Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −12.5454 | −0.554435 | −0.277217 | − | 0.960807i | \(-0.589412\pi\) | ||||
−0.277217 | + | 0.960807i | \(0.589412\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −354.612 | −0.692602 | ||||||||
\(5\) | 2378.79 | 1.70213 | 0.851063 | − | 0.525064i | \(-0.175959\pi\) | ||||
0.851063 | + | 0.525064i | \(0.175959\pi\) | |||||||
\(6\) | 1016.18 | 0.320103 | ||||||||
\(7\) | 4679.29 | 0.736612 | 0.368306 | − | 0.929705i | \(-0.379938\pi\) | ||||
0.368306 | + | 0.929705i | \(0.379938\pi\) | |||||||
\(8\) | 10872.0 | 0.938438 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −29843.0 | −0.943718 | ||||||||
\(11\) | 27377.3 | 0.563797 | 0.281899 | − | 0.959444i | \(-0.409036\pi\) | ||||
0.281899 | + | 0.959444i | \(0.409036\pi\) | |||||||
\(12\) | 28723.6 | 0.399874 | ||||||||
\(13\) | −94968.3 | −0.922218 | −0.461109 | − | 0.887344i | \(-0.652548\pi\) | ||||
−0.461109 | + | 0.887344i | \(0.652548\pi\) | |||||||
\(14\) | −58703.7 | −0.408403 | ||||||||
\(15\) | −192682. | −0.982723 | ||||||||
\(16\) | 45167.3 | 0.172299 | ||||||||
\(17\) | −363572. | −1.05577 | −0.527886 | − | 0.849315i | \(-0.677015\pi\) | ||||
−0.527886 | + | 0.849315i | \(0.677015\pi\) | |||||||
\(18\) | −82310.6 | −0.184812 | ||||||||
\(19\) | −703094. | −1.23772 | −0.618859 | − | 0.785502i | \(-0.712405\pi\) | ||||
−0.618859 | + | 0.785502i | \(0.712405\pi\) | |||||||
\(20\) | −843549. | −1.17890 | ||||||||
\(21\) | −379022. | −0.425283 | ||||||||
\(22\) | −343460. | −0.312589 | ||||||||
\(23\) | 1.27907e6 | 0.953057 | 0.476529 | − | 0.879159i | \(-0.341895\pi\) | ||||
0.476529 | + | 0.879159i | \(0.341895\pi\) | |||||||
\(24\) | −880634. | −0.541807 | ||||||||
\(25\) | 3.70553e6 | 1.89723 | ||||||||
\(26\) | 1.19142e6 | 0.511310 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −1.65933e6 | −0.510179 | ||||||||
\(29\) | −6.03733e6 | −1.58509 | −0.792545 | − | 0.609813i | \(-0.791245\pi\) | ||||
−0.792545 | + | 0.609813i | \(0.791245\pi\) | |||||||
\(30\) | 2.41728e6 | 0.544856 | ||||||||
\(31\) | −2.91796e6 | −0.567481 | −0.283740 | − | 0.958901i | \(-0.591575\pi\) | ||||
−0.283740 | + | 0.958901i | \(0.591575\pi\) | |||||||
\(32\) | −6.13312e6 | −1.03397 | ||||||||
\(33\) | −2.21756e6 | −0.325508 | ||||||||
\(34\) | 4.56116e6 | 0.585356 | ||||||||
\(35\) | 1.11311e7 | 1.25381 | ||||||||
\(36\) | −2.32661e6 | −0.230867 | ||||||||
\(37\) | 8.60765e6 | 0.755052 | 0.377526 | − | 0.925999i | \(-0.376775\pi\) | ||||
0.377526 | + | 0.925999i | \(0.376775\pi\) | |||||||
\(38\) | 8.82061e6 | 0.686234 | ||||||||
\(39\) | 7.69243e6 | 0.532443 | ||||||||
\(40\) | 2.58623e7 | 1.59734 | ||||||||
\(41\) | −1.66287e7 | −0.919033 | −0.459516 | − | 0.888169i | \(-0.651977\pi\) | ||||
−0.459516 | + | 0.888169i | \(0.651977\pi\) | |||||||
\(42\) | 4.75500e6 | 0.235792 | ||||||||
\(43\) | 3.19196e7 | 1.42380 | 0.711900 | − | 0.702281i | \(-0.247835\pi\) | ||||
0.711900 | + | 0.702281i | \(0.247835\pi\) | |||||||
\(44\) | −9.70831e6 | −0.390487 | ||||||||
\(45\) | 1.56073e7 | 0.567375 | ||||||||
\(46\) | −1.60465e7 | −0.528408 | ||||||||
\(47\) | 4.06112e7 | 1.21396 | 0.606982 | − | 0.794716i | \(-0.292380\pi\) | ||||
0.606982 | + | 0.794716i | \(0.292380\pi\) | |||||||
\(48\) | −3.65855e6 | −0.0994771 | ||||||||
\(49\) | −1.84579e7 | −0.457403 | ||||||||
\(50\) | −4.64875e7 | −1.05189 | ||||||||
\(51\) | 2.94493e7 | 0.609550 | ||||||||
\(52\) | 3.36769e7 | 0.638730 | ||||||||
\(53\) | −6.97055e7 | −1.21346 | −0.606731 | − | 0.794907i | \(-0.707519\pi\) | ||||
−0.606731 | + | 0.794907i | \(0.707519\pi\) | |||||||
\(54\) | 6.66716e6 | 0.106701 | ||||||||
\(55\) | 6.51248e7 | 0.959654 | ||||||||
\(56\) | 5.08733e7 | 0.691264 | ||||||||
\(57\) | 5.69506e7 | 0.714597 | ||||||||
\(58\) | 7.57409e7 | 0.878830 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | 6.83275e7 | 0.680636 | ||||||||
\(61\) | −6.34803e7 | −0.587022 | −0.293511 | − | 0.955956i | \(-0.594824\pi\) | ||||
−0.293511 | + | 0.955956i | \(0.594824\pi\) | |||||||
\(62\) | 3.66070e7 | 0.314631 | ||||||||
\(63\) | 3.07008e7 | 0.245537 | ||||||||
\(64\) | 5.38170e7 | 0.400968 | ||||||||
\(65\) | −2.25910e8 | −1.56973 | ||||||||
\(66\) | 2.78202e7 | 0.180473 | ||||||||
\(67\) | −1.72165e8 | −1.04378 | −0.521888 | − | 0.853014i | \(-0.674772\pi\) | ||||
−0.521888 | + | 0.853014i | \(0.674772\pi\) | |||||||
\(68\) | 1.28927e8 | 0.731229 | ||||||||
\(69\) | −1.03605e8 | −0.550248 | ||||||||
\(70\) | −1.39644e8 | −0.695153 | ||||||||
\(71\) | −1.91685e8 | −0.895212 | −0.447606 | − | 0.894231i | \(-0.647723\pi\) | ||||
−0.447606 | + | 0.894231i | \(0.647723\pi\) | |||||||
\(72\) | 7.13313e7 | 0.312813 | ||||||||
\(73\) | 1.49098e8 | 0.614494 | 0.307247 | − | 0.951630i | \(-0.400592\pi\) | ||||
0.307247 | + | 0.951630i | \(0.400592\pi\) | |||||||
\(74\) | −1.07987e8 | −0.418627 | ||||||||
\(75\) | −3.00148e8 | −1.09537 | ||||||||
\(76\) | 2.49326e8 | 0.857246 | ||||||||
\(77\) | 1.28106e8 | 0.415300 | ||||||||
\(78\) | −9.65048e7 | −0.295205 | ||||||||
\(79\) | −7.22461e7 | −0.208685 | −0.104343 | − | 0.994541i | \(-0.533274\pi\) | ||||
−0.104343 | + | 0.994541i | \(0.533274\pi\) | |||||||
\(80\) | 1.07444e8 | 0.293275 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 2.08614e8 | 0.509544 | ||||||||
\(83\) | −1.57839e8 | −0.365059 | −0.182530 | − | 0.983200i | \(-0.558429\pi\) | ||||
−0.182530 | + | 0.983200i | \(0.558429\pi\) | |||||||
\(84\) | 1.34406e8 | 0.294552 | ||||||||
\(85\) | −8.64861e8 | −1.79706 | ||||||||
\(86\) | −4.00445e8 | −0.789405 | ||||||||
\(87\) | 4.89024e8 | 0.915152 | ||||||||
\(88\) | 2.97646e8 | 0.529089 | ||||||||
\(89\) | 5.53997e8 | 0.935949 | 0.467975 | − | 0.883742i | \(-0.344984\pi\) | ||||
0.467975 | + | 0.883742i | \(0.344984\pi\) | |||||||
\(90\) | −1.95800e8 | −0.314573 | ||||||||
\(91\) | −4.44384e8 | −0.679316 | ||||||||
\(92\) | −4.53574e8 | −0.660089 | ||||||||
\(93\) | 2.36355e8 | 0.327635 | ||||||||
\(94\) | −5.09485e8 | −0.673064 | ||||||||
\(95\) | −1.67251e9 | −2.10675 | ||||||||
\(96\) | 4.96783e8 | 0.596961 | ||||||||
\(97\) | 6.86877e8 | 0.787783 | 0.393891 | − | 0.919157i | \(-0.371129\pi\) | ||||
0.393891 | + | 0.919157i | \(0.371129\pi\) | |||||||
\(98\) | 2.31562e8 | 0.253600 | ||||||||
\(99\) | 1.79622e8 | 0.187932 | ||||||||
\(100\) | −1.31403e9 | −1.31403 | ||||||||
\(101\) | −1.08954e9 | −1.04183 | −0.520917 | − | 0.853608i | \(-0.674410\pi\) | ||||
−0.520917 | + | 0.853608i | \(0.674410\pi\) | |||||||
\(102\) | −3.69454e8 | −0.337956 | ||||||||
\(103\) | 4.39108e8 | 0.384419 | 0.192209 | − | 0.981354i | \(-0.438435\pi\) | ||||
0.192209 | + | 0.981354i | \(0.438435\pi\) | |||||||
\(104\) | −1.03250e9 | −0.865444 | ||||||||
\(105\) | −9.01615e8 | −0.723885 | ||||||||
\(106\) | 8.74486e8 | 0.672785 | ||||||||
\(107\) | −5.80854e8 | −0.428391 | −0.214195 | − | 0.976791i | \(-0.568713\pi\) | ||||
−0.214195 | + | 0.976791i | \(0.568713\pi\) | |||||||
\(108\) | 1.88455e8 | 0.133291 | ||||||||
\(109\) | 2.45513e9 | 1.66592 | 0.832960 | − | 0.553333i | \(-0.186644\pi\) | ||||
0.832960 | + | 0.553333i | \(0.186644\pi\) | |||||||
\(110\) | −8.17019e8 | −0.532065 | ||||||||
\(111\) | −6.97220e8 | −0.435930 | ||||||||
\(112\) | 2.11351e8 | 0.126918 | ||||||||
\(113\) | −1.05448e9 | −0.608396 | −0.304198 | − | 0.952609i | \(-0.598388\pi\) | ||||
−0.304198 | + | 0.952609i | \(0.598388\pi\) | |||||||
\(114\) | −7.14470e8 | −0.396198 | ||||||||
\(115\) | 3.04264e9 | 1.62222 | ||||||||
\(116\) | 2.14091e9 | 1.09784 | ||||||||
\(117\) | −6.23087e8 | −0.307406 | ||||||||
\(118\) | 1.52017e8 | 0.0721813 | ||||||||
\(119\) | −1.70126e9 | −0.777693 | ||||||||
\(120\) | −2.09485e9 | −0.922224 | ||||||||
\(121\) | −1.60843e9 | −0.682133 | ||||||||
\(122\) | 7.96387e8 | 0.325466 | ||||||||
\(123\) | 1.34692e9 | 0.530604 | ||||||||
\(124\) | 1.03474e9 | 0.393038 | ||||||||
\(125\) | 4.16861e9 | 1.52720 | ||||||||
\(126\) | −3.85155e8 | −0.136134 | ||||||||
\(127\) | −3.43386e9 | −1.17129 | −0.585646 | − | 0.810567i | \(-0.699159\pi\) | ||||
−0.585646 | + | 0.810567i | \(0.699159\pi\) | |||||||
\(128\) | 2.46500e9 | 0.811656 | ||||||||
\(129\) | −2.58549e9 | −0.822031 | ||||||||
\(130\) | 2.83414e9 | 0.870313 | ||||||||
\(131\) | −2.83733e9 | −0.841760 | −0.420880 | − | 0.907116i | \(-0.638279\pi\) | ||||
−0.420880 | + | 0.907116i | \(0.638279\pi\) | |||||||
\(132\) | 7.86373e8 | 0.225448 | ||||||||
\(133\) | −3.28998e9 | −0.911718 | ||||||||
\(134\) | 2.15988e9 | 0.578706 | ||||||||
\(135\) | −1.26419e9 | −0.327574 | ||||||||
\(136\) | −3.95276e9 | −0.990775 | ||||||||
\(137\) | −2.92430e9 | −0.709217 | −0.354608 | − | 0.935015i | \(-0.615386\pi\) | ||||
−0.354608 | + | 0.935015i | \(0.615386\pi\) | |||||||
\(138\) | 1.29976e9 | 0.305077 | ||||||||
\(139\) | 2.71055e9 | 0.615873 | 0.307937 | − | 0.951407i | \(-0.400362\pi\) | ||||
0.307937 | + | 0.951407i | \(0.400362\pi\) | |||||||
\(140\) | −3.94721e9 | −0.868388 | ||||||||
\(141\) | −3.28951e9 | −0.700882 | ||||||||
\(142\) | 2.40477e9 | 0.496337 | ||||||||
\(143\) | −2.59997e9 | −0.519944 | ||||||||
\(144\) | 2.96342e8 | 0.0574331 | ||||||||
\(145\) | −1.43616e10 | −2.69802 | ||||||||
\(146\) | −1.87049e9 | −0.340697 | ||||||||
\(147\) | 1.49509e9 | 0.264082 | ||||||||
\(148\) | −3.05238e9 | −0.522951 | ||||||||
\(149\) | −1.64768e9 | −0.273864 | −0.136932 | − | 0.990580i | \(-0.543724\pi\) | ||||
−0.136932 | + | 0.990580i | \(0.543724\pi\) | |||||||
\(150\) | 3.76548e9 | 0.607310 | ||||||||
\(151\) | −8.11578e9 | −1.27038 | −0.635191 | − | 0.772355i | \(-0.719078\pi\) | ||||
−0.635191 | + | 0.772355i | \(0.719078\pi\) | |||||||
\(152\) | −7.64405e9 | −1.16152 | ||||||||
\(153\) | −2.38539e9 | −0.351924 | ||||||||
\(154\) | −1.60715e9 | −0.230257 | ||||||||
\(155\) | −6.94121e9 | −0.965924 | ||||||||
\(156\) | −2.72783e9 | −0.368771 | ||||||||
\(157\) | 1.60158e9 | 0.210378 | 0.105189 | − | 0.994452i | \(-0.466455\pi\) | ||||
0.105189 | + | 0.994452i | \(0.466455\pi\) | |||||||
\(158\) | 9.06358e8 | 0.115703 | ||||||||
\(159\) | 5.64615e9 | 0.700592 | ||||||||
\(160\) | −1.45894e10 | −1.75994 | ||||||||
\(161\) | 5.98513e9 | 0.702033 | ||||||||
\(162\) | −5.40040e8 | −0.0616039 | ||||||||
\(163\) | −6.76642e9 | −0.750783 | −0.375392 | − | 0.926866i | \(-0.622492\pi\) | ||||
−0.375392 | + | 0.926866i | \(0.622492\pi\) | |||||||
\(164\) | 5.89674e9 | 0.636524 | ||||||||
\(165\) | −5.27511e9 | −0.554056 | ||||||||
\(166\) | 1.98016e9 | 0.202401 | ||||||||
\(167\) | −4.09332e9 | −0.407241 | −0.203621 | − | 0.979050i | \(-0.565271\pi\) | ||||
−0.203621 | + | 0.979050i | \(0.565271\pi\) | |||||||
\(168\) | −4.12074e9 | −0.399101 | ||||||||
\(169\) | −1.58553e9 | −0.149515 | ||||||||
\(170\) | 1.08501e10 | 0.996350 | ||||||||
\(171\) | −4.61300e9 | −0.412573 | ||||||||
\(172\) | −1.13191e10 | −0.986127 | ||||||||
\(173\) | 1.52173e10 | 1.29160 | 0.645802 | − | 0.763505i | \(-0.276523\pi\) | ||||
0.645802 | + | 0.763505i | \(0.276523\pi\) | |||||||
\(174\) | −6.13501e9 | −0.507392 | ||||||||
\(175\) | 1.73392e10 | 1.39752 | ||||||||
\(176\) | 1.23656e9 | 0.0971419 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | −6.95013e9 | −0.518923 | ||||||||
\(179\) | 2.22183e10 | 1.61761 | 0.808804 | − | 0.588079i | \(-0.200116\pi\) | ||||
0.808804 | + | 0.588079i | \(0.200116\pi\) | |||||||
\(180\) | −5.53452e9 | −0.392965 | ||||||||
\(181\) | −2.47904e10 | −1.71684 | −0.858420 | − | 0.512947i | \(-0.828554\pi\) | ||||
−0.858420 | + | 0.512947i | \(0.828554\pi\) | |||||||
\(182\) | 5.57499e9 | 0.376637 | ||||||||
\(183\) | 5.14190e9 | 0.338917 | ||||||||
\(184\) | 1.39061e10 | 0.894385 | ||||||||
\(185\) | 2.04758e10 | 1.28519 | ||||||||
\(186\) | −2.96517e9 | −0.181652 | ||||||||
\(187\) | −9.95360e9 | −0.595241 | ||||||||
\(188\) | −1.44012e10 | −0.840794 | ||||||||
\(189\) | −2.48677e9 | −0.141761 | ||||||||
\(190\) | 2.09824e10 | 1.16806 | ||||||||
\(191\) | −1.94115e10 | −1.05538 | −0.527691 | − | 0.849436i | \(-0.676942\pi\) | ||||
−0.527691 | + | 0.849436i | \(0.676942\pi\) | |||||||
\(192\) | −4.35917e9 | −0.231499 | ||||||||
\(193\) | −1.35292e10 | −0.701884 | −0.350942 | − | 0.936397i | \(-0.614139\pi\) | ||||
−0.350942 | + | 0.936397i | \(0.614139\pi\) | |||||||
\(194\) | −8.61717e9 | −0.436774 | ||||||||
\(195\) | 1.82987e10 | 0.906284 | ||||||||
\(196\) | 6.54539e9 | 0.316798 | ||||||||
\(197\) | 2.17864e10 | 1.03059 | 0.515297 | − | 0.857012i | \(-0.327682\pi\) | ||||
0.515297 | + | 0.857012i | \(0.327682\pi\) | |||||||
\(198\) | −2.25344e9 | −0.104196 | ||||||||
\(199\) | 1.59326e10 | 0.720190 | 0.360095 | − | 0.932916i | \(-0.382744\pi\) | ||||
0.360095 | + | 0.932916i | \(0.382744\pi\) | |||||||
\(200\) | 4.02866e10 | 1.78043 | ||||||||
\(201\) | 1.39453e10 | 0.602625 | ||||||||
\(202\) | 1.36688e10 | 0.577629 | ||||||||
\(203\) | −2.82504e10 | −1.16760 | ||||||||
\(204\) | −1.04431e10 | −0.422175 | ||||||||
\(205\) | −3.95562e10 | −1.56431 | ||||||||
\(206\) | −5.50880e9 | −0.213135 | ||||||||
\(207\) | 8.39198e9 | 0.317686 | ||||||||
\(208\) | −4.28946e9 | −0.158898 | ||||||||
\(209\) | −1.92488e10 | −0.697822 | ||||||||
\(210\) | 1.13112e10 | 0.401347 | ||||||||
\(211\) | −2.42054e10 | −0.840699 | −0.420350 | − | 0.907362i | \(-0.638093\pi\) | ||||
−0.420350 | + | 0.907362i | \(0.638093\pi\) | |||||||
\(212\) | 2.47184e10 | 0.840446 | ||||||||
\(213\) | 1.55265e10 | 0.516851 | ||||||||
\(214\) | 7.28707e9 | 0.237515 | ||||||||
\(215\) | 7.59301e10 | 2.42349 | ||||||||
\(216\) | −5.77784e9 | −0.180602 | ||||||||
\(217\) | −1.36540e10 | −0.418013 | ||||||||
\(218\) | −3.08006e10 | −0.923645 | ||||||||
\(219\) | −1.20769e10 | −0.354778 | ||||||||
\(220\) | −2.30941e10 | −0.664658 | ||||||||
\(221\) | 3.45278e10 | 0.973651 | ||||||||
\(222\) | 8.74692e9 | 0.241695 | ||||||||
\(223\) | −1.04006e10 | −0.281636 | −0.140818 | − | 0.990036i | \(-0.544973\pi\) | ||||
−0.140818 | + | 0.990036i | \(0.544973\pi\) | |||||||
\(224\) | −2.86986e10 | −0.761632 | ||||||||
\(225\) | 2.43120e10 | 0.632410 | ||||||||
\(226\) | 1.32289e10 | 0.337316 | ||||||||
\(227\) | 1.85297e10 | 0.463182 | 0.231591 | − | 0.972813i | \(-0.425607\pi\) | ||||
0.231591 | + | 0.972813i | \(0.425607\pi\) | |||||||
\(228\) | −2.01954e10 | −0.494931 | ||||||||
\(229\) | −4.59022e10 | −1.10300 | −0.551498 | − | 0.834176i | \(-0.685944\pi\) | ||||
−0.551498 | + | 0.834176i | \(0.685944\pi\) | |||||||
\(230\) | −3.81712e10 | −0.899417 | ||||||||
\(231\) | −1.03766e10 | −0.239773 | ||||||||
\(232\) | −6.56380e10 | −1.48751 | ||||||||
\(233\) | 7.97085e10 | 1.77175 | 0.885876 | − | 0.463922i | \(-0.153558\pi\) | ||||
0.885876 | + | 0.463922i | \(0.153558\pi\) | |||||||
\(234\) | 7.81689e9 | 0.170437 | ||||||||
\(235\) | 9.66057e10 | 2.06632 | ||||||||
\(236\) | 4.29696e9 | 0.0901691 | ||||||||
\(237\) | 5.85193e9 | 0.120485 | ||||||||
\(238\) | 2.13430e10 | 0.431180 | ||||||||
\(239\) | −2.10848e10 | −0.418002 | −0.209001 | − | 0.977915i | \(-0.567021\pi\) | ||||
−0.209001 | + | 0.977915i | \(0.567021\pi\) | |||||||
\(240\) | −8.70293e9 | −0.169323 | ||||||||
\(241\) | 8.05924e10 | 1.53892 | 0.769462 | − | 0.638693i | \(-0.220524\pi\) | ||||
0.769462 | + | 0.638693i | \(0.220524\pi\) | |||||||
\(242\) | 2.01785e10 | 0.378198 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 2.25109e10 | 0.406573 | ||||||||
\(245\) | −4.39075e10 | −0.778558 | ||||||||
\(246\) | −1.68977e10 | −0.294185 | ||||||||
\(247\) | 6.67716e10 | 1.14145 | ||||||||
\(248\) | −3.17241e10 | −0.532545 | ||||||||
\(249\) | 1.27850e10 | 0.210767 | ||||||||
\(250\) | −5.22970e10 | −0.846733 | ||||||||
\(251\) | −7.67172e10 | −1.22000 | −0.610002 | − | 0.792400i | \(-0.708831\pi\) | ||||
−0.610002 | + | 0.792400i | \(0.708831\pi\) | |||||||
\(252\) | −1.08869e10 | −0.170060 | ||||||||
\(253\) | 3.50174e10 | 0.537331 | ||||||||
\(254\) | 4.30792e10 | 0.649405 | ||||||||
\(255\) | 7.00538e10 | 1.03753 | ||||||||
\(256\) | −5.84788e10 | −0.850978 | ||||||||
\(257\) | −1.42887e10 | −0.204312 | −0.102156 | − | 0.994768i | \(-0.532574\pi\) | ||||
−0.102156 | + | 0.994768i | \(0.532574\pi\) | |||||||
\(258\) | 3.24360e10 | 0.455763 | ||||||||
\(259\) | 4.02777e10 | 0.556180 | ||||||||
\(260\) | 8.01104e10 | 1.08720 | ||||||||
\(261\) | −3.96109e10 | −0.528364 | ||||||||
\(262\) | 3.55955e10 | 0.466701 | ||||||||
\(263\) | −1.53883e11 | −1.98331 | −0.991655 | − | 0.128923i | \(-0.958848\pi\) | ||||
−0.991655 | + | 0.128923i | \(0.958848\pi\) | |||||||
\(264\) | −2.41093e10 | −0.305469 | ||||||||
\(265\) | −1.65815e11 | −2.06546 | ||||||||
\(266\) | 4.12742e10 | 0.505488 | ||||||||
\(267\) | −4.48738e10 | −0.540371 | ||||||||
\(268\) | 6.10517e10 | 0.722922 | ||||||||
\(269\) | 1.59562e10 | 0.185800 | 0.0928998 | − | 0.995675i | \(-0.470386\pi\) | ||||
0.0928998 | + | 0.995675i | \(0.470386\pi\) | |||||||
\(270\) | 1.58598e10 | 0.181619 | ||||||||
\(271\) | −4.94957e10 | −0.557450 | −0.278725 | − | 0.960371i | \(-0.589912\pi\) | ||||
−0.278725 | + | 0.960371i | \(0.589912\pi\) | |||||||
\(272\) | −1.64215e10 | −0.181909 | ||||||||
\(273\) | 3.59951e10 | 0.392203 | ||||||||
\(274\) | 3.66866e10 | 0.393214 | ||||||||
\(275\) | 1.01447e11 | 1.06965 | ||||||||
\(276\) | 3.67395e10 | 0.381103 | ||||||||
\(277\) | −4.78501e10 | −0.488342 | −0.244171 | − | 0.969732i | \(-0.578516\pi\) | ||||
−0.244171 | + | 0.969732i | \(0.578516\pi\) | |||||||
\(278\) | −3.40051e10 | −0.341462 | ||||||||
\(279\) | −1.91447e10 | −0.189160 | ||||||||
\(280\) | 1.21017e11 | 1.17662 | ||||||||
\(281\) | 1.87649e11 | 1.79543 | 0.897716 | − | 0.440575i | \(-0.145225\pi\) | ||||
0.897716 | + | 0.440575i | \(0.145225\pi\) | |||||||
\(282\) | 4.12683e10 | 0.388594 | ||||||||
\(283\) | 9.35083e10 | 0.866585 | 0.433292 | − | 0.901253i | \(-0.357352\pi\) | ||||
0.433292 | + | 0.901253i | \(0.357352\pi\) | |||||||
\(284\) | 6.79739e10 | 0.620026 | ||||||||
\(285\) | 1.35474e11 | 1.21633 | ||||||||
\(286\) | 3.26178e10 | 0.288275 | ||||||||
\(287\) | −7.78105e10 | −0.676970 | ||||||||
\(288\) | −4.02394e10 | −0.344655 | ||||||||
\(289\) | 1.35964e10 | 0.114653 | ||||||||
\(290\) | 1.80172e11 | 1.49588 | ||||||||
\(291\) | −5.56371e10 | −0.454826 | ||||||||
\(292\) | −5.28718e10 | −0.425600 | ||||||||
\(293\) | −6.02379e10 | −0.477491 | −0.238746 | − | 0.971082i | \(-0.576736\pi\) | ||||
−0.238746 | + | 0.971082i | \(0.576736\pi\) | |||||||
\(294\) | −1.87565e10 | −0.146416 | ||||||||
\(295\) | −2.88247e10 | −0.221598 | ||||||||
\(296\) | 9.35826e10 | 0.708570 | ||||||||
\(297\) | −1.45494e10 | −0.108503 | ||||||||
\(298\) | 2.06709e10 | 0.151840 | ||||||||
\(299\) | −1.21471e11 | −0.878926 | ||||||||
\(300\) | 1.06436e11 | 0.758653 | ||||||||
\(301\) | 1.49361e11 | 1.04879 | ||||||||
\(302\) | 1.01816e11 | 0.704344 | ||||||||
\(303\) | 8.82530e10 | 0.601503 | ||||||||
\(304\) | −3.17568e10 | −0.213258 | ||||||||
\(305\) | −1.51006e11 | −0.999185 | ||||||||
\(306\) | 2.99258e10 | 0.195119 | ||||||||
\(307\) | −2.53708e10 | −0.163009 | −0.0815044 | − | 0.996673i | \(-0.525972\pi\) | ||||
−0.0815044 | + | 0.996673i | \(0.525972\pi\) | |||||||
\(308\) | −4.54280e10 | −0.287637 | ||||||||
\(309\) | −3.55678e10 | −0.221944 | ||||||||
\(310\) | 8.70805e10 | 0.535542 | ||||||||
\(311\) | −1.97030e11 | −1.19429 | −0.597147 | − | 0.802132i | \(-0.703699\pi\) | ||||
−0.597147 | + | 0.802132i | \(0.703699\pi\) | |||||||
\(312\) | 8.36323e10 | 0.499664 | ||||||||
\(313\) | 1.03704e10 | 0.0610728 | 0.0305364 | − | 0.999534i | \(-0.490278\pi\) | ||||
0.0305364 | + | 0.999534i | \(0.490278\pi\) | |||||||
\(314\) | −2.00925e10 | −0.116641 | ||||||||
\(315\) | 7.30309e10 | 0.417935 | ||||||||
\(316\) | 2.56193e10 | 0.144536 | ||||||||
\(317\) | 2.39312e11 | 1.33106 | 0.665530 | − | 0.746371i | \(-0.268206\pi\) | ||||
0.665530 | + | 0.746371i | \(0.268206\pi\) | |||||||
\(318\) | −7.08334e10 | −0.388433 | ||||||||
\(319\) | −1.65286e11 | −0.893670 | ||||||||
\(320\) | 1.28019e11 | 0.682497 | ||||||||
\(321\) | 4.70492e10 | 0.247332 | ||||||||
\(322\) | −7.50861e10 | −0.389232 | ||||||||
\(323\) | 2.55625e11 | 1.30675 | ||||||||
\(324\) | −1.52649e10 | −0.0769558 | ||||||||
\(325\) | −3.51908e11 | −1.74966 | ||||||||
\(326\) | 8.48876e10 | 0.416260 | ||||||||
\(327\) | −1.98865e11 | −0.961820 | ||||||||
\(328\) | −1.80788e11 | −0.862455 | ||||||||
\(329\) | 1.90032e11 | 0.894220 | ||||||||
\(330\) | 6.61785e10 | 0.307188 | ||||||||
\(331\) | 1.79055e11 | 0.819901 | 0.409951 | − | 0.912108i | \(-0.365546\pi\) | ||||
0.409951 | + | 0.912108i | \(0.365546\pi\) | |||||||
\(332\) | 5.59717e10 | 0.252841 | ||||||||
\(333\) | 5.64748e10 | 0.251684 | ||||||||
\(334\) | 5.13525e10 | 0.225789 | ||||||||
\(335\) | −4.09544e11 | −1.77664 | ||||||||
\(336\) | −1.71194e10 | −0.0732760 | ||||||||
\(337\) | −3.60414e11 | −1.52218 | −0.761091 | − | 0.648645i | \(-0.775336\pi\) | ||||
−0.761091 | + | 0.648645i | \(0.775336\pi\) | |||||||
\(338\) | 1.98911e10 | 0.0828962 | ||||||||
\(339\) | 8.54131e10 | 0.351258 | ||||||||
\(340\) | 3.06690e11 | 1.24464 | ||||||||
\(341\) | −7.98857e10 | −0.319944 | ||||||||
\(342\) | 5.78720e10 | 0.228745 | ||||||||
\(343\) | −2.75196e11 | −1.07354 | ||||||||
\(344\) | 3.47030e11 | 1.33615 | ||||||||
\(345\) | −2.46454e11 | −0.936591 | ||||||||
\(346\) | −1.90907e11 | −0.716111 | ||||||||
\(347\) | −6.49091e10 | −0.240338 | −0.120169 | − | 0.992753i | \(-0.538344\pi\) | ||||
−0.120169 | + | 0.992753i | \(0.538344\pi\) | |||||||
\(348\) | −1.73414e11 | −0.633836 | ||||||||
\(349\) | −3.82648e11 | −1.38066 | −0.690328 | − | 0.723497i | \(-0.742534\pi\) | ||||
−0.690328 | + | 0.723497i | \(0.742534\pi\) | |||||||
\(350\) | −2.17528e11 | −0.774835 | ||||||||
\(351\) | 5.04700e10 | 0.177481 | ||||||||
\(352\) | −1.67908e11 | −0.582947 | ||||||||
\(353\) | −3.78040e11 | −1.29584 | −0.647919 | − | 0.761709i | \(-0.724361\pi\) | ||||
−0.647919 | + | 0.761709i | \(0.724361\pi\) | |||||||
\(354\) | −1.23134e10 | −0.0416739 | ||||||||
\(355\) | −4.55979e11 | −1.52376 | ||||||||
\(356\) | −1.96454e11 | −0.648240 | ||||||||
\(357\) | 1.37802e11 | 0.449001 | ||||||||
\(358\) | −2.78739e11 | −0.896858 | ||||||||
\(359\) | 1.86227e11 | 0.591723 | 0.295861 | − | 0.955231i | \(-0.404393\pi\) | ||||
0.295861 | + | 0.955231i | \(0.404393\pi\) | |||||||
\(360\) | 1.69682e11 | 0.532446 | ||||||||
\(361\) | 1.71653e11 | 0.531948 | ||||||||
\(362\) | 3.11006e11 | 0.951876 | ||||||||
\(363\) | 1.30283e11 | 0.393829 | ||||||||
\(364\) | 1.57584e11 | 0.470496 | ||||||||
\(365\) | 3.54672e11 | 1.04595 | ||||||||
\(366\) | −6.45074e10 | −0.187908 | ||||||||
\(367\) | 3.89606e11 | 1.12106 | 0.560529 | − | 0.828135i | \(-0.310598\pi\) | ||||
0.560529 | + | 0.828135i | \(0.310598\pi\) | |||||||
\(368\) | 5.77721e10 | 0.164211 | ||||||||
\(369\) | −1.09101e11 | −0.306344 | ||||||||
\(370\) | −2.56878e11 | −0.712556 | ||||||||
\(371\) | −3.26172e11 | −0.893850 | ||||||||
\(372\) | −8.38142e10 | −0.226921 | ||||||||
\(373\) | −2.61650e11 | −0.699893 | −0.349946 | − | 0.936770i | \(-0.613800\pi\) | ||||
−0.349946 | + | 0.936770i | \(0.613800\pi\) | |||||||
\(374\) | 1.24872e11 | 0.330022 | ||||||||
\(375\) | −3.37657e11 | −0.881729 | ||||||||
\(376\) | 4.41526e11 | 1.13923 | ||||||||
\(377\) | 5.73355e11 | 1.46180 | ||||||||
\(378\) | 3.11975e10 | 0.0785972 | ||||||||
\(379\) | −5.94167e11 | −1.47922 | −0.739608 | − | 0.673037i | \(-0.764989\pi\) | ||||
−0.739608 | + | 0.673037i | \(0.764989\pi\) | |||||||
\(380\) | 5.93094e11 | 1.45914 | ||||||||
\(381\) | 2.78142e11 | 0.676246 | ||||||||
\(382\) | 2.43526e11 | 0.585141 | ||||||||
\(383\) | −7.50953e11 | −1.78327 | −0.891637 | − | 0.452750i | \(-0.850443\pi\) | ||||
−0.891637 | + | 0.452750i | \(0.850443\pi\) | |||||||
\(384\) | −1.99665e11 | −0.468610 | ||||||||
\(385\) | 3.04738e11 | 0.706892 | ||||||||
\(386\) | 1.69730e11 | 0.389149 | ||||||||
\(387\) | 2.09424e11 | 0.474600 | ||||||||
\(388\) | −2.43575e11 | −0.545620 | ||||||||
\(389\) | 6.24639e11 | 1.38311 | 0.691554 | − | 0.722325i | \(-0.256926\pi\) | ||||
0.691554 | + | 0.722325i | \(0.256926\pi\) | |||||||
\(390\) | −2.29565e11 | −0.502476 | ||||||||
\(391\) | −4.65033e11 | −1.00621 | ||||||||
\(392\) | −2.00674e11 | −0.429244 | ||||||||
\(393\) | 2.29823e11 | 0.485991 | ||||||||
\(394\) | −2.73320e11 | −0.571398 | ||||||||
\(395\) | −1.71858e11 | −0.355209 | ||||||||
\(396\) | −6.36962e10 | −0.130162 | ||||||||
\(397\) | 5.02778e11 | 1.01583 | 0.507913 | − | 0.861408i | \(-0.330417\pi\) | ||||
0.507913 | + | 0.861408i | \(0.330417\pi\) | |||||||
\(398\) | −1.99881e11 | −0.399298 | ||||||||
\(399\) | 2.66488e11 | 0.526381 | ||||||||
\(400\) | 1.67369e11 | 0.326892 | ||||||||
\(401\) | −8.79008e11 | −1.69763 | −0.848815 | − | 0.528690i | \(-0.822683\pi\) | ||||
−0.848815 | + | 0.528690i | \(0.822683\pi\) | |||||||
\(402\) | −1.74950e11 | −0.334116 | ||||||||
\(403\) | 2.77113e11 | 0.523341 | ||||||||
\(404\) | 3.86365e11 | 0.721576 | ||||||||
\(405\) | 1.02399e11 | 0.189125 | ||||||||
\(406\) | 3.54414e11 | 0.647356 | ||||||||
\(407\) | 2.35654e11 | 0.425696 | ||||||||
\(408\) | 3.20173e11 | 0.572024 | ||||||||
\(409\) | 3.67932e11 | 0.650150 | 0.325075 | − | 0.945688i | \(-0.394611\pi\) | ||||
0.325075 | + | 0.945688i | \(0.394611\pi\) | |||||||
\(410\) | 4.96250e11 | 0.867307 | ||||||||
\(411\) | 2.36868e11 | 0.409466 | ||||||||
\(412\) | −1.55713e11 | −0.266249 | ||||||||
\(413\) | −5.67006e10 | −0.0958987 | ||||||||
\(414\) | −1.05281e11 | −0.176136 | ||||||||
\(415\) | −3.75466e11 | −0.621376 | ||||||||
\(416\) | 5.82452e11 | 0.953542 | ||||||||
\(417\) | −2.19555e11 | −0.355575 | ||||||||
\(418\) | 2.41484e11 | 0.386897 | ||||||||
\(419\) | −1.62115e11 | −0.256957 | −0.128478 | − | 0.991712i | \(-0.541009\pi\) | ||||
−0.128478 | + | 0.991712i | \(0.541009\pi\) | |||||||
\(420\) | 3.19724e11 | 0.501364 | ||||||||
\(421\) | −6.72976e11 | −1.04407 | −0.522035 | − | 0.852924i | \(-0.674827\pi\) | ||||
−0.522035 | + | 0.852924i | \(0.674827\pi\) | |||||||
\(422\) | 3.03667e11 | 0.466113 | ||||||||
\(423\) | 2.66450e11 | 0.404655 | ||||||||
\(424\) | −7.57840e11 | −1.13876 | ||||||||
\(425\) | −1.34723e12 | −2.00304 | ||||||||
\(426\) | −1.94787e11 | −0.286560 | ||||||||
\(427\) | −2.97042e11 | −0.432407 | ||||||||
\(428\) | 2.05978e11 | 0.296704 | ||||||||
\(429\) | 2.10598e11 | 0.300190 | ||||||||
\(430\) | −9.52575e11 | −1.34367 | ||||||||
\(431\) | −5.75800e11 | −0.803755 | −0.401877 | − | 0.915693i | \(-0.631642\pi\) | ||||
−0.401877 | + | 0.915693i | \(0.631642\pi\) | |||||||
\(432\) | −2.40037e10 | −0.0331590 | ||||||||
\(433\) | 1.04209e12 | 1.42465 | 0.712326 | − | 0.701849i | \(-0.247642\pi\) | ||||
0.712326 | + | 0.701849i | \(0.247642\pi\) | |||||||
\(434\) | 1.71295e11 | 0.231761 | ||||||||
\(435\) | 1.16329e12 | 1.55770 | ||||||||
\(436\) | −8.70617e11 | −1.15382 | ||||||||
\(437\) | −8.99306e11 | −1.17962 | ||||||||
\(438\) | 1.51510e11 | 0.196702 | ||||||||
\(439\) | −7.00416e11 | −0.900048 | −0.450024 | − | 0.893017i | \(-0.648584\pi\) | ||||
−0.450024 | + | 0.893017i | \(0.648584\pi\) | |||||||
\(440\) | 7.08039e11 | 0.900575 | ||||||||
\(441\) | −1.21102e11 | −0.152468 | ||||||||
\(442\) | −4.33166e11 | −0.539826 | ||||||||
\(443\) | −2.07557e11 | −0.256048 | −0.128024 | − | 0.991771i | \(-0.540863\pi\) | ||||
−0.128024 | + | 0.991771i | \(0.540863\pi\) | |||||||
\(444\) | 2.47243e11 | 0.301926 | ||||||||
\(445\) | 1.31784e12 | 1.59310 | ||||||||
\(446\) | 1.30480e11 | 0.156149 | ||||||||
\(447\) | 1.33462e11 | 0.158115 | ||||||||
\(448\) | 2.51825e11 | 0.295357 | ||||||||
\(449\) | −7.72881e11 | −0.897437 | −0.448718 | − | 0.893673i | \(-0.648119\pi\) | ||||
−0.448718 | + | 0.893673i | \(0.648119\pi\) | |||||||
\(450\) | −3.05004e11 | −0.350630 | ||||||||
\(451\) | −4.55248e11 | −0.518148 | ||||||||
\(452\) | 3.73932e11 | 0.421376 | ||||||||
\(453\) | 6.57378e11 | 0.733455 | ||||||||
\(454\) | −2.32463e11 | −0.256805 | ||||||||
\(455\) | −1.05710e12 | −1.15628 | ||||||||
\(456\) | 6.19168e11 | 0.670605 | ||||||||
\(457\) | 1.64560e11 | 0.176482 | 0.0882412 | − | 0.996099i | \(-0.471875\pi\) | ||||
0.0882412 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(458\) | 5.75863e11 | 0.611540 | ||||||||
\(459\) | 1.93217e11 | 0.203183 | ||||||||
\(460\) | −1.07896e12 | −1.12355 | ||||||||
\(461\) | −1.67596e12 | −1.72827 | −0.864133 | − | 0.503264i | \(-0.832132\pi\) | ||||
−0.864133 | + | 0.503264i | \(0.832132\pi\) | |||||||
\(462\) | 1.30179e11 | 0.132939 | ||||||||
\(463\) | 1.94865e11 | 0.197070 | 0.0985348 | − | 0.995134i | \(-0.468584\pi\) | ||||
0.0985348 | + | 0.995134i | \(0.468584\pi\) | |||||||
\(464\) | −2.72690e11 | −0.273110 | ||||||||
\(465\) | 5.62238e11 | 0.557676 | ||||||||
\(466\) | −9.99977e11 | −0.982321 | ||||||||
\(467\) | 1.16272e12 | 1.13122 | 0.565611 | − | 0.824672i | \(-0.308641\pi\) | ||||
0.565611 | + | 0.824672i | \(0.308641\pi\) | |||||||
\(468\) | 2.20954e11 | 0.212910 | ||||||||
\(469\) | −8.05608e11 | −0.768858 | ||||||||
\(470\) | −1.21196e12 | −1.14564 | ||||||||
\(471\) | −1.29728e11 | −0.121462 | ||||||||
\(472\) | −1.31740e11 | −0.122174 | ||||||||
\(473\) | 8.73871e11 | 0.802735 | ||||||||
\(474\) | −7.34150e10 | −0.0668009 | ||||||||
\(475\) | −2.60533e12 | −2.34824 | ||||||||
\(476\) | 6.03286e11 | 0.538632 | ||||||||
\(477\) | −4.57338e11 | −0.404487 | ||||||||
\(478\) | 2.64517e11 | 0.231755 | ||||||||
\(479\) | −2.02118e12 | −1.75427 | −0.877133 | − | 0.480247i | \(-0.840547\pi\) | ||||
−0.877133 | + | 0.480247i | \(0.840547\pi\) | |||||||
\(480\) | 1.18174e12 | 1.01610 | ||||||||
\(481\) | −8.17454e11 | −0.696323 | ||||||||
\(482\) | −1.01107e12 | −0.853233 | ||||||||
\(483\) | −4.84796e11 | −0.405319 | ||||||||
\(484\) | 5.70370e11 | 0.472446 | ||||||||
\(485\) | 1.63394e12 | 1.34090 | ||||||||
\(486\) | 4.37432e10 | 0.0355670 | ||||||||
\(487\) | −1.82880e12 | −1.47328 | −0.736642 | − | 0.676283i | \(-0.763590\pi\) | ||||
−0.736642 | + | 0.676283i | \(0.763590\pi\) | |||||||
\(488\) | −6.90159e11 | −0.550884 | ||||||||
\(489\) | 5.48080e11 | 0.433465 | ||||||||
\(490\) | 5.50838e11 | 0.431660 | ||||||||
\(491\) | −3.89531e11 | −0.302465 | −0.151232 | − | 0.988498i | \(-0.548324\pi\) | ||||
−0.151232 | + | 0.988498i | \(0.548324\pi\) | |||||||
\(492\) | −4.77636e11 | −0.367497 | ||||||||
\(493\) | 2.19500e12 | 1.67349 | ||||||||
\(494\) | −8.37678e11 | −0.632857 | ||||||||
\(495\) | 4.27284e11 | 0.319885 | ||||||||
\(496\) | −1.31796e11 | −0.0977766 | ||||||||
\(497\) | −8.96950e11 | −0.659424 | ||||||||
\(498\) | −1.60393e11 | −0.116857 | ||||||||
\(499\) | −7.68705e11 | −0.555019 | −0.277509 | − | 0.960723i | \(-0.589509\pi\) | ||||
−0.277509 | + | 0.960723i | \(0.589509\pi\) | |||||||
\(500\) | −1.47824e12 | −1.05774 | ||||||||
\(501\) | 3.31559e11 | 0.235121 | ||||||||
\(502\) | 9.62450e11 | 0.676412 | ||||||||
\(503\) | −1.59173e12 | −1.10870 | −0.554349 | − | 0.832285i | \(-0.687033\pi\) | ||||
−0.554349 | + | 0.832285i | \(0.687033\pi\) | |||||||
\(504\) | 3.33780e11 | 0.230421 | ||||||||
\(505\) | −2.59180e12 | −1.77333 | ||||||||
\(506\) | −4.39309e11 | −0.297915 | ||||||||
\(507\) | 1.28428e11 | 0.0863224 | ||||||||
\(508\) | 1.21769e12 | 0.811239 | ||||||||
\(509\) | 1.48575e12 | 0.981105 | 0.490552 | − | 0.871412i | \(-0.336795\pi\) | ||||
0.490552 | + | 0.871412i | \(0.336795\pi\) | |||||||
\(510\) | −8.78855e11 | −0.575243 | ||||||||
\(511\) | 6.97671e11 | 0.452644 | ||||||||
\(512\) | −5.28439e11 | −0.339844 | ||||||||
\(513\) | 3.73653e11 | 0.238199 | ||||||||
\(514\) | 1.79258e11 | 0.113277 | ||||||||
\(515\) | 1.04455e12 | 0.654329 | ||||||||
\(516\) | 9.16845e11 | 0.569341 | ||||||||
\(517\) | 1.11182e12 | 0.684429 | ||||||||
\(518\) | −5.05301e11 | −0.308366 | ||||||||
\(519\) | −1.23260e12 | −0.745708 | ||||||||
\(520\) | −2.45610e12 | −1.47309 | ||||||||
\(521\) | 2.56479e11 | 0.152505 | 0.0762523 | − | 0.997089i | \(-0.475705\pi\) | ||||
0.0762523 | + | 0.997089i | \(0.475705\pi\) | |||||||
\(522\) | 4.96936e11 | 0.292943 | ||||||||
\(523\) | −4.08961e10 | −0.0239015 | −0.0119507 | − | 0.999929i | \(-0.503804\pi\) | ||||
−0.0119507 | + | 0.999929i | \(0.503804\pi\) | |||||||
\(524\) | 1.00615e12 | 0.583005 | ||||||||
\(525\) | −1.40448e12 | −0.806860 | ||||||||
\(526\) | 1.93053e12 | 1.09962 | ||||||||
\(527\) | 1.06089e12 | 0.599130 | ||||||||
\(528\) | −1.00161e11 | −0.0560849 | ||||||||
\(529\) | −1.65134e11 | −0.0916822 | ||||||||
\(530\) | 2.08022e12 | 1.14516 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | 1.16667e12 | 0.631458 | ||||||||
\(533\) | 1.57920e12 | 0.847548 | ||||||||
\(534\) | 5.62960e11 | 0.299600 | ||||||||
\(535\) | −1.38173e12 | −0.729175 | ||||||||
\(536\) | −1.87178e12 | −0.979519 | ||||||||
\(537\) | −1.79969e12 | −0.933926 | ||||||||
\(538\) | −2.00178e11 | −0.103014 | ||||||||
\(539\) | −5.05326e11 | −0.257883 | ||||||||
\(540\) | 4.48296e11 | 0.226879 | ||||||||
\(541\) | 1.22129e12 | 0.612957 | 0.306478 | − | 0.951878i | \(-0.400849\pi\) | ||||
0.306478 | + | 0.951878i | \(0.400849\pi\) | |||||||
\(542\) | 6.20945e11 | 0.309070 | ||||||||
\(543\) | 2.00802e12 | 0.991218 | ||||||||
\(544\) | 2.22983e12 | 1.09163 | ||||||||
\(545\) | 5.84023e12 | 2.83561 | ||||||||
\(546\) | −4.51574e11 | −0.217451 | ||||||||
\(547\) | 2.08681e12 | 0.996645 | 0.498323 | − | 0.866992i | \(-0.333949\pi\) | ||||
0.498323 | + | 0.866992i | \(0.333949\pi\) | |||||||
\(548\) | 1.03699e12 | 0.491205 | ||||||||
\(549\) | −4.16494e11 | −0.195674 | ||||||||
\(550\) | −1.27270e12 | −0.593053 | ||||||||
\(551\) | 4.24481e12 | 1.96190 | ||||||||
\(552\) | −1.12639e12 | −0.516373 | ||||||||
\(553\) | −3.38060e11 | −0.153720 | ||||||||
\(554\) | 6.00300e11 | 0.270754 | ||||||||
\(555\) | −1.65854e12 | −0.742007 | ||||||||
\(556\) | −9.61195e11 | −0.426555 | ||||||||
\(557\) | 3.43626e12 | 1.51265 | 0.756323 | − | 0.654199i | \(-0.226994\pi\) | ||||
0.756323 | + | 0.654199i | \(0.226994\pi\) | |||||||
\(558\) | 2.40179e11 | 0.104877 | ||||||||
\(559\) | −3.03135e12 | −1.31305 | ||||||||
\(560\) | 5.02759e11 | 0.216030 | ||||||||
\(561\) | 8.06241e11 | 0.343662 | ||||||||
\(562\) | −2.35414e12 | −0.995450 | ||||||||
\(563\) | −5.32352e11 | −0.223311 | −0.111656 | − | 0.993747i | \(-0.535615\pi\) | ||||
−0.111656 | + | 0.993747i | \(0.535615\pi\) | |||||||
\(564\) | 1.16650e12 | 0.485432 | ||||||||
\(565\) | −2.50840e12 | −1.03557 | ||||||||
\(566\) | −1.17310e12 | −0.480465 | ||||||||
\(567\) | 2.01428e11 | 0.0818457 | ||||||||
\(568\) | −2.08401e12 | −0.840101 | ||||||||
\(569\) | 4.30475e11 | 0.172164 | 0.0860820 | − | 0.996288i | \(-0.472565\pi\) | ||||
0.0860820 | + | 0.996288i | \(0.472565\pi\) | |||||||
\(570\) | −1.69957e12 | −0.674378 | ||||||||
\(571\) | 4.07772e12 | 1.60530 | 0.802649 | − | 0.596452i | \(-0.203423\pi\) | ||||
0.802649 | + | 0.596452i | \(0.203423\pi\) | |||||||
\(572\) | 9.21981e11 | 0.360114 | ||||||||
\(573\) | 1.57234e12 | 0.609325 | ||||||||
\(574\) | 9.76166e11 | 0.375336 | ||||||||
\(575\) | 4.73963e12 | 1.80817 | ||||||||
\(576\) | 3.53093e11 | 0.133656 | ||||||||
\(577\) | 2.87140e12 | 1.07845 | 0.539227 | − | 0.842160i | \(-0.318716\pi\) | ||||
0.539227 | + | 0.842160i | \(0.318716\pi\) | |||||||
\(578\) | −1.70573e11 | −0.0635675 | ||||||||
\(579\) | 1.09587e12 | 0.405233 | ||||||||
\(580\) | 5.09278e12 | 1.86866 | ||||||||
\(581\) | −7.38574e11 | −0.268907 | ||||||||
\(582\) | 6.97991e11 | 0.252172 | ||||||||
\(583\) | −1.90835e12 | −0.684146 | ||||||||
\(584\) | 1.62099e12 | 0.576665 | ||||||||
\(585\) | −1.48219e12 | −0.523243 | ||||||||
\(586\) | 7.55710e11 | 0.264738 | ||||||||
\(587\) | 1.97794e12 | 0.687609 | 0.343804 | − | 0.939041i | \(-0.388284\pi\) | ||||
0.343804 | + | 0.939041i | \(0.388284\pi\) | |||||||
\(588\) | −5.30176e11 | −0.182904 | ||||||||
\(589\) | 2.05160e12 | 0.702382 | ||||||||
\(590\) | 3.61618e11 | 0.122862 | ||||||||
\(591\) | −1.76470e12 | −0.595014 | ||||||||
\(592\) | 3.88784e11 | 0.130095 | ||||||||
\(593\) | −1.12402e12 | −0.373275 | −0.186637 | − | 0.982429i | \(-0.559759\pi\) | ||||
−0.186637 | + | 0.982429i | \(0.559759\pi\) | |||||||
\(594\) | 1.82528e11 | 0.0601578 | ||||||||
\(595\) | −4.04694e12 | −1.32373 | ||||||||
\(596\) | 5.84287e11 | 0.189679 | ||||||||
\(597\) | −1.29054e12 | −0.415802 | ||||||||
\(598\) | 1.52391e12 | 0.487307 | ||||||||
\(599\) | 4.59815e12 | 1.45936 | 0.729680 | − | 0.683789i | \(-0.239669\pi\) | ||||
0.729680 | + | 0.683789i | \(0.239669\pi\) | |||||||
\(600\) | −3.26321e12 | −1.02793 | ||||||||
\(601\) | −3.40227e12 | −1.06374 | −0.531868 | − | 0.846827i | \(-0.678510\pi\) | ||||
−0.531868 | + | 0.846827i | \(0.678510\pi\) | |||||||
\(602\) | −1.87380e12 | −0.581485 | ||||||||
\(603\) | −1.12957e12 | −0.347925 | ||||||||
\(604\) | 2.87795e12 | 0.879868 | ||||||||
\(605\) | −3.82613e12 | −1.16108 | ||||||||
\(606\) | −1.10717e12 | −0.333494 | ||||||||
\(607\) | −4.76313e12 | −1.42411 | −0.712055 | − | 0.702124i | \(-0.752235\pi\) | ||||
−0.712055 | + | 0.702124i | \(0.752235\pi\) | |||||||
\(608\) | 4.31216e12 | 1.27976 | ||||||||
\(609\) | 2.28828e12 | 0.674112 | ||||||||
\(610\) | 1.89444e12 | 0.553983 | ||||||||
\(611\) | −3.85678e12 | −1.11954 | ||||||||
\(612\) | 8.45890e11 | 0.243743 | ||||||||
\(613\) | −1.30004e12 | −0.371863 | −0.185932 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185932 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(614\) | 3.18287e11 | 0.0903777 | ||||||||
\(615\) | 3.20405e12 | 0.903154 | ||||||||
\(616\) | 1.39277e12 | 0.389733 | ||||||||
\(617\) | 6.20428e12 | 1.72349 | 0.861744 | − | 0.507343i | \(-0.169372\pi\) | ||||
0.861744 | + | 0.507343i | \(0.169372\pi\) | |||||||
\(618\) | 4.46213e11 | 0.123054 | ||||||||
\(619\) | 4.36576e12 | 1.19523 | 0.597615 | − | 0.801783i | \(-0.296115\pi\) | ||||
0.597615 | + | 0.801783i | \(0.296115\pi\) | |||||||
\(620\) | 2.46144e12 | 0.669001 | ||||||||
\(621\) | −6.79750e11 | −0.183416 | ||||||||
\(622\) | 2.47183e12 | 0.662158 | ||||||||
\(623\) | 2.59231e12 | 0.689431 | ||||||||
\(624\) | 3.47446e11 | 0.0917395 | ||||||||
\(625\) | 2.67889e12 | 0.702255 | ||||||||
\(626\) | −1.30102e11 | −0.0338609 | ||||||||
\(627\) | 1.55915e12 | 0.402888 | ||||||||
\(628\) | −5.67939e11 | −0.145708 | ||||||||
\(629\) | −3.12950e12 | −0.797163 | ||||||||
\(630\) | −9.16203e11 | −0.231718 | ||||||||
\(631\) | 4.38403e12 | 1.10088 | 0.550441 | − | 0.834874i | \(-0.314459\pi\) | ||||
0.550441 | + | 0.834874i | \(0.314459\pi\) | |||||||
\(632\) | −7.85461e11 | −0.195838 | ||||||||
\(633\) | 1.96063e12 | 0.485378 | ||||||||
\(634\) | −3.00227e12 | −0.737986 | ||||||||
\(635\) | −8.16843e12 | −1.99369 | ||||||||
\(636\) | −2.00219e12 | −0.485232 | ||||||||
\(637\) | 1.75291e12 | 0.421825 | ||||||||
\(638\) | 2.07358e12 | 0.495482 | ||||||||
\(639\) | −1.25765e12 | −0.298404 | ||||||||
\(640\) | 5.86372e12 | 1.38154 | ||||||||
\(641\) | −2.65746e12 | −0.621734 | −0.310867 | − | 0.950453i | \(-0.600619\pi\) | ||||
−0.310867 | + | 0.950453i | \(0.600619\pi\) | |||||||
\(642\) | −5.90252e11 | −0.137129 | ||||||||
\(643\) | −4.60843e12 | −1.06317 | −0.531586 | − | 0.847004i | \(-0.678404\pi\) | ||||
−0.531586 | + | 0.847004i | \(0.678404\pi\) | |||||||
\(644\) | −2.12240e12 | −0.486229 | ||||||||
\(645\) | −6.15033e12 | −1.39920 | ||||||||
\(646\) | −3.20692e12 | −0.724507 | ||||||||
\(647\) | −1.13960e12 | −0.255672 | −0.127836 | − | 0.991795i | \(-0.540803\pi\) | ||||
−0.127836 | + | 0.991795i | \(0.540803\pi\) | |||||||
\(648\) | 4.68005e11 | 0.104271 | ||||||||
\(649\) | −3.31740e11 | −0.0734001 | ||||||||
\(650\) | 4.41483e12 | 0.970072 | ||||||||
\(651\) | 1.10597e12 | 0.241340 | ||||||||
\(652\) | 2.39945e12 | 0.519994 | ||||||||
\(653\) | −1.92790e12 | −0.414929 | −0.207465 | − | 0.978243i | \(-0.566521\pi\) | ||||
−0.207465 | + | 0.978243i | \(0.566521\pi\) | |||||||
\(654\) | 2.49485e12 | 0.533267 | ||||||||
\(655\) | −6.74941e12 | −1.43278 | ||||||||
\(656\) | −7.51073e11 | −0.158349 | ||||||||
\(657\) | 9.78229e11 | 0.204831 | ||||||||
\(658\) | −2.38403e12 | −0.495787 | ||||||||
\(659\) | −6.04821e12 | −1.24923 | −0.624615 | − | 0.780933i | \(-0.714744\pi\) | ||||
−0.624615 | + | 0.780933i | \(0.714744\pi\) | |||||||
\(660\) | 1.87062e12 | 0.383740 | ||||||||
\(661\) | 8.21417e12 | 1.67362 | 0.836810 | − | 0.547493i | \(-0.184418\pi\) | ||||
0.836810 | + | 0.547493i | \(0.184418\pi\) | |||||||
\(662\) | −2.24633e12 | −0.454582 | ||||||||
\(663\) | −2.79675e12 | −0.562138 | ||||||||
\(664\) | −1.71603e12 | −0.342585 | ||||||||
\(665\) | −7.82617e12 | −1.55186 | ||||||||
\(666\) | −7.08501e11 | −0.139542 | ||||||||
\(667\) | −7.72217e12 | −1.51068 | ||||||||
\(668\) | 1.45154e12 | 0.282056 | ||||||||
\(669\) | 8.42451e11 | 0.162602 | ||||||||
\(670\) | 5.13791e12 | 0.985030 | ||||||||
\(671\) | −1.73792e12 | −0.330961 | ||||||||
\(672\) | 2.32459e12 | 0.439728 | ||||||||
\(673\) | 3.76497e12 | 0.707447 | 0.353724 | − | 0.935350i | \(-0.384915\pi\) | ||||
0.353724 | + | 0.935350i | \(0.384915\pi\) | |||||||
\(674\) | 4.52155e12 | 0.843951 | ||||||||
\(675\) | −1.96927e12 | −0.365122 | ||||||||
\(676\) | 5.62248e11 | 0.103554 | ||||||||
\(677\) | 6.21117e12 | 1.13638 | 0.568191 | − | 0.822897i | \(-0.307644\pi\) | ||||
0.568191 | + | 0.822897i | \(0.307644\pi\) | |||||||
\(678\) | −1.07154e12 | −0.194749 | ||||||||
\(679\) | 3.21410e12 | 0.580290 | ||||||||
\(680\) | −9.40279e12 | −1.68642 | ||||||||
\(681\) | −1.50091e12 | −0.267419 | ||||||||
\(682\) | 1.00220e12 | 0.177388 | ||||||||
\(683\) | 8.19423e12 | 1.44084 | 0.720419 | − | 0.693539i | \(-0.243950\pi\) | ||||
0.720419 | + | 0.693539i | \(0.243950\pi\) | |||||||
\(684\) | 1.63583e12 | 0.285749 | ||||||||
\(685\) | −6.95630e12 | −1.20718 | ||||||||
\(686\) | 3.45245e12 | 0.595208 | ||||||||
\(687\) | 3.71808e12 | 0.636816 | ||||||||
\(688\) | 1.44172e12 | 0.245320 | ||||||||
\(689\) | 6.61981e12 | 1.11908 | ||||||||
\(690\) | 3.09187e12 | 0.519279 | ||||||||
\(691\) | −3.72136e12 | −0.620942 | −0.310471 | − | 0.950583i | \(-0.600487\pi\) | ||||
−0.310471 | + | 0.950583i | \(0.600487\pi\) | |||||||
\(692\) | −5.39623e12 | −0.894568 | ||||||||
\(693\) | 8.40504e11 | 0.138433 | ||||||||
\(694\) | 8.14312e11 | 0.133252 | ||||||||
\(695\) | 6.44784e12 | 1.04829 | ||||||||
\(696\) | 5.31668e12 | 0.858813 | ||||||||
\(697\) | 6.04572e12 | 0.970288 | ||||||||
\(698\) | 4.80049e12 | 0.765483 | ||||||||
\(699\) | −6.45639e12 | −1.02292 | ||||||||
\(700\) | −6.14871e12 | −0.967927 | ||||||||
\(701\) | 3.58404e12 | 0.560585 | 0.280293 | − | 0.959915i | \(-0.409568\pi\) | ||||
0.280293 | + | 0.959915i | \(0.409568\pi\) | |||||||
\(702\) | −6.33168e11 | −0.0984016 | ||||||||
\(703\) | −6.05199e12 | −0.934542 | ||||||||
\(704\) | 1.47336e12 | 0.226064 | ||||||||
\(705\) | −7.82506e12 | −1.19299 | ||||||||
\(706\) | 4.74267e12 | 0.718458 | ||||||||
\(707\) | −5.09828e12 | −0.767426 | ||||||||
\(708\) | −3.48054e11 | −0.0520592 | ||||||||
\(709\) | −1.86082e12 | −0.276565 | −0.138282 | − | 0.990393i | \(-0.544158\pi\) | ||||
−0.138282 | + | 0.990393i | \(0.544158\pi\) | |||||||
\(710\) | 5.72046e12 | 0.844828 | ||||||||
\(711\) | −4.74006e11 | −0.0695618 | ||||||||
\(712\) | 6.02307e12 | 0.878330 | ||||||||
\(713\) | −3.73227e12 | −0.540842 | ||||||||
\(714\) | −1.72878e12 | −0.248942 | ||||||||
\(715\) | −6.18479e12 | −0.885009 | ||||||||
\(716\) | −7.87890e12 | −1.12036 | ||||||||
\(717\) | 1.70787e12 | 0.241334 | ||||||||
\(718\) | −2.33630e12 | −0.328072 | ||||||||
\(719\) | 8.32527e12 | 1.16176 | 0.580882 | − | 0.813988i | \(-0.302708\pi\) | ||||
0.580882 | + | 0.813988i | \(0.302708\pi\) | |||||||
\(720\) | 7.04937e11 | 0.0977584 | ||||||||
\(721\) | 2.05471e12 | 0.283167 | ||||||||
\(722\) | −2.15346e12 | −0.294930 | ||||||||
\(723\) | −6.52798e12 | −0.888498 | ||||||||
\(724\) | 8.79098e12 | 1.18909 | ||||||||
\(725\) | −2.23715e13 | −3.00728 | ||||||||
\(726\) | −1.63446e12 | −0.218353 | ||||||||
\(727\) | 1.05496e13 | 1.40066 | 0.700329 | − | 0.713821i | \(-0.253037\pi\) | ||||
0.700329 | + | 0.713821i | \(0.253037\pi\) | |||||||
\(728\) | −4.83135e12 | −0.637496 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −4.44952e12 | −0.579909 | ||||||||
\(731\) | −1.16051e13 | −1.50321 | ||||||||
\(732\) | −1.82338e12 | −0.234735 | ||||||||
\(733\) | −3.93351e12 | −0.503283 | −0.251641 | − | 0.967821i | \(-0.580970\pi\) | ||||
−0.251641 | + | 0.967821i | \(0.580970\pi\) | |||||||
\(734\) | −4.88777e12 | −0.621554 | ||||||||
\(735\) | 3.55650e12 | 0.449501 | ||||||||
\(736\) | −7.84468e12 | −0.985429 | ||||||||
\(737\) | −4.71340e12 | −0.588478 | ||||||||
\(738\) | 1.36872e12 | 0.169848 | ||||||||
\(739\) | −6.24664e12 | −0.770454 | −0.385227 | − | 0.922822i | \(-0.625877\pi\) | ||||
−0.385227 | + | 0.922822i | \(0.625877\pi\) | |||||||
\(740\) | −7.26098e12 | −0.890128 | ||||||||
\(741\) | −5.40850e12 | −0.659014 | ||||||||
\(742\) | 4.09197e12 | 0.495581 | ||||||||
\(743\) | −8.32453e12 | −1.00210 | −0.501049 | − | 0.865419i | \(-0.667052\pi\) | ||||
−0.501049 | + | 0.865419i | \(0.667052\pi\) | |||||||
\(744\) | 2.56965e12 | 0.307465 | ||||||||
\(745\) | −3.91949e12 | −0.466151 | ||||||||
\(746\) | 3.28251e12 | 0.388045 | ||||||||
\(747\) | −1.03558e12 | −0.121686 | ||||||||
\(748\) | 3.52967e12 | 0.412265 | ||||||||
\(749\) | −2.71798e12 | −0.315558 | ||||||||
\(750\) | 4.23605e12 | 0.488861 | ||||||||
\(751\) | 9.51081e12 | 1.09103 | 0.545516 | − | 0.838100i | \(-0.316334\pi\) | ||||
0.545516 | + | 0.838100i | \(0.316334\pi\) | |||||||
\(752\) | 1.83430e12 | 0.209165 | ||||||||
\(753\) | 6.21409e12 | 0.704369 | ||||||||
\(754\) | −7.19298e12 | −0.810472 | ||||||||
\(755\) | −1.93058e13 | −2.16235 | ||||||||
\(756\) | 8.81837e11 | 0.0981839 | ||||||||
\(757\) | 4.64714e12 | 0.514345 | 0.257172 | − | 0.966366i | \(-0.417209\pi\) | ||||
0.257172 | + | 0.966366i | \(0.417209\pi\) | |||||||
\(758\) | 7.45408e12 | 0.820129 | ||||||||
\(759\) | −2.83641e12 | −0.310228 | ||||||||
\(760\) | −1.81836e13 | −1.97706 | ||||||||
\(761\) | 8.45553e12 | 0.913924 | 0.456962 | − | 0.889486i | \(-0.348938\pi\) | ||||
0.456962 | + | 0.889486i | \(0.348938\pi\) | |||||||
\(762\) | −3.48941e12 | −0.374934 | ||||||||
\(763\) | 1.14882e13 | 1.22714 | ||||||||
\(764\) | 6.88357e12 | 0.730960 | ||||||||
\(765\) | −5.67436e12 | −0.599018 | ||||||||
\(766\) | 9.42103e12 | 0.988710 | ||||||||
\(767\) | 1.15076e12 | 0.120063 | ||||||||
\(768\) | 4.73678e12 | 0.491312 | ||||||||
\(769\) | 1.48631e13 | 1.53264 | 0.766321 | − | 0.642457i | \(-0.222085\pi\) | ||||
0.766321 | + | 0.642457i | \(0.222085\pi\) | |||||||
\(770\) | −3.82307e12 | −0.391926 | ||||||||
\(771\) | 1.15738e12 | 0.117959 | ||||||||
\(772\) | 4.79763e12 | 0.486126 | ||||||||
\(773\) | −1.81427e13 | −1.82765 | −0.913827 | − | 0.406103i | \(-0.866887\pi\) | ||||
−0.913827 | + | 0.406103i | \(0.866887\pi\) | |||||||
\(774\) | −2.62732e12 | −0.263135 | ||||||||
\(775\) | −1.08126e13 | −1.07664 | ||||||||
\(776\) | 7.46775e12 | 0.739285 | ||||||||
\(777\) | −3.26249e12 | −0.321111 | ||||||||
\(778\) | −7.83637e12 | −0.766843 | ||||||||
\(779\) | 1.16915e13 | 1.13750 | ||||||||
\(780\) | −6.48894e12 | −0.627694 | ||||||||
\(781\) | −5.24782e12 | −0.504718 | ||||||||
\(782\) | 5.83404e12 | 0.557878 | ||||||||
\(783\) | 3.20849e12 | 0.305051 | ||||||||
\(784\) | −8.33691e11 | −0.0788103 | ||||||||
\(785\) | 3.80982e12 | 0.358089 | ||||||||
\(786\) | −2.88323e12 | −0.269450 | ||||||||
\(787\) | 1.05260e13 | 0.978087 | 0.489044 | − | 0.872259i | \(-0.337346\pi\) | ||||
0.489044 | + | 0.872259i | \(0.337346\pi\) | |||||||
\(788\) | −7.72573e12 | −0.713792 | ||||||||
\(789\) | 1.24645e13 | 1.14506 | ||||||||
\(790\) | 2.15604e12 | 0.196940 | ||||||||
\(791\) | −4.93423e12 | −0.448152 | ||||||||
\(792\) | 1.95286e12 | 0.176363 | ||||||||
\(793\) | 6.02861e12 | 0.541362 | ||||||||
\(794\) | −6.30757e12 | −0.563209 | ||||||||
\(795\) | 1.34310e13 | 1.19250 | ||||||||
\(796\) | −5.64988e12 | −0.498805 | ||||||||
\(797\) | 5.90203e12 | 0.518131 | 0.259065 | − | 0.965860i | \(-0.416586\pi\) | ||||
0.259065 | + | 0.965860i | \(0.416586\pi\) | |||||||
\(798\) | −3.34321e12 | −0.291844 | ||||||||
\(799\) | −1.47651e13 | −1.28167 | ||||||||
\(800\) | −2.27264e13 | −1.96167 | ||||||||
\(801\) | 3.63477e12 | 0.311983 | ||||||||
\(802\) | 1.10275e13 | 0.941225 | ||||||||
\(803\) | 4.08188e12 | 0.346450 | ||||||||
\(804\) | −4.94519e12 | −0.417379 | ||||||||
\(805\) | 1.42374e13 | 1.19495 | ||||||||
\(806\) | −3.47651e12 | −0.290158 | ||||||||
\(807\) | −1.29245e12 | −0.107271 | ||||||||
\(808\) | −1.18455e13 | −0.977695 | ||||||||
\(809\) | 1.36585e13 | 1.12107 | 0.560536 | − | 0.828130i | \(-0.310595\pi\) | ||||
0.560536 | + | 0.828130i | \(0.310595\pi\) | |||||||
\(810\) | −1.28464e12 | −0.104858 | ||||||||
\(811\) | −1.76828e13 | −1.43535 | −0.717675 | − | 0.696379i | \(-0.754793\pi\) | ||||
−0.717675 | + | 0.696379i | \(0.754793\pi\) | |||||||
\(812\) | 1.00179e13 | 0.808679 | ||||||||
\(813\) | 4.00915e12 | 0.321844 | ||||||||
\(814\) | −2.95638e12 | −0.236021 | ||||||||
\(815\) | −1.60959e13 | −1.27793 | ||||||||
\(816\) | 1.33014e12 | 0.105025 | ||||||||
\(817\) | −2.24425e13 | −1.76226 | ||||||||
\(818\) | −4.61587e12 | −0.360466 | ||||||||
\(819\) | −2.91560e12 | −0.226439 | ||||||||
\(820\) | 1.40271e13 | 1.08344 | ||||||||
\(821\) | 2.37038e12 | 0.182085 | 0.0910423 | − | 0.995847i | \(-0.470980\pi\) | ||||
0.0910423 | + | 0.995847i | \(0.470980\pi\) | |||||||
\(822\) | −2.97161e12 | −0.227022 | ||||||||
\(823\) | −4.92072e12 | −0.373878 | −0.186939 | − | 0.982372i | \(-0.559857\pi\) | ||||
−0.186939 | + | 0.982372i | \(0.559857\pi\) | |||||||
\(824\) | 4.77400e12 | 0.360753 | ||||||||
\(825\) | −8.21723e12 | −0.617565 | ||||||||
\(826\) | 7.11334e11 | 0.0531696 | ||||||||
\(827\) | 1.33372e13 | 0.991496 | 0.495748 | − | 0.868466i | \(-0.334894\pi\) | ||||
0.495748 | + | 0.868466i | \(0.334894\pi\) | |||||||
\(828\) | −2.97590e12 | −0.220030 | ||||||||
\(829\) | −1.21354e13 | −0.892395 | −0.446198 | − | 0.894934i | \(-0.647222\pi\) | ||||
−0.446198 | + | 0.894934i | \(0.647222\pi\) | |||||||
\(830\) | 4.71039e12 | 0.344513 | ||||||||
\(831\) | 3.87586e12 | 0.281944 | ||||||||
\(832\) | −5.11090e12 | −0.369779 | ||||||||
\(833\) | 6.71076e12 | 0.482913 | ||||||||
\(834\) | 2.75441e12 | 0.197143 | ||||||||
\(835\) | −9.73716e12 | −0.693175 | ||||||||
\(836\) | 6.82585e12 | 0.483313 | ||||||||
\(837\) | 1.55072e12 | 0.109212 | ||||||||
\(838\) | 2.03380e12 | 0.142466 | ||||||||
\(839\) | 1.56293e12 | 0.108896 | 0.0544479 | − | 0.998517i | \(-0.482660\pi\) | ||||
0.0544479 | + | 0.998517i | \(0.482660\pi\) | |||||||
\(840\) | −9.80238e12 | −0.679321 | ||||||||
\(841\) | 2.19422e13 | 1.51251 | ||||||||
\(842\) | 8.44277e12 | 0.578869 | ||||||||
\(843\) | −1.51996e13 | −1.03659 | ||||||||
\(844\) | 8.58352e12 | 0.582270 | ||||||||
\(845\) | −3.77164e12 | −0.254493 | ||||||||
\(846\) | −3.34273e12 | −0.224355 | ||||||||
\(847\) | −7.52632e12 | −0.502467 | ||||||||
\(848\) | −3.14841e12 | −0.209079 | ||||||||
\(849\) | −7.57417e12 | −0.500323 | ||||||||
\(850\) | 1.69015e13 | 1.11056 | ||||||||
\(851\) | 1.10098e13 | 0.719608 | ||||||||
\(852\) | −5.50589e12 | −0.357972 | ||||||||
\(853\) | −1.21011e13 | −0.782624 | −0.391312 | − | 0.920258i | \(-0.627979\pi\) | ||||
−0.391312 | + | 0.920258i | \(0.627979\pi\) | |||||||
\(854\) | 3.72652e12 | 0.239742 | ||||||||
\(855\) | −1.09734e13 | −0.702251 | ||||||||
\(856\) | −6.31506e12 | −0.402018 | ||||||||
\(857\) | −4.10860e12 | −0.260184 | −0.130092 | − | 0.991502i | \(-0.541527\pi\) | ||||
−0.130092 | + | 0.991502i | \(0.541527\pi\) | |||||||
\(858\) | −2.64204e12 | −0.166436 | ||||||||
\(859\) | 2.13660e13 | 1.33892 | 0.669460 | − | 0.742848i | \(-0.266526\pi\) | ||||
0.669460 | + | 0.742848i | \(0.266526\pi\) | |||||||
\(860\) | −2.69257e13 | −1.67851 | ||||||||
\(861\) | 6.30265e12 | 0.390849 | ||||||||
\(862\) | 7.22365e12 | 0.445630 | ||||||||
\(863\) | −2.75466e13 | −1.69052 | −0.845259 | − | 0.534356i | \(-0.820554\pi\) | ||||
−0.845259 | + | 0.534356i | \(0.820554\pi\) | |||||||
\(864\) | 3.25939e12 | 0.198987 | ||||||||
\(865\) | 3.61988e13 | 2.19847 | ||||||||
\(866\) | −1.30734e13 | −0.789876 | ||||||||
\(867\) | −1.10131e12 | −0.0661948 | ||||||||
\(868\) | 4.84186e12 | 0.289517 | ||||||||
\(869\) | −1.97790e12 | −0.117656 | ||||||||
\(870\) | −1.45939e13 | −0.863646 | ||||||||
\(871\) | 1.63502e13 | 0.962589 | ||||||||
\(872\) | 2.66922e13 | 1.56336 | ||||||||
\(873\) | 4.50660e12 | 0.262594 | ||||||||
\(874\) | 1.12822e13 | 0.654021 | ||||||||
\(875\) | 1.95061e13 | 1.12495 | ||||||||
\(876\) | 4.28262e12 | 0.245720 | ||||||||
\(877\) | −2.30078e13 | −1.31334 | −0.656670 | − | 0.754178i | \(-0.728035\pi\) | ||||
−0.656670 | + | 0.754178i | \(0.728035\pi\) | |||||||
\(878\) | 8.78701e12 | 0.499018 | ||||||||
\(879\) | 4.87927e12 | 0.275680 | ||||||||
\(880\) | 2.94151e12 | 0.165348 | ||||||||
\(881\) | −8.63759e12 | −0.483060 | −0.241530 | − | 0.970393i | \(-0.577649\pi\) | ||||
−0.241530 | + | 0.970393i | \(0.577649\pi\) | |||||||
\(882\) | 1.51928e12 | 0.0845335 | ||||||||
\(883\) | 2.79887e13 | 1.54938 | 0.774692 | − | 0.632338i | \(-0.217905\pi\) | ||||
0.774692 | + | 0.632338i | \(0.217905\pi\) | |||||||
\(884\) | −1.22440e13 | −0.674352 | ||||||||
\(885\) | 2.33480e12 | 0.127940 | ||||||||
\(886\) | 2.60390e12 | 0.141962 | ||||||||
\(887\) | −2.43474e13 | −1.32068 | −0.660338 | − | 0.750968i | \(-0.729587\pi\) | ||||
−0.660338 | + | 0.750968i | \(0.729587\pi\) | |||||||
\(888\) | −7.58019e12 | −0.409093 | ||||||||
\(889\) | −1.60680e13 | −0.862787 | ||||||||
\(890\) | −1.65329e13 | −0.883272 | ||||||||
\(891\) | 1.17850e12 | 0.0626441 | ||||||||
\(892\) | 3.68819e12 | 0.195061 | ||||||||
\(893\) | −2.85535e13 | −1.50255 | ||||||||
\(894\) | −1.67434e12 | −0.0876647 | ||||||||
\(895\) | 5.28528e13 | 2.75337 | ||||||||
\(896\) | 1.15344e13 | 0.597875 | ||||||||
\(897\) | 9.83915e12 | 0.507448 | ||||||||
\(898\) | 9.69612e12 | 0.497570 | ||||||||
\(899\) | 1.76167e13 | 0.899509 | ||||||||
\(900\) | −8.62132e12 | −0.438009 | ||||||||
\(901\) | 2.53430e13 | 1.28114 | ||||||||
\(902\) | 5.71129e12 | 0.287279 | ||||||||
\(903\) | −1.20982e13 | −0.605518 | ||||||||
\(904\) | −1.14644e13 | −0.570942 | ||||||||
\(905\) | −5.89712e13 | −2.92228 | ||||||||
\(906\) | −8.24709e12 | −0.406653 | ||||||||
\(907\) | 2.29403e13 | 1.12556 | 0.562778 | − | 0.826608i | \(-0.309733\pi\) | ||||
0.562778 | + | 0.826608i | \(0.309733\pi\) | |||||||
\(908\) | −6.57086e12 | −0.320801 | ||||||||
\(909\) | −7.14849e12 | −0.347278 | ||||||||
\(910\) | 1.32617e13 | 0.641083 | ||||||||
\(911\) | 3.68575e13 | 1.77293 | 0.886467 | − | 0.462792i | \(-0.153152\pi\) | ||||
0.886467 | + | 0.462792i | \(0.153152\pi\) | |||||||
\(912\) | 2.57230e12 | 0.123125 | ||||||||
\(913\) | −4.32120e12 | −0.205819 | ||||||||
\(914\) | −2.06448e12 | −0.0978480 | ||||||||
\(915\) | 1.22315e13 | 0.576880 | ||||||||
\(916\) | 1.62775e13 | 0.763938 | ||||||||
\(917\) | −1.32767e13 | −0.620050 | ||||||||
\(918\) | −2.42399e12 | −0.112652 | ||||||||
\(919\) | 1.18969e12 | 0.0550192 | 0.0275096 | − | 0.999622i | \(-0.491242\pi\) | ||||
0.0275096 | + | 0.999622i | \(0.491242\pi\) | |||||||
\(920\) | 3.30797e13 | 1.52235 | ||||||||
\(921\) | 2.05503e12 | 0.0941131 | ||||||||
\(922\) | 2.10257e13 | 0.958210 | ||||||||
\(923\) | 1.82040e13 | 0.825581 | ||||||||
\(924\) | 3.67967e12 | 0.166067 | ||||||||
\(925\) | 3.18959e13 | 1.43251 | ||||||||
\(926\) | −2.44467e12 | −0.109262 | ||||||||
\(927\) | 2.88099e12 | 0.128140 | ||||||||
\(928\) | 3.70277e13 | 1.63893 | ||||||||
\(929\) | 3.55367e13 | 1.56533 | 0.782667 | − | 0.622441i | \(-0.213859\pi\) | ||||
0.782667 | + | 0.622441i | \(0.213859\pi\) | |||||||
\(930\) | −7.05352e12 | −0.309195 | ||||||||
\(931\) | 1.29776e13 | 0.566137 | ||||||||
\(932\) | −2.82656e13 | −1.22712 | ||||||||
\(933\) | 1.59595e13 | 0.689526 | ||||||||
\(934\) | −1.45868e13 | −0.627189 | ||||||||
\(935\) | −2.36775e13 | −1.01317 | ||||||||
\(936\) | −6.77421e12 | −0.288481 | ||||||||
\(937\) | −3.70448e13 | −1.57000 | −0.784999 | − | 0.619498i | \(-0.787336\pi\) | ||||
−0.784999 | + | 0.619498i | \(0.787336\pi\) | |||||||
\(938\) | 1.01067e13 | 0.426282 | ||||||||
\(939\) | −8.40005e11 | −0.0352604 | ||||||||
\(940\) | −3.42575e13 | −1.43114 | ||||||||
\(941\) | −4.72046e13 | −1.96260 | −0.981298 | − | 0.192496i | \(-0.938342\pi\) | ||||
−0.981298 | + | 0.192496i | \(0.938342\pi\) | |||||||
\(942\) | 1.62749e12 | 0.0673426 | ||||||||
\(943\) | −2.12693e13 | −0.875891 | ||||||||
\(944\) | −5.47308e11 | −0.0224315 | ||||||||
\(945\) | −5.91550e12 | −0.241295 | ||||||||
\(946\) | −1.09631e13 | −0.445064 | ||||||||
\(947\) | 3.75098e13 | 1.51555 | 0.757774 | − | 0.652517i | \(-0.226287\pi\) | ||||
0.757774 | + | 0.652517i | \(0.226287\pi\) | |||||||
\(948\) | −2.07517e12 | −0.0834479 | ||||||||
\(949\) | −1.41595e13 | −0.566697 | ||||||||
\(950\) | 3.26850e13 | 1.30195 | ||||||||
\(951\) | −1.93843e13 | −0.768488 | ||||||||
\(952\) | −1.84961e13 | −0.729817 | ||||||||
\(953\) | −1.68178e13 | −0.660467 | −0.330233 | − | 0.943899i | \(-0.607127\pi\) | ||||
−0.330233 | + | 0.943899i | \(0.607127\pi\) | |||||||
\(954\) | 5.73750e12 | 0.224262 | ||||||||
\(955\) | −4.61760e13 | −1.79639 | ||||||||
\(956\) | 7.47692e12 | 0.289509 | ||||||||
\(957\) | 1.33881e13 | 0.515960 | ||||||||
\(958\) | 2.53566e13 | 0.972626 | ||||||||
\(959\) | −1.36836e13 | −0.522417 | ||||||||
\(960\) | −1.03696e13 | −0.394040 | ||||||||
\(961\) | −1.79251e13 | −0.677965 | ||||||||
\(962\) | 1.02553e13 | 0.386066 | ||||||||
\(963\) | −3.81099e12 | −0.142797 | ||||||||
\(964\) | −2.85790e13 | −1.06586 | ||||||||
\(965\) | −3.21832e13 | −1.19469 | ||||||||
\(966\) | 6.08197e12 | 0.224723 | ||||||||
\(967\) | 1.43412e13 | 0.527430 | 0.263715 | − | 0.964601i | \(-0.415052\pi\) | ||||
0.263715 | + | 0.964601i | \(0.415052\pi\) | |||||||
\(968\) | −1.74869e13 | −0.640139 | ||||||||
\(969\) | −2.07056e13 | −0.754451 | ||||||||
\(970\) | −2.04985e13 | −0.743444 | ||||||||
\(971\) | −1.95428e13 | −0.705504 | −0.352752 | − | 0.935717i | \(-0.614754\pi\) | ||||
−0.352752 | + | 0.935717i | \(0.614754\pi\) | |||||||
\(972\) | 1.23646e12 | 0.0444304 | ||||||||
\(973\) | 1.26835e13 | 0.453659 | ||||||||
\(974\) | 2.29431e13 | 0.816840 | ||||||||
\(975\) | 2.85045e13 | 1.01017 | ||||||||
\(976\) | −2.86723e12 | −0.101144 | ||||||||
\(977\) | 1.37309e13 | 0.482140 | 0.241070 | − | 0.970508i | \(-0.422502\pi\) | ||||
0.241070 | + | 0.970508i | \(0.422502\pi\) | |||||||
\(978\) | −6.87590e12 | −0.240328 | ||||||||
\(979\) | 1.51669e13 | 0.527686 | ||||||||
\(980\) | 1.55701e13 | 0.539231 | ||||||||
\(981\) | 1.61081e13 | 0.555307 | ||||||||
\(982\) | 4.88683e12 | 0.167697 | ||||||||
\(983\) | −3.86404e12 | −0.131993 | −0.0659965 | − | 0.997820i | \(-0.521023\pi\) | ||||
−0.0659965 | + | 0.997820i | \(0.521023\pi\) | |||||||
\(984\) | 1.46438e13 | 0.497938 | ||||||||
\(985\) | 5.18254e13 | 1.75420 | ||||||||
\(986\) | −2.75372e13 | −0.927843 | ||||||||
\(987\) | −1.53926e13 | −0.516278 | ||||||||
\(988\) | −2.36780e13 | −0.790568 | ||||||||
\(989\) | 4.08274e13 | 1.35696 | ||||||||
\(990\) | −5.36046e12 | −0.177355 | ||||||||
\(991\) | −3.55386e13 | −1.17049 | −0.585246 | − | 0.810855i | \(-0.699002\pi\) | ||||
−0.585246 | + | 0.810855i | \(0.699002\pi\) | |||||||
\(992\) | 1.78962e13 | 0.586756 | ||||||||
\(993\) | −1.45035e13 | −0.473370 | ||||||||
\(994\) | 1.12526e13 | 0.365608 | ||||||||
\(995\) | 3.79003e13 | 1.22585 | ||||||||
\(996\) | −4.53370e12 | −0.145978 | ||||||||
\(997\) | −4.68278e12 | −0.150098 | −0.0750491 | − | 0.997180i | \(-0.523911\pi\) | ||||
−0.0750491 | + | 0.997180i | \(0.523911\pi\) | |||||||
\(998\) | 9.64374e12 | 0.307722 | ||||||||
\(999\) | −4.57446e12 | −0.145310 |
(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 | 177.10.a.b.1.8 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.b.1.8 | ✓ | 21 | 1.1 | even | 1 | trivial |