\(839\) | −2.07436e16 | −1.72263 | −0.861316 | − | 0.508069i | \(-0.830359\pi\) | ||||
−0.861316 | + | 0.508069i | \(0.830359\pi\) | |||||||
\(840\) | 3.16754e15 | 0.261328 | ||||||||
\(841\) | −1.06503e16 | −0.872936 | ||||||||
\(842\) | 1.70648e16 | 1.38958 | ||||||||
\(843\) | 1.92324e15 | 0.155590 | ||||||||
\(844\) | 2.08487e16 | 1.67570 | ||||||||
\(845\) | −1.04099e15 | −0.0831257 | ||||||||
\(846\) | −1.01501e16 | −0.805254 | ||||||||
\(847\) | −4.78319e15 | −0.377015 | ||||||||
\(848\) | −3.24025e15 | −0.253747 | ||||||||
\(849\) | 1.00190e15 | 0.0779532 | ||||||||
\(850\) | 2.97260e15 | 0.229791 | ||||||||
\(851\) | 2.44081e14 | 0.0187465 | ||||||||
\(852\) | −7.82892e15 | −0.597426 | ||||||||
\(853\) | −2.46016e16 | −1.86528 | −0.932639 | − | 0.360810i | \(-0.882500\pi\) | ||||
−0.932639 | + | 0.360810i | \(0.882500\pi\) | |||||||
\(854\) | −6.47692e15 | −0.487922 | ||||||||
\(855\) | −3.43374e15 | −0.257012 | ||||||||
\(856\) | −6.23593e14 | −0.0463762 | ||||||||
\(857\) | 1.68045e16 | 1.24174 | 0.620871 | − | 0.783913i | \(-0.286779\pi\) | ||||
0.620871 | + | 0.783913i | \(0.286779\pi\) | |||||||
\(858\) | 1.78832e14 | 0.0131300 | ||||||||
\(859\) | 6.85287e15 | 0.499931 | 0.249966 | − | 0.968255i | \(-0.419581\pi\) | ||||
0.249966 | + | 0.968255i | \(0.419581\pi\) | |||||||
\(860\) | −1.08842e16 | −0.788962 | ||||||||
\(861\) | −3.29096e14 | −0.0237031 | ||||||||
\(862\) | 1.63747e16 | 1.17188 | ||||||||
\(863\) | −6.49574e15 | −0.461922 | −0.230961 | − | 0.972963i | \(-0.574187\pi\) | ||||
−0.230961 | + | 0.972963i | \(0.574187\pi\) | |||||||
\(864\) | 2.41223e15 | 0.170448 | ||||||||
\(865\) | 2.08277e16 | 1.46236 | ||||||||
\(866\) | −1.93623e16 | −1.35086 | ||||||||
\(867\) | 2.49242e15 | 0.172789 | ||||||||
\(868\) | 9.47608e15 | 0.652785 | ||||||||
\(869\) | −6.75377e14 | −0.0462314 | ||||||||
\(870\) | 5.34974e15 | 0.363895 | ||||||||
\(871\) | −3.42650e14 | −0.0231607 | ||||||||
\(872\) | −1.87235e16 | −1.25761 | ||||||||
\(873\) | −4.28518e15 | −0.286017 | ||||||||
\(874\) | −2.40578e15 | −0.159567 | ||||||||
\(875\) | 5.15724e15 | 0.339917 | ||||||||
\(876\) | 5.51206e14 | 0.0361028 | ||||||||
\(877\) | 2.71964e15 | 0.177017 | 0.0885084 | − | 0.996075i | \(-0.471790\pi\) | ||||
0.0885084 | + | 0.996075i | \(0.471790\pi\) | |||||||
\(878\) | 4.37557e16 | 2.83018 | ||||||||
\(879\) | −1.90767e14 | −0.0122621 | ||||||||
\(880\) | −1.15295e14 | −0.00736473 | ||||||||
\(881\) | −2.82071e16 | −1.79057 | −0.895283 | − | 0.445498i | \(-0.853027\pi\) | ||||
−0.895283 | + | 0.445498i | \(0.853027\pi\) | |||||||
\(882\) | 1.23511e15 | 0.0779162 | ||||||||
\(883\) | 8.56937e15 | 0.537236 | 0.268618 | − | 0.963247i | \(-0.413433\pi\) | ||||
0.268618 | + | 0.963247i | \(0.413433\pi\) | |||||||
\(884\) | −6.25021e15 | −0.389410 | ||||||||
\(885\) | 1.31052e16 | 0.811437 | ||||||||
\(886\) | −1.75239e16 | −1.07832 | ||||||||
\(887\) | 1.03919e16 | 0.635501 | 0.317750 | − | 0.948174i | \(-0.397073\pi\) | ||||
0.317750 | + | 0.948174i | \(0.397073\pi\) | |||||||
\(888\) | 1.44395e15 | 0.0877566 | ||||||||
\(889\) | −1.39474e15 | −0.0842430 | ||||||||
\(890\) | 1.86801e16 | 1.12133 | ||||||||
\(891\) | 9.33330e13 | 0.00556811 | ||||||||
\(892\) | −1.26631e16 | −0.750813 | ||||||||
\(893\) | −1.78767e16 | −1.05343 | ||||||||
\(894\) | −1.44039e16 | −0.843574 | ||||||||
\(895\) | 2.43866e16 | 1.41946 | ||||||||
\(896\) | −1.11595e16 | −0.645583 | ||||||||
\(897\) | −3.80649e14 | −0.0218860 | ||||||||
\(898\) | 4.48424e16 | 2.56253 | ||||||||
\(899\) | 6.46253e15 | 0.367049 | ||||||||
\(900\) | 1.66162e15 | 0.0937991 | ||||||||
\(901\) | −2.78376e16 | −1.56187 | ||||||||
\(902\) | 1.59716e14 | 0.00890662 | ||||||||
\(903\) | −1.71374e15 | −0.0949864 | ||||||||
\(904\) | −3.13828e16 | −1.72888 | ||||||||
\(905\) | 2.95150e14 | 0.0161613 | ||||||||
\(906\) | −1.86879e15 | −0.101708 | ||||||||
\(907\) | 1.59311e16 | 0.861801 | 0.430900 | − | 0.902399i | \(-0.358196\pi\) | ||||
0.430900 | + | 0.902399i | \(0.358196\pi\) | |||||||
\(908\) | 2.88908e16 | 1.55342 | ||||||||
\(909\) | 5.57069e15 | 0.297720 | ||||||||
\(910\) | 3.48926e15 | 0.185355 | ||||||||
\(911\) | 1.39159e16 | 0.734783 | 0.367391 | − | 0.930066i | \(-0.380251\pi\) | ||||
0.367391 | + | 0.930066i | \(0.380251\pi\) | |||||||
\(912\) | −1.06742e15 | −0.0560227 | ||||||||
\(913\) | −1.18921e15 | −0.0620398 | ||||||||
\(914\) | −1.63053e16 | −0.845521 | ||||||||
\(915\) | −9.54962e15 | −0.492232 | ||||||||
\(916\) | 8.82997e15 | 0.452412 | ||||||||
\(917\) | −5.96567e15 | −0.303828 | ||||||||
\(918\) | −5.20682e15 | −0.263595 | ||||||||
\(919\) | −1.78142e16 | −0.896461 | −0.448231 | − | 0.893918i | \(-0.647946\pi\) | ||||
−0.448231 | + | 0.893918i | \(0.647946\pi\) | |||||||
\(920\) | 3.27211e15 | 0.163680 | ||||||||
\(921\) | −8.97177e15 | −0.446119 | ||||||||
\(922\) | 7.59402e15 | 0.375363 | ||||||||
\(923\) | −3.48238e15 | −0.171106 | ||||||||
\(924\) | −3.75529e14 | −0.0183420 | ||||||||
\(925\) | −4.73931e14 | −0.0230110 | ||||||||
\(926\) | 3.68517e16 | 1.77868 | ||||||||
\(927\) | 3.56371e15 | 0.170988 | ||||||||
\(928\) | −6.61912e15 | −0.315708 | ||||||||
\(929\) | −1.85742e15 | −0.0880689 | −0.0440344 | − | 0.999030i | \(-0.514021\pi\) | ||||
−0.0440344 | + | 0.999030i | \(0.514021\pi\) | |||||||
\(930\) | 2.23015e16 | 1.05118 | ||||||||
\(931\) | 2.17531e15 | 0.101929 | ||||||||
\(932\) | −3.68751e15 | −0.171770 | ||||||||
\(933\) | 1.96617e15 | 0.0910485 | ||||||||
\(934\) | 6.26022e16 | 2.88192 | ||||||||
\(935\) | −9.90525e14 | −0.0453317 | ||||||||
\(936\) | −2.25186e15 | −0.102453 | ||||||||
\(937\) | 5.68991e15 | 0.257358 | 0.128679 | − | 0.991686i | \(-0.458926\pi\) | ||||
0.128679 | + | 0.991686i | \(0.458926\pi\) | |||||||
\(938\) | 1.14851e15 | 0.0516441 | ||||||||
\(939\) | 8.01626e15 | 0.358353 | ||||||||
\(940\) | 6.02137e16 | 2.67604 | ||||||||
\(941\) | 5.60191e15 | 0.247510 | 0.123755 | − | 0.992313i | \(-0.460506\pi\) | ||||
0.123755 | + | 0.992313i | \(0.460506\pi\) | |||||||
\(942\) | −1.06186e16 | −0.466429 | ||||||||
\(943\) | −3.39960e14 | −0.0148461 | ||||||||
\(944\) | 4.07390e15 | 0.176874 | ||||||||
\(945\) | 1.82105e15 | 0.0786045 | ||||||||
\(946\) | 8.31707e14 | 0.0356918 | ||||||||
\(947\) | 4.81691e15 | 0.205515 | 0.102758 | − | 0.994706i | \(-0.467233\pi\) | ||||
0.102758 | + | 0.994706i | \(0.467233\pi\) | |||||||
\(948\) | 2.10610e16 | 0.893373 | ||||||||
\(949\) | 2.45182e14 | 0.0103401 | ||||||||
\(950\) | 4.67129e15 | 0.195865 | ||||||||
\(951\) | −2.24624e16 | −0.936405 | ||||||||
\(952\) | 8.45949e15 | 0.350624 | ||||||||
\(953\) | −3.95501e16 | −1.62981 | −0.814905 | − | 0.579594i | \(-0.803211\pi\) | ||||
−0.814905 | + | 0.579594i | \(0.803211\pi\) | |||||||
\(954\) | −2.48379e16 | −1.01765 | ||||||||
\(955\) | 1.99883e16 | 0.814250 | ||||||||
\(956\) | −4.39250e15 | −0.177907 | ||||||||
\(957\) | −2.56104e14 | −0.0103134 | ||||||||
\(958\) | −5.86242e16 | −2.34729 | ||||||||
\(959\) | −3.04895e15 | −0.121380 | ||||||||
\(960\) | −2.49854e16 | −0.988998 | ||||||||
\(961\) | 1.53193e15 | 0.0602920 | ||||||||
\(962\) | 1.59060e15 | 0.0622441 | ||||||||
\(963\) | −3.58510e14 | −0.0139494 | ||||||||
\(964\) | 2.48032e16 | 0.959585 | ||||||||
\(965\) | 1.00831e16 | 0.387877 | ||||||||
\(966\) | 1.27588e15 | 0.0488018 | ||||||||
\(967\) | −1.96372e16 | −0.746851 | −0.373425 | − | 0.927660i | \(-0.621817\pi\) | ||||
−0.373425 | + | 0.927660i | \(0.621817\pi\) | |||||||
\(968\) | −2.92308e16 | −1.10542 | ||||||||
\(969\) | −9.17043e15 | −0.344833 | ||||||||
\(970\) | 4.05773e16 | 1.51718 | ||||||||
\(971\) | −4.13717e16 | −1.53814 | −0.769072 | − | 0.639162i | \(-0.779281\pi\) | ||||
−0.769072 | + | 0.639162i | \(0.779281\pi\) | |||||||
\(972\) | −2.91050e15 | −0.107598 | ||||||||
\(973\) | −2.63664e15 | −0.0969237 | ||||||||
\(974\) | −5.37612e16 | −1.96515 | ||||||||
\(975\) | 7.39105e14 | 0.0268646 | ||||||||
\(976\) | −2.96862e15 | −0.107295 | ||||||||
\(977\) | 6.47244e15 | 0.232620 | 0.116310 | − | 0.993213i | \(-0.462893\pi\) | ||||
0.116310 | + | 0.993213i | \(0.462893\pi\) | |||||||
\(978\) | 4.39357e16 | 1.57020 | ||||||||
\(979\) | −8.94261e14 | −0.0317804 | ||||||||
\(980\) | −7.32707e15 | −0.258933 | ||||||||
\(981\) | −1.07643e16 | −0.378275 | ||||||||
\(982\) | 1.95652e16 | 0.683708 | ||||||||
\(983\) | −2.03123e16 | −0.705852 | −0.352926 | − | 0.935651i | \(-0.614813\pi\) | ||||
−0.352926 | + | 0.935651i | \(0.614813\pi\) | |||||||
\(984\) | −2.01115e15 | −0.0694980 | ||||||||
\(985\) | 5.97824e16 | 2.05435 | ||||||||
\(986\) | 1.42874e16 | 0.488237 | ||||||||
\(987\) | 9.48073e15 | 0.322179 | ||||||||
\(988\) | −9.82189e15 | −0.331919 | ||||||||
\(989\) | −1.77031e15 | −0.0594935 | ||||||||
\(990\) | −8.83789e14 | −0.0295362 | ||||||||
\(991\) | 1.53995e16 | 0.511801 | 0.255901 | − | 0.966703i | \(-0.417628\pi\) | ||||
0.255901 | + | 0.966703i | \(0.417628\pi\) | |||||||
\(992\) | −2.75932e16 | −0.911985 | ||||||||
\(993\) | −2.13247e16 | −0.700909 | ||||||||
\(994\) | 1.16724e16 | 0.381537 | ||||||||
\(995\) | −3.03955e16 | −0.988057 | ||||||||
\(996\) | 3.70845e16 | 1.19885 | ||||||||
\(997\) | −1.44352e15 | −0.0464088 | −0.0232044 | − | 0.999731i | \(-0.507387\pi\) | ||||
−0.0232044 | + | 0.999731i | \(0.507387\pi\) | |||||||
\(998\) | −2.68404e16 | −0.858166 | ||||||||
\(999\) | 8.30139e14 | 0.0263962 |
(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 | 273.12.a.c.1.15 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.12.a.c.1.15 | ✓ | 16 | 1.1 | even | 1 | trivial |